Properties

Label 1638.2.bj.f.1135.4
Level $1638$
Weight $2$
Character 1638.1135
Analytic conductor $13.079$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.195105024.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 4 x^{5} - 20 x^{4} + 12 x^{3} + 45 x^{2} - 108 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1135.4
Root \(1.30512 - 1.13871i\) of defining polynomial
Character \(\chi\) \(=\) 1638.1135
Dual form 1638.2.bj.f.127.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.166404 - 0.288220i) q^{10} +(-2.26053 - 1.30512i) q^{11} +(3.41140 + 1.16719i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.94383 + 3.36681i) q^{17} +(4.85997 - 2.80591i) q^{19} +(0.288220 - 0.166404i) q^{20} +(-1.30512 - 2.26053i) q^{22} +(-2.10628 + 3.64819i) q^{23} +4.88924 q^{25} +(2.37076 + 2.71652i) q^{26} +(-0.866025 - 0.500000i) q^{28} +(-0.593337 + 1.02769i) q^{29} +7.07434i q^{31} +(-0.866025 + 0.500000i) q^{32} +3.88766i q^{34} +(0.166404 + 0.288220i) q^{35} +(0.499211 + 0.288220i) q^{37} +5.61181 q^{38} +0.332808 q^{40} +(-0.451251 - 0.260530i) q^{41} +(1.53717 + 2.66245i) q^{43} -2.61023i q^{44} +(-3.64819 + 2.10628i) q^{46} +12.0528i q^{47} +(0.500000 - 0.866025i) q^{49} +(4.23421 + 2.44462i) q^{50} +(0.694883 + 3.53796i) q^{52} +9.71047 q^{53} +(-0.434353 + 0.752321i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.02769 + 0.593337i) q^{58} +(-9.07175 + 5.23758i) q^{59} +(-3.71989 - 6.44304i) q^{61} +(-3.53717 + 6.12656i) q^{62} -1.00000 q^{64} +(0.388451 - 1.13534i) q^{65} +(10.3233 + 5.96015i) q^{67} +(-1.94383 + 3.36681i) q^{68} +0.332808i q^{70} +(0.818065 - 0.472310i) q^{71} -4.66562i q^{73} +(0.288220 + 0.499211i) q^{74} +(4.85997 + 2.80591i) q^{76} +2.61023 q^{77} -0.943042 q^{79} +(0.288220 + 0.166404i) q^{80} +(-0.260530 - 0.451251i) q^{82} -13.7172i q^{83} +(1.12050 - 0.646922i) q^{85} +3.07434i q^{86} +(1.30512 - 2.26053i) q^{88} +(-2.92741 - 1.69014i) q^{89} +(-3.53796 + 0.694883i) q^{91} -4.21257 q^{92} +(-6.02638 + 10.4380i) q^{94} +(-0.933827 - 1.61744i) q^{95} +(-5.03669 + 2.90793i) q^{97} +(0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + O(q^{10}) \) \( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.332808i 0.148836i −0.997227 0.0744180i \(-0.976290\pi\)
0.997227 0.0744180i \(-0.0237099\pi\)
\(6\) 0 0
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.166404 0.288220i 0.0526215 0.0911431i
\(11\) −2.26053 1.30512i −0.681575 0.393508i 0.118873 0.992909i \(-0.462072\pi\)
−0.800448 + 0.599402i \(0.795405\pi\)
\(12\) 0 0
\(13\) 3.41140 + 1.16719i 0.946153 + 0.323721i
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.94383 + 3.36681i 0.471448 + 0.816572i 0.999466 0.0326607i \(-0.0103981\pi\)
−0.528018 + 0.849233i \(0.677065\pi\)
\(18\) 0 0
\(19\) 4.85997 2.80591i 1.11495 0.643719i 0.174846 0.984596i \(-0.444057\pi\)
0.940108 + 0.340877i \(0.110724\pi\)
\(20\) 0.288220 0.166404i 0.0644479 0.0372090i
\(21\) 0 0
\(22\) −1.30512 2.26053i −0.278252 0.481947i
\(23\) −2.10628 + 3.64819i −0.439191 + 0.760701i −0.997627 0.0688467i \(-0.978068\pi\)
0.558437 + 0.829547i \(0.311401\pi\)
\(24\) 0 0
\(25\) 4.88924 0.977848
\(26\) 2.37076 + 2.71652i 0.464945 + 0.532753i
\(27\) 0 0
\(28\) −0.866025 0.500000i −0.163663 0.0944911i
\(29\) −0.593337 + 1.02769i −0.110180 + 0.190837i −0.915843 0.401537i \(-0.868476\pi\)
0.805663 + 0.592374i \(0.201809\pi\)
\(30\) 0 0
\(31\) 7.07434i 1.27059i 0.772270 + 0.635294i \(0.219121\pi\)
−0.772270 + 0.635294i \(0.780879\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 3.88766i 0.666729i
\(35\) 0.166404 + 0.288220i 0.0281274 + 0.0487180i
\(36\) 0 0
\(37\) 0.499211 + 0.288220i 0.0820699 + 0.0473831i 0.540473 0.841361i \(-0.318245\pi\)
−0.458403 + 0.888744i \(0.651579\pi\)
\(38\) 5.61181 0.910356
\(39\) 0 0
\(40\) 0.332808 0.0526215
\(41\) −0.451251 0.260530i −0.0704735 0.0406879i 0.464349 0.885652i \(-0.346288\pi\)
−0.534823 + 0.844964i \(0.679622\pi\)
\(42\) 0 0
\(43\) 1.53717 + 2.66245i 0.234416 + 0.406020i 0.959103 0.283058i \(-0.0913489\pi\)
−0.724687 + 0.689078i \(0.758016\pi\)
\(44\) 2.61023i 0.393508i
\(45\) 0 0
\(46\) −3.64819 + 2.10628i −0.537896 + 0.310555i
\(47\) 12.0528i 1.75807i 0.476753 + 0.879037i \(0.341814\pi\)
−0.476753 + 0.879037i \(0.658186\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 4.23421 + 2.44462i 0.598807 + 0.345721i
\(51\) 0 0
\(52\) 0.694883 + 3.53796i 0.0963629 + 0.490626i
\(53\) 9.71047 1.33384 0.666918 0.745132i \(-0.267613\pi\)
0.666918 + 0.745132i \(0.267613\pi\)
\(54\) 0 0
\(55\) −0.434353 + 0.752321i −0.0585681 + 0.101443i
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 0 0
\(58\) −1.02769 + 0.593337i −0.134942 + 0.0779090i
\(59\) −9.07175 + 5.23758i −1.18104 + 0.681875i −0.956255 0.292533i \(-0.905502\pi\)
−0.224786 + 0.974408i \(0.572168\pi\)
\(60\) 0 0
\(61\) −3.71989 6.44304i −0.476283 0.824947i 0.523347 0.852119i \(-0.324683\pi\)
−0.999631 + 0.0271724i \(0.991350\pi\)
\(62\) −3.53717 + 6.12656i −0.449221 + 0.778073i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.388451 1.13534i 0.0481814 0.140822i
\(66\) 0 0
\(67\) 10.3233 + 5.96015i 1.26119 + 0.728148i 0.973305 0.229517i \(-0.0737145\pi\)
0.287885 + 0.957665i \(0.407048\pi\)
\(68\) −1.94383 + 3.36681i −0.235724 + 0.408286i
\(69\) 0 0
\(70\) 0.332808i 0.0397781i
\(71\) 0.818065 0.472310i 0.0970864 0.0560529i −0.450671 0.892690i \(-0.648815\pi\)
0.547757 + 0.836637i \(0.315482\pi\)
\(72\) 0 0
\(73\) 4.66562i 0.546069i −0.962004 0.273034i \(-0.911973\pi\)
0.962004 0.273034i \(-0.0880273\pi\)
\(74\) 0.288220 + 0.499211i 0.0335049 + 0.0580321i
\(75\) 0 0
\(76\) 4.85997 + 2.80591i 0.557477 + 0.321859i
\(77\) 2.61023 0.297464
\(78\) 0 0
\(79\) −0.943042 −0.106101 −0.0530503 0.998592i \(-0.516894\pi\)
−0.0530503 + 0.998592i \(0.516894\pi\)
\(80\) 0.288220 + 0.166404i 0.0322240 + 0.0186045i
\(81\) 0 0
\(82\) −0.260530 0.451251i −0.0287707 0.0498323i
\(83\) 13.7172i 1.50566i −0.658215 0.752830i \(-0.728688\pi\)
0.658215 0.752830i \(-0.271312\pi\)
\(84\) 0 0
\(85\) 1.12050 0.646922i 0.121535 0.0701685i
\(86\) 3.07434i 0.331514i
\(87\) 0 0
\(88\) 1.30512 2.26053i 0.139126 0.240973i
\(89\) −2.92741 1.69014i −0.310305 0.179155i 0.336758 0.941591i \(-0.390670\pi\)
−0.647063 + 0.762436i \(0.724003\pi\)
\(90\) 0 0
\(91\) −3.53796 + 0.694883i −0.370879 + 0.0728435i
\(92\) −4.21257 −0.439191
\(93\) 0 0
\(94\) −6.02638 + 10.4380i −0.621573 + 1.07660i
\(95\) −0.933827 1.61744i −0.0958086 0.165945i
\(96\) 0 0
\(97\) −5.03669 + 2.90793i −0.511398 + 0.295256i −0.733408 0.679789i \(-0.762072\pi\)
0.222010 + 0.975044i \(0.428738\pi\)
\(98\) 0.866025 0.500000i 0.0874818 0.0505076i
\(99\) 0 0
\(100\) 2.44462 + 4.23421i 0.244462 + 0.423421i
\(101\) 7.98516 13.8307i 0.794553 1.37621i −0.128569 0.991701i \(-0.541038\pi\)
0.923122 0.384506i \(-0.125628\pi\)
\(102\) 0 0
\(103\) −7.50641 −0.739629 −0.369814 0.929106i \(-0.620579\pi\)
−0.369814 + 0.929106i \(0.620579\pi\)
\(104\) −1.16719 + 3.41140i −0.114453 + 0.334515i
\(105\) 0 0
\(106\) 8.40951 + 4.85523i 0.816804 + 0.471582i
\(107\) 4.32539 7.49179i 0.418151 0.724259i −0.577602 0.816318i \(-0.696012\pi\)
0.995754 + 0.0920593i \(0.0293449\pi\)
\(108\) 0 0
\(109\) 18.6144i 1.78293i 0.453088 + 0.891466i \(0.350322\pi\)
−0.453088 + 0.891466i \(0.649678\pi\)
\(110\) −0.752321 + 0.434353i −0.0717310 + 0.0414139i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 4.57512 + 7.92435i 0.430392 + 0.745460i 0.996907 0.0785911i \(-0.0250422\pi\)
−0.566515 + 0.824051i \(0.691709\pi\)
\(114\) 0 0
\(115\) 1.21415 + 0.700987i 0.113220 + 0.0653674i
\(116\) −1.18667 −0.110180
\(117\) 0 0
\(118\) −10.4752 −0.964316
\(119\) −3.36681 1.94383i −0.308635 0.178191i
\(120\) 0 0
\(121\) −2.09334 3.62577i −0.190303 0.329615i
\(122\) 7.43978i 0.673566i
\(123\) 0 0
\(124\) −6.12656 + 3.53717i −0.550181 + 0.317647i
\(125\) 3.29121i 0.294375i
\(126\) 0 0
\(127\) 3.38977 5.87125i 0.300793 0.520989i −0.675523 0.737339i \(-0.736082\pi\)
0.976316 + 0.216350i \(0.0694153\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0.904078 0.789008i 0.0792929 0.0692006i
\(131\) −7.22879 −0.631583 −0.315791 0.948829i \(-0.602270\pi\)
−0.315791 + 0.948829i \(0.602270\pi\)
\(132\) 0 0
\(133\) −2.80591 + 4.85997i −0.243303 + 0.421413i
\(134\) 5.96015 + 10.3233i 0.514879 + 0.891796i
\(135\) 0 0
\(136\) −3.36681 + 1.94383i −0.288702 + 0.166682i
\(137\) 10.2964 5.94462i 0.879679 0.507883i 0.00912669 0.999958i \(-0.497095\pi\)
0.870553 + 0.492075i \(0.163762\pi\)
\(138\) 0 0
\(139\) −7.16056 12.4025i −0.607351 1.05196i −0.991675 0.128764i \(-0.958899\pi\)
0.384324 0.923198i \(-0.374434\pi\)
\(140\) −0.166404 + 0.288220i −0.0140637 + 0.0243590i
\(141\) 0 0
\(142\) 0.944620 0.0792707
\(143\) −6.18825 7.09075i −0.517488 0.592959i
\(144\) 0 0
\(145\) 0.342023 + 0.197467i 0.0284035 + 0.0163988i
\(146\) 2.33281 4.04054i 0.193065 0.334398i
\(147\) 0 0
\(148\) 0.576440i 0.0473831i
\(149\) 5.24548 3.02848i 0.429726 0.248103i −0.269504 0.962999i \(-0.586860\pi\)
0.699230 + 0.714897i \(0.253526\pi\)
\(150\) 0 0
\(151\) 21.4953i 1.74926i 0.484791 + 0.874630i \(0.338896\pi\)
−0.484791 + 0.874630i \(0.661104\pi\)
\(152\) 2.80591 + 4.85997i 0.227589 + 0.394196i
\(153\) 0 0
\(154\) 2.26053 + 1.30512i 0.182159 + 0.105169i
\(155\) 2.35439 0.189109
\(156\) 0 0
\(157\) 2.29227 0.182943 0.0914714 0.995808i \(-0.470843\pi\)
0.0914714 + 0.995808i \(0.470843\pi\)
\(158\) −0.816699 0.471521i −0.0649731 0.0375122i
\(159\) 0 0
\(160\) 0.166404 + 0.288220i 0.0131554 + 0.0227858i
\(161\) 4.21257i 0.331997i
\(162\) 0 0
\(163\) 2.89314 1.67035i 0.226608 0.130832i −0.382398 0.923998i \(-0.624902\pi\)
0.609006 + 0.793165i \(0.291568\pi\)
\(164\) 0.521059i 0.0406879i
\(165\) 0 0
\(166\) 6.85861 11.8795i 0.532331 0.922024i
\(167\) −5.57802 3.22047i −0.431640 0.249207i 0.268405 0.963306i \(-0.413503\pi\)
−0.700045 + 0.714099i \(0.746837\pi\)
\(168\) 0 0
\(169\) 10.2753 + 7.96352i 0.790410 + 0.612579i
\(170\) 1.29384 0.0992333
\(171\) 0 0
\(172\) −1.53717 + 2.66245i −0.117208 + 0.203010i
\(173\) 9.30718 + 16.1205i 0.707611 + 1.22562i 0.965741 + 0.259509i \(0.0835606\pi\)
−0.258129 + 0.966110i \(0.583106\pi\)
\(174\) 0 0
\(175\) −4.23421 + 2.44462i −0.320076 + 0.184796i
\(176\) 2.26053 1.30512i 0.170394 0.0983769i
\(177\) 0 0
\(178\) −1.69014 2.92741i −0.126682 0.219419i
\(179\) 11.1081 19.2398i 0.830261 1.43805i −0.0675707 0.997714i \(-0.521525\pi\)
0.897831 0.440339i \(-0.145142\pi\)
\(180\) 0 0
\(181\) −4.05853 −0.301669 −0.150834 0.988559i \(-0.548196\pi\)
−0.150834 + 0.988559i \(0.548196\pi\)
\(182\) −3.41140 1.16719i −0.252870 0.0865181i
\(183\) 0 0
\(184\) −3.64819 2.10628i −0.268948 0.155277i
\(185\) 0.0959218 0.166141i 0.00705231 0.0122150i
\(186\) 0 0
\(187\) 10.1477i 0.742074i
\(188\) −10.4380 + 6.02638i −0.761269 + 0.439519i
\(189\) 0 0
\(190\) 1.86765i 0.135494i
\(191\) −5.86018 10.1501i −0.424028 0.734438i 0.572301 0.820044i \(-0.306051\pi\)
−0.996329 + 0.0856056i \(0.972718\pi\)
\(192\) 0 0
\(193\) −20.6123 11.9005i −1.48371 0.856618i −0.483877 0.875136i \(-0.660772\pi\)
−0.999829 + 0.0185185i \(0.994105\pi\)
\(194\) −5.81587 −0.417555
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −8.73184 5.04133i −0.622118 0.359180i 0.155575 0.987824i \(-0.450277\pi\)
−0.777693 + 0.628644i \(0.783610\pi\)
\(198\) 0 0
\(199\) 6.92504 + 11.9945i 0.490903 + 0.850269i 0.999945 0.0104725i \(-0.00333355\pi\)
−0.509042 + 0.860742i \(0.670000\pi\)
\(200\) 4.88924i 0.345721i
\(201\) 0 0
\(202\) 13.8307 7.98516i 0.973125 0.561834i
\(203\) 1.18667i 0.0832882i
\(204\) 0 0
\(205\) −0.0867062 + 0.150180i −0.00605583 + 0.0104890i
\(206\) −6.50074 3.75321i −0.452928 0.261498i
\(207\) 0 0
\(208\) −2.71652 + 2.37076i −0.188357 + 0.164383i
\(209\) −14.6481 −1.01323
\(210\) 0 0
\(211\) −2.27743 + 3.94462i −0.156785 + 0.271559i −0.933707 0.358037i \(-0.883446\pi\)
0.776923 + 0.629596i \(0.216779\pi\)
\(212\) 4.85523 + 8.40951i 0.333459 + 0.577568i
\(213\) 0 0
\(214\) 7.49179 4.32539i 0.512128 0.295677i
\(215\) 0.886085 0.511581i 0.0604305 0.0348896i
\(216\) 0 0
\(217\) −3.53717 6.12656i −0.240119 0.415898i
\(218\) −9.30718 + 16.1205i −0.630361 + 1.09182i
\(219\) 0 0
\(220\) −0.868706 −0.0585681
\(221\) 2.70147 + 13.7544i 0.181720 + 0.925220i
\(222\) 0 0
\(223\) −7.30359 4.21673i −0.489085 0.282373i 0.235110 0.971969i \(-0.424455\pi\)
−0.724195 + 0.689596i \(0.757788\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) 0 0
\(226\) 9.15025i 0.608666i
\(227\) −24.2394 + 13.9946i −1.60883 + 0.928857i −0.619194 + 0.785238i \(0.712541\pi\)
−0.989633 + 0.143619i \(0.954126\pi\)
\(228\) 0 0
\(229\) 28.7785i 1.90174i −0.309598 0.950868i \(-0.600194\pi\)
0.309598 0.950868i \(-0.399806\pi\)
\(230\) 0.700987 + 1.21415i 0.0462217 + 0.0800584i
\(231\) 0 0
\(232\) −1.02769 0.593337i −0.0674712 0.0389545i
\(233\) 18.8877 1.23737 0.618686 0.785638i \(-0.287665\pi\)
0.618686 + 0.785638i \(0.287665\pi\)
\(234\) 0 0
\(235\) 4.01125 0.261665
\(236\) −9.07175 5.23758i −0.590521 0.340937i
\(237\) 0 0
\(238\) −1.94383 3.36681i −0.126000 0.218238i
\(239\) 11.0933i 0.717565i −0.933421 0.358783i \(-0.883192\pi\)
0.933421 0.358783i \(-0.116808\pi\)
\(240\) 0 0
\(241\) −7.02686 + 4.05696i −0.452640 + 0.261332i −0.708944 0.705264i \(-0.750828\pi\)
0.256305 + 0.966596i \(0.417495\pi\)
\(242\) 4.18667i 0.269130i
\(243\) 0 0
\(244\) 3.71989 6.44304i 0.238142 0.412474i
\(245\) −0.288220 0.166404i −0.0184137 0.0106311i
\(246\) 0 0
\(247\) 19.8543 3.89955i 1.26330 0.248122i
\(248\) −7.07434 −0.449221
\(249\) 0 0
\(250\) 1.64561 2.85027i 0.104077 0.180267i
\(251\) 1.58465 + 2.74469i 0.100022 + 0.173243i 0.911694 0.410871i \(-0.134775\pi\)
−0.811671 + 0.584114i \(0.801442\pi\)
\(252\) 0 0
\(253\) 9.52264 5.49790i 0.598683 0.345650i
\(254\) 5.87125 3.38977i 0.368395 0.212693i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.0967103 0.167507i 0.00603263 0.0104488i −0.862993 0.505215i \(-0.831413\pi\)
0.869026 + 0.494766i \(0.164746\pi\)
\(258\) 0 0
\(259\) −0.576440 −0.0358182
\(260\) 1.17746 0.231262i 0.0730229 0.0143423i
\(261\) 0 0
\(262\) −6.26032 3.61440i −0.386764 0.223298i
\(263\) 6.02185 10.4301i 0.371323 0.643150i −0.618446 0.785827i \(-0.712238\pi\)
0.989769 + 0.142677i \(0.0455709\pi\)
\(264\) 0 0
\(265\) 3.23172i 0.198523i
\(266\) −4.85997 + 2.80591i −0.297984 + 0.172041i
\(267\) 0 0
\(268\) 11.9203i 0.728148i
\(269\) 8.60487 + 14.9041i 0.524648 + 0.908718i 0.999588 + 0.0286993i \(0.00913654\pi\)
−0.474940 + 0.880018i \(0.657530\pi\)
\(270\) 0 0
\(271\) −14.8453 8.57096i −0.901790 0.520649i −0.0240098 0.999712i \(-0.507643\pi\)
−0.877781 + 0.479063i \(0.840977\pi\)
\(272\) −3.88766 −0.235724
\(273\) 0 0
\(274\) 11.8892 0.718255
\(275\) −11.0523 6.38103i −0.666477 0.384791i
\(276\) 0 0
\(277\) −7.85660 13.6080i −0.472057 0.817627i 0.527432 0.849598i \(-0.323155\pi\)
−0.999489 + 0.0319704i \(0.989822\pi\)
\(278\) 14.3211i 0.858924i
\(279\) 0 0
\(280\) −0.288220 + 0.166404i −0.0172244 + 0.00994453i
\(281\) 4.07337i 0.242997i 0.992592 + 0.121499i \(0.0387700\pi\)
−0.992592 + 0.121499i \(0.961230\pi\)
\(282\) 0 0
\(283\) 10.7674 18.6497i 0.640057 1.10861i −0.345363 0.938469i \(-0.612244\pi\)
0.985420 0.170142i \(-0.0544226\pi\)
\(284\) 0.818065 + 0.472310i 0.0485432 + 0.0280264i
\(285\) 0 0
\(286\) −1.81381 9.23490i −0.107253 0.546071i
\(287\) 0.521059 0.0307572
\(288\) 0 0
\(289\) 0.943042 1.63340i 0.0554731 0.0960822i
\(290\) 0.197467 + 0.342023i 0.0115957 + 0.0200843i
\(291\) 0 0
\(292\) 4.04054 2.33281i 0.236455 0.136517i
\(293\) −0.152457 + 0.0880210i −0.00890662 + 0.00514224i −0.504447 0.863443i \(-0.668303\pi\)
0.495540 + 0.868585i \(0.334970\pi\)
\(294\) 0 0
\(295\) 1.74311 + 3.01915i 0.101488 + 0.175782i
\(296\) −0.288220 + 0.499211i −0.0167524 + 0.0290161i
\(297\) 0 0
\(298\) 6.05696 0.350870
\(299\) −11.4435 + 9.98701i −0.661796 + 0.577564i
\(300\) 0 0
\(301\) −2.66245 1.53717i −0.153461 0.0886009i
\(302\) −10.7476 + 18.6154i −0.618457 + 1.07120i
\(303\) 0 0
\(304\) 5.61181i 0.321859i
\(305\) −2.14429 + 1.23801i −0.122782 + 0.0708882i
\(306\) 0 0
\(307\) 20.7405i 1.18372i −0.806040 0.591861i \(-0.798394\pi\)
0.806040 0.591861i \(-0.201606\pi\)
\(308\) 1.30512 + 2.26053i 0.0743660 + 0.128806i
\(309\) 0 0
\(310\) 2.03896 + 1.17720i 0.115805 + 0.0668603i
\(311\) −10.9678 −0.621926 −0.310963 0.950422i \(-0.600652\pi\)
−0.310963 + 0.950422i \(0.600652\pi\)
\(312\) 0 0
\(313\) 16.2189 0.916746 0.458373 0.888760i \(-0.348432\pi\)
0.458373 + 0.888760i \(0.348432\pi\)
\(314\) 1.98516 + 1.14613i 0.112029 + 0.0646800i
\(315\) 0 0
\(316\) −0.471521 0.816699i −0.0265251 0.0459429i
\(317\) 10.5358i 0.591750i −0.955227 0.295875i \(-0.904389\pi\)
0.955227 0.295875i \(-0.0956112\pi\)
\(318\) 0 0
\(319\) 2.68251 1.54875i 0.150192 0.0867133i
\(320\) 0.332808i 0.0186045i
\(321\) 0 0
\(322\) 2.10628 3.64819i 0.117379 0.203306i
\(323\) 18.8939 + 10.9084i 1.05129 + 0.606960i
\(324\) 0 0
\(325\) 16.6792 + 5.70668i 0.925193 + 0.316550i
\(326\) 3.34071 0.185025
\(327\) 0 0
\(328\) 0.260530 0.451251i 0.0143853 0.0249161i
\(329\) −6.02638 10.4380i −0.332245 0.575465i
\(330\) 0 0
\(331\) −13.9687 + 8.06486i −0.767792 + 0.443285i −0.832086 0.554646i \(-0.812854\pi\)
0.0642946 + 0.997931i \(0.479520\pi\)
\(332\) 11.8795 6.85861i 0.651970 0.376415i
\(333\) 0 0
\(334\) −3.22047 5.57802i −0.176216 0.305216i
\(335\) 1.98358 3.43567i 0.108375 0.187711i
\(336\) 0 0
\(337\) 1.78785 0.0973906 0.0486953 0.998814i \(-0.484494\pi\)
0.0486953 + 0.998814i \(0.484494\pi\)
\(338\) 4.91693 + 12.0343i 0.267446 + 0.654578i
\(339\) 0 0
\(340\) 1.12050 + 0.646922i 0.0607677 + 0.0350843i
\(341\) 9.23284 15.9917i 0.499986 0.866002i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −2.66245 + 1.53717i −0.143550 + 0.0828786i
\(345\) 0 0
\(346\) 18.6144i 1.00071i
\(347\) 12.7030 + 22.0023i 0.681935 + 1.18115i 0.974389 + 0.224867i \(0.0721947\pi\)
−0.292454 + 0.956280i \(0.594472\pi\)
\(348\) 0 0
\(349\) −24.5419 14.1693i −1.31370 0.758463i −0.330990 0.943634i \(-0.607383\pi\)
−0.982706 + 0.185172i \(0.940716\pi\)
\(350\) −4.88924 −0.261341
\(351\) 0 0
\(352\) 2.61023 0.139126
\(353\) 1.69146 + 0.976568i 0.0900276 + 0.0519774i 0.544338 0.838866i \(-0.316781\pi\)
−0.454310 + 0.890843i \(0.650114\pi\)
\(354\) 0 0
\(355\) −0.157188 0.272258i −0.00834269 0.0144500i
\(356\) 3.38029i 0.179155i
\(357\) 0 0
\(358\) 19.2398 11.1081i 1.01686 0.587083i
\(359\) 27.6565i 1.45965i −0.683633 0.729826i \(-0.739601\pi\)
0.683633 0.729826i \(-0.260399\pi\)
\(360\) 0 0
\(361\) 6.24622 10.8188i 0.328748 0.569409i
\(362\) −3.51479 2.02927i −0.184733 0.106656i
\(363\) 0 0
\(364\) −2.37076 2.71652i −0.124262 0.142384i
\(365\) −1.55275 −0.0812748
\(366\) 0 0
\(367\) −2.87888 + 4.98636i −0.150276 + 0.260286i −0.931329 0.364179i \(-0.881350\pi\)
0.781053 + 0.624465i \(0.214683\pi\)
\(368\) −2.10628 3.64819i −0.109798 0.190175i
\(369\) 0 0
\(370\) 0.166141 0.0959218i 0.00863728 0.00498673i
\(371\) −8.40951 + 4.85523i −0.436600 + 0.252071i
\(372\) 0 0
\(373\) −13.9243 24.1177i −0.720975 1.24877i −0.960609 0.277903i \(-0.910361\pi\)
0.239634 0.970863i \(-0.422973\pi\)
\(374\) 5.07386 8.78817i 0.262363 0.454426i
\(375\) 0 0
\(376\) −12.0528 −0.621573
\(377\) −3.22362 + 2.81333i −0.166025 + 0.144894i
\(378\) 0 0
\(379\) −10.7836 6.22590i −0.553915 0.319803i 0.196784 0.980447i \(-0.436950\pi\)
−0.750700 + 0.660644i \(0.770283\pi\)
\(380\) 0.933827 1.61744i 0.0479043 0.0829727i
\(381\) 0 0
\(382\) 11.7204i 0.599666i
\(383\) 8.42273 4.86286i 0.430381 0.248481i −0.269128 0.963104i \(-0.586735\pi\)
0.699509 + 0.714624i \(0.253402\pi\)
\(384\) 0 0
\(385\) 0.868706i 0.0442734i
\(386\) −11.9005 20.6123i −0.605720 1.04914i
\(387\) 0 0
\(388\) −5.03669 2.90793i −0.255699 0.147628i
\(389\) 13.8910 0.704302 0.352151 0.935943i \(-0.385450\pi\)
0.352151 + 0.935943i \(0.385450\pi\)
\(390\) 0 0
\(391\) −16.3770 −0.828223
\(392\) 0.866025 + 0.500000i 0.0437409 + 0.0252538i
\(393\) 0 0
\(394\) −5.04133 8.73184i −0.253979 0.439904i
\(395\) 0.313852i 0.0157916i
\(396\) 0 0
\(397\) 5.87033 3.38924i 0.294624 0.170101i −0.345401 0.938455i \(-0.612257\pi\)
0.640025 + 0.768354i \(0.278924\pi\)
\(398\) 13.8501i 0.694242i
\(399\) 0 0
\(400\) −2.44462 + 4.23421i −0.122231 + 0.211710i
\(401\) −12.5254 7.23152i −0.625487 0.361125i 0.153515 0.988146i \(-0.450941\pi\)
−0.779002 + 0.627021i \(0.784274\pi\)
\(402\) 0 0
\(403\) −8.25711 + 24.1334i −0.411316 + 1.20217i
\(404\) 15.9703 0.794553
\(405\) 0 0
\(406\) 0.593337 1.02769i 0.0294468 0.0510034i
\(407\) −0.752321 1.30306i −0.0372912 0.0645902i
\(408\) 0 0
\(409\) 20.2032 11.6643i 0.998982 0.576763i 0.0910351 0.995848i \(-0.470982\pi\)
0.907947 + 0.419085i \(0.137649\pi\)
\(410\) −0.150180 + 0.0867062i −0.00741684 + 0.00428212i
\(411\) 0 0
\(412\) −3.75321 6.50074i −0.184907 0.320269i
\(413\) 5.23758 9.07175i 0.257724 0.446392i
\(414\) 0 0
\(415\) −4.56519 −0.224096
\(416\) −3.53796 + 0.694883i −0.173463 + 0.0340694i
\(417\) 0 0
\(418\) −12.6857 7.32407i −0.620476 0.358232i
\(419\) −11.2898 + 19.5544i −0.551540 + 0.955296i 0.446623 + 0.894722i \(0.352626\pi\)
−0.998164 + 0.0605740i \(0.980707\pi\)
\(420\) 0 0
\(421\) 34.1708i 1.66538i 0.553738 + 0.832691i \(0.313201\pi\)
−0.553738 + 0.832691i \(0.686799\pi\)
\(422\) −3.94462 + 2.27743i −0.192021 + 0.110863i
\(423\) 0 0
\(424\) 9.71047i 0.471582i
\(425\) 9.50385 + 16.4612i 0.461005 + 0.798483i
\(426\) 0 0
\(427\) 6.44304 + 3.71989i 0.311801 + 0.180018i
\(428\) 8.65078 0.418151
\(429\) 0 0
\(430\) 1.02316 0.0493413
\(431\) −4.53528 2.61844i −0.218457 0.126126i 0.386779 0.922173i \(-0.373588\pi\)
−0.605235 + 0.796047i \(0.706921\pi\)
\(432\) 0 0
\(433\) 8.41030 + 14.5671i 0.404173 + 0.700048i 0.994225 0.107317i \(-0.0342260\pi\)
−0.590052 + 0.807365i \(0.700893\pi\)
\(434\) 7.07434i 0.339579i
\(435\) 0 0
\(436\) −16.1205 + 9.30718i −0.772032 + 0.445733i
\(437\) 23.6401i 1.13086i
\(438\) 0 0
\(439\) −7.36282 + 12.7528i −0.351408 + 0.608657i −0.986496 0.163783i \(-0.947630\pi\)
0.635088 + 0.772440i \(0.280964\pi\)
\(440\) −0.752321 0.434353i −0.0358655 0.0207070i
\(441\) 0 0
\(442\) −4.53765 + 13.2624i −0.215834 + 0.630827i
\(443\) −36.2393 −1.72178 −0.860891 0.508789i \(-0.830093\pi\)
−0.860891 + 0.508789i \(0.830093\pi\)
\(444\) 0 0
\(445\) −0.562493 + 0.974266i −0.0266647 + 0.0461846i
\(446\) −4.21673 7.30359i −0.199668 0.345835i
\(447\) 0 0
\(448\) 0.866025 0.500000i 0.0409159 0.0236228i
\(449\) 21.0351 12.1446i 0.992708 0.573140i 0.0866255 0.996241i \(-0.472392\pi\)
0.906083 + 0.423101i \(0.139058\pi\)
\(450\) 0 0
\(451\) 0.680043 + 1.17787i 0.0320220 + 0.0554637i
\(452\) −4.57512 + 7.92435i −0.215196 + 0.372730i
\(453\) 0 0
\(454\) −27.9893 −1.31360
\(455\) 0.231262 + 1.17746i 0.0108417 + 0.0552001i
\(456\) 0 0
\(457\) −28.8744 16.6706i −1.35069 0.779819i −0.362340 0.932046i \(-0.618022\pi\)
−0.988345 + 0.152227i \(0.951355\pi\)
\(458\) 14.3892 24.9229i 0.672365 1.16457i
\(459\) 0 0
\(460\) 1.40197i 0.0653674i
\(461\) 25.6317 14.7985i 1.19379 0.689234i 0.234625 0.972086i \(-0.424614\pi\)
0.959164 + 0.282852i \(0.0912804\pi\)
\(462\) 0 0
\(463\) 36.6027i 1.70107i 0.525918 + 0.850535i \(0.323722\pi\)
−0.525918 + 0.850535i \(0.676278\pi\)
\(464\) −0.593337 1.02769i −0.0275450 0.0477093i
\(465\) 0 0
\(466\) 16.3572 + 9.44383i 0.757732 + 0.437477i
\(467\) 6.21635 0.287658 0.143829 0.989603i \(-0.454058\pi\)
0.143829 + 0.989603i \(0.454058\pi\)
\(468\) 0 0
\(469\) −11.9203 −0.550428
\(470\) 3.47384 + 2.00562i 0.160236 + 0.0925125i
\(471\) 0 0
\(472\) −5.23758 9.07175i −0.241079 0.417561i
\(473\) 8.02474i 0.368978i
\(474\) 0 0
\(475\) 23.7616 13.7187i 1.09026 0.629459i
\(476\) 3.88766i 0.178191i
\(477\) 0 0
\(478\) 5.54665 9.60707i 0.253698 0.439417i
\(479\) 29.0757 + 16.7869i 1.32850 + 0.767011i 0.985068 0.172165i \(-0.0550764\pi\)
0.343434 + 0.939177i \(0.388410\pi\)
\(480\) 0 0
\(481\) 1.36660 + 1.56591i 0.0623117 + 0.0713993i
\(482\) −8.11392 −0.369579
\(483\) 0 0
\(484\) 2.09334 3.62577i 0.0951517 0.164808i
\(485\) 0.967782 + 1.67625i 0.0439447 + 0.0761145i
\(486\) 0 0
\(487\) 17.5020 10.1048i 0.793089 0.457890i −0.0479597 0.998849i \(-0.515272\pi\)
0.841049 + 0.540959i \(0.181939\pi\)
\(488\) 6.44304 3.71989i 0.291663 0.168392i
\(489\) 0 0
\(490\) −0.166404 0.288220i −0.00751736 0.0130204i
\(491\) 3.38977 5.87125i 0.152978 0.264966i −0.779343 0.626598i \(-0.784447\pi\)
0.932321 + 0.361632i \(0.117780\pi\)
\(492\) 0 0
\(493\) −4.61339 −0.207777
\(494\) 19.1441 + 6.55006i 0.861336 + 0.294701i
\(495\) 0 0
\(496\) −6.12656 3.53717i −0.275090 0.158824i
\(497\) −0.472310 + 0.818065i −0.0211860 + 0.0366952i
\(498\) 0 0
\(499\) 11.0813i 0.496066i −0.968752 0.248033i \(-0.920216\pi\)
0.968752 0.248033i \(-0.0797841\pi\)
\(500\) 2.85027 1.64561i 0.127468 0.0735938i
\(501\) 0 0
\(502\) 3.16930i 0.141453i
\(503\) −14.9958 25.9735i −0.668629 1.15810i −0.978288 0.207252i \(-0.933548\pi\)
0.309658 0.950848i \(-0.399785\pi\)
\(504\) 0 0
\(505\) −4.60296 2.65752i −0.204829 0.118258i
\(506\) 10.9958 0.488823
\(507\) 0 0
\(508\) 6.77953 0.300793
\(509\) −27.2629 15.7402i −1.20840 0.697673i −0.245994 0.969271i \(-0.579114\pi\)
−0.962411 + 0.271599i \(0.912448\pi\)
\(510\) 0 0
\(511\) 2.33281 + 4.04054i 0.103197 + 0.178743i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 0.167507 0.0967103i 0.00738843 0.00426571i
\(515\) 2.49819i 0.110083i
\(516\) 0 0
\(517\) 15.7303 27.2456i 0.691816 1.19826i
\(518\) −0.499211 0.288220i −0.0219341 0.0126637i
\(519\) 0 0
\(520\) 1.13534 + 0.388451i 0.0497880 + 0.0170347i
\(521\) −17.8010 −0.779877 −0.389939 0.920841i \(-0.627504\pi\)
−0.389939 + 0.920841i \(0.627504\pi\)
\(522\) 0 0
\(523\) −16.4702 + 28.5272i −0.720192 + 1.24741i 0.240731 + 0.970592i \(0.422613\pi\)
−0.960923 + 0.276817i \(0.910720\pi\)
\(524\) −3.61440 6.26032i −0.157896 0.273483i
\(525\) 0 0
\(526\) 10.4301 6.02185i 0.454776 0.262565i
\(527\) −23.8180 + 13.7513i −1.03753 + 0.599017i
\(528\) 0 0
\(529\) 2.62713 + 4.55033i 0.114223 + 0.197840i
\(530\) 1.61586 2.79875i 0.0701884 0.121570i
\(531\) 0 0
\(532\) −5.61181 −0.243303
\(533\) −1.23531 1.41547i −0.0535072 0.0613107i
\(534\) 0 0
\(535\) −2.49333 1.43952i −0.107796 0.0622360i
\(536\) −5.96015 + 10.3233i −0.257439 + 0.445898i
\(537\) 0 0
\(538\) 17.2097i 0.741965i
\(539\) −2.26053 + 1.30512i −0.0973679 + 0.0562154i
\(540\) 0 0
\(541\) 15.5204i 0.667276i 0.942701 + 0.333638i \(0.108276\pi\)
−0.942701 + 0.333638i \(0.891724\pi\)
\(542\) −8.57096 14.8453i −0.368154 0.637662i
\(543\) 0 0
\(544\) −3.36681 1.94383i −0.144351 0.0833411i
\(545\) 6.19500 0.265365
\(546\) 0 0
\(547\) 22.9529 0.981397 0.490698 0.871329i \(-0.336742\pi\)
0.490698 + 0.871329i \(0.336742\pi\)
\(548\) 10.2964 + 5.94462i 0.439840 + 0.253942i
\(549\) 0 0
\(550\) −6.38103 11.0523i −0.272088 0.471270i
\(551\) 6.65939i 0.283700i
\(552\) 0 0
\(553\) 0.816699 0.471521i 0.0347296 0.0200511i
\(554\) 15.7132i 0.667590i
\(555\) 0 0
\(556\) 7.16056 12.4025i 0.303675 0.525981i
\(557\) 20.8161 + 12.0182i 0.882005 + 0.509226i 0.871319 0.490717i \(-0.163265\pi\)
0.0106863 + 0.999943i \(0.496598\pi\)
\(558\) 0 0
\(559\) 2.13630 + 10.8769i 0.0903560 + 0.460043i
\(560\) −0.332808 −0.0140637
\(561\) 0 0
\(562\) −2.03669 + 3.52765i −0.0859125 + 0.148805i
\(563\) 18.9379 + 32.8015i 0.798139 + 1.38242i 0.920827 + 0.389972i \(0.127515\pi\)
−0.122687 + 0.992445i \(0.539151\pi\)
\(564\) 0 0
\(565\) 2.63728 1.52264i 0.110951 0.0640578i
\(566\) 18.6497 10.7674i 0.783906 0.452589i
\(567\) 0 0
\(568\) 0.472310 + 0.818065i 0.0198177 + 0.0343252i
\(569\) 13.6833 23.7001i 0.573632 0.993560i −0.422557 0.906336i \(-0.638867\pi\)
0.996189 0.0872233i \(-0.0277994\pi\)
\(570\) 0 0
\(571\) 17.6639 0.739213 0.369607 0.929188i \(-0.379492\pi\)
0.369607 + 0.929188i \(0.379492\pi\)
\(572\) 3.04665 8.90456i 0.127387 0.372318i
\(573\) 0 0
\(574\) 0.451251 + 0.260530i 0.0188348 + 0.0108743i
\(575\) −10.2981 + 17.8369i −0.429462 + 0.743849i
\(576\) 0 0
\(577\) 11.3804i 0.473772i −0.971537 0.236886i \(-0.923873\pi\)
0.971537 0.236886i \(-0.0761268\pi\)
\(578\) 1.63340 0.943042i 0.0679404 0.0392254i
\(579\) 0 0
\(580\) 0.394934i 0.0163988i
\(581\) 6.85861 + 11.8795i 0.284543 + 0.492843i
\(582\) 0 0
\(583\) −21.9508 12.6733i −0.909109 0.524874i
\(584\) 4.66562 0.193065
\(585\) 0 0
\(586\) −0.176042 −0.00727222
\(587\) −15.9949 9.23469i −0.660182 0.381156i 0.132164 0.991228i \(-0.457807\pi\)
−0.792346 + 0.610072i \(0.791141\pi\)
\(588\) 0 0
\(589\) 19.8499 + 34.3811i 0.817902 + 1.41665i
\(590\) 3.48621i 0.143525i
\(591\) 0 0
\(592\) −0.499211 + 0.288220i −0.0205175 + 0.0118458i
\(593\) 19.3561i 0.794859i −0.917633 0.397429i \(-0.869902\pi\)
0.917633 0.397429i \(-0.130098\pi\)
\(594\) 0 0
\(595\) −0.646922 + 1.12050i −0.0265212 + 0.0459361i
\(596\) 5.24548 + 3.02848i 0.214863 + 0.124051i
\(597\) 0 0
\(598\) −14.9039 + 2.92724i −0.609465 + 0.119704i
\(599\) −21.1818 −0.865466 −0.432733 0.901522i \(-0.642451\pi\)
−0.432733 + 0.901522i \(0.642451\pi\)
\(600\) 0 0
\(601\) −11.0721 + 19.1774i −0.451639 + 0.782261i −0.998488 0.0549699i \(-0.982494\pi\)
0.546849 + 0.837231i \(0.315827\pi\)
\(602\) −1.53717 2.66245i −0.0626503 0.108513i
\(603\) 0 0
\(604\) −18.6154 + 10.7476i −0.757452 + 0.437315i
\(605\) −1.20668 + 0.696679i −0.0490586 + 0.0283240i
\(606\) 0 0
\(607\) −17.1439 29.6942i −0.695851 1.20525i −0.969893 0.243531i \(-0.921694\pi\)
0.274042 0.961718i \(-0.411639\pi\)
\(608\) −2.80591 + 4.85997i −0.113795 + 0.197098i
\(609\) 0 0
\(610\) −2.47602 −0.100251
\(611\) −14.0679 + 41.1168i −0.569125 + 1.66341i
\(612\) 0 0
\(613\) 14.7308 + 8.50484i 0.594972 + 0.343507i 0.767061 0.641574i \(-0.221718\pi\)
−0.172089 + 0.985081i \(0.555052\pi\)
\(614\) 10.3702 17.9618i 0.418509 0.724878i
\(615\) 0 0
\(616\) 2.61023i 0.105169i
\(617\) −15.0005 + 8.66052i −0.603896 + 0.348659i −0.770573 0.637352i \(-0.780030\pi\)
0.166677 + 0.986012i \(0.446696\pi\)
\(618\) 0 0
\(619\) 0.621482i 0.0249795i −0.999922 0.0124897i \(-0.996024\pi\)
0.999922 0.0124897i \(-0.00397571\pi\)
\(620\) 1.17720 + 2.03896i 0.0472773 + 0.0818868i
\(621\) 0 0
\(622\) −9.49838 5.48389i −0.380850 0.219884i
\(623\) 3.38029 0.135428
\(624\) 0 0
\(625\) 23.3509 0.934034
\(626\) 14.0460 + 8.10945i 0.561390 + 0.324119i
\(627\) 0 0
\(628\) 1.14613 + 1.98516i 0.0457357 + 0.0792165i
\(629\) 2.24100i 0.0893546i
\(630\) 0 0
\(631\) 11.7575 6.78817i 0.468057 0.270233i −0.247369 0.968921i \(-0.579566\pi\)
0.715426 + 0.698688i \(0.246233\pi\)
\(632\) 0.943042i 0.0375122i
\(633\) 0 0
\(634\) 5.26790 9.12428i 0.209215 0.362371i
\(635\) −1.95400 1.12814i −0.0775419 0.0447689i
\(636\) 0 0
\(637\) 2.71652 2.37076i 0.107632 0.0939331i
\(638\) 3.09750 0.122631
\(639\) 0 0
\(640\) −0.166404 + 0.288220i −0.00657769 + 0.0113929i
\(641\) 10.2558 + 17.7636i 0.405081 + 0.701622i 0.994331 0.106330i \(-0.0339098\pi\)
−0.589250 + 0.807951i \(0.700577\pi\)
\(642\) 0 0
\(643\) −37.0253 + 21.3766i −1.46013 + 0.843009i −0.999017 0.0443295i \(-0.985885\pi\)
−0.461118 + 0.887339i \(0.652552\pi\)
\(644\) 3.64819 2.10628i 0.143759 0.0829992i
\(645\) 0 0
\(646\) 10.9084 + 18.8939i 0.429186 + 0.743372i
\(647\) 13.1115 22.7098i 0.515466 0.892814i −0.484372 0.874862i \(-0.660952\pi\)
0.999839 0.0179521i \(-0.00571465\pi\)
\(648\) 0 0
\(649\) 27.3426 1.07329
\(650\) 11.5912 + 13.2817i 0.454646 + 0.520952i
\(651\) 0 0
\(652\) 2.89314 + 1.67035i 0.113304 + 0.0654161i
\(653\) −4.36935 + 7.56794i −0.170986 + 0.296156i −0.938765 0.344558i \(-0.888029\pi\)
0.767779 + 0.640715i \(0.221362\pi\)
\(654\) 0 0
\(655\) 2.40580i 0.0940023i
\(656\) 0.451251 0.260530i 0.0176184 0.0101720i
\(657\) 0 0
\(658\) 12.0528i 0.469865i
\(659\) 0.251052 + 0.434834i 0.00977958 + 0.0169387i 0.870874 0.491507i \(-0.163554\pi\)
−0.861094 + 0.508445i \(0.830220\pi\)
\(660\) 0 0
\(661\) 27.1062 + 15.6498i 1.05431 + 0.608705i 0.923853 0.382749i \(-0.125022\pi\)
0.130456 + 0.991454i \(0.458356\pi\)
\(662\) −16.1297 −0.626899
\(663\) 0 0
\(664\) 13.7172 0.532331
\(665\) 1.61744 + 0.933827i 0.0627215 + 0.0362123i
\(666\) 0 0
\(667\) −2.49947 4.32922i −0.0967800 0.167628i
\(668\) 6.44094i 0.249207i
\(669\) 0 0
\(670\) 3.43567 1.98358i 0.132731 0.0766325i
\(671\) 19.4196i 0.749685i
\(672\) 0 0
\(673\) −11.8585 + 20.5395i −0.457112 + 0.791741i −0.998807 0.0488340i \(-0.984449\pi\)
0.541695 + 0.840575i \(0.317783\pi\)
\(674\) 1.54833 + 0.893927i 0.0596393 + 0.0344328i
\(675\) 0 0
\(676\) −1.75895 + 12.8805i −0.0676520 + 0.495402i
\(677\) −17.8136 −0.684631 −0.342315 0.939585i \(-0.611211\pi\)
−0.342315 + 0.939585i \(0.611211\pi\)
\(678\) 0 0
\(679\) 2.90793 5.03669i 0.111596 0.193290i
\(680\) 0.646922 + 1.12050i 0.0248083 + 0.0429693i
\(681\) 0 0
\(682\) 15.9917 9.23284i 0.612356 0.353544i
\(683\) −10.3174 + 5.95673i −0.394783 + 0.227928i −0.684230 0.729266i \(-0.739862\pi\)
0.289448 + 0.957194i \(0.406528\pi\)
\(684\) 0 0
\(685\) −1.97841 3.42671i −0.0755913 0.130928i
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) −3.07434 −0.117208
\(689\) 33.1263 + 11.3340i 1.26201 + 0.431790i
\(690\) 0 0
\(691\) −17.3085 9.99306i −0.658446 0.380154i 0.133239 0.991084i \(-0.457462\pi\)
−0.791685 + 0.610930i \(0.790796\pi\)
\(692\) −9.30718 + 16.1205i −0.353806 + 0.612810i
\(693\) 0 0
\(694\) 25.4061i 0.964402i
\(695\) −4.12763 + 2.38309i −0.156570 + 0.0903957i
\(696\) 0 0
\(697\) 2.02570i 0.0767289i
\(698\) −14.1693 24.5419i −0.536314 0.928923i
\(699\) 0 0
\(700\) −4.23421 2.44462i −0.160038 0.0923979i
\(701\) 23.9244 0.903613 0.451806 0.892116i \(-0.350780\pi\)
0.451806 + 0.892116i \(0.350780\pi\)
\(702\) 0 0
\(703\) 3.23487 0.122005
\(704\) 2.26053 + 1.30512i 0.0851969 + 0.0491885i
\(705\) 0 0
\(706\) 0.976568 + 1.69146i 0.0367536 + 0.0636591i
\(707\) 15.9703i 0.600626i
\(708\) 0 0
\(709\) 30.7406 17.7481i 1.15449 0.666544i 0.204512 0.978864i \(-0.434439\pi\)
0.949977 + 0.312320i \(0.101106\pi\)
\(710\) 0.314377i 0.0117983i
\(711\) 0 0
\(712\) 1.69014 2.92741i 0.0633408 0.109710i
\(713\) −25.8085 14.9006i −0.966537 0.558031i
\(714\) 0 0
\(715\) −2.35986 + 2.05950i −0.0882536 + 0.0770208i
\(716\) 22.2163 0.830261
\(717\) 0 0
\(718\) 13.8282 23.9512i 0.516065 0.893851i
\(719\) 3.09097 + 5.35372i 0.115274 + 0.199660i 0.917889 0.396837i \(-0.129892\pi\)
−0.802615 + 0.596497i \(0.796559\pi\)
\(720\) 0 0
\(721\) 6.50074 3.75321i 0.242100 0.139777i
\(722\) 10.8188 6.24622i 0.402633 0.232460i
\(723\) 0 0
\(724\) −2.02927 3.51479i −0.0754171 0.130626i
\(725\) −2.90097 + 5.02462i −0.107739 + 0.186610i
\(726\) 0 0
\(727\) −43.2387 −1.60363 −0.801817 0.597569i \(-0.796133\pi\)
−0.801817 + 0.597569i \(0.796133\pi\)
\(728\) −0.694883 3.53796i −0.0257541 0.131125i
\(729\) 0 0
\(730\) −1.34472 0.776376i −0.0497704 0.0287350i
\(731\) −5.97599 + 10.3507i −0.221030 + 0.382835i
\(732\) 0 0
\(733\) 32.0306i 1.18308i 0.806277 + 0.591538i \(0.201479\pi\)
−0.806277 + 0.591538i \(0.798521\pi\)
\(734\) −4.98636 + 2.87888i −0.184050 + 0.106261i
\(735\) 0 0
\(736\) 4.21257i 0.155277i
\(737\) −15.5574 26.9462i −0.573064 0.992576i
\(738\) 0 0
\(739\) −22.0558 12.7339i −0.811334 0.468424i 0.0360848 0.999349i \(-0.488511\pi\)
−0.847419 + 0.530925i \(0.821845\pi\)
\(740\) 0.191844 0.00705231
\(741\) 0 0
\(742\) −9.71047 −0.356482
\(743\) 12.5533 + 7.24763i 0.460535 + 0.265890i 0.712269 0.701906i \(-0.247668\pi\)
−0.251734 + 0.967796i \(0.581001\pi\)
\(744\) 0 0
\(745\) −1.00790 1.74574i −0.0369266 0.0639588i
\(746\) 27.8487i 1.01961i
\(747\) 0 0
\(748\) 8.78817 5.07386i 0.321327 0.185519i
\(749\) 8.65078i 0.316092i
\(750\) 0 0
\(751\) 14.5632 25.2243i 0.531420 0.920447i −0.467907 0.883777i \(-0.654992\pi\)
0.999327 0.0366690i \(-0.0116747\pi\)
\(752\) −10.4380 6.02638i −0.380634 0.219759i
\(753\) 0 0
\(754\) −4.19840 + 0.824599i −0.152897 + 0.0300301i
\(755\) 7.15379 0.260353
\(756\) 0 0
\(757\) 10.0230 17.3603i 0.364292 0.630973i −0.624370 0.781129i \(-0.714644\pi\)
0.988662 + 0.150156i \(0.0479776\pi\)
\(758\) −6.22590 10.7836i −0.226135 0.391677i
\(759\) 0 0
\(760\) 1.61744 0.933827i 0.0586706 0.0338735i
\(761\) −16.4954 + 9.52360i −0.597956 + 0.345230i −0.768237 0.640165i \(-0.778866\pi\)
0.170281 + 0.985396i \(0.445532\pi\)
\(762\) 0 0
\(763\) −9.30718 16.1205i −0.336942 0.583601i
\(764\) 5.86018 10.1501i 0.212014 0.367219i
\(765\) 0 0
\(766\) 9.72573 0.351405
\(767\) −37.0607 + 7.27900i −1.33818 + 0.262830i
\(768\) 0 0
\(769\) 13.2055 + 7.62418i 0.476201 + 0.274935i 0.718832 0.695184i \(-0.244677\pi\)
−0.242631 + 0.970119i \(0.578010\pi\)
\(770\) 0.434353 0.752321i 0.0156530 0.0271118i
\(771\) 0 0
\(772\) 23.8010i 0.856618i
\(773\) 5.77259 3.33281i 0.207626 0.119873i −0.392582 0.919717i \(-0.628418\pi\)
0.600207 + 0.799844i \(0.295085\pi\)
\(774\) 0 0
\(775\) 34.5881i 1.24244i
\(776\) −2.90793 5.03669i −0.104389 0.180807i
\(777\) 0 0
\(778\) 12.0300 + 6.94550i 0.431295 + 0.249008i
\(779\) −2.92409 −0.104766
\(780\) 0 0
\(781\) −2.46568 −0.0882289
\(782\) −14.1829 8.18852i −0.507181 0.292821i
\(783\) 0 0
\(784\) 0.500000 + 0.866025i 0.0178571 + 0.0309295i
\(785\) 0.762884i 0.0272285i
\(786\) 0 0
\(787\) 5.06001 2.92140i 0.180370 0.104137i −0.407097 0.913385i \(-0.633459\pi\)
0.587466 + 0.809249i \(0.300125\pi\)
\(788\) 10.0827i 0.359180i