Properties

Label 729.2.i.a.685.14
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.14
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.129177 + 0.0359588i) q^{2} +(-1.69694 - 1.02411i) q^{4} +(2.51593 - 0.0976297i) q^{5} +(4.08453 + 0.638809i) q^{7} +(-0.366413 - 0.388376i) q^{8} +O(q^{10})\) \(q+(0.129177 + 0.0359588i) q^{2} +(-1.69694 - 1.02411i) q^{4} +(2.51593 - 0.0976297i) q^{5} +(4.08453 + 0.638809i) q^{7} +(-0.366413 - 0.388376i) q^{8} +(0.328511 + 0.0778585i) q^{10} +(-0.654096 - 4.78883i) q^{11} +(-0.189852 + 0.276812i) q^{13} +(0.504656 + 0.229394i) q^{14} +(1.81405 + 3.44389i) q^{16} +(-1.56801 + 0.787482i) q^{17} +(0.123676 + 2.12343i) q^{19} +(-4.36937 - 2.41092i) q^{20} +(0.0877066 - 0.642126i) q^{22} +(0.620409 - 1.60690i) q^{23} +(1.33543 - 0.103798i) q^{25} +(-0.0344783 + 0.0289308i) q^{26} +(-6.27700 - 5.26703i) q^{28} +(0.238461 + 0.170442i) q^{29} +(5.27798 - 6.04789i) q^{31} +(0.336570 + 1.55378i) q^{32} +(-0.230867 + 0.0453408i) q^{34} +(10.3388 + 1.20843i) q^{35} +(6.18920 + 8.31354i) q^{37} +(-0.0603800 + 0.278745i) q^{38} +(-0.959789 - 0.941355i) q^{40} +(1.90818 - 7.40802i) q^{41} +(-0.684120 - 0.620806i) q^{43} +(-3.79432 + 8.79622i) q^{44} +(0.137925 - 0.185265i) q^{46} +(-4.38427 - 5.02381i) q^{47} +(9.60959 + 3.08119i) q^{49} +(0.176239 + 0.0346122i) q^{50} +(0.605653 - 0.275303i) q^{52} +(2.13636 - 12.1159i) q^{53} +(-2.11319 - 11.9845i) q^{55} +(-1.24853 - 1.82040i) q^{56} +(0.0246748 + 0.0305919i) q^{58} +(1.52698 - 0.623838i) q^{59} +(-0.475859 + 0.287182i) q^{61} +(0.899267 - 0.591457i) q^{62} +(0.440256 - 7.55890i) q^{64} +(-0.450631 + 0.714975i) q^{65} +(6.22983 - 4.45281i) q^{67} +(3.46728 + 0.269498i) q^{68} +(1.29208 + 0.527872i) q^{70} +(3.03543 + 10.1390i) q^{71} +(-10.8037 + 2.56052i) q^{73} +(0.500556 + 1.29647i) q^{74} +(1.96475 - 3.72999i) q^{76} +(0.387472 - 19.9780i) q^{77} +(-11.3308 + 11.1132i) q^{79} +(4.90025 + 8.48749i) q^{80} +(0.512876 - 0.888328i) q^{82} +(3.20132 + 12.4283i) q^{83} +(-3.86812 + 2.13434i) q^{85} +(-0.0660490 - 0.104794i) q^{86} +(-1.62019 + 2.00873i) q^{88} +(-2.10552 + 7.03291i) q^{89} +(-0.952288 + 1.00937i) q^{91} +(-2.69844 + 2.09145i) q^{92} +(-0.385695 - 0.806613i) q^{94} +(0.518470 + 5.33034i) q^{95} +(0.615629 + 0.0238892i) q^{97} +(1.13054 + 0.743568i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.129177 + 0.0359588i 0.0913418 + 0.0254267i 0.313542 0.949574i \(-0.398484\pi\)
−0.222200 + 0.975001i \(0.571324\pi\)
\(3\) 0 0
\(4\) −1.69694 1.02411i −0.848470 0.512054i
\(5\) 2.51593 0.0976297i 1.12516 0.0436613i 0.530534 0.847664i \(-0.321991\pi\)
0.594626 + 0.804002i \(0.297300\pi\)
\(6\) 0 0
\(7\) 4.08453 + 0.638809i 1.54381 + 0.241447i 0.868350 0.495951i \(-0.165181\pi\)
0.675458 + 0.737399i \(0.263946\pi\)
\(8\) −0.366413 0.388376i −0.129547 0.137312i
\(9\) 0 0
\(10\) 0.328511 + 0.0778585i 0.103884 + 0.0246210i
\(11\) −0.654096 4.78883i −0.197217 1.44389i −0.777198 0.629256i \(-0.783360\pi\)
0.579981 0.814630i \(-0.303060\pi\)
\(12\) 0 0
\(13\) −0.189852 + 0.276812i −0.0526556 + 0.0767737i −0.850109 0.526607i \(-0.823464\pi\)
0.797453 + 0.603381i \(0.206180\pi\)
\(14\) 0.504656 + 0.229394i 0.134875 + 0.0613082i
\(15\) 0 0
\(16\) 1.81405 + 3.44389i 0.453512 + 0.860972i
\(17\) −1.56801 + 0.787482i −0.380297 + 0.190993i −0.628670 0.777672i \(-0.716400\pi\)
0.248373 + 0.968664i \(0.420104\pi\)
\(18\) 0 0
\(19\) 0.123676 + 2.12343i 0.0283732 + 0.487149i 0.982324 + 0.187187i \(0.0599369\pi\)
−0.953951 + 0.299962i \(0.903026\pi\)
\(20\) −4.36937 2.41092i −0.977022 0.539098i
\(21\) 0 0
\(22\) 0.0877066 0.642126i 0.0186991 0.136902i
\(23\) 0.620409 1.60690i 0.129364 0.335062i −0.853035 0.521853i \(-0.825241\pi\)
0.982400 + 0.186791i \(0.0598088\pi\)
\(24\) 0 0
\(25\) 1.33543 0.103798i 0.267086 0.0207596i
\(26\) −0.0344783 + 0.0289308i −0.00676176 + 0.00567379i
\(27\) 0 0
\(28\) −6.27700 5.26703i −1.18624 0.995374i
\(29\) 0.238461 + 0.170442i 0.0442811 + 0.0316502i 0.603417 0.797426i \(-0.293805\pi\)
−0.559136 + 0.829076i \(0.688867\pi\)
\(30\) 0 0
\(31\) 5.27798 6.04789i 0.947953 1.08623i −0.0482206 0.998837i \(-0.515355\pi\)
0.996174 0.0873969i \(-0.0278548\pi\)
\(32\) 0.336570 + 1.55378i 0.0594978 + 0.274672i
\(33\) 0 0
\(34\) −0.230867 + 0.0453408i −0.0395933 + 0.00777588i
\(35\) 10.3388 + 1.20843i 1.74757 + 0.204262i
\(36\) 0 0
\(37\) 6.18920 + 8.31354i 1.01750 + 1.36674i 0.928760 + 0.370682i \(0.120876\pi\)
0.0887385 + 0.996055i \(0.471716\pi\)
\(38\) −0.0603800 + 0.278745i −0.00979493 + 0.0452185i
\(39\) 0 0
\(40\) −0.959789 0.941355i −0.151756 0.148841i
\(41\) 1.90818 7.40802i 0.298008 1.15694i −0.627625 0.778516i \(-0.715973\pi\)
0.925633 0.378422i \(-0.123533\pi\)
\(42\) 0 0
\(43\) −0.684120 0.620806i −0.104327 0.0946720i 0.618175 0.786041i \(-0.287872\pi\)
−0.722502 + 0.691369i \(0.757008\pi\)
\(44\) −3.79432 + 8.79622i −0.572015 + 1.32608i
\(45\) 0 0
\(46\) 0.137925 0.185265i 0.0203359 0.0273158i
\(47\) −4.38427 5.02381i −0.639511 0.732799i 0.338589 0.940935i \(-0.390051\pi\)
−0.978100 + 0.208136i \(0.933260\pi\)
\(48\) 0 0
\(49\) 9.60959 + 3.08119i 1.37280 + 0.440170i
\(50\) 0.176239 + 0.0346122i 0.0249240 + 0.00489491i
\(51\) 0 0
\(52\) 0.605653 0.275303i 0.0839890 0.0381777i
\(53\) 2.13636 12.1159i 0.293452 1.66425i −0.379978 0.924995i \(-0.624068\pi\)
0.673430 0.739251i \(-0.264820\pi\)
\(54\) 0 0
\(55\) −2.11319 11.9845i −0.284943 1.61599i
\(56\) −1.24853 1.82040i −0.166842 0.243261i
\(57\) 0 0
\(58\) 0.0246748 + 0.0305919i 0.00323995 + 0.00401691i
\(59\) 1.52698 0.623838i 0.198795 0.0812168i −0.276616 0.960981i \(-0.589213\pi\)
0.475411 + 0.879764i \(0.342299\pi\)
\(60\) 0 0
\(61\) −0.475859 + 0.287182i −0.0609275 + 0.0367699i −0.546836 0.837240i \(-0.684168\pi\)
0.485908 + 0.874010i \(0.338489\pi\)
\(62\) 0.899267 0.591457i 0.114207 0.0751152i
\(63\) 0 0
\(64\) 0.440256 7.55890i 0.0550320 0.944863i
\(65\) −0.450631 + 0.714975i −0.0558939 + 0.0886818i
\(66\) 0 0
\(67\) 6.22983 4.45281i 0.761094 0.543998i −0.133408 0.991061i \(-0.542592\pi\)
0.894502 + 0.447064i \(0.147530\pi\)
\(68\) 3.46728 + 0.269498i 0.420469 + 0.0326815i
\(69\) 0 0
\(70\) 1.29208 + 0.527872i 0.154433 + 0.0630927i
\(71\) 3.03543 + 10.1390i 0.360239 + 1.20328i 0.925621 + 0.378452i \(0.123544\pi\)
−0.565382 + 0.824829i \(0.691271\pi\)
\(72\) 0 0
\(73\) −10.8037 + 2.56052i −1.26448 + 0.299686i −0.807540 0.589813i \(-0.799201\pi\)
−0.456936 + 0.889500i \(0.651053\pi\)
\(74\) 0.500556 + 1.29647i 0.0581884 + 0.150712i
\(75\) 0 0
\(76\) 1.96475 3.72999i 0.225373 0.427860i
\(77\) 0.387472 19.9780i 0.0441566 2.27670i
\(78\) 0 0
\(79\) −11.3308 + 11.1132i −1.27482 + 1.25033i −0.322014 + 0.946735i \(0.604360\pi\)
−0.952801 + 0.303595i \(0.901813\pi\)
\(80\) 4.90025 + 8.48749i 0.547865 + 0.948930i
\(81\) 0 0
\(82\) 0.512876 0.888328i 0.0566377 0.0980994i
\(83\) 3.20132 + 12.4283i 0.351390 + 1.36418i 0.863105 + 0.505024i \(0.168517\pi\)
−0.511715 + 0.859155i \(0.670990\pi\)
\(84\) 0 0
\(85\) −3.86812 + 2.13434i −0.419556 + 0.231501i
\(86\) −0.0660490 0.104794i −0.00712225 0.0113002i
\(87\) 0 0
\(88\) −1.62019 + 2.00873i −0.172713 + 0.214131i
\(89\) −2.10552 + 7.03291i −0.223184 + 0.745487i 0.770908 + 0.636947i \(0.219803\pi\)
−0.994092 + 0.108540i \(0.965382\pi\)
\(90\) 0 0
\(91\) −0.952288 + 1.00937i −0.0998269 + 0.105810i
\(92\) −2.69844 + 2.09145i −0.281331 + 0.218048i
\(93\) 0 0
\(94\) −0.385695 0.806613i −0.0397814 0.0831958i
\(95\) 0.518470 + 5.33034i 0.0531939 + 0.546881i
\(96\) 0 0
\(97\) 0.615629 + 0.0238892i 0.0625076 + 0.00242558i 0.0700102 0.997546i \(-0.477697\pi\)
−0.00750258 + 0.999972i \(0.502388\pi\)
\(98\) 1.13054 + 0.743568i 0.114202 + 0.0751117i
\(99\) 0 0
\(100\) −2.37245 1.19149i −0.237245 0.119149i
\(101\) 0.234665 + 12.0992i 0.0233500 + 1.20392i 0.809966 + 0.586477i \(0.199486\pi\)
−0.786616 + 0.617443i \(0.788169\pi\)
\(102\) 0 0
\(103\) 13.0622 + 10.1240i 1.28706 + 0.997544i 0.999205 + 0.0398687i \(0.0126940\pi\)
0.287851 + 0.957675i \(0.407059\pi\)
\(104\) 0.177071 0.0276935i 0.0173633 0.00271557i
\(105\) 0 0
\(106\) 0.711641 1.48827i 0.0691207 0.144554i
\(107\) −15.6849 5.70884i −1.51632 0.551895i −0.556093 0.831120i \(-0.687700\pi\)
−0.960225 + 0.279226i \(0.909922\pi\)
\(108\) 0 0
\(109\) −9.46428 + 3.44472i −0.906514 + 0.329944i −0.752860 0.658181i \(-0.771326\pi\)
−0.153654 + 0.988125i \(0.549104\pi\)
\(110\) 0.157973 1.62411i 0.0150622 0.154853i
\(111\) 0 0
\(112\) 5.20956 + 15.2255i 0.492257 + 1.43867i
\(113\) −2.24224 + 2.03472i −0.210932 + 0.191411i −0.770624 0.637290i \(-0.780055\pi\)
0.559692 + 0.828701i \(0.310920\pi\)
\(114\) 0 0
\(115\) 1.40403 4.10342i 0.130926 0.382646i
\(116\) −0.230103 0.533440i −0.0213646 0.0495286i
\(117\) 0 0
\(118\) 0.219682 0.0256772i 0.0202234 0.00236378i
\(119\) −6.90762 + 2.21484i −0.633221 + 0.203034i
\(120\) 0 0
\(121\) −11.9080 + 3.31480i −1.08254 + 0.301346i
\(122\) −0.0717967 + 0.0199860i −0.00650017 + 0.00180944i
\(123\) 0 0
\(124\) −15.1501 + 4.85769i −1.36052 + 0.436233i
\(125\) −9.15429 + 1.06998i −0.818785 + 0.0957022i
\(126\) 0 0
\(127\) −2.74791 6.37036i −0.243837 0.565278i 0.751715 0.659488i \(-0.229227\pi\)
−0.995552 + 0.0942098i \(0.969968\pi\)
\(128\) 1.35803 3.96901i 0.120034 0.350814i
\(129\) 0 0
\(130\) −0.0839208 + 0.0761540i −0.00736034 + 0.00667915i
\(131\) 5.46948 + 15.9851i 0.477870 + 1.39663i 0.877334 + 0.479880i \(0.159320\pi\)
−0.399464 + 0.916749i \(0.630804\pi\)
\(132\) 0 0
\(133\) −0.851310 + 8.75223i −0.0738179 + 0.758915i
\(134\) 0.964867 0.351183i 0.0833518 0.0303376i
\(135\) 0 0
\(136\) 0.880377 + 0.320431i 0.0754917 + 0.0274767i
\(137\) 2.38460 4.98697i 0.203730 0.426066i −0.774789 0.632219i \(-0.782144\pi\)
0.978520 + 0.206154i \(0.0660947\pi\)
\(138\) 0 0
\(139\) 3.77746 0.590784i 0.320400 0.0501097i 0.00772616 0.999970i \(-0.497541\pi\)
0.312674 + 0.949860i \(0.398775\pi\)
\(140\) −16.3067 12.6387i −1.37817 1.06816i
\(141\) 0 0
\(142\) 0.0275191 + 1.41888i 0.00230935 + 0.119070i
\(143\) 1.44978 + 0.728109i 0.121237 + 0.0608876i
\(144\) 0 0
\(145\) 0.616593 + 0.405539i 0.0512052 + 0.0336782i
\(146\) −1.48766 0.0577279i −0.123119 0.00477760i
\(147\) 0 0
\(148\) −1.98874 20.4460i −0.163473 1.68065i
\(149\) −2.89351 6.05126i −0.237045 0.495738i 0.748926 0.662654i \(-0.230570\pi\)
−0.985971 + 0.166915i \(0.946619\pi\)
\(150\) 0 0
\(151\) 10.5579 8.18298i 0.859189 0.665922i −0.0846200 0.996413i \(-0.526968\pi\)
0.943809 + 0.330492i \(0.107215\pi\)
\(152\) 0.779373 0.826087i 0.0632155 0.0670045i
\(153\) 0 0
\(154\) 0.768436 2.56676i 0.0619224 0.206835i
\(155\) 12.6886 15.7314i 1.01917 1.26358i
\(156\) 0 0
\(157\) −6.75693 10.7206i −0.539262 0.855597i 0.460220 0.887805i \(-0.347771\pi\)
−0.999481 + 0.0322083i \(0.989746\pi\)
\(158\) −1.86329 + 1.02812i −0.148236 + 0.0817930i
\(159\) 0 0
\(160\) 0.998484 + 3.87635i 0.0789371 + 0.306453i
\(161\) 3.56058 6.16711i 0.280613 0.486036i
\(162\) 0 0
\(163\) 4.63994 + 8.03661i 0.363428 + 0.629476i 0.988523 0.151073i \(-0.0482729\pi\)
−0.625094 + 0.780549i \(0.714940\pi\)
\(164\) −10.8247 + 10.6168i −0.845266 + 0.829031i
\(165\) 0 0
\(166\) −0.0333702 + 1.72056i −0.00259003 + 0.133541i
\(167\) −4.11104 + 7.80461i −0.318121 + 0.603939i −0.990696 0.136090i \(-0.956546\pi\)
0.672575 + 0.740029i \(0.265188\pi\)
\(168\) 0 0
\(169\) 4.64173 + 12.0224i 0.357056 + 0.924799i
\(170\) −0.576419 + 0.136614i −0.0442094 + 0.0104778i
\(171\) 0 0
\(172\) 0.525138 + 1.75408i 0.0400414 + 0.133748i
\(173\) −19.5864 8.00192i −1.48913 0.608375i −0.519830 0.854270i \(-0.674005\pi\)
−0.969297 + 0.245895i \(0.920918\pi\)
\(174\) 0 0
\(175\) 5.52092 + 0.429120i 0.417342 + 0.0324384i
\(176\) 15.3056 10.9398i 1.15370 0.824618i
\(177\) 0 0
\(178\) −0.524879 + 0.832777i −0.0393413 + 0.0624193i
\(179\) −0.554070 + 9.51302i −0.0414131 + 0.711036i 0.912153 + 0.409851i \(0.134419\pi\)
−0.953566 + 0.301185i \(0.902618\pi\)
\(180\) 0 0
\(181\) −14.9396 + 9.82593i −1.11045 + 0.730356i −0.965842 0.259133i \(-0.916563\pi\)
−0.144610 + 0.989489i \(0.546193\pi\)
\(182\) −0.159309 + 0.0961436i −0.0118088 + 0.00712664i
\(183\) 0 0
\(184\) −0.851407 + 0.347838i −0.0627665 + 0.0256429i
\(185\) 16.3833 + 20.3121i 1.20452 + 1.49337i
\(186\) 0 0
\(187\) 4.79674 + 6.99382i 0.350773 + 0.511439i
\(188\) 2.29491 + 13.0151i 0.167374 + 0.949222i
\(189\) 0 0
\(190\) −0.124698 + 0.707200i −0.00904657 + 0.0513057i
\(191\) −5.16330 + 2.34701i −0.373604 + 0.169824i −0.591807 0.806080i \(-0.701585\pi\)
0.218203 + 0.975903i \(0.429980\pi\)
\(192\) 0 0
\(193\) −0.284735 0.0559201i −0.0204957 0.00402522i 0.182454 0.983214i \(-0.441596\pi\)
−0.202950 + 0.979189i \(0.565053\pi\)
\(194\) 0.0786659 + 0.0252232i 0.00564788 + 0.00181092i
\(195\) 0 0
\(196\) −13.1514 15.0699i −0.939388 1.07642i
\(197\) 8.83840 11.8720i 0.629710 0.845847i −0.366715 0.930333i \(-0.619518\pi\)
0.996425 + 0.0844863i \(0.0269249\pi\)
\(198\) 0 0
\(199\) −1.82865 + 4.23928i −0.129629 + 0.300515i −0.970653 0.240483i \(-0.922694\pi\)
0.841024 + 0.540998i \(0.181953\pi\)
\(200\) −0.529633 0.480616i −0.0374507 0.0339847i
\(201\) 0 0
\(202\) −0.404761 + 1.57138i −0.0284789 + 0.110562i
\(203\) 0.865122 + 0.848506i 0.0607197 + 0.0595535i
\(204\) 0 0
\(205\) 4.07762 18.8244i 0.284793 1.31475i
\(206\) 1.32329 + 1.77748i 0.0921977 + 0.123843i
\(207\) 0 0
\(208\) −1.29771 0.151680i −0.0899800 0.0105172i
\(209\) 10.0879 1.98119i 0.697791 0.137042i
\(210\) 0 0
\(211\) −2.80717 12.9593i −0.193253 0.892157i −0.966222 0.257712i \(-0.917031\pi\)
0.772968 0.634445i \(-0.218771\pi\)
\(212\) −16.0333 + 18.3721i −1.10117 + 1.26180i
\(213\) 0 0
\(214\) −1.82084 1.30146i −0.124470 0.0889660i
\(215\) −1.78181 1.49512i −0.121519 0.101966i
\(216\) 0 0
\(217\) 25.4215 21.3312i 1.72573 1.44806i
\(218\) −1.34643 + 0.104653i −0.0911920 + 0.00708800i
\(219\) 0 0
\(220\) −8.68749 + 22.5012i −0.585710 + 1.51703i
\(221\) 0.0797055 0.583548i 0.00536157 0.0392537i
\(222\) 0 0
\(223\) −12.8209 7.07426i −0.858549 0.473727i −0.00821212 0.999966i \(-0.502614\pi\)
−0.850337 + 0.526239i \(0.823602\pi\)
\(224\) 0.382162 + 6.56147i 0.0255343 + 0.438407i
\(225\) 0 0
\(226\) −0.362812 + 0.182211i −0.0241339 + 0.0121205i
\(227\) 0.807278 + 1.53258i 0.0535809 + 0.101721i 0.910089 0.414412i \(-0.136013\pi\)
−0.856508 + 0.516133i \(0.827371\pi\)
\(228\) 0 0
\(229\) −24.0047 10.9115i −1.58628 0.721052i −0.590012 0.807395i \(-0.700877\pi\)
−0.996265 + 0.0863431i \(0.972482\pi\)
\(230\) 0.328922 0.479580i 0.0216885 0.0316226i
\(231\) 0 0
\(232\) −0.0211799 0.155065i −0.00139053 0.0101805i
\(233\) 9.88318 + 2.34236i 0.647469 + 0.153453i 0.541213 0.840886i \(-0.317965\pi\)
0.106256 + 0.994339i \(0.466114\pi\)
\(234\) 0 0
\(235\) −11.5210 12.2116i −0.751548 0.796594i
\(236\) −3.23006 0.505173i −0.210259 0.0328840i
\(237\) 0 0
\(238\) −0.971947 + 0.0377160i −0.0630020 + 0.00244476i
\(239\) 23.4580 + 14.1570i 1.51737 + 0.915738i 0.998131 + 0.0611094i \(0.0194638\pi\)
0.519240 + 0.854629i \(0.326215\pi\)
\(240\) 0 0
\(241\) 5.09037 + 1.41700i 0.327900 + 0.0912772i 0.428211 0.903679i \(-0.359144\pi\)
−0.100311 + 0.994956i \(0.531984\pi\)
\(242\) −1.65743 −0.106543
\(243\) 0 0
\(244\) 1.10161 0.0705234
\(245\) 24.4779 + 6.81390i 1.56384 + 0.435324i
\(246\) 0 0
\(247\) −0.611271 0.368904i −0.0388942 0.0234728i
\(248\) −4.28278 + 0.166191i −0.271957 + 0.0105532i
\(249\) 0 0
\(250\) −1.22100 0.190961i −0.0772227 0.0120774i
\(251\) 11.0176 + 11.6780i 0.695427 + 0.737110i 0.974802 0.223072i \(-0.0716086\pi\)
−0.279375 + 0.960182i \(0.590127\pi\)
\(252\) 0 0
\(253\) −8.10097 1.91997i −0.509304 0.120707i
\(254\) −0.125895 0.921714i −0.00789935 0.0578335i
\(255\) 0 0
\(256\) −8.24708 + 12.0245i −0.515443 + 0.751534i
\(257\) −7.13854 3.24487i −0.445290 0.202409i 0.178599 0.983922i \(-0.442843\pi\)
−0.623889 + 0.781513i \(0.714448\pi\)
\(258\) 0 0
\(259\) 19.9692 + 37.9106i 1.24083 + 2.35565i
\(260\) 1.49691 0.751775i 0.0928342 0.0466231i
\(261\) 0 0
\(262\) 0.131722 + 2.26159i 0.00813783 + 0.139721i
\(263\) −17.4609 9.63450i −1.07668 0.594089i −0.157340 0.987545i \(-0.550292\pi\)
−0.919344 + 0.393456i \(0.871279\pi\)
\(264\) 0 0
\(265\) 4.19207 30.6914i 0.257517 1.88536i
\(266\) −0.424689 + 1.09997i −0.0260394 + 0.0674437i
\(267\) 0 0
\(268\) −15.1318 + 1.17614i −0.924322 + 0.0718440i
\(269\) −20.2280 + 16.9733i −1.23332 + 1.03488i −0.235308 + 0.971921i \(0.575610\pi\)
−0.998016 + 0.0629612i \(0.979946\pi\)
\(270\) 0 0
\(271\) 4.34296 + 3.64417i 0.263816 + 0.221368i 0.765094 0.643918i \(-0.222692\pi\)
−0.501278 + 0.865286i \(0.667137\pi\)
\(272\) −5.55644 3.97150i −0.336909 0.240808i
\(273\) 0 0
\(274\) 0.487361 0.558453i 0.0294425 0.0337374i
\(275\) −1.37057 6.32726i −0.0826485 0.381548i
\(276\) 0 0
\(277\) −5.64605 + 1.10885i −0.339238 + 0.0666242i −0.359430 0.933172i \(-0.617029\pi\)
0.0201922 + 0.999796i \(0.493572\pi\)
\(278\) 0.509204 + 0.0595175i 0.0305401 + 0.00356962i
\(279\) 0 0
\(280\) −3.31894 4.45812i −0.198345 0.266423i
\(281\) −0.615206 + 2.84010i −0.0367001 + 0.169426i −0.992006 0.126194i \(-0.959724\pi\)
0.955306 + 0.295620i \(0.0955263\pi\)
\(282\) 0 0
\(283\) 5.61545 + 5.50759i 0.333804 + 0.327392i 0.847716 0.530450i \(-0.177977\pi\)
−0.513912 + 0.857843i \(0.671804\pi\)
\(284\) 5.23253 20.3139i 0.310494 1.20541i
\(285\) 0 0
\(286\) 0.161097 + 0.146187i 0.00952584 + 0.00864424i
\(287\) 12.5263 29.0393i 0.739407 1.71414i
\(288\) 0 0
\(289\) −8.31318 + 11.1665i −0.489011 + 0.656855i
\(290\) 0.0650667 + 0.0745582i 0.00382085 + 0.00437821i
\(291\) 0 0
\(292\) 20.9555 + 6.71910i 1.22633 + 0.393205i
\(293\) −15.3525 3.01514i −0.896905 0.176146i −0.277044 0.960857i \(-0.589355\pi\)
−0.619862 + 0.784711i \(0.712811\pi\)
\(294\) 0 0
\(295\) 3.78087 1.71861i 0.220131 0.100062i
\(296\) 0.960969 5.44993i 0.0558552 0.316771i
\(297\) 0 0
\(298\) −0.156178 0.885729i −0.00904715 0.0513089i
\(299\) 0.327022 + 0.476810i 0.0189122 + 0.0275746i
\(300\) 0 0
\(301\) −2.39774 2.97273i −0.138203 0.171345i
\(302\) 1.65808 0.677402i 0.0954120 0.0389801i
\(303\) 0 0
\(304\) −7.08850 + 4.27793i −0.406554 + 0.245356i
\(305\) −1.16919 + 0.768990i −0.0669478 + 0.0440323i
\(306\) 0 0
\(307\) −0.800802 + 13.7492i −0.0457042 + 0.784710i 0.895122 + 0.445821i \(0.147088\pi\)
−0.940826 + 0.338889i \(0.889949\pi\)
\(308\) −21.1171 + 33.5046i −1.20326 + 1.90910i
\(309\) 0 0
\(310\) 2.20475 1.57586i 0.125222 0.0895030i
\(311\) 32.2743 + 2.50856i 1.83011 + 0.142247i 0.945819 0.324694i \(-0.105261\pi\)
0.884288 + 0.466941i \(0.154644\pi\)
\(312\) 0 0
\(313\) 28.7879 + 11.7611i 1.62719 + 0.664779i 0.994016 0.109233i \(-0.0348395\pi\)
0.633171 + 0.774012i \(0.281753\pi\)
\(314\) −0.487338 1.62782i −0.0275021 0.0918634i
\(315\) 0 0
\(316\) 30.6088 7.25442i 1.72188 0.408093i
\(317\) 3.17460 + 8.22242i 0.178303 + 0.461817i 0.993006 0.118061i \(-0.0376679\pi\)
−0.814703 + 0.579879i \(0.803100\pi\)
\(318\) 0 0
\(319\) 0.660240 1.25343i 0.0369663 0.0701789i
\(320\) 0.369682 19.0607i 0.0206658 1.06553i
\(321\) 0 0
\(322\) 0.681706 0.668613i 0.0379900 0.0372603i
\(323\) −1.86609 3.23216i −0.103832 0.179842i
\(324\) 0 0
\(325\) −0.224802 + 0.389369i −0.0124698 + 0.0215983i
\(326\) 0.310385 + 1.20499i 0.0171907 + 0.0667382i
\(327\) 0 0
\(328\) −3.57628 + 1.97331i −0.197467 + 0.108958i
\(329\) −14.6984 23.3206i −0.810351 1.28571i
\(330\) 0 0
\(331\) 5.89935 7.31404i 0.324257 0.402016i −0.589834 0.807525i \(-0.700807\pi\)
0.914091 + 0.405509i \(0.132906\pi\)
\(332\) 7.29546 24.3685i 0.400390 1.33740i
\(333\) 0 0
\(334\) −0.811695 + 0.860346i −0.0444140 + 0.0470760i
\(335\) 15.2391 11.8112i 0.832601 0.645315i
\(336\) 0 0
\(337\) 2.46933 + 5.16416i 0.134513 + 0.281310i 0.958392 0.285456i \(-0.0921451\pi\)
−0.823879 + 0.566766i \(0.808194\pi\)
\(338\) 0.167293 + 1.71992i 0.00909954 + 0.0935515i
\(339\) 0 0
\(340\) 8.74976 + 0.339531i 0.474522 + 0.0184136i
\(341\) −32.4146 21.3194i −1.75535 1.15451i
\(342\) 0 0
\(343\) 11.4213 + 5.73600i 0.616693 + 0.309715i
\(344\) 0.00956497 + 0.493167i 0.000515709 + 0.0265898i
\(345\) 0 0
\(346\) −2.24237 1.73797i −0.120550 0.0934336i
\(347\) −18.4122 + 2.87961i −0.988416 + 0.154585i −0.628006 0.778208i \(-0.716129\pi\)
−0.360410 + 0.932794i \(0.617363\pi\)
\(348\) 0 0
\(349\) 6.22793 13.0246i 0.333373 0.697191i −0.665411 0.746477i \(-0.731744\pi\)
0.998785 + 0.0492855i \(0.0156944\pi\)
\(350\) 0.697744 + 0.253958i 0.0372960 + 0.0135746i
\(351\) 0 0
\(352\) 7.22064 2.62810i 0.384861 0.140078i
\(353\) −1.66478 + 17.1154i −0.0886072 + 0.910962i 0.840662 + 0.541560i \(0.182166\pi\)
−0.929270 + 0.369402i \(0.879562\pi\)
\(354\) 0 0
\(355\) 8.62681 + 25.2128i 0.457863 + 1.33816i
\(356\) 10.7754 9.77815i 0.571095 0.518241i
\(357\) 0 0
\(358\) −0.413650 + 1.20894i −0.0218621 + 0.0638943i
\(359\) 5.03723 + 11.6776i 0.265855 + 0.616320i 0.997889 0.0649478i \(-0.0206881\pi\)
−0.732034 + 0.681268i \(0.761429\pi\)
\(360\) 0 0
\(361\) 14.3779 1.68053i 0.756730 0.0884490i
\(362\) −2.28318 + 0.732071i −0.120001 + 0.0384768i
\(363\) 0 0
\(364\) 2.64968 0.737588i 0.138881 0.0386601i
\(365\) −26.9314 + 7.49686i −1.40965 + 0.392404i
\(366\) 0 0
\(367\) −3.89388 + 1.24852i −0.203259 + 0.0651724i −0.405212 0.914223i \(-0.632802\pi\)
0.201953 + 0.979395i \(0.435271\pi\)
\(368\) 6.65943 0.778376i 0.347147 0.0405756i
\(369\) 0 0
\(370\) 1.38594 + 3.21297i 0.0720516 + 0.167034i
\(371\) 16.4658 48.1231i 0.854861 2.49842i
\(372\) 0 0
\(373\) −13.4603 + 12.2146i −0.696949 + 0.632447i −0.941431 0.337207i \(-0.890518\pi\)
0.244482 + 0.969654i \(0.421382\pi\)
\(374\) 0.368138 + 1.07592i 0.0190360 + 0.0556347i
\(375\) 0 0
\(376\) −0.344672 + 3.54354i −0.0177751 + 0.182744i
\(377\) −0.0924527 + 0.0336500i −0.00476156 + 0.00173306i
\(378\) 0 0
\(379\) 5.06892 + 1.84493i 0.260373 + 0.0947679i 0.468908 0.883247i \(-0.344647\pi\)
−0.208536 + 0.978015i \(0.566870\pi\)
\(380\) 4.57903 9.57624i 0.234900 0.491251i
\(381\) 0 0
\(382\) −0.751375 + 0.117513i −0.0384437 + 0.00601248i
\(383\) 12.8134 + 9.93117i 0.654736 + 0.507459i 0.884953 0.465680i \(-0.154190\pi\)
−0.230217 + 0.973139i \(0.573943\pi\)
\(384\) 0 0
\(385\) −0.975588 50.3011i −0.0497206 2.56358i
\(386\) −0.0347703 0.0174623i −0.00176976 0.000888808i
\(387\) 0 0
\(388\) −1.02022 0.671009i −0.0517938 0.0340653i
\(389\) 7.24458 + 0.281123i 0.367315 + 0.0142535i 0.221772 0.975099i \(-0.428816\pi\)
0.145543 + 0.989352i \(0.453507\pi\)
\(390\) 0 0
\(391\) 0.292600 + 3.00819i 0.0147974 + 0.152131i
\(392\) −2.32442 4.86112i −0.117401 0.245524i
\(393\) 0 0
\(394\) 1.56862 1.21577i 0.0790259 0.0612497i
\(395\) −27.4226 + 29.0662i −1.37978 + 1.46248i
\(396\) 0 0
\(397\) −0.582715 + 1.94640i −0.0292456 + 0.0976872i −0.971366 0.237587i \(-0.923644\pi\)
0.942121 + 0.335274i \(0.108829\pi\)
\(398\) −0.388658 + 0.481861i −0.0194817 + 0.0241535i
\(399\) 0 0
\(400\) 2.78001 + 4.41078i 0.139000 + 0.220539i
\(401\) −24.1889 + 13.3469i −1.20794 + 0.666511i −0.953737 0.300641i \(-0.902799\pi\)
−0.254199 + 0.967152i \(0.581812\pi\)
\(402\) 0 0
\(403\) 0.672090 + 2.60921i 0.0334792 + 0.129974i
\(404\) 11.9927 20.7720i 0.596661 1.03345i
\(405\) 0 0
\(406\) 0.0812425 + 0.140716i 0.00403200 + 0.00698362i
\(407\) 35.7638 35.0769i 1.77274 1.73870i
\(408\) 0 0
\(409\) 0.625129 32.2315i 0.0309107 1.59375i −0.588381 0.808584i \(-0.700234\pi\)
0.619291 0.785161i \(-0.287420\pi\)
\(410\) 1.20364 2.28505i 0.0594434 0.112850i
\(411\) 0 0
\(412\) −11.7977 30.5569i −0.581232 1.50543i
\(413\) 6.63550 1.57264i 0.326511 0.0773846i
\(414\) 0 0
\(415\) 9.26767 + 30.9562i 0.454932 + 1.51958i
\(416\) −0.494003 0.201823i −0.0242205 0.00989517i
\(417\) 0 0
\(418\) 1.37436 + 0.106824i 0.0672220 + 0.00522491i
\(419\) −0.903935 + 0.646094i −0.0441601 + 0.0315638i −0.603358 0.797471i \(-0.706171\pi\)
0.559198 + 0.829034i \(0.311109\pi\)
\(420\) 0 0
\(421\) 10.6385 16.8791i 0.518488 0.822637i −0.480019 0.877258i \(-0.659370\pi\)
0.998507 + 0.0546211i \(0.0173951\pi\)
\(422\) 0.103381 1.77499i 0.00503252 0.0864050i
\(423\) 0 0
\(424\) −5.48831 + 3.60972i −0.266536 + 0.175303i
\(425\) −2.01223 + 1.21438i −0.0976073 + 0.0589063i
\(426\) 0 0
\(427\) −2.12712 + 0.869023i −0.102938 + 0.0420550i
\(428\) 20.7699 + 25.7506i 1.00395 + 1.24470i
\(429\) 0 0
\(430\) −0.176406 0.257206i −0.00850705 0.0124036i
\(431\) −6.21196 35.2298i −0.299220 1.69696i −0.649539 0.760329i \(-0.725038\pi\)
0.350319 0.936631i \(-0.386073\pi\)
\(432\) 0 0
\(433\) −2.32585 + 13.1905i −0.111773 + 0.633897i 0.876524 + 0.481357i \(0.159856\pi\)
−0.988297 + 0.152539i \(0.951255\pi\)
\(434\) 4.05092 1.84137i 0.194450 0.0883884i
\(435\) 0 0
\(436\) 19.5881 + 3.84697i 0.938099 + 0.184237i
\(437\) 3.48887 + 1.11866i 0.166895 + 0.0535128i
\(438\) 0 0
\(439\) 9.18898 + 10.5294i 0.438566 + 0.502541i 0.929585 0.368608i \(-0.120166\pi\)
−0.491019 + 0.871149i \(0.663375\pi\)
\(440\) −3.88019 + 5.21200i −0.184981 + 0.248472i
\(441\) 0 0
\(442\) 0.0312798 0.0725147i 0.00148783 0.00344917i
\(443\) 18.7432 + 17.0085i 0.890516 + 0.808100i 0.982229 0.187685i \(-0.0600986\pi\)
−0.0917134 + 0.995785i \(0.529234\pi\)
\(444\) 0 0
\(445\) −4.61072 + 17.8999i −0.218569 + 0.848537i
\(446\) −1.40178 1.37485i −0.0663760 0.0651012i
\(447\) 0 0
\(448\) 6.62694 30.5934i 0.313093 1.44540i
\(449\) −3.75326 5.04150i −0.177127 0.237923i 0.704689 0.709516i \(-0.251086\pi\)
−0.881816 + 0.471593i \(0.843679\pi\)
\(450\) 0 0
\(451\) −36.7239 4.29240i −1.72926 0.202121i
\(452\) 5.88873 1.15651i 0.276982 0.0543976i
\(453\) 0 0
\(454\) 0.0491718 + 0.227003i 0.00230775 + 0.0106538i
\(455\) −2.29735 + 2.63247i −0.107701 + 0.123412i
\(456\) 0 0
\(457\) −24.3755 17.4226i −1.14024 0.814993i −0.155294 0.987868i \(-0.549632\pi\)
−0.984944 + 0.172876i \(0.944694\pi\)
\(458\) −2.70849 2.27269i −0.126559 0.106196i
\(459\) 0 0
\(460\) −6.58490 + 5.52539i −0.307023 + 0.257623i
\(461\) 15.9948 1.24321i 0.744952 0.0579022i 0.300595 0.953752i \(-0.402815\pi\)
0.444357 + 0.895850i \(0.353432\pi\)
\(462\) 0 0
\(463\) −0.921713 + 2.38730i −0.0428356 + 0.110947i −0.952651 0.304067i \(-0.901655\pi\)
0.909815 + 0.415014i \(0.136223\pi\)
\(464\) −0.154402 + 1.13042i −0.00716793 + 0.0524786i
\(465\) 0 0
\(466\) 1.19245 + 0.657966i 0.0552391 + 0.0304797i
\(467\) −1.07208 18.4068i −0.0496098 0.851767i −0.927713 0.373295i \(-0.878228\pi\)
0.878103 0.478472i \(-0.158809\pi\)
\(468\) 0 0
\(469\) 28.2904 14.2080i 1.30633 0.656064i
\(470\) −1.04913 1.99173i −0.0483929 0.0918717i
\(471\) 0 0
\(472\) −0.801788 0.364457i −0.0369053 0.0167755i
\(473\) −2.52545 + 3.68220i −0.116120 + 0.169308i
\(474\) 0 0
\(475\) 0.385568 + 2.82286i 0.0176911 + 0.129522i
\(476\) 13.9901 + 3.31571i 0.641233 + 0.151975i
\(477\) 0 0
\(478\) 2.52116 + 2.67227i 0.115315 + 0.122227i
\(479\) −16.6909 2.61040i −0.762625 0.119272i −0.238766 0.971077i \(-0.576743\pi\)
−0.523859 + 0.851805i \(0.675508\pi\)
\(480\) 0 0
\(481\) −3.47632 + 0.134897i −0.158506 + 0.00615077i
\(482\) 0.606604 + 0.366088i 0.0276301 + 0.0166748i
\(483\) 0 0
\(484\) 23.6018 + 6.57001i 1.07281 + 0.298637i
\(485\) 1.55121 0.0704370
\(486\) 0 0
\(487\) 24.3790 1.10472 0.552359 0.833606i \(-0.313728\pi\)
0.552359 + 0.833606i \(0.313728\pi\)
\(488\) 0.285896 + 0.0795845i 0.0129419 + 0.00360262i
\(489\) 0 0
\(490\) 2.91696 + 1.76039i 0.131775 + 0.0795265i
\(491\) −38.0608 + 1.47693i −1.71766 + 0.0666531i −0.878652 0.477464i \(-0.841556\pi\)
−0.839010 + 0.544117i \(0.816865\pi\)
\(492\) 0 0
\(493\) −0.508128 0.0794698i −0.0228850 0.00357914i
\(494\) −0.0656966 0.0696344i −0.00295583 0.00313300i
\(495\) 0 0
\(496\) 30.4028 + 7.20559i 1.36512 + 0.323540i
\(497\) 5.92139 + 43.3523i 0.265611 + 1.94461i
\(498\) 0 0
\(499\) 21.8302 31.8292i 0.977254 1.42487i 0.0732667 0.997312i \(-0.476658\pi\)
0.903987 0.427559i \(-0.140626\pi\)
\(500\) 16.6301 + 7.55929i 0.743719 + 0.338062i
\(501\) 0 0
\(502\) 1.00330 + 1.90471i 0.0447793 + 0.0850114i
\(503\) −15.5388 + 7.80390i −0.692843 + 0.347959i −0.760126 0.649775i \(-0.774863\pi\)
0.0672838 + 0.997734i \(0.478567\pi\)
\(504\) 0 0
\(505\) 1.77165 + 30.4180i 0.0788373 + 1.35358i
\(506\) −0.977418 0.539316i −0.0434515 0.0239755i
\(507\) 0 0
\(508\) −1.86091 + 13.6243i −0.0825645 + 0.604479i
\(509\) 4.09579 10.6084i 0.181543 0.470207i −0.812001 0.583656i \(-0.801622\pi\)
0.993544 + 0.113449i \(0.0361897\pi\)
\(510\) 0 0
\(511\) −45.7637 + 3.55704i −2.02447 + 0.157354i
\(512\) −7.92470 + 6.64961i −0.350225 + 0.293874i
\(513\) 0 0
\(514\) −0.805452 0.675855i −0.0355270 0.0298107i
\(515\) 33.8520 + 24.1960i 1.49170 + 1.06620i
\(516\) 0 0
\(517\) −21.1905 + 24.2816i −0.931955 + 1.06790i
\(518\) 1.21634 + 5.61524i 0.0534428 + 0.246720i
\(519\) 0 0
\(520\) 0.442796 0.0869624i 0.0194179 0.00381355i
\(521\) −2.84600 0.332649i −0.124685 0.0145736i 0.0535213 0.998567i \(-0.482955\pi\)
−0.178207 + 0.983993i \(0.557030\pi\)
\(522\) 0 0
\(523\) −6.53580 8.77910i −0.285791 0.383883i 0.635924 0.771751i \(-0.280619\pi\)
−0.921715 + 0.387868i \(0.873212\pi\)
\(524\) 7.08915 32.7272i 0.309691 1.42969i
\(525\) 0 0
\(526\) −1.90909 1.87243i −0.0832404 0.0816416i
\(527\) −3.51329 + 13.6394i −0.153042 + 0.594144i
\(528\) 0 0
\(529\) 14.8353 + 13.4623i 0.645013 + 0.585318i
\(530\) 1.64514 3.81387i 0.0714605 0.165664i
\(531\) 0 0
\(532\) 10.4079 13.9802i 0.451238 0.606118i
\(533\) 1.68835 + 1.93464i 0.0731307 + 0.0837985i
\(534\) 0 0
\(535\) −40.0196 12.8318i −1.73020 0.554765i
\(536\) −4.01206 0.787942i −0.173294 0.0340339i
\(537\) 0 0
\(538\) −3.22333 + 1.46518i −0.138968 + 0.0631686i
\(539\) 8.46971 48.0341i 0.364816 2.06897i
\(540\) 0 0
\(541\) −5.70382 32.3479i −0.245226 1.39075i −0.819967 0.572411i \(-0.806008\pi\)
0.574741 0.818336i \(-0.305103\pi\)
\(542\) 0.429969 + 0.626910i 0.0184688 + 0.0269281i
\(543\) 0 0
\(544\) −1.75132 2.17130i −0.0750872 0.0930935i
\(545\) −23.4752 + 9.59068i −1.00557 + 0.410820i
\(546\) 0 0
\(547\) 37.3642 22.5494i 1.59758 0.964144i 0.612819 0.790223i \(-0.290035\pi\)
0.984760 0.173920i \(-0.0556435\pi\)
\(548\) −9.15373 + 6.02050i −0.391028 + 0.257183i
\(549\) 0 0
\(550\) 0.0504748 0.866619i 0.00215225 0.0369527i
\(551\) −0.332430 + 0.527435i −0.0141620 + 0.0224695i
\(552\) 0 0
\(553\) −53.3802 + 38.1539i −2.26996 + 1.62247i
\(554\) −0.769211 0.0597878i −0.0326806 0.00254014i
\(555\) 0 0
\(556\) −7.01516 2.86601i −0.297509 0.121546i
\(557\) 0.143024 + 0.477734i 0.00606013 + 0.0202423i 0.960966 0.276666i \(-0.0892296\pi\)
−0.954906 + 0.296908i \(0.904044\pi\)
\(558\) 0 0
\(559\) 0.301728 0.0715109i 0.0127617 0.00302459i
\(560\) 14.5934 + 37.7978i 0.616682 + 1.59725i
\(561\) 0 0
\(562\) −0.181597 + 0.344754i −0.00766021 + 0.0145425i
\(563\) −0.123215 + 6.35296i −0.00519291 + 0.267745i 0.988212 + 0.153089i \(0.0489222\pi\)
−0.993405 + 0.114656i \(0.963423\pi\)
\(564\) 0 0
\(565\) −5.44268 + 5.33814i −0.228975 + 0.224577i
\(566\) 0.527339 + 0.913378i 0.0221657 + 0.0383921i
\(567\) 0 0
\(568\) 2.82553 4.89396i 0.118557 0.205346i
\(569\) −4.20744 16.3343i −0.176385 0.684768i −0.994036 0.109054i \(-0.965218\pi\)
0.817651 0.575714i \(-0.195276\pi\)
\(570\) 0 0
\(571\) 12.9031 7.11965i 0.539979 0.297948i −0.189580 0.981865i \(-0.560713\pi\)
0.729560 + 0.683917i \(0.239725\pi\)
\(572\) −1.71454 2.72030i −0.0716883 0.113741i
\(573\) 0 0
\(574\) 2.66233 3.30077i 0.111124 0.137772i
\(575\) 0.661721 2.21030i 0.0275957 0.0921759i
\(576\) 0 0
\(577\) −5.17676 + 5.48704i −0.215511 + 0.228429i −0.826106 0.563515i \(-0.809449\pi\)
0.610595 + 0.791943i \(0.290930\pi\)
\(578\) −1.47541 + 1.14353i −0.0613688 + 0.0475644i
\(579\) 0 0
\(580\) −0.631005 1.31963i −0.0262010 0.0547948i
\(581\) 5.13658 + 52.8087i 0.213101 + 2.19087i
\(582\) 0 0
\(583\) −59.4183 2.30570i −2.46086 0.0954924i
\(584\) 4.95306 + 3.25768i 0.204959 + 0.134804i
\(585\) 0 0
\(586\) −1.87477 0.941546i −0.0774461 0.0388949i
\(587\) 0.0591577 + 3.05016i 0.00244170 + 0.125893i 0.999049 + 0.0435938i \(0.0138807\pi\)
−0.996608 + 0.0822995i \(0.973774\pi\)
\(588\) 0 0
\(589\) 13.4950 + 10.4594i 0.556054 + 0.430974i
\(590\) 0.550199 0.0860496i 0.0226513 0.00354261i
\(591\) 0 0
\(592\) −17.4034 + 36.3961i −0.715274 + 1.49587i
\(593\) 26.8460 + 9.77113i 1.10243 + 0.401252i 0.828212 0.560415i \(-0.189358\pi\)
0.274220 + 0.961667i \(0.411580\pi\)
\(594\) 0 0
\(595\) −17.1629 + 6.24678i −0.703610 + 0.256093i
\(596\) −1.28704 + 13.2319i −0.0527191 + 0.541999i
\(597\) 0 0
\(598\) 0.0250982 + 0.0733521i 0.00102634 + 0.00299959i
\(599\) 3.25471 2.95350i 0.132984 0.120677i −0.602802 0.797891i \(-0.705949\pi\)
0.735786 + 0.677215i \(0.236813\pi\)
\(600\) 0 0
\(601\) −0.0226431 + 0.0661770i −0.000923632 + 0.00269942i −0.946609 0.322384i \(-0.895516\pi\)
0.945685 + 0.325083i \(0.105392\pi\)
\(602\) −0.202836 0.470227i −0.00826698 0.0191650i
\(603\) 0 0
\(604\) −26.2964 + 3.07360i −1.06998 + 0.125063i
\(605\) −29.6360 + 9.50240i −1.20487 + 0.386328i
\(606\) 0 0
\(607\) 0.798015 0.222143i 0.0323904 0.00901650i −0.251939 0.967743i \(-0.581068\pi\)
0.284330 + 0.958726i \(0.408229\pi\)
\(608\) −3.25772 + 0.906849i −0.132118 + 0.0367776i
\(609\) 0 0
\(610\) −0.178685 + 0.0572929i −0.00723473 + 0.00231972i
\(611\) 2.22301 0.259833i 0.0899335 0.0105117i
\(612\) 0 0
\(613\) −10.6245 24.6303i −0.429119 0.994810i −0.986381 0.164474i \(-0.947407\pi\)
0.557262 0.830337i \(-0.311852\pi\)
\(614\) −0.597851 + 1.74729i −0.0241273 + 0.0705147i
\(615\) 0 0
\(616\) −7.90093 + 7.16971i −0.318338 + 0.288876i
\(617\) −9.61763 28.1086i −0.387191 1.13161i −0.951924 0.306335i \(-0.900897\pi\)
0.564733 0.825274i \(-0.308979\pi\)
\(618\) 0 0
\(619\) 2.30241 23.6708i 0.0925417 0.951412i −0.827990 0.560743i \(-0.810515\pi\)
0.920531 0.390668i \(-0.127756\pi\)
\(620\) −37.6424 + 13.7007i −1.51176 + 0.550235i
\(621\) 0 0
\(622\) 4.07888 + 1.48459i 0.163548 + 0.0595267i
\(623\) −13.0927 + 27.3811i −0.524549 + 1.09700i
\(624\) 0 0
\(625\) −29.5440 + 4.62060i −1.18176 + 0.184824i
\(626\) 3.29581 + 2.55444i 0.131727 + 0.102096i
\(627\) 0 0
\(628\) 0.487048 + 25.1120i 0.0194353 + 1.00208i
\(629\) −16.2515 8.16179i −0.647988 0.325432i
\(630\) 0 0
\(631\) 28.0854 + 18.4720i 1.11806 + 0.735360i 0.967407 0.253226i \(-0.0814917\pi\)
0.150654 + 0.988587i \(0.451862\pi\)
\(632\) 8.46785 + 0.328591i 0.336833 + 0.0130706i
\(633\) 0 0
\(634\) 0.114416 + 1.17630i 0.00454405 + 0.0467169i
\(635\) −7.53549 15.7591i −0.299037 0.625382i
\(636\) 0 0
\(637\) −2.67731 + 2.07508i −0.106079 + 0.0822175i
\(638\) 0.130360 0.138173i 0.00516099 0.00547033i
\(639\) 0 0
\(640\) 3.02923 10.1183i 0.119741 0.399963i
\(641\) 2.90631 3.60326i 0.114793 0.142320i −0.717709 0.696343i \(-0.754809\pi\)
0.832502 + 0.554023i \(0.186908\pi\)
\(642\) 0 0
\(643\) −3.42985 5.44183i −0.135260 0.214605i 0.771524 0.636200i \(-0.219495\pi\)
−0.906784 + 0.421596i \(0.861470\pi\)
\(644\) −12.3579 + 6.81879i −0.486969 + 0.268698i
\(645\) 0 0
\(646\) −0.124831 0.484622i −0.00491140 0.0190672i
\(647\) 5.92926 10.2698i 0.233103 0.403746i −0.725617 0.688099i \(-0.758445\pi\)
0.958720 + 0.284353i \(0.0917787\pi\)
\(648\) 0 0
\(649\) −3.98624 6.90437i −0.156474 0.271020i
\(650\) −0.0430405 + 0.0422138i −0.00168819 + 0.00165576i
\(651\) 0 0
\(652\) 0.356663 18.3894i 0.0139680 0.720186i
\(653\) 0.466091 0.884852i 0.0182396 0.0346269i −0.875473 0.483268i \(-0.839450\pi\)
0.893712 + 0.448641i \(0.148092\pi\)
\(654\) 0 0
\(655\) 15.3215 + 39.6836i 0.598659 + 1.55057i
\(656\) 28.9739 6.86694i 1.13124 0.268109i
\(657\) 0 0
\(658\) −1.06011 3.54102i −0.0413275 0.138043i
\(659\) −2.08796 0.853024i −0.0813353 0.0332291i 0.337167 0.941445i \(-0.390531\pi\)
−0.418502 + 0.908216i \(0.637445\pi\)
\(660\) 0 0
\(661\) −13.7052 1.06526i −0.533072 0.0414336i −0.191864 0.981421i \(-0.561453\pi\)
−0.341208 + 0.939988i \(0.610836\pi\)
\(662\) 1.02506 0.732671i 0.0398402 0.0284761i
\(663\) 0 0
\(664\) 3.65383 5.79720i 0.141796 0.224975i
\(665\) −1.28736 + 22.1032i −0.0499218 + 0.857124i
\(666\) 0 0
\(667\) 0.421826 0.277439i 0.0163332 0.0107425i
\(668\) 14.9689 9.03381i 0.579166 0.349528i
\(669\) 0 0
\(670\) 2.39326 0.977752i 0.0924595 0.0377739i
\(671\) 1.68652 + 2.09096i 0.0651076 + 0.0807207i
\(672\) 0 0
\(673\) −2.52388 3.67991i −0.0972885 0.141850i 0.772975 0.634436i \(-0.218768\pi\)
−0.870264 + 0.492586i \(0.836052\pi\)
\(674\) 0.133283 + 0.755883i 0.00513385 + 0.0291155i
\(675\) 0 0
\(676\) 4.43549 25.1549i 0.170596 0.967496i
\(677\) −13.8386 + 6.29042i −0.531861 + 0.241760i −0.661692 0.749776i \(-0.730161\pi\)
0.129831 + 0.991536i \(0.458556\pi\)
\(678\) 0 0
\(679\) 2.49930 + 0.490846i 0.0959141 + 0.0188369i
\(680\) 2.24626 + 0.720233i 0.0861400 + 0.0276197i
\(681\) 0 0
\(682\) −3.42059 3.91957i −0.130981 0.150088i
\(683\) −12.3690 + 16.6145i −0.473288 + 0.635736i −0.973096 0.230400i \(-0.925997\pi\)
0.499808 + 0.866136i \(0.333404\pi\)
\(684\) 0 0
\(685\) 5.51263 12.7797i 0.210627 0.488287i
\(686\) 1.26911 + 1.15165i 0.0484548 + 0.0439704i
\(687\) 0 0
\(688\) 0.896958 3.48221i 0.0341962 0.132758i
\(689\) 2.94823 + 2.89160i 0.112319 + 0.110161i
\(690\) 0 0
\(691\) 1.89085 8.72915i 0.0719315 0.332073i −0.927161 0.374663i \(-0.877759\pi\)
0.999093 + 0.0425902i \(0.0135610\pi\)
\(692\) 25.0421 + 33.6374i 0.951958 + 1.27870i
\(693\) 0 0
\(694\) −2.48197 0.290101i −0.0942143 0.0110121i
\(695\) 9.44617 1.85517i 0.358314 0.0703705i
\(696\) 0 0
\(697\) 2.84164 + 13.1185i 0.107635 + 0.496898i
\(698\) 1.27285 1.45853i 0.0481782 0.0552061i
\(699\) 0 0
\(700\) −8.92920 6.38221i −0.337492 0.241225i
\(701\) 12.6180 + 10.5878i 0.476576 + 0.399895i 0.849186 0.528093i \(-0.177093\pi\)
−0.372611 + 0.927988i \(0.621537\pi\)
\(702\) 0 0
\(703\) −16.8878 + 14.1705i −0.636934 + 0.534451i
\(704\) −36.4863 + 2.83594i −1.37513 + 0.106883i
\(705\) 0 0
\(706\) −0.830501 + 2.15105i −0.0312563 + 0.0809559i
\(707\) −6.77062 + 49.5697i −0.254635 + 1.86426i
\(708\) 0 0
\(709\) −3.11614 1.71942i −0.117029 0.0645740i 0.423518 0.905888i \(-0.360795\pi\)
−0.540547 + 0.841314i \(0.681783\pi\)
\(710\) 0.207761 + 3.56712i 0.00779713 + 0.133872i
\(711\) 0 0
\(712\) 3.50290 1.75922i 0.131277 0.0659297i
\(713\) −6.44385 12.2333i −0.241324 0.458142i
\(714\) 0 0
\(715\) 3.71865 + 1.69033i 0.139070 + 0.0632149i
\(716\) 10.6826 15.5756i 0.399227 0.582087i
\(717\) 0 0
\(718\) 0.230780 + 1.68961i 0.00861263 + 0.0630556i
\(719\) 12.5713 + 2.97946i 0.468832 + 0.111115i 0.458240 0.888829i \(-0.348480\pi\)
0.0105923 + 0.999944i \(0.496628\pi\)
\(720\) 0 0
\(721\) 46.8857 + 49.6959i 1.74611 + 1.85077i
\(722\) 1.91772 + 0.299925i 0.0713700 + 0.0111621i
\(723\) 0 0
\(724\) 35.4144 1.37424i 1.31617 0.0510733i
\(725\) 0.336140 + 0.202861i 0.0124839 + 0.00753409i
\(726\) 0 0
\(727\) 36.1680 + 10.0680i 1.34140 + 0.373403i 0.863205 0.504853i \(-0.168453\pi\)
0.478190 + 0.878256i \(0.341293\pi\)
\(728\) 0.740945 0.0274612
\(729\) 0 0
\(730\) −3.74849 −0.138738
\(731\) 1.56158 + 0.434695i 0.0577571 + 0.0160778i
\(732\) 0 0
\(733\) 15.7084 + 9.48006i 0.580203 + 0.350154i 0.776235 0.630443i \(-0.217127\pi\)
−0.196033 + 0.980597i \(0.562806\pi\)
\(734\) −0.547894 + 0.0212608i −0.0202232 + 0.000784750i
\(735\) 0 0
\(736\) 2.70558 + 0.423145i 0.0997290 + 0.0155973i
\(737\) −25.3987 26.9210i −0.935571 0.991648i
\(738\) 0 0
\(739\) −4.96243 1.17612i −0.182546 0.0432642i 0.138326 0.990387i \(-0.455828\pi\)
−0.320872 + 0.947123i \(0.603976\pi\)
\(740\) −6.99967 51.2466i −0.257313 1.88386i
\(741\) 0 0
\(742\) 3.85744 5.62429i 0.141611 0.206474i
\(743\) −32.0122 14.5513i −1.17441 0.533836i −0.270988 0.962583i \(-0.587351\pi\)
−0.903425 + 0.428746i \(0.858955\pi\)
\(744\) 0 0
\(745\) −7.87066 14.9421i −0.288359 0.547436i
\(746\) −2.17798 + 1.09382i −0.0797416 + 0.0400477i
\(747\) 0 0
\(748\) −0.977352 16.7805i −0.0357355 0.613555i
\(749\) −60.4187 33.3376i −2.20765 1.21813i
\(750\) 0 0
\(751\) −2.10247 + 15.3928i −0.0767203 + 0.561692i 0.911803 + 0.410627i \(0.134690\pi\)
−0.988524 + 0.151065i \(0.951730\pi\)
\(752\) 9.34817 24.2124i 0.340893 0.882934i
\(753\) 0 0
\(754\) −0.0131528 + 0.00102231i −0.000478995 + 3.72304e-5i
\(755\) 25.7641 21.6186i 0.937650 0.786782i
\(756\) 0 0
\(757\) −18.8351 15.8045i −0.684572 0.574424i 0.232766 0.972533i \(-0.425222\pi\)
−0.917338 + 0.398109i \(0.869667\pi\)
\(758\) 0.588445 + 0.420595i 0.0213733 + 0.0152767i
\(759\) 0 0
\(760\) 1.88020 2.15447i 0.0682020 0.0781508i
\(761\) −6.02516 27.8152i −0.218412 1.00830i −0.946471 0.322788i \(-0.895380\pi\)
0.728059 0.685514i \(-0.240423\pi\)
\(762\) 0 0
\(763\) −40.8577 + 8.02419i −1.47915 + 0.290495i
\(764\) 11.1654 + 1.30505i 0.403950 + 0.0472150i
\(765\) 0 0
\(766\) 1.29809 + 1.74363i 0.0469018 + 0.0630000i
\(767\) −0.117214 + 0.541122i −0.00423237 + 0.0195388i
\(768\) 0 0
\(769\) 4.18644 + 4.10603i 0.150967 + 0.148067i 0.771776 0.635894i \(-0.219369\pi\)
−0.620809 + 0.783962i \(0.713196\pi\)
\(770\) 1.68274 6.53281i 0.0606419 0.235426i
\(771\) 0 0
\(772\) 0.425910 + 0.386493i 0.0153288 + 0.0139102i
\(773\) 13.3154 30.8686i 0.478922 1.11027i −0.491940 0.870629i \(-0.663712\pi\)
0.970862 0.239638i \(-0.0770287\pi\)
\(774\) 0 0
\(775\) 6.42062 8.62439i 0.230635 0.309797i
\(776\) −0.216297 0.247849i −0.00776460 0.00889724i
\(777\) 0 0
\(778\) 0.925722 + 0.296821i 0.0331888 + 0.0106415i
\(779\) 15.9664 + 3.13570i 0.572056 + 0.112348i
\(780\) 0 0
\(781\) 46.5686 21.1680i 1.66636 0.757452i
\(782\) −0.0703738 + 0.399110i −0.00251656 + 0.0142721i
\(783\) 0 0
\(784\) 6.82100 + 38.6838i 0.243607 + 1.38156i
\(785\) −18.0466 26.3126i −0.644112 0.939139i
\(786\) 0 0