Properties

Label 91.2.q.a.36.6
Level $91$
Weight $2$
Character 91.36
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 36.6
Root \(-1.30089 + 0.554694i\) of defining polynomial
Character \(\chi\) \(=\) 91.36
Dual form 91.2.q.a.43.6

$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.312770 0.949829i \(-0.398743\pi\)
0.978961 + 0.204047i \(0.0654097\pi\)
\(3\) −1.13082 1.95864i −0.652882 1.13082i −0.982420 0.186682i \(-0.940227\pi\)
0.329539 0.944142i \(-0.393107\pi\)
\(4\) 1.22476 2.12135i 0.612380 1.06067i
\(5\) 3.60178i 1.61076i 0.592756 + 0.805382i \(0.298040\pi\)
−0.592756 + 0.805382i \(0.701960\pi\)
\(6\) −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 −0.379791 0.925072i \(-0.624004\pi\)
0.611241 + 0.791445i \(0.290671\pi\)
\(12\) −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 0.391085 + 0.920355i \(0.372100\pi\)
−0.992593 + 0.121488i \(0.961233\pi\)
\(18\) 4.46147i 1.05158i
\(19\) 2.06008 + 1.18939i 0.472615 + 0.272864i 0.717334 0.696730i \(-0.245362\pi\)
−0.244719 + 0.969594i \(0.578696\pi\)
\(20\) 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 0.591723 0.806142i \(-0.298448\pi\)
−0.994000 + 0.109376i \(0.965115\pi\)
\(24\) −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 0.800355 0.599527i \(-0.204645\pi\)
−0.919383 + 0.393364i \(0.871311\pi\)
\(30\) 8.59150 14.8809i 1.56859 2.71687i
\(31\) 8.46921i 1.52111i −0.649271 0.760557i \(-0.724926\pi\)
0.649271 0.760557i \(-0.275074\pi\)
\(32\) 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 −0.991207 0.132323i \(-0.957757\pi\)
−0.381009 + 0.924571i \(0.624423\pi\)
\(38\) 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 0.651666 0.758506i \(-0.274071\pi\)
0.982719 0.185106i \(-0.0592628\pi\)
\(42\) 2.38535 + 4.13154i 0.368067 + 0.637511i
\(43\) −1.82125 + 3.15450i −0.277738 + 0.481056i −0.970822 0.239800i \(-0.922918\pi\)
0.693084 + 0.720856i \(0.256251\pi\)
\(44\) 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 \(0.0697922\pi\)
−0.976059 + 0.217506i \(0.930208\pi\)
\(48\) 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 0.852532 0.522675i \(-0.175066\pi\)
−0.0263837 + 0.999652i \(0.508399\pi\)
\(60\) 19.9537i 2.57601i
\(61\) 0.769632 1.33304i 0.0985412 0.170678i −0.812540 0.582906i \(-0.801916\pi\)
0.911081 + 0.412227i \(0.135249\pi\)
\(62\) −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 0.0170931 0.999854i \(-0.494559\pi\)
0.874445 + 0.485124i \(0.161225\pi\)
\(68\) 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 0.130540 0.991443i \(-0.458329\pi\)
−0.793345 + 0.608772i \(0.791662\pi\)
\(72\) 1.73683 + 1.00276i 0.204687 + 0.118176i
\(73\) 7.14859i 0.836679i −0.908291 0.418340i \(-0.862612\pi\)
0.908291 0.418340i \(-0.137388\pi\)
\(74\) −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 \(0.0842697\pi\)
−0.965160 + 0.261659i \(0.915730\pi\)
\(84\) 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 −0.324615 0.945846i \(-0.605235\pi\)
0.656819 + 0.754048i \(0.271902\pi\)
\(90\) −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 0.479492 0.877546i \(-0.340821\pi\)
−0.520231 + 0.854026i \(0.674154\pi\)
\(98\) 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 0.973740 0.227664i \(-0.0731089\pi\)
−0.684033 + 0.729451i \(0.739776\pi\)
\(102\) 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 0.943663 0.330909i \(-0.107355\pi\)
−0.758407 + 0.651781i \(0.774022\pi\)
\(108\) −2.45128 + 4.24574i −0.235875 + 0.408547i
\(109\) 10.4180i 0.997867i 0.866640 + 0.498934i \(0.166275\pi\)
−0.866640 + 0.498934i \(0.833725\pi\)
\(110\) 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 −0.727136 0.686493i \(-0.759149\pi\)
0.958089 + 0.286472i \(0.0924826\pi\)
\(114\) −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 −0.998532 0.0541658i \(-0.982750\pi\)
0.452357 0.891837i \(-0.350583\pi\)
\(128\) 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 0.749780 0.661687i \(-0.230159\pi\)
−0.198147 + 0.980172i \(0.563492\pi\)
\(138\) 18.4078i 1.56697i
\(139\) −8.34028 + 14.4458i −0.707413 + 1.22528i 0.258400 + 0.966038i \(0.416805\pi\)
−0.965813 + 0.259238i \(0.916529\pi\)
\(140\) −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 0.407874 0.913038i \(-0.366270\pi\)
−0.586777 + 0.809748i \(0.699604\pi\)
\(150\) 32.9400 + 19.0179i 2.68954 + 1.55281i
\(151\) 15.8972i 1.29370i −0.762618 0.646849i \(-0.776086\pi\)
0.762618 0.646849i \(-0.223914\pi\)
\(152\) 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 0.419265 0.907864i \(-0.362288\pi\)
−0.576601 + 0.817026i \(0.695621\pi\)
\(164\) 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 −0.884992 0.465607i \(-0.845836\pi\)
−0.0392682 + 0.999229i \(0.512503\pi\)
\(168\) 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 −0.927518 0.373779i \(-0.878062\pi\)
0.787461 + 0.616364i \(0.211395\pi\)
\(174\) 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 0.734653 0.678443i \(-0.237345\pi\)
−0.954876 + 0.297006i \(0.904012\pi\)
\(180\) −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 −0.583794 0.811902i \(-0.698432\pi\)
0.995025 + 0.0996290i \(0.0317656\pi\)
\(192\) −12.5535 21.7433i −0.905970 1.56919i
\(193\) 12.2017 7.04468i 0.878301 0.507087i 0.00820314 0.999966i \(-0.497389\pi\)
0.870098 + 0.492879i \(0.164055\pi\)
\(194\) −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 −0.995989 0.0894753i \(-0.971481\pi\)
−0.420507 + 0.907289i \(0.638148\pi\)
\(198\) 1.97729 + 3.42476i 0.140520 + 0.243387i
\(199\) −1.57492 + 2.72785i −0.111643 + 0.193372i −0.916433 0.400188i \(-0.868945\pi\)
0.804790 + 0.593560i \(0.202278\pi\)
\(200\) 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 0.999909 + 0.0134864i \(0.00429298\pi\)
−0.488275 + 0.872690i \(0.662374\pi\)
\(212\) 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 −0.367561 0.930000i \(-0.619807\pi\)
0.621623 + 0.783317i \(0.286474\pi\)
\(224\) −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 0.836357 0.548185i \(-0.184681\pi\)
−0.0565636 + 0.998399i \(0.518014\pi\)
\(228\) −11.4127 6.58915i −0.755827 0.436377i
\(229\) 16.5180i 1.09154i 0.837935 + 0.545770i \(0.183763\pi\)
−0.837935 + 0.545770i \(0.816237\pi\)
\(230\) 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 \(-0.557220\pi\)
0.178796 0.983886i \(-0.442780\pi\)
\(240\) 20.4506 + 11.8071i 1.32008 + 0.762147i
\(241\) −25.5602 14.7572i −1.64648 0.950593i −0.978458 0.206448i \(-0.933810\pi\)
−0.668018 0.744145i \(-0.732857\pi\)
\(242\) 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 −0.994859 0.101267i \(-0.967710\pi\)
0.585130 + 0.810940i \(0.301044\pi\)
\(252\) 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 0.785620 0.618710i \(-0.212344\pi\)
−0.928628 + 0.371011i \(0.879011\pi\)
\(258\) 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 0.904180 0.427152i \(-0.140483\pi\)
−0.822015 + 0.569466i \(0.807150\pi\)
\(264\) −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 −0.988544 0.150934i \(-0.951772\pi\)
0.624984 + 0.780637i \(0.285105\pi\)
\(270\) −7.60301 13.1688i −0.462705 0.801428i
\(271\) −11.2828 + 6.51416i −0.685384 + 0.395707i −0.801881 0.597484i \(-0.796167\pi\)
0.116496 + 0.993191i \(0.462834\pi\)
\(272\) −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 −0.343174 0.939272i \(-0.611502\pi\)
0.985020 0.172438i \(-0.0551646\pi\)
\(278\) 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 \(0.172228\pi\)
−0.857158 + 0.515054i \(0.827772\pi\)
\(282\) 7.11380 12.3215i 0.423621 0.733733i
\(283\) −10.6201 18.3946i −0.631299 1.09344i −0.987286 0.158952i \(-0.949189\pi\)
0.355987 0.934491i \(-0.384145\pi\)
\(284\) −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 0.489336 0.872095i \(-0.337239\pi\)
−0.510589 + 0.859825i \(0.670572\pi\)
\(294\) 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 \(-0.868380\pi\)
0.915721 0.401814i \(-0.131620\pi\)
\(308\) −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 \(0.00626889\pi\)
−0.999806 + 0.0196930i \(0.993731\pi\)
\(318\) −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 0.596590 0.802546i \(-0.296522\pi\)
−0.396730 + 0.917935i \(0.629855\pi\)
\(332\) 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 −0.952940 0.303160i \(-0.901959\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(348\) 3.55103 + 6.15057i 0.190355 + 0.329705i
\(349\) 18.7038 10.7986i 1.00119 0.578037i 0.0925892 0.995704i \(-0.470486\pi\)
0.908600 + 0.417668i \(0.137152\pi\)
\(350\) 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 0.0892465 0.996010i \(-0.471554\pi\)
0.907193 + 0.420715i \(0.138221\pi\)
\(354\) −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 \(0.117595\pi\)
−0.932531 + 0.361090i \(0.882405\pi\)
\(360\) −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 0.975649 0.219339i \(-0.0703902\pi\)
−0.677778 + 0.735267i \(0.737057\pi\)
\(368\) 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 −0.103151 0.994666i \(-0.532892\pi\)
0.912981 0.408002i \(-0.133774\pi\)
\(374\) 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 0.254729 0.967012i \(-0.418014\pi\)
0.964822 + 0.262904i \(0.0846803\pi\)
\(380\) 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 0.811980 0.583686i \(-0.198390\pi\)
−0.0994967 + 0.995038i \(0.531723\pi\)
\(384\) −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 0.756876 0.653558i \(-0.226724\pi\)
−0.187560 + 0.982253i \(0.560058\pi\)
\(398\) 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 −0.0166501 0.999861i \(-0.505300\pi\)
0.857580 + 0.514350i \(0.171967\pi\)
\(402\) −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 0.917020 0.398840i \(-0.130587\pi\)
0.113105 + 0.993583i \(0.463921\pi\)
\(410\) 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 −0.738394 0.674370i \(-0.764415\pi\)
−0.214825 0.976653i \(-0.568918\pi\)
\(420\) −9.97684 + 17.2804i −0.486820 + 0.843197i
\(421\) 22.0284i 1.07360i −0.843710 0.536799i \(-0.819633\pi\)
0.843710 0.536799i \(-0.180367\pi\)
\(422\) 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 −0.999993 0.00377645i \(-0.998798\pi\)
−0.496726 + 0.867907i \(0.665465\pi\)
\(432\) −2.90098 5.02464i −0.139573 0.241748i
\(433\) 6.10678 10.5773i 0.293473 0.508310i −0.681155 0.732139i \(-0.738522\pi\)
0.974629 + 0.223828i \(0.0718555\pi\)
\(434\) 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 0.614493 0.788922i \(-0.289361\pi\)
−0.990473 + 0.137706i \(0.956027\pi\)
\(440\) 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 0.972703 0.232052i \(-0.0745441\pi\)
0.285388 + 0.958412i \(0.407877\pi\)
\(450\) 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 −0.648805 0.760955i \(-0.724731\pi\)
0.334603 + 0.942359i \(0.391398\pi\)
\(458\) 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 0.529397 0.848374i \(-0.322418\pi\)
−0.470015 + 0.882658i \(0.655752\pi\)
\(462\) 3.66213 + 2.11433i 0.170378 + 0.0983677i
\(463\) 14.0366i 0.652335i −0.945312 0.326168i \(-0.894243\pi\)
0.945312 0.326168i \(-0.105757\pi\)
\(464\) 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 0.646009 0.763330i \(-0.276437\pi\)
0.984068 0.177795i \(-0.0568964\pi\)
\(480\) 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 0.939250 0.343234i \(-0.111522\pi\)
0.172376 + 0.985031i \(0.444856\pi\)
\(488\) −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 0.929034 + 0.369993i \(0.120640\pi\)
−0.144094 + 0.989564i \(0.546027\pi\)
\(492\) −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 \(-0.999505\pi\)
0.999999 0.00155537i \(-0.000495089\pi\)
\(500\) −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 0.422391 + 0.906414i \(0.361191\pi\)
−0.996173 + 0.0874060i \(0.972142\pi\)
\(504\) −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 −0.628995 0.777409i \(-0.716533\pi\)
0.358759 + 0.933430i \(0.383200\pi\)
\(510\) 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 0.933059 0.359723i \(-0.117129\pi\)
−0.778059 + 0.628191i \(0.783796\pi\)
\(524\) −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 \(-0.815194\pi\)
0.836141 0.548515i \(-0.184806\pi\)
\(542\) −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 −0.778451 0.627705i \(-0.783994\pi\)
0.154383 + 0.988011i \(0.450661\pi\)
\(558\) 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 0.474461 + 0.880276i \(0.342643\pi\)
−0.999572 + 0.0292428i \(0.990690\pi\)
\(564\) 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 0.921059 0.389424i \(-0.127326\pi\)
−0.797780 + 0.602948i \(0.793993\pi\)
\(570\) 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 \(0.271575\pi\)
−0.657592 + 0.753374i \(0.728425\pi\)
\(578\) −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 0.323166 0.946342i \(-0.395253\pi\)
0.981139 + 0.193301i \(0.0619195\pi\)
\(588\) −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 \(-0.744832\pi\)
0.695533 0.718495i \(-0.255168\pi\)
\(594\) −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 0.585334 0.810792i \(-0.300963\pi\)
−0.994834 + 0.101518i \(0.967630\pi\)
\(602\) 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 −0.947613 0.319420i \(-0.896512\pi\)
0.750433 + 0.660947i \(0.229845\pi\)
\(608\) 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 −0.693193 0.720752i \(-0.743797\pi\)
0.277593 + 0.960699i \(0.410463\pi\)
\(614\) −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 0.109295 0.994009i \(-0.465141\pi\)
−0.806190 + 0.591657i \(0.798474\pi\)
\(618\) 34.0393 + 19.6526i 1.36926 + 0.790543i
\(619\) 41.7176i 1.67677i −0.545078 0.838386i \(-0.683500\pi\)
0.545078 0.838386i \(-0.316500\pi\)
\(620\) 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 0.772263 0.635303i \(-0.219125\pi\)
−0.164057 + 0.986451i \(0.552458\pi\)
\(632\) 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 −0.953477 0.301465i \(-0.902524\pi\)
0.737815 + 0.675003i \(0.235858\pi\)
\(642\) 18.2842i 0.721618i
\(643\) 15.2725 + 8.81757i 0.602288 + 0.347731i 0.769941 0.638115i \(-0.220286\pi\)
−0.167653 + 0.985846i \(0.553619\pi\)
\(644\) 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 0.982062 0.188558i \(-0.0603815\pi\)
−0.654327 + 0.756211i \(0.727048\pi\)
\(648\) 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 0.924651 0.380816i \(-0.124357\pi\)
−0.792121 + 0.610364i \(0.791023\pi\)
\(654\) 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 0.329154 + 0.944276i \(0.393236\pi\)
−0.982344 + 0.187082i \(0.940097\pi\)
\(660\) −8.84332 15.3171i −0.344226 0.596216i
\(661\) −21.7945 + 12.5830i −0.847707 + 0.489424i −0.859876 0.510502i \(-0.829460\pi\)
0.0121696 + 0.999926i \(0.496126\pi\)
\(662\) 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 0.847599 0.530638i \(-0.178048\pi\)
−0.883345 + 0.468723i \(0.844714\pi\)
\(674\) −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 0.625807 0.779978i \(-0.284770\pi\)
−0.362578 + 0.931954i \(0.618103\pi\)
\(684\) 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 −0.321916 0.946768i \(-0.604327\pi\)
0.658967 + 0.752172i \(0.270994\pi\)
\(692\) 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 0.997560 + 0.0698158i \(0.0222412\pi\)
0.559242 + 0.829004i \(0.311092\pi\)
\(710\) 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 0.254444 + 0.967087i \(0.418107\pi\)
−0.964744 + 0.263188i \(0.915226\pi\)
\(720\) 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 \(-0.931097\pi\)
0.976663 0.214778i \(-0.0689029\pi\)
\(734\) 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 −0.456556 0.889695i \(-0.650917\pi\)
0.542220 + 0.840236i \(0.317584\pi\)
\(740\) −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 −0.538681 0.842510i \(-0.681077\pi\)
0.460295 + 0.887766i \(0.347744\pi\)
\(744\) 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 −0.971237 0.238115i \(-0.923471\pi\)
0.279405 0.960173i \(-0.409863\pi\)
\(752\) −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 −0.987632 0.156788i \(-0.949886\pi\)
0.358034 0.933709i \(-0.383447\pi\)
\(758\) 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 0.813882 0.581030i \(-0.197350\pi\)
−0.0962458 + 0.995358i \(0.530683\pi\)
\(762\) 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 −0.631260 + 0.775571i \(0.717462\pi\)
−0.987294 + 0.158902i \(0.949205\pi\)
\(770\) −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 0.408598 0.912715i \(-0.366018\pi\)
−0.586135 + 0.810213i \(0.699351\pi\)
\(774\) −14.0737 8.12545i −0.505868 0.292063i
\(775\) 67.5234i 2.42551i
\(776\) −0.219653 + 0.380450i −0.00788508 +