Properties

Label 756.2.ba.a.575.16
Level $756$
Weight $2$
Character 756.575
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(71,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
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

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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 575.16
Character \(\chi\) \(=\) 756.575
Dual form 756.2.ba.a.71.16

$q$-expansion

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

Character values

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

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

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 0.470075 0.882626i \(-0.344227\pi\)
0.999414 + 0.0342161i \(0.0108934\pi\)
\(6\) 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 −0.887368 0.461062i \(-0.847469\pi\)
0.842975 + 0.537953i \(0.180802\pi\)
\(12\) 0 0
\(13\) −1.99299 3.45197i −0.552757 0.957404i −0.998074 0.0620307i \(-0.980242\pi\)
0.445317 0.895373i \(-0.353091\pi\)
\(14\) 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 \(0.144173\pi\)
−0.899168 + 0.437603i \(0.855827\pi\)
\(18\) 0 0
\(19\) 6.02570i 1.38239i −0.722668 0.691195i \(-0.757085\pi\)
0.722668 0.691195i \(-0.242915\pi\)
\(20\) −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 0.504696 0.863297i \(-0.331604\pi\)
−0.999985 + 0.00543156i \(0.998271\pi\)
\(24\) 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 0.413667 0.910428i \(-0.364248\pi\)
−0.581621 + 0.813460i \(0.697581\pi\)
\(30\) 0 0
\(31\) 5.56802 3.21470i 1.00005 0.577376i 0.0917836 0.995779i \(-0.470743\pi\)
0.908262 + 0.418403i \(0.137410\pi\)
\(32\) −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 0.702687 0.711499i \(-0.251983\pi\)
0.967520 0.252796i \(-0.0813501\pi\)
\(42\) 0 0
\(43\) −0.852502 0.492192i −0.130005 0.0750586i 0.433587 0.901112i \(-0.357248\pi\)
−0.563592 + 0.826053i \(0.690581\pi\)
\(44\) 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 −0.962298 0.271996i \(-0.912316\pi\)
0.716705 + 0.697377i \(0.245650\pi\)
\(48\) 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 \(0.0445306\pi\)
−0.990230 + 0.139441i \(0.955469\pi\)
\(54\) 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 0.998867 + 0.0475837i \(0.0151521\pi\)
−0.458225 + 0.888836i \(0.651515\pi\)
\(60\) 0 0
\(61\) −5.48589 + 9.50184i −0.702397 + 1.21659i 0.265226 + 0.964186i \(0.414553\pi\)
−0.967623 + 0.252400i \(0.918780\pi\)
\(62\) 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 0.187170 0.982327i \(-0.440068\pi\)
0.944306 + 0.329069i \(0.106735\pi\)
\(68\) 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 0.742701 0.669623i \(-0.233544\pi\)
−0.208560 + 0.978010i \(0.566878\pi\)
\(80\) 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 −0.998179 0.0603253i \(-0.980786\pi\)
0.551333 + 0.834286i \(0.314120\pi\)
\(84\) 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 \(0.0569151\pi\)
−0.984057 + 0.177853i \(0.943085\pi\)
\(90\) 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 −0.289198 0.957269i \(-0.593389\pi\)
0.973619 0.228182i \(-0.0732781\pi\)
\(98\) −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 0.938482 0.345328i \(-0.112232\pi\)
0.170178 + 0.985413i \(0.445566\pi\)
\(102\) 0 0
\(103\) −7.71860 + 4.45634i −0.760537 + 0.439096i −0.829488 0.558524i \(-0.811368\pi\)
0.0689517 + 0.997620i \(0.478035\pi\)
\(104\) −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 −0.757821 0.652463i \(-0.773736\pi\)
0.186139 + 0.982523i \(0.440403\pi\)
\(114\) 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 \(-0.899627\pi\)
0.950694 0.310131i \(-0.100373\pi\)
\(128\) 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 −0.999738 0.0228940i \(-0.992712\pi\)
0.480042 0.877245i \(-0.340621\pi\)
\(132\) 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 0.510235 0.860035i \(-0.329558\pi\)
−0.489695 + 0.871894i \(0.662892\pi\)
\(138\) 0 0
\(139\) −9.51784 + 5.49513i −0.807293 + 0.466091i −0.846015 0.533159i \(-0.821005\pi\)
0.0387220 + 0.999250i \(0.487671\pi\)
\(140\) 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 −0.765812 0.643065i \(-0.777663\pi\)
0.174004 + 0.984745i \(0.444329\pi\)
\(150\) 0 0
\(151\) 4.58601 + 2.64773i 0.373204 + 0.215469i 0.674857 0.737948i \(-0.264205\pi\)
−0.301653 + 0.953418i \(0.597539\pi\)
\(152\) −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 0.989975 0.141242i \(-0.0451097\pi\)
−0.617307 + 0.786722i \(0.711776\pi\)
\(158\) −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 \(-0.789813\pi\)
0.789794 0.613372i \(-0.210187\pi\)
\(164\) −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 0.805172 0.593042i \(-0.202073\pi\)
−0.916175 + 0.400778i \(0.868740\pi\)
\(168\) 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 0.256193 0.966626i \(-0.417532\pi\)
−0.709026 + 0.705182i \(0.750865\pi\)
\(174\) 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 −0.976351 0.216193i \(-0.930636\pi\)
0.675404 + 0.737448i \(0.263969\pi\)
\(192\) 0 0
\(193\) 5.39565 + 9.34554i 0.388387 + 0.672707i 0.992233 0.124395i \(-0.0396989\pi\)
−0.603845 + 0.797101i \(0.706366\pi\)
\(194\) 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 \(0.171378\pi\)
−0.858530 + 0.512763i \(0.828622\pi\)
\(198\) 0 0
\(199\) 14.9925i 1.06279i −0.847124 0.531395i \(-0.821668\pi\)
0.847124 0.531395i \(-0.178332\pi\)
\(200\) −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 −0.412030 0.911170i \(-0.635180\pi\)
0.583081 + 0.812414i \(0.301847\pi\)
\(212\) 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 0.900480 0.434897i \(-0.143215\pi\)
0.0736082 + 0.997287i \(0.476549\pi\)
\(224\) 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 −0.220742 + 0.975332i \(0.570848\pi\)
−0.734291 + 0.678834i \(0.762485\pi\)
\(228\) 0 0
\(229\) −9.30663 16.1196i −0.614999 1.06521i −0.990385 0.138341i \(-0.955823\pi\)
0.375385 0.926869i \(-0.377510\pi\)
\(230\) 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 \(-0.688181\pi\)
0.557348 0.830279i \(-0.311819\pi\)
\(234\) 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 0.909845 + 0.414949i \(0.136201\pi\)
−0.0955656 + 0.995423i \(0.530466\pi\)
\(240\) 0 0
\(241\) −4.83687 + 8.37771i −0.311570 + 0.539656i −0.978703 0.205284i \(-0.934188\pi\)
0.667132 + 0.744939i \(0.267522\pi\)
\(242\) −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 −0.828977 0.559282i \(-0.811077\pi\)
0.0698640 + 0.997557i \(0.477743\pi\)
\(258\) 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 −0.961997 0.273058i \(-0.911965\pi\)
0.717474 + 0.696585i \(0.245298\pi\)
\(264\) 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 \(-0.937844\pi\)
0.980995 0.194031i \(-0.0621563\pi\)
\(270\) 0 0
\(271\) 2.98241i 0.181169i 0.995889 + 0.0905844i \(0.0288735\pi\)
−0.995889 + 0.0905844i \(0.971127\pi\)
\(272\) −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 0.335397 + 0.942077i \(0.391130\pi\)
−0.983561 + 0.180576i \(0.942204\pi\)
\(278\) −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 0.694051 0.719926i \(-0.255824\pi\)
−0.276449 + 0.961029i \(0.589158\pi\)
\(282\) 0 0
\(283\) −0.719769 + 0.415559i −0.0427858 + 0.0247024i −0.521240 0.853410i \(-0.674530\pi\)
0.478455 + 0.878112i \(0.341197\pi\)
\(284\) 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 −0.792225 0.610229i \(-0.791077\pi\)
0.132361 + 0.991202i \(0.457744\pi\)
\(294\) 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 \(0.380636\pi\)
−0.366266 + 0.930510i \(0.619364\pi\)
\(308\) −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 0.989163 0.146823i \(-0.0469047\pi\)
−0.621734 + 0.783229i \(0.713571\pi\)
\(312\) 0 0
\(313\) −3.72105 + 6.44505i −0.210326 + 0.364296i −0.951817 0.306668i \(-0.900786\pi\)
0.741490 + 0.670963i \(0.234119\pi\)
\(314\) −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 0.507626 0.861578i \(-0.330523\pi\)
−0.492335 + 0.870406i \(0.663857\pi\)
\(318\) 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 0.909137 0.416497i \(-0.136742\pi\)
0.0938717 + 0.995584i \(0.470076\pi\)
\(332\) 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 0.706416 0.707797i \(-0.250311\pi\)
−0.966178 + 0.257876i \(0.916977\pi\)
\(338\) −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 0.989407 0.145171i \(-0.0463733\pi\)
−0.620425 + 0.784266i \(0.713040\pi\)
\(348\) 0 0
\(349\) 8.69604 15.0620i 0.465488 0.806249i −0.533735 0.845652i \(-0.679212\pi\)
0.999223 + 0.0394024i \(0.0125454\pi\)
\(350\) −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 0.866033 0.499987i \(-0.166662\pi\)
1.46597e−5 1.00000i \(0.499995\pi\)
\(354\) 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 0.450219 0.892918i \(-0.351346\pi\)
−0.548180 + 0.836360i \(0.684679\pi\)
\(368\) 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 −0.865680 0.500598i \(-0.833114\pi\)
−0.000690393 1.00000i \(-0.500220\pi\)
\(374\) 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 \(-0.943873\pi\)
0.984494 0.175416i \(-0.0561271\pi\)
\(380\) 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 0.944922 0.327295i \(-0.106137\pi\)
−0.755907 + 0.654679i \(0.772804\pi\)
\(384\) 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 0.0679209 0.997691i \(-0.478363\pi\)
−0.830065 + 0.557667i \(0.811697\pi\)
\(390\) 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 0.127742 0.991807i \(-0.459227\pi\)
0.922802 + 0.385276i \(0.125894\pi\)
\(402\) 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 0.753909 + 0.656979i \(0.228166\pi\)
0.192006 + 0.981394i \(0.438501\pi\)
\(410\) 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 0.999102 0.0423659i \(-0.0134895\pi\)
−0.536241 + 0.844065i \(0.680156\pi\)
\(420\) 0 0
\(421\) 10.6034 18.3656i 0.516777 0.895084i −0.483033 0.875602i \(-0.660465\pi\)
0.999810 0.0194821i \(-0.00620175\pi\)
\(422\) 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 0.855047 0.518551i \(-0.173528\pi\)
−0.0215550 + 0.999768i \(0.506862\pi\)
\(440\) 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 −0.301733 0.953392i \(-0.597565\pi\)
0.976529 0.215387i \(-0.0691014\pi\)
\(444\) 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 \(0.0672413\pi\)
−0.977771 + 0.209677i \(0.932759\pi\)
\(450\) 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 −0.710381 0.703817i \(-0.751477\pi\)
0.964714 + 0.263299i \(0.0848106\pi\)
\(458\) 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 −0.459974 0.887932i \(-0.652141\pi\)
−0.998959 + 0.0456166i \(0.985475\pi\)
\(462\) 0 0
\(463\) −7.50957 + 4.33565i −0.348999 + 0.201495i −0.664244 0.747516i \(-0.731247\pi\)
0.315245 + 0.949010i \(0.397913\pi\)
\(464\) −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 0.0173444 0.999850i \(-0.494479\pi\)
0.857223 0.514945i \(-0.172188\pi\)
\(480\) 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 \(-0.902480\pi\)
0.953436 0.301597i \(-0.0975196\pi\)
\(488\) 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 0.831014 0.556251i \(-0.187761\pi\)
−0.897235 + 0.441554i \(0.854427\pi\)
\(492\) 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 0.449775 0.893142i \(-0.351504\pi\)
0.998371 + 0.0570538i \(0.0181707\pi\)
\(500\) −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 −0.00317707 0.999995i \(-0.501011\pi\)
0.864432 + 0.502749i \(0.167678\pi\)
\(510\) 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 \(0.137731\pi\)
−0.907839 + 0.419318i \(0.862269\pi\)
\(522\) 0 0
\(523\) 7.09271i 0.310143i 0.987903 + 0.155071i \(0.0495607\pi\)
−0.987903 + 0.155071i \(0.950439\pi\)
\(524\) 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 0.612238 0.790673i \(-0.290269\pi\)
−0.378624 + 0.925551i \(0.623603\pi\)
\(548\) −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 \(-0.843764\pi\)
0.881942 0.471357i \(-0.156236\pi\)
\(558\) 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 −0.919887 0.392185i \(-0.871719\pi\)
0.120301 0.992737i \(-0.461614\pi\)
\(564\) 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 0.317064 0.948404i \(-0.397303\pi\)
−0.662810 + 0.748788i \(0.730636\pi\)
\(570\) 0 0
\(571\) −21.0510 + 12.1538i −0.880958 + 0.508621i −0.870974 0.491329i \(-0.836511\pi\)
−0.00998391 + 0.999950i \(0.503178\pi\)
\(572\) −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 −0.925647 0.378388i \(-0.876479\pi\)
0.790517 + 0.612440i \(0.209812\pi\)
\(588\) 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 \(0.0732818\pi\)
−0.973616 + 0.228193i \(0.926718\pi\)
\(594\) 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 0.966304 0.257405i \(-0.0828675\pi\)
−0.706071 + 0.708141i \(0.749534\pi\)
\(600\) 0 0
\(601\) −14.5547 + 25.2095i −0.593699 + 1.02832i 0.400030 + 0.916502i \(0.369000\pi\)
−0.993729 + 0.111815i \(0.964334\pi\)
\(602\) −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 −0.983775 0.179406i \(-0.942583\pi\)
−0.336518 + 0.941677i \(0.609249\pi\)
\(608\) 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 −0.957631 0.288000i \(-0.907010\pi\)
−0.229400 + 0.973332i \(0.573677\pi\)
\(618\) 0 0
\(619\) 32.9073 + 18.9990i 1.32265 + 0.763635i 0.984151 0.177330i \(-0.0567461\pi\)
0.338503 + 0.940965i \(0.390079\pi\)
\(620\) −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 \(-0.617155\pi\)
0.359799 0.933030i \(-0.382845\pi\)
\(632\) 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 0.877457 0.479655i \(-0.159238\pi\)
0.0233352 + 0.999728i \(0.492571\pi\)
\(642\) 0 0
\(643\) 33.1788 19.1558i 1.30844 0.755430i 0.326608 0.945160i \(-0.394094\pi\)
0.981836 + 0.189730i \(0.0607611\pi\)
\(644\) 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 −0.594458 0.804127i \(-0.702633\pi\)
0.399165 + 0.916879i \(0.369300\pi\)
\(654\) 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 −0.655477 0.755216i \(-0.727532\pi\)
0.981774 + 0.190052i \(0.0608655\pi\)
\(660\) 0 0
\(661\) −8.26733 14.3194i −0.321562 0.556961i 0.659249 0.751925i \(-0.270874\pi\)
−0.980810 + 0.194964i \(0.937541\pi\)
\(662\) −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 −0.958697 0.284430i \(-0.908196\pi\)
0.725672 + 0.688041i \(0.241529\pi\)
\(674\) 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 0.848885 0.528577i \(-0.177274\pi\)
−0.0333185 + 0.999445i \(0.510608\pi\)
\(678\) 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 0.637913 0.770108i \(-0.279798\pi\)
−0.347977 + 0.937503i \(0.613131\pi\)
\(692\) 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 \(-0.726885\pi\)
0.653940 0.756546i \(-0.273115\pi\)
\(702\) 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 0.495284 + 0.868731i \(0.335064\pi\)
−0.999985 + 0.00543734i \(0.998269\pi\)
\(710\) −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 0.436213 0.899843i \(-0.356319\pi\)
−0.561181 + 0.827693i \(0.689653\pi\)
\(728\) 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 0.580381 0.814345i \(-0.302904\pi\)
−0.995434 + 0.0954521i \(0.969570\pi\)
\(734\) 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 \(0.216768\pi\)
−0.776947 + 0.629567i \(0.783232\pi\)
\(740\) 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 0.999615 + 0.0277637i \(0.00883859\pi\)
−0.475763 + 0.879573i \(0.657828\pi\)
\(744\) 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 −0.565011 0.825083i \(-0.691128\pi\)
0.432038 + 0.901856i \(0.357795\pi\)
\(752\) −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 −0.510092 0.860120i \(-0.670389\pi\)
0.489839 + 0.871813i \(0.337056\pi\)
\(762\) 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 0.543552 0.839376i \(-0.317079\pi\)
−0.998697 + 0.0510420i \(0.983746\pi\)
\(770\) 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 \(0.0501591\pi\)
−0.987610 + 0.156928i \(0.949841\pi\)
\(774\) 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 −0.769141 0.639079i \(-0.779316\pi\)
0.168888 + 0.985635i \(0.445982\pi\)
\(788\) 9.88636 27.0370i 0.352187 0.963155i
\(789\) 0 0
\(790\) −5.12953 + 28.9647i −0.182501 + 1.03052i
\(791\) 7.01719 0.249502
\(792\) 0 0
\(793\) 43.7334 1.55302
\(794\) −1.21088 + 6.83745i −0.0429727 + 0.242652i
\(795\) 0 0
\(796\) −10.2975 + 28.1614i −0.364984 + 0.998153i
\(797\) 46.9719 27.1193i 1.66383 0.960614i 0.692972 0.720964i \(-0.256301\pi\)
0.970859 0.239649i \(-0.0770325\pi\)
\(798\) 0 0
\(799\) −10.5235 6.07577i −0.372296 0.214945i
\(800\) 9.03453 + 52.3783i 0.319419 + 1.85185i
\(801\) 0 0
\(802\) 11.7255 + 32.2905i 0.414042 + 1.14022i
\(803\) −1.27107 + 2.20155i −0.0448550 + 0.0776911i
\(804\) 0 0
\(805\) 9.01246 + 15.6100i 0.317647 + 0.550182i
\(806\) 23.3171 27.7462i 0.821309 0.977317i
\(807\) 0 0
\(808\) 31.5547 18.1241i 1.11009 0.637604i
\(809\) 33.5957i 1.18116i 0.806979 + 0.590581i \(0.201101\pi\)
−0.806979 + 0.590581i \(0.798899\pi\)
\(810\) 0 0
\(811\) 6.28139i 0.220570i −0.993900 0.110285i \(-0.964824\pi\)
0.993900 0.110285i \(-0.0351763\pi\)
\(812\) −0.359641 2.05756i −0.0126209 0.0722062i
\(813\) 0 0
\(814\) 1.23265 + 1.03588i 0.0432044 + 0.0363077i
\(815\) −29.7125 51.4635i −1.04078 1.80269i
\(816\) 0 0
\(817\) −2.96580 + 5.13692i −0.103760 + 0.179718i
\(818\) −50.8583 + 18.4680i −1.77822 + 0.645718i
\(819\) 0 0
\(820\) −71.8752 + 60.1281i −2.50999 + 2.09976i
\(821\) −16.5450 9.55229i −0.577426 0.333377i 0.182684 0.983172i \(-0.441522\pi\)
−0.760110 + 0.649795i \(0.774855\pi\)
\(822\) 0 0
\(823\) 43.0543 24.8574i 1.50078 0.866476i 0.500780 0.865574i \(-0.333046\pi\)
1.00000 0.000901331i \(-0.000286903\pi\)
\(824\) −0.0563808 + 25.2088i −0.00196412 + 0.878190i
\(825\) 0 0
\(826\) 11.5658 + 2.04825i 0.402425 + 0.0712678i
\(827\) −4.74479 −0.164992 −0.0824962 0.996591i \(-0.526289\pi\)
−0.0824962 + 0.996591i \(0.526289\pi\)
\(828\) 0 0
\(829\) 11.3890 0.395558 0.197779 0.980247i \(-0.436627\pi\)
0.197779 + 0.980247i \(0.436627\pi\)
\(830\) −43.0187 7.61843i −1.49320 0.264440i
\(831\) 0 0
\(832\) −16.0673 + 27.5442i −0.557034 + 0.954922i
\(833\) −3.12511 + 1.80429i −0.108279 + 0.0625148i
\(834\) 0 0
\(835\) −9.42707 5.44272i −0.326237 0.188353i
\(836\) −2.27705 2.72192i −0.0787535 0.0941395i
\(837\) 0 0
\(838\) −25.1887 + 9.14669i −0.870130 + 0.315967i
\(839\) 17.0108 29.4636i 0.587279 1.01720i −0.407308 0.913291i \(-0.633532\pi\)
0.994587 0.103906i \(-0.0331343\pi\)
\(840\) 0 0
\(841\) −13.9546 24.1701i −0.481194 0.833453i
\(842\) 22.9600 + 19.2949i 0.791253 + 0.664946i
\(843\) 0 0
\(844\) −5.65238 + 0.987980i −0.194563 + 0.0340077i
\(845\) 10.9581i 0.376970i
\(846\) 0 0
\(847\) 10.9133i 0.374985i
\(848\) −5.23872 + 6.20559i −0.179898 + 0.213101i
\(849\) 0 0
\(850\) −30.8494 + 36.7092i −1.05812 + 1.25912i
\(851\) 9.18385 + 15.9069i 0.314818 + 0.545281i
\(852\) 0 0
\(853\) 8.54802 14.8056i 0.292679 0.506934i −0.681764 0.731573i \(-0.738787\pi\)
0.974442 + 0.224638i \(0.0721201\pi\)
\(854\) 5.29607 + 14.5846i 0.181228 + 0.499076i
\(855\) 0 0
\(856\) 3.23850 5.58038i 0.110690 0.190734i
\(857\) 4.25999 + 2.45951i 0.145518 + 0.0840151i 0.570991 0.820956i \(-0.306559\pi\)
−0.425473 + 0.904971i \(0.639892\pi\)
\(858\) 0 0
\(859\) 25.8381 14.9176i 0.881585 0.508983i 0.0104044 0.999946i \(-0.496688\pi\)
0.871181 + 0.490963i \(0.163355\pi\)
\(860\) 7.01561 + 2.56533i 0.239230 + 0.0874769i
\(861\) 0 0
\(862\) −1.53898 + 8.69008i −0.0524177 + 0.295985i
\(863\) −7.21912 −0.245742 −0.122871 0.992423i \(-0.539210\pi\)
−0.122871 + 0.992423i \(0.539210\pi\)
\(864\) 0 0
\(865\) −26.0946 −0.887244
\(866\) −3.01639 + 17.0325i −0.102501 + 0.578788i
\(867\) 0 0
\(868\) 12.0767 + 4.41597i 0.409911 + 0.149888i
\(869\) −1.39801 + 0.807143i −0.0474243 + 0.0273804i
\(870\) 0 0
\(871\) −36.9164 21.3137i −1.25086 0.722186i
\(872\) −14.2741 + 24.5962i −0.483380 + 0.832932i
\(873\) 0 0
\(874\) −13.8177 38.0521i −0.467391 1.28713i
\(875\) −8.33966 + 14.4447i −0.281932 + 0.488321i
\(876\) 0 0
\(877\) −4.56875 7.91331i −0.154276 0.267214i 0.778519 0.627621i \(-0.215971\pi\)
−0.932795 + 0.360407i \(0.882638\pi\)
\(878\) −18.3472 + 21.8323i −0.619190 + 0.736805i
\(879\) 0 0
\(880\) −2.88289 + 3.41496i −0.0971822 + 0.115118i
\(881\) 18.1037i 0.609930i 0.952364 + 0.304965i \(0.0986447\pi\)
−0.952364 + 0.304965i \(0.901355\pi\)
\(882\) 0 0
\(883\) 10.5545i 0.355187i −0.984104 0.177593i \(-0.943169\pi\)
0.984104 0.177593i \(-0.0568311\pi\)
\(884\) −28.3378 + 4.95317i −0.953104 + 0.166593i
\(885\) 0 0
\(886\) 30.7540 + 25.8447i 1.03320 + 0.868271i
\(887\) 4.71464 + 8.16599i 0.158302 + 0.274187i 0.934256 0.356602i \(-0.116065\pi\)
−0.775954 + 0.630789i \(0.782731\pi\)
\(888\) 0 0
\(889\) −3.49500 + 6.05351i −0.117218 + 0.203028i
\(890\) −16.9249 + 6.14586i −0.567323 + 0.206010i
\(891\) 0 0
\(892\) −21.5548 25.7660i −0.721709 0.862709i
\(893\) 17.5725 + 10.1455i 0.588042 + 0.339506i
\(894\) 0 0
\(895\) 63.5735 36.7042i 2.12503 1.22689i
\(896\) −11.1314 2.02272i −0.371875 0.0675744i
\(897\) 0 0
\(898\) −12.3741 2.19140i −0.412929 0.0731280i
\(899\) −6.71471 −0.223948
\(900\) 0 0
\(901\) −7.32646 −0.244080
\(902\) −5.06386 0.896788i −0.168608 0.0298598i
\(903\) 0 0
\(904\) −0.0443901 + 19.8476i −0.00147639 + 0.660120i
\(905\) −41.6886 + 24.0689i −1.38578 + 0.800078i
\(906\) 0 0
\(907\) 5.60015 + 3.23325i 0.185950 + 0.107358i 0.590085 0.807341i \(-0.299094\pi\)
−0.404135 + 0.914699i \(0.632428\pi\)
\(908\) 44.1457 36.9306i 1.46503 1.22558i
\(909\) 0 0
\(910\) −20.1037 + 7.30017i −0.666431 + 0.241998i
\(911\) −17.1240 + 29.6597i −0.567345 + 0.982670i 0.429482 + 0.903075i \(0.358696\pi\)
−0.996827 + 0.0795950i \(0.974637\pi\)
\(912\) 0 0
\(913\) −1.19878 2.07634i −0.0396737 0.0687168i
\(914\) 11.7730 + 9.89371i 0.389417 + 0.327255i
\(915\) 0 0
\(916\) 6.40965 + 36.6706i 0.211781 + 1.21163i
\(917\) 11.8964i 0.392853i
\(918\) 0 0
\(919\) 7.16854i 0.236468i −0.992986 0.118234i \(-0.962277\pi\)
0.992986 0.118234i \(-0.0377233\pi\)
\(920\) −44.2088 + 25.3923i −1.45752 + 0.837158i
\(921\) 0 0
\(922\) 32.9097 39.1609i 1.08382 1.28969i
\(923\) 5.44654 + 9.43369i 0.179275 + 0.310514i
\(924\) 0 0
\(925\) −18.1642 + 31.4612i −0.597234 + 1.03444i
\(926\) −4.18562 11.5266i −0.137548 0.378789i
\(927\) 0 0
\(928\) 5.82192 1.00420i 0.191114 0.0329645i
\(929\) −20.4211 11.7901i −0.669993 0.386821i 0.126081 0.992020i \(-0.459760\pi\)
−0.796074 + 0.605199i \(0.793093\pi\)
\(930\) 0 0
\(931\) 5.21841 3.01285i 0.171026 0.0987422i
\(932\) −17.4096 + 47.6115i −0.570270 + 1.55957i
\(933\) 0 0
\(934\) 3.32910 18.7983i 0.108932 0.615100i
\(935\) −4.03178 −0.131853
\(936\) 0 0
\(937\) 28.9176 0.944698 0.472349 0.881411i \(-0.343406\pi\)
0.472349 + 0.881411i \(0.343406\pi\)
\(938\) 2.63736 14.8923i 0.0861129 0.486250i
\(939\) 0 0
\(940\) 8.77554 23.9992i 0.286227 0.782767i
\(941\) 7.14862 4.12726i 0.233038 0.134545i −0.378935 0.925423i \(-0.623709\pi\)
0.611973 + 0.790879i \(0.290376\pi\)
\(942\) 0 0
\(943\) −50.8060 29.3328i −1.65447 0.955208i
\(944\) −5.86648 + 32.7000i −0.190938 + 1.06429i
\(945\) 0 0
\(946\) 0.139921 + 0.385322i 0.00454921 + 0.0125279i
\(947\) 13.0431 22.5914i 0.423845 0.734121i −0.572467 0.819928i \(-0.694013\pi\)
0.996312 + 0.0858067i \(0.0273468\pi\)
\(948\) 0 0
\(949\) −17.2054 29.8006i −0.558510 0.967367i
\(950\) 51.5132 61.2982i 1.67131 1.98878i
\(951\) 0 0
\(952\) −5.08351 8.85055i −0.164757 0.286848i
\(953\) 8.16427i 0.264467i −0.991219 0.132233i \(-0.957785\pi\)
0.991219 0.132233i \(-0.0422148\pi\)
\(954\) 0 0
\(955\) 31.5615i 1.02131i
\(956\) −8.66990 49.6018i −0.280404 1.60424i
\(957\) 0 0
\(958\) 41.4465 + 34.8304i 1.33908 + 1.12532i
\(959\) −0.138806 0.240419i −0.00448228 0.00776354i
\(960\) 0 0
\(961\) 5.16854 8.95217i 0.166727 0.288780i
\(962\) −20.4860 + 7.43900i −0.660495 + 0.239843i
\(963\) 0 0
\(964\) 14.8396 12.4142i 0.477950 0.399835i
\(965\) 35.4589 + 20.4722i 1.14146 + 0.659024i
\(966\) 0 0
\(967\) −47.9368 + 27.6763i −1.54154 + 0.890010i −0.542800 + 0.839862i \(0.682636\pi\)
−0.998742 + 0.0501481i \(0.984031\pi\)
\(968\) 30.8674 + 0.0690365i 0.992115 + 0.00221892i
\(969\) 0 0
\(970\) 71.2310 + 12.6147i 2.28709 + 0.405034i
\(971\) −11.2138 −0.359869 −0.179935 0.983679i \(-0.557589\pi\)
−0.179935 + 0.983679i \(0.557589\pi\)
\(972\) 0 0
\(973\) 10.9903 0.352332
\(974\) 18.5366 + 3.28275i 0.593951 + 0.105186i
\(975\) 0 0
\(976\) −41.2850 + 14.8872i −1.32150 + 0.476529i
\(977\) 20.0276 11.5629i 0.640740 0.369931i −0.144160 0.989554i \(-0.546048\pi\)
0.784899 + 0.619623i \(0.212715\pi\)
\(978\) 0 0
\(979\) −0.855770 0.494079i −0.0273505 0.0157908i
\(980\) −4.86906 5.82033i −0.155537 0.185924i
\(981\) 0 0
\(982\) 3.90106 1.41658i 0.124488 0.0452048i
\(983\) −16.6695 + 28.8724i −0.531673 + 0.920885i 0.467643 + 0.883917i \(0.345103\pi\)
−0.999316 + 0.0369680i \(0.988230\pi\)
\(984\) 0 0
\(985\) 27.3068 + 47.2967i 0.870067 + 1.50700i
\(986\) 4.08028 + 3.42895i 0.129943 + 0.109200i
\(987\) 0 0
\(988\) 47.3193 8.27095i 1.50543 0.263134i
\(989\) 4.67646i 0.148703i
\(990\) 0 0
\(991\) 27.6317i 0.877749i −0.898548 0.438875i \(-0.855377\pi\)
0.898548 0.438875i \(-0.144623\pi\)
\(992\) −12.5666 + 34.1301i −0.398991 + 1.08363i
\(993\) 0 0
\(994\) −2.48647 + 2.95877i −0.0788660 + 0.0938466i
\(995\) −28.4423 49.2635i −0.901682 1.56176i
\(996\) 0 0
\(997\) 10.1065 17.5050i 0.320077 0.554390i −0.660426 0.750891i \(-0.729624\pi\)
0.980504 + 0.196500i \(0.0629577\pi\)
\(998\) 18.0305 + 49.6536i 0.570746 + 1.57176i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 756.2.ba.a.575.16 72
3.2 odd 2 252.2.ba.a.155.21 yes 72
4.3 odd 2 inner 756.2.ba.a.575.27 72
9.4 even 3 252.2.ba.a.239.10 yes 72
9.5 odd 6 inner 756.2.ba.a.71.27 72
12.11 even 2 252.2.ba.a.155.10 72
36.23 even 6 inner 756.2.ba.a.71.16 72
36.31 odd 6 252.2.ba.a.239.21 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.ba.a.155.10 72 12.11 even 2
252.2.ba.a.155.21 yes 72 3.2 odd 2
252.2.ba.a.239.10 yes 72 9.4 even 3
252.2.ba.a.239.21 yes 72 36.31 odd 6
756.2.ba.a.71.16 72 36.23 even 6 inner
756.2.ba.a.71.27 72 9.5 odd 6 inner
756.2.ba.a.575.16 72 1.1 even 1 trivial
756.2.ba.a.575.27 72 4.3 odd 2 inner