Properties

Label 605.2.g.q.251.3
Level $605$
Weight $2$
Character 605.251
Analytic conductor $4.831$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(81,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 251.3
Character \(\chi\) \(=\) 605.251
Dual form 605.2.g.q.511.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.148607 + 0.457364i) q^{2} +(1.29579 - 0.941443i) q^{3} +(1.43094 + 1.03964i) q^{4} +(0.309017 + 0.951057i) q^{5} +(0.238020 + 0.732550i) q^{6} +(-0.389057 - 0.282666i) q^{7} +(-1.46625 + 1.06529i) q^{8} +(-0.134306 + 0.413352i) q^{9} +O(q^{10})\) \(q+(-0.148607 + 0.457364i) q^{2} +(1.29579 - 0.941443i) q^{3} +(1.43094 + 1.03964i) q^{4} +(0.309017 + 0.951057i) q^{5} +(0.238020 + 0.732550i) q^{6} +(-0.389057 - 0.282666i) q^{7} +(-1.46625 + 1.06529i) q^{8} +(-0.134306 + 0.413352i) q^{9} -0.480901 q^{10} +2.83294 q^{12} +(-1.48192 + 4.56088i) q^{13} +(0.187098 - 0.135935i) q^{14} +(1.29579 + 0.941443i) q^{15} +(0.823805 + 2.53541i) q^{16} +(0.773253 + 2.37983i) q^{17} +(-0.169094 - 0.122854i) q^{18} +(4.65783 - 3.38411i) q^{19} +(-0.546569 + 1.68217i) q^{20} -0.770249 q^{21} +4.43462 q^{23} +(-0.897034 + 2.76079i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-1.86576 - 1.35555i) q^{26} +(1.69995 + 5.23192i) q^{27} +(-0.262846 - 0.808955i) q^{28} +(-7.29125 - 5.29740i) q^{29} +(-0.623145 + 0.452741i) q^{30} +(2.46351 - 7.58191i) q^{31} -4.90680 q^{32} -1.20336 q^{34} +(0.148607 - 0.457364i) q^{35} +(-0.621919 + 0.451851i) q^{36} +(-4.20961 - 3.05846i) q^{37} +(0.855586 + 2.63322i) q^{38} +(2.37356 + 7.30506i) q^{39} +(-1.46625 - 1.06529i) q^{40} +(6.83720 - 4.96752i) q^{41} +(0.114464 - 0.352284i) q^{42} +8.53158 q^{43} -0.434624 q^{45} +(-0.659014 + 2.02824i) q^{46} +(-7.76792 + 5.64373i) q^{47} +(3.45442 + 2.50978i) q^{48} +(-2.09165 - 6.43745i) q^{49} +(-0.148607 - 0.457364i) q^{50} +(3.24244 + 2.35577i) q^{51} +(-6.86218 + 4.98567i) q^{52} +(1.88516 - 5.80193i) q^{53} -2.64552 q^{54} +0.871579 q^{56} +(2.84960 - 8.77016i) q^{57} +(3.50637 - 2.54753i) q^{58} +(-2.23995 - 1.62742i) q^{59} +(0.875428 + 2.69429i) q^{60} +(1.24390 + 3.82833i) q^{61} +(3.10160 + 2.25344i) q^{62} +(0.169094 - 0.122854i) q^{63} +(-0.918427 + 2.82663i) q^{64} -4.79559 q^{65} +7.60168 q^{67} +(-1.36768 + 4.20928i) q^{68} +(5.74632 - 4.17495i) q^{69} +(0.187098 + 0.135935i) q^{70} +(-0.855586 - 2.63322i) q^{71} +(-0.243415 - 0.749154i) q^{72} +(4.04881 + 2.94163i) q^{73} +(2.02440 - 1.47081i) q^{74} +(-0.494946 + 1.52329i) q^{75} +10.1833 q^{76} -3.69380 q^{78} +(-1.12012 + 3.44737i) q^{79} +(-2.15675 + 1.56697i) q^{80} +(6.07348 + 4.41264i) q^{81} +(1.25591 + 3.86529i) q^{82} +(-0.529838 - 1.63067i) q^{83} +(-1.10218 - 0.800779i) q^{84} +(-2.02440 + 1.47081i) q^{85} +(-1.26785 + 3.90204i) q^{86} -14.4351 q^{87} -15.7408 q^{89} +(0.0645880 - 0.198781i) q^{90} +(1.86576 - 1.35555i) q^{91} +(6.34566 + 4.61039i) q^{92} +(-3.94576 - 12.1438i) q^{93} +(-1.42687 - 4.39146i) q^{94} +(4.65783 + 3.38411i) q^{95} +(-6.35817 + 4.61948i) q^{96} +(-1.12420 + 3.45993i) q^{97} +3.25509 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.148607 + 0.457364i −0.105081 + 0.323405i −0.989749 0.142815i \(-0.954385\pi\)
0.884669 + 0.466220i \(0.154385\pi\)
\(3\) 1.29579 0.941443i 0.748122 0.543543i −0.147122 0.989118i \(-0.547001\pi\)
0.895244 + 0.445576i \(0.147001\pi\)
\(4\) 1.43094 + 1.03964i 0.715468 + 0.519818i
\(5\) 0.309017 + 0.951057i 0.138197 + 0.425325i
\(6\) 0.238020 + 0.732550i 0.0971713 + 0.299062i
\(7\) −0.389057 0.282666i −0.147050 0.106838i 0.511828 0.859088i \(-0.328969\pi\)
−0.658878 + 0.752250i \(0.728969\pi\)
\(8\) −1.46625 + 1.06529i −0.518399 + 0.376639i
\(9\) −0.134306 + 0.413352i −0.0447687 + 0.137784i
\(10\) −0.480901 −0.152074
\(11\) 0 0
\(12\) 2.83294 0.817801
\(13\) −1.48192 + 4.56088i −0.411010 + 1.26496i 0.504761 + 0.863259i \(0.331581\pi\)
−0.915771 + 0.401700i \(0.868419\pi\)
\(14\) 0.187098 0.135935i 0.0500040 0.0363300i
\(15\) 1.29579 + 0.941443i 0.334570 + 0.243080i
\(16\) 0.823805 + 2.53541i 0.205951 + 0.633853i
\(17\) 0.773253 + 2.37983i 0.187541 + 0.577193i 0.999983 0.00584959i \(-0.00186199\pi\)
−0.812441 + 0.583043i \(0.801862\pi\)
\(18\) −0.169094 0.122854i −0.0398557 0.0289569i
\(19\) 4.65783 3.38411i 1.06858 0.776368i 0.0929225 0.995673i \(-0.470379\pi\)
0.975656 + 0.219305i \(0.0703791\pi\)
\(20\) −0.546569 + 1.68217i −0.122217 + 0.376144i
\(21\) −0.770249 −0.168082
\(22\) 0 0
\(23\) 4.43462 0.924683 0.462342 0.886702i \(-0.347009\pi\)
0.462342 + 0.886702i \(0.347009\pi\)
\(24\) −0.897034 + 2.76079i −0.183106 + 0.563543i
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) −1.86576 1.35555i −0.365905 0.265846i
\(27\) 1.69995 + 5.23192i 0.327156 + 1.00688i
\(28\) −0.262846 0.808955i −0.0496731 0.152878i
\(29\) −7.29125 5.29740i −1.35395 0.983703i −0.998804 0.0488927i \(-0.984431\pi\)
−0.355147 0.934810i \(-0.615569\pi\)
\(30\) −0.623145 + 0.452741i −0.113770 + 0.0826588i
\(31\) 2.46351 7.58191i 0.442460 1.36175i −0.442786 0.896627i \(-0.646010\pi\)
0.885246 0.465124i \(-0.153990\pi\)
\(32\) −4.90680 −0.867409
\(33\) 0 0
\(34\) −1.20336 −0.206374
\(35\) 0.148607 0.457364i 0.0251191 0.0773086i
\(36\) −0.621919 + 0.451851i −0.103653 + 0.0753084i
\(37\) −4.20961 3.05846i −0.692055 0.502807i 0.185280 0.982686i \(-0.440681\pi\)
−0.877335 + 0.479878i \(0.840681\pi\)
\(38\) 0.855586 + 2.63322i 0.138794 + 0.427165i
\(39\) 2.37356 + 7.30506i 0.380073 + 1.16975i
\(40\) −1.46625 1.06529i −0.231835 0.168438i
\(41\) 6.83720 4.96752i 1.06779 0.775796i 0.0922772 0.995733i \(-0.470585\pi\)
0.975514 + 0.219938i \(0.0705854\pi\)
\(42\) 0.114464 0.352284i 0.0176622 0.0543586i
\(43\) 8.53158 1.30105 0.650527 0.759483i \(-0.274548\pi\)
0.650527 + 0.759483i \(0.274548\pi\)
\(44\) 0 0
\(45\) −0.434624 −0.0647899
\(46\) −0.659014 + 2.02824i −0.0971663 + 0.299047i
\(47\) −7.76792 + 5.64373i −1.13307 + 0.823222i −0.986138 0.165925i \(-0.946939\pi\)
−0.146929 + 0.989147i \(0.546939\pi\)
\(48\) 3.45442 + 2.50978i 0.498603 + 0.362256i
\(49\) −2.09165 6.43745i −0.298808 0.919636i
\(50\) −0.148607 0.457364i −0.0210161 0.0646810i
\(51\) 3.24244 + 2.35577i 0.454033 + 0.329874i
\(52\) −6.86218 + 4.98567i −0.951613 + 0.691387i
\(53\) 1.88516 5.80193i 0.258947 0.796957i −0.734079 0.679064i \(-0.762386\pi\)
0.993026 0.117893i \(-0.0376140\pi\)
\(54\) −2.64552 −0.360009
\(55\) 0 0
\(56\) 0.871579 0.116470
\(57\) 2.84960 8.77016i 0.377438 1.16164i
\(58\) 3.50637 2.54753i 0.460409 0.334507i
\(59\) −2.23995 1.62742i −0.291617 0.211872i 0.432352 0.901705i \(-0.357684\pi\)
−0.723969 + 0.689833i \(0.757684\pi\)
\(60\) 0.875428 + 2.69429i 0.113017 + 0.347831i
\(61\) 1.24390 + 3.82833i 0.159265 + 0.490167i 0.998568 0.0534969i \(-0.0170367\pi\)
−0.839303 + 0.543664i \(0.817037\pi\)
\(62\) 3.10160 + 2.25344i 0.393903 + 0.286188i
\(63\) 0.169094 0.122854i 0.0213038 0.0154781i
\(64\) −0.918427 + 2.82663i −0.114803 + 0.353329i
\(65\) −4.79559 −0.594820
\(66\) 0 0
\(67\) 7.60168 0.928693 0.464346 0.885654i \(-0.346289\pi\)
0.464346 + 0.885654i \(0.346289\pi\)
\(68\) −1.36768 + 4.20928i −0.165855 + 0.510451i
\(69\) 5.74632 4.17495i 0.691776 0.502605i
\(70\) 0.187098 + 0.135935i 0.0223625 + 0.0162473i
\(71\) −0.855586 2.63322i −0.101539 0.312506i 0.887363 0.461071i \(-0.152535\pi\)
−0.988903 + 0.148565i \(0.952535\pi\)
\(72\) −0.243415 0.749154i −0.0286867 0.0882886i
\(73\) 4.04881 + 2.94163i 0.473877 + 0.344292i 0.798950 0.601397i \(-0.205389\pi\)
−0.325073 + 0.945689i \(0.605389\pi\)
\(74\) 2.02440 1.47081i 0.235332 0.170979i
\(75\) −0.494946 + 1.52329i −0.0571514 + 0.175894i
\(76\) 10.1833 1.16810
\(77\) 0 0
\(78\) −3.69380 −0.418240
\(79\) −1.12012 + 3.44737i −0.126023 + 0.387859i −0.994086 0.108595i \(-0.965365\pi\)
0.868063 + 0.496454i \(0.165365\pi\)
\(80\) −2.15675 + 1.56697i −0.241132 + 0.175193i
\(81\) 6.07348 + 4.41264i 0.674831 + 0.490293i
\(82\) 1.25591 + 3.86529i 0.138692 + 0.426850i
\(83\) −0.529838 1.63067i −0.0581573 0.178990i 0.917758 0.397141i \(-0.129998\pi\)
−0.975915 + 0.218151i \(0.929998\pi\)
\(84\) −1.10218 0.800779i −0.120257 0.0873721i
\(85\) −2.02440 + 1.47081i −0.219577 + 0.159532i
\(86\) −1.26785 + 3.90204i −0.136716 + 0.420767i
\(87\) −14.4351 −1.54761
\(88\) 0 0
\(89\) −15.7408 −1.66852 −0.834262 0.551368i \(-0.814106\pi\)
−0.834262 + 0.551368i \(0.814106\pi\)
\(90\) 0.0645880 0.198781i 0.00680817 0.0209534i
\(91\) 1.86576 1.35555i 0.195585 0.142100i
\(92\) 6.34566 + 4.61039i 0.661581 + 0.480667i
\(93\) −3.94576 12.1438i −0.409156 1.25925i
\(94\) −1.42687 4.39146i −0.147171 0.452945i
\(95\) 4.65783 + 3.38411i 0.477883 + 0.347202i
\(96\) −6.35817 + 4.61948i −0.648928 + 0.471474i
\(97\) −1.12420 + 3.45993i −0.114145 + 0.351302i −0.991768 0.128050i \(-0.959128\pi\)
0.877623 + 0.479352i \(0.159128\pi\)
\(98\) 3.25509 0.328814
\(99\) 0 0
\(100\) −1.76873 −0.176873
\(101\) 2.37895 7.32166i 0.236715 0.728533i −0.760175 0.649719i \(-0.774887\pi\)
0.996889 0.0788140i \(-0.0251133\pi\)
\(102\) −1.55929 + 1.13289i −0.154393 + 0.112173i
\(103\) −7.36436 5.35052i −0.725632 0.527202i 0.162547 0.986701i \(-0.448029\pi\)
−0.888178 + 0.459499i \(0.848029\pi\)
\(104\) −2.68581 8.26608i −0.263365 0.810555i
\(105\) −0.238020 0.732550i −0.0232284 0.0714896i
\(106\) 2.37345 + 1.72441i 0.230530 + 0.167490i
\(107\) −13.5844 + 9.86966i −1.31326 + 0.954136i −0.313266 + 0.949666i \(0.601423\pi\)
−0.999990 + 0.00447062i \(0.998577\pi\)
\(108\) −3.00677 + 9.25388i −0.289326 + 0.890455i
\(109\) 17.8817 1.71276 0.856380 0.516346i \(-0.172708\pi\)
0.856380 + 0.516346i \(0.172708\pi\)
\(110\) 0 0
\(111\) −8.33411 −0.791039
\(112\) 0.396169 1.21928i 0.0374344 0.115211i
\(113\) 0.374196 0.271869i 0.0352014 0.0255753i −0.570045 0.821613i \(-0.693074\pi\)
0.605247 + 0.796038i \(0.293074\pi\)
\(114\) 3.58769 + 2.60661i 0.336018 + 0.244131i
\(115\) 1.37037 + 4.21758i 0.127788 + 0.393291i
\(116\) −4.92594 15.1605i −0.457362 1.40762i
\(117\) −1.68622 1.22511i −0.155891 0.113261i
\(118\) 1.07720 0.782628i 0.0991639 0.0720468i
\(119\) 0.371858 1.14446i 0.0340882 0.104913i
\(120\) −2.90286 −0.264994
\(121\) 0 0
\(122\) −1.93579 −0.175258
\(123\) 4.18291 12.8737i 0.377160 1.16078i
\(124\) 11.4076 8.28807i 1.02443 0.744291i
\(125\) −0.809017 0.587785i −0.0723607 0.0525731i
\(126\) 0.0310604 + 0.0955941i 0.00276708 + 0.00851620i
\(127\) −4.89157 15.0547i −0.434057 1.33589i −0.894050 0.447968i \(-0.852148\pi\)
0.459993 0.887923i \(-0.347852\pi\)
\(128\) −9.09569 6.60841i −0.803953 0.584106i
\(129\) 11.0551 8.03200i 0.973347 0.707178i
\(130\) 0.712656 2.19333i 0.0625041 0.192368i
\(131\) −9.60460 −0.839158 −0.419579 0.907719i \(-0.637822\pi\)
−0.419579 + 0.907719i \(0.637822\pi\)
\(132\) 0 0
\(133\) −2.76873 −0.240080
\(134\) −1.12966 + 3.47673i −0.0975877 + 0.300344i
\(135\) −4.45054 + 3.23350i −0.383041 + 0.278296i
\(136\) −3.66900 2.66569i −0.314614 0.228581i
\(137\) 1.22744 + 3.77768i 0.104868 + 0.322749i 0.989699 0.143161i \(-0.0457268\pi\)
−0.884832 + 0.465911i \(0.845727\pi\)
\(138\) 1.05553 + 3.24859i 0.0898526 + 0.276538i
\(139\) 7.46034 + 5.42026i 0.632778 + 0.459740i 0.857362 0.514715i \(-0.172102\pi\)
−0.224583 + 0.974455i \(0.572102\pi\)
\(140\) 0.688138 0.499962i 0.0581583 0.0422545i
\(141\) −4.75231 + 14.6261i −0.400217 + 1.23174i
\(142\) 1.33149 0.111736
\(143\) 0 0
\(144\) −1.15866 −0.0965550
\(145\) 2.78501 8.57138i 0.231282 0.711814i
\(146\) −1.94707 + 1.41463i −0.161141 + 0.117076i
\(147\) −8.77083 6.37238i −0.723406 0.525585i
\(148\) −2.84399 8.75291i −0.233775 0.719485i
\(149\) −2.36402 7.27569i −0.193668 0.596048i −0.999990 0.00457087i \(-0.998545\pi\)
0.806322 0.591477i \(-0.201455\pi\)
\(150\) −0.623145 0.452741i −0.0508795 0.0369661i
\(151\) −2.32348 + 1.68811i −0.189082 + 0.137376i −0.678299 0.734786i \(-0.737283\pi\)
0.489217 + 0.872162i \(0.337283\pi\)
\(152\) −3.22448 + 9.92392i −0.261540 + 0.804936i
\(153\) −1.08756 −0.0879240
\(154\) 0 0
\(155\) 7.97209 0.640334
\(156\) −4.19819 + 12.9207i −0.336124 + 1.03448i
\(157\) −14.1430 + 10.2755i −1.12873 + 0.820071i −0.985510 0.169620i \(-0.945746\pi\)
−0.143221 + 0.989691i \(0.545746\pi\)
\(158\) −1.41024 1.02460i −0.112193 0.0815130i
\(159\) −3.01943 9.29284i −0.239456 0.736970i
\(160\) −1.51629 4.66665i −0.119873 0.368931i
\(161\) −1.72532 1.25352i −0.135974 0.0987912i
\(162\) −2.92074 + 2.12204i −0.229475 + 0.166723i
\(163\) 4.06884 12.5226i 0.318696 0.980847i −0.655510 0.755187i \(-0.727546\pi\)
0.974206 0.225660i \(-0.0724538\pi\)
\(164\) 14.9480 1.16724
\(165\) 0 0
\(166\) 0.824549 0.0639974
\(167\) 4.90651 15.1007i 0.379677 1.16853i −0.560591 0.828093i \(-0.689426\pi\)
0.940268 0.340434i \(-0.110574\pi\)
\(168\) 1.12938 0.820542i 0.0871335 0.0633062i
\(169\) −8.08828 5.87648i −0.622176 0.452037i
\(170\) −0.371858 1.14446i −0.0285202 0.0877762i
\(171\) 0.773253 + 2.37983i 0.0591321 + 0.181990i
\(172\) 12.2081 + 8.86974i 0.930862 + 0.676311i
\(173\) 18.4622 13.4136i 1.40366 1.01982i 0.409449 0.912333i \(-0.365721\pi\)
0.994207 0.107483i \(-0.0342791\pi\)
\(174\) 2.14515 6.60210i 0.162623 0.500504i
\(175\) 0.480901 0.0363527
\(176\) 0 0
\(177\) −4.43462 −0.333327
\(178\) 2.33919 7.19929i 0.175330 0.539609i
\(179\) 0.374196 0.271869i 0.0279687 0.0203205i −0.573713 0.819056i \(-0.694498\pi\)
0.601682 + 0.798736i \(0.294498\pi\)
\(180\) −0.621919 0.451851i −0.0463551 0.0336790i
\(181\) −0.966735 2.97531i −0.0718569 0.221153i 0.908678 0.417498i \(-0.137093\pi\)
−0.980535 + 0.196345i \(0.937093\pi\)
\(182\) 0.342717 + 1.05477i 0.0254039 + 0.0781851i
\(183\) 5.21598 + 3.78963i 0.385576 + 0.280137i
\(184\) −6.50228 + 4.72418i −0.479354 + 0.348271i
\(185\) 1.60793 4.94869i 0.118217 0.363835i
\(186\) 6.14050 0.450243
\(187\) 0 0
\(188\) −16.9828 −1.23860
\(189\) 0.817509 2.51603i 0.0594650 0.183015i
\(190\) −2.23995 + 1.62742i −0.162503 + 0.118066i
\(191\) 4.39859 + 3.19576i 0.318271 + 0.231237i 0.735437 0.677593i \(-0.236977\pi\)
−0.417167 + 0.908830i \(0.636977\pi\)
\(192\) 1.47103 + 4.52735i 0.106162 + 0.326733i
\(193\) 0.990941 + 3.04980i 0.0713295 + 0.219530i 0.980366 0.197187i \(-0.0631807\pi\)
−0.909036 + 0.416717i \(0.863181\pi\)
\(194\) −1.41538 1.02834i −0.101619 0.0738302i
\(195\) −6.21405 + 4.51478i −0.444998 + 0.323310i
\(196\) 3.69958 11.3861i 0.264256 0.813295i
\(197\) −19.4048 −1.38253 −0.691267 0.722600i \(-0.742947\pi\)
−0.691267 + 0.722600i \(0.742947\pi\)
\(198\) 0 0
\(199\) 20.3509 1.44264 0.721319 0.692603i \(-0.243536\pi\)
0.721319 + 0.692603i \(0.243536\pi\)
\(200\) 0.560059 1.72368i 0.0396021 0.121883i
\(201\) 9.85015 7.15655i 0.694776 0.504784i
\(202\) 2.99514 + 2.17609i 0.210737 + 0.153109i
\(203\) 1.33931 + 4.12198i 0.0940014 + 0.289307i
\(204\) 2.19058 + 6.74192i 0.153372 + 0.472029i
\(205\) 6.83720 + 4.96752i 0.477531 + 0.346946i
\(206\) 3.54153 2.57307i 0.246750 0.179274i
\(207\) −0.595597 + 1.83306i −0.0413969 + 0.127407i
\(208\) −12.7845 −0.886446
\(209\) 0 0
\(210\) 0.370413 0.0255610
\(211\) 2.12600 6.54314i 0.146360 0.450448i −0.850824 0.525451i \(-0.823897\pi\)
0.997183 + 0.0750027i \(0.0238966\pi\)
\(212\) 8.72945 6.34231i 0.599541 0.435592i
\(213\) −3.58769 2.60661i −0.245824 0.178602i
\(214\) −2.49529 7.67972i −0.170575 0.524975i
\(215\) 2.63640 + 8.11401i 0.179801 + 0.553371i
\(216\) −8.06610 5.86036i −0.548828 0.398747i
\(217\) −3.10160 + 2.25344i −0.210550 + 0.152974i
\(218\) −2.65734 + 8.17847i −0.179978 + 0.553916i
\(219\) 8.01576 0.541655
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 1.23850 3.81172i 0.0831229 0.255826i
\(223\) 0.840273 0.610494i 0.0562688 0.0408817i −0.559295 0.828968i \(-0.688928\pi\)
0.615564 + 0.788087i \(0.288928\pi\)
\(224\) 1.90903 + 1.38699i 0.127552 + 0.0926721i
\(225\) −0.134306 0.413352i −0.00895375 0.0275568i
\(226\) 0.0687352 + 0.211545i 0.00457220 + 0.0140718i
\(227\) −0.389057 0.282666i −0.0258226 0.0187612i 0.574799 0.818295i \(-0.305080\pi\)
−0.600622 + 0.799533i \(0.705080\pi\)
\(228\) 13.1954 9.58699i 0.873884 0.634914i
\(229\) 4.18403 12.8771i 0.276488 0.850944i −0.712333 0.701841i \(-0.752362\pi\)
0.988822 0.149102i \(-0.0476384\pi\)
\(230\) −2.13261 −0.140620
\(231\) 0 0
\(232\) 16.3341 1.07239
\(233\) −6.53704 + 20.1189i −0.428256 + 1.31803i 0.471587 + 0.881820i \(0.343681\pi\)
−0.899842 + 0.436215i \(0.856319\pi\)
\(234\) 0.810903 0.589155i 0.0530104 0.0385143i
\(235\) −7.76792 5.64373i −0.506723 0.368156i
\(236\) −1.51330 4.65747i −0.0985077 0.303176i
\(237\) 1.79407 + 5.52157i 0.116537 + 0.358665i
\(238\) 0.468175 + 0.340149i 0.0303473 + 0.0220486i
\(239\) −2.16525 + 1.57315i −0.140058 + 0.101758i −0.655608 0.755101i \(-0.727588\pi\)
0.515550 + 0.856860i \(0.327588\pi\)
\(240\) −1.31947 + 4.06092i −0.0851715 + 0.262131i
\(241\) −4.56912 −0.294323 −0.147161 0.989112i \(-0.547014\pi\)
−0.147161 + 0.989112i \(0.547014\pi\)
\(242\) 0 0
\(243\) −4.47932 −0.287349
\(244\) −2.20013 + 6.77129i −0.140849 + 0.433487i
\(245\) 5.47602 3.97856i 0.349850 0.254181i
\(246\) 5.26635 + 3.82622i 0.335770 + 0.243951i
\(247\) 8.53198 + 26.2587i 0.542877 + 1.67080i
\(248\) 4.46484 + 13.7414i 0.283518 + 0.872577i
\(249\) −2.22174 1.61419i −0.140797 0.102295i
\(250\) 0.389057 0.282666i 0.0246061 0.0178774i
\(251\) −3.53421 + 10.8772i −0.223078 + 0.686562i 0.775403 + 0.631466i \(0.217547\pi\)
−0.998481 + 0.0550961i \(0.982453\pi\)
\(252\) 0.369685 0.0232880
\(253\) 0 0
\(254\) 7.61241 0.477645
\(255\) −1.23850 + 3.81172i −0.0775581 + 0.238699i
\(256\) −0.434821 + 0.315916i −0.0271763 + 0.0197448i
\(257\) 16.2165 + 11.7820i 1.01156 + 0.734940i 0.964535 0.263954i \(-0.0850268\pi\)
0.0470224 + 0.998894i \(0.485027\pi\)
\(258\) 2.03069 + 6.24981i 0.126425 + 0.389096i
\(259\) 0.773253 + 2.37983i 0.0480476 + 0.147875i
\(260\) −6.86218 4.98567i −0.425574 0.309198i
\(261\) 3.16895 2.30238i 0.196153 0.142514i
\(262\) 1.42731 4.39280i 0.0881793 0.271388i
\(263\) −6.55852 −0.404416 −0.202208 0.979343i \(-0.564812\pi\)
−0.202208 + 0.979343i \(0.564812\pi\)
\(264\) 0 0
\(265\) 6.10051 0.374752
\(266\) 0.411452 1.26632i 0.0252277 0.0776430i
\(267\) −20.3967 + 14.8191i −1.24826 + 0.906914i
\(268\) 10.8775 + 7.90298i 0.664450 + 0.482751i
\(269\) 0.586253 + 1.80430i 0.0357445 + 0.110010i 0.967337 0.253495i \(-0.0815800\pi\)
−0.931592 + 0.363505i \(0.881580\pi\)
\(270\) −0.817509 2.51603i −0.0497520 0.153121i
\(271\) −9.18567 6.67378i −0.557989 0.405403i 0.272733 0.962090i \(-0.412072\pi\)
−0.830723 + 0.556687i \(0.812072\pi\)
\(272\) −5.39684 + 3.92103i −0.327231 + 0.237747i
\(273\) 1.14145 3.51301i 0.0690835 0.212617i
\(274\) −1.91018 −0.115398
\(275\) 0 0
\(276\) 12.5630 0.756206
\(277\) −7.05609 + 21.7164i −0.423959 + 1.30481i 0.480028 + 0.877253i \(0.340626\pi\)
−0.903987 + 0.427559i \(0.859374\pi\)
\(278\) −3.58769 + 2.60661i −0.215175 + 0.156334i
\(279\) 2.80313 + 2.03660i 0.167819 + 0.121928i
\(280\) 0.269333 + 0.828921i 0.0160957 + 0.0495375i
\(281\) 6.98735 + 21.5049i 0.416830 + 1.28287i 0.910603 + 0.413281i \(0.135617\pi\)
−0.493773 + 0.869591i \(0.664383\pi\)
\(282\) −5.98323 4.34707i −0.356296 0.258864i
\(283\) −22.3019 + 16.2033i −1.32571 + 0.963186i −0.325869 + 0.945415i \(0.605657\pi\)
−0.999842 + 0.0177706i \(0.994343\pi\)
\(284\) 1.51330 4.65747i 0.0897981 0.276370i
\(285\) 9.22149 0.546234
\(286\) 0 0
\(287\) −4.06421 −0.239903
\(288\) 0.659014 2.02824i 0.0388328 0.119515i
\(289\) 8.68763 6.31193i 0.511037 0.371290i
\(290\) 3.50637 + 2.54753i 0.205901 + 0.149596i
\(291\) 1.80061 + 5.54169i 0.105553 + 0.324860i
\(292\) 2.73536 + 8.41857i 0.160075 + 0.492659i
\(293\) −17.6841 12.8482i −1.03312 0.750603i −0.0641861 0.997938i \(-0.520445\pi\)
−0.968930 + 0.247335i \(0.920445\pi\)
\(294\) 4.21790 3.06448i 0.245993 0.178724i
\(295\) 0.855586 2.63322i 0.0498141 0.153312i
\(296\) 9.43050 0.548137
\(297\) 0 0
\(298\) 3.67895 0.213116
\(299\) −6.57175 + 20.2258i −0.380054 + 1.16969i
\(300\) −2.29190 + 1.66516i −0.132323 + 0.0961382i
\(301\) −3.31927 2.41159i −0.191320 0.139002i
\(302\) −0.426796 1.31354i −0.0245593 0.0755859i
\(303\) −3.81032 11.7270i −0.218897 0.673696i
\(304\) 12.4173 + 9.02166i 0.712178 + 0.517428i
\(305\) −3.25657 + 2.36604i −0.186471 + 0.135479i
\(306\) 0.161618 0.497410i 0.00923911 0.0284351i
\(307\) 9.80019 0.559326 0.279663 0.960098i \(-0.409777\pi\)
0.279663 + 0.960098i \(0.409777\pi\)
\(308\) 0 0
\(309\) −14.5798 −0.829418
\(310\) −1.18471 + 3.64615i −0.0672867 + 0.207087i
\(311\) −7.90496 + 5.74329i −0.448249 + 0.325672i −0.788904 0.614516i \(-0.789351\pi\)
0.340655 + 0.940188i \(0.389351\pi\)
\(312\) −11.2623 8.18252i −0.637601 0.463244i
\(313\) −0.277236 0.853245i −0.0156703 0.0482283i 0.942916 0.333032i \(-0.108072\pi\)
−0.958586 + 0.284804i \(0.908072\pi\)
\(314\) −2.59789 7.99548i −0.146607 0.451211i
\(315\) 0.169094 + 0.122854i 0.00952734 + 0.00692202i
\(316\) −5.18682 + 3.76845i −0.291782 + 0.211992i
\(317\) −0.824526 + 2.53763i −0.0463100 + 0.142527i −0.971538 0.236885i \(-0.923874\pi\)
0.925228 + 0.379412i \(0.123874\pi\)
\(318\) 4.69891 0.263502
\(319\) 0 0
\(320\) −2.97209 −0.166145
\(321\) −8.31077 + 25.5779i −0.463862 + 1.42762i
\(322\) 0.829709 0.602819i 0.0462379 0.0335938i
\(323\) 11.6553 + 8.46806i 0.648517 + 0.471175i
\(324\) 4.10322 + 12.6284i 0.227957 + 0.701578i
\(325\) −1.48192 4.56088i −0.0822020 0.252992i
\(326\) 5.12274 + 3.72188i 0.283722 + 0.206136i
\(327\) 23.1709 16.8347i 1.28135 0.930958i
\(328\) −4.73319 + 14.5673i −0.261347 + 0.804343i
\(329\) 4.61746 0.254569
\(330\) 0 0
\(331\) 18.9744 1.04293 0.521464 0.853273i \(-0.325386\pi\)
0.521464 + 0.853273i \(0.325386\pi\)
\(332\) 0.937143 2.88423i 0.0514324 0.158293i
\(333\) 1.82960 1.32928i 0.100261 0.0728440i
\(334\) 6.17737 + 4.48812i 0.338011 + 0.245579i
\(335\) 2.34905 + 7.22963i 0.128342 + 0.394997i
\(336\) −0.634535 1.95290i −0.0346167 0.106539i
\(337\) −3.87971 2.81878i −0.211341 0.153549i 0.477079 0.878860i \(-0.341696\pi\)
−0.688420 + 0.725312i \(0.741696\pi\)
\(338\) 3.88966 2.82601i 0.211570 0.153714i
\(339\) 0.228928 0.704568i 0.0124337 0.0382669i
\(340\) −4.42590 −0.240028
\(341\) 0 0
\(342\) −1.20336 −0.0650702
\(343\) −2.04612 + 6.29732i −0.110480 + 0.340023i
\(344\) −12.5095 + 9.08865i −0.674464 + 0.490027i
\(345\) 5.74632 + 4.17495i 0.309372 + 0.224772i
\(346\) 3.39128 + 10.4373i 0.182317 + 0.561113i
\(347\) 0.0798714 + 0.245819i 0.00428772 + 0.0131962i 0.953177 0.302411i \(-0.0977917\pi\)
−0.948890 + 0.315608i \(0.897792\pi\)
\(348\) −20.6557 15.0073i −1.10726 0.804473i
\(349\) 1.08805 0.790517i 0.0582421 0.0423154i −0.558283 0.829650i \(-0.688540\pi\)
0.616525 + 0.787335i \(0.288540\pi\)
\(350\) −0.0714650 + 0.219947i −0.00381997 + 0.0117566i
\(351\) −26.3813 −1.40813
\(352\) 0 0
\(353\) 35.4537 1.88701 0.943506 0.331355i \(-0.107506\pi\)
0.943506 + 0.331355i \(0.107506\pi\)
\(354\) 0.659014 2.02824i 0.0350262 0.107800i
\(355\) 2.23995 1.62742i 0.118884 0.0863745i
\(356\) −22.5241 16.3647i −1.19378 0.867329i
\(357\) −0.595597 1.83306i −0.0315224 0.0970158i
\(358\) 0.0687352 + 0.211545i 0.00363277 + 0.0111805i
\(359\) −6.34404 4.60922i −0.334826 0.243265i 0.407650 0.913138i \(-0.366348\pi\)
−0.742476 + 0.669873i \(0.766348\pi\)
\(360\) 0.637268 0.463003i 0.0335870 0.0244024i
\(361\) 4.37183 13.4551i 0.230096 0.708164i
\(362\) 1.50446 0.0790727
\(363\) 0 0
\(364\) 4.07906 0.213801
\(365\) −1.54651 + 4.75966i −0.0809478 + 0.249132i
\(366\) −2.50837 + 1.82244i −0.131115 + 0.0952603i
\(367\) −0.862850 0.626897i −0.0450404 0.0327238i 0.565037 0.825065i \(-0.308862\pi\)
−0.610078 + 0.792342i \(0.708862\pi\)
\(368\) 3.65327 + 11.2436i 0.190440 + 0.586113i
\(369\) 1.13505 + 3.49334i 0.0590886 + 0.181856i
\(370\) 2.02440 + 1.47081i 0.105244 + 0.0764640i
\(371\) −2.37345 + 1.72441i −0.123223 + 0.0895269i
\(372\) 6.97899 21.4791i 0.361844 1.11364i
\(373\) 37.6388 1.94886 0.974431 0.224689i \(-0.0721366\pi\)
0.974431 + 0.224689i \(0.0721366\pi\)
\(374\) 0 0
\(375\) −1.60168 −0.0827104
\(376\) 5.37750 16.5503i 0.277324 0.853514i
\(377\) 34.9658 25.4042i 1.80083 1.30838i
\(378\) 1.02926 + 0.747799i 0.0529392 + 0.0384626i
\(379\) 10.8612 + 33.4273i 0.557902 + 1.71705i 0.688154 + 0.725564i \(0.258421\pi\)
−0.130253 + 0.991481i \(0.541579\pi\)
\(380\) 3.14681 + 9.68489i 0.161428 + 0.496824i
\(381\) −20.5116 14.9025i −1.05084 0.763481i
\(382\) −2.11529 + 1.53684i −0.108227 + 0.0786318i
\(383\) 0.254800 0.784193i 0.0130197 0.0400704i −0.944336 0.328984i \(-0.893294\pi\)
0.957355 + 0.288913i \(0.0932939\pi\)
\(384\) −18.0075 −0.918942
\(385\) 0 0
\(386\) −1.54213 −0.0784924
\(387\) −1.14584 + 3.52655i −0.0582465 + 0.179264i
\(388\) −5.20572 + 3.78218i −0.264280 + 0.192011i
\(389\) −3.91861 2.84704i −0.198682 0.144351i 0.483996 0.875070i \(-0.339185\pi\)
−0.682678 + 0.730719i \(0.739185\pi\)
\(390\) −1.14145 3.51301i −0.0577994 0.177888i
\(391\) 3.42909 + 10.5536i 0.173416 + 0.533721i
\(392\) 9.92467 + 7.21070i 0.501272 + 0.364195i
\(393\) −12.4455 + 9.04218i −0.627792 + 0.456118i
\(394\) 2.88368 8.87505i 0.145278 0.447119i
\(395\) −3.62478 −0.182382
\(396\) 0 0
\(397\) −7.33178 −0.367971 −0.183986 0.982929i \(-0.558900\pi\)
−0.183986 + 0.982929i \(0.558900\pi\)
\(398\) −3.02428 + 9.30777i −0.151593 + 0.466556i
\(399\) −3.58769 + 2.60661i −0.179609 + 0.130494i
\(400\) −2.15675 1.56697i −0.107838 0.0783485i
\(401\) −9.62584 29.6253i −0.480692 1.47942i −0.838125 0.545478i \(-0.816348\pi\)
0.357434 0.933939i \(-0.383652\pi\)
\(402\) 1.80935 + 5.56861i 0.0902423 + 0.277737i
\(403\) 30.9294 + 22.4715i 1.54070 + 1.11939i
\(404\) 11.0160 8.00359i 0.548066 0.398193i
\(405\) −2.31986 + 7.13980i −0.115275 + 0.354780i
\(406\) −2.08428 −0.103441
\(407\) 0 0
\(408\) −7.26384 −0.359613
\(409\) 2.23484 6.87813i 0.110506 0.340102i −0.880477 0.474088i \(-0.842778\pi\)
0.990983 + 0.133986i \(0.0427779\pi\)
\(410\) −3.28802 + 2.38888i −0.162384 + 0.117979i
\(411\) 5.14698 + 3.73950i 0.253882 + 0.184456i
\(412\) −4.97533 15.3125i −0.245117 0.754393i
\(413\) 0.411452 + 1.26632i 0.0202462 + 0.0623115i
\(414\) −0.749866 0.544810i −0.0368539 0.0267759i
\(415\) 1.38713 1.00781i 0.0680918 0.0494716i
\(416\) 7.27148 22.3793i 0.356514 1.09724i
\(417\) 14.7699 0.723284
\(418\) 0 0
\(419\) −2.30620 −0.112665 −0.0563327 0.998412i \(-0.517941\pi\)
−0.0563327 + 0.998412i \(0.517941\pi\)
\(420\) 0.420994 1.29569i 0.0205424 0.0632230i
\(421\) −5.37024 + 3.90171i −0.261730 + 0.190158i −0.710909 0.703284i \(-0.751716\pi\)
0.449180 + 0.893441i \(0.351716\pi\)
\(422\) 2.67666 + 1.94471i 0.130298 + 0.0946669i
\(423\) −1.28956 3.96887i −0.0627008 0.192973i
\(424\) 3.41665 + 10.5154i 0.165927 + 0.510671i
\(425\) −2.02440 1.47081i −0.0981980 0.0713450i
\(426\) 1.72532 1.25352i 0.0835921 0.0607332i
\(427\) 0.598192 1.84105i 0.0289485 0.0890944i
\(428\) −29.6993 −1.43557
\(429\) 0 0
\(430\) −4.10284 −0.197857
\(431\) 10.1491 31.2357i 0.488865 1.50457i −0.337439 0.941347i \(-0.609561\pi\)
0.826304 0.563224i \(-0.190439\pi\)
\(432\) −11.8646 + 8.62016i −0.570838 + 0.414738i
\(433\) −1.91091 1.38836i −0.0918326 0.0667203i 0.540922 0.841073i \(-0.318076\pi\)
−0.632754 + 0.774353i \(0.718076\pi\)
\(434\) −0.569726 1.75344i −0.0273477 0.0841676i
\(435\) −4.46069 13.7286i −0.213874 0.658236i
\(436\) 25.5876 + 18.5905i 1.22543 + 0.890324i
\(437\) 20.6557 15.0073i 0.988097 0.717894i
\(438\) −1.19119 + 3.66612i −0.0569175 + 0.175174i
\(439\) −30.8847 −1.47404 −0.737022 0.675869i \(-0.763769\pi\)
−0.737022 + 0.675869i \(0.763769\pi\)
\(440\) 0 0
\(441\) 2.94185 0.140088
\(442\) 1.78328 5.48837i 0.0848219 0.261055i
\(443\) 11.1440 8.09662i 0.529470 0.384682i −0.290690 0.956817i \(-0.593885\pi\)
0.820159 + 0.572135i \(0.193885\pi\)
\(444\) −11.9256 8.66444i −0.565963 0.411196i
\(445\) −4.86418 14.9704i −0.230584 0.709666i
\(446\) 0.154348 + 0.475034i 0.00730858 + 0.0224935i
\(447\) −9.91291 7.20215i −0.468865 0.340650i
\(448\) 1.15631 0.840111i 0.0546307 0.0396915i
\(449\) −12.0258 + 37.0116i −0.567532 + 1.74668i 0.0927733 + 0.995687i \(0.470427\pi\)
−0.660305 + 0.750997i \(0.729573\pi\)
\(450\) 0.209011 0.00985288
\(451\) 0 0
\(452\) 0.818095 0.0384800
\(453\) −1.42148 + 4.37486i −0.0667868 + 0.205549i
\(454\) 0.187098 0.135935i 0.00878094 0.00637973i
\(455\) 1.86576 + 1.35555i 0.0874681 + 0.0635493i
\(456\) 5.16458 + 15.8949i 0.241853 + 0.744348i
\(457\) 0.411452 + 1.26632i 0.0192469 + 0.0592359i 0.960219 0.279249i \(-0.0900855\pi\)
−0.940972 + 0.338485i \(0.890086\pi\)
\(458\) 5.26775 + 3.82725i 0.246146 + 0.178836i
\(459\) −11.1366 + 8.09120i −0.519811 + 0.377665i
\(460\) −2.42383 + 7.45977i −0.113012 + 0.347814i
\(461\) 5.73993 0.267335 0.133668 0.991026i \(-0.457325\pi\)
0.133668 + 0.991026i \(0.457325\pi\)
\(462\) 0 0
\(463\) −3.44535 −0.160119 −0.0800595 0.996790i \(-0.525511\pi\)
−0.0800595 + 0.996790i \(0.525511\pi\)
\(464\) 7.42453 22.8503i 0.344675 1.06080i
\(465\) 10.3301 7.50527i 0.479048 0.348049i
\(466\) −8.23023 5.97961i −0.381258 0.277000i
\(467\) −8.41034 25.8843i −0.389184 1.19778i −0.933399 0.358839i \(-0.883173\pi\)
0.544215 0.838946i \(-0.316827\pi\)
\(468\) −1.13920 3.50610i −0.0526596 0.162070i
\(469\) −2.95749 2.14874i −0.136564 0.0992196i
\(470\) 3.73560 2.71407i 0.172310 0.125191i
\(471\) −8.65248 + 26.6296i −0.398685 + 1.22703i
\(472\) 5.01802 0.230973
\(473\) 0 0
\(474\) −2.79198 −0.128240
\(475\) −1.77913 + 5.47560i −0.0816321 + 0.251238i
\(476\) 1.72193 1.25105i 0.0789245 0.0573420i
\(477\) 2.14505 + 1.55847i 0.0982152 + 0.0713575i
\(478\) −0.397730 1.22409i −0.0181917 0.0559884i
\(479\) 4.32073 + 13.2978i 0.197419 + 0.607593i 0.999940 + 0.0109692i \(0.00349166\pi\)
−0.802521 + 0.596624i \(0.796508\pi\)
\(480\) −6.35817 4.61948i −0.290209 0.210849i
\(481\) 20.1875 14.6671i 0.920472 0.668762i
\(482\) 0.679001 2.08975i 0.0309277 0.0951855i
\(483\) −3.41576 −0.155423
\(484\) 0 0
\(485\) −3.63798 −0.165192
\(486\) 0.665657 2.04868i 0.0301948 0.0929300i
\(487\) 6.03021 4.38120i 0.273255 0.198531i −0.442715 0.896662i \(-0.645985\pi\)
0.715970 + 0.698131i \(0.245985\pi\)
\(488\) −5.90216 4.28817i −0.267178 0.194116i
\(489\) −6.51698 20.0572i −0.294708 0.907018i
\(490\) 1.00588 + 3.09578i 0.0454409 + 0.139853i
\(491\) 12.9245 + 9.39022i 0.583276 + 0.423775i 0.839904 0.542736i \(-0.182611\pi\)
−0.256628 + 0.966510i \(0.582611\pi\)
\(492\) 19.3694 14.0727i 0.873240 0.634446i
\(493\) 6.96893 21.4482i 0.313865 0.965976i
\(494\) −13.2777 −0.597392
\(495\) 0 0
\(496\) 21.2527 0.954275
\(497\) −0.411452 + 1.26632i −0.0184561 + 0.0568022i
\(498\) 1.06844 0.776266i 0.0478779 0.0347853i
\(499\) 19.7003 + 14.3131i 0.881906 + 0.640742i 0.933755 0.357913i \(-0.116511\pi\)
−0.0518489 + 0.998655i \(0.516511\pi\)
\(500\) −0.546569 1.68217i −0.0244433 0.0752288i
\(501\) −7.85866 24.1865i −0.351099 1.08057i
\(502\) −4.44963 3.23284i −0.198597 0.144289i
\(503\) −22.3019 + 16.2033i −0.994393 + 0.722469i −0.960879 0.276969i \(-0.910670\pi\)
−0.0335144 + 0.999438i \(0.510670\pi\)
\(504\) −0.117058 + 0.360269i −0.00521420 + 0.0160477i
\(505\) 7.69845 0.342577
\(506\) 0 0
\(507\) −16.0131 −0.711165
\(508\) 8.65190 26.6278i 0.383866 1.18142i
\(509\) −14.3075 + 10.3950i −0.634168 + 0.460750i −0.857842 0.513914i \(-0.828195\pi\)
0.223674 + 0.974664i \(0.428195\pi\)
\(510\) −1.55929 1.13289i −0.0690467 0.0501654i
\(511\) −0.743716 2.28892i −0.0329001 0.101256i
\(512\) −7.02836 21.6311i −0.310613 0.955967i
\(513\) 25.6235 + 18.6165i 1.13130 + 0.821941i
\(514\) −7.79853 + 5.66596i −0.343978 + 0.249915i
\(515\) 2.81293 8.65732i 0.123953 0.381487i
\(516\) 24.1695 1.06400
\(517\) 0 0
\(518\) −1.20336 −0.0528725
\(519\) 11.2949 34.7623i 0.495793 1.52589i
\(520\) 7.03154 5.10872i 0.308354 0.224032i
\(521\) 4.36054 + 3.16812i 0.191039 + 0.138798i 0.679193 0.733959i \(-0.262330\pi\)
−0.488155 + 0.872757i \(0.662330\pi\)
\(522\) 0.582098 + 1.79151i 0.0254777 + 0.0784124i
\(523\) −11.6418 35.8298i −0.509061 1.56673i −0.793835 0.608133i \(-0.791919\pi\)
0.284775 0.958595i \(-0.408081\pi\)
\(524\) −13.7436 9.98528i −0.600390 0.436209i
\(525\) 0.623145 0.452741i 0.0271963 0.0197592i
\(526\) 0.974639 2.99963i 0.0424963 0.130790i
\(527\) 19.9486 0.868973
\(528\) 0 0
\(529\) −3.33411 −0.144961
\(530\) −0.906576 + 2.79016i −0.0393792 + 0.121197i
\(531\) 0.973537 0.707316i 0.0422479 0.0306949i
\(532\) −3.96188 2.87848i −0.171769 0.124798i
\(533\) 12.5241 + 38.5451i 0.542477 + 1.66957i
\(534\) −3.74663 11.5309i −0.162133 0.498993i
\(535\) −13.5844 9.86966i −0.587306 0.426703i
\(536\) −11.1460 + 8.09803i −0.481433 + 0.349782i
\(537\) 0.228928 0.704568i 0.00987898 0.0304044i
\(538\) −0.912344 −0.0393339
\(539\) 0 0
\(540\) −9.73010 −0.418717
\(541\) −8.95070 + 27.5474i −0.384821 + 1.18436i 0.551789 + 0.833983i \(0.313945\pi\)
−0.936610 + 0.350373i \(0.886055\pi\)
\(542\) 4.41739 3.20943i 0.189743 0.137857i
\(543\) −4.05376 2.94523i −0.173964 0.126392i
\(544\) −3.79420 11.6774i −0.162675 0.500662i
\(545\) 5.52576 + 17.0066i 0.236698 + 0.728481i
\(546\) 1.43710 + 1.04411i 0.0615021 + 0.0446839i
\(547\) −15.9696 + 11.6026i −0.682812 + 0.496092i −0.874289 0.485405i \(-0.838672\pi\)
0.191477 + 0.981497i \(0.438672\pi\)
\(548\) −2.17102 + 6.68172i −0.0927415 + 0.285429i
\(549\) −1.74951 −0.0746672
\(550\) 0 0
\(551\) −51.8884 −2.21052
\(552\) −3.97801 + 12.2431i −0.169315 + 0.521099i
\(553\) 1.41024 1.02460i 0.0599697 0.0435705i
\(554\) −8.88372 6.45440i −0.377433 0.274221i
\(555\) −2.57538 7.92621i −0.109319 0.336449i
\(556\) 5.04018 + 15.5121i 0.213751 + 0.657859i
\(557\) 13.4944 + 9.80429i 0.571778 + 0.415421i 0.835751 0.549109i \(-0.185033\pi\)
−0.263973 + 0.964530i \(0.585033\pi\)
\(558\) −1.34803 + 0.979400i −0.0570666 + 0.0414613i
\(559\) −12.6431 + 38.9115i −0.534746 + 1.64578i
\(560\) 1.28203 0.0541756
\(561\) 0 0
\(562\) −10.8739 −0.458688
\(563\) 1.51629 4.66665i 0.0639038 0.196676i −0.914007 0.405699i \(-0.867028\pi\)
0.977911 + 0.209023i \(0.0670283\pi\)
\(564\) −22.0061 + 15.9884i −0.926624 + 0.673232i
\(565\) 0.374196 + 0.271869i 0.0157425 + 0.0114376i
\(566\) −4.09659 12.6080i −0.172193 0.529954i
\(567\) −1.11562 3.43354i −0.0468518 0.144195i
\(568\) 4.05966 + 2.94952i 0.170340 + 0.123759i
\(569\) −18.1490 + 13.1860i −0.760846 + 0.552787i −0.899170 0.437600i \(-0.855829\pi\)
0.138324 + 0.990387i \(0.455829\pi\)
\(570\) −1.37037 + 4.21758i −0.0573987 + 0.176655i
\(571\) −0.195590 −0.00818520 −0.00409260 0.999992i \(-0.501303\pi\)
−0.00409260 + 0.999992i \(0.501303\pi\)
\(572\) 0 0
\(573\) 8.70826 0.363793
\(574\) 0.603968 1.85882i 0.0252092 0.0775858i
\(575\) −3.58769 + 2.60661i −0.149617 + 0.108703i
\(576\) −1.04504 0.759267i −0.0435434 0.0316361i
\(577\) −12.7464 39.2292i −0.530638 1.63313i −0.752891 0.658145i \(-0.771341\pi\)
0.222253 0.974989i \(-0.428659\pi\)
\(578\) 1.59581 + 4.91140i 0.0663770 + 0.204287i
\(579\) 4.15527 + 3.01898i 0.172687 + 0.125464i
\(580\) 12.8963 9.36970i 0.535489 0.389056i
\(581\) −0.254800 + 0.784193i −0.0105709 + 0.0325338i
\(582\) −2.80215 −0.116153
\(583\) 0 0
\(584\) −9.07028 −0.375331
\(585\) 0.644077 1.98227i 0.0266293 0.0819566i
\(586\) 8.50430 6.17874i 0.351309 0.255241i
\(587\) 1.43584 + 1.04320i 0.0592636 + 0.0430575i 0.617023 0.786945i \(-0.288339\pi\)
−0.557759 + 0.830003i \(0.688339\pi\)
\(588\) −5.92554 18.2369i −0.244365 0.752079i
\(589\) −14.1834 43.6520i −0.584417 1.79865i
\(590\) 1.07720 + 0.782628i 0.0443474 + 0.0322203i
\(591\) −25.1444 + 18.2685i −1.03430 + 0.751466i
\(592\) 4.28655 13.1927i 0.176176 0.542215i
\(593\) 29.0094 1.19127 0.595636 0.803254i \(-0.296900\pi\)
0.595636 + 0.803254i \(0.296900\pi\)
\(594\) 0 0
\(595\) 1.20336 0.0493329
\(596\) 4.18132 12.8688i 0.171273 0.527125i
\(597\) 26.3704 19.1592i 1.07927 0.784135i
\(598\) −8.27393 6.01136i −0.338346 0.245823i
\(599\) 12.4432 + 38.2964i 0.508417 + 1.56475i 0.794949 + 0.606676i \(0.207498\pi\)
−0.286532 + 0.958071i \(0.592502\pi\)
\(600\) −0.897034 2.76079i −0.0366213 0.112709i
\(601\) −11.0801 8.05015i −0.451966 0.328372i 0.338406 0.941000i \(-0.390112\pi\)
−0.790371 + 0.612628i \(0.790112\pi\)
\(602\) 1.59624 1.15974i 0.0650579 0.0472673i
\(603\) −1.02095 + 3.14217i −0.0415764 + 0.127959i
\(604\) −5.07978 −0.206693
\(605\) 0 0
\(606\) 5.92972 0.240879
\(607\) −6.53704 + 20.1189i −0.265330 + 0.816602i 0.726287 + 0.687392i \(0.241244\pi\)
−0.991617 + 0.129211i \(0.958756\pi\)
\(608\) −22.8550 + 16.6052i −0.926894 + 0.673428i
\(609\) 5.61608 + 4.08032i 0.227575 + 0.165343i
\(610\) −0.598192 1.84105i −0.0242201 0.0745417i
\(611\) −14.2289 43.7921i −0.575640 1.77164i
\(612\) −1.55623 1.13067i −0.0629068 0.0457045i
\(613\) −18.8113 + 13.6672i −0.759780 + 0.552012i −0.898843 0.438271i \(-0.855591\pi\)
0.139063 + 0.990284i \(0.455591\pi\)
\(614\) −1.45637 + 4.48225i −0.0587744 + 0.180889i
\(615\) 13.5362 0.545831
\(616\) 0 0
\(617\) −13.1028 −0.527501 −0.263750 0.964591i \(-0.584960\pi\)
−0.263750 + 0.964591i \(0.584960\pi\)
\(618\) 2.16666 6.66829i 0.0871558 0.268238i
\(619\) −13.4849 + 9.79733i −0.542003 + 0.393788i −0.824828 0.565383i \(-0.808728\pi\)
0.282825 + 0.959171i \(0.408728\pi\)
\(620\) 11.4076 + 8.28807i 0.458138 + 0.332857i
\(621\) 7.53866 + 23.2016i 0.302516 + 0.931048i
\(622\) −1.45204 4.46893i −0.0582217 0.179188i
\(623\) 6.12408 + 4.44940i 0.245356 + 0.178262i
\(624\) −16.5660 + 12.0359i −0.663170 + 0.481821i
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 0.431443 0.0172439
\(627\) 0 0
\(628\) −30.9204 −1.23386
\(629\) 4.02351 12.3831i 0.160428 0.493747i
\(630\) −0.0813172 + 0.0590804i −0.00323976 + 0.00235382i
\(631\) 2.15486 + 1.56560i 0.0857838 + 0.0623256i 0.629850 0.776716i \(-0.283116\pi\)
−0.544067 + 0.839042i \(0.683116\pi\)
\(632\) −2.03009 6.24796i −0.0807525 0.248531i
\(633\) −3.40516 10.4800i −0.135343 0.416543i
\(634\) −1.03809 0.754217i −0.0412278 0.0299538i
\(635\) 12.8063 9.30433i 0.508203 0.369231i
\(636\) 5.34056 16.4366i 0.211767 0.651752i
\(637\) 32.4601 1.28611
\(638\) 0 0
\(639\) 1.20336 0.0476041
\(640\) 3.47424 10.6926i 0.137332 0.422663i
\(641\) 0.374196 0.271869i 0.0147798 0.0107382i −0.580371 0.814352i \(-0.697092\pi\)
0.595151 + 0.803614i \(0.297092\pi\)
\(642\) −10.4634 7.60210i −0.412957 0.300031i
\(643\) −10.3404 31.8244i −0.407784 1.25503i −0.918548 0.395310i \(-0.870637\pi\)
0.510763 0.859721i \(-0.329363\pi\)
\(644\) −1.16562 3.58741i −0.0459319 0.141364i
\(645\) 11.0551 + 8.03200i 0.435294 + 0.316260i
\(646\) −5.60503 + 4.07230i −0.220527 + 0.160222i
\(647\) −12.4406 + 38.2884i −0.489092 + 1.50527i 0.336873 + 0.941550i \(0.390631\pi\)
−0.825965 + 0.563721i \(0.809369\pi\)
\(648\) −13.6060 −0.534495
\(649\) 0 0
\(650\) 2.30620 0.0904567
\(651\) −1.89752 + 5.83996i −0.0743696 + 0.228886i
\(652\) 18.8412 13.6889i 0.737879 0.536100i
\(653\) −12.4173 9.02166i −0.485925 0.353045i 0.317690 0.948195i \(-0.397093\pi\)
−0.803615 + 0.595150i \(0.797093\pi\)
\(654\) 4.25621 + 13.0993i 0.166431 + 0.512222i
\(655\) −2.96798 9.13452i −0.115969 0.356915i
\(656\) 18.2272 + 13.2428i 0.711653 + 0.517046i
\(657\) −1.75971 + 1.27850i −0.0686528 + 0.0498791i
\(658\) −0.686184 + 2.11186i −0.0267502 + 0.0823288i
\(659\) −36.6635 −1.42821 −0.714104 0.700039i \(-0.753166\pi\)
−0.714104 + 0.700039i \(0.753166\pi\)
\(660\) 0 0
\(661\) −8.03024 −0.312340 −0.156170 0.987730i \(-0.549915\pi\)
−0.156170 + 0.987730i \(0.549915\pi\)
\(662\) −2.81972 + 8.67822i −0.109592 + 0.337288i
\(663\) −15.5494 + 11.2973i −0.603890 + 0.438752i
\(664\) 2.51403 + 1.82655i 0.0975631 + 0.0708838i
\(665\) −0.855586 2.63322i −0.0331782 0.102112i
\(666\) 0.336074 + 1.03433i 0.0130226 + 0.0400795i
\(667\) −32.3340 23.4920i −1.25198 0.909614i
\(668\) 22.7201 16.5071i 0.879068 0.638680i
\(669\) 0.514068 1.58214i 0.0198750 0.0611690i
\(670\) −3.65565 −0.141230
\(671\) 0 0
\(672\) 3.77946 0.145796
\(673\) 3.63364 11.1832i 0.140067 0.431081i −0.856277 0.516517i \(-0.827228\pi\)
0.996344 + 0.0854362i \(0.0272284\pi\)
\(674\) 1.86576 1.35555i 0.0718663 0.0522139i
\(675\) −4.45054 3.23350i −0.171301 0.124458i
\(676\) −5.46442 16.8177i −0.210170 0.646836i
\(677\) 8.43455 + 25.9589i 0.324166 + 0.997681i 0.971816 + 0.235743i \(0.0757522\pi\)
−0.647649 + 0.761939i \(0.724248\pi\)
\(678\) 0.288224 + 0.209407i 0.0110692 + 0.00804222i
\(679\) 1.41538 1.02834i 0.0543174 0.0394639i
\(680\) 1.40143 4.31317i 0.0537426 0.165403i
\(681\) −0.770249 −0.0295160
\(682\) 0 0
\(683\) 49.5738 1.89689 0.948444 0.316945i \(-0.102657\pi\)
0.948444 + 0.316945i \(0.102657\pi\)
\(684\) −1.36768 + 4.20928i −0.0522945 + 0.160946i
\(685\) −3.21349 + 2.33474i −0.122781 + 0.0892057i
\(686\) −2.57610 1.87165i −0.0983560 0.0714598i
\(687\) −6.70147 20.6250i −0.255677 0.786893i
\(688\) 7.02836 + 21.6311i 0.267954 + 0.824677i
\(689\) 23.6682 + 17.1960i 0.901688 + 0.655115i
\(690\) −2.76341 + 2.00774i −0.105201 + 0.0764332i
\(691\) −7.82596 + 24.0858i −0.297713 + 0.916268i 0.684583 + 0.728935i \(0.259984\pi\)
−0.982297 + 0.187333i \(0.940016\pi\)
\(692\) 40.3635 1.53439
\(693\) 0 0
\(694\) −0.124298 −0.00471829
\(695\) −2.84960 + 8.77016i −0.108091 + 0.332671i
\(696\) 21.1655 15.3776i 0.802276 0.582888i
\(697\) 17.1087 + 12.4302i 0.648039 + 0.470828i
\(698\) 0.199862 + 0.615112i 0.00756489 + 0.0232823i
\(699\) 10.4702 + 32.2241i 0.396021 + 1.21883i
\(700\) 0.688138 + 0.499962i 0.0260092 + 0.0188968i
\(701\) −14.7690 + 10.7303i −0.557817 + 0.405278i −0.830659 0.556781i \(-0.812036\pi\)
0.272842 + 0.962059i \(0.412036\pi\)
\(702\) 3.92044 12.0659i 0.147967 0.455397i
\(703\) −29.9578 −1.12988
\(704\) 0 0
\(705\) −15.3788 −0.579199
\(706\) −5.26866 + 16.2153i −0.198289 + 0.610270i
\(707\) −2.99514 + 2.17609i −0.112644 + 0.0818404i
\(708\) −6.34566 4.61039i −0.238485 0.173269i
\(709\) 1.33859 + 4.11977i 0.0502719 + 0.154721i 0.973041 0.230632i \(-0.0740795\pi\)
−0.922769 + 0.385354i \(0.874079\pi\)
\(710\) 0.411452 + 1.26632i 0.0154415 + 0.0475241i
\(711\) −1.27454 0.926005i −0.0477989 0.0347279i
\(712\) 23.0800 16.7686i 0.864961 0.628431i
\(713\) 10.9247 33.6229i 0.409135 1.25919i
\(714\) 0.926885 0.0346878
\(715\) 0 0
\(716\) 0.818095 0.0305737
\(717\) −1.32467 + 4.07692i −0.0494707 + 0.152255i
\(718\) 3.05086 2.21658i 0.113857 0.0827219i
\(719\) 19.4977 + 14.1659i 0.727142 + 0.528300i 0.888658 0.458570i \(-0.151638\pi\)
−0.161516 + 0.986870i \(0.551638\pi\)
\(720\) −0.358045 1.10195i −0.0133436 0.0410673i
\(721\) 1.35274 + 4.16331i 0.0503788 + 0.155050i
\(722\) 5.50420 + 3.99904i 0.204845 + 0.148829i
\(723\) −5.92060 + 4.30157i −0.220189 + 0.159977i
\(724\) 1.70990 5.26252i 0.0635479 0.195580i
\(725\) 9.01248 0.334715
\(726\) 0 0
\(727\) −25.1066 −0.931151 −0.465576 0.885008i \(-0.654153\pi\)
−0.465576 + 0.885008i \(0.654153\pi\)
\(728\) −1.29161 + 3.97516i −0.0478702 + 0.147329i
\(729\) −24.0247 + 17.4549i −0.889803 + 0.646479i
\(730\) −1.94707 1.41463i −0.0720645 0.0523579i
\(731\) 6.59707 + 20.3037i 0.244001 + 0.750959i
\(732\) 3.52390 + 10.8454i 0.130247 + 0.400859i
\(733\) −14.1143 10.2547i −0.521325 0.378764i 0.295778 0.955257i \(-0.404421\pi\)
−0.817103 + 0.576492i \(0.804421\pi\)
\(734\) 0.414945 0.301476i 0.0153159 0.0111277i
\(735\) 3.35016 10.3107i 0.123572 0.380317i
\(736\) −21.7598 −0.802078
\(737\) 0 0
\(738\) −1.76640 −0.0650222
\(739\) 1.60695 4.94567i 0.0591125 0.181930i −0.917140 0.398565i \(-0.869508\pi\)
0.976253 + 0.216635i \(0.0695083\pi\)
\(740\) 7.44567 5.40960i 0.273708 0.198861i
\(741\) 35.7767 + 25.9933i 1.31429 + 0.954889i
\(742\) −0.435973 1.34179i −0.0160051 0.0492586i
\(743\) 11.4932 + 35.3724i 0.421645 + 1.29769i 0.906171 + 0.422912i \(0.138992\pi\)
−0.484526 + 0.874777i \(0.661008\pi\)
\(744\) 18.7222 + 13.6025i 0.686389 + 0.498691i
\(745\) 6.18907 4.49662i 0.226750 0.164744i
\(746\) −5.59337 + 17.2146i −0.204788 + 0.630272i
\(747\) 0.745203 0.0272656
\(748\) 0 0
\(749\) 8.07494 0.295052
\(750\) 0.238020 0.732550i 0.00869126 0.0267490i
\(751\) −33.5104 + 24.3468i −1.22281 + 0.888426i −0.996330 0.0855894i \(-0.972723\pi\)
−0.226483 + 0.974015i \(0.572723\pi\)
\(752\) −20.7084 15.0455i −0.755158 0.548655i
\(753\) 5.66068 + 17.4218i 0.206286 + 0.634885i
\(754\) 6.42280 + 19.7673i 0.233904 + 0.719884i
\(755\) −2.32348 1.68811i −0.0845603 0.0614366i
\(756\) 3.78556 2.75037i 0.137680 0.100030i
\(757\) 1.21020 3.72460i 0.0439853 0.135373i −0.926652 0.375920i \(-0.877327\pi\)
0.970638 + 0.240547i \(0.0773268\pi\)
\(758\) −16.9025 −0.613926
\(759\) 0 0
\(760\) −10.4346 −0.378504
\(761\) 12.0921 37.2157i 0.438339 1.34907i −0.451287 0.892379i \(-0.649035\pi\)
0.889626 0.456690i \(-0.150965\pi\)
\(762\) 9.86405 7.16665i 0.357337 0.259620i
\(763\) −6.95702 5.05457i −0.251861 0.182988i
\(764\) 2.97167 + 9.14586i 0.107511 + 0.330886i
\(765\) −0.336074 1.03433i −0.0121508 0.0373963i
\(766\) 0.320797 + 0.233072i 0.0115909 + 0.00842125i
\(767\) 10.7419 7.80444i 0.387867 0.281802i
\(768\) −0.266018 + 0.818719i −0.00959910 + 0.0295430i
\(769\) −11.6755 −0.421028 −0.210514 0.977591i \(-0.567514\pi\)
−0.210514 + 0.977591i \(0.567514\pi\)
\(770\) 0 0
\(771\) 32.1052 1.15624
\(772\) −1.75271 + 5.39429i −0.0630815 + 0.194145i
\(773\) 6.28315 4.56498i 0.225989 0.164191i −0.469029 0.883183i \(-0.655396\pi\)
0.695019 + 0.718992i \(0.255396\pi\)
\(774\) −1.44263 1.04814i −0.0518544 0.0376745i
\(775\) 2.46351 + 7.58191i 0.0884920 + 0.272350i
\(776\) −2.03748 6.27073i −0.0731414 0.225106i
\(777\) 3.24244 + 2.35577i 0.116322 + 0.0845129i
\(778\) 1.88446 1.36914i 0.0675613 0.0490862i
\(779\) 15.0359 46.2757i 0.538716 1.65800i
\(780\) −13.5856 −0.486444
\(781\) 0 0
\(782\) −5.33644 −0.190831
\(783\) 15.3208 47.1526i 0.547521 1.68510i
\(784\) 14.5985 10.6064i 0.521374 0.378800i
\(785\) −14.1430 10.2755i −0.504784 0.366747i
\(786\) −2.28609 7.03585i −0.0815420 0.250960i
\(787\) 0.441672 + 1.35933i 0.0157439 + 0.0484548i 0.958620 0.284689i \(-0.0918904\pi\)
−0.942876 + 0.333144i \(0.891890\pi\)
\(788\) −27.7670 20.1739i −0.989159 0.718666i
\(789\) −8.49843 + 6.17447i −0.302552 + 0.219817i
\(790\) 0.538665 1.65784i 0.0191649 0.0589834i
\(791\) −0.222432 −0.00790876
\(792\) 0 0
\(793\) −19.3039 −0.685501
\(794\) 1.08955 3.35329i 0.0386667 0.119004i
\(795\) 7.90496 5.74329i 0.280360 0.203693i
\(796\) 29.1208 + 21.1575i 1.03216 + 0.749909i
\(797\) −11.2417 34.5983i −0.398200 1.22553i −0.926441 0.376440i \(-0.877148\pi\)
0.528241 0.849095i \(-0.322852\pi\)
\(798\) −0.659014 2.02824i −0.0233288 0.0717988i
\(799\) −19.4377 14.1223i −0.687655 0.499611i
\(800\) 3.96969 2.88415i 0.140350 0.101970i
\(801\) 2.11409 6.50650i 0.0746977 0.229896i
\(802\) 14.9800 0.528962
\(803\) 0 0
\(804\) 21.5351 0.759486
\(805\) 0.659014 2.02824i 0.0232272 0.0714860i
\(806\) −14.8740 + 10.8066i −0.523914 + 0.380646i
\(807\) 2.45831 + 1.78606i 0.0865365 + 0.0628724i
\(808\) 4.31158 + 13.2697i 0.151681 + 0.466826i
\(809\) −8.61338 26.5093i −0.302830 0.932016i −0.980478 0.196629i \(-0.937000\pi\)
0.677648 0.735387i \(-0.263000\pi\)
\(810\) −2.92074 2.12204i −0.102624 0.0745610i
\(811\) 31.6967 23.0290i 1.11302 0.808657i 0.129884 0.991529i \(-0.458539\pi\)
0.983137 + 0.182872i \(0.0585394\pi\)
\(812\) −2.36889 + 7.29069i −0.0831317 + 0.255853i
\(813\) −18.1856 −0.637798
\(814\) 0 0
\(815\) 13.1671 0.461222
\(816\) −3.30171 + 10.1616i −0.115583 + 0.355728i
\(817\) 39.7386 28.8718i 1.39028 1.01010i
\(818\) 2.81370 + 2.04427i 0.0983786 + 0.0714762i
\(819\) 0.309737 + 0.953273i 0.0108231 + 0.0333101i
\(820\) 4.61919 + 14.2164i 0.161309 + 0.496458i
\(821\) −11.1460 8.09803i −0.388997 0.282623i 0.376047 0.926601i \(-0.377283\pi\)
−0.765045 + 0.643977i \(0.777283\pi\)
\(822\) −2.47519 + 1.79833i −0.0863321 + 0.0627239i
\(823\) −6.14325 + 18.9070i −0.214140 + 0.659056i 0.785073 + 0.619403i \(0.212625\pi\)
−0.999214 + 0.0396530i \(0.987375\pi\)
\(824\) 16.4979 0.574731
\(825\) 0 0
\(826\) −0.640313 −0.0222793
\(827\) −4.11832 + 12.6749i −0.143208 + 0.440749i −0.996776 0.0802321i \(-0.974434\pi\)
0.853568 + 0.520981i \(0.174434\pi\)
\(828\) −2.75798 + 2.00379i −0.0958463 + 0.0696364i
\(829\) −41.4135 30.0887i −1.43835 1.04502i −0.988384 0.151978i \(-0.951436\pi\)
−0.449967 0.893045i \(-0.648564\pi\)
\(830\) 0.254800 + 0.784193i 0.00884423 + 0.0272197i
\(831\) 11.3016 + 34.7827i 0.392048 + 1.20660i
\(832\) −11.5309 8.37766i −0.399761 0.290443i
\(833\) 13.7026 9.95556i 0.474769 0.344940i
\(834\) −2.19490 + 6.75521i −0.0760032 + 0.233914i
\(835\) 15.8778 0.549474
\(836\) 0 0
\(837\) 43.8558 1.51588
\(838\) 0.342717 1.05477i 0.0118390 0.0364366i
\(839\) 13.6513 9.91824i 0.471295 0.342416i −0.326651 0.945145i \(-0.605920\pi\)
0.797946 + 0.602729i \(0.205920\pi\)
\(840\) 1.12938 + 0.820542i 0.0389673 + 0.0283114i
\(841\) 16.1384 + 49.6687i 0.556495 + 1.71272i
\(842\) −0.986448 3.03597i −0.0339952 0.104627i
\(843\) 29.2997 + 21.2875i 1.00914 + 0.733180i
\(844\) 9.84465 7.15256i 0.338867 0.246201i
\(845\) 3.08945 9.50835i 0.106280 0.327097i
\(846\) 2.00686 0.0689972
\(847\) 0 0
\(848\) 16.2633 0.558484
\(849\) −13.6440 + 41.9920i −0.468262 + 1.44116i
\(850\) 0.973537 0.707316i 0.0333921 0.0242607i
\(851\) −18.6680 13.5631i −0.639931 0.464937i
\(852\) −2.42383 7.45977i −0.0830390 0.255568i
\(853\) −1.67568 5.15722i −0.0573743 0.176580i 0.918262 0.395972i \(-0.129592\pi\)
−0.975637 + 0.219393i \(0.929592\pi\)
\(854\) 0.753132 + 0.547183i 0.0257717 + 0.0187242i
\(855\) −2.02440 + 1.47081i −0.0692331 + 0.0503008i
\(856\) 9.40410 28.9428i 0.321425 0.989246i
\(857\) −27.8386 −0.950947 −0.475474 0.879730i \(-0.657723\pi\)
−0.475474 + 0.879730i \(0.657723\pi\)
\(858\) 0 0
\(859\) 48.1899 1.64422 0.822109 0.569330i \(-0.192797\pi\)
0.822109 + 0.569330i \(0.192797\pi\)
\(860\) −4.66310 + 14.3515i −0.159010 + 0.489383i
\(861\) −5.26635 + 3.82622i −0.179477 + 0.130397i
\(862\) 12.7779 + 9.28366i 0.435216 + 0.316203i
\(863\) 8.30046 + 25.5462i 0.282551 + 0.869602i 0.987122 + 0.159969i \(0.0511394\pi\)
−0.704571 + 0.709633i \(0.748861\pi\)
\(864\) −8.34134 25.6720i −0.283778 0.873379i
\(865\) 18.4622 + 13.4136i 0.627734 + 0.456076i
\(866\) 0.918960 0.667663i 0.0312275 0.0226881i
\(867\) 5.31498 16.3578i 0.180506 0.555541i
\(868\) −6.78095 −0.230160
\(869\) 0 0
\(870\) 6.94185 0.235351
\(871\) −11.2651 + 34.6703i −0.381702 + 1.17476i
\(872\) −26.2192 + 19.0493i −0.887893 + 0.645092i
\(873\) −1.27918 0.929379i −0.0432937 0.0314547i
\(874\) 3.79420 + 11.6774i 0.128341 + 0.394992i
\(875\) 0.148607 + 0.457364i 0.00502382 + 0.0154617i
\(876\) 11.4700 + 8.33347i 0.387537 + 0.281562i
\(877\) 32.2666 23.4431i 1.08957 0.791616i 0.110240 0.993905i \(-0.464838\pi\)
0.979326 + 0.202289i \(0.0648381\pi\)
\(878\) 4.58966 14.1255i 0.154894 0.476713i
\(879\) −35.0107 −1.18088
\(880\) 0 0
\(881\) −2.82222 −0.0950829 −0.0475415 0.998869i \(-0.515139\pi\)
−0.0475415 + 0.998869i \(0.515139\pi\)
\(882\) −0.437179 + 1.34550i −0.0147206 + 0.0453053i
\(883\) −40.8786 + 29.7000i −1.37567 + 0.999485i −0.378403 + 0.925641i \(0.623527\pi\)
−0.997270 + 0.0738443i \(0.976473\pi\)
\(884\) −17.1712 12.4756i −0.577531 0.419601i
\(885\) −1.37037 4.21758i −0.0460646 0.141772i
\(886\) 2.04703 + 6.30010i 0.0687712 + 0.211656i
\(887\) −22.9109 16.6458i −0.769274 0.558910i 0.132467 0.991187i \(-0.457710\pi\)
−0.901741 + 0.432277i \(0.857710\pi\)
\(888\) 12.2199 8.87828i 0.410073 0.297936i
\(889\) −2.35236 + 7.23983i −0.0788957 + 0.242816i
\(890\) 7.56978 0.253740
\(891\) 0 0
\(892\) 1.83707 0.0615096
\(893\) −17.0826 + 52.5750i −0.571649 + 1.75935i
\(894\) 4.76713 3.46352i 0.159437 0.115837i
\(895\) 0.374196 + 0.271869i 0.0125080 + 0.00908758i
\(896\) 1.67077 + 5.14209i 0.0558164 + 0.171785i
\(897\) 10.5258 + 32.3952i 0.351447 + 1.08164i
\(898\) −15.1407 11.0003i −0.505250 0.367086i
\(899\) −58.1265 + 42.2314i −1.93863 + 1.40850i
\(900\) 0.237552 0.731110i 0.00791840 0.0243703i
\(901\) 15.2653 0.508561
\(902\) 0 0
\(903\) −6.57144 −0.218684
\(904\) −0.259045 + 0.797258i −0.00861570 + 0.0265164i
\(905\) 2.53095 1.83884i 0.0841315 0.0611251i
\(906\) −1.78966 1.30027i −0.0594575 0.0431984i
\(907\) 15.7756 + 48.5522i 0.523819 + 1.61215i 0.766640 + 0.642077i \(0.221927\pi\)
−0.242821 + 0.970071i \(0.578073\pi\)
\(908\) −0.262846 0.808955i −0.00872283 0.0268461i
\(909\) 2.70692 + 1.96669i 0.0897827 + 0.0652310i
\(910\) −0.897244 + 0.651886i −0.0297434 + 0.0216098i
\(911\) −7.76958 + 23.9123i −0.257418 + 0.792250i 0.735926 + 0.677062i \(0.236747\pi\)
−0.993344 + 0.115188i \(0.963253\pi\)
\(912\) 24.5835 0.814040
\(913\) 0 0
\(914\) −0.640313 −0.0211797
\(915\) −1.99233 + 6.13175i −0.0658643 + 0.202709i
\(916\) 19.3746 14.0765i 0.640154 0.465099i
\(917\) 3.73674 + 2.71490i 0.123398 + 0.0896538i
\(918\) −2.04565 6.29587i −0.0675166 0.207795i
\(919\) 7.91551 + 24.3614i 0.261108 + 0.803609i 0.992564 + 0.121720i \(0.0388411\pi\)
−0.731456 + 0.681889i \(0.761159\pi\)
\(920\) −6.50228 4.72418i −0.214374 0.155752i
\(921\) 12.6989 9.22632i 0.418444 0.304018i
\(922\) −0.852992 + 2.62524i −0.0280918 + 0.0864576i
\(923\) 13.2777 0.437041
\(924\) 0 0
\(925\) 5.20336 0.171085
\(926\) 0.512002 1.57578i 0.0168254 0.0517833i
\(927\) 3.20073 2.32546i 0.105126 0.0763782i
\(928\) 35.7767 + 25.9933i 1.17443 + 0.853273i
\(929\) −2.65994 8.18645i −0.0872698 0.268589i 0.897892 0.440215i \(-0.145098\pi\)
−0.985162 + 0.171626i \(0.945098\pi\)
\(930\) 1.89752 + 5.83996i 0.0622221 + 0.191500i
\(931\) −31.5276 22.9061i −1.03328 0.750718i
\(932\) −30.2704 + 21.9928i −0.991541 + 0.720397i
\(933\) −4.83615 + 14.8841i −0.158328 + 0.487285i
\(934\) 13.0884 0.428266
\(935\) 0 0
\(936\) 3.77752 0.123472
\(937\) −1.84372 + 5.67438i −0.0602317 + 0.185374i −0.976645 0.214859i \(-0.931071\pi\)
0.916413 + 0.400233i \(0.131071\pi\)
\(938\) 1.42226 1.03333i 0.0464384 0.0337395i
\(939\) −1.16252 0.844621i −0.0379374 0.0275632i
\(940\) −5.24798 16.1516i −0.171170 0.526808i
\(941\) −7.05733 21.7202i −0.230062 0.708059i −0.997738 0.0672209i \(-0.978587\pi\)
0.767676 0.640839i \(-0.221413\pi\)
\(942\) −10.8936 7.91466i −0.354933 0.257874i
\(943\) 30.3204 22.0291i 0.987368 0.717365i
\(944\) 2.28090 7.01988i 0.0742369 0.228478i
\(945\) 2.64552 0.0860586
\(946\) 0 0
\(947\) −2.30620 −0.0749415 −0.0374708 0.999298i \(-0.511930\pi\)
−0.0374708 + 0.999298i \(0.511930\pi\)
\(948\) −3.17323 + 9.76620i −0.103062 + 0.317191i
\(949\) −19.4164 + 14.1068i −0.630283 + 0.457928i
\(950\) −2.23995 1.62742i −0.0726737 0.0528005i
\(951\) 1.32063 + 4.06447i 0.0428242 + 0.131799i
\(952\) 0.673951 + 2.07421i 0.0218429 + 0.0672255i
\(953\) −23.1483 16.8182i −0.749847 0.544795i 0.145933 0.989295i \(-0.453382\pi\)
−0.895779 + 0.444499i \(0.853382\pi\)
\(954\) −1.03156 + 0.749470i −0.0333979 + 0.0242650i
\(955\) −1.68011 + 5.17085i −0.0543671 + 0.167325i
\(956\) −4.73383 −0.153103
\(957\) 0 0
\(958\) −6.72404 −0.217244
\(959\) 0.590279 1.81669i 0.0190611 0.0586640i
\(960\) −3.85119 + 2.79806i −0.124297 + 0.0903069i
\(961\) −26.3369 19.1349i −0.849579 0.617255i
\(962\) 3.70820 + 11.4127i 0.119557 + 0.367960i
\(963\) −2.25517 6.94070i −0.0726719 0.223661i
\(964\) −6.53812 4.75022i −0.210579 0.152994i
\(965\) −2.59432 + 1.88488i −0.0835141 + 0.0606765i
\(966\) 0.507605 1.56225i 0.0163319 0.0502645i
\(967\) −31.7422 −1.02076 −0.510380 0.859949i \(-0.670495\pi\)
−0.510380 + 0.859949i \(0.670495\pi\)
\(968\) 0 0
\(969\) 23.0749 0.741274
\(970\) 0.540628 1.66388i 0.0173585 0.0534240i
\(971\) 29.9355 21.7494i 0.960676 0.697972i 0.00736865 0.999973i \(-0.497654\pi\)
0.953308 + 0.302001i \(0.0976545\pi\)
\(972\) −6.40962 4.65686i −0.205589 0.149369i
\(973\) −1.37037 4.21758i −0.0439322 0.135209i
\(974\) 1.10768 + 3.40907i 0.0354922 + 0.109234i
\(975\) −6.21405 4.51478i −0.199009 0.144589i
\(976\) −8.68165 + 6.30759i −0.277893 + 0.201901i
\(977\) 10.4669 32.2138i 0.334866 1.03061i −0.631923 0.775031i \(-0.717734\pi\)
0.966788 0.255579i \(-0.0822660\pi\)
\(978\) 10.1419 0.324303
\(979\) 0 0
\(980\) 11.9721 0.382434
\(981\) −2.40163 + 7.39145i −0.0766781 + 0.235991i
\(982\) −6.21542 + 4.51577i −0.198342 + 0.144104i
\(983\) 30.5416 + 22.1898i 0.974127 + 0.707745i 0.956388 0.292098i \(-0.0943533\pi\)
0.0177388 + 0.999843i \(0.494353\pi\)
\(984\) 7.58105 + 23.3321i 0.241675 + 0.743800i
\(985\) −5.99641 18.4550i −0.191061 0.588027i
\(986\) 8.77399 + 6.37467i 0.279421 + 0.203011i
\(987\) 5.98323 4.34707i 0.190448 0.138369i
\(988\) −15.0908 + 46.4447i −0.480103 + 1.47760i
\(989\) 37.8343 1.20306
\(990\) 0 0
\(991\) −44.9354 −1.42742 −0.713710 0.700441i \(-0.752987\pi\)
−0.713710 + 0.700441i \(0.752987\pi\)
\(992\) −12.0880 + 37.2030i −0.383793 + 1.18119i
\(993\) 24.5868 17.8633i 0.780238 0.566876i
\(994\) −0.518024 0.376367i −0.0164307 0.0119376i
\(995\) 6.28877 + 19.3549i 0.199368 + 0.613590i
\(996\) −1.50100 4.61961i −0.0475611 0.146378i
\(997\) 0.320797 + 0.233072i 0.0101597 + 0.00738148i 0.592854 0.805310i \(-0.298001\pi\)
−0.582694 + 0.812692i \(0.698001\pi\)
\(998\) −9.47389 + 6.88318i −0.299891 + 0.217883i
\(999\) 8.84547 27.2236i 0.279858 0.861315i
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 605.2.g.q.251.3 24
11.2 odd 10 inner 605.2.g.q.366.3 24
11.3 even 5 inner 605.2.g.q.81.4 24
11.4 even 5 605.2.a.m.1.3 6
11.5 even 5 inner 605.2.g.q.511.3 24
11.6 odd 10 inner 605.2.g.q.511.4 24
11.7 odd 10 605.2.a.m.1.4 yes 6
11.8 odd 10 inner 605.2.g.q.81.3 24
11.9 even 5 inner 605.2.g.q.366.4 24
11.10 odd 2 inner 605.2.g.q.251.4 24
33.26 odd 10 5445.2.a.bx.1.4 6
33.29 even 10 5445.2.a.bx.1.3 6
44.7 even 10 9680.2.a.cw.1.6 6
44.15 odd 10 9680.2.a.cw.1.5 6
55.4 even 10 3025.2.a.bg.1.4 6
55.29 odd 10 3025.2.a.bg.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.a.m.1.3 6 11.4 even 5
605.2.a.m.1.4 yes 6 11.7 odd 10
605.2.g.q.81.3 24 11.8 odd 10 inner
605.2.g.q.81.4 24 11.3 even 5 inner
605.2.g.q.251.3 24 1.1 even 1 trivial
605.2.g.q.251.4 24 11.10 odd 2 inner
605.2.g.q.366.3 24 11.2 odd 10 inner
605.2.g.q.366.4 24 11.9 even 5 inner
605.2.g.q.511.3 24 11.5 even 5 inner
605.2.g.q.511.4 24 11.6 odd 10 inner
3025.2.a.bg.1.3 6 55.29 odd 10
3025.2.a.bg.1.4 6 55.4 even 10
5445.2.a.bx.1.3 6 33.29 even 10
5445.2.a.bx.1.4 6 33.26 odd 10
9680.2.a.cw.1.5 6 44.15 odd 10
9680.2.a.cw.1.6 6 44.7 even 10