Properties

Label 189.2.e.e.109.2
Level 189
Weight 2
Character 189.109
Analytic conductor 1.509
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 189.e (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(1.5091725982\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.2
Root \(0.500000 + 1.41036i\)
Character \(\chi\) = 189.109
Dual form 189.2.e.e.163.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-0.380438 - 0.658939i) q^{2}\) \(+(0.710533 - 1.23068i) q^{4}\) \(+(-1.59097 - 2.75564i) q^{5}\) \(+(-2.56238 + 0.658939i) q^{7}\) \(-2.60301 q^{8}\) \(+O(q^{10})\) \(q\)\(+(-0.380438 - 0.658939i) q^{2}\) \(+(0.710533 - 1.23068i) q^{4}\) \(+(-1.59097 - 2.75564i) q^{5}\) \(+(-2.56238 + 0.658939i) q^{7}\) \(-2.60301 q^{8}\) \(+(-1.21053 + 2.09671i) q^{10}\) \(+(-1.11956 + 1.93914i) q^{11}\) \(+3.70370 q^{13}\) \(+(1.40903 + 1.43777i) q^{14}\) \(+(-0.430782 - 0.746136i) q^{16}\) \(+(2.80150 - 4.85235i) q^{17}\) \(+(-2.21053 - 3.82876i) q^{19}\) \(-4.52175 q^{20}\) \(+1.70370 q^{22}\) \(+(0.471410 + 0.816506i) q^{23}\) \(+(-2.56238 + 4.43818i) q^{25}\) \(+(-1.40903 - 2.44051i) q^{26}\) \(+(-1.00972 + 3.62167i) q^{28}\) \(+10.1248 q^{29}\) \(+(2.85185 - 4.93955i) q^{31}\) \(+(-2.93078 + 5.07626i) q^{32}\) \(-4.26320 q^{34}\) \(+(5.89248 + 6.01266i) q^{35}\) \(+(-1.56238 - 2.70612i) q^{37}\) \(+(-1.68194 + 2.91321i) q^{38}\) \(+(4.14132 + 7.17297i) q^{40}\) \(+3.98633 q^{41}\) \(-3.28263 q^{43}\) \(+(1.59097 + 2.75564i) q^{44}\) \(+(0.358685 - 0.621261i) q^{46}\) \(+(0.112725 + 0.195246i) q^{47}\) \(+(6.13160 - 3.37690i) q^{49}\) \(+3.89931 q^{50}\) \(+(2.63160 - 4.55806i) q^{52}\) \(+(-5.33009 + 9.23200i) q^{53}\) \(+7.12476 q^{55}\) \(+(6.66991 - 1.71522i) q^{56}\) \(+(-3.85185 - 6.67160i) q^{58}\) \(+(1.02859 - 1.78157i) q^{59}\) \(+(2.92107 + 5.05944i) q^{61}\) \(-4.33981 q^{62}\) \(+2.73680 q^{64}\) \(+(-5.89248 - 10.2061i) q^{65}\) \(+(-3.71053 + 6.42683i) q^{67}\) \(+(-3.98113 - 6.89551i) q^{68}\) \(+(1.72025 - 6.17023i) q^{70}\) \(+7.26320 q^{71}\) \(+(-3.77975 + 6.54672i) q^{73}\) \(+(-1.18878 + 2.05903i) q^{74}\) \(-6.28263 q^{76}\) \(+(1.59097 - 5.70653i) q^{77}\) \(+(3.41423 + 5.91362i) q^{79}\) \(+(-1.37072 + 2.37416i) q^{80}\) \(+(-1.51655 - 2.62674i) q^{82}\) \(-8.11109 q^{83}\) \(-17.8285 q^{85}\) \(+(1.24884 + 2.16305i) q^{86}\) \(+(2.91423 - 5.04759i) q^{88}\) \(+(-4.86389 - 8.42450i) q^{89}\) \(+(-9.49028 + 2.44051i) q^{91}\) \(+1.33981 q^{92}\) \(+(0.0857699 - 0.148558i) q^{94}\) \(+(-7.03379 + 12.1829i) q^{95}\) \(+0.842133 q^{97}\) \(+(-4.55787 - 2.75564i) q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut -\mathstrut 10q^{16} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 26q^{20} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 17q^{26} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut +\mathstrut 24q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 18q^{43} \) \(\mathstrut +\mathstrut q^{44} \) \(\mathstrut +\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 9q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 9q^{52} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut q^{61} \) \(\mathstrut -\mathstrut 42q^{62} \) \(\mathstrut +\mathstrut 66q^{64} \) \(\mathstrut -\mathstrut 10q^{65} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut -\mathstrut 39q^{68} \) \(\mathstrut +\mathstrut 26q^{70} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 7q^{73} \) \(\mathstrut -\mathstrut 36q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 43q^{82} \) \(\mathstrut +\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 54q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 28q^{97} \) \(\mathstrut +\mathstrut 49q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.380438 0.658939i −0.269011 0.465940i 0.699596 0.714539i \(-0.253363\pi\)
−0.968607 + 0.248599i \(0.920030\pi\)
\(3\) 0 0
\(4\) 0.710533 1.23068i 0.355267 0.615340i
\(5\) −1.59097 2.75564i −0.711504 1.23236i −0.964292 0.264840i \(-0.914681\pi\)
0.252788 0.967522i \(-0.418652\pi\)
\(6\) 0 0
\(7\) −2.56238 + 0.658939i −0.968489 + 0.249055i
\(8\) −2.60301 −0.920303
\(9\) 0 0
\(10\) −1.21053 + 2.09671i −0.382804 + 0.663036i
\(11\) −1.11956 + 1.93914i −0.337561 + 0.584672i −0.983973 0.178316i \(-0.942935\pi\)
0.646413 + 0.762988i \(0.276268\pi\)
\(12\) 0 0
\(13\) 3.70370 1.02722 0.513610 0.858024i \(-0.328308\pi\)
0.513610 + 0.858024i \(0.328308\pi\)
\(14\) 1.40903 + 1.43777i 0.376579 + 0.384259i
\(15\) 0 0
\(16\) −0.430782 0.746136i −0.107695 0.186534i
\(17\) 2.80150 4.85235i 0.679465 1.17687i −0.295678 0.955288i \(-0.595545\pi\)
0.975142 0.221580i \(-0.0711213\pi\)
\(18\) 0 0
\(19\) −2.21053 3.82876i −0.507131 0.878377i −0.999966 0.00825398i \(-0.997373\pi\)
0.492835 0.870123i \(-0.335961\pi\)
\(20\) −4.52175 −1.01109
\(21\) 0 0
\(22\) 1.70370 0.363229
\(23\) 0.471410 + 0.816506i 0.0982958 + 0.170253i 0.910979 0.412452i \(-0.135328\pi\)
−0.812684 + 0.582705i \(0.801994\pi\)
\(24\) 0 0
\(25\) −2.56238 + 4.43818i −0.512476 + 0.887635i
\(26\) −1.40903 2.44051i −0.276333 0.478623i
\(27\) 0 0
\(28\) −1.00972 + 3.62167i −0.190818 + 0.684431i
\(29\) 10.1248 1.88012 0.940061 0.341007i \(-0.110768\pi\)
0.940061 + 0.341007i \(0.110768\pi\)
\(30\) 0 0
\(31\) 2.85185 4.93955i 0.512207 0.887169i −0.487693 0.873015i \(-0.662161\pi\)
0.999900 0.0141534i \(-0.00450531\pi\)
\(32\) −2.93078 + 5.07626i −0.518094 + 0.897365i
\(33\) 0 0
\(34\) −4.26320 −0.731133
\(35\) 5.89248 + 6.01266i 0.996010 + 1.01632i
\(36\) 0 0
\(37\) −1.56238 2.70612i −0.256854 0.444884i 0.708543 0.705667i \(-0.249353\pi\)
−0.965397 + 0.260783i \(0.916019\pi\)
\(38\) −1.68194 + 2.91321i −0.272847 + 0.472585i
\(39\) 0 0
\(40\) 4.14132 + 7.17297i 0.654799 + 1.13415i
\(41\) 3.98633 0.622560 0.311280 0.950318i \(-0.399242\pi\)
0.311280 + 0.950318i \(0.399242\pi\)
\(42\) 0 0
\(43\) −3.28263 −0.500596 −0.250298 0.968169i \(-0.580529\pi\)
−0.250298 + 0.968169i \(0.580529\pi\)
\(44\) 1.59097 + 2.75564i 0.239848 + 0.415429i
\(45\) 0 0
\(46\) 0.358685 0.621261i 0.0528852 0.0915999i
\(47\) 0.112725 + 0.195246i 0.0164426 + 0.0284795i 0.874130 0.485693i \(-0.161433\pi\)
−0.857687 + 0.514172i \(0.828099\pi\)
\(48\) 0 0
\(49\) 6.13160 3.37690i 0.875943 0.482415i
\(50\) 3.89931 0.551446
\(51\) 0 0
\(52\) 2.63160 4.55806i 0.364937 0.632090i
\(53\) −5.33009 + 9.23200i −0.732145 + 1.26811i 0.223820 + 0.974631i \(0.428147\pi\)
−0.955965 + 0.293482i \(0.905186\pi\)
\(54\) 0 0
\(55\) 7.12476 0.960703
\(56\) 6.66991 1.71522i 0.891304 0.229206i
\(57\) 0 0
\(58\) −3.85185 6.67160i −0.505772 0.876024i
\(59\) 1.02859 1.78157i 0.133911 0.231941i −0.791270 0.611467i \(-0.790580\pi\)
0.925181 + 0.379526i \(0.123913\pi\)
\(60\) 0 0
\(61\) 2.92107 + 5.05944i 0.374004 + 0.647794i 0.990177 0.139816i \(-0.0446512\pi\)
−0.616173 + 0.787611i \(0.711318\pi\)
\(62\) −4.33981 −0.551156
\(63\) 0 0
\(64\) 2.73680 0.342100
\(65\) −5.89248 10.2061i −0.730872 1.26591i
\(66\) 0 0
\(67\) −3.71053 + 6.42683i −0.453314 + 0.785163i −0.998590 0.0530942i \(-0.983092\pi\)
0.545276 + 0.838257i \(0.316425\pi\)
\(68\) −3.98113 6.89551i −0.482782 0.836204i
\(69\) 0 0
\(70\) 1.72025 6.17023i 0.205609 0.737483i
\(71\) 7.26320 0.861983 0.430992 0.902356i \(-0.358164\pi\)
0.430992 + 0.902356i \(0.358164\pi\)
\(72\) 0 0
\(73\) −3.77975 + 6.54672i −0.442386 + 0.766236i −0.997866 0.0652944i \(-0.979201\pi\)
0.555480 + 0.831530i \(0.312535\pi\)
\(74\) −1.18878 + 2.05903i −0.138193 + 0.239357i
\(75\) 0 0
\(76\) −6.28263 −0.720667
\(77\) 1.59097 5.70653i 0.181308 0.650320i
\(78\) 0 0
\(79\) 3.41423 + 5.91362i 0.384131 + 0.665334i 0.991648 0.128972i \(-0.0411678\pi\)
−0.607517 + 0.794306i \(0.707834\pi\)
\(80\) −1.37072 + 2.37416i −0.153252 + 0.265439i
\(81\) 0 0
\(82\) −1.51655 2.62674i −0.167475 0.290075i
\(83\) −8.11109 −0.890308 −0.445154 0.895454i \(-0.646851\pi\)
−0.445154 + 0.895454i \(0.646851\pi\)
\(84\) 0 0
\(85\) −17.8285 −1.93377
\(86\) 1.24884 + 2.16305i 0.134666 + 0.233248i
\(87\) 0 0
\(88\) 2.91423 5.04759i 0.310658 0.538075i
\(89\) −4.86389 8.42450i −0.515571 0.892995i −0.999837 0.0180741i \(-0.994247\pi\)
0.484266 0.874921i \(-0.339087\pi\)
\(90\) 0 0
\(91\) −9.49028 + 2.44051i −0.994852 + 0.255835i
\(92\) 1.33981 0.139685
\(93\) 0 0
\(94\) 0.0857699 0.148558i 0.00884649 0.0153226i
\(95\) −7.03379 + 12.1829i −0.721652 + 1.24994i
\(96\) 0 0
\(97\) 0.842133 0.0855057 0.0427528 0.999086i \(-0.486387\pi\)
0.0427528 + 0.999086i \(0.486387\pi\)
\(98\) −4.55787 2.75564i −0.460414 0.278362i
\(99\) 0 0
\(100\) 3.64132 + 6.30694i 0.364132 + 0.630694i
\(101\) 3.87360 6.70928i 0.385438 0.667598i −0.606392 0.795166i \(-0.707384\pi\)
0.991830 + 0.127568i \(0.0407171\pi\)
\(102\) 0 0
\(103\) 1.21737 + 2.10855i 0.119951 + 0.207761i 0.919748 0.392509i \(-0.128393\pi\)
−0.799797 + 0.600271i \(0.795060\pi\)
\(104\) −9.64076 −0.945354
\(105\) 0 0
\(106\) 8.11109 0.787819
\(107\) −5.73229 9.92861i −0.554161 0.959835i −0.997968 0.0637128i \(-0.979706\pi\)
0.443807 0.896122i \(-0.353628\pi\)
\(108\) 0 0
\(109\) 9.12476 15.8046i 0.873994 1.51380i 0.0161631 0.999869i \(-0.494855\pi\)
0.857831 0.513932i \(-0.171812\pi\)
\(110\) −2.71053 4.69478i −0.258439 0.447630i
\(111\) 0 0
\(112\) 1.59549 + 1.62803i 0.150759 + 0.153834i
\(113\) −5.24953 −0.493834 −0.246917 0.969037i \(-0.579417\pi\)
−0.246917 + 0.969037i \(0.579417\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) 7.19398 12.4603i 0.667944 1.15691i
\(117\) 0 0
\(118\) −1.56526 −0.144094
\(119\) −3.98113 + 14.2796i −0.364949 + 1.30901i
\(120\) 0 0
\(121\) 2.99316 + 5.18431i 0.272106 + 0.471301i
\(122\) 2.22257 3.84961i 0.201222 0.348527i
\(123\) 0 0
\(124\) −4.05267 7.01942i −0.363940 0.630363i
\(125\) 0.396990 0.0355079
\(126\) 0 0
\(127\) 20.1053 1.78406 0.892030 0.451976i \(-0.149281\pi\)
0.892030 + 0.451976i \(0.149281\pi\)
\(128\) 4.82038 + 8.34914i 0.426065 + 0.737967i
\(129\) 0 0
\(130\) −4.48345 + 7.76556i −0.393224 + 0.681085i
\(131\) 2.04063 + 3.53447i 0.178291 + 0.308808i 0.941295 0.337585i \(-0.109610\pi\)
−0.763005 + 0.646393i \(0.776277\pi\)
\(132\) 0 0
\(133\) 8.18715 + 8.35413i 0.709916 + 0.724395i
\(134\) 5.64652 0.487785
\(135\) 0 0
\(136\) −7.29235 + 12.6307i −0.625313 + 1.08307i
\(137\) 0.942820 1.63301i 0.0805506 0.139518i −0.822936 0.568134i \(-0.807665\pi\)
0.903487 + 0.428616i \(0.140999\pi\)
\(138\) 0 0
\(139\) −12.7954 −1.08529 −0.542644 0.839963i \(-0.682577\pi\)
−0.542644 + 0.839963i \(0.682577\pi\)
\(140\) 11.5865 2.97956i 0.979234 0.251819i
\(141\) 0 0
\(142\) −2.76320 4.78600i −0.231883 0.401632i
\(143\) −4.14652 + 7.18198i −0.346749 + 0.600587i
\(144\) 0 0
\(145\) −16.1082 27.9002i −1.33771 2.31699i
\(146\) 5.75185 0.476026
\(147\) 0 0
\(148\) −4.44050 −0.365007
\(149\) −4.02859 6.97772i −0.330035 0.571637i 0.652483 0.757803i \(-0.273727\pi\)
−0.982518 + 0.186166i \(0.940394\pi\)
\(150\) 0 0
\(151\) 3.14132 5.44092i 0.255637 0.442776i −0.709432 0.704774i \(-0.751048\pi\)
0.965068 + 0.261999i \(0.0843816\pi\)
\(152\) 5.75404 + 9.96629i 0.466714 + 0.808373i
\(153\) 0 0
\(154\) −4.36552 + 1.12263i −0.351784 + 0.0904642i
\(155\) −18.1488 −1.45775
\(156\) 0 0
\(157\) −0.351848 + 0.609419i −0.0280806 + 0.0486370i −0.879724 0.475484i \(-0.842273\pi\)
0.851644 + 0.524121i \(0.175606\pi\)
\(158\) 2.59781 4.49954i 0.206671 0.357964i
\(159\) 0 0
\(160\) 18.6512 1.47450
\(161\) −1.74596 1.78157i −0.137601 0.140407i
\(162\) 0 0
\(163\) 9.61793 + 16.6587i 0.753334 + 1.30481i 0.946198 + 0.323588i \(0.104889\pi\)
−0.192864 + 0.981225i \(0.561778\pi\)
\(164\) 2.83242 4.90589i 0.221175 0.383086i
\(165\) 0 0
\(166\) 3.08577 + 5.34471i 0.239502 + 0.414830i
\(167\) 23.3880 1.80981 0.904907 0.425608i \(-0.139940\pi\)
0.904907 + 0.425608i \(0.139940\pi\)
\(168\) 0 0
\(169\) 0.717370 0.0551823
\(170\) 6.78263 + 11.7479i 0.520204 + 0.901020i
\(171\) 0 0
\(172\) −2.33242 + 4.03987i −0.177845 + 0.308037i
\(173\) 4.11956 + 7.13529i 0.313204 + 0.542486i 0.979054 0.203600i \(-0.0652641\pi\)
−0.665850 + 0.746086i \(0.731931\pi\)
\(174\) 0 0
\(175\) 3.64132 13.0608i 0.275258 0.987300i
\(176\) 1.92915 0.145415
\(177\) 0 0
\(178\) −3.70082 + 6.41001i −0.277388 + 0.480450i
\(179\) −4.95486 + 8.58207i −0.370344 + 0.641454i −0.989618 0.143721i \(-0.954093\pi\)
0.619275 + 0.785174i \(0.287427\pi\)
\(180\) 0 0
\(181\) −9.38796 −0.697802 −0.348901 0.937160i \(-0.613445\pi\)
−0.348901 + 0.937160i \(0.613445\pi\)
\(182\) 5.21861 + 5.32505i 0.386829 + 0.394719i
\(183\) 0 0
\(184\) −1.22708 2.12537i −0.0904619 0.156685i
\(185\) −4.97141 + 8.61073i −0.365505 + 0.633074i
\(186\) 0 0
\(187\) 6.27292 + 10.8650i 0.458721 + 0.794528i
\(188\) 0.320380 0.0233661
\(189\) 0 0
\(190\) 10.7037 0.776528
\(191\) 12.3691 + 21.4239i 0.894996 + 1.55018i 0.833810 + 0.552052i \(0.186155\pi\)
0.0611861 + 0.998126i \(0.480512\pi\)
\(192\) 0 0
\(193\) 0.414230 0.717468i 0.0298169 0.0516444i −0.850732 0.525600i \(-0.823841\pi\)
0.880549 + 0.473955i \(0.157174\pi\)
\(194\) −0.320380 0.554914i −0.0230019 0.0398405i
\(195\) 0 0
\(196\) 0.200818 9.94544i 0.0143442 0.710389i
\(197\) 5.86156 0.417619 0.208810 0.977956i \(-0.433041\pi\)
0.208810 + 0.977956i \(0.433041\pi\)
\(198\) 0 0
\(199\) 4.62476 8.01033i 0.327841 0.567837i −0.654242 0.756285i \(-0.727012\pi\)
0.982083 + 0.188448i \(0.0603457\pi\)
\(200\) 6.66991 11.5526i 0.471634 0.816893i
\(201\) 0 0
\(202\) −5.89467 −0.414747
\(203\) −25.9435 + 6.67160i −1.82088 + 0.468254i
\(204\) 0 0
\(205\) −6.34213 10.9849i −0.442954 0.767218i
\(206\) 0.926268 1.60434i 0.0645362 0.111780i
\(207\) 0 0
\(208\) −1.59549 2.76346i −0.110627 0.191612i
\(209\) 9.89931 0.684750
\(210\) 0 0
\(211\) −12.5595 −0.864632 −0.432316 0.901722i \(-0.642303\pi\)
−0.432316 + 0.901722i \(0.642303\pi\)
\(212\) 7.57442 + 13.1193i 0.520213 + 0.901036i
\(213\) 0 0
\(214\) −4.36156 + 7.55445i −0.298150 + 0.516412i
\(215\) 5.22257 + 9.04576i 0.356176 + 0.616916i
\(216\) 0 0
\(217\) −4.05267 + 14.5362i −0.275113 + 0.986781i
\(218\) −13.8856 −0.940454
\(219\) 0 0
\(220\) 5.06238 8.76830i 0.341306 0.591159i
\(221\) 10.3759 17.9716i 0.697960 1.20890i
\(222\) 0 0
\(223\) −21.3880 −1.43224 −0.716122 0.697975i \(-0.754085\pi\)
−0.716122 + 0.697975i \(0.754085\pi\)
\(224\) 4.16484 14.9385i 0.278275 0.998122i
\(225\) 0 0
\(226\) 1.99712 + 3.45912i 0.132847 + 0.230097i
\(227\) 6.31122 10.9314i 0.418890 0.725539i −0.576938 0.816788i \(-0.695752\pi\)
0.995828 + 0.0912487i \(0.0290858\pi\)
\(228\) 0 0
\(229\) 14.4601 + 25.0456i 0.955548 + 1.65506i 0.733110 + 0.680110i \(0.238068\pi\)
0.222438 + 0.974947i \(0.428599\pi\)
\(230\) −2.28263 −0.150512
\(231\) 0 0
\(232\) −26.3549 −1.73028
\(233\) −10.7255 18.5770i −0.702648 1.21702i −0.967534 0.252742i \(-0.918668\pi\)
0.264886 0.964280i \(-0.414666\pi\)
\(234\) 0 0
\(235\) 0.358685 0.621261i 0.0233980 0.0405266i
\(236\) −1.46169 2.53173i −0.0951482 0.164802i
\(237\) 0 0
\(238\) 10.9239 2.80919i 0.708094 0.182093i
\(239\) −7.73680 −0.500452 −0.250226 0.968187i \(-0.580505\pi\)
−0.250226 + 0.968187i \(0.580505\pi\)
\(240\) 0 0
\(241\) −3.04583 + 5.27553i −0.196199 + 0.339827i −0.947293 0.320369i \(-0.896193\pi\)
0.751094 + 0.660195i \(0.229527\pi\)
\(242\) 2.27743 3.94462i 0.146399 0.253570i
\(243\) 0 0
\(244\) 8.30206 0.531485
\(245\) −19.0607 11.5239i −1.21775 0.736238i
\(246\) 0 0
\(247\) −8.18715 14.1806i −0.520936 0.902287i
\(248\) −7.42339 + 12.8577i −0.471386 + 0.816464i
\(249\) 0 0
\(250\) −0.151030 0.261592i −0.00955199 0.0165445i
\(251\) −1.40164 −0.0884705 −0.0442352 0.999021i \(-0.514085\pi\)
−0.0442352 + 0.999021i \(0.514085\pi\)
\(252\) 0 0
\(253\) −2.11109 −0.132723
\(254\) −7.64884 13.2482i −0.479931 0.831265i
\(255\) 0 0
\(256\) 6.40451 11.0929i 0.400282 0.693309i
\(257\) 8.97825 + 15.5508i 0.560048 + 0.970031i 0.997492 + 0.0707853i \(0.0225505\pi\)
−0.437444 + 0.899246i \(0.644116\pi\)
\(258\) 0 0
\(259\) 5.78659 + 5.90461i 0.359561 + 0.366895i
\(260\) −16.7472 −1.03862
\(261\) 0 0
\(262\) 1.55267 2.68930i 0.0959241 0.166145i
\(263\) 3.58809 6.21476i 0.221251 0.383218i −0.733937 0.679218i \(-0.762319\pi\)
0.955188 + 0.295999i \(0.0956526\pi\)
\(264\) 0 0
\(265\) 33.9201 2.08370
\(266\) 2.39015 8.57306i 0.146550 0.525648i
\(267\) 0 0
\(268\) 5.27292 + 9.13296i 0.322095 + 0.557884i
\(269\) −1.69850 + 2.94188i −0.103559 + 0.179370i −0.913149 0.407627i \(-0.866356\pi\)
0.809590 + 0.586996i \(0.199690\pi\)
\(270\) 0 0
\(271\) 5.11793 + 8.86451i 0.310892 + 0.538481i 0.978556 0.205982i \(-0.0660389\pi\)
−0.667664 + 0.744463i \(0.732706\pi\)
\(272\) −4.82735 −0.292701
\(273\) 0 0
\(274\) −1.43474 −0.0866758
\(275\) −5.73749 9.93762i −0.345984 0.599261i
\(276\) 0 0
\(277\) 1.77975 3.08262i 0.106935 0.185217i −0.807592 0.589741i \(-0.799230\pi\)
0.914527 + 0.404525i \(0.132563\pi\)
\(278\) 4.86784 + 8.43135i 0.291954 + 0.505679i
\(279\) 0 0
\(280\) −15.3382 15.6510i −0.916631 0.935327i
\(281\) 6.98633 0.416769 0.208385 0.978047i \(-0.433179\pi\)
0.208385 + 0.978047i \(0.433179\pi\)
\(282\) 0 0
\(283\) 15.1082 26.1682i 0.898090 1.55554i 0.0681568 0.997675i \(-0.478288\pi\)
0.829933 0.557863i \(-0.188378\pi\)
\(284\) 5.16075 8.93867i 0.306234 0.530413i
\(285\) 0 0
\(286\) 6.30998 0.373117
\(287\) −10.2145 + 2.62674i −0.602942 + 0.155052i
\(288\) 0 0
\(289\) −7.19686 12.4653i −0.423345 0.733255i
\(290\) −12.2564 + 21.2286i −0.719718 + 1.24659i
\(291\) 0 0
\(292\) 5.37128 + 9.30333i 0.314330 + 0.544436i
\(293\) −15.2359 −0.890088 −0.445044 0.895509i \(-0.646812\pi\)
−0.445044 + 0.895509i \(0.646812\pi\)
\(294\) 0 0
\(295\) −6.54583 −0.381113
\(296\) 4.06690 + 7.04407i 0.236383 + 0.409428i
\(297\) 0 0
\(298\) −3.06526 + 5.30919i −0.177566 + 0.307553i
\(299\) 1.74596 + 3.02409i 0.100971 + 0.174888i
\(300\) 0 0
\(301\) 8.41135 2.16305i 0.484822 0.124676i
\(302\) −4.78031 −0.275076
\(303\) 0 0
\(304\) −1.90451 + 3.29872i −0.109231 + 0.189194i
\(305\) 9.29467 16.0988i 0.532211 0.921817i
\(306\) 0 0
\(307\) −1.03310 −0.0589623 −0.0294812 0.999565i \(-0.509386\pi\)
−0.0294812 + 0.999565i \(0.509386\pi\)
\(308\) −5.89248 6.01266i −0.335755 0.342603i
\(309\) 0 0
\(310\) 6.90451 + 11.9590i 0.392150 + 0.679224i
\(311\) 4.66019 8.07169i 0.264255 0.457703i −0.703113 0.711078i \(-0.748207\pi\)
0.967368 + 0.253375i \(0.0815406\pi\)
\(312\) 0 0
\(313\) −3.04583 5.27553i −0.172160 0.298191i 0.767014 0.641630i \(-0.221741\pi\)
−0.939175 + 0.343439i \(0.888408\pi\)
\(314\) 0.535426 0.0302159
\(315\) 0 0
\(316\) 9.70370 0.545876
\(317\) −11.6505 20.1792i −0.654356 1.13338i −0.982055 0.188595i \(-0.939607\pi\)
0.327699 0.944782i \(-0.393727\pi\)
\(318\) 0 0
\(319\) −11.3353 + 19.6333i −0.634655 + 1.09925i
\(320\) −4.35417 7.54165i −0.243406 0.421591i
\(321\) 0 0
\(322\) −0.509715 + 1.82826i −0.0284053 + 0.101885i
\(323\) −24.7713 −1.37831
\(324\) 0 0
\(325\) −9.49028 + 16.4377i −0.526426 + 0.911797i
\(326\) 7.31806 12.6752i 0.405310 0.702017i
\(327\) 0 0
\(328\) −10.3764 −0.572944
\(329\) −0.417500 0.426015i −0.0230175 0.0234870i
\(330\) 0 0
\(331\) −7.33818 12.7101i −0.403343 0.698610i 0.590784 0.806829i \(-0.298818\pi\)
−0.994127 + 0.108220i \(0.965485\pi\)
\(332\) −5.76320 + 9.98215i −0.316297 + 0.547842i
\(333\) 0 0
\(334\) −8.89768 15.4112i −0.486859 0.843265i
\(335\) 23.6134 1.29014
\(336\) 0 0
\(337\) 25.6238 1.39582 0.697909 0.716186i \(-0.254114\pi\)
0.697909 + 0.716186i \(0.254114\pi\)
\(338\) −0.272915 0.472703i −0.0148446 0.0257116i
\(339\) 0 0
\(340\) −12.6677 + 21.9411i −0.687003 + 1.18992i
\(341\) 6.38564 + 11.0603i 0.345802 + 0.598946i
\(342\) 0 0
\(343\) −13.4863 + 12.6933i −0.728193 + 0.685372i
\(344\) 8.54472 0.460700
\(345\) 0 0
\(346\) 3.13448 5.42908i 0.168511 0.291869i
\(347\) 5.64652 9.78005i 0.303121 0.525021i −0.673720 0.738986i \(-0.735305\pi\)
0.976841 + 0.213966i \(0.0686381\pi\)
\(348\) 0 0
\(349\) −11.2963 −0.604677 −0.302339 0.953201i \(-0.597767\pi\)
−0.302339 + 0.953201i \(0.597767\pi\)
\(350\) −9.99153 + 2.56941i −0.534070 + 0.137341i
\(351\) 0 0
\(352\) −6.56238 11.3664i −0.349776 0.605830i
\(353\) −9.25116 + 16.0235i −0.492390 + 0.852844i −0.999962 0.00876550i \(-0.997210\pi\)
0.507572 + 0.861609i \(0.330543\pi\)
\(354\) 0 0
\(355\) −11.5555 20.0148i −0.613305 1.06227i
\(356\) −13.8238 −0.732661
\(357\) 0 0
\(358\) 7.54007 0.398505
\(359\) 9.94802 + 17.2305i 0.525037 + 0.909390i 0.999575 + 0.0291551i \(0.00928167\pi\)
−0.474538 + 0.880235i \(0.657385\pi\)
\(360\) 0 0
\(361\) −0.272915 + 0.472703i −0.0143639 + 0.0248791i
\(362\) 3.57154 + 6.18609i 0.187716 + 0.325134i
\(363\) 0 0
\(364\) −3.73968 + 13.4136i −0.196012 + 0.703062i
\(365\) 24.0539 1.25904
\(366\) 0 0
\(367\) −2.87524 + 4.98006i −0.150086 + 0.259957i −0.931259 0.364358i \(-0.881288\pi\)
0.781173 + 0.624315i \(0.214622\pi\)
\(368\) 0.406150 0.703472i 0.0211720 0.0366710i
\(369\) 0 0
\(370\) 7.56526 0.393299
\(371\) 7.57442 27.1681i 0.393244 1.41050i
\(372\) 0 0
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) 4.77292 8.26693i 0.246802 0.427473i
\(375\) 0 0
\(376\) −0.293425 0.508226i −0.0151322 0.0262098i
\(377\) 37.4991 1.93130
\(378\) 0 0
\(379\) 8.95322 0.459896 0.229948 0.973203i \(-0.426144\pi\)
0.229948 + 0.973203i \(0.426144\pi\)
\(380\) 9.99549 + 17.3127i 0.512758 + 0.888122i
\(381\) 0 0
\(382\) 9.41135 16.3009i 0.481527 0.834029i
\(383\) 10.0825 + 17.4634i 0.515192 + 0.892338i 0.999845 + 0.0176316i \(0.00561261\pi\)
−0.484653 + 0.874707i \(0.661054\pi\)
\(384\) 0 0
\(385\) −18.2564 + 4.69478i −0.930430 + 0.239268i
\(386\) −0.630356 −0.0320843
\(387\) 0 0
\(388\) 0.598364 1.03640i 0.0303773 0.0526151i
\(389\) −16.7999 + 29.0982i −0.851787 + 1.47534i 0.0278066 + 0.999613i \(0.491148\pi\)
−0.879594 + 0.475725i \(0.842186\pi\)
\(390\) 0 0
\(391\) 5.28263 0.267154
\(392\) −15.9606 + 8.79012i −0.806133 + 0.443968i
\(393\) 0 0
\(394\) −2.22996 3.86241i −0.112344 0.194585i
\(395\) 10.8639 18.8168i 0.546621 0.946776i
\(396\) 0 0
\(397\) 2.06922 + 3.58399i 0.103851 + 0.179875i 0.913268 0.407359i \(-0.133550\pi\)
−0.809417 + 0.587234i \(0.800217\pi\)
\(398\) −7.03775 −0.352771
\(399\) 0 0
\(400\) 4.41531 0.220765
\(401\) 7.73461 + 13.3967i 0.386248 + 0.669001i 0.991941 0.126697i \(-0.0404376\pi\)
−0.605693 + 0.795698i \(0.707104\pi\)
\(402\) 0 0
\(403\) 10.5624 18.2946i 0.526150 0.911318i
\(404\) −5.50465 9.53433i −0.273866 0.474350i
\(405\) 0 0
\(406\) 14.2661 + 14.5570i 0.708014 + 0.722454i
\(407\) 6.99673 0.346815
\(408\) 0 0
\(409\) −13.6969 + 23.7237i −0.677266 + 1.17306i 0.298535 + 0.954399i \(0.403502\pi\)
−0.975801 + 0.218661i \(0.929831\pi\)
\(410\) −4.82558 + 8.35815i −0.238318 + 0.412780i
\(411\) 0 0
\(412\) 3.45993 0.170458
\(413\) −1.46169 + 5.24284i −0.0719253 + 0.257983i
\(414\) 0 0
\(415\) 12.9045 + 22.3513i 0.633458 + 1.09718i
\(416\) −10.8547 + 18.8009i −0.532197 + 0.921792i
\(417\) 0 0
\(418\) −3.76608 6.52304i −0.184205 0.319052i
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) 0 0
\(421\) 19.9590 0.972741 0.486371 0.873753i \(-0.338321\pi\)
0.486371 + 0.873753i \(0.338321\pi\)
\(422\) 4.77812 + 8.27594i 0.232595 + 0.402867i
\(423\) 0 0
\(424\) 13.8743 24.0310i 0.673795 1.16705i
\(425\) 14.3571 + 24.8671i 0.696419 + 1.20623i
\(426\) 0 0
\(427\) −10.8187 11.0394i −0.523556 0.534234i
\(428\) −16.2919 −0.787500
\(429\) 0 0
\(430\) 3.97373 6.88271i 0.191630 0.331914i
\(431\) 10.0647 17.4326i 0.484800 0.839698i −0.515048 0.857162i \(-0.672226\pi\)
0.999847 + 0.0174637i \(0.00555914\pi\)
\(432\) 0 0
\(433\) 11.8558 0.569754 0.284877 0.958564i \(-0.408047\pi\)
0.284877 + 0.958564i \(0.408047\pi\)
\(434\) 11.1202 2.85967i 0.533789 0.137268i
\(435\) 0 0
\(436\) −12.9669 22.4593i −0.621002 1.07561i
\(437\) 2.08414 3.60983i 0.0996977 0.172681i
\(438\) 0 0
\(439\) 1.07893 + 1.86877i 0.0514947 + 0.0891914i 0.890624 0.454741i \(-0.150268\pi\)
−0.839129 + 0.543932i \(0.816935\pi\)
\(440\) −18.5458 −0.884138
\(441\) 0 0
\(442\) −15.7896 −0.751035
\(443\) 0.981125 + 1.69936i 0.0466147 + 0.0807390i 0.888391 0.459087i \(-0.151823\pi\)
−0.841777 + 0.539826i \(0.818490\pi\)
\(444\) 0 0
\(445\) −15.4766 + 26.8063i −0.733662 + 1.27074i
\(446\) 8.13680 + 14.0934i 0.385289 + 0.667340i
\(447\) 0 0
\(448\) −7.01273 + 1.80338i −0.331320 + 0.0852018i
\(449\) 2.15211 0.101564 0.0507822 0.998710i \(-0.483829\pi\)
0.0507822 + 0.998710i \(0.483829\pi\)
\(450\) 0 0
\(451\) −4.46294 + 7.73004i −0.210152 + 0.363993i
\(452\) −3.72996 + 6.46049i −0.175443 + 0.303876i
\(453\) 0 0
\(454\) −9.60412 −0.450744
\(455\) 21.8239 + 22.2691i 1.02312 + 1.04399i
\(456\) 0 0
\(457\) 6.55267 + 11.3496i 0.306521 + 0.530910i 0.977599 0.210477i \(-0.0675018\pi\)
−0.671078 + 0.741387i \(0.734168\pi\)
\(458\) 11.0023 19.0566i 0.514105 0.890456i
\(459\) 0 0
\(460\) −2.13160 3.69204i −0.0993864 0.172142i
\(461\) −5.48727 −0.255568 −0.127784 0.991802i \(-0.540786\pi\)
−0.127784 + 0.991802i \(0.540786\pi\)
\(462\) 0 0
\(463\) −20.4991 −0.952672 −0.476336 0.879263i \(-0.658035\pi\)
−0.476336 + 0.879263i \(0.658035\pi\)
\(464\) −4.36156 7.55445i −0.202481 0.350707i
\(465\) 0 0
\(466\) −8.16075 + 14.1348i −0.378039 + 0.654783i
\(467\) −19.6758 34.0795i −0.910487 1.57701i −0.813377 0.581736i \(-0.802374\pi\)
−0.0971099 0.995274i \(-0.530960\pi\)
\(468\) 0 0
\(469\) 5.27292 18.9130i 0.243481 0.873322i
\(470\) −0.545830 −0.0251773
\(471\) 0 0
\(472\) −2.67743 + 4.63744i −0.123239 + 0.213456i
\(473\) 3.67511 6.36547i 0.168982 0.292685i
\(474\) 0 0
\(475\) 22.6569 1.03957
\(476\) 14.7449 + 15.0456i 0.675830 + 0.689615i
\(477\) 0 0
\(478\) 2.94338 + 5.09808i 0.134627 + 0.233181i
\(479\) 8.37360 14.5035i 0.382600 0.662682i −0.608833 0.793298i \(-0.708362\pi\)
0.991433 + 0.130616i \(0.0416955\pi\)
\(480\) 0 0
\(481\) −5.78659 10.0227i −0.263846 0.456994i
\(482\) 4.63500 0.211119
\(483\) 0 0
\(484\) 8.50697 0.386680
\(485\) −1.33981 2.32062i −0.0608376 0.105374i
\(486\) 0 0
\(487\) −2.00288 + 3.46909i −0.0907591 + 0.157199i −0.907831 0.419337i \(-0.862263\pi\)
0.817072 + 0.576536i \(0.195596\pi\)
\(488\) −7.60357 13.1698i −0.344197 0.596167i
\(489\) 0 0
\(490\) −0.342133 + 16.9440i −0.0154560 + 0.765452i
\(491\) −24.6512 −1.11249 −0.556246 0.831018i \(-0.687759\pi\)
−0.556246 + 0.831018i \(0.687759\pi\)
\(492\) 0 0
\(493\) 28.3646 49.1289i 1.27748 2.21265i
\(494\) −6.22941 + 10.7897i −0.280274 + 0.485449i
\(495\) 0 0
\(496\) −4.91410 −0.220649
\(497\) −18.6111 + 4.78600i −0.834821 + 0.214682i
\(498\) 0 0
\(499\) 12.2798 + 21.2692i 0.549717 + 0.952138i 0.998294 + 0.0583936i \(0.0185978\pi\)
−0.448576 + 0.893744i \(0.648069\pi\)
\(500\) 0.282075 0.488568i 0.0126148 0.0218494i
\(501\) 0 0
\(502\) 0.533236 + 0.923592i 0.0237995 + 0.0412219i
\(503\) 12.3743 0.551742 0.275871 0.961195i \(-0.411034\pi\)
0.275871 + 0.961195i \(0.411034\pi\)
\(504\) 0 0
\(505\) −24.6512 −1.09696
\(506\) 0.803140 + 1.39108i 0.0357039 + 0.0618410i
\(507\) 0 0
\(508\) 14.2855 24.7432i 0.633817 1.09780i
\(509\) −5.59781 9.69569i −0.248118 0.429754i 0.714885 0.699242i \(-0.246479\pi\)
−0.963004 + 0.269488i \(0.913146\pi\)
\(510\) 0 0
\(511\) 5.37128 19.2658i 0.237611 0.852270i
\(512\) 9.53543 0.421410
\(513\) 0 0
\(514\) 6.83134 11.8322i 0.301317 0.521897i
\(515\) 3.87360 6.70928i 0.170691 0.295646i
\(516\) 0 0
\(517\) −0.504811 −0.0222016
\(518\) 1.68934 6.05935i 0.0742251 0.266232i
\(519\) 0 0
\(520\) 15.3382 + 26.5665i 0.672623 + 1.16502i
\(521\) −15.8096 + 27.3830i −0.692631 + 1.19967i 0.278342 + 0.960482i \(0.410215\pi\)
−0.970973 + 0.239189i \(0.923118\pi\)
\(522\) 0 0
\(523\) 14.1179 + 24.4530i 0.617334 + 1.06925i 0.989970 + 0.141276i \(0.0451205\pi\)
−0.372636 + 0.927977i \(0.621546\pi\)
\(524\) 5.79974 0.253363
\(525\) 0 0
\(526\) −5.46019 −0.238076
\(527\) −15.9789 27.6763i −0.696053 1.20560i
\(528\) 0 0
\(529\) 11.0555 19.1488i 0.480676 0.832555i
\(530\) −12.9045 22.3513i −0.560536 0.970877i
\(531\) 0 0
\(532\) 16.0985 4.13987i 0.697958 0.179486i
\(533\) 14.7641 0.639506
\(534\) 0 0
\(535\) −18.2398 + 31.5923i −0.788576 + 1.36585i
\(536\) 9.65856 16.7291i 0.417186 0.722587i
\(537\) 0 0
\(538\) 2.58469 0.111434
\(539\) −0.316422 + 15.6707i −0.0136293 + 0.674983i
\(540\) 0 0
\(541\) −21.4045 37.0737i −0.920252 1.59392i −0.799025 0.601298i \(-0.794650\pi\)
−0.121227 0.992625i \(-0.538683\pi\)
\(542\) 3.89411 6.74480i 0.167266 0.289714i
\(543\) 0 0
\(544\) 16.4212 + 28.4424i 0.704053 + 1.21946i
\(545\) −58.0690 −2.48740
\(546\) 0 0
\(547\) 13.5516 0.579424 0.289712 0.957114i \(-0.406440\pi\)
0.289712 + 0.957114i \(0.406440\pi\)
\(548\) −1.33981 2.32062i −0.0572339 0.0991319i
\(549\) 0 0
\(550\) −4.36552 + 7.56130i −0.186146 + 0.322415i
\(551\) −22.3811 38.7652i −0.953468 1.65146i
\(552\) 0 0
\(553\) −12.6453 12.9032i −0.537732 0.548699i
\(554\) −2.70834 −0.115066
\(555\) 0 0
\(556\) −9.09153 + 15.7470i −0.385567 + 0.667821i
\(557\) −16.3925 + 28.3926i −0.694572 + 1.20303i 0.275753 + 0.961228i \(0.411073\pi\)
−0.970325 + 0.241805i \(0.922261\pi\)
\(558\) 0 0
\(559\) −12.1579 −0.514223
\(560\) 1.94789 6.98673i 0.0823133 0.295243i
\(561\) 0 0
\(562\) −2.65787 4.60356i −0.112115 0.194189i
\(563\) 8.57730 14.8563i 0.361490 0.626119i −0.626716 0.779248i \(-0.715601\pi\)
0.988206 + 0.153128i \(0.0489348\pi\)
\(564\) 0 0
\(565\) 8.35185 + 14.4658i 0.351365 + 0.608582i
\(566\) −22.9910 −0.966383
\(567\) 0 0
\(568\) −18.9062 −0.793286
\(569\) −6.44966 11.1711i −0.270384 0.468318i 0.698576 0.715535i \(-0.253817\pi\)
−0.968960 + 0.247217i \(0.920484\pi\)
\(570\) 0 0
\(571\) 0.141315 0.244765i 0.00591385 0.0102431i −0.863053 0.505113i \(-0.831451\pi\)
0.868967 + 0.494870i \(0.164784\pi\)
\(572\) 5.89248 + 10.2061i 0.246377 + 0.426737i
\(573\) 0 0
\(574\) 5.61685 + 5.73141i 0.234443 + 0.239224i
\(575\) −4.83173 −0.201497
\(576\) 0 0
\(577\) 1.08289 1.87562i 0.0450814 0.0780832i −0.842604 0.538533i \(-0.818979\pi\)
0.887686 + 0.460450i \(0.152312\pi\)
\(578\) −5.47592 + 9.48458i −0.227768 + 0.394506i
\(579\) 0 0
\(580\) −45.7817 −1.90098
\(581\) 20.7837 5.34471i 0.862254 0.221736i
\(582\) 0 0
\(583\) −11.9347 20.6716i −0.494286 0.856129i
\(584\) 9.83873 17.0412i 0.407130 0.705169i
\(585\) 0 0
\(586\) 5.79630 + 10.0395i 0.239443 + 0.414728i
\(587\) −16.7759 −0.692417 −0.346208 0.938158i \(-0.612531\pi\)
−0.346208 + 0.938158i \(0.612531\pi\)
\(588\) 0 0
\(589\) −25.2164 −1.03902
\(590\) 2.49028 + 4.31330i 0.102523 + 0.177576i
\(591\) 0 0
\(592\) −1.34609 + 2.33150i −0.0553240 + 0.0958240i
\(593\) 12.5933 + 21.8122i 0.517145 + 0.895721i 0.999802 + 0.0199114i \(0.00633841\pi\)
−0.482657 + 0.875809i \(0.660328\pi\)
\(594\) 0 0
\(595\) 45.6833 11.7479i 1.87283 0.481615i
\(596\) −11.4498 −0.469002
\(597\) 0 0
\(598\) 1.32846 2.30096i 0.0543248 0.0940933i
\(599\) −14.3662 + 24.8830i −0.586987 + 1.01669i 0.407637 + 0.913144i \(0.366353\pi\)
−0.994624 + 0.103548i \(0.966980\pi\)
\(600\) 0 0
\(601\) −36.7954 −1.50091 −0.750457 0.660919i \(-0.770167\pi\)
−0.750457 + 0.660919i \(0.770167\pi\)
\(602\) −4.62532 4.71966i −0.188514 0.192359i
\(603\) 0 0
\(604\) −4.46402 7.73191i −0.181638 0.314607i
\(605\) 9.52408 16.4962i 0.387209 0.670665i
\(606\) 0 0
\(607\) −18.9503 32.8230i −0.769171 1.33224i −0.938013 0.346600i \(-0.887336\pi\)
0.168842 0.985643i \(-0.445997\pi\)
\(608\) 25.9144 1.05097
\(609\) 0 0
\(610\) −14.1442 −0.572682
\(611\) 0.417500 + 0.723131i 0.0168902 + 0.0292547i
\(612\) 0 0
\(613\) −19.0196 + 32.9428i −0.768193 + 1.33055i 0.170349 + 0.985384i \(0.445511\pi\)
−0.938542 + 0.345165i \(0.887823\pi\)
\(614\) 0.393032 + 0.680752i 0.0158615 + 0.0274729i
\(615\) 0 0
\(616\) −4.14132 + 14.8542i −0.166858 + 0.598491i
\(617\) 26.5264 1.06791 0.533956 0.845512i \(-0.320705\pi\)
0.533956 + 0.845512i \(0.320705\pi\)
\(618\) 0 0
\(619\) −6.35185 + 11.0017i −0.255302 + 0.442197i −0.964978 0.262332i \(-0.915508\pi\)
0.709675 + 0.704529i \(0.248842\pi\)
\(620\) −12.8954 + 22.3354i −0.517890 + 0.897012i
\(621\) 0 0
\(622\) −7.09166 −0.284350
\(623\) 18.0144 + 18.3818i 0.721730 + 0.736450i
\(624\) 0 0
\(625\) 12.1803 + 21.0969i 0.487212 + 0.843877i
\(626\) −2.31750 + 4.01403i −0.0926260 + 0.160433i
\(627\) 0 0
\(628\) 0.500000 + 0.866025i 0.0199522 + 0.0345582i
\(629\) −17.5081 −0.698093
\(630\) 0 0
\(631\) 20.6764 0.823113 0.411556 0.911384i \(-0.364985\pi\)
0.411556 + 0.911384i \(0.364985\pi\)
\(632\) −8.88727 15.3932i −0.353517 0.612309i
\(633\) 0 0
\(634\) −8.86458 + 15.3539i −0.352057 + 0.609781i
\(635\) −31.9870 55.4031i −1.26937 2.19861i
\(636\) 0 0
\(637\) 22.7096 12.5070i 0.899787 0.495547i
\(638\) 17.2495 0.682915
\(639\) 0 0
\(640\) 15.3382 26.5665i 0.606295 1.05013i
\(641\) −13.9870 + 24.2262i −0.552454 + 0.956878i 0.445643 + 0.895211i \(0.352975\pi\)
−0.998097 + 0.0616674i \(0.980358\pi\)
\(642\) 0 0
\(643\) 27.9806 1.10345 0.551723 0.834027i \(-0.313971\pi\)
0.551723 + 0.834027i \(0.313971\pi\)
\(644\) −3.43310 + 0.882853i −0.135283 + 0.0347893i
\(645\) 0 0
\(646\) 9.42395 + 16.3228i 0.370780 + 0.642210i
\(647\) 2.30834 3.99816i 0.0907503 0.157184i −0.817077 0.576529i \(-0.804407\pi\)
0.907827 + 0.419345i \(0.137740\pi\)
\(648\) 0 0
\(649\) 2.30314 + 3.98916i 0.0904061 + 0.156588i
\(650\) 14.4419 0.566457
\(651\) 0 0
\(652\) 27.3354 1.07054
\(653\) 5.79016 + 10.0288i 0.226586 + 0.392459i 0.956794 0.290766i \(-0.0939101\pi\)
−0.730208 + 0.683225i \(0.760577\pi\)
\(654\) 0 0
\(655\) 6.49316 11.2465i 0.253709 0.439437i
\(656\) −1.71724 2.97434i −0.0670468 0.116129i
\(657\) 0 0
\(658\) −0.121885 + 0.437179i −0.00475156 + 0.0170430i
\(659\) −4.73680 −0.184520 −0.0922598 0.995735i \(-0.529409\pi\)
−0.0922598 + 0.995735i \(0.529409\pi\)
\(660\) 0 0
\(661\) 6.91135 11.9708i 0.268820 0.465611i −0.699737 0.714400i \(-0.746700\pi\)
0.968557 + 0.248790i \(0.0800329\pi\)
\(662\) −5.58345 + 9.67081i −0.217007 + 0.375867i
\(663\) 0 0
\(664\) 21.1132 0.819353
\(665\) 9.99549 35.8520i 0.387608 1.39028i
\(666\) 0 0
\(667\) 4.77292 + 8.26693i 0.184808 + 0.320097i
\(668\) 16.6179 28.7831i 0.642967 1.11365i
\(669\) 0 0
\(670\) −8.98345 15.5598i −0.347061 0.601127i
\(671\) −13.0813 −0.504996
\(672\) 0 0
\(673\) 6.02735 0.232337 0.116169 0.993230i \(-0.462939\pi\)
0.116169 + 0.993230i \(0.462939\pi\)
\(674\) −9.74828 16.8845i −0.375490 0.650367i
\(675\) 0 0
\(676\) 0.509715 0.882853i 0.0196044 0.0339559i
\(677\) −11.4428 19.8195i −0.439783 0.761727i 0.557889 0.829915i \(-0.311611\pi\)
−0.997672 + 0.0681884i \(0.978278\pi\)
\(678\) 0 0
\(679\) −2.15787 + 0.554914i −0.0828113 + 0.0212956i
\(680\) 46.4077 1.77965
\(681\) 0 0
\(682\) 4.85868 8.41549i 0.186049 0.322246i
\(683\) 5.14940 8.91901i 0.197036 0.341277i −0.750530 0.660836i \(-0.770202\pi\)
0.947566 + 0.319560i \(0.103535\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 13.4948 + 4.05766i 0.515234 + 0.154922i
\(687\) 0 0
\(688\) 1.41410 + 2.44929i 0.0539120 + 0.0933782i
\(689\) −19.7411 + 34.1925i −0.752074 + 1.30263i
\(690\) 0 0
\(691\) −14.5361 25.1773i −0.552980 0.957789i −0.998058 0.0622973i \(-0.980157\pi\)
0.445078 0.895492i \(-0.353176\pi\)
\(692\) 11.7083 0.445084
\(693\) 0 0
\(694\) −8.59261 −0.326171
\(695\) 20.3571 + 35.2594i 0.772187 + 1.33747i
\(696\) 0 0
\(697\) 11.1677 19.3430i 0.423007 0.732670i
\(698\) 4.29755 + 7.44357i 0.162665 + 0.281743i
\(699\) 0 0
\(700\) −13.4863 13.7614i −0.509735 0.520132i
\(701\) 27.4153 1.03546 0.517731 0.855543i \(-0.326777\pi\)
0.517731 + 0.855543i \(0.326777\pi\)
\(702\) 0 0
\(703\) −6.90739 + 11.9640i −0.260517 + 0.451229i
\(704\) −3.06402 + 5.30703i −0.115479 + 0.200016i
\(705\) 0 0
\(706\) 14.0780 0.529832
\(707\) −5.50465 + 19.7442i −0.207024 + 0.742557i
\(708\) 0 0
\(709\) 18.4834 + 32.0143i 0.694160 + 1.20232i 0.970463 + 0.241250i \(0.0775575\pi\)
−0.276302 + 0.961071i \(0.589109\pi\)
\(710\) −8.79235 + 15.2288i −0.329971 + 0.571526i
\(711\) 0 0
\(712\) 12.6607 + 21.9291i 0.474481 + 0.821826i
\(713\) 5.37756 0.201391
\(714\) 0 0
\(715\) 26.3880 0.986854
\(716\) 7.04118 + 12.1957i 0.263141 + 0.455774i
\(717\) 0 0
\(718\) 7.56922 13.1103i 0.282481 0.489271i
\(719\) 20.2599 + 35.0912i 0.755568 + 1.30868i 0.945092 + 0.326806i \(0.105972\pi\)
−0.189524 + 0.981876i \(0.560694\pi\)
\(720\) 0 0
\(721\) −4.50877 4.60073i −0.167915 0.171340i
\(722\) 0.415309 0.0154562
\(723\) 0 0
\(724\) −6.67046 + 11.5536i −0.247906 + 0.429385i
\(725\) −25.9435 + 44.9355i −0.963518 + 1.66886i
\(726\) 0 0
\(727\) −15.2416 −0.565280 −0.282640 0.959226i \(-0.591210\pi\)
−0.282640 + 0.959226i \(0.591210\pi\)
\(728\) 24.7033 6.35267i 0.915565 0.235446i
\(729\) 0 0
\(730\) −9.15103 15.8500i −0.338695 0.586637i
\(731\) −9.19630 + 15.9285i −0.340138 + 0.589136i
\(732\) 0 0
\(733\) −16.2895 28.2142i −0.601665 1.04211i −0.992569 0.121683i \(-0.961171\pi\)
0.390904 0.920432i \(-0.372163\pi\)
\(734\) 4.37540 0.161499
\(735\) 0 0
\(736\) −5.52640 −0.203706
\(737\) −8.30834 14.3905i −0.306042 0.530080i
\(738\) 0 0
\(739\) −3.50684 + 6.07402i −0.129001 + 0.223436i −0.923290 0.384104i \(-0.874510\pi\)
0.794289 + 0.607540i \(0.207844\pi\)
\(740\) 7.06470 + 12.2364i 0.259704 + 0.449820i
\(741\) 0 0
\(742\) −20.7837 + 5.34471i −0.762994 + 0.196210i
\(743\) 35.0118 1.28446 0.642229 0.766513i \(-0.278010\pi\)
0.642229 + 0.766513i \(0.278010\pi\)
\(744\) 0 0
\(745\) −12.8187 + 22.2027i −0.469642 + 0.813445i
\(746\) −0.760877 + 1.31788i −0.0278577 + 0.0482509i
\(747\) 0 0
\(748\) 17.8285 0.651873
\(749\) 21.2307 + 21.6637i 0.775751 + 0.791573i
\(750\) 0 0
\(751\) 2.13844 + 3.70388i 0.0780327 + 0.135157i 0.902401 0.430897i \(-0.141803\pi\)
−0.824368 + 0.566054i \(0.808469\pi\)
\(752\) 0.0971198 0.168217i 0.00354160 0.00613422i
\(753\) 0 0
\(754\) −14.2661 24.7096i −0.519540 0.899870i
\(755\) −19.9910 −0.727546
\(756\) 0 0
\(757\) −34.9611 −1.27068 −0.635342 0.772231i \(-0.719141\pi\)
−0.635342 + 0.772231i \(0.719141\pi\)
\(758\) −3.40615 5.89962i −0.123717 0.214284i
\(759\) 0 0
\(760\) 18.3090 31.7122i 0.664138 1.15032i
\(761\) −2.29179 3.96950i −0.0830773 0.143894i 0.821493 0.570219i \(-0.193142\pi\)
−0.904570 + 0.426324i \(0.859808\pi\)
\(762\) 0 0
\(763\) −12.9669 + 46.5100i −0.469433 + 1.68377i
\(764\) 35.1546 1.27185
\(765\) 0 0
\(766\) 7.67154 13.2875i 0.277184 0.480097i
\(767\) 3.80959 6.59840i 0.137556 0.238254i
\(768\) 0 0
\(769\) 16.9590 0.611556 0.305778 0.952103i \(-0.401083\pi\)
0.305778 + 0.952103i \(0.401083\pi\)
\(770\) 10.0390 + 10.2437i 0.361780 + 0.369159i
\(771\) 0 0
\(772\) −0.588649 1.01957i −0.0211859 0.0366951i
\(773\) −20.1420 + 34.8870i −0.724458 + 1.25480i 0.234739 + 0.972058i \(0.424576\pi\)
−0.959197 + 0.282739i \(0.908757\pi\)
\(774\) 0 0
\(775\) 14.6150 + 25.3140i 0.524988 + 0.909306i
\(776\) −2.19208 −0.0786911
\(777\) 0 0
\(778\) 25.5653 0.916559
\(779\) −8.81191 15.2627i −0.315719 0.546842i
\(780\) 0 0
\(781\) −8.13160 + 14.0843i −0.290972 + 0.503977i
\(782\) −2.00972 3.48093i −0.0718673 0.124478i
\(783\) 0 0
\(784\) −5.16101 3.12030i −0.184322 0.111439i
\(785\) 2.23912 0.0799177
\(786\) 0 0
\(787\) −23.6053 + 40.8856i −0.841439 + 1.45742i 0.0472387 + 0.998884i \(0.484958\pi\)
−0.888678 + 0.458532i \(0.848375\pi\)
\(788\) 4.16484 7.21371i 0.148366 0.256978i
\(789\) 0 0
\(790\) −16.5322 −0.588188
\(791\) 13.4513 3.45912i 0.478273 0.122992i