Properties

Label 462.2.i.g.67.3
Level $462$
Weight $2$
Character 462.67
Analytic conductor $3.689$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.21870000.1
Defining polynomial: \(x^{6} - 3 x^{5} + 24 x^{4} - 43 x^{3} + 138 x^{2} - 117 x + 73\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.3
Root \(0.500000 + 0.679547i\) of defining polynomial
Character \(\chi\) \(=\) 462.67
Dual form 462.2.i.g.331.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.40280 + 2.42972i) q^{5} -1.00000 q^{6} +(-1.40280 + 2.24325i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.40280 + 2.42972i) q^{5} -1.00000 q^{6} +(-1.40280 + 2.24325i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.40280 - 2.42972i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.64411 + 0.0932392i) q^{14} +2.80560 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.98261 + 6.89809i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.24131 + 5.61411i) q^{19} -2.80560 q^{20} +(1.24131 + 2.33648i) q^{21} -1.00000 q^{22} +(2.64411 + 4.57973i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-1.43570 + 2.48671i) q^{25} -1.00000 q^{27} +(-1.24131 - 2.33648i) q^{28} +5.12859 q^{29} +(-1.40280 - 2.42972i) q^{30} +(4.48261 - 7.76411i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +7.96523 q^{34} +(-7.41832 - 0.261592i) q^{35} +1.00000 q^{36} +(-5.24131 - 9.07821i) q^{37} +(3.24131 - 5.61411i) q^{38} +(1.40280 + 2.42972i) q^{40} -5.09382 q^{41} +(1.40280 - 2.24325i) q^{42} +11.4478 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.40280 - 2.42972i) q^{45} +(2.64411 - 4.57973i) q^{46} +(-0.161495 - 0.279717i) q^{47} -1.00000 q^{48} +(-3.06430 - 6.29365i) q^{49} +2.87141 q^{50} +(3.98261 + 6.89809i) q^{51} +(-4.00000 + 6.92820i) q^{53} +(0.500000 + 0.866025i) q^{54} +2.80560 q^{55} +(-1.40280 + 2.24325i) q^{56} +6.48261 q^{57} +(-2.56430 - 4.44149i) q^{58} +(0.435704 - 0.754661i) q^{59} +(-1.40280 + 2.42972i) q^{60} +(-1.07981 - 1.87029i) q^{61} -8.96523 q^{62} +(2.64411 + 0.0932392i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(3.54691 - 6.14343i) q^{67} +(-3.98261 - 6.89809i) q^{68} +5.28822 q^{69} +(3.48261 + 6.55525i) q^{70} -7.44784 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-6.28822 + 10.8915i) q^{73} +(-5.24131 + 9.07821i) q^{74} +(1.43570 + 2.48671i) q^{75} -6.48261 q^{76} +(1.24131 + 2.33648i) q^{77} +(-3.40280 - 5.89382i) q^{79} +(1.40280 - 2.42972i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.54691 + 4.41138i) q^{82} +15.0938 q^{83} +(-2.64411 - 0.0932392i) q^{84} -22.3473 q^{85} +(-5.72392 - 9.91412i) q^{86} +(2.56430 - 4.44149i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-0.805603 - 1.39535i) q^{89} -2.80560 q^{90} -5.28822 q^{92} +(-4.48261 - 7.76411i) q^{93} +(-0.161495 + 0.279717i) q^{94} +(-9.09382 + 15.7510i) q^{95} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(-3.91832 + 5.80059i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} - 3 q^{9} + O(q^{10}) \) \( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} - 3 q^{9} + 3 q^{11} + 3 q^{12} - 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{21} - 6 q^{22} - 3 q^{23} + 3 q^{24} - 15 q^{25} - 6 q^{27} + 3 q^{28} + 18 q^{29} + 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} - 30 q^{35} + 6 q^{36} - 21 q^{37} + 9 q^{38} + 24 q^{41} + 6 q^{43} + 3 q^{44} - 3 q^{46} - 3 q^{47} - 6 q^{48} - 12 q^{49} + 30 q^{50} + 3 q^{51} - 24 q^{53} + 3 q^{54} + 18 q^{57} - 9 q^{58} + 9 q^{59} + 6 q^{61} - 12 q^{62} - 3 q^{63} + 6 q^{64} - 3 q^{66} - 6 q^{67} - 3 q^{68} - 6 q^{69} + 18 q^{71} - 3 q^{72} - 21 q^{74} + 15 q^{75} - 18 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} + 36 q^{83} + 3 q^{84} - 3 q^{86} + 9 q^{87} + 3 q^{88} + 12 q^{89} + 6 q^{92} - 6 q^{93} - 3 q^{94} + 3 q^{96} + 42 q^{97} - 9 q^{98} - 6 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.40280 + 2.42972i 0.627352 + 1.08661i 0.988081 + 0.153935i \(0.0491945\pi\)
−0.360729 + 0.932671i \(0.617472\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.40280 + 2.24325i −0.530209 + 0.847867i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.40280 2.42972i 0.443605 0.768346i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 2.64411 + 0.0932392i 0.706668 + 0.0249192i
\(15\) 2.80560 0.724404
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.98261 + 6.89809i −0.965926 + 1.67303i −0.258818 + 0.965926i \(0.583333\pi\)
−0.707108 + 0.707106i \(0.750000\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 3.24131 + 5.61411i 0.743607 + 1.28796i 0.950843 + 0.309674i \(0.100220\pi\)
−0.207236 + 0.978291i \(0.566447\pi\)
\(20\) −2.80560 −0.627352
\(21\) 1.24131 + 2.33648i 0.270875 + 0.509863i
\(22\) −1.00000 −0.213201
\(23\) 2.64411 + 4.57973i 0.551335 + 0.954940i 0.998179 + 0.0603277i \(0.0192146\pi\)
−0.446844 + 0.894612i \(0.647452\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −1.43570 + 2.48671i −0.287141 + 0.497342i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.24131 2.33648i −0.234585 0.441554i
\(29\) 5.12859 0.952356 0.476178 0.879349i \(-0.342022\pi\)
0.476178 + 0.879349i \(0.342022\pi\)
\(30\) −1.40280 2.42972i −0.256115 0.443605i
\(31\) 4.48261 7.76411i 0.805101 1.39448i −0.111122 0.993807i \(-0.535444\pi\)
0.916223 0.400669i \(-0.131222\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.500000 0.866025i −0.0870388 0.150756i
\(34\) 7.96523 1.36602
\(35\) −7.41832 0.261592i −1.25392 0.0442171i
\(36\) 1.00000 0.166667
\(37\) −5.24131 9.07821i −0.861665 1.49245i −0.870320 0.492486i \(-0.836088\pi\)
0.00865499 0.999963i \(-0.497245\pi\)
\(38\) 3.24131 5.61411i 0.525809 0.910728i
\(39\) 0 0
\(40\) 1.40280 + 2.42972i 0.221802 + 0.384173i
\(41\) −5.09382 −0.795521 −0.397760 0.917489i \(-0.630212\pi\)
−0.397760 + 0.917489i \(0.630212\pi\)
\(42\) 1.40280 2.24325i 0.216457 0.346140i
\(43\) 11.4478 1.74578 0.872890 0.487918i \(-0.162243\pi\)
0.872890 + 0.487918i \(0.162243\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 1.40280 2.42972i 0.209117 0.362202i
\(46\) 2.64411 4.57973i 0.389852 0.675244i
\(47\) −0.161495 0.279717i −0.0235565 0.0408010i 0.854007 0.520262i \(-0.174166\pi\)
−0.877563 + 0.479461i \(0.840832\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.06430 6.29365i −0.437757 0.899094i
\(50\) 2.87141 0.406078
\(51\) 3.98261 + 6.89809i 0.557677 + 0.965926i
\(52\) 0 0
\(53\) −4.00000 + 6.92820i −0.549442 + 0.951662i 0.448871 + 0.893597i \(0.351826\pi\)
−0.998313 + 0.0580651i \(0.981507\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 2.80560 0.378307
\(56\) −1.40280 + 2.24325i −0.187457 + 0.299766i
\(57\) 6.48261 0.858643
\(58\) −2.56430 4.44149i −0.336709 0.583196i
\(59\) 0.435704 0.754661i 0.0567238 0.0982485i −0.836269 0.548319i \(-0.815268\pi\)
0.892993 + 0.450071i \(0.148601\pi\)
\(60\) −1.40280 + 2.42972i −0.181101 + 0.313676i
\(61\) −1.07981 1.87029i −0.138256 0.239466i 0.788581 0.614931i \(-0.210816\pi\)
−0.926836 + 0.375465i \(0.877483\pi\)
\(62\) −8.96523 −1.13858
\(63\) 2.64411 + 0.0932392i 0.333126 + 0.0117470i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.500000 + 0.866025i −0.0615457 + 0.106600i
\(67\) 3.54691 6.14343i 0.433324 0.750539i −0.563833 0.825889i \(-0.690674\pi\)
0.997157 + 0.0753496i \(0.0240073\pi\)
\(68\) −3.98261 6.89809i −0.482963 0.836516i
\(69\) 5.28822 0.636626
\(70\) 3.48261 + 6.55525i 0.416252 + 0.783502i
\(71\) −7.44784 −0.883896 −0.441948 0.897041i \(-0.645712\pi\)
−0.441948 + 0.897041i \(0.645712\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −6.28822 + 10.8915i −0.735980 + 1.27475i 0.218312 + 0.975879i \(0.429945\pi\)
−0.954292 + 0.298876i \(0.903388\pi\)
\(74\) −5.24131 + 9.07821i −0.609289 + 1.05532i
\(75\) 1.43570 + 2.48671i 0.165781 + 0.287141i
\(76\) −6.48261 −0.743607
\(77\) 1.24131 + 2.33648i 0.141460 + 0.266267i
\(78\) 0 0
\(79\) −3.40280 5.89382i −0.382845 0.663107i 0.608623 0.793460i \(-0.291722\pi\)
−0.991468 + 0.130353i \(0.958389\pi\)
\(80\) 1.40280 2.42972i 0.156838 0.271651i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.54691 + 4.41138i 0.281259 + 0.487155i
\(83\) 15.0938 1.65676 0.828381 0.560165i \(-0.189262\pi\)
0.828381 + 0.560165i \(0.189262\pi\)
\(84\) −2.64411 0.0932392i −0.288496 0.0101732i
\(85\) −22.3473 −2.42390
\(86\) −5.72392 9.91412i −0.617226 1.06907i
\(87\) 2.56430 4.44149i 0.274921 0.476178i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) −0.805603 1.39535i −0.0853937 0.147906i 0.820165 0.572127i \(-0.193881\pi\)
−0.905559 + 0.424221i \(0.860548\pi\)
\(90\) −2.80560 −0.295737
\(91\) 0 0
\(92\) −5.28822 −0.551335
\(93\) −4.48261 7.76411i −0.464825 0.805101i
\(94\) −0.161495 + 0.279717i −0.0166569 + 0.0288507i
\(95\) −9.09382 + 15.7510i −0.933006 + 1.61601i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −3.91832 + 5.80059i −0.395810 + 0.585948i
\(99\) −1.00000 −0.100504
\(100\) −1.43570 2.48671i −0.143570 0.248671i
\(101\) −5.36990 + 9.30094i −0.534325 + 0.925478i 0.464871 + 0.885379i \(0.346101\pi\)
−0.999196 + 0.0400994i \(0.987233\pi\)
\(102\) 3.98261 6.89809i 0.394337 0.683012i
\(103\) −1.48261 2.56796i −0.146086 0.253029i 0.783691 0.621150i \(-0.213334\pi\)
−0.929778 + 0.368122i \(0.880001\pi\)
\(104\) 0 0
\(105\) −3.93570 + 6.29365i −0.384085 + 0.614198i
\(106\) 8.00000 0.777029
\(107\) −2.41832 4.18865i −0.233787 0.404932i 0.725132 0.688610i \(-0.241779\pi\)
−0.958920 + 0.283678i \(0.908445\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 5.07981 8.79849i 0.486558 0.842743i −0.513323 0.858196i \(-0.671586\pi\)
0.999881 + 0.0154529i \(0.00491901\pi\)
\(110\) −1.40280 2.42972i −0.133752 0.231665i
\(111\) −10.4826 −0.994966
\(112\) 2.64411 + 0.0932392i 0.249845 + 0.00881027i
\(113\) 10.9652 1.03152 0.515761 0.856733i \(-0.327509\pi\)
0.515761 + 0.856733i \(0.327509\pi\)
\(114\) −3.24131 5.61411i −0.303576 0.525809i
\(115\) −7.41832 + 12.8489i −0.691762 + 1.19817i
\(116\) −2.56430 + 4.44149i −0.238089 + 0.412382i
\(117\) 0 0
\(118\) −0.871407 −0.0802195
\(119\) −9.88729 18.6106i −0.906366 1.70603i
\(120\) 2.80560 0.256115
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −1.07981 + 1.87029i −0.0977615 + 0.169328i
\(123\) −2.54691 + 4.41138i −0.229647 + 0.397760i
\(124\) 4.48261 + 7.76411i 0.402551 + 0.697238i
\(125\) 5.97199 0.534151
\(126\) −1.24131 2.33648i −0.110584 0.208151i
\(127\) −9.28822 −0.824196 −0.412098 0.911140i \(-0.635204\pi\)
−0.412098 + 0.911140i \(0.635204\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 5.72392 9.91412i 0.503963 0.872890i
\(130\) 0 0
\(131\) −6.48261 11.2282i −0.566389 0.981014i −0.996919 0.0784377i \(-0.975007\pi\)
0.430530 0.902576i \(-0.358326\pi\)
\(132\) 1.00000 0.0870388
\(133\) −17.1407 0.604433i −1.48629 0.0524110i
\(134\) −7.09382 −0.612813
\(135\) −1.40280 2.42972i −0.120734 0.209117i
\(136\) −3.98261 + 6.89809i −0.341506 + 0.591506i
\(137\) −2.80560 + 4.85945i −0.239699 + 0.415171i −0.960628 0.277838i \(-0.910382\pi\)
0.720929 + 0.693009i \(0.243715\pi\)
\(138\) −2.64411 4.57973i −0.225081 0.389852i
\(139\) 13.1286 1.11355 0.556776 0.830662i \(-0.312038\pi\)
0.556776 + 0.830662i \(0.312038\pi\)
\(140\) 3.93570 6.29365i 0.332628 0.531911i
\(141\) −0.322990 −0.0272007
\(142\) 3.72392 + 6.45002i 0.312504 + 0.541273i
\(143\) 0 0
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 7.19440 + 12.4611i 0.597462 + 1.03483i
\(146\) 12.5764 1.04083
\(147\) −6.98261 0.493069i −0.575916 0.0406676i
\(148\) 10.4826 0.861665
\(149\) −8.36990 14.4971i −0.685689 1.18765i −0.973220 0.229877i \(-0.926168\pi\)
0.287531 0.957771i \(-0.407166\pi\)
\(150\) 1.43570 2.48671i 0.117225 0.203039i
\(151\) −5.44971 + 9.43918i −0.443491 + 0.768149i −0.997946 0.0640648i \(-0.979594\pi\)
0.554455 + 0.832214i \(0.312927\pi\)
\(152\) 3.24131 + 5.61411i 0.262905 + 0.455364i
\(153\) 7.96523 0.643950
\(154\) 1.40280 2.24325i 0.113041 0.180766i
\(155\) 25.1529 2.02033
\(156\) 0 0
\(157\) −0.887286 + 1.53682i −0.0708132 + 0.122652i −0.899258 0.437419i \(-0.855893\pi\)
0.828445 + 0.560071i \(0.189226\pi\)
\(158\) −3.40280 + 5.89382i −0.270712 + 0.468888i
\(159\) 4.00000 + 6.92820i 0.317221 + 0.549442i
\(160\) −2.80560 −0.221802
\(161\) −13.9826 0.493069i −1.10198 0.0388593i
\(162\) 1.00000 0.0785674
\(163\) 2.02952 + 3.51524i 0.158964 + 0.275335i 0.934496 0.355975i \(-0.115851\pi\)
−0.775531 + 0.631309i \(0.782518\pi\)
\(164\) 2.54691 4.41138i 0.198880 0.344471i
\(165\) 1.40280 2.42972i 0.109208 0.189154i
\(166\) −7.54691 13.0716i −0.585754 1.01456i
\(167\) 13.8684 1.07317 0.536584 0.843847i \(-0.319714\pi\)
0.536584 + 0.843847i \(0.319714\pi\)
\(168\) 1.24131 + 2.33648i 0.0957689 + 0.180264i
\(169\) −13.0000 −1.00000
\(170\) 11.1736 + 19.3533i 0.856978 + 1.48433i
\(171\) 3.24131 5.61411i 0.247869 0.429322i
\(172\) −5.72392 + 9.91412i −0.436445 + 0.755945i
\(173\) −8.48261 14.6923i −0.644921 1.11704i −0.984320 0.176394i \(-0.943557\pi\)
0.339399 0.940643i \(-0.389776\pi\)
\(174\) −5.12859 −0.388798
\(175\) −3.56430 6.70900i −0.269435 0.507153i
\(176\) −1.00000 −0.0753778
\(177\) −0.435704 0.754661i −0.0327495 0.0567238i
\(178\) −0.805603 + 1.39535i −0.0603825 + 0.104586i
\(179\) 6.33513 10.9728i 0.473509 0.820142i −0.526031 0.850466i \(-0.676320\pi\)
0.999540 + 0.0303231i \(0.00965363\pi\)
\(180\) 1.40280 + 2.42972i 0.104559 + 0.181101i
\(181\) −2.57643 −0.191505 −0.0957523 0.995405i \(-0.530526\pi\)
−0.0957523 + 0.995405i \(0.530526\pi\)
\(182\) 0 0
\(183\) −2.15962 −0.159644
\(184\) 2.64411 + 4.57973i 0.194926 + 0.337622i
\(185\) 14.7050 25.4698i 1.08113 1.87258i
\(186\) −4.48261 + 7.76411i −0.328681 + 0.569292i
\(187\) 3.98261 + 6.89809i 0.291238 + 0.504438i
\(188\) 0.322990 0.0235565
\(189\) 1.40280 2.24325i 0.102039 0.163172i
\(190\) 18.1876 1.31947
\(191\) 1.19440 + 2.06876i 0.0864235 + 0.149690i 0.905997 0.423284i \(-0.139123\pi\)
−0.819573 + 0.572974i \(0.805790\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 7.28822 12.6236i 0.524617 0.908664i −0.474972 0.880001i \(-0.657542\pi\)
0.999589 0.0286628i \(-0.00912489\pi\)
\(194\) −3.50000 6.06218i −0.251285 0.435239i
\(195\) 0 0
\(196\) 6.98261 + 0.493069i 0.498758 + 0.0352192i
\(197\) −12.4826 −0.889349 −0.444675 0.895692i \(-0.646681\pi\)
−0.444675 + 0.895692i \(0.646681\pi\)
\(198\) 0.500000 + 0.866025i 0.0355335 + 0.0615457i
\(199\) 7.09382 12.2869i 0.502867 0.870992i −0.497127 0.867678i \(-0.665612\pi\)
0.999995 0.00331424i \(-0.00105496\pi\)
\(200\) −1.43570 + 2.48671i −0.101520 + 0.175837i
\(201\) −3.54691 6.14343i −0.250180 0.433324i
\(202\) 10.7398 0.755650
\(203\) −7.19440 + 11.5047i −0.504948 + 0.807471i
\(204\) −7.96523 −0.557677
\(205\) −7.14562 12.3766i −0.499071 0.864417i
\(206\) −1.48261 + 2.56796i −0.103299 + 0.178918i
\(207\) 2.64411 4.57973i 0.183778 0.318313i
\(208\) 0 0
\(209\) 6.48261 0.448412
\(210\) 7.41832 + 0.261592i 0.511912 + 0.0180516i
\(211\) −20.8336 −1.43425 −0.717123 0.696947i \(-0.754541\pi\)
−0.717123 + 0.696947i \(0.754541\pi\)
\(212\) −4.00000 6.92820i −0.274721 0.475831i
\(213\) −3.72392 + 6.45002i −0.255159 + 0.441948i
\(214\) −2.41832 + 4.18865i −0.165313 + 0.286330i
\(215\) 16.0590 + 27.8151i 1.09522 + 1.89697i
\(216\) −1.00000 −0.0680414
\(217\) 11.1286 + 20.9471i 0.755458 + 1.42198i
\(218\) −10.1596 −0.688096
\(219\) 6.28822 + 10.8915i 0.424918 + 0.735980i
\(220\) −1.40280 + 2.42972i −0.0945769 + 0.163812i
\(221\) 0 0
\(222\) 5.24131 + 9.07821i 0.351773 + 0.609289i
\(223\) 12.5764 0.842180 0.421090 0.907019i \(-0.361648\pi\)
0.421090 + 0.907019i \(0.361648\pi\)
\(224\) −1.24131 2.33648i −0.0829383 0.156113i
\(225\) 2.87141 0.191427
\(226\) −5.48261 9.49616i −0.364698 0.631675i
\(227\) −10.0295 + 17.3716i −0.665683 + 1.15300i 0.313417 + 0.949616i \(0.398526\pi\)
−0.979100 + 0.203381i \(0.934807\pi\)
\(228\) −3.24131 + 5.61411i −0.214661 + 0.371803i
\(229\) 11.2882 + 19.5518i 0.745946 + 1.29202i 0.949751 + 0.313005i \(0.101336\pi\)
−0.203805 + 0.979011i \(0.565331\pi\)
\(230\) 14.8366 0.978299
\(231\) 2.64411 + 0.0932392i 0.173970 + 0.00613469i
\(232\) 5.12859 0.336709
\(233\) 0.371407 + 0.643296i 0.0243317 + 0.0421437i 0.877935 0.478780i \(-0.158921\pi\)
−0.853603 + 0.520924i \(0.825588\pi\)
\(234\) 0 0
\(235\) 0.453091 0.784776i 0.0295564 0.0511931i
\(236\) 0.435704 + 0.754661i 0.0283619 + 0.0491242i
\(237\) −6.80560 −0.442071
\(238\) −11.1736 + 17.8680i −0.724279 + 1.15821i
\(239\) 4.31925 0.279389 0.139694 0.990195i \(-0.455388\pi\)
0.139694 + 0.990195i \(0.455388\pi\)
\(240\) −1.40280 2.42972i −0.0905504 0.156838i
\(241\) 9.09382 15.7510i 0.585784 1.01461i −0.408993 0.912538i \(-0.634120\pi\)
0.994777 0.102071i \(-0.0325468\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 2.15962 0.138256
\(245\) 10.9932 16.2741i 0.702332 1.03972i
\(246\) 5.09382 0.324770
\(247\) 0 0
\(248\) 4.48261 7.76411i 0.284646 0.493022i
\(249\) 7.54691 13.0716i 0.478266 0.828381i
\(250\) −2.98599 5.17189i −0.188851 0.327099i
\(251\) 28.6703 1.80965 0.904825 0.425784i \(-0.140001\pi\)
0.904825 + 0.425784i \(0.140001\pi\)
\(252\) −1.40280 + 2.24325i −0.0883682 + 0.141311i
\(253\) 5.28822 0.332467
\(254\) 4.64411 + 8.04383i 0.291397 + 0.504715i
\(255\) −11.1736 + 19.3533i −0.699720 + 1.21195i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.80560 + 11.7876i 0.424522 + 0.735293i 0.996376 0.0850621i \(-0.0271089\pi\)
−0.571854 + 0.820356i \(0.693776\pi\)
\(258\) −11.4478 −0.712711
\(259\) 27.7172 + 0.977390i 1.72226 + 0.0607321i
\(260\) 0 0
\(261\) −2.56430 4.44149i −0.158726 0.274921i
\(262\) −6.48261 + 11.2282i −0.400497 + 0.693681i
\(263\) 1.80560 3.12740i 0.111338 0.192843i −0.804972 0.593313i \(-0.797820\pi\)
0.916310 + 0.400470i \(0.131153\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) −22.4448 −1.37877
\(266\) 8.04691 + 15.1465i 0.493388 + 0.928693i
\(267\) −1.61121 −0.0986042
\(268\) 3.54691 + 6.14343i 0.216662 + 0.375270i
\(269\) 4.69102 8.12508i 0.286016 0.495395i −0.686839 0.726810i \(-0.741002\pi\)
0.972855 + 0.231415i \(0.0743355\pi\)
\(270\) −1.40280 + 2.42972i −0.0853718 + 0.147868i
\(271\) −2.80560 4.85945i −0.170428 0.295190i 0.768141 0.640280i \(-0.221182\pi\)
−0.938570 + 0.345090i \(0.887848\pi\)
\(272\) 7.96523 0.482963
\(273\) 0 0
\(274\) 5.61121 0.338985
\(275\) 1.43570 + 2.48671i 0.0865762 + 0.149954i
\(276\) −2.64411 + 4.57973i −0.159157 + 0.275667i
\(277\) 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) −6.56430 11.3697i −0.393700 0.681909i
\(279\) −8.96523 −0.536734
\(280\) −7.41832 0.261592i −0.443329 0.0156331i
\(281\) 24.1529 1.44084 0.720420 0.693539i \(-0.243949\pi\)
0.720420 + 0.693539i \(0.243949\pi\)
\(282\) 0.161495 + 0.279717i 0.00961688 + 0.0166569i
\(283\) −3.77083 + 6.53127i −0.224152 + 0.388244i −0.956065 0.293155i \(-0.905295\pi\)
0.731912 + 0.681399i \(0.238628\pi\)
\(284\) 3.72392 6.45002i 0.220974 0.382738i
\(285\) 9.09382 + 15.7510i 0.538671 + 0.933006i
\(286\) 0 0
\(287\) 7.14562 11.4267i 0.421792 0.674496i
\(288\) 1.00000 0.0589256
\(289\) −23.2224 40.2224i −1.36602 2.36602i
\(290\) 7.19440 12.4611i 0.422470 0.731739i
\(291\) 3.50000 6.06218i 0.205174 0.355371i
\(292\) −6.28822 10.8915i −0.367990 0.637377i
\(293\) 7.90618 0.461884 0.230942 0.972968i \(-0.425819\pi\)
0.230942 + 0.972968i \(0.425819\pi\)
\(294\) 3.06430 + 6.29365i 0.178713 + 0.367053i
\(295\) 2.44482 0.142343
\(296\) −5.24131 9.07821i −0.304645 0.527660i
\(297\) −0.500000 + 0.866025i −0.0290129 + 0.0502519i
\(298\) −8.36990 + 14.4971i −0.484855 + 0.839794i
\(299\) 0 0
\(300\) −2.87141 −0.165781
\(301\) −16.0590 + 25.6803i −0.925628 + 1.48019i
\(302\) 10.8994 0.627191
\(303\) 5.36990 + 9.30094i 0.308493 + 0.534325i
\(304\) 3.24131 5.61411i 0.185902 0.321991i
\(305\) 3.02952 5.24729i 0.173470 0.300459i
\(306\) −3.98261 6.89809i −0.227671 0.394337i
\(307\) 12.8957 0.735995 0.367998 0.929827i \(-0.380043\pi\)
0.367998 + 0.929827i \(0.380043\pi\)
\(308\) −2.64411 0.0932392i −0.150662 0.00531279i
\(309\) −2.96523 −0.168686
\(310\) −12.5764 21.7830i −0.714293 1.23719i
\(311\) −5.44971 + 9.43918i −0.309025 + 0.535247i −0.978149 0.207904i \(-0.933336\pi\)
0.669125 + 0.743150i \(0.266669\pi\)
\(312\) 0 0
\(313\) 4.56430 + 7.90559i 0.257989 + 0.446851i 0.965703 0.259649i \(-0.0836067\pi\)
−0.707714 + 0.706499i \(0.750273\pi\)
\(314\) 1.77457 0.100145
\(315\) 3.48261 + 6.55525i 0.196223 + 0.369346i
\(316\) 6.80560 0.382845
\(317\) 4.75682 + 8.23906i 0.267170 + 0.462752i 0.968130 0.250449i \(-0.0805782\pi\)
−0.700960 + 0.713201i \(0.747245\pi\)
\(318\) 4.00000 6.92820i 0.224309 0.388514i
\(319\) 2.56430 4.44149i 0.143573 0.248676i
\(320\) 1.40280 + 2.42972i 0.0784190 + 0.135826i
\(321\) −4.83663 −0.269955
\(322\) 6.56430 + 12.3558i 0.365814 + 0.688564i
\(323\) −51.6355 −2.87307
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) 2.02952 3.51524i 0.112405 0.194691i
\(327\) −5.07981 8.79849i −0.280914 0.486558i
\(328\) −5.09382 −0.281259
\(329\) 0.854020 + 0.0301153i 0.0470837 + 0.00166031i
\(330\) −2.80560 −0.154443
\(331\) −0.546909 0.947275i −0.0300609 0.0520669i 0.850604 0.525807i \(-0.176237\pi\)
−0.880664 + 0.473741i \(0.842903\pi\)
\(332\) −7.54691 + 13.0716i −0.414190 + 0.717399i
\(333\) −5.24131 + 9.07821i −0.287222 + 0.497483i
\(334\) −6.93420 12.0104i −0.379422 0.657179i
\(335\) 19.9024 1.08739
\(336\) 1.40280 2.24325i 0.0765291 0.122379i
\(337\) −25.7988 −1.40535 −0.702676 0.711510i \(-0.748012\pi\)
−0.702676 + 0.711510i \(0.748012\pi\)
\(338\) 6.50000 + 11.2583i 0.353553 + 0.612372i
\(339\) 5.48261 9.49616i 0.297775 0.515761i
\(340\) 11.1736 19.3533i 0.605975 1.04958i
\(341\) −4.48261 7.76411i −0.242747 0.420450i
\(342\) −6.48261 −0.350540
\(343\) 18.4168 + 1.95478i 0.994414 + 0.105548i
\(344\) 11.4478 0.617226
\(345\) 7.41832 + 12.8489i 0.399389 + 0.691762i
\(346\) −8.48261 + 14.6923i −0.456028 + 0.789864i
\(347\) −10.3835 + 17.9848i −0.557418 + 0.965476i 0.440293 + 0.897854i \(0.354874\pi\)
−0.997711 + 0.0676219i \(0.978459\pi\)
\(348\) 2.56430 + 4.44149i 0.137461 + 0.238089i
\(349\) −9.51364 −0.509254 −0.254627 0.967039i \(-0.581953\pi\)
−0.254627 + 0.967039i \(0.581953\pi\)
\(350\) −4.02801 + 6.44127i −0.215306 + 0.344300i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 6.28822 10.8915i 0.334688 0.579697i −0.648737 0.761013i \(-0.724702\pi\)
0.983425 + 0.181316i \(0.0580358\pi\)
\(354\) −0.435704 + 0.754661i −0.0231574 + 0.0401098i
\(355\) −10.4478 18.0962i −0.554514 0.960446i
\(356\) 1.61121 0.0853937
\(357\) −21.0609 0.742671i −1.11466 0.0393063i
\(358\) −12.6703 −0.669644
\(359\) 0.0347742 + 0.0602306i 0.00183531 + 0.00317885i 0.866942 0.498410i \(-0.166082\pi\)
−0.865106 + 0.501589i \(0.832749\pi\)
\(360\) 1.40280 2.42972i 0.0739341 0.128058i
\(361\) −11.5121 + 19.9396i −0.605902 + 1.04945i
\(362\) 1.28822 + 2.23126i 0.0677071 + 0.117272i
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) −35.2845 −1.84687
\(366\) 1.07981 + 1.87029i 0.0564427 + 0.0977615i
\(367\) 15.7708 27.3159i 0.823231 1.42588i −0.0800336 0.996792i \(-0.525503\pi\)
0.903264 0.429085i \(-0.141164\pi\)
\(368\) 2.64411 4.57973i 0.137834 0.238735i
\(369\) 2.54691 + 4.41138i 0.132587 + 0.229647i
\(370\) −29.4100 −1.52896
\(371\) −9.93045 18.6919i −0.515563 0.970434i
\(372\) 8.96523 0.464825
\(373\) −7.65624 13.2610i −0.396425 0.686629i 0.596857 0.802348i \(-0.296416\pi\)
−0.993282 + 0.115719i \(0.963083\pi\)
\(374\) 3.98261 6.89809i 0.205936 0.356692i
\(375\) 2.98599 5.17189i 0.154196 0.267075i
\(376\) −0.161495 0.279717i −0.00832847 0.0144253i
\(377\) 0 0
\(378\) −2.64411 0.0932392i −0.135998 0.00479570i
\(379\) 16.0590 0.824898 0.412449 0.910981i \(-0.364674\pi\)
0.412449 + 0.910981i \(0.364674\pi\)
\(380\) −9.09382 15.7510i −0.466503 0.808007i
\(381\) −4.64411 + 8.04383i −0.237925 + 0.412098i
\(382\) 1.19440 2.06876i 0.0611107 0.105847i
\(383\) 0.369899 + 0.640684i 0.0189010 + 0.0327374i 0.875321 0.483542i \(-0.160650\pi\)
−0.856420 + 0.516279i \(0.827317\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −3.93570 + 6.29365i −0.200582 + 0.320754i
\(386\) −14.5764 −0.741921
\(387\) −5.72392 9.91412i −0.290963 0.503963i
\(388\) −3.50000 + 6.06218i −0.177686 + 0.307760i
\(389\) −1.79160 + 3.10313i −0.0908375 + 0.157335i −0.907864 0.419265i \(-0.862288\pi\)
0.817026 + 0.576600i \(0.195621\pi\)
\(390\) 0 0
\(391\) −42.1218 −2.13019
\(392\) −3.06430 6.29365i −0.154770 0.317878i
\(393\) −12.9652 −0.654009
\(394\) 6.24131 + 10.8103i 0.314432 + 0.544613i
\(395\) 9.54691 16.5357i 0.480357 0.832003i
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 12.5643 + 21.7620i 0.630584 + 1.09220i 0.987433 + 0.158041i \(0.0505179\pi\)
−0.356849 + 0.934162i \(0.616149\pi\)
\(398\) −14.1876 −0.711162
\(399\) −9.09382 + 14.5421i −0.455260 + 0.728015i
\(400\) 2.87141 0.143570
\(401\) 1.93420 + 3.35013i 0.0965891 + 0.167297i 0.910271 0.414014i \(-0.135873\pi\)
−0.813682 + 0.581311i \(0.802540\pi\)
\(402\) −3.54691 + 6.14343i −0.176904 + 0.306406i
\(403\) 0 0
\(404\) −5.36990 9.30094i −0.267162 0.462739i
\(405\) −2.80560 −0.139412
\(406\) 13.5606 + 0.478186i 0.672999 + 0.0237320i
\(407\) −10.4826 −0.519604
\(408\) 3.98261 + 6.89809i 0.197169 + 0.341506i
\(409\) −2.32299 + 4.02354i −0.114864 + 0.198951i −0.917726 0.397215i \(-0.869977\pi\)
0.802861 + 0.596166i \(0.203310\pi\)
\(410\) −7.14562 + 12.3766i −0.352897 + 0.611235i
\(411\) 2.80560 + 4.85945i 0.138390 + 0.239699i
\(412\) 2.96523 0.146086
\(413\) 1.08168 + 2.03603i 0.0532262 + 0.100186i
\(414\) −5.28822 −0.259902
\(415\) 21.1736 + 36.6738i 1.03937 + 1.80025i
\(416\) 0 0
\(417\) 6.56430 11.3697i 0.321455 0.556776i
\(418\) −3.24131 5.61411i −0.158537 0.274595i
\(419\) −19.5174 −0.953487 −0.476743 0.879043i \(-0.658183\pi\)
−0.476743 + 0.879043i \(0.658183\pi\)
\(420\) −3.48261 6.55525i −0.169934 0.319863i
\(421\) 15.5174 0.756271 0.378136 0.925750i \(-0.376565\pi\)
0.378136 + 0.925750i \(0.376565\pi\)
\(422\) 10.4168 + 18.0424i 0.507082 + 0.878292i
\(423\) −0.161495 + 0.279717i −0.00785215 + 0.0136003i
\(424\) −4.00000 + 6.92820i −0.194257 + 0.336463i
\(425\) −11.4357 19.8072i −0.554713 0.960791i
\(426\) 7.44784 0.360849
\(427\) 5.71028 + 0.201361i 0.276340 + 0.00974456i
\(428\) 4.83663 0.233787
\(429\) 0 0
\(430\) 16.0590 27.8151i 0.774436 1.34136i
\(431\) 7.19440 12.4611i 0.346542 0.600228i −0.639091 0.769131i \(-0.720689\pi\)
0.985633 + 0.168903i \(0.0540225\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 2.03477 0.0977850 0.0488925 0.998804i \(-0.484431\pi\)
0.0488925 + 0.998804i \(0.484431\pi\)
\(434\) 12.5764 20.1112i 0.603688 0.965368i
\(435\) 14.3888 0.689890
\(436\) 5.07981 + 8.79849i 0.243279 + 0.421371i
\(437\) −17.1407 + 29.6886i −0.819952 + 1.42020i
\(438\) 6.28822 10.8915i 0.300463 0.520416i
\(439\) −1.61308 2.79393i −0.0769880 0.133347i 0.824961 0.565190i \(-0.191197\pi\)
−0.901949 + 0.431842i \(0.857864\pi\)
\(440\) 2.80560 0.133752
\(441\) −3.91832 + 5.80059i −0.186587 + 0.276218i
\(442\) 0 0
\(443\) 11.0469 + 19.1338i 0.524854 + 0.909075i 0.999581 + 0.0289413i \(0.00921360\pi\)
−0.474727 + 0.880133i \(0.657453\pi\)
\(444\) 5.24131 9.07821i 0.248741 0.430833i
\(445\) 2.26020 3.91478i 0.107144 0.185579i
\(446\) −6.28822 10.8915i −0.297756 0.515728i
\(447\) −16.7398 −0.791765
\(448\) −1.40280 + 2.24325i −0.0662761 + 0.105983i
\(449\) 22.2497 1.05003 0.525014 0.851094i \(-0.324060\pi\)
0.525014 + 0.851094i \(0.324060\pi\)
\(450\) −1.43570 2.48671i −0.0676797 0.117225i
\(451\) −2.54691 + 4.41138i −0.119929 + 0.207724i
\(452\) −5.48261 + 9.49616i −0.257880 + 0.446662i
\(453\) 5.44971 + 9.43918i 0.256050 + 0.443491i
\(454\) 20.0590 0.941418
\(455\) 0 0
\(456\) 6.48261 0.303576
\(457\) 9.31925 + 16.1414i 0.435936 + 0.755063i 0.997372 0.0724572i \(-0.0230841\pi\)
−0.561436 + 0.827520i \(0.689751\pi\)
\(458\) 11.2882 19.5518i 0.527464 0.913594i
\(459\) 3.98261 6.89809i 0.185892 0.321975i
\(460\) −7.41832 12.8489i −0.345881 0.599083i
\(461\) −20.9895 −0.977578 −0.488789 0.872402i \(-0.662561\pi\)
−0.488789 + 0.872402i \(0.662561\pi\)
\(462\) −1.24131 2.33648i −0.0577508 0.108703i
\(463\) −5.35402 −0.248822 −0.124411 0.992231i \(-0.539704\pi\)
−0.124411 + 0.992231i \(0.539704\pi\)
\(464\) −2.56430 4.44149i −0.119044 0.206191i
\(465\) 12.5764 21.7830i 0.583218 1.01016i
\(466\) 0.371407 0.643296i 0.0172051 0.0298001i
\(467\) −13.0121 22.5377i −0.602130 1.04292i −0.992498 0.122261i \(-0.960986\pi\)
0.390368 0.920659i \(-0.372348\pi\)
\(468\) 0 0
\(469\) 8.80560 + 16.5746i 0.406605 + 0.765344i
\(470\) −0.906181 −0.0417990
\(471\) 0.887286 + 1.53682i 0.0408840 + 0.0708132i
\(472\) 0.435704 0.754661i 0.0200549 0.0347361i
\(473\) 5.72392 9.91412i 0.263186 0.455852i
\(474\) 3.40280 + 5.89382i 0.156296 + 0.270712i
\(475\) −18.6142 −0.854079
\(476\) 21.0609 + 0.742671i 0.965326 + 0.0340403i
\(477\) 8.00000 0.366295
\(478\) −2.15962 3.74058i −0.0987789 0.171090i
\(479\) 1.80560 3.12740i 0.0825001 0.142894i −0.821823 0.569743i \(-0.807043\pi\)
0.904323 + 0.426848i \(0.140376\pi\)
\(480\) −1.40280 + 2.42972i −0.0640288 + 0.110901i
\(481\) 0 0
\(482\) −18.1876 −0.828424
\(483\) −7.41832 + 11.8628i −0.337545 + 0.539774i
\(484\) 1.00000 0.0454545
\(485\) 9.81961 + 17.0081i 0.445886 + 0.772296i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 4.03103 6.98195i 0.182663 0.316382i −0.760123 0.649779i \(-0.774861\pi\)
0.942787 + 0.333397i \(0.108195\pi\)
\(488\) −1.07981 1.87029i −0.0488808 0.0846640i
\(489\) 4.05904 0.183556
\(490\) −19.5904 1.38336i −0.885006 0.0624936i
\(491\) 20.9062 0.943483 0.471741 0.881737i \(-0.343626\pi\)
0.471741 + 0.881737i \(0.343626\pi\)
\(492\) −2.54691 4.41138i −0.114824 0.198880i
\(493\) −20.4252 + 35.3775i −0.919905 + 1.59332i
\(494\) 0 0
\(495\) −1.40280 2.42972i −0.0630512 0.109208i
\(496\) −8.96523 −0.402551
\(497\) 10.4478 16.7073i 0.468650 0.749426i
\(498\) −15.0938 −0.676370
\(499\) −2.48261 4.30001i −0.111137 0.192495i 0.805092 0.593150i \(-0.202116\pi\)
−0.916229 + 0.400655i \(0.868783\pi\)
\(500\) −2.98599 + 5.17189i −0.133538 + 0.231294i
\(501\) 6.93420 12.0104i 0.309797 0.536584i
\(502\) −14.3351 24.8292i −0.639808 1.10818i
\(503\) −17.7988 −0.793611 −0.396806 0.917903i \(-0.629881\pi\)
−0.396806 + 0.917903i \(0.629881\pi\)
\(504\) 2.64411 + 0.0932392i 0.117778 + 0.00415320i
\(505\) −30.1316 −1.34084
\(506\) −2.64411 4.57973i −0.117545 0.203594i
\(507\) −6.50000 + 11.2583i −0.288675 + 0.500000i
\(508\) 4.64411 8.04383i 0.206049 0.356887i
\(509\) −2.25719 3.90956i −0.100048 0.173288i 0.811656 0.584135i \(-0.198566\pi\)
−0.911704 + 0.410847i \(0.865233\pi\)
\(510\) 22.3473 0.989553
\(511\) −15.6112 29.3846i −0.690599 1.29990i
\(512\) 1.00000 0.0441942
\(513\) −3.24131 5.61411i −0.143107 0.247869i
\(514\) 6.80560 11.7876i 0.300182 0.519931i
\(515\) 4.15962 7.20468i 0.183295 0.317476i
\(516\) 5.72392 + 9.91412i 0.251982 + 0.436445i
\(517\) −0.322990 −0.0142051
\(518\) −13.0121 24.4925i −0.571720 1.07614i
\(519\) −16.9652 −0.744691
\(520\) 0 0
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) −2.56430 + 4.44149i −0.112236 + 0.194399i
\(523\) −3.45158 5.97832i −0.150927 0.261414i 0.780641 0.624979i \(-0.214893\pi\)
−0.931569 + 0.363566i \(0.881559\pi\)
\(524\) 12.9652 0.566389
\(525\) −7.59231 0.267728i −0.331356 0.0116846i
\(526\) −3.61121 −0.157456
\(527\) 35.7050 + 61.8429i 1.55534 + 2.69392i
\(528\) −0.500000 + 0.866025i −0.0217597 + 0.0376889i
\(529\) −2.48261 + 4.30001i −0.107940 + 0.186957i
\(530\) 11.2224 + 19.4378i 0.487470 + 0.844323i
\(531\) −0.871407 −0.0378159
\(532\) 9.09382 14.5421i 0.394267 0.630480i
\(533\) 0 0
\(534\) 0.805603 + 1.39535i 0.0348618 + 0.0603825i
\(535\) 6.78484 11.7517i 0.293334 0.508069i
\(536\) 3.54691 6.14343i 0.153203 0.265356i
\(537\) −6.33513 10.9728i −0.273381 0.473509i
\(538\) −9.38203 −0.404488
\(539\) −6.98261 0.493069i −0.300762 0.0212380i
\(540\) 2.80560 0.120734
\(541\) −1.40280 2.42972i −0.0603111 0.104462i 0.834293 0.551321i \(-0.185876\pi\)
−0.894604 + 0.446859i \(0.852543\pi\)
\(542\) −2.80560 + 4.85945i −0.120511 + 0.208731i
\(543\) −1.28822 + 2.23126i −0.0552826 + 0.0957523i
\(544\) −3.98261 6.89809i −0.170753 0.295753i
\(545\) 28.5039 1.22097
\(546\) 0 0
\(547\) 32.9274 1.40788 0.703938 0.710262i \(-0.251423\pi\)
0.703938 + 0.710262i \(0.251423\pi\)
\(548\) −2.80560 4.85945i −0.119849 0.207585i
\(549\) −1.07981 + 1.87029i −0.0460852 + 0.0798220i
\(550\) 1.43570 2.48671i 0.0612186 0.106034i
\(551\) 16.6233 + 28.7925i 0.708178 + 1.22660i
\(552\) 5.28822 0.225081
\(553\) 17.9947 + 0.634549i 0.765215 + 0.0269838i
\(554\) −16.0000 −0.679775
\(555\) −14.7050 25.4698i −0.624194 1.08113i
\(556\) −6.56430 + 11.3697i −0.278388 + 0.482182i
\(557\) −11.8525 + 20.5292i −0.502207 + 0.869848i 0.497790 + 0.867298i \(0.334145\pi\)
−0.999997 + 0.00255037i \(0.999188\pi\)
\(558\) 4.48261 + 7.76411i 0.189764 + 0.328681i
\(559\) 0 0
\(560\) 3.48261 + 6.55525i 0.147167 + 0.277010i
\(561\) 7.96523 0.336292
\(562\) −12.0764 20.9170i −0.509414 0.882330i
\(563\) −15.2224 + 26.3660i −0.641548 + 1.11119i 0.343539 + 0.939138i \(0.388374\pi\)
−0.985087 + 0.172056i \(0.944959\pi\)
\(564\) 0.161495 0.279717i 0.00680016 0.0117782i
\(565\) 15.3820 + 26.6425i 0.647127 + 1.12086i
\(566\) 7.54166 0.317000
\(567\) −1.24131 2.33648i −0.0521300 0.0981231i
\(568\) −7.44784 −0.312504
\(569\) −11.1407 19.2963i −0.467044 0.808943i 0.532248 0.846589i \(-0.321348\pi\)
−0.999291 + 0.0376455i \(0.988014\pi\)
\(570\) 9.09382 15.7510i 0.380898 0.659735i
\(571\) 1.43570 2.48671i 0.0600823 0.104066i −0.834420 0.551130i \(-0.814197\pi\)
0.894502 + 0.447064i \(0.147530\pi\)
\(572\) 0 0
\(573\) 2.38879 0.0997933
\(574\) −13.4686 0.474943i −0.562169 0.0198238i
\(575\) −15.1846 −0.633242
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 7.51214 13.0114i 0.312734 0.541672i −0.666219 0.745756i \(-0.732088\pi\)
0.978953 + 0.204084i \(0.0654217\pi\)
\(578\) −23.2224 + 40.2224i −0.965925 + 1.67303i
\(579\) −7.28822 12.6236i −0.302888 0.524617i
\(580\) −14.3888 −0.597462
\(581\) −21.1736 + 33.8591i −0.878430 + 1.40471i
\(582\) −7.00000 −0.290159
\(583\) 4.00000 + 6.92820i 0.165663 + 0.286937i
\(584\) −6.28822 + 10.8915i −0.260208 + 0.450694i
\(585\) 0 0
\(586\) −3.95309 6.84695i −0.163301 0.282845i
\(587\) −42.5069 −1.75445 −0.877223 0.480082i \(-0.840607\pi\)
−0.877223 + 0.480082i \(0.840607\pi\)
\(588\) 3.91832 5.80059i 0.161589 0.239212i
\(589\) 58.1181 2.39471
\(590\) −1.22241 2.11728i −0.0503259 0.0871670i
\(591\) −6.24131 + 10.8103i −0.256733 + 0.444675i
\(592\) −5.24131 + 9.07821i −0.215416 + 0.373112i
\(593\) −7.69289 13.3245i −0.315909 0.547171i 0.663721 0.747980i \(-0.268976\pi\)
−0.979630 + 0.200809i \(0.935643\pi\)
\(594\) 1.00000 0.0410305
\(595\) 31.3488 50.1304i 1.28517 2.05515i
\(596\) 16.7398 0.685689
\(597\) −7.09382 12.2869i −0.290331 0.502867i
\(598\) 0 0
\(599\) 19.8196 34.3286i 0.809807 1.40263i −0.103190 0.994662i \(-0.532905\pi\)
0.912997 0.407966i \(-0.133762\pi\)
\(600\) 1.43570 + 2.48671i 0.0586124 + 0.101520i
\(601\) 33.3405 1.35999 0.679994 0.733218i \(-0.261983\pi\)
0.679994 + 0.733218i \(0.261983\pi\)
\(602\) 30.2693 + 1.06739i 1.23369 + 0.0435034i
\(603\) −7.09382 −0.288883
\(604\) −5.44971 9.43918i −0.221746 0.384075i
\(605\) 1.40280 2.42972i 0.0570320 0.0987823i
\(606\) 5.36990 9.30094i 0.218137 0.377825i
\(607\) −7.97923 13.8204i −0.323867 0.560954i 0.657415 0.753528i \(-0.271650\pi\)
−0.981282 + 0.192574i \(0.938316\pi\)
\(608\) −6.48261 −0.262905
\(609\) 6.36616 + 11.9829i 0.257970 + 0.485571i
\(610\) −6.05904 −0.245324
\(611\) 0 0
\(612\) −3.98261 + 6.89809i −0.160988 + 0.278839i
\(613\) −23.3333 + 40.4144i −0.942421 + 1.63232i −0.181587 + 0.983375i \(0.558123\pi\)
−0.760834 + 0.648947i \(0.775210\pi\)
\(614\) −6.44784 11.1680i −0.260214 0.450703i
\(615\) −14.2912 −0.576278
\(616\) 1.24131 + 2.33648i 0.0500137 + 0.0941396i
\(617\) −9.28447 −0.373779 −0.186889 0.982381i \(-0.559841\pi\)
−0.186889 + 0.982381i \(0.559841\pi\)
\(618\) 1.48261 + 2.56796i 0.0596394 + 0.103299i
\(619\) −16.9947 + 29.4358i −0.683077 + 1.18312i 0.290961 + 0.956735i \(0.406025\pi\)
−0.974037 + 0.226388i \(0.927308\pi\)
\(620\) −12.5764 + 21.7830i −0.505082 + 0.874827i
\(621\) −2.64411 4.57973i −0.106104 0.183778i
\(622\) 10.8994 0.437027
\(623\) 4.26020 + 0.150227i 0.170681 + 0.00601874i
\(624\) 0 0
\(625\) 15.5560 + 26.9438i 0.622241 + 1.07775i
\(626\) 4.56430 7.90559i 0.182426 0.315971i
\(627\) 3.24131 5.61411i 0.129445 0.224206i
\(628\) −0.887286 1.53682i −0.0354066 0.0613260i
\(629\) 83.4964 3.32922
\(630\) 3.93570 6.29365i 0.156802 0.250745i
\(631\) −14.6460 −0.583047 −0.291524 0.956564i \(-0.594162\pi\)
−0.291524 + 0.956564i \(0.594162\pi\)
\(632\) −3.40280 5.89382i −0.135356 0.234444i
\(633\) −10.4168 + 18.0424i −0.414031 + 0.717123i
\(634\) 4.75682 8.23906i 0.188918 0.327215i
\(635\) −13.0295 22.5678i −0.517061 0.895576i
\(636\) −8.00000 −0.317221
\(637\) 0 0
\(638\) −5.12859 −0.203043
\(639\) 3.72392 + 6.45002i 0.147316 + 0.255159i
\(640\) 1.40280 2.42972i 0.0554506 0.0960432i
\(641\) −10.4826 + 18.1564i −0.414038 + 0.717135i −0.995327 0.0965620i \(-0.969215\pi\)
0.581289 + 0.813697i \(0.302549\pi\)
\(642\) 2.41832 + 4.18865i 0.0954433 + 0.165313i
\(643\) −23.6733 −0.933582 −0.466791 0.884368i \(-0.654590\pi\)
−0.466791 + 0.884368i \(0.654590\pi\)
\(644\) 7.41832 11.8628i 0.292323 0.467458i
\(645\) 32.1181 1.26465
\(646\) 25.8177 + 44.7176i 1.01579 + 1.75939i
\(647\) 6.20840 10.7533i 0.244078 0.422755i −0.717794 0.696255i \(-0.754848\pi\)
0.961872 + 0.273500i \(0.0881815\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −0.435704 0.754661i −0.0171029 0.0296230i
\(650\) 0 0
\(651\) 23.7050 + 0.835910i 0.929073 + 0.0327619i
\(652\) −4.05904 −0.158964
\(653\) 0.0487812 + 0.0844916i 0.00190896 + 0.00330641i 0.866978 0.498346i \(-0.166059\pi\)
−0.865069 + 0.501652i \(0.832726\pi\)
\(654\) −5.07981 + 8.79849i −0.198636 + 0.344048i
\(655\) 18.1876 31.5019i 0.710650 1.23088i
\(656\) 2.54691 + 4.41138i 0.0994401 + 0.172235i
\(657\) 12.5764 0.490653
\(658\) −0.400929 0.754661i −0.0156299 0.0294197i
\(659\) −35.0243 −1.36435 −0.682176 0.731188i \(-0.738966\pi\)
−0.682176 + 0.731188i \(0.738966\pi\)
\(660\) 1.40280 + 2.42972i 0.0546040 + 0.0945769i
\(661\) −14.8177 + 25.6651i −0.576343 + 0.998256i 0.419551 + 0.907732i \(0.362188\pi\)
−0.995894 + 0.0905240i \(0.971146\pi\)
\(662\) −0.546909 + 0.947275i −0.0212562 + 0.0368169i
\(663\) 0 0
\(664\) 15.0938 0.585754
\(665\) −22.5764 42.4951i −0.875476 1.64789i
\(666\) 10.4826 0.406193
\(667\) 13.5606 + 23.4876i 0.525067 + 0.909442i
\(668\) −6.93420 + 12.0104i −0.268292 + 0.464696i
\(669\) 6.28822 10.8915i 0.243116 0.421090i
\(670\) −9.95122 17.2360i −0.384449 0.665885i
\(671\) −2.15962 −0.0833713
\(672\) −2.64411 0.0932392i −0.101999 0.00359678i
\(673\) 16.8957 0.651281 0.325640 0.945494i \(-0.394420\pi\)
0.325640 + 0.945494i \(0.394420\pi\)
\(674\) 12.8994 + 22.3425i 0.496867 + 0.860599i
\(675\) 1.43570 2.48671i 0.0552603 0.0957136i
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) −6.59533 11.4234i −0.253479 0.439038i 0.711002 0.703190i \(-0.248242\pi\)
−0.964481 + 0.264151i \(0.914908\pi\)
\(678\) −10.9652 −0.421117
\(679\) −9.81961 + 15.7027i −0.376842 + 0.602615i
\(680\) −22.3473 −0.856978
\(681\) 10.0295 + 17.3716i 0.384332 + 0.665683i
\(682\) −4.48261 + 7.76411i −0.171648 + 0.297303i
\(683\) −4.91832 + 8.51877i −0.188194 + 0.325962i −0.944648 0.328085i \(-0.893597\pi\)
0.756454 + 0.654047i \(0.226930\pi\)
\(684\) 3.24131 + 5.61411i 0.123934 + 0.214661i
\(685\) −15.7428 −0.601502
\(686\) −7.51552 16.9268i −0.286944 0.646269i
\(687\) 22.5764 0.861345
\(688\) −5.72392 9.91412i −0.218222 0.377972i
\(689\) 0 0
\(690\) 7.41832 12.8489i 0.282410 0.489149i
\(691\) 24.9947 + 43.2922i 0.950845 + 1.64691i 0.743602 + 0.668622i \(0.233116\pi\)
0.207243 + 0.978290i \(0.433551\pi\)
\(692\) 16.9652 0.644921
\(693\) 1.40280 2.24325i 0.0532880 0.0852138i
\(694\) 20.7671 0.788308
\(695\) 18.4168 + 31.8988i 0.698589 + 1.20999i
\(696\) 2.56430 4.44149i 0.0971994 0.168354i
\(697\) 20.2867 35.1376i 0.768414 1.33093i
\(698\) 4.75682 + 8.23906i 0.180048 + 0.311853i
\(699\) 0.742815 0.0280958
\(700\) 7.59231 + 0.267728i 0.286962 + 0.0101192i
\(701\) −17.7050 −0.668710 −0.334355 0.942447i \(-0.608518\pi\)
−0.334355 + 0.942447i \(0.608518\pi\)
\(702\) 0 0
\(703\) 33.9774 58.8505i 1.28148 2.21959i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −0.453091 0.784776i −0.0170644 0.0295564i
\(706\) −12.5764 −0.473320
\(707\) −13.3314 25.0934i −0.501378 0.943733i
\(708\) 0.871407 0.0327495
\(709\) 15.9774 + 27.6736i 0.600042 + 1.03930i 0.992814 + 0.119668i \(0.0381830\pi\)
−0.392772 + 0.919636i \(0.628484\pi\)
\(710\) −10.4478 + 18.0962i −0.392100 + 0.679138i
\(711\) −3.40280 + 5.89382i −0.127615 + 0.221036i
\(712\) −0.805603 1.39535i −0.0301912 0.0522928i
\(713\) 47.4100 1.77552
\(714\) 9.88729 + 18.6106i 0.370022 + 0.696485i
\(715\) 0 0
\(716\) 6.33513 + 10.9728i 0.236755 + 0.410071i
\(717\) 2.15962 3.74058i 0.0806526 0.139694i
\(718\) 0.0347742 0.0602306i 0.00129776 0.00224779i
\(719\) −10.8975 18.8751i −0.406410 0.703923i 0.588074 0.808807i \(-0.299886\pi\)
−0.994484 + 0.104884i \(0.966553\pi\)
\(720\) −2.80560 −0.104559
\(721\) 7.84038 + 0.276475i 0.291991 + 0.0102965i
\(722\) 23.0243 0.856875
\(723\) −9.09382 15.7510i −0.338203 0.585784i
\(724\) 1.28822 2.23126i 0.0478762 0.0829239i
\(725\) −7.36314 + 12.7533i −0.273460 + 0.473647i
\(726\) 0.500000 + 0.866025i 0.0185567 + 0.0321412i
\(727\) −4.84714 −0.179770 −0.0898852 0.995952i \(-0.528650\pi\)
−0.0898852 + 0.995952i \(0.528650\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 17.6422 + 30.5572i 0.652968 + 1.13097i
\(731\) −45.5923 + 78.9682i −1.68629 + 2.92074i
\(732\) 1.07981 1.87029i 0.0399110 0.0691278i
\(733\) −6.11459 10.5908i −0.225847 0.391179i 0.730726 0.682671i \(-0.239182\pi\)
−0.956573 + 0.291492i \(0.905848\pi\)
\(734\) −31.5417 −1.16422
\(735\) −8.59720 17.6575i −0.317112 0.651307i
\(736\) −5.28822 −0.194926
\(737\) −3.54691 6.14343i −0.130652 0.226296i
\(738\) 2.54691 4.41138i 0.0937530 0.162385i
\(739\) 0.517387 0.896141i 0.0190324 0.0329651i −0.856352 0.516392i \(-0.827275\pi\)
0.875385 + 0.483427i \(0.160608\pi\)
\(740\) 14.7050 + 25.4698i 0.540567 + 0.936290i
\(741\) 0 0
\(742\) −11.2224 + 17.9460i −0.411988 + 0.658817i
\(743\) −23.9925 −0.880200 −0.440100 0.897949i \(-0.645057\pi\)
−0.440100 + 0.897949i \(0.645057\pi\)
\(744\) −4.48261 7.76411i −0.164341 0.284646i
\(745\) 23.4826 40.6731i 0.860336 1.49015i
\(746\) −7.65624 + 13.2610i −0.280315 + 0.485520i
\(747\) −7.54691 13.0716i −0.276127 0.478266i
\(748\) −7.96523 −0.291238
\(749\) 12.7886 + 0.450964i 0.467285 + 0.0164779i
\(750\) −5.97199 −0.218066
\(751\) −10.2534 17.7595i −0.374153 0.648053i 0.616047 0.787710i \(-0.288733\pi\)
−0.990200 + 0.139657i \(0.955400\pi\)
\(752\) −0.161495 + 0.279717i −0.00588912 + 0.0102002i
\(753\) 14.3351 24.8292i 0.522401 0.904825i
\(754\) 0 0
\(755\) −30.5794 −1.11290
\(756\) 1.24131 + 2.33648i 0.0451459 + 0.0849771i
\(757\) −16.8019 −0.610674 −0.305337 0.952244i \(-0.598769\pi\)
−0.305337 + 0.952244i \(0.598769\pi\)
\(758\) −8.02952 13.9075i −0.291645 0.505145i
\(759\) 2.64411 4.57973i 0.0959750 0.166234i
\(760\) −9.09382 + 15.7510i −0.329867 + 0.571347i
\(761\) 7.25495 + 12.5659i 0.262992 + 0.455515i 0.967036 0.254642i \(-0.0819575\pi\)
−0.704044 + 0.710157i \(0.748624\pi\)
\(762\) 9.28822 0.336477
\(763\) 12.6112 + 23.7378i 0.456556 + 0.859366i
\(764\) −2.38879 −0.0864235
\(765\) 11.1736 + 19.3533i 0.403983 + 0.699720i
\(766\) 0.369899 0.640684i 0.0133650 0.0231489i
\(767\) 0 0
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 3.35402 0.120949 0.0604745 0.998170i \(-0.480739\pi\)
0.0604745 + 0.998170i \(0.480739\pi\)
\(770\) 7.41832 + 0.261592i 0.267338 + 0.00942712i
\(771\) 13.6112 0.490196
\(772\) 7.28822 + 12.6236i 0.262309 + 0.454332i
\(773\) −0.920188 + 1.59381i −0.0330969 + 0.0573255i −0.882099 0.471063i \(-0.843870\pi\)
0.849003 + 0.528389i \(0.177204\pi\)
\(774\) −5.72392 + 9.91412i −0.205742 + 0.356356i
\(775\) 12.8714 + 22.2939i 0.462355 + 0.800822i
\(776\) 7.00000 0.251285
\(777\) 14.7050 23.5151i 0.527540 0.843598i
\(778\) 3.58319 0.128464
\(779\) −16.5106 28.5972i −0.591555 1.02460i
\(780\) 0 0