Properties

Label 405.2.r.a.368.11
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 368.11
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.03355 + 0.0904240i) q^{2} +(-0.909563 - 0.160381i) q^{4} +(-1.76770 + 1.36939i) q^{5} +(-2.38295 - 1.66856i) q^{7} +(-2.92987 - 0.785057i) q^{8} +O(q^{10})\) \(q+(1.03355 + 0.0904240i) q^{2} +(-0.909563 - 0.160381i) q^{4} +(-1.76770 + 1.36939i) q^{5} +(-2.38295 - 1.66856i) q^{7} +(-2.92987 - 0.785057i) q^{8} +(-1.95083 + 1.25550i) q^{10} +(0.357163 - 0.981298i) q^{11} +(-0.102905 - 1.17621i) q^{13} +(-2.31203 - 1.94002i) q^{14} +(-1.22140 - 0.444552i) q^{16} +(-5.46688 + 1.46485i) q^{17} +(-3.77562 + 2.17985i) q^{19} +(1.82746 - 0.962045i) q^{20} +(0.457879 - 0.981926i) q^{22} +(-2.49254 - 3.55972i) q^{23} +(1.24952 - 4.84135i) q^{25} -1.22498i q^{26} +(1.89984 + 1.89984i) q^{28} +(5.99110 - 5.02713i) q^{29} +(-1.88318 + 10.6800i) q^{31} +(4.27590 + 1.99388i) q^{32} +(-5.78276 + 1.01966i) q^{34} +(6.49726 - 0.313684i) q^{35} +(1.84738 + 6.89452i) q^{37} +(-4.09941 + 1.91158i) q^{38} +(6.25419 - 2.62440i) q^{40} +(2.34606 - 2.79593i) q^{41} +(-0.986834 - 2.11627i) q^{43} +(-0.482244 + 0.835270i) q^{44} +(-2.25429 - 3.90454i) q^{46} +(0.209148 - 0.298694i) q^{47} +(0.500224 + 1.37435i) q^{49} +(1.72922 - 4.89080i) q^{50} +(-0.0950427 + 1.08634i) q^{52} +(-1.16516 + 1.16516i) q^{53} +(0.712425 + 2.22374i) q^{55} +(5.67183 + 6.75943i) q^{56} +(6.64669 - 4.65406i) q^{58} +(-9.77378 + 3.55737i) q^{59} +(-0.654019 - 3.70913i) q^{61} +(-2.91210 + 10.8681i) q^{62} +(6.49036 + 3.74721i) q^{64} +(1.79260 + 1.93827i) q^{65} +(0.570007 - 0.0498691i) q^{67} +(5.20741 - 0.455589i) q^{68} +(6.74362 + 0.263300i) q^{70} +(-2.83490 - 1.63673i) q^{71} +(3.56015 - 13.2867i) q^{73} +(1.28593 + 7.29289i) q^{74} +(3.78377 - 1.37718i) q^{76} +(-2.48846 + 1.74244i) q^{77} +(-2.43289 - 2.89941i) q^{79} +(2.76783 - 0.886738i) q^{80} +(2.67759 - 2.67759i) q^{82} +(0.416330 - 4.75867i) q^{83} +(7.65785 - 10.0757i) q^{85} +(-0.828582 - 2.27651i) q^{86} +(-1.81682 + 2.59468i) q^{88} +(1.62360 + 2.81215i) q^{89} +(-1.71736 + 2.97456i) q^{91} +(1.69622 + 3.63755i) q^{92} +(0.243174 - 0.289803i) q^{94} +(3.68908 - 9.02363i) q^{95} +(-10.8407 + 5.05512i) q^{97} +(0.392732 + 1.46570i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.03355 + 0.0904240i 0.730831 + 0.0639395i 0.446496 0.894786i \(-0.352672\pi\)
0.284335 + 0.958725i \(0.408227\pi\)
\(3\) 0 0
\(4\) −0.909563 0.160381i −0.454782 0.0801903i
\(5\) −1.76770 + 1.36939i −0.790539 + 0.612411i
\(6\) 0 0
\(7\) −2.38295 1.66856i −0.900671 0.630657i 0.0287865 0.999586i \(-0.490836\pi\)
−0.929458 + 0.368929i \(0.879725\pi\)
\(8\) −2.92987 0.785057i −1.03587 0.277560i
\(9\) 0 0
\(10\) −1.95083 + 1.25550i −0.616908 + 0.397023i
\(11\) 0.357163 0.981298i 0.107689 0.295872i −0.874130 0.485691i \(-0.838568\pi\)
0.981819 + 0.189819i \(0.0607901\pi\)
\(12\) 0 0
\(13\) −0.102905 1.17621i −0.0285408 0.326222i −0.997021 0.0771317i \(-0.975424\pi\)
0.968480 0.249091i \(-0.0801317\pi\)
\(14\) −2.31203 1.94002i −0.617915 0.518492i
\(15\) 0 0
\(16\) −1.22140 0.444552i −0.305349 0.111138i
\(17\) −5.46688 + 1.46485i −1.32591 + 0.355277i −0.851190 0.524858i \(-0.824118\pi\)
−0.474723 + 0.880135i \(0.657452\pi\)
\(18\) 0 0
\(19\) −3.77562 + 2.17985i −0.866186 + 0.500093i −0.866079 0.499907i \(-0.833367\pi\)
−0.000107079 1.00000i \(0.500034\pi\)
\(20\) 1.82746 0.962045i 0.408632 0.215120i
\(21\) 0 0
\(22\) 0.457879 0.981926i 0.0976202 0.209347i
\(23\) −2.49254 3.55972i −0.519731 0.742253i 0.470391 0.882458i \(-0.344113\pi\)
−0.990123 + 0.140205i \(0.955224\pi\)
\(24\) 0 0
\(25\) 1.24952 4.84135i 0.249905 0.968270i
\(26\) 1.22498i 0.240238i
\(27\) 0 0
\(28\) 1.89984 + 1.89984i 0.359036 + 0.359036i
\(29\) 5.99110 5.02713i 1.11252 0.933515i 0.114317 0.993444i \(-0.463532\pi\)
0.998203 + 0.0599291i \(0.0190875\pi\)
\(30\) 0 0
\(31\) −1.88318 + 10.6800i −0.338229 + 1.91819i 0.0544490 + 0.998517i \(0.482660\pi\)
−0.392678 + 0.919676i \(0.628451\pi\)
\(32\) 4.27590 + 1.99388i 0.755879 + 0.352472i
\(33\) 0 0
\(34\) −5.78276 + 1.01966i −0.991735 + 0.174870i
\(35\) 6.49726 0.313684i 1.09824 0.0530223i
\(36\) 0 0
\(37\) 1.84738 + 6.89452i 0.303708 + 1.13345i 0.934052 + 0.357137i \(0.116247\pi\)
−0.630344 + 0.776316i \(0.717086\pi\)
\(38\) −4.09941 + 1.91158i −0.665011 + 0.310100i
\(39\) 0 0
\(40\) 6.25419 2.62440i 0.988874 0.414955i
\(41\) 2.34606 2.79593i 0.366393 0.436650i −0.551077 0.834454i \(-0.685783\pi\)
0.917471 + 0.397804i \(0.130228\pi\)
\(42\) 0 0
\(43\) −0.986834 2.11627i −0.150491 0.322729i 0.816582 0.577230i \(-0.195866\pi\)
−0.967072 + 0.254501i \(0.918089\pi\)
\(44\) −0.482244 + 0.835270i −0.0727010 + 0.125922i
\(45\) 0 0
\(46\) −2.25429 3.90454i −0.332377 0.575693i
\(47\) 0.209148 0.298694i 0.0305073 0.0435690i −0.803609 0.595158i \(-0.797089\pi\)
0.834116 + 0.551589i \(0.185978\pi\)
\(48\) 0 0
\(49\) 0.500224 + 1.37435i 0.0714605 + 0.196336i
\(50\) 1.72922 4.89080i 0.244549 0.691664i
\(51\) 0 0
\(52\) −0.0950427 + 1.08634i −0.0131800 + 0.150649i
\(53\) −1.16516 + 1.16516i −0.160047 + 0.160047i −0.782588 0.622540i \(-0.786101\pi\)
0.622540 + 0.782588i \(0.286101\pi\)
\(54\) 0 0
\(55\) 0.712425 + 2.22374i 0.0960634 + 0.299849i
\(56\) 5.67183 + 6.75943i 0.757930 + 0.903266i
\(57\) 0 0
\(58\) 6.64669 4.65406i 0.872753 0.611108i
\(59\) −9.77378 + 3.55737i −1.27244 + 0.463130i −0.887924 0.459990i \(-0.847853\pi\)
−0.384514 + 0.923119i \(0.625631\pi\)
\(60\) 0 0
\(61\) −0.654019 3.70913i −0.0837385 0.474905i −0.997622 0.0689275i \(-0.978042\pi\)
0.913883 0.405977i \(-0.133069\pi\)
\(62\) −2.91210 + 10.8681i −0.369837 + 1.38025i
\(63\) 0 0
\(64\) 6.49036 + 3.74721i 0.811295 + 0.468401i
\(65\) 1.79260 + 1.93827i 0.222345 + 0.240413i
\(66\) 0 0
\(67\) 0.570007 0.0498691i 0.0696374 0.00609249i −0.0522838 0.998632i \(-0.516650\pi\)
0.121921 + 0.992540i \(0.461094\pi\)
\(68\) 5.20741 0.455589i 0.631491 0.0552483i
\(69\) 0 0
\(70\) 6.74362 + 0.263300i 0.806016 + 0.0314703i
\(71\) −2.83490 1.63673i −0.336441 0.194244i 0.322256 0.946652i \(-0.395559\pi\)
−0.658697 + 0.752408i \(0.728892\pi\)
\(72\) 0 0
\(73\) 3.56015 13.2867i 0.416684 1.55509i −0.364755 0.931104i \(-0.618847\pi\)
0.781439 0.623982i \(-0.214486\pi\)
\(74\) 1.28593 + 7.29289i 0.149487 + 0.847782i
\(75\) 0 0
\(76\) 3.78377 1.37718i 0.434028 0.157973i
\(77\) −2.48846 + 1.74244i −0.283586 + 0.198569i
\(78\) 0 0
\(79\) −2.43289 2.89941i −0.273722 0.326209i 0.611618 0.791153i \(-0.290519\pi\)
−0.885340 + 0.464944i \(0.846074\pi\)
\(80\) 2.76783 0.886738i 0.309453 0.0991403i
\(81\) 0 0
\(82\) 2.67759 2.67759i 0.295691 0.295691i
\(83\) 0.416330 4.75867i 0.0456981 0.522332i −0.938502 0.345273i \(-0.887786\pi\)
0.984200 0.177059i \(-0.0566583\pi\)
\(84\) 0 0
\(85\) 7.65785 10.0757i 0.830611 1.09286i
\(86\) −0.828582 2.27651i −0.0893483 0.245482i
\(87\) 0 0
\(88\) −1.81682 + 2.59468i −0.193673 + 0.276594i
\(89\) 1.62360 + 2.81215i 0.172101 + 0.298087i 0.939154 0.343496i \(-0.111611\pi\)
−0.767053 + 0.641583i \(0.778278\pi\)
\(90\) 0 0
\(91\) −1.71736 + 2.97456i −0.180029 + 0.311819i
\(92\) 1.69622 + 3.63755i 0.176843 + 0.379241i
\(93\) 0 0
\(94\) 0.243174 0.289803i 0.0250815 0.0298909i
\(95\) 3.68908 9.02363i 0.378492 0.925805i
\(96\) 0 0
\(97\) −10.8407 + 5.05512i −1.10071 + 0.513270i −0.886130 0.463436i \(-0.846616\pi\)
−0.214581 + 0.976706i \(0.568839\pi\)
\(98\) 0.392732 + 1.46570i 0.0396719 + 0.148058i
\(99\) 0 0
\(100\) −1.91298 + 4.20312i −0.191298 + 0.420312i
\(101\) −0.264044 + 0.0465580i −0.0262733 + 0.00463269i −0.186769 0.982404i \(-0.559802\pi\)
0.160496 + 0.987036i \(0.448691\pi\)
\(102\) 0 0
\(103\) −11.5058 5.36526i −1.13370 0.528655i −0.237099 0.971485i \(-0.576197\pi\)
−0.896606 + 0.442830i \(0.853974\pi\)
\(104\) −0.621894 + 3.52694i −0.0609817 + 0.345845i
\(105\) 0 0
\(106\) −1.30961 + 1.09890i −0.127201 + 0.106734i
\(107\) −5.03532 5.03532i −0.486782 0.486782i 0.420507 0.907289i \(-0.361852\pi\)
−0.907289 + 0.420507i \(0.861852\pi\)
\(108\) 0 0
\(109\) 8.81333i 0.844164i 0.906558 + 0.422082i \(0.138701\pi\)
−0.906558 + 0.422082i \(0.861299\pi\)
\(110\) 0.535249 + 2.36277i 0.0510340 + 0.225281i
\(111\) 0 0
\(112\) 2.16877 + 3.09732i 0.204929 + 0.292669i
\(113\) −0.0274297 + 0.0588232i −0.00258037 + 0.00553362i −0.907594 0.419849i \(-0.862083\pi\)
0.905013 + 0.425383i \(0.139861\pi\)
\(114\) 0 0
\(115\) 9.28073 + 2.87925i 0.865433 + 0.268491i
\(116\) −6.25554 + 3.61164i −0.580813 + 0.335332i
\(117\) 0 0
\(118\) −10.4234 + 2.79294i −0.959550 + 0.257111i
\(119\) 15.4715 + 5.63116i 1.41827 + 0.516208i
\(120\) 0 0
\(121\) 7.59111 + 6.36970i 0.690101 + 0.579063i
\(122\) −0.340568 3.89271i −0.0308336 0.352430i
\(123\) 0 0
\(124\) 3.42574 9.41215i 0.307641 0.845236i
\(125\) 4.42093 + 10.2691i 0.395420 + 0.918500i
\(126\) 0 0
\(127\) −16.2081 4.34294i −1.43823 0.385374i −0.546320 0.837577i \(-0.683972\pi\)
−0.891915 + 0.452203i \(0.850638\pi\)
\(128\) −1.36013 0.952371i −0.120219 0.0841785i
\(129\) 0 0
\(130\) 1.67748 + 2.16540i 0.147125 + 0.189918i
\(131\) 3.72744 + 0.657248i 0.325668 + 0.0574240i 0.334092 0.942541i \(-0.391570\pi\)
−0.00842419 + 0.999965i \(0.502682\pi\)
\(132\) 0 0
\(133\) 12.6343 + 1.10536i 1.09554 + 0.0958470i
\(134\) 0.593641 0.0512828
\(135\) 0 0
\(136\) 17.1673 1.47208
\(137\) −21.5441 1.88486i −1.84064 0.161035i −0.886955 0.461856i \(-0.847184\pi\)
−0.953681 + 0.300821i \(0.902739\pi\)
\(138\) 0 0
\(139\) −11.0217 1.94342i −0.934847 0.164839i −0.314581 0.949231i \(-0.601864\pi\)
−0.620265 + 0.784392i \(0.712975\pi\)
\(140\) −5.95998 0.756718i −0.503710 0.0639544i
\(141\) 0 0
\(142\) −2.78201 1.94799i −0.233461 0.163471i
\(143\) −1.19097 0.319119i −0.0995937 0.0266861i
\(144\) 0 0
\(145\) −3.70635 + 17.0906i −0.307796 + 1.41930i
\(146\) 4.88103 13.4105i 0.403957 1.10986i
\(147\) 0 0
\(148\) −0.574563 6.56729i −0.0472288 0.539828i
\(149\) 10.1272 + 8.49772i 0.829651 + 0.696160i 0.955211 0.295926i \(-0.0956282\pi\)
−0.125560 + 0.992086i \(0.540073\pi\)
\(150\) 0 0
\(151\) 11.4353 + 4.16211i 0.930591 + 0.338708i 0.762444 0.647054i \(-0.223999\pi\)
0.168147 + 0.985762i \(0.446222\pi\)
\(152\) 12.7734 3.42262i 1.03606 0.277611i
\(153\) 0 0
\(154\) −2.72951 + 1.57588i −0.219950 + 0.126988i
\(155\) −11.2963 21.4579i −0.907339 1.72354i
\(156\) 0 0
\(157\) 5.01098 10.7461i 0.399920 0.857631i −0.598483 0.801136i \(-0.704230\pi\)
0.998403 0.0564955i \(-0.0179927\pi\)
\(158\) −2.25234 3.21668i −0.179187 0.255905i
\(159\) 0 0
\(160\) −10.2889 + 2.33080i −0.813410 + 0.184266i
\(161\) 12.6416i 0.996298i
\(162\) 0 0
\(163\) −10.1170 10.1170i −0.792424 0.792424i 0.189463 0.981888i \(-0.439325\pi\)
−0.981888 + 0.189463i \(0.939325\pi\)
\(164\) −2.58230 + 2.16681i −0.201644 + 0.169199i
\(165\) 0 0
\(166\) 0.860597 4.88069i 0.0667953 0.378815i
\(167\) 19.2590 + 8.98064i 1.49031 + 0.694943i 0.985716 0.168415i \(-0.0538648\pi\)
0.504593 + 0.863357i \(0.331643\pi\)
\(168\) 0 0
\(169\) 11.4296 2.01535i 0.879201 0.155027i
\(170\) 8.82587 9.72132i 0.676913 0.745591i
\(171\) 0 0
\(172\) 0.558179 + 2.08315i 0.0425608 + 0.158839i
\(173\) −7.68830 + 3.58511i −0.584530 + 0.272571i −0.692306 0.721604i \(-0.743405\pi\)
0.107775 + 0.994175i \(0.465627\pi\)
\(174\) 0 0
\(175\) −11.0556 + 9.45180i −0.835728 + 0.714489i
\(176\) −0.872476 + 1.03978i −0.0657653 + 0.0783761i
\(177\) 0 0
\(178\) 1.42378 + 3.05331i 0.106717 + 0.228856i
\(179\) 6.71299 11.6272i 0.501753 0.869061i −0.498245 0.867036i \(-0.666022\pi\)
0.999998 0.00202486i \(-0.000644535\pi\)
\(180\) 0 0
\(181\) −9.97071 17.2698i −0.741117 1.28365i −0.951987 0.306138i \(-0.900963\pi\)
0.210870 0.977514i \(-0.432370\pi\)
\(182\) −2.04395 + 2.91907i −0.151508 + 0.216376i
\(183\) 0 0
\(184\) 4.50825 + 12.3863i 0.332353 + 0.913132i
\(185\) −12.7069 9.65765i −0.934232 0.710045i
\(186\) 0 0
\(187\) −0.515118 + 5.88783i −0.0376692 + 0.430560i
\(188\) −0.238138 + 0.238138i −0.0173680 + 0.0173680i
\(189\) 0 0
\(190\) 4.62881 8.99281i 0.335809 0.652407i
\(191\) −0.583207 0.695039i −0.0421994 0.0502912i 0.744532 0.667587i \(-0.232673\pi\)
−0.786731 + 0.617296i \(0.788228\pi\)
\(192\) 0 0
\(193\) −6.05638 + 4.24072i −0.435948 + 0.305254i −0.770871 0.636992i \(-0.780179\pi\)
0.334923 + 0.942245i \(0.391290\pi\)
\(194\) −11.6616 + 4.24447i −0.837252 + 0.304735i
\(195\) 0 0
\(196\) −0.234566 1.33029i −0.0167547 0.0950205i
\(197\) 4.43194 16.5402i 0.315763 1.17844i −0.607515 0.794309i \(-0.707833\pi\)
0.923277 0.384134i \(-0.125500\pi\)
\(198\) 0 0
\(199\) 0.887783 + 0.512562i 0.0629332 + 0.0363345i 0.531136 0.847286i \(-0.321765\pi\)
−0.468203 + 0.883621i \(0.655098\pi\)
\(200\) −7.46168 + 13.2036i −0.527621 + 0.933636i
\(201\) 0 0
\(202\) −0.277113 + 0.0242442i −0.0194976 + 0.00170582i
\(203\) −22.6646 + 1.98289i −1.59074 + 0.139172i
\(204\) 0 0
\(205\) −0.318408 + 8.15504i −0.0222386 + 0.569573i
\(206\) −11.4067 6.58568i −0.794745 0.458846i
\(207\) 0 0
\(208\) −0.397199 + 1.48237i −0.0275408 + 0.102784i
\(209\) 0.790574 + 4.48357i 0.0546852 + 0.310135i
\(210\) 0 0
\(211\) −9.20369 + 3.34987i −0.633608 + 0.230614i −0.638801 0.769372i \(-0.720569\pi\)
0.00519293 + 0.999987i \(0.498347\pi\)
\(212\) 1.24666 0.872919i 0.0856208 0.0599523i
\(213\) 0 0
\(214\) −4.74895 5.65957i −0.324631 0.386880i
\(215\) 4.64244 + 2.38957i 0.316611 + 0.162967i
\(216\) 0 0
\(217\) 22.3078 22.3078i 1.51435 1.51435i
\(218\) −0.796937 + 9.10903i −0.0539754 + 0.616942i
\(219\) 0 0
\(220\) −0.291352 2.13689i −0.0196429 0.144069i
\(221\) 2.28554 + 6.27947i 0.153742 + 0.422403i
\(222\) 0 0
\(223\) −5.62275 + 8.03011i −0.376527 + 0.537736i −0.962033 0.272932i \(-0.912007\pi\)
0.585507 + 0.810668i \(0.300896\pi\)
\(224\) −6.86234 11.8859i −0.458510 0.794162i
\(225\) 0 0
\(226\) −0.0336690 + 0.0583165i −0.00223963 + 0.00387916i
\(227\) −7.23760 15.5211i −0.480376 1.03017i −0.985897 0.167356i \(-0.946477\pi\)
0.505520 0.862815i \(-0.331301\pi\)
\(228\) 0 0
\(229\) −11.7568 + 14.0112i −0.776912 + 0.925888i −0.998790 0.0491866i \(-0.984337\pi\)
0.221877 + 0.975075i \(0.428782\pi\)
\(230\) 9.33176 + 3.81505i 0.615318 + 0.251557i
\(231\) 0 0
\(232\) −21.4998 + 10.0255i −1.41153 + 0.658207i
\(233\) 1.27701 + 4.76585i 0.0836594 + 0.312221i 0.995057 0.0993059i \(-0.0316622\pi\)
−0.911398 + 0.411527i \(0.864996\pi\)
\(234\) 0 0
\(235\) 0.0393191 + 0.814406i 0.00256489 + 0.0531260i
\(236\) 9.46041 1.66812i 0.615820 0.108586i
\(237\) 0 0
\(238\) 15.4814 + 7.21909i 1.00351 + 0.467944i
\(239\) −1.04890 + 5.94858i −0.0678474 + 0.384782i 0.931909 + 0.362693i \(0.118143\pi\)
−0.999756 + 0.0220886i \(0.992968\pi\)
\(240\) 0 0
\(241\) −13.1764 + 11.0563i −0.848766 + 0.712199i −0.959518 0.281649i \(-0.909119\pi\)
0.110751 + 0.993848i \(0.464674\pi\)
\(242\) 7.26983 + 7.26983i 0.467322 + 0.467322i
\(243\) 0 0
\(244\) 3.47858i 0.222693i
\(245\) −2.76627 1.74444i −0.176731 0.111448i
\(246\) 0 0
\(247\) 2.95250 + 4.21661i 0.187863 + 0.268296i
\(248\) 13.9019 29.8128i 0.882773 1.89311i
\(249\) 0 0
\(250\) 3.64068 + 11.0134i 0.230257 + 0.696552i
\(251\) 0.245642 0.141822i 0.0155048 0.00895170i −0.492228 0.870467i \(-0.663817\pi\)
0.507732 + 0.861515i \(0.330484\pi\)
\(252\) 0 0
\(253\) −4.38339 + 1.17453i −0.275582 + 0.0738419i
\(254\) −16.3592 5.95426i −1.02647 0.373603i
\(255\) 0 0
\(256\) −12.8018 10.7420i −0.800110 0.671372i
\(257\) 0.568503 + 6.49802i 0.0354623 + 0.405335i 0.993092 + 0.117335i \(0.0374350\pi\)
−0.957630 + 0.288001i \(0.907009\pi\)
\(258\) 0 0
\(259\) 7.10171 19.5118i 0.441279 1.21240i
\(260\) −1.31962 2.05048i −0.0818396 0.127165i
\(261\) 0 0
\(262\) 3.79307 + 1.01635i 0.234336 + 0.0627903i
\(263\) 3.72625 + 2.60915i 0.229770 + 0.160887i 0.682792 0.730612i \(-0.260765\pi\)
−0.453022 + 0.891499i \(0.649654\pi\)
\(264\) 0 0
\(265\) 0.464091 3.65522i 0.0285089 0.224538i
\(266\) 12.9583 + 2.28489i 0.794523 + 0.140096i
\(267\) 0 0
\(268\) −0.526455 0.0460589i −0.0321584 0.00281349i
\(269\) −7.68259 −0.468416 −0.234208 0.972187i \(-0.575250\pi\)
−0.234208 + 0.972187i \(0.575250\pi\)
\(270\) 0 0
\(271\) 18.8470 1.14487 0.572437 0.819949i \(-0.305998\pi\)
0.572437 + 0.819949i \(0.305998\pi\)
\(272\) 7.32843 + 0.641154i 0.444351 + 0.0388757i
\(273\) 0 0
\(274\) −22.0965 3.89621i −1.33490 0.235378i
\(275\) −4.30452 2.95531i −0.259573 0.178212i
\(276\) 0 0
\(277\) 8.10294 + 5.67374i 0.486858 + 0.340902i 0.791094 0.611695i \(-0.209512\pi\)
−0.304235 + 0.952597i \(0.598401\pi\)
\(278\) −11.2157 3.00525i −0.672675 0.180243i
\(279\) 0 0
\(280\) −19.2824 4.18167i −1.15234 0.249902i
\(281\) 1.61241 4.43006i 0.0961883 0.264275i −0.882262 0.470759i \(-0.843980\pi\)
0.978450 + 0.206484i \(0.0662022\pi\)
\(282\) 0 0
\(283\) 0.00130413 + 0.0149063i 7.75226e−5 + 0.000886087i 0.996233 0.0867127i \(-0.0276362\pi\)
−0.996156 + 0.0875988i \(0.972081\pi\)
\(284\) 2.31602 + 1.94337i 0.137431 + 0.115318i
\(285\) 0 0
\(286\) −1.20207 0.437518i −0.0710799 0.0258710i
\(287\) −10.2557 + 2.74801i −0.605376 + 0.162210i
\(288\) 0 0
\(289\) 13.0186 7.51627i 0.765798 0.442134i
\(290\) −5.37611 + 17.3289i −0.315696 + 1.01759i
\(291\) 0 0
\(292\) −5.36910 + 11.5141i −0.314203 + 0.673810i
\(293\) 13.1517 + 18.7826i 0.768330 + 1.09729i 0.992441 + 0.122726i \(0.0391636\pi\)
−0.224110 + 0.974564i \(0.571948\pi\)
\(294\) 0 0
\(295\) 12.4057 19.6725i 0.722286 1.14538i
\(296\) 21.6504i 1.25840i
\(297\) 0 0
\(298\) 9.69857 + 9.69857i 0.561823 + 0.561823i
\(299\) −3.93049 + 3.29807i −0.227306 + 0.190733i
\(300\) 0 0
\(301\) −1.17955 + 6.68957i −0.0679882 + 0.385580i
\(302\) 11.4426 + 5.33578i 0.658448 + 0.307040i
\(303\) 0 0
\(304\) 5.58058 0.984008i 0.320068 0.0564367i
\(305\) 6.23536 + 5.66101i 0.357036 + 0.324149i
\(306\) 0 0
\(307\) −7.06051 26.3502i −0.402965 1.50388i −0.807779 0.589486i \(-0.799330\pi\)
0.404814 0.914399i \(-0.367336\pi\)
\(308\) 2.54286 1.18576i 0.144893 0.0675647i
\(309\) 0 0
\(310\) −9.73498 23.1993i −0.552910 1.31763i
\(311\) −20.3862 + 24.2954i −1.15600 + 1.37766i −0.242835 + 0.970068i \(0.578077\pi\)
−0.913162 + 0.407596i \(0.866367\pi\)
\(312\) 0 0
\(313\) 4.83829 + 10.3757i 0.273476 + 0.586472i 0.994297 0.106650i \(-0.0340125\pi\)
−0.720820 + 0.693122i \(0.756235\pi\)
\(314\) 6.15081 10.6535i 0.347110 0.601213i
\(315\) 0 0
\(316\) 1.74786 + 3.02739i 0.0983249 + 0.170304i
\(317\) 7.17947 10.2533i 0.403239 0.575885i −0.565257 0.824915i \(-0.691223\pi\)
0.968496 + 0.249030i \(0.0801117\pi\)
\(318\) 0 0
\(319\) −2.79331 7.67456i −0.156395 0.429693i
\(320\) −16.6044 + 2.26391i −0.928214 + 0.126556i
\(321\) 0 0
\(322\) −1.14311 + 13.0658i −0.0637028 + 0.728126i
\(323\) 17.4477 17.4477i 0.970816 0.970816i
\(324\) 0 0
\(325\) −5.82304 0.971504i −0.323004 0.0538893i
\(326\) −9.54162 11.3713i −0.528461 0.629796i
\(327\) 0 0
\(328\) −9.06863 + 6.34992i −0.500731 + 0.350616i
\(329\) −0.996777 + 0.362797i −0.0549541 + 0.0200017i
\(330\) 0 0
\(331\) −4.38923 24.8926i −0.241254 1.36822i −0.829034 0.559199i \(-0.811109\pi\)
0.587780 0.809021i \(-0.300002\pi\)
\(332\) −1.14188 + 4.26154i −0.0626686 + 0.233883i
\(333\) 0 0
\(334\) 19.0931 + 11.0234i 1.04473 + 0.603175i
\(335\) −0.939311 + 0.868717i −0.0513200 + 0.0474631i
\(336\) 0 0
\(337\) −1.72746 + 0.151133i −0.0941006 + 0.00823274i −0.134109 0.990967i \(-0.542817\pi\)
0.0400082 + 0.999199i \(0.487262\pi\)
\(338\) 11.9953 1.04946i 0.652460 0.0570829i
\(339\) 0 0
\(340\) −8.58125 + 7.93633i −0.465384 + 0.430408i
\(341\) 9.80770 + 5.66248i 0.531117 + 0.306640i
\(342\) 0 0
\(343\) −4.16923 + 15.5598i −0.225118 + 0.840150i
\(344\) 1.22990 + 6.97513i 0.0663120 + 0.376074i
\(345\) 0 0
\(346\) −8.27043 + 3.01019i −0.444621 + 0.161829i
\(347\) −8.10639 + 5.67616i −0.435174 + 0.304712i −0.770559 0.637369i \(-0.780023\pi\)
0.335385 + 0.942081i \(0.391134\pi\)
\(348\) 0 0
\(349\) 19.9263 + 23.7472i 1.06663 + 1.27116i 0.960939 + 0.276759i \(0.0892603\pi\)
0.105689 + 0.994399i \(0.466295\pi\)
\(350\) −12.2812 + 8.76923i −0.656460 + 0.468735i
\(351\) 0 0
\(352\) 3.48379 3.48379i 0.185687 0.185687i
\(353\) −0.319565 + 3.65264i −0.0170087 + 0.194411i 0.982937 + 0.183945i \(0.0588869\pi\)
−0.999945 + 0.0104654i \(0.996669\pi\)
\(354\) 0 0
\(355\) 7.25257 0.988845i 0.384927 0.0524825i
\(356\) −1.02575 2.81822i −0.0543646 0.149365i
\(357\) 0 0
\(358\) 7.98960 11.4103i 0.422264 0.603055i
\(359\) −3.73590 6.47077i −0.197173 0.341514i 0.750438 0.660941i \(-0.229843\pi\)
−0.947611 + 0.319427i \(0.896509\pi\)
\(360\) 0 0
\(361\) 0.00352408 0.00610389i 0.000185478 0.000321258i
\(362\) −8.74364 18.7508i −0.459555 0.985520i
\(363\) 0 0
\(364\) 2.03911 2.43012i 0.106878 0.127373i
\(365\) 11.9014 + 28.3621i 0.622947 + 1.48454i
\(366\) 0 0
\(367\) 15.3011 7.13502i 0.798711 0.372445i 0.0199776 0.999800i \(-0.493640\pi\)
0.778733 + 0.627356i \(0.215863\pi\)
\(368\) 1.46190 + 5.45590i 0.0762070 + 0.284408i
\(369\) 0 0
\(370\) −12.2600 11.1307i −0.637366 0.578657i
\(371\) 4.72067 0.832381i 0.245085 0.0432151i
\(372\) 0 0
\(373\) −1.92488 0.897584i −0.0996663 0.0464752i 0.372146 0.928174i \(-0.378622\pi\)
−0.471812 + 0.881699i \(0.656400\pi\)
\(374\) −1.06480 + 6.03879i −0.0550596 + 0.312259i
\(375\) 0 0
\(376\) −0.847268 + 0.710942i −0.0436945 + 0.0366640i
\(377\) −6.52949 6.52949i −0.336286 0.336286i
\(378\) 0 0
\(379\) 9.60506i 0.493379i −0.969095 0.246689i \(-0.920657\pi\)
0.969095 0.246689i \(-0.0793427\pi\)
\(380\) −4.80267 + 7.61591i −0.246372 + 0.390688i
\(381\) 0 0
\(382\) −0.539926 0.771094i −0.0276250 0.0394526i
\(383\) 0.0510389 0.109453i 0.00260797 0.00559281i −0.904999 0.425413i \(-0.860129\pi\)
0.907607 + 0.419820i \(0.137907\pi\)
\(384\) 0 0
\(385\) 2.01276 6.48778i 0.102580 0.330648i
\(386\) −6.64304 + 3.83536i −0.338122 + 0.195215i
\(387\) 0 0
\(388\) 10.6711 2.85931i 0.541742 0.145159i
\(389\) 24.1005 + 8.77187i 1.22194 + 0.444752i 0.870832 0.491581i \(-0.163581\pi\)
0.351113 + 0.936333i \(0.385803\pi\)
\(390\) 0 0
\(391\) 18.8409 + 15.8094i 0.952825 + 0.799515i
\(392\) −0.386646 4.41938i −0.0195286 0.223213i
\(393\) 0 0
\(394\) 6.07627 16.6944i 0.306118 0.841053i
\(395\) 8.27106 + 1.79370i 0.416162 + 0.0902507i
\(396\) 0 0
\(397\) 25.5064 + 6.83441i 1.28013 + 0.343009i 0.833903 0.551911i \(-0.186101\pi\)
0.446225 + 0.894921i \(0.352768\pi\)
\(398\) 0.871221 + 0.610036i 0.0436704 + 0.0305783i
\(399\) 0 0
\(400\) −3.67840 + 5.35773i −0.183920 + 0.267887i
\(401\) 33.5008 + 5.90709i 1.67295 + 0.294986i 0.928124 0.372272i \(-0.121421\pi\)
0.744826 + 0.667259i \(0.232532\pi\)
\(402\) 0 0
\(403\) 12.7558 + 1.11599i 0.635411 + 0.0555912i
\(404\) 0.247631 0.0123201
\(405\) 0 0
\(406\) −23.6043 −1.17146
\(407\) 7.42540 + 0.649638i 0.368063 + 0.0322014i
\(408\) 0 0
\(409\) 33.1027 + 5.83690i 1.63682 + 0.288616i 0.914998 0.403458i \(-0.132192\pi\)
0.721826 + 0.692075i \(0.243303\pi\)
\(410\) −1.06650 + 8.39986i −0.0526708 + 0.414840i
\(411\) 0 0
\(412\) 9.60481 + 6.72536i 0.473195 + 0.331335i
\(413\) 29.2261 + 7.83112i 1.43812 + 0.385344i
\(414\) 0 0
\(415\) 5.78055 + 8.98202i 0.283756 + 0.440910i
\(416\) 1.90522 5.23454i 0.0934110 0.256645i
\(417\) 0 0
\(418\) 0.411677 + 4.70549i 0.0201358 + 0.230153i
\(419\) −23.6855 19.8745i −1.15711 0.970932i −0.157249 0.987559i \(-0.550263\pi\)
−0.999862 + 0.0166274i \(0.994707\pi\)
\(420\) 0 0
\(421\) −13.7828 5.01653i −0.671732 0.244490i −0.0164386 0.999865i \(-0.505233\pi\)
−0.655293 + 0.755374i \(0.727455\pi\)
\(422\) −9.81539 + 2.63003i −0.477806 + 0.128028i
\(423\) 0 0
\(424\) 4.32849 2.49906i 0.210210 0.121365i
\(425\) 0.260840 + 28.2974i 0.0126526 + 1.37263i
\(426\) 0 0
\(427\) −4.63041 + 9.92994i −0.224081 + 0.480543i
\(428\) 3.77237 + 5.38751i 0.182345 + 0.260415i
\(429\) 0 0
\(430\) 4.58212 + 2.88953i 0.220970 + 0.139346i
\(431\) 30.3267i 1.46078i 0.683028 + 0.730392i \(0.260663\pi\)
−0.683028 + 0.730392i \(0.739337\pi\)
\(432\) 0 0
\(433\) 5.35178 + 5.35178i 0.257190 + 0.257190i 0.823910 0.566720i \(-0.191788\pi\)
−0.566720 + 0.823910i \(0.691788\pi\)
\(434\) 25.0735 21.0391i 1.20356 1.00991i
\(435\) 0 0
\(436\) 1.41349 8.01628i 0.0676938 0.383910i
\(437\) 17.1706 + 8.00677i 0.821380 + 0.383016i
\(438\) 0 0
\(439\) −9.78003 + 1.72448i −0.466775 + 0.0823051i −0.402089 0.915601i \(-0.631716\pi\)
−0.0646863 + 0.997906i \(0.520605\pi\)
\(440\) −0.341556 7.07456i −0.0162830 0.337266i
\(441\) 0 0
\(442\) 1.79441 + 6.69682i 0.0853513 + 0.318535i
\(443\) −8.40263 + 3.91821i −0.399221 + 0.186160i −0.611851 0.790973i \(-0.709575\pi\)
0.212630 + 0.977133i \(0.431797\pi\)
\(444\) 0 0
\(445\) −6.72097 2.74770i −0.318605 0.130253i
\(446\) −6.53751 + 7.79110i −0.309560 + 0.368919i
\(447\) 0 0
\(448\) −9.21376 19.7590i −0.435309 0.933524i
\(449\) 15.0787 26.1171i 0.711609 1.23254i −0.252644 0.967559i \(-0.581300\pi\)
0.964253 0.264984i \(-0.0853667\pi\)
\(450\) 0 0
\(451\) −1.90571 3.30079i −0.0897364 0.155428i
\(452\) 0.0343832 0.0491042i 0.00161725 0.00230967i
\(453\) 0 0
\(454\) −6.07695 16.6963i −0.285206 0.783596i
\(455\) −1.03756 7.60987i −0.0486416 0.356756i
\(456\) 0 0
\(457\) 2.64140 30.1913i 0.123559 1.41229i −0.640902 0.767622i \(-0.721440\pi\)
0.764462 0.644669i \(-0.223005\pi\)
\(458\) −13.4182 + 13.4182i −0.626993 + 0.626993i
\(459\) 0 0
\(460\) −7.97964 4.10731i −0.372052 0.191504i
\(461\) −8.35560 9.95782i −0.389159 0.463782i 0.535524 0.844520i \(-0.320114\pi\)
−0.924683 + 0.380738i \(0.875670\pi\)
\(462\) 0 0
\(463\) 22.5069 15.7595i 1.04598 0.732405i 0.0815330 0.996671i \(-0.474018\pi\)
0.964450 + 0.264266i \(0.0851295\pi\)
\(464\) −9.55234 + 3.47677i −0.443456 + 0.161405i
\(465\) 0 0
\(466\) 0.888904 + 5.04122i 0.0411777 + 0.233530i
\(467\) −7.76986 + 28.9975i −0.359546 + 1.34184i 0.515119 + 0.857118i \(0.327748\pi\)
−0.874666 + 0.484727i \(0.838919\pi\)
\(468\) 0 0
\(469\) −1.44151 0.832256i −0.0665627 0.0384300i
\(470\) −0.0330036 + 0.845286i −0.00152234 + 0.0389901i
\(471\) 0 0
\(472\) 31.4287 2.74965i 1.44662 0.126563i
\(473\) −2.42915 + 0.212523i −0.111693 + 0.00977184i
\(474\) 0 0
\(475\) 5.83572 + 21.0029i 0.267761 + 0.963678i
\(476\) −13.1692 7.60323i −0.603608 0.348493i
\(477\) 0 0
\(478\) −1.62198 + 6.05332i −0.0741878 + 0.276872i
\(479\) −1.81506 10.2937i −0.0829324 0.470333i −0.997784 0.0665419i \(-0.978803\pi\)
0.914851 0.403791i \(-0.132308\pi\)
\(480\) 0 0
\(481\) 7.91931 2.88239i 0.361090 0.131426i
\(482\) −14.6182 + 10.2358i −0.665843 + 0.466228i
\(483\) 0 0
\(484\) −5.88302 7.01111i −0.267410 0.318687i
\(485\) 12.2407 23.7812i 0.555823 1.07985i
\(486\) 0 0
\(487\) −13.7181 + 13.7181i −0.621625 + 0.621625i −0.945947 0.324322i \(-0.894864\pi\)
0.324322 + 0.945947i \(0.394864\pi\)
\(488\) −0.995683 + 11.3807i −0.0450725 + 0.515181i
\(489\) 0 0
\(490\) −2.70135 2.05311i −0.122034 0.0927499i
\(491\) −14.3153 39.3310i −0.646040 1.77498i −0.631861 0.775082i \(-0.717708\pi\)
−0.0141799 0.999899i \(-0.504514\pi\)
\(492\) 0 0
\(493\) −25.3887 + 36.2588i −1.14345 + 1.63301i
\(494\) 2.67028 + 4.62506i 0.120141 + 0.208091i
\(495\) 0 0
\(496\) 7.04794 12.2074i 0.316462 0.548128i
\(497\) 4.02444 + 8.63045i 0.180521 + 0.387129i
\(498\) 0 0
\(499\) −17.0051 + 20.2659i −0.761253 + 0.907226i −0.997927 0.0643635i \(-0.979498\pi\)
0.236674 + 0.971589i \(0.423943\pi\)
\(500\) −2.37415 10.0495i −0.106175 0.449426i
\(501\) 0 0
\(502\) 0.266708 0.124368i 0.0119038 0.00555082i
\(503\) 6.58100 + 24.5606i 0.293432 + 1.09510i 0.942455 + 0.334334i \(0.108511\pi\)
−0.649023 + 0.760769i \(0.724822\pi\)
\(504\) 0 0
\(505\) 0.402993 0.443880i 0.0179330 0.0197524i
\(506\) −4.63667 + 0.817570i −0.206125 + 0.0363454i
\(507\) 0 0
\(508\) 14.0458 + 6.54964i 0.623180 + 0.290593i
\(509\) 5.29524 30.0308i 0.234707 1.33109i −0.608522 0.793537i \(-0.708237\pi\)
0.843229 0.537554i \(-0.180652\pi\)
\(510\) 0 0
\(511\) −30.6533 + 25.7211i −1.35602 + 1.13784i
\(512\) −9.91177 9.91177i −0.438043 0.438043i
\(513\) 0 0
\(514\) 6.76745i 0.298499i
\(515\) 27.6860 6.27185i 1.21999 0.276371i
\(516\) 0 0
\(517\) −0.218408 0.311918i −0.00960556 0.0137182i
\(518\) 9.10432 19.5243i 0.400021 0.857847i
\(519\) 0 0
\(520\) −3.73044 7.08618i −0.163591 0.310750i
\(521\) 1.09146 0.630155i 0.0478178 0.0276076i −0.475901 0.879499i \(-0.657878\pi\)
0.523718 + 0.851892i \(0.324544\pi\)
\(522\) 0 0
\(523\) −9.13037 + 2.44648i −0.399243 + 0.106977i −0.452853 0.891585i \(-0.649594\pi\)
0.0536101 + 0.998562i \(0.482927\pi\)
\(524\) −3.28493 1.19562i −0.143503 0.0522308i
\(525\) 0 0
\(526\) 3.61534 + 3.03363i 0.157636 + 0.132272i
\(527\) −5.34950 61.1451i −0.233028 2.66352i
\(528\) 0 0
\(529\) 1.40762 3.86740i 0.0612007 0.168148i
\(530\) 0.810182 3.73589i 0.0351920 0.162277i
\(531\) 0 0
\(532\) −11.3144 3.03170i −0.490544 0.131441i
\(533\) −3.53002 2.47175i −0.152902 0.107063i
\(534\) 0 0
\(535\) 15.7963 + 2.00560i 0.682932 + 0.0867096i
\(536\) −1.70920 0.301378i −0.0738261 0.0130175i
\(537\) 0 0
\(538\) −7.94036 0.694691i −0.342333 0.0299503i
\(539\) 1.52731 0.0657859
\(540\) 0 0
\(541\) −14.5318 −0.624771 −0.312385 0.949955i \(-0.601128\pi\)
−0.312385 + 0.949955i \(0.601128\pi\)
\(542\) 19.4793 + 1.70422i 0.836710 + 0.0732026i
\(543\) 0 0
\(544\) −26.2966 4.63679i −1.12746 0.198801i
\(545\) −12.0689 15.5793i −0.516976 0.667345i
\(546\) 0 0
\(547\) −11.9957 8.39950i −0.512900 0.359136i 0.288293 0.957542i \(-0.406912\pi\)
−0.801193 + 0.598406i \(0.795801\pi\)
\(548\) 19.2934 + 5.16965i 0.824174 + 0.220837i
\(549\) 0 0
\(550\) −4.18172 3.44369i −0.178309 0.146840i
\(551\) −11.6617 + 32.0403i −0.496805 + 1.36496i
\(552\) 0 0
\(553\) 0.959627 + 10.9686i 0.0408075 + 0.466432i
\(554\) 7.86176 + 6.59680i 0.334014 + 0.280271i
\(555\) 0 0
\(556\) 9.71323 + 3.53533i 0.411933 + 0.149931i
\(557\) −3.61631 + 0.968988i −0.153228 + 0.0410573i −0.334618 0.942354i \(-0.608607\pi\)
0.181390 + 0.983411i \(0.441941\pi\)
\(558\) 0 0
\(559\) −2.38763 + 1.37850i −0.100986 + 0.0583044i
\(560\) −8.07518 2.50524i −0.341239 0.105866i
\(561\) 0 0
\(562\) 2.06709 4.43289i 0.0871950 0.186990i
\(563\) 5.55357 + 7.93132i 0.234055 + 0.334265i 0.918948 0.394378i \(-0.129040\pi\)
−0.684893 + 0.728644i \(0.740151\pi\)
\(564\) 0 0
\(565\) −0.0320646 0.141544i −0.00134897 0.00595479i
\(566\) 0.0155243i 0.000652537i
\(567\) 0 0
\(568\) 7.02097 + 7.02097i 0.294593 + 0.294593i
\(569\) −29.7838 + 24.9915i −1.24860 + 1.04770i −0.251799 + 0.967780i \(0.581022\pi\)
−0.996801 + 0.0799199i \(0.974534\pi\)
\(570\) 0 0
\(571\) −1.13871 + 6.45794i −0.0476535 + 0.270256i −0.999320 0.0368775i \(-0.988259\pi\)
0.951666 + 0.307134i \(0.0993700\pi\)
\(572\) 1.03208 + 0.481267i 0.0431534 + 0.0201228i
\(573\) 0 0
\(574\) −10.8483 + 1.91285i −0.452800 + 0.0798408i
\(575\) −20.3484 + 7.61933i −0.848585 + 0.317748i
\(576\) 0 0
\(577\) 2.53716 + 9.46880i 0.105623 + 0.394191i 0.998415 0.0562782i \(-0.0179234\pi\)
−0.892792 + 0.450469i \(0.851257\pi\)
\(578\) 14.1350 6.59126i 0.587939 0.274160i
\(579\) 0 0
\(580\) 6.11217 14.9506i 0.253794 0.620790i
\(581\) −8.93223 + 10.6450i −0.370571 + 0.441630i
\(582\) 0 0
\(583\) 0.727218 + 1.55952i 0.0301183 + 0.0645888i
\(584\) −20.8616 + 36.1333i −0.863258 + 1.49521i
\(585\) 0 0
\(586\) 11.8946 + 20.6020i 0.491360 + 0.851060i
\(587\) 10.1521 14.4987i 0.419023 0.598427i −0.553038 0.833156i \(-0.686531\pi\)
0.972061 + 0.234729i \(0.0754204\pi\)
\(588\) 0 0
\(589\) −16.1708 44.4288i −0.666305 1.83066i
\(590\) 14.6008 19.2108i 0.601104 0.790895i
\(591\) 0 0
\(592\) 0.808588 9.24221i 0.0332328 0.379852i
\(593\) −3.34033 + 3.34033i −0.137171 + 0.137171i −0.772358 0.635187i \(-0.780923\pi\)
0.635187 + 0.772358i \(0.280923\pi\)
\(594\) 0 0
\(595\) −35.0602 + 11.2324i −1.43733 + 0.460482i
\(596\) −7.84845 9.35341i −0.321485 0.383131i
\(597\) 0 0
\(598\) −4.36059 + 3.05332i −0.178318 + 0.124859i
\(599\) −18.0781 + 6.57991i −0.738653 + 0.268848i −0.683823 0.729648i \(-0.739684\pi\)
−0.0548301 + 0.998496i \(0.517462\pi\)
\(600\) 0 0
\(601\) −1.93521 10.9751i −0.0789387 0.447684i −0.998501 0.0547387i \(-0.982567\pi\)
0.919562 0.392945i \(-0.128544\pi\)
\(602\) −1.82402 + 6.80735i −0.0743417 + 0.277447i
\(603\) 0 0
\(604\) −9.73361 5.61970i −0.396055 0.228662i
\(605\) −22.1414 0.864496i −0.900177 0.0351468i
\(606\) 0 0
\(607\) 18.3352 1.60413i 0.744204 0.0651094i 0.291255 0.956646i \(-0.405927\pi\)
0.452950 + 0.891536i \(0.350372\pi\)
\(608\) −20.4905 + 1.79269i −0.831001 + 0.0727032i
\(609\) 0 0
\(610\) 5.93268 + 6.41477i 0.240207 + 0.259727i
\(611\) −0.372849 0.215265i −0.0150839 0.00870868i
\(612\) 0 0
\(613\) −2.08262 + 7.77243i −0.0841161 + 0.313926i −0.995145 0.0984162i \(-0.968622\pi\)
0.911029 + 0.412342i \(0.135289\pi\)
\(614\) −4.91471 27.8727i −0.198342 1.12485i
\(615\) 0 0
\(616\) 8.65878 3.15154i 0.348872 0.126979i
\(617\) −5.25082 + 3.67666i −0.211390 + 0.148017i −0.674477 0.738296i \(-0.735631\pi\)
0.463087 + 0.886313i \(0.346742\pi\)
\(618\) 0 0
\(619\) −17.8281 21.2467i −0.716573 0.853979i 0.277720 0.960662i \(-0.410421\pi\)
−0.994293 + 0.106683i \(0.965977\pi\)
\(620\) 6.83325 + 21.3290i 0.274430 + 0.856595i
\(621\) 0 0
\(622\) −23.2671 + 23.2671i −0.932926 + 0.932926i
\(623\) 0.823294 9.41029i 0.0329846 0.377015i
\(624\) 0 0
\(625\) −21.8774 12.0988i −0.875095 0.483951i
\(626\) 4.06240 + 11.1614i 0.162366 + 0.446098i
\(627\) 0 0
\(628\) −6.28127 + 8.97058i −0.250650 + 0.357965i
\(629\) −20.1988 34.9854i −0.805380 1.39496i
\(630\) 0 0
\(631\) 7.53540 13.0517i 0.299979 0.519580i −0.676151 0.736763i \(-0.736353\pi\)
0.976131 + 0.217183i \(0.0696868\pi\)
\(632\) 4.85187 + 10.4049i 0.192997 + 0.413883i
\(633\) 0 0
\(634\) 8.34750 9.94816i 0.331522 0.395092i
\(635\) 34.5982 14.5182i 1.37299 0.576138i
\(636\) 0 0
\(637\) 1.56505 0.729797i 0.0620097 0.0289156i
\(638\) −2.19307 8.18464i −0.0868244 0.324033i
\(639\) 0 0
\(640\) 3.70847 0.179043i 0.146590 0.00707729i
\(641\) −28.9474 + 5.10420i −1.14335 + 0.201604i −0.713071 0.701091i \(-0.752696\pi\)
−0.430281 + 0.902695i \(0.641585\pi\)
\(642\) 0 0
\(643\) −19.6987 9.18567i −0.776842 0.362248i −0.00658305 0.999978i \(-0.502095\pi\)
−0.770259 + 0.637731i \(0.779873\pi\)
\(644\) 2.02747 11.4983i 0.0798935 0.453098i
\(645\) 0 0
\(646\) 19.6108 16.4554i 0.771576 0.647429i
\(647\) 16.4745 + 16.4745i 0.647680 + 0.647680i 0.952432 0.304752i \(-0.0985735\pi\)
−0.304752 + 0.952432i \(0.598574\pi\)
\(648\) 0 0
\(649\) 10.8616i 0.426353i
\(650\) −5.93056 1.53064i −0.232616 0.0600367i
\(651\) 0 0
\(652\) 7.57948 + 10.8246i 0.296835 + 0.423925i
\(653\) −5.62864 + 12.0707i −0.220266 + 0.472362i −0.985126 0.171835i \(-0.945030\pi\)
0.764860 + 0.644197i \(0.222808\pi\)
\(654\) 0 0
\(655\) −7.48902 + 3.94251i −0.292620 + 0.154047i
\(656\) −4.10841 + 2.37199i −0.160406 + 0.0926106i
\(657\) 0 0
\(658\) −1.06303 + 0.284837i −0.0414411 + 0.0111041i
\(659\) 12.4761 + 4.54094i 0.486001 + 0.176890i 0.573387 0.819285i \(-0.305629\pi\)
−0.0873859 + 0.996175i \(0.527851\pi\)
\(660\) 0 0
\(661\) −9.01628 7.56556i −0.350693 0.294266i 0.450375 0.892839i \(-0.351290\pi\)
−0.801068 + 0.598573i \(0.795735\pi\)
\(662\) −2.28561 26.1246i −0.0888328 1.01536i
\(663\) 0 0
\(664\) −4.95562 + 13.6155i −0.192316 + 0.528383i
\(665\) −23.8474 + 15.3474i −0.924762 + 0.595148i
\(666\) 0 0
\(667\) −32.8283 8.79631i −1.27112 0.340595i
\(668\) −16.0770 11.2572i −0.622038 0.435555i
\(669\) 0 0
\(670\) −1.04938 + 0.812928i −0.0405410 + 0.0314061i
\(671\) −3.87335 0.682976i −0.149529 0.0263660i
\(672\) 0 0
\(673\) 11.5900 + 1.01400i 0.446763 + 0.0390867i 0.308318 0.951283i \(-0.400234\pi\)
0.138445 + 0.990370i \(0.455790\pi\)
\(674\) −1.79908 −0.0692981
\(675\) 0 0
\(676\) −10.7192 −0.412276
\(677\) −5.37998 0.470687i −0.206769 0.0180900i −0.0166995 0.999861i \(-0.505316\pi\)
−0.190070 + 0.981771i \(0.560871\pi\)
\(678\) 0 0
\(679\) 34.2678 + 6.04233i 1.31508 + 0.231883i
\(680\) −30.3465 + 23.5087i −1.16374 + 0.901518i
\(681\) 0 0
\(682\) 9.62474 + 6.73932i 0.368550 + 0.258062i
\(683\) −16.0348 4.29650i −0.613553 0.164401i −0.0613579 0.998116i \(-0.519543\pi\)
−0.552195 + 0.833715i \(0.686210\pi\)
\(684\) 0 0
\(685\) 40.6646 26.1705i 1.55371 0.999922i
\(686\) −5.71610 + 15.7049i −0.218242 + 0.599614i
\(687\) 0 0
\(688\) 0.264523 + 3.02351i 0.0100848 + 0.115270i
\(689\) 1.49038 + 1.25058i 0.0567789 + 0.0476431i
\(690\) 0 0
\(691\) 4.89099 + 1.78018i 0.186062 + 0.0677211i 0.433371 0.901216i \(-0.357324\pi\)
−0.247309 + 0.968937i \(0.579546\pi\)
\(692\) 7.56797 2.02783i 0.287691 0.0770866i
\(693\) 0 0
\(694\) −8.89164 + 5.13359i −0.337522 + 0.194868i
\(695\) 22.1443 11.6576i 0.839982 0.442199i
\(696\) 0 0
\(697\) −8.73003 + 18.7216i −0.330674 + 0.709132i
\(698\) 18.4475 + 26.3458i 0.698248 + 0.997202i
\(699\) 0 0
\(700\) 11.5717 6.82390i 0.437369 0.257919i
\(701\) 30.8522i 1.16527i −0.812733 0.582636i \(-0.802021\pi\)
0.812733 0.582636i \(-0.197979\pi\)
\(702\) 0 0
\(703\) −22.0041 22.0041i −0.829899 0.829899i
\(704\) 5.99524 5.03061i 0.225954 0.189598i
\(705\) 0 0
\(706\) −0.660573 + 3.74630i −0.0248610 + 0.140994i
\(707\) 0.706888 + 0.329627i 0.0265853 + 0.0123969i
\(708\) 0 0
\(709\) −19.4630 + 3.43186i −0.730949 + 0.128886i −0.526722 0.850038i \(-0.676579\pi\)
−0.204227 + 0.978924i \(0.565468\pi\)
\(710\) 7.58533 0.366215i 0.284672 0.0137438i
\(711\) 0 0
\(712\) −2.54923 9.51386i −0.0955365 0.356547i
\(713\) 42.7119 19.9169i 1.59957 0.745893i
\(714\) 0 0
\(715\) 2.54227 1.06680i 0.0950756 0.0398959i
\(716\) −7.97067 + 9.49908i −0.297878 + 0.354997i
\(717\) 0 0
\(718\) −3.27613 7.02568i −0.122264 0.262196i
\(719\) −3.29514 + 5.70736i −0.122888 + 0.212849i −0.920905 0.389786i \(-0.872549\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(720\) 0 0
\(721\) 18.4656 + 31.9834i 0.687695 + 1.19112i
\(722\) 0.00419426 0.00599003i 0.000156094 0.000222926i
\(723\) 0 0
\(724\) 6.29925 + 17.3071i 0.234110 + 0.643212i
\(725\) −16.8521 35.2866i −0.625871 1.31051i
\(726\) 0 0
\(727\) 1.33493 15.2584i 0.0495099 0.565901i −0.930411 0.366517i \(-0.880550\pi\)
0.979921 0.199384i \(-0.0638942\pi\)
\(728\) 7.36685 7.36685i 0.273034 0.273034i
\(729\) 0 0
\(730\) 9.73608 + 30.3898i 0.360349 + 1.12478i
\(731\) 8.49492 + 10.1238i 0.314196 + 0.374444i
\(732\) 0 0
\(733\) 0.908462 0.636112i 0.0335548 0.0234953i −0.556679 0.830728i \(-0.687925\pi\)
0.590234 + 0.807233i \(0.299036\pi\)
\(734\) 16.4596 5.99082i 0.607537 0.221125i
\(735\) 0 0
\(736\) −3.56019 20.1909i −0.131230 0.744245i
\(737\) 0.154649 0.577158i 0.00569657 0.0212599i
\(738\) 0 0
\(739\) 0.148882 + 0.0859569i 0.00547670 + 0.00316198i 0.502736 0.864440i \(-0.332327\pi\)
−0.497259 + 0.867602i \(0.665660\pi\)
\(740\) 10.0089 + 10.8222i 0.367933 + 0.397832i
\(741\) 0 0
\(742\) 4.95432 0.433447i 0.181879 0.0159123i
\(743\) −20.1450 + 1.76246i −0.739048 + 0.0646584i −0.450462 0.892796i \(-0.648741\pi\)
−0.288586 + 0.957454i \(0.593185\pi\)
\(744\) 0 0
\(745\) −29.5385 1.15331i −1.08221 0.0422540i
\(746\) −1.90830 1.10175i −0.0698677 0.0403381i
\(747\) 0 0
\(748\) 1.41283 5.27274i 0.0516580 0.192790i
\(749\) 3.59719 + 20.4007i 0.131438 + 0.745424i
\(750\) 0 0
\(751\) 16.8648 6.13828i 0.615405 0.223989i −0.0154616 0.999880i \(-0.504922\pi\)
0.630867 + 0.775891i \(0.282700\pi\)
\(752\) −0.388237 + 0.271846i −0.0141575 + 0.00991322i
\(753\) 0 0
\(754\) −6.15814 7.33898i −0.224266 0.267270i
\(755\) −25.9137 + 8.30206i −0.943097 + 0.302143i
\(756\) 0 0
\(757\) −19.5487 + 19.5487i −0.710508 + 0.710508i −0.966641 0.256133i \(-0.917551\pi\)
0.256133 + 0.966641i \(0.417551\pi\)
\(758\) 0.868528 9.92732i 0.0315464 0.360577i
\(759\) 0 0
\(760\) −17.8926 + 23.5420i −0.649033 + 0.853957i
\(761\) −0.210722 0.578955i −0.00763868 0.0209871i 0.935815 0.352492i \(-0.114666\pi\)
−0.943453 + 0.331505i \(0.892444\pi\)
\(762\) 0 0
\(763\) 14.7056 21.0017i 0.532378 0.760314i
\(764\) 0.418993 + 0.725717i 0.0151586 + 0.0262555i
\(765\) 0 0
\(766\) 0.0626486 0.108511i 0.00226359 0.00392064i
\(767\) 5.18999 + 11.1300i 0.187400 + 0.401880i
\(768\) 0 0
\(769\) 26.3803 31.4388i 0.951298 1.13371i −0.0396163 0.999215i \(-0.512614\pi\)
0.990914 0.134497i \(-0.0429420\pi\)
\(770\) 2.66695 6.52346i 0.0961101 0.235089i
\(771\) 0 0
\(772\) 6.18879 2.88588i 0.222739 0.103865i
\(773\) −8.41362 31.4000i −0.302617 1.12938i −0.934977 0.354707i \(-0.884581\pi\)
0.632361 0.774674i \(-0.282086\pi\)
\(774\) 0 0
\(775\) 49.3528 + 22.4621i 1.77280 + 0.806863i
\(776\) 35.7306 6.30026i 1.28265 0.226166i
\(777\) 0 0
\(778\) 24.1159 + 11.2454i 0.864598 + 0.403169i
\(779\) −2.76312 + 15.6704i −0.0989990 + 0.561451i
\(780\) 0 0
\(781\) −2.61864 + 2.19730i −0.0937023 + 0.0786256i
\(782\) 18.0435 + 18.0435i 0.645233 + 0.645233i
\(783\) 0 0
\(784\) 1.90101i 0.0678930i
\(785\) 5.85771 + 25.8579i 0.209071 + 0.922907i
\(786\) 0 0