Properties

Label 450.2.p.a.257.1
Level $450$
Weight $2$
Character 450.257
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
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] = [450,2,Mod(257,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.p (of order \(12\), degree \(4\), 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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 257.1
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 450.257
Dual form 450.2.p.a.443.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(1.33195 + 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(-0.283763 + 1.05902i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(1.33195 + 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(-0.283763 + 1.05902i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.548188 + 2.94949i) q^{9} +(-5.44949 + 3.14626i) q^{11} +(0.599900 + 1.62484i) q^{12} +(0.896575 + 3.34607i) q^{13} +(0.548188 - 0.949490i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.14626 - 3.14626i) q^{17} +(0.233875 - 2.99087i) q^{18} +1.55051i q^{19} +(-1.55051 + 1.09638i) q^{21} +(6.07812 - 1.62863i) q^{22} +(-0.965926 + 0.258819i) q^{23} +(-0.158919 - 1.72474i) q^{24} -3.46410i q^{26} +(-2.53553 + 4.53553i) q^{27} +(-0.775255 + 0.775255i) q^{28} +(1.57313 + 2.72474i) q^{29} +(2.22474 - 3.85337i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-10.7420 - 1.84304i) q^{33} +(-3.85337 + 2.22474i) q^{34} +(-1.00000 + 2.82843i) q^{36} +(3.00000 + 3.00000i) q^{37} +(0.401302 - 1.49768i) q^{38} +(-2.51059 + 5.44949i) q^{39} +(-3.39898 - 1.96240i) q^{41} +(1.78144 - 0.657717i) q^{42} +(3.34607 + 0.896575i) q^{43} -6.29253 q^{44} +1.00000 q^{46} +(-8.69333 - 2.32937i) q^{47} +(-0.292893 + 1.70711i) q^{48} +(5.02118 + 2.89898i) q^{49} +(7.67423 - 0.707107i) q^{51} +(-0.896575 + 3.34607i) q^{52} +(6.61037 + 6.61037i) q^{53} +(3.62302 - 3.72474i) q^{54} +(0.949490 - 0.548188i) q^{56} +(-1.71673 + 2.06520i) q^{57} +(-0.814313 - 3.03906i) q^{58} +(5.90326 - 10.2247i) q^{59} +(2.72474 + 4.71940i) q^{61} +(-3.14626 + 3.14626i) q^{62} +(-3.27912 - 0.256415i) q^{63} +1.00000i q^{64} +(9.89898 + 4.56048i) q^{66} +(3.65307 - 0.978838i) q^{67} +(4.29788 - 1.15161i) q^{68} +(-1.57313 - 0.724745i) q^{69} -0.635674i q^{71} +(1.69798 - 2.47323i) q^{72} +(-2.89898 + 2.89898i) q^{73} +(-2.12132 - 3.67423i) q^{74} +(-0.775255 + 1.34278i) q^{76} +(-1.78559 - 6.66390i) q^{77} +(3.83548 - 4.61401i) q^{78} +(-2.12132 + 1.22474i) q^{79} +(-8.39898 + 3.23375i) q^{81} +(2.77526 + 2.77526i) q^{82} +(0.142483 - 0.531752i) q^{83} +(-1.89097 + 0.174235i) q^{84} +(-3.00000 - 1.73205i) q^{86} +(-0.921519 + 5.37101i) q^{87} +(6.07812 + 1.62863i) q^{88} +2.36773 q^{89} -3.79796 q^{91} +(-0.965926 - 0.258819i) q^{92} +(7.22973 - 2.66925i) q^{93} +(7.79423 + 4.50000i) q^{94} +(0.724745 - 1.57313i) q^{96} +(2.89123 - 10.7902i) q^{97} +(-4.09978 - 4.09978i) q^{98} +(-12.2672 - 14.3485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7} - 24 q^{11} + 4 q^{12} + 4 q^{16} + 8 q^{18} - 32 q^{21} + 8 q^{22} + 8 q^{27} - 16 q^{28} + 8 q^{31} - 16 q^{33} - 8 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{41} - 20 q^{42} + 8 q^{46} - 8 q^{48} + 32 q^{51} - 12 q^{56} - 28 q^{57} + 4 q^{58} + 12 q^{61} + 32 q^{63} + 40 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{72} + 16 q^{73} - 16 q^{76} - 24 q^{77} + 24 q^{78} - 28 q^{81} + 32 q^{82} - 12 q^{83} - 24 q^{86} + 8 q^{87} + 8 q^{88} + 48 q^{91} + 20 q^{93} - 4 q^{96} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) 1.33195 + 1.10721i 0.769002 + 0.639246i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) −1.00000 1.41421i −0.408248 0.577350i
\(7\) −0.283763 + 1.05902i −0.107252 + 0.400271i −0.998591 0.0530669i \(-0.983100\pi\)
0.891339 + 0.453338i \(0.149767\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.548188 + 2.94949i 0.182729 + 0.983163i
\(10\) 0 0
\(11\) −5.44949 + 3.14626i −1.64308 + 0.948634i −0.663354 + 0.748305i \(0.730868\pi\)
−0.979729 + 0.200329i \(0.935799\pi\)
\(12\) 0.599900 + 1.62484i 0.173176 + 0.469052i
\(13\) 0.896575 + 3.34607i 0.248665 + 0.928032i 0.971506 + 0.237016i \(0.0761695\pi\)
−0.722840 + 0.691015i \(0.757164\pi\)
\(14\) 0.548188 0.949490i 0.146509 0.253762i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 3.14626 3.14626i 0.763081 0.763081i −0.213797 0.976878i \(-0.568583\pi\)
0.976878 + 0.213797i \(0.0685831\pi\)
\(18\) 0.233875 2.99087i 0.0551249 0.704955i
\(19\) 1.55051i 0.355711i 0.984057 + 0.177856i \(0.0569160\pi\)
−0.984057 + 0.177856i \(0.943084\pi\)
\(20\) 0 0
\(21\) −1.55051 + 1.09638i −0.338349 + 0.239249i
\(22\) 6.07812 1.62863i 1.29586 0.347224i
\(23\) −0.965926 + 0.258819i −0.201409 + 0.0539675i −0.358113 0.933678i \(-0.616580\pi\)
0.156704 + 0.987646i \(0.449913\pi\)
\(24\) −0.158919 1.72474i −0.0324391 0.352062i
\(25\) 0 0
\(26\) 3.46410i 0.679366i
\(27\) −2.53553 + 4.53553i −0.487964 + 0.872864i
\(28\) −0.775255 + 0.775255i −0.146509 + 0.146509i
\(29\) 1.57313 + 2.72474i 0.292123 + 0.505972i 0.974312 0.225204i \(-0.0723049\pi\)
−0.682188 + 0.731177i \(0.738972\pi\)
\(30\) 0 0
\(31\) 2.22474 3.85337i 0.399576 0.692086i −0.594098 0.804393i \(-0.702491\pi\)
0.993674 + 0.112307i \(0.0358240\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) −10.7420 1.84304i −1.86995 0.320832i
\(34\) −3.85337 + 2.22474i −0.660848 + 0.381541i
\(35\) 0 0
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) 3.00000 + 3.00000i 0.493197 + 0.493197i 0.909312 0.416115i \(-0.136609\pi\)
−0.416115 + 0.909312i \(0.636609\pi\)
\(38\) 0.401302 1.49768i 0.0650997 0.242955i
\(39\) −2.51059 + 5.44949i −0.402016 + 0.872617i
\(40\) 0 0
\(41\) −3.39898 1.96240i −0.530831 0.306476i 0.210524 0.977589i \(-0.432483\pi\)
−0.741355 + 0.671113i \(0.765816\pi\)
\(42\) 1.78144 0.657717i 0.274882 0.101488i
\(43\) 3.34607 + 0.896575i 0.510270 + 0.136726i 0.504762 0.863258i \(-0.331580\pi\)
0.00550783 + 0.999985i \(0.498247\pi\)
\(44\) −6.29253 −0.948634
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) −8.69333 2.32937i −1.26805 0.339774i −0.438768 0.898600i \(-0.644585\pi\)
−0.829285 + 0.558827i \(0.811252\pi\)
\(48\) −0.292893 + 1.70711i −0.0422755 + 0.246400i
\(49\) 5.02118 + 2.89898i 0.717311 + 0.414140i
\(50\) 0 0
\(51\) 7.67423 0.707107i 1.07461 0.0990148i
\(52\) −0.896575 + 3.34607i −0.124333 + 0.464016i
\(53\) 6.61037 + 6.61037i 0.908004 + 0.908004i 0.996111 0.0881074i \(-0.0280819\pi\)
−0.0881074 + 0.996111i \(0.528082\pi\)
\(54\) 3.62302 3.72474i 0.493031 0.506874i
\(55\) 0 0
\(56\) 0.949490 0.548188i 0.126881 0.0732547i
\(57\) −1.71673 + 2.06520i −0.227387 + 0.273543i
\(58\) −0.814313 3.03906i −0.106925 0.399048i
\(59\) 5.90326 10.2247i 0.768539 1.33115i −0.169816 0.985476i \(-0.554317\pi\)
0.938355 0.345673i \(-0.112349\pi\)
\(60\) 0 0
\(61\) 2.72474 + 4.71940i 0.348868 + 0.604257i 0.986049 0.166458i \(-0.0532329\pi\)
−0.637181 + 0.770714i \(0.719900\pi\)
\(62\) −3.14626 + 3.14626i −0.399576 + 0.399576i
\(63\) −3.27912 0.256415i −0.413130 0.0323053i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 9.89898 + 4.56048i 1.21848 + 0.561356i
\(67\) 3.65307 0.978838i 0.446294 0.119584i −0.0286709 0.999589i \(-0.509127\pi\)
0.474965 + 0.880005i \(0.342461\pi\)
\(68\) 4.29788 1.15161i 0.521194 0.139654i
\(69\) −1.57313 0.724745i −0.189383 0.0872490i
\(70\) 0 0
\(71\) 0.635674i 0.0754407i −0.999288 0.0377203i \(-0.987990\pi\)
0.999288 0.0377203i \(-0.0120096\pi\)
\(72\) 1.69798 2.47323i 0.200108 0.291473i
\(73\) −2.89898 + 2.89898i −0.339300 + 0.339300i −0.856104 0.516804i \(-0.827122\pi\)
0.516804 + 0.856104i \(0.327122\pi\)
\(74\) −2.12132 3.67423i −0.246598 0.427121i
\(75\) 0 0
\(76\) −0.775255 + 1.34278i −0.0889279 + 0.154028i
\(77\) −1.78559 6.66390i −0.203487 0.759422i
\(78\) 3.83548 4.61401i 0.434282 0.522434i
\(79\) −2.12132 + 1.22474i −0.238667 + 0.137795i −0.614564 0.788867i \(-0.710668\pi\)
0.375897 + 0.926662i \(0.377335\pi\)
\(80\) 0 0
\(81\) −8.39898 + 3.23375i −0.933220 + 0.359306i
\(82\) 2.77526 + 2.77526i 0.306476 + 0.306476i
\(83\) 0.142483 0.531752i 0.0156395 0.0583674i −0.957665 0.287885i \(-0.907048\pi\)
0.973305 + 0.229517i \(0.0737147\pi\)
\(84\) −1.89097 + 0.174235i −0.206322 + 0.0190106i
\(85\) 0 0
\(86\) −3.00000 1.73205i −0.323498 0.186772i
\(87\) −0.921519 + 5.37101i −0.0987973 + 0.575833i
\(88\) 6.07812 + 1.62863i 0.647929 + 0.173612i
\(89\) 2.36773 0.250978 0.125489 0.992095i \(-0.459950\pi\)
0.125489 + 0.992095i \(0.459950\pi\)
\(90\) 0 0
\(91\) −3.79796 −0.398134
\(92\) −0.965926 0.258819i −0.100705 0.0269838i
\(93\) 7.22973 2.66925i 0.749688 0.276788i
\(94\) 7.79423 + 4.50000i 0.803913 + 0.464140i
\(95\) 0 0
\(96\) 0.724745 1.57313i 0.0739690 0.160557i
\(97\) 2.89123 10.7902i 0.293560 1.09558i −0.648795 0.760963i \(-0.724727\pi\)
0.942355 0.334616i \(-0.108607\pi\)
\(98\) −4.09978 4.09978i −0.414140 0.414140i
\(99\) −12.2672 14.3485i −1.23290 1.44208i
\(100\) 0 0
\(101\) 1.10102 0.635674i 0.109556 0.0632520i −0.444221 0.895917i \(-0.646519\pi\)
0.553777 + 0.832665i \(0.313186\pi\)
\(102\) −7.59575 1.30323i −0.752092 0.129039i
\(103\) −1.06110 3.96008i −0.104553 0.390198i 0.893741 0.448584i \(-0.148071\pi\)
−0.998294 + 0.0583855i \(0.981405\pi\)
\(104\) 1.73205 3.00000i 0.169842 0.294174i
\(105\) 0 0
\(106\) −4.67423 8.09601i −0.454002 0.786354i
\(107\) 3.71051 3.71051i 0.358708 0.358708i −0.504628 0.863337i \(-0.668370\pi\)
0.863337 + 0.504628i \(0.168370\pi\)
\(108\) −4.46360 + 2.66012i −0.429510 + 0.255970i
\(109\) 20.3485i 1.94903i −0.224323 0.974515i \(-0.572017\pi\)
0.224323 0.974515i \(-0.427983\pi\)
\(110\) 0 0
\(111\) 0.674235 + 7.31747i 0.0639955 + 0.694544i
\(112\) −1.05902 + 0.283763i −0.100068 + 0.0268131i
\(113\) 13.3278 3.57117i 1.25377 0.335948i 0.429981 0.902838i \(-0.358520\pi\)
0.823793 + 0.566890i \(0.191854\pi\)
\(114\) 2.19275 1.55051i 0.205370 0.145219i
\(115\) 0 0
\(116\) 3.14626i 0.292123i
\(117\) −9.37769 + 4.47871i −0.866968 + 0.414057i
\(118\) −8.34847 + 8.34847i −0.768539 + 0.768539i
\(119\) 2.43916 + 4.22474i 0.223597 + 0.387282i
\(120\) 0 0
\(121\) 14.2980 24.7648i 1.29981 2.25134i
\(122\) −1.41043 5.26380i −0.127694 0.476562i
\(123\) −2.35449 6.37720i −0.212297 0.575012i
\(124\) 3.85337 2.22474i 0.346043 0.199788i
\(125\) 0 0
\(126\) 3.10102 + 1.09638i 0.276261 + 0.0976730i
\(127\) −14.1237 14.1237i −1.25328 1.25328i −0.954242 0.299036i \(-0.903335\pi\)
−0.299036 0.954242i \(-0.596665\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) 3.46410 + 4.89898i 0.304997 + 0.431331i
\(130\) 0 0
\(131\) 9.12372 + 5.26758i 0.797143 + 0.460231i 0.842471 0.538741i \(-0.181100\pi\)
−0.0453278 + 0.998972i \(0.514433\pi\)
\(132\) −8.38134 6.96713i −0.729502 0.606411i
\(133\) −1.64202 0.439978i −0.142381 0.0381509i
\(134\) −3.78194 −0.326710
\(135\) 0 0
\(136\) −4.44949 −0.381541
\(137\) 2.12701 + 0.569930i 0.181723 + 0.0486924i 0.348533 0.937297i \(-0.386680\pi\)
−0.166810 + 0.985989i \(0.553347\pi\)
\(138\) 1.33195 + 1.10721i 0.113383 + 0.0942517i
\(139\) −11.1708 6.44949i −0.947499 0.547039i −0.0551956 0.998476i \(-0.517578\pi\)
−0.892303 + 0.451437i \(0.850912\pi\)
\(140\) 0 0
\(141\) −9.00000 12.7279i −0.757937 1.07188i
\(142\) −0.164525 + 0.614014i −0.0138066 + 0.0515269i
\(143\) −15.4135 15.4135i −1.28894 1.28894i
\(144\) −2.28024 + 1.94949i −0.190020 + 0.162457i
\(145\) 0 0
\(146\) 3.55051 2.04989i 0.293842 0.169650i
\(147\) 3.47820 + 9.42078i 0.286877 + 0.777013i
\(148\) 1.09808 + 4.09808i 0.0902613 + 0.336860i
\(149\) −6.45145 + 11.1742i −0.528523 + 0.915429i 0.470924 + 0.882174i \(0.343921\pi\)
−0.999447 + 0.0332550i \(0.989413\pi\)
\(150\) 0 0
\(151\) 10.7980 + 18.7026i 0.878725 + 1.52200i 0.852741 + 0.522335i \(0.174939\pi\)
0.0259849 + 0.999662i \(0.491728\pi\)
\(152\) 1.09638 1.09638i 0.0889279 0.0889279i
\(153\) 11.0046 + 7.55513i 0.889671 + 0.610796i
\(154\) 6.89898i 0.555936i
\(155\) 0 0
\(156\) −4.89898 + 3.46410i −0.392232 + 0.277350i
\(157\) 5.94012 1.59165i 0.474073 0.127028i −0.0138684 0.999904i \(-0.504415\pi\)
0.487942 + 0.872876i \(0.337748\pi\)
\(158\) 2.36603 0.633975i 0.188231 0.0504363i
\(159\) 1.48565 + 16.1237i 0.117819 + 1.27869i
\(160\) 0 0
\(161\) 1.09638i 0.0864066i
\(162\) 8.94975 0.949747i 0.703159 0.0746192i
\(163\) 0.449490 0.449490i 0.0352068 0.0352068i −0.689284 0.724491i \(-0.742075\pi\)
0.724491 + 0.689284i \(0.242075\pi\)
\(164\) −1.96240 3.39898i −0.153238 0.265416i
\(165\) 0 0
\(166\) −0.275255 + 0.476756i −0.0213639 + 0.0370034i
\(167\) 2.79472 + 10.4300i 0.216262 + 0.807100i 0.985719 + 0.168401i \(0.0538603\pi\)
−0.769457 + 0.638699i \(0.779473\pi\)
\(168\) 1.87163 + 0.321121i 0.144400 + 0.0247750i
\(169\) 0.866025 0.500000i 0.0666173 0.0384615i
\(170\) 0 0
\(171\) −4.57321 + 0.849971i −0.349722 + 0.0649989i
\(172\) 2.44949 + 2.44949i 0.186772 + 0.186772i
\(173\) −0.802603 + 2.99536i −0.0610208 + 0.227733i −0.989701 0.143148i \(-0.954277\pi\)
0.928680 + 0.370881i \(0.120944\pi\)
\(174\) 2.28024 4.94949i 0.172864 0.375220i
\(175\) 0 0
\(176\) −5.44949 3.14626i −0.410771 0.237159i
\(177\) 19.1838 7.08274i 1.44194 0.532371i
\(178\) −2.28705 0.612812i −0.171421 0.0459322i
\(179\) 17.6062 1.31595 0.657976 0.753039i \(-0.271413\pi\)
0.657976 + 0.753039i \(0.271413\pi\)
\(180\) 0 0
\(181\) −10.5505 −0.784213 −0.392107 0.919920i \(-0.628254\pi\)
−0.392107 + 0.919920i \(0.628254\pi\)
\(182\) 3.66855 + 0.982984i 0.271931 + 0.0728636i
\(183\) −1.59612 + 9.30286i −0.117988 + 0.687687i
\(184\) 0.866025 + 0.500000i 0.0638442 + 0.0368605i
\(185\) 0 0
\(186\) −7.67423 + 0.707107i −0.562702 + 0.0518476i
\(187\) −7.24656 + 27.0445i −0.529921 + 1.97769i
\(188\) −6.36396 6.36396i −0.464140 0.464140i
\(189\) −4.08372 3.97219i −0.297047 0.288935i
\(190\) 0 0
\(191\) −2.87628 + 1.66062i −0.208120 + 0.120158i −0.600437 0.799672i \(-0.705007\pi\)
0.392317 + 0.919830i \(0.371673\pi\)
\(192\) −1.10721 + 1.33195i −0.0799057 + 0.0961253i
\(193\) −4.48288 16.7303i −0.322685 1.20428i −0.916619 0.399762i \(-0.869093\pi\)
0.593934 0.804513i \(-0.297574\pi\)
\(194\) −5.58542 + 9.67423i −0.401010 + 0.694570i
\(195\) 0 0
\(196\) 2.89898 + 5.02118i 0.207070 + 0.358656i
\(197\) 6.92820 6.92820i 0.493614 0.493614i −0.415829 0.909443i \(-0.636508\pi\)
0.909443 + 0.415829i \(0.136508\pi\)
\(198\) 8.13557 + 17.0345i 0.578170 + 1.21059i
\(199\) 3.55051i 0.251689i 0.992050 + 0.125844i \(0.0401640\pi\)
−0.992050 + 0.125844i \(0.959836\pi\)
\(200\) 0 0
\(201\) 5.94949 + 2.74094i 0.419645 + 0.193331i
\(202\) −1.22803 + 0.329049i −0.0864038 + 0.0231518i
\(203\) −3.33195 + 0.892794i −0.233857 + 0.0626618i
\(204\) 6.99964 + 3.22474i 0.490073 + 0.225777i
\(205\) 0 0
\(206\) 4.09978i 0.285645i
\(207\) −1.29289 2.70711i −0.0898623 0.188157i
\(208\) −2.44949 + 2.44949i −0.169842 + 0.169842i
\(209\) −4.87832 8.44949i −0.337440 0.584463i
\(210\) 0 0
\(211\) −9.44949 + 16.3670i −0.650530 + 1.12675i 0.332465 + 0.943116i \(0.392120\pi\)
−0.982995 + 0.183635i \(0.941214\pi\)
\(212\) 2.41956 + 9.02993i 0.166176 + 0.620178i
\(213\) 0.703823 0.846687i 0.0482251 0.0580141i
\(214\) −4.54442 + 2.62372i −0.310650 + 0.179354i
\(215\) 0 0
\(216\) 5.00000 1.41421i 0.340207 0.0962250i
\(217\) 3.44949 + 3.44949i 0.234167 + 0.234167i
\(218\) −5.26657 + 19.6551i −0.356697 + 1.33121i
\(219\) −7.07107 + 0.651531i −0.477818 + 0.0440264i
\(220\) 0 0
\(221\) 13.3485 + 7.70674i 0.897915 + 0.518412i
\(222\) 1.24264 7.24264i 0.0834006 0.486094i
\(223\) 8.02714 + 2.15087i 0.537537 + 0.144033i 0.517367 0.855764i \(-0.326912\pi\)
0.0201706 + 0.999797i \(0.493579\pi\)
\(224\) 1.09638 0.0732547
\(225\) 0 0
\(226\) −13.7980 −0.917827
\(227\) 14.5865 + 3.90843i 0.968138 + 0.259412i 0.708041 0.706171i \(-0.249579\pi\)
0.260096 + 0.965583i \(0.416246\pi\)
\(228\) −2.51934 + 0.930152i −0.166847 + 0.0616008i
\(229\) 14.1582 + 8.17423i 0.935600 + 0.540169i 0.888578 0.458725i \(-0.151694\pi\)
0.0470214 + 0.998894i \(0.485027\pi\)
\(230\) 0 0
\(231\) 5.00000 10.8530i 0.328976 0.714075i
\(232\) 0.814313 3.03906i 0.0534623 0.199524i
\(233\) 10.9959 + 10.9959i 0.720363 + 0.720363i 0.968679 0.248316i \(-0.0798770\pi\)
−0.248316 + 0.968679i \(0.579877\pi\)
\(234\) 10.2173 1.89898i 0.667928 0.124140i
\(235\) 0 0
\(236\) 10.2247 5.90326i 0.665574 0.384269i
\(237\) −4.18154 0.717439i −0.271620 0.0466027i
\(238\) −1.26260 4.71209i −0.0818423 0.305439i
\(239\) −8.48528 + 14.6969i −0.548867 + 0.950666i 0.449485 + 0.893288i \(0.351607\pi\)
−0.998353 + 0.0573782i \(0.981726\pi\)
\(240\) 0 0
\(241\) −9.50000 16.4545i −0.611949 1.05993i −0.990912 0.134515i \(-0.957053\pi\)
0.378963 0.925412i \(-0.376281\pi\)
\(242\) −20.2204 + 20.2204i −1.29981 + 1.29981i
\(243\) −14.7675 4.99221i −0.947333 0.320250i
\(244\) 5.44949i 0.348868i
\(245\) 0 0
\(246\) 0.623724 + 6.76928i 0.0397672 + 0.431594i
\(247\) −5.18811 + 1.39015i −0.330111 + 0.0884531i
\(248\) −4.29788 + 1.15161i −0.272915 + 0.0731275i
\(249\) 0.778539 0.550510i 0.0493379 0.0348872i
\(250\) 0 0
\(251\) 11.1708i 0.705097i −0.935793 0.352549i \(-0.885315\pi\)
0.935793 0.352549i \(-0.114685\pi\)
\(252\) −2.71159 1.86162i −0.170814 0.117271i
\(253\) 4.44949 4.44949i 0.279737 0.279737i
\(254\) 9.98698 + 17.2980i 0.626639 + 1.08537i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.74105 + 25.1579i 0.420495 + 1.56931i 0.773568 + 0.633713i \(0.218470\pi\)
−0.353073 + 0.935596i \(0.614863\pi\)
\(258\) −2.07812 5.62863i −0.129378 0.350423i
\(259\) −4.02834 + 2.32577i −0.250309 + 0.144516i
\(260\) 0 0
\(261\) −7.17423 + 6.13361i −0.444074 + 0.379661i
\(262\) −7.44949 7.44949i −0.460231 0.460231i
\(263\) −3.28621 + 12.2643i −0.202636 + 0.756249i 0.787521 + 0.616288i \(0.211364\pi\)
−0.990157 + 0.139961i \(0.955302\pi\)
\(264\) 6.29253 + 8.89898i 0.387278 + 0.547694i
\(265\) 0 0
\(266\) 1.47219 + 0.849971i 0.0902660 + 0.0521151i
\(267\) 3.15369 + 2.62156i 0.193003 + 0.160437i
\(268\) 3.65307 + 0.978838i 0.223147 + 0.0597920i
\(269\) −4.70334 −0.286768 −0.143384 0.989667i \(-0.545798\pi\)
−0.143384 + 0.989667i \(0.545798\pi\)
\(270\) 0 0
\(271\) −16.0454 −0.974689 −0.487345 0.873210i \(-0.662034\pi\)
−0.487345 + 0.873210i \(0.662034\pi\)
\(272\) 4.29788 + 1.15161i 0.260597 + 0.0698268i
\(273\) −5.05870 4.20512i −0.306166 0.254506i
\(274\) −1.90702 1.10102i −0.115208 0.0665151i
\(275\) 0 0
\(276\) −1.00000 1.41421i −0.0601929 0.0851257i
\(277\) 3.69723 13.7983i 0.222145 0.829057i −0.761383 0.648302i \(-0.775479\pi\)
0.983528 0.180754i \(-0.0578539\pi\)
\(278\) 9.12096 + 9.12096i 0.547039 + 0.547039i
\(279\) 12.5851 + 4.44949i 0.753448 + 0.266384i
\(280\) 0 0
\(281\) −0.151531 + 0.0874863i −0.00903957 + 0.00521900i −0.504513 0.863404i \(-0.668328\pi\)
0.495473 + 0.868623i \(0.334995\pi\)
\(282\) 5.39910 + 14.6236i 0.321512 + 0.870823i
\(283\) −1.78484 6.66112i −0.106098 0.395962i 0.892370 0.451305i \(-0.149041\pi\)
−0.998467 + 0.0553430i \(0.982375\pi\)
\(284\) 0.317837 0.550510i 0.0188602 0.0326668i
\(285\) 0 0
\(286\) 10.8990 + 18.8776i 0.644470 + 1.11626i
\(287\) 3.04272 3.04272i 0.179606 0.179606i
\(288\) 2.70711 1.29289i 0.159518 0.0761845i
\(289\) 2.79796i 0.164586i
\(290\) 0 0
\(291\) 15.7980 11.1708i 0.926093 0.654846i
\(292\) −3.96008 + 1.06110i −0.231746 + 0.0620962i
\(293\) −21.2942 + 5.70577i −1.24402 + 0.333335i −0.820024 0.572329i \(-0.806040\pi\)
−0.423998 + 0.905663i \(0.639374\pi\)
\(294\) −0.921404 10.0000i −0.0537374 0.583212i
\(295\) 0 0
\(296\) 4.24264i 0.246598i
\(297\) −0.452623 32.6938i −0.0262638 1.89709i
\(298\) 9.12372 9.12372i 0.528523 0.528523i
\(299\) −1.73205 3.00000i −0.100167 0.173494i
\(300\) 0 0
\(301\) −1.89898 + 3.28913i −0.109455 + 0.189582i
\(302\) −5.58943 20.8601i −0.321636 1.20036i
\(303\) 2.17033 + 0.372369i 0.124682 + 0.0213921i
\(304\) −1.34278 + 0.775255i −0.0770138 + 0.0444639i
\(305\) 0 0
\(306\) −8.67423 10.1459i −0.495873 0.580002i
\(307\) −0.674235 0.674235i −0.0384806 0.0384806i 0.687605 0.726085i \(-0.258662\pi\)
−0.726085 + 0.687605i \(0.758662\pi\)
\(308\) 1.78559 6.66390i 0.101743 0.379711i
\(309\) 2.97129 6.44949i 0.169031 0.366899i
\(310\) 0 0
\(311\) −17.8207 10.2888i −1.01052 0.583422i −0.0991741 0.995070i \(-0.531620\pi\)
−0.911343 + 0.411648i \(0.864953\pi\)
\(312\) 5.62863 2.07812i 0.318658 0.117650i
\(313\) 4.85009 + 1.29958i 0.274143 + 0.0734564i 0.393271 0.919422i \(-0.371343\pi\)
−0.119128 + 0.992879i \(0.538010\pi\)
\(314\) −6.14966 −0.347046
\(315\) 0 0
\(316\) −2.44949 −0.137795
\(317\) −1.06350 0.284965i −0.0597323 0.0160052i 0.228829 0.973467i \(-0.426510\pi\)
−0.288561 + 0.957461i \(0.593177\pi\)
\(318\) 2.73810 15.9588i 0.153545 0.894927i
\(319\) −17.1455 9.89898i −0.959966 0.554236i
\(320\) 0 0
\(321\) 9.05051 0.833917i 0.505150 0.0465447i
\(322\) −0.283763 + 1.05902i −0.0158135 + 0.0590168i
\(323\) 4.87832 + 4.87832i 0.271437 + 0.271437i
\(324\) −8.89060 1.39898i −0.493922 0.0777211i
\(325\) 0 0
\(326\) −0.550510 + 0.317837i −0.0304899 + 0.0176034i
\(327\) 22.5300 27.1032i 1.24591 1.49881i
\(328\) 1.01581 + 3.79107i 0.0560889 + 0.209327i
\(329\) 4.93369 8.54541i 0.272003 0.471124i
\(330\) 0 0
\(331\) 2.22474 + 3.85337i 0.122283 + 0.211800i 0.920668 0.390347i \(-0.127645\pi\)
−0.798385 + 0.602148i \(0.794312\pi\)
\(332\) 0.389270 0.389270i 0.0213639 0.0213639i
\(333\) −7.20390 + 10.4930i −0.394772 + 0.575015i
\(334\) 10.7980i 0.590838i
\(335\) 0 0
\(336\) −1.72474 0.794593i −0.0940925 0.0433486i
\(337\) −29.7766 + 7.97861i −1.62203 + 0.434622i −0.951598 0.307346i \(-0.900559\pi\)
−0.670435 + 0.741968i \(0.733892\pi\)
\(338\) −0.965926 + 0.258819i −0.0525394 + 0.0140779i
\(339\) 21.7060 + 10.0000i 1.17891 + 0.543125i
\(340\) 0 0
\(341\) 27.9985i 1.51621i
\(342\) 4.63737 + 0.362626i 0.250760 + 0.0196085i
\(343\) −9.92168 + 9.92168i −0.535721 + 0.535721i
\(344\) −1.73205 3.00000i −0.0933859 0.161749i
\(345\) 0 0
\(346\) 1.55051 2.68556i 0.0833559 0.144377i
\(347\) 1.08757 + 4.05886i 0.0583837 + 0.217891i 0.988954 0.148222i \(-0.0473550\pi\)
−0.930570 + 0.366113i \(0.880688\pi\)
\(348\) −3.48356 + 4.19067i −0.186739 + 0.224644i
\(349\) −13.0297 + 7.52270i −0.697464 + 0.402681i −0.806402 0.591367i \(-0.798588\pi\)
0.108938 + 0.994049i \(0.465255\pi\)
\(350\) 0 0
\(351\) −17.4495 4.41761i −0.931385 0.235795i
\(352\) 4.44949 + 4.44949i 0.237159 + 0.237159i
\(353\) 8.87564 33.1244i 0.472403 1.76303i −0.158694 0.987328i \(-0.550728\pi\)
0.631097 0.775704i \(-0.282605\pi\)
\(354\) −20.3632 + 1.87628i −1.08229 + 0.0997229i
\(355\) 0 0
\(356\) 2.05051 + 1.18386i 0.108677 + 0.0627446i
\(357\) −1.42883 + 8.32780i −0.0756215 + 0.440754i
\(358\) −17.0063 4.55683i −0.898812 0.240836i
\(359\) −17.4634 −0.921682 −0.460841 0.887483i \(-0.652452\pi\)
−0.460841 + 0.887483i \(0.652452\pi\)
\(360\) 0 0
\(361\) 16.5959 0.873469
\(362\) 10.1910 + 2.73067i 0.535628 + 0.143521i
\(363\) 46.4639 17.1547i 2.43872 0.900388i
\(364\) −3.28913 1.89898i −0.172397 0.0995336i
\(365\) 0 0
\(366\) 3.94949 8.57277i 0.206443 0.448106i
\(367\) −2.52520 + 9.42418i −0.131814 + 0.491938i −0.999991 0.00431778i \(-0.998626\pi\)
0.868176 + 0.496256i \(0.165292\pi\)
\(368\) −0.707107 0.707107i −0.0368605 0.0368605i
\(369\) 3.92480 11.1010i 0.204317 0.577896i
\(370\) 0 0
\(371\) −8.87628 + 5.12472i −0.460833 + 0.266062i
\(372\) 7.59575 + 1.30323i 0.393822 + 0.0675691i
\(373\) −5.25190 19.6004i −0.271933 1.01487i −0.957869 0.287206i \(-0.907273\pi\)
0.685935 0.727662i \(-0.259393\pi\)
\(374\) 13.9993 24.2474i 0.723885 1.25381i
\(375\) 0 0
\(376\) 4.50000 + 7.79423i 0.232070 + 0.401957i
\(377\) −7.70674 + 7.70674i −0.396917 + 0.396917i
\(378\) 2.91649 + 4.89379i 0.150008 + 0.251709i
\(379\) 6.65153i 0.341666i −0.985300 0.170833i \(-0.945354\pi\)
0.985300 0.170833i \(-0.0546459\pi\)
\(380\) 0 0
\(381\) −3.17423 34.4500i −0.162621 1.76493i
\(382\) 3.20807 0.859599i 0.164139 0.0439809i
\(383\) −26.8508 + 7.19464i −1.37201 + 0.367629i −0.868212 0.496193i \(-0.834731\pi\)
−0.503798 + 0.863822i \(0.668064\pi\)
\(384\) 1.41421 1.00000i 0.0721688 0.0510310i
\(385\) 0 0
\(386\) 17.3205i 0.881591i
\(387\) −0.810167 + 10.3607i −0.0411831 + 0.526663i
\(388\) 7.89898 7.89898i 0.401010 0.401010i
\(389\) 2.81237 + 4.87117i 0.142593 + 0.246978i 0.928472 0.371402i \(-0.121123\pi\)
−0.785879 + 0.618380i \(0.787789\pi\)
\(390\) 0 0
\(391\) −2.22474 + 3.85337i −0.112510 + 0.194873i
\(392\) −1.50062 5.60040i −0.0757929 0.282863i
\(393\) 6.32005 + 17.1180i 0.318804 + 0.863489i
\(394\) −8.48528 + 4.89898i −0.427482 + 0.246807i
\(395\) 0 0
\(396\) −3.44949 18.5597i −0.173343 0.932662i
\(397\) −15.4495 15.4495i −0.775388 0.775388i 0.203655 0.979043i \(-0.434718\pi\)
−0.979043 + 0.203655i \(0.934718\pi\)
\(398\) 0.918940 3.42953i 0.0460623 0.171907i
\(399\) −1.69994 2.40408i −0.0851036 0.120355i
\(400\) 0 0
\(401\) 22.3485 + 12.9029i 1.11603 + 0.644340i 0.940384 0.340114i \(-0.110466\pi\)
0.175645 + 0.984454i \(0.443799\pi\)
\(402\) −5.03736 4.18739i −0.251241 0.208848i
\(403\) 14.8883 + 3.98930i 0.741638 + 0.198721i
\(404\) 1.27135 0.0632520
\(405\) 0 0
\(406\) 3.44949 0.171195
\(407\) −25.7873 6.90968i −1.27823 0.342500i
\(408\) −5.92650 4.92650i −0.293406 0.243898i
\(409\) 16.5420 + 9.55051i 0.817948 + 0.472242i 0.849708 0.527253i \(-0.176778\pi\)
−0.0317605 + 0.999496i \(0.510111\pi\)
\(410\) 0 0
\(411\) 2.20204 + 3.11416i 0.108619 + 0.153610i
\(412\) 1.06110 3.96008i 0.0522767 0.195099i
\(413\) 9.15306 + 9.15306i 0.450393 + 0.450393i
\(414\) 0.548188 + 2.94949i 0.0269420 + 0.144960i
\(415\) 0 0
\(416\) 3.00000 1.73205i 0.147087 0.0849208i
\(417\) −7.73810 20.9588i −0.378937 1.02636i
\(418\) 2.52520 + 9.42418i 0.123512 + 0.460952i
\(419\) 5.97469 10.3485i 0.291883 0.505556i −0.682372 0.731005i \(-0.739052\pi\)
0.974255 + 0.225449i \(0.0723850\pi\)
\(420\) 0 0
\(421\) 7.44949 + 12.9029i 0.363066 + 0.628849i 0.988464 0.151457i \(-0.0483966\pi\)
−0.625398 + 0.780306i \(0.715063\pi\)
\(422\) 13.3636 13.3636i 0.650530 0.650530i
\(423\) 2.10488 26.9178i 0.102343 1.30879i
\(424\) 9.34847i 0.454002i
\(425\) 0 0
\(426\) −0.898979 + 0.635674i −0.0435557 + 0.0307985i
\(427\) −5.77111 + 1.54636i −0.279284 + 0.0748338i
\(428\) 5.06865 1.35814i 0.245002 0.0656482i
\(429\) −3.46410 37.5959i −0.167248 1.81515i
\(430\) 0 0
\(431\) 15.5563i 0.749323i −0.927162 0.374661i \(-0.877759\pi\)
0.927162 0.374661i \(-0.122241\pi\)
\(432\) −5.19565 + 0.0719302i −0.249976 + 0.00346074i
\(433\) −8.55051 + 8.55051i −0.410911 + 0.410911i −0.882056 0.471145i \(-0.843841\pi\)
0.471145 + 0.882056i \(0.343841\pi\)
\(434\) −2.43916 4.22474i −0.117083 0.202794i
\(435\) 0 0
\(436\) 10.1742 17.6223i 0.487257 0.843955i
\(437\) −0.401302 1.49768i −0.0191969 0.0716436i
\(438\) 6.99876 + 1.20080i 0.334413 + 0.0573763i
\(439\) 8.83523 5.10102i 0.421682 0.243458i −0.274114 0.961697i \(-0.588385\pi\)
0.695797 + 0.718239i \(0.255051\pi\)
\(440\) 0 0
\(441\) −5.79796 + 16.3991i −0.276093 + 0.780910i
\(442\) −10.8990 10.8990i −0.518412 0.518412i
\(443\) −0.142483 + 0.531752i −0.00676955 + 0.0252643i −0.969228 0.246165i \(-0.920830\pi\)
0.962458 + 0.271429i \(0.0874962\pi\)
\(444\) −3.07483 + 6.67423i −0.145925 + 0.316745i
\(445\) 0 0
\(446\) −7.19694 4.15515i −0.340785 0.196752i
\(447\) −20.9652 + 7.74045i −0.991620 + 0.366111i
\(448\) −1.05902 0.283763i −0.0500339 0.0134065i
\(449\) 21.7060 1.02437 0.512185 0.858875i \(-0.328836\pi\)
0.512185 + 0.858875i \(0.328836\pi\)
\(450\) 0 0
\(451\) 24.6969 1.16293
\(452\) 13.3278 + 3.57117i 0.626887 + 0.167974i
\(453\) −6.32530 + 36.8665i −0.297188 + 1.73214i
\(454\) −13.0779 7.55051i −0.613775 0.354363i
\(455\) 0 0
\(456\) 2.67423 0.246405i 0.125233 0.0115390i
\(457\) −1.59165 + 5.94012i −0.0744543 + 0.277867i −0.993109 0.117194i \(-0.962610\pi\)
0.918655 + 0.395061i \(0.129277\pi\)
\(458\) −11.5601 11.5601i −0.540169 0.540169i
\(459\) 6.29253 + 22.2474i 0.293710 + 1.03842i
\(460\) 0 0
\(461\) 16.3763 9.45485i 0.762719 0.440356i −0.0675520 0.997716i \(-0.521519\pi\)
0.830271 + 0.557360i \(0.188186\pi\)
\(462\) −7.63859 + 9.18910i −0.355380 + 0.427516i
\(463\) 8.54613 + 31.8946i 0.397172 + 1.48227i 0.818048 + 0.575150i \(0.195056\pi\)
−0.420876 + 0.907118i \(0.638277\pi\)
\(464\) −1.57313 + 2.72474i −0.0730308 + 0.126493i
\(465\) 0 0
\(466\) −7.77526 13.4671i −0.360182 0.623853i
\(467\) −2.82843 + 2.82843i −0.130884 + 0.130884i −0.769514 0.638630i \(-0.779501\pi\)
0.638630 + 0.769514i \(0.279501\pi\)
\(468\) −10.3607 0.810167i −0.478922 0.0374500i
\(469\) 4.14643i 0.191464i
\(470\) 0 0
\(471\) 9.67423 + 4.45694i 0.445765 + 0.205365i
\(472\) −11.4042 + 3.05575i −0.524922 + 0.140652i
\(473\) −21.0552 + 5.64173i −0.968120 + 0.259407i
\(474\) 3.85337 + 1.77526i 0.176991 + 0.0815402i
\(475\) 0 0
\(476\) 4.87832i 0.223597i
\(477\) −15.8735 + 23.1209i −0.726797 + 1.05863i
\(478\) 12.0000 12.0000i 0.548867 0.548867i
\(479\) −3.53553 6.12372i −0.161543 0.279800i 0.773879 0.633333i \(-0.218314\pi\)
−0.935422 + 0.353533i \(0.884980\pi\)
\(480\) 0 0
\(481\) −7.34847 + 12.7279i −0.335061 + 0.580343i
\(482\) 4.91756 + 18.3526i 0.223989 + 0.835938i
\(483\) 1.21391 1.46032i 0.0552350 0.0664469i
\(484\) 24.7648 14.2980i 1.12567 0.649907i
\(485\) 0 0
\(486\) 12.9722 + 8.64420i 0.588431 + 0.392109i
\(487\) 12.0000 + 12.0000i 0.543772 + 0.543772i 0.924632 0.380861i \(-0.124372\pi\)
−0.380861 + 0.924632i \(0.624372\pi\)
\(488\) 1.41043 5.26380i 0.0638472 0.238281i
\(489\) 1.09638 0.101021i 0.0495799 0.00456831i
\(490\) 0 0
\(491\) 0.247449 + 0.142865i 0.0111672 + 0.00644739i 0.505573 0.862784i \(-0.331281\pi\)
−0.494406 + 0.869231i \(0.664614\pi\)
\(492\) 1.14955 6.70006i 0.0518256 0.302062i
\(493\) 13.5223 + 3.62328i 0.609012 + 0.163184i
\(494\) 5.37113 0.241658
\(495\) 0 0
\(496\) 4.44949 0.199788
\(497\) 0.673191 + 0.180381i 0.0301967 + 0.00809119i
\(498\) −0.894494 + 0.330251i −0.0400832 + 0.0147989i
\(499\) 7.70674 + 4.44949i 0.345001 + 0.199187i 0.662481 0.749078i \(-0.269503\pi\)
−0.317480 + 0.948265i \(0.602837\pi\)
\(500\) 0 0
\(501\) −7.82577 + 16.9866i −0.349629 + 0.758906i
\(502\) −2.89123 + 10.7902i −0.129042 + 0.481590i
\(503\) 16.7563 + 16.7563i 0.747125 + 0.747125i 0.973938 0.226813i \(-0.0728307\pi\)
−0.226813 + 0.973938i \(0.572831\pi\)
\(504\) 2.13737 + 2.50000i 0.0952062 + 0.111359i
\(505\) 0 0
\(506\) −5.44949 + 3.14626i −0.242259 + 0.139869i
\(507\) 1.70711 + 0.292893i 0.0758153 + 0.0130078i
\(508\) −5.16964 19.2934i −0.229366 0.856005i
\(509\) −19.8150 + 34.3207i −0.878286 + 1.52124i −0.0250662 + 0.999686i \(0.507980\pi\)
−0.853220 + 0.521551i \(0.825354\pi\)
\(510\) 0 0
\(511\) −2.24745 3.89270i −0.0994213 0.172203i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −7.03239 3.93137i −0.310488 0.173574i
\(514\) 26.0454i 1.14881i
\(515\) 0 0
\(516\) 0.550510 + 5.97469i 0.0242349 + 0.263021i
\(517\) 54.7030 14.6576i 2.40584 0.644642i
\(518\) 4.49303 1.20390i 0.197413 0.0528965i
\(519\) −4.38551 + 3.10102i −0.192502 + 0.136120i
\(520\) 0 0
\(521\) 29.4449i 1.29000i −0.764181 0.645001i \(-0.776857\pi\)
0.764181 0.645001i \(-0.223143\pi\)
\(522\) 8.51727 4.06778i 0.372791 0.178042i
\(523\) −1.77526 + 1.77526i −0.0776265 + 0.0776265i −0.744854 0.667228i \(-0.767481\pi\)
0.667228 + 0.744854i \(0.267481\pi\)
\(524\) 5.26758 + 9.12372i 0.230116 + 0.398572i
\(525\) 0 0
\(526\) 6.34847 10.9959i 0.276806 0.479443i
\(527\) −5.12409 19.1234i −0.223209 0.833027i
\(528\) −3.77489 10.2244i −0.164281 0.444959i
\(529\) −19.0526 + 11.0000i −0.828372 + 0.478261i
\(530\) 0 0
\(531\) 33.3939 + 11.8065i 1.44917 + 0.512359i
\(532\) −1.20204 1.20204i −0.0521151 0.0521151i
\(533\) 3.51888 13.1326i 0.152420 0.568838i
\(534\) −2.36773 3.34847i −0.102461 0.144902i
\(535\) 0 0
\(536\) −3.27526 1.89097i −0.141469 0.0816774i
\(537\) 23.4506 + 19.4937i 1.01197 + 0.841217i
\(538\) 4.54308 + 1.21731i 0.195866 + 0.0524822i
\(539\) −36.4838 −1.57147
\(540\) 0 0
\(541\) −25.9444 −1.11544 −0.557718 0.830030i \(-0.688323\pi\)
−0.557718 + 0.830030i \(0.688323\pi\)
\(542\) 15.4987 + 4.15286i 0.665725 + 0.178380i
\(543\) −14.0528 11.6816i −0.603062 0.501305i
\(544\) −3.85337 2.22474i −0.165212 0.0953851i
\(545\) 0 0
\(546\) 3.79796 + 5.37113i 0.162538 + 0.229863i
\(547\) 5.53567 20.6594i 0.236688 0.883332i −0.740693 0.671844i \(-0.765502\pi\)
0.977381 0.211488i \(-0.0678308\pi\)
\(548\) 1.55708 + 1.55708i 0.0665151 + 0.0665151i
\(549\) −12.4261 + 10.6237i −0.530335 + 0.453410i
\(550\) 0 0
\(551\) −4.22474 + 2.43916i −0.179980 + 0.103912i
\(552\) 0.599900 + 1.62484i 0.0255335 + 0.0691580i
\(553\) −0.695075 2.59405i −0.0295576 0.110310i
\(554\) −7.14250 + 12.3712i −0.303456 + 0.525601i
\(555\) 0 0
\(556\) −6.44949 11.1708i −0.273519 0.473749i
\(557\) −16.3670 + 16.3670i −0.693492 + 0.693492i −0.962999 0.269507i \(-0.913139\pi\)
0.269507 + 0.962999i \(0.413139\pi\)
\(558\) −11.0046 7.55513i −0.465863 0.319834i
\(559\) 12.0000i 0.507546i
\(560\) 0 0
\(561\) −39.5959 + 27.9985i −1.67174 + 1.18210i
\(562\) 0.169011 0.0452863i 0.00712928 0.00191029i
\(563\) 33.1781 8.89004i 1.39829 0.374670i 0.520559 0.853826i \(-0.325724\pi\)
0.877730 + 0.479155i \(0.159057\pi\)
\(564\) −1.43027 15.5227i −0.0602251 0.653624i
\(565\) 0 0
\(566\) 6.89610i 0.289864i
\(567\) −1.04128 9.81229i −0.0437297 0.412077i
\(568\) −0.449490 + 0.449490i −0.0188602 + 0.0188602i
\(569\) −13.0458 22.5959i −0.546907 0.947270i −0.998484 0.0550383i \(-0.982472\pi\)
0.451578 0.892232i \(-0.350861\pi\)
\(570\) 0 0
\(571\) −13.5505 + 23.4702i −0.567071 + 0.982196i 0.429782 + 0.902932i \(0.358590\pi\)
−0.996854 + 0.0792637i \(0.974743\pi\)
\(572\) −5.64173 21.0552i −0.235892 0.880363i
\(573\) −5.66971 0.972768i −0.236855 0.0406380i
\(574\) −3.72656 + 2.15153i −0.155544 + 0.0898032i
\(575\) 0 0
\(576\) −2.94949 + 0.548188i −0.122895 + 0.0228412i
\(577\) 17.0000 + 17.0000i 0.707719 + 0.707719i 0.966055 0.258336i \(-0.0831741\pi\)
−0.258336 + 0.966055i \(0.583174\pi\)
\(578\) −0.724165 + 2.70262i −0.0301213 + 0.112414i
\(579\) 12.5529 27.2474i 0.521683 1.13237i
\(580\) 0 0
\(581\) 0.522704 + 0.301783i 0.0216854 + 0.0125201i
\(582\) −18.1509 + 6.70139i −0.752378 + 0.277782i
\(583\) −56.8211 15.2252i −2.35329 0.630562i
\(584\) 4.09978 0.169650
\(585\) 0 0
\(586\) 22.0454 0.910687
\(587\) −29.9876 8.03514i −1.23772 0.331646i −0.420138 0.907460i \(-0.638019\pi\)
−0.817581 + 0.575814i \(0.804685\pi\)
\(588\) −1.69818 + 9.89774i −0.0700319 + 0.408176i
\(589\) 5.97469 + 3.44949i 0.246183 + 0.142134i
\(590\) 0 0
\(591\) 16.8990 1.55708i 0.695131 0.0640496i
\(592\) −1.09808 + 4.09808i −0.0451307 + 0.168430i
\(593\) −10.0745 10.0745i −0.413709 0.413709i 0.469320 0.883028i \(-0.344499\pi\)
−0.883028 + 0.469320i \(0.844499\pi\)
\(594\) −8.02458 + 31.6969i −0.329252 + 1.30054i
\(595\) 0 0
\(596\) −11.1742 + 6.45145i −0.457714 + 0.264262i
\(597\) −3.93115 + 4.72911i −0.160891 + 0.193549i
\(598\) 0.896575 + 3.34607i 0.0366637 + 0.136831i
\(599\) 16.8991 29.2702i 0.690480 1.19595i −0.281201 0.959649i \(-0.590733\pi\)
0.971681 0.236297i \(-0.0759339\pi\)
\(600\) 0 0
\(601\) −17.3485 30.0484i −0.707659 1.22570i −0.965723 0.259573i \(-0.916418\pi\)
0.258065 0.966128i \(-0.416915\pi\)
\(602\) 2.68556 2.68556i 0.109455 0.109455i
\(603\) 4.88964 + 10.2381i 0.199122 + 0.416928i
\(604\) 21.5959i 0.878725i
\(605\) 0 0
\(606\) −2.00000 0.921404i −0.0812444 0.0374295i
\(607\) 21.4114 5.73717i 0.869062 0.232864i 0.203380 0.979100i \(-0.434807\pi\)
0.665682 + 0.746235i \(0.268141\pi\)
\(608\) 1.49768 0.401302i 0.0607389 0.0162749i
\(609\) −5.42650 2.50000i −0.219893 0.101305i
\(610\) 0 0
\(611\) 31.1769i 1.26128i
\(612\) 5.75272 + 12.0452i 0.232540 + 0.486900i
\(613\) 12.7980 12.7980i 0.516905 0.516905i −0.399729 0.916633i \(-0.630896\pi\)
0.916633 + 0.399729i \(0.130896\pi\)
\(614\) 0.476756 + 0.825765i 0.0192403 + 0.0333252i
\(615\) 0 0
\(616\) −3.44949 + 5.97469i −0.138984 + 0.240727i
\(617\) −1.83788 6.85906i −0.0739902 0.276135i 0.919012 0.394229i \(-0.128988\pi\)
−0.993002 + 0.118094i \(0.962322\pi\)
\(618\) −4.53930 + 5.46070i −0.182597 + 0.219662i
\(619\) 21.4275 12.3712i 0.861244 0.497239i −0.00318471 0.999995i \(-0.501014\pi\)
0.864429 + 0.502756i \(0.167680\pi\)
\(620\) 0 0
\(621\) 1.27526 5.03723i 0.0511742 0.202137i
\(622\) 14.5505 + 14.5505i 0.583422 + 0.583422i
\(623\) −0.671873 + 2.50746i −0.0269180 + 0.100459i
\(624\) −5.97469 + 0.550510i −0.239179 + 0.0220380i
\(625\) 0 0
\(626\) −4.34847 2.51059i −0.173800 0.100343i
\(627\) 2.85765 16.6556i 0.114124 0.665161i
\(628\) 5.94012 + 1.59165i 0.237037 + 0.0635138i
\(629\) 18.8776 0.752699
\(630\) 0 0
\(631\) −12.8990 −0.513500 −0.256750 0.966478i \(-0.582652\pi\)
−0.256750 + 0.966478i \(0.582652\pi\)
\(632\) 2.36603 + 0.633975i 0.0941154 + 0.0252182i
\(633\) −30.7079 + 11.3375i −1.22053 + 0.450625i
\(634\) 0.953512 + 0.550510i 0.0378688 + 0.0218636i
\(635\) 0 0
\(636\) −6.77526 + 14.7064i −0.268656 + 0.583146i
\(637\) −5.19831 + 19.4003i −0.205964 + 0.768670i
\(638\) 13.9993 + 13.9993i 0.554236 + 0.554236i
\(639\) 1.87492 0.348469i 0.0741705 0.0137852i
\(640\) 0 0
\(641\) −7.74745 + 4.47299i −0.306006 + 0.176673i −0.645138 0.764066i \(-0.723200\pi\)
0.339132 + 0.940739i \(0.389867\pi\)
\(642\) −8.95796 1.53694i −0.353542 0.0606583i
\(643\) 8.22539 + 30.6976i 0.324378 + 1.21059i 0.914936 + 0.403599i \(0.132241\pi\)
−0.590558 + 0.806995i \(0.701092\pi\)
\(644\) 0.548188 0.949490i 0.0216016 0.0374151i
\(645\) 0 0
\(646\) −3.44949 5.97469i −0.135718 0.235071i
\(647\) 24.9558 24.9558i 0.981114 0.981114i −0.0187105 0.999825i \(-0.505956\pi\)
0.999825 + 0.0187105i \(0.00595608\pi\)
\(648\) 8.22558 + 3.65237i 0.323131 + 0.143479i
\(649\) 74.2929i 2.91625i
\(650\) 0 0
\(651\) 0.775255 + 8.41385i 0.0303846 + 0.329765i
\(652\) 0.614014 0.164525i 0.0240467 0.00644328i
\(653\) 20.8162 5.57768i 0.814601 0.218272i 0.172616 0.984989i \(-0.444778\pi\)
0.641985 + 0.766718i \(0.278111\pi\)
\(654\) −28.7771 + 20.3485i −1.12527 + 0.795688i
\(655\) 0 0
\(656\) 3.92480i 0.153238i
\(657\) −10.1397 6.96132i −0.395587 0.271587i
\(658\) −6.97730 + 6.97730i −0.272003 + 0.272003i
\(659\) 5.65685 + 9.79796i 0.220360 + 0.381674i 0.954917 0.296872i \(-0.0959435\pi\)
−0.734557 + 0.678546i \(0.762610\pi\)
\(660\) 0 0
\(661\) 15.3485 26.5843i 0.596986 1.03401i −0.396277 0.918131i \(-0.629698\pi\)
0.993263 0.115880i \(-0.0369687\pi\)
\(662\) −1.15161 4.29788i −0.0447587 0.167042i
\(663\) 9.24656 + 25.0445i 0.359106 + 0.972648i
\(664\) −0.476756 + 0.275255i −0.0185017 + 0.0106820i
\(665\) 0 0
\(666\) 9.67423 8.27098i 0.374869 0.320494i
\(667\) −2.22474 2.22474i −0.0861425 0.0861425i
\(668\) −2.79472 + 10.4300i −0.108131 + 0.403550i
\(669\) 8.31031 + 11.7526i 0.321295 + 0.454380i
\(670\) 0 0
\(671\) −29.6969 17.1455i −1.14644 0.661896i
\(672\) 1.46032 + 1.21391i 0.0563331 + 0.0468278i
\(673\) −15.7783 4.22778i −0.608208 0.162969i −0.0584468 0.998291i \(-0.518615\pi\)
−0.549762 + 0.835322i \(0.685281\pi\)
\(674\) 30.8270 1.18741
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) −6.18587 1.65750i −0.237742 0.0637028i 0.137981 0.990435i \(-0.455939\pi\)
−0.375723 + 0.926732i \(0.622606\pi\)
\(678\) −18.3782 15.2772i −0.705811 0.586717i
\(679\) 10.6066 + 6.12372i 0.407044 + 0.235007i
\(680\) 0 0
\(681\) 15.1010 + 21.3561i 0.578672 + 0.818366i
\(682\) 7.24656 27.0445i 0.277485 1.03559i
\(683\) −13.8564 13.8564i −0.530201 0.530201i 0.390431 0.920632i \(-0.372326\pi\)
−0.920632 + 0.390431i \(0.872326\pi\)
\(684\) −4.38551 1.55051i −0.167684 0.0592852i
\(685\) 0 0
\(686\) 12.1515 7.01569i 0.463948 0.267860i
\(687\) 9.80745 + 26.5637i 0.374178 + 1.01347i
\(688\) 0.896575 + 3.34607i 0.0341816 + 0.127568i
\(689\) −16.1920 + 28.0454i −0.616867 + 1.06844i
\(690\) 0 0
\(691\) −16.4722 28.5307i −0.626632 1.08536i −0.988223 0.153021i \(-0.951100\pi\)
0.361591 0.932337i \(-0.382234\pi\)
\(692\) −2.19275 + 2.19275i −0.0833559 + 0.0833559i
\(693\) 18.6763 8.91964i 0.709453 0.338829i
\(694\) 4.20204i 0.159507i
\(695\) 0 0
\(696\) 4.44949 3.14626i 0.168657 0.119259i
\(697\) −16.8683 + 4.51985i −0.638933 + 0.171202i
\(698\) 14.5327 3.89404i 0.550073 0.147392i
\(699\) 2.47127 + 26.8207i 0.0934719 + 1.01445i
\(700\) 0 0
\(701\) 23.9309i 0.903857i 0.892054 + 0.451928i \(0.149264\pi\)
−0.892054 + 0.451928i \(0.850736\pi\)
\(702\) 15.7116 + 8.78335i 0.592994 + 0.331506i
\(703\) −4.65153 + 4.65153i −0.175436 + 0.175436i
\(704\) −3.14626 5.44949i −0.118579 0.205385i
\(705\) 0 0
\(706\) −17.1464 + 29.6985i −0.645314 + 1.11772i
\(707\) 0.360762 + 1.34638i 0.0135678 + 0.0506359i
\(708\) 20.1550 + 3.45805i 0.757471 + 0.129961i
\(709\) 38.4069 22.1742i 1.44240 0.832771i 0.444392 0.895833i \(-0.353420\pi\)
0.998010 + 0.0630617i \(0.0200865\pi\)
\(710\) 0 0
\(711\) −4.77526 5.58542i −0.179086 0.209470i
\(712\) −1.67423 1.67423i −0.0627446 0.0627446i
\(713\) −1.15161 + 4.29788i −0.0431282 + 0.160957i
\(714\) 3.53553 7.67423i 0.132314 0.287201i
\(715\) 0 0
\(716\) 15.2474 + 8.80312i 0.569824 + 0.328988i
\(717\) −27.5745 + 10.1806i −1.02979 + 0.380203i
\(718\) 16.8683 + 4.51985i 0.629520 + 0.168679i
\(719\) 32.5269 1.21305 0.606525 0.795065i \(-0.292563\pi\)
0.606525 + 0.795065i \(0.292563\pi\)
\(720\) 0 0
\(721\) 4.49490 0.167399
\(722\) −16.0304 4.29534i −0.596591 0.159856i
\(723\) 5.56497 32.4350i 0.206964 1.20627i
\(724\) −9.13701 5.27526i −0.339574 0.196053i
\(725\) 0 0
\(726\) −49.3207 + 4.54442i −1.83046 + 0.168659i
\(727\) 8.11447 30.2836i 0.300949 1.12316i −0.635428 0.772160i \(-0.719176\pi\)
0.936377 0.350996i \(-0.114157\pi\)
\(728\) 2.68556 + 2.68556i 0.0995336 + 0.0995336i
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) 0 0
\(731\) 13.3485 7.70674i 0.493711 0.285044i
\(732\) −6.03371 + 7.25845i −0.223012 + 0.268280i
\(733\) 3.71385 + 13.8603i 0.137174 + 0.511941i 0.999979 + 0.00640470i \(0.00203869\pi\)
−0.862805 + 0.505536i \(0.831295\pi\)
\(734\) 4.87832 8.44949i 0.180062 0.311876i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) −16.8277 + 16.8277i −0.619856 + 0.619856i
\(738\) −6.66422 + 9.70695i −0.245313 + 0.357318i
\(739\) 24.9444i 0.917594i −0.888541 0.458797i \(-0.848280\pi\)
0.888541 0.458797i \(-0.151720\pi\)
\(740\) 0 0
\(741\) −8.44949 3.89270i −0.310400 0.143002i
\(742\) 9.90020 2.65275i 0.363448 0.0973855i
\(743\) −0.0975783 + 0.0261460i −0.00357980 + 0.000959205i −0.260609 0.965445i \(-0.583923\pi\)
0.257029 + 0.966404i \(0.417257\pi\)
\(744\) −6.99964 3.22474i −0.256619 0.118225i
\(745\) 0 0
\(746\) 20.2918i 0.742936i
\(747\) 1.64650 + 0.128751i 0.0602425 + 0.00471074i
\(748\) −19.7980 + 19.7980i −0.723885 + 0.723885i
\(749\) 2.87659 + 4.98240i 0.105108 + 0.182053i
\(750\) 0 0
\(751\) 4.34847 7.53177i 0.158678 0.274838i −0.775714 0.631084i \(-0.782610\pi\)
0.934392 + 0.356246i \(0.115944\pi\)
\(752\) −2.32937 8.69333i −0.0849434 0.317013i
\(753\) 12.3684 14.8790i 0.450731 0.542222i
\(754\) 9.43879 5.44949i 0.343741 0.198459i
\(755\) 0 0
\(756\) −1.55051 5.48188i −0.0563915 0.199374i
\(757\) 22.0454 + 22.0454i 0.801254 + 0.801254i 0.983292 0.182038i \(-0.0582693\pi\)
−0.182038 + 0.983292i \(0.558269\pi\)
\(758\) −1.72154 + 6.42489i −0.0625293 + 0.233362i
\(759\) 10.8530 1.00000i 0.393939 0.0362977i
\(760\) 0 0
\(761\) −15.3990 8.89060i −0.558213 0.322284i 0.194215 0.980959i \(-0.437784\pi\)
−0.752428 + 0.658675i \(0.771117\pi\)
\(762\) −5.85024 + 34.0977i −0.211932 + 1.23523i
\(763\) 21.5494 + 5.77414i 0.780141 + 0.209038i
\(764\) −3.32124 −0.120158
\(765\) 0 0
\(766\) 27.7980 1.00438
\(767\) 39.5054 + 10.5854i 1.42646 + 0.382218i
\(768\) −1.62484 + 0.599900i −0.0586315 + 0.0216470i
\(769\) −17.0580 9.84847i −0.615129 0.355145i 0.159841 0.987143i \(-0.448902\pi\)
−0.774970 + 0.631998i \(0.782235\pi\)
\(770\) 0 0
\(771\) −18.8763 + 40.9729i −0.679812 + 1.47560i
\(772\) 4.48288 16.7303i 0.161342 0.602138i
\(773\) −3.11416 3.11416i −0.112008 0.112008i 0.648881 0.760890i \(-0.275237\pi\)
−0.760890 + 0.648881i \(0.775237\pi\)
\(774\) 3.46410 9.79796i 0.124515 0.352180i
\(775\) 0 0
\(776\) −9.67423 + 5.58542i −0.347285 + 0.200505i
\(777\) −7.94066 1.36240i −0.284870 0.0488759i
\(778\) −1.45579 5.43309i −0.0521927 0.194786i
\(779\) 3.04272 5.27015i 0.109017 0.188823i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) 3.14626 3.14626i 0.112510 0.112510i
\(783\) −16.3469 + 0.226311i −0.584191 + 0.00808771i
\(784\) 5.79796i 0.207070i
\(785\) 0 0
\(786\) −1.67423 18.1705i −0.0597180 0.648120i
\(787\) 3.96008 1.06110i 0.141162 0.0378241i −0.187546 0.982256i \(-0.560053\pi\)
0.328708 + 0.944432i \(0.393387\pi\)
\(788\) 9.46410 2.53590i 0.337145 0.0903376i
\(789\) −17.9562 + 12.6969i −0.639257 + 0.452023i
\(790\) 0 0
\(791\) 15.1278i 0.537881i
\(792\) −1.47167 + 18.8201i −0.0522933 + 0.668744i
\(793\) −13.3485 + 13.3485i −0.474018 + 0.474018i
\(794\) 10.9244 + 18.9217i 0.387694 + 0.671505i
\(795\) 0 0
\(796\) −1.77526 + 3.07483i −0.0629222 + 0.108985i
\(797\) 5.22867 + 19.5137i 0.185209 + 0.691210i 0.994586 + 0.103920i \(0.0331385\pi\)
−0.809377 + 0.587290i \(0.800195\pi\)
\(798\) 1.01980 + 2.76214i 0.0361004 + 0.0977788i
\(799\) −34.6803 + 20.0227i −1.22690 + 0.708352i
\(800\) 0 0
\(801\) 1.29796 + 6.98358i 0.0458611 + 0.246753i
\(802\) −18.2474 18.2474i −0.644340 0.644340i
\(803\) 6.67700 24.9189i 0.235626 0.879369i
\(804\) 3.78194 + 5.34847i 0.133379 + 0.188626i
\(805\) 0 0
\(806\) −13.3485 7.70674i −0.470180 0.271458i
\(807\) −6.26462 5.20757i −0.220525 0.183315i
\(808\) −1.22803 0.329049i −0.0432019 0.0115759i
\(809\) −54.0901 −1.90171 −0.950853 0.309644i \(-0.899790\pi\)
−0.950853 + 0.309644i \(0.899790\pi\)
\(810\) 0 0
\(811\) 43.6413 1.53245 0.766227 0.642570i \(-0.222132\pi\)
0.766227 + 0.642570i \(0.222132\pi\)
\(812\) −3.33195 0.892794i −0.116929 0.0313309i
\(813\) −21.3717 17.7656i −0.749538 0.623066i
\(814\) 23.1202 + 13.3485i 0.810364 + 0.467864i
\(815\) 0 0
\(816\) 4.44949 + 6.29253i 0.155763 + 0.220283i
\(817\) −1.39015 + 5.18811i −0.0486352 + 0.181509i
\(818\) −13.5065 13.5065i −0.472242 0.472242i
\(819\) −2.08200 11.2020i −0.0727508 0.391431i
\(820\) 0 0
\(821\) −22.3207 + 12.8868i −0.778997 + 0.449754i −0.836075 0.548616i \(-0.815155\pi\)
0.0570780 + 0.998370i \(0.481822\pi\)
\(822\) −1.32101 3.57797i −0.0460754 0.124796i
\(823\) 12.5807 + 46.9519i 0.438536 + 1.63664i 0.732459 + 0.680811i \(0.238373\pi\)
−0.293923 + 0.955829i \(0.594961\pi\)
\(824\) −2.04989 + 3.55051i −0.0714112 + 0.123688i
\(825\) 0 0
\(826\) −6.47219 11.2102i −0.225196 0.390052i
\(827\) 27.3235 27.3235i 0.950133 0.950133i −0.0486816 0.998814i \(-0.515502\pi\)
0.998814 + 0.0486816i \(0.0155020\pi\)
\(828\) 0.233875 2.99087i 0.00812772 0.103940i
\(829\) 15.4495i 0.536583i −0.963338 0.268291i \(-0.913541\pi\)
0.963338 0.268291i \(-0.0864590\pi\)
\(830\) 0 0
\(831\) 20.2020 14.2850i 0.700801 0.495541i
\(832\) −3.34607 + 0.896575i −0.116004 + 0.0310832i
\(833\) 24.9189 6.67700i 0.863389 0.231344i
\(834\) 2.04989 + 22.2474i 0.0709818 + 0.770366i
\(835\) 0 0
\(836\) 9.75663i 0.337440i
\(837\) 11.8362 + 19.8608i 0.409118 + 0.686488i
\(838\) −8.44949 + 8.44949i −0.291883 + 0.291883i
\(839\) −10.1459 17.5732i −0.350275 0.606695i 0.636022 0.771671i \(-0.280579\pi\)
−0.986298 + 0.164976i \(0.947245\pi\)
\(840\) 0 0
\(841\) 9.55051 16.5420i 0.329328 0.570413i
\(842\) −3.85614 14.3913i −0.132891 0.495957i
\(843\) −0.298697 0.0512483i −0.0102877 0.00176509i
\(844\) −16.3670 + 9.44949i −0.563375 + 0.325265i
\(845\) 0 0
\(846\) −9.00000 + 25.4558i −0.309426 + 0.875190i
\(847\) 22.1691 + 22.1691i 0.761740 + 0.761740i
\(848\) −2.41956 + 9.02993i −0.0830881 + 0.310089i
\(849\) 4.99791 10.8485i 0.171528 0.372319i
\(850\) 0 0
\(851\) −3.67423 2.12132i −0.125951 0.0727179i
\(852\) 1.03287 0.381341i 0.0353856 0.0130645i
\(853\) −35.8547 9.60723i −1.22764 0.328945i −0.413980 0.910286i \(-0.635862\pi\)
−0.813660 + 0.581340i \(0.802528\pi\)
\(854\) 5.97469 0.204450
\(855\) 0 0
\(856\) −5.24745 −0.179354
\(857\) −3.66855 0.982984i −0.125315 0.0335781i 0.195616 0.980680i \(-0.437329\pi\)
−0.320932 + 0.947102i \(0.603996\pi\)
\(858\) −6.38447 + 37.2114i −0.217962 + 1.27038i
\(859\) −2.16064 1.24745i −0.0737202 0.0425624i 0.462687 0.886522i \(-0.346885\pi\)
−0.536407 + 0.843959i \(0.680219\pi\)
\(860\) 0 0
\(861\) 7.42168 0.683837i 0.252930 0.0233051i
\(862\) −4.02628 + 15.0263i −0.137136 + 0.511797i
\(863\) −27.7842 27.7842i −0.945787 0.945787i 0.0528175 0.998604i \(-0.483180\pi\)
−0.998604 + 0.0528175i \(0.983180\pi\)
\(864\) 5.03723 + 1.27526i 0.171370 + 0.0433851i
\(865\) 0 0
\(866\) 10.4722 6.04612i 0.355860 0.205456i
\(867\) 3.09792 3.72674i 0.105211 0.126567i
\(868\) 1.26260 + 4.71209i 0.0428555 + 0.159939i
\(869\) 7.70674 13.3485i 0.261433 0.452816i
\(870\) 0 0
\(871\) 6.55051 + 11.3458i 0.221956 + 0.384438i
\(872\) −14.3885 + 14.3885i −0.487257 + 0.487257i
\(873\) 33.4105 + 2.61258i 1.13078 + 0.0884225i
\(874\) 1.55051i 0.0524468i
\(875\) 0 0
\(876\) −6.44949 2.97129i −0.217908 0.100391i
\(877\) 7.85813 2.10558i 0.265350 0.0711004i −0.123691 0.992321i \(-0.539473\pi\)
0.389041 + 0.921220i \(0.372806\pi\)
\(878\) −9.85441 + 2.64048i −0.332570 + 0.0891120i
\(879\) −34.6803 15.9773i −1.16974 0.538901i
\(880\) 0 0
\(881\) 58.3006i 1.96420i 0.188368 + 0.982098i \(0.439680\pi\)
−0.188368 + 0.982098i \(0.560320\pi\)
\(882\) 9.84480 14.3397i 0.331492 0.482843i
\(883\) 40.2702 40.2702i 1.35520 1.35520i 0.475463 0.879736i \(-0.342281\pi\)
0.879736 0.475463i \(-0.157719\pi\)
\(884\) 7.70674 + 13.3485i 0.259206 + 0.448958i
\(885\) 0 0
\(886\) 0.275255 0.476756i 0.00924738 0.0160169i
\(887\) −7.19464 26.8508i −0.241572 0.901561i −0.975075 0.221874i \(-0.928783\pi\)
0.733503 0.679686i \(-0.237884\pi\)
\(888\) 4.69748 5.65099i 0.157637 0.189635i
\(889\) 18.9651 10.9495i 0.636068 0.367234i
\(890\) 0 0
\(891\) 35.5959 44.0477i 1.19251 1.47565i
\(892\) 5.87628 + 5.87628i 0.196752 + 0.196752i
\(893\) 3.61171 13.4791i 0.120861 0.451061i
\(894\) 22.2542 2.05051i 0.744292 0.0685793i
\(895\) 0 0
\(896\) 0.949490 + 0.548188i 0.0317202 + 0.0183137i
\(897\) 1.01461 5.91359i 0.0338769 0.197449i
\(898\) −20.9664 5.61793i −0.699658 0.187473i
\(899\) 13.9993 0.466902
\(900\) 0 0
\(901\) 41.5959 1.38576
\(902\) −23.8554 6.39204i −0.794298 0.212832i
\(903\) −6.17109 + 2.27840i −0.205361 + 0.0758203i
\(904\) −11.9494 6.89898i −0.397431 0.229457i
\(905\) 0 0
\(906\) 15.6515 33.9732i 0.519987 1.12869i
\(907\) −1.71089 + 6.38512i −0.0568091 + 0.212015i −0.988496 0.151248i \(-0.951671\pi\)
0.931687 + 0.363263i \(0.118337\pi\)
\(908\) 10.6780 + 10.6780i 0.354363 + 0.354363i
\(909\) 2.47848 + 2.89898i 0.0822061 + 0.0961531i
\(910\) 0 0
\(911\) 6.12372 3.53553i 0.202888 0.117137i −0.395114 0.918632i \(-0.629295\pi\)
0.598002 + 0.801495i \(0.295962\pi\)
\(912\) −2.64689 0.454134i −0.0876472 0.0150379i
\(913\) 0.896575 + 3.34607i 0.0296723 + 0.110739i
\(914\) 3.07483 5.32577i 0.101706 0.176161i
\(915\) 0 0
\(916\) 8.17423 + 14.1582i 0.270084 + 0.467800i
\(917\) −8.16744 + 8.16744i −0.269713 + 0.269713i
\(918\) −0.320053 23.1180i −0.0105633 0.763008i
\(919\) 27.3485i 0.902143i 0.892488 + 0.451071i \(0.148958\pi\)
−0.892488 + 0.451071i \(0.851042\pi\)
\(920\) 0 0
\(921\) −0.151531 1.64456i −0.00499311 0.0541902i
\(922\) −18.2654 + 4.89419i −0.601538 + 0.161182i
\(923\) 2.12701 0.569930i 0.0700113 0.0187595i
\(924\) 9.75663 6.89898i 0.320970 0.226960i
\(925\) 0 0
\(926\) 33.0197i 1.08510i
\(927\) 11.0985 5.30057i 0.364524 0.174094i
\(928\) 2.22474 2.22474i 0.0730308 0.0730308i
\(929\) −23.9309 41.4495i −0.785147 1.35991i −0.928912 0.370302i \(-0.879254\pi\)
0.143765 0.989612i \(-0.454079\pi\)
\(930\) 0 0
\(931\) −4.49490 + 7.78539i −0.147314 + 0.255156i
\(932\) 4.02477 + 15.0206i 0.131836 + 0.492017i
\(933\) −12.3445 33.4353i −0.404140 1.09462i
\(934\) 3.46410 2.00000i 0.113349 0.0654420i
\(935\) 0 0
\(936\) 9.79796 + 3.46410i 0.320256 + 0.113228i
\(937\) 12.8990 + 12.8990i 0.421391 + 0.421391i 0.885683 0.464291i \(-0.153691\pi\)
−0.464291 + 0.885683i \(0.653691\pi\)
\(938\) 1.07317 4.00514i 0.0350404 0.130773i
\(939\) 5.02118 + 7.10102i 0.163860 + 0.231733i
\(940\) 0 0
\(941\) 5.47730 + 3.16232i 0.178555 + 0.103089i 0.586613 0.809867i \(-0.300461\pi\)
−0.408059 + 0.912956i \(0.633794\pi\)
\(942\) −8.19105 6.80895i −0.266879 0.221847i
\(943\) 3.79107 + 1.01581i 0.123454 + 0.0330795i
\(944\) 11.8065 0.384269
\(945\) 0 0
\(946\) 21.7980 0.708713
\(947\) −39.6468 10.6233i −1.28835 0.345212i −0.451316 0.892364i \(-0.649045\pi\)
−0.837033 + 0.547152i \(0.815712\pi\)
\(948\) −3.26260 2.71209i −0.105964 0.0880846i
\(949\) −12.2993 7.10102i −0.399253 0.230509i
\(950\) 0 0
\(951\) −1.10102 1.55708i −0.0357030 0.0504917i
\(952\) 1.26260 4.71209i 0.0409211 0.152720i
\(953\) 19.6561 + 19.6561i 0.636724 + 0.636724i 0.949746 0.313022i \(-0.101341\pi\)
−0.313022 + 0.949746i \(0.601341\pi\)
\(954\) 21.3167 18.2247i 0.690155 0.590048i
\(955\) 0 0
\(956\) −14.6969 + 8.48528i −0.475333 + 0.274434i
\(957\) −11.8768 32.1686i −0.383923 1.03986i
\(958\) 1.83013 + 6.83013i 0.0591287 + 0.220671i
\(959\) −1.20713 + 2.09082i −0.0389804 + 0.0675159i
\(960\) 0 0
\(961\) 5.60102 + 9.70125i 0.180678 + 0.312944i
\(962\) 10.3923 10.3923i 0.335061 0.335061i
\(963\) 12.9782 + 8.91005i 0.418215 + 0.287122i
\(964\) 19.0000i 0.611949i
\(965\) 0 0
\(966\) −1.55051 + 1.09638i −0.0498868 + 0.0352753i
\(967\) −48.7319 + 13.0577i −1.56711 + 0.419907i −0.934907 0.354894i \(-0.884517\pi\)
−0.632206 + 0.774800i \(0.717850\pi\)
\(968\) −27.6215 + 7.40117i −0.887790 + 0.237883i
\(969\) 1.09638 + 11.8990i 0.0352207 + 0.382250i
\(970\) 0 0
\(971\) 49.2117i 1.57928i −0.613570 0.789640i \(-0.710267\pi\)
0.613570 0.789640i \(-0.289733\pi\)
\(972\) −10.2929 11.7071i −0.330145 0.375506i
\(973\) 10.0000 10.0000i 0.320585 0.320585i
\(974\) −8.48528 14.6969i −0.271886 0.470920i
\(975\) 0 0
\(976\) −2.72474 + 4.71940i −0.0872170 + 0.151064i
\(977\) −10.9985 41.0469i −0.351873 1.31321i −0.884374 0.466778i \(-0.845415\pi\)
0.532502 0.846429i \(-0.321252\pi\)
\(978\) −1.08516 0.186185i −0.0346997 0.00595353i
\(979\) −12.9029 + 7.44949i −0.412378 + 0.238087i
\(980\) 0 0
\(981\) 60.0176 11.1548i 1.91621 0.356145i
\(982\) −0.202041 0.202041i −0.00644739 0.00644739i
\(983\) −12.1122 + 45.2034i −0.386319 + 1.44176i 0.449757 + 0.893151i \(0.351510\pi\)
−0.836077 + 0.548612i \(0.815156\pi\)
\(984\) −2.84448 + 6.17423i −0.0906787 + 0.196827i
\(985\) 0 0
\(986\) −12.1237 6.99964i −0.386098 0.222914i
\(987\) 16.0330 5.91945i 0.510335 0.188418i
\(988\) −5.18811 1.39015i −0.165056 0.0442265i
\(989\) −3.46410 −0.110152
\(990\) 0 0
\(991\) −56.7423 −1.80248 −0.901240 0.433320i \(-0.857342\pi\)
−0.901240 + 0.433320i \(0.857342\pi\)
\(992\) −4.29788 1.15161i −0.136458 0.0365637i
\(993\) −1.30323 + 7.59575i −0.0413566 + 0.241044i
\(994\) −0.603566 0.348469i −0.0191440 0.0110528i
\(995\) 0 0
\(996\) 0.949490 0.0874863i 0.0300857 0.00277211i
\(997\) 10.7053 39.9528i 0.339041 1.26532i −0.560381 0.828235i \(-0.689345\pi\)
0.899422 0.437082i \(-0.143988\pi\)
\(998\) −6.29253 6.29253i −0.199187 0.199187i
\(999\) −21.2132 + 6.00000i −0.671156 + 0.189832i
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 450.2.p.a.257.1 8
3.2 odd 2 1350.2.q.g.557.2 8
5.2 odd 4 90.2.l.a.23.2 8
5.3 odd 4 inner 450.2.p.a.293.1 8
5.4 even 2 90.2.l.a.77.2 yes 8
9.2 odd 6 inner 450.2.p.a.407.1 8
9.7 even 3 1350.2.q.g.1007.2 8
15.2 even 4 270.2.m.a.233.1 8
15.8 even 4 1350.2.q.g.1043.2 8
15.14 odd 2 270.2.m.a.17.1 8
20.7 even 4 720.2.cu.a.113.2 8
20.19 odd 2 720.2.cu.a.257.2 8
45.2 even 12 90.2.l.a.83.2 yes 8
45.4 even 6 810.2.f.b.647.1 8
45.7 odd 12 270.2.m.a.143.1 8
45.14 odd 6 810.2.f.b.647.4 8
45.22 odd 12 810.2.f.b.323.3 8
45.29 odd 6 90.2.l.a.47.2 yes 8
45.32 even 12 810.2.f.b.323.2 8
45.34 even 6 270.2.m.a.197.1 8
45.38 even 12 inner 450.2.p.a.443.1 8
45.43 odd 12 1350.2.q.g.143.2 8
180.47 odd 12 720.2.cu.a.353.2 8
180.119 even 6 720.2.cu.a.497.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.l.a.23.2 8 5.2 odd 4
90.2.l.a.47.2 yes 8 45.29 odd 6
90.2.l.a.77.2 yes 8 5.4 even 2
90.2.l.a.83.2 yes 8 45.2 even 12
270.2.m.a.17.1 8 15.14 odd 2
270.2.m.a.143.1 8 45.7 odd 12
270.2.m.a.197.1 8 45.34 even 6
270.2.m.a.233.1 8 15.2 even 4
450.2.p.a.257.1 8 1.1 even 1 trivial
450.2.p.a.293.1 8 5.3 odd 4 inner
450.2.p.a.407.1 8 9.2 odd 6 inner
450.2.p.a.443.1 8 45.38 even 12 inner
720.2.cu.a.113.2 8 20.7 even 4
720.2.cu.a.257.2 8 20.19 odd 2
720.2.cu.a.353.2 8 180.47 odd 12
720.2.cu.a.497.2 8 180.119 even 6
810.2.f.b.323.2 8 45.32 even 12
810.2.f.b.323.3 8 45.22 odd 12
810.2.f.b.647.1 8 45.4 even 6
810.2.f.b.647.4 8 45.14 odd 6
1350.2.q.g.143.2 8 45.43 odd 12
1350.2.q.g.557.2 8 3.2 odd 2
1350.2.q.g.1007.2 8 9.7 even 3
1350.2.q.g.1043.2 8 15.8 even 4