Properties

Label 637.2.k.i.459.3
Level $637$
Weight $2$
Character 637.459
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 459.3
Root \(0.655911 + 1.25291i\) of defining polynomial
Character \(\chi\) \(=\) 637.459
Dual form 637.2.k.i.569.4

$q$-expansion

\(f(q)\) \(=\) \(q-0.180824i q^{2} +(-0.913006 - 1.58137i) q^{3} +1.96730 q^{4} +(2.32670 - 1.34332i) q^{5} +(-0.285950 + 0.165093i) q^{6} -0.717383i q^{8} +(-0.167162 + 0.289532i) q^{9} +O(q^{10})\) \(q-0.180824i q^{2} +(-0.913006 - 1.58137i) q^{3} +1.96730 q^{4} +(2.32670 - 1.34332i) q^{5} +(-0.285950 + 0.165093i) q^{6} -0.717383i q^{8} +(-0.167162 + 0.289532i) q^{9} +(-0.242904 - 0.420723i) q^{10} +(2.33328 - 1.34712i) q^{11} +(-1.79616 - 3.11104i) q^{12} +(-1.92153 + 3.05086i) q^{13} +(-4.24858 - 2.45292i) q^{15} +3.80489 q^{16} +4.76493 q^{17} +(0.0523543 + 0.0302268i) q^{18} +(-0.163180 - 0.0942122i) q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} -4.39929 q^{23} +(-1.13445 + 0.654975i) q^{24} +(1.10902 - 1.92088i) q^{25} +(0.551667 + 0.347458i) q^{26} -4.86756 q^{27} +(-3.54280 + 6.13631i) q^{29} +(-0.443546 + 0.768245i) q^{30} +(3.20369 + 1.84965i) q^{31} -2.12278i q^{32} +(-4.26060 - 2.45986i) q^{33} -0.861613i q^{34} +(-0.328857 + 0.569598i) q^{36} +7.95413i q^{37} +(-0.0170358 + 0.0295069i) q^{38} +(6.57891 + 0.253207i) q^{39} +(-0.963675 - 1.66913i) q^{40} +(-4.70215 - 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +(4.59027 - 2.65020i) q^{44} +0.898206i q^{45} +0.795496i q^{46} +(1.60118 - 0.924445i) q^{47} +(-3.47389 - 6.01695i) q^{48} +(-0.347341 - 0.200538i) q^{50} +(-4.35041 - 7.53514i) q^{51} +(-3.78023 + 6.00196i) q^{52} +(3.53622 - 6.12491i) q^{53} +0.880171i q^{54} +(3.61923 - 6.26869i) q^{55} +0.344066i q^{57} +(1.10959 + 0.640623i) q^{58} -7.58888i q^{59} +(-8.35825 - 4.82564i) q^{60} +(-0.205782 + 0.356425i) q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(-0.372548 + 9.67966i) q^{65} +(-0.444801 + 0.770418i) q^{66} +(-9.87358 + 5.70051i) q^{67} +9.37407 q^{68} +(4.01658 + 6.95692i) q^{69} +(2.89675 - 1.67244i) q^{71} +(0.207705 + 0.119919i) q^{72} +(-12.3112 - 7.10790i) q^{73} +1.43830 q^{74} -4.05018 q^{75} +(-0.321025 - 0.185344i) q^{76} +(0.0457859 - 1.18962i) q^{78} +(-4.55529 - 7.89000i) q^{79} +(8.85283 - 5.11118i) q^{80} +(4.94560 + 8.56603i) q^{81} +(-0.490899 + 0.850261i) q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(-1.25445 + 0.724258i) q^{86} +12.9384 q^{87} +(-0.966401 - 1.67386i) q^{88} +5.89165i q^{89} +0.162417 q^{90} -8.65473 q^{92} -6.75498i q^{93} +(-0.167162 - 0.289532i) q^{94} -0.506229 q^{95} +(-3.35691 + 1.93811i) q^{96} +(-0.390659 + 0.225547i) q^{97} +0.900747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 3q^{3} - 8q^{4} + 3q^{5} + 9q^{6} - q^{9} + O(q^{10}) \) \( 12q + 3q^{3} - 8q^{4} + 3q^{5} + 9q^{6} - q^{9} - 12q^{10} + 12q^{11} + q^{12} + 2q^{13} - 12q^{15} + 16q^{16} + 34q^{17} + 3q^{18} - 9q^{19} + 3q^{20} - 15q^{22} - 6q^{23} - 15q^{24} - 5q^{25} + 6q^{26} - 12q^{27} - q^{29} + 11q^{30} - 18q^{31} + 6q^{33} - 13q^{36} - 19q^{38} - 4q^{39} + q^{40} + 6q^{41} + 11q^{43} - 33q^{44} + 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} + 7q^{52} - 8q^{53} + 15q^{55} - 24q^{58} - 30q^{60} - 5q^{61} - 41q^{62} + 2q^{64} + 21q^{65} + 34q^{66} + 15q^{67} - 22q^{68} - 7q^{69} + 30q^{71} + 57q^{72} - 42q^{73} + 66q^{74} + 2q^{75} + 45q^{76} + 44q^{78} - 35q^{79} + 63q^{80} + 14q^{81} - 5q^{82} - 21q^{85} - 57q^{86} + 20q^{87} - 14q^{88} - 66q^{92} - q^{94} - 4q^{95} - 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.180824i 0.127862i −0.997954 0.0639308i \(-0.979636\pi\)
0.997954 0.0639308i \(-0.0203637\pi\)
\(3\) −0.913006 1.58137i −0.527125 0.913006i −0.999500 0.0316092i \(-0.989937\pi\)
0.472376 0.881397i \(-0.343397\pi\)
\(4\) 1.96730 0.983651
\(5\) 2.32670 1.34332i 1.04053 0.600751i 0.120548 0.992708i \(-0.461535\pi\)
0.919984 + 0.391956i \(0.128201\pi\)
\(6\) −0.285950 + 0.165093i −0.116739 + 0.0673990i
\(7\) 0 0
\(8\) 0.717383i 0.253633i
\(9\) −0.167162 + 0.289532i −0.0557205 + 0.0965108i
\(10\) −0.242904 0.420723i −0.0768131 0.133044i
\(11\) 2.33328 1.34712i 0.703511 0.406172i −0.105143 0.994457i \(-0.533530\pi\)
0.808654 + 0.588285i \(0.200197\pi\)
\(12\) −1.79616 3.11104i −0.518507 0.898080i
\(13\) −1.92153 + 3.05086i −0.532937 + 0.846155i
\(14\) 0 0
\(15\) −4.24858 2.45292i −1.09698 0.633342i
\(16\) 3.80489 0.951221
\(17\) 4.76493 1.15567 0.577833 0.816155i \(-0.303898\pi\)
0.577833 + 0.816155i \(0.303898\pi\)
\(18\) 0.0523543 + 0.0302268i 0.0123400 + 0.00712452i
\(19\) −0.163180 0.0942122i −0.0374361 0.0216138i 0.481165 0.876630i \(-0.340214\pi\)
−0.518601 + 0.855016i \(0.673547\pi\)
\(20\) 4.57732 2.64272i 1.02352 0.590930i
\(21\) 0 0
\(22\) −0.243592 0.421913i −0.0519339 0.0899521i
\(23\) −4.39929 −0.917315 −0.458657 0.888613i \(-0.651669\pi\)
−0.458657 + 0.888613i \(0.651669\pi\)
\(24\) −1.13445 + 0.654975i −0.231569 + 0.133696i
\(25\) 1.10902 1.92088i 0.221804 0.384177i
\(26\) 0.551667 + 0.347458i 0.108191 + 0.0681422i
\(27\) −4.86756 −0.936762
\(28\) 0 0
\(29\) −3.54280 + 6.13631i −0.657882 + 1.13948i 0.323281 + 0.946303i \(0.395214\pi\)
−0.981163 + 0.193182i \(0.938119\pi\)
\(30\) −0.443546 + 0.768245i −0.0809801 + 0.140262i
\(31\) 3.20369 + 1.84965i 0.575400 + 0.332207i 0.759303 0.650737i \(-0.225540\pi\)
−0.183903 + 0.982944i \(0.558873\pi\)
\(32\) 2.12278i 0.375258i
\(33\) −4.26060 2.45986i −0.741676 0.428207i
\(34\) 0.861613i 0.147765i
\(35\) 0 0
\(36\) −0.328857 + 0.569598i −0.0548096 + 0.0949329i
\(37\) 7.95413i 1.30765i 0.756645 + 0.653826i \(0.226837\pi\)
−0.756645 + 0.653826i \(0.773163\pi\)
\(38\) −0.0170358 + 0.0295069i −0.00276357 + 0.00478665i
\(39\) 6.57891 + 0.253207i 1.05347 + 0.0405456i
\(40\) −0.963675 1.66913i −0.152370 0.263913i
\(41\) −4.70215 2.71479i −0.734353 0.423979i 0.0856594 0.996324i \(-0.472700\pi\)
−0.820013 + 0.572345i \(0.806034\pi\)
\(42\) 0 0
\(43\) −4.00533 6.93743i −0.610807 1.05795i −0.991105 0.133084i \(-0.957512\pi\)
0.380298 0.924864i \(-0.375821\pi\)
\(44\) 4.59027 2.65020i 0.692010 0.399532i
\(45\) 0.898206i 0.133897i
\(46\) 0.795496i 0.117289i
\(47\) 1.60118 0.924445i 0.233557 0.134844i −0.378655 0.925538i \(-0.623613\pi\)
0.612212 + 0.790694i \(0.290280\pi\)
\(48\) −3.47389 6.01695i −0.501412 0.868471i
\(49\) 0 0
\(50\) −0.347341 0.200538i −0.0491215 0.0283603i
\(51\) −4.35041 7.53514i −0.609180 1.05513i
\(52\) −3.78023 + 6.00196i −0.524224 + 0.832322i
\(53\) 3.53622 6.12491i 0.485737 0.841321i −0.514128 0.857713i \(-0.671885\pi\)
0.999866 + 0.0163917i \(0.00521788\pi\)
\(54\) 0.880171i 0.119776i
\(55\) 3.61923 6.26869i 0.488017 0.845271i
\(56\) 0 0
\(57\) 0.344066i 0.0455726i
\(58\) 1.10959 + 0.640623i 0.145696 + 0.0841179i
\(59\) 7.58888i 0.987988i −0.869465 0.493994i \(-0.835536\pi\)
0.869465 0.493994i \(-0.164464\pi\)
\(60\) −8.35825 4.82564i −1.07905 0.622987i
\(61\) −0.205782 + 0.356425i −0.0263477 + 0.0456355i −0.878899 0.477009i \(-0.841721\pi\)
0.852551 + 0.522644i \(0.175054\pi\)
\(62\) 0.334461 0.579304i 0.0424766 0.0735716i
\(63\) 0 0
\(64\) 7.22592 0.903240
\(65\) −0.372548 + 9.67966i −0.0462089 + 1.20061i
\(66\) −0.444801 + 0.770418i −0.0547512 + 0.0948319i
\(67\) −9.87358 + 5.70051i −1.20625 + 0.696429i −0.961938 0.273268i \(-0.911895\pi\)
−0.244312 + 0.969697i \(0.578562\pi\)
\(68\) 9.37407 1.13677
\(69\) 4.01658 + 6.95692i 0.483539 + 0.837514i
\(70\) 0 0
\(71\) 2.89675 1.67244i 0.343781 0.198482i −0.318162 0.948037i \(-0.603065\pi\)
0.661943 + 0.749554i \(0.269732\pi\)
\(72\) 0.207705 + 0.119919i 0.0244783 + 0.0141326i
\(73\) −12.3112 7.10790i −1.44092 0.831917i −0.443011 0.896516i \(-0.646090\pi\)
−0.997911 + 0.0645994i \(0.979423\pi\)
\(74\) 1.43830 0.167199
\(75\) −4.05018 −0.467674
\(76\) −0.321025 0.185344i −0.0368241 0.0212604i
\(77\) 0 0
\(78\) 0.0457859 1.18962i 0.00518423 0.134698i
\(79\) −4.55529 7.89000i −0.512511 0.887695i −0.999895 0.0145069i \(-0.995382\pi\)
0.487384 0.873188i \(-0.337951\pi\)
\(80\) 8.85283 5.11118i 0.989776 0.571448i
\(81\) 4.94560 + 8.56603i 0.549511 + 0.951781i
\(82\) −0.490899 + 0.850261i −0.0542107 + 0.0938956i
\(83\) 16.5866i 1.82061i 0.413934 + 0.910307i \(0.364155\pi\)
−0.413934 + 0.910307i \(0.635845\pi\)
\(84\) 0 0
\(85\) 11.0866 6.40083i 1.20251 0.694268i
\(86\) −1.25445 + 0.724258i −0.135271 + 0.0780988i
\(87\) 12.9384 1.38714
\(88\) −0.966401 1.67386i −0.103019 0.178434i
\(89\) 5.89165i 0.624513i 0.949998 + 0.312257i \(0.101085\pi\)
−0.949998 + 0.312257i \(0.898915\pi\)
\(90\) 0.162417 0.0171203
\(91\) 0 0
\(92\) −8.65473 −0.902318
\(93\) 6.75498i 0.700459i
\(94\) −0.167162 0.289532i −0.0172414 0.0298630i
\(95\) −0.506229 −0.0519380
\(96\) −3.35691 + 1.93811i −0.342613 + 0.197808i
\(97\) −0.390659 + 0.225547i −0.0396654 + 0.0229008i −0.519702 0.854348i \(-0.673957\pi\)
0.480036 + 0.877249i \(0.340624\pi\)
\(98\) 0 0
\(99\) 0.900747i 0.0905285i
\(100\) 2.18178 3.77896i 0.218178 0.377896i
\(101\) 3.82840 + 6.63098i 0.380940 + 0.659807i 0.991197 0.132396i \(-0.0422671\pi\)
−0.610257 + 0.792204i \(0.708934\pi\)
\(102\) −1.36253 + 0.786658i −0.134911 + 0.0778908i
\(103\) −2.57870 4.46644i −0.254087 0.440091i 0.710560 0.703636i \(-0.248442\pi\)
−0.964647 + 0.263545i \(0.915108\pi\)
\(104\) 2.18863 + 1.37847i 0.214613 + 0.135170i
\(105\) 0 0
\(106\) −1.10753 0.639433i −0.107573 0.0621072i
\(107\) 8.03289 0.776569 0.388284 0.921540i \(-0.373068\pi\)
0.388284 + 0.921540i \(0.373068\pi\)
\(108\) −9.57597 −0.921448
\(109\) 1.15490 + 0.666781i 0.110619 + 0.0638660i 0.554289 0.832324i \(-0.312990\pi\)
−0.443670 + 0.896190i \(0.646324\pi\)
\(110\) −1.13353 0.654443i −0.108078 0.0623987i
\(111\) 12.5785 7.26217i 1.19389 0.689295i
\(112\) 0 0
\(113\) 9.96917 + 17.2671i 0.937821 + 1.62435i 0.769525 + 0.638617i \(0.220493\pi\)
0.168296 + 0.985736i \(0.446173\pi\)
\(114\) 0.0622152 0.00582699
\(115\) −10.2358 + 5.90965i −0.954495 + 0.551078i
\(116\) −6.96976 + 12.0720i −0.647126 + 1.12086i
\(117\) −0.562115 1.06633i −0.0519676 0.0985823i
\(118\) −1.37225 −0.126326
\(119\) 0 0
\(120\) −1.75968 + 3.04786i −0.160636 + 0.278230i
\(121\) −1.87053 + 3.23985i −0.170048 + 0.294532i
\(122\) 0.0644501 + 0.0372103i 0.00583503 + 0.00336886i
\(123\) 9.91448i 0.893959i
\(124\) 6.30263 + 3.63883i 0.565993 + 0.326776i
\(125\) 7.47412i 0.668505i
\(126\) 0 0
\(127\) −3.98361 + 6.89981i −0.353488 + 0.612259i −0.986858 0.161590i \(-0.948338\pi\)
0.633370 + 0.773849i \(0.281671\pi\)
\(128\) 5.55218i 0.490748i
\(129\) −7.31378 + 12.6678i −0.643942 + 1.11534i
\(130\) 1.75031 + 0.0673655i 0.153513 + 0.00590835i
\(131\) 5.00897 + 8.67579i 0.437636 + 0.758007i 0.997507 0.0705727i \(-0.0224827\pi\)
−0.559871 + 0.828580i \(0.689149\pi\)
\(132\) −8.38190 4.83929i −0.729551 0.421206i
\(133\) 0 0
\(134\) 1.03079 + 1.78538i 0.0890465 + 0.154233i
\(135\) −11.3254 + 6.53870i −0.974731 + 0.562761i
\(136\) 3.41828i 0.293115i
\(137\) 5.06696i 0.432899i −0.976294 0.216450i \(-0.930552\pi\)
0.976294 0.216450i \(-0.0694477\pi\)
\(138\) 1.25798 0.726293i 0.107086 0.0618261i
\(139\) 3.86289 + 6.69073i 0.327646 + 0.567500i 0.982044 0.188650i \(-0.0604113\pi\)
−0.654398 + 0.756150i \(0.727078\pi\)
\(140\) 0 0
\(141\) −2.92378 1.68805i −0.246227 0.142159i
\(142\) −0.302417 0.523802i −0.0253783 0.0439565i
\(143\) −0.373602 + 9.70704i −0.0312422 + 0.811744i
\(144\) −0.636031 + 1.10164i −0.0530025 + 0.0918031i
\(145\) 19.0365i 1.58089i
\(146\) −1.28528 + 2.22617i −0.106370 + 0.184239i
\(147\) 0 0
\(148\) 15.6482i 1.28627i
\(149\) 12.4002 + 7.15924i 1.01586 + 0.586507i 0.912902 0.408178i \(-0.133836\pi\)
0.102958 + 0.994686i \(0.467169\pi\)
\(150\) 0.732368i 0.0597976i
\(151\) 5.60534 + 3.23624i 0.456156 + 0.263362i 0.710427 0.703771i \(-0.248502\pi\)
−0.254271 + 0.967133i \(0.581835\pi\)
\(152\) −0.0675862 + 0.117063i −0.00548197 + 0.00949504i
\(153\) −0.796513 + 1.37960i −0.0643943 + 0.111534i
\(154\) 0 0
\(155\) 9.93871 0.798296
\(156\) 12.9427 + 0.498136i 1.03625 + 0.0398828i
\(157\) 7.95937 13.7860i 0.635227 1.10025i −0.351240 0.936285i \(-0.614240\pi\)
0.986467 0.163960i \(-0.0524267\pi\)
\(158\) −1.42670 + 0.823705i −0.113502 + 0.0655305i
\(159\) −12.9144 −1.02418
\(160\) −2.85157 4.93907i −0.225437 0.390468i
\(161\) 0 0
\(162\) 1.54894 0.894282i 0.121696 0.0702614i
\(163\) −4.14100 2.39081i −0.324348 0.187263i 0.328981 0.944337i \(-0.393295\pi\)
−0.653329 + 0.757074i \(0.726628\pi\)
\(164\) −9.25056 5.34081i −0.722348 0.417048i
\(165\) −13.2175 −1.02898
\(166\) 2.99925 0.232787
\(167\) 2.34729 + 1.35521i 0.181639 + 0.104869i 0.588062 0.808816i \(-0.299891\pi\)
−0.406424 + 0.913685i \(0.633224\pi\)
\(168\) 0 0
\(169\) −5.61544 11.7246i −0.431957 0.901894i
\(170\) −1.15742 2.00472i −0.0887703 0.153755i
\(171\) 0.0545550 0.0314973i 0.00417192 0.00240866i
\(172\) −7.87969 13.6480i −0.600821 1.04065i
\(173\) 0.449908 0.779264i 0.0342059 0.0592463i −0.848416 0.529331i \(-0.822443\pi\)
0.882622 + 0.470084i \(0.155776\pi\)
\(174\) 2.33957i 0.177362i
\(175\) 0 0
\(176\) 8.87787 5.12564i 0.669195 0.386360i
\(177\) −12.0009 + 6.92870i −0.902039 + 0.520793i
\(178\) 1.06535 0.0798513
\(179\) −5.52791 9.57462i −0.413175 0.715641i 0.582060 0.813146i \(-0.302247\pi\)
−0.995235 + 0.0975054i \(0.968914\pi\)
\(180\) 1.76704i 0.131708i
\(181\) 3.52898 0.262307 0.131153 0.991362i \(-0.458132\pi\)
0.131153 + 0.991362i \(0.458132\pi\)
\(182\) 0 0
\(183\) 0.751521 0.0555540
\(184\) 3.15597i 0.232661i
\(185\) 10.6850 + 18.5069i 0.785573 + 1.36065i
\(186\) −1.22146 −0.0895619
\(187\) 11.1179 6.41894i 0.813024 0.469400i
\(188\) 3.15002 1.81866i 0.229738 0.132640i
\(189\) 0 0
\(190\) 0.0915382i 0.00664088i
\(191\) 10.2002 17.6672i 0.738059 1.27836i −0.215309 0.976546i \(-0.569076\pi\)
0.953368 0.301810i \(-0.0975909\pi\)
\(192\) −6.59731 11.4269i −0.476120 0.824664i
\(193\) −14.9515 + 8.63228i −1.07624 + 0.621365i −0.929878 0.367867i \(-0.880088\pi\)
−0.146357 + 0.989232i \(0.546755\pi\)
\(194\) 0.0407842 + 0.0706403i 0.00292814 + 0.00507168i
\(195\) 15.6473 8.24845i 1.12053 0.590684i
\(196\) 0 0
\(197\) −4.29264 2.47836i −0.305838 0.176576i 0.339224 0.940705i \(-0.389835\pi\)
−0.645063 + 0.764130i \(0.723169\pi\)
\(198\) 0.162877 0.0115751
\(199\) 7.18195 0.509115 0.254557 0.967058i \(-0.418070\pi\)
0.254557 + 0.967058i \(0.418070\pi\)
\(200\) −1.37801 0.795593i −0.0974399 0.0562569i
\(201\) 18.0293 + 10.4092i 1.27169 + 0.734209i
\(202\) 1.19904 0.692265i 0.0843641 0.0487076i
\(203\) 0 0
\(204\) −8.55858 14.8239i −0.599221 1.03788i
\(205\) −14.5873 −1.01882
\(206\) −0.807638 + 0.466290i −0.0562708 + 0.0324880i
\(207\) 0.735392 1.27374i 0.0511132 0.0885307i
\(208\) −7.31121 + 11.6082i −0.506941 + 0.804881i
\(209\) −0.507661 −0.0351157
\(210\) 0 0
\(211\) 8.79636 15.2357i 0.605566 1.04887i −0.386395 0.922333i \(-0.626280\pi\)
0.991962 0.126539i \(-0.0403868\pi\)
\(212\) 6.95682 12.0496i 0.477796 0.827567i
\(213\) −5.28951 3.05390i −0.362431 0.209250i
\(214\) 1.45254i 0.0992934i
\(215\) −18.6384 10.7609i −1.27113 0.733886i
\(216\) 3.49190i 0.237594i
\(217\) 0 0
\(218\) 0.120570 0.208833i 0.00816602 0.0141440i
\(219\) 25.9582i 1.75410i
\(220\) 7.12013 12.3324i 0.480039 0.831452i
\(221\) −9.15597 + 14.5371i −0.615897 + 0.977873i
\(222\) −1.31317 2.27448i −0.0881344 0.152653i
\(223\) −12.2157 7.05271i −0.818020 0.472284i 0.0317129 0.999497i \(-0.489904\pi\)
−0.849733 + 0.527213i \(0.823237\pi\)
\(224\) 0 0
\(225\) 0.370772 + 0.642195i 0.0247181 + 0.0428130i
\(226\) 3.12230 1.80266i 0.207693 0.119911i
\(227\) 2.86877i 0.190407i 0.995458 + 0.0952035i \(0.0303502\pi\)
−0.995458 + 0.0952035i \(0.969650\pi\)
\(228\) 0.676881i 0.0448275i
\(229\) −7.59860 + 4.38706i −0.502130 + 0.289905i −0.729593 0.683882i \(-0.760290\pi\)
0.227463 + 0.973787i \(0.426957\pi\)
\(230\) 1.06861 + 1.85088i 0.0704618 + 0.122043i
\(231\) 0 0
\(232\) 4.40208 + 2.54154i 0.289011 + 0.166861i
\(233\) 2.55371 + 4.42316i 0.167299 + 0.289771i 0.937469 0.348068i \(-0.113162\pi\)
−0.770170 + 0.637839i \(0.779829\pi\)
\(234\) −0.192818 + 0.101644i −0.0126049 + 0.00664466i
\(235\) 2.48365 4.30181i 0.162016 0.280619i
\(236\) 14.9296i 0.971836i
\(237\) −8.31803 + 14.4072i −0.540314 + 0.935851i
\(238\) 0 0
\(239\) 2.49797i 0.161580i −0.996731 0.0807901i \(-0.974256\pi\)
0.996731 0.0807901i \(-0.0257443\pi\)
\(240\) −16.1654 9.33309i −1.04347 0.602448i
\(241\) 7.98512i 0.514367i 0.966363 + 0.257183i \(0.0827944\pi\)
−0.966363 + 0.257183i \(0.917206\pi\)
\(242\) 0.585842 + 0.338236i 0.0376593 + 0.0217426i
\(243\) 1.72939 2.99538i 0.110940 0.192154i
\(244\) −0.404835 + 0.701195i −0.0259169 + 0.0448894i
\(245\) 0 0
\(246\) 1.79277 0.114303
\(247\) 0.600984 0.316808i 0.0382397 0.0201580i
\(248\) 1.32691 2.29827i 0.0842588 0.145941i
\(249\) 26.2296 15.1437i 1.66223 0.959690i
\(250\) 1.35150 0.0854762
\(251\) −12.6285 21.8732i −0.797105 1.38063i −0.921494 0.388393i \(-0.873030\pi\)
0.124389 0.992234i \(-0.460303\pi\)
\(252\) 0 0
\(253\) −10.2648 + 5.92637i −0.645341 + 0.372588i
\(254\) 1.24765 + 0.720331i 0.0782845 + 0.0451976i
\(255\) −20.2442 11.6880i −1.26774 0.731931i
\(256\) 13.4479 0.840493
\(257\) −3.37363 −0.210442 −0.105221 0.994449i \(-0.533555\pi\)
−0.105221 + 0.994449i \(0.533555\pi\)
\(258\) 2.29065 + 1.32250i 0.142609 + 0.0823355i
\(259\) 0 0
\(260\) −0.732915 + 19.0428i −0.0454535 + 1.18099i
\(261\) −1.18444 2.05151i −0.0733150 0.126985i
\(262\) 1.56879 0.905740i 0.0969201 0.0559568i
\(263\) 0.0794677 + 0.137642i 0.00490019 + 0.00848737i 0.868465 0.495750i \(-0.165107\pi\)
−0.863565 + 0.504238i \(0.831774\pi\)
\(264\) −1.76466 + 3.05648i −0.108607 + 0.188114i
\(265\) 19.0011i 1.16723i
\(266\) 0 0
\(267\) 9.31689 5.37911i 0.570185 0.329196i
\(268\) −19.4243 + 11.2146i −1.18653 + 0.685043i
\(269\) 23.3266 1.42225 0.711124 0.703066i \(-0.248186\pi\)
0.711124 + 0.703066i \(0.248186\pi\)
\(270\) 1.18235 + 2.04789i 0.0719556 + 0.124631i
\(271\) 11.8210i 0.718074i −0.933323 0.359037i \(-0.883105\pi\)
0.933323 0.359037i \(-0.116895\pi\)
\(272\) 18.1300 1.09929
\(273\) 0 0
\(274\) −0.916226 −0.0553513
\(275\) 5.97595i 0.360363i
\(276\) 7.90182 + 13.6864i 0.475634 + 0.823822i
\(277\) 27.3653 1.64422 0.822111 0.569327i \(-0.192796\pi\)
0.822111 + 0.569327i \(0.192796\pi\)
\(278\) 1.20984 0.698503i 0.0725615 0.0418934i
\(279\) −1.07107 + 0.618382i −0.0641232 + 0.0370215i
\(280\) 0 0
\(281\) 28.5383i 1.70245i 0.524801 + 0.851225i \(0.324140\pi\)
−0.524801 + 0.851225i \(0.675860\pi\)
\(282\) −0.305239 + 0.528690i −0.0181767 + 0.0314830i
\(283\) −8.98604 15.5643i −0.534165 0.925201i −0.999203 0.0399101i \(-0.987293\pi\)
0.465038 0.885290i \(-0.346040\pi\)
\(284\) 5.69879 3.29020i 0.338161 0.195237i
\(285\) 0.462190 + 0.800537i 0.0273778 + 0.0474197i
\(286\) 1.75526 + 0.0675561i 0.103791 + 0.00399468i
\(287\) 0 0
\(288\) 0.614613 + 0.354847i 0.0362164 + 0.0209096i
\(289\) 5.70459 0.335564
\(290\) 3.44225 0.202136
\(291\) 0.713347 + 0.411851i 0.0418172 + 0.0241432i
\(292\) −24.2199 13.9834i −1.41737 0.818316i
\(293\) −12.8943 + 7.44453i −0.753293 + 0.434914i −0.826882 0.562375i \(-0.809888\pi\)
0.0735896 + 0.997289i \(0.476554\pi\)
\(294\) 0 0
\(295\) −10.1943 17.6570i −0.593535 1.02803i
\(296\) 5.70616 0.331664
\(297\) −11.3574 + 6.55719i −0.659023 + 0.380487i
\(298\) 1.29456 2.24224i 0.0749918 0.129890i
\(299\) 8.45337 13.4216i 0.488871 0.776191i
\(300\) −7.96793 −0.460028
\(301\) 0 0
\(302\) 0.585190 1.01358i 0.0336739 0.0583249i
\(303\) 6.99071 12.1083i 0.401606 0.695601i
\(304\) −0.620883 0.358467i −0.0356101 0.0205595i
\(305\) 1.10572i 0.0633136i
\(306\) 0.249465 + 0.144029i 0.0142610 + 0.00823356i
\(307\) 23.5161i 1.34214i 0.741396 + 0.671068i \(0.234164\pi\)
−0.741396 + 0.671068i \(0.765836\pi\)
\(308\) 0 0
\(309\) −4.70874 + 8.15577i −0.267871 + 0.463966i
\(310\) 1.79715i 0.102072i
\(311\) −0.815450 + 1.41240i −0.0462399 + 0.0800899i −0.888219 0.459420i \(-0.848057\pi\)
0.841979 + 0.539510i \(0.181391\pi\)
\(312\) 0.181647 4.71960i 0.0102837 0.267195i
\(313\) −0.348367 0.603389i −0.0196909 0.0341056i 0.856012 0.516956i \(-0.172935\pi\)
−0.875703 + 0.482850i \(0.839602\pi\)
\(314\) −2.49284 1.43924i −0.140679 0.0812212i
\(315\) 0 0
\(316\) −8.96164 15.5220i −0.504132 0.873182i
\(317\) 18.5579 10.7144i 1.04231 0.601780i 0.121826 0.992551i \(-0.461125\pi\)
0.920488 + 0.390771i \(0.127792\pi\)
\(318\) 2.33522i 0.130953i
\(319\) 19.0903i 1.06885i
\(320\) 16.8126 9.70673i 0.939850 0.542623i
\(321\) −7.33408 12.7030i −0.409348 0.709012i
\(322\) 0 0
\(323\) −0.777544 0.448915i −0.0432637 0.0249783i
\(324\) 9.72949 + 16.8520i 0.540527 + 0.936221i
\(325\) 3.72932 + 7.07450i 0.206865 + 0.392423i
\(326\) −0.432315 + 0.748792i −0.0239437 + 0.0414717i
\(327\) 2.43510i 0.134661i
\(328\) −1.94754 + 3.37324i −0.107535 + 0.186256i
\(329\) 0 0
\(330\) 2.39004i 0.131568i
\(331\) −1.31676 0.760232i −0.0723757 0.0417861i 0.463375 0.886162i \(-0.346638\pi\)
−0.535751 + 0.844376i \(0.679971\pi\)
\(332\) 32.6308i 1.79085i
\(333\) −2.30298 1.32962i −0.126202 0.0728630i
\(334\) 0.245054 0.424446i 0.0134088 0.0232247i
\(335\) −15.3152 + 26.5268i −0.836761 + 1.44931i
\(336\) 0 0
\(337\) −32.2304 −1.75570 −0.877850 0.478936i \(-0.841023\pi\)
−0.877850 + 0.478936i \(0.841023\pi\)
\(338\) −2.12009 + 1.01540i −0.115318 + 0.0552307i
\(339\) 18.2038 31.5300i 0.988697 1.71247i
\(340\) 21.8106 12.5924i 1.18285 0.682918i
\(341\) 9.96683 0.539734
\(342\) −0.00569546 0.00986483i −0.000307975 0.000533429i
\(343\) 0 0
\(344\) −4.97679 + 2.87335i −0.268331 + 0.154921i
\(345\) 18.6907 + 10.7911i 1.00628 + 0.580974i
\(346\) −0.140909 0.0813541i −0.00757534 0.00437362i
\(347\) 8.18431 0.439357 0.219678 0.975572i \(-0.429499\pi\)
0.219678 + 0.975572i \(0.429499\pi\)
\(348\) 25.4538 1.36446
\(349\) 18.9220 + 10.9246i 1.01287 + 0.584782i 0.912031 0.410120i \(-0.134513\pi\)
0.100841 + 0.994903i \(0.467847\pi\)
\(350\) 0 0
\(351\) 9.35317 14.8502i 0.499235 0.792646i
\(352\) −2.85964 4.95304i −0.152419 0.263998i
\(353\) 0.491192 0.283590i 0.0261435 0.0150940i −0.486871 0.873474i \(-0.661862\pi\)
0.513015 + 0.858380i \(0.328529\pi\)
\(354\) 1.25287 + 2.17004i 0.0665894 + 0.115336i
\(355\) 4.49325 7.78254i 0.238477 0.413054i
\(356\) 11.5907i 0.614303i
\(357\) 0 0
\(358\) −1.73132 + 0.999577i −0.0915030 + 0.0528293i
\(359\) −28.0630 + 16.2022i −1.48111 + 0.855118i −0.999771 0.0214184i \(-0.993182\pi\)
−0.481336 + 0.876536i \(0.659848\pi\)
\(360\) 0.644358 0.0339606
\(361\) −9.48225 16.4237i −0.499066 0.864407i
\(362\) 0.638123i 0.0335390i
\(363\) 6.83122 0.358546
\(364\) 0 0
\(365\) −38.1928 −1.99910
\(366\) 0.135893i 0.00710323i
\(367\) −3.93444 6.81465i −0.205376 0.355722i 0.744876 0.667202i \(-0.232508\pi\)
−0.950252 + 0.311481i \(0.899175\pi\)
\(368\) −16.7388 −0.872569
\(369\) 1.57204 0.907617i 0.0818371 0.0472487i
\(370\) 3.34648 1.93209i 0.173975 0.100445i
\(371\) 0 0
\(372\) 13.2891i 0.689007i
\(373\) 1.04581 1.81140i 0.0541502 0.0937909i −0.837680 0.546162i \(-0.816088\pi\)
0.891830 + 0.452371i \(0.149422\pi\)
\(374\) −1.16070 2.01039i −0.0600182 0.103955i
\(375\) 11.8194 6.82392i 0.610350 0.352386i
\(376\) −0.663180 1.14866i −0.0342009 0.0592377i
\(377\) −11.9134 22.5997i −0.613571 1.16394i
\(378\) 0 0
\(379\) 12.3983 + 7.15817i 0.636859 + 0.367691i 0.783404 0.621513i \(-0.213482\pi\)
−0.146545 + 0.989204i \(0.546815\pi\)
\(380\) −0.995906 −0.0510889
\(381\) 14.5482 0.745329
\(382\) −3.19466 1.84444i −0.163453 0.0943695i
\(383\) −21.8129 12.5937i −1.11459 0.643507i −0.174573 0.984644i \(-0.555854\pi\)
−0.940013 + 0.341138i \(0.889188\pi\)
\(384\) −8.78006 + 5.06917i −0.448056 + 0.258685i
\(385\) 0 0
\(386\) 1.56092 + 2.70359i 0.0794488 + 0.137609i
\(387\) 2.67815 0.136138
\(388\) −0.768544 + 0.443719i −0.0390169 + 0.0225264i
\(389\) 14.0512 24.3373i 0.712422 1.23395i −0.251524 0.967851i \(-0.580932\pi\)
0.963946 0.266099i \(-0.0857350\pi\)
\(390\) −1.49152 2.82940i −0.0755259 0.143272i
\(391\) −20.9623 −1.06011
\(392\) 0 0
\(393\) 9.14644 15.8421i 0.461377 0.799128i
\(394\) −0.448146 + 0.776212i −0.0225773 + 0.0391050i
\(395\) −21.1976 12.2384i −1.06657 0.615783i
\(396\) 1.77204i 0.0890485i
\(397\) 18.8590 + 10.8882i 0.946504 + 0.546465i 0.891993 0.452049i \(-0.149307\pi\)
0.0545111 + 0.998513i \(0.482640\pi\)
\(398\) 1.29867i 0.0650963i
\(399\) 0 0
\(400\) 4.21970 7.30874i 0.210985 0.365437i
\(401\) 20.5290i 1.02517i −0.858637 0.512584i \(-0.828688\pi\)
0.858637 0.512584i \(-0.171312\pi\)
\(402\) 1.88223 3.26012i 0.0938772 0.162600i
\(403\) −11.7990 + 6.21984i −0.587751 + 0.309832i
\(404\) 7.53162 + 13.0451i 0.374712 + 0.649020i
\(405\) 23.0138 + 13.2871i 1.14357 + 0.660239i
\(406\) 0 0
\(407\) 10.7152 + 18.5592i 0.531132 + 0.919947i
\(408\) −5.40558 + 3.12091i −0.267616 + 0.154508i
\(409\) 6.26862i 0.309963i 0.987917 + 0.154982i \(0.0495319\pi\)
−0.987917 + 0.154982i \(0.950468\pi\)
\(410\) 2.63774i 0.130269i
\(411\) −8.01275 + 4.62616i −0.395240 + 0.228192i
\(412\) −5.07308 8.78683i −0.249933 0.432896i
\(413\) 0 0
\(414\) −0.230322 0.132976i −0.0113197 0.00653543i
\(415\) 22.2811 + 38.5920i 1.09374 + 1.89441i
\(416\) 6.47629 + 4.07899i 0.317526 + 0.199989i
\(417\) 7.05369 12.2174i 0.345421 0.598286i
\(418\) 0.0917972i 0.00448995i
\(419\) 17.0817 29.5864i 0.834497 1.44539i −0.0599424 0.998202i \(-0.519092\pi\)
0.894439 0.447189i \(-0.147575\pi\)
\(420\) 0 0
\(421\) 11.5233i 0.561613i −0.959764 0.280806i \(-0.909398\pi\)
0.959764 0.280806i \(-0.0906019\pi\)
\(422\) −2.75498 1.59059i −0.134111 0.0774288i
\(423\) 0.618126i 0.0300543i
\(424\) −4.39391 2.53682i −0.213387 0.123199i
\(425\) 5.28442 9.15288i 0.256332 0.443980i
\(426\) −0.552218 + 0.956469i −0.0267550 + 0.0463411i
\(427\) 0 0
\(428\) 15.8031 0.763873
\(429\) 15.6916 8.27179i 0.757596 0.399366i
\(430\) −1.94582 + 3.37026i −0.0938359 + 0.162529i
\(431\) −7.59505 + 4.38500i −0.365841 + 0.211218i −0.671640 0.740878i \(-0.734410\pi\)
0.305799 + 0.952096i \(0.401076\pi\)
\(432\) −18.5205 −0.891069
\(433\) −11.0535 19.1452i −0.531196 0.920058i −0.999337 0.0364046i \(-0.988409\pi\)
0.468141 0.883654i \(-0.344924\pi\)
\(434\) 0 0
\(435\) 30.1038 17.3804i 1.44337 0.833328i
\(436\) 2.27203 + 1.31176i 0.108811 + 0.0628219i
\(437\) 0.717877 + 0.414467i 0.0343407 + 0.0198266i
\(438\) 4.69387 0.224282
\(439\) −10.3709 −0.494978 −0.247489 0.968891i \(-0.579605\pi\)
−0.247489 + 0.968891i \(0.579605\pi\)
\(440\) −4.49705 2.59637i −0.214389 0.123777i
\(441\) 0 0
\(442\) 2.62866 + 1.65562i 0.125032 + 0.0787496i
\(443\) −17.9068 31.0156i −0.850780 1.47359i −0.880506 0.474036i \(-0.842797\pi\)
0.0297257 0.999558i \(-0.490537\pi\)
\(444\) 24.7456 14.2869i 1.17438 0.678026i
\(445\) 7.91437 + 13.7081i 0.375177 + 0.649826i
\(446\) −1.27530 + 2.20888i −0.0603871 + 0.104593i
\(447\) 26.1457i 1.23665i
\(448\) 0 0
\(449\) −19.7023 + 11.3751i −0.929809 + 0.536825i −0.886751 0.462247i \(-0.847043\pi\)
−0.0430575 + 0.999073i \(0.513710\pi\)
\(450\) 0.116124 0.0670443i 0.00547415 0.00316050i
\(451\) −14.6286 −0.688834
\(452\) 19.6124 + 33.9696i 0.922489 + 1.59780i
\(453\) 11.8188i 0.555298i
\(454\) 0.518742 0.0243458
\(455\) 0 0
\(456\) 0.246827 0.0115587
\(457\) 31.3172i 1.46496i −0.680791 0.732478i \(-0.738364\pi\)
0.680791 0.732478i \(-0.261636\pi\)
\(458\) 0.793284 + 1.37401i 0.0370677 + 0.0642032i
\(459\) −23.1936 −1.08258
\(460\) −20.1370 + 11.6261i −0.938891 + 0.542069i
\(461\) 7.28113 4.20376i 0.339116 0.195789i −0.320765 0.947159i \(-0.603940\pi\)
0.659881 + 0.751370i \(0.270607\pi\)
\(462\) 0 0
\(463\) 10.0392i 0.466563i 0.972409 + 0.233281i \(0.0749463\pi\)
−0.972409 + 0.233281i \(0.925054\pi\)
\(464\) −13.4800 + 23.3480i −0.625791 + 1.08390i
\(465\) −9.07411 15.7168i −0.420802 0.728850i
\(466\) 0.799813 0.461772i 0.0370506 0.0213912i
\(467\) 13.1756 + 22.8209i 0.609696 + 1.05602i 0.991290 + 0.131695i \(0.0420418\pi\)
−0.381594 + 0.924330i \(0.624625\pi\)
\(468\) −1.10585 2.09780i −0.0511180 0.0969706i
\(469\) 0 0
\(470\) −0.777869 0.449103i −0.0358804 0.0207156i
\(471\) −29.0678 −1.33937
\(472\) −5.44413 −0.250586
\(473\) −18.6911 10.7913i −0.859418 0.496185i
\(474\) 2.60517 + 1.50410i 0.119660 + 0.0690855i
\(475\) −0.361941 + 0.208967i −0.0166070 + 0.00958806i
\(476\) 0 0
\(477\) 1.18224 + 2.04770i 0.0541310 + 0.0937577i
\(478\) −0.451692 −0.0206599
\(479\) 7.43409 4.29207i 0.339672 0.196110i −0.320455 0.947264i \(-0.603836\pi\)
0.660127 + 0.751154i \(0.270502\pi\)
\(480\) −5.20701 + 9.01880i −0.237666 + 0.411650i
\(481\) −24.2669 15.2841i −1.10648 0.696895i
\(482\) 1.44390 0.0657678
\(483\) 0 0
\(484\) −3.67990 + 6.37377i −0.167268 + 0.289717i
\(485\) −0.605963 + 1.04956i −0.0275154 + 0.0476580i
\(486\) −0.541637 0.312714i −0.0245691 0.0141850i
\(487\) 21.2562i 0.963212i −0.876388 0.481606i \(-0.840054\pi\)
0.876388 0.481606i \(-0.159946\pi\)
\(488\) 0.255693 + 0.147624i 0.0115747 + 0.00668264i
\(489\) 8.73130i 0.394843i
\(490\) 0 0
\(491\) −11.2268 + 19.4453i −0.506657 + 0.877556i 0.493313 + 0.869852i \(0.335786\pi\)
−0.999970 + 0.00770409i \(0.997548\pi\)
\(492\) 19.5048i 0.879344i
\(493\) −16.8812 + 29.2391i −0.760292 + 1.31686i
\(494\) −0.0572864 0.108672i −0.00257744 0.00488939i
\(495\) 1.20999 + 2.09577i 0.0543851 + 0.0941978i
\(496\) 12.1897 + 7.03772i 0.547333 + 0.316003i
\(497\) 0 0
\(498\) −2.73833 4.74293i −0.122708 0.212536i
\(499\) −33.6694 + 19.4390i −1.50725 + 0.870210i −0.507284 + 0.861779i \(0.669350\pi\)
−0.999964 + 0.00843082i \(0.997316\pi\)
\(500\) 14.7039i 0.657576i
\(501\) 4.94926i 0.221117i
\(502\) −3.95520 + 2.28354i −0.176529 + 0.101919i
\(503\) 2.72850 + 4.72591i 0.121658 + 0.210718i 0.920422 0.390927i \(-0.127846\pi\)
−0.798764 + 0.601645i \(0.794512\pi\)
\(504\) 0 0
\(505\) 17.8151 + 10.2855i 0.792760 + 0.457700i
\(506\) 1.07163 + 1.85612i 0.0476397 + 0.0825144i
\(507\) −13.4141 + 19.5848i −0.595740 + 0.869790i
\(508\) −7.83697 + 13.5740i −0.347709 + 0.602250i
\(509\) 10.8925i 0.482800i −0.970426 0.241400i \(-0.922393\pi\)
0.970426 0.241400i \(-0.0776066\pi\)
\(510\) −2.11347 + 3.66064i −0.0935860 + 0.162096i
\(511\) 0 0
\(512\) 13.5360i 0.598214i
\(513\) 0.794290 + 0.458584i 0.0350688 + 0.0202470i
\(514\) 0.610033i 0.0269074i
\(515\) −11.9997 6.92804i −0.528771 0.305286i
\(516\) −14.3884 + 24.9215i −0.633415 + 1.09711i
\(517\) 2.49068 4.31398i 0.109540 0.189729i
\(518\) 0 0
\(519\) −1.64308 −0.0721230
\(520\) 6.94402 + 0.267260i 0.304515 + 0.0117201i
\(521\) 13.9480 24.1587i 0.611074 1.05841i −0.379985 0.924993i \(-0.624071\pi\)
0.991060 0.133419i \(-0.0425957\pi\)
\(522\) −0.370962 + 0.214175i −0.0162366 + 0.00937418i
\(523\) −16.7236 −0.731272 −0.365636 0.930758i \(-0.619148\pi\)
−0.365636 + 0.930758i \(0.619148\pi\)
\(524\) 9.85416 + 17.0679i 0.430481 + 0.745615i
\(525\) 0 0
\(526\) 0.0248890 0.0143696i 0.00108521 0.000626546i
\(527\) 15.2654 + 8.81347i 0.664970 + 0.383921i
\(528\) −16.2111 9.35949i −0.705498 0.407319i
\(529\) −3.64627 −0.158534
\(530\) −3.43585 −0.149244
\(531\) 2.19723 + 1.26857i 0.0953515 + 0.0550512i
\(532\) 0 0
\(533\) 17.3178 9.12904i 0.750116 0.395423i
\(534\) −0.972671 1.68472i −0.0420916 0.0729048i
\(535\) 18.6901 10.7907i 0.808045 0.466525i
\(536\) 4.08945 + 7.08313i 0.176637 + 0.305945i
\(537\) −10.0940 + 17.4834i −0.435590 + 0.754464i
\(538\) 4.21800i 0.181851i
\(539\) 0 0
\(540\) −22.2804 + 12.8636i −0.958796 + 0.553561i
\(541\) 9.66528 5.58025i 0.415543 0.239914i −0.277626 0.960689i \(-0.589547\pi\)
0.693169 + 0.720776i \(0.256214\pi\)
\(542\) −2.13751 −0.0918141
\(543\) −3.22198 5.58063i −0.138268 0.239488i
\(544\) 10.1149i 0.433673i
\(545\) 3.58280 0.153470
\(546\) 0 0
\(547\) 36.6556 1.56728 0.783640 0.621215i \(-0.213361\pi\)
0.783640 + 0.621215i \(0.213361\pi\)
\(548\) 9.96824i 0.425822i
\(549\) −0.0687976 0.119161i −0.00293621 0.00508567i
\(550\) −1.08059 −0.0460767
\(551\) 1.15623 0.667551i 0.0492571 0.0284386i
\(552\) 4.99077 2.88142i 0.212421 0.122641i
\(553\) 0 0
\(554\) 4.94830i 0.210233i
\(555\) 19.5109 33.7938i 0.828190 1.43447i
\(556\) 7.59948 + 13.1627i 0.322290 + 0.558222i
\(557\) −28.6461 + 16.5388i −1.21377 + 0.700772i −0.963579 0.267424i \(-0.913827\pi\)
−0.250193 + 0.968196i \(0.580494\pi\)
\(558\) 0.111818 + 0.193675i 0.00473364 + 0.00819890i
\(559\) 28.8615 + 1.11081i 1.22071 + 0.0469823i
\(560\) 0 0
\(561\) −20.3015 11.7211i −0.857130 0.494864i
\(562\) 5.16039 0.217678
\(563\) 17.7967 0.750043 0.375021 0.927016i \(-0.377635\pi\)
0.375021 + 0.927016i \(0.377635\pi\)
\(564\) −5.75197 3.32090i −0.242202 0.139835i
\(565\) 46.3906 + 26.7836i 1.95167 + 1.12679i
\(566\) −2.81439 + 1.62489i −0.118298 + 0.0682992i
\(567\) 0 0
\(568\) −1.19978 2.07808i −0.0503417 0.0871943i
\(569\) 8.22094 0.344640 0.172320 0.985041i \(-0.444874\pi\)
0.172320 + 0.985041i \(0.444874\pi\)
\(570\) 0.144756 0.0835750i 0.00606317 0.00350057i
\(571\) −12.8776 + 22.3047i −0.538912 + 0.933424i 0.460051 + 0.887893i \(0.347831\pi\)
−0.998963 + 0.0455309i \(0.985502\pi\)
\(572\) −0.734988 + 19.0967i −0.0307314 + 0.798473i
\(573\) −37.2513 −1.55620
\(574\) 0 0
\(575\) −4.87891 + 8.45051i −0.203464 + 0.352411i
\(576\) −1.20790 + 2.09214i −0.0503290 + 0.0871724i
\(577\) 0.666314 + 0.384697i 0.0277390 + 0.0160151i 0.513805 0.857907i \(-0.328235\pi\)
−0.486066 + 0.873922i \(0.661569\pi\)
\(578\) 1.03152i 0.0429058i
\(579\) 27.3017 + 15.7626i 1.13462 + 0.655073i
\(580\) 37.4505i 1.55505i
\(581\) 0 0
\(582\) 0.0744725 0.128990i 0.00308698 0.00534681i
\(583\) 19.0549i 0.789172i
\(584\) −5.09908 + 8.83187i −0.211002 + 0.365465i
\(585\) −2.74030 1.72593i −0.113297 0.0713585i
\(586\) 1.34615 + 2.33159i 0.0556088 + 0.0963173i
\(587\) 10.4727 + 6.04644i 0.432256 + 0.249563i 0.700307 0.713841i \(-0.253046\pi\)
−0.268051 + 0.963405i \(0.586380\pi\)
\(588\) 0 0
\(589\) −0.348520 0.603654i −0.0143605 0.0248731i
\(590\) −3.19281 + 1.84337i −0.131446 + 0.0758904i
\(591\) 9.05103i 0.372310i
\(592\) 30.2646i 1.24387i
\(593\) 13.8115 7.97406i 0.567170 0.327456i −0.188848 0.982006i \(-0.560475\pi\)
0.756018 + 0.654551i \(0.227142\pi\)
\(594\) 1.18570 + 2.05369i 0.0486497 + 0.0842638i
\(595\) 0 0
\(596\) 24.3949 + 14.0844i 0.999253 + 0.576919i
\(597\) −6.55717 11.3573i −0.268367 0.464825i
\(598\) −2.42694 1.52857i −0.0992450 0.0625078i
\(599\) 3.55511 6.15763i 0.145258 0.251594i −0.784211 0.620494i \(-0.786932\pi\)
0.929469 + 0.368900i \(0.120266\pi\)
\(600\) 2.90553i 0.118618i
\(601\) 10.3953 18.0051i 0.424032 0.734445i −0.572297 0.820046i \(-0.693948\pi\)
0.996329 + 0.0856011i \(0.0272811\pi\)
\(602\) 0 0
\(603\) 3.81163i 0.155221i
\(604\) 11.0274 + 6.36667i 0.448698 + 0.259056i
\(605\) 10.0509i 0.408626i
\(606\) −2.18946 1.26409i −0.0889408 0.0513500i
\(607\) −3.85702 + 6.68056i −0.156552 + 0.271156i −0.933623 0.358257i \(-0.883371\pi\)
0.777071 + 0.629413i \(0.216704\pi\)
\(608\) −0.199992 + 0.346396i −0.00811074 + 0.0140482i
\(609\) 0 0
\(610\) 0.199941 0.00809539
\(611\) −0.256380 + 6.66133i −0.0103720 + 0.269489i
\(612\) −1.56698 + 2.71409i −0.0633415 + 0.109711i
\(613\) −17.6997 + 10.2189i −0.714883 + 0.412738i −0.812867 0.582450i \(-0.802094\pi\)
0.0979832 + 0.995188i \(0.468761\pi\)
\(614\) 4.25227 0.171608
\(615\) 13.3183 + 23.0680i 0.537047 + 0.930193i
\(616\) 0 0
\(617\) −3.98209 + 2.29906i −0.160313 + 0.0925567i −0.578010 0.816030i \(-0.696171\pi\)
0.417697 + 0.908586i \(0.362837\pi\)
\(618\) 1.47476 + 0.851451i 0.0593234 + 0.0342504i
\(619\) 8.70599 + 5.02641i 0.349923 + 0.202028i 0.664651 0.747154i \(-0.268580\pi\)
−0.314728 + 0.949182i \(0.601913\pi\)
\(620\) 19.5525 0.785245
\(621\) 21.4138 0.859306
\(622\) 0.255396 + 0.147453i 0.0102404 + 0.00591232i
\(623\) 0 0
\(624\) 25.0320 + 0.963425i 1.00208 + 0.0385679i
\(625\) 15.5853 + 26.9944i 0.623410 + 1.07978i
\(626\) −0.109107 + 0.0629930i −0.00436080 + 0.00251771i
\(627\) 0.463498 + 0.802802i 0.0185103 + 0.0320608i
\(628\) 15.6585 27.1213i 0.624842 1.08226i
\(629\) 37.9009i 1.51121i
\(630\) 0 0
\(631\) −6.29923 + 3.63686i −0.250768 + 0.144781i −0.620116 0.784510i \(-0.712914\pi\)
0.369348 + 0.929291i \(0.379581\pi\)
\(632\) −5.66015 + 3.26789i −0.225149 + 0.129990i
\(633\) −32.1245 −1.27684
\(634\) −1.93742 3.35570i −0.0769447 0.133272i
\(635\) 21.4051i 0.849434i
\(636\) −25.4065 −1.00743
\(637\) 0 0
\(638\) 3.45199 0.136665
\(639\) 1.11827i 0.0442381i
\(640\) −7.45835 12.9182i −0.294817 0.510639i
\(641\) −3.85033 −0.152079 −0.0760394 0.997105i \(-0.524227\pi\)
−0.0760394 + 0.997105i \(0.524227\pi\)
\(642\) −2.29700 + 1.32618i −0.0906555 + 0.0523400i
\(643\) −2.49163 + 1.43855i −0.0982605 + 0.0567307i −0.548325 0.836265i \(-0.684734\pi\)
0.450065 + 0.892996i \(0.351401\pi\)
\(644\) 0 0
\(645\) 39.2990i 1.54740i
\(646\) −0.0811745 + 0.140598i −0.00319377 + 0.00553177i
\(647\) −18.5501 32.1296i −0.729278 1.26315i −0.957189 0.289464i \(-0.906523\pi\)
0.227911 0.973682i \(-0.426810\pi\)
\(648\) 6.14512 3.54789i 0.241403 0.139374i
\(649\) −10.2231 17.7070i −0.401293 0.695061i
\(650\) 1.27924 0.674349i 0.0501758 0.0264501i
\(651\) 0 0
\(652\) −8.14661 4.70345i −0.319046 0.184201i
\(653\) 20.0950 0.786377 0.393189 0.919458i \(-0.371372\pi\)
0.393189 + 0.919458i \(0.371372\pi\)
\(654\) −0.440324 −0.0172180
\(655\) 23.3087 + 13.4573i 0.910748 + 0.525820i
\(656\) −17.8912 10.3295i −0.698532 0.403298i
\(657\) 4.11593 2.37634i 0.160578 0.0927097i
\(658\) 0 0
\(659\) −4.95529 8.58281i −0.193031 0.334339i 0.753223 0.657766i \(-0.228498\pi\)
−0.946253 + 0.323427i \(0.895165\pi\)
\(660\) −26.0029 −1.01216
\(661\) −40.8994 + 23.6133i −1.59080 + 0.918450i −0.597633 + 0.801770i \(0.703892\pi\)
−0.993170 + 0.116680i \(0.962775\pi\)
\(662\) −0.137468 + 0.238102i −0.00534284 + 0.00925408i
\(663\) 31.3481 + 1.20652i 1.21746 + 0.0468572i
\(664\) 11.8989 0.461768
\(665\) 0 0
\(666\) −0.240428 + 0.416433i −0.00931639 + 0.0161365i
\(667\) 15.5858 26.9954i 0.603485 1.04527i
\(668\) 4.61783 + 2.66611i 0.178669 + 0.103155i
\(669\) 25.7567i 0.995811i
\(670\) 4.79667 + 2.76936i 0.185312 + 0.106990i
\(671\) 1.10885i 0.0428068i
\(672\) 0 0
\(673\) 3.45845 5.99020i 0.133313 0.230905i −0.791639 0.610990i \(-0.790772\pi\)
0.924952 + 0.380084i \(0.124105\pi\)
\(674\) 5.82801i 0.224487i
\(675\) −5.39823 + 9.35001i −0.207778 + 0.359882i
\(676\) −11.0473 23.0659i −0.424895 0.887150i
\(677\) −6.16453 10.6773i −0.236922 0.410361i 0.722908 0.690945i \(-0.242805\pi\)
−0.959830 + 0.280584i \(0.909472\pi\)
\(678\) −5.70137 3.29169i −0.218960 0.126416i
\(679\) 0 0
\(680\) −4.59185 7.95331i −0.176089 0.304996i
\(681\) 4.53660 2.61921i 0.173843 0.100368i
\(682\) 1.80224i 0.0690113i
\(683\) 24.5364i 0.938859i −0.882970 0.469430i \(-0.844460\pi\)
0.882970 0.469430i \(-0.155540\pi\)
\(684\) 0.107326 0.0619648i 0.00410372 0.00236928i
\(685\) −6.80655 11.7893i −0.260065 0.450446i
\(686\) 0 0
\(687\) 13.8751 + 8.01082i 0.529370 + 0.305632i
\(688\) −15.2398 26.3961i −0.581012 1.00634i
\(689\) 11.8913 + 22.5577i 0.453021 + 0.859380i
\(690\) 1.95129 3.37973i 0.0742843 0.128664i
\(691\) 9.10716i 0.346453i 0.984882 + 0.173226i \(0.0554192\pi\)
−0.984882 + 0.173226i \(0.944581\pi\)
\(692\) 0.885106 1.53305i 0.0336467 0.0582777i
\(693\) 0 0
\(694\) 1.47992i 0.0561769i
\(695\) 17.9756 + 10.3782i 0.681853 + 0.393668i
\(696\) 9.28179i 0.351825i
\(697\) −22.4055 12.9358i −0.848667 0.489978i
\(698\) 1.97543 3.42155i 0.0747712 0.129508i
\(699\) 4.66312 8.07675i 0.176375 0.305491i
\(700\) 0 0
\(701\) 0.286950 0.0108380 0.00541898 0.999985i \(-0.498275\pi\)
0.00541898 + 0.999985i \(0.498275\pi\)
\(702\) −2.68527 1.69127i −0.101349 0.0638331i
\(703\) 0.749377 1.29796i 0.0282633 0.0489534i
\(704\) 16.8601 9.73419i 0.635440 0.366871i
\(705\) −9.07036 −0.341609
\(706\) −0.0512797 0.0888191i −0.00192994 0.00334275i
\(707\) 0 0
\(708\) −23.6093 + 13.6308i −0.887292 + 0.512278i
\(709\) 16.0949 + 9.29241i 0.604457 + 0.348984i 0.770793 0.637086i \(-0.219860\pi\)
−0.166336 + 0.986069i \(0.553194\pi\)
\(710\) −1.40727 0.812486i −0.0528138 0.0304921i
\(711\) 3.04588 0.114229
\(712\) 4.22656 0.158397
\(713\) −14.0940 8.13715i −0.527823 0.304739i
\(714\) 0 0
\(715\) 12.1704 + 23.0872i 0.455148 + 0.863414i
\(716\) −10.8751 18.8362i −0.406421 0.703941i
\(717\) −3.95022 + 2.28066i −0.147524 + 0.0851729i
\(718\) 2.92974 + 5.07445i 0.109337 + 0.189377i
\(719\) −20.8475 + 36.1088i −0.777479 + 1.34663i 0.155912 + 0.987771i \(0.450168\pi\)
−0.933391 + 0.358862i \(0.883165\pi\)
\(720\) 3.41757i 0.127365i
\(721\) 0 0
\(722\) −2.96980 + 1.71462i −0.110525 + 0.0638114i
\(723\) 12.6275 7.29046i 0.469620 0.271135i
\(724\) 6.94257 0.258019
\(725\) 7.85809 + 13.6106i 0.291842 + 0.505486i
\(726\) 1.23525i 0.0458443i
\(727\) −32.7039 −1.21292 −0.606461 0.795113i \(-0.707411\pi\)
−0.606461 + 0.795113i \(0.707411\pi\)
\(728\) 0 0
\(729\) 23.3578 0.865105
\(730\) 6.90616i 0.255608i
\(731\) −19.0851 33.0564i −0.705888 1.22263i
\(732\) 1.47847 0.0546458
\(733\) −8.60423 + 4.96765i −0.317804 + 0.183484i −0.650413 0.759580i \(-0.725404\pi\)
0.332609 + 0.943065i \(0.392071\pi\)
\(734\) −1.23225 + 0.711440i −0.0454832 + 0.0262597i
\(735\) 0 0
\(736\) 9.33871i 0.344230i
\(737\) −15.3586 + 26.6018i −0.565740 + 0.979891i
\(738\) −0.164119 0.284262i −0.00604129 0.0104638i
\(739\) −9.00853 + 5.20108i −0.331384 + 0.191325i −0.656455 0.754365i \(-0.727945\pi\)
0.325071 + 0.945690i \(0.394612\pi\)
\(740\) 21.0205 + 36.4086i 0.772730 + 1.33841i
\(741\) −1.04969 0.661133i −0.0385615 0.0242873i
\(742\) 0 0
\(743\) −1.47972 0.854317i −0.0542857 0.0313419i 0.472612 0.881271i \(-0.343311\pi\)
−0.526897 + 0.849929i \(0.676645\pi\)
\(744\) −4.84590 −0.177659
\(745\) 38.4686 1.40938
\(746\) −0.327545 0.189108i −0.0119923 0.00692374i
\(747\) −4.80235 2.77264i −0.175709 0.101446i
\(748\) 21.8723 12.6280i 0.799732 0.461726i
\(749\) 0 0
\(750\) −1.23393 2.13722i −0.0450566 0.0780404i
\(751\) −29.9812 −1.09403 −0.547015 0.837123i \(-0.684236\pi\)
−0.547015 + 0.837123i \(0.684236\pi\)
\(752\) 6.09233 3.51741i 0.222164 0.128267i
\(753\) −23.0598 + 39.9408i −0.840347 + 1.45552i
\(754\) −4.08656 + 2.15423i −0.148824 + 0.0784523i
\(755\) 17.3893 0.632860
\(756\) 0 0
\(757\) −4.20229 + 7.27858i −0.152735 + 0.264545i −0.932232 0.361861i \(-0.882141\pi\)
0.779497 + 0.626406i \(0.215475\pi\)
\(758\) 1.29437 2.24191i 0.0470136 0.0814299i
\(759\) 18.7436 + 10.8216i 0.680350 + 0.392800i
\(760\) 0.363160i 0.0131732i
\(761\) −44.2184 25.5295i −1.60292 0.925444i −0.990900 0.134598i \(-0.957026\pi\)
−0.612015 0.790846i \(-0.709641\pi\)
\(762\) 2.63067i 0.0952990i
\(763\) 0 0
\(764\) 20.0668 34.7568i 0.725993 1.25746i
\(765\) 4.27989i 0.154740i
\(766\) −2.27723 + 3.94429i −0.0822798 + 0.142513i
\(767\) 23.1526 + 14.5823i 0.835991 + 0.526535i
\(768\) −12.2780 21.2661i −0.443044 0.767375i
\(769\) 0.610062 + 0.352220i 0.0219994 + 0.0127014i 0.510959 0.859605i \(-0.329290\pi\)
−0.488960 + 0.872306i \(0.662624\pi\)
\(770\) 0 0
\(771\) 3.08015 + 5.33498i 0.110929 + 0.192134i
\(772\) −29.4142 + 16.9823i −1.05864 + 0.611206i
\(773\) 1.26521i 0.0455066i −0.999741 0.0227533i \(-0.992757\pi\)
0.999741 0.0227533i \(-0.00724323\pi\)
\(774\) 0.484272i 0.0174068i
\(775\) 7.10593 4.10261i 0.255253 0.147370i
\(776\) 0.161803 + 0.280252i 0.00580840 + 0.0100604i
\(777\) 0 0
\(778\) −4.40076 2.54078i −0.157775 0.0910914i
\(779\) 0.511533 + 0.886001i 0.0183276 + 0.0317443i
\(780\) 30.7830 16.2272i 1.10221 0.581027i
\(781\) 4.50596 7.80456i 0.161236