Properties

Label 441.2.bg.a.395.8
Level $441$
Weight $2$
Character 441.395
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 395.8
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.568908 - 0.223280i) q^{2} +(-1.19230 - 1.10629i) q^{4} +(2.30954 + 1.57462i) q^{5} +(0.0953467 + 2.64403i) q^{7} +(0.961636 + 1.99686i) q^{8} +O(q^{10})\) \(q+(-0.568908 - 0.223280i) q^{2} +(-1.19230 - 1.10629i) q^{4} +(2.30954 + 1.57462i) q^{5} +(0.0953467 + 2.64403i) q^{7} +(0.961636 + 1.99686i) q^{8} +(-0.962336 - 1.41149i) q^{10} +(-0.355186 - 2.35651i) q^{11} +(-2.96799 + 2.36690i) q^{13} +(0.536116 - 1.52550i) q^{14} +(0.141871 + 1.89314i) q^{16} +(2.98520 + 0.920812i) q^{17} +(-5.52972 + 3.19259i) q^{19} +(-1.01168 - 4.43246i) q^{20} +(-0.324092 + 1.41994i) q^{22} +(2.41439 + 7.82724i) q^{23} +(1.02786 + 2.61894i) q^{25} +(2.21699 - 0.683852i) q^{26} +(2.81140 - 3.25797i) q^{28} +(8.18266 - 1.86764i) q^{29} +(3.00894 + 1.73721i) q^{31} +(1.64855 - 5.34446i) q^{32} +(-1.49270 - 1.19039i) q^{34} +(-3.94314 + 6.25665i) q^{35} +(5.29640 - 4.91434i) q^{37} +(3.85874 - 0.581612i) q^{38} +(-0.923353 + 6.12604i) q^{40} +(-2.49594 + 1.20198i) q^{41} +(8.98188 + 4.32545i) q^{43} +(-2.18350 + 3.20261i) q^{44} +(0.374103 - 4.99206i) q^{46} +(-1.52269 + 3.87975i) q^{47} +(-6.98182 + 0.504199i) q^{49} -1.71944i q^{50} +(6.15723 + 0.461421i) q^{52} +(-0.503602 + 0.542754i) q^{53} +(2.89028 - 6.00174i) q^{55} +(-5.18807 + 2.73299i) q^{56} +(-5.07218 - 0.764509i) q^{58} +(-2.77969 + 1.89516i) q^{59} +(-8.06655 - 8.69368i) q^{61} +(-1.32392 - 1.66015i) q^{62} +(0.236150 - 0.296123i) q^{64} +(-10.5817 + 0.792987i) q^{65} +(-1.63319 + 2.82877i) q^{67} +(-2.54057 - 4.40039i) q^{68} +(3.64026 - 2.67903i) q^{70} +(-4.32106 - 0.986253i) q^{71} +(-8.43376 + 3.31001i) q^{73} +(-4.11044 + 1.61323i) q^{74} +(10.1250 + 2.31097i) q^{76} +(6.19681 - 1.16381i) q^{77} +(-5.27084 - 9.12936i) q^{79} +(-2.65332 + 4.59569i) q^{80} +(1.68834 - 0.126523i) q^{82} +(6.22852 - 7.81031i) q^{83} +(5.44452 + 6.82721i) q^{85} +(-4.14407 - 4.46625i) q^{86} +(4.36405 - 2.97536i) q^{88} +(11.8511 + 1.78627i) q^{89} +(-6.54114 - 7.62180i) q^{91} +(5.78056 - 12.0035i) q^{92} +(1.73254 - 1.86723i) q^{94} +(-17.7983 - 1.33379i) q^{95} -3.74135i q^{97} +(4.08459 + 1.27206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 216q - 16q^{4} + 2q^{7} + 12q^{10} + 12q^{16} - 6q^{19} + 44q^{22} + 26q^{25} + 84q^{28} - 6q^{31} - 112q^{34} + 60q^{37} - 304q^{40} + 20q^{43} - 20q^{46} - 86q^{49} - 168q^{52} - 84q^{55} - 120q^{58} - 2q^{61} + 32q^{64} + 22q^{67} - 136q^{70} - 6q^{73} + 84q^{76} + 2q^{79} - 104q^{82} + 96q^{85} - 12q^{88} + 58q^{91} + 52q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.568908 0.223280i −0.402278 0.157883i 0.155571 0.987825i \(-0.450278\pi\)
−0.557850 + 0.829942i \(0.688373\pi\)
\(3\) 0 0
\(4\) −1.19230 1.10629i −0.596151 0.553147i
\(5\) 2.30954 + 1.57462i 1.03286 + 0.704192i 0.956155 0.292862i \(-0.0946077\pi\)
0.0767049 + 0.997054i \(0.475560\pi\)
\(6\) 0 0
\(7\) 0.0953467 + 2.64403i 0.0360377 + 0.999350i
\(8\) 0.961636 + 1.99686i 0.339990 + 0.705996i
\(9\) 0 0
\(10\) −0.962336 1.41149i −0.304317 0.446352i
\(11\) −0.355186 2.35651i −0.107093 0.710513i −0.976357 0.216165i \(-0.930645\pi\)
0.869264 0.494348i \(-0.164593\pi\)
\(12\) 0 0
\(13\) −2.96799 + 2.36690i −0.823173 + 0.656459i −0.941686 0.336494i \(-0.890759\pi\)
0.118512 + 0.992953i \(0.462187\pi\)
\(14\) 0.536116 1.52550i 0.143283 0.407707i
\(15\) 0 0
\(16\) 0.141871 + 1.89314i 0.0354679 + 0.473286i
\(17\) 2.98520 + 0.920812i 0.724017 + 0.223330i 0.634793 0.772682i \(-0.281085\pi\)
0.0892236 + 0.996012i \(0.471561\pi\)
\(18\) 0 0
\(19\) −5.52972 + 3.19259i −1.26861 + 0.732430i −0.974724 0.223412i \(-0.928280\pi\)
−0.293881 + 0.955842i \(0.594947\pi\)
\(20\) −1.01168 4.43246i −0.226218 0.991128i
\(21\) 0 0
\(22\) −0.324092 + 1.41994i −0.0690967 + 0.302732i
\(23\) 2.41439 + 7.82724i 0.503434 + 1.63209i 0.748896 + 0.662687i \(0.230584\pi\)
−0.245462 + 0.969406i \(0.578940\pi\)
\(24\) 0 0
\(25\) 1.02786 + 2.61894i 0.205572 + 0.523789i
\(26\) 2.21699 0.683852i 0.434788 0.134114i
\(27\) 0 0
\(28\) 2.81140 3.25797i 0.531304 0.615698i
\(29\) 8.18266 1.86764i 1.51948 0.346812i 0.620293 0.784371i \(-0.287014\pi\)
0.899190 + 0.437559i \(0.144157\pi\)
\(30\) 0 0
\(31\) 3.00894 + 1.73721i 0.540422 + 0.312013i 0.745250 0.666785i \(-0.232330\pi\)
−0.204828 + 0.978798i \(0.565664\pi\)
\(32\) 1.64855 5.34446i 0.291425 0.944776i
\(33\) 0 0
\(34\) −1.49270 1.19039i −0.255996 0.204150i
\(35\) −3.94314 + 6.25665i −0.666512 + 1.05757i
\(36\) 0 0
\(37\) 5.29640 4.91434i 0.870723 0.807913i −0.111862 0.993724i \(-0.535682\pi\)
0.982586 + 0.185811i \(0.0594911\pi\)
\(38\) 3.85874 0.581612i 0.625970 0.0943499i
\(39\) 0 0
\(40\) −0.923353 + 6.12604i −0.145995 + 0.968613i
\(41\) −2.49594 + 1.20198i −0.389801 + 0.187718i −0.618510 0.785777i \(-0.712264\pi\)
0.228710 + 0.973495i \(0.426549\pi\)
\(42\) 0 0
\(43\) 8.98188 + 4.32545i 1.36972 + 0.659624i 0.966782 0.255601i \(-0.0822735\pi\)
0.402942 + 0.915226i \(0.367988\pi\)
\(44\) −2.18350 + 3.20261i −0.329175 + 0.482811i
\(45\) 0 0
\(46\) 0.374103 4.99206i 0.0551585 0.736039i
\(47\) −1.52269 + 3.87975i −0.222107 + 0.565920i −0.997879 0.0650934i \(-0.979265\pi\)
0.775772 + 0.631013i \(0.217361\pi\)
\(48\) 0 0
\(49\) −6.98182 + 0.504199i −0.997403 + 0.0720285i
\(50\) 1.71944i 0.243165i
\(51\) 0 0
\(52\) 6.15723 + 0.461421i 0.853854 + 0.0639875i
\(53\) −0.503602 + 0.542754i −0.0691751 + 0.0745530i −0.766691 0.642016i \(-0.778098\pi\)
0.697516 + 0.716569i \(0.254289\pi\)
\(54\) 0 0
\(55\) 2.89028 6.00174i 0.389726 0.809274i
\(56\) −5.18807 + 2.73299i −0.693285 + 0.365211i
\(57\) 0 0
\(58\) −5.07218 0.764509i −0.666011 0.100385i
\(59\) −2.77969 + 1.89516i −0.361884 + 0.246729i −0.730588 0.682818i \(-0.760754\pi\)
0.368704 + 0.929547i \(0.379802\pi\)
\(60\) 0 0
\(61\) −8.06655 8.69368i −1.03282 1.11311i −0.993494 0.113885i \(-0.963671\pi\)
−0.0393222 0.999227i \(-0.512520\pi\)
\(62\) −1.32392 1.66015i −0.168139 0.210839i
\(63\) 0 0
\(64\) 0.236150 0.296123i 0.0295187 0.0370153i
\(65\) −10.5817 + 0.792987i −1.31250 + 0.0983579i
\(66\) 0 0
\(67\) −1.63319 + 2.82877i −0.199526 + 0.345589i −0.948375 0.317152i \(-0.897274\pi\)
0.748849 + 0.662741i \(0.230607\pi\)
\(68\) −2.54057 4.40039i −0.308089 0.533626i
\(69\) 0 0
\(70\) 3.64026 2.67903i 0.435095 0.320205i
\(71\) −4.32106 0.986253i −0.512815 0.117047i −0.0417204 0.999129i \(-0.513284\pi\)
−0.471095 + 0.882083i \(0.656141\pi\)
\(72\) 0 0
\(73\) −8.43376 + 3.31001i −0.987097 + 0.387407i −0.803311 0.595559i \(-0.796930\pi\)
−0.183786 + 0.982966i \(0.558835\pi\)
\(74\) −4.11044 + 1.61323i −0.477829 + 0.187534i
\(75\) 0 0
\(76\) 10.1250 + 2.31097i 1.16142 + 0.265087i
\(77\) 6.19681 1.16381i 0.706192 0.132628i
\(78\) 0 0
\(79\) −5.27084 9.12936i −0.593016 1.02713i −0.993824 0.110971i \(-0.964604\pi\)
0.400808 0.916162i \(-0.368730\pi\)
\(80\) −2.65332 + 4.59569i −0.296651 + 0.513814i
\(81\) 0 0
\(82\) 1.68834 0.126523i 0.186446 0.0139722i
\(83\) 6.22852 7.81031i 0.683669 0.857293i −0.312018 0.950076i \(-0.601005\pi\)
0.995686 + 0.0927830i \(0.0295763\pi\)
\(84\) 0 0
\(85\) 5.44452 + 6.82721i 0.590541 + 0.740515i
\(86\) −4.14407 4.46625i −0.446867 0.481608i
\(87\) 0 0
\(88\) 4.36405 2.97536i 0.465209 0.317174i
\(89\) 11.8511 + 1.78627i 1.25622 + 0.189345i 0.743222 0.669045i \(-0.233297\pi\)
0.512998 + 0.858390i \(0.328535\pi\)
\(90\) 0 0
\(91\) −6.54114 7.62180i −0.685698 0.798981i
\(92\) 5.78056 12.0035i 0.602665 1.25145i
\(93\) 0 0
\(94\) 1.73254 1.86723i 0.178698 0.192591i
\(95\) −17.7983 1.33379i −1.82606 0.136844i
\(96\) 0 0
\(97\) 3.74135i 0.379877i −0.981796 0.189938i \(-0.939171\pi\)
0.981796 0.189938i \(-0.0608289\pi\)
\(98\) 4.08459 + 1.27206i 0.412606 + 0.128497i
\(99\) 0 0
\(100\) 1.67180 4.25969i 0.167180 0.425969i
\(101\) 0.997657 13.3128i 0.0992706 1.32467i −0.695834 0.718202i \(-0.744965\pi\)
0.795105 0.606472i \(-0.207416\pi\)
\(102\) 0 0
\(103\) −6.25546 + 9.17507i −0.616369 + 0.904047i −0.999809 0.0195185i \(-0.993787\pi\)
0.383441 + 0.923565i \(0.374739\pi\)
\(104\) −7.58049 3.65057i −0.743328 0.357968i
\(105\) 0 0
\(106\) 0.407689 0.196333i 0.0395982 0.0190695i
\(107\) 0.909514 6.03423i 0.0879261 0.583351i −0.900871 0.434086i \(-0.857071\pi\)
0.988797 0.149265i \(-0.0476907\pi\)
\(108\) 0 0
\(109\) 11.1749 1.68435i 1.07036 0.161331i 0.409856 0.912150i \(-0.365579\pi\)
0.660508 + 0.750819i \(0.270341\pi\)
\(110\) −2.98437 + 2.76909i −0.284549 + 0.264023i
\(111\) 0 0
\(112\) −4.99201 + 0.555618i −0.471700 + 0.0525009i
\(113\) −0.325037 0.259208i −0.0305769 0.0243843i 0.608082 0.793874i \(-0.291939\pi\)
−0.638659 + 0.769490i \(0.720511\pi\)
\(114\) 0 0
\(115\) −6.74881 + 21.8791i −0.629330 + 2.04024i
\(116\) −11.8224 6.82564i −1.09768 0.633745i
\(117\) 0 0
\(118\) 2.00454 0.457522i 0.184532 0.0421183i
\(119\) −2.15003 + 7.98076i −0.197093 + 0.731595i
\(120\) 0 0
\(121\) 5.08434 1.56831i 0.462212 0.142574i
\(122\) 2.64800 + 6.74700i 0.239739 + 0.610844i
\(123\) 0 0
\(124\) −1.66570 5.40006i −0.149584 0.484939i
\(125\) 1.36005 5.95878i 0.121647 0.532970i
\(126\) 0 0
\(127\) −4.30837 18.8762i −0.382306 1.67499i −0.690238 0.723583i \(-0.742494\pi\)
0.307932 0.951408i \(-0.400363\pi\)
\(128\) −9.88772 + 5.70868i −0.873959 + 0.504580i
\(129\) 0 0
\(130\) 6.19705 + 1.91154i 0.543518 + 0.167653i
\(131\) 1.62385 + 21.6688i 0.141876 + 1.89321i 0.384555 + 0.923102i \(0.374355\pi\)
−0.242678 + 0.970107i \(0.578026\pi\)
\(132\) 0 0
\(133\) −8.96854 14.3164i −0.777671 1.24139i
\(134\) 1.56074 1.24465i 0.134827 0.107521i
\(135\) 0 0
\(136\) 1.03194 + 6.84650i 0.0884885 + 0.587083i
\(137\) 1.44583 + 2.12064i 0.123526 + 0.181179i 0.883020 0.469335i \(-0.155506\pi\)
−0.759495 + 0.650513i \(0.774554\pi\)
\(138\) 0 0
\(139\) −2.52220 5.23739i −0.213930 0.444230i 0.766196 0.642607i \(-0.222147\pi\)
−0.980126 + 0.198377i \(0.936433\pi\)
\(140\) 11.6231 3.09753i 0.982332 0.261789i
\(141\) 0 0
\(142\) 2.23807 + 1.52589i 0.187815 + 0.128050i
\(143\) 6.63180 + 6.15341i 0.554579 + 0.514574i
\(144\) 0 0
\(145\) 21.8390 + 8.57119i 1.81363 + 0.711799i
\(146\) 5.53709 0.458253
\(147\) 0 0
\(148\) −11.7516 −0.965977
\(149\) −4.13806 1.62407i −0.339003 0.133049i 0.189732 0.981836i \(-0.439238\pi\)
−0.528735 + 0.848787i \(0.677333\pi\)
\(150\) 0 0
\(151\) −7.68138 7.12727i −0.625101 0.580009i 0.302699 0.953086i \(-0.402112\pi\)
−0.927800 + 0.373077i \(0.878303\pi\)
\(152\) −11.6927 7.97196i −0.948405 0.646612i
\(153\) 0 0
\(154\) −3.78527 0.721523i −0.305026 0.0581420i
\(155\) 4.21383 + 8.75011i 0.338463 + 0.702826i
\(156\) 0 0
\(157\) 6.49697 + 9.52930i 0.518514 + 0.760521i 0.992791 0.119855i \(-0.0382429\pi\)
−0.474277 + 0.880376i \(0.657291\pi\)
\(158\) 0.960219 + 6.37064i 0.0763909 + 0.506821i
\(159\) 0 0
\(160\) 12.2229 9.74743i 0.966304 0.770602i
\(161\) −20.4653 + 7.13002i −1.61289 + 0.561924i
\(162\) 0 0
\(163\) 0.476350 + 6.35645i 0.0373106 + 0.497875i 0.984287 + 0.176574i \(0.0565013\pi\)
−0.946977 + 0.321302i \(0.895880\pi\)
\(164\) 4.30566 + 1.32812i 0.336216 + 0.103709i
\(165\) 0 0
\(166\) −5.28734 + 3.05264i −0.410377 + 0.236931i
\(167\) −3.32556 14.5702i −0.257340 1.12748i −0.924083 0.382192i \(-0.875169\pi\)
0.666743 0.745288i \(-0.267688\pi\)
\(168\) 0 0
\(169\) 0.314019 1.37581i 0.0241553 0.105831i
\(170\) −1.57305 5.09970i −0.120647 0.391129i
\(171\) 0 0
\(172\) −5.92390 15.0938i −0.451693 1.15089i
\(173\) 3.91986 1.20912i 0.298021 0.0919274i −0.142139 0.989847i \(-0.545398\pi\)
0.440160 + 0.897919i \(0.354922\pi\)
\(174\) 0 0
\(175\) −6.82657 + 2.96740i −0.516040 + 0.224314i
\(176\) 4.41081 1.00674i 0.332478 0.0758858i
\(177\) 0 0
\(178\) −6.34337 3.66235i −0.475456 0.274504i
\(179\) 3.04420 9.86906i 0.227534 0.737648i −0.767759 0.640739i \(-0.778628\pi\)
0.995293 0.0969091i \(-0.0308956\pi\)
\(180\) 0 0
\(181\) 13.1115 + 10.4561i 0.974573 + 0.777196i 0.974863 0.222804i \(-0.0715211\pi\)
−0.000290678 1.00000i \(0.500093\pi\)
\(182\) 2.01951 + 5.79660i 0.149696 + 0.429673i
\(183\) 0 0
\(184\) −13.3081 + 12.3481i −0.981089 + 0.910317i
\(185\) 19.9705 3.01007i 1.46826 0.221305i
\(186\) 0 0
\(187\) 1.10960 7.36170i 0.0811418 0.538341i
\(188\) 6.10765 2.94129i 0.445446 0.214516i
\(189\) 0 0
\(190\) 9.82775 + 4.73280i 0.712980 + 0.343353i
\(191\) −2.12421 + 3.11564i −0.153702 + 0.225440i −0.895365 0.445333i \(-0.853085\pi\)
0.741663 + 0.670773i \(0.234038\pi\)
\(192\) 0 0
\(193\) −0.671898 + 8.96585i −0.0483643 + 0.645376i 0.919369 + 0.393397i \(0.128700\pi\)
−0.967733 + 0.251979i \(0.918919\pi\)
\(194\) −0.835369 + 2.12848i −0.0599760 + 0.152816i
\(195\) 0 0
\(196\) 8.88223 + 7.12279i 0.634445 + 0.508771i
\(197\) 24.7868i 1.76599i −0.469384 0.882994i \(-0.655524\pi\)
0.469384 0.882994i \(-0.344476\pi\)
\(198\) 0 0
\(199\) 6.43723 + 0.482404i 0.456323 + 0.0341967i 0.300909 0.953653i \(-0.402710\pi\)
0.155414 + 0.987849i \(0.450329\pi\)
\(200\) −4.24123 + 4.57096i −0.299900 + 0.323216i
\(201\) 0 0
\(202\) −3.54006 + 7.35100i −0.249077 + 0.517215i
\(203\) 5.71829 + 21.4572i 0.401345 + 1.50600i
\(204\) 0 0
\(205\) −7.65715 1.15413i −0.534799 0.0806079i
\(206\) 5.60739 3.82305i 0.390685 0.266365i
\(207\) 0 0
\(208\) −4.90195 5.28304i −0.339889 0.366313i
\(209\) 9.48743 + 11.8969i 0.656259 + 0.822923i
\(210\) 0 0
\(211\) −9.74313 + 12.2175i −0.670745 + 0.841087i −0.994465 0.105065i \(-0.966495\pi\)
0.323721 + 0.946153i \(0.395066\pi\)
\(212\) 1.20089 0.0899943i 0.0824775 0.00618084i
\(213\) 0 0
\(214\) −1.86475 + 3.22984i −0.127472 + 0.220788i
\(215\) 13.9331 + 24.1329i 0.950230 + 1.64585i
\(216\) 0 0
\(217\) −4.30636 + 8.12138i −0.292334 + 0.551315i
\(218\) −6.73358 1.53690i −0.456056 0.104092i
\(219\) 0 0
\(220\) −10.0858 + 3.95838i −0.679983 + 0.266874i
\(221\) −11.0395 + 4.33269i −0.742598 + 0.291448i
\(222\) 0 0
\(223\) −2.26598 0.517194i −0.151741 0.0346339i 0.145976 0.989288i \(-0.453368\pi\)
−0.297717 + 0.954654i \(0.596225\pi\)
\(224\) 14.2881 + 3.84924i 0.954664 + 0.257188i
\(225\) 0 0
\(226\) 0.127040 + 0.220040i 0.00845058 + 0.0146368i
\(227\) 6.15258 10.6566i 0.408361 0.707302i −0.586345 0.810061i \(-0.699434\pi\)
0.994706 + 0.102759i \(0.0327672\pi\)
\(228\) 0 0
\(229\) −5.76042 + 0.431684i −0.380659 + 0.0285265i −0.263686 0.964609i \(-0.584938\pi\)
−0.116973 + 0.993135i \(0.537319\pi\)
\(230\) 8.72461 10.9403i 0.575284 0.721383i
\(231\) 0 0
\(232\) 11.5982 + 14.5436i 0.761456 + 0.954836i
\(233\) −4.48540 4.83411i −0.293848 0.316693i 0.568821 0.822461i \(-0.307400\pi\)
−0.862670 + 0.505768i \(0.831209\pi\)
\(234\) 0 0
\(235\) −9.62586 + 6.56280i −0.627922 + 0.428110i
\(236\) 5.41083 + 0.815551i 0.352215 + 0.0530879i
\(237\) 0 0
\(238\) 3.00511 4.06026i 0.194792 0.263187i
\(239\) −1.49317 + 3.10061i −0.0965853 + 0.200562i −0.943663 0.330907i \(-0.892645\pi\)
0.847078 + 0.531469i \(0.178360\pi\)
\(240\) 0 0
\(241\) 9.39452 10.1249i 0.605155 0.652201i −0.353946 0.935266i \(-0.615160\pi\)
0.959101 + 0.283064i \(0.0913510\pi\)
\(242\) −3.24269 0.243006i −0.208448 0.0156210i
\(243\) 0 0
\(244\) 19.2895i 1.23488i
\(245\) −16.9187 9.82924i −1.08090 0.627967i
\(246\) 0 0
\(247\) 8.85566 22.5639i 0.563472 1.43570i
\(248\) −0.575461 + 7.67900i −0.0365418 + 0.487617i
\(249\) 0 0
\(250\) −2.10422 + 3.08633i −0.133083 + 0.195196i
\(251\) 2.90508 + 1.39901i 0.183367 + 0.0883049i 0.523315 0.852139i \(-0.324695\pi\)
−0.339948 + 0.940444i \(0.610409\pi\)
\(252\) 0 0
\(253\) 17.5874 8.46964i 1.10571 0.532482i
\(254\) −1.76361 + 11.7008i −0.110659 + 0.734172i
\(255\) 0 0
\(256\) 6.15078 0.927081i 0.384424 0.0579426i
\(257\) 13.8489 12.8499i 0.863871 0.801555i −0.117621 0.993059i \(-0.537527\pi\)
0.981492 + 0.191503i \(0.0613363\pi\)
\(258\) 0 0
\(259\) 13.4987 + 13.5353i 0.838767 + 0.841042i
\(260\) 13.4938 + 10.7610i 0.836852 + 0.667367i
\(261\) 0 0
\(262\) 3.91438 12.6901i 0.241831 0.783997i
\(263\) 25.5040 + 14.7247i 1.57264 + 0.907965i 0.995844 + 0.0910776i \(0.0290311\pi\)
0.576797 + 0.816887i \(0.304302\pi\)
\(264\) 0 0
\(265\) −2.01772 + 0.460532i −0.123948 + 0.0282903i
\(266\) 1.90572 + 10.1472i 0.116847 + 0.622164i
\(267\) 0 0
\(268\) 5.07671 1.56596i 0.310109 0.0956560i
\(269\) 9.65058 + 24.5893i 0.588406 + 1.49923i 0.846109 + 0.533010i \(0.178939\pi\)
−0.257703 + 0.966224i \(0.582965\pi\)
\(270\) 0 0
\(271\) −0.761616 2.46910i −0.0462649 0.149987i 0.929493 0.368840i \(-0.120245\pi\)
−0.975758 + 0.218852i \(0.929769\pi\)
\(272\) −1.31971 + 5.78204i −0.0800194 + 0.350588i
\(273\) 0 0
\(274\) −0.349047 1.52927i −0.0210867 0.0923868i
\(275\) 5.80647 3.35237i 0.350144 0.202155i
\(276\) 0 0
\(277\) 9.27993 + 2.86248i 0.557577 + 0.171990i 0.560720 0.828005i \(-0.310524\pi\)
−0.00314320 + 0.999995i \(0.501001\pi\)
\(278\) 0.265492 + 3.54275i 0.0159232 + 0.212480i
\(279\) 0 0
\(280\) −16.2855 1.85728i −0.973245 0.110994i
\(281\) 16.1573 12.8850i 0.963863 0.768655i −0.00901855 0.999959i \(-0.502871\pi\)
0.972881 + 0.231304i \(0.0742993\pi\)
\(282\) 0 0
\(283\) 0.766715 + 5.08682i 0.0455765 + 0.302380i 0.999992 + 0.00390027i \(0.00124150\pi\)
−0.954416 + 0.298480i \(0.903520\pi\)
\(284\) 4.06092 + 5.95627i 0.240971 + 0.353440i
\(285\) 0 0
\(286\) −2.39895 4.98147i −0.141853 0.294560i
\(287\) −3.41606 6.48475i −0.201644 0.382782i
\(288\) 0 0
\(289\) −5.98255 4.07883i −0.351914 0.239931i
\(290\) −10.5106 9.75243i −0.617205 0.572683i
\(291\) 0 0
\(292\) 13.7174 + 5.38369i 0.802752 + 0.315057i
\(293\) −23.2876 −1.36048 −0.680238 0.732991i \(-0.738124\pi\)
−0.680238 + 0.732991i \(0.738124\pi\)
\(294\) 0 0
\(295\) −9.40397 −0.547520
\(296\) 14.9065 + 5.85035i 0.866420 + 0.340045i
\(297\) 0 0
\(298\) 1.99155 + 1.84789i 0.115367 + 0.107045i
\(299\) −25.6922 17.5166i −1.48582 1.01301i
\(300\) 0 0
\(301\) −10.5802 + 24.1608i −0.609834 + 1.39261i
\(302\) 2.77862 + 5.76986i 0.159891 + 0.332018i
\(303\) 0 0
\(304\) −6.82853 10.0156i −0.391643 0.574435i
\(305\) −4.94082 32.7802i −0.282910 1.87699i
\(306\) 0 0
\(307\) −8.07903 + 6.44281i −0.461094 + 0.367710i −0.826313 0.563211i \(-0.809566\pi\)
0.365219 + 0.930922i \(0.380994\pi\)
\(308\) −8.67599 5.46789i −0.494360 0.311562i
\(309\) 0 0
\(310\) −0.443558 5.91887i −0.0251924 0.336169i
\(311\) 1.80833 + 0.557795i 0.102541 + 0.0316297i 0.345601 0.938382i \(-0.387675\pi\)
−0.243060 + 0.970011i \(0.578151\pi\)
\(312\) 0 0
\(313\) −21.9225 + 12.6570i −1.23913 + 0.715413i −0.968917 0.247387i \(-0.920428\pi\)
−0.270215 + 0.962800i \(0.587095\pi\)
\(314\) −1.56847 6.87193i −0.0885141 0.387805i
\(315\) 0 0
\(316\) −3.81533 + 16.7161i −0.214629 + 0.940352i
\(317\) −0.837254 2.71431i −0.0470249 0.152451i 0.929015 0.370041i \(-0.120656\pi\)
−0.976040 + 0.217590i \(0.930180\pi\)
\(318\) 0 0
\(319\) −7.30747 18.6191i −0.409140 1.04247i
\(320\) 1.01168 0.312062i 0.0565546 0.0174448i
\(321\) 0 0
\(322\) 13.2348 + 0.513165i 0.737549 + 0.0285976i
\(323\) −19.4471 + 4.43867i −1.08207 + 0.246974i
\(324\) 0 0
\(325\) −9.24945 5.34017i −0.513067 0.296219i
\(326\) 1.14827 3.72259i 0.0635966 0.206175i
\(327\) 0 0
\(328\) −4.80038 3.82817i −0.265056 0.211375i
\(329\) −10.4034 3.65612i −0.573557 0.201569i
\(330\) 0 0
\(331\) 7.16952 6.65235i 0.394073 0.365646i −0.458105 0.888898i \(-0.651472\pi\)
0.852178 + 0.523252i \(0.175281\pi\)
\(332\) −16.0668 + 2.42168i −0.881779 + 0.132907i
\(333\) 0 0
\(334\) −1.36130 + 9.03166i −0.0744872 + 0.494190i
\(335\) −8.22616 + 3.96151i −0.449443 + 0.216440i
\(336\) 0 0
\(337\) 1.92190 + 0.925541i 0.104693 + 0.0504174i 0.485497 0.874238i \(-0.338639\pi\)
−0.380804 + 0.924656i \(0.624353\pi\)
\(338\) −0.485837 + 0.712592i −0.0264260 + 0.0387599i
\(339\) 0 0
\(340\) 1.06140 14.1633i 0.0575622 0.768115i
\(341\) 3.02502 7.70762i 0.163814 0.417391i
\(342\) 0 0
\(343\) −1.99881 18.4121i −0.107926 0.994159i
\(344\) 22.0950i 1.19129i
\(345\) 0 0
\(346\) −2.50001 0.187350i −0.134401 0.0100720i
\(347\) 18.9046 20.3743i 1.01485 1.09375i 0.0192725 0.999814i \(-0.493865\pi\)
0.995578 0.0939348i \(-0.0299445\pi\)
\(348\) 0 0
\(349\) 12.8147 26.6100i 0.685955 1.42440i −0.208853 0.977947i \(-0.566973\pi\)
0.894807 0.446452i \(-0.147313\pi\)
\(350\) 4.54625 0.163943i 0.243007 0.00876310i
\(351\) 0 0
\(352\) −13.1798 1.98653i −0.702485 0.105883i
\(353\) 10.8537 7.39996i 0.577687 0.393860i −0.238933 0.971036i \(-0.576798\pi\)
0.816620 + 0.577176i \(0.195845\pi\)
\(354\) 0 0
\(355\) −8.42670 9.08182i −0.447243 0.482013i
\(356\) −12.1540 15.2406i −0.644161 0.807752i
\(357\) 0 0
\(358\) −3.93543 + 4.93487i −0.207994 + 0.260816i
\(359\) −17.2207 + 1.29051i −0.908871 + 0.0681105i −0.520955 0.853584i \(-0.674424\pi\)
−0.387916 + 0.921695i \(0.626805\pi\)
\(360\) 0 0
\(361\) 10.8852 18.8538i 0.572906 0.992303i
\(362\) −5.12461 8.87609i −0.269344 0.466517i
\(363\) 0 0
\(364\) −0.632940 + 16.3239i −0.0331751 + 0.855605i
\(365\) −24.6901 5.63536i −1.29234 0.294968i
\(366\) 0 0
\(367\) −2.22898 + 0.874809i −0.116352 + 0.0456647i −0.422803 0.906222i \(-0.638954\pi\)
0.306451 + 0.951886i \(0.400858\pi\)
\(368\) −14.4756 + 5.68124i −0.754591 + 0.296155i
\(369\) 0 0
\(370\) −12.0335 2.74656i −0.625590 0.142787i
\(371\) −1.48308 1.27979i −0.0769975 0.0664434i
\(372\) 0 0
\(373\) 5.26798 + 9.12442i 0.272766 + 0.472444i 0.969569 0.244818i \(-0.0787282\pi\)
−0.696803 + 0.717262i \(0.745395\pi\)
\(374\) −2.27498 + 3.94037i −0.117636 + 0.203752i
\(375\) 0 0
\(376\) −9.21159 + 0.690313i −0.475051 + 0.0356002i
\(377\) −19.8656 + 24.9107i −1.02313 + 1.28296i
\(378\) 0 0
\(379\) −2.36405 2.96442i −0.121433 0.152272i 0.717399 0.696663i \(-0.245332\pi\)
−0.838832 + 0.544390i \(0.816761\pi\)
\(380\) 19.7453 + 21.2804i 1.01291 + 1.09166i
\(381\) 0 0
\(382\) 1.90414 1.29822i 0.0974241 0.0664226i
\(383\) 24.3620 + 3.67198i 1.24484 + 0.187629i 0.738232 0.674547i \(-0.235661\pi\)
0.506608 + 0.862176i \(0.330899\pi\)
\(384\) 0 0
\(385\) 16.1444 + 7.06976i 0.822793 + 0.360308i
\(386\) 2.38414 4.95072i 0.121350 0.251985i
\(387\) 0 0
\(388\) −4.13904 + 4.46082i −0.210128 + 0.226464i
\(389\) 9.28049 + 0.695476i 0.470539 + 0.0352621i 0.307890 0.951422i \(-0.400377\pi\)
0.162649 + 0.986684i \(0.447996\pi\)
\(390\) 0 0
\(391\) 25.5891i 1.29409i
\(392\) −7.72078 13.4568i −0.389958 0.679673i
\(393\) 0 0
\(394\) −5.53440 + 14.1014i −0.278819 + 0.710419i
\(395\) 2.20204 29.3842i 0.110797 1.47848i
\(396\) 0 0
\(397\) 12.1166 17.7717i 0.608112 0.891937i −0.391489 0.920183i \(-0.628040\pi\)
0.999601 + 0.0282461i \(0.00899219\pi\)
\(398\) −3.55448 1.71175i −0.178170 0.0858021i
\(399\) 0 0
\(400\) −4.81221 + 2.31744i −0.240611 + 0.115872i
\(401\) 3.39335 22.5134i 0.169456 1.12426i −0.728779 0.684749i \(-0.759912\pi\)
0.898235 0.439516i \(-0.144850\pi\)
\(402\) 0 0
\(403\) −13.0423 + 1.96581i −0.649684 + 0.0979242i
\(404\) −15.9174 + 14.7692i −0.791920 + 0.734794i
\(405\) 0 0
\(406\) 1.53777 13.4839i 0.0763183 0.669196i
\(407\) −13.4619 10.7355i −0.667281 0.532139i
\(408\) 0 0
\(409\) 9.28497 30.1011i 0.459112 1.48841i −0.369845 0.929094i \(-0.620589\pi\)
0.828957 0.559312i \(-0.188935\pi\)
\(410\) 4.09852 + 2.36628i 0.202411 + 0.116862i
\(411\) 0 0
\(412\) 17.6087 4.01908i 0.867520 0.198006i
\(413\) −5.27590 7.16889i −0.259610 0.352758i
\(414\) 0 0
\(415\) 26.6833 8.23071i 1.30983 0.404030i
\(416\) 7.75690 + 19.7643i 0.380313 + 0.969023i
\(417\) 0 0
\(418\) −2.74114 8.88657i −0.134074 0.434656i
\(419\) −8.17719 + 35.8266i −0.399482 + 1.75024i 0.229963 + 0.973199i \(0.426140\pi\)
−0.629445 + 0.777045i \(0.716718\pi\)
\(420\) 0 0
\(421\) 1.91314 + 8.38202i 0.0932408 + 0.408515i 0.999911 0.0133251i \(-0.00424165\pi\)
−0.906670 + 0.421840i \(0.861385\pi\)
\(422\) 8.27086 4.77518i 0.402619 0.232452i
\(423\) 0 0
\(424\) −1.56808 0.483690i −0.0761529 0.0234901i
\(425\) 0.656811 + 8.76453i 0.0318600 + 0.425142i
\(426\) 0 0
\(427\) 22.2172 22.1571i 1.07517 1.07226i
\(428\) −7.76005 + 6.18844i −0.375096 + 0.299129i
\(429\) 0 0
\(430\) −2.53827 16.8403i −0.122406 0.812114i
\(431\) 18.1310 + 26.5933i 0.873339 + 1.28095i 0.958647 + 0.284598i \(0.0918601\pi\)
−0.0853083 + 0.996355i \(0.527188\pi\)
\(432\) 0 0
\(433\) 5.06241 + 10.5122i 0.243284 + 0.505184i 0.986478 0.163891i \(-0.0524046\pi\)
−0.743194 + 0.669076i \(0.766690\pi\)
\(434\) 4.26326 3.65879i 0.204643 0.175628i
\(435\) 0 0
\(436\) −15.1873 10.3545i −0.727339 0.495891i
\(437\) −38.3400 35.5744i −1.83405 1.70175i
\(438\) 0 0
\(439\) 11.7316 + 4.60431i 0.559919 + 0.219752i 0.628386 0.777901i \(-0.283716\pi\)
−0.0684676 + 0.997653i \(0.521811\pi\)
\(440\) 14.7640 0.703847
\(441\) 0 0
\(442\) 7.24787 0.344746
\(443\) −13.3936 5.25659i −0.636348 0.249748i 0.0251633 0.999683i \(-0.491989\pi\)
−0.661511 + 0.749935i \(0.730085\pi\)
\(444\) 0 0
\(445\) 24.5581 + 22.7865i 1.16416 + 1.08019i
\(446\) 1.17365 + 0.800183i 0.0555740 + 0.0378897i
\(447\) 0 0
\(448\) 0.805474 + 0.596154i 0.0380551 + 0.0281656i
\(449\) 8.39188 + 17.4259i 0.396037 + 0.822380i 0.999684 + 0.0251283i \(0.00799941\pi\)
−0.603647 + 0.797252i \(0.706286\pi\)
\(450\) 0 0
\(451\) 3.71900 + 5.45477i 0.175121 + 0.256855i
\(452\) 0.100781 + 0.668641i 0.00474036 + 0.0314502i
\(453\) 0 0
\(454\) −5.87964 + 4.68886i −0.275945 + 0.220059i
\(455\) −3.10561 27.9027i −0.145593 1.30810i
\(456\) 0 0
\(457\) 2.55635 + 34.1121i 0.119581 + 1.59569i 0.658000 + 0.753018i \(0.271403\pi\)
−0.538419 + 0.842677i \(0.680978\pi\)
\(458\) 3.37353 + 1.04060i 0.157635 + 0.0486239i
\(459\) 0 0
\(460\) 32.2514 18.6203i 1.50373 0.868177i
\(461\) 2.13925 + 9.37267i 0.0996348 + 0.436529i 0.999999 + 0.00139152i \(0.000442934\pi\)
−0.900364 + 0.435137i \(0.856700\pi\)
\(462\) 0 0
\(463\) 4.14177 18.1463i 0.192484 0.843330i −0.782782 0.622296i \(-0.786200\pi\)
0.975266 0.221033i \(-0.0709429\pi\)
\(464\) 4.69660 + 15.2260i 0.218034 + 0.706849i
\(465\) 0 0
\(466\) 1.47242 + 3.75166i 0.0682085 + 0.173792i
\(467\) −10.9618 + 3.38127i −0.507252 + 0.156466i −0.537809 0.843067i \(-0.680748\pi\)
0.0305574 + 0.999533i \(0.490272\pi\)
\(468\) 0 0
\(469\) −7.63508 4.04849i −0.352555 0.186942i
\(470\) 6.94156 1.58437i 0.320190 0.0730814i
\(471\) 0 0
\(472\) −6.45741 3.72819i −0.297226 0.171604i
\(473\) 7.00270 22.7022i 0.321984 1.04385i
\(474\) 0 0
\(475\) −14.0450 11.2005i −0.644428 0.513914i
\(476\) 11.3925 7.13691i 0.522177 0.327120i
\(477\) 0 0
\(478\) 1.54178 1.43056i 0.0705194 0.0654324i
\(479\) −33.4701 + 5.04481i −1.52929 + 0.230503i −0.859147 0.511729i \(-0.829005\pi\)
−0.670142 + 0.742233i \(0.733767\pi\)
\(480\) 0 0
\(481\) −4.08795 + 27.1218i −0.186394 + 1.23665i
\(482\) −7.60530 + 3.66252i −0.346412 + 0.166823i
\(483\) 0 0
\(484\) −7.79708 3.75487i −0.354413 0.170676i
\(485\) 5.89121 8.64082i 0.267506 0.392360i
\(486\) 0 0
\(487\) 1.45316 19.3911i 0.0658489 0.878692i −0.862280 0.506433i \(-0.830964\pi\)
0.928129 0.372260i \(-0.121417\pi\)
\(488\) 9.60295 24.4679i 0.434705 1.10761i
\(489\) 0 0
\(490\) 7.43053 + 9.36954i 0.335677 + 0.423273i
\(491\) 13.0886i 0.590679i −0.955392 0.295340i \(-0.904567\pi\)
0.955392 0.295340i \(-0.0954328\pi\)
\(492\) 0 0
\(493\) 26.1466 + 1.95942i 1.17758 + 0.0882477i
\(494\) −10.0761 + 10.8595i −0.453345 + 0.488590i
\(495\) 0 0
\(496\) −2.86191 + 5.94282i −0.128504 + 0.266840i
\(497\) 2.19569 11.5191i 0.0984900 0.516700i
\(498\) 0 0
\(499\) −10.3061 1.55340i −0.461365 0.0695396i −0.0857528 0.996316i \(-0.527330\pi\)
−0.375612 + 0.926777i \(0.622568\pi\)
\(500\) −8.21376 + 5.60005i −0.367331 + 0.250442i
\(501\) 0 0
\(502\) −1.34035 1.44456i −0.0598228 0.0644736i
\(503\) 3.11566 + 3.90692i 0.138921 + 0.174201i 0.846425 0.532508i \(-0.178750\pi\)
−0.707504 + 0.706709i \(0.750179\pi\)
\(504\) 0 0
\(505\) 23.2668 29.1756i 1.03536 1.29830i
\(506\) −11.8967 + 0.891534i −0.528873 + 0.0396335i
\(507\) 0 0
\(508\) −15.7458 + 27.2724i −0.698605 + 1.21002i
\(509\) 0.772687 + 1.33833i 0.0342487 + 0.0593205i 0.882642 0.470046i \(-0.155763\pi\)
−0.848393 + 0.529367i \(0.822429\pi\)
\(510\) 0 0
\(511\) −9.55590 21.9835i −0.422728 0.972494i
\(512\) 18.5560 + 4.23528i 0.820066 + 0.187175i
\(513\) 0 0
\(514\) −10.7479 + 4.21823i −0.474068 + 0.186058i
\(515\) −28.8945 + 11.3403i −1.27324 + 0.499712i
\(516\) 0 0
\(517\) 9.68350 + 2.21020i 0.425880 + 0.0972043i
\(518\) −4.65734 10.7143i −0.204632 0.470760i
\(519\) 0 0
\(520\) −11.7592 20.3675i −0.515675 0.893176i
\(521\) −15.6375 + 27.0849i −0.685090 + 1.18661i 0.288319 + 0.957534i \(0.406904\pi\)
−0.973409 + 0.229076i \(0.926430\pi\)
\(522\) 0 0
\(523\) 3.05590 0.229008i 0.133625 0.0100138i −0.00774962 0.999970i \(-0.502467\pi\)
0.141375 + 0.989956i \(0.454848\pi\)
\(524\) 22.0359 27.6322i 0.962644 1.20712i
\(525\) 0 0
\(526\) −11.2217 14.0715i −0.489288 0.613547i
\(527\) 7.38264 + 7.95659i 0.321593 + 0.346595i
\(528\) 0 0
\(529\) −36.4330 + 24.8396i −1.58404 + 1.07998i
\(530\) 1.25073 + 0.188516i 0.0543280 + 0.00818863i
\(531\) 0 0
\(532\) −5.14490 + 26.9913i −0.223060 + 1.17022i
\(533\) 4.56297 9.47511i 0.197644 0.410413i
\(534\) 0 0
\(535\) 11.6022 12.5042i 0.501606 0.540603i
\(536\) −7.21918 0.541003i −0.311821 0.0233678i
\(537\) 0 0
\(538\) 16.1438i 0.696009i
\(539\) 3.66799 + 16.2736i 0.157992 + 0.700954i
\(540\) 0 0
\(541\) −13.4069 + 34.1603i −0.576408 + 1.46866i 0.283881 + 0.958859i \(0.408378\pi\)
−0.860290 + 0.509805i \(0.829717\pi\)
\(542\) −0.118011 + 1.57474i −0.00506899 + 0.0676410i
\(543\) 0 0
\(544\) 9.84248 14.4363i 0.421993 0.618950i
\(545\) 28.4612 + 13.7062i 1.21914 + 0.587109i
\(546\) 0 0
\(547\) −33.1589 + 15.9685i −1.41777 + 0.682763i −0.976680 0.214699i \(-0.931123\pi\)
−0.441092 + 0.897462i \(0.645409\pi\)
\(548\) 0.622190 4.12796i 0.0265786 0.176338i
\(549\) 0 0
\(550\) −4.05186 + 0.610720i −0.172772 + 0.0260412i
\(551\) −39.2853 + 36.4514i −1.67361 + 1.55288i
\(552\) 0 0
\(553\) 23.6358 14.8067i 1.00510 0.629646i
\(554\) −4.64029 3.70051i −0.197147 0.157219i
\(555\) 0 0
\(556\) −2.78688 + 9.03484i −0.118190 + 0.383163i
\(557\) 33.1476 + 19.1378i 1.40451 + 0.810894i 0.994851 0.101344i \(-0.0323143\pi\)
0.409659 + 0.912239i \(0.365648\pi\)
\(558\) 0 0
\(559\) −36.8960 + 8.42128i −1.56054 + 0.356182i
\(560\) −12.4041 6.57729i −0.524171 0.277941i
\(561\) 0 0
\(562\) −12.0690 + 3.72278i −0.509098 + 0.157036i
\(563\) −4.75307 12.1106i −0.200318 0.510402i 0.795050 0.606544i \(-0.207445\pi\)
−0.995368 + 0.0961425i \(0.969350\pi\)
\(564\) 0 0
\(565\) −0.342533 1.11046i −0.0144105 0.0467175i
\(566\) 0.699594 3.06512i 0.0294061 0.128837i
\(567\) 0 0
\(568\) −2.18588 9.57696i −0.0917174 0.401840i
\(569\) 22.4059 12.9361i 0.939305 0.542308i 0.0495625 0.998771i \(-0.484217\pi\)
0.889742 + 0.456463i \(0.150884\pi\)
\(570\) 0 0
\(571\) 37.0368 + 11.4243i 1.54994 + 0.478093i 0.947415 0.320006i \(-0.103685\pi\)
0.602525 + 0.798100i \(0.294161\pi\)
\(572\) −1.09962 14.6734i −0.0459775 0.613527i
\(573\) 0 0
\(574\) 0.495510 + 4.45196i 0.0206822 + 0.185821i
\(575\) −18.0175 + 14.3684i −0.751380 + 0.599206i
\(576\) 0 0
\(577\) −0.910238 6.03904i −0.0378937 0.251408i 0.961861 0.273537i \(-0.0881937\pi\)
−0.999755 + 0.0221289i \(0.992956\pi\)
\(578\) 2.49279 + 3.65626i 0.103687 + 0.152080i
\(579\) 0 0
\(580\) −16.5565 34.3799i −0.687470 1.42755i
\(581\) 21.2446 + 15.7237i 0.881374 + 0.652330i
\(582\) 0 0
\(583\) 1.45788 + 0.993963i 0.0603790 + 0.0411657i
\(584\) −14.7198 13.6580i −0.609111 0.565172i
\(585\) 0 0
\(586\) 13.2485 + 5.19965i 0.547290 + 0.214796i
\(587\) 8.51684 0.351528 0.175764 0.984432i \(-0.443760\pi\)
0.175764 + 0.984432i \(0.443760\pi\)
\(588\) 0 0
\(589\) −22.1848 −0.914109
\(590\) 5.34999 + 2.09972i 0.220256 + 0.0864439i
\(591\) 0 0
\(592\) 10.0550 + 9.32964i 0.413256 + 0.383446i
\(593\) −26.0237 17.7427i −1.06867 0.728605i −0.104667 0.994507i \(-0.533378\pi\)
−0.964000 + 0.265903i \(0.914330\pi\)
\(594\) 0 0
\(595\) −17.5322 + 15.0464i −0.718752 + 0.616844i
\(596\) 3.13711 + 6.51429i 0.128501 + 0.266836i
\(597\) 0 0
\(598\) 10.7054 + 15.7019i 0.437775 + 0.642097i
\(599\) 4.66133 + 30.9259i 0.190457 + 1.26360i 0.855897 + 0.517146i \(0.173006\pi\)
−0.665441 + 0.746451i \(0.731756\pi\)
\(600\) 0 0
\(601\) −8.61014 + 6.86636i −0.351215 + 0.280084i −0.783166 0.621812i \(-0.786397\pi\)
0.431951 + 0.901897i \(0.357825\pi\)
\(602\) 11.4138 11.3829i 0.465191 0.463933i
\(603\) 0 0
\(604\) 1.27365 + 16.9957i 0.0518242 + 0.691546i
\(605\) 14.2120 + 4.38382i 0.577800 + 0.178228i
\(606\) 0 0
\(607\) 23.6262 13.6406i 0.958956 0.553654i 0.0631048 0.998007i \(-0.479900\pi\)
0.895852 + 0.444353i \(0.146566\pi\)
\(608\) 7.94664 + 34.8165i 0.322279 + 1.41200i
\(609\) 0 0
\(610\) −4.50828 + 19.7521i −0.182535 + 0.799738i
\(611\) −4.66363 15.1191i −0.188670 0.611655i
\(612\) 0 0
\(613\) 1.53110 + 3.90117i 0.0618404 + 0.157567i 0.958454 0.285247i \(-0.0920756\pi\)
−0.896614 + 0.442814i \(0.853980\pi\)
\(614\) 6.03477 1.86148i 0.243543 0.0751232i
\(615\) 0 0
\(616\) 8.28304 + 11.2550i 0.333733 + 0.453477i
\(617\) −23.7804 + 5.42771i −0.957361 + 0.218511i −0.672533 0.740067i \(-0.734794\pi\)
−0.284828 + 0.958579i \(0.591936\pi\)
\(618\) 0 0
\(619\) 11.2869 + 6.51647i 0.453657 + 0.261919i 0.709374 0.704833i \(-0.248978\pi\)
−0.255716 + 0.966752i \(0.582311\pi\)
\(620\) 4.65604 15.0945i 0.186991 0.606210i
\(621\) 0 0
\(622\) −0.904227 0.721097i −0.0362562 0.0289133i
\(623\) −3.59300 + 31.5051i −0.143950 + 1.26223i
\(624\) 0 0
\(625\) 22.8359 21.1886i 0.913434 0.847543i
\(626\) 15.2979 2.30579i 0.611427 0.0921578i
\(627\) 0 0
\(628\) 2.79587 18.5494i 0.111567 0.740200i
\(629\) 20.3360 9.79330i 0.810849 0.390484i
\(630\) 0 0
\(631\) −36.0077 17.3404i −1.43344 0.690310i −0.453810 0.891099i \(-0.649935\pi\)
−0.979635 + 0.200788i \(0.935650\pi\)
\(632\) 13.1614 19.3042i 0.523533 0.767882i
\(633\) 0 0
\(634\) −0.129731 + 1.73113i −0.00515226 + 0.0687521i
\(635\) 19.7725 50.3794i 0.784647 1.99925i
\(636\) 0 0
\(637\) 19.5286 18.0217i 0.773752 0.714046i
\(638\) 12.2242i 0.483960i
\(639\) 0 0
\(640\) −31.8251 2.38496i −1.25800 0.0942739i
\(641\) 8.37354 9.02453i 0.330735 0.356447i −0.545689 0.837988i \(-0.683732\pi\)
0.876424 + 0.481540i \(0.159923\pi\)
\(642\) 0 0
\(643\) 8.45630 17.5597i 0.333484 0.692486i −0.665040 0.746808i \(-0.731585\pi\)
0.998523 + 0.0543217i \(0.0172997\pi\)
\(644\) 32.2887 + 14.1395i 1.27235 + 0.557174i
\(645\) 0 0
\(646\) 12.0547 + 1.81695i 0.474284 + 0.0714869i
\(647\) 9.75819 6.65302i 0.383634 0.261557i −0.356112 0.934443i \(-0.615898\pi\)
0.739746 + 0.672886i \(0.234946\pi\)
\(648\) 0 0
\(649\) 5.45326 + 5.87722i 0.214059 + 0.230701i
\(650\) 4.06973 + 5.10328i 0.159628 + 0.200167i
\(651\) 0 0
\(652\) 6.46415 8.10579i 0.253156 0.317447i
\(653\) 33.2661 2.49295i 1.30180 0.0975566i 0.594286 0.804253i \(-0.297435\pi\)
0.707517 + 0.706697i \(0.249816\pi\)
\(654\) 0 0
\(655\) −30.3697 + 52.6019i −1.18664 + 2.05533i
\(656\) −2.62963 4.55465i −0.102670 0.177829i
\(657\) 0 0
\(658\) 5.10222 + 4.40286i 0.198905 + 0.171641i
\(659\) 6.03998 + 1.37859i 0.235284 + 0.0537021i 0.338537 0.940953i \(-0.390068\pi\)
−0.103253 + 0.994655i \(0.532925\pi\)
\(660\) 0 0
\(661\) −2.24012 + 0.879184i −0.0871307 + 0.0341963i −0.408506 0.912756i \(-0.633950\pi\)
0.321375 + 0.946952i \(0.395855\pi\)
\(662\) −5.56413 + 2.18376i −0.216256 + 0.0848743i
\(663\) 0 0
\(664\) 21.5857 + 4.92679i 0.837686 + 0.191196i
\(665\) 1.82959 47.1863i 0.0709486 1.82981i
\(666\) 0 0
\(667\) 34.3746 + 59.5385i 1.33099 + 2.30534i
\(668\) −12.1539 + 21.0512i −0.470249 + 0.814495i
\(669\) 0 0
\(670\) 5.56445 0.416998i 0.214973 0.0161100i
\(671\) −17.6216 + 22.0968i −0.680273 + 0.853036i
\(672\) 0 0
\(673\) −18.0133 22.5879i −0.694360 0.870700i 0.302228 0.953236i \(-0.402270\pi\)
−0.996588 + 0.0825354i \(0.973698\pi\)
\(674\) −0.886732 0.955669i −0.0341556 0.0368110i
\(675\) 0 0
\(676\) −1.89645 + 1.29298i −0.0729404 + 0.0497299i
\(677\) 42.8377 + 6.45674i 1.64639 + 0.248153i 0.905768 0.423773i \(-0.139295\pi\)
0.740618 + 0.671926i \(0.234533\pi\)
\(678\) 0 0
\(679\) 9.89226 0.356726i 0.379630 0.0136899i
\(680\) −8.39732 + 17.4372i −0.322023 + 0.668687i
\(681\) 0 0
\(682\) −3.44191 + 3.70950i −0.131798 + 0.142044i
\(683\) 28.6509 + 2.14709i 1.09630 + 0.0821560i 0.610575 0.791958i \(-0.290938\pi\)
0.485720 + 0.874114i \(0.338557\pi\)
\(684\) 0 0
\(685\) 7.17435i 0.274118i
\(686\) −2.97391 + 10.9211i −0.113544 + 0.416968i
\(687\) 0 0
\(688\) −6.91441 + 17.6176i −0.263610 + 0.671666i
\(689\) 0.210046 2.80286i 0.00800210 0.106781i
\(690\) 0 0
\(691\) −0.648065 + 0.950537i −0.0246536 + 0.0361601i −0.838368 0.545105i \(-0.816490\pi\)
0.813714 + 0.581265i \(0.197442\pi\)
\(692\) −6.01129 2.89489i −0.228515 0.110047i
\(693\) 0 0
\(694\) −15.3041 + 7.37008i −0.580937 + 0.279764i
\(695\) 2.42178 16.0675i 0.0918635 0.609475i
\(696\) 0 0
\(697\) −8.55768 + 1.28986i −0.324145 + 0.0488570i
\(698\) −13.2318 + 12.2774i −0.500833 + 0.464705i
\(699\) 0 0
\(700\) 11.4221 + 4.01416i 0.431717 + 0.151721i
\(701\) 3.83572 + 3.05888i 0.144873 + 0.115532i 0.693245 0.720702i \(-0.256181\pi\)
−0.548371 + 0.836235i \(0.684752\pi\)
\(702\) 0 0
\(703\) −13.5982 + 44.0842i −0.512865 + 1.66267i
\(704\) −0.781692 0.451310i −0.0294611 0.0170094i
\(705\) 0 0
\(706\) −7.82704 + 1.78647i −0.294575 + 0.0672347i
\(707\) 35.2946 + 1.36851i 1.32739 + 0.0514680i
\(708\) 0 0
\(709\) −42.0232 + 12.9624i −1.57822 + 0.486815i −0.955341 0.295507i \(-0.904512\pi\)
−0.622875 + 0.782322i \(0.714035\pi\)
\(710\) 2.76623 + 7.04823i 0.103815 + 0.264515i
\(711\) 0 0
\(712\) 7.82956 + 25.3828i 0.293425 + 0.951261i
\(713\) −6.33285 + 27.7460i −0.237167 + 1.03910i
\(714\) 0 0
\(715\) 5.62714 + 24.6541i 0.210443 + 0.922012i
\(716\) −14.5477 + 8.39911i −0.543673 + 0.313890i
\(717\) 0 0
\(718\) 10.0851 + 3.11084i 0.376373 + 0.116096i
\(719\) −2.00621 26.7709i −0.0748188 0.998388i −0.900671 0.434501i \(-0.856925\pi\)
0.825852 0.563886i \(-0.190694\pi\)
\(720\) 0 0
\(721\) −24.8556 15.6648i −0.925672 0.583389i
\(722\) −10.4023 + 8.29560i −0.387135 + 0.308730i
\(723\) 0 0
\(724\) −4.06538 26.9720i −0.151089 1.00241i
\(725\) 13.3019 + 19.5103i 0.494019 + 0.724593i
\(726\) 0 0
\(727\) 7.19562 + 14.9419i 0.266871 + 0.554163i 0.990740 0.135775i \(-0.0433523\pi\)
−0.723869 + 0.689937i \(0.757638\pi\)
\(728\) 8.92945 20.3911i 0.330948 0.755745i
\(729\) 0 0
\(730\) 12.7881 + 8.71881i 0.473311 + 0.322698i
\(731\) 22.8298 + 21.1829i 0.844390 + 0.783479i
\(732\) 0 0
\(733\) −22.0506 8.65424i −0.814459 0.319652i −0.0787029 0.996898i \(-0.525078\pi\)
−0.735756 + 0.677246i \(0.763173\pi\)
\(734\) 1.46341 0.0540154
\(735\) 0 0
\(736\) 45.8126 1.68868
\(737\) 7.24610 + 2.84388i 0.266913 + 0.104756i
\(738\) 0 0
\(739\) −27.1206 25.1642i −0.997647 0.925681i −0.000412314 1.00000i \(-0.500131\pi\)
−0.997235 + 0.0743189i \(0.976322\pi\)
\(740\) −27.1409 18.5043i −0.997719 0.680233i
\(741\) 0 0
\(742\) 0.557982 + 1.05922i 0.0204842 + 0.0388853i
\(743\) −13.3347 27.6899i −0.489204 1.01584i −0.988753 0.149557i \(-0.952215\pi\)
0.499549 0.866286i \(-0.333499\pi\)
\(744\) 0 0
\(745\) −6.99973 10.2667i −0.256450 0.376144i
\(746\) −0.959699 6.36718i −0.0351371 0.233119i
\(747\) 0 0
\(748\) −9.46718 + 7.54982i −0.346154 + 0.276049i
\(749\) 16.0414 + 1.82944i 0.586141 + 0.0668463i
\(750\) 0 0
\(751\) −2.96210 39.5264i −0.108088 1.44234i −0.742760 0.669558i \(-0.766484\pi\)
0.634671 0.772782i \(-0.281135\pi\)
\(752\) −7.56095 2.33224i −0.275720 0.0850482i
\(753\) 0 0
\(754\) 16.8637 9.73628i 0.614141 0.354574i
\(755\) −6.51772 28.5560i −0.237204 1.03926i
\(756\) 0 0
\(757\) 11.6607 51.0888i 0.423814 1.85685i −0.0855975 0.996330i \(-0.527280\pi\)
0.509412 0.860523i \(-0.329863\pi\)
\(758\) 0.683030 + 2.21433i 0.0248088 + 0.0804280i
\(759\) 0 0
\(760\) −14.4520 36.8232i −0.524231 1.33572i
\(761\) −23.6151 + 7.28430i −0.856047 + 0.264055i −0.691556 0.722323i \(-0.743074\pi\)
−0.164491 + 0.986379i \(0.552598\pi\)
\(762\) 0 0
\(763\) 5.51897 + 29.3863i 0.199800 + 1.06385i
\(764\) 5.97951 1.36478i 0.216331 0.0493762i
\(765\) 0 0
\(766\) −13.0398 7.52856i −0.471149 0.272018i
\(767\) 3.76445 12.2041i 0.135926 0.440663i
\(768\) 0 0
\(769\) −6.59012 5.25545i −0.237646 0.189516i 0.497424 0.867507i \(-0.334279\pi\)
−0.735070 + 0.677991i \(0.762851\pi\)
\(770\) −7.60612 7.62675i −0.274106 0.274849i
\(771\) 0 0
\(772\) 10.7200 9.94669i 0.385820 0.357989i
\(773\) −46.9211 + 7.07222i −1.68764 + 0.254370i −0.921520 0.388332i \(-0.873051\pi\)
−0.766116 + 0.642702i \(0.777813\pi\)
\(774\) 0 0
\(775\) −1.45689 + 9.66586i −0.0523332 + 0.347208i
\(776\) 7.47095 3.59782i 0.268192 0.129154i
\(777\) 0 0
\(778\) −5.12445 2.46781i −0.183721 0.0884752i
\(779\) 9.96443 14.6151i 0.357013 0.523642i
\(780\) 0 0
\(781\) −0.789332 + 10.5329i −0.0282445 + 0.376897i
\(782\) 5.71352 14.5578i 0.204315 0.520586i
\(783\) 0 0
\(784\) −1.94504 13.1460i −0.0694658 0.469502i
\(785\) 32.2386i 1.15064i
\(786\) 0 0
\(787\) 42.5877 + 3.19151i 1.51809 + 0.113765i 0.807510 0.589854i \(-0.200815\pi\)
0.710577 + 0.703619i \(0.248434\pi\)
\(788\) −27.4215 + 29.5534i