Properties

Label 756.2.ba.a.71.16
Level $756$
Weight $2$
Character 756.71
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.16
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.16

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.246614 - 1.39255i) q^{2} +(-1.87836 + 0.686842i) q^{4} +(3.28588 + 1.89710i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.41969 + 2.44632i) q^{8} +O(q^{10})\) \(q+(-0.246614 - 1.39255i) q^{2} +(-1.87836 + 0.686842i) q^{4} +(3.28588 + 1.89710i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.41969 + 2.44632i) q^{8} +(1.83146 - 5.04359i) q^{10} +(-0.147235 - 0.255018i) q^{11} +(-1.99299 + 3.45197i) q^{13} +(0.909846 + 1.08267i) q^{14} +(3.05650 - 2.58028i) q^{16} -3.60857i q^{17} +6.02570i q^{19} +(-7.47508 - 1.30657i) q^{20} +(-0.318814 + 0.267922i) q^{22} +(-2.37532 + 4.11418i) q^{23} +(4.69800 + 8.13717i) q^{25} +(5.29852 + 1.92403i) q^{26} +(1.28329 - 1.53400i) q^{28} +(-0.904457 + 0.522189i) q^{29} +(5.56802 + 3.21470i) q^{31} +(-4.34693 - 3.61998i) q^{32} +(-5.02510 + 0.889923i) q^{34} -3.79421 q^{35} -3.86636 q^{37} +(8.39106 - 1.48602i) q^{38} +(0.0240018 + 10.7316i) q^{40} +(10.6945 + 6.17450i) q^{41} +(-0.852502 + 0.492192i) q^{43} +(0.451718 + 0.377890i) q^{44} +(6.31496 + 2.29313i) q^{46} +(-1.68371 - 2.91626i) q^{47} +(0.500000 - 0.866025i) q^{49} +(10.1728 - 8.54892i) q^{50} +(1.37261 - 7.85292i) q^{52} -2.03029i q^{53} -1.11728i q^{55} +(-2.45265 - 1.40873i) q^{56} +(0.950223 + 1.13072i) q^{58} +(4.15275 - 7.19278i) q^{59} +(-5.48589 - 9.50184i) q^{61} +(3.10346 - 8.54650i) q^{62} +(-3.96897 + 6.94603i) q^{64} +(-13.0975 + 7.56183i) q^{65} +(9.26153 + 5.34715i) q^{67} +(2.47852 + 6.77821i) q^{68} +(0.935704 + 5.28360i) q^{70} -2.73284 q^{71} +8.63292 q^{73} +(0.953498 + 5.38408i) q^{74} +(-4.13870 - 11.3185i) q^{76} +(0.255018 + 0.147235i) q^{77} +(4.74756 - 2.74100i) q^{79} +(14.9383 - 2.67999i) q^{80} +(5.96084 - 16.4153i) q^{82} +(-4.07096 - 7.05111i) q^{83} +(6.84583 - 11.8573i) q^{85} +(0.895639 + 1.06577i) q^{86} +(0.414829 - 0.722231i) q^{88} -3.35572i q^{89} -3.98599i q^{91} +(1.63593 - 9.35939i) q^{92} +(-3.64580 + 3.06383i) q^{94} +(-11.4314 + 19.7997i) q^{95} +(6.74076 + 11.6753i) q^{97} +(-1.32929 - 0.482699i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.246614 1.39255i −0.174382 0.984678i
\(3\) 0 0
\(4\) −1.87836 + 0.686842i −0.939182 + 0.343421i
\(5\) 3.28588 + 1.89710i 1.46949 + 0.848410i 0.999414 0.0342161i \(-0.0108934\pi\)
0.470075 + 0.882626i \(0.344227\pi\)
\(6\) 0 0
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 1.41969 + 2.44632i 0.501936 + 0.864905i
\(9\) 0 0
\(10\) 1.83146 5.04359i 0.579158 1.59492i
\(11\) −0.147235 0.255018i −0.0443930 0.0768909i 0.842975 0.537953i \(-0.180802\pi\)
−0.887368 + 0.461062i \(0.847469\pi\)
\(12\) 0 0
\(13\) −1.99299 + 3.45197i −0.552757 + 0.957404i 0.445317 + 0.895373i \(0.353091\pi\)
−0.998074 + 0.0620307i \(0.980242\pi\)
\(14\) 0.909846 + 1.08267i 0.243167 + 0.289356i
\(15\) 0 0
\(16\) 3.05650 2.58028i 0.764124 0.645069i
\(17\) 3.60857i 0.875207i −0.899168 0.437603i \(-0.855827\pi\)
0.899168 0.437603i \(-0.144173\pi\)
\(18\) 0 0
\(19\) 6.02570i 1.38239i 0.722668 + 0.691195i \(0.242915\pi\)
−0.722668 + 0.691195i \(0.757085\pi\)
\(20\) −7.47508 1.30657i −1.67148 0.292158i
\(21\) 0 0
\(22\) −0.318814 + 0.267922i −0.0679715 + 0.0571212i
\(23\) −2.37532 + 4.11418i −0.495289 + 0.857865i −0.999985 0.00543156i \(-0.998271\pi\)
0.504696 + 0.863297i \(0.331604\pi\)
\(24\) 0 0
\(25\) 4.69800 + 8.13717i 0.939600 + 1.62743i
\(26\) 5.29852 + 1.92403i 1.03913 + 0.377334i
\(27\) 0 0
\(28\) 1.28329 1.53400i 0.242519 0.289900i
\(29\) −0.904457 + 0.522189i −0.167954 + 0.0969680i −0.581621 0.813460i \(-0.697581\pi\)
0.413667 + 0.910428i \(0.364248\pi\)
\(30\) 0 0
\(31\) 5.56802 + 3.21470i 1.00005 + 0.577376i 0.908262 0.418403i \(-0.137410\pi\)
0.0917836 + 0.995779i \(0.470743\pi\)
\(32\) −4.34693 3.61998i −0.768435 0.639928i
\(33\) 0 0
\(34\) −5.02510 + 0.889923i −0.861797 + 0.152621i
\(35\) −3.79421 −0.641338
\(36\) 0 0
\(37\) −3.86636 −0.635626 −0.317813 0.948153i \(-0.602948\pi\)
−0.317813 + 0.948153i \(0.602948\pi\)
\(38\) 8.39106 1.48602i 1.36121 0.241064i
\(39\) 0 0
\(40\) 0.0240018 + 10.7316i 0.00379502 + 1.69682i
\(41\) 10.6945 + 6.17450i 1.67021 + 0.964295i 0.967520 + 0.252796i \(0.0813501\pi\)
0.702687 + 0.711499i \(0.251983\pi\)
\(42\) 0 0
\(43\) −0.852502 + 0.492192i −0.130005 + 0.0750586i −0.563592 0.826053i \(-0.690581\pi\)
0.433587 + 0.901112i \(0.357248\pi\)
\(44\) 0.451718 + 0.377890i 0.0680991 + 0.0569691i
\(45\) 0 0
\(46\) 6.31496 + 2.29313i 0.931091 + 0.338103i
\(47\) −1.68371 2.91626i −0.245594 0.425381i 0.716705 0.697377i \(-0.245650\pi\)
−0.962298 + 0.271996i \(0.912316\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 10.1728 8.54892i 1.43865 1.20900i
\(51\) 0 0
\(52\) 1.37261 7.85292i 0.190347 1.08900i
\(53\) 2.03029i 0.278882i −0.990230 0.139441i \(-0.955469\pi\)
0.990230 0.139441i \(-0.0445306\pi\)
\(54\) 0 0
\(55\) 1.11728i 0.150654i
\(56\) −2.45265 1.40873i −0.327749 0.188250i
\(57\) 0 0
\(58\) 0.950223 + 1.13072i 0.124770 + 0.148471i
\(59\) 4.15275 7.19278i 0.540642 0.936420i −0.458225 0.888836i \(-0.651515\pi\)
0.998867 0.0475837i \(-0.0151521\pi\)
\(60\) 0 0
\(61\) −5.48589 9.50184i −0.702397 1.21659i −0.967623 0.252400i \(-0.918780\pi\)
0.265226 0.964186i \(-0.414553\pi\)
\(62\) 3.10346 8.54650i 0.394140 1.08541i
\(63\) 0 0
\(64\) −3.96897 + 6.94603i −0.496121 + 0.868253i
\(65\) −13.0975 + 7.56183i −1.62454 + 0.937930i
\(66\) 0 0
\(67\) 9.26153 + 5.34715i 1.13148 + 0.653258i 0.944306 0.329069i \(-0.106735\pi\)
0.187170 + 0.982327i \(0.440068\pi\)
\(68\) 2.47852 + 6.77821i 0.300564 + 0.821978i
\(69\) 0 0
\(70\) 0.935704 + 5.28360i 0.111838 + 0.631511i
\(71\) −2.73284 −0.324329 −0.162164 0.986764i \(-0.551848\pi\)
−0.162164 + 0.986764i \(0.551848\pi\)
\(72\) 0 0
\(73\) 8.63292 1.01041 0.505203 0.863000i \(-0.331417\pi\)
0.505203 + 0.863000i \(0.331417\pi\)
\(74\) 0.953498 + 5.38408i 0.110842 + 0.625886i
\(75\) 0 0
\(76\) −4.13870 11.3185i −0.474742 1.29832i
\(77\) 0.255018 + 0.147235i 0.0290620 + 0.0167790i
\(78\) 0 0
\(79\) 4.74756 2.74100i 0.534142 0.308387i −0.208560 0.978010i \(-0.566878\pi\)
0.742701 + 0.669623i \(0.233544\pi\)
\(80\) 14.9383 2.67999i 1.67016 0.299632i
\(81\) 0 0
\(82\) 5.96084 16.4153i 0.658265 1.81277i
\(83\) −4.07096 7.05111i −0.446846 0.773960i 0.551333 0.834286i \(-0.314120\pi\)
−0.998179 + 0.0603253i \(0.980786\pi\)
\(84\) 0 0
\(85\) 6.84583 11.8573i 0.742534 1.28611i
\(86\) 0.895639 + 1.06577i 0.0965792 + 0.114925i
\(87\) 0 0
\(88\) 0.414829 0.722231i 0.0442209 0.0769900i
\(89\) 3.35572i 0.355706i −0.984057 0.177853i \(-0.943085\pi\)
0.984057 0.177853i \(-0.0569151\pi\)
\(90\) 0 0
\(91\) 3.98599i 0.417845i
\(92\) 1.63593 9.35939i 0.170557 0.975784i
\(93\) 0 0
\(94\) −3.64580 + 3.06383i −0.376036 + 0.316010i
\(95\) −11.4314 + 19.7997i −1.17283 + 2.03141i
\(96\) 0 0
\(97\) 6.74076 + 11.6753i 0.684421 + 1.18545i 0.973619 + 0.228182i \(0.0732781\pi\)
−0.289198 + 0.957269i \(0.593389\pi\)
\(98\) −1.32929 0.482699i −0.134278 0.0487599i
\(99\) 0 0
\(100\) −14.4135 12.0578i −1.44135 1.20578i
\(101\) 11.1419 6.43278i 1.10866 0.640085i 0.170178 0.985413i \(-0.445566\pi\)
0.938482 + 0.345328i \(0.112232\pi\)
\(102\) 0 0
\(103\) −7.71860 4.45634i −0.760537 0.439096i 0.0689517 0.997620i \(-0.478035\pi\)
−0.829488 + 0.558524i \(0.811368\pi\)
\(104\) −11.2741 + 0.0252150i −1.10551 + 0.00247254i
\(105\) 0 0
\(106\) −2.82728 + 0.500699i −0.274609 + 0.0486322i
\(107\) 2.28113 0.220525 0.110263 0.993902i \(-0.464831\pi\)
0.110263 + 0.993902i \(0.464831\pi\)
\(108\) 0 0
\(109\) −10.0544 −0.963032 −0.481516 0.876437i \(-0.659914\pi\)
−0.481516 + 0.876437i \(0.659914\pi\)
\(110\) −1.55586 + 0.275537i −0.148346 + 0.0262714i
\(111\) 0 0
\(112\) −1.35687 + 3.76283i −0.128212 + 0.355554i
\(113\) −6.07706 3.50859i −0.571682 0.330061i 0.186139 0.982523i \(-0.440403\pi\)
−0.757821 + 0.652463i \(0.773736\pi\)
\(114\) 0 0
\(115\) −15.6100 + 9.01246i −1.45564 + 0.840416i
\(116\) 1.34024 1.60208i 0.124438 0.148749i
\(117\) 0 0
\(118\) −11.0404 4.00906i −1.01635 0.369064i
\(119\) 1.80429 + 3.12511i 0.165399 + 0.286479i
\(120\) 0 0
\(121\) 5.45664 9.45118i 0.496059 0.859199i
\(122\) −11.8788 + 9.98264i −1.07546 + 0.903786i
\(123\) 0 0
\(124\) −12.6667 2.21402i −1.13751 0.198825i
\(125\) 16.6793i 1.49184i
\(126\) 0 0
\(127\) 6.98999i 0.620262i 0.950694 + 0.310131i \(0.100373\pi\)
−0.950694 + 0.310131i \(0.899627\pi\)
\(128\) 10.6515 + 3.81398i 0.941465 + 0.337112i
\(129\) 0 0
\(130\) 13.7602 + 16.3740i 1.20685 + 1.43609i
\(131\) −5.94819 + 10.3026i −0.519696 + 0.900139i 0.480042 + 0.877245i \(0.340621\pi\)
−0.999738 + 0.0228940i \(0.992712\pi\)
\(132\) 0 0
\(133\) −3.01285 5.21841i −0.261247 0.452493i
\(134\) 5.16212 14.2158i 0.445939 1.22806i
\(135\) 0 0
\(136\) 8.82772 5.12305i 0.756971 0.439297i
\(137\) 0.240419 0.138806i 0.0205404 0.0118590i −0.489695 0.871894i \(-0.662892\pi\)
0.510235 + 0.860035i \(0.329558\pi\)
\(138\) 0 0
\(139\) −9.51784 5.49513i −0.807293 0.466091i 0.0387220 0.999250i \(-0.487671\pi\)
−0.846015 + 0.533159i \(0.821005\pi\)
\(140\) 7.12690 2.60602i 0.602333 0.220249i
\(141\) 0 0
\(142\) 0.673957 + 3.80561i 0.0565572 + 0.319360i
\(143\) 1.17375 0.0981542
\(144\) 0 0
\(145\) −3.96258 −0.329075
\(146\) −2.12900 12.0217i −0.176197 0.994925i
\(147\) 0 0
\(148\) 7.26243 2.65558i 0.596968 0.218287i
\(149\) −7.22393 4.17074i −0.591808 0.341680i 0.174004 0.984745i \(-0.444329\pi\)
−0.765812 + 0.643065i \(0.777663\pi\)
\(150\) 0 0
\(151\) 4.58601 2.64773i 0.373204 0.215469i −0.301653 0.953418i \(-0.597539\pi\)
0.674857 + 0.737948i \(0.264205\pi\)
\(152\) −14.7408 + 8.55462i −1.19564 + 0.693871i
\(153\) 0 0
\(154\) 0.142140 0.391435i 0.0114540 0.0315427i
\(155\) 12.1972 + 21.1262i 0.979704 + 1.69690i
\(156\) 0 0
\(157\) 4.66952 8.08784i 0.372668 0.645480i −0.617307 0.786722i \(-0.711776\pi\)
0.989975 + 0.141242i \(0.0451097\pi\)
\(158\) −4.98778 5.93522i −0.396807 0.472180i
\(159\) 0 0
\(160\) −7.41600 20.1414i −0.586286 1.59232i
\(161\) 4.75064i 0.374403i
\(162\) 0 0
\(163\) 15.6620i 1.22674i 0.789794 + 0.613372i \(0.210187\pi\)
−0.789794 + 0.613372i \(0.789813\pi\)
\(164\) −24.3291 4.25249i −1.89979 0.332064i
\(165\) 0 0
\(166\) −8.81504 + 7.40790i −0.684179 + 0.574965i
\(167\) −1.43448 + 2.48460i −0.111004 + 0.192264i −0.916175 0.400778i \(-0.868740\pi\)
0.805172 + 0.593042i \(0.202073\pi\)
\(168\) 0 0
\(169\) −1.44406 2.50118i −0.111081 0.192398i
\(170\) −18.2001 6.60895i −1.39589 0.506883i
\(171\) 0 0
\(172\) 1.26325 1.51005i 0.0963219 0.115140i
\(173\) −5.95609 + 3.43875i −0.452833 + 0.261443i −0.709026 0.705182i \(-0.750865\pi\)
0.256193 + 0.966626i \(0.417532\pi\)
\(174\) 0 0
\(175\) −8.13717 4.69800i −0.615113 0.355135i
\(176\) −1.10804 0.399556i −0.0835217 0.0301177i
\(177\) 0 0
\(178\) −4.67299 + 0.827567i −0.350255 + 0.0620288i
\(179\) 19.3475 1.44610 0.723050 0.690796i \(-0.242740\pi\)
0.723050 + 0.690796i \(0.242740\pi\)
\(180\) 0 0
\(181\) −12.6872 −0.943032 −0.471516 0.881858i \(-0.656293\pi\)
−0.471516 + 0.881858i \(0.656293\pi\)
\(182\) −5.55067 + 0.983000i −0.411443 + 0.0728648i
\(183\) 0 0
\(184\) −13.4368 + 0.0300522i −0.990575 + 0.00221547i
\(185\) −12.7044 7.33488i −0.934045 0.539271i
\(186\) 0 0
\(187\) −0.920252 + 0.531308i −0.0672955 + 0.0388531i
\(188\) 5.16562 + 4.32136i 0.376742 + 0.315168i
\(189\) 0 0
\(190\) 30.3911 + 11.0358i 2.20480 + 0.800622i
\(191\) −4.15917 7.20389i −0.300947 0.521255i 0.675404 0.737448i \(-0.263969\pi\)
−0.976351 + 0.216193i \(0.930636\pi\)
\(192\) 0 0
\(193\) 5.39565 9.34554i 0.388387 0.672707i −0.603845 0.797101i \(-0.706366\pi\)
0.992233 + 0.124395i \(0.0396989\pi\)
\(194\) 14.5961 12.2661i 1.04794 0.880656i
\(195\) 0 0
\(196\) −0.344359 + 1.97013i −0.0245971 + 0.140724i
\(197\) 14.3939i 1.02553i −0.858530 0.512763i \(-0.828622\pi\)
0.858530 0.512763i \(-0.171378\pi\)
\(198\) 0 0
\(199\) 14.9925i 1.06279i 0.847124 + 0.531395i \(0.178332\pi\)
−0.847124 + 0.531395i \(0.821668\pi\)
\(200\) −13.2364 + 23.0451i −0.935958 + 1.62953i
\(201\) 0 0
\(202\) −11.7057 13.9292i −0.823609 0.980054i
\(203\) 0.522189 0.904457i 0.0366505 0.0634805i
\(204\) 0 0
\(205\) 23.4273 + 40.5773i 1.63623 + 2.83404i
\(206\) −4.30214 + 11.8475i −0.299744 + 0.825454i
\(207\) 0 0
\(208\) 2.81545 + 15.6934i 0.195216 + 1.08814i
\(209\) 1.53666 0.887194i 0.106293 0.0613685i
\(210\) 0 0
\(211\) 2.48466 + 1.43452i 0.171051 + 0.0987564i 0.583081 0.812414i \(-0.301847\pi\)
−0.412030 + 0.911170i \(0.635180\pi\)
\(212\) 1.39449 + 3.81363i 0.0957740 + 0.261921i
\(213\) 0 0
\(214\) −0.562559 3.17658i −0.0384557 0.217147i
\(215\) −3.73496 −0.254722
\(216\) 0 0
\(217\) −6.42939 −0.436456
\(218\) 2.47954 + 14.0011i 0.167936 + 0.948277i
\(219\) 0 0
\(220\) 0.767394 + 2.09866i 0.0517377 + 0.141491i
\(221\) 12.4567 + 7.19186i 0.837926 + 0.483777i
\(222\) 0 0
\(223\) 14.5462 8.39828i 0.974088 0.562390i 0.0736082 0.997287i \(-0.476549\pi\)
0.900480 + 0.434897i \(0.143215\pi\)
\(224\) 5.57454 + 0.961530i 0.372464 + 0.0642449i
\(225\) 0 0
\(226\) −3.38719 + 9.32785i −0.225312 + 0.620479i
\(227\) −14.3890 24.9225i −0.955033 1.65417i −0.734291 0.678834i \(-0.762485\pi\)
−0.220742 0.975332i \(-0.570848\pi\)
\(228\) 0 0
\(229\) −9.30663 + 16.1196i −0.614999 + 1.06521i 0.375385 + 0.926869i \(0.377510\pi\)
−0.990385 + 0.138341i \(0.955823\pi\)
\(230\) 16.3999 + 19.5151i 1.08138 + 1.28679i
\(231\) 0 0
\(232\) −2.56149 1.47125i −0.168170 0.0965921i
\(233\) 25.3473i 1.66056i 0.557348 + 0.830279i \(0.311819\pi\)
−0.557348 + 0.830279i \(0.688181\pi\)
\(234\) 0 0
\(235\) 12.7767i 0.833457i
\(236\) −2.86008 + 16.3629i −0.186175 + 1.06514i
\(237\) 0 0
\(238\) 3.90690 3.28324i 0.253247 0.212821i
\(239\) 12.5884 21.8038i 0.814279 1.41037i −0.0955656 0.995423i \(-0.530466\pi\)
0.909845 0.414949i \(-0.136201\pi\)
\(240\) 0 0
\(241\) −4.83687 8.37771i −0.311570 0.539656i 0.667132 0.744939i \(-0.267522\pi\)
−0.978703 + 0.205284i \(0.934188\pi\)
\(242\) −14.5069 5.26783i −0.932538 0.338629i
\(243\) 0 0
\(244\) 16.8308 + 14.0800i 1.07748 + 0.901378i
\(245\) 3.28588 1.89710i 0.209927 0.121201i
\(246\) 0 0
\(247\) −20.8005 12.0092i −1.32351 0.764126i
\(248\) 0.0406718 + 18.1850i 0.00258266 + 1.15475i
\(249\) 0 0
\(250\) 23.2267 4.11335i 1.46899 0.260151i
\(251\) −9.27090 −0.585174 −0.292587 0.956239i \(-0.594516\pi\)
−0.292587 + 0.956239i \(0.594516\pi\)
\(252\) 0 0
\(253\) 1.39892 0.0879494
\(254\) 9.73388 1.72383i 0.610758 0.108163i
\(255\) 0 0
\(256\) 2.68435 15.7732i 0.167772 0.985826i
\(257\) −12.1695 7.02607i −0.759113 0.438274i 0.0698640 0.997557i \(-0.477743\pi\)
−0.828977 + 0.559282i \(0.811077\pi\)
\(258\) 0 0
\(259\) 3.34837 1.93318i 0.208057 0.120122i
\(260\) 19.4080 23.1998i 1.20364 1.43879i
\(261\) 0 0
\(262\) 15.8137 + 5.74237i 0.976973 + 0.354765i
\(263\) −3.96550 6.86845i −0.244523 0.423527i 0.717474 0.696585i \(-0.245298\pi\)
−0.961997 + 0.273058i \(0.911965\pi\)
\(264\) 0 0
\(265\) 3.85168 6.67130i 0.236607 0.409815i
\(266\) −6.52386 + 5.48246i −0.400003 + 0.336151i
\(267\) 0 0
\(268\) −21.0692 3.68268i −1.28700 0.224955i
\(269\) 6.36470i 0.388062i 0.980995 + 0.194031i \(0.0621563\pi\)
−0.980995 + 0.194031i \(0.937844\pi\)
\(270\) 0 0
\(271\) 2.98241i 0.181169i −0.995889 0.0905844i \(-0.971127\pi\)
0.995889 0.0905844i \(-0.0288735\pi\)
\(272\) −9.31111 11.0296i −0.564569 0.668767i
\(273\) 0 0
\(274\) −0.252584 0.300563i −0.0152592 0.0181577i
\(275\) 1.38342 2.39615i 0.0834233 0.144493i
\(276\) 0 0
\(277\) −10.7876 18.6847i −0.648164 1.12265i −0.983561 0.180576i \(-0.942204\pi\)
0.335397 0.942077i \(-0.391130\pi\)
\(278\) −5.30498 + 14.6092i −0.318172 + 0.876202i
\(279\) 0 0
\(280\) −5.38659 9.28184i −0.321910 0.554696i
\(281\) 7.00028 4.04161i 0.417602 0.241103i −0.276449 0.961029i \(-0.589158\pi\)
0.694051 + 0.719926i \(0.255824\pi\)
\(282\) 0 0
\(283\) −0.719769 0.415559i −0.0427858 0.0247024i 0.478455 0.878112i \(-0.341197\pi\)
−0.521240 + 0.853410i \(0.674530\pi\)
\(284\) 5.13327 1.87703i 0.304604 0.111381i
\(285\) 0 0
\(286\) −0.289464 1.63451i −0.0171164 0.0966503i
\(287\) −12.3490 −0.728938
\(288\) 0 0
\(289\) 3.97822 0.234013
\(290\) 0.977228 + 5.51808i 0.0573848 + 0.324033i
\(291\) 0 0
\(292\) −16.2158 + 5.92945i −0.948956 + 0.346995i
\(293\) −11.2950 6.52120i −0.659864 0.380972i 0.132361 0.991202i \(-0.457744\pi\)
−0.792225 + 0.610229i \(0.791077\pi\)
\(294\) 0 0
\(295\) 27.2909 15.7564i 1.58894 0.917373i
\(296\) −5.48903 9.45835i −0.319043 0.549756i
\(297\) 0 0
\(298\) −4.02642 + 11.0882i −0.233244 + 0.642323i
\(299\) −9.46801 16.3991i −0.547549 0.948383i
\(300\) 0 0
\(301\) 0.492192 0.852502i 0.0283695 0.0491374i
\(302\) −4.81806 5.73325i −0.277248 0.329912i
\(303\) 0 0
\(304\) 15.5480 + 18.4175i 0.891737 + 1.05632i
\(305\) 41.6292i 2.38368i
\(306\) 0 0
\(307\) 32.6077i 1.86102i −0.366266 0.930510i \(-0.619364\pi\)
0.366266 0.930510i \(-0.380636\pi\)
\(308\) −0.580144 0.101403i −0.0330568 0.00577800i
\(309\) 0 0
\(310\) 26.4112 22.1952i 1.50005 1.26060i
\(311\) 6.47968 11.2231i 0.367429 0.636406i −0.621734 0.783229i \(-0.713571\pi\)
0.989163 + 0.146823i \(0.0469047\pi\)
\(312\) 0 0
\(313\) −3.72105 6.44505i −0.210326 0.364296i 0.741490 0.670963i \(-0.234119\pi\)
−0.951817 + 0.306668i \(0.900786\pi\)
\(314\) −12.4142 4.50794i −0.700576 0.254398i
\(315\) 0 0
\(316\) −7.03500 + 8.40942i −0.395750 + 0.473067i
\(317\) 0.272234 0.157175i 0.0152902 0.00882780i −0.492335 0.870406i \(-0.663857\pi\)
0.507626 + 0.861578i \(0.330523\pi\)
\(318\) 0 0
\(319\) 0.266336 + 0.153769i 0.0149119 + 0.00860940i
\(320\) −26.2189 + 15.2943i −1.46568 + 0.854975i
\(321\) 0 0
\(322\) −6.61548 + 1.17157i −0.368667 + 0.0652893i
\(323\) 21.7442 1.20988
\(324\) 0 0
\(325\) −37.4524 −2.07748
\(326\) 21.8101 3.86247i 1.20795 0.213923i
\(327\) 0 0
\(328\) 0.0781187 + 34.9281i 0.00431338 + 1.92858i
\(329\) 2.91626 + 1.68371i 0.160779 + 0.0928257i
\(330\) 0 0
\(331\) 18.2481 10.5356i 1.00301 0.579087i 0.0938717 0.995584i \(-0.470076\pi\)
0.909137 + 0.416497i \(0.136742\pi\)
\(332\) 12.4897 + 10.4484i 0.685464 + 0.573433i
\(333\) 0 0
\(334\) 3.81367 + 1.38484i 0.208675 + 0.0757753i
\(335\) 20.2882 + 35.1402i 1.10846 + 1.91991i
\(336\) 0 0
\(337\) −4.76860 + 8.25945i −0.259762 + 0.449921i −0.966178 0.257876i \(-0.916977\pi\)
0.706416 + 0.707797i \(0.250311\pi\)
\(338\) −3.12688 + 2.62774i −0.170080 + 0.142930i
\(339\) 0 0
\(340\) −4.71485 + 26.9744i −0.255699 + 1.46289i
\(341\) 1.89326i 0.102526i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −2.41435 1.38673i −0.130173 0.0747677i
\(345\) 0 0
\(346\) 6.25746 + 7.44608i 0.336403 + 0.400303i
\(347\) 6.87336 11.9050i 0.368981 0.639095i −0.620425 0.784266i \(-0.713040\pi\)
0.989407 + 0.145171i \(0.0463733\pi\)
\(348\) 0 0
\(349\) 8.69604 + 15.0620i 0.465488 + 0.806249i 0.999223 0.0394024i \(-0.0125454\pi\)
−0.533735 + 0.845652i \(0.679212\pi\)
\(350\) −4.53544 + 12.4900i −0.242429 + 0.667617i
\(351\) 0 0
\(352\) −0.283142 + 1.64153i −0.0150915 + 0.0874940i
\(353\) 16.2716 9.39439i 0.866047 0.500013i 1.46597e−5 1.00000i \(-0.499995\pi\)
0.866033 + 0.499987i \(0.166662\pi\)
\(354\) 0 0
\(355\) −8.97979 5.18449i −0.476598 0.275164i
\(356\) 2.30485 + 6.30326i 0.122157 + 0.334072i
\(357\) 0 0
\(358\) −4.77136 26.9423i −0.252174 1.42394i
\(359\) 14.2512 0.752151 0.376076 0.926589i \(-0.377273\pi\)
0.376076 + 0.926589i \(0.377273\pi\)
\(360\) 0 0
\(361\) −17.3091 −0.911003
\(362\) 3.12884 + 17.6675i 0.164448 + 0.928582i
\(363\) 0 0
\(364\) 2.73774 + 7.48714i 0.143497 + 0.392433i
\(365\) 28.3667 + 16.3775i 1.48478 + 0.857240i
\(366\) 0 0
\(367\) −1.87665 + 1.08348i −0.0979604 + 0.0565574i −0.548180 0.836360i \(-0.684679\pi\)
0.450219 + 0.892918i \(0.351346\pi\)
\(368\) 3.35555 + 18.7040i 0.174920 + 0.975011i
\(369\) 0 0
\(370\) −7.08107 + 19.5003i −0.368128 + 1.01377i
\(371\) 1.01515 + 1.75829i 0.0527038 + 0.0912857i
\(372\) 0 0
\(373\) −16.7324 + 28.9814i −0.866370 + 1.50060i −0.000690393 1.00000i \(0.500220\pi\)
−0.865680 + 0.500598i \(0.833114\pi\)
\(374\) 0.966817 + 1.15046i 0.0499929 + 0.0594891i
\(375\) 0 0
\(376\) 4.74378 8.25907i 0.244642 0.425929i
\(377\) 4.16288i 0.214399i
\(378\) 0 0
\(379\) 6.82998i 0.350832i 0.984494 + 0.175416i \(0.0561271\pi\)
−0.984494 + 0.175416i \(0.943873\pi\)
\(380\) 7.87300 45.0426i 0.403876 2.31064i
\(381\) 0 0
\(382\) −9.00603 + 7.56841i −0.460789 + 0.387233i
\(383\) 3.69911 6.40704i 0.189016 0.327384i −0.755907 0.654679i \(-0.772804\pi\)
0.944922 + 0.327295i \(0.106137\pi\)
\(384\) 0 0
\(385\) 0.558640 + 0.967592i 0.0284709 + 0.0493131i
\(386\) −14.3447 5.20895i −0.730128 0.265128i
\(387\) 0 0
\(388\) −20.6807 17.3007i −1.04990 0.878310i
\(389\) −15.0318 + 8.67863i −0.762144 + 0.440024i −0.830065 0.557667i \(-0.811697\pi\)
0.0679209 + 0.997691i \(0.478363\pi\)
\(390\) 0 0
\(391\) 14.8463 + 8.57151i 0.750810 + 0.433480i
\(392\) 2.82842 0.00632591i 0.142857 0.000319507i
\(393\) 0 0
\(394\) −20.0442 + 3.54975i −1.00981 + 0.178834i
\(395\) 20.7999 1.04655
\(396\) 0 0
\(397\) 4.91004 0.246428 0.123214 0.992380i \(-0.460680\pi\)
0.123214 + 0.992380i \(0.460680\pi\)
\(398\) 20.8777 3.69736i 1.04651 0.185332i
\(399\) 0 0
\(400\) 35.3556 + 12.7491i 1.76778 + 0.637455i
\(401\) 21.0371 + 12.1458i 1.05054 + 0.606532i 0.922802 0.385276i \(-0.125894\pi\)
0.127742 + 0.991807i \(0.459227\pi\)
\(402\) 0 0
\(403\) −22.1941 + 12.8137i −1.10556 + 0.638298i
\(404\) −16.5102 + 19.7358i −0.821415 + 0.981894i
\(405\) 0 0
\(406\) −1.38828 0.504120i −0.0688990 0.0250190i
\(407\) 0.569263 + 0.985993i 0.0282173 + 0.0488738i
\(408\) 0 0
\(409\) 19.1299 33.1340i 0.945915 1.63837i 0.192006 0.981394i \(-0.438501\pi\)
0.753909 0.656979i \(-0.228166\pi\)
\(410\) 50.7282 42.6305i 2.50529 2.10537i
\(411\) 0 0
\(412\) 17.5591 + 3.06916i 0.865077 + 0.151207i
\(413\) 8.30551i 0.408687i
\(414\) 0 0
\(415\) 30.8921i 1.51644i
\(416\) 21.1594 7.79085i 1.03743 0.381978i
\(417\) 0 0
\(418\) −1.61442 1.92108i −0.0789638 0.0939631i
\(419\) 9.47453 16.4104i 0.462861 0.801699i −0.536241 0.844065i \(-0.680156\pi\)
0.999102 + 0.0423659i \(0.0134895\pi\)
\(420\) 0 0
\(421\) 10.6034 + 18.3656i 0.516777 + 0.895084i 0.999810 + 0.0194821i \(0.00620175\pi\)
−0.483033 + 0.875602i \(0.660465\pi\)
\(422\) 1.38488 3.81377i 0.0674150 0.185652i
\(423\) 0 0
\(424\) 4.96675 2.88239i 0.241207 0.139981i
\(425\) 29.3636 16.9531i 1.42434 0.822344i
\(426\) 0 0
\(427\) 9.50184 + 5.48589i 0.459827 + 0.265481i
\(428\) −4.28480 + 1.56678i −0.207113 + 0.0757330i
\(429\) 0 0
\(430\) 0.921092 + 5.20110i 0.0444190 + 0.250819i
\(431\) 6.24043 0.300591 0.150295 0.988641i \(-0.451977\pi\)
0.150295 + 0.988641i \(0.451977\pi\)
\(432\) 0 0
\(433\) 12.2312 0.587795 0.293897 0.955837i \(-0.405048\pi\)
0.293897 + 0.955837i \(0.405048\pi\)
\(434\) 1.58558 + 8.95322i 0.0761101 + 0.429768i
\(435\) 0 0
\(436\) 18.8857 6.90575i 0.904462 0.330725i
\(437\) −24.7908 14.3130i −1.18590 0.684682i
\(438\) 0 0
\(439\) 17.4636 10.0826i 0.833492 0.481217i −0.0215550 0.999768i \(-0.506862\pi\)
0.855047 + 0.518551i \(0.173528\pi\)
\(440\) 2.73322 1.58619i 0.130301 0.0756186i
\(441\) 0 0
\(442\) 6.94300 19.1201i 0.330245 0.909450i
\(443\) 14.2028 + 24.6000i 0.674795 + 1.16878i 0.976529 + 0.215387i \(0.0691014\pi\)
−0.301733 + 0.953392i \(0.597565\pi\)
\(444\) 0 0
\(445\) 6.36615 11.0265i 0.301784 0.522706i
\(446\) −15.2823 18.1852i −0.723637 0.861093i
\(447\) 0 0
\(448\) −0.0357847 7.99992i −0.00169067 0.377961i
\(449\) 8.88596i 0.419354i −0.977771 0.209677i \(-0.932759\pi\)
0.977771 0.209677i \(-0.0672413\pi\)
\(450\) 0 0
\(451\) 3.63641i 0.171232i
\(452\) 13.8248 + 2.41643i 0.650263 + 0.113659i
\(453\) 0 0
\(454\) −31.1572 + 26.1836i −1.46228 + 1.22886i
\(455\) 7.56183 13.0975i 0.354504 0.614019i
\(456\) 0 0
\(457\) 5.43702 + 9.41720i 0.254333 + 0.440518i 0.964714 0.263299i \(-0.0848106\pi\)
−0.710381 + 0.703817i \(0.751477\pi\)
\(458\) 24.7423 + 8.98459i 1.15613 + 0.419822i
\(459\) 0 0
\(460\) 23.1312 27.6503i 1.07850 1.28920i
\(461\) −31.3246 + 18.0853i −1.45893 + 0.842316i −0.998959 0.0456166i \(-0.985475\pi\)
−0.459974 + 0.887932i \(0.652141\pi\)
\(462\) 0 0
\(463\) −7.50957 4.33565i −0.348999 0.201495i 0.315245 0.949010i \(-0.397913\pi\)
−0.664244 + 0.747516i \(0.731247\pi\)
\(464\) −1.41708 + 3.92982i −0.0657863 + 0.182437i
\(465\) 0 0
\(466\) 35.2973 6.25100i 1.63511 0.289572i
\(467\) −13.4993 −0.624671 −0.312336 0.949972i \(-0.601111\pi\)
−0.312336 + 0.949972i \(0.601111\pi\)
\(468\) 0 0
\(469\) −10.6943 −0.493817
\(470\) −17.7921 + 3.15090i −0.820687 + 0.145340i
\(471\) 0 0
\(472\) 23.4915 0.0525399i 1.08128 0.00241835i
\(473\) 0.251036 + 0.144936i 0.0115427 + 0.00666416i
\(474\) 0 0
\(475\) −49.0322 + 28.3087i −2.24975 + 1.29889i
\(476\) −5.53556 4.63084i −0.253722 0.212254i
\(477\) 0 0
\(478\) −33.4673 12.1529i −1.53076 0.555859i
\(479\) 19.1408 + 33.1529i 0.874567 + 1.51480i 0.857223 + 0.514945i \(0.172188\pi\)
0.0173444 + 0.999850i \(0.494479\pi\)
\(480\) 0 0
\(481\) 7.70563 13.3465i 0.351347 0.608550i
\(482\) −10.4735 + 8.80163i −0.477055 + 0.400903i
\(483\) 0 0
\(484\) −3.75809 + 21.5006i −0.170822 + 0.977300i
\(485\) 51.1517i 2.32268i
\(486\) 0 0
\(487\) 13.3113i 0.603193i 0.953436 + 0.301597i \(0.0975196\pi\)
−0.953436 + 0.301597i \(0.902480\pi\)
\(488\) 15.4563 26.9099i 0.699674 1.21815i
\(489\) 0 0
\(490\) −3.45214 4.10788i −0.155952 0.185575i
\(491\) −1.46735 + 2.54153i −0.0662207 + 0.114698i −0.897235 0.441554i \(-0.854427\pi\)
0.831014 + 0.556251i \(0.187761\pi\)
\(492\) 0 0
\(493\) 1.88435 + 3.26380i 0.0848671 + 0.146994i
\(494\) −11.5936 + 31.9273i −0.521622 + 1.43648i
\(495\) 0 0
\(496\) 25.3134 4.54131i 1.13661 0.203911i
\(497\) 2.36671 1.36642i 0.106162 0.0612924i
\(498\) 0 0
\(499\) 32.3491 + 18.6768i 1.44815 + 0.836088i 0.998371 0.0570538i \(-0.0181707\pi\)
0.449775 + 0.893142i \(0.351504\pi\)
\(500\) −11.4561 31.3298i −0.512331 1.40111i
\(501\) 0 0
\(502\) 2.28633 + 12.9101i 0.102044 + 0.576208i
\(503\) −29.1509 −1.29978 −0.649888 0.760030i \(-0.725184\pi\)
−0.649888 + 0.760030i \(0.725184\pi\)
\(504\) 0 0
\(505\) 48.8146 2.17222
\(506\) −0.344993 1.94806i −0.0153368 0.0866019i
\(507\) 0 0
\(508\) −4.80102 13.1297i −0.213011 0.582538i
\(509\) 19.4308 + 11.2184i 0.861255 + 0.497246i 0.864432 0.502749i \(-0.167678\pi\)
−0.00317707 + 0.999995i \(0.501011\pi\)
\(510\) 0 0
\(511\) −7.47633 + 4.31646i −0.330733 + 0.190949i
\(512\) −22.6269 + 0.151821i −0.999977 + 0.00670960i
\(513\) 0 0
\(514\) −6.78295 + 18.6793i −0.299183 + 0.823909i
\(515\) −16.9083 29.2860i −0.745067 1.29049i
\(516\) 0 0
\(517\) −0.495801 + 0.858752i −0.0218053 + 0.0377679i
\(518\) −3.51779 4.18600i −0.154563 0.183922i
\(519\) 0 0
\(520\) −37.0930 21.3052i −1.62664 0.934294i
\(521\) 19.1422i 0.838636i −0.907839 0.419318i \(-0.862269\pi\)
0.907839 0.419318i \(-0.137731\pi\)
\(522\) 0 0
\(523\) 7.09271i 0.310143i −0.987903 0.155071i \(-0.950439\pi\)
0.987903 0.155071i \(-0.0495607\pi\)
\(524\) 4.09663 23.4374i 0.178962 1.02387i
\(525\) 0 0
\(526\) −8.58668 + 7.21600i −0.374397 + 0.314632i
\(527\) 11.6005 20.0926i 0.505324 0.875246i
\(528\) 0 0
\(529\) 0.215696 + 0.373597i 0.00937809 + 0.0162433i
\(530\) −10.2400 3.71840i −0.444796 0.161517i
\(531\) 0 0
\(532\) 9.24345 + 7.73272i 0.400754 + 0.335256i
\(533\) −42.6283 + 24.6115i −1.84644 + 1.06604i
\(534\) 0 0
\(535\) 7.49553 + 4.32754i 0.324060 + 0.187096i
\(536\) 0.0676512 + 30.2480i 0.00292209 + 1.30651i
\(537\) 0 0
\(538\) 8.86313 1.56962i 0.382116 0.0676712i
\(539\) −0.294470 −0.0126837
\(540\) 0 0
\(541\) 15.6391 0.672376 0.336188 0.941795i \(-0.390862\pi\)
0.336188 + 0.941795i \(0.390862\pi\)
\(542\) −4.15315 + 0.735505i −0.178393 + 0.0315926i
\(543\) 0 0
\(544\) −13.0629 + 15.6862i −0.560069 + 0.672540i
\(545\) −33.0374 19.0741i −1.41517 0.817047i
\(546\) 0 0
\(547\) 5.46377 3.15451i 0.233614 0.134877i −0.378624 0.925551i \(-0.623603\pi\)
0.612238 + 0.790673i \(0.290269\pi\)
\(548\) −0.356257 + 0.425858i −0.0152185 + 0.0181918i
\(549\) 0 0
\(550\) −3.67792 1.33555i −0.156827 0.0569480i
\(551\) −3.14655 5.44999i −0.134048 0.232177i
\(552\) 0 0
\(553\) −2.74100 + 4.74756i −0.116559 + 0.201887i
\(554\) −23.3589 + 19.6301i −0.992424 + 0.834004i
\(555\) 0 0
\(556\) 21.6523 + 3.78460i 0.918260 + 0.160503i
\(557\) 22.2489i 0.942714i 0.881942 + 0.471357i \(0.156236\pi\)
−0.881942 + 0.471357i \(0.843764\pi\)
\(558\) 0 0
\(559\) 3.92375i 0.165957i
\(560\) −11.5970 + 9.79010i −0.490062 + 0.413707i
\(561\) 0 0
\(562\) −7.35450 8.75149i −0.310231 0.369159i
\(563\) −18.9723 + 32.8609i −0.799585 + 1.38492i 0.120301 + 0.992737i \(0.461614\pi\)
−0.919887 + 0.392185i \(0.871719\pi\)
\(564\) 0 0
\(565\) −13.3123 23.0576i −0.560054 0.970042i
\(566\) −0.401179 + 1.10479i −0.0168628 + 0.0464379i
\(567\) 0 0
\(568\) −3.87979 6.68541i −0.162792 0.280514i
\(569\) −8.24731 + 4.76159i −0.345745 + 0.199616i −0.662810 0.748788i \(-0.730636\pi\)
0.317064 + 0.948404i \(0.397303\pi\)
\(570\) 0 0
\(571\) −21.0510 12.1538i −0.880958 0.508621i −0.00998391 0.999950i \(-0.503178\pi\)
−0.870974 + 0.491329i \(0.836511\pi\)
\(572\) −2.20474 + 0.806183i −0.0921847 + 0.0337082i
\(573\) 0 0
\(574\) 3.04543 + 17.1965i 0.127114 + 0.717769i
\(575\) −44.6370 −1.86149
\(576\) 0 0
\(577\) −13.6033 −0.566311 −0.283156 0.959074i \(-0.591381\pi\)
−0.283156 + 0.959074i \(0.591381\pi\)
\(578\) −0.981085 5.53985i −0.0408077 0.230428i
\(579\) 0 0
\(580\) 7.44317 2.72167i 0.309061 0.113011i
\(581\) 7.05111 + 4.07096i 0.292529 + 0.168892i
\(582\) 0 0
\(583\) −0.517763 + 0.298930i −0.0214435 + 0.0123804i
\(584\) 12.2561 + 21.1189i 0.507159 + 0.873906i
\(585\) 0 0
\(586\) −6.29555 + 17.3371i −0.260067 + 0.716188i
\(587\) −3.27395 5.67065i −0.135130 0.234053i 0.790517 0.612440i \(-0.209812\pi\)
−0.925647 + 0.378388i \(0.876479\pi\)
\(588\) 0 0
\(589\) −19.3708 + 33.5512i −0.798159 + 1.38245i
\(590\) −28.6718 34.1180i −1.18040 1.40462i
\(591\) 0 0
\(592\) −11.8175 + 9.97628i −0.485697 + 0.410022i
\(593\) 11.1137i 0.456386i −0.973616 0.228193i \(-0.926718\pi\)
0.973616 0.228193i \(-0.0732818\pi\)
\(594\) 0 0
\(595\) 13.6917i 0.561303i
\(596\) 16.4338 + 2.87247i 0.673155 + 0.117661i
\(597\) 0 0
\(598\) −20.5015 + 17.2289i −0.838369 + 0.704541i
\(599\) 6.36905 11.0315i 0.260232 0.450736i −0.706071 0.708141i \(-0.749534\pi\)
0.966304 + 0.257405i \(0.0828675\pi\)
\(600\) 0 0
\(601\) −14.5547 25.2095i −0.593699 1.02832i −0.993729 0.111815i \(-0.964334\pi\)
0.400030 0.916502i \(-0.369000\pi\)
\(602\) −1.30853 0.475161i −0.0533317 0.0193661i
\(603\) 0 0
\(604\) −6.79561 + 8.12326i −0.276510 + 0.330531i
\(605\) 35.8597 20.7036i 1.45791 0.841722i
\(606\) 0 0
\(607\) −32.5285 18.7804i −1.32029 0.762272i −0.336518 0.941677i \(-0.609249\pi\)
−0.983775 + 0.179406i \(0.942583\pi\)
\(608\) 21.8129 26.1933i 0.884630 1.06228i
\(609\) 0 0
\(610\) −57.9706 + 10.2663i −2.34716 + 0.415672i
\(611\) 13.4225 0.543015
\(612\) 0 0
\(613\) 20.5622 0.830501 0.415250 0.909707i \(-0.363694\pi\)
0.415250 + 0.909707i \(0.363694\pi\)
\(614\) −45.4077 + 8.04151i −1.83251 + 0.324529i
\(615\) 0 0
\(616\) 0.00186279 + 0.832885i 7.50540e−5 + 0.0335579i
\(617\) −29.4852 17.0233i −1.18703 0.685333i −0.229400 0.973332i \(-0.573677\pi\)
−0.957631 + 0.288000i \(0.907010\pi\)
\(618\) 0 0
\(619\) 32.9073 18.9990i 1.32265 0.763635i 0.338503 0.940965i \(-0.390079\pi\)
0.984151 + 0.177330i \(0.0567461\pi\)
\(620\) −37.4212 31.3051i −1.50287 1.25724i
\(621\) 0 0
\(622\) −17.2267 6.25547i −0.690728 0.250821i
\(623\) 1.67786 + 2.90614i 0.0672220 + 0.116432i
\(624\) 0 0
\(625\) −8.15241 + 14.1204i −0.326096 + 0.564815i
\(626\) −8.05736 + 6.77117i −0.322037 + 0.270630i
\(627\) 0 0
\(628\) −3.21598 + 18.3991i −0.128332 + 0.734205i
\(629\) 13.9520i 0.556304i
\(630\) 0 0
\(631\) 46.8749i 1.86606i 0.359799 + 0.933030i \(0.382845\pi\)
−0.359799 + 0.933030i \(0.617155\pi\)
\(632\) 13.4454 + 7.72267i 0.534830 + 0.307191i
\(633\) 0 0
\(634\) −0.286009 0.340337i −0.0113589 0.0135165i
\(635\) −13.2607 + 22.9683i −0.526236 + 0.911468i
\(636\) 0 0
\(637\) 1.99299 + 3.45197i 0.0789653 + 0.136772i
\(638\) 0.148448 0.408806i 0.00587712 0.0161848i
\(639\) 0 0
\(640\) 27.7639 + 32.7392i 1.09746 + 1.29413i
\(641\) 22.8062 13.1672i 0.900792 0.520073i 0.0233352 0.999728i \(-0.492571\pi\)
0.877457 + 0.479655i \(0.159238\pi\)
\(642\) 0 0
\(643\) 33.1788 + 19.1558i 1.30844 + 0.755430i 0.981836 0.189730i \(-0.0607611\pi\)
0.326608 + 0.945160i \(0.394094\pi\)
\(644\) 3.26294 + 8.92343i 0.128578 + 0.351633i
\(645\) 0 0
\(646\) −5.36241 30.2797i −0.210981 1.19134i
\(647\) −31.8925 −1.25382 −0.626912 0.779090i \(-0.715682\pi\)
−0.626912 + 0.779090i \(0.715682\pi\)
\(648\) 0 0
\(649\) −2.44572 −0.0960030
\(650\) 9.23627 + 52.1541i 0.362276 + 2.04565i
\(651\) 0 0
\(652\) −10.7573 29.4190i −0.421290 1.15214i
\(653\) −4.99048 2.88125i −0.195292 0.112752i 0.399165 0.916879i \(-0.369300\pi\)
−0.594458 + 0.804127i \(0.702633\pi\)
\(654\) 0 0
\(655\) −39.0901 + 22.5687i −1.52738 + 0.881830i
\(656\) 48.6197 8.72255i 1.89828 0.340558i
\(657\) 0 0
\(658\) 1.62545 4.47625i 0.0633664 0.174503i
\(659\) 8.37638 + 14.5083i 0.326298 + 0.565164i 0.981774 0.190052i \(-0.0608655\pi\)
−0.655477 + 0.755216i \(0.727532\pi\)
\(660\) 0 0
\(661\) −8.26733 + 14.3194i −0.321562 + 0.556961i −0.980810 0.194964i \(-0.937541\pi\)
0.659249 + 0.751925i \(0.270874\pi\)
\(662\) −19.1715 22.8131i −0.745122 0.886658i
\(663\) 0 0
\(664\) 11.4698 19.9693i 0.445114 0.774958i
\(665\) 22.8627i 0.886579i
\(666\) 0 0
\(667\) 4.96146i 0.192109i
\(668\) 0.987954 5.65223i 0.0382251 0.218692i
\(669\) 0 0
\(670\) 43.9309 36.9183i 1.69720 1.42628i
\(671\) −1.61543 + 2.79801i −0.0623630 + 0.108016i
\(672\) 0 0
\(673\) −6.04519 10.4706i −0.233025 0.403611i 0.725672 0.688041i \(-0.241529\pi\)
−0.958697 + 0.284430i \(0.908196\pi\)
\(674\) 12.6777 + 4.60359i 0.488325 + 0.177324i
\(675\) 0 0
\(676\) 4.43038 + 3.70628i 0.170399 + 0.142549i
\(677\) 21.2204 12.2516i 0.815567 0.470868i −0.0333185 0.999445i \(-0.510608\pi\)
0.848885 + 0.528577i \(0.177274\pi\)
\(678\) 0 0
\(679\) −11.6753 6.74076i −0.448058 0.258687i
\(680\) 38.7258 0.0866122i 1.48507 0.00332143i
\(681\) 0 0
\(682\) −2.63645 + 0.466905i −0.100955 + 0.0178787i
\(683\) −50.4915 −1.93200 −0.966002 0.258534i \(-0.916761\pi\)
−0.966002 + 0.258534i \(0.916761\pi\)
\(684\) 0 0
\(685\) 1.05332 0.0402452
\(686\) 1.39255 0.246614i 0.0531676 0.00941576i
\(687\) 0 0
\(688\) −1.33568 + 3.70408i −0.0509222 + 0.141217i
\(689\) 7.00851 + 4.04637i 0.267003 + 0.154154i
\(690\) 0 0
\(691\) 7.62153 4.40029i 0.289937 0.167395i −0.347977 0.937503i \(-0.613131\pi\)
0.637913 + 0.770108i \(0.279798\pi\)
\(692\) 8.82582 10.5501i 0.335507 0.401055i
\(693\) 0 0
\(694\) −18.2733 6.63553i −0.693646 0.251881i
\(695\) −20.8497 36.1127i −0.790872 1.36983i
\(696\) 0 0
\(697\) 22.2811 38.5920i 0.843957 1.46178i
\(698\) 18.8299 15.8241i 0.712723 0.598952i
\(699\) 0 0
\(700\) 18.5114 + 3.23560i 0.699663 + 0.122294i
\(701\) 40.0613i 1.51309i 0.653940 + 0.756546i \(0.273115\pi\)
−0.653940 + 0.756546i \(0.726885\pi\)
\(702\) 0 0
\(703\) 23.2975i 0.878682i
\(704\) 2.35574 0.0105375i 0.0887851 0.000397147i
\(705\) 0 0
\(706\) −17.0949 20.3421i −0.643375 0.765584i
\(707\) −6.43278 + 11.1419i −0.241930 + 0.419034i
\(708\) 0 0
\(709\) −13.4387 23.2765i −0.504701 0.874169i −0.999985 0.00543734i \(-0.998269\pi\)
0.495284 0.868731i \(-0.335064\pi\)
\(710\) −5.00509 + 13.7833i −0.187838 + 0.517279i
\(711\) 0 0
\(712\) 8.20917 4.76408i 0.307652 0.178541i
\(713\) −26.4517 + 15.2719i −0.990622 + 0.571936i
\(714\) 0 0
\(715\) 3.85681 + 2.22673i 0.144237 + 0.0832751i
\(716\) −36.3416 + 13.2887i −1.35815 + 0.496621i
\(717\) 0 0
\(718\) −3.51455 19.8455i −0.131162 0.740627i
\(719\) 40.6857 1.51732 0.758661 0.651486i \(-0.225854\pi\)
0.758661 + 0.651486i \(0.225854\pi\)
\(720\) 0 0
\(721\) 8.91268 0.331925
\(722\) 4.26865 + 24.1036i 0.158863 + 0.897044i
\(723\) 0 0
\(724\) 23.8312 8.71409i 0.885678 0.323857i
\(725\) −8.49828 4.90649i −0.315618 0.182222i
\(726\) 0 0
\(727\) −3.36949 + 1.94538i −0.124968 + 0.0721501i −0.561181 0.827693i \(-0.689653\pi\)
0.436213 + 0.899843i \(0.356319\pi\)
\(728\) 9.75101 5.65886i 0.361396 0.209731i
\(729\) 0 0
\(730\) 15.8108 43.5409i 0.585185 1.61152i
\(731\) 1.77611 + 3.07631i 0.0656918 + 0.113782i
\(732\) 0 0
\(733\) −11.2371 + 19.4633i −0.415053 + 0.718893i −0.995434 0.0954521i \(-0.969570\pi\)
0.580381 + 0.814345i \(0.302904\pi\)
\(734\) 1.97161 + 2.34612i 0.0727734 + 0.0865968i
\(735\) 0 0
\(736\) 25.2186 9.28541i 0.929569 0.342265i
\(737\) 3.14915i 0.116000i
\(738\) 0 0
\(739\) 34.2290i 1.25913i −0.776947 0.629567i \(-0.783232\pi\)
0.776947 0.629567i \(-0.216768\pi\)
\(740\) 28.9014 + 5.05167i 1.06244 + 0.185703i
\(741\) 0 0
\(742\) 2.19814 1.84726i 0.0806964 0.0678149i
\(743\) 14.2792 24.7322i 0.523851 0.907337i −0.475763 0.879573i \(-0.657828\pi\)
0.999615 0.0277637i \(-0.00883859\pi\)
\(744\) 0 0
\(745\) −15.8246 27.4091i −0.579770 1.00419i
\(746\) 44.4843 + 16.1534i 1.62869 + 0.591418i
\(747\) 0 0
\(748\) 1.36364 1.63006i 0.0498597 0.0596008i
\(749\) −1.97552 + 1.14057i −0.0721839 + 0.0416754i
\(750\) 0 0
\(751\) −3.64406 2.10390i −0.132974 0.0767723i 0.432038 0.901856i \(-0.357795\pi\)
−0.565011 + 0.825083i \(0.691128\pi\)
\(752\) −12.6710 4.56913i −0.462064 0.166619i
\(753\) 0 0
\(754\) −5.79700 + 1.02662i −0.211114 + 0.0373874i
\(755\) 20.0921 0.731226
\(756\) 0 0
\(757\) −5.18894 −0.188595 −0.0942977 0.995544i \(-0.530061\pi\)
−0.0942977 + 0.995544i \(0.530061\pi\)
\(758\) 9.51105 1.68437i 0.345457 0.0611790i
\(759\) 0 0
\(760\) −64.6654 + 0.144628i −2.34566 + 0.00524620i
\(761\) −0.558714 0.322574i −0.0202534 0.0116933i 0.489839 0.871813i \(-0.337056\pi\)
−0.510092 + 0.860120i \(0.670389\pi\)
\(762\) 0 0
\(763\) 8.70733 5.02718i 0.315226 0.181996i
\(764\) 12.7604 + 10.6748i 0.461654 + 0.386202i
\(765\) 0 0
\(766\) −9.83434 3.57111i −0.355329 0.129029i
\(767\) 16.5528 + 28.6703i 0.597688 + 1.03523i
\(768\) 0 0
\(769\) −12.6215 + 21.8612i −0.455145 + 0.788333i −0.998697 0.0510420i \(-0.983746\pi\)
0.543552 + 0.839376i \(0.317079\pi\)
\(770\) 1.20965 1.01655i 0.0435927 0.0366340i
\(771\) 0 0
\(772\) −3.71608 + 21.2603i −0.133745 + 0.765174i
\(773\) 8.72610i 0.313856i −0.987610 0.156928i \(-0.949841\pi\)
0.987610 0.156928i \(-0.0501591\pi\)
\(774\) 0 0
\(775\) 60.4106i 2.17001i
\(776\) −18.9918 + 33.0654i −0.681768 + 1.18698i
\(777\) 0 0
\(778\) 15.7924 + 18.7922i 0.566187 + 0.673734i
\(779\) −37.2057 + 64.4421i −1.33303 + 2.30888i
\(780\) 0 0
\(781\) 0.402370 + 0.696926i 0.0143979 + 0.0249380i
\(782\) 8.27492 22.7880i 0.295910 0.814897i
\(783\) 0 0
\(784\) −0.706337 3.93714i −0.0252263 0.140612i
\(785\) 30.6869 17.7171i 1.09526 0.632351i
\(786\) 0 0
\(787\) −16.8392 9.72212i −0.600253 0.346556i 0.168888 0.985635i \(-0.445982\pi\)
−0.769141 + 0.639079i \(0.779316\pi\)
\(788\) 9.88636 + 27.0370i 0.352187 + 0.963155i
\(789\) 0 0
\(790\)