Properties

Label 546.2.q.j.335.4
Level $546$
Weight $2$
Character 546.335
Analytic conductor $4.360$
Analytic rank $0$
Dimension $24$
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] = [546,2,Mod(251,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.q (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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 335.4
Character \(\chi\) \(=\) 546.335
Dual form 546.2.q.j.251.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.17531 - 1.27226i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.58412i q^{5} +(0.514158 - 1.65398i) q^{6} +(-2.54363 - 0.727985i) q^{7} -1.00000 q^{8} +(-0.237306 + 2.99060i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.17531 - 1.27226i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.58412i q^{5} +(0.514158 - 1.65398i) q^{6} +(-2.54363 - 0.727985i) q^{7} -1.00000 q^{8} +(-0.237306 + 2.99060i) q^{9} +(3.10394 - 1.79206i) q^{10} +(0.630804 + 1.09258i) q^{11} +(1.68947 - 0.381715i) q^{12} +(-2.88239 + 2.16606i) q^{13} +(-0.641360 - 2.56684i) q^{14} +(-4.55994 + 4.21244i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.57988 + 2.73643i) q^{17} +(-2.70859 + 1.28979i) q^{18} +(0.386956 - 0.670228i) q^{19} +(3.10394 + 1.79206i) q^{20} +(2.06336 + 4.09177i) q^{21} +(-0.630804 + 1.09258i) q^{22} +(-7.28626 + 4.20672i) q^{23} +(1.17531 + 1.27226i) q^{24} -7.84590 q^{25} +(-3.31706 - 1.41319i) q^{26} +(4.08374 - 3.21296i) q^{27} +(1.90227 - 1.83885i) q^{28} +(6.76234 - 3.90424i) q^{29} +(-5.92805 - 1.84280i) q^{30} -7.70977 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.648666 - 2.08667i) q^{33} -3.15976 q^{34} +(-2.60918 + 9.11666i) q^{35} +(-2.47128 - 1.70081i) q^{36} +(-0.424035 + 0.244817i) q^{37} +0.773913 q^{38} +(6.14350 + 1.12137i) q^{39} +3.58412i q^{40} +(-1.17143 + 0.676327i) q^{41} +(-2.51190 + 3.83280i) q^{42} +(0.125032 - 0.216561i) q^{43} -1.26161 q^{44} +(10.7187 + 0.850531i) q^{45} +(-7.28626 - 4.20672i) q^{46} -10.9168i q^{47} +(-0.514158 + 1.65398i) q^{48} +(5.94008 + 3.70344i) q^{49} +(-3.92295 - 6.79475i) q^{50} +(5.33831 - 1.20613i) q^{51} +(-0.434672 - 3.57925i) q^{52} -12.1730i q^{53} +(4.82437 + 1.93014i) q^{54} +(3.91595 - 2.26088i) q^{55} +(2.54363 + 0.727985i) q^{56} +(-1.30750 + 0.295414i) q^{57} +(6.76234 + 3.90424i) q^{58} +(-10.4372 - 6.02594i) q^{59} +(-1.36811 - 6.05524i) q^{60} +(3.27341 + 1.88990i) q^{61} +(-3.85488 - 6.67685i) q^{62} +(2.78073 - 7.43422i) q^{63} +1.00000 q^{64} +(7.76343 + 10.3308i) q^{65} +(2.13144 - 0.481574i) q^{66} +(-10.4963 + 6.06005i) q^{67} +(-1.57988 - 2.73643i) q^{68} +(13.9157 + 4.32584i) q^{69} +(-9.19985 + 2.29871i) q^{70} +(0.0759653 - 0.131576i) q^{71} +(0.237306 - 2.99060i) q^{72} -10.3607 q^{73} +(-0.424035 - 0.244817i) q^{74} +(9.22134 + 9.98204i) q^{75} +(0.386956 + 0.670228i) q^{76} +(-0.809145 - 3.23834i) q^{77} +(2.10062 + 5.88111i) q^{78} +5.53840 q^{79} +(-3.10394 + 1.79206i) q^{80} +(-8.88737 - 1.41937i) q^{81} +(-1.17143 - 0.676327i) q^{82} -3.23534i q^{83} +(-4.57525 - 0.258966i) q^{84} +(9.80769 + 5.66247i) q^{85} +0.250064 q^{86} +(-12.9150 - 4.01479i) q^{87} +(-0.630804 - 1.09258i) q^{88} +(5.69791 - 3.28969i) q^{89} +(4.62275 + 9.70790i) q^{90} +(8.90858 - 3.41132i) q^{91} -8.41345i q^{92} +(9.06134 + 9.80885i) q^{93} +(9.45425 - 5.45842i) q^{94} +(-2.40218 - 1.38690i) q^{95} +(-1.68947 + 0.381715i) q^{96} +(-2.21400 + 3.83477i) q^{97} +(-0.237237 + 6.99598i) q^{98} +(-3.41718 + 1.62721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −1.17531 1.27226i −0.678564 0.734541i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 3.58412i 1.60287i −0.598085 0.801433i \(-0.704071\pi\)
0.598085 0.801433i \(-0.295929\pi\)
\(6\) 0.514158 1.65398i 0.209904 0.675233i
\(7\) −2.54363 0.727985i −0.961401 0.275152i
\(8\) −1.00000 −0.353553
\(9\) −0.237306 + 2.99060i −0.0791019 + 0.996867i
\(10\) 3.10394 1.79206i 0.981551 0.566699i
\(11\) 0.630804 + 1.09258i 0.190195 + 0.329427i 0.945315 0.326160i \(-0.105755\pi\)
−0.755120 + 0.655587i \(0.772421\pi\)
\(12\) 1.68947 0.381715i 0.487707 0.110191i
\(13\) −2.88239 + 2.16606i −0.799431 + 0.600758i
\(14\) −0.641360 2.56684i −0.171411 0.686016i
\(15\) −4.55994 + 4.21244i −1.17737 + 1.08765i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.57988 + 2.73643i −0.383177 + 0.663682i −0.991514 0.129996i \(-0.958503\pi\)
0.608337 + 0.793679i \(0.291837\pi\)
\(18\) −2.70859 + 1.28979i −0.638420 + 0.304006i
\(19\) 0.386956 0.670228i 0.0887739 0.153761i −0.818219 0.574906i \(-0.805038\pi\)
0.906993 + 0.421145i \(0.138372\pi\)
\(20\) 3.10394 + 1.79206i 0.694061 + 0.400716i
\(21\) 2.06336 + 4.09177i 0.450261 + 0.892897i
\(22\) −0.630804 + 1.09258i −0.134488 + 0.232940i
\(23\) −7.28626 + 4.20672i −1.51929 + 0.877162i −0.519548 + 0.854441i \(0.673900\pi\)
−0.999742 + 0.0227213i \(0.992767\pi\)
\(24\) 1.17531 + 1.27226i 0.239909 + 0.259700i
\(25\) −7.84590 −1.56918
\(26\) −3.31706 1.41319i −0.650529 0.277149i
\(27\) 4.08374 3.21296i 0.785915 0.618334i
\(28\) 1.90227 1.83885i 0.359495 0.347511i
\(29\) 6.76234 3.90424i 1.25574 0.724999i 0.283493 0.958974i \(-0.408507\pi\)
0.972243 + 0.233975i \(0.0751735\pi\)
\(30\) −5.92805 1.84280i −1.08231 0.336448i
\(31\) −7.70977 −1.38471 −0.692357 0.721555i \(-0.743428\pi\)
−0.692357 + 0.721555i \(0.743428\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0.648666 2.08667i 0.112918 0.363243i
\(34\) −3.15976 −0.541894
\(35\) −2.60918 + 9.11666i −0.441032 + 1.54100i
\(36\) −2.47128 1.70081i −0.411880 0.283469i
\(37\) −0.424035 + 0.244817i −0.0697109 + 0.0402476i −0.534450 0.845200i \(-0.679481\pi\)
0.464739 + 0.885447i \(0.346148\pi\)
\(38\) 0.773913 0.125545
\(39\) 6.14350 + 1.12137i 0.983747 + 0.179562i
\(40\) 3.58412i 0.566699i
\(41\) −1.17143 + 0.676327i −0.182947 + 0.105625i −0.588677 0.808369i \(-0.700351\pi\)
0.405730 + 0.913993i \(0.367017\pi\)
\(42\) −2.51190 + 3.83280i −0.387594 + 0.591414i
\(43\) 0.125032 0.216561i 0.0190672 0.0330253i −0.856334 0.516422i \(-0.827264\pi\)
0.875402 + 0.483396i \(0.160597\pi\)
\(44\) −1.26161 −0.190195
\(45\) 10.7187 + 0.850531i 1.59784 + 0.126790i
\(46\) −7.28626 4.20672i −1.07430 0.620248i
\(47\) 10.9168i 1.59238i −0.605044 0.796192i \(-0.706845\pi\)
0.605044 0.796192i \(-0.293155\pi\)
\(48\) −0.514158 + 1.65398i −0.0742124 + 0.238731i
\(49\) 5.94008 + 3.70344i 0.848582 + 0.529063i
\(50\) −3.92295 6.79475i −0.554789 0.960922i
\(51\) 5.33831 1.20613i 0.747512 0.168891i
\(52\) −0.434672 3.57925i −0.0602781 0.496353i
\(53\) 12.1730i 1.67208i −0.548665 0.836042i \(-0.684864\pi\)
0.548665 0.836042i \(-0.315136\pi\)
\(54\) 4.82437 + 1.93014i 0.656514 + 0.262659i
\(55\) 3.91595 2.26088i 0.528027 0.304856i
\(56\) 2.54363 + 0.727985i 0.339906 + 0.0972810i
\(57\) −1.30750 + 0.295414i −0.173182 + 0.0391285i
\(58\) 6.76234 + 3.90424i 0.887939 + 0.512652i
\(59\) −10.4372 6.02594i −1.35881 0.784510i −0.369348 0.929291i \(-0.620419\pi\)
−0.989464 + 0.144781i \(0.953752\pi\)
\(60\) −1.36811 6.05524i −0.176622 0.781728i
\(61\) 3.27341 + 1.88990i 0.419117 + 0.241977i 0.694699 0.719300i \(-0.255537\pi\)
−0.275583 + 0.961277i \(0.588871\pi\)
\(62\) −3.85488 6.67685i −0.489571 0.847961i
\(63\) 2.78073 7.43422i 0.350339 0.936623i
\(64\) 1.00000 0.125000
\(65\) 7.76343 + 10.3308i 0.962935 + 1.28138i
\(66\) 2.13144 0.481574i 0.262363 0.0592777i
\(67\) −10.4963 + 6.06005i −1.28233 + 0.740353i −0.977274 0.211981i \(-0.932008\pi\)
−0.305056 + 0.952335i \(0.598675\pi\)
\(68\) −1.57988 2.73643i −0.191589 0.331841i
\(69\) 13.9157 + 4.32584i 1.67525 + 0.520770i
\(70\) −9.19985 + 2.29871i −1.09959 + 0.274748i
\(71\) 0.0759653 0.131576i 0.00901542 0.0156152i −0.861482 0.507787i \(-0.830464\pi\)
0.870498 + 0.492172i \(0.163797\pi\)
\(72\) 0.237306 2.99060i 0.0279667 0.352446i
\(73\) −10.3607 −1.21263 −0.606315 0.795224i \(-0.707353\pi\)
−0.606315 + 0.795224i \(0.707353\pi\)
\(74\) −0.424035 0.244817i −0.0492930 0.0284593i
\(75\) 9.22134 + 9.98204i 1.06479 + 1.15263i
\(76\) 0.386956 + 0.670228i 0.0443869 + 0.0768804i
\(77\) −0.809145 3.23834i −0.0922107 0.369043i
\(78\) 2.10062 + 5.88111i 0.237848 + 0.665904i
\(79\) 5.53840 0.623118 0.311559 0.950227i \(-0.399149\pi\)
0.311559 + 0.950227i \(0.399149\pi\)
\(80\) −3.10394 + 1.79206i −0.347031 + 0.200358i
\(81\) −8.88737 1.41937i −0.987486 0.157708i
\(82\) −1.17143 0.676327i −0.129363 0.0746878i
\(83\) 3.23534i 0.355125i −0.984110 0.177562i \(-0.943179\pi\)
0.984110 0.177562i \(-0.0568211\pi\)
\(84\) −4.57525 0.258966i −0.499201 0.0282555i
\(85\) 9.80769 + 5.66247i 1.06379 + 0.614182i
\(86\) 0.250064 0.0269651
\(87\) −12.9150 4.01479i −1.38464 0.430431i
\(88\) −0.630804 1.09258i −0.0672439 0.116470i
\(89\) 5.69791 3.28969i 0.603977 0.348706i −0.166627 0.986020i \(-0.553288\pi\)
0.770605 + 0.637314i \(0.219954\pi\)
\(90\) 4.62275 + 9.70790i 0.487280 + 1.02330i
\(91\) 8.90858 3.41132i 0.933873 0.357604i
\(92\) 8.41345i 0.877162i
\(93\) 9.06134 + 9.80885i 0.939618 + 1.01713i
\(94\) 9.45425 5.45842i 0.975132 0.562993i
\(95\) −2.40218 1.38690i −0.246458 0.142293i
\(96\) −1.68947 + 0.381715i −0.172430 + 0.0389586i
\(97\) −2.21400 + 3.83477i −0.224798 + 0.389361i −0.956259 0.292522i \(-0.905506\pi\)
0.731461 + 0.681883i \(0.238839\pi\)
\(98\) −0.237237 + 6.99598i −0.0239646 + 0.706701i
\(99\) −3.41718 + 1.62721i −0.343439 + 0.163540i
\(100\) 3.92295 6.79475i 0.392295 0.679475i
\(101\) −0.490495 0.849562i −0.0488061 0.0845346i 0.840590 0.541671i \(-0.182208\pi\)
−0.889396 + 0.457137i \(0.848875\pi\)
\(102\) 3.71369 + 4.02005i 0.367710 + 0.398044i
\(103\) 15.6826i 1.54525i 0.634860 + 0.772627i \(0.281058\pi\)
−0.634860 + 0.772627i \(0.718942\pi\)
\(104\) 2.88239 2.16606i 0.282642 0.212400i
\(105\) 14.6654 7.39531i 1.43119 0.721708i
\(106\) 10.5421 6.08648i 1.02394 0.591171i
\(107\) −4.25464 + 2.45642i −0.411311 + 0.237471i −0.691353 0.722517i \(-0.742985\pi\)
0.280042 + 0.959988i \(0.409652\pi\)
\(108\) 0.740636 + 5.14310i 0.0712677 + 0.494895i
\(109\) 5.99158i 0.573889i −0.957947 0.286945i \(-0.907360\pi\)
0.957947 0.286945i \(-0.0926395\pi\)
\(110\) 3.91595 + 2.26088i 0.373371 + 0.215566i
\(111\) 0.809842 + 0.251749i 0.0768668 + 0.0238950i
\(112\) 0.641360 + 2.56684i 0.0606029 + 0.242543i
\(113\) 13.7438 + 7.93500i 1.29291 + 0.746462i 0.979169 0.203047i \(-0.0650843\pi\)
0.313741 + 0.949509i \(0.398418\pi\)
\(114\) −0.909585 0.984620i −0.0851905 0.0922181i
\(115\) 15.0774 + 26.1148i 1.40597 + 2.43522i
\(116\) 7.80848i 0.724999i
\(117\) −5.79382 9.13409i −0.535639 0.844447i
\(118\) 12.0519i 1.10946i
\(119\) 6.01071 5.81033i 0.551000 0.532633i
\(120\) 4.55994 4.21244i 0.416264 0.384541i
\(121\) 4.70417 8.14787i 0.427652 0.740715i
\(122\) 3.77980i 0.342207i
\(123\) 2.23726 + 0.695478i 0.201727 + 0.0627092i
\(124\) 3.85488 6.67685i 0.346179 0.599599i
\(125\) 10.2000i 0.912318i
\(126\) 7.82858 1.30893i 0.697426 0.116608i
\(127\) −5.41129 9.37263i −0.480174 0.831686i 0.519567 0.854430i \(-0.326093\pi\)
−0.999741 + 0.0227433i \(0.992760\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −0.422474 + 0.0954529i −0.0371967 + 0.00840416i
\(130\) −5.06504 + 11.8887i −0.444233 + 1.04271i
\(131\) −13.6129 −1.18936 −0.594682 0.803961i \(-0.702722\pi\)
−0.594682 + 0.803961i \(0.702722\pi\)
\(132\) 1.48278 + 1.60510i 0.129059 + 0.139706i
\(133\) −1.47219 + 1.42311i −0.127655 + 0.123399i
\(134\) −10.4963 6.06005i −0.906744 0.523509i
\(135\) −11.5156 14.6366i −0.991107 1.25972i
\(136\) 1.57988 2.73643i 0.135474 0.234647i
\(137\) 1.10639 1.91632i 0.0945251 0.163722i −0.814885 0.579622i \(-0.803200\pi\)
0.909410 + 0.415900i \(0.136533\pi\)
\(138\) 3.21153 + 14.2142i 0.273384 + 1.21000i
\(139\) 2.92041 + 1.68610i 0.247706 + 0.143013i 0.618713 0.785617i \(-0.287654\pi\)
−0.371007 + 0.928630i \(0.620988\pi\)
\(140\) −6.59067 6.81795i −0.557013 0.576222i
\(141\) −13.8891 + 12.8306i −1.16967 + 1.08053i
\(142\) 0.151931 0.0127497
\(143\) −4.18483 1.78289i −0.349953 0.149093i
\(144\) 2.70859 1.28979i 0.225716 0.107482i
\(145\) −13.9933 24.2370i −1.16208 2.01277i
\(146\) −5.18036 8.97264i −0.428730 0.742581i
\(147\) −2.26966 11.9100i −0.187199 0.982322i
\(148\) 0.489633i 0.0402476i
\(149\) 2.67228 4.62852i 0.218922 0.379183i −0.735557 0.677463i \(-0.763079\pi\)
0.954479 + 0.298279i \(0.0964127\pi\)
\(150\) −4.03403 + 12.9769i −0.329377 + 1.05956i
\(151\) 13.2645i 1.07945i −0.841842 0.539723i \(-0.818529\pi\)
0.841842 0.539723i \(-0.181471\pi\)
\(152\) −0.386956 + 0.670228i −0.0313863 + 0.0543627i
\(153\) −7.80866 5.37416i −0.631293 0.434475i
\(154\) 2.39991 2.31991i 0.193391 0.186944i
\(155\) 27.6327i 2.21951i
\(156\) −4.04288 + 4.75974i −0.323689 + 0.381084i
\(157\) 5.83056i 0.465329i −0.972557 0.232665i \(-0.925256\pi\)
0.972557 0.232665i \(-0.0747444\pi\)
\(158\) 2.76920 + 4.79639i 0.220306 + 0.381581i
\(159\) −15.4872 + 14.3070i −1.22822 + 1.13462i
\(160\) −3.10394 1.79206i −0.245388 0.141675i
\(161\) 21.5960 5.39605i 1.70200 0.425268i
\(162\) −3.21447 8.40638i −0.252553 0.660467i
\(163\) 16.1748 + 9.33852i 1.26691 + 0.731449i 0.974402 0.224815i \(-0.0721777\pi\)
0.292506 + 0.956264i \(0.405511\pi\)
\(164\) 1.35265i 0.105625i
\(165\) −7.47887 2.32490i −0.582230 0.180993i
\(166\) 2.80189 1.61767i 0.217468 0.125555i
\(167\) 2.79787 1.61535i 0.216505 0.124999i −0.387826 0.921733i \(-0.626774\pi\)
0.604331 + 0.796733i \(0.293440\pi\)
\(168\) −2.06336 4.09177i −0.159191 0.315687i
\(169\) 3.61634 12.4869i 0.278180 0.960529i
\(170\) 11.3249i 0.868584i
\(171\) 1.91256 + 1.31628i 0.146257 + 0.100658i
\(172\) 0.125032 + 0.216561i 0.00953359 + 0.0165127i
\(173\) −7.02069 + 12.1602i −0.533773 + 0.924522i 0.465449 + 0.885075i \(0.345893\pi\)
−0.999222 + 0.0394472i \(0.987440\pi\)
\(174\) −2.98061 13.1922i −0.225959 1.00009i
\(175\) 19.9570 + 5.71169i 1.50861 + 0.431763i
\(176\) 0.630804 1.09258i 0.0475486 0.0823567i
\(177\) 4.60038 + 20.3612i 0.345785 + 1.53044i
\(178\) 5.69791 + 3.28969i 0.427076 + 0.246573i
\(179\) −7.80209 + 4.50454i −0.583156 + 0.336685i −0.762386 0.647122i \(-0.775972\pi\)
0.179231 + 0.983807i \(0.442639\pi\)
\(180\) −6.09591 + 8.85737i −0.454362 + 0.660189i
\(181\) 13.9831i 1.03935i 0.854363 + 0.519676i \(0.173947\pi\)
−0.854363 + 0.519676i \(0.826053\pi\)
\(182\) 7.40858 + 6.00940i 0.549161 + 0.445446i
\(183\) −1.44281 6.38585i −0.106655 0.472055i
\(184\) 7.28626 4.20672i 0.537150 0.310124i
\(185\) 0.877451 + 1.51979i 0.0645115 + 0.111737i
\(186\) −3.96404 + 12.7518i −0.290658 + 0.935006i
\(187\) −3.98638 −0.291513
\(188\) 9.45425 + 5.45842i 0.689522 + 0.398096i
\(189\) −12.7265 + 5.19967i −0.925716 + 0.378220i
\(190\) 2.77379i 0.201232i
\(191\) −19.5584 11.2921i −1.41520 0.817066i −0.419328 0.907835i \(-0.637734\pi\)
−0.995872 + 0.0907692i \(0.971067\pi\)
\(192\) −1.17531 1.27226i −0.0848205 0.0918177i
\(193\) −6.75717 + 3.90126i −0.486392 + 0.280819i −0.723076 0.690768i \(-0.757273\pi\)
0.236684 + 0.971587i \(0.423939\pi\)
\(194\) −4.42801 −0.317912
\(195\) 4.01911 22.0190i 0.287814 1.57681i
\(196\) −6.17731 + 3.29254i −0.441237 + 0.235181i
\(197\) −8.91140 15.4350i −0.634911 1.09970i −0.986534 0.163557i \(-0.947703\pi\)
0.351623 0.936142i \(-0.385630\pi\)
\(198\) −3.11779 2.14576i −0.221572 0.152492i
\(199\) 8.97099 + 5.17941i 0.635937 + 0.367158i 0.783048 0.621962i \(-0.213664\pi\)
−0.147111 + 0.989120i \(0.546997\pi\)
\(200\) 7.84590 0.554789
\(201\) 20.0464 + 6.23165i 1.41396 + 0.439547i
\(202\) 0.490495 0.849562i 0.0345111 0.0597750i
\(203\) −20.0431 + 5.00805i −1.40675 + 0.351496i
\(204\) −1.62462 + 5.22617i −0.113746 + 0.365905i
\(205\) 2.42403 + 4.19855i 0.169302 + 0.293240i
\(206\) −13.5815 + 7.84131i −0.946271 + 0.546330i
\(207\) −10.8516 22.7886i −0.754235 1.58391i
\(208\) 3.31706 + 1.41319i 0.229997 + 0.0979871i
\(209\) 0.976374 0.0675372
\(210\) 13.7372 + 9.00293i 0.947958 + 0.621261i
\(211\) −1.30125 2.25382i −0.0895814 0.155160i 0.817753 0.575570i \(-0.195220\pi\)
−0.907334 + 0.420410i \(0.861886\pi\)
\(212\) 10.5421 + 6.08648i 0.724034 + 0.418021i
\(213\) −0.256681 + 0.0579941i −0.0175875 + 0.00397369i
\(214\) −4.25464 2.45642i −0.290841 0.167917i
\(215\) −0.776182 0.448129i −0.0529351 0.0305621i
\(216\) −4.08374 + 3.21296i −0.277863 + 0.218614i
\(217\) 19.6108 + 5.61259i 1.33127 + 0.381007i
\(218\) 5.18886 2.99579i 0.351434 0.202900i
\(219\) 12.1770 + 13.1816i 0.822847 + 0.890727i
\(220\) 4.52175i 0.304856i
\(221\) −1.37346 11.3096i −0.0923888 0.760765i
\(222\) 0.186900 + 0.827218i 0.0125439 + 0.0555193i
\(223\) −6.59396 11.4211i −0.441564 0.764812i 0.556242 0.831021i \(-0.312243\pi\)
−0.997806 + 0.0662090i \(0.978910\pi\)
\(224\) −1.90227 + 1.83885i −0.127101 + 0.122864i
\(225\) 1.86188 23.4639i 0.124125 1.56426i
\(226\) 15.8700i 1.05566i
\(227\) 19.5736 + 11.3008i 1.29914 + 0.750060i 0.980256 0.197733i \(-0.0633578\pi\)
0.318886 + 0.947793i \(0.396691\pi\)
\(228\) 0.397914 1.28003i 0.0263525 0.0847723i
\(229\) −0.457707 −0.0302461 −0.0151230 0.999886i \(-0.504814\pi\)
−0.0151230 + 0.999886i \(0.504814\pi\)
\(230\) −15.0774 + 26.1148i −0.994174 + 1.72196i
\(231\) −3.16903 + 4.83549i −0.208507 + 0.318152i
\(232\) −6.76234 + 3.90424i −0.443969 + 0.256326i
\(233\) 15.7117i 1.02931i −0.857398 0.514654i \(-0.827921\pi\)
0.857398 0.514654i \(-0.172079\pi\)
\(234\) 5.01344 9.58464i 0.327739 0.626568i
\(235\) −39.1272 −2.55238
\(236\) 10.4372 6.02594i 0.679406 0.392255i
\(237\) −6.50932 7.04630i −0.422826 0.457706i
\(238\) 8.03725 + 2.30026i 0.520978 + 0.149103i
\(239\) 18.8837 1.22148 0.610741 0.791830i \(-0.290872\pi\)
0.610741 + 0.791830i \(0.290872\pi\)
\(240\) 5.92805 + 1.84280i 0.382654 + 0.118952i
\(241\) 9.49057 16.4382i 0.611341 1.05887i −0.379673 0.925121i \(-0.623964\pi\)
0.991015 0.133754i \(-0.0427031\pi\)
\(242\) 9.40835 0.604791
\(243\) 8.63958 + 12.9753i 0.554229 + 0.832364i
\(244\) −3.27341 + 1.88990i −0.209558 + 0.120989i
\(245\) 13.2736 21.2899i 0.848017 1.36016i
\(246\) 0.516328 + 2.28526i 0.0329198 + 0.145703i
\(247\) 0.336398 + 2.77003i 0.0214045 + 0.176253i
\(248\) 7.70977 0.489571
\(249\) −4.11620 + 3.80252i −0.260854 + 0.240975i
\(250\) −8.83348 + 5.10001i −0.558678 + 0.322553i
\(251\) −2.20065 + 3.81164i −0.138904 + 0.240588i −0.927082 0.374859i \(-0.877691\pi\)
0.788178 + 0.615447i \(0.211025\pi\)
\(252\) 5.04786 + 6.12529i 0.317985 + 0.385857i
\(253\) −9.19240 5.30724i −0.577921 0.333663i
\(254\) 5.41129 9.37263i 0.339535 0.588091i
\(255\) −4.32290 19.1331i −0.270710 1.19816i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −4.37736 7.58182i −0.273052 0.472941i 0.696589 0.717470i \(-0.254700\pi\)
−0.969642 + 0.244529i \(0.921367\pi\)
\(258\) −0.293902 0.318147i −0.0182975 0.0198069i
\(259\) 1.25681 0.314031i 0.0780943 0.0195130i
\(260\) −12.8285 + 1.55791i −0.795588 + 0.0966177i
\(261\) 10.0713 + 21.1500i 0.623396 + 1.30915i
\(262\) −6.80645 11.7891i −0.420504 0.728334i
\(263\) −10.3649 + 5.98418i −0.639128 + 0.369000i −0.784278 0.620409i \(-0.786967\pi\)
0.145151 + 0.989410i \(0.453633\pi\)
\(264\) −0.648666 + 2.08667i −0.0399226 + 0.128426i
\(265\) −43.6293 −2.68013
\(266\) −1.96855 0.563396i −0.120699 0.0345441i
\(267\) −10.8821 3.38284i −0.665976 0.207027i
\(268\) 12.1201i 0.740353i
\(269\) 1.75697 3.04316i 0.107124 0.185545i −0.807480 0.589895i \(-0.799169\pi\)
0.914604 + 0.404350i \(0.132502\pi\)
\(270\) 6.91785 17.2911i 0.421007 1.05230i
\(271\) −1.27260 2.20420i −0.0773046 0.133896i 0.824782 0.565452i \(-0.191298\pi\)
−0.902086 + 0.431556i \(0.857965\pi\)
\(272\) 3.15976 0.191589
\(273\) −14.8104 7.32471i −0.896368 0.443311i
\(274\) 2.21278 0.133679
\(275\) −4.94922 8.57230i −0.298449 0.516929i
\(276\) −10.7041 + 9.88839i −0.644312 + 0.595211i
\(277\) −6.92333 + 11.9916i −0.415983 + 0.720503i −0.995531 0.0944347i \(-0.969896\pi\)
0.579548 + 0.814938i \(0.303229\pi\)
\(278\) 3.37220i 0.202251i
\(279\) 1.82957 23.0568i 0.109534 1.38038i
\(280\) 2.60918 9.11666i 0.155928 0.544824i
\(281\) −15.0793 −0.899556 −0.449778 0.893140i \(-0.648497\pi\)
−0.449778 + 0.893140i \(0.648497\pi\)
\(282\) −18.0562 5.61298i −1.07523 0.334248i
\(283\) −2.40604 + 1.38913i −0.143024 + 0.0825752i −0.569805 0.821780i \(-0.692981\pi\)
0.426780 + 0.904355i \(0.359648\pi\)
\(284\) 0.0759653 + 0.131576i 0.00450771 + 0.00780758i
\(285\) 1.05880 + 4.68623i 0.0627177 + 0.277588i
\(286\) −0.548385 4.51562i −0.0324267 0.267014i
\(287\) 3.47204 0.867538i 0.204948 0.0512092i
\(288\) 2.47128 + 1.70081i 0.145622 + 0.100221i
\(289\) 3.50796 + 6.07596i 0.206351 + 0.357410i
\(290\) 13.9933 24.2370i 0.821712 1.42325i
\(291\) 7.48096 1.69023i 0.438542 0.0990833i
\(292\) 5.18036 8.97264i 0.303158 0.525084i
\(293\) 3.84106 + 2.21763i 0.224397 + 0.129556i 0.607985 0.793949i \(-0.291978\pi\)
−0.383588 + 0.923504i \(0.625312\pi\)
\(294\) 9.17955 7.92060i 0.535362 0.461939i
\(295\) −21.5977 + 37.4083i −1.25746 + 2.17799i
\(296\) 0.424035 0.244817i 0.0246465 0.0142297i
\(297\) 6.08647 + 2.43508i 0.353173 + 0.141298i
\(298\) 5.34456 0.309602
\(299\) 11.8898 27.9079i 0.687605 1.61396i
\(300\) −13.2554 + 2.99489i −0.765299 + 0.172910i
\(301\) −0.475688 + 0.459830i −0.0274182 + 0.0265042i
\(302\) 11.4874 6.63223i 0.661024 0.381642i
\(303\) −0.504384 + 1.62254i −0.0289761 + 0.0932122i
\(304\) −0.773913 −0.0443869
\(305\) 6.77363 11.7323i 0.387857 0.671788i
\(306\) 0.749829 9.44958i 0.0428649 0.540196i
\(307\) 18.1869 1.03798 0.518990 0.854780i \(-0.326308\pi\)
0.518990 + 0.854780i \(0.326308\pi\)
\(308\) 3.20906 + 0.918431i 0.182853 + 0.0523325i
\(309\) 19.9524 18.4319i 1.13505 1.04855i
\(310\) −23.9306 + 13.8164i −1.35917 + 0.784716i
\(311\) −7.71151 −0.437279 −0.218640 0.975806i \(-0.570162\pi\)
−0.218640 + 0.975806i \(0.570162\pi\)
\(312\) −6.14350 1.12137i −0.347807 0.0634849i
\(313\) 15.8942i 0.898391i 0.893433 + 0.449196i \(0.148289\pi\)
−0.893433 + 0.449196i \(0.851711\pi\)
\(314\) 5.04941 2.91528i 0.284955 0.164519i
\(315\) −26.6451 9.96645i −1.50128 0.561546i
\(316\) −2.76920 + 4.79639i −0.155780 + 0.269818i
\(317\) −6.00739 −0.337409 −0.168704 0.985667i \(-0.553958\pi\)
−0.168704 + 0.985667i \(0.553958\pi\)
\(318\) −20.1338 6.25883i −1.12905 0.350978i
\(319\) 8.53142 + 4.92562i 0.477668 + 0.275782i
\(320\) 3.58412i 0.200358i
\(321\) 8.12571 + 2.52597i 0.453533 + 0.140986i
\(322\) 15.4711 + 16.0046i 0.862170 + 0.891903i
\(323\) 1.22269 + 2.11776i 0.0680322 + 0.117835i
\(324\) 5.67290 6.98700i 0.315161 0.388167i
\(325\) 22.6149 16.9947i 1.25445 0.942697i
\(326\) 18.6770i 1.03443i
\(327\) −7.62286 + 7.04194i −0.421545 + 0.389420i
\(328\) 1.17143 0.676327i 0.0646815 0.0373439i
\(329\) −7.94728 + 27.7683i −0.438148 + 1.53092i
\(330\) −1.72602 7.63934i −0.0950142 0.420532i
\(331\) −14.2730 8.24050i −0.784513 0.452939i 0.0535143 0.998567i \(-0.482958\pi\)
−0.838027 + 0.545628i \(0.816291\pi\)
\(332\) 2.80189 + 1.61767i 0.153773 + 0.0887811i
\(333\) −0.631522 1.32621i −0.0346072 0.0726761i
\(334\) 2.79787 + 1.61535i 0.153092 + 0.0883880i
\(335\) 21.7199 + 37.6200i 1.18669 + 2.05540i
\(336\) 2.51190 3.83280i 0.137035 0.209097i
\(337\) −28.6451 −1.56040 −0.780200 0.625530i \(-0.784883\pi\)
−0.780200 + 0.625530i \(0.784883\pi\)
\(338\) 12.6221 3.11160i 0.686553 0.169249i
\(339\) −6.05781 26.8118i −0.329015 1.45622i
\(340\) −9.80769 + 5.66247i −0.531897 + 0.307091i
\(341\) −4.86335 8.42357i −0.263365 0.456162i
\(342\) −0.183654 + 2.31446i −0.00993086 + 0.125152i
\(343\) −12.4133 13.7445i −0.670255 0.742131i
\(344\) −0.125032 + 0.216561i −0.00674126 + 0.0116762i
\(345\) 15.5043 49.8753i 0.834725 2.68520i
\(346\) −14.0414 −0.754869
\(347\) −18.8271 10.8698i −1.01069 0.583522i −0.0992964 0.995058i \(-0.531659\pi\)
−0.911394 + 0.411536i \(0.864993\pi\)
\(348\) 9.93444 9.17736i 0.532542 0.491958i
\(349\) 13.3083 + 23.0507i 0.712377 + 1.23387i 0.963962 + 0.266038i \(0.0857147\pi\)
−0.251585 + 0.967835i \(0.580952\pi\)
\(350\) 5.03205 + 20.1391i 0.268974 + 1.07648i
\(351\) −4.81144 + 18.1066i −0.256816 + 0.966460i
\(352\) 1.26161 0.0672439
\(353\) 22.2718 12.8586i 1.18541 0.684396i 0.228149 0.973626i \(-0.426733\pi\)
0.957259 + 0.289231i \(0.0933995\pi\)
\(354\) −15.3332 + 14.1647i −0.814948 + 0.752843i
\(355\) −0.471583 0.272268i −0.0250290 0.0144505i
\(356\) 6.57938i 0.348706i
\(357\) −14.4567 0.818269i −0.765130 0.0433074i
\(358\) −7.80209 4.50454i −0.412353 0.238072i
\(359\) 9.32911 0.492372 0.246186 0.969223i \(-0.420823\pi\)
0.246186 + 0.969223i \(0.420823\pi\)
\(360\) −10.7187 0.850531i −0.564923 0.0448269i
\(361\) 9.20053 + 15.9358i 0.484238 + 0.838726i
\(362\) −12.1097 + 6.99153i −0.636470 + 0.367466i
\(363\) −15.8951 + 3.59130i −0.834275 + 0.188494i
\(364\) −1.50000 + 9.42072i −0.0786213 + 0.493780i
\(365\) 37.1340i 1.94368i
\(366\) 4.80890 4.44243i 0.251365 0.232210i
\(367\) −8.31827 + 4.80255i −0.434210 + 0.250691i −0.701139 0.713025i \(-0.747325\pi\)
0.266928 + 0.963716i \(0.413991\pi\)
\(368\) 7.28626 + 4.20672i 0.379822 + 0.219291i
\(369\) −1.74464 3.66378i −0.0908221 0.190729i
\(370\) −0.877451 + 1.51979i −0.0456165 + 0.0790101i
\(371\) −8.86173 + 30.9635i −0.460078 + 1.60754i
\(372\) −13.0254 + 2.94293i −0.675335 + 0.152584i
\(373\) 8.44383 14.6251i 0.437205 0.757262i −0.560268 0.828312i \(-0.689302\pi\)
0.997473 + 0.0710501i \(0.0226350\pi\)
\(374\) −1.99319 3.45230i −0.103065 0.178514i
\(375\) 12.9771 11.9882i 0.670135 0.619066i
\(376\) 10.9168i 0.562993i
\(377\) −11.0349 + 25.9012i −0.568325 + 1.33398i
\(378\) −10.8663 8.42162i −0.558902 0.433162i
\(379\) 25.2872 14.5996i 1.29892 0.749930i 0.318700 0.947856i \(-0.396754\pi\)
0.980217 + 0.197925i \(0.0634203\pi\)
\(380\) 2.40218 1.38690i 0.123229 0.0711463i
\(381\) −5.56452 + 17.9003i −0.285079 + 0.917060i
\(382\) 22.5841i 1.15551i
\(383\) −7.31222 4.22171i −0.373637 0.215719i 0.301409 0.953495i \(-0.402543\pi\)
−0.675046 + 0.737775i \(0.735876\pi\)
\(384\) 0.514158 1.65398i 0.0262380 0.0844042i
\(385\) −11.6066 + 2.90007i −0.591527 + 0.147801i
\(386\) −6.75717 3.90126i −0.343931 0.198569i
\(387\) 0.617978 + 0.425311i 0.0314136 + 0.0216198i
\(388\) −2.21400 3.83477i −0.112399 0.194681i
\(389\) 0.653576i 0.0331376i −0.999863 0.0165688i \(-0.994726\pi\)
0.999863 0.0165688i \(-0.00527425\pi\)
\(390\) 21.0786 7.52885i 1.06736 0.381238i
\(391\) 26.5845i 1.34443i
\(392\) −5.94008 3.70344i −0.300019 0.187052i
\(393\) 15.9993 + 17.3192i 0.807060 + 0.873637i
\(394\) 8.91140 15.4350i 0.448950 0.777604i
\(395\) 19.8503i 0.998775i
\(396\) 0.299387 3.77296i 0.0150447 0.189599i
\(397\) −2.51686 + 4.35932i −0.126317 + 0.218788i −0.922247 0.386601i \(-0.873649\pi\)
0.795930 + 0.605389i \(0.206982\pi\)
\(398\) 10.3588i 0.519240i
\(399\) 3.54085 + 0.200417i 0.177264 + 0.0100334i
\(400\) 3.92295 + 6.79475i 0.196147 + 0.339737i
\(401\) 10.4095 + 18.0297i 0.519824 + 0.900361i 0.999734 + 0.0230440i \(0.00733579\pi\)
−0.479911 + 0.877317i \(0.659331\pi\)
\(402\) 4.62642 + 20.4765i 0.230745 + 1.02127i
\(403\) 22.2225 16.6998i 1.10698 0.831878i
\(404\) 0.980990 0.0488061
\(405\) −5.08720 + 31.8534i −0.252785 + 1.58281i
\(406\) −14.3586 14.8538i −0.712608 0.737182i
\(407\) −0.534966 0.308863i −0.0265173 0.0153097i
\(408\) −5.33831 + 1.20613i −0.264286 + 0.0597121i
\(409\) −14.6945 + 25.4516i −0.726594 + 1.25850i 0.231720 + 0.972783i \(0.425565\pi\)
−0.958314 + 0.285716i \(0.907769\pi\)
\(410\) −2.42403 + 4.19855i −0.119715 + 0.207352i
\(411\) −3.73841 + 0.844649i −0.184402 + 0.0416635i
\(412\) −13.5815 7.84131i −0.669115 0.386314i
\(413\) 22.1616 + 22.9259i 1.09050 + 1.12811i
\(414\) 14.3097 20.7920i 0.703283 1.02187i
\(415\) −11.5958 −0.569217
\(416\) 0.434672 + 3.57925i 0.0213115 + 0.175487i
\(417\) −1.28722 5.69722i −0.0630353 0.278994i
\(418\) 0.488187 + 0.845565i 0.0238780 + 0.0413579i
\(419\) 11.2918 + 19.5580i 0.551640 + 0.955469i 0.998156 + 0.0606934i \(0.0193312\pi\)
−0.446516 + 0.894776i \(0.647335\pi\)
\(420\) −0.928163 + 16.3982i −0.0452897 + 0.800152i
\(421\) 28.5241i 1.39018i 0.718922 + 0.695091i \(0.244636\pi\)
−0.718922 + 0.695091i \(0.755364\pi\)
\(422\) 1.30125 2.25382i 0.0633436 0.109714i
\(423\) 32.6479 + 2.59063i 1.58739 + 0.125961i
\(424\) 12.1730i 0.591171i
\(425\) 12.3956 21.4698i 0.601274 1.04144i
\(426\) −0.178565 0.193296i −0.00865151 0.00936520i
\(427\) −6.95050 7.19019i −0.336358 0.347958i
\(428\) 4.91283i 0.237471i
\(429\) 2.65015 + 7.41965i 0.127951 + 0.358224i
\(430\) 0.896257i 0.0432214i
\(431\) −3.76847 6.52718i −0.181521 0.314403i 0.760878 0.648895i \(-0.224769\pi\)
−0.942399 + 0.334492i \(0.891435\pi\)
\(432\) −4.82437 1.93014i −0.232113 0.0928639i
\(433\) −28.3474 16.3664i −1.36229 0.786518i −0.372361 0.928088i \(-0.621452\pi\)
−0.989928 + 0.141570i \(0.954785\pi\)
\(434\) 4.94474 + 19.7897i 0.237355 + 0.949937i
\(435\) −14.3895 + 46.2890i −0.689923 + 2.21939i
\(436\) 5.18886 + 2.99579i 0.248501 + 0.143472i
\(437\) 6.51127i 0.311476i
\(438\) −5.32705 + 17.1364i −0.254536 + 0.818808i
\(439\) 21.2278 12.2559i 1.01315 0.584940i 0.101035 0.994883i \(-0.467785\pi\)
0.912111 + 0.409943i \(0.134451\pi\)
\(440\) −3.91595 + 2.26088i −0.186686 + 0.107783i
\(441\) −12.4851 + 16.8855i −0.594530 + 0.804074i
\(442\) 9.10766 6.84424i 0.433207 0.325547i
\(443\) 10.7332i 0.509951i 0.966948 + 0.254975i \(0.0820674\pi\)
−0.966948 + 0.254975i \(0.917933\pi\)
\(444\) −0.622942 + 0.575469i −0.0295635 + 0.0273106i
\(445\) −11.7906 20.4220i −0.558930 0.968095i
\(446\) 6.59396 11.4211i 0.312233 0.540803i
\(447\) −9.02945 + 2.04010i −0.427078 + 0.0964932i
\(448\) −2.54363 0.727985i −0.120175 0.0343940i
\(449\) −19.7420 + 34.1941i −0.931683 + 1.61372i −0.151237 + 0.988497i \(0.548326\pi\)
−0.780445 + 0.625224i \(0.785008\pi\)
\(450\) 21.2513 10.1195i 1.00180 0.477040i
\(451\) −1.47789 0.853259i −0.0695910 0.0401784i
\(452\) −13.7438 + 7.93500i −0.646455 + 0.373231i
\(453\) −16.8759 + 15.5898i −0.792898 + 0.732474i
\(454\) 22.6016i 1.06075i
\(455\) −12.2266 31.9294i −0.573191 1.49687i
\(456\) 1.30750 0.295414i 0.0612292 0.0138340i
\(457\) 9.89907 5.71523i 0.463059 0.267347i −0.250271 0.968176i \(-0.580520\pi\)
0.713330 + 0.700829i \(0.247186\pi\)
\(458\) −0.228853 0.396385i −0.0106936 0.0185219i
\(459\) 2.34023 + 16.2510i 0.109233 + 0.758530i
\(460\) −30.1548 −1.40597
\(461\) −8.42605 4.86478i −0.392440 0.226576i 0.290777 0.956791i \(-0.406086\pi\)
−0.683217 + 0.730215i \(0.739420\pi\)
\(462\) −5.77217 0.326713i −0.268546 0.0152001i
\(463\) 26.6572i 1.23887i −0.785050 0.619433i \(-0.787363\pi\)
0.785050 0.619433i \(-0.212637\pi\)
\(464\) −6.76234 3.90424i −0.313934 0.181250i
\(465\) 35.1561 32.4769i 1.63032 1.50608i
\(466\) 13.6067 7.85585i 0.630319 0.363915i
\(467\) 6.02179 0.278655 0.139328 0.990246i \(-0.455506\pi\)
0.139328 + 0.990246i \(0.455506\pi\)
\(468\) 10.8073 0.450552i 0.499566 0.0208268i
\(469\) 31.1103 7.77335i 1.43654 0.358940i
\(470\) −19.5636 33.8851i −0.902402 1.56301i
\(471\) −7.41800 + 6.85270i −0.341803 + 0.315756i
\(472\) 10.4372 + 6.02594i 0.480412 + 0.277366i
\(473\) 0.315482 0.0145059
\(474\) 2.84761 9.16038i 0.130795 0.420750i
\(475\) −3.03602 + 5.25854i −0.139302 + 0.241278i
\(476\) 2.02654 + 8.11059i 0.0928865 + 0.371748i
\(477\) 36.4045 + 2.88871i 1.66685 + 0.132265i
\(478\) 9.44183 + 16.3537i 0.431859 + 0.748002i
\(479\) −7.74812 + 4.47338i −0.354021 + 0.204394i −0.666455 0.745546i \(-0.732189\pi\)
0.312434 + 0.949939i \(0.398856\pi\)
\(480\) 1.36811 + 6.05524i 0.0624454 + 0.276383i
\(481\) 0.691945 1.62414i 0.0315500 0.0740545i
\(482\) 18.9811 0.864567
\(483\) −32.2471 21.1337i −1.46729 0.961617i
\(484\) 4.70417 + 8.14787i 0.213826 + 0.370358i
\(485\) 13.7442 + 7.93525i 0.624094 + 0.360321i
\(486\) −6.91713 + 13.9697i −0.313767 + 0.633680i
\(487\) 25.3833 + 14.6550i 1.15023 + 0.664083i 0.948942 0.315450i \(-0.102155\pi\)
0.201284 + 0.979533i \(0.435489\pi\)
\(488\) −3.27341 1.88990i −0.148180 0.0855518i
\(489\) −7.12930 31.5542i −0.322398 1.42693i
\(490\) 25.0744 + 0.850285i 1.13275 + 0.0384120i
\(491\) −5.50320 + 3.17727i −0.248356 + 0.143388i −0.619011 0.785382i \(-0.712466\pi\)
0.370655 + 0.928770i \(0.379133\pi\)
\(492\) −1.72093 + 1.58978i −0.0775856 + 0.0716730i
\(493\) 24.6729i 1.11121i
\(494\) −2.23072 + 1.67634i −0.100365 + 0.0754223i
\(495\) 5.83210 + 12.2476i 0.262133 + 0.550487i
\(496\) 3.85488 + 6.67685i 0.173089 + 0.299800i
\(497\) −0.289012 + 0.279378i −0.0129640 + 0.0125318i
\(498\) −5.35118 1.66348i −0.239792 0.0745422i
\(499\) 5.92485i 0.265233i −0.991167 0.132616i \(-0.957662\pi\)
0.991167 0.132616i \(-0.0423378\pi\)
\(500\) −8.83348 5.10001i −0.395045 0.228080i
\(501\) −5.34350 1.66109i −0.238730 0.0742121i
\(502\) −4.40130 −0.196440
\(503\) 19.6190 33.9811i 0.874767 1.51514i 0.0177557 0.999842i \(-0.494348\pi\)
0.857011 0.515298i \(-0.172319\pi\)
\(504\) −2.78073 + 7.43422i −0.123863 + 0.331146i
\(505\) −3.04493 + 1.75799i −0.135498 + 0.0782296i
\(506\) 10.6145i 0.471871i
\(507\) −20.1369 + 10.0750i −0.894311 + 0.447446i
\(508\) 10.8226 0.480174
\(509\) −8.72379 + 5.03668i −0.386675 + 0.223247i −0.680718 0.732545i \(-0.738332\pi\)
0.294043 + 0.955792i \(0.404999\pi\)
\(510\) 14.4083 13.3103i 0.638011 0.589390i
\(511\) 26.3538 + 7.54244i 1.16582 + 0.333658i
\(512\) −1.00000 −0.0441942
\(513\) −0.573187 3.98031i −0.0253068 0.175735i
\(514\) 4.37736 7.58182i 0.193077 0.334420i
\(515\) 56.2083 2.47684
\(516\) 0.128572 0.413600i 0.00566008 0.0182077i
\(517\) 11.9276 6.88638i 0.524573 0.302863i
\(518\) 0.900363 + 0.931413i 0.0395597 + 0.0409239i
\(519\) 23.7224 5.35980i 1.04130 0.235269i
\(520\) −7.76343 10.3308i −0.340449 0.453036i
\(521\) −12.2704 −0.537578 −0.268789 0.963199i \(-0.586623\pi\)
−0.268789 + 0.963199i \(0.586623\pi\)
\(522\) −13.2808 + 19.2970i −0.581283 + 0.844605i
\(523\) −12.6762 + 7.31862i −0.554292 + 0.320021i −0.750851 0.660471i \(-0.770357\pi\)
0.196559 + 0.980492i \(0.437023\pi\)
\(524\) 6.80645 11.7891i 0.297341 0.515010i
\(525\) −16.1889 32.1036i −0.706540 1.40112i
\(526\) −10.3649 5.98418i −0.451931 0.260923i
\(527\) 12.1805 21.0973i 0.530591 0.919011i
\(528\) −2.13144 + 0.481574i −0.0927592 + 0.0209578i
\(529\) 23.8930 41.3840i 1.03883 1.79930i
\(530\) −21.8147 37.7841i −0.947568 1.64124i
\(531\) 20.4980 29.7836i 0.889537 1.29250i
\(532\) −0.496357 1.98651i −0.0215198 0.0861261i
\(533\) 1.91156 4.48683i 0.0827987 0.194346i
\(534\) −2.51144 11.1156i −0.108681 0.481021i
\(535\) 8.80408 + 15.2491i 0.380634 + 0.659277i
\(536\) 10.4963 6.06005i 0.453372 0.261754i
\(537\) 14.9008 + 4.63209i 0.643018 + 0.199890i
\(538\) 3.51394 0.151497
\(539\) −0.299300 + 8.82618i −0.0128918 + 0.380171i
\(540\) 18.4335 2.65452i 0.793250 0.114233i
\(541\) 34.8104i 1.49661i 0.663352 + 0.748307i \(0.269133\pi\)
−0.663352 + 0.748307i \(0.730867\pi\)
\(542\) 1.27260 2.20420i 0.0546626 0.0946785i
\(543\) 17.7901 16.4344i 0.763447 0.705267i
\(544\) 1.57988 + 2.73643i 0.0677368 + 0.117324i
\(545\) −21.4745 −0.919867
\(546\) −1.06183 16.4886i −0.0454421 0.705645i
\(547\) −27.0523 −1.15667 −0.578336 0.815799i \(-0.696298\pi\)
−0.578336 + 0.815799i \(0.696298\pi\)
\(548\) 1.10639 + 1.91632i 0.0472626 + 0.0818612i
\(549\) −6.42874 + 9.34096i −0.274372 + 0.398662i
\(550\) 4.94922 8.57230i 0.211036 0.365524i
\(551\) 6.04308i 0.257444i
\(552\) −13.9157 4.32584i −0.592289 0.184120i
\(553\) −14.0876 4.03187i −0.599066 0.171452i
\(554\) −13.8467 −0.588288
\(555\) 0.902298 2.90257i 0.0383004 0.123207i
\(556\) −2.92041 + 1.68610i −0.123853 + 0.0715066i
\(557\) −6.46740 11.2019i −0.274032 0.474638i 0.695858 0.718179i \(-0.255024\pi\)
−0.969891 + 0.243541i \(0.921691\pi\)
\(558\) 20.8826 9.94396i 0.884030 0.420961i
\(559\) 0.108696 + 0.895041i 0.00459733 + 0.0378562i
\(560\) 9.19985 2.29871i 0.388765 0.0971383i
\(561\) 4.68522 + 5.07172i 0.197810 + 0.214128i
\(562\) −7.53965 13.0591i −0.318041 0.550863i
\(563\) −2.33044 + 4.03644i −0.0982162 + 0.170115i −0.910946 0.412525i \(-0.864647\pi\)
0.812730 + 0.582640i \(0.197980\pi\)
\(564\) −4.16711 18.4436i −0.175467 0.776616i
\(565\) 28.4400 49.2595i 1.19648 2.07236i
\(566\) −2.40604 1.38913i −0.101134 0.0583895i
\(567\) 21.5729 + 10.0802i 0.905976 + 0.423330i
\(568\) −0.0759653 + 0.131576i −0.00318743 + 0.00552080i
\(569\) −13.1884 + 7.61435i −0.552888 + 0.319210i −0.750286 0.661113i \(-0.770084\pi\)
0.197398 + 0.980323i \(0.436751\pi\)
\(570\) −3.52899 + 3.26006i −0.147813 + 0.136549i
\(571\) 35.0542 1.46697 0.733487 0.679703i \(-0.237891\pi\)
0.733487 + 0.679703i \(0.237891\pi\)
\(572\) 3.63645 2.73272i 0.152047 0.114261i
\(573\) 8.62070 + 38.1551i 0.360135 + 1.59395i
\(574\) 2.48733 + 2.57311i 0.103819 + 0.107399i
\(575\) 57.1672 33.0055i 2.38404 1.37643i
\(576\) −0.237306 + 2.99060i −0.00988773 + 0.124608i
\(577\) 9.20999 0.383417 0.191709 0.981452i \(-0.438597\pi\)
0.191709 + 0.981452i \(0.438597\pi\)
\(578\) −3.50796 + 6.07596i −0.145912 + 0.252727i
\(579\) 12.9052 + 4.01173i 0.536321 + 0.166722i
\(580\) 27.9865 1.16208
\(581\) −2.35528 + 8.22949i −0.0977133 + 0.341417i
\(582\) 5.20427 + 5.63359i 0.215724 + 0.233520i
\(583\) 13.3000 7.67875i 0.550829 0.318021i
\(584\) 10.3607 0.428730
\(585\) −32.7377 + 20.7657i −1.35354 + 0.858558i
\(586\) 4.43527i 0.183219i
\(587\) 2.67162 1.54246i 0.110270 0.0636642i −0.443851 0.896101i \(-0.646388\pi\)
0.554120 + 0.832436i \(0.313055\pi\)
\(588\) 11.4492 + 3.98943i 0.472158 + 0.164521i
\(589\) −2.98334 + 5.16730i −0.122926 + 0.212915i
\(590\) −43.1953 −1.77832
\(591\) −9.16375 + 29.4785i −0.376946 + 1.21258i
\(592\) 0.424035 + 0.244817i 0.0174277 + 0.0100619i
\(593\) 6.04376i 0.248187i −0.992271 0.124094i \(-0.960398\pi\)
0.992271 0.124094i \(-0.0396023\pi\)
\(594\) 0.934392 + 6.48857i 0.0383386 + 0.266229i
\(595\) −20.8249 21.5431i −0.853739 0.883180i
\(596\) 2.67228 + 4.62852i 0.109461 + 0.189592i
\(597\) −3.95411 17.5009i −0.161831 0.716262i
\(598\) 30.1139 3.65709i 1.23145 0.149549i
\(599\) 14.1048i 0.576307i −0.957584 0.288154i \(-0.906959\pi\)
0.957584 0.288154i \(-0.0930414\pi\)
\(600\) −9.22134 9.98204i −0.376460 0.407515i
\(601\) −18.7865 + 10.8464i −0.766319 + 0.442435i −0.831560 0.555435i \(-0.812552\pi\)
0.0652409 + 0.997870i \(0.479218\pi\)
\(602\) −0.636069 0.182042i −0.0259242 0.00741950i
\(603\) −15.6324 32.8284i −0.636599 1.33687i
\(604\) 11.4874 + 6.63223i 0.467414 + 0.269862i
\(605\) −29.2029 16.8603i −1.18727 0.685469i
\(606\) −1.65735 + 0.374458i −0.0673252 + 0.0152113i
\(607\) 17.4314 + 10.0640i 0.707518 + 0.408486i 0.810141 0.586235i \(-0.199390\pi\)
−0.102623 + 0.994720i \(0.532724\pi\)
\(608\) −0.386956 0.670228i −0.0156932 0.0271813i
\(609\) 29.9284 + 19.6141i 1.21276 + 0.794803i
\(610\) 13.5473 0.548512
\(611\) 23.6466 + 31.4666i 0.956637 + 1.27300i
\(612\) 8.55849 4.07542i 0.345956 0.164739i
\(613\) 25.1943 14.5459i 1.01759 0.587505i 0.104184 0.994558i \(-0.466777\pi\)
0.913404 + 0.407053i \(0.133444\pi\)
\(614\) 9.09344 + 15.7503i 0.366981 + 0.635630i
\(615\) 2.49268 8.01860i 0.100514 0.323341i
\(616\) 0.809145 + 3.23834i 0.0326014 + 0.130477i
\(617\) −12.2531 + 21.2230i −0.493292 + 0.854407i −0.999970 0.00772817i \(-0.997540\pi\)
0.506678 + 0.862135i \(0.330873\pi\)
\(618\) 25.9387 + 8.06335i 1.04341 + 0.324355i
\(619\) −36.1887 −1.45455 −0.727273 0.686349i \(-0.759212\pi\)
−0.727273 + 0.686349i \(0.759212\pi\)
\(620\) −23.9306 13.8164i −0.961077 0.554878i
\(621\) −16.2391 + 40.5896i −0.651654 + 1.62880i
\(622\) −3.85575 6.67836i −0.154602 0.267778i
\(623\) −16.8882 + 4.21975i −0.676612 + 0.169061i
\(624\) −2.10062 5.88111i −0.0840919 0.235433i
\(625\) −2.67139 −0.106856
\(626\) −13.7648 + 7.94708i −0.550150 + 0.317629i
\(627\) −1.14754 1.24220i −0.0458283 0.0496089i
\(628\) 5.04941 + 2.91528i 0.201493 + 0.116332i
\(629\) 1.54712i 0.0616878i
\(630\) −4.69135 28.0586i −0.186908 1.11788i
\(631\) 10.9062 + 6.29670i 0.434169 + 0.250668i 0.701121 0.713042i \(-0.252683\pi\)
−0.266952 + 0.963710i \(0.586017\pi\)
\(632\) −5.53840 −0.220306
\(633\) −1.33809 + 4.30446i −0.0531844 + 0.171087i
\(634\) −3.00370 5.20256i −0.119292 0.206620i
\(635\) −33.5926 + 19.3947i −1.33308 + 0.769655i
\(636\) −4.64660 20.5658i −0.184250 0.815487i
\(637\) −25.1435 + 2.19182i −0.996222 + 0.0868432i
\(638\) 9.85124i 0.390014i
\(639\) 0.375463 + 0.258405i 0.0148531 + 0.0102224i
\(640\) 3.10394 1.79206i 0.122694 0.0708373i
\(641\) 6.51225 + 3.75985i 0.257218 + 0.148505i 0.623065 0.782170i \(-0.285887\pi\)
−0.365847 + 0.930675i \(0.619221\pi\)
\(642\) 1.87530 + 8.30006i 0.0740121 + 0.327577i
\(643\) 4.12995 7.15328i 0.162869 0.282098i −0.773027 0.634373i \(-0.781258\pi\)
0.935897 + 0.352275i \(0.114592\pi\)
\(644\) −6.12486 + 21.4007i −0.241353 + 0.843305i
\(645\) 0.342114 + 1.51420i 0.0134707 + 0.0596214i
\(646\) −1.22269 + 2.11776i −0.0481061 + 0.0833221i
\(647\) 14.7602 + 25.5654i 0.580284 + 1.00508i 0.995445 + 0.0953335i \(0.0303918\pi\)
−0.415161 + 0.909748i \(0.636275\pi\)
\(648\) 8.88737 + 1.41937i 0.349129 + 0.0557582i
\(649\) 15.2047i 0.596838i
\(650\) 26.0253 + 11.0877i 1.02080 + 0.434897i
\(651\) −15.9080 31.5466i −0.623483 1.23641i
\(652\) −16.1748 + 9.33852i −0.633454 + 0.365725i
\(653\) 4.09902 2.36657i 0.160407 0.0926111i −0.417648 0.908609i \(-0.637145\pi\)
0.578055 + 0.815998i \(0.303812\pi\)
\(654\) −9.90993 3.08062i −0.387509 0.120462i
\(655\) 48.7902i 1.90639i
\(656\) 1.17143 + 0.676327i 0.0457368 + 0.0264061i
\(657\) 2.45866 30.9848i 0.0959213 1.20883i
\(658\) −28.0217 + 7.00162i −1.09240 + 0.272952i
\(659\) 37.4903 + 21.6450i 1.46042 + 0.843171i 0.999030 0.0440285i \(-0.0140192\pi\)
0.461385 + 0.887200i \(0.347353\pi\)
\(660\) 5.75286 5.31445i 0.223930 0.206865i
\(661\) −18.6135 32.2396i −0.723982 1.25397i −0.959392 0.282078i \(-0.908976\pi\)
0.235409 0.971896i \(-0.424357\pi\)
\(662\) 16.4810i 0.640552i
\(663\) −12.7745 + 15.0396i −0.496122 + 0.584091i
\(664\) 3.23534i 0.125555i
\(665\) 5.10060 + 5.27650i 0.197793 + 0.204614i
\(666\) 0.832774 1.21002i 0.0322693 0.0468874i
\(667\) −32.8481 + 56.8946i −1.27188 + 2.20297i
\(668\) 3.23070i 0.124999i
\(669\) −6.78068 + 21.8125i −0.262156 + 0.843321i
\(670\) −21.7199 + 37.6200i −0.839114 + 1.45339i
\(671\) 4.76863i 0.184091i
\(672\) 4.57525 + 0.258966i 0.176494 + 0.00998981i
\(673\) 9.00579 + 15.5985i 0.347148 + 0.601277i 0.985742 0.168267i \(-0.0538170\pi\)
−0.638594 + 0.769544i \(0.720484\pi\)
\(674\) −14.3226 24.8074i −0.551685 0.955546i
\(675\) −32.0406 + 25.2085i −1.23324 + 0.970277i
\(676\) 9.00579 + 9.37528i 0.346376 + 0.360588i
\(677\) 43.2431 1.66197 0.830984 0.556296i \(-0.187778\pi\)
0.830984 + 0.556296i \(0.187778\pi\)
\(678\) 20.1908 18.6521i 0.775424 0.716331i
\(679\) 8.42325 8.14245i 0.323255 0.312479i
\(680\) −9.80769 5.66247i −0.376108 0.217146i
\(681\) −8.62736 38.1846i −0.330601 1.46324i
\(682\) 4.86335 8.42357i 0.186227 0.322555i
\(683\) −9.67584 + 16.7591i −0.370236 + 0.641267i −0.989602 0.143835i \(-0.954056\pi\)
0.619366 + 0.785103i \(0.287390\pi\)
\(684\) −2.09621 + 0.998183i −0.0801506 + 0.0381665i
\(685\) −6.86832 3.96543i −0.262425 0.151511i
\(686\) 5.69641 17.6225i 0.217490 0.672828i
\(687\) 0.537946 + 0.582323i 0.0205239 + 0.0222170i
\(688\) −0.250064 −0.00953359
\(689\) 26.3674 + 35.0872i 1.00452 + 1.33672i
\(690\) 50.9455 11.5105i 1.93946 0.438198i
\(691\) 0.643698 + 1.11492i 0.0244874 + 0.0424135i 0.878009 0.478643i \(-0.158871\pi\)
−0.853522 + 0.521057i \(0.825538\pi\)
\(692\) −7.02069 12.1602i −0.266887 0.462261i
\(693\) 9.87660 1.65135i 0.375181 0.0627297i
\(694\) 21.7396i 0.825225i
\(695\) 6.04318 10.4671i 0.229231 0.397040i
\(696\) 12.9150 + 4.01479i 0.489544 + 0.152180i
\(697\) 4.27406i 0.161892i
\(698\) −13.3083 + 23.0507i −0.503727 + 0.872480i
\(699\) −19.9894 + 18.4661i −0.756069 + 0.698451i
\(700\) −14.9250 + 14.4275i −0.564112 + 0.545306i
\(701\) 9.09155i 0.343383i −0.985151 0.171692i \(-0.945077\pi\)
0.985151 0.171692i \(-0.0549232\pi\)
\(702\) −18.0865 + 4.88648i −0.682632 + 0.184428i
\(703\) 0.378933i 0.0142917i
\(704\) 0.630804 + 1.09258i 0.0237743 + 0.0411783i
\(705\) 45.9865 + 49.7801i 1.73195 + 1.87483i
\(706\) 22.2718 + 12.8586i 0.838210 + 0.483941i
\(707\) 0.629168 + 2.51804i 0.0236623 + 0.0947007i
\(708\) −19.9335 6.19657i −0.749148 0.232881i
\(709\) −32.1245 18.5471i −1.20646 0.696550i −0.244475 0.969655i \(-0.578616\pi\)
−0.961984 + 0.273106i \(0.911949\pi\)
\(710\) 0.544537i 0.0204361i
\(711\) −1.31429 + 16.5631i −0.0492898 + 0.621166i
\(712\) −5.69791 + 3.28969i −0.213538 + 0.123286i
\(713\) 56.1753 32.4329i 2.10378 1.21462i
\(714\) −6.51971 12.9290i −0.243994 0.483856i
\(715\) −6.39009 + 14.9989i −0.238976 + 0.560928i
\(716\) 9.00908i 0.336685i
\(717\) −22.1941 24.0250i −0.828854 0.897229i
\(718\) 4.66456 + 8.07925i 0.174080 + 0.301515i
\(719\) −19.1457 + 33.1613i −0.714013 + 1.23671i 0.249325 + 0.968420i \(0.419791\pi\)
−0.963339 + 0.268288i \(0.913542\pi\)
\(720\) −4.62275 9.70790i −0.172280 0.361792i
\(721\) 11.4167 39.8907i 0.425180 1.48561i
\(722\) −9.20053 + 15.9358i −0.342408 + 0.593068i
\(723\) −32.0680 + 7.24538i −1.19262 + 0.269459i
\(724\) −12.1097 6.99153i −0.450053 0.259838i
\(725\) −53.0566 + 30.6323i −1.97047 + 1.13765i
\(726\) −11.0577 11.9699i −0.410390 0.444244i
\(727\) 35.6262i 1.32130i 0.750693 + 0.660651i \(0.229720\pi\)
−0.750693 + 0.660651i \(0.770280\pi\)
\(728\) −8.90858 + 3.41132i −0.330174 + 0.126432i
\(729\) 6.35380 26.2417i 0.235326 0.971917i
\(730\) −32.1590 + 18.5670i −1.19026 + 0.687196i
\(731\) 0.395070 + 0.684282i 0.0146122 + 0.0253091i
\(732\) 6.25171 + 1.94342i 0.231070 + 0.0718308i
\(733\) −8.76856 −0.323874 −0.161937 0.986801i \(-0.551774\pi\)
−0.161937 + 0.986801i \(0.551774\pi\)
\(734\) −8.31827 4.80255i −0.307033 0.177266i
\(735\) −42.6869 + 8.13474i −1.57453 + 0.300054i
\(736\) 8.41345i 0.310124i
\(737\) −13.2422 7.64541i −0.487784 0.281622i
\(738\) 2.30061 3.34279i 0.0846866 0.123050i
\(739\) −5.20359 + 3.00429i −0.191417 + 0.110515i −0.592646 0.805463i \(-0.701917\pi\)
0.401229 + 0.915978i \(0.368583\pi\)
\(740\) −1.75490 −0.0645115
\(741\) 3.12884 3.68362i 0.114941 0.135321i
\(742\) −31.2460 + 7.80726i −1.14708 + 0.286613i
\(743\) −22.9464 39.7443i −0.841821 1.45808i −0.888353 0.459160i \(-0.848150\pi\)
0.0465322 0.998917i \(-0.485183\pi\)
\(744\) −9.06134 9.80885i −0.332205 0.359610i
\(745\) −16.5892 9.57776i −0.607780 0.350902i
\(746\) 16.8877 0.618301
\(747\) 9.67560 + 0.767764i 0.354012 + 0.0280910i
\(748\) 1.99319 3.45230i 0.0728782 0.126229i
\(749\) 12.6104 3.15089i 0.460775 0.115131i
\(750\) 16.8706 + 5.24443i 0.616028 + 0.191499i
\(751\) −21.7817 37.7271i −0.794826 1.37668i −0.922949 0.384921i \(-0.874229\pi\)
0.128123 0.991758i \(-0.459105\pi\)
\(752\) −9.45425 + 5.45842i −0.344761 + 0.199048i
\(753\) 7.43584 1.68004i 0.270977 0.0612241i
\(754\) −27.9485 + 3.39412i −1.01783 + 0.123607i
\(755\) −47.5414 −1.73021
\(756\) 1.86020 13.6213i 0.0676547 0.495402i
\(757\) 1.39668 + 2.41912i 0.0507632 + 0.0879244i 0.890290 0.455393i \(-0.150501\pi\)
−0.839527 + 0.543318i \(0.817168\pi\)
\(758\) 25.2872 + 14.5996i 0.918473 + 0.530281i
\(759\) 4.05170 + 17.9328i 0.147067 + 0.650919i
\(760\) 2.40218 + 1.38690i 0.0871361 + 0.0503080i
\(761\) −46.3396 26.7542i −1.67981 0.969839i −0.961778 0.273829i \(-0.911710\pi\)
−0.718032 0.696010i \(-0.754957\pi\)
\(762\) −18.2844 + 4.13114i −0.662373 + 0.149655i
\(763\) −4.36178 + 15.2403i −0.157907 + 0.551737i
\(764\) 19.5584 11.2921i 0.707600 0.408533i
\(765\) −19.2616 + 27.9871i −0.696405 + 1.01188i
\(766\) 8.44343i 0.305073i
\(767\) 43.1367 5.23861i 1.55758 0.189155i
\(768\) 1.68947 0.381715i 0.0609633 0.0137739i
\(769\) −5.91403 10.2434i −0.213265 0.369386i 0.739469 0.673190i \(-0.235077\pi\)
−0.952735 + 0.303804i \(0.901743\pi\)
\(770\) −8.31484 8.60158i −0.299646 0.309979i
\(771\) −4.50132 + 14.4801i −0.162111 + 0.521489i
\(772\) 7.80251i 0.280819i
\(773\) −27.7265 16.0079i −0.997251 0.575763i −0.0898175 0.995958i \(-0.528628\pi\)
−0.907434 + 0.420195i \(0.861962\pi\)
\(774\) −0.0593415 + 0.747840i −0.00213299 + 0.0268806i
\(775\) 60.4900 2.17287
\(776\) 2.21400 3.83477i 0.0794781 0.137660i
\(777\) −1.87667 1.22991i −0.0673250 0.0441227i
\(778\) 0.566013 0.326788i 0.0202926 0.0117159i
\(779\) 1.04684i 0.0375068i
\(780\) 17.0595 + 14.4902i 0.610827 + 0.518831i
\(781\) 0.191677 0.00685874
\(782\) 23.0228 13.2922i 0.823295 0.475329i
\(783\) 15.0715 37.6710i 0.538610 1.34625i
\(784\) 0.237237 6.99598i 0.00847275 0.249856i
\(785\) −20.8974 −0.745860
\(786\) −6.99918 + 22.5154i −0.249653 + 0.803099i
\(787\) −6.78351 + 11.7494i −0.241806 + 0.418820i −0.961229 0.275752i \(-0.911073\pi\)
0.719423 + 0.694573i \(0.244406\pi\)
\(788\) 17.8228 0.634911
\(789\) 19.7954 + 6.15363i 0.704735 + 0.219075i
\(790\) 17.1908 9.92513i 0.611622 0.353120i
\(791\) −29.1826 30.1890i −1.03761 1.07340i
\(792\) 3.41718 1.62721i 0.121424 0.0578202i
\(793\) −13.5289 + 1.64297i −0.480424 + 0.0583437i
\(794\) −5.03371 −0.178640
\(795\) 51.2779 + 55.5080i 1.81864 + 1.96866i
\(796\) −8.97099 + 5.17941i −0.317968 + 0.183579i
\(797\) 15.7158 27.2205i 0.556682 0.964201i −0.441089 0.897463i \(-0.645408\pi\)
0.997771 0.0667377i \(-0.0212591\pi\)
\(798\) 1.59686 + 3.16667i 0.0565281 + 0.112099i
\(799\) 29.8732 + 17.2473i 1.05684 + 0.610165i
\(800\) −3.92295 + 6.79475i −0.138697 + 0.240231i
\(801\) 8.48600 + 17.8208i 0.299838 + 0.629668i
\(802\) −10.4095 + 18.0297i −0.367571 + 0.636652i
\(803\) −6.53558 11.3200i −0.230636 0.399473i
\(804\) −15.4200 + 14.2448i −0.543820 + 0.502377i
\(805\) −19.3401 77.4024i −0.681648 2.72808i
\(806\) 25.5738 + 10.8954i 0.900797 + 0.383773i
\(807\) −5.93668 + 1.34132i −0.208981 + 0.0472168i
\(808\) 0.490495 + 0.849562i 0.0172556 + 0.0298875i
\(809\) −17.4070 + 10.0499i −0.611996 + 0.353336i −0.773746 0.633496i \(-0.781619\pi\)
0.161750 + 0.986832i \(0.448286\pi\)
\(810\) −30.1294 + 11.5211i −1.05864 + 0.404808i
\(811\) 33.5036 1.17647 0.588236 0.808689i \(-0.299823\pi\)
0.588236 + 0.808689i \(0.299823\pi\)
\(812\) 5.68445 19.8619i 0.199485 0.697014i
\(813\) −1.30863 + 4.20969i −0.0458957 + 0.147640i
\(814\) 0.617725i 0.0216513i
\(815\) 33.4703 57.9723i 1.17241 2.03068i
\(816\) −3.71369 4.02005i −0.130005 0.140730i
\(817\) −0.0967637 0.167600i −0.00338533 0.00586357i
\(818\) −29.3889 −1.02756
\(819\) 8.08785 + 27.4515i 0.282612 + 0.959234i
\(820\) −4.84807 −0.169302
\(821\) −7.45863 12.9187i −0.260308 0.450867i 0.706016 0.708196i \(-0.250491\pi\)
−0.966324 + 0.257329i \(0.917157\pi\)
\(822\) −2.60069 2.81523i −0.0907096 0.0981925i
\(823\) −4.82700 + 8.36061i −0.168259 + 0.291433i −0.937808 0.347155i \(-0.887148\pi\)
0.769549 + 0.638588i \(0.220481\pi\)
\(824\) 15.6826i 0.546330i
\(825\) −5.08937 + 16.3718i −0.177189 + 0.569993i
\(826\) −8.77358 + 30.6555i −0.305272 + 1.06664i
\(827\) −7.56315 −0.262996 −0.131498 0.991316i \(-0.541979\pi\)
−0.131498 + 0.991316i \(0.541979\pi\)
\(828\) 25.1613 + 1.99656i 0.874414 + 0.0693852i
\(829\) −10.8268 + 6.25083i −0.376029 + 0.217100i −0.676089 0.736820i \(-0.736327\pi\)
0.300060 + 0.953920i \(0.402993\pi\)
\(830\) −5.79792 10.0423i −0.201249 0.348573i
\(831\) 23.3935 5.28547i 0.811510 0.183351i
\(832\) −2.88239 + 2.16606i −0.0999289 + 0.0750948i
\(833\) −19.5188 + 10.4036i −0.676287 + 0.360464i
\(834\) 4.29033 3.96337i 0.148562 0.137240i
\(835\) −5.78960 10.0279i −0.200357 0.347029i
\(836\) −0.488187 + 0.845565i −0.0168843 + 0.0292445i
\(837\) −31.4846 + 24.7712i −1.08827 + 0.856216i
\(838\) −11.2918 + 19.5580i −0.390069 + 0.675619i
\(839\) 14.0117 + 8.08964i 0.483736 + 0.279285i 0.721972 0.691922i \(-0.243236\pi\)
−0.238236 + 0.971207i \(0.576569\pi\)
\(840\) −14.6654 + 7.39531i −0.506004 + 0.255162i
\(841\) 15.9862 27.6888i 0.551247 0.954788i
\(842\) −24.7026 + 14.2621i −0.851309 + 0.491503i
\(843\) 17.7228 + 19.1848i 0.610406 + 0.660761i
\(844\) 2.60249 0.0895814
\(845\) −44.7544 12.9614i −1.53960 0.445885i
\(846\) 14.0804 + 29.5692i 0.484094 + 1.01661i
\(847\) −17.8972 + 17.3006i −0.614954 + 0.594455i
\(848\) −10.5421 + 6.08648i −0.362017 + 0.209011i
\(849\) 4.59518 + 1.42847i 0.157706 + 0.0490248i
\(850\) 24.7911 0.850329
\(851\) 2.05975 3.56759i 0.0706074 0.122296i
\(852\) 0.0781164 0.251290i 0.00267622 0.00860904i
\(853\) 27.7026 0.948520 0.474260 0.880385i \(-0.342716\pi\)
0.474260 + 0.880385i \(0.342716\pi\)
\(854\) 2.75164 9.61441i 0.0941591 0.328998i
\(855\) 4.71770 6.85483i 0.161342 0.234430i
\(856\) 4.25464 2.45642i 0.145420 0.0839585i
\(857\) −13.2750 −0.453464 −0.226732 0.973957i \(-0.572804\pi\)
−0.226732 + 0.973957i \(0.572804\pi\)
\(858\) −5.10053 + 6.00493i −0.174129 + 0.205005i
\(859\) 51.4810i 1.75651i −0.478194 0.878254i \(-0.658708\pi\)
0.478194 0.878254i \(-0.341292\pi\)
\(860\) 0.776182 0.448129i 0.0264676 0.0152811i
\(861\) −5.18445 3.39773i −0.176686 0.115794i
\(862\) 3.76847 6.52718i 0.128354 0.222316i
\(863\) −14.4211 −0.490900 −0.245450 0.969409i \(-0.578936\pi\)
−0.245450 + 0.969409i \(0.578936\pi\)
\(864\) −0.740636 5.14310i −0.0251969 0.174972i
\(865\) 43.5836 + 25.1630i 1.48189 + 0.855567i
\(866\) 32.7328i 1.11230i
\(867\) 3.60729 11.6042i 0.122510 0.394098i
\(868\) −14.6660 + 14.1771i −0.497797 + 0.481203i
\(869\) 3.49364 + 6.05117i 0.118514 + 0.205272i
\(870\) −47.2822 + 10.6829i −1.60302 + 0.362183i
\(871\) 17.1280 40.2031i 0.580361 1.36223i
\(872\) 5.99158i 0.202900i
\(873\) −10.9429 7.53121i −0.370359 0.254893i
\(874\) −5.63893 + 3.25564i −0.190740 + 0.110124i
\(875\) 7.42546 25.9451i 0.251026 0.877103i
\(876\) −17.5041 + 3.95484i −0.591408 + 0.133622i
\(877\) −39.8280 22.9947i −1.34489 0.776475i −0.357374 0.933962i \(-0.616328\pi\)
−0.987521 + 0.157486i \(0.949661\pi\)
\(878\) 21.2278 + 12.2559i 0.716403 + 0.413615i
\(879\) −1.69301 7.49323i −0.0571037 0.252741i
\(880\) −3.91595 2.26088i −0.132007 0.0762141i
\(881\) −18.8103 32.5804i −0.633735 1.09766i −0.986782 0.162056i \(-0.948188\pi\)
0.353046 0.935606i \(-0.385146\pi\)
\(882\) −20.8659 2.36967i −0.702591 0.0797908i
\(883\) −23.2787 −0.783389 −0.391695 0.920095i \(-0.628111\pi\)
−0.391695 + 0.920095i \(0.628111\pi\)
\(884\) 10.4811 + 4.46534i 0.352518 + 0.150186i
\(885\) 72.9770 16.4883i 2.45310 0.554248i
\(886\) −9.29525 + 5.36661i −0.312280 + 0.180295i
\(887\) 7.93228 + 13.7391i 0.266340 + 0.461314i 0.967914 0.251282i \(-0.0808523\pi\)
−0.701574 + 0.712597i \(0.747519\pi\)
\(888\) −0.809842 0.251749i −0.0271765 0.00844814i
\(889\) 6.94117 + 27.7798i 0.232800 + 0.931705i
\(890\) 11.7906 20.4220i 0.395223 0.684546i
\(891\) −4.05541 10.6056i −0.135861 0.355299i
\(892\) 13.1879 0.441564
\(893\) −7.31677 4.22434i −0.244846 0.141362i
\(894\) −6.28150 6.79968i −0.210085 0.227415i
\(895\) 16.1448 + 27.9636i 0.539661 + 0.934720i
\(896\) −0.641360 2.56684i −0.0214263 0.0857520i
\(897\) −49.4804 + 17.6734i −1.65210 + 0.590098i
\(898\) −39.4840 −1.31760
\(899\) −52.1361 + 30.1008i −1.73883 + 1.00392i
\(900\) 19.3894 + 13.3444i 0.646314 + 0.444813i
\(901\) 33.3105 + 19.2318i 1.10973 + 0.640705i
\(902\) 1.70652i 0.0568209i
\(903\) 1.14410 + 0.0647579i 0.0380734 + 0.00215501i
\(904\) −13.7438 7.93500i −0.457113 0.263914i
\(905\) 50.1169 1.66594
\(906\) −21.9391 6.82004i −0.728879 0.226580i
\(907\) −3.67040 6.35732i −0.121874 0.211091i 0.798633 0.601819i \(-0.205557\pi\)
−0.920507 + 0.390727i \(0.872224\pi\)
\(908\) −19.5736 + 11.3008i −0.649571 + 0.375030i
\(909\) 2.65710 1.26527i 0.0881304 0.0419663i
\(910\) 21.5384 26.5532i 0.713991 0.880231i
\(911\) 4.10735i 0.136082i −0.997683 0.0680412i \(-0.978325\pi\)
0.997683 0.0680412i \(-0.0216749\pi\)
\(912\) 0.909585 + 0.984620i 0.0301194 + 0.0326040i
\(913\) 3.53488 2.04086i 0.116987 0.0675428i
\(914\) 9.89907 + 5.71523i 0.327432 + 0.189043i
\(915\) −22.8876 + 5.17118i −0.756641 + 0.170954i
\(916\) 0.228853 0.396385i 0.00756152 0.0130969i
\(917\) 34.6261 + 9.90998i 1.14346 + 0.327256i
\(918\) −12.9036 + 10.1522i −0.425883 + 0.335072i
\(919\) −19.1541 + 33.1759i −0.631835 + 1.09437i 0.355341 + 0.934737i \(0.384365\pi\)
−0.987176 + 0.159634i \(0.948969\pi\)
\(920\) −15.0774 26.1148i −0.497087 0.860980i
\(921\) −21.3752 23.1385i −0.704336 0.762439i
\(922\) 9.72957i 0.320426i
\(923\) 0.0660399 + 0.543798i 0.00217373 + 0.0178993i
\(924\) −2.60315 5.16221i −0.0856372 0.169824i
\(925\) 3.32693 1.92081i 0.109389 0.0631557i
\(926\) 23.0858 13.3286i 0.758647 0.438005i
\(927\) −46.9004 3.72157i −1.54041 0.122233i
\(928\) 7.80848i 0.256326i
\(929\) 22.8552 + 13.1955i 0.749856 + 0.432930i 0.825642 0.564195i \(-0.190813\pi\)
−0.0757859 + 0.997124i \(0.524147\pi\)
\(930\) 45.7039 + 14.2076i 1.49869 + 0.465885i
\(931\) 4.78070 2.54814i 0.156681 0.0835118i
\(932\) 13.6067 + 7.85585i 0.445703 + 0.257327i
\(933\) 9.06339 + 9.81106i 0.296722 + 0.321200i
\(934\) 3.01089 + 5.21502i 0.0985194 + 0.170641i
\(935\) 14.2876i 0.467256i
\(936\) 5.79382 + 9.13409i 0.189377 + 0.298557i
\(937\) 53.4346i 1.74563i −0.488049 0.872816i \(-0.662291\pi\)
0.488049 0.872816i \(-0.337709\pi\)
\(938\) 22.2871 + 23.0557i 0.727699 + 0.752794i
\(939\) 20.2216 18.6805i 0.659906 0.609616i
\(940\) 19.5636 33.8851i 0.638094 1.10521i
\(941\) 11.0561i 0.360419i −0.983628 0.180209i \(-0.942322\pi\)
0.983628 0.180209i \(-0.0576775\pi\)
\(942\) −9.64361 2.99783i −0.314206 0.0976746i
\(943\) 5.69024 9.85578i 0.185300 0.320949i
\(944\) 12.0519i 0.392255i
\(945\) 18.6362 + 45.6132i 0.606237 + 1.48380i
\(946\) 0.157741 + 0.273216i 0.00512861 + 0.00888301i
\(947\) −4.57740 7.92829i −0.148746 0.257635i 0.782019 0.623255i \(-0.214190\pi\)
−0.930764 + 0.365620i \(0.880857\pi\)
\(948\) 9.35693 2.11409i 0.303899 0.0686623i
\(949\) 29.8636 22.4420i 0.969414 0.728497i
\(950\) −6.07204 −0.197003
\(951\) 7.06053 + 7.64298i 0.228953 + 0.247841i
\(952\) −6.01071 + 5.81033i −0.194808 + 0.188314i
\(953\) −44.8045 25.8679i −1.45136 0.837943i −0.452801 0.891612i \(-0.649575\pi\)
−0.998559 + 0.0536692i \(0.982908\pi\)
\(954\) 15.7005 + 32.9715i 0.508323 + 1.06749i
\(955\) −40.4721 + 70.0998i −1.30965 + 2.26838i
\(956\) −9.44183 + 16.3537i −0.305371 + 0.528917i
\(957\) −3.76036 16.6433i −0.121555 0.538002i
\(958\) −7.74812 4.47338i −0.250330 0.144528i
\(959\) −4.20929 + 4.06897i −0.135925 + 0.131394i
\(960\) −4.55994 + 4.21244i −0.147171 + 0.135956i
\(961\) 28.4405 0.917435
\(962\) 1.75252 0.212830i 0.0565036 0.00686190i
\(963\) −6.33651 13.3068i −0.204191 0.428807i
\(964\) 9.49057 + 16.4382i 0.305671 + 0.529437i
\(965\) 13.9826 + 24.2185i 0.450114 + 0.779621i
\(966\) 2.17879 38.4936i 0.0701015 1.23851i
\(967\) 0.447825i 0.0144011i −0.999974 0.00720054i \(-0.997708\pi\)
0.999974 0.00720054i \(-0.00229202\pi\)
\(968\) −4.70417 + 8.14787i −0.151198 + 0.261882i
\(969\) 1.25731 4.04460i 0.0403907 0.129931i
\(970\) 15.8705i 0.509571i
\(971\) 19.5151 33.8011i 0.626269 1.08473i −0.362025 0.932169i \(-0.617914\pi\)
0.988294 0.152562i \(-0.0487523\pi\)
\(972\) −15.5567 + 0.994458i −0.498982 + 0.0318973i
\(973\) −6.20098 6.41482i −0.198794 0.205650i
\(974\) 29.3101i 0.939155i
\(975\) −48.2012 8.79812i −1.54367 0.281765i
\(976\) 3.77980i 0.120989i
\(977\) −7.19880 12.4687i −0.230310 0.398909i 0.727589 0.686013i \(-0.240641\pi\)
−0.957899 + 0.287104i \(0.907307\pi\)
\(978\) 23.7621 21.9513i 0.759828 0.701924i
\(979\) 7.18853 + 4.15030i 0.229746 + 0.132644i
\(980\) 11.8008 + 22.1402i 0.376964 + 0.707243i
\(981\) 17.9184 + 1.42184i 0.572091 + 0.0453957i
\(982\) −5.50320 3.17727i −0.175614 0.101391i
\(983\) 55.8894i 1.78259i −0.453420 0.891297i \(-0.649796\pi\)
0.453420 0.891297i \(-0.350204\pi\)
\(984\) −2.23726 0.695478i −0.0713212 0.0221710i
\(985\) −55.3209 + 31.9395i −1.76267 + 1.01768i
\(986\) −21.3674 + 12.3365i −0.680476 + 0.392873i
\(987\) 44.6691 22.5253i 1.42183 0.716988i
\(988\) −2.56712 1.09369i −0.0816708 0.0347948i
\(989\) 2.10390i 0.0669000i
\(990\) −7.69065 + 11.1745i −0.244425 + 0.355150i
\(991\) 4.29142 + 7.43296i 0.136322 + 0.236116i 0.926102 0.377274i \(-0.123139\pi\)
−0.789780 + 0.613390i \(0.789805\pi\)
\(992\) −3.85488 + 6.67685i −0.122393 + 0.211990i
\(993\) 6.29104 + 27.8441i 0.199640 + 0.883605i
\(994\) −0.386455 0.110603i −0.0122576 0.00350812i
\(995\) 18.5636 32.1531i 0.588506 1.01932i
\(996\) −1.23498 5.46599i −0.0391317 0.173197i
\(997\) −44.8411 25.8890i −1.42013 0.819914i −0.423824 0.905745i \(-0.639312\pi\)
−0.996310 + 0.0858304i \(0.972646\pi\)
\(998\) 5.13107 2.96242i 0.162421 0.0937739i
\(999\) −0.945060 + 2.36217i −0.0299004 + 0.0747358i
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 546.2.q.j.335.4 yes 24
3.2 odd 2 546.2.q.i.335.9 yes 24
7.6 odd 2 inner 546.2.q.j.335.9 yes 24
13.4 even 6 546.2.q.i.251.4 24
21.20 even 2 546.2.q.i.335.4 yes 24
39.17 odd 6 inner 546.2.q.j.251.9 yes 24
91.69 odd 6 546.2.q.i.251.9 yes 24
273.251 even 6 inner 546.2.q.j.251.4 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.q.i.251.4 24 13.4 even 6
546.2.q.i.251.9 yes 24 91.69 odd 6
546.2.q.i.335.4 yes 24 21.20 even 2
546.2.q.i.335.9 yes 24 3.2 odd 2
546.2.q.j.251.4 yes 24 273.251 even 6 inner
546.2.q.j.251.9 yes 24 39.17 odd 6 inner
546.2.q.j.335.4 yes 24 1.1 even 1 trivial
546.2.q.j.335.9 yes 24 7.6 odd 2 inner