Properties

Label 1183.2.e.i.170.4
Level $1183$
Weight $2$
Character 1183.170
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 170.4
Root \(-0.166188 - 0.287846i\) of defining polynomial
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.i.508.4

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.166188 + 0.287846i −0.117512 + 0.203538i −0.918781 0.394767i \(-0.870825\pi\)
0.801269 + 0.598304i \(0.204159\pi\)
\(3\) −0.729919 1.26426i −0.421419 0.729919i 0.574660 0.818392i \(-0.305134\pi\)
−0.996079 + 0.0884737i \(0.971801\pi\)
\(4\) 0.944763 + 1.63638i 0.472382 + 0.818189i
\(5\) −0.722811 + 1.25195i −0.323251 + 0.559887i −0.981157 0.193213i \(-0.938109\pi\)
0.657906 + 0.753100i \(0.271442\pi\)
\(6\) 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 0.830333 + 0.557267i \(0.188150\pi\)
0.0674405 + 0.997723i \(0.478517\pi\)
\(12\) 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 −0.999578 0.0290341i \(-0.990757\pi\)
0.474645 0.880177i \(-0.342576\pi\)
\(18\) 0.144396 + 0.250102i 0.0340345 + 0.0589496i
\(19\) −0.978767 + 1.69527i −0.224545 + 0.388923i −0.956183 0.292771i \(-0.905423\pi\)
0.731638 + 0.681693i \(0.238756\pi\)
\(20\) −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 −0.836493 0.547977i \(-0.815398\pi\)
0.892809 + 0.450436i \(0.148731\pi\)
\(24\) 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 0.998377 + 0.0569568i \(0.0181397\pi\)
−0.449862 + 0.893098i \(0.648527\pi\)
\(32\) −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 0.320660 + 0.947194i \(0.396095\pi\)
−0.980624 + 0.195897i \(0.937238\pi\)
\(38\) −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 −0.998780 0.0493882i \(-0.984273\pi\)
0.542161 + 0.840274i \(0.317606\pi\)
\(48\) 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 0.945538 0.325513i \(-0.105537\pi\)
−0.754671 + 0.656103i \(0.772204\pi\)
\(54\) 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 0.892398 0.451250i \(-0.149022\pi\)
−0.836993 + 0.547214i \(0.815688\pi\)
\(60\) 1.99380 + 3.45337i 0.257399 + 0.445828i
\(61\) −3.38953 + 5.87083i −0.433984 + 0.751683i −0.997212 0.0746187i \(-0.976226\pi\)
0.563228 + 0.826302i \(0.309559\pi\)
\(62\) −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 0.894598 0.446871i \(-0.147462\pi\)
−0.834301 + 0.551309i \(0.814129\pi\)
\(68\) 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 0.999183 + 0.0404208i \(0.0128699\pi\)
−0.464586 + 0.885528i \(0.653797\pi\)
\(74\) −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 −0.862314 0.506375i \(-0.830985\pi\)
0.869690 + 0.493598i \(0.164319\pi\)
\(80\) −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 0.484828 + 0.874610i \(0.338882\pi\)
−0.999848 + 0.0174319i \(0.994451\pi\)
\(90\) −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 0.867782 0.496945i \(-0.165545\pi\)
−0.864258 + 0.503049i \(0.832212\pi\)
\(102\) −1.05018 1.81896i −0.103983 0.180104i
\(103\) −3.16910 + 5.48905i −0.312261 + 0.540852i −0.978852 0.204572i \(-0.934420\pi\)
0.666590 + 0.745424i \(0.267753\pi\)
\(104\) 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 −0.990265 0.139193i \(-0.955549\pi\)
0.615678 + 0.787998i \(0.288882\pi\)
\(108\) −5.33596 9.24215i −0.513453 0.889326i
\(109\) 0.0167811 + 0.0290658i 0.00160734 + 0.00278400i 0.866828 0.498607i \(-0.166155\pi\)
−0.865221 + 0.501391i \(0.832822\pi\)
\(110\) 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 −0.581659 0.813433i \(-0.697596\pi\)
0.995283 + 0.0970151i \(0.0309295\pi\)
\(132\) 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 −0.965086 0.261934i \(-0.915640\pi\)
0.255702 0.966756i \(-0.417693\pi\)
\(138\) 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 −0.796005 0.605290i \(-0.793057\pi\)
0.922199 + 0.386715i \(0.126390\pi\)
\(150\) 0.706030 + 1.22288i 0.0576471 + 0.0998477i
\(151\) −1.27442 2.20737i −0.103711 0.179633i 0.809500 0.587120i \(-0.199738\pi\)
−0.913211 + 0.407487i \(0.866405\pi\)
\(152\) 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 0.990396 0.138260i \(-0.0441509\pi\)
−0.614935 + 0.788578i \(0.710818\pi\)
\(158\) 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 −0.879317 0.476238i \(-0.842000\pi\)
0.852092 + 0.523392i \(0.175334\pi\)
\(164\) −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 −0.743998 0.668182i \(-0.767073\pi\)
0.950662 + 0.310230i \(0.100406\pi\)
\(174\) 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 0.748361 0.663292i \(-0.230841\pi\)
−0.948608 + 0.316454i \(0.897508\pi\)
\(180\) −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 −0.999935 0.0114067i \(-0.996369\pi\)
0.509846 + 0.860266i \(0.329702\pi\)
\(192\) 3.99217 + 6.91464i 0.288110 + 0.499021i
\(193\) −9.27812 16.0702i −0.667853 1.15676i −0.978503 0.206232i \(-0.933880\pi\)
0.310650 0.950524i \(-0.399453\pi\)
\(194\) −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 −0.962586 0.270976i \(-0.912654\pi\)
0.246621 0.969112i \(-0.420680\pi\)
\(200\) −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 −0.828141 0.560520i \(-0.810601\pi\)
−0.0713539 0.997451i \(-0.522732\pi\)
\(228\) 2.69983 + 4.67625i 0.178801 + 0.309692i
\(229\) 9.49437 16.4447i 0.627406 1.08670i −0.360665 0.932696i \(-0.617450\pi\)
0.988070 0.154003i \(-0.0492166\pi\)
\(230\) −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 0.251942 + 0.967742i \(0.418931\pi\)
−0.964060 + 0.265683i \(0.914403\pi\)
\(234\) 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 0.809302 0.587393i \(-0.199846\pi\)
−0.913348 + 0.407179i \(0.866513\pi\)
\(242\) −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 −0.942479 0.334266i \(-0.891512\pi\)
0.760722 + 0.649078i \(0.224845\pi\)
\(258\) 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 −0.998903 0.0468234i \(-0.985090\pi\)
0.458901 0.888487i \(-0.348243\pi\)
\(264\) −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 −0.974767 0.223226i \(-0.928341\pi\)
0.294064 0.955786i \(-0.404992\pi\)
\(270\) 1.35688 + 2.35019i 0.0825773 + 0.143028i
\(271\) 13.1847 22.8366i 0.800916 1.38723i −0.118098 0.993002i \(-0.537680\pi\)
0.919014 0.394225i \(-0.128987\pi\)
\(272\) 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 0.971799 0.235812i \(-0.0757750\pi\)
−0.690119 + 0.723696i \(0.742442\pi\)
\(278\) −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 0.972737 0.231911i \(-0.0744979\pi\)
−0.687210 + 0.726459i \(0.741165\pi\)
\(284\) 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 −0.861143 0.508363i \(-0.830251\pi\)
−0.00968369 0.999953i \(-0.503082\pi\)
\(312\) 0 0
\(313\) −5.54334 + 9.60135i −0.313328 + 0.542701i −0.979081 0.203472i \(-0.934777\pi\)
0.665752 + 0.746173i \(0.268111\pi\)
\(314\) −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 −0.306991 0.951712i \(-0.599322\pi\)
0.977703 0.209994i \(-0.0673445\pi\)
\(318\) 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 −0.496403 0.868092i \(-0.665346\pi\)
0.999991 0.00414903i \(-0.00132068\pi\)
\(332\) 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 0.996978 + 0.0776892i \(0.0247542\pi\)
−0.431208 + 0.902253i \(0.641912\pi\)
\(348\) 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 0.772999 0.634407i \(-0.218756\pi\)
−0.935912 + 0.352233i \(0.885422\pi\)
\(354\) 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 −0.487189 0.873297i \(-0.661978\pi\)
0.999891 0.0147308i \(-0.00468913\pi\)
\(360\) −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 0.927896 0.372838i \(-0.121615\pi\)
−0.786836 + 0.617163i \(0.788282\pi\)
\(368\) 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 −0.996009 0.0892478i \(-0.971554\pi\)
0.575296 + 0.817946i \(0.304887\pi\)
\(374\) 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 −0.910630 0.413223i \(-0.864403\pi\)
0.813177 + 0.582017i \(0.197736\pi\)
\(384\) −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 0.900119 0.435643i \(-0.143479\pi\)
−0.827338 + 0.561705i \(0.810146\pi\)
\(390\) 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 −0.519968 0.854185i \(-0.674056\pi\)
0.999731 + 0.0232131i \(0.00738963\pi\)
\(398\) 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 −0.901026 0.433764i \(-0.857185\pi\)
0.826164 + 0.563430i \(0.190518\pi\)
\(402\) 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 0.887700 + 0.460422i \(0.152302\pi\)
−0.0451127 + 0.998982i \(0.514365\pi\)
\(410\) 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 0.917682 0.397316i \(-0.130058\pi\)
−0.802927 + 0.596078i \(0.796725\pi\)
\(432\) 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 −0.904070 0.427384i \(-0.859435\pi\)
0.822161 + 0.569256i \(0.192769\pi\)
\(440\) 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 −0.743894 0.668298i \(-0.767023\pi\)
0.950710 + 0.310082i \(0.100357\pi\)
\(444\) 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 −0.952403 0.304842i \(-0.901396\pi\)
0.740202 + 0.672384i \(0.234730\pi\)
\(458\) 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 0.282960 + 0.959132i \(0.408684\pi\)
−0.972112 + 0.234515i \(0.924650\pi\)
\(468\) 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 0.917076 + 0.398712i \(0.130543\pi\)
−0.113243 + 0.993567i \(0.536124\pi\)
\(480\) −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 0.844895 0.534933i \(-0.179663\pi\)
−0.885713 + 0.464234i \(0.846330\pi\)
\(488\) 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 0.0902781 + 0.995917i \(0.471224\pi\)
−0.907628 + 0.419775i \(0.862109\pi\)
\(500\) −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 −0.332699 0.943033i \(-0.607959\pi\)
0.983040 0.183391i \(-0.0587074\pi\)
\(510\) 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 0.983066 + 0.183254i \(0.0586632\pi\)
−0.332830 + 0.942987i \(0.608003\pi\)
\(522\) 1.03367 + 1.79037i 0.0452425 + 0.0783624i
\(523\) −10.2864 + 17.8165i −0.449791 + 0.779062i −0.998372 0.0570361i \(-0.981835\pi\)
0.548581 + 0.836098i \(0.315168\pi\)
\(524\) 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 0.223564 + 0.974689i \(0.428231\pi\)
−0.955888 + 0.293732i \(0.905103\pi\)
\(542\) 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 0.990414 0.138132i \(-0.0441098\pi\)
−0.614833 + 0.788658i \(0.710776\pi\)
\(558\) −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 0.999939 + 0.0110571i \(0.00351966\pi\)
−0.490394 + 0.871501i \(0.663147\pi\)
\(564\) 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 0.0648066 0.997898i \(-0.479357\pi\)
0.831802 0.555073i \(-0.187310\pi\)
\(570\) −0.686542 1.18913i −0.0287561 0.0498070i
\(571\) −3.68140 6.37637i −0.154062 0.266843i 0.778655 0.627452i \(-0.215902\pi\)
−0.932717 + 0.360609i \(0.882569\pi\)
\(572\) 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 0.938615 0.344965i \(-0.112109\pi\)
−0.768057 + 0.640382i \(0.778776\pi\)
\(578\) −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 −0.853300 0.521421i \(-0.825402\pi\)
0.878213 + 0.478269i \(0.158736\pi\)
\(594\) 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 −0.978655 0.205508i \(-0.934115\pi\)
0.311352 0.950295i \(-0.399218\pi\)
\(600\) −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 −0.965338 0.261001i \(-0.915947\pi\)
0.708703 + 0.705507i \(0.249281\pi\)
\(608\) 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 0.589797 0.807552i \(-0.299208\pi\)
−0.994259 + 0.107003i \(0.965874\pi\)
\(614\) −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 0.907127 0.420856i \(-0.138270\pi\)
−0.818036 + 0.575167i \(0.804937\pi\)
\(620\) −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 −0.930250 0.366926i \(-0.880410\pi\)
0.147357 0.989083i \(-0.452923\pi\)
\(642\) −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 0.978249 0.207433i \(-0.0665109\pi\)
−0.668767 + 0.743472i \(0.733178\pi\)
\(648\) −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 −0.470623 0.882334i \(-0.655971\pi\)
0.999436 0.0335954i \(-0.0106958\pi\)
\(654\) 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 0.927544 0.373714i \(-0.121916\pi\)
−0.787418 + 0.616420i \(0.788583\pi\)
\(662\) 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 −0.419474 0.907767i \(-0.637785\pi\)
0.995887 0.0906086i \(-0.0288812\pi\)
\(678\) −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 −0.971721 0.236132i \(-0.924120\pi\)
0.281365 0.959601i \(-0.409213\pi\)
\(684\) −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 −0.999935 0.0113665i \(-0.996382\pi\)
0.509811 + 0.860286i \(0.329715\pi\)
\(692\) 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 −0.862779 0.505581i \(-0.831278\pi\)
0.869236 + 0.494398i \(0.164611\pi\)
\(710\) −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 −0.936200 0.351467i \(-0.885683\pi\)
0.772479 + 0.635040i \(0.219016\pi\)
\(720\) −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 −0.937470 0.348067i \(-0.886838\pi\)
0.770170 + 0.637839i \(0.220172\pi\)
\(734\) −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 0.793558 0.608494i \(-0.208226\pi\)
−0.923751 + 0.382995i \(0.874893\pi\)
\(740\) 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 −0.417062 0.908878i \(-0.636940\pi\)
0.995643 0.0932523i \(-0.0297263\pi\)
\(752\) −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 −0.863748 0.503925i \(-0.831889\pi\)
0.868285 + 0.496065i \(0.165222\pi\)
\(762\) 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 0.998370 + 0.0570784i \(0.0181785\pi\)
−0.449753 + 0.893153i \(0.648488\pi\)
\(774\) 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