Properties

Label 637.2.r.f.324.3
Level $637$
Weight $2$
Character 637.324
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
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: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 324.3
Root \(0.929293 - 0.536527i\) of defining polynomial
Character \(\chi\) \(=\) 637.324
Dual form 637.2.r.f.116.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.929293 - 0.536527i) q^{2} +(-1.21570 - 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(-0.541640 - 0.312716i) q^{5} +2.60903i q^{6} +3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +O(q^{10})\) \(q+(-0.929293 - 0.536527i) q^{2} +(-1.21570 - 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(-0.541640 - 0.312716i) q^{5} +2.60903i q^{6} +3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +(0.335561 + 0.581209i) q^{10} +(-0.613597 + 0.354260i) q^{11} +(-1.03159 + 1.78676i) q^{12} +(-0.848553 + 3.50428i) q^{13} +1.52068i q^{15} +(0.791426 - 1.37079i) q^{16} +(1.67157 + 2.89524i) q^{17} +(2.70585 - 1.56222i) q^{18} +(4.50573 + 2.60138i) q^{19} +0.530712i q^{20} +0.760282 q^{22} +(-2.21570 + 3.83771i) q^{23} +(6.43627 - 3.71598i) q^{24} +(-2.30442 - 3.99137i) q^{25} +(2.66870 - 2.80123i) q^{26} -0.214623 q^{27} -6.59711 q^{29} +(0.815886 - 1.41316i) q^{30} +(-3.80238 + 2.19530i) q^{31} +(3.82335 - 2.20741i) q^{32} +(1.49190 + 0.861351i) q^{33} -3.58737i q^{34} +2.47076 q^{36} +(-0.366683 - 0.211704i) q^{37} +(-2.79143 - 4.83489i) q^{38} +(8.41040 - 2.47340i) q^{39} +(0.955864 - 1.65561i) q^{40} -5.01604i q^{41} +11.2059 q^{43} +(0.520670 + 0.300609i) q^{44} +(1.57711 - 0.910544i) q^{45} +(4.11807 - 2.37757i) q^{46} +(6.99116 + 4.03635i) q^{47} -3.84855 q^{48} +4.94553i q^{50} +(4.06426 - 7.03950i) q^{51} +(2.93520 - 0.863208i) q^{52} +(0.348553 + 0.603712i) q^{53} +(0.199447 + 0.115151i) q^{54} +0.443132 q^{55} -12.6500i q^{57} +(6.13065 + 3.53953i) q^{58} +(-8.54177 + 4.93159i) q^{59} +(1.11750 - 0.645188i) q^{60} +(2.34855 - 4.06781i) q^{61} +4.71136 q^{62} -7.90305 q^{64} +(1.55545 - 1.63270i) q^{65} +(-0.924277 - 1.60089i) q^{66} +(-9.02470 + 5.21041i) q^{67} +(1.41841 - 2.45676i) q^{68} +10.7745 q^{69} +14.0876i q^{71} +(-7.70775 - 4.45007i) q^{72} +(4.40273 - 2.54191i) q^{73} +(0.227170 + 0.393471i) q^{74} +(-5.60297 + 9.70463i) q^{75} -4.41482i q^{76} +(-9.14277 - 2.21390i) q^{78} +(1.95586 - 3.38766i) q^{79} +(-0.857336 + 0.494983i) q^{80} +(4.62851 + 8.01682i) q^{81} +(-2.69124 + 4.66137i) q^{82} +10.2035i q^{83} -2.09090i q^{85} +(-10.4136 - 6.01230i) q^{86} +(8.02012 + 13.8913i) q^{87} +(-1.08285 - 1.87555i) q^{88} +(-11.5866 - 6.68955i) q^{89} -1.95413 q^{90} +3.76028 q^{92} +(9.24512 + 5.33767i) q^{93} +(-4.33122 - 7.50190i) q^{94} +(-1.62699 - 2.81802i) q^{95} +(-9.29610 - 5.36711i) q^{96} -0.202023i q^{97} -2.06302i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} + 12 q^{13} + 2 q^{16} - 8 q^{17} - 36 q^{22} - 12 q^{23} + 6 q^{26} - 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} - 34 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{43} - 36 q^{48} + 16 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{55} + 12 q^{61} - 44 q^{62} + 88 q^{64} - 30 q^{65} - 2 q^{66} + 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 20 q^{78} + 20 q^{79} - 24 q^{81} + 16 q^{82} + 68 q^{87} + 4 q^{88} + 216 q^{90} + 12 q^{92} + 26 q^{94} - 16 q^{95}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.929293 0.536527i −0.657109 0.379382i 0.134065 0.990972i \(-0.457197\pi\)
−0.791175 + 0.611590i \(0.790530\pi\)
\(3\) −1.21570 2.10566i −0.701886 1.21570i −0.967804 0.251707i \(-0.919008\pi\)
0.265918 0.963996i \(-0.414325\pi\)
\(4\) −0.424277 0.734868i −0.212138 0.367434i
\(5\) −0.541640 0.312716i −0.242229 0.139851i 0.373972 0.927440i \(-0.377996\pi\)
−0.616201 + 0.787589i \(0.711329\pi\)
\(6\) 2.60903i 1.06513i
\(7\) 0 0
\(8\) 3.05665i 1.08069i
\(9\) −1.45586 + 2.52163i −0.485288 + 0.840544i
\(10\) 0.335561 + 0.581209i 0.106114 + 0.183795i
\(11\) −0.613597 + 0.354260i −0.185006 + 0.106814i −0.589643 0.807664i \(-0.700731\pi\)
0.404636 + 0.914478i \(0.367398\pi\)
\(12\) −1.03159 + 1.78676i −0.297794 + 0.515794i
\(13\) −0.848553 + 3.50428i −0.235346 + 0.971912i
\(14\) 0 0
\(15\) 1.52068i 0.392637i
\(16\) 0.791426 1.37079i 0.197856 0.342697i
\(17\) 1.67157 + 2.89524i 0.405414 + 0.702199i 0.994370 0.105967i \(-0.0337939\pi\)
−0.588955 + 0.808166i \(0.700461\pi\)
\(18\) 2.70585 1.56222i 0.637775 0.368219i
\(19\) 4.50573 + 2.60138i 1.03368 + 0.596798i 0.918038 0.396492i \(-0.129773\pi\)
0.115646 + 0.993290i \(0.463106\pi\)
\(20\) 0.530712i 0.118671i
\(21\) 0 0
\(22\) 0.760282 0.162093
\(23\) −2.21570 + 3.83771i −0.462006 + 0.800218i −0.999061 0.0433296i \(-0.986203\pi\)
0.537055 + 0.843547i \(0.319537\pi\)
\(24\) 6.43627 3.71598i 1.31380 0.758522i
\(25\) −2.30442 3.99137i −0.460883 0.798274i
\(26\) 2.66870 2.80123i 0.523374 0.549366i
\(27\) −0.214623 −0.0413042
\(28\) 0 0
\(29\) −6.59711 −1.22505 −0.612526 0.790450i \(-0.709847\pi\)
−0.612526 + 0.790450i \(0.709847\pi\)
\(30\) 0.815886 1.41316i 0.148960 0.258006i
\(31\) −3.80238 + 2.19530i −0.682927 + 0.394288i −0.800957 0.598722i \(-0.795675\pi\)
0.118030 + 0.993010i \(0.462342\pi\)
\(32\) 3.82335 2.20741i 0.675879 0.390219i
\(33\) 1.49190 + 0.861351i 0.259707 + 0.149942i
\(34\) 3.58737i 0.615228i
\(35\) 0 0
\(36\) 2.47076 0.411793
\(37\) −0.366683 0.211704i −0.0602823 0.0348040i 0.469556 0.882903i \(-0.344414\pi\)
−0.529838 + 0.848099i \(0.677747\pi\)
\(38\) −2.79143 4.83489i −0.452829 0.784323i
\(39\) 8.41040 2.47340i 1.34674 0.396060i
\(40\) 0.955864 1.65561i 0.151135 0.261774i
\(41\) 5.01604i 0.783374i −0.920099 0.391687i \(-0.871892\pi\)
0.920099 0.391687i \(-0.128108\pi\)
\(42\) 0 0
\(43\) 11.2059 1.70889 0.854445 0.519542i \(-0.173897\pi\)
0.854445 + 0.519542i \(0.173897\pi\)
\(44\) 0.520670 + 0.300609i 0.0784939 + 0.0453185i
\(45\) 1.57711 0.910544i 0.235101 0.135736i
\(46\) 4.11807 2.37757i 0.607177 0.350554i
\(47\) 6.99116 + 4.03635i 1.01977 + 0.588762i 0.914036 0.405633i \(-0.132949\pi\)
0.105729 + 0.994395i \(0.466282\pi\)
\(48\) −3.84855 −0.555491
\(49\) 0 0
\(50\) 4.94553i 0.699404i
\(51\) 4.06426 7.03950i 0.569110 0.985727i
\(52\) 2.93520 0.863208i 0.407040 0.119705i
\(53\) 0.348553 + 0.603712i 0.0478774 + 0.0829262i 0.888971 0.457964i \(-0.151421\pi\)
−0.841094 + 0.540890i \(0.818088\pi\)
\(54\) 0.199447 + 0.115151i 0.0271414 + 0.0156701i
\(55\) 0.443132 0.0597519
\(56\) 0 0
\(57\) 12.6500i 1.67554i
\(58\) 6.13065 + 3.53953i 0.804993 + 0.464763i
\(59\) −8.54177 + 4.93159i −1.11204 + 0.642039i −0.939358 0.342938i \(-0.888578\pi\)
−0.172686 + 0.984977i \(0.555244\pi\)
\(60\) 1.11750 0.645188i 0.144268 0.0832934i
\(61\) 2.34855 4.06781i 0.300701 0.520830i −0.675594 0.737274i \(-0.736113\pi\)
0.976295 + 0.216444i \(0.0694459\pi\)
\(62\) 4.71136 0.598344
\(63\) 0 0
\(64\) −7.90305 −0.987881
\(65\) 1.55545 1.63270i 0.192930 0.202512i
\(66\) −0.924277 1.60089i −0.113771 0.197056i
\(67\) −9.02470 + 5.21041i −1.10254 + 0.636553i −0.936888 0.349631i \(-0.886307\pi\)
−0.165655 + 0.986184i \(0.552974\pi\)
\(68\) 1.41841 2.45676i 0.172008 0.297926i
\(69\) 10.7745 1.29710
\(70\) 0 0
\(71\) 14.0876i 1.67189i 0.548812 + 0.835946i \(0.315080\pi\)
−0.548812 + 0.835946i \(0.684920\pi\)
\(72\) −7.70775 4.45007i −0.908368 0.524446i
\(73\) 4.40273 2.54191i 0.515300 0.297509i −0.219710 0.975565i \(-0.570511\pi\)
0.735010 + 0.678057i \(0.237178\pi\)
\(74\) 0.227170 + 0.393471i 0.0264080 + 0.0457400i
\(75\) −5.60297 + 9.70463i −0.646975 + 1.12059i
\(76\) 4.41482i 0.506415i
\(77\) 0 0
\(78\) −9.14277 2.21390i −1.03521 0.250675i
\(79\) 1.95586 3.38766i 0.220052 0.381141i −0.734772 0.678315i \(-0.762711\pi\)
0.954823 + 0.297174i \(0.0960440\pi\)
\(80\) −0.857336 + 0.494983i −0.0958530 + 0.0553408i
\(81\) 4.62851 + 8.01682i 0.514279 + 0.890757i
\(82\) −2.69124 + 4.66137i −0.297198 + 0.514762i
\(83\) 10.2035i 1.11998i 0.828499 + 0.559990i \(0.189195\pi\)
−0.828499 + 0.559990i \(0.810805\pi\)
\(84\) 0 0
\(85\) 2.09090i 0.226790i
\(86\) −10.4136 6.01230i −1.12293 0.648323i
\(87\) 8.02012 + 13.8913i 0.859847 + 1.48930i
\(88\) −1.08285 1.87555i −0.115432 0.199935i
\(89\) −11.5866 6.68955i −1.22818 0.709090i −0.261532 0.965195i \(-0.584228\pi\)
−0.966649 + 0.256104i \(0.917561\pi\)
\(90\) −1.95413 −0.205983
\(91\) 0 0
\(92\) 3.76028 0.392036
\(93\) 9.24512 + 5.33767i 0.958674 + 0.553491i
\(94\) −4.33122 7.50190i −0.446731 0.773761i
\(95\) −1.62699 2.81802i −0.166925 0.289123i
\(96\) −9.29610 5.36711i −0.948780 0.547778i
\(97\) 0.202023i 0.0205123i −0.999947 0.0102562i \(-0.996735\pi\)
0.999947 0.0102562i \(-0.00326470\pi\)
\(98\) 0 0
\(99\) 2.06302i 0.207341i
\(100\) −1.95542 + 3.38689i −0.195542 + 0.338689i
\(101\) 8.66723 + 15.0121i 0.862421 + 1.49376i 0.869585 + 0.493783i \(0.164386\pi\)
−0.00716374 + 0.999974i \(0.502280\pi\)
\(102\) −7.55377 + 4.36117i −0.747934 + 0.431820i
\(103\) 5.40739 9.36587i 0.532806 0.922847i −0.466460 0.884542i \(-0.654471\pi\)
0.999266 0.0383047i \(-0.0121957\pi\)
\(104\) −10.7114 2.59373i −1.05034 0.254336i
\(105\) 0 0
\(106\) 0.748033i 0.0726554i
\(107\) 3.05839 5.29729i 0.295666 0.512108i −0.679474 0.733700i \(-0.737792\pi\)
0.975140 + 0.221592i \(0.0711252\pi\)
\(108\) 0.0910594 + 0.157720i 0.00876220 + 0.0151766i
\(109\) −9.87196 + 5.69958i −0.945563 + 0.545921i −0.891700 0.452628i \(-0.850487\pi\)
−0.0538629 + 0.998548i \(0.517153\pi\)
\(110\) −0.411799 0.237752i −0.0392635 0.0226688i
\(111\) 1.02948i 0.0977137i
\(112\) 0 0
\(113\) −0.923456 −0.0868714 −0.0434357 0.999056i \(-0.513830\pi\)
−0.0434357 + 0.999056i \(0.513830\pi\)
\(114\) −6.78709 + 11.7556i −0.635669 + 1.10101i
\(115\) 2.40023 1.38577i 0.223822 0.129224i
\(116\) 2.79900 + 4.84801i 0.259880 + 0.450126i
\(117\) −7.60112 7.24149i −0.702723 0.669476i
\(118\) 10.5837 0.974312
\(119\) 0 0
\(120\) −4.64819 −0.424319
\(121\) −5.24900 + 9.09153i −0.477182 + 0.826503i
\(122\) −4.36499 + 2.52013i −0.395187 + 0.228162i
\(123\) −10.5621 + 6.09801i −0.952349 + 0.549839i
\(124\) 3.22652 + 1.86283i 0.289750 + 0.167287i
\(125\) 6.00967i 0.537521i
\(126\) 0 0
\(127\) 8.50972 0.755116 0.377558 0.925986i \(-0.376764\pi\)
0.377558 + 0.925986i \(0.376764\pi\)
\(128\) −0.302447 0.174618i −0.0267328 0.0154342i
\(129\) −13.6231 23.5959i −1.19945 2.07750i
\(130\) −2.32146 + 0.682713i −0.203606 + 0.0598779i
\(131\) −3.50152 + 6.06482i −0.305930 + 0.529885i −0.977468 0.211084i \(-0.932301\pi\)
0.671538 + 0.740970i \(0.265634\pi\)
\(132\) 1.46180i 0.127234i
\(133\) 0 0
\(134\) 11.1821 0.965988
\(135\) 0.116248 + 0.0671160i 0.0100051 + 0.00577642i
\(136\) −8.84974 + 5.10940i −0.758859 + 0.438128i
\(137\) −5.38403 + 3.10847i −0.459989 + 0.265575i −0.712040 0.702139i \(-0.752228\pi\)
0.252051 + 0.967714i \(0.418895\pi\)
\(138\) −10.0127 5.78084i −0.852338 0.492097i
\(139\) −6.53140 −0.553986 −0.276993 0.960872i \(-0.589338\pi\)
−0.276993 + 0.960872i \(0.589338\pi\)
\(140\) 0 0
\(141\) 19.6280i 1.65297i
\(142\) 7.55839 13.0915i 0.634286 1.09862i
\(143\) −0.720757 2.45082i −0.0602727 0.204948i
\(144\) 2.30442 + 3.99137i 0.192035 + 0.332614i
\(145\) 3.57326 + 2.06302i 0.296743 + 0.171325i
\(146\) −5.45523 −0.451478
\(147\) 0 0
\(148\) 0.359285i 0.0295330i
\(149\) −3.20203 1.84869i −0.262320 0.151451i 0.363072 0.931761i \(-0.381728\pi\)
−0.625393 + 0.780310i \(0.715061\pi\)
\(150\) 10.4136 6.01230i 0.850267 0.490902i
\(151\) −4.22425 + 2.43887i −0.343764 + 0.198473i −0.661935 0.749561i \(-0.730265\pi\)
0.318171 + 0.948033i \(0.396931\pi\)
\(152\) −7.95152 + 13.7724i −0.644954 + 1.11709i
\(153\) −9.73430 −0.786971
\(154\) 0 0
\(155\) 2.74603 0.220566
\(156\) −5.38595 5.13113i −0.431221 0.410819i
\(157\) −4.75984 8.24428i −0.379876 0.657965i 0.611168 0.791501i \(-0.290700\pi\)
−0.991044 + 0.133536i \(0.957367\pi\)
\(158\) −3.63514 + 2.09875i −0.289196 + 0.166968i
\(159\) 0.847473 1.46787i 0.0672090 0.116409i
\(160\) −2.76117 −0.218290
\(161\) 0 0
\(162\) 9.93329i 0.780433i
\(163\) 20.5325 + 11.8544i 1.60823 + 0.928511i 0.989767 + 0.142696i \(0.0455770\pi\)
0.618461 + 0.785815i \(0.287756\pi\)
\(164\) −3.68613 + 2.12819i −0.287838 + 0.166184i
\(165\) −0.538716 0.933084i −0.0419390 0.0726405i
\(166\) 5.47446 9.48204i 0.424901 0.735949i
\(167\) 1.13193i 0.0875914i −0.999041 0.0437957i \(-0.986055\pi\)
0.999041 0.0437957i \(-0.0139451\pi\)
\(168\) 0 0
\(169\) −11.5599 5.94713i −0.889224 0.457472i
\(170\) −1.12183 + 1.94306i −0.0860402 + 0.149026i
\(171\) −13.1195 + 7.57452i −1.00327 + 0.579238i
\(172\) −4.75442 8.23489i −0.362521 0.627905i
\(173\) −5.99458 + 10.3829i −0.455760 + 0.789399i −0.998732 0.0503522i \(-0.983966\pi\)
0.542972 + 0.839751i \(0.317299\pi\)
\(174\) 17.2121i 1.30484i
\(175\) 0 0
\(176\) 1.12148i 0.0845350i
\(177\) 20.7685 + 11.9907i 1.56106 + 0.901276i
\(178\) 7.17825 + 12.4331i 0.538033 + 0.931900i
\(179\) 4.73538 + 8.20192i 0.353939 + 0.613040i 0.986936 0.161114i \(-0.0515088\pi\)
−0.632997 + 0.774154i \(0.718175\pi\)
\(180\) −1.33826 0.772645i −0.0997480 0.0575896i
\(181\) 11.4314 0.849690 0.424845 0.905266i \(-0.360329\pi\)
0.424845 + 0.905266i \(0.360329\pi\)
\(182\) 0 0
\(183\) −11.4206 −0.844233
\(184\) −11.7305 6.77264i −0.864788 0.499285i
\(185\) 0.132407 + 0.229335i 0.00973473 + 0.0168611i
\(186\) −5.72761 9.92052i −0.419969 0.727408i
\(187\) −2.05134 1.18434i −0.150009 0.0866075i
\(188\) 6.85011i 0.499595i
\(189\) 0 0
\(190\) 3.49169i 0.253314i
\(191\) −7.84377 + 13.5858i −0.567555 + 0.983034i 0.429252 + 0.903185i \(0.358777\pi\)
−0.996807 + 0.0798496i \(0.974556\pi\)
\(192\) 9.60776 + 16.6411i 0.693380 + 1.20097i
\(193\) 19.9248 11.5036i 1.43422 0.828045i 0.436776 0.899570i \(-0.356120\pi\)
0.997439 + 0.0715256i \(0.0227868\pi\)
\(194\) −0.108391 + 0.187739i −0.00778202 + 0.0134788i
\(195\) −5.32888 1.29038i −0.381609 0.0924057i
\(196\) 0 0
\(197\) 10.2035i 0.726970i 0.931600 + 0.363485i \(0.118413\pi\)
−0.931600 + 0.363485i \(0.881587\pi\)
\(198\) −1.10687 + 1.91715i −0.0786616 + 0.136246i
\(199\) −5.96173 10.3260i −0.422616 0.731992i 0.573579 0.819150i \(-0.305555\pi\)
−0.996194 + 0.0871586i \(0.972221\pi\)
\(200\) 12.2002 7.04381i 0.862687 0.498072i
\(201\) 21.9427 + 12.6686i 1.54772 + 0.893576i
\(202\) 18.6008i 1.30875i
\(203\) 0 0
\(204\) −6.89747 −0.482920
\(205\) −1.56860 + 2.71689i −0.109555 + 0.189756i
\(206\) −10.0501 + 5.80243i −0.700223 + 0.404274i
\(207\) −6.45152 11.1744i −0.448412 0.776672i
\(208\) 4.13206 + 3.93656i 0.286507 + 0.272952i
\(209\) −3.68627 −0.254984
\(210\) 0 0
\(211\) −15.5893 −1.07321 −0.536606 0.843833i \(-0.680294\pi\)
−0.536606 + 0.843833i \(0.680294\pi\)
\(212\) 0.295766 0.512281i 0.0203133 0.0351836i
\(213\) 29.6637 17.1263i 2.03252 1.17348i
\(214\) −5.68428 + 3.28182i −0.388570 + 0.224341i
\(215\) −6.06959 3.50428i −0.413942 0.238990i
\(216\) 0.656028i 0.0446370i
\(217\) 0 0
\(218\) 12.2319 0.828451
\(219\) −10.7048 6.18042i −0.723364 0.417634i
\(220\) −0.188010 0.325643i −0.0126757 0.0219549i
\(221\) −11.5641 + 3.40087i −0.777888 + 0.228767i
\(222\) 0.552343 0.956687i 0.0370709 0.0642086i
\(223\) 6.76662i 0.453126i 0.973996 + 0.226563i \(0.0727490\pi\)
−0.973996 + 0.226563i \(0.927251\pi\)
\(224\) 0 0
\(225\) 13.4197 0.894645
\(226\) 0.858161 + 0.495459i 0.0570840 + 0.0329575i
\(227\) −14.5704 + 8.41225i −0.967074 + 0.558340i −0.898343 0.439295i \(-0.855228\pi\)
−0.0687311 + 0.997635i \(0.521895\pi\)
\(228\) −9.29610 + 5.36711i −0.615650 + 0.355445i
\(229\) −9.54855 5.51286i −0.630986 0.364300i 0.150148 0.988664i \(-0.452025\pi\)
−0.781134 + 0.624364i \(0.785358\pi\)
\(230\) −2.97402 −0.196101
\(231\) 0 0
\(232\) 20.1651i 1.32390i
\(233\) 8.67743 15.0298i 0.568477 0.984632i −0.428239 0.903665i \(-0.640866\pi\)
0.996717 0.0809664i \(-0.0258006\pi\)
\(234\) 3.17840 + 10.8077i 0.207779 + 0.706520i
\(235\) −2.52446 4.37249i −0.164678 0.285230i
\(236\) 7.24814 + 4.18472i 0.471814 + 0.272402i
\(237\) −9.51100 −0.617806
\(238\) 0 0
\(239\) 19.7223i 1.27573i 0.770148 + 0.637865i \(0.220182\pi\)
−0.770148 + 0.637865i \(0.779818\pi\)
\(240\) 2.08453 + 1.20350i 0.134556 + 0.0776858i
\(241\) 2.41112 1.39206i 0.155314 0.0896706i −0.420329 0.907372i \(-0.638085\pi\)
0.575643 + 0.817701i \(0.304752\pi\)
\(242\) 9.75571 5.63246i 0.627121 0.362069i
\(243\) 10.9318 18.9345i 0.701278 1.21465i
\(244\) −3.98574 −0.255161
\(245\) 0 0
\(246\) 13.0870 0.834397
\(247\) −12.9393 + 13.5819i −0.823309 + 0.864196i
\(248\) −6.71028 11.6226i −0.426103 0.738033i
\(249\) 21.4851 12.4044i 1.36156 0.786098i
\(250\) 3.22435 5.58475i 0.203926 0.353210i
\(251\) 23.5608 1.48714 0.743572 0.668655i \(-0.233130\pi\)
0.743572 + 0.668655i \(0.233130\pi\)
\(252\) 0 0
\(253\) 3.13974i 0.197394i
\(254\) −7.90803 4.56570i −0.496194 0.286478i
\(255\) −4.40273 + 2.54191i −0.275709 + 0.159181i
\(256\) 8.09042 + 14.0130i 0.505651 + 0.875814i
\(257\) 1.71615 2.97245i 0.107050 0.185417i −0.807524 0.589835i \(-0.799193\pi\)
0.914574 + 0.404419i \(0.132526\pi\)
\(258\) 29.2367i 1.82019i
\(259\) 0 0
\(260\) −1.85976 0.450337i −0.115338 0.0279287i
\(261\) 9.60450 16.6355i 0.594503 1.02971i
\(262\) 6.50788 3.75733i 0.402058 0.232128i
\(263\) 10.7245 + 18.5754i 0.661303 + 1.14541i 0.980273 + 0.197646i \(0.0633298\pi\)
−0.318970 + 0.947765i \(0.603337\pi\)
\(264\) −2.63285 + 4.56023i −0.162041 + 0.280663i
\(265\) 0.435992i 0.0267828i
\(266\) 0 0
\(267\) 32.5300i 1.99080i
\(268\) 7.65794 + 4.42131i 0.467783 + 0.270075i
\(269\) 7.32843 + 12.6932i 0.446822 + 0.773919i 0.998177 0.0603517i \(-0.0192222\pi\)
−0.551355 + 0.834271i \(0.685889\pi\)
\(270\) −0.0720191 0.124741i −0.00438294 0.00759148i
\(271\) 1.76986 + 1.02183i 0.107511 + 0.0620717i 0.552792 0.833320i \(-0.313563\pi\)
−0.445280 + 0.895391i \(0.646896\pi\)
\(272\) 5.29168 0.320856
\(273\) 0 0
\(274\) 6.67112 0.403017
\(275\) 2.82797 + 1.63273i 0.170533 + 0.0984572i
\(276\) −4.57138 7.91787i −0.275165 0.476600i
\(277\) −2.71678 4.70560i −0.163236 0.282732i 0.772792 0.634660i \(-0.218860\pi\)
−0.936027 + 0.351927i \(0.885526\pi\)
\(278\) 6.06959 + 3.50428i 0.364030 + 0.210173i
\(279\) 12.7843i 0.765373i
\(280\) 0 0
\(281\) 20.2356i 1.20715i −0.797305 0.603577i \(-0.793742\pi\)
0.797305 0.603577i \(-0.206258\pi\)
\(282\) −10.5310 + 18.2401i −0.627109 + 1.08618i
\(283\) −0.867593 1.50272i −0.0515731 0.0893272i 0.839086 0.543998i \(-0.183090\pi\)
−0.890659 + 0.454671i \(0.849757\pi\)
\(284\) 10.3525 5.97704i 0.614310 0.354672i
\(285\) −3.95586 + 6.85176i −0.234325 + 0.405863i
\(286\) −0.645140 + 2.66424i −0.0381479 + 0.157540i
\(287\) 0 0
\(288\) 12.8548i 0.757474i
\(289\) 2.91173 5.04326i 0.171278 0.296662i
\(290\) −2.21373 3.83430i −0.129995 0.225158i
\(291\) −0.425392 + 0.245600i −0.0249369 + 0.0143973i
\(292\) −3.73595 2.15695i −0.218630 0.126226i
\(293\) 27.2441i 1.59162i 0.605547 + 0.795810i \(0.292954\pi\)
−0.605547 + 0.795810i \(0.707046\pi\)
\(294\) 0 0
\(295\) 6.16875 0.359159
\(296\) 0.647107 1.12082i 0.0376123 0.0651465i
\(297\) 0.131692 0.0760324i 0.00764154 0.00441185i
\(298\) 1.98375 + 3.43595i 0.114915 + 0.199039i
\(299\) −11.5683 11.0209i −0.669009 0.637357i
\(300\) 9.50884 0.548993
\(301\) 0 0
\(302\) 5.23409 0.301188
\(303\) 21.0735 36.5004i 1.21064 2.09690i
\(304\) 7.13190 4.11760i 0.409042 0.236161i
\(305\) −2.54414 + 1.46886i −0.145677 + 0.0841067i
\(306\) 9.04601 + 5.22272i 0.517126 + 0.298563i
\(307\) 12.7138i 0.725612i 0.931865 + 0.362806i \(0.118181\pi\)
−0.931865 + 0.362806i \(0.881819\pi\)
\(308\) 0 0
\(309\) −26.2951 −1.49588
\(310\) −2.55186 1.47332i −0.144936 0.0836788i
\(311\) −4.80939 8.33011i −0.272716 0.472357i 0.696841 0.717226i \(-0.254588\pi\)
−0.969556 + 0.244869i \(0.921255\pi\)
\(312\) 7.56031 + 25.7077i 0.428018 + 1.45541i
\(313\) −4.51273 + 7.81628i −0.255075 + 0.441802i −0.964916 0.262559i \(-0.915433\pi\)
0.709841 + 0.704362i \(0.248767\pi\)
\(314\) 10.2151i 0.576473i
\(315\) 0 0
\(316\) −3.31931 −0.186726
\(317\) −21.3269 12.3131i −1.19784 0.691572i −0.237766 0.971323i \(-0.576415\pi\)
−0.960073 + 0.279750i \(0.909748\pi\)
\(318\) −1.57510 + 0.909386i −0.0883273 + 0.0509958i
\(319\) 4.04797 2.33709i 0.226643 0.130852i
\(320\) 4.28061 + 2.47141i 0.239293 + 0.138156i
\(321\) −14.8724 −0.830095
\(322\) 0 0
\(323\) 17.3935i 0.967802i
\(324\) 3.92754 6.80269i 0.218196 0.377927i
\(325\) 15.9423 4.68843i 0.884319 0.260067i
\(326\) −12.7205 22.0325i −0.704521 1.22027i
\(327\) 24.0027 + 13.8580i 1.32735 + 0.766348i
\(328\) 15.3323 0.846584
\(329\) 0 0
\(330\) 1.15614i 0.0636436i
\(331\) −11.4071 6.58591i −0.626993 0.361994i 0.152594 0.988289i \(-0.451237\pi\)
−0.779586 + 0.626295i \(0.784571\pi\)
\(332\) 7.49823 4.32911i 0.411519 0.237591i
\(333\) 1.06768 0.616426i 0.0585085 0.0337799i
\(334\) −0.607311 + 1.05189i −0.0332306 + 0.0575571i
\(335\) 6.51752 0.356090
\(336\) 0 0
\(337\) 17.0307 0.927720 0.463860 0.885909i \(-0.346464\pi\)
0.463860 + 0.885909i \(0.346464\pi\)
\(338\) 7.55175 + 11.7288i 0.410761 + 0.637965i
\(339\) 1.12265 + 1.94448i 0.0609738 + 0.105610i
\(340\) −1.53654 + 0.887121i −0.0833305 + 0.0481109i
\(341\) 1.55542 2.69406i 0.0842306 0.145892i
\(342\) 16.2558 0.879010
\(343\) 0 0
\(344\) 34.2527i 1.84678i
\(345\) −5.83592 3.36937i −0.314195 0.181401i
\(346\) 11.1414 6.43251i 0.598968 0.345814i
\(347\) −0.229959 0.398300i −0.0123448 0.0213819i 0.859787 0.510653i \(-0.170596\pi\)
−0.872132 + 0.489271i \(0.837263\pi\)
\(348\) 6.80550 11.7875i 0.364813 0.631875i
\(349\) 6.87822i 0.368183i −0.982909 0.184091i \(-0.941066\pi\)
0.982909 0.184091i \(-0.0589342\pi\)
\(350\) 0 0
\(351\) 0.182119 0.752098i 0.00972078 0.0401440i
\(352\) −1.56400 + 2.70892i −0.0833613 + 0.144386i
\(353\) −1.32784 + 0.766631i −0.0706740 + 0.0408036i −0.534921 0.844902i \(-0.679658\pi\)
0.464247 + 0.885706i \(0.346325\pi\)
\(354\) −12.8667 22.2857i −0.683856 1.18447i
\(355\) 4.40542 7.63041i 0.233815 0.404980i
\(356\) 11.3529i 0.601701i
\(357\) 0 0
\(358\) 10.1626i 0.537112i
\(359\) −23.5617 13.6034i −1.24354 0.717959i −0.273728 0.961807i \(-0.588257\pi\)
−0.969813 + 0.243848i \(0.921590\pi\)
\(360\) 2.78322 + 4.82068i 0.146688 + 0.254072i
\(361\) 4.03438 + 6.98774i 0.212336 + 0.367776i
\(362\) −10.6231 6.13326i −0.558339 0.322357i
\(363\) 25.5249 1.33971
\(364\) 0 0
\(365\) −3.17959 −0.166427
\(366\) 10.6131 + 6.12745i 0.554753 + 0.320287i
\(367\) 13.4907 + 23.3666i 0.704208 + 1.21972i 0.966977 + 0.254865i \(0.0820311\pi\)
−0.262769 + 0.964859i \(0.584636\pi\)
\(368\) 3.50713 + 6.07452i 0.182822 + 0.316656i
\(369\) 12.6486 + 7.30267i 0.658460 + 0.380162i
\(370\) 0.284159i 0.0147727i
\(371\) 0 0
\(372\) 9.05859i 0.469666i
\(373\) −1.98619 + 3.44018i −0.102841 + 0.178126i −0.912854 0.408286i \(-0.866127\pi\)
0.810013 + 0.586412i \(0.199460\pi\)
\(374\) 1.27086 + 2.20120i 0.0657147 + 0.113821i
\(375\) 12.6543 7.30597i 0.653466 0.377279i
\(376\) −12.3377 + 21.3695i −0.636269 + 1.10205i
\(377\) 5.59800 23.1181i 0.288311 1.19064i
\(378\) 0 0
\(379\) 11.4059i 0.585884i −0.956130 0.292942i \(-0.905366\pi\)
0.956130 0.292942i \(-0.0946343\pi\)
\(380\) −1.38058 + 2.39124i −0.0708225 + 0.122668i
\(381\) −10.3453 17.9186i −0.530005 0.917996i
\(382\) 14.5783 8.41680i 0.745892 0.430641i
\(383\) −20.6044 11.8960i −1.05284 0.607856i −0.129395 0.991593i \(-0.541304\pi\)
−0.923442 + 0.383737i \(0.874637\pi\)
\(384\) 0.849134i 0.0433322i
\(385\) 0 0
\(386\) −24.6879 −1.25658
\(387\) −16.3143 + 28.2573i −0.829304 + 1.43640i
\(388\) −0.148460 + 0.0857137i −0.00753694 + 0.00435145i
\(389\) −14.2055 24.6046i −0.720247 1.24751i −0.960901 0.276894i \(-0.910695\pi\)
0.240653 0.970611i \(-0.422638\pi\)
\(390\) 4.25977 + 4.05823i 0.215702 + 0.205496i
\(391\) −14.8148 −0.749216
\(392\) 0 0
\(393\) 17.0272 0.858911
\(394\) 5.47446 9.48204i 0.275799 0.477698i
\(395\) −2.11875 + 1.22326i −0.106606 + 0.0615489i
\(396\) −1.51605 + 0.875291i −0.0761843 + 0.0439850i
\(397\) 8.53825 + 4.92956i 0.428522 + 0.247408i 0.698717 0.715398i \(-0.253755\pi\)
−0.270195 + 0.962806i \(0.587088\pi\)
\(398\) 12.7945i 0.641332i
\(399\) 0 0
\(400\) −7.29510 −0.364755
\(401\) 10.9287 + 6.30971i 0.545756 + 0.315092i 0.747408 0.664365i \(-0.231298\pi\)
−0.201653 + 0.979457i \(0.564631\pi\)
\(402\) −13.5941 23.5457i −0.678013 1.17435i
\(403\) −4.46643 15.1874i −0.222489 0.756539i
\(404\) 7.35460 12.7385i 0.365905 0.633766i
\(405\) 5.78964i 0.287689i
\(406\) 0 0
\(407\) 0.299994 0.0148701
\(408\) 21.5173 + 12.4230i 1.06527 + 0.615031i
\(409\) 15.6381 9.02867i 0.773255 0.446439i −0.0607793 0.998151i \(-0.519359\pi\)
0.834035 + 0.551712i \(0.186025\pi\)
\(410\) 2.91537 1.68319i 0.143980 0.0831268i
\(411\) 13.0908 + 7.55795i 0.645720 + 0.372806i
\(412\) −9.17691 −0.452114
\(413\) 0 0
\(414\) 13.8457i 0.680478i
\(415\) 3.19080 5.52663i 0.156630 0.271291i
\(416\) 4.49107 + 15.2712i 0.220193 + 0.748731i
\(417\) 7.94024 + 13.7529i 0.388835 + 0.673483i
\(418\) 3.42562 + 1.97778i 0.167553 + 0.0967366i
\(419\) −14.2805 −0.697647 −0.348823 0.937188i \(-0.613419\pi\)
−0.348823 + 0.937188i \(0.613419\pi\)
\(420\) 0 0
\(421\) 4.27439i 0.208321i 0.994561 + 0.104160i \(0.0332155\pi\)
−0.994561 + 0.104160i \(0.966784\pi\)
\(422\) 14.4870 + 8.36410i 0.705218 + 0.407158i
\(423\) −20.3564 + 11.7527i −0.989760 + 0.571438i
\(424\) −1.84534 + 1.06541i −0.0896175 + 0.0517407i
\(425\) 7.70398 13.3437i 0.373698 0.647263i
\(426\) −36.7550 −1.78079
\(427\) 0 0
\(428\) −5.19042 −0.250888
\(429\) −4.28437 + 4.49714i −0.206851 + 0.217124i
\(430\) 3.76028 + 6.51300i 0.181337 + 0.314085i
\(431\) 12.6498 7.30335i 0.609318 0.351790i −0.163381 0.986563i \(-0.552240\pi\)
0.772698 + 0.634773i \(0.218906\pi\)
\(432\) −0.169858 + 0.294203i −0.00817230 + 0.0141548i
\(433\) −28.0099 −1.34607 −0.673035 0.739611i \(-0.735009\pi\)
−0.673035 + 0.739611i \(0.735009\pi\)
\(434\) 0 0
\(435\) 10.0321i 0.481001i
\(436\) 8.37688 + 4.83640i 0.401180 + 0.231621i
\(437\) −19.9667 + 11.5278i −0.955137 + 0.551448i
\(438\) 6.63193 + 11.4868i 0.316886 + 0.548863i
\(439\) −8.53872 + 14.7895i −0.407531 + 0.705864i −0.994612 0.103664i \(-0.966943\pi\)
0.587082 + 0.809528i \(0.300277\pi\)
\(440\) 1.35450i 0.0645733i
\(441\) 0 0
\(442\) 12.5711 + 3.04407i 0.597947 + 0.144792i
\(443\) −6.90783 + 11.9647i −0.328201 + 0.568461i −0.982155 0.188073i \(-0.939776\pi\)
0.653954 + 0.756534i \(0.273109\pi\)
\(444\) 0.756531 0.436783i 0.0359034 0.0207288i
\(445\) 4.18386 + 7.24665i 0.198334 + 0.343524i
\(446\) 3.63048 6.28817i 0.171908 0.297754i
\(447\) 8.98984i 0.425205i
\(448\) 0 0
\(449\) 32.6410i 1.54042i −0.637789 0.770211i \(-0.720151\pi\)
0.637789 0.770211i \(-0.279849\pi\)
\(450\) −12.4708 7.20003i −0.587880 0.339412i
\(451\) 1.77698 + 3.07783i 0.0836749 + 0.144929i
\(452\) 0.391801 + 0.678619i 0.0184287 + 0.0319195i
\(453\) 10.2709 + 5.92988i 0.482567 + 0.278610i
\(454\) 18.0536 0.847298
\(455\) 0 0
\(456\) 38.6667 1.81074
\(457\) 2.74559 + 1.58517i 0.128433 + 0.0741511i 0.562840 0.826566i \(-0.309709\pi\)
−0.434407 + 0.900717i \(0.643042\pi\)
\(458\) 5.91560 + 10.2461i 0.276418 + 0.478769i
\(459\) −0.358756 0.621384i −0.0167453 0.0290037i
\(460\) −2.03672 1.17590i −0.0949625 0.0548266i
\(461\) 0.202023i 0.00940915i 0.999989 + 0.00470458i \(0.00149752\pi\)
−0.999989 + 0.00470458i \(0.998502\pi\)
\(462\) 0 0
\(463\) 17.2121i 0.799912i 0.916534 + 0.399956i \(0.130975\pi\)
−0.916534 + 0.399956i \(0.869025\pi\)
\(464\) −5.22112 + 9.04325i −0.242384 + 0.419822i
\(465\) −3.33835 5.78219i −0.154812 0.268143i
\(466\) −16.1277 + 9.31136i −0.747103 + 0.431340i
\(467\) 0.0955845 0.165557i 0.00442312 0.00766108i −0.863805 0.503826i \(-0.831925\pi\)
0.868228 + 0.496165i \(0.165259\pi\)
\(468\) −2.09657 + 8.65821i −0.0969139 + 0.400226i
\(469\) 0 0
\(470\) 5.41777i 0.249903i
\(471\) −11.5731 + 20.0452i −0.533260 + 0.923633i
\(472\) −15.0742 26.1092i −0.693845 1.20177i
\(473\) −6.87593 + 3.96982i −0.316156 + 0.182533i
\(474\) 8.83850 + 5.10291i 0.405966 + 0.234384i
\(475\) 23.9787i 1.10022i
\(476\) 0 0
\(477\) −2.02978 −0.0929374
\(478\) 10.5816 18.3278i 0.483989 0.838294i
\(479\) 18.6009 10.7392i 0.849897 0.490688i −0.0107189 0.999943i \(-0.503412\pi\)
0.860616 + 0.509254i \(0.170079\pi\)
\(480\) 3.35676 + 5.81408i 0.153214 + 0.265375i
\(481\) 1.05302 1.10532i 0.0480136 0.0503981i
\(482\) −2.98752 −0.136078
\(483\) 0 0
\(484\) 8.90811 0.404914
\(485\) −0.0631758 + 0.109424i −0.00286867 + 0.00496868i
\(486\) −20.3178 + 11.7305i −0.921633 + 0.532105i
\(487\) 16.4964 9.52422i 0.747525 0.431584i −0.0772740 0.997010i \(-0.524622\pi\)
0.824799 + 0.565426i \(0.191288\pi\)
\(488\) 12.4339 + 7.17871i 0.562856 + 0.324965i
\(489\) 57.6458i 2.60684i
\(490\) 0 0
\(491\) −35.7559 −1.61364 −0.806821 0.590796i \(-0.798814\pi\)
−0.806821 + 0.590796i \(0.798814\pi\)
\(492\) 8.96247 + 5.17448i 0.404059 + 0.233284i
\(493\) −11.0275 19.1002i −0.496654 0.860230i
\(494\) 19.3115 5.67927i 0.868864 0.255522i
\(495\) −0.645140 + 1.11741i −0.0289969 + 0.0502240i
\(496\) 6.94968i 0.312050i
\(497\) 0 0
\(498\) −26.6213 −1.19293
\(499\) −15.3192 8.84457i −0.685784 0.395937i 0.116247 0.993220i \(-0.462914\pi\)
−0.802031 + 0.597283i \(0.796247\pi\)
\(500\) 4.41632 2.54976i 0.197504 0.114029i
\(501\) −2.38346 + 1.37609i −0.106485 + 0.0614792i
\(502\) −21.8949 12.6410i −0.977217 0.564196i
\(503\) −11.3305 −0.505203 −0.252601 0.967570i \(-0.581286\pi\)
−0.252601 + 0.967570i \(0.581286\pi\)
\(504\) 0 0
\(505\) 10.8415i 0.482441i
\(506\) −1.68456 + 2.91774i −0.0748878 + 0.129709i
\(507\) 1.53079 + 31.5712i 0.0679849 + 1.40212i
\(508\) −3.61048 6.25353i −0.160189 0.277455i
\(509\) −16.7588 9.67569i −0.742821 0.428868i 0.0802734 0.996773i \(-0.474421\pi\)
−0.823094 + 0.567905i \(0.807754\pi\)
\(510\) 5.45523 0.241562
\(511\) 0 0
\(512\) 16.6645i 0.736472i
\(513\) −0.967032 0.558316i −0.0426955 0.0246502i
\(514\) −3.18961 + 1.84152i −0.140687 + 0.0812259i
\(515\) −5.85772 + 3.38195i −0.258122 + 0.149027i
\(516\) −11.5599 + 20.0224i −0.508897 + 0.881435i
\(517\) −5.71967 −0.251551
\(518\) 0 0
\(519\) 29.1505 1.27957
\(520\) 4.99060 + 4.75448i 0.218852 + 0.208498i
\(521\) −3.85550 6.67791i −0.168912 0.292565i 0.769125 0.639098i \(-0.220692\pi\)
−0.938038 + 0.346533i \(0.887359\pi\)
\(522\) −17.8508 + 10.3062i −0.781307 + 0.451088i
\(523\) −17.5251 + 30.3543i −0.766317 + 1.32730i 0.173230 + 0.984881i \(0.444580\pi\)
−0.939547 + 0.342419i \(0.888754\pi\)
\(524\) 5.94246 0.259597
\(525\) 0 0
\(526\) 23.0160i 1.00355i
\(527\) −12.7119 7.33919i −0.553737 0.319700i
\(528\) 2.36146 1.36339i 0.102769 0.0593339i
\(529\) 1.68133 + 2.91214i 0.0731011 + 0.126615i
\(530\) −0.233922 + 0.405165i −0.0101609 + 0.0175992i
\(531\) 28.7189i 1.24630i
\(532\) 0 0
\(533\) 17.5776 + 4.25637i 0.761370 + 0.184364i
\(534\) 17.4532 30.2299i 0.755275 1.30818i
\(535\) −3.31309 + 1.91282i −0.143238 + 0.0826982i
\(536\) −15.9264 27.5854i −0.687917 1.19151i
\(537\) 11.5136 19.9422i 0.496849 0.860568i
\(538\) 15.7276i 0.678066i
\(539\) 0 0
\(540\) 0.113903i 0.00490160i
\(541\) 10.5079 + 6.06674i 0.451770 + 0.260829i 0.708577 0.705633i \(-0.249337\pi\)
−0.256807 + 0.966463i \(0.582671\pi\)
\(542\) −1.09648 1.89916i −0.0470978 0.0815758i
\(543\) −13.8972 24.0706i −0.596385 1.03297i
\(544\) 12.7820 + 7.37967i 0.548022 + 0.316401i
\(545\) 7.12940 0.305390
\(546\) 0 0
\(547\) −5.12546 −0.219149 −0.109575 0.993979i \(-0.534949\pi\)
−0.109575 + 0.993979i \(0.534949\pi\)
\(548\) 4.56864 + 2.63770i 0.195162 + 0.112677i
\(549\) 6.83835 + 11.8444i 0.291854 + 0.505505i
\(550\) −1.75201 3.03457i −0.0747058 0.129394i
\(551\) −29.7248 17.1616i −1.26632 0.731109i
\(552\) 32.9340i 1.40177i
\(553\) 0 0
\(554\) 5.83051i 0.247715i
\(555\) 0.321934 0.557606i 0.0136653 0.0236691i
\(556\) 2.77112 + 4.79972i 0.117522 + 0.203554i
\(557\) −32.5267 + 18.7793i −1.37820 + 0.795705i −0.991943 0.126686i \(-0.959566\pi\)
−0.386258 + 0.922391i \(0.626233\pi\)
\(558\) −6.85911 + 11.8803i −0.290369 + 0.502934i
\(559\) −9.50884 + 39.2687i −0.402181 + 1.66089i
\(560\) 0 0
\(561\) 5.75922i 0.243154i
\(562\) −10.8569 + 18.8048i −0.457973 + 0.793232i
\(563\) −14.3504 24.8557i −0.604799 1.04754i −0.992083 0.125583i \(-0.959920\pi\)
0.387284 0.921960i \(-0.373413\pi\)
\(564\) −14.4240 + 8.32769i −0.607359 + 0.350659i
\(565\) 0.500180 + 0.288779i 0.0210428 + 0.0121490i
\(566\) 1.86195i 0.0782636i
\(567\) 0 0
\(568\) −43.0610 −1.80680
\(569\) 8.97417 15.5437i 0.376217 0.651627i −0.614291 0.789079i \(-0.710558\pi\)
0.990508 + 0.137452i \(0.0438914\pi\)
\(570\) 7.35231 4.24486i 0.307955 0.177798i
\(571\) 8.91370 + 15.4390i 0.373027 + 0.646101i 0.990030 0.140860i \(-0.0449867\pi\)
−0.617003 + 0.786961i \(0.711653\pi\)
\(572\) −1.49523 + 1.56949i −0.0625188 + 0.0656236i
\(573\) 38.1428 1.59344
\(574\) 0 0
\(575\) 20.4236 0.851724
\(576\) 11.5058 19.9286i 0.479407 0.830357i
\(577\) −28.6282 + 16.5285i −1.19181 + 0.688091i −0.958717 0.284363i \(-0.908218\pi\)
−0.233092 + 0.972455i \(0.574884\pi\)
\(578\) −5.41170 + 3.12445i −0.225097 + 0.129960i
\(579\) −48.4451 27.9698i −2.01331 1.16239i
\(580\) 3.50117i 0.145378i
\(581\) 0 0
\(582\) 0.527085 0.0218484
\(583\) −0.427742 0.246957i −0.0177153 0.0102279i
\(584\) 7.76975 + 13.4576i 0.321515 + 0.556880i
\(585\) 1.85254 + 6.29927i 0.0765930 + 0.260443i
\(586\) 14.6172 25.3178i 0.603832 1.04587i
\(587\) 14.7295i 0.607953i −0.952680 0.303976i \(-0.901686\pi\)
0.952680 0.303976i \(-0.0983144\pi\)
\(588\) 0 0
\(589\) −22.8433 −0.941241
\(590\) −5.73258 3.30970i −0.236006 0.136258i
\(591\) 21.4851 12.4044i 0.883779 0.510250i
\(592\) −0.580404 + 0.335097i −0.0238545 + 0.0137724i
\(593\) 7.97598 + 4.60494i 0.327534 + 0.189102i 0.654746 0.755849i \(-0.272776\pi\)
−0.327212 + 0.944951i \(0.606109\pi\)
\(594\) −0.163174 −0.00669510
\(595\) 0 0
\(596\) 3.13743i 0.128514i
\(597\) −14.4954 + 25.1067i −0.593256 + 1.02755i
\(598\) 4.83726 + 16.4484i 0.197810 + 0.672624i
\(599\) 5.28727 + 9.15782i 0.216032 + 0.374178i 0.953591 0.301104i \(-0.0973551\pi\)
−0.737559 + 0.675282i \(0.764022\pi\)
\(600\) −29.6637 17.1263i −1.21102 0.699180i
\(601\) −4.08916 −0.166800 −0.0834001 0.996516i \(-0.526578\pi\)
−0.0834001 + 0.996516i \(0.526578\pi\)
\(602\) 0 0
\(603\) 30.3426i 1.23565i
\(604\) 3.58450 + 2.06951i 0.145851 + 0.0842072i
\(605\) 5.68613 3.28289i 0.231174 0.133469i
\(606\) −39.1670 + 22.6131i −1.59105 + 0.918593i
\(607\) 1.80353 3.12380i 0.0732030 0.126791i −0.827100 0.562054i \(-0.810011\pi\)
0.900303 + 0.435263i \(0.143345\pi\)
\(608\) 22.9693 0.931527
\(609\) 0 0
\(610\) 3.15233 0.127634
\(611\) −20.0768 + 21.0739i −0.812222 + 0.852559i
\(612\) 4.13003 + 7.15343i 0.166947 + 0.289160i
\(613\) −33.3285 + 19.2422i −1.34613 + 0.777186i −0.987698 0.156371i \(-0.950020\pi\)
−0.358428 + 0.933557i \(0.616687\pi\)
\(614\) 6.82128 11.8148i 0.275284 0.476806i
\(615\) 7.62778 0.307582
\(616\) 0 0
\(617\) 3.09503i 0.124601i −0.998057 0.0623007i \(-0.980156\pi\)
0.998057 0.0623007i \(-0.0198438\pi\)
\(618\) 24.4359 + 14.1080i 0.982954 + 0.567509i
\(619\) 10.6255 6.13462i 0.427074 0.246571i −0.271025 0.962572i \(-0.587363\pi\)
0.698099 + 0.716001i \(0.254029\pi\)
\(620\) −1.16507 2.01797i −0.0467905 0.0810435i
\(621\) 0.475540 0.823660i 0.0190828 0.0330523i
\(622\) 10.3215i 0.413854i
\(623\) 0 0
\(624\) 3.26570 13.4864i 0.130733 0.539888i
\(625\) −9.64277 + 16.7018i −0.385711 + 0.668071i
\(626\) 8.38730 4.84241i 0.335224 0.193542i
\(627\) 4.48140 + 7.76202i 0.178970 + 0.309985i
\(628\) −4.03897 + 6.99571i −0.161173 + 0.279159i
\(629\) 1.41551i 0.0564402i
\(630\) 0 0
\(631\) 5.31780i 0.211698i 0.994382 + 0.105849i \(0.0337561\pi\)
−0.994382 + 0.105849i \(0.966244\pi\)
\(632\) 10.3549 + 5.97840i 0.411896 + 0.237808i
\(633\) 18.9520 + 32.8258i 0.753273 + 1.30471i
\(634\) 13.2126 + 22.8849i 0.524740 + 0.908877i
\(635\) −4.60921 2.66113i −0.182911 0.105604i
\(636\) −1.43825 −0.0570304
\(637\) 0 0
\(638\) −5.01566 −0.198572
\(639\) −35.5238 20.5097i −1.40530 0.811349i
\(640\) 0.109212 + 0.189160i 0.00431697 + 0.00747721i
\(641\) 6.09521 + 10.5572i 0.240746 + 0.416985i 0.960927 0.276801i \(-0.0892744\pi\)
−0.720181 + 0.693787i \(0.755941\pi\)
\(642\) 13.8208 + 7.97944i 0.545463 + 0.314923i
\(643\) 18.9733i 0.748235i 0.927381 + 0.374117i \(0.122054\pi\)
−0.927381 + 0.374117i \(0.877946\pi\)
\(644\) 0 0
\(645\) 17.0406i 0.670974i
\(646\) 9.33211 16.1637i 0.367167 0.635952i
\(647\) −9.85587 17.0709i −0.387474 0.671125i 0.604635 0.796503i \(-0.293319\pi\)
−0.992109 + 0.125378i \(0.959986\pi\)
\(648\) −24.5046 + 14.1478i −0.962633 + 0.555776i
\(649\) 3.49414 6.05202i 0.137157 0.237563i
\(650\) −17.3305 4.19655i −0.679759 0.164602i
\(651\) 0 0
\(652\) 20.1182i 0.787891i
\(653\) 10.1986 17.6645i 0.399103 0.691267i −0.594512 0.804087i \(-0.702655\pi\)
0.993616 + 0.112819i \(0.0359882\pi\)
\(654\) −14.8704 25.7563i −0.581478 1.00715i
\(655\) 3.79313 2.18996i 0.148210 0.0855690i
\(656\) −6.87593 3.96982i −0.268460 0.154996i
\(657\) 14.8027i 0.577510i
\(658\) 0 0
\(659\) 32.6628 1.27236 0.636181 0.771540i \(-0.280513\pi\)
0.636181 + 0.771540i \(0.280513\pi\)
\(660\) −0.457129 + 0.791771i −0.0177937 + 0.0308196i
\(661\) −8.43242 + 4.86846i −0.327983 + 0.189361i −0.654945 0.755676i \(-0.727308\pi\)
0.326962 + 0.945037i \(0.393975\pi\)
\(662\) 7.06704 + 12.2405i 0.274668 + 0.475740i
\(663\) 21.2196 + 20.2157i 0.824101 + 0.785111i
\(664\) −31.1886 −1.21035
\(665\) 0 0
\(666\) −1.32292 −0.0512620
\(667\) 14.6172 25.3178i 0.565981 0.980308i
\(668\) −0.831819 + 0.480251i −0.0321841 + 0.0185815i
\(669\) 14.2482 8.22620i 0.550867 0.318043i
\(670\) −6.05668 3.49683i −0.233990 0.135094i
\(671\) 3.32800i 0.128476i
\(672\) 0 0
\(673\) −39.4512 −1.52073 −0.760367 0.649494i \(-0.774981\pi\)
−0.760367 + 0.649494i \(0.774981\pi\)
\(674\) −15.8265 9.13742i −0.609613 0.351960i
\(675\) 0.494581 + 0.856639i 0.0190364 + 0.0329720i
\(676\) 0.534242 + 11.0182i 0.0205478 + 0.423779i
\(677\) −24.3169 + 42.1182i −0.934576 + 1.61873i −0.159187 + 0.987248i \(0.550887\pi\)
−0.775389 + 0.631484i \(0.782446\pi\)
\(678\) 2.40932i 0.0925296i
\(679\) 0 0
\(680\) 6.39117 0.245090
\(681\) 35.4266 + 20.4536i 1.35755 + 0.783783i
\(682\) −2.89088 + 1.66905i −0.110697 + 0.0639112i
\(683\) −4.94304 + 2.85387i −0.189140 + 0.109200i −0.591580 0.806246i \(-0.701496\pi\)
0.402440 + 0.915446i \(0.368162\pi\)
\(684\) 11.1326 + 6.42738i 0.425664 + 0.245757i
\(685\) 3.88828 0.148563
\(686\) 0 0
\(687\) 26.8080i 1.02279i
\(688\) 8.86867 15.3610i 0.338115 0.585632i
\(689\) −2.41134 + 0.709145i −0.0918647 + 0.0270163i
\(690\) 3.61552 + 6.26226i 0.137640 + 0.238400i
\(691\) −36.1766 20.8866i −1.37622 0.794563i −0.384521 0.923116i \(-0.625633\pi\)
−0.991703 + 0.128553i \(0.958967\pi\)
\(692\) 10.1734 0.386736
\(693\) 0 0
\(694\) 0.493517i 0.0187336i
\(695\) 3.53767 + 2.04247i 0.134191 + 0.0774754i
\(696\) −42.4608 + 24.5147i −1.60947 + 0.929228i
\(697\) 14.5226 8.38464i 0.550084 0.317591i
\(698\) −3.69035 + 6.39188i −0.139682 + 0.241936i
\(699\) −42.1967 −1.59603
\(700\) 0 0
\(701\) 22.4361 0.847399 0.423700 0.905803i \(-0.360731\pi\)
0.423700 + 0.905803i \(0.360731\pi\)
\(702\) −0.572763 + 0.601207i −0.0216175 + 0.0226911i
\(703\) −1.10145 1.90776i −0.0415419 0.0719527i
\(704\) 4.84929 2.79974i 0.182764 0.105519i
\(705\) −6.13798 + 10.6313i −0.231170 + 0.400398i
\(706\) 1.64527 0.0619207
\(707\) 0 0
\(708\) 20.3495i 0.764780i
\(709\) −24.8955 14.3734i −0.934969 0.539804i −0.0465891 0.998914i \(-0.514835\pi\)
−0.888380 + 0.459110i \(0.848168\pi\)
\(710\) −8.18785 + 4.72726i −0.307285 + 0.177411i
\(711\) 5.69495 + 9.86394i 0.213577 + 0.369927i
\(712\) 20.4476 35.4163i 0.766307 1.32728i
\(713\) 19.4566i 0.728654i
\(714\) 0 0
\(715\) −0.376021 + 1.55286i −0.0140624 + 0.0580735i
\(716\) 4.01822 6.95976i 0.150168 0.260098i
\(717\) 41.5284 23.9765i 1.55091 0.895417i
\(718\) 14.5972 + 25.2830i 0.544762 + 0.943555i
\(719\) 2.10450 3.64509i 0.0784844 0.135939i −0.824112 0.566427i \(-0.808325\pi\)
0.902596 + 0.430488i \(0.141659\pi\)
\(720\) 2.88251i 0.107425i
\(721\) 0 0
\(722\) 8.65821i 0.322225i
\(723\) −5.86242 3.38467i −0.218026 0.125877i
\(724\) −4.85008 8.40058i −0.180252 0.312205i
\(725\) 15.2025 + 26.3315i 0.564606 + 0.977927i
\(726\) −23.7201 13.6948i −0.880335 0.508262i
\(727\) 43.4680 1.61214 0.806070 0.591820i \(-0.201591\pi\)
0.806070 + 0.591820i \(0.201591\pi\)
\(728\) 0 0
\(729\) −25.3884 −0.940312
\(730\) 2.95477 + 1.70594i 0.109361 + 0.0631396i
\(731\) 18.7315 + 32.4439i 0.692809 + 1.19998i
\(732\) 4.84548 + 8.39261i 0.179094 + 0.310200i
\(733\) −7.87581 4.54710i −0.290900 0.167951i 0.347448 0.937699i \(-0.387048\pi\)
−0.638348 + 0.769748i \(0.720382\pi\)
\(734\) 28.9525i 1.06866i
\(735\) 0 0
\(736\) 19.5639i 0.721133i
\(737\) 3.69169 6.39419i 0.135985 0.235533i
\(738\) −7.83617 13.5726i −0.288453 0.499616i
\(739\) 8.32135 4.80433i 0.306106 0.176730i −0.339077 0.940759i \(-0.610115\pi\)
0.645183 + 0.764028i \(0.276781\pi\)
\(740\) 0.112354 0.194603i 0.00413022 0.00715375i
\(741\) 44.3292 + 10.7342i 1.62847 + 0.394331i
\(742\) 0 0
\(743\) 32.1771i 1.18046i −0.807234 0.590231i \(-0.799036\pi\)
0.807234 0.590231i \(-0.200964\pi\)
\(744\) −16.3154 + 28.2591i −0.598152 + 1.03603i
\(745\) 1.15623 + 2.00265i 0.0423610 + 0.0733714i
\(746\) 3.69150 2.13129i 0.135155 0.0780320i
\(747\) −25.7295 14.8549i −0.941392 0.543513i
\(748\) 2.00995i 0.0734911i
\(749\) 0 0
\(750\) −15.6794 −0.572531
\(751\) 3.89892 6.75313i 0.142274 0.246425i −0.786079 0.618126i \(-0.787892\pi\)
0.928352 + 0.371701i \(0.121225\pi\)
\(752\) 11.0660 6.38894i 0.403534 0.232981i
\(753\) −28.6429 49.6110i −1.04381 1.80793i
\(754\) −17.6057 + 18.4800i −0.641161 + 0.673002i
\(755\) 3.05070 0.111026
\(756\) 0 0
\(757\) 17.9970 0.654110 0.327055 0.945005i \(-0.393944\pi\)
0.327055 + 0.945005i \(0.393944\pi\)
\(758\) −6.11960 + 10.5995i −0.222274 + 0.384990i
\(759\) −6.61123 + 3.81699i −0.239972 + 0.138548i
\(760\) 8.61373 4.97314i 0.312453 0.180395i
\(761\) 35.2290 + 20.3395i 1.27705 + 0.737306i 0.976305 0.216398i \(-0.0694309\pi\)
0.300746 + 0.953704i \(0.402764\pi\)
\(762\) 22.2021i 0.804299i
\(763\) 0 0
\(764\) 13.3117 0.481601
\(765\) 5.27248 + 3.04407i 0.190627 + 0.110059i
\(766\) 12.7650 + 22.1097i 0.461220 + 0.798856i
\(767\) −10.0335 34.1174i −0.362290 1.23191i
\(768\) 19.6711 34.0713i 0.709819 1.22944i
\(769\) 39.3098i 1.41755i −0.705435 0.708774i \(-0.749248\pi\)
0.705435 0.708774i \(-0.250752\pi\)
\(770\) 0 0
\(771\) −8.34529 −0.300548
\(772\) −16.9072 9.76138i −0.608504 0.351320i
\(773\) −11.6685 + 6.73679i −0.419685 + 0.242306i −0.694943 0.719065i \(-0.744570\pi\)
0.275257 + 0.961371i \(0.411237\pi\)
\(774\) 30.3216 17.5062i 1.08989 0.629247i
\(775\) 17.5245 + 10.1178i 0.629500 + 0.363442i
\(776\) 0.617515 0.0221675
\(777\) 0 0
\(778\) 30.4866i 1.09300i
\(779\) 13.0486 22.6009i 0.467516 0.809761i
\(780\) 1.31266 + 4.46350i 0.0470008 + 0.159819i
\(781\) −4.99068 8.64412i −0.178581 0.309311i
\(782\) 13.7673 + 7.94854i 0.492316 + 0.284239i
\(783\) 1.41589 0.0505998
\(784\) 0 0
\(785\) 5.95391i 0.212504i
\(786\) −15.8233 9.13558i −0.564398 0.325855i
\(787\) 34.4930 19.9145i 1.22954 0.709877i 0.262608 0.964903i \(-0.415417\pi\)
0.966934 + 0.255026i \(0.0820839\pi\)
\(788\) 7.49823 4.32911i 0.267114 0.154218i
\(789\) 26.0757 45.1644i 0.928319 1.60790i
\(790\) 2.62525 0.0934022
\(791\) 0 0
\(792\) 6.30594 0.224072
\(793\) 12.2619 + 11.6817i 0.435432 + 0.414831i
\(794\) −5.28969 9.16201i −0.187724 0.325148i
\(795\) −0.918051 + 0.530037i −0.0325599 + 0.0187985i
\(796\) −5.05884 + 8.76217i −0.179306 + 0.310567i
\(797\) −21.2530 −0.752821 −0.376410 0.926453i \(-0.622842\pi\)
−0.376410 + 0.926453i \(0.622842\pi\)
\(798\) 0 0
\(799\) 26.9881i 0.954770i
\(800\) −17.6212 10.1736i −0.623003 0.359691i
\(801\) 33.7371 19.4781i 1.19204 0.688226i
\(802\) −6.77067 11.7271i −0.239081 0.414100i
\(803\) −1.80100 + 3.11942i −0.0635559 + 0.110082i
\(804\) 21.5000i 0.758246i
\(805\) 0 0
\(806\) −3.99784 + 16.5099i −0.140818 + 0.581537i
\(807\) 17.8184 30.8624i 0.627237 1.08641i
\(808\) −45.8867 + 26.4927i −1.61429 + 0.932010i
\(809\) −10.7088 18.5481i −0.376500 0.652117i 0.614050 0.789267i \(-0.289539\pi\)
−0.990550 + 0.137150i \(0.956206\pi\)
\(810\) −3.10630 + 5.38027i −0.109144 + 0.189043i
\(811\) 11.0116i 0.386669i 0.981133 + 0.193335i \(0.0619303\pi\)
−0.981133 + 0.193335i \(0.938070\pi\)
\(812\) 0 0
\(813\) 4.96896i 0.174269i
\(814\) −0.278782 0.160955i −0.00977131 0.00564147i
\(815\) −7.41414 12.8417i −0.259706 0.449824i
\(816\) −6.43311 11.1425i −0.225204 0.390065i
\(817\) 50.4909 + 29.1509i 1.76645 + 1.01986i
\(818\) −19.3765 −0.677484
\(819\) 0 0
\(820\) 2.66207 0.0929636
\(821\) 33.4879 + 19.3342i 1.16873 + 0.674769i 0.953382 0.301767i \(-0.0975764\pi\)
0.215353 + 0.976536i \(0.430910\pi\)
\(822\) −8.11010 14.0471i −0.282872 0.489949i
\(823\) −10.2283 17.7160i −0.356537 0.617540i 0.630843 0.775911i \(-0.282709\pi\)
−0.987380 + 0.158371i \(0.949376\pi\)
\(824\) 28.6282 + 16.5285i 0.997312 + 0.575798i
\(825\) 7.93965i 0.276423i
\(826\) 0 0
\(827\) 27.3451i 0.950881i −0.879748 0.475440i \(-0.842289\pi\)
0.879748 0.475440i \(-0.157711\pi\)
\(828\) −5.47446 + 9.48204i −0.190251 + 0.329524i
\(829\) 12.5043 + 21.6581i 0.434292 + 0.752217i 0.997238 0.0742776i \(-0.0236651\pi\)
−0.562945 + 0.826494i \(0.690332\pi\)
\(830\) −5.93037 + 3.42390i −0.205846 + 0.118845i
\(831\) −6.60560 + 11.4412i −0.229146 + 0.396892i
\(832\) 6.70616 27.6945i 0.232494 0.960133i
\(833\) 0 0
\(834\) 17.0406i 0.590069i
\(835\) −0.353972 + 0.613098i −0.0122497 + 0.0212171i
\(836\) 1.56400 + 2.70892i 0.0540920 + 0.0936900i
\(837\) 0.816077 0.471162i 0.0282077 0.0162857i
\(838\) 13.2707 + 7.66187i 0.458430 + 0.264675i
\(839\) 8.76981i 0.302768i 0.988475 + 0.151384i \(0.0483729\pi\)
−0.988475 + 0.151384i \(0.951627\pi\)
\(840\) 0 0
\(841\) 14.5218 0.500753
\(842\) 2.29333 3.97216i 0.0790332 0.136890i
\(843\) −42.6092 + 24.6004i −1.46754 + 0.847284i
\(844\) 6.61418 + 11.4561i 0.227669 + 0.394335i
\(845\) 4.40155 + 6.83617i 0.151418 + 0.235171i
\(846\) 25.2227 0.867174
\(847\) 0 0
\(848\) 1.10342 0.0378914
\(849\) −2.10947 + 3.65371i −0.0723968 + 0.125395i
\(850\) −14.3185 + 8.26679i −0.491120 + 0.283549i
\(851\) 1.62492 0.938148i 0.0557015 0.0321593i
\(852\) −25.1712 14.5326i −0.862352 0.497879i
\(853\) 19.8232i 0.678734i 0.940654 + 0.339367i \(0.110213\pi\)
−0.940654 + 0.339367i \(0.889787\pi\)
\(854\) 0 0
\(855\) 9.47469 0.324028
\(856\) 16.1920 + 9.34845i 0.553431 + 0.319523i
\(857\) 1.33518 + 2.31261i 0.0456090 + 0.0789972i 0.887929 0.459981i \(-0.152144\pi\)
−0.842320 + 0.538978i \(0.818810\pi\)
\(858\) 6.39427 1.88048i 0.218297 0.0641984i
\(859\) −19.4798 + 33.7401i −0.664644 + 1.15120i 0.314738 + 0.949179i \(0.398083\pi\)
−0.979382 + 0.202018i \(0.935250\pi\)
\(860\) 5.94713i 0.202795i
\(861\) 0 0
\(862\) −15.6738 −0.533851
\(863\) 21.4754 + 12.3988i 0.731030 + 0.422060i 0.818799 0.574081i \(-0.194640\pi\)
−0.0877689 + 0.996141i \(0.527974\pi\)
\(864\) −0.820578 + 0.473761i −0.0279166 + 0.0161177i
\(865\) 6.49381 3.74920i 0.220796 0.127477i
\(866\) 26.0294 + 15.0281i 0.884514 + 0.510675i
\(867\) −14.1592 −0.480871
\(868\) 0 0
\(869\) 2.77154i 0.0940181i
\(870\) −5.38249 + 9.32274i −0.182483 + 0.316070i
\(871\) −10.6008 36.0464i −0.359194 1.22138i
\(872\) −17.4216 30.1752i −0.589971 1.02186i
\(873\) 0.509428 + 0.294118i 0.0172415 + 0.00995439i
\(874\) 24.7399 0.836839
\(875\) 0 0
\(876\) 10.4888i 0.354385i
\(877\) −1.71335 0.989201i −0.0578556 0.0334029i 0.470793 0.882244i \(-0.343968\pi\)
−0.528649 + 0.848841i \(0.677301\pi\)
\(878\) 15.8699 9.16251i 0.535584 0.309220i
\(879\) 57.3668 33.1208i 1.93494 1.11714i
\(880\) 0.350706 0.607440i 0.0118223 0.0204768i
\(881\) 17.1466 0.577683 0.288841 0.957377i \(-0.406730\pi\)
0.288841 + 0.957377i \(0.406730\pi\)
\(882\) 0 0
\(883\) 10.2168 0.343822 0.171911 0.985112i \(-0.445006\pi\)
0.171911 + 0.985112i \(0.445006\pi\)
\(884\) 7.40558 + 7.05521i 0.249077 + 0.237292i
\(885\) −7.49936 12.9893i −0.252088 0.436630i
\(886\) 12.8388 7.41248i 0.431328 0.249027i
\(887\) 25.4965 44.1613i 0.856090 1.48279i −0.0195395 0.999809i \(-0.506220\pi\)
0.875630 0.482983i \(-0.160447\pi\)
\(888\) −3.14676 −0.105598
\(889\) 0 0
\(890\) 8.97901i 0.300977i
\(891\) −5.68008 3.27940i −0.190290 0.109864i
\(892\) 4.97258 2.87092i 0.166494 0.0961255i
\(893\) 21.0002 + 36.3733i 0.702743 + 1.21719i
\(894\) 4.82329 8.35419i 0.161315 0.279406i
\(895\) 5.92331i 0.197995i
\(896\) 0 0
\(897\) −9.14277 + 37.7570i −0.305268 + 1.26067i
\(898\) −17.5128 + 30.3330i −0.584409 + 1.01223i
\(899\) 25.0847 14.4827i 0.836621 0.483024i
\(900\) −5.69365 9.86170i −0.189788 0.328723i
\(901\) −1.16526 + 2.01829i −0.0388204 + 0.0672389i
\(902\) 3.81360i 0.126979i
\(903\) 0 0
\(904\) 2.82268i 0.0938811i
\(905\) −6.19170 3.57478i −0.205819 0.118830i
\(906\) −6.36309 11.0212i −0.211400 0.366155i
\(907\) −2.89269 5.01028i −0.0960501 0.166364i 0.813996 0.580870i \(-0.197288\pi\)
−0.910046 + 0.414506i \(0.863954\pi\)
\(908\) 12.3638 + 7.13824i 0.410307 + 0.236891i
\(909\) −50.4732 −1.67409
\(910\) 0 0
\(911\) −1.70706 −0.0565573 −0.0282787 0.999600i \(-0.509003\pi\)
−0.0282787 + 0.999600i \(0.509003\pi\)
\(912\) −17.3405 10.0116i −0.574202 0.331516i
\(913\) −3.61470 6.26084i −0.119629 0.207204i
\(914\) −1.70097 2.94617i −0.0562632 0.0974507i
\(915\) 6.18583 + 3.57139i 0.204497 + 0.118067i
\(916\) 9.35590i 0.309128i
\(917\) 0 0
\(918\) 0.769931i 0.0254115i
\(919\) −18.6025 + 32.2205i −0.613640 + 1.06286i 0.376982 + 0.926221i \(0.376962\pi\)
−0.990622 + 0.136634i \(0.956371\pi\)
\(920\) 4.23582 + 7.33666i 0.139651 + 0.241882i
\(921\) 26.7708 15.4561i 0.882128 0.509297i
\(922\) 0.108391 0.187739i 0.00356967 0.00618284i
\(923\) −49.3669 11.9541i −1.62493 0.393474i
\(924\) 0 0
\(925\) 1.95142i 0.0641623i
\(926\) 9.23474 15.9950i 0.303472 0.525630i
\(927\) 15.7449 + 27.2709i 0.517129 + 0.895693i
\(928\) −25.2230 + 14.5625i −0.827987 + 0.478038i
\(929\) −17.2379 9.95229i −0.565556 0.326524i 0.189816 0.981820i \(-0.439211\pi\)
−0.755373 + 0.655296i \(0.772544\pi\)
\(930\) 7.16447i 0.234932i
\(931\) 0 0
\(932\) −14.7265 −0.482383
\(933\) −11.6936 + 20.2539i −0.382831 + 0.663082i
\(934\) −0.177652 + 0.102567i −0.00581295 + 0.00335611i
\(935\) 0.740724 + 1.28297i 0.0242243 + 0.0419577i
\(936\) 22.1347 23.2340i 0.723496 0.759426i
\(937\) −7.16949 −0.234217 −0.117109 0.993119i \(-0.537363\pi\)
−0.117109 + 0.993119i \(0.537363\pi\)
\(938\) 0 0
\(939\) 21.9446 0.716134
\(940\) −2.14214 + 3.71029i −0.0698688 + 0.121016i
\(941\) 2.65066 1.53036i 0.0864091 0.0498883i −0.456173 0.889891i \(-0.650780\pi\)
0.542582 + 0.840003i \(0.317447\pi\)
\(942\) 21.5096 12.4186i 0.700820 0.404619i
\(943\) 19.2501 + 11.1140i 0.626869 + 0.361923i
\(944\) 15.6120i 0.508126i
\(945\) 0 0
\(946\) 8.51968 0.276999
\(947\) 38.2832 + 22.1028i 1.24404 + 0.718244i 0.969913 0.243451i \(-0.0782794\pi\)
0.274122 + 0.961695i \(0.411613\pi\)
\(948\) 4.03529 + 6.98933i 0.131060 + 0.227003i
\(949\) 5.17163 + 17.5853i 0.167878 + 0.570844i
\(950\) −12.8652 + 22.2832i −0.417403 + 0.722963i
\(951\) 59.8762i 1.94162i
\(952\) 0 0
\(953\) 13.7002 0.443791 0.221896 0.975070i \(-0.428776\pi\)
0.221896 + 0.975070i \(0.428776\pi\)
\(954\) 1.88626 + 1.08903i 0.0610700 + 0.0352588i
\(955\) 8.49700 4.90574i 0.274956 0.158746i
\(956\) 14.4933 8.36771i 0.468747 0.270631i
\(957\) −9.84225 5.68242i −0.318155 0.183687i
\(958\) −23.0476 −0.744634
\(959\) 0 0
\(960\) 12.0180i 0.387879i
\(961\) −5.86129 + 10.1520i −0.189074 + 0.327485i
\(962\) −1.57160 + 0.462187i −0.0506703 + 0.0149015i
\(963\) 8.90521 + 15.4243i 0.286966 + 0.497040i
\(964\) −2.04597 1.18124i −0.0658961 0.0380451i
\(965\) −14.3894 −0.463211
\(966\) 0 0
\(967\) 43.9429i 1.41311i 0.707659 + 0.706554i \(0.249751\pi\)
−0.707659 + 0.706554i \(0.750249\pi\)
\(968\) −27.7897 16.0444i −0.893194 0.515686i
\(969\) 36.6248 21.1454i 1.17656 0.679287i
\(970\) 0.117418 0.0677912i 0.00377006 0.00217664i
\(971\) −10.6585 + 18.4611i −0.342049 + 0.592446i −0.984813 0.173618i \(-0.944454\pi\)
0.642764 + 0.766064i \(0.277788\pi\)
\(972\) −18.5525 −0.595072
\(973\) 0 0
\(974\) −20.4400 −0.654941
\(975\) −29.2533 27.8693i −0.936855 0.892531i
\(976\) −3.71741 6.43874i −0.118991 0.206099i
\(977\) 14.2432 8.22330i 0.455679 0.263087i −0.254547 0.967061i \(-0.581926\pi\)
0.710226 + 0.703974i \(0.248593\pi\)
\(978\) −30.9286 + 53.5699i −0.988987 + 1.71298i
\(979\) 9.47937 0.302962
\(980\) 0 0
\(981\) 33.1913i 1.05972i
\(982\) 33.2277 + 19.1840i 1.06034 + 0.612187i
\(983\) −10.1415 + 5.85521i −0.323464 + 0.186752i −0.652936 0.757413i \(-0.726463\pi\)
0.329471 + 0.944166i \(0.393129\pi\)
\(984\) −18.6395 32.2846i −0.594206 1.02919i
\(985\) 3.19080 5.52663i 0.101667 0.176093i
\(986\) 23.6662i 0.753687i
\(987\) 0 0
\(988\) 15.4708 + 3.74621i 0.492190 + 0.119183i
\(989\) −24.8290 + 43.0051i −0.789517 + 1.36748i
\(990\) 1.19905 0.692270i 0.0381082 0.0220018i
\(991\) 15.6873 + 27.1713i 0.498325 + 0.863124i 0.999998 0.00193305i \(-0.000615311\pi\)
−0.501673 + 0.865057i \(0.667282\pi\)
\(992\) −9.69187 + 16.7868i −0.307717 + 0.532982i
\(993\) 32.0260i 1.01632i
\(994\) 0 0
\(995\) 7.45731i 0.236413i
\(996\) −18.2312 10.5258i −0.577679 0.333523i
\(997\) −2.34855 4.06781i −0.0743794 0.128829i 0.826437 0.563029i \(-0.190364\pi\)
−0.900816 + 0.434201i \(0.857031\pi\)
\(998\) 9.49071 + 16.4384i 0.300423 + 0.520348i
\(999\) 0.0786985 + 0.0454366i 0.00248991 + 0.00143755i
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.f.324.3 16
7.2 even 3 637.2.c.e.246.6 8
7.3 odd 6 91.2.r.a.25.6 yes 16
7.4 even 3 inner 637.2.r.f.116.6 16
7.5 odd 6 637.2.c.f.246.6 8
7.6 odd 2 91.2.r.a.51.3 yes 16
13.12 even 2 inner 637.2.r.f.324.6 16
21.17 even 6 819.2.dl.e.298.3 16
21.20 even 2 819.2.dl.e.415.6 16
91.5 even 12 8281.2.a.ck.1.6 8
91.12 odd 6 637.2.c.f.246.3 8
91.25 even 6 inner 637.2.r.f.116.3 16
91.31 even 12 1183.2.e.i.508.3 16
91.34 even 4 1183.2.e.i.170.6 16
91.38 odd 6 91.2.r.a.25.3 16
91.44 odd 12 8281.2.a.cj.1.6 8
91.47 even 12 8281.2.a.ck.1.3 8
91.51 even 6 637.2.c.e.246.3 8
91.73 even 12 1183.2.e.i.508.6 16
91.83 even 4 1183.2.e.i.170.3 16
91.86 odd 12 8281.2.a.cj.1.3 8
91.90 odd 2 91.2.r.a.51.6 yes 16
273.38 even 6 819.2.dl.e.298.6 16
273.272 even 2 819.2.dl.e.415.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.r.a.25.3 16 91.38 odd 6
91.2.r.a.25.6 yes 16 7.3 odd 6
91.2.r.a.51.3 yes 16 7.6 odd 2
91.2.r.a.51.6 yes 16 91.90 odd 2
637.2.c.e.246.3 8 91.51 even 6
637.2.c.e.246.6 8 7.2 even 3
637.2.c.f.246.3 8 91.12 odd 6
637.2.c.f.246.6 8 7.5 odd 6
637.2.r.f.116.3 16 91.25 even 6 inner
637.2.r.f.116.6 16 7.4 even 3 inner
637.2.r.f.324.3 16 1.1 even 1 trivial
637.2.r.f.324.6 16 13.12 even 2 inner
819.2.dl.e.298.3 16 21.17 even 6
819.2.dl.e.298.6 16 273.38 even 6
819.2.dl.e.415.3 16 273.272 even 2
819.2.dl.e.415.6 16 21.20 even 2
1183.2.e.i.170.3 16 91.83 even 4
1183.2.e.i.170.6 16 91.34 even 4
1183.2.e.i.508.3 16 91.31 even 12
1183.2.e.i.508.6 16 91.73 even 12
8281.2.a.cj.1.3 8 91.86 odd 12
8281.2.a.cj.1.6 8 91.44 odd 12
8281.2.a.ck.1.3 8 91.47 even 12
8281.2.a.ck.1.6 8 91.5 even 12