Properties

Label 91.2.r.a.51.6
Level $91$
Weight $2$
Character 91.51
Analytic conductor $0.727$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,2,Mod(25,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, 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("91.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.r (of order \(6\), degree \(2\), 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: \(0.726638658394\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 51.6
Root \(-0.929293 + 0.536527i\) of defining polynomial
Character \(\chi\) \(=\) 91.51
Dual form 91.2.r.a.25.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.929293 + 0.536527i) q^{2} +(1.21570 + 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(-0.541640 - 0.312716i) q^{5} +2.60903i q^{6} +(-2.34996 - 1.21561i) q^{7} -3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +O(q^{10})\) \(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} +(-2.34996 - 1.21561i) q^{7} -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} +(-1.53159 - 2.39047i) q^{14} -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} +(-0.297185 - 6.42602i) q^{21} +0.760282 q^{22} +(-2.21570 + 3.83771i) q^{23} +(6.43627 - 3.71598i) q^{24} +(-2.30442 - 3.99137i) q^{25} +(-1.09159 + 3.71177i) q^{26} +0.214623 q^{27} +(0.103717 + 2.24266i) q^{28} -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} +(0.892689 + 1.39329i) q^{35} +2.47076 q^{36} +(0.366683 + 0.211704i) q^{37} +(2.79143 + 4.83489i) q^{38} +(-6.34722 + 6.04692i) q^{39} +(-0.955864 + 1.65561i) q^{40} -5.01604i q^{41} +(3.17157 - 6.13111i) q^{42} +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} +(4.04458 + 5.71326i) q^{49} -4.94553i q^{50} +(4.06426 - 7.03950i) q^{51} +(2.21516 - 2.11036i) q^{52} +(0.348553 + 0.603712i) q^{53} +(0.199447 + 0.115151i) q^{54} -0.443132 q^{55} +(-3.71570 + 7.18300i) q^{56} +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} +(6.48654 - 4.15596i) q^{63} -7.90305 q^{64} +(0.636233 - 2.16341i) q^{65} +(0.924277 + 1.60089i) q^{66} +(9.02470 - 5.21041i) q^{67} +(-1.41841 + 2.45676i) q^{68} -10.7745 q^{69} +(0.0820297 + 1.77373i) q^{70} -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} +(-1.87257 + 0.0866008i) q^{77} +(-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} +(-4.59619 + 2.94480i) q^{84} +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} +(2.26578 - 9.26640i) q^{91} +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} +(0.693276 + 7.47932i) q^{98} +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 \( 16 q - 4 q^{3} + 6 q^{4} - 12 q^{9} - 6 q^{10} + 18 q^{12} - 12 q^{13} - 26 q^{14} + 2 q^{16} + 8 q^{17} - 36 q^{22} - 12 q^{23} - 6 q^{26} + 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} + 34 q^{38} + 18 q^{39} - 4 q^{40} + 16 q^{42} + 16 q^{43} + 36 q^{48} + 40 q^{49} + 16 q^{51} - 42 q^{52} - 20 q^{53} + 24 q^{55} - 36 q^{56} - 12 q^{61} + 44 q^{62} + 88 q^{64} - 30 q^{65} + 2 q^{66} - 2 q^{68} - 56 q^{69} + 42 q^{74} + 8 q^{75} - 76 q^{77} + 20 q^{78} + 20 q^{79} - 24 q^{81} - 16 q^{82} - 68 q^{87} + 4 q^{88} - 216 q^{90} + 56 q^{91} + 12 q^{92} - 26 q^{94} - 16 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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 0.791175 0.611590i \(-0.209470\pi\)
−0.134065 + 0.990972i \(0.542803\pi\)
\(3\) 1.21570 + 2.10566i 0.701886 + 1.21570i 0.967804 + 0.251707i \(0.0809918\pi\)
−0.265918 + 0.963996i \(0.585675\pi\)
\(4\) −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
\(7\) −2.34996 1.21561i −0.888200 0.459458i
\(8\) 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 −0.404636 0.914478i \(-0.632602\pi\)
0.589643 + 0.807664i \(0.299269\pi\)
\(12\) 1.03159 1.78676i 0.297794 0.515794i
\(13\) 0.848553 + 3.50428i 0.235346 + 0.971912i
\(14\) −1.53159 2.39047i −0.409334 0.638881i
\(15\) 1.52068i 0.392637i
\(16\) 0.791426 1.37079i 0.197856 0.342697i
\(17\) −1.67157 2.89524i −0.405414 0.702199i 0.588955 0.808166i \(-0.299539\pi\)
−0.994370 + 0.105967i \(0.966206\pi\)
\(18\) −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
\(21\) −0.297185 6.42602i −0.0648510 1.40227i
\(22\) 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
\(26\) −1.09159 + 3.71177i −0.214078 + 0.727938i
\(27\) 0.214623 0.0413042
\(28\) 0.103717 + 2.24266i 0.0196006 + 0.423824i
\(29\) −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
\(35\) 0.892689 + 1.39329i 0.150892 + 0.235509i
\(36\) 2.47076 0.411793
\(37\) 0.366683 + 0.211704i 0.0602823 + 0.0348040i 0.529838 0.848099i \(-0.322253\pi\)
−0.469556 + 0.882903i \(0.655586\pi\)
\(38\) 2.79143 + 4.83489i 0.452829 + 0.784323i
\(39\) −6.34722 + 6.04692i −1.01637 + 0.968282i
\(40\) −0.955864 + 1.65561i −0.151135 + 0.261774i
\(41\) 5.01604i 0.783374i −0.920099 0.391687i \(-0.871892\pi\)
0.920099 0.391687i \(-0.128108\pi\)
\(42\) 3.17157 6.13111i 0.489383 0.946050i
\(43\) 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
\(49\) 4.04458 + 5.71326i 0.577797 + 0.816180i
\(50\) 4.94553i 0.699404i
\(51\) 4.06426 7.03950i 0.569110 0.985727i
\(52\) 2.21516 2.11036i 0.307188 0.292654i
\(53\) 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
\(56\) −3.71570 + 7.18300i −0.496532 + 0.959869i
\(57\) 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 −0.976295 0.216444i \(-0.930554\pi\)
0.675594 + 0.737274i \(0.263887\pi\)
\(62\) −4.71136 −0.598344
\(63\) 6.48654 4.15596i 0.817227 0.523601i
\(64\) −7.90305 −0.987881
\(65\) 0.636233 2.16341i 0.0789150 0.268338i
\(66\) 0.924277 + 1.60089i 0.113771 + 0.197056i
\(67\) 9.02470 5.21041i 1.10254 0.636553i 0.165655 0.986184i \(-0.447026\pi\)
0.936888 + 0.349631i \(0.113693\pi\)
\(68\) −1.41841 + 2.45676i −0.172008 + 0.297926i
\(69\) −10.7745 −1.29710
\(70\) 0.0820297 + 1.77373i 0.00980443 + 0.212001i
\(71\) 14.0876i 1.67189i −0.548812 0.835946i \(-0.684920\pi\)
0.548812 0.835946i \(-0.315080\pi\)
\(72\) 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
\(77\) −1.87257 + 0.0866008i −0.213399 + 0.00986908i
\(78\) −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 \(0.810805\pi\)
\(84\) −4.59619 + 2.94480i −0.501486 + 0.321304i
\(85\) 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
\(91\) 2.26578 9.26640i 0.237518 0.971383i
\(92\) 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 \(-0.00326470\pi\)
\(98\) 0.693276 + 7.47932i 0.0700315 + 0.755526i
\(99\) 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 \(-0.835614\pi\)
0.00716374 0.999974i \(-0.497720\pi\)
\(102\) 7.55377 4.36117i 0.747934 0.431820i
\(103\) −5.40739 + 9.36587i −0.532806 + 0.922847i 0.466460 + 0.884542i \(0.345529\pi\)
−0.999266 + 0.0383047i \(0.987804\pi\)
\(104\) 10.7114 2.59373i 1.05034 0.254336i
\(105\) −1.84855 + 3.57353i −0.180400 + 0.348740i
\(106\) 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 0.0538629 0.998548i \(-0.482847\pi\)
0.891700 + 0.452628i \(0.149513\pi\)
\(110\) −0.411799 0.237752i −0.0392635 0.0226688i
\(111\) 1.02948i 0.0977137i
\(112\) −3.52616 + 2.25923i −0.333191 + 0.213477i
\(113\) −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
\(117\) −10.0719 2.96201i −0.931145 0.273838i
\(118\) −10.5837 −0.974312
\(119\) 0.408623 + 8.83566i 0.0374584 + 0.809963i
\(120\) −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
\(126\) 8.25768 0.381893i 0.735652 0.0340218i
\(127\) 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
\(130\) 1.75198 1.66909i 0.153659 0.146389i
\(131\) 3.50152 6.06482i 0.305930 0.529885i −0.671538 0.740970i \(-0.734366\pi\)
0.977468 + 0.211084i \(0.0676995\pi\)
\(132\) 1.46180i 0.127234i
\(133\) −7.42599 11.5903i −0.643915 1.00501i
\(134\) 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 −0.252051 0.967714i \(-0.581105\pi\)
0.712040 + 0.702139i \(0.247772\pi\)
\(138\) −10.0127 5.78084i −0.852338 0.492097i
\(139\) 6.53140 0.553986 0.276993 0.960872i \(-0.410662\pi\)
0.276993 + 0.960872i \(0.410662\pi\)
\(140\) 0.645140 1.24715i 0.0545242 0.105403i
\(141\) 19.6280i 1.65297i
\(142\) 7.55839 13.0915i 0.634286 1.09862i
\(143\) 1.76210 + 1.84961i 0.147354 + 0.154672i
\(144\) 2.30442 + 3.99137i 0.192035 + 0.332614i
\(145\) 3.57326 + 2.06302i 0.296743 + 0.171325i
\(146\) 5.45523 0.451478
\(147\) −7.11317 + 15.4621i −0.586685 + 1.27529i
\(148\) 0.359285i 0.0295330i
\(149\) 3.20203 + 1.84869i 0.262320 + 0.151451i 0.625393 0.780310i \(-0.284939\pi\)
−0.363072 + 0.931761i \(0.618272\pi\)
\(150\) 10.4136 6.01230i 0.850267 0.490902i
\(151\) 4.22425 2.43887i 0.343764 0.198473i −0.318171 0.948033i \(-0.603069\pi\)
0.661935 + 0.749561i \(0.269735\pi\)
\(152\) 7.95152 13.7724i 0.644954 1.11709i
\(153\) 9.73430 0.786971
\(154\) −1.78663 0.924207i −0.143971 0.0744747i
\(155\) 2.74603 0.220566
\(156\) 7.13667 + 2.09881i 0.571391 + 0.168039i
\(157\) 4.75984 + 8.24428i 0.379876 + 0.657965i 0.991044 0.133536i \(-0.0426332\pi\)
−0.611168 + 0.791501i \(0.709300\pi\)
\(158\) 3.63514 2.09875i 0.289196 0.166968i
\(159\) −0.847473 + 1.46787i −0.0672090 + 0.116409i
\(160\) 2.76117 0.218290
\(161\) 9.87196 6.32501i 0.778020 0.498481i
\(162\) 9.93329i 0.780433i
\(163\) −20.5325 11.8544i −1.60823 0.928511i −0.989767 0.142696i \(-0.954423\pi\)
−0.618461 0.785815i \(-0.712244\pi\)
\(164\) −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 \(-0.0139451\pi\)
\(168\) −19.6421 + 0.908391i −1.51542 + 0.0700839i
\(169\) −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 −0.542972 0.839751i \(-0.682701\pi\)
0.998732 + 0.0503522i \(0.0160344\pi\)
\(174\) 17.2121i 1.30484i
\(175\) 0.563327 + 12.1808i 0.0425835 + 0.920783i
\(176\) 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 \(-0.639671\pi\)
−0.424845 + 0.905266i \(0.639671\pi\)
\(182\) 7.07725 7.39555i 0.524601 0.548195i
\(183\) −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
\(189\) −0.504354 0.260898i −0.0366864 0.0189775i
\(190\) 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 −0.997439 0.0715256i \(-0.977213\pi\)
−0.436776 + 0.899570i \(0.643880\pi\)
\(194\) 0.108391 0.187739i 0.00778202 0.0134788i
\(195\) 5.32888 1.29038i 0.381609 0.0924057i
\(196\) 2.48248 5.39624i 0.177320 0.385446i
\(197\) 10.2035i 0.726970i −0.931600 0.363485i \(-0.881587\pi\)
0.931600 0.363485i \(-0.118413\pi\)
\(198\) −1.10687 + 1.91715i −0.0786616 + 0.136246i
\(199\) 5.96173 + 10.3260i 0.422616 + 0.731992i 0.996194 0.0871586i \(-0.0277787\pi\)
−0.573579 + 0.819150i \(0.694445\pi\)
\(200\) −12.2002 + 7.04381i −0.862687 + 0.498072i
\(201\) 21.9427 + 12.6686i 1.54772 + 0.893576i
\(202\) 18.6008i 1.30875i
\(203\) 15.5029 + 8.01952i 1.08809 + 0.562860i
\(204\) −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
\(208\) 5.47519 + 1.61019i 0.379636 + 0.111646i
\(209\) 3.68627 0.254984
\(210\) −3.63514 + 2.32905i −0.250849 + 0.160720i
\(211\) −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
\(217\) 11.6041 0.536653i 0.787734 0.0364304i
\(218\) 12.2319 0.828451
\(219\) 10.7048 + 6.18042i 0.723364 + 0.417634i
\(220\) 0.188010 + 0.325643i 0.0126757 + 0.0219549i
\(221\) 8.72731 8.31440i 0.587062 0.559287i
\(222\) −0.552343 + 0.956687i −0.0370709 + 0.0642086i
\(223\) 6.76662i 0.453126i 0.973996 + 0.226563i \(0.0727490\pi\)
−0.973996 + 0.226563i \(0.927251\pi\)
\(224\) 11.6680 0.539613i 0.779604 0.0360544i
\(225\) 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
\(231\) −2.45884 3.83771i −0.161780 0.252503i
\(232\) 20.1651i 1.32390i
\(233\) 8.67743 15.0298i 0.568477 0.984632i −0.428239 0.903665i \(-0.640866\pi\)
0.996717 0.0809664i \(-0.0258006\pi\)
\(234\) −7.77052 8.15642i −0.507975 0.533202i
\(235\) −2.52446 4.37249i −0.164678 0.285230i
\(236\) 7.24814 + 4.18472i 0.471814 + 0.272402i
\(237\) 9.51100 0.617806
\(238\) −4.36084 + 8.43015i −0.282671 + 0.546445i
\(239\) 19.7223i 1.27573i −0.770148 0.637865i \(-0.779818\pi\)
0.770148 0.637865i \(-0.220182\pi\)
\(240\) −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
\(245\) −0.404077 4.35934i −0.0258155 0.278508i
\(246\) 13.0870 0.834397
\(247\) −5.29262 + 17.9967i −0.336761 + 1.14510i
\(248\) 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 \(-0.766870\pi\)
−0.743572 + 0.668655i \(0.766870\pi\)
\(252\) −5.80617 3.00348i −0.365754 0.189201i
\(253\) 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 −0.914574 0.404419i \(-0.867474\pi\)
0.807524 + 0.589835i \(0.200807\pi\)
\(258\) 29.2367i 1.82019i
\(259\) −0.604338 0.943239i −0.0375517 0.0586100i
\(260\) −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
\(266\) −0.682378 14.7551i −0.0418393 0.904691i
\(267\) 32.5300i 1.99080i
\(268\) −7.65794 4.42131i −0.467783 0.270075i
\(269\) −7.32843 12.6932i −0.446822 0.773919i 0.551355 0.834271i \(-0.314111\pi\)
−0.998177 + 0.0603517i \(0.980778\pi\)
\(270\) −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
\(273\) 22.2664 6.49424i 1.34762 0.393049i
\(274\) 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
\(280\) 4.25881 2.72864i 0.254513 0.163067i
\(281\) 20.2356i 1.20715i 0.797305 + 0.603577i \(0.206258\pi\)
−0.797305 + 0.603577i \(0.793742\pi\)
\(282\) −10.5310 + 18.2401i −0.627109 + 1.08618i
\(283\) 0.867593 + 1.50272i 0.0515731 + 0.0893272i 0.890659 0.454671i \(-0.150243\pi\)
−0.839086 + 0.543998i \(0.816910\pi\)
\(284\) −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
\(287\) −6.09755 + 11.7875i −0.359927 + 0.695792i
\(288\) 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 \(0.707046\pi\)
\(294\) −14.9061 + 10.5524i −0.869340 + 0.615430i
\(295\) 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
\(299\) −15.3285 4.50794i −0.886472 0.260701i
\(300\) −9.50884 −0.548993
\(301\) −26.3335 13.6221i −1.51784 0.785163i
\(302\) 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 \(0.881819\pi\)
\(308\) 0.858127 + 1.33935i 0.0488963 + 0.0763165i
\(309\) −26.2951 −1.49588
\(310\) 2.55186 + 1.47332i 0.144936 + 0.0836788i
\(311\) 4.80939 + 8.33011i 0.272716 + 0.472357i 0.969556 0.244869i \(-0.0787448\pi\)
−0.696841 + 0.717226i \(0.745412\pi\)
\(312\) 18.4833 + 19.4013i 1.04641 + 1.09838i
\(313\) 4.51273 7.81628i 0.255075 0.441802i −0.709841 0.704362i \(-0.751233\pi\)
0.964916 + 0.262559i \(0.0845666\pi\)
\(314\) 10.2151i 0.576473i
\(315\) −4.81300 + 0.222587i −0.271182 + 0.0125414i
\(316\) −3.31931 −0.186726
\(317\) 21.3269 + 12.3131i 1.19784 + 0.691572i 0.960073 0.279750i \(-0.0902517\pi\)
0.237766 + 0.971323i \(0.423585\pi\)
\(318\) −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
\(322\) 12.5675 0.581209i 0.700359 0.0323895i
\(323\) 17.3935i 0.967802i
\(324\) 3.92754 6.80269i 0.218196 0.377927i
\(325\) 12.0314 11.4622i 0.667384 0.635809i
\(326\) −12.7205 22.0325i −0.704521 1.22027i
\(327\) 24.0027 + 13.8580i 1.32735 + 0.766348i
\(328\) −15.3323 −0.846584
\(329\) −11.5223 17.9838i −0.635244 0.991477i
\(330\) 1.15614i 0.0636436i
\(331\) 11.4071 + 6.58591i 0.626993 + 0.361994i 0.779586 0.626295i \(-0.215429\pi\)
−0.152594 + 0.988289i \(0.548763\pi\)
\(332\) 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
\(336\) −9.04393 4.67834i −0.493387 0.255225i
\(337\) 17.0307 0.927720 0.463860 0.885909i \(-0.346464\pi\)
0.463860 + 0.885909i \(0.346464\pi\)
\(338\) −13.9333 0.675587i −0.757874 0.0367471i
\(339\) −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
\(343\) −2.55948 18.3425i −0.138199 0.990405i
\(344\) 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 \(-0.0589342\pi\)
\(350\) −6.01184 + 11.6218i −0.321347 + 0.621210i
\(351\) 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
\(357\) −18.1081 + 11.6019i −0.958383 + 0.614040i
\(358\) 10.1626i 0.537112i
\(359\) 23.5617 + 13.6034i 1.24354 + 0.717959i 0.969813 0.243848i \(-0.0784099\pi\)
0.273728 + 0.961807i \(0.411743\pi\)
\(360\) −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
\(364\) −7.77090 + 2.26647i −0.407306 + 0.118795i
\(365\) −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 \(-0.917969\pi\)
0.262769 0.964859i \(-0.415364\pi\)
\(368\) 3.50713 + 6.07452i 0.182822 + 0.316656i
\(369\) 12.6486 + 7.30267i 0.658460 + 0.380162i
\(370\) 0.284159i 0.0147727i
\(371\) −0.0852056 1.84240i −0.00442365 0.0956526i
\(372\) 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
\(378\) −0.328714 0.513050i −0.0169072 0.0263885i
\(379\) 11.4059i 0.585884i 0.956130 + 0.292942i \(0.0946343\pi\)
−0.956130 + 0.292942i \(0.905366\pi\)
\(380\) −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
\(385\) 1.04134 + 0.538676i 0.0530716 + 0.0274535i
\(386\) −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 \(-0.422638\pi\)
\(390\) 5.64441 + 1.65995i 0.285816 + 0.0840549i
\(391\) 14.8148 0.749216
\(392\) 17.4635 12.3629i 0.882038 0.624420i
\(393\) 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
\(399\) 15.3775 29.7270i 0.769838 1.48821i
\(400\) −7.29510 −0.364755
\(401\) −10.9287 6.30971i −0.545756 0.315092i 0.201653 0.979457i \(-0.435369\pi\)
−0.747408 + 0.664365i \(0.768702\pi\)
\(402\) 13.5941 + 23.5457i 0.678013 + 1.17435i
\(403\) −10.9195 11.4618i −0.543938 0.570950i
\(404\) −7.35460 + 12.7385i −0.365905 + 0.633766i
\(405\) 5.78964i 0.287689i
\(406\) 10.1041 + 15.7702i 0.501456 + 0.782663i
\(407\) 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
\(413\) 26.0677 1.20555i 1.28271 0.0593214i
\(414\) 13.8457i 0.680478i
\(415\) 3.19080 5.52663i 0.156630 0.271291i
\(416\) −10.9797 11.5250i −0.538324 0.565058i
\(417\) 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 \(-0.386581\pi\)
0.348823 + 0.937188i \(0.386581\pi\)
\(420\) 3.41037 0.157720i 0.166409 0.00769593i
\(421\) 4.27439i 0.208321i −0.994561 0.104160i \(-0.966784\pi\)
0.994561 0.104160i \(-0.0332155\pi\)
\(422\) −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
\(427\) 10.4639 6.70425i 0.506382 0.324441i
\(428\) −5.19042 −0.250888
\(429\) −1.75245 + 5.95894i −0.0846092 + 0.287700i
\(430\) −3.76028 6.51300i −0.181337 0.314085i
\(431\) −12.6498 + 7.30335i −0.609318 + 0.351790i −0.772698 0.634773i \(-0.781094\pi\)
0.163381 + 0.986563i \(0.447760\pi\)
\(432\) 0.169858 0.294203i 0.00817230 0.0141548i
\(433\) 28.0099 1.34607 0.673035 0.739611i \(-0.264991\pi\)
0.673035 + 0.739611i \(0.264991\pi\)
\(434\) 11.0715 + 5.72718i 0.531449 + 0.274914i
\(435\) 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 −0.587082 0.809528i \(-0.699723\pi\)
0.994612 + 0.103664i \(0.0330566\pi\)
\(440\) 1.35450i 0.0645733i
\(441\) −20.2951 + 1.88120i −0.966433 + 0.0895810i
\(442\) 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
\(448\) 18.5718 + 9.60703i 0.877436 + 0.453890i
\(449\) 32.6410i 1.54042i 0.637789 + 0.770211i \(0.279849\pi\)
−0.637789 + 0.770211i \(0.720151\pi\)
\(450\) 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
\(455\) −4.12499 + 4.31051i −0.193382 + 0.202080i
\(456\) 38.6667 1.81074
\(457\) −2.74559 1.58517i −0.128433 0.0741511i 0.434407 0.900717i \(-0.356958\pi\)
−0.562840 + 0.826566i \(0.690291\pi\)
\(458\) −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 \(0.998502\pi\)
\(462\) −0.225944 4.88559i −0.0105119 0.227298i
\(463\) 17.2121i 0.799912i −0.916534 0.399956i \(-0.869025\pi\)
0.916534 0.399956i \(-0.130975\pi\)
\(464\) −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 −0.868228 0.496165i \(-0.834741\pi\)
0.863805 + 0.503826i \(0.168075\pi\)
\(468\) 2.09657 + 8.65821i 0.0969139 + 0.400226i
\(469\) −27.5415 + 1.27371i −1.27175 + 0.0588146i
\(470\) 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
\(476\) 6.31968 4.04905i 0.289662 0.185588i
\(477\) −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
\(481\) −0.430721 + 1.46460i −0.0196392 + 0.0667800i
\(482\) 2.98752 0.136078
\(483\) 25.3197 + 13.0976i 1.15209 + 0.595964i
\(484\) 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 −0.824799 0.565426i \(-0.808712\pi\)
0.0772740 + 0.997010i \(0.475378\pi\)
\(488\) 12.4339 + 7.17871i 0.562856 + 0.324965i
\(489\) 57.6458i 2.60684i
\(490\) 1.96340 4.26790i 0.0886973 0.192804i
\(491\) −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
\(494\) −14.5741 + 13.8846i −0.655721 + 0.624697i
\(495\) 0.645140 1.11741i 0.0289969 0.0502240i
\(496\) 6.94968i 0.312050i
\(497\) −17.1251 + 33.1053i −0.768164 + 1.48497i
\(498\) −26.6213 −1.19293
\(499\) 15.3192 + 8.84457i 0.685784 + 0.395937i 0.802031 0.597283i \(-0.203753\pi\)
−0.116247 + 0.993220i \(0.537086\pi\)
\(500\) 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 \(-0.418714\pi\)
0.252601 + 0.967570i \(0.418714\pi\)
\(504\) −12.7033 19.8271i −0.565851 0.883169i
\(505\) 10.8415i 0.482441i
\(506\) −1.68456 + 2.91774i −0.0748878 + 0.129709i
\(507\) −26.5760 17.1113i −1.18028 0.759939i
\(508\) −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
\(511\) −13.4362 + 0.621384i −0.594382 + 0.0274884i
\(512\) 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
\(518\) −0.0555330 1.20079i −0.00243998 0.0527597i
\(519\) 29.1505 1.27957
\(520\) −6.61280 1.94474i −0.289991 0.0852827i
\(521\) 3.85550 + 6.67791i 0.168912 + 0.292565i 0.938038 0.346533i \(-0.112641\pi\)
−0.769125 + 0.639098i \(0.779308\pi\)
\(522\) 17.8508 10.3062i 0.781307 0.451088i
\(523\) 17.5251 30.3543i 0.766317 1.32730i −0.173230 0.984881i \(-0.555420\pi\)
0.939547 0.342419i \(-0.111246\pi\)
\(524\) −5.94246 −0.259597
\(525\) −24.9638 + 15.9944i −1.08951 + 0.698054i
\(526\) 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
\(532\) −5.36671 + 10.3746i −0.232676 + 0.449797i
\(533\) 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
\(539\) 4.50573 + 2.07281i 0.194075 + 0.0892821i
\(540\) 0.113903i 0.00490160i
\(541\) −10.5079 6.06674i −0.451770 0.260829i 0.256807 0.966463i \(-0.417329\pi\)
−0.708577 + 0.705633i \(0.750663\pi\)
\(542\) 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
\(546\) 24.1763 + 5.91148i 1.03465 + 0.252988i
\(547\) −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
\(553\) −8.71427 + 5.58327i −0.370568 + 0.237425i
\(554\) 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 0.386258 0.922391i \(-0.373767\pi\)
0.991943 + 0.126686i \(0.0404341\pi\)
\(558\) 6.85911 11.8803i 0.290369 0.502934i
\(559\) 9.50884 + 39.2687i 0.402181 + 1.66089i
\(560\) 2.61641 0.121001i 0.110563 0.00511323i
\(561\) 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 \(0.0400800\pi\)
−0.387284 + 0.921960i \(0.626587\pi\)
\(564\) 14.4240 8.32769i 0.607359 0.350659i
\(565\) 0.500180 + 0.288779i 0.0210428 + 0.0121490i
\(566\) 1.86195i 0.0782636i
\(567\) −1.13146 24.4656i −0.0475170 1.02746i
\(568\) −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 \(0.711653\pi\)
\(572\) 0.611601 2.07965i 0.0255723 0.0869547i
\(573\) −38.1428 −1.59344
\(574\) −11.9907 + 7.68250i −0.500483 + 0.320662i
\(575\) 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
\(581\) 12.4035 23.9778i 0.514584 0.994766i
\(582\) 0.527085 0.0218484
\(583\) 0.427742 + 0.246957i 0.0177153 + 0.0102279i
\(584\) −7.76975 13.4576i −0.321515 0.556880i
\(585\) 4.52906 + 4.75398i 0.187254 + 0.196553i
\(586\) −14.6172 + 25.3178i −0.603832 + 1.04587i
\(587\) 14.7295i 0.607953i −0.952680 0.303976i \(-0.901686\pi\)
0.952680 0.303976i \(-0.0983144\pi\)
\(588\) 14.3806 1.33297i 0.593045 0.0549708i
\(589\) −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
\(595\) 2.54172 4.91353i 0.104201 0.201435i
\(596\) 3.13743i 0.128514i
\(597\) −14.4954 + 25.1067i −0.593256 + 1.02755i
\(598\) −11.8261 12.4134i −0.483604 0.507621i
\(599\) 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 \(-0.473422\pi\)
0.0834001 + 0.996516i \(0.473422\pi\)
\(602\) −17.1629 26.7875i −0.699507 1.09178i
\(603\) 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 −0.900303 0.435263i \(-0.856655\pi\)
0.827100 + 0.562054i \(0.189989\pi\)
\(608\) −22.9693 −0.931527
\(609\) 1.96056 + 42.3932i 0.0794459 + 1.71786i
\(610\) 3.15233 0.127634
\(611\) −8.21211 + 27.9240i −0.332226 + 1.12968i
\(612\) −4.13003 7.15343i −0.166947 0.289160i
\(613\) 33.3285 19.2422i 1.34613 0.777186i 0.358428 0.933557i \(-0.383313\pi\)
0.987698 + 0.156371i \(0.0499796\pi\)
\(614\) −6.82128 + 11.8148i −0.275284 + 0.476806i
\(615\) −7.62778 −0.307582
\(616\) 0.264709 + 5.72379i 0.0106654 + 0.230618i
\(617\) 3.09503i 0.124601i 0.998057 + 0.0623007i \(0.0198438\pi\)
−0.998057 + 0.0623007i \(0.980156\pi\)
\(618\) −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
\(623\) 19.0962 + 29.8050i 0.765073 + 1.19411i
\(624\) 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
\(630\) −4.59211 2.37546i −0.182954 0.0946406i
\(631\) 5.31780i 0.211698i −0.994382 0.105849i \(-0.966244\pi\)
0.994382 0.105849i \(-0.0337561\pi\)
\(632\) −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
\(637\) −16.5888 + 19.0213i −0.657273 + 0.753653i
\(638\) −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 \(0.877946\pi\)
\(644\) −8.83649 4.57104i −0.348207 0.180124i
\(645\) 17.0406i 0.670974i
\(646\) 9.33211 16.1637i 0.367167 0.635952i
\(647\) 9.85587 + 17.0709i 0.387474 + 0.671125i 0.992109 0.125378i \(-0.0400143\pi\)
−0.604635 + 0.796503i \(0.706681\pi\)
\(648\) 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
\(651\) 15.2371 + 23.7818i 0.597188 + 0.932080i
\(652\) 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
\(658\) −1.05879 22.8942i −0.0412759 0.892509i
\(659\) 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
\(663\) 28.1171 + 8.26889i 1.09198 + 0.321137i
\(664\) 31.1886 1.21035
\(665\) 0.397725 + 8.60002i 0.0154231 + 0.333494i
\(666\) −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
\(672\) 15.3211 + 23.9129i 0.591025 + 0.922461i
\(673\) −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
\(676\) 9.27496 + 5.97179i 0.356729 + 0.229684i
\(677\) 24.3169 42.1182i 0.934576 1.61873i 0.159187 0.987248i \(-0.449113\pi\)
0.775389 0.631484i \(-0.217554\pi\)
\(678\) 2.40932i 0.0925296i
\(679\) −0.245582 + 0.474745i −0.00942455 + 0.0182191i
\(680\) 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 −0.402440 0.915446i \(-0.631838\pi\)
0.591580 + 0.806246i \(0.298504\pi\)
\(684\) 11.1326 + 6.42738i 0.425664 + 0.245757i
\(685\) −3.88828 −0.148563
\(686\) 7.46278 18.4188i 0.284930 0.703234i
\(687\) 26.8080i 1.02279i
\(688\) 8.86867 15.3610i 0.338115 0.585632i
\(689\) −1.81981 + 1.73371i −0.0693291 + 0.0660490i
\(690\) 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
\(693\) 2.50783 4.84801i 0.0952646 0.184161i
\(694\) 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
\(700\) 8.71229 5.58200i 0.329294 0.210980i
\(701\) 22.4361 0.847399 0.423700 0.905803i \(-0.360731\pi\)
0.423700 + 0.905803i \(0.360731\pi\)
\(702\) −0.234279 + 0.796631i −0.00884231 + 0.0300669i
\(703\) 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
\(707\) 2.11875 + 45.8137i 0.0796837 + 1.72300i
\(708\) 20.3495i 0.764780i
\(709\) 24.8955 + 14.3734i 0.934969 + 0.539804i 0.888380 0.459110i \(-0.151832\pi\)
0.0465891 + 0.998914i \(0.485165\pi\)
\(710\) −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
\(714\) −23.0525 + 1.06611i −0.862718 + 0.0398982i
\(715\) −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 −0.902596 0.430488i \(-0.858341\pi\)
0.824112 + 0.566427i \(0.191675\pi\)
\(720\) 2.88251i 0.107425i
\(721\) 24.0924 15.4361i 0.897247 0.574870i
\(722\) 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 \(-0.798409\pi\)
−0.806070 + 0.591820i \(0.798409\pi\)
\(728\) −28.3242 6.92569i −1.04976 0.256683i
\(729\) −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
\(735\) 8.68803 6.15050i 0.320463 0.226865i
\(736\) 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 −0.645183 0.764028i \(-0.723219\pi\)
0.339077 + 0.940759i \(0.389885\pi\)
\(740\) −0.112354 + 0.194603i −0.00413022 + 0.00715375i
\(741\) −44.3292 + 10.7342i −1.62847 + 0.394331i
\(742\) 0.909317 1.75784i 0.0333821 0.0645325i
\(743\) 32.1771i 1.18046i 0.807234 + 0.590231i \(0.200964\pi\)
−0.807234 + 0.590231i \(0.799036\pi\)
\(744\) −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
\(749\) −13.6265 + 8.73058i −0.497903 + 0.319008i
\(750\) −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
\(754\) 7.20132 24.4870i 0.262256 0.891762i
\(755\) −3.05070 −0.111026
\(756\) 0.0222599 + 0.481327i 0.000809586 + 0.0175057i
\(757\) 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
\(763\) −30.1271 + 1.39329i −1.09068 + 0.0504406i
\(764\) 13.3117 0.481601
\(765\) −5.27248 3.04407i −0.190627 0.110059i
\(766\) −12.7650 22.1097i −0.461220 0.798856i
\(767\) −24.5298 25.7480i −0.885720 0.929707i
\(768\) −19.6711 + 34.0713i −0.709819 + 1.22944i
\(769\) 39.3098i 1.41755i −0.705435 0.708774i \(-0.749248\pi\)
0.705435 0.708774i \(-0.250752\pi\)
\(770\) 0.678695 + 1.05929i 0.0244585 + 0.0381743i
\(771\) −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
\(777\) 1.25144 2.41923i 0.0448953 0.0867893i
\(778\) 30.4866i 1.09300i
\(779\) 13.0486 22.6009i 0.467516 0.809761i
\(780\) −3.20917 3.36855i −0.114907 0.120613i
\(781\) −4.99068 8.64412i −0.178581 0.309311i
\(782\) 13.7673 + 7.94854i 0.492316 + 0.284239i
\(783\) −1.41589 −0.0505998
\(784\) 11.0327 1.02264i 0.394024 0.0365230i
\(785\) 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
\(791\) 2.17008 + 1.12256i 0.0771592 + 0.0399137i
\(792\) 6.30594 0.224072
\(793\) −16.2476 4.77823i −0.576970 0.169680i
\(794\) 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 \(-0.377158\pi\)
0.376410 + 0.926453i \(0.377158\pi\)
\(798\) 30.2396 19.3746i 1.07047 0.685854i
\(799\) 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
\(805\) −7.32498 + 0.338759i −0.258172 + 0.0119397i
\(806\) −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 \(0.938070\pi\)
\(812\) −0.684230 14.7951i −0.0240118 0.519206i
\(813\) 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
\(819\) 20.0678 + 19.2041i 0.701225 + 0.671045i
\(820\) 2.66207 0.0929636
\(821\) −33.4879 19.3342i −1.16873 0.674769i −0.215353 0.976536i \(-0.569090\pi\)
−0.953382 + 0.301767i \(0.902424\pi\)
\(822\) 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
\(826\) 24.8713 + 12.8657i 0.865384 + 0.447655i
\(827\) 27.3451i 0.950881i 0.879748 + 0.475440i \(0.157711\pi\)
−0.879748 + 0.475440i \(0.842289\pi\)
\(828\) −5.47446 + 9.48204i −0.190251 + 0.329524i
\(829\) −12.5043 21.6581i −0.434292 0.752217i 0.562945 0.826494i \(-0.309668\pi\)
−0.997238 + 0.0742776i \(0.976335\pi\)
\(830\) 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
\(833\) 9.78048 21.2601i 0.338873 0.736620i
\(834\) 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 \(0.951627\pi\)
\(840\) 10.9230 + 5.65039i 0.376880 + 0.194957i
\(841\) 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
\(845\) 8.12107 + 0.393767i 0.279373 + 0.0135460i
\(846\) −25.2227 −0.867174
\(847\) 23.3867 14.9840i 0.803576 0.514855i
\(848\) 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 \(0.889787\pi\)
\(854\) 13.3210 0.616058i 0.455836 0.0210811i
\(855\) 9.47469 0.324028
\(856\) −16.1920 9.34845i −0.553431 0.319523i
\(857\) −1.33518 2.31261i −0.0456090 0.0789972i 0.842320 0.538978i \(-0.181190\pi\)
−0.887929 + 0.459981i \(0.847856\pi\)
\(858\) −4.82568 + 4.59736i −0.164746 + 0.156951i
\(859\) 19.4798 33.7401i 0.664644 1.15120i −0.314738 0.949179i \(-0.601917\pi\)
0.979382 0.202018i \(-0.0647500\pi\)
\(860\) 5.94713i 0.202795i
\(861\) −32.2332 + 1.49069i −1.09850 + 0.0508026i
\(862\) −15.6738 −0.533851
\(863\) −21.4754 12.3988i −0.731030 0.422060i 0.0877689 0.996141i \(-0.472026\pi\)
−0.818799 + 0.574081i \(0.805360\pi\)
\(864\) −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
\(868\) −5.31770 8.29976i −0.180494 0.281712i
\(869\) 2.77154i 0.0940181i
\(870\) −5.38249 + 9.32274i −0.182483 + 0.316070i
\(871\) 25.9167 + 27.2037i 0.878153 + 0.921763i
\(872\) −17.4216 30.1752i −0.589971 1.02186i
\(873\) 0.509428 + 0.294118i 0.0172415 + 0.00995439i
\(874\) −24.7399 −0.836839
\(875\) 7.30542 14.1225i 0.246968 0.477426i
\(876\) 10.4888i 0.354385i
\(877\) 1.71335 + 0.989201i 0.0578556 + 0.0334029i 0.528649 0.848841i \(-0.322699\pi\)
−0.470793 + 0.882244i \(0.656032\pi\)
\(878\) 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 \(-0.593270\pi\)
−0.288841 + 0.957377i \(0.593270\pi\)
\(882\) −19.8694 9.14069i −0.669038 0.307783i
\(883\) 10.2168 0.343822 0.171911 0.985112i \(-0.445006\pi\)
0.171911 + 0.985112i \(0.445006\pi\)
\(884\) −9.81278 2.88582i −0.330039 0.0970606i
\(885\) 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 \(0.493780\pi\)
−0.875630 + 0.482983i \(0.839553\pi\)
\(888\) 3.14676 0.105598
\(889\) −19.9975 10.3445i −0.670694 0.346944i
\(890\) 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
\(896\) −0.498470 0.778003i −0.0166527 0.0259913i
\(897\) −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
\(903\) −3.33024 72.0097i −0.110823 2.39633i
\(904\) 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
\(910\) −6.14603 + 1.79256i −0.203739 + 0.0594227i
\(911\) −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
\(917\) −15.6009 + 9.99556i −0.515187 + 0.330082i
\(918\) 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
\(924\) −1.77698 + 3.43517i −0.0584585 + 0.113009i
\(925\) 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
\(931\) 3.36139 + 36.2639i 0.110165 + 1.18850i
\(932\) −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
\(936\) −9.05385 + 30.7862i −0.295934 + 1.00628i
\(937\) 7.16949 0.234217 0.117109 0.993119i \(-0.462637\pi\)
0.117109 + 0.993119i \(0.462637\pi\)
\(938\) −26.2775 13.5931i −0.857990 0.443831i
\(939\) 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
\(945\) 0.191591 + 0.299032i 0.00623247 + 0.00972752i
\(946\) 8.51968 0.276999
\(947\) −38.2832 22.1028i −1.24404 0.718244i −0.274122 0.961695i \(-0.588387\pi\)
−0.969913 + 0.243451i \(0.921721\pi\)
\(948\) −4.03529 6.98933i −0.131060 0.227003i
\(949\) 12.6435 + 13.2714i 0.410426 + 0.430809i
\(950\) 12.8652 22.2832i 0.417403 0.722963i
\(951\) 59.8762i 1.94162i
\(952\) 27.0075 1.24902i 0.875320 0.0404810i
\(953\) 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
\(959\) −16.4309 + 0.759882i −0.530582 + 0.0245379i
\(960\) 12.0180i 0.387879i
\(961\) −5.86129 + 10.1520i −0.189074 + 0.327485i
\(962\) −1.18606 + 1.12995i −0.0382403 + 0.0364310i
\(963\) 8.90521 + 15.4243i 0.286966 + 0.497040i
\(964\) −2.04597 1.18124i −0.0658961 0.0380451i
\(965\) 14.3894 0.463211
\(966\) 16.5022 + 25.7563i 0.530948 + 0.828694i
\(967\) 43.9429i 1.41311i −0.707659 0.706554i \(-0.750249\pi\)
0.707659 0.706554i \(-0.249751\pi\)
\(968\) 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 −0.642764 0.766064i \(-0.722212\pi\)
0.984813 + 0.173618i \(0.0555458\pi\)
\(972\) 18.5525 0.595072
\(973\) −15.3485 7.93965i −0.492050 0.254533i
\(974\) −20.4400 −0.654941
\(975\) 38.7621 + 11.3995i 1.24138 + 0.365075i
\(976\) 3.71741 + 6.43874i 0.118991 + 0.206099i
\(977\) −14.2432 + 8.22330i −0.455679 + 0.263087i −0.710226 0.703974i \(-0.751407\pi\)
0.254547 + 0.967061i \(0.418074\pi\)
\(978\) 30.9286 53.5699i 0.988987 1.71298i
\(979\) −9.47937 −0.302962
\(980\) −3.03210 + 2.14651i −0.0968568 + 0.0685677i
\(981\) 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
\(987\) 23.8600 46.1249i 0.759472 1.46817i
\(988\) 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
\(994\) −33.6761 + 21.5764i −1.06814 + 0.684362i
\(995\) 7.45731i 0.236413i
\(996\) 18.2312 + 10.5258i 0.577679 + 0.333523i
\(997\) 2.34855 + 4.06781i 0.0743794 + 0.128829i 0.900816 0.434201i \(-0.142969\pi\)
−0.826437 + 0.563029i \(0.809636\pi\)
\(998\) 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 91.2.r.a.51.6 yes 16
3.2 odd 2 819.2.dl.e.415.3 16
7.2 even 3 637.2.c.f.246.3 8
7.3 odd 6 637.2.r.f.116.3 16
7.4 even 3 inner 91.2.r.a.25.3 16
7.5 odd 6 637.2.c.e.246.3 8
7.6 odd 2 637.2.r.f.324.6 16
13.5 odd 4 1183.2.e.i.170.6 16
13.8 odd 4 1183.2.e.i.170.3 16
13.12 even 2 inner 91.2.r.a.51.3 yes 16
21.11 odd 6 819.2.dl.e.298.6 16
39.38 odd 2 819.2.dl.e.415.6 16
91.5 even 12 8281.2.a.cj.1.3 8
91.12 odd 6 637.2.c.e.246.6 8
91.18 odd 12 1183.2.e.i.508.6 16
91.25 even 6 inner 91.2.r.a.25.6 yes 16
91.38 odd 6 637.2.r.f.116.6 16
91.44 odd 12 8281.2.a.ck.1.3 8
91.47 even 12 8281.2.a.cj.1.6 8
91.51 even 6 637.2.c.f.246.6 8
91.60 odd 12 1183.2.e.i.508.3 16
91.86 odd 12 8281.2.a.ck.1.6 8
91.90 odd 2 637.2.r.f.324.3 16
273.116 odd 6 819.2.dl.e.298.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.r.a.25.3 16 7.4 even 3 inner
91.2.r.a.25.6 yes 16 91.25 even 6 inner
91.2.r.a.51.3 yes 16 13.12 even 2 inner
91.2.r.a.51.6 yes 16 1.1 even 1 trivial
637.2.c.e.246.3 8 7.5 odd 6
637.2.c.e.246.6 8 91.12 odd 6
637.2.c.f.246.3 8 7.2 even 3
637.2.c.f.246.6 8 91.51 even 6
637.2.r.f.116.3 16 7.3 odd 6
637.2.r.f.116.6 16 91.38 odd 6
637.2.r.f.324.3 16 91.90 odd 2
637.2.r.f.324.6 16 7.6 odd 2
819.2.dl.e.298.3 16 273.116 odd 6
819.2.dl.e.298.6 16 21.11 odd 6
819.2.dl.e.415.3 16 3.2 odd 2
819.2.dl.e.415.6 16 39.38 odd 2
1183.2.e.i.170.3 16 13.8 odd 4
1183.2.e.i.170.6 16 13.5 odd 4
1183.2.e.i.508.3 16 91.60 odd 12
1183.2.e.i.508.6 16 91.18 odd 12
8281.2.a.cj.1.3 8 91.5 even 12
8281.2.a.cj.1.6 8 91.47 even 12
8281.2.a.ck.1.3 8 91.44 odd 12
8281.2.a.ck.1.6 8 91.86 odd 12