Properties

Label 950.2.l.i.651.1
Level $950$
Weight $2$
Character 950.651
Analytic conductor $7.586$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), degree \(6\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} - 12862 x^{9} + 77397 x^{8} - 24822 x^{7} + 178501 x^{6} - 39408 x^{5} + \cdots + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 651.1
Root \(-1.58985 + 2.75370i\) of defining polynomial
Character \(\chi\) \(=\) 950.651
Dual form 950.2.l.i.251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.939693 + 0.342020i) q^{2} +(-0.552148 + 3.13139i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.552148 - 3.13139i) q^{6} +(-1.67305 - 2.89781i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-6.68164 - 2.43192i) q^{9} +O(q^{10})\) \(q+(-0.939693 + 0.342020i) q^{2} +(-0.552148 + 3.13139i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.552148 - 3.13139i) q^{6} +(-1.67305 - 2.89781i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-6.68164 - 2.43192i) q^{9} +(-3.09216 + 5.35578i) q^{11} +(1.58985 + 2.75370i) q^{12} +(0.128260 + 0.727397i) q^{13} +(2.56327 + 2.15083i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.815778 - 0.296919i) q^{17} +7.11045 q^{18} +(-2.59916 - 3.49919i) q^{19} +(9.99794 - 3.63895i) q^{21} +(1.07390 - 6.09037i) q^{22} +(0.875950 - 0.735009i) q^{23} +(-2.43579 - 2.04387i) q^{24} +(-0.369309 - 0.639662i) q^{26} +(6.53498 - 11.3189i) q^{27} +(-3.14431 - 1.14444i) q^{28} +(7.32010 + 2.66430i) q^{29} +(-3.23887 - 5.60988i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-15.0637 - 12.6399i) q^{33} +(-0.665029 + 0.558025i) q^{34} +(-6.68164 + 2.43192i) q^{36} -1.68113 q^{37} +(3.63921 + 2.39920i) q^{38} -2.34858 q^{39} +(1.68282 - 9.54373i) q^{41} +(-8.15040 + 6.83899i) q^{42} +(-1.42354 - 1.19449i) q^{43} +(1.07390 + 6.09037i) q^{44} +(-0.571736 + 0.990275i) q^{46} +(0.311691 + 0.113446i) q^{47} +(2.98793 + 1.08752i) q^{48} +(-2.09821 + 3.63420i) q^{49} +(0.479338 + 2.71846i) q^{51} +(0.565815 + 0.474775i) q^{52} +(5.44265 - 4.56693i) q^{53} +(-2.26958 + 12.8714i) q^{54} +3.34610 q^{56} +(12.3925 - 6.20691i) q^{57} -7.78988 q^{58} +(-4.56719 + 1.66232i) q^{59} +(5.53664 - 4.64579i) q^{61} +(4.96223 + 4.16381i) q^{62} +(4.13149 + 23.4308i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(18.4784 + 6.72557i) q^{66} +(2.74854 + 1.00039i) q^{67} +(0.434067 - 0.751825i) q^{68} +(1.81794 + 3.14877i) q^{69} +(-5.27849 - 4.42918i) q^{71} +(5.44692 - 4.57051i) q^{72} +(-1.35735 + 7.69790i) q^{73} +(1.57975 - 0.574982i) q^{74} +(-4.24031 - 1.00983i) q^{76} +20.6934 q^{77} +(2.20694 - 0.803262i) q^{78} +(-0.399207 + 2.26401i) q^{79} +(15.4949 + 13.0018i) q^{81} +(1.68282 + 9.54373i) q^{82} +(-5.72338 - 9.91318i) q^{83} +(5.31979 - 9.21415i) q^{84} +(1.74623 + 0.635576i) q^{86} +(-12.3847 + 21.4510i) q^{87} +(-3.09216 - 5.35578i) q^{88} +(0.404290 + 2.29284i) q^{89} +(1.89328 - 1.58865i) q^{91} +(0.198562 - 1.12610i) q^{92} +(19.3550 - 7.04466i) q^{93} -0.331695 q^{94} -3.17969 q^{96} +(-6.43131 + 2.34081i) q^{97} +(0.728700 - 4.13266i) q^{98} +(33.6855 - 28.2655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.939693 + 0.342020i −0.664463 + 0.241845i
\(3\) −0.552148 + 3.13139i −0.318783 + 1.80791i 0.231396 + 0.972860i \(0.425671\pi\)
−0.550178 + 0.835047i \(0.685440\pi\)
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) 0 0
\(6\) −0.552148 3.13139i −0.225413 1.27838i
\(7\) −1.67305 2.89781i −0.632354 1.09527i −0.987069 0.160295i \(-0.948755\pi\)
0.354715 0.934975i \(-0.384578\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) −6.68164 2.43192i −2.22721 0.810639i
\(10\) 0 0
\(11\) −3.09216 + 5.35578i −0.932322 + 1.61483i −0.152981 + 0.988229i \(0.548887\pi\)
−0.779341 + 0.626600i \(0.784446\pi\)
\(12\) 1.58985 + 2.75370i 0.458949 + 0.794923i
\(13\) 0.128260 + 0.727397i 0.0355729 + 0.201744i 0.997415 0.0718630i \(-0.0228944\pi\)
−0.961842 + 0.273607i \(0.911783\pi\)
\(14\) 2.56327 + 2.15083i 0.685061 + 0.574835i
\(15\) 0 0
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) 0.815778 0.296919i 0.197855 0.0720134i −0.241192 0.970477i \(-0.577538\pi\)
0.439047 + 0.898464i \(0.355316\pi\)
\(18\) 7.11045 1.67595
\(19\) −2.59916 3.49919i −0.596289 0.802770i
\(20\) 0 0
\(21\) 9.99794 3.63895i 2.18173 0.794085i
\(22\) 1.07390 6.09037i 0.228956 1.29847i
\(23\) 0.875950 0.735009i 0.182648 0.153260i −0.546879 0.837211i \(-0.684184\pi\)
0.729528 + 0.683951i \(0.239740\pi\)
\(24\) −2.43579 2.04387i −0.497203 0.417203i
\(25\) 0 0
\(26\) −0.369309 0.639662i −0.0724275 0.125448i
\(27\) 6.53498 11.3189i 1.25766 2.17833i
\(28\) −3.14431 1.14444i −0.594219 0.216278i
\(29\) 7.32010 + 2.66430i 1.35931 + 0.494748i 0.915840 0.401543i \(-0.131526\pi\)
0.443468 + 0.896290i \(0.353748\pi\)
\(30\) 0 0
\(31\) −3.23887 5.60988i −0.581718 1.00756i −0.995276 0.0970869i \(-0.969048\pi\)
0.413558 0.910478i \(-0.364286\pi\)
\(32\) 0.173648 + 0.984808i 0.0306970 + 0.174091i
\(33\) −15.0637 12.6399i −2.62225 2.20033i
\(34\) −0.665029 + 0.558025i −0.114051 + 0.0957005i
\(35\) 0 0
\(36\) −6.68164 + 2.43192i −1.11361 + 0.405319i
\(37\) −1.68113 −0.276377 −0.138188 0.990406i \(-0.544128\pi\)
−0.138188 + 0.990406i \(0.544128\pi\)
\(38\) 3.63921 + 2.39920i 0.590357 + 0.389202i
\(39\) −2.34858 −0.376074
\(40\) 0 0
\(41\) 1.68282 9.54373i 0.262812 1.49048i −0.512383 0.858757i \(-0.671237\pi\)
0.775194 0.631723i \(-0.217652\pi\)
\(42\) −8.15040 + 6.83899i −1.25763 + 1.05528i
\(43\) −1.42354 1.19449i −0.217088 0.182158i 0.527758 0.849395i \(-0.323033\pi\)
−0.744846 + 0.667236i \(0.767477\pi\)
\(44\) 1.07390 + 6.09037i 0.161896 + 0.918158i
\(45\) 0 0
\(46\) −0.571736 + 0.990275i −0.0842978 + 0.146008i
\(47\) 0.311691 + 0.113446i 0.0454649 + 0.0165479i 0.364652 0.931144i \(-0.381188\pi\)
−0.319188 + 0.947692i \(0.603410\pi\)
\(48\) 2.98793 + 1.08752i 0.431271 + 0.156970i
\(49\) −2.09821 + 3.63420i −0.299744 + 0.519172i
\(50\) 0 0
\(51\) 0.479338 + 2.71846i 0.0671207 + 0.380661i
\(52\) 0.565815 + 0.474775i 0.0784644 + 0.0658394i
\(53\) 5.44265 4.56693i 0.747606 0.627316i −0.187263 0.982310i \(-0.559962\pi\)
0.934868 + 0.354994i \(0.115517\pi\)
\(54\) −2.26958 + 12.8714i −0.308850 + 1.75158i
\(55\) 0 0
\(56\) 3.34610 0.447142
\(57\) 12.3925 6.20691i 1.64142 0.822125i
\(58\) −7.78988 −1.02286
\(59\) −4.56719 + 1.66232i −0.594597 + 0.216416i −0.621750 0.783216i \(-0.713578\pi\)
0.0271531 + 0.999631i \(0.491356\pi\)
\(60\) 0 0
\(61\) 5.53664 4.64579i 0.708894 0.594833i −0.215394 0.976527i \(-0.569104\pi\)
0.924289 + 0.381694i \(0.124659\pi\)
\(62\) 4.96223 + 4.16381i 0.630204 + 0.528804i
\(63\) 4.13149 + 23.4308i 0.520519 + 2.95201i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 0 0
\(66\) 18.4784 + 6.72557i 2.27453 + 0.827861i
\(67\) 2.74854 + 1.00039i 0.335787 + 0.122217i 0.504410 0.863464i \(-0.331710\pi\)
−0.168623 + 0.985681i \(0.553932\pi\)
\(68\) 0.434067 0.751825i 0.0526383 0.0911722i
\(69\) 1.81794 + 3.14877i 0.218855 + 0.379068i
\(70\) 0 0
\(71\) −5.27849 4.42918i −0.626442 0.525647i 0.273379 0.961906i \(-0.411859\pi\)
−0.899821 + 0.436259i \(0.856303\pi\)
\(72\) 5.44692 4.57051i 0.641926 0.538640i
\(73\) −1.35735 + 7.69790i −0.158866 + 0.900972i 0.796301 + 0.604901i \(0.206787\pi\)
−0.955166 + 0.296070i \(0.904324\pi\)
\(74\) 1.57975 0.574982i 0.183642 0.0668403i
\(75\) 0 0
\(76\) −4.24031 1.00983i −0.486397 0.115835i
\(77\) 20.6934 2.35823
\(78\) 2.20694 0.803262i 0.249887 0.0909515i
\(79\) −0.399207 + 2.26401i −0.0449143 + 0.254721i −0.998995 0.0448292i \(-0.985726\pi\)
0.954080 + 0.299551i \(0.0968368\pi\)
\(80\) 0 0
\(81\) 15.4949 + 13.0018i 1.72165 + 1.44464i
\(82\) 1.68282 + 9.54373i 0.185836 + 1.05393i
\(83\) −5.72338 9.91318i −0.628223 1.08811i −0.987908 0.155040i \(-0.950449\pi\)
0.359686 0.933074i \(-0.382884\pi\)
\(84\) 5.31979 9.21415i 0.580437 1.00535i
\(85\) 0 0
\(86\) 1.74623 + 0.635576i 0.188301 + 0.0685359i
\(87\) −12.3847 + 21.4510i −1.32778 + 2.29978i
\(88\) −3.09216 5.35578i −0.329626 0.570928i
\(89\) 0.404290 + 2.29284i 0.0428546 + 0.243041i 0.998709 0.0508007i \(-0.0161773\pi\)
−0.955854 + 0.293841i \(0.905066\pi\)
\(90\) 0 0
\(91\) 1.89328 1.58865i 0.198469 0.166535i
\(92\) 0.198562 1.12610i 0.0207015 0.117404i
\(93\) 19.3550 7.04466i 2.00702 0.730497i
\(94\) −0.331695 −0.0342117
\(95\) 0 0
\(96\) −3.17969 −0.324526
\(97\) −6.43131 + 2.34081i −0.653000 + 0.237673i −0.647211 0.762311i \(-0.724065\pi\)
−0.00578901 + 0.999983i \(0.501843\pi\)
\(98\) 0.728700 4.13266i 0.0736098 0.417462i
\(99\) 33.6855 28.2655i 3.38552 2.84079i
\(100\) 0 0
\(101\) 1.76892 + 10.0321i 0.176015 + 0.998228i 0.936966 + 0.349420i \(0.113621\pi\)
−0.760952 + 0.648809i \(0.775268\pi\)
\(102\) −1.38020 2.39057i −0.136660 0.236702i
\(103\) 1.03525 1.79310i 0.102006 0.176680i −0.810505 0.585732i \(-0.800807\pi\)
0.912511 + 0.409052i \(0.134141\pi\)
\(104\) −0.694074 0.252622i −0.0680596 0.0247717i
\(105\) 0 0
\(106\) −3.55244 + 6.15300i −0.345043 + 0.597632i
\(107\) −7.31857 12.6761i −0.707513 1.22545i −0.965777 0.259374i \(-0.916484\pi\)
0.258264 0.966075i \(-0.416850\pi\)
\(108\) −2.26958 12.8714i −0.218390 1.23855i
\(109\) −6.66091 5.58917i −0.637999 0.535345i 0.265404 0.964137i \(-0.414495\pi\)
−0.903403 + 0.428792i \(0.858939\pi\)
\(110\) 0 0
\(111\) 0.928235 5.26428i 0.0881041 0.499663i
\(112\) −3.14431 + 1.14444i −0.297109 + 0.108139i
\(113\) −10.8308 −1.01888 −0.509439 0.860507i \(-0.670147\pi\)
−0.509439 + 0.860507i \(0.670147\pi\)
\(114\) −9.52221 + 10.0711i −0.891836 + 0.943240i
\(115\) 0 0
\(116\) 7.32010 2.66430i 0.679654 0.247374i
\(117\) 0.911985 5.17212i 0.0843130 0.478163i
\(118\) 3.72320 3.12414i 0.342749 0.287600i
\(119\) −2.22526 1.86721i −0.203989 0.171167i
\(120\) 0 0
\(121\) −13.6229 23.5956i −1.23845 2.14506i
\(122\) −3.61379 + 6.25926i −0.327177 + 0.566687i
\(123\) 28.9559 + 10.5391i 2.61087 + 0.950279i
\(124\) −6.08708 2.21552i −0.546636 0.198959i
\(125\) 0 0
\(126\) −11.8962 20.6047i −1.05979 1.83562i
\(127\) 1.94911 + 11.0540i 0.172956 + 0.980880i 0.940477 + 0.339857i \(0.110379\pi\)
−0.767522 + 0.641023i \(0.778510\pi\)
\(128\) 0.766044 + 0.642788i 0.0677094 + 0.0568149i
\(129\) 4.52642 3.79812i 0.398529 0.334406i
\(130\) 0 0
\(131\) −14.2703 + 5.19396i −1.24680 + 0.453798i −0.879319 0.476233i \(-0.842002\pi\)
−0.367481 + 0.930031i \(0.619780\pi\)
\(132\) −19.6643 −1.71155
\(133\) −5.79147 + 13.3862i −0.502184 + 1.16073i
\(134\) −2.92493 −0.252676
\(135\) 0 0
\(136\) −0.150750 + 0.854944i −0.0129267 + 0.0733109i
\(137\) 6.54988 5.49600i 0.559594 0.469555i −0.318580 0.947896i \(-0.603206\pi\)
0.878174 + 0.478341i \(0.158762\pi\)
\(138\) −2.78525 2.33710i −0.237096 0.198948i
\(139\) 1.52883 + 8.67044i 0.129674 + 0.735417i 0.978421 + 0.206619i \(0.0662460\pi\)
−0.848748 + 0.528798i \(0.822643\pi\)
\(140\) 0 0
\(141\) −0.527344 + 0.913387i −0.0444104 + 0.0769210i
\(142\) 6.47503 + 2.35672i 0.543372 + 0.197771i
\(143\) −4.29238 1.56230i −0.358947 0.130646i
\(144\) −3.55522 + 6.15783i −0.296269 + 0.513152i
\(145\) 0 0
\(146\) −1.35735 7.69790i −0.112335 0.637083i
\(147\) −10.2216 8.57692i −0.843061 0.707413i
\(148\) −1.28782 + 1.08061i −0.105858 + 0.0888258i
\(149\) 0.132240 0.749969i 0.0108335 0.0614398i −0.978912 0.204284i \(-0.934514\pi\)
0.989745 + 0.142844i \(0.0456246\pi\)
\(150\) 0 0
\(151\) −6.08784 −0.495421 −0.247711 0.968834i \(-0.579678\pi\)
−0.247711 + 0.968834i \(0.579678\pi\)
\(152\) 4.32997 0.501343i 0.351207 0.0406643i
\(153\) −6.17282 −0.499043
\(154\) −19.4454 + 7.07756i −1.56696 + 0.570326i
\(155\) 0 0
\(156\) −1.79912 + 1.50964i −0.144045 + 0.120868i
\(157\) −18.6728 15.6683i −1.49025 1.25047i −0.894317 0.447434i \(-0.852338\pi\)
−0.595933 0.803034i \(-0.703218\pi\)
\(158\) −0.399207 2.26401i −0.0317592 0.180115i
\(159\) 11.2957 + 19.5647i 0.895804 + 1.55158i
\(160\) 0 0
\(161\) −3.59543 1.30863i −0.283360 0.103134i
\(162\) −19.0073 6.91809i −1.49335 0.543536i
\(163\) −2.15496 + 3.73250i −0.168789 + 0.292352i −0.937994 0.346650i \(-0.887319\pi\)
0.769205 + 0.639002i \(0.220652\pi\)
\(164\) −4.84548 8.39261i −0.378368 0.655353i
\(165\) 0 0
\(166\) 8.76873 + 7.35783i 0.680585 + 0.571079i
\(167\) −3.99229 + 3.34993i −0.308933 + 0.259225i −0.784051 0.620697i \(-0.786850\pi\)
0.475118 + 0.879922i \(0.342405\pi\)
\(168\) −1.84754 + 10.4779i −0.142541 + 0.808391i
\(169\) 11.7033 4.25967i 0.900258 0.327667i
\(170\) 0 0
\(171\) 8.85690 + 29.7013i 0.677304 + 2.27131i
\(172\) −1.85830 −0.141694
\(173\) 6.61144 2.40637i 0.502658 0.182953i −0.0782309 0.996935i \(-0.524927\pi\)
0.580889 + 0.813983i \(0.302705\pi\)
\(174\) 4.30117 24.3931i 0.326071 1.84924i
\(175\) 0 0
\(176\) 4.73747 + 3.97521i 0.357100 + 0.299642i
\(177\) −2.68360 15.2195i −0.201712 1.14397i
\(178\) −1.16411 2.01629i −0.0872534 0.151127i
\(179\) −1.59972 + 2.77080i −0.119569 + 0.207099i −0.919597 0.392863i \(-0.871485\pi\)
0.800028 + 0.599963i \(0.204818\pi\)
\(180\) 0 0
\(181\) 4.44963 + 1.61953i 0.330738 + 0.120379i 0.502052 0.864838i \(-0.332579\pi\)
−0.171313 + 0.985217i \(0.554801\pi\)
\(182\) −1.23575 + 2.14038i −0.0915997 + 0.158655i
\(183\) 11.4907 + 19.9025i 0.849419 + 1.47124i
\(184\) 0.198562 + 1.12610i 0.0146382 + 0.0830172i
\(185\) 0 0
\(186\) −15.7784 + 13.2396i −1.15693 + 0.970777i
\(187\) −0.932285 + 5.28725i −0.0681754 + 0.386642i
\(188\) 0.311691 0.113446i 0.0227324 0.00827393i
\(189\) −43.7335 −3.18114
\(190\) 0 0
\(191\) −18.4307 −1.33360 −0.666800 0.745237i \(-0.732336\pi\)
−0.666800 + 0.745237i \(0.732336\pi\)
\(192\) 2.98793 1.08752i 0.215636 0.0784849i
\(193\) 2.35285 13.3437i 0.169362 0.960501i −0.775090 0.631851i \(-0.782295\pi\)
0.944452 0.328649i \(-0.106593\pi\)
\(194\) 5.24285 4.39927i 0.376415 0.315849i
\(195\) 0 0
\(196\) 0.728700 + 4.13266i 0.0520500 + 0.295190i
\(197\) 4.09550 + 7.09361i 0.291792 + 0.505399i 0.974234 0.225541i \(-0.0724151\pi\)
−0.682441 + 0.730940i \(0.739082\pi\)
\(198\) −21.9867 + 38.0820i −1.56252 + 2.70637i
\(199\) −5.58408 2.03244i −0.395845 0.144076i 0.136425 0.990650i \(-0.456439\pi\)
−0.532270 + 0.846575i \(0.678661\pi\)
\(200\) 0 0
\(201\) −4.65019 + 8.05437i −0.327999 + 0.568112i
\(202\) −5.09342 8.82205i −0.358371 0.620718i
\(203\) −4.52627 25.6698i −0.317682 1.80166i
\(204\) 2.11459 + 1.77435i 0.148051 + 0.124229i
\(205\) 0 0
\(206\) −0.359538 + 2.03904i −0.0250502 + 0.142067i
\(207\) −7.64026 + 2.78083i −0.531035 + 0.193281i
\(208\) 0.738619 0.0512140
\(209\) 26.7779 3.10047i 1.85227 0.214464i
\(210\) 0 0
\(211\) 1.63846 0.596352i 0.112796 0.0410545i −0.285005 0.958526i \(-0.591995\pi\)
0.397802 + 0.917471i \(0.369773\pi\)
\(212\) 1.23375 6.99694i 0.0847342 0.480552i
\(213\) 16.7840 14.0834i 1.15002 0.964981i
\(214\) 11.2127 + 9.40858i 0.766485 + 0.643157i
\(215\) 0 0
\(216\) 6.53498 + 11.3189i 0.444649 + 0.770155i
\(217\) −10.8376 + 18.7713i −0.735703 + 1.27428i
\(218\) 8.17082 + 2.97393i 0.553397 + 0.201420i
\(219\) −23.3557 8.50076i −1.57823 0.574428i
\(220\) 0 0
\(221\) 0.320610 + 0.555312i 0.0215665 + 0.0373543i
\(222\) 0.928235 + 5.26428i 0.0622990 + 0.353315i
\(223\) −20.2549 16.9959i −1.35637 1.13813i −0.977085 0.212848i \(-0.931726\pi\)
−0.379283 0.925281i \(-0.623829\pi\)
\(224\) 2.56327 2.15083i 0.171265 0.143709i
\(225\) 0 0
\(226\) 10.1777 3.70436i 0.677007 0.246411i
\(227\) 27.4472 1.82174 0.910869 0.412697i \(-0.135413\pi\)
0.910869 + 0.412697i \(0.135413\pi\)
\(228\) 5.50345 12.7205i 0.364475 0.842434i
\(229\) −11.5722 −0.764711 −0.382355 0.924015i \(-0.624887\pi\)
−0.382355 + 0.924015i \(0.624887\pi\)
\(230\) 0 0
\(231\) −11.4258 + 64.7990i −0.751764 + 4.26346i
\(232\) −5.96740 + 5.00724i −0.391779 + 0.328741i
\(233\) −9.84970 8.26488i −0.645275 0.541450i 0.260358 0.965512i \(-0.416159\pi\)
−0.905633 + 0.424062i \(0.860604\pi\)
\(234\) 0.911985 + 5.17212i 0.0596183 + 0.338112i
\(235\) 0 0
\(236\) −2.43015 + 4.20914i −0.158189 + 0.273992i
\(237\) −6.86908 2.50014i −0.446195 0.162402i
\(238\) 2.72968 + 0.993522i 0.176939 + 0.0644005i
\(239\) 5.65708 9.79836i 0.365926 0.633803i −0.622998 0.782223i \(-0.714086\pi\)
0.988924 + 0.148420i \(0.0474189\pi\)
\(240\) 0 0
\(241\) −4.13196 23.4335i −0.266163 1.50948i −0.765704 0.643193i \(-0.777609\pi\)
0.499541 0.866290i \(-0.333502\pi\)
\(242\) 20.8715 + 17.5133i 1.34167 + 1.12580i
\(243\) −19.2325 + 16.1379i −1.23376 + 1.03525i
\(244\) 1.25506 7.11777i 0.0803467 0.455669i
\(245\) 0 0
\(246\) −30.8143 −1.96465
\(247\) 2.21194 2.33943i 0.140742 0.148854i
\(248\) 6.47773 0.411337
\(249\) 34.2022 12.4486i 2.16747 0.788896i
\(250\) 0 0
\(251\) 19.9736 16.7599i 1.26072 1.05787i 0.265120 0.964215i \(-0.414588\pi\)
0.995604 0.0936578i \(-0.0298560\pi\)
\(252\) 18.2260 + 15.2934i 1.14813 + 0.963394i
\(253\) 1.22797 + 6.96417i 0.0772018 + 0.437833i
\(254\) −5.61224 9.72069i −0.352143 0.609930i
\(255\) 0 0
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) −9.54054 3.47247i −0.595122 0.216607i 0.0268585 0.999639i \(-0.491450\pi\)
−0.621981 + 0.783032i \(0.713672\pi\)
\(258\) −2.95441 + 5.11719i −0.183934 + 0.318582i
\(259\) 2.81263 + 4.87161i 0.174768 + 0.302707i
\(260\) 0 0
\(261\) −42.4309 35.6037i −2.62641 2.20382i
\(262\) 11.6332 9.76144i 0.718704 0.603064i
\(263\) −2.97399 + 16.8663i −0.183384 + 1.04002i 0.744630 + 0.667477i \(0.232626\pi\)
−0.928014 + 0.372545i \(0.878485\pi\)
\(264\) 18.4784 6.72557i 1.13726 0.413930i
\(265\) 0 0
\(266\) 0.863848 14.5597i 0.0529659 0.892714i
\(267\) −7.40300 −0.453056
\(268\) 2.74854 1.00039i 0.167894 0.0611083i
\(269\) 3.96080 22.4628i 0.241495 1.36958i −0.587000 0.809587i \(-0.699691\pi\)
0.828495 0.559997i \(-0.189198\pi\)
\(270\) 0 0
\(271\) 13.6282 + 11.4354i 0.827852 + 0.694650i 0.954797 0.297260i \(-0.0960727\pi\)
−0.126945 + 0.991910i \(0.540517\pi\)
\(272\) −0.150750 0.854944i −0.00914054 0.0518386i
\(273\) 3.92930 + 6.80574i 0.237812 + 0.411902i
\(274\) −4.27513 + 7.40475i −0.258270 + 0.447337i
\(275\) 0 0
\(276\) 3.41662 + 1.24355i 0.205656 + 0.0748527i
\(277\) −10.4365 + 18.0765i −0.627066 + 1.08611i 0.361071 + 0.932538i \(0.382411\pi\)
−0.988137 + 0.153572i \(0.950922\pi\)
\(278\) −4.40210 7.62466i −0.264020 0.457296i
\(279\) 7.99817 + 45.3598i 0.478838 + 2.71562i
\(280\) 0 0
\(281\) −20.8354 + 17.4830i −1.24294 + 1.04295i −0.245650 + 0.969359i \(0.579001\pi\)
−0.997289 + 0.0735907i \(0.976554\pi\)
\(282\) 0.183145 1.03867i 0.0109061 0.0618516i
\(283\) −18.5060 + 6.73563i −1.10007 + 0.400392i −0.827341 0.561700i \(-0.810148\pi\)
−0.272726 + 0.962092i \(0.587925\pi\)
\(284\) −6.89058 −0.408881
\(285\) 0 0
\(286\) 4.56786 0.270103
\(287\) −30.4714 + 11.0907i −1.79867 + 0.654662i
\(288\) 1.23472 7.00242i 0.0727564 0.412622i
\(289\) −12.4454 + 10.4429i −0.732084 + 0.614291i
\(290\) 0 0
\(291\) −3.77893 21.4314i −0.221525 1.25633i
\(292\) 3.90833 + 6.76942i 0.228718 + 0.396151i
\(293\) −7.38854 + 12.7973i −0.431643 + 0.747628i −0.997015 0.0772085i \(-0.975399\pi\)
0.565372 + 0.824836i \(0.308733\pi\)
\(294\) 12.5386 + 4.56368i 0.731267 + 0.266159i
\(295\) 0 0
\(296\) 0.840567 1.45590i 0.0488570 0.0846227i
\(297\) 40.4145 + 69.9999i 2.34508 + 4.06181i
\(298\) 0.132240 + 0.749969i 0.00766044 + 0.0434445i
\(299\) 0.646993 + 0.542892i 0.0374166 + 0.0313962i
\(300\) 0 0
\(301\) −1.07976 + 6.12360i −0.0622361 + 0.352958i
\(302\) 5.72070 2.08216i 0.329189 0.119815i
\(303\) −32.3910 −1.86081
\(304\) −3.89737 + 1.95205i −0.223530 + 0.111958i
\(305\) 0 0
\(306\) 5.80055 2.11123i 0.331595 0.120691i
\(307\) 0.736086 4.17455i 0.0420106 0.238254i −0.956571 0.291500i \(-0.905846\pi\)
0.998581 + 0.0532459i \(0.0169567\pi\)
\(308\) 15.8521 13.3015i 0.903255 0.757921i
\(309\) 5.04328 + 4.23182i 0.286902 + 0.240740i
\(310\) 0 0
\(311\) 3.49343 + 6.05079i 0.198094 + 0.343109i 0.947910 0.318537i \(-0.103192\pi\)
−0.749816 + 0.661646i \(0.769858\pi\)
\(312\) 1.17429 2.03393i 0.0664811 0.115149i
\(313\) −7.16016 2.60608i −0.404716 0.147305i 0.131638 0.991298i \(-0.457976\pi\)
−0.536354 + 0.843993i \(0.680199\pi\)
\(314\) 22.9056 + 8.33694i 1.29264 + 0.470481i
\(315\) 0 0
\(316\) 1.14947 + 1.99094i 0.0646627 + 0.111999i
\(317\) −2.38566 13.5297i −0.133992 0.759905i −0.975557 0.219749i \(-0.929476\pi\)
0.841565 0.540156i \(-0.181635\pi\)
\(318\) −17.3060 14.5214i −0.970470 0.814321i
\(319\) −36.9043 + 30.9664i −2.06625 + 1.73379i
\(320\) 0 0
\(321\) 43.7348 15.9182i 2.44104 0.888466i
\(322\) 3.82618 0.213224
\(323\) −3.15932 2.08283i −0.175789 0.115892i
\(324\) 20.2271 1.12373
\(325\) 0 0
\(326\) 0.748409 4.24444i 0.0414506 0.235078i
\(327\) 21.1796 17.7718i 1.17124 0.982785i
\(328\) 7.42370 + 6.22923i 0.409905 + 0.343952i
\(329\) −0.192730 1.09302i −0.0106255 0.0602604i
\(330\) 0 0
\(331\) 3.32212 5.75409i 0.182600 0.316273i −0.760165 0.649730i \(-0.774882\pi\)
0.942765 + 0.333457i \(0.108215\pi\)
\(332\) −10.7564 3.91502i −0.590336 0.214865i
\(333\) 11.2327 + 4.08838i 0.615550 + 0.224042i
\(334\) 2.60578 4.51335i 0.142582 0.246959i
\(335\) 0 0
\(336\) −1.84754 10.4779i −0.100792 0.571619i
\(337\) 14.1012 + 11.8323i 0.768139 + 0.644545i 0.940232 0.340536i \(-0.110608\pi\)
−0.172093 + 0.985081i \(0.555053\pi\)
\(338\) −9.54066 + 8.00556i −0.518943 + 0.435445i
\(339\) 5.98022 33.9155i 0.324801 1.84204i
\(340\) 0 0
\(341\) 40.0604 2.16939
\(342\) −18.4812 24.8808i −0.999349 1.34540i
\(343\) −9.38108 −0.506531
\(344\) 1.74623 0.635576i 0.0941504 0.0342680i
\(345\) 0 0
\(346\) −5.38969 + 4.52249i −0.289752 + 0.243131i
\(347\) −5.68212 4.76787i −0.305032 0.255952i 0.477403 0.878684i \(-0.341578\pi\)
−0.782435 + 0.622732i \(0.786023\pi\)
\(348\) 4.30117 + 24.3931i 0.230567 + 1.30761i
\(349\) −9.57581 16.5858i −0.512581 0.887817i −0.999894 0.0145891i \(-0.995356\pi\)
0.487312 0.873228i \(-0.337977\pi\)
\(350\) 0 0
\(351\) 9.07153 + 3.30177i 0.484202 + 0.176235i
\(352\) −5.81136 2.11516i −0.309747 0.112739i
\(353\) −0.801691 + 1.38857i −0.0426697 + 0.0739061i −0.886572 0.462592i \(-0.846920\pi\)
0.843902 + 0.536498i \(0.180253\pi\)
\(354\) 7.72713 + 13.3838i 0.410692 + 0.711340i
\(355\) 0 0
\(356\) 1.78351 + 1.49655i 0.0945261 + 0.0793168i
\(357\) 7.07563 5.93716i 0.374482 0.314228i
\(358\) 0.555577 3.15084i 0.0293632 0.166527i
\(359\) 20.2961 7.38717i 1.07119 0.389880i 0.254566 0.967055i \(-0.418067\pi\)
0.816620 + 0.577175i \(0.195845\pi\)
\(360\) 0 0
\(361\) −5.48872 + 18.1899i −0.288880 + 0.957365i
\(362\) −4.73520 −0.248876
\(363\) 81.4089 29.6304i 4.27286 1.55519i
\(364\) 0.429171 2.43395i 0.0224947 0.127574i
\(365\) 0 0
\(366\) −17.6048 14.7722i −0.920219 0.772155i
\(367\) −3.42815 19.4420i −0.178948 1.01486i −0.933488 0.358610i \(-0.883251\pi\)
0.754540 0.656255i \(-0.227860\pi\)
\(368\) −0.571736 0.990275i −0.0298038 0.0516217i
\(369\) −34.4535 + 59.6753i −1.79358 + 3.10657i
\(370\) 0 0
\(371\) −22.3399 8.13107i −1.15983 0.422144i
\(372\) 10.2986 17.8377i 0.533958 0.924842i
\(373\) −11.5800 20.0572i −0.599592 1.03852i −0.992881 0.119109i \(-0.961996\pi\)
0.393289 0.919415i \(-0.371337\pi\)
\(374\) −0.932285 5.28725i −0.0482073 0.273397i
\(375\) 0 0
\(376\) −0.254093 + 0.213209i −0.0131039 + 0.0109954i
\(377\) −0.999129 + 5.66634i −0.0514578 + 0.291831i
\(378\) 41.0960 14.9577i 2.11375 0.769343i
\(379\) −3.52957 −0.181302 −0.0906508 0.995883i \(-0.528895\pi\)
−0.0906508 + 0.995883i \(0.528895\pi\)
\(380\) 0 0
\(381\) −35.6904 −1.82847
\(382\) 17.3192 6.30368i 0.886128 0.322524i
\(383\) −6.36973 + 36.1246i −0.325478 + 1.84588i 0.180815 + 0.983517i \(0.442127\pi\)
−0.506293 + 0.862362i \(0.668985\pi\)
\(384\) −2.43579 + 2.04387i −0.124301 + 0.104301i
\(385\) 0 0
\(386\) 2.35285 + 13.3437i 0.119757 + 0.679176i
\(387\) 6.60667 + 11.4431i 0.335836 + 0.581685i
\(388\) −3.42203 + 5.92713i −0.173727 + 0.300904i
\(389\) 23.1021 + 8.40847i 1.17132 + 0.426327i 0.853129 0.521699i \(-0.174702\pi\)
0.318193 + 0.948026i \(0.396924\pi\)
\(390\) 0 0
\(391\) 0.496343 0.859691i 0.0251011 0.0434764i
\(392\) −2.09821 3.63420i −0.105976 0.183555i
\(393\) −8.38498 47.5536i −0.422966 2.39876i
\(394\) −6.27467 5.26507i −0.316113 0.265251i
\(395\) 0 0
\(396\) 7.63589 43.3053i 0.383718 2.17617i
\(397\) 19.1282 6.96208i 0.960015 0.349417i 0.185976 0.982554i \(-0.440455\pi\)
0.774039 + 0.633137i \(0.218233\pi\)
\(398\) 5.94246 0.297868
\(399\) −38.7197 25.5265i −1.93841 1.27792i
\(400\) 0 0
\(401\) −18.9313 + 6.89045i −0.945386 + 0.344092i −0.768291 0.640101i \(-0.778892\pi\)
−0.177096 + 0.984194i \(0.556670\pi\)
\(402\) 1.61500 9.15910i 0.0805487 0.456814i
\(403\) 3.66520 3.07547i 0.182576 0.153200i
\(404\) 7.80356 + 6.54797i 0.388242 + 0.325774i
\(405\) 0 0
\(406\) 13.0329 + 22.5736i 0.646811 + 1.12031i
\(407\) 5.19834 9.00379i 0.257672 0.446301i
\(408\) −2.59392 0.944111i −0.128418 0.0467405i
\(409\) −12.1073 4.40670i −0.598668 0.217897i 0.0248698 0.999691i \(-0.492083\pi\)
−0.623537 + 0.781794i \(0.714305\pi\)
\(410\) 0 0
\(411\) 13.5936 + 23.5448i 0.670523 + 1.16138i
\(412\) −0.359538 2.03904i −0.0177132 0.100456i
\(413\) 12.4582 + 10.4537i 0.613030 + 0.514393i
\(414\) 6.22840 5.22625i 0.306109 0.256856i
\(415\) 0 0
\(416\) −0.694074 + 0.252622i −0.0340298 + 0.0123858i
\(417\) −27.9946 −1.37090
\(418\) −24.1026 + 12.0721i −1.17890 + 0.590465i
\(419\) 20.0166 0.977876 0.488938 0.872319i \(-0.337384\pi\)
0.488938 + 0.872319i \(0.337384\pi\)
\(420\) 0 0
\(421\) 1.16311 6.59634i 0.0566867 0.321486i −0.943257 0.332062i \(-0.892256\pi\)
0.999944 + 0.0105764i \(0.00336662\pi\)
\(422\) −1.33569 + 1.12077i −0.0650202 + 0.0545585i
\(423\) −1.80672 1.51601i −0.0878455 0.0737112i
\(424\) 1.23375 + 6.99694i 0.0599161 + 0.339801i
\(425\) 0 0
\(426\) −10.9550 + 18.9746i −0.530770 + 0.919321i
\(427\) −22.7257 8.27149i −1.09978 0.400285i
\(428\) −13.7544 5.00620i −0.664845 0.241984i
\(429\) 7.26219 12.5785i 0.350622 0.607295i
\(430\) 0 0
\(431\) −4.86528 27.5924i −0.234352 1.32908i −0.843974 0.536385i \(-0.819790\pi\)
0.609621 0.792693i \(-0.291321\pi\)
\(432\) −10.0122 8.40121i −0.481711 0.404203i
\(433\) 17.3262 14.5384i 0.832646 0.698673i −0.123251 0.992376i \(-0.539332\pi\)
0.955897 + 0.293702i \(0.0948875\pi\)
\(434\) 3.76386 21.3459i 0.180671 1.02464i
\(435\) 0 0
\(436\) −8.69520 −0.416425
\(437\) −4.84868 1.15471i −0.231944 0.0552373i
\(438\) 24.8546 1.18760
\(439\) 3.88563 1.41425i 0.185451 0.0674986i −0.247626 0.968856i \(-0.579650\pi\)
0.433076 + 0.901357i \(0.357428\pi\)
\(440\) 0 0
\(441\) 22.8575 19.1798i 1.08845 0.913322i
\(442\) −0.491202 0.412168i −0.0233641 0.0196048i
\(443\) 5.02534 + 28.5001i 0.238761 + 1.35408i 0.834547 + 0.550937i \(0.185730\pi\)
−0.595786 + 0.803144i \(0.703159\pi\)
\(444\) −2.67274 4.62933i −0.126843 0.219698i
\(445\) 0 0
\(446\) 24.8463 + 9.04332i 1.17651 + 0.428214i
\(447\) 2.27543 + 0.828187i 0.107624 + 0.0391719i
\(448\) −1.67305 + 2.89781i −0.0790443 + 0.136909i
\(449\) 2.78070 + 4.81632i 0.131229 + 0.227296i 0.924151 0.382028i \(-0.124774\pi\)
−0.792921 + 0.609324i \(0.791441\pi\)
\(450\) 0 0
\(451\) 45.9106 + 38.5236i 2.16185 + 1.81400i
\(452\) −8.29690 + 6.96192i −0.390253 + 0.327461i
\(453\) 3.36139 19.0634i 0.157932 0.895676i
\(454\) −25.7920 + 9.38751i −1.21048 + 0.440578i
\(455\) 0 0
\(456\) −0.820886 + 13.8356i −0.0384415 + 0.647913i
\(457\) 3.44090 0.160959 0.0804793 0.996756i \(-0.474355\pi\)
0.0804793 + 0.996756i \(0.474355\pi\)
\(458\) 10.8743 3.95792i 0.508122 0.184941i
\(459\) 1.97029 11.1741i 0.0919654 0.521562i
\(460\) 0 0
\(461\) −3.88985 3.26397i −0.181169 0.152018i 0.547693 0.836679i \(-0.315506\pi\)
−0.728862 + 0.684661i \(0.759950\pi\)
\(462\) −11.4258 64.7990i −0.531577 3.01472i
\(463\) −2.56405 4.44107i −0.119162 0.206394i 0.800274 0.599634i \(-0.204687\pi\)
−0.919436 + 0.393240i \(0.871354\pi\)
\(464\) 3.89494 6.74624i 0.180818 0.313186i
\(465\) 0 0
\(466\) 12.0824 + 4.39765i 0.559708 + 0.203717i
\(467\) 14.8110 25.6535i 0.685373 1.18710i −0.287947 0.957646i \(-0.592973\pi\)
0.973320 0.229454i \(-0.0736940\pi\)
\(468\) −2.62595 4.54829i −0.121385 0.210245i
\(469\) −1.69952 9.63844i −0.0784764 0.445062i
\(470\) 0 0
\(471\) 59.3737 49.8205i 2.73580 2.29561i
\(472\) 0.843982 4.78646i 0.0388474 0.220315i
\(473\) 10.7993 3.93061i 0.496550 0.180729i
\(474\) 7.30992 0.335756
\(475\) 0 0
\(476\) −2.90486 −0.133144
\(477\) −47.4722 + 17.2785i −2.17360 + 0.791127i
\(478\) −1.96468 + 11.1423i −0.0898626 + 0.509636i
\(479\) −28.8677 + 24.2229i −1.31900 + 1.10677i −0.332485 + 0.943109i \(0.607887\pi\)
−0.986516 + 0.163664i \(0.947669\pi\)
\(480\) 0 0
\(481\) −0.215622 1.22285i −0.00983151 0.0557573i
\(482\) 11.8975 + 20.6071i 0.541916 + 0.938626i
\(483\) 6.08303 10.5361i 0.276788 0.479410i
\(484\) −25.6027 9.31863i −1.16376 0.423574i
\(485\) 0 0
\(486\) 12.5531 21.7426i 0.569420 0.986264i
\(487\) −8.87714 15.3757i −0.402262 0.696738i 0.591737 0.806131i \(-0.298442\pi\)
−0.993999 + 0.109393i \(0.965109\pi\)
\(488\) 1.25506 + 7.11777i 0.0568137 + 0.322206i
\(489\) −10.4980 8.80890i −0.474738 0.398352i
\(490\) 0 0
\(491\) −3.87201 + 21.9592i −0.174741 + 0.991006i 0.763701 + 0.645570i \(0.223380\pi\)
−0.938442 + 0.345436i \(0.887731\pi\)
\(492\) 28.9559 10.5391i 1.30543 0.475139i
\(493\) 6.76266 0.304575
\(494\) −1.27841 + 2.95487i −0.0575183 + 0.132946i
\(495\) 0 0
\(496\) −6.08708 + 2.21552i −0.273318 + 0.0994796i
\(497\) −4.00374 + 22.7063i −0.179592 + 1.01852i
\(498\) −27.8819 + 23.3957i −1.24942 + 1.04838i
\(499\) −14.4603 12.1337i −0.647334 0.543177i 0.258927 0.965897i \(-0.416631\pi\)
−0.906261 + 0.422719i \(0.861076\pi\)
\(500\) 0 0
\(501\) −8.28559 14.3511i −0.370173 0.641158i
\(502\) −13.0369 + 22.5805i −0.581864 + 1.00782i
\(503\) 38.3963 + 13.9751i 1.71201 + 0.623119i 0.997100 0.0761023i \(-0.0242476\pi\)
0.714905 + 0.699221i \(0.246470\pi\)
\(504\) −22.3575 8.13745i −0.995880 0.362471i
\(505\) 0 0
\(506\) −3.53580 6.12418i −0.157185 0.272253i
\(507\) 6.87669 + 38.9997i 0.305405 + 1.73204i
\(508\) 8.59845 + 7.21496i 0.381495 + 0.320112i
\(509\) −10.1977 + 8.55692i −0.452007 + 0.379279i −0.840180 0.542308i \(-0.817551\pi\)
0.388173 + 0.921586i \(0.373106\pi\)
\(510\) 0 0
\(511\) 24.5780 8.94566i 1.08727 0.395733i
\(512\) 1.00000 0.0441942
\(513\) −56.5926 + 6.55254i −2.49862 + 0.289302i
\(514\) 10.1528 0.447822
\(515\) 0 0
\(516\) 1.02606 5.81905i 0.0451696 0.256170i
\(517\) −1.57139 + 1.31856i −0.0691098 + 0.0579900i
\(518\) −4.30919 3.61584i −0.189335 0.158871i
\(519\) 3.88477 + 22.0316i 0.170523 + 0.967082i
\(520\) 0 0
\(521\) 13.8343 23.9617i 0.606091 1.04978i −0.385787 0.922588i \(-0.626070\pi\)
0.991878 0.127193i \(-0.0405968\pi\)
\(522\) 52.0492 + 18.9443i 2.27813 + 0.829172i
\(523\) −1.00974 0.367514i −0.0441527 0.0160703i 0.319849 0.947468i \(-0.396368\pi\)
−0.364002 + 0.931398i \(0.618590\pi\)
\(524\) −7.59305 + 13.1516i −0.331704 + 0.574528i
\(525\) 0 0
\(526\) −2.97399 16.8663i −0.129672 0.735407i
\(527\) −4.30788 3.61474i −0.187654 0.157460i
\(528\) −15.0637 + 12.6399i −0.655563 + 0.550083i
\(529\) −3.76686 + 21.3629i −0.163776 + 0.928822i
\(530\) 0 0
\(531\) 34.5589 1.49973
\(532\) 4.16797 + 13.9771i 0.180704 + 0.605985i
\(533\) 7.15792 0.310044
\(534\) 6.95655 2.53198i 0.301039 0.109569i
\(535\) 0 0
\(536\) −2.24063 + 1.88011i −0.0967804 + 0.0812084i
\(537\) −7.79316 6.53924i −0.336300 0.282189i
\(538\) 3.96080 + 22.4628i 0.170762 + 0.968442i
\(539\) −12.9760 22.4751i −0.558916 0.968071i
\(540\) 0 0
\(541\) −14.5180 5.28411i −0.624177 0.227182i 0.0105181 0.999945i \(-0.496652\pi\)
−0.634695 + 0.772763i \(0.718874\pi\)
\(542\) −16.7174 6.08464i −0.718074 0.261358i
\(543\) −7.52824 + 13.0393i −0.323068 + 0.559569i
\(544\) 0.434067 + 0.751825i 0.0186104 + 0.0322342i
\(545\) 0 0
\(546\) −6.02003 5.05141i −0.257634 0.216180i
\(547\) 25.7407 21.5990i 1.10059 0.923508i 0.103129 0.994668i \(-0.467115\pi\)
0.997465 + 0.0711601i \(0.0226701\pi\)
\(548\) 1.48474 8.42037i 0.0634248 0.359700i
\(549\) −48.2920 + 17.5769i −2.06105 + 0.750162i
\(550\) 0 0
\(551\) −9.70322 32.5394i −0.413371 1.38622i
\(552\) −3.63589 −0.154754
\(553\) 7.22858 2.63099i 0.307391 0.111881i
\(554\) 3.62454 20.5558i 0.153992 0.873333i
\(555\) 0 0
\(556\) 6.74440 + 5.65923i 0.286026 + 0.240005i
\(557\) 2.47429 + 14.0324i 0.104839 + 0.594571i 0.991285 + 0.131739i \(0.0420559\pi\)
−0.886446 + 0.462833i \(0.846833\pi\)
\(558\) −23.0298 39.8888i −0.974929 1.68863i
\(559\) 0.686287 1.18868i 0.0290269 0.0502760i
\(560\) 0 0
\(561\) −16.0417 5.83869i −0.677280 0.246510i
\(562\) 13.5994 23.5548i 0.573655 0.993599i
\(563\) 7.38607 + 12.7930i 0.311286 + 0.539163i 0.978641 0.205577i \(-0.0659070\pi\)
−0.667355 + 0.744740i \(0.732574\pi\)
\(564\) 0.183145 + 1.03867i 0.00771178 + 0.0437357i
\(565\) 0 0
\(566\) 15.0862 12.6588i 0.634122 0.532091i
\(567\) 11.7529 66.6539i 0.493574 2.79920i
\(568\) 6.47503 2.35672i 0.271686 0.0988857i
\(569\) 19.4550 0.815598 0.407799 0.913072i \(-0.366296\pi\)
0.407799 + 0.913072i \(0.366296\pi\)
\(570\) 0 0
\(571\) −39.3956 −1.64866 −0.824328 0.566112i \(-0.808447\pi\)
−0.824328 + 0.566112i \(0.808447\pi\)
\(572\) −4.29238 + 1.56230i −0.179473 + 0.0653230i
\(573\) 10.1765 57.7137i 0.425129 2.41102i
\(574\) 24.8405 20.8436i 1.03682 0.869997i
\(575\) 0 0
\(576\) 1.23472 + 7.00242i 0.0514465 + 0.291768i
\(577\) −7.94763 13.7657i −0.330864 0.573073i 0.651818 0.758376i \(-0.274007\pi\)
−0.982682 + 0.185303i \(0.940673\pi\)
\(578\) 8.12317 14.0697i 0.337879 0.585224i
\(579\) 40.4852 + 14.7354i 1.68251 + 0.612382i
\(580\) 0 0
\(581\) −19.1510 + 33.1706i −0.794519 + 1.37615i
\(582\) 10.8810 + 18.8464i 0.451032 + 0.781210i
\(583\) 7.62990 + 43.2713i 0.315998 + 1.79212i
\(584\) −5.98791 5.02445i −0.247781 0.207913i
\(585\) 0 0
\(586\) 2.56601 14.5526i 0.106001 0.601161i
\(587\) −12.0891 + 4.40009i −0.498973 + 0.181611i −0.579232 0.815163i \(-0.696647\pi\)
0.0802592 + 0.996774i \(0.474425\pi\)
\(588\) −13.3433 −0.550269
\(589\) −11.2117 + 25.9144i −0.461971 + 1.06778i
\(590\) 0 0
\(591\) −24.4742 + 8.90787i −1.00673 + 0.366421i
\(592\) −0.291926 + 1.65559i −0.0119981 + 0.0680445i
\(593\) −1.66829 + 1.39986i −0.0685086 + 0.0574855i −0.676399 0.736535i \(-0.736460\pi\)
0.607890 + 0.794021i \(0.292016\pi\)
\(594\) −61.9185 51.9558i −2.54055 2.13177i
\(595\) 0 0
\(596\) −0.380769 0.659512i −0.0155969 0.0270146i
\(597\) 9.44759 16.3637i 0.386664 0.669722i
\(598\) −0.793654 0.288867i −0.0324549 0.0118126i
\(599\) −3.32108 1.20877i −0.135696 0.0493891i 0.273280 0.961935i \(-0.411892\pi\)
−0.408975 + 0.912545i \(0.634114\pi\)
\(600\) 0 0
\(601\) −11.2019 19.4022i −0.456935 0.791434i 0.541863 0.840467i \(-0.317719\pi\)
−0.998797 + 0.0490333i \(0.984386\pi\)
\(602\) −1.07976 6.12360i −0.0440076 0.249579i
\(603\) −15.9319 13.3684i −0.648796 0.544405i
\(604\) −4.66356 + 3.91319i −0.189757 + 0.159225i
\(605\) 0 0
\(606\) 30.4376 11.0784i 1.23644 0.450028i
\(607\) 12.5717 0.510269 0.255134 0.966906i \(-0.417880\pi\)
0.255134 + 0.966906i \(0.417880\pi\)
\(608\) 2.99469 3.16730i 0.121451 0.128451i
\(609\) 82.8812 3.35851
\(610\) 0 0
\(611\) −0.0425431 + 0.241274i −0.00172111 + 0.00976090i
\(612\) −4.72865 + 3.96781i −0.191144 + 0.160389i
\(613\) 35.9199 + 30.1404i 1.45079 + 1.21736i 0.932000 + 0.362458i \(0.118062\pi\)
0.518791 + 0.854901i \(0.326382\pi\)
\(614\) 0.736086 + 4.17455i 0.0297060 + 0.168471i
\(615\) 0 0
\(616\) −10.3467 + 17.9210i −0.416880 + 0.722058i
\(617\) 0.496525 + 0.180720i 0.0199893 + 0.00727553i 0.351995 0.936002i \(-0.385503\pi\)
−0.332006 + 0.943277i \(0.607725\pi\)
\(618\) −6.18650 2.25170i −0.248858 0.0905768i
\(619\) −10.9317 + 18.9343i −0.439383 + 0.761034i −0.997642 0.0686330i \(-0.978136\pi\)
0.558259 + 0.829667i \(0.311470\pi\)
\(620\) 0 0
\(621\) −2.59520 14.7181i −0.104142 0.590616i
\(622\) −5.35224 4.49106i −0.214605 0.180075i
\(623\) 5.96783 5.00760i 0.239096 0.200625i
\(624\) −0.407827 + 2.31290i −0.0163261 + 0.0925901i
\(625\) 0 0
\(626\) 7.61968 0.304544
\(627\) −5.07663 + 85.5640i −0.202741 + 3.41710i
\(628\) −24.3756 −0.972692
\(629\) −1.37143 + 0.499161i −0.0546826 + 0.0199028i
\(630\) 0 0
\(631\) 23.0776 19.3644i 0.918705 0.770885i −0.0550497 0.998484i \(-0.517532\pi\)
0.973755 + 0.227598i \(0.0730873\pi\)
\(632\) −1.76109 1.47773i −0.0700524 0.0587810i
\(633\) 0.962734 + 5.45993i 0.0382652 + 0.217013i
\(634\) 6.86922 + 11.8978i 0.272812 + 0.472524i
\(635\) 0 0
\(636\) 21.2289 + 7.72669i 0.841781 + 0.306383i
\(637\) −2.91263 1.06011i −0.115402 0.0420031i
\(638\) 24.0876 41.7209i 0.953637 1.65175i
\(639\) 24.4976 + 42.4310i 0.969109 + 1.67855i
\(640\) 0 0
\(641\) 24.6653 + 20.6967i 0.974223 + 0.817470i 0.983208 0.182490i \(-0.0584156\pi\)
−0.00898505 + 0.999960i \(0.502860\pi\)
\(642\) −35.6530 + 29.9164i −1.40711 + 1.18071i
\(643\) 4.44391 25.2027i 0.175251 0.993896i −0.762604 0.646866i \(-0.776079\pi\)
0.937854 0.347030i \(-0.112810\pi\)
\(644\) −3.59543 + 1.30863i −0.141680 + 0.0515672i
\(645\) 0 0
\(646\) 3.68115 + 0.876666i 0.144833 + 0.0344920i
\(647\) 18.8860 0.742483 0.371242 0.928536i \(-0.378932\pi\)
0.371242 + 0.928536i \(0.378932\pi\)
\(648\) −19.0073 + 6.91809i −0.746677 + 0.271768i
\(649\) 5.21946 29.6010i 0.204882 1.16194i
\(650\) 0 0
\(651\) −52.7961 44.3012i −2.06924 1.73630i
\(652\) 0.748409 + 4.24444i 0.0293100 + 0.166225i
\(653\) 12.4152 + 21.5038i 0.485846 + 0.841510i 0.999868 0.0162674i \(-0.00517829\pi\)
−0.514022 + 0.857777i \(0.671845\pi\)
\(654\) −13.8240 + 23.9439i −0.540562 + 0.936282i
\(655\) 0 0
\(656\) −9.10652 3.31450i −0.355550 0.129410i
\(657\) 27.7900 48.1336i 1.08419 1.87787i
\(658\) 0.554943 + 0.961190i 0.0216339 + 0.0374711i
\(659\) 5.44946 + 30.9054i 0.212281 + 1.20391i 0.885563 + 0.464519i \(0.153773\pi\)
−0.673282 + 0.739386i \(0.735116\pi\)
\(660\) 0 0
\(661\) −14.2738 + 11.9771i −0.555186 + 0.465857i −0.876693 0.481051i \(-0.840255\pi\)
0.321506 + 0.946907i \(0.395811\pi\)
\(662\) −1.15376 + 6.54331i −0.0448422 + 0.254313i
\(663\) −1.91592 + 0.697338i −0.0744082 + 0.0270824i
\(664\) 11.4468 0.444220
\(665\) 0 0
\(666\) −11.9536 −0.463193
\(667\) 8.37032 3.04655i 0.324100 0.117963i
\(668\) −0.904979 + 5.13239i −0.0350147 + 0.198578i
\(669\) 64.4044 54.0417i 2.49002 2.08937i
\(670\) 0 0
\(671\) 7.76167 + 44.0186i 0.299636 + 1.69932i
\(672\) 5.31979 + 9.21415i 0.205215 + 0.355444i
\(673\) −7.28810 + 12.6234i −0.280935 + 0.486594i −0.971615 0.236566i \(-0.923978\pi\)
0.690680 + 0.723161i \(0.257311\pi\)
\(674\) −17.2976 6.29582i −0.666280 0.242506i
\(675\) 0 0
\(676\) 6.22722 10.7859i 0.239509 0.414841i
\(677\) 1.21821 + 2.11001i 0.0468197 + 0.0810941i 0.888486 0.458905i \(-0.151758\pi\)
−0.841666 + 0.539999i \(0.818425\pi\)
\(678\) 5.98022 + 33.9155i 0.229669 + 1.30252i
\(679\) 17.5431 + 14.7204i 0.673244 + 0.564918i
\(680\) 0 0
\(681\) −15.1549 + 85.9479i −0.580738 + 3.29353i
\(682\) −37.6445 + 13.7015i −1.44148 + 0.524656i
\(683\) −15.0962 −0.577639 −0.288820 0.957384i \(-0.593263\pi\)
−0.288820 + 0.957384i \(0.593263\pi\)
\(684\) 25.8764 + 17.0594i 0.989409 + 0.652282i
\(685\) 0 0
\(686\) 8.81533 3.20852i 0.336571 0.122502i
\(687\) 6.38955 36.2370i 0.243777 1.38253i
\(688\) −1.42354 + 1.19449i −0.0542720 + 0.0455396i
\(689\) 4.02004 + 3.37322i 0.153151 + 0.128509i
\(690\) 0 0
\(691\) 6.12019 + 10.6005i 0.232823 + 0.403261i 0.958638 0.284629i \(-0.0918704\pi\)
−0.725815 + 0.687890i \(0.758537\pi\)
\(692\) 3.51787 6.09314i 0.133729 0.231626i
\(693\) −138.266 50.3246i −5.25228 1.91167i
\(694\) 6.97015 + 2.53693i 0.264583 + 0.0963005i
\(695\) 0 0
\(696\) −12.3847 21.4510i −0.469442 0.813097i
\(697\) −1.46091 8.28523i −0.0553359 0.313825i
\(698\) 14.6710 + 12.3104i 0.555305 + 0.465956i
\(699\) 31.3190 26.2798i 1.18459 0.993992i
\(700\) 0 0
\(701\) −41.9967 + 15.2856i −1.58620 + 0.577328i −0.976539 0.215339i \(-0.930914\pi\)
−0.609656 + 0.792666i \(0.708692\pi\)
\(702\) −9.65372 −0.364356
\(703\) 4.36954 + 5.88261i 0.164800 + 0.221867i
\(704\) 6.18432 0.233080
\(705\) 0 0
\(706\) 0.278424 1.57902i 0.0104786 0.0594273i
\(707\) 26.1115 21.9102i 0.982026 0.824017i
\(708\) −11.8386 9.93381i −0.444924 0.373335i
\(709\) −2.78707 15.8063i −0.104671 0.593617i −0.991351 0.131235i \(-0.958106\pi\)
0.886681 0.462382i \(-0.153005\pi\)
\(710\) 0 0
\(711\) 8.17325 14.1565i 0.306521 0.530910i
\(712\) −2.18780 0.796295i −0.0819914 0.0298424i
\(713\) −6.96040 2.53338i −0.260669 0.0948758i
\(714\) −4.61829 + 7.99911i −0.172835 + 0.299359i
\(715\) 0 0
\(716\) 0.555577 + 3.15084i 0.0207629 + 0.117752i
\(717\) 27.5589 + 23.1247i 1.02921 + 0.863606i
\(718\) −16.5455 + 13.8833i −0.617474 + 0.518122i
\(719\) −0.265213 + 1.50410i −0.00989079 + 0.0560934i −0.989354 0.145531i \(-0.953511\pi\)
0.979463 + 0.201624i \(0.0646221\pi\)
\(720\) 0 0
\(721\) −6.92809 −0.258016
\(722\) −1.06362 18.9702i −0.0395838 0.705998i
\(723\) 75.6608 2.81385
\(724\) 4.44963 1.61953i 0.165369 0.0601894i
\(725\) 0 0
\(726\) −66.3651 + 55.6869i −2.46304 + 2.06674i
\(727\) 29.0850 + 24.4052i 1.07870 + 0.905139i 0.995812 0.0914199i \(-0.0291405\pi\)
0.0828900 + 0.996559i \(0.473585\pi\)
\(728\) 0.429171 + 2.43395i 0.0159061 + 0.0902081i
\(729\) −9.57428 16.5831i −0.354603 0.614190i
\(730\) 0 0
\(731\) −1.51596 0.551764i −0.0560698 0.0204077i
\(732\) 21.5955 + 7.86012i 0.798193 + 0.290519i
\(733\) −16.0110 + 27.7319i −0.591381 + 1.02430i 0.402666 + 0.915347i \(0.368084\pi\)
−0.994047 + 0.108955i \(0.965250\pi\)
\(734\) 9.87097 + 17.0970i 0.364344 + 0.631062i
\(735\) 0 0
\(736\) 0.875950 + 0.735009i 0.0322879 + 0.0270928i
\(737\) −13.8568 + 11.6272i −0.510421 + 0.428294i
\(738\) 11.9656 67.8602i 0.440459 2.49797i
\(739\) 36.3892 13.2446i 1.33860 0.487210i 0.429228 0.903196i \(-0.358786\pi\)
0.909371 + 0.415986i \(0.136564\pi\)
\(740\) 0 0
\(741\) 6.10434 + 8.21814i 0.224249 + 0.301901i
\(742\) 23.7737 0.872758
\(743\) −29.3436 + 10.6802i −1.07651 + 0.391819i −0.818609 0.574351i \(-0.805254\pi\)
−0.257905 + 0.966170i \(0.583032\pi\)
\(744\) −3.57667 + 20.2843i −0.131127 + 0.743658i
\(745\) 0 0
\(746\) 17.7417 + 14.8870i 0.649568 + 0.545052i
\(747\) 14.1335 + 80.1551i 0.517118 + 2.93272i
\(748\) 2.68441 + 4.64953i 0.0981517 + 0.170004i
\(749\) −24.4887 + 42.4157i −0.894798 + 1.54984i
\(750\) 0 0
\(751\) 32.3847 + 11.7871i 1.18173 + 0.430116i 0.856814 0.515625i \(-0.172440\pi\)
0.324920 + 0.945741i \(0.394663\pi\)
\(752\) 0.165847 0.287256i 0.00604784 0.0104752i
\(753\) 41.4532 + 71.7991i 1.51064 + 2.61650i
\(754\) −0.999129 5.66634i −0.0363861 0.206356i
\(755\) 0 0
\(756\) −33.5018 + 28.1113i −1.21845 + 1.02240i
\(757\) 0.469366 2.66191i 0.0170594 0.0967487i −0.975089 0.221813i \(-0.928803\pi\)
0.992149 + 0.125064i \(0.0399137\pi\)
\(758\) 3.31671 1.20718i 0.120468 0.0438468i
\(759\) −22.4855 −0.816173
\(760\) 0 0
\(761\) 9.19327 0.333256 0.166628 0.986020i \(-0.446712\pi\)
0.166628 + 0.986020i \(0.446712\pi\)
\(762\) 33.5380 12.2068i 1.21495 0.442207i
\(763\) −5.05230 + 28.6530i −0.182906 + 1.03731i
\(764\) −14.1187 + 11.8470i −0.510798 + 0.428611i
\(765\) 0 0
\(766\) −6.36973 36.1246i −0.230148 1.30523i
\(767\) −1.79495 3.10895i −0.0648120 0.112258i
\(768\) 1.58985 2.75370i 0.0573686 0.0993654i
\(769\) −0.0570740 0.0207732i −0.00205814 0.000749102i 0.340991 0.940067i \(-0.389237\pi\)
−0.343049 + 0.939318i \(0.611460\pi\)
\(770\) 0 0
\(771\) 16.1414 27.9578i 0.581320 1.00688i
\(772\) −6.77477 11.7343i −0.243829 0.422325i
\(773\) −1.71922 9.75016i −0.0618359 0.350689i −0.999990 0.00447097i \(-0.998577\pi\)
0.938154 0.346218i \(-0.112534\pi\)
\(774\) −10.1220 8.49337i −0.363828 0.305288i
\(775\) 0 0
\(776\) 1.18846 6.74008i 0.0426632 0.241955i
\(777\) −16.8079 + 6.11757i −0.602979 + 0.219466i
\(778\) −24.5847 −0.881405
\(779\) −37.7693 + 18.9172i −1.35322 + 0.677779i
\(780\) 0 0
\(781\) 40.0437 14.5747i 1.43288 0.521524i
\(782\) −0.172378 + 0.977604i −0.00616423 + 0.0349591i
\(783\) 77.9937 65.4445i 2.78727 2.33879i
\(784\) 3.21464 + 2.69741i 0.114809 + 0.0963359i
\(785\) 0 0
\(786\) 24.1436 + 41.8179i 0.861173 + 1.49160i
\(787\) 5.59115 9.68415i 0.199303 0.345203i −0.749000 0.662570i \(-0.769466\pi\)
0.948303 + 0.317368i \(0.102799\pi\)
\(788\) 7.69702 + 2.80149i 0.274195 + 0.0997988i
\(789\) −51.1729 18.6254i −1.82180 0.663082i
\(790\) 0 0
\(791\) 18.1205 + 31.3857i 0.644293 + 1.11595i
\(792\) 7.63589 + 43.3053i 0.271329 + 1.53879i
\(793\) 4.08947 + 3.43147i 0.145221 + 0.121855i
\(794\) −15.5934 + 13.0844i −0.553390 + 0.464349i
\(795\) 0 0
\(796\) −5.58408 + 2.03244i −0.197923 + 0.0720379i
\(797\) −16.8348 −0.596320 −0.298160 0.954516i \(-0.596373\pi\)
−0.298160 + 0.954516i \(0.596373\pi\)
\(798\) 45.1152 + 10.7442i 1.59706 + 0.380339i
\(799\) 0.287955 0.0101871
\(800\) 0 0
\(801\) 2.87468 16.3031i 0.101572 0.576043i
\(802\) 15.4330 12.9498i 0.544957 0.457273i
\(803\) −37.0312 31.0728i −1.30680 1.09654i
\(804\) 1.61500 + 9.15910i 0.0569565 + 0.323016i
\(805\) 0 0
\(806\) −2.39229 + 4.14356i −0.0842647 + 0.145951i
\(807\) 68.1529 + 24.8056i 2.39910 + 0.873199i
\(808\) −9.57249 3.48410i −0.336759 0.122570i
\(809\) −13.1217 + 22.7275i −0.461335 + 0.799056i −0.999028 0.0440848i \(-0.985963\pi\)
0.537692 + 0.843141i \(0.319296\pi\)
\(810\) 0 0
\(811\) 7.65768 + 43.4288i 0.268897 + 1.52499i 0.757703 + 0.652600i \(0.226322\pi\)
−0.488805 + 0.872393i \(0.662567\pi\)
\(812\) −19.9675 16.7548i −0.700723 0.587977i
\(813\) −43.3334 + 36.3610i −1.51977 + 1.27524i
\(814\) −1.80536 + 10.2387i −0.0632780 + 0.358867i
\(815\) 0 0
\(816\) 2.76040 0.0966332
\(817\) −0.479748 + 8.08592i −0.0167843 + 0.282891i
\(818\) 12.8843 0.450490
\(819\) −16.5136 + 6.01047i −0.577033 + 0.210023i
\(820\) 0 0
\(821\) −35.5474 + 29.8278i −1.24061 + 1.04100i −0.243138 + 0.969992i \(0.578177\pi\)
−0.997476 + 0.0710073i \(0.977379\pi\)
\(822\) −20.8266 17.4756i −0.726412 0.609532i
\(823\) −5.43149 30.8035i −0.189330 1.07374i −0.920265 0.391296i \(-0.872027\pi\)
0.730935 0.682447i \(-0.239084\pi\)
\(824\) 1.03525 + 1.79310i 0.0360646 + 0.0624656i
\(825\) 0 0
\(826\) −15.2823 5.56230i −0.531739 0.193537i
\(827\) −18.5253 6.74267i −0.644189 0.234466i −0.000793747 1.00000i \(-0.500253\pi\)
−0.643395 + 0.765534i \(0.722475\pi\)
\(828\) −4.06530 + 7.04130i −0.141279 + 0.244702i
\(829\) 27.3133 + 47.3081i 0.948632 + 1.64308i 0.748311 + 0.663348i \(0.230865\pi\)
0.200320 + 0.979730i \(0.435802\pi\)
\(830\) 0 0
\(831\) −50.8420 42.6615i −1.76369 1.47991i
\(832\) 0.565815 0.474775i 0.0196161 0.0164599i
\(833\) −0.632609 + 3.58770i −0.0219186 + 0.124307i
\(834\) 26.3064 9.57473i 0.910915 0.331546i
\(835\) 0 0
\(836\) 18.5202 19.5876i 0.640533 0.677452i
\(837\) −84.6638 −2.92641
\(838\) −18.8095 + 6.84609i −0.649762 + 0.236494i
\(839\) 6.63032 37.6024i 0.228904 1.29818i −0.626175 0.779682i \(-0.715381\pi\)
0.855079 0.518497i \(-0.173508\pi\)
\(840\) 0 0
\(841\) 24.2700 + 20.3650i 0.836898 + 0.702241i
\(842\) 1.16311 + 6.59634i 0.0400835 + 0.227325i
\(843\) −43.2418 74.8970i −1.48933 2.57959i
\(844\) 0.871808 1.51002i 0.0300089 0.0519769i
\(845\) 0 0
\(846\) 2.21627 + 0.806655i 0.0761968 + 0.0277334i
\(847\) −45.5838 + 78.9534i −1.56628 + 2.71287i
\(848\) −3.55244 6.15300i −0.121991 0.211295i
\(849\) −10.8738 61.6685i −0.373189 2.11646i
\(850\) 0 0
\(851\) −1.47259 + 1.23565i −0.0504797 + 0.0423575i
\(852\) 3.80462 21.5771i 0.130344 0.739219i
\(853\) −31.2888 + 11.3882i −1.07131 + 0.389925i −0.816666 0.577111i \(-0.804180\pi\)
−0.254643 + 0.967035i \(0.581958\pi\)
\(854\) 24.1842 0.827567
\(855\) 0 0
\(856\) 14.6371 0.500287
\(857\) −37.9460 + 13.8112i −1.29621 + 0.471782i −0.895761 0.444537i \(-0.853368\pi\)
−0.400450 + 0.916319i \(0.631146\pi\)
\(858\) −2.52213 + 14.3037i −0.0861042 + 0.488321i
\(859\) −5.94441 + 4.98795i −0.202821 + 0.170187i −0.738541 0.674209i \(-0.764485\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(860\) 0 0
\(861\) −17.9045 101.541i −0.610183 3.46052i
\(862\) 14.0090 + 24.2643i 0.477149 + 0.826446i
\(863\) −23.2056 + 40.1932i −0.789926 + 1.36819i 0.136085 + 0.990697i \(0.456548\pi\)
−0.926011 + 0.377495i \(0.876785\pi\)
\(864\) 12.2818 + 4.47019i 0.417834 + 0.152079i
\(865\) 0 0
\(866\) −11.3089 + 19.5876i −0.384292 + 0.665614i
\(867\) −25.8292 44.7375i −0.877205 1.51936i
\(868\) 3.76386 + 21.3459i 0.127754 + 0.724526i
\(869\) −10.8912 9.13876i −0.369457 0.310011i
\(870\) 0 0
\(871\) −0.375151 + 2.12759i −0.0127115 + 0.0720906i
\(872\) 8.17082 2.97393i 0.276699 0.100710i
\(873\) 48.6643 1.64704
\(874\) 4.95120 0.573271i 0.167477 0.0193912i
\(875\) 0 0
\(876\) −23.3557 + 8.50076i −0.789115 + 0.287214i
\(877\) 4.69718 26.6390i 0.158612 0.899536i −0.796796 0.604248i \(-0.793473\pi\)
0.955408 0.295288i \(-0.0954155\pi\)
\(878\) −3.16759 + 2.65793i −0.106901 + 0.0897006i
\(879\) −35.9938 30.2024i −1.21404 1.01870i
\(880\) 0 0
\(881\) −10.1018 17.4968i −0.340338 0.589482i 0.644158 0.764893i \(-0.277208\pi\)
−0.984495 + 0.175410i \(0.943875\pi\)
\(882\) −14.9192 + 25.8408i −0.502356 + 0.870106i
\(883\) −14.1304 5.14304i −0.475525 0.173077i 0.0931285 0.995654i \(-0.470313\pi\)
−0.568654 + 0.822577i \(0.692535\pi\)
\(884\) 0.602549 + 0.219310i 0.0202659 + 0.00737619i
\(885\) 0 0
\(886\) −14.4699 25.0626i −0.486125 0.841994i
\(887\) −5.06838 28.7442i −0.170180 0.965137i −0.943562 0.331197i \(-0.892548\pi\)
0.773382 0.633940i \(-0.218563\pi\)
\(888\) 4.09488 + 3.43601i 0.137415 + 0.115305i
\(889\) 28.7713 24.1420i 0.964959 0.809697i
\(890\) 0 0
\(891\) −117.547 + 42.7837i −3.93798 + 1.43331i
\(892\) −26.4409 −0.885307
\(893\) −0.413165 1.38553i −0.0138260 0.0463651i
\(894\) −2.42146 −0.0809857
\(895\) 0 0
\(896\) 0.581045 3.29527i 0.0194114 0.110087i
\(897\) −2.05724 + 1.72623i −0.0686892 + 0.0576371i
\(898\) −4.26028 3.57480i −0.142167 0.119293i
\(899\) −8.76243 49.6942i −0.292243 1.65739i
\(900\) 0 0
\(901\) 3.08399 5.34162i 0.102743 0.177955i
\(902\) −56.3177 20.4980i −1.87517 0.682507i
\(903\) −18.5792 6.76226i −0.618276 0.225034i
\(904\) 5.41542 9.37977i 0.180114 0.311967i
\(905\) 0 0
\(906\) 3.36139 + 19.0634i 0.111675 + 0.633338i
\(907\) −40.2537 33.7769i −1.33660 1.12154i −0.982485 0.186343i \(-0.940336\pi\)
−0.354119 0.935200i \(-0.615219\pi\)
\(908\) 21.0258 17.6427i 0.697766 0.585495i
\(909\) 12.5778 71.3325i 0.417181 2.36595i
\(910\) 0 0
\(911\) −28.5338 −0.945366 −0.472683 0.881233i \(-0.656714\pi\)
−0.472683 + 0.881233i \(0.656714\pi\)
\(912\) −3.96068 13.2820i −0.131151 0.439811i
\(913\) 70.7905 2.34282
\(914\) −3.23339 + 1.17686i −0.106951 + 0.0389270i
\(915\) 0 0
\(916\) −8.86480 + 7.43845i −0.292901 + 0.245773i
\(917\) 38.9260 + 32.6628i 1.28545 + 1.07862i
\(918\) 1.97029 + 11.1741i 0.0650294 + 0.368800i
\(919\) −13.5016 23.3855i −0.445378 0.771418i 0.552700 0.833380i \(-0.313597\pi\)
−0.998078 + 0.0619624i \(0.980264\pi\)
\(920\) 0 0
\(921\) 12.6657 + 4.60994i 0.417349 + 0.151903i
\(922\) 4.77161 + 1.73672i 0.157145 + 0.0571960i
\(923\) 2.54476 4.40765i 0.0837617 0.145079i
\(924\) 32.8993 + 56.9833i 1.08231 + 1.87461i
\(925\) 0 0
\(926\) 3.92835 + 3.29628i 0.129094 + 0.108323i
\(927\) −11.2778 + 9.46322i −0.370412 + 0.310813i
\(928\) −1.35270 + 7.67154i −0.0444045 + 0.251831i
\(929\) 10.4901 3.81810i 0.344170 0.125268i −0.164151 0.986435i \(-0.552488\pi\)
0.508321 + 0.861168i \(0.330266\pi\)
\(930\) 0 0
\(931\) 18.1704 2.10384i 0.595510 0.0689507i
\(932\) −12.8579 −0.421173
\(933\) −20.8763 + 7.59834i −0.683458 + 0.248758i
\(934\) −5.14382 + 29.1720i −0.168311 + 0.954538i
\(935\) 0 0
\(936\) 4.02320 + 3.37586i 0.131502 + 0.110344i
\(937\) −2.37497 13.4691i −0.0775869 0.440017i −0.998711 0.0507491i \(-0.983839\pi\)
0.921125 0.389268i \(-0.127272\pi\)
\(938\) 4.89357 + 8.47591i 0.159781 + 0.276748i
\(939\) 12.1141 20.9823i 0.395330 0.684731i
\(940\) 0 0
\(941\) 3.22980 + 1.17555i 0.105288 + 0.0383218i 0.394127 0.919056i \(-0.371047\pi\)
−0.288839 + 0.957378i \(0.593269\pi\)
\(942\) −38.7534 + 67.1229i −1.26266 + 2.18698i
\(943\) −5.54067 9.59672i −0.180429 0.312512i
\(944\) 0.843982 + 4.78646i 0.0274693 + 0.155786i
\(945\) 0 0
\(946\) −8.80363 + 7.38712i −0.286231 + 0.240176i
\(947\) −7.09857 + 40.2580i −0.230673 + 1.30821i 0.620866 + 0.783917i \(0.286781\pi\)
−0.851538 + 0.524292i \(0.824330\pi\)
\(948\) −6.86908 + 2.50014i −0.223097 + 0.0812008i
\(949\) −5.77353 −0.187417
\(950\) 0 0
\(951\) 43.6840 1.41655
\(952\) 2.72968 0.993522i 0.0884694 0.0322002i
\(953\) 7.57113 42.9380i 0.245253 1.39090i −0.574652 0.818398i \(-0.694862\pi\)
0.819905 0.572500i \(-0.194026\pi\)
\(954\) 38.6997 32.4729i 1.25295 1.05135i
\(955\) 0 0
\(956\) −1.96468 11.1423i −0.0635424 0.360367i
\(957\) −76.5911 132.660i −2.47584 4.28828i
\(958\) 18.8421 32.6354i 0.608760 1.05440i
\(959\) −26.8847 9.78522i −0.868152 0.315981i
\(960\) 0 0
\(961\) −5.48052 + 9.49254i −0.176791 + 0.306211i
\(962\) 0.620858 + 1.07536i 0.0200173 + 0.0346709i
\(963\) 18.0727 + 102.496i 0.582386 + 3.30287i
\(964\) −18.2280 15.2951i −0.587085 0.492623i
\(965\) 0 0
\(966\) −2.11262 + 11.9812i −0.0679723 + 0.385490i
\(967\) 21.6746 7.88890i 0.697008 0.253690i 0.0308750 0.999523i \(-0.490171\pi\)
0.666133 + 0.745833i \(0.267948\pi\)
\(968\) 27.2459 0.875715
\(969\) 8.26654 8.74301i 0.265560 0.280866i
\(970\) 0 0
\(971\) 30.8948 11.2448i 0.991462 0.360863i 0.205176 0.978725i \(-0.434223\pi\)
0.786286 + 0.617862i \(0.212001\pi\)
\(972\) −4.35964 + 24.7248i −0.139836 + 0.793047i
\(973\) 22.5675 18.9364i 0.723480 0.607072i
\(974\) 13.6006 + 11.4122i 0.435790 + 0.365672i
\(975\) 0 0
\(976\) −3.61379 6.25926i −0.115675 0.200354i
\(977\) 28.1552 48.7663i 0.900765 1.56017i 0.0742618 0.997239i \(-0.476340\pi\)
0.826503 0.562932i \(-0.190327\pi\)
\(978\) 12.8777 + 4.68712i 0.411785 + 0.149877i
\(979\) −13.5301 4.92455i −0.432424 0.157389i
\(980\) 0 0
\(981\) 30.9134 + 53.5436i 0.986988 + 1.70951i
\(982\) −3.87201 21.9592i −0.123561 0.700747i
\(983\) 26.4336 + 22.1804i 0.843100 + 0.707445i 0.958259 0.285902i \(-0.0922933\pi\)
−0.115159 + 0.993347i \(0.536738\pi\)
\(984\) −23.6051 + 19.8070i −0.752503 + 0.631425i
\(985\) 0 0
\(986\) −6.35482 + 2.31296i −0.202379 + 0.0736598i
\(987\) 3.52910 0.112332
\(988\) 0.190686 3.21391i 0.00606652 0.102248i
\(989\) −2.12491 −0.0675683
\(990\) 0 0
\(991\) 7.27532 41.2604i 0.231108 1.31068i −0.619549 0.784958i \(-0.712684\pi\)
0.850657 0.525721i \(-0.176205\pi\)
\(992\) 4.96223 4.16381i 0.157551 0.132201i
\(993\) 16.1840 + 13.5800i 0.513583 + 0.430947i
\(994\) −4.00374 22.7063i −0.126991 0.720201i
\(995\) 0 0
\(996\) 18.1986 31.5209i 0.576644 0.998777i
\(997\) −30.8447 11.2266i −0.976862 0.355549i −0.196243 0.980555i \(-0.562874\pi\)
−0.780619 + 0.625007i \(0.785096\pi\)
\(998\) 17.7382 + 6.45619i 0.561494 + 0.204367i
\(999\) −10.9862 + 19.0286i −0.347587 + 0.602039i
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 950.2.l.i.651.1 18
5.2 odd 4 950.2.u.g.499.3 36
5.3 odd 4 950.2.u.g.499.4 36
5.4 even 2 190.2.k.d.81.3 yes 18
19.4 even 9 inner 950.2.l.i.251.1 18
95.4 even 18 190.2.k.d.61.3 18
95.23 odd 36 950.2.u.g.99.3 36
95.42 odd 36 950.2.u.g.99.4 36
95.59 odd 18 3610.2.a.bj.1.2 9
95.74 even 18 3610.2.a.bi.1.8 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.k.d.61.3 18 95.4 even 18
190.2.k.d.81.3 yes 18 5.4 even 2
950.2.l.i.251.1 18 19.4 even 9 inner
950.2.l.i.651.1 18 1.1 even 1 trivial
950.2.u.g.99.3 36 95.23 odd 36
950.2.u.g.99.4 36 95.42 odd 36
950.2.u.g.499.3 36 5.2 odd 4
950.2.u.g.499.4 36 5.3 odd 4
3610.2.a.bi.1.8 9 95.74 even 18
3610.2.a.bj.1.2 9 95.59 odd 18