Properties

Label 1183.2.e.i.508.4
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 11 x^{14} + 85 x^{12} + 334 x^{10} + 952 x^{8} + 1050 x^{6} + 853 x^{4} + 93 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.4
Root \(-0.166188 + 0.287846i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.i.170.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.166188 - 0.287846i) q^{2} +(-0.729919 + 1.26426i) q^{3} +(0.944763 - 1.63638i) q^{4} +(-0.722811 - 1.25195i) q^{5} +0.485214 q^{6} +(-1.36920 + 2.26391i) q^{7} -1.29278 q^{8} +(0.434437 + 0.752468i) q^{9} +O(q^{10})\) \(q+(-0.166188 - 0.287846i) q^{2} +(-0.729919 + 1.26426i) q^{3} +(0.944763 - 1.63638i) q^{4} +(-0.722811 - 1.25195i) q^{5} +0.485214 q^{6} +(-1.36920 + 2.26391i) q^{7} -1.29278 q^{8} +(0.434437 + 0.752468i) q^{9} +(-0.240245 + 0.416116i) q^{10} +(2.97758 - 5.15732i) q^{11} +(1.37920 + 2.38885i) q^{12} +(0.879201 + 0.0178849i) q^{14} +2.11037 q^{15} +(-1.67468 - 2.90063i) q^{16} +(-2.16436 + 3.74877i) q^{17} +(0.144396 - 0.250102i) q^{18} +(-0.978767 - 1.69527i) q^{19} -2.73154 q^{20} +(-1.86276 - 3.38349i) q^{21} -1.97935 q^{22} +(0.270081 + 0.467795i) q^{23} +(0.943626 - 1.63441i) q^{24} +(1.45509 - 2.52029i) q^{25} -5.64793 q^{27} +(2.41104 + 4.37939i) q^{28} +7.15857 q^{29} +(-0.350718 - 0.607461i) q^{30} +(3.05400 - 5.28968i) q^{31} +(-1.84941 + 3.20327i) q^{32} +(4.34678 + 7.52885i) q^{33} +1.43876 q^{34} +(3.82396 + 0.0777879i) q^{35} +1.64176 q^{36} +(-4.01441 - 6.95316i) q^{37} +(-0.325318 + 0.563467i) q^{38} +(0.934437 + 1.61849i) q^{40} -7.55362 q^{41} +(-0.664356 + 1.09848i) q^{42} +4.24839 q^{43} +(-5.62622 - 9.74489i) q^{44} +(0.628032 - 1.08778i) q^{45} +(0.0897684 - 0.155483i) q^{46} +(-3.13042 - 5.42204i) q^{47} +4.88953 q^{48} +(-3.25057 - 6.19950i) q^{49} -0.967272 q^{50} +(-3.15961 - 5.47260i) q^{51} +(1.38953 - 2.40673i) q^{53} +(0.938616 + 1.62573i) q^{54} -8.60891 q^{55} +(1.77008 - 2.92674i) q^{56} +2.85768 q^{57} +(-1.18967 - 2.06056i) q^{58} +(0.425576 - 0.737119i) q^{59} +(1.99380 - 3.45337i) q^{60} +(-3.38953 - 5.87083i) q^{61} -2.03015 q^{62} +(-2.29835 - 0.0467536i) q^{63} -5.46933 q^{64} +(1.44476 - 2.50240i) q^{66} +(0.493553 - 0.854859i) q^{67} +(4.08961 + 7.08341i) q^{68} -0.788550 q^{69} +(-0.613105 - 1.11364i) q^{70} +3.76223 q^{71} +(-0.561633 - 0.972777i) q^{72} +(4.56760 - 7.91131i) q^{73} +(-1.33429 + 2.31106i) q^{74} +(2.12419 + 3.67921i) q^{75} -3.69881 q^{76} +(7.59879 + 13.8024i) q^{77} +(0.0655625 + 0.113558i) q^{79} +(-2.42096 + 4.19322i) q^{80} +(2.81922 - 4.88303i) q^{81} +(1.25532 + 2.17428i) q^{82} +2.66812 q^{83} +(-7.29653 - 0.148428i) q^{84} +6.25768 q^{85} +(-0.706030 - 1.22288i) q^{86} +(-5.22517 + 9.05026i) q^{87} +(-3.84936 + 6.66729i) q^{88} +(-4.85869 - 8.41550i) q^{89} -0.417485 q^{90} +1.02065 q^{92} +(4.45834 + 7.72207i) q^{93} +(-1.04047 + 1.80215i) q^{94} +(-1.41493 + 2.45072i) q^{95} +(-2.69983 - 4.67625i) q^{96} +6.58319 q^{97} +(-1.24429 + 1.96594i) q^{98} +5.17429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 6q^{4} - 12q^{9} + O(q^{10}) \) \( 16q - 4q^{3} - 6q^{4} - 12q^{9} + 6q^{10} - 18q^{12} - 26q^{14} + 2q^{16} - 8q^{17} - 36q^{22} + 12q^{23} + 32q^{27} - 16q^{29} - 38q^{30} + 56q^{36} - 34q^{38} - 4q^{40} + 16q^{42} - 16q^{43} + 36q^{48} - 40q^{49} - 16q^{51} - 20q^{53} + 24q^{55} + 36q^{56} - 12q^{61} - 44q^{62} - 88q^{64} + 2q^{66} - 2q^{68} + 56q^{69} + 42q^{74} - 8q^{75} + 76q^{77} + 20q^{79} - 24q^{81} + 16q^{82} - 68q^{87} - 4q^{88} + 216q^{90} + 12q^{92} - 26q^{94} + 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.166188 0.287846i −0.117512 0.203538i 0.801269 0.598304i \(-0.204159\pi\)
−0.918781 + 0.394767i \(0.870825\pi\)
\(3\) −0.729919 + 1.26426i −0.421419 + 0.729919i −0.996079 0.0884737i \(-0.971801\pi\)
0.574660 + 0.818392i \(0.305134\pi\)
\(4\) 0.944763 1.63638i 0.472382 0.818189i
\(5\) −0.722811 1.25195i −0.323251 0.559887i 0.657906 0.753100i \(-0.271442\pi\)
−0.981157 + 0.193213i \(0.938109\pi\)
\(6\) 0.485214 0.198088
\(7\) −1.36920 + 2.26391i −0.517510 + 0.855677i
\(8\) −1.29278 −0.457068
\(9\) 0.434437 + 0.752468i 0.144812 + 0.250823i
\(10\) −0.240245 + 0.416116i −0.0759720 + 0.131587i
\(11\) 2.97758 5.15732i 0.897774 1.55499i 0.0674405 0.997723i \(-0.478517\pi\)
0.830333 0.557267i \(-0.188150\pi\)
\(12\) 1.37920 + 2.38885i 0.398141 + 0.689600i
\(13\) 0 0
\(14\) 0.879201 + 0.0178849i 0.234976 + 0.00477994i
\(15\) 2.11037 0.544896
\(16\) −1.67468 2.90063i −0.418670 0.725159i
\(17\) −2.16436 + 3.74877i −0.524933 + 0.909211i 0.474645 + 0.880177i \(0.342576\pi\)
−0.999578 + 0.0290341i \(0.990757\pi\)
\(18\) 0.144396 0.250102i 0.0340345 0.0589496i
\(19\) −0.978767 1.69527i −0.224545 0.388923i 0.731638 0.681693i \(-0.238756\pi\)
−0.956183 + 0.292771i \(0.905423\pi\)
\(20\) −2.73154 −0.610791
\(21\) −1.86276 3.38349i −0.406486 0.738339i
\(22\) −1.97935 −0.421998
\(23\) 0.270081 + 0.467795i 0.0563158 + 0.0975419i 0.892809 0.450436i \(-0.148731\pi\)
−0.836493 + 0.547977i \(0.815398\pi\)
\(24\) 0.943626 1.63441i 0.192617 0.333622i
\(25\) 1.45509 2.52029i 0.291018 0.504058i
\(26\) 0 0
\(27\) −5.64793 −1.08694
\(28\) 2.41104 + 4.37939i 0.455644 + 0.827627i
\(29\) 7.15857 1.32931 0.664656 0.747149i \(-0.268578\pi\)
0.664656 + 0.747149i \(0.268578\pi\)
\(30\) −0.350718 0.607461i −0.0640320 0.110907i
\(31\) 3.05400 5.28968i 0.548514 0.950055i −0.449862 0.893098i \(-0.648527\pi\)
0.998377 0.0569568i \(-0.0181397\pi\)
\(32\) −1.84941 + 3.20327i −0.326932 + 0.566263i
\(33\) 4.34678 + 7.52885i 0.756678 + 1.31060i
\(34\) 1.43876 0.246745
\(35\) 3.82396 + 0.0777879i 0.646368 + 0.0131486i
\(36\) 1.64176 0.273627
\(37\) −4.01441 6.95316i −0.659964 1.14309i −0.980624 0.195897i \(-0.937238\pi\)
0.320660 0.947194i \(-0.396095\pi\)
\(38\) −0.325318 + 0.563467i −0.0527736 + 0.0914065i
\(39\) 0 0
\(40\) 0.934437 + 1.61849i 0.147748 + 0.255906i
\(41\) −7.55362 −1.17968 −0.589839 0.807521i \(-0.700809\pi\)
−0.589839 + 0.807521i \(0.700809\pi\)
\(42\) −0.664356 + 1.09848i −0.102512 + 0.169499i
\(43\) 4.24839 0.647873 0.323936 0.946079i \(-0.394994\pi\)
0.323936 + 0.946079i \(0.394994\pi\)
\(44\) −5.62622 9.74489i −0.848184 1.46910i
\(45\) 0.628032 1.08778i 0.0936215 0.162157i
\(46\) 0.0897684 0.155483i 0.0132356 0.0229248i
\(47\) −3.13042 5.42204i −0.456618 0.790886i 0.542161 0.840274i \(-0.317606\pi\)
−0.998780 + 0.0493882i \(0.984273\pi\)
\(48\) 4.88953 0.705742
\(49\) −3.25057 6.19950i −0.464367 0.885643i
\(50\) −0.967272 −0.136793
\(51\) −3.15961 5.47260i −0.442434 0.766317i
\(52\) 0 0
\(53\) 1.38953 2.40673i 0.190866 0.330590i −0.754671 0.656103i \(-0.772204\pi\)
0.945538 + 0.325513i \(0.105537\pi\)
\(54\) 0.938616 + 1.62573i 0.127729 + 0.221234i
\(55\) −8.60891 −1.16082
\(56\) 1.77008 2.92674i 0.236537 0.391103i
\(57\) 2.85768 0.378509
\(58\) −1.18967 2.06056i −0.156211 0.270565i
\(59\) 0.425576 0.737119i 0.0554053 0.0959647i −0.836993 0.547214i \(-0.815688\pi\)
0.892398 + 0.451250i \(0.149022\pi\)
\(60\) 1.99380 3.45337i 0.257399 0.445828i
\(61\) −3.38953 5.87083i −0.433984 0.751683i 0.563228 0.826302i \(-0.309559\pi\)
−0.997212 + 0.0746187i \(0.976226\pi\)
\(62\) −2.03015 −0.257829
\(63\) −2.29835 0.0467536i −0.289565 0.00589039i
\(64\) −5.46933 −0.683667
\(65\) 0 0
\(66\) 1.44476 2.50240i 0.177838 0.308025i
\(67\) 0.493553 0.854859i 0.0602971 0.104438i −0.834301 0.551309i \(-0.814129\pi\)
0.894598 + 0.446871i \(0.147462\pi\)
\(68\) 4.08961 + 7.08341i 0.495938 + 0.858990i
\(69\) −0.788550 −0.0949302
\(70\) −0.613105 1.11364i −0.0732801 0.133105i
\(71\) 3.76223 0.446494 0.223247 0.974762i \(-0.428334\pi\)
0.223247 + 0.974762i \(0.428334\pi\)
\(72\) −0.561633 0.972777i −0.0661891 0.114643i
\(73\) 4.56760 7.91131i 0.534597 0.925949i −0.464586 0.885528i \(-0.653797\pi\)
0.999183 0.0404208i \(-0.0128699\pi\)
\(74\) −1.33429 + 2.31106i −0.155108 + 0.268655i
\(75\) 2.12419 + 3.67921i 0.245281 + 0.424839i
\(76\) −3.69881 −0.424283
\(77\) 7.59879 + 13.8024i 0.865963 + 1.57293i
\(78\) 0 0
\(79\) 0.0655625 + 0.113558i 0.00737636 + 0.0127762i 0.869690 0.493598i \(-0.164319\pi\)
−0.862314 + 0.506375i \(0.830985\pi\)
\(80\) −2.42096 + 4.19322i −0.270671 + 0.468816i
\(81\) 2.81922 4.88303i 0.313246 0.542558i
\(82\) 1.25532 + 2.17428i 0.138627 + 0.240109i
\(83\) 2.66812 0.292865 0.146432 0.989221i \(-0.453221\pi\)
0.146432 + 0.989221i \(0.453221\pi\)
\(84\) −7.29653 0.148428i −0.796117 0.0161948i
\(85\) 6.25768 0.678741
\(86\) −0.706030 1.22288i −0.0761331 0.131866i
\(87\) −5.22517 + 9.05026i −0.560197 + 0.970290i
\(88\) −3.84936 + 6.66729i −0.410344 + 0.710736i
\(89\) −4.85869 8.41550i −0.515021 0.892042i −0.999848 0.0174319i \(-0.994451\pi\)
0.484828 0.874610i \(-0.338882\pi\)
\(90\) −0.417485 −0.0440068
\(91\) 0 0
\(92\) 1.02065 0.106410
\(93\) 4.45834 + 7.72207i 0.462308 + 0.800742i
\(94\) −1.04047 + 1.80215i −0.107317 + 0.185878i
\(95\) −1.41493 + 2.45072i −0.145168 + 0.251439i
\(96\) −2.69983 4.67625i −0.275550 0.477267i
\(97\) 6.58319 0.668422 0.334211 0.942498i \(-0.391530\pi\)
0.334211 + 0.942498i \(0.391530\pi\)
\(98\) −1.24429 + 1.96594i −0.125693 + 0.198590i
\(99\) 5.17429 0.520036
\(100\) −2.74943 4.76215i −0.274943 0.476215i
\(101\) 0.0354144 0.0613396i 0.00352387 0.00610352i −0.864258 0.503049i \(-0.832212\pi\)
0.867782 + 0.496945i \(0.165545\pi\)
\(102\) −1.05018 + 1.81896i −0.103983 + 0.180104i
\(103\) −3.16910 5.48905i −0.312261 0.540852i 0.666590 0.745424i \(-0.267753\pi\)
−0.978852 + 0.204572i \(0.934420\pi\)
\(104\) 0 0
\(105\) −2.88953 + 4.77769i −0.281989 + 0.466255i
\(106\) −0.923689 −0.0897166
\(107\) −3.87476 6.71129i −0.374588 0.648805i 0.615678 0.787998i \(-0.288882\pi\)
−0.990265 + 0.139193i \(0.955549\pi\)
\(108\) −5.33596 + 9.24215i −0.513453 + 0.889326i
\(109\) 0.0167811 0.0290658i 0.00160734 0.00278400i −0.865221 0.501391i \(-0.832822\pi\)
0.866828 + 0.498607i \(0.166155\pi\)
\(110\) 1.43069 + 2.47804i 0.136411 + 0.236271i
\(111\) 11.7208 1.11249
\(112\) 8.85975 + 0.180227i 0.837168 + 0.0170298i
\(113\) −9.19987 −0.865451 −0.432725 0.901526i \(-0.642448\pi\)
−0.432725 + 0.901526i \(0.642448\pi\)
\(114\) −0.474911 0.822571i −0.0444795 0.0770408i
\(115\) 0.390435 0.676254i 0.0364083 0.0630610i
\(116\) 6.76315 11.7141i 0.627943 1.08763i
\(117\) 0 0
\(118\) −0.282902 −0.0260432
\(119\) −5.52344 10.0327i −0.506333 0.919699i
\(120\) −2.72825 −0.249054
\(121\) −12.2320 21.1864i −1.11200 1.92603i
\(122\) −1.12660 + 1.95132i −0.101997 + 0.176664i
\(123\) 5.51353 9.54971i 0.497138 0.861068i
\(124\) −5.77061 9.99499i −0.518216 0.897577i
\(125\) −11.4351 −1.02279
\(126\) 0.368500 + 0.669340i 0.0328286 + 0.0596296i
\(127\) 14.3952 1.27737 0.638683 0.769470i \(-0.279480\pi\)
0.638683 + 0.769470i \(0.279480\pi\)
\(128\) 4.60775 + 7.98085i 0.407271 + 0.705414i
\(129\) −3.10098 + 5.37105i −0.273026 + 0.472895i
\(130\) 0 0
\(131\) 4.73414 + 8.19978i 0.413624 + 0.716418i 0.995283 0.0970151i \(-0.0309295\pi\)
−0.581659 + 0.813433i \(0.697596\pi\)
\(132\) 16.4267 1.42976
\(133\) 5.17808 + 0.105334i 0.448996 + 0.00913357i
\(134\) −0.328090 −0.0283426
\(135\) 4.08238 + 7.07090i 0.351356 + 0.608566i
\(136\) 2.79804 4.84635i 0.239930 0.415571i
\(137\) −8.30313 + 14.3814i −0.709384 + 1.22869i 0.255702 + 0.966756i \(0.417693\pi\)
−0.965086 + 0.261934i \(0.915640\pi\)
\(138\) 0.131047 + 0.226980i 0.0111555 + 0.0193219i
\(139\) 18.4778 1.56726 0.783632 0.621225i \(-0.213365\pi\)
0.783632 + 0.621225i \(0.213365\pi\)
\(140\) 3.74003 6.18396i 0.316090 0.522640i
\(141\) 9.13980 0.769710
\(142\) −0.625236 1.08294i −0.0524687 0.0908784i
\(143\) 0 0
\(144\) 1.45509 2.52029i 0.121257 0.210024i
\(145\) −5.17429 8.96213i −0.429701 0.744264i
\(146\) −3.03631 −0.251287
\(147\) 10.2104 + 0.415577i 0.842140 + 0.0342762i
\(148\) −15.1707 −1.24702
\(149\) 1.54040 + 2.66805i 0.126195 + 0.218575i 0.922199 0.386715i \(-0.126390\pi\)
−0.796005 + 0.605290i \(0.793057\pi\)
\(150\) 0.706030 1.22288i 0.0576471 0.0998477i
\(151\) −1.27442 + 2.20737i −0.103711 + 0.179633i −0.913211 0.407487i \(-0.866405\pi\)
0.809500 + 0.587120i \(0.199738\pi\)
\(152\) 1.26533 + 2.19162i 0.102632 + 0.177764i
\(153\) −3.76111 −0.304068
\(154\) 2.71013 4.48106i 0.218388 0.361095i
\(155\) −8.82985 −0.709231
\(156\) 0 0
\(157\) 4.70452 8.14847i 0.375461 0.650318i −0.614935 0.788578i \(-0.710818\pi\)
0.990396 + 0.138260i \(0.0441509\pi\)
\(158\) 0.0217914 0.0377438i 0.00173363 0.00300273i
\(159\) 2.02848 + 3.51344i 0.160869 + 0.278634i
\(160\) 5.34708 0.422724
\(161\) −1.42884 0.0290658i −0.112608 0.00229070i
\(162\) −1.87408 −0.147241
\(163\) −0.347578 0.602023i −0.0272244 0.0471541i 0.852092 0.523392i \(-0.175334\pi\)
−0.879317 + 0.476238i \(0.842000\pi\)
\(164\) −7.13638 + 12.3606i −0.557258 + 0.965199i
\(165\) 6.28380 10.8839i 0.489193 0.847308i
\(166\) −0.443409 0.768007i −0.0344152 0.0596089i
\(167\) 13.9840 1.08211 0.541056 0.840986i \(-0.318025\pi\)
0.541056 + 0.840986i \(0.318025\pi\)
\(168\) 2.40814 + 4.37412i 0.185792 + 0.337471i
\(169\) 0 0
\(170\) −1.03995 1.80125i −0.0797605 0.138149i
\(171\) 0.850426 1.47298i 0.0650337 0.112642i
\(172\) 4.01372 6.95197i 0.306043 0.530083i
\(173\) 2.71824 + 4.70813i 0.206664 + 0.357952i 0.950662 0.310230i \(-0.100406\pi\)
−0.743998 + 0.668182i \(0.767073\pi\)
\(174\) 3.47344 0.263321
\(175\) 3.71339 + 6.74497i 0.280706 + 0.509872i
\(176\) −19.9460 −1.50349
\(177\) 0.621272 + 1.07607i 0.0466976 + 0.0808827i
\(178\) −1.61491 + 2.79711i −0.121043 + 0.209652i
\(179\) −2.67912 + 4.64037i −0.200247 + 0.346838i −0.948608 0.316454i \(-0.897508\pi\)
0.748361 + 0.663292i \(0.230841\pi\)
\(180\) −1.18668 2.05540i −0.0884502 0.153200i
\(181\) 7.54016 0.560456 0.280228 0.959933i \(-0.409590\pi\)
0.280228 + 0.959933i \(0.409590\pi\)
\(182\) 0 0
\(183\) 9.89632 0.731557
\(184\) −0.349157 0.604757i −0.0257402 0.0445833i
\(185\) −5.80331 + 10.0516i −0.426668 + 0.739011i
\(186\) 1.48184 2.56663i 0.108654 0.188194i
\(187\) 12.8891 + 22.3245i 0.942543 + 1.63253i
\(188\) −11.8300 −0.862793
\(189\) 7.73316 12.7864i 0.562504 0.930074i
\(190\) 0.940574 0.0682364
\(191\) −6.77316 11.7315i −0.490089 0.848859i 0.509846 0.860266i \(-0.329702\pi\)
−0.999935 + 0.0114067i \(0.996369\pi\)
\(192\) 3.99217 6.91464i 0.288110 0.499021i
\(193\) −9.27812 + 16.0702i −0.667853 + 1.15676i 0.310650 + 0.950524i \(0.399453\pi\)
−0.978503 + 0.206232i \(0.933880\pi\)
\(194\) −1.09405 1.89494i −0.0785479 0.136049i
\(195\) 0 0
\(196\) −13.2157 0.537898i −0.943982 0.0384213i
\(197\) −2.66812 −0.190096 −0.0950480 0.995473i \(-0.530300\pi\)
−0.0950480 + 0.995473i \(0.530300\pi\)
\(198\) −0.859903 1.48940i −0.0611106 0.105847i
\(199\) −10.0999 + 17.4936i −0.715965 + 1.24009i 0.246621 + 0.969112i \(0.420680\pi\)
−0.962586 + 0.270976i \(0.912654\pi\)
\(200\) −1.88111 + 3.25819i −0.133015 + 0.230389i
\(201\) 0.720507 + 1.24795i 0.0508206 + 0.0880239i
\(202\) −0.0235418 −0.00165639
\(203\) −9.80152 + 16.2063i −0.687932 + 1.13746i
\(204\) −11.9403 −0.835990
\(205\) 5.45984 + 9.45672i 0.381332 + 0.660486i
\(206\) −1.05333 + 1.82443i −0.0733891 + 0.127114i
\(207\) −0.234667 + 0.406455i −0.0163105 + 0.0282506i
\(208\) 0 0
\(209\) −11.6574 −0.806361
\(210\) 1.85544 + 0.0377438i 0.128038 + 0.00260457i
\(211\) 13.1268 0.903683 0.451842 0.892098i \(-0.350767\pi\)
0.451842 + 0.892098i \(0.350767\pi\)
\(212\) −2.62555 4.54758i −0.180323 0.312329i
\(213\) −2.74612 + 4.75642i −0.188161 + 0.325905i
\(214\) −1.28788 + 2.23067i −0.0880374 + 0.152485i
\(215\) −3.07078 5.31875i −0.209425 0.362736i
\(216\) 7.30155 0.496807
\(217\) 7.79382 + 14.1566i 0.529079 + 0.961014i
\(218\) −0.0111553 −0.000755530
\(219\) 6.66795 + 11.5492i 0.450578 + 0.780424i
\(220\) −8.13338 + 14.0874i −0.548352 + 0.949774i
\(221\) 0 0
\(222\) −1.94785 3.37377i −0.130731 0.226433i
\(223\) −2.22334 −0.148886 −0.0744428 0.997225i \(-0.523718\pi\)
−0.0744428 + 0.997225i \(0.523718\pi\)
\(224\) −4.71969 8.57281i −0.315348 0.572795i
\(225\) 2.52858 0.168572
\(226\) 1.52890 + 2.64814i 0.101701 + 0.176152i
\(227\) −13.5523 + 23.4732i −0.899495 + 1.55797i −0.0713539 + 0.997451i \(0.522732\pi\)
−0.828141 + 0.560520i \(0.810601\pi\)
\(228\) 2.69983 4.67625i 0.178801 0.309692i
\(229\) 9.49437 + 16.4447i 0.627406 + 1.08670i 0.988070 + 0.154003i \(0.0492166\pi\)
−0.360665 + 0.932696i \(0.617450\pi\)
\(230\) −0.259542 −0.0171137
\(231\) −22.9962 0.467795i −1.51304 0.0307786i
\(232\) −9.25447 −0.607586
\(233\) −10.8700 18.8274i −0.712118 1.23343i −0.964060 0.265683i \(-0.914403\pi\)
0.251942 0.967742i \(-0.418931\pi\)
\(234\) 0 0
\(235\) −4.52540 + 7.83822i −0.295205 + 0.511309i
\(236\) −0.804137 1.39281i −0.0523449 0.0906639i
\(237\) −0.191421 −0.0124342
\(238\) −1.96995 + 3.25722i −0.127693 + 0.211134i
\(239\) 19.9695 1.29172 0.645861 0.763455i \(-0.276499\pi\)
0.645861 + 0.763455i \(0.276499\pi\)
\(240\) −3.53420 6.12142i −0.228132 0.395136i
\(241\) −1.61524 + 2.79768i −0.104047 + 0.180214i −0.913348 0.407179i \(-0.866513\pi\)
0.809302 + 0.587393i \(0.199846\pi\)
\(242\) −4.06560 + 7.04183i −0.261347 + 0.452666i
\(243\) −4.35630 7.54533i −0.279456 0.484033i
\(244\) −12.8092 −0.820025
\(245\) −5.41188 + 8.55060i −0.345753 + 0.546278i
\(246\) −3.66512 −0.233680
\(247\) 0 0
\(248\) −3.94816 + 6.83841i −0.250708 + 0.434239i
\(249\) −1.94751 + 3.37319i −0.123419 + 0.213767i
\(250\) 1.90038 + 3.29155i 0.120190 + 0.208176i
\(251\) 12.4916 0.788466 0.394233 0.919011i \(-0.371010\pi\)
0.394233 + 0.919011i \(0.371010\pi\)
\(252\) −2.24790 + 3.71680i −0.141605 + 0.234136i
\(253\) 3.21675 0.202236
\(254\) −2.39230 4.14359i −0.150106 0.259992i
\(255\) −4.56760 + 7.91131i −0.286034 + 0.495425i
\(256\) −3.93783 + 6.82052i −0.246114 + 0.426283i
\(257\) −2.91379 5.04682i −0.181757 0.314812i 0.760722 0.649078i \(-0.224845\pi\)
−0.942479 + 0.334266i \(0.891512\pi\)
\(258\) 2.06138 0.128336
\(259\) 21.2378 + 0.432025i 1.31966 + 0.0268447i
\(260\) 0 0
\(261\) 3.10995 + 5.38659i 0.192501 + 0.333422i
\(262\) 1.57351 2.72540i 0.0972119 0.168376i
\(263\) −8.75736 + 15.1682i −0.540002 + 0.935311i 0.458901 + 0.888487i \(0.348243\pi\)
−0.998903 + 0.0468234i \(0.985090\pi\)
\(264\) −5.61945 9.73316i −0.345853 0.599035i
\(265\) −4.01746 −0.246791
\(266\) −0.830213 1.50799i −0.0509036 0.0924609i
\(267\) 14.1858 0.868157
\(268\) −0.932581 1.61528i −0.0569665 0.0986688i
\(269\) −11.1644 + 19.3372i −0.680703 + 1.17901i 0.294064 + 0.955786i \(0.404992\pi\)
−0.974767 + 0.223226i \(0.928341\pi\)
\(270\) 1.35688 2.35019i 0.0825773 0.143028i
\(271\) 13.1847 + 22.8366i 0.800916 + 1.38723i 0.919014 + 0.394225i \(0.128987\pi\)
−0.118098 + 0.993002i \(0.537680\pi\)
\(272\) 14.4984 0.879097
\(273\) 0 0
\(274\) 5.51951 0.333446
\(275\) −8.66529 15.0087i −0.522536 0.905060i
\(276\) −0.744993 + 1.29037i −0.0448433 + 0.0776709i
\(277\) 4.68809 8.12001i 0.281680 0.487884i −0.690119 0.723696i \(-0.742442\pi\)
0.971799 + 0.235812i \(0.0757750\pi\)
\(278\) −3.07078 5.31875i −0.184173 0.318997i
\(279\) 5.30709 0.317727
\(280\) −4.94356 0.100563i −0.295434 0.00600978i
\(281\) −17.7754 −1.06039 −0.530195 0.847876i \(-0.677881\pi\)
−0.530195 + 0.847876i \(0.677881\pi\)
\(282\) −1.51892 2.63085i −0.0904505 0.156665i
\(283\) 4.80331 8.31958i 0.285527 0.494548i −0.687210 0.726459i \(-0.741165\pi\)
0.972737 + 0.231911i \(0.0744979\pi\)
\(284\) 3.55442 6.15643i 0.210916 0.365317i
\(285\) −2.06556 3.57766i −0.122353 0.211922i
\(286\) 0 0
\(287\) 10.3424 17.1007i 0.610494 1.00942i
\(288\) −3.21380 −0.189375
\(289\) −0.868875 1.50494i −0.0511103 0.0885256i
\(290\) −1.71981 + 2.97879i −0.100990 + 0.174921i
\(291\) −4.80519 + 8.32284i −0.281685 + 0.487894i
\(292\) −8.63060 14.9486i −0.505067 0.874803i
\(293\) −11.6338 −0.679654 −0.339827 0.940488i \(-0.610369\pi\)
−0.339827 + 0.940488i \(0.610369\pi\)
\(294\) −1.57722 3.00808i −0.0919855 0.175435i
\(295\) −1.23044 −0.0716392
\(296\) 5.18976 + 8.98892i 0.301648 + 0.522470i
\(297\) −16.8172 + 29.1282i −0.975830 + 1.69019i
\(298\) 0.511991 0.886795i 0.0296588 0.0513706i
\(299\) 0 0
\(300\) 8.02744 0.463464
\(301\) −5.81690 + 9.61796i −0.335281 + 0.554370i
\(302\) 0.847174 0.0487494
\(303\) 0.0516993 + 0.0895459i 0.00297005 + 0.00514427i
\(304\) −3.27825 + 5.67809i −0.188020 + 0.325661i
\(305\) −4.89997 + 8.48700i −0.280572 + 0.485964i
\(306\) 0.625050 + 1.08262i 0.0357317 + 0.0618892i
\(307\) 13.8280 0.789204 0.394602 0.918852i \(-0.370882\pi\)
0.394602 + 0.918852i \(0.370882\pi\)
\(308\) 29.7650 + 0.605485i 1.69602 + 0.0345007i
\(309\) 9.25275 0.526371
\(310\) 1.46741 + 2.54163i 0.0833435 + 0.144355i
\(311\) −15.3572 + 26.5994i −0.870827 + 1.50832i −0.00968369 + 0.999953i \(0.503082\pi\)
−0.861143 + 0.508363i \(0.830251\pi\)
\(312\) 0 0
\(313\) −5.54334 9.60135i −0.313328 0.542701i 0.665752 0.746173i \(-0.268111\pi\)
−0.979081 + 0.203472i \(0.934777\pi\)
\(314\) −3.12733 −0.176486
\(315\) 1.60274 + 2.91120i 0.0903042 + 0.164028i
\(316\) 0.247764 0.0139378
\(317\) 11.9417 + 20.6836i 0.670712 + 1.16171i 0.977703 + 0.209994i \(0.0673445\pi\)
−0.306991 + 0.951712i \(0.599322\pi\)
\(318\) 0.674218 1.16778i 0.0378083 0.0654858i
\(319\) 21.3152 36.9190i 1.19342 2.06707i
\(320\) 3.95329 + 6.84731i 0.220996 + 0.382776i
\(321\) 11.3130 0.631433
\(322\) 0.229089 + 0.416116i 0.0127666 + 0.0231892i
\(323\) 8.47360 0.471484
\(324\) −5.32698 9.22661i −0.295944 0.512589i
\(325\) 0 0
\(326\) −0.115526 + 0.200098i −0.00639842 + 0.0110824i
\(327\) 0.0244977 + 0.0424313i 0.00135473 + 0.00234646i
\(328\) 9.76519 0.539192
\(329\) 16.5612 + 0.336891i 0.913048 + 0.0185734i
\(330\) −4.17716 −0.229945
\(331\) 9.16200 + 15.8690i 0.503589 + 0.872241i 0.999991 + 0.00414903i \(0.00132068\pi\)
−0.496403 + 0.868092i \(0.665346\pi\)
\(332\) 2.52075 4.36606i 0.138344 0.239619i
\(333\) 3.48802 6.04142i 0.191142 0.331068i
\(334\) −2.32396 4.02522i −0.127162 0.220250i
\(335\) −1.42698 −0.0779643
\(336\) −6.69475 + 11.0694i −0.365229 + 0.603888i
\(337\) −7.21762 −0.393169 −0.196584 0.980487i \(-0.562985\pi\)
−0.196584 + 0.980487i \(0.562985\pi\)
\(338\) 0 0
\(339\) 6.71516 11.6310i 0.364717 0.631709i
\(340\) 5.91203 10.2399i 0.320625 0.555338i
\(341\) −18.1870 31.5009i −0.984884 1.70587i
\(342\) −0.565321 −0.0305691
\(343\) 18.4858 + 1.12937i 0.998139 + 0.0609804i
\(344\) −5.49224 −0.296122
\(345\) 0.569972 + 0.987221i 0.0306863 + 0.0531502i
\(346\) 0.903476 1.56487i 0.0485712 0.0841277i
\(347\) 10.5391 18.2543i 0.565770 0.979942i −0.431208 0.902253i \(-0.641912\pi\)
0.996978 0.0776892i \(-0.0247542\pi\)
\(348\) 9.87310 + 17.1007i 0.529254 + 0.916694i
\(349\) −30.7629 −1.64670 −0.823350 0.567534i \(-0.807898\pi\)
−0.823350 + 0.567534i \(0.807898\pi\)
\(350\) 1.32439 2.18982i 0.0707917 0.117051i
\(351\) 0 0
\(352\) 11.0135 + 19.0760i 0.587022 + 1.01675i
\(353\) −3.06086 + 5.30157i −0.162913 + 0.282174i −0.935912 0.352233i \(-0.885422\pi\)
0.772999 + 0.634407i \(0.218756\pi\)
\(354\) 0.206495 0.357660i 0.0109751 0.0190094i
\(355\) −2.71938 4.71010i −0.144330 0.249986i
\(356\) −18.3613 −0.973145
\(357\) 16.7156 + 0.340033i 0.884684 + 0.0179964i
\(358\) 1.78095 0.0941259
\(359\) 9.71433 + 16.8257i 0.512703 + 0.888028i 0.999891 + 0.0147308i \(0.00468913\pi\)
−0.487189 + 0.873297i \(0.661978\pi\)
\(360\) −0.811909 + 1.40627i −0.0427914 + 0.0741168i
\(361\) 7.58403 13.1359i 0.399160 0.691365i
\(362\) −1.25308 2.17040i −0.0658605 0.114074i
\(363\) 35.7133 1.87446
\(364\) 0 0
\(365\) −13.2060 −0.691235
\(366\) −1.64465 2.84861i −0.0859670 0.148899i
\(367\) 2.70234 4.68058i 0.141061 0.244324i −0.786836 0.617163i \(-0.788282\pi\)
0.927896 + 0.372838i \(0.121615\pi\)
\(368\) 0.904601 1.56681i 0.0471556 0.0816758i
\(369\) −3.28158 5.68385i −0.170832 0.295890i
\(370\) 3.85776 0.200555
\(371\) 3.54608 + 6.44106i 0.184103 + 0.334403i
\(372\) 16.8483 0.873544
\(373\) −8.12533 14.0735i −0.420714 0.728698i 0.575296 0.817946i \(-0.304887\pi\)
−0.996009 + 0.0892478i \(0.971554\pi\)
\(374\) 4.28401 7.42013i 0.221521 0.383686i
\(375\) 8.34671 14.4569i 0.431022 0.746553i
\(376\) 4.04695 + 7.00952i 0.208706 + 0.361489i
\(377\) 0 0
\(378\) −4.96566 0.101013i −0.255406 0.00519553i
\(379\) 25.1730 1.29305 0.646525 0.762893i \(-0.276222\pi\)
0.646525 + 0.762893i \(0.276222\pi\)
\(380\) 2.67354 + 4.63071i 0.137150 + 0.237550i
\(381\) −10.5073 + 18.1992i −0.538306 + 0.932373i
\(382\) −2.25123 + 3.89925i −0.115183 + 0.199503i
\(383\) −1.90719 3.30335i −0.0974529 0.168793i 0.813177 0.582017i \(-0.197736\pi\)
−0.910630 + 0.413223i \(0.864403\pi\)
\(384\) −13.4531 −0.686527
\(385\) 11.7873 19.4898i 0.600738 0.993291i
\(386\) 6.16764 0.313924
\(387\) 1.84566 + 3.19677i 0.0938201 + 0.162501i
\(388\) 6.21956 10.7726i 0.315750 0.546895i
\(389\) 1.43548 2.48632i 0.0727817 0.126062i −0.827338 0.561705i \(-0.810146\pi\)
0.900119 + 0.435643i \(0.143479\pi\)
\(390\) 0 0
\(391\) −2.33821 −0.118248
\(392\) 4.20228 + 8.01461i 0.212247 + 0.404799i
\(393\) −13.8222 −0.697236
\(394\) 0.443409 + 0.768007i 0.0223386 + 0.0386917i
\(395\) 0.0947786 0.164161i 0.00476883 0.00825986i
\(396\) 4.88848 8.46709i 0.245655 0.425487i
\(397\) 9.55919 + 16.5570i 0.479762 + 0.830972i 0.999731 0.0232131i \(-0.00738963\pi\)
−0.519968 + 0.854185i \(0.674056\pi\)
\(398\) 6.71394 0.336539
\(399\) −3.91274 + 6.46953i −0.195882 + 0.323882i
\(400\) −9.74725 −0.487362
\(401\) −1.49912 2.59655i −0.0748625 0.129666i 0.826164 0.563430i \(-0.190518\pi\)
−0.901026 + 0.433764i \(0.857185\pi\)
\(402\) 0.239479 0.414789i 0.0119441 0.0206878i
\(403\) 0 0
\(404\) −0.0669165 0.115903i −0.00332922 0.00576638i
\(405\) −8.15104 −0.405028
\(406\) 6.29382 + 0.128030i 0.312357 + 0.00635403i
\(407\) −47.8129 −2.37000
\(408\) 4.08469 + 7.07489i 0.202222 + 0.350259i
\(409\) 17.0403 29.5146i 0.842587 1.45940i −0.0451127 0.998982i \(-0.514365\pi\)
0.887700 0.460422i \(-0.152302\pi\)
\(410\) 1.81472 3.14318i 0.0896224 0.155231i
\(411\) −12.1212 20.9946i −0.597896 1.03559i
\(412\) −11.9762 −0.590026
\(413\) 1.08607 + 1.97273i 0.0534421 + 0.0970717i
\(414\) 0.155995 0.00766674
\(415\) −1.92855 3.34034i −0.0946687 0.163971i
\(416\) 0 0
\(417\) −13.4873 + 23.3606i −0.660475 + 1.14398i
\(418\) 1.93732 + 3.35554i 0.0947574 + 0.164125i
\(419\) 34.7759 1.69891 0.849457 0.527657i \(-0.176929\pi\)
0.849457 + 0.527657i \(0.176929\pi\)
\(420\) 5.08819 + 9.24215i 0.248278 + 0.450971i
\(421\) −24.1400 −1.17651 −0.588257 0.808674i \(-0.700186\pi\)
−0.588257 + 0.808674i \(0.700186\pi\)
\(422\) −2.18151 3.77848i −0.106194 0.183933i
\(423\) 2.71994 4.71108i 0.132248 0.229060i
\(424\) −1.79636 + 3.11138i −0.0872388 + 0.151102i
\(425\) 6.29866 + 10.9096i 0.305530 + 0.529193i
\(426\) 1.82549 0.0884451
\(427\) 17.9320 + 0.364776i 0.867789 + 0.0176528i
\(428\) −14.6429 −0.707793
\(429\) 0 0
\(430\) −1.02065 + 1.76782i −0.0492202 + 0.0852519i
\(431\) 2.38238 4.12641i 0.114755 0.198762i −0.802927 0.596078i \(-0.796725\pi\)
0.917682 + 0.397316i \(0.130058\pi\)
\(432\) 9.45848 + 16.3826i 0.455071 + 0.788207i
\(433\) 22.0231 1.05836 0.529181 0.848509i \(-0.322499\pi\)
0.529181 + 0.848509i \(0.322499\pi\)
\(434\) 2.77968 4.59607i 0.133429 0.220618i
\(435\) 15.1072 0.724337
\(436\) −0.0317084 0.0549206i −0.00151856 0.00263022i
\(437\) 0.528693 0.915724i 0.0252908 0.0438050i
\(438\) 2.21626 3.83868i 0.105897 0.183419i
\(439\) −1.71620 2.97254i −0.0819097 0.141872i 0.822161 0.569256i \(-0.192769\pi\)
−0.904070 + 0.427384i \(0.859435\pi\)
\(440\) 11.1294 0.530576
\(441\) 3.25275 5.13924i 0.154893 0.244726i
\(442\) 0 0
\(443\) 4.35297 + 7.53957i 0.206816 + 0.358216i 0.950710 0.310082i \(-0.100357\pi\)
−0.743894 + 0.668298i \(0.767023\pi\)
\(444\) 11.0733 19.1796i 0.525518 0.910223i
\(445\) −7.02383 + 12.1656i −0.332962 + 0.576706i
\(446\) 0.369491 + 0.639977i 0.0174959 + 0.0303038i
\(447\) −4.49747 −0.212723
\(448\) 7.48862 12.3821i 0.353804 0.584998i
\(449\) −17.6120 −0.831159 −0.415580 0.909557i \(-0.636421\pi\)
−0.415580 + 0.909557i \(0.636421\pi\)
\(450\) −0.420219 0.727841i −0.0198093 0.0343107i
\(451\) −22.4915 + 38.9564i −1.05908 + 1.83439i
\(452\) −8.69170 + 15.0545i −0.408823 + 0.708102i
\(453\) −1.86045 3.22240i −0.0874116 0.151401i
\(454\) 9.00887 0.422807
\(455\) 0 0
\(456\) −3.69436 −0.173004
\(457\) −4.53634 7.85717i −0.212201 0.367543i 0.740202 0.672384i \(-0.234730\pi\)
−0.952403 + 0.304842i \(0.901396\pi\)
\(458\) 3.15570 5.46583i 0.147456 0.255401i
\(459\) 12.2241 21.1728i 0.570573 0.988262i
\(460\) −0.737738 1.27780i −0.0343972 0.0595777i
\(461\) −6.58319 −0.306610 −0.153305 0.988179i \(-0.548992\pi\)
−0.153305 + 0.988179i \(0.548992\pi\)
\(462\) 3.68704 + 6.69711i 0.171537 + 0.311578i
\(463\) −3.47344 −0.161424 −0.0807121 0.996737i \(-0.525719\pi\)
−0.0807121 + 0.996737i \(0.525719\pi\)
\(464\) −11.9883 20.7644i −0.556544 0.963962i
\(465\) 6.44507 11.1632i 0.298883 0.517681i
\(466\) −3.61293 + 6.25777i −0.167366 + 0.289886i
\(467\) −14.8927 25.7949i −0.689152 1.19365i −0.972112 0.234515i \(-0.924650\pi\)
0.282960 0.959132i \(-0.408684\pi\)
\(468\) 0 0
\(469\) 1.25955 + 2.28783i 0.0581606 + 0.105642i
\(470\) 3.00826 0.138761
\(471\) 6.86783 + 11.8954i 0.316453 + 0.548113i
\(472\) −0.550177 + 0.952935i −0.0253240 + 0.0438624i
\(473\) 12.6499 21.9103i 0.581643 1.00744i
\(474\) 0.0318119 + 0.0550998i 0.00146117 + 0.00253082i
\(475\) −5.69677 −0.261386
\(476\) −21.6357 0.440118i −0.991671 0.0201728i
\(477\) 2.41465 0.110559
\(478\) −3.31869 5.74814i −0.151793 0.262914i
\(479\) 17.5927 30.4715i 0.803833 1.39228i −0.113243 0.993567i \(-0.536124\pi\)
0.917076 0.398712i \(-0.130543\pi\)
\(480\) −3.90294 + 6.76008i −0.178144 + 0.308554i
\(481\) 0 0
\(482\) 1.07373 0.0489072
\(483\) 1.07968 1.78520i 0.0491273 0.0812296i
\(484\) −46.2252 −2.10115
\(485\) −4.75840 8.24179i −0.216068 0.374241i
\(486\) −1.44793 + 2.50788i −0.0656792 + 0.113760i
\(487\) −0.900769 + 1.56018i −0.0408178 + 0.0706984i −0.885713 0.464234i \(-0.846330\pi\)
0.844895 + 0.534933i \(0.179663\pi\)
\(488\) 4.38192 + 7.58971i 0.198360 + 0.343570i
\(489\) 1.01482 0.0458916
\(490\) 3.36064 + 0.136782i 0.151818 + 0.00617920i
\(491\) −8.19322 −0.369755 −0.184877 0.982762i \(-0.559189\pi\)
−0.184877 + 0.982762i \(0.559189\pi\)
\(492\) −10.4180 18.0444i −0.469678 0.813506i
\(493\) −15.4937 + 26.8358i −0.697800 + 1.20863i
\(494\) 0 0
\(495\) −3.74003 6.47792i −0.168102 0.291161i
\(496\) −20.4579 −0.918587
\(497\) −5.15125 + 8.51734i −0.231065 + 0.382055i
\(498\) 1.29461 0.0580129
\(499\) −18.2582 31.6242i −0.817350 1.41569i −0.907628 0.419775i \(-0.862109\pi\)
0.0902781 0.995917i \(-0.471224\pi\)
\(500\) −10.8035 + 18.7122i −0.483147 + 0.836834i
\(501\) −10.2072 + 17.6793i −0.456022 + 0.789854i
\(502\) −2.07596 3.59566i −0.0926545 0.160482i
\(503\) −3.02972 −0.135089 −0.0675443 0.997716i \(-0.521516\pi\)
−0.0675443 + 0.997716i \(0.521516\pi\)
\(504\) 2.97127 + 0.0604422i 0.132351 + 0.00269231i
\(505\) −0.102392 −0.00455637
\(506\) −0.534585 0.925928i −0.0237652 0.0411625i
\(507\) 0 0
\(508\) 13.6000 23.5559i 0.603404 1.04513i
\(509\) 14.6724 + 25.4133i 0.650341 + 1.12642i 0.983040 + 0.183391i \(0.0587074\pi\)
−0.332699 + 0.943033i \(0.607959\pi\)
\(510\) 3.03631 0.134450
\(511\) 11.6565 + 21.1728i 0.515654 + 0.936630i
\(512\) 21.0487 0.930229
\(513\) 5.52800 + 9.57479i 0.244067 + 0.422737i
\(514\) −0.968471 + 1.67744i −0.0427174 + 0.0739887i
\(515\) −4.58133 + 7.93509i −0.201877 + 0.349662i
\(516\) 5.85938 + 10.1487i 0.257945 + 0.446773i
\(517\) −37.2843 −1.63976
\(518\) −3.40511 6.18502i −0.149612 0.271754i
\(519\) −7.93637 −0.348368
\(520\) 0 0
\(521\) 14.8419 25.7069i 0.650236 1.12624i −0.332830 0.942987i \(-0.608003\pi\)
0.983066 0.183254i \(-0.0586632\pi\)
\(522\) 1.03367 1.79037i 0.0452425 0.0783624i
\(523\) −10.2864 17.8165i −0.449791 0.779062i 0.548581 0.836098i \(-0.315168\pi\)
−0.998372 + 0.0570361i \(0.981835\pi\)
\(524\) 17.8906 0.781553
\(525\) −11.2379 0.228603i −0.490460 0.00997704i
\(526\) 5.82146 0.253828
\(527\) 13.2199 + 22.8975i 0.575867 + 0.997431i
\(528\) 14.5590 25.2168i 0.633597 1.09742i
\(529\) 11.3541 19.6659i 0.493657 0.855039i
\(530\) 0.667652 + 1.15641i 0.0290010 + 0.0502311i
\(531\) 0.739544 0.0320935
\(532\) 5.06442 8.37377i 0.219571 0.363049i
\(533\) 0 0
\(534\) −2.35751 4.08332i −0.102019 0.176703i
\(535\) −5.60144 + 9.70198i −0.242171 + 0.419453i
\(536\) −0.638057 + 1.10515i −0.0275599 + 0.0477351i
\(537\) −3.91108 6.77419i −0.168775 0.292328i
\(538\) 7.42151 0.319964
\(539\) −41.6516 1.69527i −1.79406 0.0730206i
\(540\) 15.4275 0.663896
\(541\) −17.0334 29.5027i −0.732324 1.26842i −0.955888 0.293732i \(-0.905103\pi\)
0.223564 0.974689i \(-0.428231\pi\)
\(542\) 4.38228 7.59034i 0.188235 0.326033i
\(543\) −5.50371 + 9.53270i −0.236187 + 0.409087i
\(544\) −8.00555 13.8660i −0.343235 0.594500i
\(545\) −0.0485183 −0.00207830
\(546\) 0 0
\(547\) −0.850931 −0.0363832 −0.0181916 0.999835i \(-0.505791\pi\)
−0.0181916 + 0.999835i \(0.505791\pi\)
\(548\) 15.6890 + 27.1741i 0.670200 + 1.16082i
\(549\) 2.94507 5.10102i 0.125693 0.217706i
\(550\) −2.88013 + 4.98853i −0.122809 + 0.212712i
\(551\) −7.00657 12.1357i −0.298490 0.516999i
\(552\) 1.01942 0.0433895
\(553\) −0.346853 0.00705575i −0.0147497 0.000300041i
\(554\) −3.11641 −0.132404
\(555\) −8.47189 14.6737i −0.359612 0.622866i
\(556\) 17.4571 30.2366i 0.740347 1.28232i
\(557\) 8.86404 15.3530i 0.375581 0.650526i −0.614833 0.788658i \(-0.710776\pi\)
0.990414 + 0.138132i \(0.0441098\pi\)
\(558\) −0.881972 1.52762i −0.0373369 0.0646694i
\(559\) 0 0
\(560\) −6.17829 11.2222i −0.261080 0.474224i
\(561\) −37.6319 −1.58882
\(562\) 2.95405 + 5.11656i 0.124609 + 0.215829i
\(563\) 12.0903 20.9410i 0.509545 0.882558i −0.490394 0.871501i \(-0.663147\pi\)
0.999939 0.0110571i \(-0.00351966\pi\)
\(564\) 8.63495 14.9562i 0.363597 0.629768i
\(565\) 6.64976 + 11.5177i 0.279758 + 0.484555i
\(566\) −3.19301 −0.134212
\(567\) 7.19465 + 13.0683i 0.302147 + 0.548817i
\(568\) −4.86375 −0.204078
\(569\) 21.3874 + 37.0441i 0.896608 + 1.55297i 0.831802 + 0.555073i \(0.187310\pi\)
0.0648066 + 0.997898i \(0.479357\pi\)
\(570\) −0.686542 + 1.18913i −0.0287561 + 0.0498070i
\(571\) −3.68140 + 6.37637i −0.154062 + 0.266843i −0.932717 0.360609i \(-0.882569\pi\)
0.778655 + 0.627452i \(0.215902\pi\)
\(572\) 0 0
\(573\) 19.7754 0.826131
\(574\) −6.64115 0.135096i −0.277196 0.00563878i
\(575\) 1.57197 0.0655557
\(576\) −2.37608 4.11550i −0.0990035 0.171479i
\(577\) 4.09696 7.09615i 0.170559 0.295417i −0.768057 0.640382i \(-0.778776\pi\)
0.938615 + 0.344965i \(0.112109\pi\)
\(578\) −0.288793 + 0.500204i −0.0120122 + 0.0208057i
\(579\) −13.5445 23.4598i −0.562892 0.974957i
\(580\) −19.5539 −0.811932
\(581\) −3.65320 + 6.04039i −0.151560 + 0.250598i
\(582\) 3.19426 0.132406
\(583\) −8.27485 14.3325i −0.342709 0.593590i
\(584\) −5.90491 + 10.2276i −0.244347 + 0.423221i
\(585\) 0 0
\(586\) 1.93339 + 3.34874i 0.0798678 + 0.138335i
\(587\) 39.1141 1.61441 0.807205 0.590271i \(-0.200979\pi\)
0.807205 + 0.590271i \(0.200979\pi\)
\(588\) 10.3265 16.3155i 0.425856 0.672838i
\(589\) −11.9566 −0.492664
\(590\) 0.204485 + 0.354178i 0.00841849 + 0.0145813i
\(591\) 1.94751 3.37319i 0.0801100 0.138755i
\(592\) −13.4457 + 23.2886i −0.552615 + 0.957158i
\(593\) 0.606691 + 1.05082i 0.0249138 + 0.0431520i 0.878213 0.478269i \(-0.158736\pi\)
−0.853300 + 0.521421i \(0.825402\pi\)
\(594\) 11.1792 0.458689
\(595\) −8.56803 + 14.1668i −0.351255 + 0.580783i
\(596\) 5.82125 0.238448
\(597\) −14.7443 25.5378i −0.603442 1.04519i
\(598\) 0 0
\(599\) −16.3319 + 28.2877i −0.667303 + 1.15580i 0.311352 + 0.950295i \(0.399218\pi\)
−0.978655 + 0.205508i \(0.934115\pi\)
\(600\) −2.74612 4.75642i −0.112110 0.194180i
\(601\) 2.50114 0.102024 0.0510118 0.998698i \(-0.483755\pi\)
0.0510118 + 0.998698i \(0.483755\pi\)
\(602\) 3.73519 + 0.0759819i 0.152235 + 0.00309679i
\(603\) 0.857671 0.0349271
\(604\) 2.40806 + 4.17088i 0.0979825 + 0.169711i
\(605\) −17.6828 + 30.6275i −0.718907 + 1.24518i
\(606\) 0.0171836 0.0297628i 0.000698035 0.00120903i
\(607\) −6.32282 10.9515i −0.256635 0.444506i 0.708703 0.705507i \(-0.249281\pi\)
−0.965338 + 0.261001i \(0.915947\pi\)
\(608\) 7.24055 0.293643
\(609\) −13.3347 24.2209i −0.540347 0.981482i
\(610\) 3.25726 0.131883
\(611\) 0 0
\(612\) −3.55336 + 6.15460i −0.143636 + 0.248785i
\(613\) −10.0140 + 17.3448i −0.404462 + 0.700548i −0.994259 0.107003i \(-0.965874\pi\)
0.589797 + 0.807552i \(0.299208\pi\)
\(614\) −2.29804 3.98032i −0.0927413 0.160633i
\(615\) −15.9409 −0.642801
\(616\) −9.82359 17.8435i −0.395804 0.718934i
\(617\) −45.2926 −1.82341 −0.911705 0.410846i \(-0.865233\pi\)
−0.911705 + 0.410846i \(0.865233\pi\)
\(618\) −1.53769 2.66336i −0.0618551 0.107136i
\(619\) 2.21658 3.83922i 0.0890917 0.154311i −0.818036 0.575167i \(-0.804937\pi\)
0.907127 + 0.420856i \(0.138270\pi\)
\(620\) −8.34212 + 14.4490i −0.335028 + 0.580285i
\(621\) −1.52540 2.64207i −0.0612122 0.106023i
\(622\) 10.2087 0.409332
\(623\) 25.7045 + 0.522886i 1.02983 + 0.0209490i
\(624\) 0 0
\(625\) 0.989985 + 1.71471i 0.0395994 + 0.0685882i
\(626\) −1.84247 + 3.19125i −0.0736400 + 0.127548i
\(627\) 8.50897 14.7380i 0.339816 0.588578i
\(628\) −8.88931 15.3967i −0.354722 0.614397i
\(629\) 34.7544 1.38575
\(630\) 0.571621 0.945148i 0.0227739 0.0376556i
\(631\) 19.7358 0.785672 0.392836 0.919609i \(-0.371494\pi\)
0.392836 + 0.919609i \(0.371494\pi\)
\(632\) −0.0847581 0.146805i −0.00337150 0.00583961i
\(633\) −9.58147 + 16.5956i −0.380829 + 0.659615i
\(634\) 3.96912 6.87472i 0.157634 0.273030i
\(635\) −10.4050 18.0220i −0.412909 0.715180i
\(636\) 7.66574 0.303967
\(637\) 0 0
\(638\) −14.1693 −0.560968
\(639\) 1.63445 + 2.83096i 0.0646580 + 0.111991i
\(640\) 6.66106 11.5373i 0.263302 0.456052i
\(641\) −19.8213 + 34.3314i −0.782893 + 1.35601i 0.147357 + 0.989083i \(0.452923\pi\)
−0.930250 + 0.366926i \(0.880410\pi\)
\(642\) −1.88009 3.25641i −0.0742012 0.128520i
\(643\) −20.8300 −0.821453 −0.410727 0.911759i \(-0.634725\pi\)
−0.410727 + 0.911759i \(0.634725\pi\)
\(644\) −1.39748 + 2.31066i −0.0550684 + 0.0910529i
\(645\) 8.96568 0.353023
\(646\) −1.40821 2.43909i −0.0554052 0.0959646i
\(647\) 7.87206 13.6348i 0.309482 0.536039i −0.668767 0.743472i \(-0.733178\pi\)
0.978249 + 0.207433i \(0.0665109\pi\)
\(648\) −3.64463 + 6.31269i −0.143175 + 0.247986i
\(649\) −2.53437 4.38966i −0.0994828 0.172309i
\(650\) 0 0
\(651\) −23.5864 0.479800i −0.924426 0.0188049i
\(652\) −1.31352 −0.0514413
\(653\) 13.5132 + 23.4055i 0.528812 + 0.915930i 0.999436 + 0.0335954i \(0.0106958\pi\)
−0.470623 + 0.882334i \(0.655971\pi\)
\(654\) 0.00814244 0.0141031i 0.000318395 0.000551476i
\(655\) 6.84378 11.8538i 0.267409 0.463165i
\(656\) 12.6499 + 21.9103i 0.493896 + 0.855453i
\(657\) 7.93734 0.309665
\(658\) −2.65529 4.82305i −0.103514 0.188022i
\(659\) −6.79491 −0.264692 −0.132346 0.991204i \(-0.542251\pi\)
−0.132346 + 0.991204i \(0.542251\pi\)
\(660\) −11.8734 20.5653i −0.462172 0.800505i
\(661\) 3.60263 6.23994i 0.140126 0.242705i −0.787418 0.616420i \(-0.788583\pi\)
0.927544 + 0.373714i \(0.121916\pi\)
\(662\) 3.04522 5.27448i 0.118356 0.204998i
\(663\) 0 0
\(664\) −3.44930 −0.133859
\(665\) −3.61090 6.55880i −0.140025 0.254339i
\(666\) −2.31866 −0.0898463
\(667\) 1.93339 + 3.34874i 0.0748613 + 0.129664i
\(668\) 13.2115 22.8831i 0.511170 0.885372i
\(669\) 1.62285 2.81087i 0.0627432 0.108674i
\(670\) 0.237147 + 0.410750i 0.00916178 + 0.0158687i
\(671\) −40.3703 −1.55848
\(672\) 14.2832 + 0.290552i 0.550987 + 0.0112083i
\(673\) 8.32130 0.320763 0.160381 0.987055i \(-0.448728\pi\)
0.160381 + 0.987055i \(0.448728\pi\)
\(674\) 1.19948 + 2.07756i 0.0462022 + 0.0800246i
\(675\) −8.21824 + 14.2344i −0.316320 + 0.547883i
\(676\) 0 0
\(677\) 14.9978 + 25.9770i 0.576413 + 0.998376i 0.995887 + 0.0906086i \(0.0288812\pi\)
−0.419474 + 0.907767i \(0.637785\pi\)
\(678\) −4.46391 −0.171435
\(679\) −9.01372 + 14.9037i −0.345915 + 0.571953i
\(680\) −8.08982 −0.310231
\(681\) −19.7841 34.2671i −0.758128 1.31312i
\(682\) −6.04493 + 10.4701i −0.231472 + 0.400922i
\(683\) −18.0420 + 31.2496i −0.690356 + 1.19573i 0.281365 + 0.959601i \(0.409213\pi\)
−0.971721 + 0.236132i \(0.924120\pi\)
\(684\) −1.60690 2.78324i −0.0614415 0.106420i
\(685\) 24.0064 0.917236
\(686\) −2.74703 5.50874i −0.104882 0.210325i
\(687\) −27.7205 −1.05760
\(688\) −7.11470 12.3230i −0.271245 0.469811i
\(689\) 0 0
\(690\) 0.189445 0.328128i 0.00721204 0.0124916i
\(691\) −12.8838 22.3155i −0.490124 0.848920i 0.509811 0.860286i \(-0.329715\pi\)
−0.999935 + 0.0113665i \(0.996382\pi\)
\(692\) 10.2724 0.390497
\(693\) −7.08465 + 11.7141i −0.269123 + 0.444983i
\(694\) −7.00589 −0.265940
\(695\) −13.3559 23.1332i −0.506620 0.877491i
\(696\) 6.75501 11.7000i 0.256048 0.443488i
\(697\) 16.3487 28.3168i 0.619252 1.07258i
\(698\) 5.11242 + 8.85496i 0.193508 + 0.335165i
\(699\) 31.7369 1.20040
\(700\) 14.5456 + 0.295890i 0.549772 + 0.0111836i
\(701\) 41.7872 1.57828 0.789141 0.614213i \(-0.210526\pi\)
0.789141 + 0.614213i \(0.210526\pi\)
\(702\) 0 0
\(703\) −7.85834 + 13.6110i −0.296383 + 0.513350i
\(704\) −16.2854 + 28.2071i −0.613778 + 1.06310i
\(705\) −6.60635 11.4425i −0.248809 0.430951i
\(706\) 2.03471 0.0765774
\(707\) 0.0903778 + 0.164161i 0.00339901 + 0.00617393i
\(708\) 2.34782 0.0882364
\(709\) 0.171924 + 0.297781i 0.00645673 + 0.0111834i 0.869236 0.494398i \(-0.164611\pi\)
−0.862779 + 0.505581i \(0.831278\pi\)
\(710\) −0.903855 + 1.56552i −0.0339211 + 0.0587530i
\(711\) −0.0569657 + 0.0986674i −0.00213638 + 0.00370032i
\(712\) 6.28124 + 10.8794i 0.235399 + 0.407724i
\(713\) 3.29931 0.123560
\(714\) −2.68005 4.86802i −0.100298 0.182181i
\(715\) 0 0
\(716\) 5.06227 + 8.76810i 0.189186 + 0.327679i
\(717\) −14.5761 + 25.2466i −0.544356 + 0.942852i
\(718\) 3.22881 5.59246i 0.120498 0.208709i
\(719\) −4.39005 7.60379i −0.163721 0.283574i 0.772479 0.635040i \(-0.219016\pi\)
−0.936200 + 0.351467i \(0.885683\pi\)
\(720\) −4.20702 −0.156786
\(721\) 16.7659 + 0.341055i 0.624393 + 0.0127015i
\(722\) −5.04149 −0.187625
\(723\) −2.35799 4.08416i −0.0876946 0.151891i
\(724\) 7.12367 12.3386i 0.264749 0.458559i
\(725\) 10.4164 18.0416i 0.386854 0.670050i
\(726\) −5.93512 10.2799i −0.220273 0.381524i
\(727\) −17.3658 −0.644064 −0.322032 0.946729i \(-0.604366\pi\)
−0.322032 + 0.946729i \(0.604366\pi\)
\(728\) 0 0
\(729\) 29.6343 1.09757
\(730\) 2.19468 + 3.80130i 0.0812288 + 0.140692i
\(731\) −9.19502 + 15.9262i −0.340090 + 0.589053i
\(732\) 9.34968 16.1941i 0.345574 0.598552i
\(733\) −4.52947 7.84528i −0.167300 0.289772i 0.770170 0.637839i \(-0.220172\pi\)
−0.937470 + 0.348067i \(0.886838\pi\)
\(734\) −1.79638 −0.0663056
\(735\) −6.85991 13.0833i −0.253032 0.482583i
\(736\) −1.99796 −0.0736458
\(737\) −2.93919 5.09082i −0.108266 0.187523i
\(738\) −1.09071 + 1.88917i −0.0401498 + 0.0695414i
\(739\) −3.53921 + 6.13010i −0.130192 + 0.225499i −0.923751 0.382995i \(-0.874893\pi\)
0.793558 + 0.608494i \(0.208226\pi\)
\(740\) 10.9655 + 18.9928i 0.403100 + 0.698190i
\(741\) 0 0
\(742\) 1.26472 2.09115i 0.0464292 0.0767685i
\(743\) 14.6779 0.538479 0.269240 0.963073i \(-0.413228\pi\)
0.269240 + 0.963073i \(0.413228\pi\)
\(744\) −5.76367 9.98297i −0.211306 0.365993i
\(745\) 2.22684 3.85699i 0.0815849 0.141309i
\(746\) −2.70066 + 4.67768i −0.0988782 + 0.171262i
\(747\) 1.15913 + 2.00768i 0.0424105 + 0.0734571i
\(748\) 48.7085 1.78096
\(749\) 20.4991 + 0.416997i 0.749020 + 0.0152367i
\(750\) −5.54848 −0.202602
\(751\) 15.8556 + 27.4628i 0.578580 + 1.00213i 0.995643 + 0.0932523i \(0.0297263\pi\)
−0.417062 + 0.908878i \(0.636940\pi\)
\(752\) −10.4849 + 18.1604i −0.382345 + 0.662241i
\(753\) −9.11788 + 15.7926i −0.332274 + 0.575516i
\(754\) 0 0
\(755\) 3.68467 0.134099
\(756\) −13.6174 24.7345i −0.495259 0.899585i
\(757\) 15.5317 0.564510 0.282255 0.959339i \(-0.408918\pi\)
0.282255 + 0.959339i \(0.408918\pi\)
\(758\) −4.18344 7.24593i −0.151949 0.263184i
\(759\) −2.34797 + 4.06680i −0.0852259 + 0.147616i
\(760\) 1.82919 3.16825i 0.0663518 0.114925i
\(761\) 0.125185 + 0.216826i 0.00453794 + 0.00785993i 0.868285 0.496065i \(-0.165222\pi\)
−0.863748 + 0.503925i \(0.831889\pi\)
\(762\) 6.98474 0.253030
\(763\) 0.0428255 + 0.0777879i 0.00155039 + 0.00281611i
\(764\) −25.5961 −0.926036
\(765\) 2.71857 + 4.70870i 0.0982901 + 0.170243i
\(766\) −0.633903 + 1.09795i −0.0229039 + 0.0396706i
\(767\) 0 0
\(768\) −5.74859 9.95686i −0.207435 0.359287i
\(769\) 24.0146 0.865988 0.432994 0.901397i \(-0.357457\pi\)
0.432994 + 0.901397i \(0.357457\pi\)
\(770\) −7.56896 0.153969i −0.272766 0.00554867i
\(771\) 8.50731 0.306383
\(772\) 17.5312 + 30.3650i 0.630963 + 1.09286i
\(773\) 15.2531 26.4192i 0.548616 0.950231i −0.449753 0.893153i \(-0.648488\pi\)
0.998370 0.0570784i \(-0.0181785\pi\)
\(774\) 0.613451 1.06253i 0.0220501 0.0381918i
\(775\) −8.88768 15.3939i −0.319255 0.552966i
\(776\) −8.51064 −0.305514
\(777\) −16.0481 + 26.5347i −0.575722 + 0.951928i
\(778\) −0.954237 −0.0342110
\(779\) 7.39323 + 12.8055i 0.264890 + 0.458803i
\(780\) 0 0