Properties

Label 637.2.r.e.324.3
Level $637$
Weight $2$
Character 637.324
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(116,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.116");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.89539436150784.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 324.3
Root \(1.98293 - 0.531325i\) of defining polynomial
Character \(\chi\) \(=\) 637.324
Dual form 637.2.r.e.116.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.596598 - 0.344446i) q^{2} +(1.10716 + 1.91766i) q^{3} +(-0.762714 - 1.32106i) q^{4} +(-2.78368 - 1.60716i) q^{5} -1.52543i q^{6} +2.42864i q^{8} +(-0.951606 + 1.64823i) q^{9} +O(q^{10})\) \(q+(-0.596598 - 0.344446i) q^{2} +(1.10716 + 1.91766i) q^{3} +(-0.762714 - 1.32106i) q^{4} +(-2.78368 - 1.60716i) q^{5} -1.52543i q^{6} +2.42864i q^{8} +(-0.951606 + 1.64823i) q^{9} +(1.10716 + 1.91766i) q^{10} +(-2.32865 + 1.34445i) q^{11} +(1.68889 - 2.92525i) q^{12} +(3.59210 + 0.311108i) q^{13} -7.11753i q^{15} +(-0.688892 + 1.19320i) q^{16} +(1.79605 + 3.11085i) q^{17} +(1.13545 - 0.655554i) q^{18} +(7.40120 + 4.27309i) q^{19} +4.90321i q^{20} +1.85236 q^{22} +(-1.64050 + 2.84143i) q^{23} +(-4.65730 + 2.68889i) q^{24} +(2.66593 + 4.61752i) q^{25} +(-2.03588 - 1.42289i) q^{26} +2.42864 q^{27} +2.05086 q^{29} +(-2.45161 + 4.24631i) q^{30} +(5.05459 - 2.91827i) q^{31} +(5.02851 - 2.90321i) q^{32} +(-5.15637 - 2.97703i) q^{33} -2.47457i q^{34} +2.90321 q^{36} +(3.40636 + 1.96666i) q^{37} +(-2.94370 - 5.09863i) q^{38} +(3.38044 + 7.23287i) q^{39} +(3.90321 - 6.76056i) q^{40} +0.755569i q^{41} -8.80642 q^{43} +(3.55219 + 2.05086i) q^{44} +(5.29794 - 3.05877i) q^{45} +(1.95744 - 1.13013i) q^{46} +(1.63027 + 0.941234i) q^{47} -3.05086 q^{48} -3.67307i q^{50} +(-3.97703 + 6.88842i) q^{51} +(-2.32876 - 4.98267i) q^{52} +(-1.26271 - 2.18708i) q^{53} +(-1.44892 - 0.836535i) q^{54} +8.64296 q^{55} +18.9240i q^{57} +(-1.22354 - 0.706409i) q^{58} +(-6.34957 + 3.66593i) q^{59} +(-9.40268 + 5.42864i) q^{60} +(-4.52543 + 7.83827i) q^{61} -4.02074 q^{62} -1.24443 q^{64} +(-9.49928 - 6.63911i) q^{65} +(2.05086 + 3.55219i) q^{66} +(0.371213 - 0.214320i) q^{67} +(2.73975 - 4.74538i) q^{68} -7.26517 q^{69} +8.98418i q^{71} +(-4.00296 - 2.31111i) q^{72} +(-5.01481 + 2.89530i) q^{73} +(-1.35482 - 2.34661i) q^{74} +(-5.90321 + 10.2247i) q^{75} -13.0366i q^{76} +(0.474572 - 5.47949i) q^{78} +(2.23975 - 3.87936i) q^{79} +(3.83531 - 2.21432i) q^{80} +(5.54371 + 9.60199i) q^{81} +(0.260253 - 0.450771i) q^{82} -10.8272i q^{83} -11.5462i q^{85} +(5.25390 + 3.03334i) q^{86} +(2.27062 + 3.93284i) q^{87} +(-3.26517 - 5.65545i) q^{88} +(4.64360 + 2.68098i) q^{89} -4.21432 q^{90} +5.00492 q^{92} +(11.1925 + 6.46198i) q^{93} +(-0.648409 - 1.12308i) q^{94} +(-13.7351 - 23.7898i) q^{95} +(11.1347 + 6.42864i) q^{96} +9.62867i q^{97} -5.11753i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} + 2 q^{9} + 20 q^{12} + 16 q^{13} - 8 q^{16} + 8 q^{17} + 48 q^{22} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 24 q^{27} - 28 q^{29} - 16 q^{30} + 8 q^{36} + 4 q^{38} + 8 q^{39} + 20 q^{40} - 52 q^{43} + 16 q^{48} - 8 q^{51} + 20 q^{52} - 2 q^{53} + 24 q^{55} - 28 q^{61} + 32 q^{62} - 16 q^{64} + 6 q^{65} - 28 q^{66} - 20 q^{68} - 8 q^{69} + 24 q^{74} - 44 q^{75} + 32 q^{78} - 26 q^{79} + 26 q^{81} + 56 q^{82} + 40 q^{87} + 40 q^{88} - 24 q^{90} - 72 q^{92} - 20 q^{94} - 58 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.596598 0.344446i −0.421859 0.243560i 0.274014 0.961726i \(-0.411649\pi\)
−0.695872 + 0.718166i \(0.744982\pi\)
\(3\) 1.10716 + 1.91766i 0.639219 + 1.10716i 0.985604 + 0.169068i \(0.0540756\pi\)
−0.346385 + 0.938092i \(0.612591\pi\)
\(4\) −0.762714 1.32106i −0.381357 0.660530i
\(5\) −2.78368 1.60716i −1.24490 0.718744i −0.274813 0.961498i \(-0.588616\pi\)
−0.970088 + 0.242754i \(0.921949\pi\)
\(6\) 1.52543i 0.622753i
\(7\) 0 0
\(8\) 2.42864i 0.858654i
\(9\) −0.951606 + 1.64823i −0.317202 + 0.549410i
\(10\) 1.10716 + 1.91766i 0.350115 + 0.606416i
\(11\) −2.32865 + 1.34445i −0.702114 + 0.405366i −0.808134 0.588998i \(-0.799522\pi\)
0.106020 + 0.994364i \(0.466189\pi\)
\(12\) 1.68889 2.92525i 0.487541 0.844446i
\(13\) 3.59210 + 0.311108i 0.996270 + 0.0862858i
\(14\) 0 0
\(15\) 7.11753i 1.83774i
\(16\) −0.688892 + 1.19320i −0.172223 + 0.298299i
\(17\) 1.79605 + 3.11085i 0.435607 + 0.754493i 0.997345 0.0728222i \(-0.0232006\pi\)
−0.561738 + 0.827315i \(0.689867\pi\)
\(18\) 1.13545 0.655554i 0.267629 0.154516i
\(19\) 7.40120 + 4.27309i 1.69795 + 0.980313i 0.947701 + 0.319160i \(0.103401\pi\)
0.750251 + 0.661153i \(0.229933\pi\)
\(20\) 4.90321i 1.09639i
\(21\) 0 0
\(22\) 1.85236 0.394924
\(23\) −1.64050 + 2.84143i −0.342068 + 0.592478i −0.984817 0.173599i \(-0.944460\pi\)
0.642749 + 0.766077i \(0.277794\pi\)
\(24\) −4.65730 + 2.68889i −0.950667 + 0.548868i
\(25\) 2.66593 + 4.61752i 0.533185 + 0.923504i
\(26\) −2.03588 1.42289i −0.399269 0.279052i
\(27\) 2.42864 0.467392
\(28\) 0 0
\(29\) 2.05086 0.380834 0.190417 0.981703i \(-0.439016\pi\)
0.190417 + 0.981703i \(0.439016\pi\)
\(30\) −2.45161 + 4.24631i −0.447600 + 0.775266i
\(31\) 5.05459 2.91827i 0.907831 0.524136i 0.0280982 0.999605i \(-0.491055\pi\)
0.879733 + 0.475469i \(0.157722\pi\)
\(32\) 5.02851 2.90321i 0.888923 0.513220i
\(33\) −5.15637 2.97703i −0.897609 0.518235i
\(34\) 2.47457i 0.424386i
\(35\) 0 0
\(36\) 2.90321 0.483869
\(37\) 3.40636 + 1.96666i 0.560002 + 0.323317i 0.753146 0.657853i \(-0.228535\pi\)
−0.193144 + 0.981170i \(0.561869\pi\)
\(38\) −2.94370 5.09863i −0.477530 0.827107i
\(39\) 3.38044 + 7.23287i 0.541303 + 1.15819i
\(40\) 3.90321 6.76056i 0.617152 1.06894i
\(41\) 0.755569i 0.118000i 0.998258 + 0.0590000i \(0.0187912\pi\)
−0.998258 + 0.0590000i \(0.981209\pi\)
\(42\) 0 0
\(43\) −8.80642 −1.34297 −0.671484 0.741019i \(-0.734343\pi\)
−0.671484 + 0.741019i \(0.734343\pi\)
\(44\) 3.55219 + 2.05086i 0.535512 + 0.309178i
\(45\) 5.29794 3.05877i 0.789770 0.455974i
\(46\) 1.95744 1.13013i 0.288608 0.166628i
\(47\) 1.63027 + 0.941234i 0.237799 + 0.137293i 0.614165 0.789178i \(-0.289493\pi\)
−0.376366 + 0.926471i \(0.622826\pi\)
\(48\) −3.05086 −0.440353
\(49\) 0 0
\(50\) 3.67307i 0.519451i
\(51\) −3.97703 + 6.88842i −0.556896 + 0.964572i
\(52\) −2.32876 4.98267i −0.322940 0.690972i
\(53\) −1.26271 2.18708i −0.173447 0.300419i 0.766176 0.642631i \(-0.222157\pi\)
−0.939623 + 0.342212i \(0.888824\pi\)
\(54\) −1.44892 0.836535i −0.197173 0.113838i
\(55\) 8.64296 1.16542
\(56\) 0 0
\(57\) 18.9240i 2.50654i
\(58\) −1.22354 0.706409i −0.160658 0.0927560i
\(59\) −6.34957 + 3.66593i −0.826644 + 0.477263i −0.852702 0.522398i \(-0.825038\pi\)
0.0260585 + 0.999660i \(0.491704\pi\)
\(60\) −9.40268 + 5.42864i −1.21388 + 0.700834i
\(61\) −4.52543 + 7.83827i −0.579422 + 1.00359i 0.416124 + 0.909308i \(0.363388\pi\)
−0.995546 + 0.0942799i \(0.969945\pi\)
\(62\) −4.02074 −0.510635
\(63\) 0 0
\(64\) −1.24443 −0.155554
\(65\) −9.49928 6.63911i −1.17824 0.823480i
\(66\) 2.05086 + 3.55219i 0.252443 + 0.437244i
\(67\) 0.371213 0.214320i 0.0453508 0.0261833i −0.477153 0.878820i \(-0.658331\pi\)
0.522504 + 0.852637i \(0.324998\pi\)
\(68\) 2.73975 4.74538i 0.332243 0.575462i
\(69\) −7.26517 −0.874624
\(70\) 0 0
\(71\) 8.98418i 1.06623i 0.846044 + 0.533113i \(0.178978\pi\)
−0.846044 + 0.533113i \(0.821022\pi\)
\(72\) −4.00296 2.31111i −0.471753 0.272367i
\(73\) −5.01481 + 2.89530i −0.586939 + 0.338869i −0.763886 0.645351i \(-0.776711\pi\)
0.176947 + 0.984220i \(0.443378\pi\)
\(74\) −1.35482 2.34661i −0.157494 0.272788i
\(75\) −5.90321 + 10.2247i −0.681644 + 1.18064i
\(76\) 13.0366i 1.49540i
\(77\) 0 0
\(78\) 0.474572 5.47949i 0.0537347 0.620431i
\(79\) 2.23975 3.87936i 0.251991 0.436462i −0.712083 0.702096i \(-0.752248\pi\)
0.964074 + 0.265634i \(0.0855812\pi\)
\(80\) 3.83531 2.21432i 0.428801 0.247568i
\(81\) 5.54371 + 9.60199i 0.615968 + 1.06689i
\(82\) 0.260253 0.450771i 0.0287401 0.0497793i
\(83\) 10.8272i 1.18844i −0.804304 0.594218i \(-0.797462\pi\)
0.804304 0.594218i \(-0.202538\pi\)
\(84\) 0 0
\(85\) 11.5462i 1.25236i
\(86\) 5.25390 + 3.03334i 0.566542 + 0.327093i
\(87\) 2.27062 + 3.93284i 0.243436 + 0.421644i
\(88\) −3.26517 5.65545i −0.348069 0.602873i
\(89\) 4.64360 + 2.68098i 0.492220 + 0.284183i 0.725495 0.688227i \(-0.241611\pi\)
−0.233275 + 0.972411i \(0.574944\pi\)
\(90\) −4.21432 −0.444228
\(91\) 0 0
\(92\) 5.00492 0.521799
\(93\) 11.1925 + 6.46198i 1.16061 + 0.670076i
\(94\) −0.648409 1.12308i −0.0668783 0.115837i
\(95\) −13.7351 23.7898i −1.40919 2.44078i
\(96\) 11.1347 + 6.42864i 1.13643 + 0.656120i
\(97\) 9.62867i 0.977643i 0.872384 + 0.488822i \(0.162573\pi\)
−0.872384 + 0.488822i \(0.837427\pi\)
\(98\) 0 0
\(99\) 5.11753i 0.514331i
\(100\) 4.06668 7.04369i 0.406668 0.704369i
\(101\) 6.84691 + 11.8592i 0.681293 + 1.18003i 0.974587 + 0.224011i \(0.0719152\pi\)
−0.293294 + 0.956022i \(0.594751\pi\)
\(102\) 4.74538 2.73975i 0.469863 0.271275i
\(103\) 6.14764 10.6480i 0.605745 1.04918i −0.386188 0.922420i \(-0.626208\pi\)
0.991933 0.126761i \(-0.0404583\pi\)
\(104\) −0.755569 + 8.72393i −0.0740896 + 0.855451i
\(105\) 0 0
\(106\) 1.73975i 0.168979i
\(107\) 9.09457 15.7522i 0.879205 1.52283i 0.0269898 0.999636i \(-0.491408\pi\)
0.852215 0.523192i \(-0.175259\pi\)
\(108\) −1.85236 3.20838i −0.178243 0.308726i
\(109\) 7.24167 4.18098i 0.693626 0.400465i −0.111343 0.993782i \(-0.535515\pi\)
0.804969 + 0.593317i \(0.202182\pi\)
\(110\) −5.15637 2.97703i −0.491641 0.283849i
\(111\) 8.70964i 0.826682i
\(112\) 0 0
\(113\) −8.46520 −0.796339 −0.398170 0.917312i \(-0.630354\pi\)
−0.398170 + 0.917312i \(0.630354\pi\)
\(114\) 6.51828 11.2900i 0.610493 1.05741i
\(115\) 9.13325 5.27309i 0.851680 0.491718i
\(116\) −1.56422 2.70930i −0.145234 0.251552i
\(117\) −3.93104 + 5.62456i −0.363425 + 0.519991i
\(118\) 5.05086 0.464969
\(119\) 0 0
\(120\) 17.2859 1.57798
\(121\) −1.88493 + 3.26479i −0.171357 + 0.296799i
\(122\) 5.39972 3.11753i 0.488868 0.282248i
\(123\) −1.44892 + 0.836535i −0.130645 + 0.0754279i
\(124\) −7.71041 4.45161i −0.692415 0.399766i
\(125\) 1.06668i 0.0954065i
\(126\) 0 0
\(127\) −4.08742 −0.362700 −0.181350 0.983419i \(-0.558047\pi\)
−0.181350 + 0.983419i \(0.558047\pi\)
\(128\) −9.31460 5.37778i −0.823302 0.475333i
\(129\) −9.75012 16.8877i −0.858450 1.48688i
\(130\) 3.38044 + 7.23287i 0.296484 + 0.634365i
\(131\) −2.96989 + 5.14400i −0.259480 + 0.449433i −0.966103 0.258158i \(-0.916885\pi\)
0.706622 + 0.707591i \(0.250218\pi\)
\(132\) 9.08250i 0.790530i
\(133\) 0 0
\(134\) −0.295286 −0.0255089
\(135\) −6.76056 3.90321i −0.581856 0.335935i
\(136\) −7.55514 + 4.36196i −0.647848 + 0.374035i
\(137\) −14.1699 + 8.18098i −1.21061 + 0.698948i −0.962893 0.269883i \(-0.913015\pi\)
−0.247721 + 0.968831i \(0.579682\pi\)
\(138\) 4.33439 + 2.50246i 0.368968 + 0.213024i
\(139\) 3.03011 0.257011 0.128505 0.991709i \(-0.458982\pi\)
0.128505 + 0.991709i \(0.458982\pi\)
\(140\) 0 0
\(141\) 4.16839i 0.351041i
\(142\) 3.09457 5.35994i 0.259690 0.449797i
\(143\) −8.78302 + 4.10493i −0.734473 + 0.343271i
\(144\) −1.31111 2.27091i −0.109259 0.189242i
\(145\) −5.70893 3.29605i −0.474101 0.273722i
\(146\) 3.98910 0.330140
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) 12.5892 + 7.26840i 1.03135 + 0.595451i 0.917371 0.398032i \(-0.130307\pi\)
0.113979 + 0.993483i \(0.463640\pi\)
\(150\) 7.04369 4.06668i 0.575115 0.332043i
\(151\) 17.2987 9.98741i 1.40775 0.812764i 0.412577 0.910923i \(-0.364629\pi\)
0.995171 + 0.0981592i \(0.0312954\pi\)
\(152\) −10.3778 + 17.9748i −0.841749 + 1.45795i
\(153\) −6.83654 −0.552701
\(154\) 0 0
\(155\) −18.7605 −1.50688
\(156\) 6.97674 9.98236i 0.558587 0.799229i
\(157\) −3.69926 6.40731i −0.295233 0.511359i 0.679806 0.733392i \(-0.262064\pi\)
−0.975039 + 0.222033i \(0.928731\pi\)
\(158\) −2.67246 + 1.54294i −0.212609 + 0.122750i
\(159\) 2.79605 4.84290i 0.221741 0.384067i
\(160\) −18.6637 −1.47550
\(161\) 0 0
\(162\) 7.63804i 0.600101i
\(163\) 2.01518 + 1.16346i 0.157841 + 0.0911296i 0.576840 0.816857i \(-0.304286\pi\)
−0.418999 + 0.907987i \(0.637619\pi\)
\(164\) 0.998151 0.576283i 0.0779425 0.0450001i
\(165\) 9.56914 + 16.5742i 0.744956 + 1.29030i
\(166\) −3.72938 + 6.45947i −0.289456 + 0.501352i
\(167\) 3.42219i 0.264817i 0.991195 + 0.132408i \(0.0422710\pi\)
−0.991195 + 0.132408i \(0.957729\pi\)
\(168\) 0 0
\(169\) 12.8064 + 2.23506i 0.985110 + 0.171928i
\(170\) −3.97703 + 6.88842i −0.305025 + 0.528318i
\(171\) −14.0861 + 8.13259i −1.07719 + 0.621915i
\(172\) 6.71678 + 11.6338i 0.512150 + 0.887069i
\(173\) 4.13727 7.16596i 0.314551 0.544818i −0.664791 0.747029i \(-0.731479\pi\)
0.979342 + 0.202211i \(0.0648127\pi\)
\(174\) 3.12843i 0.237166i
\(175\) 0 0
\(176\) 3.70471i 0.279253i
\(177\) −14.0600 8.11753i −1.05681 0.610151i
\(178\) −1.84691 3.19894i −0.138432 0.239770i
\(179\) −8.11285 14.0519i −0.606383 1.05029i −0.991831 0.127556i \(-0.959287\pi\)
0.385449 0.922729i \(-0.374047\pi\)
\(180\) −8.08162 4.66593i −0.602368 0.347778i
\(181\) 9.20495 0.684199 0.342099 0.939664i \(-0.388862\pi\)
0.342099 + 0.939664i \(0.388862\pi\)
\(182\) 0 0
\(183\) −20.0415 −1.48151
\(184\) −6.90080 3.98418i −0.508734 0.293718i
\(185\) −6.32148 10.9491i −0.464764 0.804996i
\(186\) −4.45161 7.71041i −0.326408 0.565355i
\(187\) −8.36475 4.82939i −0.611691 0.353160i
\(188\) 2.87157i 0.209431i
\(189\) 0 0
\(190\) 18.9240i 1.37289i
\(191\) 3.33407 5.77479i 0.241245 0.417849i −0.719824 0.694157i \(-0.755778\pi\)
0.961069 + 0.276308i \(0.0891109\pi\)
\(192\) −1.37778 2.38639i −0.0994330 0.172223i
\(193\) −17.8431 + 10.3017i −1.28438 + 0.741535i −0.977645 0.210261i \(-0.932569\pi\)
−0.306732 + 0.951796i \(0.599235\pi\)
\(194\) 3.31656 5.74445i 0.238115 0.412427i
\(195\) 2.21432 25.5669i 0.158571 1.83088i
\(196\) 0 0
\(197\) 8.36842i 0.596225i −0.954531 0.298112i \(-0.903643\pi\)
0.954531 0.298112i \(-0.0963571\pi\)
\(198\) −1.76271 + 3.05311i −0.125271 + 0.216975i
\(199\) −0.300736 0.520890i −0.0213186 0.0369249i 0.855169 0.518349i \(-0.173453\pi\)
−0.876488 + 0.481424i \(0.840120\pi\)
\(200\) −11.2143 + 6.47457i −0.792970 + 0.457821i
\(201\) 0.821984 + 0.474572i 0.0579783 + 0.0334738i
\(202\) 9.43356i 0.663743i
\(203\) 0 0
\(204\) 12.1334 0.849505
\(205\) 1.21432 2.10326i 0.0848118 0.146898i
\(206\) −7.33534 + 4.23506i −0.511078 + 0.295071i
\(207\) −3.12222 5.40784i −0.217009 0.375871i
\(208\) −2.84579 + 4.07177i −0.197320 + 0.282326i
\(209\) −22.9797 −1.58954
\(210\) 0 0
\(211\) −1.90321 −0.131023 −0.0655113 0.997852i \(-0.520868\pi\)
−0.0655113 + 0.997852i \(0.520868\pi\)
\(212\) −1.92618 + 3.33624i −0.132290 + 0.229134i
\(213\) −17.2286 + 9.94692i −1.18048 + 0.681552i
\(214\) −10.8516 + 6.26517i −0.741800 + 0.428279i
\(215\) 24.5143 + 14.1533i 1.67186 + 0.965249i
\(216\) 5.89829i 0.401328i
\(217\) 0 0
\(218\) −5.76049 −0.390150
\(219\) −11.1044 6.41112i −0.750365 0.433224i
\(220\) −6.59210 11.4179i −0.444440 0.769792i
\(221\) 5.48380 + 11.7333i 0.368880 + 0.789265i
\(222\) 3.00000 5.19615i 0.201347 0.348743i
\(223\) 10.6336i 0.712078i 0.934471 + 0.356039i \(0.115873\pi\)
−0.934471 + 0.356039i \(0.884127\pi\)
\(224\) 0 0
\(225\) −10.1476 −0.676510
\(226\) 5.05033 + 2.91581i 0.335943 + 0.193957i
\(227\) 13.0344 7.52543i 0.865125 0.499480i −0.000600144 1.00000i \(-0.500191\pi\)
0.865725 + 0.500520i \(0.166858\pi\)
\(228\) 24.9997 14.4336i 1.65564 0.955886i
\(229\) −5.65930 3.26740i −0.373977 0.215916i 0.301218 0.953555i \(-0.402607\pi\)
−0.675195 + 0.737640i \(0.735940\pi\)
\(230\) −7.26517 −0.479051
\(231\) 0 0
\(232\) 4.98079i 0.327005i
\(233\) −13.9795 + 24.2132i −0.915827 + 1.58626i −0.110141 + 0.993916i \(0.535130\pi\)
−0.805686 + 0.592343i \(0.798203\pi\)
\(234\) 4.28261 2.00157i 0.279963 0.130847i
\(235\) −3.02543 5.24019i −0.197357 0.341833i
\(236\) 9.68581 + 5.59210i 0.630492 + 0.364015i
\(237\) 9.91903 0.644310
\(238\) 0 0
\(239\) 19.5812i 1.26660i −0.773905 0.633301i \(-0.781699\pi\)
0.773905 0.633301i \(-0.218301\pi\)
\(240\) 8.49261 + 4.90321i 0.548196 + 0.316501i
\(241\) 11.5679 6.67876i 0.745157 0.430217i −0.0787843 0.996892i \(-0.525104\pi\)
0.823941 + 0.566675i \(0.191770\pi\)
\(242\) 2.24909 1.29851i 0.144577 0.0834716i
\(243\) −8.63259 + 14.9521i −0.553781 + 0.959176i
\(244\) 13.8064 0.883866
\(245\) 0 0
\(246\) 1.15257 0.0734849
\(247\) 25.2565 + 17.6519i 1.60703 + 1.12317i
\(248\) 7.08742 + 12.2758i 0.450052 + 0.779512i
\(249\) 20.7628 11.9874i 1.31579 0.759671i
\(250\) −0.367413 + 0.636377i −0.0232372 + 0.0402480i
\(251\) −3.29682 −0.208093 −0.104047 0.994572i \(-0.533179\pi\)
−0.104047 + 0.994572i \(0.533179\pi\)
\(252\) 0 0
\(253\) 8.82225i 0.554650i
\(254\) 2.43855 + 1.40790i 0.153008 + 0.0883392i
\(255\) 22.1416 12.7835i 1.38656 0.800531i
\(256\) 4.94914 + 8.57217i 0.309322 + 0.535761i
\(257\) −11.8469 + 20.5194i −0.738990 + 1.27997i 0.213961 + 0.976842i \(0.431364\pi\)
−0.952951 + 0.303126i \(0.901970\pi\)
\(258\) 13.4336i 0.836337i
\(259\) 0 0
\(260\) −1.52543 + 17.6128i −0.0946030 + 1.09230i
\(261\) −1.95161 + 3.38028i −0.120801 + 0.209234i
\(262\) 3.54366 2.04593i 0.218928 0.126398i
\(263\) −4.99532 8.65214i −0.308024 0.533514i 0.669906 0.742446i \(-0.266335\pi\)
−0.977930 + 0.208932i \(0.933001\pi\)
\(264\) 7.23014 12.5230i 0.444984 0.770736i
\(265\) 8.11753i 0.498656i
\(266\) 0 0
\(267\) 11.8731i 0.726622i
\(268\) −0.566258 0.326929i −0.0345897 0.0199704i
\(269\) 9.10171 + 15.7646i 0.554941 + 0.961186i 0.997908 + 0.0646482i \(0.0205925\pi\)
−0.442967 + 0.896538i \(0.646074\pi\)
\(270\) 2.68889 + 4.65730i 0.163641 + 0.283434i
\(271\) −20.9360 12.0874i −1.27177 0.734258i −0.296451 0.955048i \(-0.595803\pi\)
−0.975322 + 0.220789i \(0.929137\pi\)
\(272\) −4.94914 −0.300086
\(273\) 0 0
\(274\) 11.2716 0.680944
\(275\) −12.4160 7.16839i −0.748714 0.432270i
\(276\) 5.54125 + 9.59772i 0.333544 + 0.577715i
\(277\) 0.847673 + 1.46821i 0.0509317 + 0.0882163i 0.890367 0.455243i \(-0.150448\pi\)
−0.839436 + 0.543459i \(0.817114\pi\)
\(278\) −1.80776 1.04371i −0.108422 0.0625976i
\(279\) 11.1082i 0.665028i
\(280\) 0 0
\(281\) 11.6479i 0.694854i −0.937707 0.347427i \(-0.887055\pi\)
0.937707 0.347427i \(-0.112945\pi\)
\(282\) 1.43578 2.48685i 0.0854997 0.148090i
\(283\) 6.06668 + 10.5078i 0.360626 + 0.624623i 0.988064 0.154043i \(-0.0492296\pi\)
−0.627438 + 0.778667i \(0.715896\pi\)
\(284\) 11.8686 6.85236i 0.704274 0.406613i
\(285\) 30.4138 52.6783i 1.80156 3.12039i
\(286\) 6.65386 + 0.576283i 0.393451 + 0.0340763i
\(287\) 0 0
\(288\) 11.0509i 0.651178i
\(289\) 2.04839 3.54792i 0.120494 0.208701i
\(290\) 2.27062 + 3.93284i 0.133336 + 0.230944i
\(291\) −18.4645 + 10.6605i −1.08241 + 0.624928i
\(292\) 7.64973 + 4.41657i 0.447666 + 0.258460i
\(293\) 11.4538i 0.669140i −0.942371 0.334570i \(-0.891409\pi\)
0.942371 0.334570i \(-0.108591\pi\)
\(294\) 0 0
\(295\) 23.5669 1.37212
\(296\) −4.77631 + 8.27282i −0.277618 + 0.480848i
\(297\) −5.65545 + 3.26517i −0.328162 + 0.189465i
\(298\) −5.00715 8.67263i −0.290056 0.502392i
\(299\) −6.77683 + 9.69633i −0.391914 + 0.560753i
\(300\) 18.0098 1.03980
\(301\) 0 0
\(302\) −13.7605 −0.791827
\(303\) −15.1612 + 26.2600i −0.870991 + 1.50860i
\(304\) −10.1973 + 5.88739i −0.584853 + 0.337665i
\(305\) 25.1947 14.5462i 1.44264 0.832911i
\(306\) 4.07866 + 2.35482i 0.233162 + 0.134616i
\(307\) 3.96989i 0.226574i −0.993562 0.113287i \(-0.963862\pi\)
0.993562 0.113287i \(-0.0361379\pi\)
\(308\) 0 0
\(309\) 27.2257 1.54882
\(310\) 11.1925 + 6.46198i 0.635690 + 0.367016i
\(311\) 13.6741 + 23.6842i 0.775386 + 1.34301i 0.934577 + 0.355760i \(0.115778\pi\)
−0.159192 + 0.987248i \(0.550889\pi\)
\(312\) −17.5660 + 8.20986i −0.994481 + 0.464792i
\(313\) 9.55162 16.5439i 0.539890 0.935116i −0.459020 0.888426i \(-0.651799\pi\)
0.998909 0.0466901i \(-0.0148673\pi\)
\(314\) 5.09679i 0.287628i
\(315\) 0 0
\(316\) −6.83314 −0.384394
\(317\) −8.58070 4.95407i −0.481940 0.278248i 0.239285 0.970949i \(-0.423087\pi\)
−0.721225 + 0.692701i \(0.756420\pi\)
\(318\) −3.33624 + 1.92618i −0.187087 + 0.108015i
\(319\) −4.77572 + 2.75726i −0.267389 + 0.154377i
\(320\) 3.46410 + 2.00000i 0.193649 + 0.111803i
\(321\) 40.2766 2.24802
\(322\) 0 0
\(323\) 30.6987i 1.70812i
\(324\) 8.45653 14.6471i 0.469807 0.813730i
\(325\) 8.13974 + 17.4160i 0.451511 + 0.966066i
\(326\) −0.801502 1.38824i −0.0443911 0.0768876i
\(327\) 16.0354 + 9.25803i 0.886758 + 0.511970i
\(328\) −1.83500 −0.101321
\(329\) 0 0
\(330\) 13.1842i 0.725767i
\(331\) −20.2817 11.7096i −1.11478 0.643620i −0.174718 0.984618i \(-0.555902\pi\)
−0.940064 + 0.340999i \(0.889235\pi\)
\(332\) −14.3033 + 8.25803i −0.784997 + 0.453218i
\(333\) −6.48302 + 3.74297i −0.355267 + 0.205114i
\(334\) 1.17876 2.04167i 0.0644988 0.111715i
\(335\) −1.37778 −0.0752764
\(336\) 0 0
\(337\) 7.51606 0.409426 0.204713 0.978822i \(-0.434374\pi\)
0.204713 + 0.978822i \(0.434374\pi\)
\(338\) −6.87043 5.74456i −0.373702 0.312463i
\(339\) −9.37233 16.2334i −0.509035 0.881675i
\(340\) −15.2532 + 8.80642i −0.827219 + 0.477595i
\(341\) −7.84691 + 13.5912i −0.424934 + 0.736007i
\(342\) 11.2050 0.605894
\(343\) 0 0
\(344\) 21.3876i 1.15314i
\(345\) 20.2239 + 11.6763i 1.08882 + 0.628631i
\(346\) −4.93658 + 2.85013i −0.265392 + 0.153224i
\(347\) −2.82225 4.88827i −0.151506 0.262416i 0.780275 0.625436i \(-0.215079\pi\)
−0.931781 + 0.363020i \(0.881746\pi\)
\(348\) 3.46367 5.99926i 0.185672 0.321594i
\(349\) 24.1590i 1.29320i −0.762828 0.646601i \(-0.776190\pi\)
0.762828 0.646601i \(-0.223810\pi\)
\(350\) 0 0
\(351\) 8.72393 + 0.755569i 0.465649 + 0.0403293i
\(352\) −7.80642 + 13.5211i −0.416084 + 0.720678i
\(353\) 31.2886 18.0645i 1.66532 0.961474i 0.695213 0.718804i \(-0.255310\pi\)
0.970109 0.242670i \(-0.0780231\pi\)
\(354\) 5.59210 + 9.68581i 0.297217 + 0.514795i
\(355\) 14.4390 25.0091i 0.766343 1.32735i
\(356\) 8.17929i 0.433501i
\(357\) 0 0
\(358\) 11.1778i 0.590763i
\(359\) 15.0799 + 8.70641i 0.795889 + 0.459507i 0.842032 0.539428i \(-0.181360\pi\)
−0.0461427 + 0.998935i \(0.514693\pi\)
\(360\) 7.42864 + 12.8668i 0.391524 + 0.678139i
\(361\) 27.0185 + 46.7975i 1.42203 + 2.46302i
\(362\) −5.49166 3.17061i −0.288635 0.166644i
\(363\) −8.34767 −0.438139
\(364\) 0 0
\(365\) 18.6128 0.974241
\(366\) 11.9567 + 6.90321i 0.624987 + 0.360837i
\(367\) −1.46912 2.54460i −0.0766876 0.132827i 0.825131 0.564941i \(-0.191101\pi\)
−0.901819 + 0.432114i \(0.857768\pi\)
\(368\) −2.26025 3.91487i −0.117824 0.204077i
\(369\) −1.24535 0.719004i −0.0648304 0.0374298i
\(370\) 8.70964i 0.452792i
\(371\) 0 0
\(372\) 19.7146i 1.02215i
\(373\) 9.38493 16.2552i 0.485933 0.841661i −0.513936 0.857828i \(-0.671813\pi\)
0.999869 + 0.0161675i \(0.00514648\pi\)
\(374\) 3.32693 + 5.76241i 0.172031 + 0.297967i
\(375\) 2.04552 1.18098i 0.105630 0.0609856i
\(376\) −2.28592 + 3.95933i −0.117887 + 0.204187i
\(377\) 7.36689 + 0.638037i 0.379414 + 0.0328606i
\(378\) 0 0
\(379\) 23.6894i 1.21684i 0.793615 + 0.608421i \(0.208197\pi\)
−0.793615 + 0.608421i \(0.791803\pi\)
\(380\) −20.9518 + 36.2897i −1.07481 + 1.86162i
\(381\) −4.52543 7.83827i −0.231845 0.401567i
\(382\) −3.97820 + 2.29682i −0.203543 + 0.117515i
\(383\) −27.3775 15.8064i −1.39893 0.807671i −0.404646 0.914473i \(-0.632605\pi\)
−0.994280 + 0.106803i \(0.965939\pi\)
\(384\) 23.8163i 1.21537i
\(385\) 0 0
\(386\) 14.1936 0.722434
\(387\) 8.38025 14.5150i 0.425992 0.737839i
\(388\) 12.7200 7.34392i 0.645762 0.372831i
\(389\) −10.0279 17.3688i −0.508434 0.880634i −0.999952 0.00976644i \(-0.996891\pi\)
0.491518 0.870867i \(-0.336442\pi\)
\(390\) −10.1275 + 14.4905i −0.512825 + 0.733753i
\(391\) −11.7857 −0.596027
\(392\) 0 0
\(393\) −13.1526 −0.663459
\(394\) −2.88247 + 4.99258i −0.145217 + 0.251523i
\(395\) −12.4695 + 7.19926i −0.627408 + 0.362234i
\(396\) −6.76056 + 3.90321i −0.339731 + 0.196144i
\(397\) 19.8087 + 11.4366i 0.994169 + 0.573984i 0.906518 0.422167i \(-0.138730\pi\)
0.0876515 + 0.996151i \(0.472064\pi\)
\(398\) 0.414349i 0.0207695i
\(399\) 0 0
\(400\) −7.34614 −0.367307
\(401\) −4.86087 2.80642i −0.242740 0.140146i 0.373695 0.927552i \(-0.378091\pi\)
−0.616436 + 0.787405i \(0.711424\pi\)
\(402\) −0.326929 0.566258i −0.0163057 0.0282424i
\(403\) 19.0645 8.91020i 0.949670 0.443849i
\(404\) 10.4445 18.0903i 0.519631 0.900028i
\(405\) 35.6385i 1.77089i
\(406\) 0 0
\(407\) −10.5763 −0.524247
\(408\) −16.7295 9.65878i −0.828234 0.478181i
\(409\) −22.6184 + 13.0588i −1.11841 + 0.645714i −0.940995 0.338422i \(-0.890107\pi\)
−0.177416 + 0.984136i \(0.556774\pi\)
\(410\) −1.44892 + 0.836535i −0.0715571 + 0.0413135i
\(411\) −31.3766 18.1153i −1.54770 0.893562i
\(412\) −18.7556 −0.924021
\(413\) 0 0
\(414\) 4.30174i 0.211419i
\(415\) −17.4010 + 30.1394i −0.854181 + 1.47948i
\(416\) 18.9661 8.86423i 0.929892 0.434605i
\(417\) 3.35482 + 5.81072i 0.164286 + 0.284552i
\(418\) 13.7097 + 7.91528i 0.670562 + 0.387149i
\(419\) −25.2464 −1.23337 −0.616685 0.787210i \(-0.711525\pi\)
−0.616685 + 0.787210i \(0.711525\pi\)
\(420\) 0 0
\(421\) 8.22861i 0.401038i −0.979690 0.200519i \(-0.935737\pi\)
0.979690 0.200519i \(-0.0642628\pi\)
\(422\) 1.13545 + 0.655554i 0.0552730 + 0.0319119i
\(423\) −3.10274 + 1.79137i −0.150860 + 0.0870993i
\(424\) 5.31164 3.06668i 0.257956 0.148931i
\(425\) −9.57628 + 16.5866i −0.464518 + 0.804569i
\(426\) 13.7047 0.663996
\(427\) 0 0
\(428\) −27.7462 −1.34116
\(429\) −17.5961 12.2980i −0.849545 0.593753i
\(430\) −9.75012 16.8877i −0.470192 0.814397i
\(431\) −1.24535 + 0.719004i −0.0599864 + 0.0346332i −0.529693 0.848189i \(-0.677693\pi\)
0.469707 + 0.882822i \(0.344360\pi\)
\(432\) −1.67307 + 2.89784i −0.0804957 + 0.139423i
\(433\) 16.5018 0.793024 0.396512 0.918029i \(-0.370220\pi\)
0.396512 + 0.918029i \(0.370220\pi\)
\(434\) 0 0
\(435\) 14.5970i 0.699874i
\(436\) −11.0466 6.37778i −0.529038 0.305440i
\(437\) −24.2833 + 14.0200i −1.16163 + 0.670666i
\(438\) 4.41657 + 7.64973i 0.211032 + 0.365518i
\(439\) −5.08097 + 8.80049i −0.242501 + 0.420025i −0.961426 0.275063i \(-0.911301\pi\)
0.718925 + 0.695088i \(0.244635\pi\)
\(440\) 20.9906i 1.00069i
\(441\) 0 0
\(442\) 0.769859 8.88892i 0.0366185 0.422803i
\(443\) −1.60393 + 2.77809i −0.0762052 + 0.131991i −0.901610 0.432550i \(-0.857614\pi\)
0.825405 + 0.564542i \(0.190947\pi\)
\(444\) 11.5059 6.64296i 0.546048 0.315261i
\(445\) −8.61753 14.9260i −0.408510 0.707560i
\(446\) 3.66270 6.34398i 0.173434 0.300396i
\(447\) 32.1891i 1.52249i
\(448\) 0 0
\(449\) 18.4099i 0.868817i 0.900716 + 0.434409i \(0.143043\pi\)
−0.900716 + 0.434409i \(0.856957\pi\)
\(450\) 6.05406 + 3.49532i 0.285391 + 0.164771i
\(451\) −1.01582 1.75945i −0.0478332 0.0828495i
\(452\) 6.45653 + 11.1830i 0.303690 + 0.526006i
\(453\) 38.3048 + 22.1153i 1.79972 + 1.03907i
\(454\) −10.3684 −0.486614
\(455\) 0 0
\(456\) −45.9595 −2.15225
\(457\) −2.94706 1.70149i −0.137858 0.0795922i 0.429485 0.903074i \(-0.358695\pi\)
−0.567343 + 0.823482i \(0.692028\pi\)
\(458\) 2.25088 + 3.89865i 0.105177 + 0.182172i
\(459\) 4.36196 + 7.55514i 0.203599 + 0.352644i
\(460\) −13.9321 8.04371i −0.649588 0.375040i
\(461\) 17.5714i 0.818380i 0.912449 + 0.409190i \(0.134189\pi\)
−0.912449 + 0.409190i \(0.865811\pi\)
\(462\) 0 0
\(463\) 15.7714i 0.732959i −0.930426 0.366479i \(-0.880563\pi\)
0.930426 0.366479i \(-0.119437\pi\)
\(464\) −1.41282 + 2.44707i −0.0655884 + 0.113602i
\(465\) −20.7709 35.9762i −0.963226 1.66836i
\(466\) 16.6803 9.63036i 0.772699 0.446118i
\(467\) −1.88347 + 3.26227i −0.0871567 + 0.150960i −0.906308 0.422617i \(-0.861111\pi\)
0.819151 + 0.573577i \(0.194445\pi\)
\(468\) 10.4286 + 0.903212i 0.482064 + 0.0417510i
\(469\) 0 0
\(470\) 4.16839i 0.192273i
\(471\) 8.19135 14.1878i 0.377438 0.653741i
\(472\) −8.90321 15.4208i −0.409804 0.709801i
\(473\) 20.5071 11.8398i 0.942916 0.544393i
\(474\) −5.91768 3.41657i −0.271808 0.156928i
\(475\) 45.5669i 2.09075i
\(476\) 0 0
\(477\) 4.80642 0.220071
\(478\) −6.74467 + 11.6821i −0.308494 + 0.534327i
\(479\) 10.4817 6.05162i 0.478922 0.276506i −0.241045 0.970514i \(-0.577490\pi\)
0.719967 + 0.694008i \(0.244157\pi\)
\(480\) −20.6637 35.7906i −0.943165 1.63361i
\(481\) 11.6241 + 8.12420i 0.530016 + 0.370432i
\(482\) −9.20189 −0.419135
\(483\) 0 0
\(484\) 5.75065 0.261393
\(485\) 15.4748 26.8032i 0.702675 1.21707i
\(486\) 10.3004 5.94692i 0.467234 0.269758i
\(487\) −15.0496 + 8.68889i −0.681963 + 0.393731i −0.800594 0.599207i \(-0.795483\pi\)
0.118631 + 0.992938i \(0.462149\pi\)
\(488\) −19.0363 10.9906i −0.861734 0.497523i
\(489\) 5.15257i 0.233007i
\(490\) 0 0
\(491\) 19.3921 0.875152 0.437576 0.899181i \(-0.355837\pi\)
0.437576 + 0.899181i \(0.355837\pi\)
\(492\) 2.21023 + 1.27607i 0.0996446 + 0.0575299i
\(493\) 3.68344 + 6.37991i 0.165894 + 0.287337i
\(494\) −8.98784 19.2306i −0.404382 0.865226i
\(495\) −8.22469 + 14.2456i −0.369672 + 0.640291i
\(496\) 8.04149i 0.361073i
\(497\) 0 0
\(498\) −16.5161 −0.740102
\(499\) 9.24063 + 5.33508i 0.413667 + 0.238831i 0.692364 0.721548i \(-0.256569\pi\)
−0.278697 + 0.960379i \(0.589903\pi\)
\(500\) −1.40914 + 0.813569i −0.0630188 + 0.0363839i
\(501\) −6.56258 + 3.78891i −0.293194 + 0.169276i
\(502\) 1.96688 + 1.13558i 0.0877859 + 0.0506832i
\(503\) −4.27655 −0.190682 −0.0953410 0.995445i \(-0.530394\pi\)
−0.0953410 + 0.995445i \(0.530394\pi\)
\(504\) 0 0
\(505\) 44.0163i 1.95870i
\(506\) −3.03879 + 5.26334i −0.135091 + 0.233984i
\(507\) 9.89267 + 27.0329i 0.439349 + 1.20057i
\(508\) 3.11753 + 5.39972i 0.138318 + 0.239574i
\(509\) −28.6451 16.5383i −1.26967 0.733046i −0.294746 0.955576i \(-0.595235\pi\)
−0.974926 + 0.222530i \(0.928568\pi\)
\(510\) −17.6128 −0.779910
\(511\) 0 0
\(512\) 14.6923i 0.649313i
\(513\) 17.9748 + 10.3778i 0.793609 + 0.458190i
\(514\) 14.1357 8.16124i 0.623498 0.359977i
\(515\) −34.2262 + 19.7605i −1.50819 + 0.870751i
\(516\) −14.8731 + 25.7610i −0.654752 + 1.13406i
\(517\) −5.06175 −0.222616
\(518\) 0 0
\(519\) 18.3225 0.804268
\(520\) 16.1240 23.0703i 0.707084 1.01170i
\(521\) −12.1891 21.1122i −0.534015 0.924942i −0.999210 0.0397336i \(-0.987349\pi\)
0.465195 0.885208i \(-0.345984\pi\)
\(522\) 2.32865 1.34445i 0.101922 0.0588448i
\(523\) −17.4701 + 30.2591i −0.763915 + 1.32314i 0.176903 + 0.984228i \(0.443392\pi\)
−0.940818 + 0.338912i \(0.889941\pi\)
\(524\) 9.06070 0.395818
\(525\) 0 0
\(526\) 6.88247i 0.300090i
\(527\) 18.1566 + 10.4827i 0.790914 + 0.456635i
\(528\) 7.10437 4.10171i 0.309178 0.178504i
\(529\) 6.11753 + 10.5959i 0.265980 + 0.460690i
\(530\) 2.79605 4.84290i 0.121453 0.210362i
\(531\) 13.9541i 0.605555i
\(532\) 0 0
\(533\) −0.235063 + 2.71408i −0.0101817 + 0.117560i
\(534\) 4.08964 7.08347i 0.176976 0.306532i
\(535\) −50.6328 + 29.2328i −2.18905 + 1.26385i
\(536\) 0.520505 + 0.901542i 0.0224824 + 0.0389407i
\(537\) 17.9644 31.1153i 0.775223 1.34273i
\(538\) 12.5402i 0.540646i
\(539\) 0 0
\(540\) 11.9081i 0.512445i
\(541\) −26.4097 15.2477i −1.13544 0.655548i −0.190144 0.981756i \(-0.560896\pi\)
−0.945298 + 0.326208i \(0.894229\pi\)
\(542\) 8.32693 + 14.4227i 0.357672 + 0.619506i
\(543\) 10.1914 + 17.6519i 0.437353 + 0.757517i
\(544\) 18.0629 + 10.4286i 0.774442 + 0.447124i
\(545\) −26.8780 −1.15133
\(546\) 0 0
\(547\) −10.0049 −0.427780 −0.213890 0.976858i \(-0.568613\pi\)
−0.213890 + 0.976858i \(0.568613\pi\)
\(548\) 21.6151 + 12.4795i 0.923352 + 0.533098i
\(549\) −8.61285 14.9179i −0.367587 0.636680i
\(550\) 4.93825 + 8.55329i 0.210568 + 0.364714i
\(551\) 15.1788 + 8.76348i 0.646638 + 0.373337i
\(552\) 17.6445i 0.750999i
\(553\) 0 0
\(554\) 1.16791i 0.0496198i
\(555\) 13.9978 24.2449i 0.594173 1.02914i
\(556\) −2.31111 4.00296i −0.0980128 0.169763i
\(557\) −12.2920 + 7.09679i −0.520829 + 0.300701i −0.737274 0.675594i \(-0.763887\pi\)
0.216445 + 0.976295i \(0.430554\pi\)
\(558\) 3.82616 6.62711i 0.161974 0.280548i
\(559\) −31.6336 2.73975i −1.33796 0.115879i
\(560\) 0 0
\(561\) 21.3876i 0.902986i
\(562\) −4.01207 + 6.94910i −0.169239 + 0.293130i
\(563\) −10.6795 18.4975i −0.450088 0.779576i 0.548303 0.836280i \(-0.315274\pi\)
−0.998391 + 0.0567041i \(0.981941\pi\)
\(564\) 5.50668 3.17929i 0.231873 0.133872i
\(565\) 23.5644 + 13.6049i 0.991364 + 0.572364i
\(566\) 8.35857i 0.351337i
\(567\) 0 0
\(568\) −21.8193 −0.915519
\(569\) 17.1336 29.6763i 0.718278 1.24409i −0.243404 0.969925i \(-0.578264\pi\)
0.961682 0.274168i \(-0.0884025\pi\)
\(570\) −36.2897 + 20.9518i −1.52001 + 0.877576i
\(571\) −18.8247 32.6053i −0.787789 1.36449i −0.927318 0.374273i \(-0.877892\pi\)
0.139529 0.990218i \(-0.455441\pi\)
\(572\) 12.1218 + 8.47200i 0.506837 + 0.354232i
\(573\) 14.7654 0.616834
\(574\) 0 0
\(575\) −17.4938 −0.729541
\(576\) 1.18421 2.05111i 0.0493420 0.0854629i
\(577\) 24.5925 14.1985i 1.02380 0.591091i 0.108598 0.994086i \(-0.465364\pi\)
0.915202 + 0.402995i \(0.132031\pi\)
\(578\) −2.44414 + 1.41112i −0.101663 + 0.0586950i
\(579\) −39.5104 22.8113i −1.64200 0.948007i
\(580\) 10.0558i 0.417543i
\(581\) 0 0
\(582\) 14.6878 0.608830
\(583\) 5.88083 + 3.39530i 0.243559 + 0.140619i
\(584\) −7.03164 12.1792i −0.290971 0.503977i
\(585\) 19.9824 9.33918i 0.826169 0.386127i
\(586\) −3.94523 + 6.83333i −0.162976 + 0.282282i
\(587\) 6.23659i 0.257412i −0.991683 0.128706i \(-0.958918\pi\)
0.991683 0.128706i \(-0.0410823\pi\)
\(588\) 0 0
\(589\) 49.8800 2.05527
\(590\) −14.0600 8.11753i −0.578840 0.334193i
\(591\) 16.0478 9.26517i 0.660116 0.381118i
\(592\) −4.69323 + 2.70964i −0.192890 + 0.111365i
\(593\) 15.2159 + 8.78491i 0.624843 + 0.360753i 0.778752 0.627332i \(-0.215853\pi\)
−0.153909 + 0.988085i \(0.549186\pi\)
\(594\) 4.49871 0.184584
\(595\) 0 0
\(596\) 22.1748i 0.908317i
\(597\) 0.665926 1.15342i 0.0272545 0.0472062i
\(598\) 7.38291 3.45056i 0.301909 0.141104i
\(599\) −8.49063 14.7062i −0.346918 0.600879i 0.638782 0.769387i \(-0.279438\pi\)
−0.985700 + 0.168508i \(0.946105\pi\)
\(600\) −24.8320 14.3368i −1.01376 0.585296i
\(601\) −18.7052 −0.763001 −0.381500 0.924369i \(-0.624592\pi\)
−0.381500 + 0.924369i \(0.624592\pi\)
\(602\) 0 0
\(603\) 0.815792i 0.0332216i
\(604\) −26.3879 15.2351i −1.07371 0.619906i
\(605\) 10.4941 6.05877i 0.426645 0.246324i
\(606\) 18.0903 10.4445i 0.734870 0.424277i
\(607\) 5.17876 8.96987i 0.210199 0.364076i −0.741577 0.670867i \(-0.765922\pi\)
0.951777 + 0.306791i \(0.0992554\pi\)
\(608\) 49.6227 2.01247
\(609\) 0 0
\(610\) −20.0415 −0.811456
\(611\) 5.56326 + 3.88820i 0.225065 + 0.157300i
\(612\) 5.21432 + 9.03147i 0.210776 + 0.365075i
\(613\) −6.08147 + 3.51114i −0.245628 + 0.141814i −0.617761 0.786366i \(-0.711960\pi\)
0.372133 + 0.928180i \(0.378627\pi\)
\(614\) −1.36741 + 2.36843i −0.0551843 + 0.0955820i
\(615\) 5.37778 0.216853
\(616\) 0 0
\(617\) 29.9813i 1.20700i 0.797363 + 0.603500i \(0.206228\pi\)
−0.797363 + 0.603500i \(0.793772\pi\)
\(618\) −16.2428 9.37778i −0.653381 0.377230i
\(619\) −0.0247512 + 0.0142901i −0.000994834 + 0.000574368i −0.500497 0.865738i \(-0.666849\pi\)
0.499503 + 0.866312i \(0.333516\pi\)
\(620\) 14.3089 + 24.7837i 0.574659 + 0.995338i
\(621\) −3.98418 + 6.90080i −0.159880 + 0.276920i
\(622\) 18.8399i 0.755412i
\(623\) 0 0
\(624\) −10.9590 0.949145i −0.438711 0.0379962i
\(625\) 11.6153 20.1183i 0.464612 0.804732i
\(626\) −11.3970 + 6.58004i −0.455514 + 0.262991i
\(627\) −25.4422 44.0672i −1.01607 1.75988i
\(628\) −5.64296 + 9.77389i −0.225179 + 0.390021i
\(629\) 14.1289i 0.563356i
\(630\) 0 0
\(631\) 12.1936i 0.485419i 0.970099 + 0.242709i \(0.0780361\pi\)
−0.970099 + 0.242709i \(0.921964\pi\)
\(632\) 9.42156 + 5.43954i 0.374769 + 0.216373i
\(633\) −2.10716 3.64971i −0.0837521 0.145063i
\(634\) 3.41282 + 5.91117i 0.135540 + 0.234763i
\(635\) 11.3781 + 6.56914i 0.451525 + 0.260688i
\(636\) −8.53035 −0.338250
\(637\) 0 0
\(638\) 3.79892 0.150401
\(639\) −14.8080 8.54940i −0.585795 0.338209i
\(640\) 17.2859 + 29.9401i 0.683286 + 1.18349i
\(641\) −1.41258 2.44666i −0.0557935 0.0966373i 0.836780 0.547540i \(-0.184436\pi\)
−0.892573 + 0.450903i \(0.851102\pi\)
\(642\) −24.0289 13.8731i −0.948346 0.547528i
\(643\) 37.7275i 1.48783i −0.668276 0.743913i \(-0.732968\pi\)
0.668276 0.743913i \(-0.267032\pi\)
\(644\) 0 0
\(645\) 62.6800i 2.46802i
\(646\) 10.5741 18.3148i 0.416031 0.720587i
\(647\) 6.18320 + 10.7096i 0.243087 + 0.421039i 0.961592 0.274483i \(-0.0885067\pi\)
−0.718505 + 0.695522i \(0.755173\pi\)
\(648\) −23.3198 + 13.4637i −0.916087 + 0.528903i
\(649\) 9.85728 17.0733i 0.386932 0.670186i
\(650\) 1.14272 13.1941i 0.0448212 0.517513i
\(651\) 0 0
\(652\) 3.54956i 0.139012i
\(653\) 16.5002 28.5793i 0.645704 1.11839i −0.338434 0.940990i \(-0.609897\pi\)
0.984138 0.177402i \(-0.0567694\pi\)
\(654\) −6.37778 11.0466i −0.249391 0.431958i
\(655\) 16.5345 9.54617i 0.646055 0.373000i
\(656\) −0.901542 0.520505i −0.0351993 0.0203223i
\(657\) 11.0207i 0.429960i
\(658\) 0 0
\(659\) 32.8118 1.27817 0.639084 0.769137i \(-0.279314\pi\)
0.639084 + 0.769137i \(0.279314\pi\)
\(660\) 14.5970 25.2828i 0.568188 0.984131i
\(661\) 12.7364 7.35336i 0.495388 0.286013i −0.231419 0.972854i \(-0.574337\pi\)
0.726807 + 0.686842i \(0.241003\pi\)
\(662\) 8.06668 + 13.9719i 0.313520 + 0.543033i
\(663\) −16.4290 + 23.5067i −0.638048 + 0.912923i
\(664\) 26.2953 1.02046
\(665\) 0 0
\(666\) 5.15701 0.199830
\(667\) −3.36442 + 5.82735i −0.130271 + 0.225636i
\(668\) 4.52091 2.61015i 0.174919 0.100990i
\(669\) −20.3916 + 11.7731i −0.788384 + 0.455174i
\(670\) 0.821984 + 0.474572i 0.0317560 + 0.0183343i
\(671\) 24.3368i 0.939511i
\(672\) 0 0
\(673\) −21.2908 −0.820702 −0.410351 0.911928i \(-0.634594\pi\)
−0.410351 + 0.911928i \(0.634594\pi\)
\(674\) −4.48407 2.58888i −0.172720 0.0997198i
\(675\) 6.47457 + 11.2143i 0.249206 + 0.431638i
\(676\) −6.81499 18.6228i −0.262115 0.716260i
\(677\) 1.53580 2.66008i 0.0590256 0.102235i −0.835003 0.550246i \(-0.814534\pi\)
0.894028 + 0.448011i \(0.147867\pi\)
\(678\) 12.9131i 0.495923i
\(679\) 0 0
\(680\) 28.0415 1.07534
\(681\) 28.8624 + 16.6637i 1.10601 + 0.638554i
\(682\) 9.36290 5.40567i 0.358524 0.206994i
\(683\) 21.4749 12.3985i 0.821713 0.474416i −0.0292935 0.999571i \(-0.509326\pi\)
0.851007 + 0.525154i \(0.175992\pi\)
\(684\) 21.4873 + 12.4057i 0.821586 + 0.474343i
\(685\) 52.5926 2.00946
\(686\) 0 0
\(687\) 14.4701i 0.552070i
\(688\) 6.06668 10.5078i 0.231290 0.400606i
\(689\) −3.85538 8.24908i −0.146878 0.314265i
\(690\) −8.04371 13.9321i −0.306219 0.530387i
\(691\) 23.4652 + 13.5476i 0.892658 + 0.515376i 0.874811 0.484465i \(-0.160986\pi\)
0.0178467 + 0.999841i \(0.494319\pi\)
\(692\) −12.6222 −0.479825
\(693\) 0 0
\(694\) 3.88845i 0.147603i
\(695\) −8.43487 4.86987i −0.319953 0.184725i
\(696\) −9.55144 + 5.51453i −0.362047 + 0.209028i
\(697\) −2.35046 + 1.35704i −0.0890302 + 0.0514016i
\(698\) −8.32148 + 14.4132i −0.314973 + 0.545549i
\(699\) −61.9101 −2.34166
\(700\) 0 0
\(701\) −13.5205 −0.510662 −0.255331 0.966854i \(-0.582185\pi\)
−0.255331 + 0.966854i \(0.582185\pi\)
\(702\) −4.94443 3.45569i −0.186615 0.130427i
\(703\) 16.8074 + 29.1113i 0.633904 + 1.09795i
\(704\) 2.89784 1.67307i 0.109217 0.0630562i
\(705\) 6.69926 11.6035i 0.252309 0.437012i
\(706\) −24.8889 −0.936707
\(707\) 0 0
\(708\) 24.7654i 0.930741i
\(709\) −44.1459 25.4876i −1.65793 0.957209i −0.973666 0.227977i \(-0.926789\pi\)
−0.684267 0.729231i \(-0.739878\pi\)
\(710\) −17.2286 + 9.94692i −0.646577 + 0.373301i
\(711\) 4.26271 + 7.38324i 0.159864 + 0.276893i
\(712\) −6.51114 + 11.2776i −0.244015 + 0.422647i
\(713\) 19.1497i 0.717160i
\(714\) 0 0
\(715\) 31.0464 + 2.68889i 1.16107 + 0.100559i
\(716\) −12.3756 + 21.4351i −0.462496 + 0.801067i
\(717\) 37.5500 21.6795i 1.40233 0.809637i
\(718\) −5.99778 10.3885i −0.223835 0.387694i
\(719\) 20.7709 35.9762i 0.774622 1.34169i −0.160384 0.987055i \(-0.551273\pi\)
0.935006 0.354631i \(-0.115393\pi\)
\(720\) 8.42864i 0.314117i
\(721\) 0 0
\(722\) 37.2257i 1.38540i
\(723\) 25.6151 + 14.7889i 0.952637 + 0.550005i
\(724\) −7.02074 12.1603i −0.260924 0.451933i
\(725\) 5.46743 + 9.46986i 0.203055 + 0.351702i
\(726\) 4.98021 + 2.87532i 0.184833 + 0.106713i
\(727\) 20.8988 0.775092 0.387546 0.921850i \(-0.373323\pi\)
0.387546 + 0.921850i \(0.373323\pi\)
\(728\) 0 0
\(729\) −4.96836 −0.184013
\(730\) −11.1044 6.41112i −0.410992 0.237286i
\(731\) −15.8168 27.3955i −0.585005 1.01326i
\(732\) 15.2859 + 26.4760i 0.564984 + 0.978581i
\(733\) −16.7641 9.67876i −0.619196 0.357493i 0.157360 0.987541i \(-0.449702\pi\)
−0.776556 + 0.630048i \(0.783035\pi\)
\(734\) 2.02413i 0.0747122i
\(735\) 0 0
\(736\) 19.0509i 0.702224i
\(737\) −0.576283 + 0.998151i −0.0212276 + 0.0367674i
\(738\) 0.495316 + 0.857913i 0.0182328 + 0.0315802i
\(739\) 1.13545 0.655554i 0.0417683 0.0241149i −0.478970 0.877831i \(-0.658990\pi\)
0.520739 + 0.853716i \(0.325657\pi\)
\(740\) −9.64296 + 16.7021i −0.354482 + 0.613981i
\(741\) −5.88739 + 67.9768i −0.216279 + 2.49719i
\(742\) 0 0
\(743\) 21.5210i 0.789528i −0.918783 0.394764i \(-0.870826\pi\)
0.918783 0.394764i \(-0.129174\pi\)
\(744\) −15.6938 + 27.1825i −0.575363 + 0.996558i
\(745\) −23.3630 40.4658i −0.855953 1.48255i
\(746\) −11.1981 + 6.46520i −0.409990 + 0.236708i
\(747\) 17.8457 + 10.3032i 0.652939 + 0.376974i
\(748\) 14.7338i 0.538720i
\(749\) 0 0
\(750\) −1.62714 −0.0594147
\(751\) −8.15878 + 14.1314i −0.297718 + 0.515663i −0.975614 0.219495i \(-0.929559\pi\)
0.677895 + 0.735158i \(0.262892\pi\)
\(752\) −2.24615 + 1.29682i −0.0819088 + 0.0472901i
\(753\) −3.65010 6.32217i −0.133017 0.230393i
\(754\) −4.17530 2.91815i −0.152055 0.106273i
\(755\) −64.2054 −2.33667
\(756\) 0 0
\(757\) −18.7462 −0.681342 −0.340671 0.940183i \(-0.610654\pi\)
−0.340671 + 0.940183i \(0.610654\pi\)
\(758\) 8.15971 14.1330i 0.296374 0.513335i
\(759\) 16.9180 9.76764i 0.614086 0.354543i
\(760\) 57.7769 33.3575i 2.09579 1.21000i
\(761\) −8.91731 5.14841i −0.323252 0.186630i 0.329589 0.944124i \(-0.393090\pi\)
−0.652841 + 0.757495i \(0.726423\pi\)
\(762\) 6.23506i 0.225873i
\(763\) 0 0
\(764\) −10.1718 −0.368002
\(765\) 19.0307 + 10.9874i 0.688058 + 0.397250i
\(766\) 10.8889 + 18.8602i 0.393433 + 0.681445i
\(767\) −23.9488 + 11.1930i −0.864742 + 0.404155i
\(768\) −10.9590 + 18.9815i −0.395448 + 0.684937i
\(769\) 9.36641i 0.337761i 0.985637 + 0.168881i \(0.0540153\pi\)
−0.985637 + 0.168881i \(0.945985\pi\)
\(770\) 0 0
\(771\) −52.4657 −1.88951
\(772\) 27.2184 + 15.7146i 0.979612 + 0.565579i
\(773\) −3.21690 + 1.85728i −0.115704 + 0.0668017i −0.556735 0.830690i \(-0.687946\pi\)
0.441031 + 0.897492i \(0.354613\pi\)
\(774\) −9.99928 + 5.77309i −0.359417 + 0.207509i
\(775\) 26.9503 + 15.5598i 0.968084 + 0.558923i
\(776\) −23.3846 −0.839457
\(777\) 0 0
\(778\) 13.8163i 0.495337i
\(779\) −3.22861 + 5.59212i −0.115677 + 0.200358i
\(780\) −35.4643 + 16.5750i −1.26983 + 0.593480i
\(781\) −12.0787 20.9210i −0.432211 0.748612i
\(782\) 7.03131 + 4.05953i 0.251439 + 0.145169i
\(783\) 4.98079 0.177999
\(784\) 0 0
\(785\) 23.7812i 0.848789i
\(786\) 7.84680 + 4.53035i 0.279886 + 0.161592i
\(787\) −5.40105 + 3.11830i −0.192527 + 0.111155i −0.593165 0.805081i \(-0.702122\pi\)
0.400638 + 0.916236i \(0.368788\pi\)
\(788\) −11.0552 + 6.38271i −0.393824 + 0.227375i
\(789\) 11.0612 19.1586i 0.393790 0.682064i
\(790\) 9.91903 0.352903
\(791\) 0 0
\(792\) 12.4286 0.441632
\(793\) −18.6944 + 26.7480i −0.663856 + 0.949849i
\(794\) −7.87855 13.6460i −0.279599 0.484280i
\(795\) −15.5666 + 8.98741i −0.552092 + 0.318750i
\(796\) −0.458751 + 0.794580i −0.0162600 + 0.0281631i
\(797\) 40.0701 1.41935 0.709677 0.704527i \(-0.248841\pi\)
0.709677 + 0.704527i \(0.248841\pi\)
\(798\) 0 0
\(799\) 6.76202i 0.239223i
\(800\) 26.8113 + 15.4795i 0.947922 + 0.547283i
\(801\) −8.83775 + 5.10248i −0.312266 + 0.180287i
\(802\) 1.93332 + 3.34861i 0.0682680 + 0.118244i
\(803\) 7.78515 13.4843i 0.274732 0.475850i
\(804\) 1.44785i 0.0510618i
\(805\) 0 0
\(806\) −14.4429 1.25088i −0.508730 0.0440605i
\(807\) −20.1541 + 34.9079i −0.709458 + 1.22882i
\(808\) −28.8017 + 16.6287i −1.01324 + 0.584995i
\(809\) 1.28568 + 2.22686i 0.0452021 + 0.0782924i 0.887741 0.460343i \(-0.152273\pi\)
−0.842539 + 0.538635i \(0.818940\pi\)
\(810\) −12.2755 + 21.2619i −0.431319 + 0.747066i
\(811\) 28.3654i 0.996042i −0.867165 0.498021i \(-0.834060\pi\)
0.867165 0.498021i \(-0.165940\pi\)
\(812\) 0 0
\(813\) 53.5308i 1.87741i
\(814\) 6.30979 + 3.64296i 0.221158 + 0.127686i
\(815\) −3.73975 6.47743i −0.130998 0.226895i
\(816\) −5.47949 9.49076i −0.191821 0.332243i
\(817\) −65.1781 37.6306i −2.28029 1.31653i
\(818\) 17.9922 0.629081
\(819\) 0 0
\(820\) −3.70471 −0.129374
\(821\) 27.5263 + 15.8923i 0.960674 + 0.554646i 0.896380 0.443285i \(-0.146187\pi\)
0.0642938 + 0.997931i \(0.479521\pi\)
\(822\) 12.4795 + 21.6151i 0.435272 + 0.753914i
\(823\) 15.4565 + 26.7715i 0.538781 + 0.933196i 0.998970 + 0.0453747i \(0.0144482\pi\)
−0.460189 + 0.887821i \(0.652218\pi\)
\(824\) 25.8602 + 14.9304i 0.900884 + 0.520125i
\(825\) 31.7462i 1.10526i
\(826\) 0 0
\(827\) 49.7560i 1.73019i −0.501610 0.865094i \(-0.667259\pi\)
0.501610 0.865094i \(-0.332741\pi\)
\(828\) −4.76271 + 8.24926i −0.165516 + 0.286682i
\(829\) −9.95952 17.2504i −0.345908 0.599131i 0.639610 0.768700i \(-0.279096\pi\)
−0.985518 + 0.169569i \(0.945763\pi\)
\(830\) 20.7628 11.9874i 0.720687 0.416089i
\(831\) −1.87702 + 3.25109i −0.0651131 + 0.112779i
\(832\) −4.47013 0.387152i −0.154974 0.0134221i
\(833\) 0 0
\(834\) 4.62222i 0.160054i
\(835\) 5.50000 9.52628i 0.190335 0.329670i
\(836\) 17.5270 + 30.3576i 0.606183 + 1.04994i
\(837\) 12.2758 7.08742i 0.424313 0.244977i
\(838\) 15.0620 + 8.69604i 0.520307 + 0.300400i
\(839\) 11.5625i 0.399181i −0.979879 0.199590i \(-0.936039\pi\)
0.979879 0.199590i \(-0.0639611\pi\)
\(840\) 0 0
\(841\) −24.7940 −0.854965
\(842\) −2.83431 + 4.90917i −0.0976769 + 0.169181i
\(843\) 22.3366 12.8961i 0.769315 0.444164i
\(844\) 1.45161 + 2.51426i 0.0499663 + 0.0865442i
\(845\) −32.0569 26.8037i −1.10279 0.922075i
\(846\) 2.46812 0.0848557
\(847\) 0 0
\(848\) 3.47949 0.119486
\(849\) −13.4336 + 23.2676i −0.461039 + 0.798542i
\(850\) 11.4264 6.59703i 0.391922 0.226276i
\(851\) −11.1762 + 6.45261i −0.383117 + 0.221193i
\(852\) 26.2809 + 15.1733i 0.900370 + 0.519829i
\(853\) 1.74467i 0.0597363i −0.999554 0.0298682i \(-0.990491\pi\)
0.999554 0.0298682i \(-0.00950875\pi\)
\(854\) 0 0
\(855\) 52.2815 1.78799
\(856\) 38.2565 + 22.0874i 1.30758 + 0.754932i
\(857\) −21.1684 36.6647i −0.723098 1.25244i −0.959752 0.280849i \(-0.909384\pi\)
0.236654 0.971594i \(-0.423949\pi\)
\(858\) 6.26177 + 13.3979i 0.213773 + 0.457395i
\(859\) 2.68889 4.65730i 0.0917438 0.158905i −0.816501 0.577344i \(-0.804089\pi\)
0.908245 + 0.418439i \(0.137423\pi\)
\(860\) 43.1798i 1.47242i
\(861\) 0 0
\(862\) 0.990632 0.0337411
\(863\) −13.3620 7.71456i −0.454848 0.262607i 0.255027 0.966934i \(-0.417915\pi\)
−0.709875 + 0.704327i \(0.751249\pi\)
\(864\) 12.2124 7.05086i 0.415476 0.239875i
\(865\) −23.0337 + 13.2985i −0.783169 + 0.452163i
\(866\) −9.84492 5.68397i −0.334544 0.193149i
\(867\) 9.07160 0.308088
\(868\) 0 0
\(869\) 12.0449i 0.408595i
\(870\) −5.02789 + 8.70856i −0.170461 + 0.295248i
\(871\) 1.40011 0.654372i 0.0474410 0.0221725i
\(872\) 10.1541 + 17.5874i 0.343861 + 0.595585i
\(873\) −15.8703 9.16270i −0.537127 0.310110i
\(874\) 19.3165 0.653391
\(875\) 0 0
\(876\) 19.5594i 0.660851i
\(877\) −33.3576 19.2590i −1.12641 0.650331i −0.183378 0.983042i \(-0.558703\pi\)
−0.943029 + 0.332711i \(0.892037\pi\)
\(878\) 6.06259 3.50024i 0.204603 0.118127i
\(879\) 21.9645 12.6812i 0.740845 0.427727i
\(880\) −5.95407 + 10.3127i −0.200712 + 0.347643i
\(881\) 41.7373 1.40617 0.703083 0.711108i \(-0.251806\pi\)
0.703083 + 0.711108i \(0.251806\pi\)
\(882\) 0 0
\(883\) −52.8439 −1.77834 −0.889170 0.457577i \(-0.848717\pi\)
−0.889170 + 0.457577i \(0.848717\pi\)
\(884\) 11.3178 16.1935i 0.380658 0.544648i
\(885\) 26.0923 + 45.1933i 0.877084 + 1.51915i
\(886\) 1.91381 1.10494i 0.0642956 0.0371211i
\(887\) −4.49532 + 7.78612i −0.150938 + 0.261432i −0.931573 0.363556i \(-0.881563\pi\)
0.780635 + 0.624988i \(0.214896\pi\)
\(888\) −21.1526 −0.709834
\(889\) 0 0
\(890\) 11.8731i 0.397987i
\(891\) −25.8187 14.9064i −0.864959 0.499384i
\(892\) 14.0476 8.11039i 0.470348 0.271556i
\(893\) 8.04395 + 13.9325i 0.269180 + 0.466234i
\(894\) 11.0874 19.2040i 0.370819 0.642277i
\(895\) 52.1546i 1.74334i
\(896\) 0 0
\(897\) −26.0973 2.26025i −0.871362 0.0754676i
\(898\) 6.34122 10.9833i 0.211609 0.366518i
\(899\) 10.3662 5.98494i 0.345733 0.199609i
\(900\) 7.73975 + 13.4056i 0.257992 + 0.446855i
\(901\) 4.53580 7.85623i 0.151109 0.261729i
\(902\) 1.39958i 0.0466010i
\(903\) 0 0
\(904\) 20.5589i 0.683780i
\(905\) −25.6237 14.7938i −0.851759 0.491764i
\(906\) −15.2351 26.3879i −0.506151 0.876679i
\(907\) −10.3501 17.9270i −0.343671 0.595255i 0.641441 0.767173i \(-0.278337\pi\)
−0.985111 + 0.171918i \(0.945004\pi\)
\(908\) −19.8831 11.4795i −0.659843 0.380960i
\(909\) −26.0622 −0.864430
\(910\) 0 0
\(911\) 29.8988 0.990590 0.495295 0.868725i \(-0.335060\pi\)
0.495295 + 0.868725i \(0.335060\pi\)
\(912\) −22.5800 13.0366i −0.747698 0.431684i
\(913\) 14.5565 + 25.2127i 0.481751 + 0.834418i
\(914\) 1.17214 + 2.03021i 0.0387710 + 0.0671533i
\(915\) 55.7891 + 32.2099i 1.84433 + 1.06483i
\(916\) 9.96836i 0.329364i
\(917\) 0 0
\(918\) 6.00984i 0.198354i
\(919\) −19.2924 + 33.4154i −0.636397 + 1.10227i 0.349821 + 0.936817i \(0.386242\pi\)
−0.986217 + 0.165455i \(0.947091\pi\)
\(920\) 12.8064 + 22.1814i 0.422215 + 0.731298i
\(921\) 7.61289 4.39530i 0.250853 0.144830i
\(922\) 6.05239 10.4830i 0.199325 0.345241i
\(923\) −2.79505 + 32.2721i −0.0920001 + 1.06225i
\(924\) 0 0
\(925\) 20.9719i 0.689552i
\(926\) −5.43239 + 9.40918i −0.178520 + 0.309205i
\(927\) 11.7003 + 20.2655i 0.384287 + 0.665605i
\(928\) 10.3127 5.95407i 0.338532 0.195452i
\(929\) −2.81961 1.62790i −0.0925085 0.0534098i 0.453032 0.891494i \(-0.350342\pi\)
−0.545541 + 0.838084i \(0.683676\pi\)
\(930\) 28.6178i 0.938414i
\(931\) 0 0
\(932\) 42.6494 1.39703
\(933\) −30.2788 + 52.4444i −0.991283 + 1.71695i
\(934\) 2.24735 1.29751i 0.0735356 0.0424558i
\(935\) 15.5232 + 26.8870i 0.507663 + 0.879298i
\(936\) −13.6600 9.54709i −0.446492 0.312056i
\(937\) −11.6840 −0.381699 −0.190849 0.981619i \(-0.561124\pi\)
−0.190849 + 0.981619i \(0.561124\pi\)
\(938\) 0 0
\(939\) 42.3007 1.38043
\(940\) −4.61507 + 7.99354i −0.150527 + 0.260720i
\(941\) −36.3470 + 20.9849i −1.18488 + 0.684090i −0.957138 0.289632i \(-0.906467\pi\)
−0.227740 + 0.973722i \(0.573134\pi\)
\(942\) −9.77389 + 5.64296i −0.318451 + 0.183858i
\(943\) −2.14689 1.23951i −0.0699124 0.0403640i
\(944\) 10.1017i 0.328783i
\(945\) 0 0
\(946\) −16.3126 −0.530370
\(947\) −17.6284 10.1778i −0.572846 0.330733i 0.185439 0.982656i \(-0.440629\pi\)
−0.758285 + 0.651923i \(0.773962\pi\)
\(948\) −7.56538 13.1036i −0.245712 0.425586i
\(949\) −18.9145 + 8.84008i −0.613990 + 0.286961i
\(950\) 15.6953 27.1851i 0.509224 0.882002i
\(951\) 21.9398i 0.711446i
\(952\) 0 0
\(953\) 30.5496 0.989597 0.494799 0.869008i \(-0.335242\pi\)
0.494799 + 0.869008i \(0.335242\pi\)
\(954\) −2.86750 1.65555i −0.0928389 0.0536005i
\(955\) −18.5620 + 10.7168i −0.600653 + 0.346787i
\(956\) −25.8679 + 14.9349i −0.836629 + 0.483028i
\(957\) −10.5750 6.10546i −0.341840 0.197362i
\(958\) −8.33783 −0.269383
\(959\) 0 0
\(960\) 8.85728i 0.285867i
\(961\) 1.53257 2.65449i 0.0494378 0.0856288i
\(962\) −4.13660 8.85077i −0.133369 0.285360i
\(963\) 17.3089 + 29.9799i 0.557771 + 0.966088i
\(964\) −17.6461 10.1880i −0.568342 0.328132i
\(965\) 66.2262 2.13190
\(966\) 0 0
\(967\) 54.4548i 1.75115i 0.483084 + 0.875574i \(0.339516\pi\)
−0.483084 + 0.875574i \(0.660484\pi\)
\(968\) −7.92901 4.57781i −0.254848 0.147137i
\(969\) −58.8697 + 33.9884i −1.89117 + 1.09187i
\(970\) −18.4645 + 10.6605i −0.592859 + 0.342287i
\(971\) 27.3017 47.2880i 0.876155 1.51754i 0.0206267 0.999787i \(-0.493434\pi\)
0.855528 0.517757i \(-0.173233\pi\)
\(972\) 26.3368 0.844752
\(973\) 0 0
\(974\) 11.9714 0.383589
\(975\) −24.3859 + 34.8915i −0.780975 + 1.11742i
\(976\) −6.23506 10.7994i −0.199580 0.345682i
\(977\) 28.2735 16.3237i 0.904549 0.522242i 0.0258756 0.999665i \(-0.491763\pi\)
0.878673 + 0.477424i \(0.158429\pi\)
\(978\) 1.77478 3.07401i 0.0567512 0.0982960i
\(979\) −14.4177 −0.460793
\(980\) 0 0
\(981\) 15.9146i 0.508114i
\(982\) −11.5693 6.67952i −0.369190 0.213152i
\(983\) 23.8202 13.7526i 0.759745 0.438639i −0.0694590 0.997585i \(-0.522127\pi\)
0.829204 + 0.558946i \(0.188794\pi\)
\(984\) −2.03164 3.51891i −0.0647664 0.112179i
\(985\) −13.4494 + 23.2950i −0.428533 + 0.742241i
\(986\) 5.07499i 0.161621i
\(987\) 0 0
\(988\) 4.05578 46.8287i 0.129031 1.48982i
\(989\) 14.4469 25.0228i 0.459385 0.795679i
\(990\) 9.81367 5.66593i 0.311899 0.180075i
\(991\) 3.14695 + 5.45068i 0.0999662 + 0.173147i 0.911670 0.410922i \(-0.134793\pi\)
−0.811704 + 0.584069i \(0.801460\pi\)
\(992\) 16.9447 29.3491i 0.537995 0.931834i
\(993\) 51.8578i 1.64566i
\(994\) 0 0
\(995\) 1.93332i 0.0612905i
\(996\) −31.6721 18.2859i −1.00357 0.579411i
\(997\) 10.4351 + 18.0741i 0.330483 + 0.572413i 0.982607 0.185700i \(-0.0594551\pi\)
−0.652124 + 0.758112i \(0.726122\pi\)
\(998\) −3.67529 6.36580i −0.116339 0.201506i
\(999\) 8.27282 + 4.77631i 0.261740 + 0.151116i
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 637.2.r.e.324.3 12
7.2 even 3 91.2.c.a.64.4 yes 6
7.3 odd 6 637.2.r.d.116.4 12
7.4 even 3 inner 637.2.r.e.116.4 12
7.5 odd 6 637.2.c.d.246.4 6
7.6 odd 2 637.2.r.d.324.3 12
13.12 even 2 inner 637.2.r.e.324.4 12
21.2 odd 6 819.2.c.b.64.3 6
28.23 odd 6 1456.2.k.c.337.6 6
91.5 even 12 8281.2.a.bi.1.2 3
91.12 odd 6 637.2.c.d.246.3 6
91.25 even 6 inner 637.2.r.e.116.3 12
91.38 odd 6 637.2.r.d.116.3 12
91.44 odd 12 1183.2.a.j.1.2 3
91.47 even 12 8281.2.a.be.1.2 3
91.51 even 6 91.2.c.a.64.3 6
91.86 odd 12 1183.2.a.h.1.2 3
91.90 odd 2 637.2.r.d.324.4 12
273.233 odd 6 819.2.c.b.64.4 6
364.51 odd 6 1456.2.k.c.337.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.c.a.64.3 6 91.51 even 6
91.2.c.a.64.4 yes 6 7.2 even 3
637.2.c.d.246.3 6 91.12 odd 6
637.2.c.d.246.4 6 7.5 odd 6
637.2.r.d.116.3 12 91.38 odd 6
637.2.r.d.116.4 12 7.3 odd 6
637.2.r.d.324.3 12 7.6 odd 2
637.2.r.d.324.4 12 91.90 odd 2
637.2.r.e.116.3 12 91.25 even 6 inner
637.2.r.e.116.4 12 7.4 even 3 inner
637.2.r.e.324.3 12 1.1 even 1 trivial
637.2.r.e.324.4 12 13.12 even 2 inner
819.2.c.b.64.3 6 21.2 odd 6
819.2.c.b.64.4 6 273.233 odd 6
1183.2.a.h.1.2 3 91.86 odd 12
1183.2.a.j.1.2 3 91.44 odd 12
1456.2.k.c.337.5 6 364.51 odd 6
1456.2.k.c.337.6 6 28.23 odd 6
8281.2.a.be.1.2 3 91.47 even 12
8281.2.a.bi.1.2 3 91.5 even 12