Properties

Label 91.2.q.a.43.6
Level $91$
Weight $2$
Character 91.43
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.6
Root \(-1.30089 - 0.554694i\) of defining polynomial
Character \(\chi\) \(=\) 91.43
Dual form 91.2.q.a.36.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.82678 + 1.05469i) q^{2} +(-1.13082 + 1.95864i) q^{3} +(1.22476 + 2.12135i) q^{4} -3.60178i q^{5} +(-4.13154 + 2.38535i) q^{6} +(-0.866025 + 0.500000i) q^{7} +0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +O(q^{10})\) \(q+(1.82678 + 1.05469i) q^{2} +(-1.13082 + 1.95864i) q^{3} +(1.22476 + 2.12135i) q^{4} -3.60178i q^{5} +(-4.13154 + 2.38535i) q^{6} +(-0.866025 + 0.500000i) q^{7} +0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +(3.79878 - 6.57967i) q^{10} +(0.767631 + 0.443192i) q^{11} -5.53995 q^{12} +(-1.17349 + 3.40924i) q^{13} -2.10939 q^{14} +(7.05461 + 4.07298i) q^{15} +(1.44945 - 2.51051i) q^{16} +(-2.48008 - 4.29563i) q^{17} -4.46147i q^{18} +(2.06008 - 1.18939i) q^{19} +(7.64062 - 4.41132i) q^{20} -2.26165i q^{21} +(0.934864 + 1.61923i) q^{22} +(-1.92926 + 3.34157i) q^{23} +(-1.85721 - 1.07226i) q^{24} -7.97282 q^{25} +(-5.73942 + 4.99028i) q^{26} -2.00144 q^{27} +(-2.12135 - 1.22476i) q^{28} +(-0.640986 + 1.11022i) q^{29} +(8.59150 + 14.8809i) q^{30} +8.46921i q^{31} +(6.93800 - 4.00566i) q^{32} +(-1.73611 + 1.00234i) q^{33} -10.4629i q^{34} +(1.80089 + 3.11923i) q^{35} +(2.59043 - 4.48676i) q^{36} +(-8.34686 - 4.81906i) q^{37} +5.01776 q^{38} +(-5.35049 - 6.15370i) q^{39} +3.41525 q^{40} +(10.4652 + 6.04207i) q^{41} +(2.38535 - 4.13154i) q^{42} +(-1.82125 - 3.15450i) q^{43} +2.17122i q^{44} +(-6.59734 + 3.80898i) q^{45} +(-7.04867 + 4.06955i) q^{46} -2.98229i q^{47} +(3.27814 + 5.67790i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-14.5646 - 8.40888i) q^{50} +11.2181 q^{51} +(-8.66942 + 1.68613i) q^{52} +4.92032 q^{53} +(-3.65619 - 2.11090i) q^{54} +(1.59628 - 2.76484i) q^{55} +(-0.474106 - 0.821175i) q^{56} +5.37995i q^{57} +(-2.34189 + 1.35209i) q^{58} +(6.34577 - 3.66373i) q^{59} +19.9537i q^{60} +(0.769632 + 1.33304i) q^{61} +(-8.93242 + 15.4714i) q^{62} +(1.83169 + 1.05753i) q^{63} +11.1012 q^{64} +(12.2793 + 4.22664i) q^{65} -4.22867 q^{66} +(7.29756 + 4.21325i) q^{67} +(6.07501 - 10.5222i) q^{68} +(-4.36330 - 7.55745i) q^{69} +7.59755i q^{70} +(-5.58490 + 3.22444i) q^{71} +(1.73683 - 1.00276i) q^{72} +7.14859i q^{73} +(-10.1653 - 17.6068i) q^{74} +(9.01585 - 15.6159i) q^{75} +(5.04621 + 2.91343i) q^{76} -0.886384 q^{77} +(-3.28391 - 16.8846i) q^{78} +0.757551 q^{79} +(-9.04232 - 5.22059i) q^{80} +(5.43585 - 9.41518i) q^{81} +(12.7451 + 22.0751i) q^{82} -4.76766i q^{83} +(4.79774 - 2.76998i) q^{84} +(-15.4719 + 8.93270i) q^{85} -7.68344i q^{86} +(-1.44969 - 2.51093i) q^{87} +(-0.420240 + 0.727877i) q^{88} +(3.13400 + 1.80942i) q^{89} -16.0692 q^{90} +(-0.688351 - 3.53923i) q^{91} -9.45150 q^{92} +(-16.5882 - 9.57719i) q^{93} +(3.14541 - 5.44800i) q^{94} +(-4.28391 - 7.41995i) q^{95} +18.1188i q^{96} +(-0.401229 + 0.231650i) q^{97} +(1.82678 - 1.05469i) q^{98} -1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + O(q^{10}) \) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + 12q^{10} + 6q^{11} - 4q^{12} + 4q^{13} - 8q^{14} + 6q^{15} - 8q^{16} - 4q^{17} - 12q^{20} + 6q^{22} - 12q^{23} + 12q^{24} - 20q^{25} - 42q^{26} + 12q^{27} + 8q^{29} + 8q^{30} + 36q^{32} - 30q^{33} + 6q^{35} - 10q^{36} - 42q^{37} + 4q^{38} - 4q^{39} + 92q^{40} + 30q^{41} + 4q^{42} + 2q^{43} + 12q^{46} - 2q^{48} + 6q^{49} - 18q^{50} + 52q^{51} + 2q^{52} - 44q^{53} + 12q^{54} - 6q^{55} - 12q^{56} - 12q^{58} + 18q^{59} + 14q^{61} - 4q^{62} + 12q^{63} - 52q^{64} + 60q^{65} - 52q^{66} - 24q^{67} - 8q^{68} + 4q^{69} - 24q^{71} + 60q^{72} + 6q^{74} + 46q^{75} - 18q^{76} + 8q^{77} - 10q^{78} - 56q^{79} - 72q^{80} + 2q^{81} + 14q^{82} + 18q^{84} - 48q^{85} - 2q^{87} - 14q^{88} - 12q^{89} + 24q^{90} + 14q^{91} + 24q^{92} - 18q^{93} + 4q^{94} - 22q^{95} + 6q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.82678 + 1.05469i 1.29173 + 0.745781i 0.978961 0.204047i \(-0.0654097\pi\)
0.312770 + 0.949829i \(0.398743\pi\)
\(3\) −1.13082 + 1.95864i −0.652882 + 1.13082i 0.329539 + 0.944142i \(0.393107\pi\)
−0.982420 + 0.186682i \(0.940227\pi\)
\(4\) 1.22476 + 2.12135i 0.612380 + 1.06067i
\(5\) 3.60178i 1.61076i −0.592756 0.805382i \(-0.701960\pi\)
0.592756 0.805382i \(-0.298040\pi\)
\(6\) −4.13154 + 2.38535i −1.68670 + 0.973814i
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 0.948212i 0.335243i
\(9\) −1.05753 1.83169i −0.352509 0.610563i
\(10\) 3.79878 6.57967i 1.20128 2.08068i
\(11\) 0.767631 + 0.443192i 0.231450 + 0.133627i 0.611241 0.791445i \(-0.290671\pi\)
−0.379791 + 0.925072i \(0.624004\pi\)
\(12\) −5.53995 −1.59925
\(13\) −1.17349 + 3.40924i −0.325467 + 0.945553i
\(14\) −2.10939 −0.563758
\(15\) 7.05461 + 4.07298i 1.82149 + 1.05164i
\(16\) 1.44945 2.51051i 0.362362 0.627629i
\(17\) −2.48008 4.29563i −0.601508 1.04184i −0.992593 0.121488i \(-0.961233\pi\)
0.391085 0.920355i \(-0.372100\pi\)
\(18\) 4.46147i 1.05158i
\(19\) 2.06008 1.18939i 0.472615 0.272864i −0.244719 0.969594i \(-0.578696\pi\)
0.717334 + 0.696730i \(0.245362\pi\)
\(20\) 7.64062 4.41132i 1.70849 0.986400i
\(21\) 2.26165i 0.493532i
\(22\) 0.934864 + 1.61923i 0.199314 + 0.345222i
\(23\) −1.92926 + 3.34157i −0.402278 + 0.696765i −0.994000 0.109376i \(-0.965115\pi\)
0.591723 + 0.806142i \(0.298448\pi\)
\(24\) −1.85721 1.07226i −0.379101 0.218874i
\(25\) −7.97282 −1.59456
\(26\) −5.73942 + 4.99028i −1.12559 + 0.978674i
\(27\) −2.00144 −0.385177
\(28\) −2.12135 1.22476i −0.400897 0.231458i
\(29\) −0.640986 + 1.11022i −0.119028 + 0.206163i −0.919383 0.393364i \(-0.871311\pi\)
0.800355 + 0.599527i \(0.204645\pi\)
\(30\) 8.59150 + 14.8809i 1.56859 + 2.71687i
\(31\) 8.46921i 1.52111i 0.649271 + 0.760557i \(0.275074\pi\)
−0.649271 + 0.760557i \(0.724926\pi\)
\(32\) 6.93800 4.00566i 1.22648 0.708107i
\(33\) −1.73611 + 1.00234i −0.302218 + 0.174486i
\(34\) 10.4629i 1.79437i
\(35\) 1.80089 + 3.11923i 0.304406 + 0.527247i
\(36\) 2.59043 4.48676i 0.431739 0.747793i
\(37\) −8.34686 4.81906i −1.37222 0.792249i −0.381009 0.924571i \(-0.624423\pi\)
−0.991207 + 0.132323i \(0.957757\pi\)
\(38\) 5.01776 0.813988
\(39\) −5.35049 6.15370i −0.856763 0.985380i
\(40\) 3.41525 0.539998
\(41\) 10.4652 + 6.04207i 1.63438 + 0.943612i 0.982719 + 0.185106i \(0.0592628\pi\)
0.651666 + 0.758506i \(0.274071\pi\)
\(42\) 2.38535 4.13154i 0.368067 0.637511i
\(43\) −1.82125 3.15450i −0.277738 0.481056i 0.693084 0.720856i \(-0.256251\pi\)
−0.970822 + 0.239800i \(0.922918\pi\)
\(44\) 2.17122i 0.327323i
\(45\) −6.59734 + 3.80898i −0.983474 + 0.567809i
\(46\) −7.04867 + 4.06955i −1.03927 + 0.600022i
\(47\) 2.98229i 0.435012i −0.976059 0.217506i \(-0.930208\pi\)
0.976059 0.217506i \(-0.0697922\pi\)
\(48\) 3.27814 + 5.67790i 0.473158 + 0.819535i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −14.5646 8.40888i −2.05975 1.18920i
\(51\) 11.2181 1.57085
\(52\) −8.66942 + 1.68613i −1.20223 + 0.233824i
\(53\) 4.92032 0.675858 0.337929 0.941172i \(-0.390274\pi\)
0.337929 + 0.941172i \(0.390274\pi\)
\(54\) −3.65619 2.11090i −0.497545 0.287258i
\(55\) 1.59628 2.76484i 0.215242 0.372811i
\(56\) −0.474106 0.821175i −0.0633551 0.109734i
\(57\) 5.37995i 0.712592i
\(58\) −2.34189 + 1.35209i −0.307505 + 0.177538i
\(59\) 6.34577 3.66373i 0.826148 0.476977i −0.0263837 0.999652i \(-0.508399\pi\)
0.852532 + 0.522675i \(0.175066\pi\)
\(60\) 19.9537i 2.57601i
\(61\) 0.769632 + 1.33304i 0.0985412 + 0.170678i 0.911081 0.412227i \(-0.135249\pi\)
−0.812540 + 0.582906i \(0.801916\pi\)
\(62\) −8.93242 + 15.4714i −1.13442 + 1.96487i
\(63\) 1.83169 + 1.05753i 0.230771 + 0.133236i
\(64\) 11.1012 1.38765
\(65\) 12.2793 + 4.22664i 1.52306 + 0.524250i
\(66\) −4.22867 −0.520513
\(67\) 7.29756 + 4.21325i 0.891539 + 0.514730i 0.874445 0.485124i \(-0.161225\pi\)
0.0170931 + 0.999854i \(0.494559\pi\)
\(68\) 6.07501 10.5222i 0.736703 1.27601i
\(69\) −4.36330 7.55745i −0.525279 0.909811i
\(70\) 7.59755i 0.908081i
\(71\) −5.58490 + 3.22444i −0.662805 + 0.382671i −0.793345 0.608772i \(-0.791662\pi\)
0.130540 + 0.991443i \(0.458329\pi\)
\(72\) 1.73683 1.00276i 0.204687 0.118176i
\(73\) 7.14859i 0.836679i 0.908291 + 0.418340i \(0.137388\pi\)
−0.908291 + 0.418340i \(0.862612\pi\)
\(74\) −10.1653 17.6068i −1.18169 2.04675i
\(75\) 9.01585 15.6159i 1.04106 1.80317i
\(76\) 5.04621 + 2.91343i 0.578840 + 0.334193i
\(77\) −0.886384 −0.101013
\(78\) −3.28391 16.8846i −0.371830 1.91180i
\(79\) 0.757551 0.0852311 0.0426156 0.999092i \(-0.486431\pi\)
0.0426156 + 0.999092i \(0.486431\pi\)
\(80\) −9.04232 5.22059i −1.01096 0.583679i
\(81\) 5.43585 9.41518i 0.603984 1.04613i
\(82\) 12.7451 + 22.0751i 1.40746 + 2.43779i
\(83\) 4.76766i 0.523319i −0.965160 0.261659i \(-0.915730\pi\)
0.965160 0.261659i \(-0.0842697\pi\)
\(84\) 4.79774 2.76998i 0.523476 0.302229i
\(85\) −15.4719 + 8.93270i −1.67816 + 0.968888i
\(86\) 7.68344i 0.828527i
\(87\) −1.44969 2.51093i −0.155423 0.269200i
\(88\) −0.420240 + 0.727877i −0.0447977 + 0.0775919i
\(89\) 3.13400 + 1.80942i 0.332204 + 0.191798i 0.656819 0.754048i \(-0.271902\pi\)
−0.324615 + 0.945846i \(0.605235\pi\)
\(90\) −16.0692 −1.69385
\(91\) −0.688351 3.53923i −0.0721588 0.371012i
\(92\) −9.45150 −0.985387
\(93\) −16.5882 9.57719i −1.72011 0.993108i
\(94\) 3.14541 5.44800i 0.324424 0.561919i
\(95\) −4.28391 7.41995i −0.439520 0.761271i
\(96\) 18.1188i 1.84924i
\(97\) −0.401229 + 0.231650i −0.0407386 + 0.0235205i −0.520231 0.854026i \(-0.674154\pi\)
0.479492 + 0.877546i \(0.340821\pi\)
\(98\) 1.82678 1.05469i 0.184533 0.106540i
\(99\) 1.87475i 0.188419i
\(100\) −9.76479 16.9131i −0.976479 1.69131i
\(101\) 2.91152 5.04289i 0.289707 0.501787i −0.684033 0.729451i \(-0.739776\pi\)
0.973740 + 0.227664i \(0.0731089\pi\)
\(102\) 20.4931 + 11.8317i 2.02912 + 1.17151i
\(103\) −8.23888 −0.811801 −0.405901 0.913917i \(-0.633042\pi\)
−0.405901 + 0.913917i \(0.633042\pi\)
\(104\) −3.23268 1.11271i −0.316991 0.109111i
\(105\) −8.14596 −0.794964
\(106\) 8.98837 + 5.18944i 0.873027 + 0.504043i
\(107\) 1.91630 3.31913i 0.185256 0.320872i −0.758407 0.651781i \(-0.774022\pi\)
0.943663 + 0.330909i \(0.107355\pi\)
\(108\) −2.45128 4.24574i −0.235875 0.408547i
\(109\) 10.4180i 0.997867i −0.866640 0.498934i \(-0.833725\pi\)
0.866640 0.498934i \(-0.166275\pi\)
\(110\) 5.83212 3.36718i 0.556071 0.321048i
\(111\) 18.8777 10.8990i 1.79179 1.03449i
\(112\) 2.89889i 0.273920i
\(113\) 2.45505 + 4.25228i 0.230952 + 0.400021i 0.958089 0.286472i \(-0.0924826\pi\)
−0.727136 + 0.686493i \(0.759149\pi\)
\(114\) −5.67421 + 9.82801i −0.531438 + 0.920478i
\(115\) 12.0356 + 6.94875i 1.12233 + 0.647975i
\(116\) −3.14022 −0.291562
\(117\) 7.48567 1.45590i 0.692050 0.134598i
\(118\) 15.4565 1.42288
\(119\) 4.29563 + 2.48008i 0.393779 + 0.227349i
\(120\) −3.86205 + 6.68926i −0.352555 + 0.610643i
\(121\) −5.10716 8.84586i −0.464287 0.804169i
\(122\) 3.24690i 0.293961i
\(123\) −23.6685 + 13.6650i −2.13412 + 1.23213i
\(124\) −17.9661 + 10.3727i −1.61341 + 0.931500i
\(125\) 10.7074i 0.957702i
\(126\) 2.23073 + 3.86375i 0.198730 + 0.344210i
\(127\) −6.15508 + 10.6609i −0.546175 + 0.946003i 0.452357 + 0.891837i \(0.350583\pi\)
−0.998532 + 0.0541658i \(0.982750\pi\)
\(128\) 6.40347 + 3.69704i 0.565992 + 0.326776i
\(129\) 8.23805 0.725320
\(130\) 17.9739 + 20.6721i 1.57641 + 1.81306i
\(131\) −8.20265 −0.716669 −0.358335 0.933593i \(-0.616655\pi\)
−0.358335 + 0.933593i \(0.616655\pi\)
\(132\) −4.25264 2.45526i −0.370145 0.213703i
\(133\) −1.18939 + 2.06008i −0.103133 + 0.178632i
\(134\) 8.88737 + 15.3934i 0.767752 + 1.32979i
\(135\) 7.20874i 0.620429i
\(136\) 4.07316 2.35164i 0.349271 0.201652i
\(137\) 6.45670 3.72778i 0.551633 0.318485i −0.198147 0.980172i \(-0.563492\pi\)
0.749780 + 0.661687i \(0.230159\pi\)
\(138\) 18.4078i 1.56697i
\(139\) −8.34028 14.4458i −0.707413 1.22528i −0.965813 0.259238i \(-0.916529\pi\)
0.258400 0.966038i \(-0.416805\pi\)
\(140\) −4.41132 + 7.64062i −0.372824 + 0.645750i
\(141\) 5.84125 + 3.37245i 0.491922 + 0.284011i
\(142\) −13.6032 −1.14156
\(143\) −2.41175 + 2.09696i −0.201681 + 0.175357i
\(144\) −6.13131 −0.510943
\(145\) 3.99877 + 2.30869i 0.332080 + 0.191726i
\(146\) −7.53958 + 13.0589i −0.623980 + 1.08076i
\(147\) 1.13082 + 1.95864i 0.0932688 + 0.161546i
\(148\) 23.6088i 1.94063i
\(149\) −2.18380 + 1.26082i −0.178904 + 0.103290i −0.586777 0.809748i \(-0.699604\pi\)
0.407874 + 0.913038i \(0.366270\pi\)
\(150\) 32.9400 19.0179i 2.68954 1.55281i
\(151\) 15.8972i 1.29370i 0.762618 + 0.646849i \(0.223914\pi\)
−0.762618 + 0.646849i \(0.776086\pi\)
\(152\) 1.12779 + 1.95339i 0.0914760 + 0.158441i
\(153\) −5.24550 + 9.08548i −0.424074 + 0.734517i
\(154\) −1.61923 0.934864i −0.130481 0.0753335i
\(155\) 30.5042 2.45016
\(156\) 6.50106 18.8870i 0.520502 1.51217i
\(157\) 12.9831 1.03616 0.518082 0.855331i \(-0.326646\pi\)
0.518082 + 0.855331i \(0.326646\pi\)
\(158\) 1.38388 + 0.798985i 0.110096 + 0.0635638i
\(159\) −5.56402 + 9.63717i −0.441256 + 0.764277i
\(160\) −14.4275 24.9892i −1.14059 1.97557i
\(161\) 3.85851i 0.304093i
\(162\) 19.8603 11.4663i 1.56037 0.900880i
\(163\) −2.00873 + 1.15974i −0.157336 + 0.0908378i −0.576601 0.817026i \(-0.695621\pi\)
0.419265 + 0.907864i \(0.362288\pi\)
\(164\) 29.6003i 2.31140i
\(165\) 3.61023 + 6.25309i 0.281056 + 0.486803i
\(166\) 5.02843 8.70949i 0.390282 0.675987i
\(167\) −11.9441 6.89591i −0.924260 0.533622i −0.0392682 0.999229i \(-0.512503\pi\)
−0.884992 + 0.465607i \(0.845836\pi\)
\(168\) 2.14452 0.165453
\(169\) −10.2459 8.00140i −0.788143 0.615493i
\(170\) −37.6851 −2.89031
\(171\) −4.35718 2.51562i −0.333202 0.192374i
\(172\) 4.46118 7.72700i 0.340162 0.589178i
\(173\) −1.84216 3.19071i −0.140057 0.242585i 0.787461 0.616364i \(-0.211395\pi\)
−0.927518 + 0.373779i \(0.878062\pi\)
\(174\) 6.11590i 0.463645i
\(175\) 6.90466 3.98641i 0.521943 0.301344i
\(176\) 2.22528 1.28477i 0.167737 0.0968429i
\(177\) 16.5721i 1.24564i
\(178\) 3.81677 + 6.61083i 0.286079 + 0.495503i
\(179\) −2.94638 + 5.10328i −0.220223 + 0.381437i −0.954876 0.297006i \(-0.904012\pi\)
0.734653 + 0.678443i \(0.237345\pi\)
\(180\) −16.1603 9.33017i −1.20452 0.695430i
\(181\) −2.11543 −0.157239 −0.0786193 0.996905i \(-0.525051\pi\)
−0.0786193 + 0.996905i \(0.525051\pi\)
\(182\) 2.47534 7.19141i 0.183484 0.533063i
\(183\) −3.48127 −0.257343
\(184\) −3.16851 1.82934i −0.233586 0.134861i
\(185\) −17.3572 + 30.0635i −1.27613 + 2.21032i
\(186\) −20.2020 34.9909i −1.48128 2.56566i
\(187\) 4.39661i 0.321512i
\(188\) 6.32647 3.65259i 0.461406 0.266393i
\(189\) 1.73330 1.00072i 0.126079 0.0727916i
\(190\) 18.0729i 1.31114i
\(191\) 5.68333 + 9.84381i 0.411231 + 0.712273i 0.995025 0.0996290i \(-0.0317656\pi\)
−0.583794 + 0.811902i \(0.698432\pi\)
\(192\) −12.5535 + 21.7433i −0.905970 + 1.56919i
\(193\) 12.2017 + 7.04468i 0.878301 + 0.507087i 0.870098 0.492879i \(-0.164055\pi\)
0.00820314 + 0.999966i \(0.497389\pi\)
\(194\) −0.977279 −0.0701645
\(195\) −22.1643 + 19.2713i −1.58722 + 1.38004i
\(196\) 2.44952 0.174966
\(197\) −19.8815 11.4786i −1.41650 0.817814i −0.420507 0.907289i \(-0.638148\pi\)
−0.995989 + 0.0894753i \(0.971481\pi\)
\(198\) 1.97729 3.42476i 0.140520 0.243387i
\(199\) −1.57492 2.72785i −0.111643 0.193372i 0.804790 0.593560i \(-0.202278\pi\)
−0.916433 + 0.400188i \(0.868945\pi\)
\(200\) 7.55992i 0.534567i
\(201\) −16.5045 + 9.52888i −1.16414 + 0.672116i
\(202\) 10.6374 6.14152i 0.748446 0.432116i
\(203\) 1.28197i 0.0899768i
\(204\) 13.7395 + 23.7976i 0.961959 + 1.66616i
\(205\) 21.7622 37.6932i 1.51994 2.63261i
\(206\) −15.0507 8.68950i −1.04863 0.605426i
\(207\) 8.16096 0.567226
\(208\) 6.85804 + 7.88757i 0.475520 + 0.546905i
\(209\) 2.10851 0.145849
\(210\) −14.8809 8.59150i −1.02688 0.592870i
\(211\) 7.43191 12.8725i 0.511634 0.886176i −0.488275 0.872690i \(-0.662374\pi\)
0.999909 0.0134864i \(-0.00429298\pi\)
\(212\) 6.02621 + 10.4377i 0.413882 + 0.716865i
\(213\) 14.5851i 0.999355i
\(214\) 7.00133 4.04222i 0.478601 0.276321i
\(215\) −11.3618 + 6.55974i −0.774868 + 0.447370i
\(216\) 1.89779i 0.129128i
\(217\) −4.23460 7.33455i −0.287464 0.497902i
\(218\) 10.9878 19.0315i 0.744191 1.28898i
\(219\) −14.0016 8.08380i −0.946137 0.546253i
\(220\) 7.82024 0.527241
\(221\) 17.5552 3.41433i 1.18089 0.229673i
\(222\) 45.9805 3.08601
\(223\) 3.79396 + 2.19044i 0.254062 + 0.146683i 0.621623 0.783317i \(-0.286474\pi\)
−0.367561 + 0.930000i \(0.619807\pi\)
\(224\) −4.00566 + 6.93800i −0.267639 + 0.463565i
\(225\) 8.43147 + 14.6037i 0.562098 + 0.973582i
\(226\) 10.3573i 0.688959i
\(227\) 11.7488 6.78316i 0.779793 0.450214i −0.0565636 0.998399i \(-0.518014\pi\)
0.836357 + 0.548185i \(0.184681\pi\)
\(228\) −11.4127 + 6.58915i −0.755827 + 0.436377i
\(229\) 16.5180i 1.09154i −0.837935 0.545770i \(-0.816237\pi\)
0.837935 0.545770i \(-0.183763\pi\)
\(230\) 14.6576 + 25.3877i 0.966495 + 1.67402i
\(231\) 1.00234 1.73611i 0.0659494 0.114228i
\(232\) −1.05272 0.607791i −0.0691147 0.0399034i
\(233\) 16.5026 1.08112 0.540561 0.841305i \(-0.318212\pi\)
0.540561 + 0.841305i \(0.318212\pi\)
\(234\) 15.2102 + 5.23548i 0.994324 + 0.342254i
\(235\) −10.7416 −0.700702
\(236\) 15.5441 + 8.97438i 1.01183 + 0.584182i
\(237\) −0.856657 + 1.48377i −0.0556458 + 0.0963814i
\(238\) 5.23145 + 9.06114i 0.339105 + 0.587347i
\(239\) 30.4210i 1.96777i 0.178796 + 0.983886i \(0.442780\pi\)
−0.178796 + 0.983886i \(0.557220\pi\)
\(240\) 20.4506 11.8071i 1.32008 0.762147i
\(241\) −25.5602 + 14.7572i −1.64648 + 0.950593i −0.668018 + 0.744145i \(0.732857\pi\)
−0.978458 + 0.206448i \(0.933810\pi\)
\(242\) 21.5460i 1.38503i
\(243\) 9.29184 + 16.0939i 0.596072 + 1.03243i
\(244\) −1.88523 + 3.26531i −0.120689 + 0.209040i
\(245\) −3.11923 1.80089i −0.199280 0.115055i
\(246\) −57.6497 −3.67561
\(247\) 1.63743 + 8.41904i 0.104187 + 0.535691i
\(248\) −8.03060 −0.509944
\(249\) 9.33816 + 5.39139i 0.591782 + 0.341665i
\(250\) −11.2931 + 19.5602i −0.714236 + 1.23709i
\(251\) −6.49134 11.2433i −0.409730 0.709673i 0.585130 0.810940i \(-0.301044\pi\)
−0.994859 + 0.101267i \(0.967710\pi\)
\(252\) 5.18087i 0.326364i
\(253\) −2.96191 + 1.71006i −0.186214 + 0.107511i
\(254\) −22.4880 + 12.9835i −1.41102 + 0.814654i
\(255\) 40.4053i 2.53028i
\(256\) −3.30268 5.72042i −0.206418 0.357526i
\(257\) −2.29261 + 3.97091i −0.143009 + 0.247698i −0.928628 0.371011i \(-0.879011\pi\)
0.785620 + 0.618710i \(0.212344\pi\)
\(258\) 15.0491 + 8.68862i 0.936918 + 0.540930i
\(259\) 9.63812 0.598884
\(260\) 6.07307 + 31.2253i 0.376636 + 1.93651i
\(261\) 2.71144 0.167834
\(262\) −14.9845 8.65129i −0.925744 0.534479i
\(263\) 1.33250 2.30795i 0.0821652 0.142314i −0.822015 0.569466i \(-0.807150\pi\)
0.904180 + 0.427152i \(0.140483\pi\)
\(264\) −0.950435 1.64620i −0.0584952 0.101317i
\(265\) 17.7219i 1.08865i
\(266\) −4.34551 + 2.50888i −0.266440 + 0.153829i
\(267\) −7.08801 + 4.09227i −0.433779 + 0.250443i
\(268\) 20.6409i 1.26084i
\(269\) −5.96282 10.3279i −0.363559 0.629703i 0.624984 0.780637i \(-0.285105\pi\)
−0.988544 + 0.150934i \(0.951772\pi\)
\(270\) −7.60301 + 13.1688i −0.462705 + 0.801428i
\(271\) −11.2828 6.51416i −0.685384 0.395707i 0.116496 0.993191i \(-0.462834\pi\)
−0.801881 + 0.597484i \(0.796167\pi\)
\(272\) −14.3790 −0.871853
\(273\) 7.71051 + 2.65402i 0.466661 + 0.160628i
\(274\) 15.7267 0.950082
\(275\) −6.12018 3.53349i −0.369061 0.213077i
\(276\) 10.6880 18.5121i 0.643341 1.11430i
\(277\) 10.6824 + 18.5025i 0.641846 + 1.11171i 0.985020 + 0.172438i \(0.0551646\pi\)
−0.343174 + 0.939272i \(0.611502\pi\)
\(278\) 35.1858i 2.11030i
\(279\) 15.5130 8.95641i 0.928737 0.536206i
\(280\) −2.95769 + 1.70762i −0.176756 + 0.102050i
\(281\) 17.2678i 1.03011i −0.857158 0.515054i \(-0.827772\pi\)
0.857158 0.515054i \(-0.172228\pi\)
\(282\) 7.11380 + 12.3215i 0.423621 + 0.733733i
\(283\) −10.6201 + 18.3946i −0.631299 + 1.09344i 0.355987 + 0.934491i \(0.384145\pi\)
−0.987286 + 0.158952i \(0.949189\pi\)
\(284\) −13.6803 7.89833i −0.811777 0.468680i
\(285\) 19.3774 1.14782
\(286\) −6.61741 + 1.28703i −0.391295 + 0.0761037i
\(287\) −12.0841 −0.713304
\(288\) −14.6742 8.47218i −0.864688 0.499228i
\(289\) −3.80160 + 6.58457i −0.223624 + 0.387327i
\(290\) 4.86993 + 8.43496i 0.285972 + 0.495318i
\(291\) 1.04782i 0.0614243i
\(292\) −15.1646 + 8.75531i −0.887443 + 0.512366i
\(293\) −0.363782 + 0.210030i −0.0212524 + 0.0122701i −0.510589 0.859825i \(-0.670572\pi\)
0.489336 + 0.872095i \(0.337239\pi\)
\(294\) 4.77070i 0.278233i
\(295\) −13.1959 22.8561i −0.768298 1.33073i
\(296\) 4.56949 7.91459i 0.265596 0.460026i
\(297\) −1.53637 0.887022i −0.0891490 0.0514702i
\(298\) −5.31910 −0.308127
\(299\) −9.12826 10.4986i −0.527901 0.607149i
\(300\) 44.1690 2.55010
\(301\) 3.15450 + 1.82125i 0.181822 + 0.104975i
\(302\) −16.7667 + 29.0408i −0.964817 + 1.67111i
\(303\) 6.58482 + 11.4053i 0.378288 + 0.655215i
\(304\) 6.89581i 0.395502i
\(305\) 4.80132 2.77204i 0.274923 0.158727i
\(306\) −19.1648 + 11.0648i −1.09558 + 0.632533i
\(307\) 14.0807i 0.803628i 0.915721 + 0.401814i \(0.131620\pi\)
−0.915721 + 0.401814i \(0.868380\pi\)
\(308\) −1.08561 1.88033i −0.0618583 0.107142i
\(309\) 9.31673 16.1370i 0.530010 0.918004i
\(310\) 55.7246 + 32.1726i 3.16495 + 1.82728i
\(311\) −10.3848 −0.588867 −0.294434 0.955672i \(-0.595131\pi\)
−0.294434 + 0.955672i \(0.595131\pi\)
\(312\) 5.83501 5.07339i 0.330342 0.287224i
\(313\) 6.84759 0.387048 0.193524 0.981096i \(-0.438008\pi\)
0.193524 + 0.981096i \(0.438008\pi\)
\(314\) 23.7173 + 13.6932i 1.33845 + 0.772752i
\(315\) 3.80898 6.59734i 0.214612 0.371718i
\(316\) 0.927818 + 1.60703i 0.0521938 + 0.0904024i
\(317\) 0.701249i 0.0393861i −0.999806 0.0196930i \(-0.993731\pi\)
0.999806 0.0196930i \(-0.00626889\pi\)
\(318\) −20.3285 + 11.7367i −1.13997 + 0.658160i
\(319\) −0.984082 + 0.568160i −0.0550980 + 0.0318109i
\(320\) 39.9840i 2.23518i
\(321\) 4.33400 + 7.50670i 0.241900 + 0.418983i
\(322\) 4.06955 7.04867i 0.226787 0.392807i
\(323\) −10.2183 5.89956i −0.568563 0.328260i
\(324\) 26.6305 1.47947
\(325\) 9.35600 27.1813i 0.518977 1.50774i
\(326\) −4.89268 −0.270980
\(327\) 20.4052 + 11.7810i 1.12841 + 0.651489i
\(328\) −5.72916 + 9.92319i −0.316340 + 0.547917i
\(329\) 1.49115 + 2.58274i 0.0822095 + 0.142391i
\(330\) 15.2307i 0.838424i
\(331\) 3.63613 2.09932i 0.199860 0.115389i −0.396730 0.917935i \(-0.629855\pi\)
0.596590 + 0.802546i \(0.296522\pi\)
\(332\) 10.1139 5.83924i 0.555070 0.320470i
\(333\) 20.3851i 1.11710i
\(334\) −14.5462 25.1947i −0.795930 1.37859i
\(335\) 15.1752 26.2842i 0.829109 1.43606i
\(336\) −5.67790 3.27814i −0.309755 0.178837i
\(337\) −20.4278 −1.11278 −0.556388 0.830923i \(-0.687813\pi\)
−0.556388 + 0.830923i \(0.687813\pi\)
\(338\) −10.2779 25.4231i −0.559046 1.38283i
\(339\) −11.1049 −0.603138
\(340\) −37.8987 21.8808i −2.05535 1.18665i
\(341\) −3.75349 + 6.50123i −0.203263 + 0.352061i
\(342\) −5.30642 9.19098i −0.286938 0.496991i
\(343\) 1.00000i 0.0539949i
\(344\) 2.99113 1.72693i 0.161271 0.0931098i
\(345\) −27.2203 + 15.7156i −1.46549 + 0.846102i
\(346\) 7.77165i 0.417807i
\(347\) −3.98500 6.90222i −0.213926 0.370531i 0.739014 0.673690i \(-0.235292\pi\)
−0.952940 + 0.303160i \(0.901959\pi\)
\(348\) 3.55103 6.15057i 0.190355 0.329705i
\(349\) 18.7038 + 10.7986i 1.00119 + 0.578037i 0.908600 0.417668i \(-0.137152\pi\)
0.0925892 + 0.995704i \(0.470486\pi\)
\(350\) 16.8178 0.898947
\(351\) 2.34866 6.82338i 0.125362 0.364205i
\(352\) 7.10110 0.378490
\(353\) 18.7214 + 10.8088i 0.996439 + 0.575295i 0.907193 0.420715i \(-0.138221\pi\)
0.0892465 + 0.996010i \(0.471554\pi\)
\(354\) −17.4785 + 30.2737i −0.928974 + 1.60903i
\(355\) 11.6137 + 20.1156i 0.616393 + 1.06762i
\(356\) 8.86441i 0.469813i
\(357\) −9.71520 + 5.60907i −0.514183 + 0.296863i
\(358\) −10.7648 + 6.21507i −0.568938 + 0.328476i
\(359\) 13.6834i 0.722180i −0.932531 0.361090i \(-0.882405\pi\)
0.932531 0.361090i \(-0.117595\pi\)
\(360\) −3.61172 6.25568i −0.190354 0.329703i
\(361\) −6.67071 + 11.5540i −0.351090 + 0.608106i
\(362\) −3.86443 2.23113i −0.203110 0.117266i
\(363\) 23.1012 1.21250
\(364\) 6.66487 5.79494i 0.349334 0.303737i
\(365\) 25.7477 1.34769
\(366\) −6.35953 3.67168i −0.332418 0.191922i
\(367\) 5.70638 9.88374i 0.297871 0.515927i −0.677778 0.735267i \(-0.737057\pi\)
0.975649 + 0.219339i \(0.0703902\pi\)
\(368\) 5.59271 + 9.68685i 0.291540 + 0.504962i
\(369\) 25.5586i 1.33053i
\(370\) −63.4157 + 36.6131i −3.29683 + 1.90342i
\(371\) −4.26112 + 2.46016i −0.221227 + 0.127725i
\(372\) 46.9190i 2.43264i
\(373\) 15.6404 + 27.0900i 0.809830 + 1.40267i 0.912981 + 0.408002i \(0.133774\pi\)
−0.103151 + 0.994666i \(0.532892\pi\)
\(374\) 4.63708 8.03166i 0.239778 0.415307i
\(375\) −20.9721 12.1082i −1.08299 0.625266i
\(376\) 2.82784 0.145835
\(377\) −3.03282 3.48811i −0.156198 0.179647i
\(378\) 4.22181 0.217146
\(379\) 23.7421 + 13.7075i 1.21955 + 0.704108i 0.964822 0.262904i \(-0.0846803\pi\)
0.254729 + 0.967012i \(0.418014\pi\)
\(380\) 10.4935 18.1753i 0.538307 0.932374i
\(381\) −13.9206 24.1112i −0.713175 1.23526i
\(382\) 23.9767i 1.22675i
\(383\) 13.9436 8.05032i 0.712483 0.411352i −0.0994967 0.995038i \(-0.531723\pi\)
0.811980 + 0.583686i \(0.198390\pi\)
\(384\) −14.4824 + 8.36142i −0.739052 + 0.426692i
\(385\) 3.19256i 0.162708i
\(386\) 14.8600 + 25.7382i 0.756353 + 1.31004i
\(387\) −3.85204 + 6.67193i −0.195810 + 0.339153i
\(388\) −0.982819 0.567431i −0.0498951 0.0288069i
\(389\) −21.1380 −1.07174 −0.535870 0.844301i \(-0.680016\pi\)
−0.535870 + 0.844301i \(0.680016\pi\)
\(390\) −60.8146 + 11.8279i −3.07947 + 0.598930i
\(391\) 19.1388 0.967893
\(392\) 0.821175 + 0.474106i 0.0414756 + 0.0239460i
\(393\) 9.27576 16.0661i 0.467900 0.810427i
\(394\) −24.2128 41.9377i −1.21982 2.11279i
\(395\) 2.72853i 0.137287i
\(396\) 3.97699 2.29612i 0.199851 0.115384i
\(397\) 11.3436 6.54921i 0.569317 0.328695i −0.187560 0.982253i \(-0.560058\pi\)
0.756876 + 0.653558i \(0.226724\pi\)
\(398\) 6.64426i 0.333046i
\(399\) −2.68998 4.65918i −0.134667 0.233251i
\(400\) −11.5562 + 20.0159i −0.577808 + 1.00079i
\(401\) 16.8396 + 9.72236i 0.840930 + 0.485511i 0.857580 0.514350i \(-0.171967\pi\)
−0.0166501 + 0.999861i \(0.505300\pi\)
\(402\) −40.2002 −2.00501
\(403\) −28.8736 9.93851i −1.43830 0.495072i
\(404\) 14.2636 0.709642
\(405\) −33.9114 19.5788i −1.68507 0.972876i
\(406\) 1.35209 2.34189i 0.0671031 0.116226i
\(407\) −4.27154 7.39853i −0.211732 0.366731i
\(408\) 10.6372i 0.526618i
\(409\) 20.8330 12.0279i 1.03013 0.594743i 0.113105 0.993583i \(-0.463921\pi\)
0.917020 + 0.398840i \(0.130587\pi\)
\(410\) 79.5096 45.9049i 3.92670 2.26708i
\(411\) 16.8618i 0.831733i
\(412\) −10.0907 17.4775i −0.497131 0.861056i
\(413\) −3.66373 + 6.34577i −0.180280 + 0.312255i
\(414\) 14.9083 + 8.60732i 0.732703 + 0.423026i
\(415\) −17.1721 −0.842944
\(416\) 5.51460 + 28.3539i 0.270375 + 1.39016i
\(417\) 37.7256 1.84743
\(418\) 3.85179 + 2.22383i 0.188397 + 0.108771i
\(419\) −19.5119 + 33.7956i −0.953218 + 1.65102i −0.214825 + 0.976653i \(0.568918\pi\)
−0.738394 + 0.674370i \(0.764415\pi\)
\(420\) −9.97684 17.2804i −0.486820 0.843197i
\(421\) 22.0284i 1.07360i 0.843710 + 0.536799i \(0.180367\pi\)
−0.843710 + 0.536799i \(0.819633\pi\)
\(422\) 27.1530 15.6768i 1.32179 0.763134i
\(423\) −5.46263 + 3.15385i −0.265602 + 0.153346i
\(424\) 4.66551i 0.226577i
\(425\) 19.7732 + 34.2482i 0.959142 + 1.66128i
\(426\) 15.3828 26.6438i 0.745301 1.29090i
\(427\) −1.33304 0.769632i −0.0645104 0.0372451i
\(428\) 9.38803 0.453787
\(429\) −1.37993 7.09506i −0.0666237 0.342553i
\(430\) −27.6741 −1.33456
\(431\) −31.0727 17.9398i −1.49672 0.864131i −0.496726 0.867907i \(-0.665465\pi\)
−0.999993 + 0.00377645i \(0.998798\pi\)
\(432\) −2.90098 + 5.02464i −0.139573 + 0.241748i
\(433\) 6.10678 + 10.5773i 0.293473 + 0.508310i 0.974629 0.223828i \(-0.0718555\pi\)
−0.681155 + 0.732139i \(0.738522\pi\)
\(434\) 17.8648i 0.857540i
\(435\) −9.04381 + 5.22145i −0.433618 + 0.250349i
\(436\) 22.1003 12.7596i 1.05841 0.611074i
\(437\) 9.17853i 0.439069i
\(438\) −17.0519 29.5347i −0.814770 1.41122i
\(439\) −7.87765 + 13.6445i −0.375980 + 0.651216i −0.990473 0.137706i \(-0.956027\pi\)
0.614493 + 0.788922i \(0.289361\pi\)
\(440\) 2.62165 + 1.51361i 0.124982 + 0.0721586i
\(441\) −2.11505 −0.100717
\(442\) 35.6706 + 12.2781i 1.69668 + 0.584009i
\(443\) −15.0706 −0.716028 −0.358014 0.933716i \(-0.616546\pi\)
−0.358014 + 0.933716i \(0.616546\pi\)
\(444\) 46.2412 + 26.6974i 2.19451 + 1.26700i
\(445\) 6.51712 11.2880i 0.308941 0.535102i
\(446\) 4.62050 + 8.00293i 0.218787 + 0.378950i
\(447\) 5.70305i 0.269745i
\(448\) −9.61391 + 5.55059i −0.454215 + 0.262241i
\(449\) 26.6585 15.3913i 1.25809 0.726360i 0.285388 0.958412i \(-0.407877\pi\)
0.972703 + 0.232052i \(0.0745441\pi\)
\(450\) 35.5705i 1.67681i
\(451\) 5.35559 + 9.27616i 0.252185 + 0.436797i
\(452\) −6.01371 + 10.4160i −0.282861 + 0.489929i
\(453\) −31.1370 17.9770i −1.46295 0.844632i
\(454\) 28.6166 1.34304
\(455\) −12.7475 + 2.47929i −0.597614 + 0.116231i
\(456\) −5.10133 −0.238892
\(457\) −6.71687 3.87799i −0.314202 0.181405i 0.334603 0.942359i \(-0.391398\pi\)
−0.648805 + 0.760955i \(0.724731\pi\)
\(458\) 17.4214 30.1748i 0.814050 1.40998i
\(459\) 4.96373 + 8.59743i 0.231687 + 0.401294i
\(460\) 34.0422i 1.58723i
\(461\) 1.27498 0.736110i 0.0593817 0.0342840i −0.470015 0.882658i \(-0.655752\pi\)
0.529397 + 0.848374i \(0.322418\pi\)
\(462\) 3.66213 2.11433i 0.170378 0.0983677i
\(463\) 14.0366i 0.652335i 0.945312 + 0.326168i \(0.105757\pi\)
−0.945312 + 0.326168i \(0.894243\pi\)
\(464\) 1.85815 + 3.21841i 0.0862625 + 0.149411i
\(465\) −34.4949 + 59.7469i −1.59966 + 2.77070i
\(466\) 30.1467 + 17.4052i 1.39652 + 0.806281i
\(467\) −31.3806 −1.45212 −0.726060 0.687631i \(-0.758651\pi\)
−0.726060 + 0.687631i \(0.758651\pi\)
\(468\) 12.2566 + 14.0966i 0.566562 + 0.651614i
\(469\) −8.42649 −0.389099
\(470\) −19.6225 11.3291i −0.905119 0.522571i
\(471\) −14.6816 + 25.4293i −0.676492 + 1.17172i
\(472\) 3.47399 + 6.01713i 0.159903 + 0.276961i
\(473\) 3.22865i 0.148454i
\(474\) −3.12985 + 1.80702i −0.143759 + 0.0829993i
\(475\) −16.4246 + 9.48277i −0.753614 + 0.435099i
\(476\) 12.1500i 0.556895i
\(477\) −5.20337 9.01251i −0.238246 0.412654i
\(478\) −32.0849 + 55.5726i −1.46753 + 2.54183i
\(479\) 35.6760 + 20.5975i 1.63008 + 0.941125i 0.984068 + 0.177795i \(0.0568964\pi\)
0.646009 + 0.763330i \(0.276437\pi\)
\(480\) 65.2598 2.97869
\(481\) 26.2243 22.8014i 1.19572 1.03965i
\(482\) −62.2572 −2.83574
\(483\) 7.55745 + 4.36330i 0.343876 + 0.198537i
\(484\) 12.5101 21.6681i 0.568641 0.984914i
\(485\) 0.834351 + 1.44514i 0.0378859 + 0.0656204i
\(486\) 39.2002i 1.77816i
\(487\) 24.5314 14.1632i 1.11163 0.641798i 0.172376 0.985031i \(-0.444856\pi\)
0.939250 + 0.343234i \(0.111522\pi\)
\(488\) −1.26400 + 0.729774i −0.0572188 + 0.0330353i
\(489\) 5.24584i 0.237225i
\(490\) −3.79878 6.57967i −0.171611 0.297239i
\(491\) 17.3931 30.1258i 0.784941 1.35956i −0.144094 0.989564i \(-0.546027\pi\)
0.929034 0.369993i \(-0.120640\pi\)
\(492\) −57.9765 33.4728i −2.61378 1.50907i
\(493\) 6.35879 0.286386
\(494\) −5.88828 + 17.1068i −0.264926 + 0.769670i
\(495\) −6.75244 −0.303499
\(496\) 21.2621 + 12.2757i 0.954695 + 0.551194i
\(497\) 3.22444 5.58490i 0.144636 0.250517i
\(498\) 11.3725 + 19.6978i 0.509615 + 0.882680i
\(499\) 0.0694885i 0.00311073i 0.999999 + 0.00155537i \(0.000495089\pi\)
−0.999999 + 0.00155537i \(0.999505\pi\)
\(500\) −22.7142 + 13.1140i −1.01581 + 0.586477i
\(501\) 27.0133 15.5961i 1.20686 0.696783i
\(502\) 27.3855i 1.22228i
\(503\) −12.8686 22.2891i −0.573782 0.993820i −0.996173 0.0874060i \(-0.972142\pi\)
0.422391 0.906414i \(-0.361191\pi\)
\(504\) −1.00276 + 1.73683i −0.0446664 + 0.0773646i
\(505\) −18.1634 10.4866i −0.808260 0.466649i
\(506\) −7.21437 −0.320718
\(507\) 27.2582 11.0198i 1.21058 0.489407i
\(508\) −30.1540 −1.33787
\(509\) −6.09682 3.52000i −0.270237 0.156021i 0.358759 0.933430i \(-0.383200\pi\)
−0.628995 + 0.777409i \(0.716533\pi\)
\(510\) 42.6152 73.8117i 1.88703 3.26844i
\(511\) −3.57430 6.19086i −0.158118 0.273868i
\(512\) 28.7215i 1.26932i
\(513\) −4.12312 + 2.38049i −0.182040 + 0.105101i
\(514\) −8.37619 + 4.83599i −0.369458 + 0.213307i
\(515\) 29.6746i 1.30762i
\(516\) 10.0896 + 17.4758i 0.444171 + 0.769327i
\(517\) 1.32173 2.28930i 0.0581295 0.100683i
\(518\) 17.6068 + 10.1653i 0.773597 + 0.446636i
\(519\) 8.33263 0.365762
\(520\) −4.00775 + 11.6434i −0.175752 + 0.510597i
\(521\) 16.3253 0.715225 0.357613 0.933870i \(-0.383591\pi\)
0.357613 + 0.933870i \(0.383591\pi\)
\(522\) 4.95322 + 2.85974i 0.216796 + 0.125167i
\(523\) 3.54473 6.13965i 0.155000 0.268468i −0.778059 0.628191i \(-0.783796\pi\)
0.933059 + 0.359723i \(0.117129\pi\)
\(524\) −10.0463 17.4007i −0.438874 0.760152i
\(525\) 18.0317i 0.786968i
\(526\) 4.86836 2.81075i 0.212271 0.122555i
\(527\) 36.3805 21.0043i 1.58476 0.914963i
\(528\) 5.81138i 0.252908i
\(529\) 4.05594 + 7.02510i 0.176345 + 0.305439i
\(530\) 18.6912 32.3741i 0.811894 1.40624i
\(531\) −13.4216 7.74899i −0.582449 0.336277i
\(532\) −5.82686 −0.252626
\(533\) −32.8796 + 28.5880i −1.42417 + 1.23828i
\(534\) −17.2644 −0.747102
\(535\) −11.9548 6.90209i −0.516850 0.298403i
\(536\) −3.99505 + 6.91963i −0.172560 + 0.298882i
\(537\) −6.66368 11.5418i −0.287559 0.498067i
\(538\) 25.1558i 1.08454i
\(539\) 0.767631 0.443192i 0.0330642 0.0190896i
\(540\) −15.2922 + 8.82897i −0.658073 + 0.379938i
\(541\) 25.5162i 1.09703i 0.836141 + 0.548515i \(0.184806\pi\)
−0.836141 + 0.548515i \(0.815194\pi\)
\(542\) −13.7409 23.7999i −0.590222 1.02229i
\(543\) 2.39218 4.14338i 0.102658 0.177809i
\(544\) −34.4136 19.8687i −1.47547 0.851864i
\(545\) −37.5235 −1.60733
\(546\) 11.2863 + 12.9805i 0.483007 + 0.555516i
\(547\) −13.3073 −0.568978 −0.284489 0.958679i \(-0.591824\pi\)
−0.284489 + 0.958679i \(0.591824\pi\)
\(548\) 15.8158 + 9.13126i 0.675618 + 0.390068i
\(549\) 1.62781 2.81945i 0.0694733 0.120331i
\(550\) −7.45350 12.9098i −0.317818 0.550478i
\(551\) 3.04952i 0.129914i
\(552\) 7.16607 4.13733i 0.305008 0.176096i
\(553\) −0.656058 + 0.378775i −0.0278984 + 0.0161072i
\(554\) 45.0669i 1.91471i
\(555\) −39.2559 67.9932i −1.66632 2.88615i
\(556\) 20.4297 35.3852i 0.866412 1.50067i
\(557\) −14.7285 8.50353i −0.624069 0.360306i 0.154383 0.988011i \(-0.450661\pi\)
−0.778451 + 0.627705i \(0.783994\pi\)
\(558\) 37.7851 1.59957
\(559\) 12.8916 2.50732i 0.545259 0.106048i
\(560\) 10.4412 0.441220
\(561\) 8.61140 + 4.97179i 0.363573 + 0.209909i
\(562\) 18.2122 31.5445i 0.768235 1.33062i
\(563\) −12.4596 21.5807i −0.525111 0.909519i −0.999572 0.0292428i \(-0.990690\pi\)
0.474461 0.880276i \(-0.342643\pi\)
\(564\) 16.5218i 0.695691i
\(565\) 15.3158 8.84257i 0.644340 0.372010i
\(566\) −38.8013 + 22.4019i −1.63094 + 0.941623i
\(567\) 10.8717i 0.456569i
\(568\) −3.05745 5.29566i −0.128288 0.222201i
\(569\) 2.94065 5.09335i 0.123278 0.213524i −0.797780 0.602948i \(-0.793993\pi\)
0.921059 + 0.389424i \(0.127326\pi\)
\(570\) 35.3983 + 20.4372i 1.48267 + 0.856022i
\(571\) −8.92622 −0.373551 −0.186775 0.982403i \(-0.559804\pi\)
−0.186775 + 0.982403i \(0.559804\pi\)
\(572\) −7.40220 2.54789i −0.309501 0.106533i
\(573\) −25.7074 −1.07394
\(574\) −22.0751 12.7451i −0.921397 0.531969i
\(575\) 15.3816 26.6417i 0.641457 1.11104i
\(576\) −11.7398 20.3339i −0.489158 0.847247i
\(577\) 36.1933i 1.50675i −0.657592 0.753374i \(-0.728425\pi\)
0.657592 0.753374i \(-0.271575\pi\)
\(578\) −13.8894 + 8.01905i −0.577723 + 0.333549i
\(579\) −27.5961 + 15.9326i −1.14685 + 0.662136i
\(580\) 11.3104i 0.469638i
\(581\) 2.38383 + 4.12892i 0.0988980 + 0.171296i
\(582\) 1.10513 1.91414i 0.0458091 0.0793437i
\(583\) 3.77699 + 2.18065i 0.156427 + 0.0903132i
\(584\) −6.77838 −0.280491
\(585\) −5.24383 26.9617i −0.216806 1.11473i
\(586\) −0.886069 −0.0366032
\(587\) 31.6008 + 18.2447i 1.30431 + 0.753041i 0.981139 0.193301i \(-0.0619195\pi\)
0.323166 + 0.946342i \(0.395253\pi\)
\(588\) −2.76998 + 4.79774i −0.114232 + 0.197855i
\(589\) 10.0732 + 17.4472i 0.415058 + 0.718901i
\(590\) 55.6708i 2.29193i
\(591\) 44.9649 25.9605i 1.84961 1.06787i
\(592\) −24.1967 + 13.9699i −0.994476 + 0.574161i
\(593\) 34.9930i 1.43699i 0.695533 + 0.718495i \(0.255168\pi\)
−0.695533 + 0.718495i \(0.744832\pi\)
\(594\) −1.87107 3.24079i −0.0767711 0.132971i
\(595\) 8.93270 15.4719i 0.366205 0.634286i
\(596\) −5.34926 3.08839i −0.219114 0.126506i
\(597\) 7.12385 0.291560
\(598\) −5.60256 28.8062i −0.229106 1.17797i
\(599\) −32.5052 −1.32812 −0.664062 0.747677i \(-0.731169\pi\)
−0.664062 + 0.747677i \(0.731169\pi\)
\(600\) 14.8072 + 8.54894i 0.604501 + 0.349009i
\(601\) −10.0390 + 17.3881i −0.409500 + 0.709275i −0.994834 0.101518i \(-0.967630\pi\)
0.585334 + 0.810792i \(0.300963\pi\)
\(602\) 3.84172 + 6.65406i 0.156577 + 0.271199i
\(603\) 17.8225i 0.725788i
\(604\) −33.7235 + 19.4703i −1.37219 + 0.792235i
\(605\) −31.8608 + 18.3949i −1.29533 + 0.747858i
\(606\) 27.7799i 1.12848i
\(607\) −4.85800 8.41431i −0.197180 0.341526i 0.750433 0.660947i \(-0.229845\pi\)
−0.947613 + 0.319420i \(0.896512\pi\)
\(608\) 9.52856 16.5039i 0.386434 0.669323i
\(609\) 2.51093 + 1.44969i 0.101748 + 0.0587442i
\(610\) 11.6946 0.473502
\(611\) 10.1674 + 3.49968i 0.411327 + 0.141582i
\(612\) −25.6979 −1.03878
\(613\) −10.2898 5.94080i −0.415600 0.239947i 0.277593 0.960699i \(-0.410463\pi\)
−0.693193 + 0.720752i \(0.743797\pi\)
\(614\) −14.8508 + 25.7224i −0.599331 + 1.03807i
\(615\) 49.2184 + 85.2488i 1.98468 + 3.43756i
\(616\) 0.840480i 0.0338639i
\(617\) −17.3105 + 9.99422i −0.696895 + 0.402352i −0.806190 0.591657i \(-0.798474\pi\)
0.109295 + 0.994009i \(0.465141\pi\)
\(618\) 34.0393 19.6526i 1.36926 0.790543i
\(619\) 41.7176i 1.67677i 0.545078 + 0.838386i \(0.316500\pi\)
−0.545078 + 0.838386i \(0.683500\pi\)
\(620\) 37.3603 + 64.7100i 1.50043 + 2.59882i
\(621\) 3.86129 6.68794i 0.154948 0.268378i
\(622\) −18.9708 10.9528i −0.760659 0.439166i
\(623\) −3.61884 −0.144986
\(624\) −23.2042 + 4.51302i −0.928911 + 0.180665i
\(625\) −1.29828 −0.0519312
\(626\) 12.5091 + 7.22211i 0.499963 + 0.288654i
\(627\) −2.38435 + 4.12982i −0.0952219 + 0.164929i
\(628\) 15.9012 + 27.5416i 0.634526 + 1.09903i
\(629\) 47.8066i 1.90618i
\(630\) 13.9164 8.03461i 0.554441 0.320107i
\(631\) 15.2780 8.82074i 0.608206 0.351148i −0.164057 0.986451i \(-0.552458\pi\)
0.772263 + 0.635303i \(0.219125\pi\)
\(632\) 0.718319i 0.0285732i
\(633\) 16.8084 + 29.1130i 0.668073 + 1.15714i
\(634\) 0.739603 1.28103i 0.0293734 0.0508762i
\(635\) 38.3982 + 22.1692i 1.52379 + 0.879759i
\(636\) −27.2584 −1.08086
\(637\) 2.36575 + 2.72089i 0.0937343 + 0.107806i
\(638\) −2.39694 −0.0948958
\(639\) 11.8124 + 6.81987i 0.467290 + 0.269790i
\(640\) 13.3159 23.0639i 0.526359 0.911680i
\(641\) −5.46012 9.45721i −0.215662 0.373537i 0.737815 0.675003i \(-0.235858\pi\)
−0.953477 + 0.301465i \(0.902524\pi\)
\(642\) 18.2842i 0.721618i
\(643\) 15.2725 8.81757i 0.602288 0.347731i −0.167653 0.985846i \(-0.553619\pi\)
0.769941 + 0.638115i \(0.220286\pi\)
\(644\) 8.18524 4.72575i 0.322544 0.186221i
\(645\) 29.6716i 1.16832i
\(646\) −12.4445 21.5544i −0.489620 0.848048i
\(647\) 8.33632 14.4389i 0.327735 0.567653i −0.654327 0.756211i \(-0.727048\pi\)
0.982062 + 0.188558i \(0.0603815\pi\)
\(648\) 8.92758 + 5.15434i 0.350708 + 0.202482i
\(649\) 6.49495 0.254949
\(650\) 45.7593 39.7866i 1.79483 1.56056i
\(651\) 19.1544 0.750719
\(652\) −4.92042 2.84080i −0.192698 0.111254i
\(653\) 3.38664 5.86584i 0.132530 0.229548i −0.792121 0.610364i \(-0.791023\pi\)
0.924651 + 0.380816i \(0.124357\pi\)
\(654\) 24.8506 + 43.0426i 0.971737 + 1.68310i
\(655\) 29.5441i 1.15439i
\(656\) 30.3374 17.5153i 1.18448 0.683858i
\(657\) 13.0940 7.55983i 0.510846 0.294937i
\(658\) 6.29081i 0.245241i
\(659\) −16.7680 29.0431i −0.653190 1.13136i −0.982344 0.187082i \(-0.940097\pi\)
0.329154 0.944276i \(-0.393236\pi\)
\(660\) −8.84332 + 15.3171i −0.344226 + 0.596216i
\(661\) −21.7945 12.5830i −0.847707 0.489424i 0.0121696 0.999926i \(-0.496126\pi\)
−0.859876 + 0.510502i \(0.829460\pi\)
\(662\) 8.85657 0.344221
\(663\) −13.1643 + 38.2454i −0.511261 + 1.48533i
\(664\) 4.52075 0.175439
\(665\) 7.41995 + 4.28391i 0.287733 + 0.166123i
\(666\) −21.5001 + 37.2393i −0.833112 + 1.44299i
\(667\) −2.47325 4.28380i −0.0957647 0.165869i
\(668\) 33.7833i 1.30712i
\(669\) −8.58060 + 4.95401i −0.331745 + 0.191533i
\(670\) 55.4436 32.0104i 2.14197 1.23667i
\(671\) 1.36438i 0.0526713i
\(672\) −9.05939 15.6913i −0.349473 0.605306i
\(673\) −0.927341 + 1.60620i −0.0357464 + 0.0619145i −0.883345 0.468723i \(-0.844714\pi\)
0.847599 + 0.530638i \(0.178048\pi\)
\(674\) −37.3172 21.5451i −1.43741 0.829887i
\(675\) 15.9571 0.614189
\(676\) 4.42503 31.5348i 0.170194 1.21288i
\(677\) −14.7209 −0.565770 −0.282885 0.959154i \(-0.591291\pi\)
−0.282885 + 0.959154i \(0.591291\pi\)
\(678\) −20.2863 11.7123i −0.779092 0.449809i
\(679\) 0.231650 0.401229i 0.00888990 0.0153978i
\(680\) −8.47009 14.6706i −0.324813 0.562593i
\(681\) 30.6822i 1.17575i
\(682\) −13.7136 + 7.91756i −0.525122 + 0.303179i
\(683\) 6.87930 3.97177i 0.263229 0.151975i −0.362578 0.931954i \(-0.618103\pi\)
0.625807 + 0.779978i \(0.284770\pi\)
\(684\) 12.3241i 0.471224i
\(685\) −13.4266 23.2556i −0.513005 0.888551i
\(686\) −1.05469 + 1.82678i −0.0402684 + 0.0697469i
\(687\) 32.3529 + 18.6790i 1.23434 + 0.712647i
\(688\) −10.5592 −0.402566
\(689\) −5.77394 + 16.7746i −0.219969 + 0.639060i
\(690\) −66.3008 −2.52403
\(691\) 8.86002 + 5.11534i 0.337051 + 0.194597i 0.658967 0.752172i \(-0.270994\pi\)
−0.321916 + 0.946768i \(0.604327\pi\)
\(692\) 4.51240 7.81571i 0.171536 0.297109i
\(693\) 0.937375 + 1.62358i 0.0356079 + 0.0616748i
\(694\) 16.8118i 0.638168i
\(695\) −52.0306 + 30.0399i −1.97363 + 1.13948i
\(696\) 2.38089 1.37461i 0.0902475 0.0521044i
\(697\) 59.9392i 2.27036i
\(698\) 22.7785 + 39.4535i 0.862178 + 1.49334i
\(699\) −18.6616 + 32.3228i −0.705845 + 1.22256i
\(700\) 16.9131 + 9.76479i 0.639255 + 0.369074i
\(701\) −16.5978 −0.626891 −0.313445 0.949606i \(-0.601483\pi\)
−0.313445 + 0.949606i \(0.601483\pi\)
\(702\) 11.4871 9.98773i 0.433552 0.376963i
\(703\) −22.9269 −0.864706
\(704\) 8.52162 + 4.91996i 0.321171 + 0.185428i
\(705\) 12.1468 21.0389i 0.457475 0.792371i
\(706\) 22.8000 + 39.4907i 0.858088 + 1.48625i
\(707\) 5.82303i 0.218998i
\(708\) −35.1552 + 20.2969i −1.32121 + 0.762804i
\(709\) 41.4531 23.9329i 1.55680 0.898820i 0.559242 0.829004i \(-0.311092\pi\)
0.997560 0.0698158i \(-0.0222412\pi\)
\(710\) 48.9957i 1.83878i
\(711\) −0.801130 1.38760i −0.0300447 0.0520390i
\(712\) −1.71571 + 2.97170i −0.0642990 + 0.111369i
\(713\) −28.3004 16.3393i −1.05986 0.611910i
\(714\) −23.6634 −0.885581
\(715\) 7.55279 + 8.68661i 0.282458 + 0.324861i
\(716\) −14.4344 −0.539441
\(717\) −59.5840 34.4008i −2.22520 1.28472i
\(718\) 14.4318 24.9965i 0.538588 0.932862i
\(719\) −19.0461 32.9888i −0.710300 1.23028i −0.964744 0.263188i \(-0.915226\pi\)
0.254444 0.967087i \(-0.418107\pi\)
\(720\) 22.0836i 0.823009i
\(721\) 7.13508 4.11944i 0.265724 0.153416i
\(722\) −24.3719 + 14.0711i −0.907028 + 0.523673i
\(723\) 66.7511i 2.48250i
\(724\) −2.59089 4.48756i −0.0962898 0.166779i
\(725\) 5.11047 8.85159i 0.189798 0.328740i
\(726\) 42.2009 + 24.3647i 1.56622 + 0.904259i
\(727\) 15.4059 0.571374 0.285687 0.958323i \(-0.407778\pi\)
0.285687 + 0.958323i \(0.407778\pi\)
\(728\) 3.35594 0.652702i 0.124379 0.0241908i
\(729\) −9.41460 −0.348689
\(730\) 47.0354 + 27.1559i 1.74086 + 1.00508i
\(731\) −9.03369 + 15.6468i −0.334123 + 0.578718i
\(732\) −4.26372 7.38498i −0.157592 0.272957i
\(733\) 11.6298i 0.429557i 0.976663 + 0.214778i \(0.0689029\pi\)
−0.976663 + 0.214778i \(0.931097\pi\)
\(734\) 20.8487 12.0370i 0.769538 0.444293i
\(735\) 7.05461 4.07298i 0.260213 0.150234i
\(736\) 30.9117i 1.13942i
\(737\) 3.73456 + 6.46844i 0.137564 + 0.238268i
\(738\) 26.9565 46.6900i 0.992282 1.71868i
\(739\) 2.32875 + 1.34451i 0.0856645 + 0.0494584i 0.542220 0.840236i \(-0.317584\pi\)
−0.456556 + 0.889695i \(0.650917\pi\)
\(740\) −85.0336 −3.12590
\(741\) −18.3416 6.31331i −0.673794 0.231925i
\(742\) −10.3789 −0.381020
\(743\) −2.13665 1.23360i −0.0783862 0.0452563i 0.460295 0.887766i \(-0.347744\pi\)
−0.538681 + 0.842510i \(0.681077\pi\)
\(744\) 9.08120 15.7291i 0.332933 0.576657i
\(745\) 4.54118 + 7.86556i 0.166376 + 0.288172i
\(746\) 65.9835i 2.41583i
\(747\) −8.73288 + 5.04193i −0.319519 + 0.184475i
\(748\) 9.32673 5.38479i 0.341019 0.196887i
\(749\) 3.83260i 0.140040i
\(750\) −25.5409 44.2382i −0.932623 1.61535i
\(751\) −18.9592 + 32.8383i −0.691832 + 1.19829i 0.279405 + 0.960173i \(0.409863\pi\)
−0.971237 + 0.238115i \(0.923471\pi\)
\(752\) −7.48709 4.32267i −0.273026 0.157632i
\(753\) 29.3623 1.07002
\(754\) −1.86142 9.57072i −0.0677890 0.348545i
\(755\) 57.2583 2.08384
\(756\) 4.24574 + 2.45128i 0.154416 + 0.0891522i
\(757\) −17.3225 + 30.0035i −0.629598 + 1.09050i 0.358034 + 0.933709i \(0.383447\pi\)
−0.987632 + 0.156788i \(0.949886\pi\)
\(758\) 28.9145 + 50.0814i 1.05022 + 1.81904i
\(759\) 7.73512i 0.280767i
\(760\) 7.03569 4.06206i 0.255211 0.147346i
\(761\) 19.7969 11.4297i 0.717636 0.414328i −0.0962458 0.995358i \(-0.530683\pi\)
0.813882 + 0.581030i \(0.197350\pi\)
\(762\) 58.7280i 2.12749i
\(763\) 5.20902 + 9.02229i 0.188579 + 0.326629i
\(764\) −13.9214 + 24.1126i −0.503659 + 0.872363i
\(765\) 32.7239 + 18.8931i 1.18313 + 0.683083i
\(766\) 33.9625 1.22712
\(767\) 5.04386 + 25.9336i 0.182123 + 0.936408i
\(768\) 14.9390 0.539065
\(769\) −44.8839 25.9137i −1.61855 0.934473i −0.987294 0.158902i \(-0.949205\pi\)
−0.631260 0.775571i \(-0.717462\pi\)
\(770\) −3.36718 + 5.83212i −0.121345 + 0.210175i
\(771\) −5.18507 8.98080i −0.186736 0.323436i
\(772\) 34.5122i 1.24212i
\(773\) −4.93605 + 2.84983i −0.177538 + 0.102501i −0.586135 0.810213i \(-0.699351\pi\)
0.408598 + 0.912715i \(0.366018\pi\)
\(774\) −14.0737 + 8.12545i −0.505868 + 0.292063i
\(775\) 67.5234i 2.42551i
\(776\) −0.219653 0.380450i −0.00788508