Properties

Label 471.2.e.b.169.11
Level $471$
Weight $2$
Character 471.169
Analytic conductor $3.761$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [471,2,Mod(169,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.e (of order \(3\), 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: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 169.11
Character \(\chi\) \(=\) 471.169
Dual form 471.2.e.b.301.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.74840 q^{2} +(0.500000 + 0.866025i) q^{3} +5.55371 q^{4} +(0.277926 + 0.481381i) q^{5} +(1.37420 + 2.38018i) q^{6} -4.42840 q^{7} +9.76701 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+2.74840 q^{2} +(0.500000 + 0.866025i) q^{3} +5.55371 q^{4} +(0.277926 + 0.481381i) q^{5} +(1.37420 + 2.38018i) q^{6} -4.42840 q^{7} +9.76701 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.763851 + 1.32303i) q^{10} +(-1.93821 - 3.35708i) q^{11} +(2.77685 + 4.80965i) q^{12} +(0.286084 - 0.495513i) q^{13} -12.1710 q^{14} +(-0.277926 + 0.481381i) q^{15} +15.7362 q^{16} +(2.88539 + 4.99764i) q^{17} +(-1.37420 + 2.38018i) q^{18} +(-2.35250 - 4.07464i) q^{19} +(1.54352 + 2.67345i) q^{20} +(-2.21420 - 3.83511i) q^{21} +(-5.32698 - 9.22660i) q^{22} -1.19495 q^{23} +(4.88351 + 8.45848i) q^{24} +(2.34551 - 4.06255i) q^{25} +(0.786274 - 1.36187i) q^{26} -1.00000 q^{27} -24.5941 q^{28} -10.3284 q^{29} +(-0.763851 + 1.32303i) q^{30} +(-1.89212 + 3.27726i) q^{31} +23.7155 q^{32} +(1.93821 - 3.35708i) q^{33} +(7.93020 + 13.7355i) q^{34} +(-1.23077 - 2.13175i) q^{35} +(-2.77685 + 4.80965i) q^{36} +(1.26780 - 2.19590i) q^{37} +(-6.46560 - 11.1987i) q^{38} +0.572169 q^{39} +(2.71450 + 4.70166i) q^{40} +8.61324 q^{41} +(-6.08551 - 10.5404i) q^{42} +(-5.04965 + 8.74625i) q^{43} +(-10.7643 - 18.6442i) q^{44} -0.555851 q^{45} -3.28419 q^{46} +(1.70863 - 2.95943i) q^{47} +(7.86812 + 13.6280i) q^{48} +12.6108 q^{49} +(6.44641 - 11.1655i) q^{50} +(-2.88539 + 4.99764i) q^{51} +(1.58883 - 2.75193i) q^{52} +(0.565189 - 0.978937i) q^{53} -2.74840 q^{54} +(1.07736 - 1.86604i) q^{55} -43.2523 q^{56} +(2.35250 - 4.07464i) q^{57} -28.3865 q^{58} +1.90366 q^{59} +(-1.54352 + 2.67345i) q^{60} +(-0.175136 - 0.303345i) q^{61} +(-5.20032 + 9.00721i) q^{62} +(2.21420 - 3.83511i) q^{63} +33.7072 q^{64} +0.318041 q^{65} +(5.32698 - 9.22660i) q^{66} +2.06043 q^{67} +(16.0246 + 27.7554i) q^{68} +(-0.597473 - 1.03485i) q^{69} +(-3.38264 - 5.85890i) q^{70} +(4.68078 - 8.10735i) q^{71} +(-4.88351 + 8.45848i) q^{72} +(6.74811 + 11.6881i) q^{73} +(3.48443 - 6.03521i) q^{74} +4.69103 q^{75} +(-13.0651 - 22.6294i) q^{76} +(8.58318 + 14.8665i) q^{77} +1.57255 q^{78} -7.07153 q^{79} +(4.37351 + 7.57513i) q^{80} +(-0.500000 - 0.866025i) q^{81} +23.6726 q^{82} +(-3.41445 + 5.91401i) q^{83} +(-12.2970 - 21.2991i) q^{84} +(-1.60385 + 2.77794i) q^{85} +(-13.8785 + 24.0382i) q^{86} +(-5.16418 - 8.94462i) q^{87} +(-18.9305 - 32.7886i) q^{88} +(2.76950 + 4.79692i) q^{89} -1.52770 q^{90} +(-1.26690 + 2.19433i) q^{91} -6.63638 q^{92} -3.78425 q^{93} +(4.69599 - 8.13369i) q^{94} +(1.30764 - 2.26489i) q^{95} +(11.8577 + 20.5382i) q^{96} +(-8.40042 + 14.5500i) q^{97} +34.6594 q^{98} +3.87642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.74840 1.94341 0.971706 0.236192i \(-0.0758994\pi\)
0.971706 + 0.236192i \(0.0758994\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 5.55371 2.77685
\(5\) 0.277926 + 0.481381i 0.124292 + 0.215280i 0.921456 0.388483i \(-0.127001\pi\)
−0.797164 + 0.603763i \(0.793667\pi\)
\(6\) 1.37420 + 2.38018i 0.561015 + 0.971706i
\(7\) −4.42840 −1.67378 −0.836890 0.547372i \(-0.815628\pi\)
−0.836890 + 0.547372i \(0.815628\pi\)
\(8\) 9.76701 3.45316
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.763851 + 1.32303i 0.241551 + 0.418378i
\(11\) −1.93821 3.35708i −0.584392 1.01220i −0.994951 0.100363i \(-0.968000\pi\)
0.410558 0.911834i \(-0.365334\pi\)
\(12\) 2.77685 + 4.80965i 0.801609 + 1.38843i
\(13\) 0.286084 0.495513i 0.0793455 0.137430i −0.823622 0.567139i \(-0.808050\pi\)
0.902968 + 0.429708i \(0.141384\pi\)
\(14\) −12.1710 −3.25284
\(15\) −0.277926 + 0.481381i −0.0717601 + 0.124292i
\(16\) 15.7362 3.93406
\(17\) 2.88539 + 4.99764i 0.699809 + 1.21210i 0.968532 + 0.248887i \(0.0800649\pi\)
−0.268723 + 0.963217i \(0.586602\pi\)
\(18\) −1.37420 + 2.38018i −0.323902 + 0.561015i
\(19\) −2.35250 4.07464i −0.539699 0.934787i −0.998920 0.0464645i \(-0.985205\pi\)
0.459221 0.888322i \(-0.348129\pi\)
\(20\) 1.54352 + 2.67345i 0.345141 + 0.597802i
\(21\) −2.21420 3.83511i −0.483178 0.836890i
\(22\) −5.32698 9.22660i −1.13572 1.96712i
\(23\) −1.19495 −0.249163 −0.124582 0.992209i \(-0.539759\pi\)
−0.124582 + 0.992209i \(0.539759\pi\)
\(24\) 4.88351 + 8.45848i 0.996841 + 1.72658i
\(25\) 2.34551 4.06255i 0.469103 0.812510i
\(26\) 0.786274 1.36187i 0.154201 0.267084i
\(27\) −1.00000 −0.192450
\(28\) −24.5941 −4.64784
\(29\) −10.3284 −1.91793 −0.958964 0.283527i \(-0.908495\pi\)
−0.958964 + 0.283527i \(0.908495\pi\)
\(30\) −0.763851 + 1.32303i −0.139459 + 0.241551i
\(31\) −1.89212 + 3.27726i −0.339836 + 0.588613i −0.984402 0.175936i \(-0.943705\pi\)
0.644566 + 0.764549i \(0.277038\pi\)
\(32\) 23.7155 4.19235
\(33\) 1.93821 3.35708i 0.337399 0.584392i
\(34\) 7.93020 + 13.7355i 1.36002 + 2.35562i
\(35\) −1.23077 2.13175i −0.208038 0.360332i
\(36\) −2.77685 + 4.80965i −0.462809 + 0.801609i
\(37\) 1.26780 2.19590i 0.208425 0.361003i −0.742793 0.669521i \(-0.766499\pi\)
0.951219 + 0.308517i \(0.0998328\pi\)
\(38\) −6.46560 11.1987i −1.04886 1.81668i
\(39\) 0.572169 0.0916203
\(40\) 2.71450 + 4.70166i 0.429200 + 0.743397i
\(41\) 8.61324 1.34516 0.672581 0.740024i \(-0.265186\pi\)
0.672581 + 0.740024i \(0.265186\pi\)
\(42\) −6.08551 10.5404i −0.939015 1.62642i
\(43\) −5.04965 + 8.74625i −0.770064 + 1.33379i 0.167463 + 0.985878i \(0.446442\pi\)
−0.937527 + 0.347912i \(0.886891\pi\)
\(44\) −10.7643 18.6442i −1.62277 2.81072i
\(45\) −0.555851 −0.0828614
\(46\) −3.28419 −0.484227
\(47\) 1.70863 2.95943i 0.249229 0.431677i −0.714083 0.700061i \(-0.753156\pi\)
0.963312 + 0.268384i \(0.0864896\pi\)
\(48\) 7.86812 + 13.6280i 1.13567 + 1.96703i
\(49\) 12.6108 1.80154
\(50\) 6.44641 11.1655i 0.911661 1.57904i
\(51\) −2.88539 + 4.99764i −0.404035 + 0.699809i
\(52\) 1.58883 2.75193i 0.220331 0.381624i
\(53\) 0.565189 0.978937i 0.0776347 0.134467i −0.824594 0.565725i \(-0.808597\pi\)
0.902229 + 0.431257i \(0.141930\pi\)
\(54\) −2.74840 −0.374010
\(55\) 1.07736 1.86604i 0.145271 0.251616i
\(56\) −43.2523 −5.77983
\(57\) 2.35250 4.07464i 0.311596 0.539699i
\(58\) −28.3865 −3.72733
\(59\) 1.90366 0.247835 0.123918 0.992293i \(-0.460454\pi\)
0.123918 + 0.992293i \(0.460454\pi\)
\(60\) −1.54352 + 2.67345i −0.199267 + 0.345141i
\(61\) −0.175136 0.303345i −0.0224239 0.0388393i 0.854596 0.519294i \(-0.173805\pi\)
−0.877020 + 0.480455i \(0.840472\pi\)
\(62\) −5.20032 + 9.00721i −0.660441 + 1.14392i
\(63\) 2.21420 3.83511i 0.278963 0.483178i
\(64\) 33.7072 4.21340
\(65\) 0.318041 0.0394481
\(66\) 5.32698 9.22660i 0.655706 1.13572i
\(67\) 2.06043 0.251722 0.125861 0.992048i \(-0.459831\pi\)
0.125861 + 0.992048i \(0.459831\pi\)
\(68\) 16.0246 + 27.7554i 1.94327 + 3.36584i
\(69\) −0.597473 1.03485i −0.0719273 0.124582i
\(70\) −3.38264 5.85890i −0.404303 0.700273i
\(71\) 4.68078 8.10735i 0.555507 0.962166i −0.442357 0.896839i \(-0.645858\pi\)
0.997864 0.0653270i \(-0.0208091\pi\)
\(72\) −4.88351 + 8.45848i −0.575527 + 0.996841i
\(73\) 6.74811 + 11.6881i 0.789807 + 1.36799i 0.926085 + 0.377315i \(0.123153\pi\)
−0.136278 + 0.990671i \(0.543514\pi\)
\(74\) 3.48443 6.03521i 0.405057 0.701579i
\(75\) 4.69103 0.541673
\(76\) −13.0651 22.6294i −1.49867 2.59577i
\(77\) 8.58318 + 14.8665i 0.978144 + 1.69419i
\(78\) 1.57255 0.178056
\(79\) −7.07153 −0.795609 −0.397805 0.917470i \(-0.630228\pi\)
−0.397805 + 0.917470i \(0.630228\pi\)
\(80\) 4.37351 + 7.57513i 0.488973 + 0.846926i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 23.6726 2.61420
\(83\) −3.41445 + 5.91401i −0.374785 + 0.649147i −0.990295 0.138982i \(-0.955617\pi\)
0.615510 + 0.788129i \(0.288950\pi\)
\(84\) −12.2970 21.2991i −1.34172 2.32392i
\(85\) −1.60385 + 2.77794i −0.173961 + 0.301310i
\(86\) −13.8785 + 24.0382i −1.49655 + 2.59210i
\(87\) −5.16418 8.94462i −0.553658 0.958964i
\(88\) −18.9305 32.7886i −2.01800 3.49528i
\(89\) 2.76950 + 4.79692i 0.293567 + 0.508473i 0.974650 0.223733i \(-0.0718244\pi\)
−0.681084 + 0.732206i \(0.738491\pi\)
\(90\) −1.52770 −0.161034
\(91\) −1.26690 + 2.19433i −0.132807 + 0.230028i
\(92\) −6.63638 −0.691890
\(93\) −3.78425 −0.392408
\(94\) 4.69599 8.13369i 0.484354 0.838926i
\(95\) 1.30764 2.26489i 0.134161 0.232373i
\(96\) 11.8577 + 20.5382i 1.21023 + 2.09617i
\(97\) −8.40042 + 14.5500i −0.852934 + 1.47732i 0.0256153 + 0.999672i \(0.491845\pi\)
−0.878549 + 0.477652i \(0.841488\pi\)
\(98\) 34.6594 3.50113
\(99\) 3.87642 0.389595
\(100\) 13.0263 22.5622i 1.30263 2.25622i
\(101\) −6.06220 −0.603211 −0.301606 0.953433i \(-0.597523\pi\)
−0.301606 + 0.953433i \(0.597523\pi\)
\(102\) −7.93020 + 13.7355i −0.785207 + 1.36002i
\(103\) 8.39372 0.827058 0.413529 0.910491i \(-0.364296\pi\)
0.413529 + 0.910491i \(0.364296\pi\)
\(104\) 2.79419 4.83968i 0.273993 0.474569i
\(105\) 1.23077 2.13175i 0.120111 0.208038i
\(106\) 1.55337 2.69051i 0.150876 0.261325i
\(107\) −2.24376 + 3.88630i −0.216912 + 0.375703i −0.953862 0.300244i \(-0.902932\pi\)
0.736950 + 0.675947i \(0.236265\pi\)
\(108\) −5.55371 −0.534406
\(109\) −0.345821 0.598979i −0.0331236 0.0573718i 0.848988 0.528412i \(-0.177212\pi\)
−0.882112 + 0.471040i \(0.843879\pi\)
\(110\) 2.96101 5.12862i 0.282321 0.488994i
\(111\) 2.53560 0.240669
\(112\) −69.6864 −6.58475
\(113\) −8.28854 14.3562i −0.779720 1.35051i −0.932103 0.362193i \(-0.882028\pi\)
0.152383 0.988321i \(-0.451305\pi\)
\(114\) 6.46560 11.1987i 0.605559 1.04886i
\(115\) −0.332106 0.575225i −0.0309690 0.0536400i
\(116\) −57.3607 −5.32581
\(117\) 0.286084 + 0.495513i 0.0264485 + 0.0458102i
\(118\) 5.23202 0.481646
\(119\) −12.7777 22.1315i −1.17133 2.02880i
\(120\) −2.71450 + 4.70166i −0.247799 + 0.429200i
\(121\) −2.01332 + 3.48717i −0.183029 + 0.317015i
\(122\) −0.481345 0.833713i −0.0435789 0.0754808i
\(123\) 4.30662 + 7.45928i 0.388315 + 0.672581i
\(124\) −10.5083 + 18.2009i −0.943674 + 1.63449i
\(125\) 5.38677 0.481807
\(126\) 6.08551 10.5404i 0.542141 0.939015i
\(127\) 0.762895 1.32137i 0.0676960 0.117253i −0.830191 0.557479i \(-0.811769\pi\)
0.897887 + 0.440227i \(0.145102\pi\)
\(128\) 45.2098 3.99602
\(129\) −10.0993 −0.889193
\(130\) 0.874103 0.0766639
\(131\) 9.47219 16.4063i 0.827589 1.43343i −0.0723352 0.997380i \(-0.523045\pi\)
0.899924 0.436046i \(-0.143622\pi\)
\(132\) 10.7643 18.6442i 0.936908 1.62277i
\(133\) 10.4178 + 18.0442i 0.903338 + 1.56463i
\(134\) 5.66289 0.489199
\(135\) −0.277926 0.481381i −0.0239200 0.0414307i
\(136\) 28.1816 + 48.8120i 2.41655 + 4.18559i
\(137\) −5.66096 9.80506i −0.483648 0.837703i 0.516176 0.856483i \(-0.327355\pi\)
−0.999824 + 0.0187797i \(0.994022\pi\)
\(138\) −1.64210 2.84419i −0.139784 0.242114i
\(139\) −1.21676 + 2.10749i −0.103204 + 0.178755i −0.913003 0.407953i \(-0.866243\pi\)
0.809799 + 0.586707i \(0.199576\pi\)
\(140\) −6.83532 11.8391i −0.577690 1.00059i
\(141\) 3.41725 0.287785
\(142\) 12.8647 22.2823i 1.07958 1.86989i
\(143\) −2.21797 −0.185476
\(144\) −7.86812 + 13.6280i −0.655677 + 1.13567i
\(145\) −2.87052 4.97188i −0.238383 0.412892i
\(146\) 18.5465 + 32.1235i 1.53492 + 2.65856i
\(147\) 6.30538 + 10.9212i 0.520059 + 0.900768i
\(148\) 7.04100 12.1954i 0.578767 1.00245i
\(149\) 9.57621 0.784514 0.392257 0.919856i \(-0.371694\pi\)
0.392257 + 0.919856i \(0.371694\pi\)
\(150\) 12.8928 1.05270
\(151\) 8.01468 + 13.8818i 0.652225 + 1.12969i 0.982582 + 0.185831i \(0.0594978\pi\)
−0.330356 + 0.943856i \(0.607169\pi\)
\(152\) −22.9768 39.7971i −1.86367 3.22797i
\(153\) −5.77077 −0.466539
\(154\) 23.5900 + 40.8591i 1.90094 + 3.29252i
\(155\) −2.10348 −0.168956
\(156\) 3.17766 0.254416
\(157\) −5.13171 + 11.4309i −0.409555 + 0.912286i
\(158\) −19.4354 −1.54620
\(159\) 1.13038 0.0896448
\(160\) 6.59114 + 11.4162i 0.521075 + 0.902529i
\(161\) 5.29170 0.417045
\(162\) −1.37420 2.38018i −0.107967 0.187005i
\(163\) 7.24553 + 12.5496i 0.567514 + 0.982962i 0.996811 + 0.0797993i \(0.0254279\pi\)
−0.429297 + 0.903163i \(0.641239\pi\)
\(164\) 47.8354 3.73532
\(165\) 2.15471 0.167744
\(166\) −9.38429 + 16.2541i −0.728362 + 1.26156i
\(167\) −1.53417 2.65725i −0.118717 0.205625i 0.800542 0.599276i \(-0.204545\pi\)
−0.919260 + 0.393652i \(0.871212\pi\)
\(168\) −21.6261 37.4576i −1.66849 2.88991i
\(169\) 6.33631 + 10.9748i 0.487409 + 0.844216i
\(170\) −4.40801 + 7.63490i −0.338079 + 0.585570i
\(171\) 4.70499 0.359800
\(172\) −28.0443 + 48.5741i −2.13835 + 3.70374i
\(173\) −5.45837 −0.414992 −0.207496 0.978236i \(-0.566531\pi\)
−0.207496 + 0.978236i \(0.566531\pi\)
\(174\) −14.1932 24.5834i −1.07599 1.86366i
\(175\) −10.3869 + 17.9906i −0.785175 + 1.35996i
\(176\) −30.5002 52.8278i −2.29904 3.98205i
\(177\) 0.951830 + 1.64862i 0.0715439 + 0.123918i
\(178\) 7.61171 + 13.1839i 0.570521 + 0.988172i
\(179\) −5.02532 8.70410i −0.375610 0.650575i 0.614808 0.788677i \(-0.289233\pi\)
−0.990418 + 0.138101i \(0.955900\pi\)
\(180\) −3.08703 −0.230094
\(181\) −7.94327 13.7582i −0.590419 1.02264i −0.994176 0.107769i \(-0.965629\pi\)
0.403757 0.914866i \(-0.367704\pi\)
\(182\) −3.48194 + 6.03090i −0.258099 + 0.447040i
\(183\) 0.175136 0.303345i 0.0129464 0.0224239i
\(184\) −11.6710 −0.860401
\(185\) 1.40942 0.103623
\(186\) −10.4006 −0.762611
\(187\) 11.1850 19.3729i 0.817926 1.41669i
\(188\) 9.48921 16.4358i 0.692072 1.19870i
\(189\) 4.42840 0.322119
\(190\) 3.59391 6.22484i 0.260730 0.451597i
\(191\) 1.29645 + 2.24552i 0.0938081 + 0.162480i 0.909111 0.416555i \(-0.136763\pi\)
−0.815302 + 0.579035i \(0.803429\pi\)
\(192\) 16.8536 + 29.1913i 1.21630 + 2.10670i
\(193\) 7.55176 13.0800i 0.543587 0.941521i −0.455107 0.890437i \(-0.650399\pi\)
0.998694 0.0510843i \(-0.0162677\pi\)
\(194\) −23.0877 + 39.9891i −1.65760 + 2.87105i
\(195\) 0.159020 + 0.275431i 0.0113877 + 0.0197240i
\(196\) 70.0364 5.00260
\(197\) 5.59983 + 9.69919i 0.398971 + 0.691039i 0.993599 0.112962i \(-0.0360339\pi\)
−0.594628 + 0.804001i \(0.702701\pi\)
\(198\) 10.6540 0.757144
\(199\) 2.13021 + 3.68964i 0.151007 + 0.261552i 0.931598 0.363491i \(-0.118415\pi\)
−0.780591 + 0.625042i \(0.785082\pi\)
\(200\) 22.9087 39.6790i 1.61989 2.80573i
\(201\) 1.03022 + 1.78439i 0.0726658 + 0.125861i
\(202\) −16.6613 −1.17229
\(203\) 45.7381 3.21019
\(204\) −16.0246 + 27.7554i −1.12195 + 1.94327i
\(205\) 2.39384 + 4.14625i 0.167193 + 0.289587i
\(206\) 23.0693 1.60732
\(207\) 0.597473 1.03485i 0.0415272 0.0719273i
\(208\) 4.50189 7.79751i 0.312150 0.540660i
\(209\) −9.11926 + 15.7950i −0.630792 + 1.09256i
\(210\) 3.38264 5.85890i 0.233424 0.404303i
\(211\) −17.2752 −1.18928 −0.594638 0.803994i \(-0.702704\pi\)
−0.594638 + 0.803994i \(0.702704\pi\)
\(212\) 3.13890 5.43673i 0.215580 0.373396i
\(213\) 9.36157 0.641444
\(214\) −6.16675 + 10.6811i −0.421550 + 0.730146i
\(215\) −5.61370 −0.382851
\(216\) −9.76701 −0.664561
\(217\) 8.37909 14.5130i 0.568810 0.985207i
\(218\) −0.950454 1.64623i −0.0643728 0.111497i
\(219\) −6.74811 + 11.6881i −0.455995 + 0.789807i
\(220\) 5.98332 10.3634i 0.403395 0.698701i
\(221\) 3.30186 0.222107
\(222\) 6.96886 0.467719
\(223\) 13.7028 23.7340i 0.917610 1.58935i 0.114575 0.993415i \(-0.463449\pi\)
0.803035 0.595932i \(-0.203217\pi\)
\(224\) −105.022 −7.01706
\(225\) 2.34551 + 4.06255i 0.156368 + 0.270837i
\(226\) −22.7802 39.4565i −1.51532 2.62461i
\(227\) −1.85385 3.21097i −0.123045 0.213119i 0.797922 0.602760i \(-0.205932\pi\)
−0.920967 + 0.389641i \(0.872599\pi\)
\(228\) 13.0651 22.6294i 0.865255 1.49867i
\(229\) −2.67308 + 4.62991i −0.176642 + 0.305953i −0.940728 0.339161i \(-0.889857\pi\)
0.764086 + 0.645114i \(0.223190\pi\)
\(230\) −0.912760 1.58095i −0.0601856 0.104245i
\(231\) −8.58318 + 14.8665i −0.564732 + 0.978144i
\(232\) −100.877 −6.62291
\(233\) 6.47919 + 11.2223i 0.424466 + 0.735196i 0.996370 0.0851239i \(-0.0271286\pi\)
−0.571905 + 0.820320i \(0.693795\pi\)
\(234\) 0.786274 + 1.36187i 0.0514004 + 0.0890281i
\(235\) 1.89948 0.123909
\(236\) 10.5724 0.688202
\(237\) −3.53577 6.12412i −0.229673 0.397805i
\(238\) −35.1181 60.8264i −2.27637 3.94279i
\(239\) −26.9233 −1.74153 −0.870763 0.491703i \(-0.836375\pi\)
−0.870763 + 0.491703i \(0.836375\pi\)
\(240\) −4.37351 + 7.57513i −0.282309 + 0.488973i
\(241\) 6.63584 + 11.4936i 0.427452 + 0.740369i 0.996646 0.0818345i \(-0.0260779\pi\)
−0.569194 + 0.822203i \(0.692745\pi\)
\(242\) −5.53341 + 9.58414i −0.355701 + 0.616092i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −0.972655 1.68469i −0.0622679 0.107851i
\(245\) 3.50485 + 6.07058i 0.223917 + 0.387835i
\(246\) 11.8363 + 20.5011i 0.754656 + 1.30710i
\(247\) −2.69205 −0.171291
\(248\) −18.4804 + 32.0090i −1.17351 + 2.03257i
\(249\) −6.82891 −0.432765
\(250\) 14.8050 0.936351
\(251\) 6.15031 10.6526i 0.388204 0.672389i −0.604004 0.796981i \(-0.706429\pi\)
0.992208 + 0.124592i \(0.0397623\pi\)
\(252\) 12.2970 21.2991i 0.774640 1.34172i
\(253\) 2.31606 + 4.01153i 0.145609 + 0.252203i
\(254\) 2.09674 3.63166i 0.131561 0.227871i
\(255\) −3.20769 −0.200873
\(256\) 56.8404 3.55253
\(257\) 13.9682 24.1936i 0.871312 1.50916i 0.0106718 0.999943i \(-0.496603\pi\)
0.860640 0.509214i \(-0.170064\pi\)
\(258\) −27.7569 −1.72807
\(259\) −5.61434 + 9.72432i −0.348858 + 0.604240i
\(260\) 1.76630 0.109542
\(261\) 5.16418 8.94462i 0.319655 0.553658i
\(262\) 26.0334 45.0911i 1.60835 2.78574i
\(263\) 12.0428 20.8587i 0.742591 1.28621i −0.208721 0.977975i \(-0.566930\pi\)
0.951312 0.308230i \(-0.0997367\pi\)
\(264\) 18.9305 32.7886i 1.16509 2.01800i
\(265\) 0.628322 0.0385975
\(266\) 28.6323 + 49.5926i 1.75556 + 3.04072i
\(267\) −2.76950 + 4.79692i −0.169491 + 0.293567i
\(268\) 11.4430 0.698994
\(269\) −5.31204 −0.323881 −0.161940 0.986801i \(-0.551775\pi\)
−0.161940 + 0.986801i \(0.551775\pi\)
\(270\) −0.763851 1.32303i −0.0464865 0.0805170i
\(271\) −10.2479 + 17.7499i −0.622517 + 1.07823i 0.366498 + 0.930419i \(0.380557\pi\)
−0.989015 + 0.147813i \(0.952777\pi\)
\(272\) 45.4051 + 78.6440i 2.75309 + 4.76849i
\(273\) −2.53379 −0.153352
\(274\) −15.5586 26.9482i −0.939928 1.62800i
\(275\) −18.1844 −1.09656
\(276\) −3.31819 5.74727i −0.199732 0.345945i
\(277\) −4.35788 + 7.54807i −0.261840 + 0.453520i −0.966731 0.255796i \(-0.917663\pi\)
0.704891 + 0.709316i \(0.250996\pi\)
\(278\) −3.34414 + 5.79222i −0.200568 + 0.347394i
\(279\) −1.89212 3.27726i −0.113279 0.196204i
\(280\) −12.0209 20.8208i −0.718387 1.24428i
\(281\) 5.63715 9.76382i 0.336284 0.582461i −0.647447 0.762111i \(-0.724163\pi\)
0.983731 + 0.179650i \(0.0574965\pi\)
\(282\) 9.39198 0.559284
\(283\) −2.43965 + 4.22560i −0.145022 + 0.251186i −0.929381 0.369121i \(-0.879659\pi\)
0.784359 + 0.620307i \(0.212992\pi\)
\(284\) 25.9957 45.0259i 1.54256 2.67179i
\(285\) 2.61527 0.154915
\(286\) −6.09586 −0.360456
\(287\) −38.1429 −2.25150
\(288\) −11.8577 + 20.5382i −0.698724 + 1.21023i
\(289\) −8.15091 + 14.1178i −0.479465 + 0.830458i
\(290\) −7.88933 13.6647i −0.463277 0.802420i
\(291\) −16.8008 −0.984883
\(292\) 37.4771 + 64.9122i 2.19318 + 3.79870i
\(293\) 3.23932 + 5.61067i 0.189243 + 0.327779i 0.944998 0.327076i \(-0.106063\pi\)
−0.755755 + 0.654854i \(0.772730\pi\)
\(294\) 17.3297 + 30.0159i 1.01069 + 1.75056i
\(295\) 0.529076 + 0.916386i 0.0308040 + 0.0533540i
\(296\) 12.3826 21.4474i 0.719726 1.24660i
\(297\) 1.93821 + 3.35708i 0.112466 + 0.194797i
\(298\) 26.3193 1.52463
\(299\) −0.341855 + 0.592111i −0.0197700 + 0.0342427i
\(300\) 26.0526 1.50415
\(301\) 22.3619 38.7319i 1.28892 2.23247i
\(302\) 22.0276 + 38.1528i 1.26754 + 2.19545i
\(303\) −3.03110 5.25002i −0.174132 0.301606i
\(304\) −37.0194 64.1195i −2.12321 3.67751i
\(305\) 0.0973497 0.168615i 0.00557423 0.00965484i
\(306\) −15.8604 −0.906678
\(307\) 8.81502 0.503100 0.251550 0.967844i \(-0.419060\pi\)
0.251550 + 0.967844i \(0.419060\pi\)
\(308\) 47.6684 + 82.5642i 2.71616 + 4.70453i
\(309\) 4.19686 + 7.26918i 0.238751 + 0.413529i
\(310\) −5.78120 −0.328350
\(311\) 3.01535 + 5.22275i 0.170985 + 0.296155i 0.938765 0.344559i \(-0.111972\pi\)
−0.767779 + 0.640714i \(0.778638\pi\)
\(312\) 5.58838 0.316380
\(313\) −1.80118 −0.101809 −0.0509044 0.998704i \(-0.516210\pi\)
−0.0509044 + 0.998704i \(0.516210\pi\)
\(314\) −14.1040 + 31.4167i −0.795934 + 1.77295i
\(315\) 2.46153 0.138692
\(316\) −39.2732 −2.20929
\(317\) −9.54975 16.5406i −0.536367 0.929015i −0.999096 0.0425153i \(-0.986463\pi\)
0.462729 0.886500i \(-0.346870\pi\)
\(318\) 3.10673 0.174217
\(319\) 20.0185 + 34.6731i 1.12082 + 1.94132i
\(320\) 9.36809 + 16.2260i 0.523692 + 0.907061i
\(321\) −4.48752 −0.250469
\(322\) 14.5437 0.810490
\(323\) 13.5757 23.5138i 0.755373 1.30834i
\(324\) −2.77685 4.80965i −0.154270 0.267203i
\(325\) −1.34203 2.32446i −0.0744424 0.128938i
\(326\) 19.9136 + 34.4914i 1.10291 + 1.91030i
\(327\) 0.345821 0.598979i 0.0191239 0.0331236i
\(328\) 84.1256 4.64506
\(329\) −7.56649 + 13.1055i −0.417154 + 0.722532i
\(330\) 5.92201 0.325996
\(331\) −3.27008 5.66394i −0.179740 0.311318i 0.762052 0.647516i \(-0.224192\pi\)
−0.941791 + 0.336198i \(0.890859\pi\)
\(332\) −18.9629 + 32.8447i −1.04072 + 1.80259i
\(333\) 1.26780 + 2.19590i 0.0694751 + 0.120334i
\(334\) −4.21650 7.30320i −0.230717 0.399613i
\(335\) 0.572646 + 0.991853i 0.0312870 + 0.0541907i
\(336\) −34.8432 60.3502i −1.90085 3.29237i
\(337\) 13.5462 0.737906 0.368953 0.929448i \(-0.379716\pi\)
0.368953 + 0.929448i \(0.379716\pi\)
\(338\) 17.4147 + 30.1632i 0.947236 + 1.64066i
\(339\) 8.28854 14.3562i 0.450172 0.779720i
\(340\) −8.90729 + 15.4279i −0.483065 + 0.836694i
\(341\) 14.6693 0.794389
\(342\) 12.9312 0.699239
\(343\) −24.8467 −1.34159
\(344\) −49.3200 + 85.4247i −2.65915 + 4.60579i
\(345\) 0.332106 0.575225i 0.0178800 0.0309690i
\(346\) −15.0018 −0.806501
\(347\) 13.5077 23.3961i 0.725134 1.25597i −0.233786 0.972288i \(-0.575111\pi\)
0.958919 0.283680i \(-0.0915553\pi\)
\(348\) −28.6803 49.6758i −1.53743 2.66290i
\(349\) −13.8261 23.9476i −0.740096 1.28188i −0.952451 0.304691i \(-0.901447\pi\)
0.212355 0.977193i \(-0.431887\pi\)
\(350\) −28.5473 + 49.4454i −1.52592 + 2.64297i
\(351\) −0.286084 + 0.495513i −0.0152701 + 0.0264485i
\(352\) −45.9656 79.6148i −2.44997 4.24348i
\(353\) −14.5495 −0.774392 −0.387196 0.921997i \(-0.626556\pi\)
−0.387196 + 0.921997i \(0.626556\pi\)
\(354\) 2.61601 + 4.53106i 0.139039 + 0.240823i
\(355\) 5.20364 0.276180
\(356\) 15.3810 + 26.6407i 0.815192 + 1.41195i
\(357\) 12.7777 22.1315i 0.676265 1.17133i
\(358\) −13.8116 23.9224i −0.729965 1.26434i
\(359\) 3.69915 0.195233 0.0976167 0.995224i \(-0.468878\pi\)
0.0976167 + 0.995224i \(0.468878\pi\)
\(360\) −5.42900 −0.286134
\(361\) −1.56847 + 2.71666i −0.0825509 + 0.142982i
\(362\) −21.8313 37.8129i −1.14743 1.98740i
\(363\) −4.02664 −0.211344
\(364\) −7.03597 + 12.1867i −0.368785 + 0.638755i
\(365\) −3.75095 + 6.49683i −0.196334 + 0.340060i
\(366\) 0.481345 0.833713i 0.0251603 0.0435789i
\(367\) 9.61899 16.6606i 0.502107 0.869675i −0.497890 0.867240i \(-0.665892\pi\)
0.999997 0.00243470i \(-0.000774989\pi\)
\(368\) −18.8040 −0.980224
\(369\) −4.30662 + 7.45928i −0.224194 + 0.388315i
\(370\) 3.87365 0.201381
\(371\) −2.50289 + 4.33513i −0.129943 + 0.225069i
\(372\) −21.0166 −1.08966
\(373\) −11.2613 −0.583085 −0.291543 0.956558i \(-0.594169\pi\)
−0.291543 + 0.956558i \(0.594169\pi\)
\(374\) 30.7408 53.2446i 1.58957 2.75321i
\(375\) 2.69339 + 4.66508i 0.139086 + 0.240904i
\(376\) 16.6882 28.9048i 0.860627 1.49065i
\(377\) −2.95478 + 5.11783i −0.152179 + 0.263582i
\(378\) 12.1710 0.626010
\(379\) 17.6749 0.907899 0.453949 0.891028i \(-0.350015\pi\)
0.453949 + 0.891028i \(0.350015\pi\)
\(380\) 7.26223 12.5786i 0.372545 0.645266i
\(381\) 1.52579 0.0781686
\(382\) 3.56317 + 6.17160i 0.182308 + 0.315766i
\(383\) 6.36056 + 11.0168i 0.325009 + 0.562933i 0.981514 0.191389i \(-0.0612992\pi\)
−0.656505 + 0.754322i \(0.727966\pi\)
\(384\) 22.6049 + 39.1529i 1.15355 + 1.99801i
\(385\) −4.77097 + 8.26356i −0.243151 + 0.421150i
\(386\) 20.7553 35.9492i 1.05641 1.82976i
\(387\) −5.04965 8.74625i −0.256688 0.444597i
\(388\) −46.6535 + 80.8062i −2.36847 + 4.10231i
\(389\) −23.2925 −1.18098 −0.590489 0.807046i \(-0.701065\pi\)
−0.590489 + 0.807046i \(0.701065\pi\)
\(390\) 0.437052 + 0.756996i 0.0221310 + 0.0383320i
\(391\) −3.44788 5.97190i −0.174367 0.302012i
\(392\) 123.169 6.22099
\(393\) 18.9444 0.955618
\(394\) 15.3906 + 26.6573i 0.775366 + 1.34297i
\(395\) −1.96536 3.40410i −0.0988880 0.171279i
\(396\) 21.5285 1.08185
\(397\) −2.83255 + 4.90613i −0.142162 + 0.246232i −0.928310 0.371806i \(-0.878739\pi\)
0.786149 + 0.618037i \(0.212072\pi\)
\(398\) 5.85468 + 10.1406i 0.293469 + 0.508303i
\(399\) −10.4178 + 18.0442i −0.521542 + 0.903338i
\(400\) 36.9096 63.9293i 1.84548 3.19646i
\(401\) −3.42273 5.92835i −0.170923 0.296048i 0.767820 0.640666i \(-0.221342\pi\)
−0.938743 + 0.344618i \(0.888008\pi\)
\(402\) 2.83144 + 4.90421i 0.141220 + 0.244600i
\(403\) 1.08261 + 1.87514i 0.0539289 + 0.0934075i
\(404\) −33.6677 −1.67503
\(405\) 0.277926 0.481381i 0.0138102 0.0239200i
\(406\) 125.707 6.23872
\(407\) −9.82907 −0.487209
\(408\) −28.1816 + 48.8120i −1.39520 + 2.41655i
\(409\) −11.3065 + 19.5834i −0.559069 + 0.968336i 0.438506 + 0.898728i \(0.355508\pi\)
−0.997574 + 0.0696071i \(0.977825\pi\)
\(410\) 6.57923 + 11.3956i 0.324925 + 0.562787i
\(411\) 5.66096 9.80506i 0.279234 0.483648i
\(412\) 46.6163 2.29662
\(413\) −8.43017 −0.414822
\(414\) 1.64210 2.84419i 0.0807046 0.139784i
\(415\) −3.79586 −0.186331
\(416\) 6.78463 11.7513i 0.332644 0.576156i
\(417\) −2.43352 −0.119170
\(418\) −25.0634 + 43.4111i −1.22589 + 2.12330i
\(419\) −14.0041 + 24.2558i −0.684146 + 1.18498i 0.289559 + 0.957160i \(0.406491\pi\)
−0.973704 + 0.227815i \(0.926842\pi\)
\(420\) 6.83532 11.8391i 0.333529 0.577690i
\(421\) 5.64983 9.78580i 0.275356 0.476931i −0.694869 0.719136i \(-0.744538\pi\)
0.970225 + 0.242206i \(0.0778709\pi\)
\(422\) −47.4792 −2.31125
\(423\) 1.70863 + 2.95943i 0.0830762 + 0.143892i
\(424\) 5.52021 9.56128i 0.268085 0.464337i
\(425\) 27.0709 1.31313
\(426\) 25.7293 1.24659
\(427\) 0.775574 + 1.34333i 0.0375326 + 0.0650084i
\(428\) −12.4612 + 21.5834i −0.602334 + 1.04327i
\(429\) −1.10898 1.92082i −0.0535422 0.0927378i
\(430\) −15.4287 −0.744038
\(431\) −17.4011 30.1397i −0.838184 1.45178i −0.891412 0.453194i \(-0.850284\pi\)
0.0532284 0.998582i \(-0.483049\pi\)
\(432\) −15.7362 −0.757110
\(433\) −14.0184 24.2806i −0.673681 1.16685i −0.976852 0.213914i \(-0.931379\pi\)
0.303171 0.952936i \(-0.401955\pi\)
\(434\) 23.0291 39.8876i 1.10543 1.91466i
\(435\) 2.87052 4.97188i 0.137631 0.238383i
\(436\) −1.92059 3.32655i −0.0919794 0.159313i
\(437\) 2.81110 + 4.86898i 0.134473 + 0.232915i
\(438\) −18.5465 + 32.1235i −0.886187 + 1.53492i
\(439\) −25.4068 −1.21260 −0.606301 0.795235i \(-0.707347\pi\)
−0.606301 + 0.795235i \(0.707347\pi\)
\(440\) 10.5226 18.2256i 0.501643 0.868871i
\(441\) −6.30538 + 10.9212i −0.300256 + 0.520059i
\(442\) 9.07482 0.431645
\(443\) −10.5502 −0.501256 −0.250628 0.968083i \(-0.580637\pi\)
−0.250628 + 0.968083i \(0.580637\pi\)
\(444\) 14.0820 0.668302
\(445\) −1.53943 + 2.66637i −0.0729761 + 0.126398i
\(446\) 37.6609 65.2306i 1.78329 3.08876i
\(447\) 4.78810 + 8.29324i 0.226470 + 0.392257i
\(448\) −149.269 −7.05229
\(449\) 1.16703 + 2.02135i 0.0550755 + 0.0953935i 0.892249 0.451544i \(-0.149127\pi\)
−0.837173 + 0.546938i \(0.815793\pi\)
\(450\) 6.44641 + 11.1655i 0.303887 + 0.526348i
\(451\) −16.6943 28.9153i −0.786102 1.36157i
\(452\) −46.0321 79.7299i −2.16517 3.75018i
\(453\) −8.01468 + 13.8818i −0.376562 + 0.652225i
\(454\) −5.09513 8.82503i −0.239126 0.414179i
\(455\) −1.40841 −0.0660274
\(456\) 22.9768 39.7971i 1.07599 1.86367i
\(457\) 37.2626 1.74307 0.871535 0.490333i \(-0.163125\pi\)
0.871535 + 0.490333i \(0.163125\pi\)
\(458\) −7.34670 + 12.7249i −0.343289 + 0.594594i
\(459\) −2.88539 4.99764i −0.134678 0.233270i
\(460\) −1.84442 3.19463i −0.0859965 0.148950i
\(461\) 5.18045 + 8.97280i 0.241278 + 0.417905i 0.961078 0.276276i \(-0.0891002\pi\)
−0.719801 + 0.694181i \(0.755767\pi\)
\(462\) −23.5900 + 40.8591i −1.09751 + 1.90094i
\(463\) −9.61981 −0.447071 −0.223535 0.974696i \(-0.571760\pi\)
−0.223535 + 0.974696i \(0.571760\pi\)
\(464\) −162.530 −7.54525
\(465\) −1.05174 1.82167i −0.0487733 0.0844778i
\(466\) 17.8074 + 30.8433i 0.824912 + 1.42879i
\(467\) −37.6168 −1.74070 −0.870348 0.492437i \(-0.836106\pi\)
−0.870348 + 0.492437i \(0.836106\pi\)
\(468\) 1.58883 + 2.75193i 0.0734436 + 0.127208i
\(469\) −9.12442 −0.421326
\(470\) 5.22054 0.240806
\(471\) −12.4653 + 1.27126i −0.574371 + 0.0585767i
\(472\) 18.5931 0.855815
\(473\) 39.1491 1.80008
\(474\) −9.71770 16.8315i −0.446349 0.773099i
\(475\) −22.0712 −1.01270
\(476\) −70.9633 122.912i −3.25260 5.63367i
\(477\) 0.565189 + 0.978937i 0.0258782 + 0.0448224i
\(478\) −73.9961 −3.38450
\(479\) −19.9238 −0.910343 −0.455172 0.890404i \(-0.650422\pi\)
−0.455172 + 0.890404i \(0.650422\pi\)
\(480\) −6.59114 + 11.4162i −0.300843 + 0.521075i
\(481\) −0.725397 1.25642i −0.0330752 0.0572880i
\(482\) 18.2380 + 31.5891i 0.830716 + 1.43884i
\(483\) 2.64585 + 4.58275i 0.120390 + 0.208522i
\(484\) −11.1814 + 19.3667i −0.508245 + 0.880305i
\(485\) −9.33877 −0.424052
\(486\) 1.37420 2.38018i 0.0623350 0.107967i
\(487\) −32.7100 −1.48223 −0.741117 0.671376i \(-0.765704\pi\)
−0.741117 + 0.671376i \(0.765704\pi\)
\(488\) −1.71056 2.96277i −0.0774333 0.134118i
\(489\) −7.24553 + 12.5496i −0.327654 + 0.567514i
\(490\) 9.63274 + 16.6844i 0.435163 + 0.753724i
\(491\) 1.19785 + 2.07473i 0.0540581 + 0.0936313i 0.891788 0.452453i \(-0.149451\pi\)
−0.837730 + 0.546085i \(0.816118\pi\)
\(492\) 23.9177 + 41.4267i 1.07829 + 1.86766i
\(493\) −29.8013 51.6174i −1.34218 2.32473i
\(494\) −7.39883 −0.332889
\(495\) 1.07736 + 1.86604i 0.0484236 + 0.0838721i
\(496\) −29.7749 + 51.5717i −1.33693 + 2.31564i
\(497\) −20.7284 + 35.9026i −0.929796 + 1.61045i
\(498\) −18.7686 −0.841040
\(499\) 7.19526 0.322104 0.161052 0.986946i \(-0.448511\pi\)
0.161052 + 0.986946i \(0.448511\pi\)
\(500\) 29.9165 1.33791
\(501\) 1.53417 2.65725i 0.0685415 0.118717i
\(502\) 16.9035 29.2777i 0.754440 1.30673i
\(503\) 27.3124 1.21780 0.608899 0.793248i \(-0.291611\pi\)
0.608899 + 0.793248i \(0.291611\pi\)
\(504\) 21.6261 37.4576i 0.963304 1.66849i
\(505\) −1.68484 2.91823i −0.0749744 0.129859i
\(506\) 6.36545 + 11.0253i 0.282979 + 0.490134i
\(507\) −6.33631 + 10.9748i −0.281405 + 0.487409i
\(508\) 4.23689 7.33852i 0.187982 0.325594i
\(509\) 17.6495 + 30.5698i 0.782299 + 1.35498i 0.930599 + 0.366040i \(0.119287\pi\)
−0.148300 + 0.988942i \(0.547380\pi\)
\(510\) −8.81602 −0.390380
\(511\) −29.8834 51.7595i −1.32196 2.28971i
\(512\) 65.8006 2.90800
\(513\) 2.35250 + 4.07464i 0.103865 + 0.179900i
\(514\) 38.3902 66.4938i 1.69332 2.93291i
\(515\) 2.33283 + 4.04058i 0.102797 + 0.178049i
\(516\) −56.0885 −2.46916
\(517\) −13.2467 −0.582590
\(518\) −15.4305 + 26.7263i −0.677975 + 1.17429i
\(519\) −2.72918 4.72709i −0.119798 0.207496i
\(520\) 3.10631 0.136221
\(521\) 4.61151 7.98737i 0.202034 0.349933i −0.747150 0.664656i \(-0.768578\pi\)
0.949184 + 0.314723i \(0.101912\pi\)
\(522\) 14.1932 24.5834i 0.621221 1.07599i
\(523\) −5.97535 + 10.3496i −0.261284 + 0.452557i −0.966583 0.256353i \(-0.917479\pi\)
0.705300 + 0.708909i \(0.250813\pi\)
\(524\) 52.6058 91.1159i 2.29809 3.98042i
\(525\) −20.7738 −0.906642
\(526\) 33.0985 57.3282i 1.44316 2.49963i
\(527\) −21.8380 −0.951280
\(528\) 30.5002 52.8278i 1.32735 2.29904i
\(529\) −21.5721 −0.937918
\(530\) 1.72688 0.0750109
\(531\) −0.951830 + 1.64862i −0.0413059 + 0.0715439i
\(532\) 57.8574 + 100.212i 2.50844 + 4.34474i
\(533\) 2.46411 4.26797i 0.106733 0.184866i
\(534\) −7.61171 + 13.1839i −0.329391 + 0.570521i
\(535\) −2.49439 −0.107842
\(536\) 20.1242 0.869235
\(537\) 5.02532 8.70410i 0.216858 0.375610i
\(538\) −14.5996 −0.629434
\(539\) −24.4423 42.3353i −1.05280 1.82351i
\(540\) −1.54352 2.67345i −0.0664224 0.115047i
\(541\) −8.17072 14.1521i −0.351287 0.608446i 0.635189 0.772357i \(-0.280922\pi\)
−0.986475 + 0.163911i \(0.947589\pi\)
\(542\) −28.1654 + 48.7839i −1.20981 + 2.09545i
\(543\) 7.94327 13.7582i 0.340878 0.590419i
\(544\) 68.4283 + 118.521i 2.93384 + 5.08156i
\(545\) 0.192225 0.332943i 0.00823400 0.0142617i
\(546\) −6.96388 −0.298027
\(547\) 11.8974 + 20.6069i 0.508697 + 0.881089i 0.999949 + 0.0100715i \(0.00320592\pi\)
−0.491252 + 0.871017i \(0.663461\pi\)
\(548\) −31.4393 54.4544i −1.34302 2.32618i
\(549\) 0.350272 0.0149493
\(550\) −49.9780 −2.13107
\(551\) 24.2974 + 42.0844i 1.03510 + 1.79285i
\(552\) −5.83552 10.1074i −0.248376 0.430201i
\(553\) 31.3156 1.33167
\(554\) −11.9772 + 20.7451i −0.508863 + 0.881376i
\(555\) 0.704709 + 1.22059i 0.0299132 + 0.0518113i
\(556\) −6.75752 + 11.7044i −0.286583 + 0.496376i
\(557\) −9.97395 + 17.2754i −0.422610 + 0.731982i −0.996194 0.0871650i \(-0.972219\pi\)
0.573584 + 0.819147i \(0.305553\pi\)
\(558\) −5.20032 9.00721i −0.220147 0.381306i
\(559\) 2.88925 + 5.00433i 0.122202 + 0.211661i
\(560\) −19.3676 33.5457i −0.818432 1.41757i
\(561\) 22.3699 0.944460
\(562\) 15.4931 26.8349i 0.653539 1.13196i
\(563\) −18.5052 −0.779900 −0.389950 0.920836i \(-0.627508\pi\)
−0.389950 + 0.920836i \(0.627508\pi\)
\(564\) 18.9784 0.799135
\(565\) 4.60719 7.97989i 0.193826 0.335717i
\(566\) −6.70514 + 11.6136i −0.281838 + 0.488158i
\(567\) 2.21420 + 3.83511i 0.0929877 + 0.161059i
\(568\) 45.7173 79.1846i 1.91825 3.32251i
\(569\) 21.2740 0.891852 0.445926 0.895070i \(-0.352874\pi\)
0.445926 + 0.895070i \(0.352874\pi\)
\(570\) 7.18782 0.301065
\(571\) −10.4991 + 18.1849i −0.439372 + 0.761014i −0.997641 0.0686458i \(-0.978132\pi\)
0.558270 + 0.829660i \(0.311466\pi\)
\(572\) −12.3179 −0.515039
\(573\) −1.29645 + 2.24552i −0.0541601 + 0.0938081i
\(574\) −104.832 −4.37560
\(575\) −2.80276 + 4.85453i −0.116883 + 0.202448i
\(576\) −16.8536 + 29.1913i −0.702233 + 1.21630i
\(577\) −17.3629 + 30.0734i −0.722827 + 1.25197i 0.237036 + 0.971501i \(0.423824\pi\)
−0.959862 + 0.280471i \(0.909509\pi\)
\(578\) −22.4020 + 38.8013i −0.931799 + 1.61392i
\(579\) 15.1035 0.627681
\(580\) −15.9420 27.6124i −0.661956 1.14654i
\(581\) 15.1206 26.1896i 0.627307 1.08653i
\(582\) −46.1754 −1.91403
\(583\) −4.38182 −0.181477
\(584\) 65.9089 + 114.158i 2.72733 + 4.72387i
\(585\) −0.159020 + 0.275431i −0.00657468 + 0.0113877i
\(586\) 8.90295 + 15.4204i 0.367777 + 0.637009i
\(587\) 11.4699 0.473413 0.236706 0.971581i \(-0.423932\pi\)
0.236706 + 0.971581i \(0.423932\pi\)
\(588\) 35.0182 + 60.6533i 1.44413 + 2.50130i
\(589\) 17.8049 0.733636
\(590\) 1.45411 + 2.51860i 0.0598648 + 0.103689i
\(591\) −5.59983 + 9.69919i −0.230346 + 0.398971i
\(592\) 19.9504 34.5552i 0.819958 1.42021i
\(593\) −2.03686 3.52795i −0.0836440 0.144876i 0.821169 0.570686i \(-0.193323\pi\)
−0.904813 + 0.425810i \(0.859989\pi\)
\(594\) 5.32698 + 9.22660i 0.218569 + 0.378572i
\(595\) 7.10247 12.3018i 0.291173 0.504326i
\(596\) 53.1835 2.17848
\(597\) −2.13021 + 3.68964i −0.0871839 + 0.151007i
\(598\) −0.939555 + 1.62736i −0.0384213 + 0.0665476i
\(599\) −30.6585 −1.25267 −0.626336 0.779553i \(-0.715446\pi\)
−0.626336 + 0.779553i \(0.715446\pi\)
\(600\) 45.8173 1.87048
\(601\) 22.7170 0.926646 0.463323 0.886189i \(-0.346657\pi\)
0.463323 + 0.886189i \(0.346657\pi\)
\(602\) 61.4594 106.451i 2.50490 4.33861i
\(603\) −1.03022 + 1.78439i −0.0419536 + 0.0726658i
\(604\) 44.5112 + 77.0956i 1.81113 + 3.13698i
\(605\) −2.23821 −0.0909962
\(606\) −8.33067 14.4292i −0.338411 0.586144i
\(607\) 9.68733 + 16.7790i 0.393197 + 0.681037i 0.992869 0.119209i \(-0.0380358\pi\)
−0.599673 + 0.800246i \(0.704702\pi\)
\(608\) −55.7906 96.6321i −2.26261 3.91895i
\(609\) 22.8691 + 39.6104i 0.926702 + 1.60509i
\(610\) 0.267556 0.463420i 0.0108330 0.0187633i
\(611\) −0.977622 1.69329i −0.0395504 0.0685032i
\(612\) −32.0492 −1.29551
\(613\) 14.6408 25.3586i 0.591336 1.02422i −0.402717 0.915325i \(-0.631934\pi\)
0.994053 0.108899i \(-0.0347325\pi\)
\(614\) 24.2272 0.977730
\(615\) −2.39384 + 4.14625i −0.0965289 + 0.167193i
\(616\) 83.8320 + 145.201i 3.37769 + 5.85032i
\(617\) −1.51295 2.62050i −0.0609089 0.105497i 0.833963 0.551820i \(-0.186067\pi\)
−0.894872 + 0.446323i \(0.852733\pi\)
\(618\) 11.5347 + 19.9786i 0.463992 + 0.803658i
\(619\) 13.2838 23.0083i 0.533922 0.924780i −0.465293 0.885157i \(-0.654051\pi\)
0.999215 0.0396231i \(-0.0126157\pi\)
\(620\) −11.6821 −0.469165
\(621\) 1.19495 0.0479515
\(622\) 8.28740 + 14.3542i 0.332294 + 0.575551i
\(623\) −12.2645 21.2427i −0.491366 0.851071i
\(624\) 9.00379 0.360440
\(625\) −10.2305 17.7197i −0.409218 0.708787i
\(626\) −4.95037 −0.197857
\(627\) −18.2385 −0.728376
\(628\) −28.5000 + 63.4839i −1.13727 + 2.53328i
\(629\) 14.6324 0.583432
\(630\) 6.76528 0.269535
\(631\) −12.2938 21.2935i −0.489410 0.847682i 0.510516 0.859868i \(-0.329454\pi\)
−0.999926 + 0.0121859i \(0.996121\pi\)
\(632\) −69.0677 −2.74737
\(633\) −8.63761 14.9608i −0.343314 0.594638i
\(634\) −26.2465 45.4603i −1.04238 1.80546i
\(635\) 0.848112 0.0336563
\(636\) 6.27779 0.248931
\(637\) 3.60774 6.24879i 0.142944 0.247586i
\(638\) 55.0190 + 95.2956i 2.17822 + 3.77279i
\(639\) 4.68078 + 8.10735i 0.185169 + 0.320722i
\(640\) 12.5650 + 21.7632i 0.496674 + 0.860265i
\(641\) 16.6301 28.8041i 0.656848 1.13769i −0.324579 0.945859i \(-0.605222\pi\)
0.981427 0.191836i \(-0.0614442\pi\)
\(642\) −12.3335 −0.486764
\(643\) 9.12819 15.8105i 0.359981 0.623505i −0.627976 0.778232i \(-0.716117\pi\)
0.987957 + 0.154727i \(0.0494499\pi\)
\(644\) 29.3886 1.15807
\(645\) −2.80685 4.86161i −0.110520 0.191426i
\(646\) 37.3115 64.6254i 1.46800 2.54265i
\(647\) 14.6648 + 25.4002i 0.576534 + 0.998586i 0.995873 + 0.0907564i \(0.0289285\pi\)
−0.419339 + 0.907830i \(0.637738\pi\)
\(648\) −4.88351 8.45848i −0.191842 0.332280i
\(649\) −3.68969 6.39073i −0.144833 0.250858i
\(650\) −3.68844 6.38856i −0.144672 0.250580i
\(651\) 16.7582 0.656805
\(652\) 40.2395 + 69.6969i 1.57590 + 2.72954i
\(653\) 4.58519 7.94178i 0.179432 0.310786i −0.762254 0.647278i \(-0.775907\pi\)
0.941686 + 0.336492i \(0.109241\pi\)
\(654\) 0.950454 1.64623i 0.0371657 0.0643728i
\(655\) 10.5303 0.411451
\(656\) 135.540 5.29195
\(657\) −13.4962 −0.526538
\(658\) −20.7957 + 36.0193i −0.810702 + 1.40418i
\(659\) −9.52136 + 16.4915i −0.370900 + 0.642417i −0.989704 0.143128i \(-0.954284\pi\)
0.618805 + 0.785545i \(0.287617\pi\)
\(660\) 11.9666 0.465801
\(661\) −2.51320 + 4.35300i −0.0977523 + 0.169312i −0.910754 0.412949i \(-0.864499\pi\)
0.813002 + 0.582261i \(0.197832\pi\)
\(662\) −8.98749 15.5668i −0.349309 0.605020i
\(663\) 1.65093 + 2.85949i 0.0641167 + 0.111053i
\(664\) −33.3490 + 57.7622i −1.29419 + 2.24161i
\(665\) −5.79074 + 10.0299i −0.224555 + 0.388941i
\(666\) 3.48443 + 6.03521i 0.135019 + 0.233860i
\(667\) 12.3418 0.477878
\(668\) −8.52031 14.7576i −0.329661 0.570989i
\(669\) 27.4057 1.05956
\(670\) 1.57386 + 2.72601i 0.0608036 + 0.105315i
\(671\) −0.678902 + 1.17589i −0.0262087 + 0.0453948i
\(672\) −52.5109 90.9515i −2.02565 3.50853i
\(673\) 33.4070 1.28774 0.643872 0.765133i \(-0.277327\pi\)
0.643872 + 0.765133i \(0.277327\pi\)
\(674\) 37.2303 1.43406
\(675\) −2.34551 + 4.06255i −0.0902789 + 0.156368i
\(676\) 35.1900 + 60.9509i 1.35346 + 2.34427i
\(677\) −1.63873 −0.0629814 −0.0314907 0.999504i \(-0.510025\pi\)
−0.0314907 + 0.999504i \(0.510025\pi\)
\(678\) 22.7802 39.4565i 0.874869 1.51532i
\(679\) 37.2005 64.4331i 1.42762 2.47271i
\(680\) −15.6648 + 27.1322i −0.600717 + 1.04047i
\(681\) 1.85385 3.21097i 0.0710398 0.123045i
\(682\) 40.3172 1.54383
\(683\) 14.2677 24.7124i 0.545938 0.945593i −0.452609 0.891709i \(-0.649507\pi\)
0.998547 0.0538837i \(-0.0171600\pi\)
\(684\) 26.1301 0.999111
\(685\) 3.14665 5.45016i 0.120227 0.208240i
\(686\) −68.2886 −2.60727
\(687\) −5.34617 −0.203969
\(688\) −79.4625 + 137.633i −3.02948 + 5.24721i
\(689\) −0.323384 0.560117i −0.0123199 0.0213388i
\(690\) 0.912760 1.58095i 0.0347482 0.0601856i
\(691\) −19.5833 + 33.9192i −0.744983 + 1.29035i 0.205220 + 0.978716i \(0.434209\pi\)
−0.950203 + 0.311632i \(0.899124\pi\)
\(692\) −30.3142 −1.15237
\(693\) −17.1664 −0.652096
\(694\) 37.1247 64.3018i 1.40923 2.44086i
\(695\) −1.35267 −0.0513098
\(696\) −50.4386 87.3622i −1.91187 3.31146i
\(697\) 24.8525 + 43.0458i 0.941356 + 1.63048i
\(698\) −37.9998 65.8175i −1.43831 2.49123i
\(699\) −6.47919 + 11.2223i −0.245065 + 0.424466i
\(700\) −57.6857 + 99.9146i −2.18031 + 3.77642i
\(701\) 16.1264 + 27.9318i 0.609086 + 1.05497i 0.991391 + 0.130932i \(0.0417971\pi\)
−0.382305 + 0.924036i \(0.624870\pi\)
\(702\) −0.786274 + 1.36187i −0.0296760 + 0.0514004i
\(703\) −11.9300 −0.449948
\(704\) −65.3316 113.158i −2.46228 4.26479i
\(705\) 0.949742 + 1.64500i 0.0357693 + 0.0619543i
\(706\) −39.9879 −1.50496
\(707\) 26.8459 1.00964
\(708\) 5.28618 + 9.15594i 0.198667 + 0.344101i
\(709\) 18.7819 + 32.5312i 0.705369 + 1.22174i 0.966558 + 0.256447i \(0.0825520\pi\)
−0.261189 + 0.965288i \(0.584115\pi\)
\(710\) 14.3017 0.536733
\(711\) 3.53577 6.12412i 0.132602 0.229673i
\(712\) 27.0498 + 46.8516i 1.01373 + 1.75584i
\(713\) 2.26099 3.91614i 0.0846746 0.146661i
\(714\) 35.1181 60.8264i 1.31426 2.27637i
\(715\) −0.616430 1.06769i −0.0230532 0.0399292i
\(716\) −27.9091 48.3400i −1.04301 1.80655i
\(717\) −13.4617 23.3163i −0.502735 0.870763i
\(718\) 10.1667 0.379419
\(719\) −2.94846 + 5.10689i −0.109959 + 0.190455i −0.915753 0.401741i \(-0.868405\pi\)
0.805794 + 0.592195i \(0.201739\pi\)
\(720\) −8.74701 −0.325982
\(721\) −37.1708 −1.38431
\(722\) −4.31077 + 7.46648i −0.160430 + 0.277874i
\(723\) −6.63584 + 11.4936i −0.246790 + 0.427452i
\(724\) −44.1146 76.4087i −1.63951 2.83971i
\(725\) −24.2253 + 41.9595i −0.899706 + 1.55834i
\(726\) −11.0668 −0.410728
\(727\) −36.0466 −1.33689 −0.668447 0.743760i \(-0.733041\pi\)
−0.668447 + 0.743760i \(0.733041\pi\)
\(728\) −12.3738 + 21.4320i −0.458603 + 0.794324i
\(729\) 1.00000 0.0370370
\(730\) −10.3091 + 17.8559i −0.381557 + 0.660876i
\(731\) −58.2807 −2.15559
\(732\) 0.972655 1.68469i 0.0359504 0.0622679i
\(733\) 11.3298 19.6238i 0.418475 0.724820i −0.577311 0.816524i \(-0.695898\pi\)
0.995786 + 0.0917041i \(0.0292314\pi\)
\(734\) 26.4368 45.7899i 0.975801 1.69014i
\(735\) −3.50485 + 6.07058i −0.129278 + 0.223917i
\(736\) −28.3387 −1.04458
\(737\) −3.99355 6.91703i −0.147104 0.254792i
\(738\) −11.8363 + 20.5011i −0.435701 + 0.754656i
\(739\) −2.87789 −0.105865 −0.0529324 0.998598i \(-0.516857\pi\)
−0.0529324 + 0.998598i \(0.516857\pi\)
\(740\) 7.82750 0.287745
\(741\) −1.34602 2.33138i −0.0494474 0.0856455i
\(742\) −6.87893 + 11.9147i −0.252534 + 0.437401i
\(743\) 24.0698 + 41.6900i 0.883034 + 1.52946i 0.847951 + 0.530075i \(0.177836\pi\)
0.0350825 + 0.999384i \(0.488831\pi\)
\(744\) −36.9608 −1.35505
\(745\) 2.66147 + 4.60981i 0.0975088 + 0.168890i
\(746\) −30.9504 −1.13318
\(747\) −3.41445 5.91401i −0.124928 0.216382i
\(748\) 62.1180 107.592i 2.27126 3.93394i
\(749\) 9.93627 17.2101i 0.363063 0.628844i
\(750\) 7.40250 + 12.8215i 0.270301 + 0.468175i
\(751\) −11.4410 19.8164i −0.417489 0.723112i 0.578197 0.815897i \(-0.303756\pi\)
−0.995686 + 0.0927849i \(0.970423\pi\)
\(752\) 26.8874 46.5703i 0.980481 1.69824i
\(753\) 12.3006 0.448259
\(754\) −8.12093 + 14.0659i −0.295747 + 0.512248i
\(755\) −4.45497 + 7.71623i −0.162133 + 0.280822i
\(756\) 24.5941 0.894477
\(757\) −34.5432 −1.25549 −0.627747 0.778417i \(-0.716023\pi\)
−0.627747 + 0.778417i \(0.716023\pi\)
\(758\) 48.5777 1.76442
\(759\) −2.31606 + 4.01153i −0.0840675 + 0.145609i
\(760\) 12.7717 22.1212i 0.463278 0.802422i
\(761\) 4.10100 + 7.10314i 0.148661 + 0.257489i 0.930733 0.365700i \(-0.119170\pi\)
−0.782072 + 0.623188i \(0.785837\pi\)
\(762\) 4.19348 0.151914
\(763\) 1.53143 + 2.65252i 0.0554416 + 0.0960277i
\(764\) 7.20012 + 12.4710i 0.260491 + 0.451184i
\(765\) −1.60385 2.77794i −0.0579872 0.100437i
\(766\) 17.4814 + 30.2786i 0.631627 + 1.09401i
\(767\) 0.544607 0.943287i 0.0196646 0.0340601i
\(768\) 28.4202 + 49.2253i 1.02553 + 1.77626i
\(769\) 1.23692 0.0446045 0.0223022 0.999751i \(-0.492900\pi\)
0.0223022 + 0.999751i \(0.492900\pi\)
\(770\) −13.1125 + 22.7116i −0.472543 + 0.818468i
\(771\) 27.9364 1.00610
\(772\) 41.9403 72.6426i 1.50946 2.61447i
\(773\) −12.8471 22.2518i −0.462078 0.800343i 0.536986 0.843591i \(-0.319563\pi\)
−0.999064 + 0.0432479i \(0.986229\pi\)
\(774\) −13.8785 24.0382i −0.498851 0.864035i
\(775\) 8.87601 + 15.3737i 0.318836 + 0.552240i
\(776\) −82.0470 + 142.110i −2.94532 + 5.10144i
\(777\) −11.2287 −0.402827
\(778\) −64.0171 −2.29513
\(779\) −20.2626 35.0959i −0.725983 1.25744i
\(780\) 0.883152 + 1.52966i 0.0316219 + 0.0547708i
\(781\) −36.2894 −1.29854
\(782\) −9.47616 16.4132i −0.338867 0.586934i
\(783\) 10.3284 0.369105
\(784\) 198.446 7.08735
\(785\) −6.92886 + 0.706633i −0.247301 + 0.0252208i
\(786\) 52.0668 1.85716
\(787\) 16.2761 0.580180 0.290090 0.956999i \(-0.406315\pi\)
0.290090 + 0.956999i \(0.406315\pi\)
\(788\) 31.0998 + 53.8665i 1.10789 + 1.91891i
\(789\) 24.0856 0.857470
\(790\) −5.40159 9.35584i −0.192180 0.332866i
\(791\) 36.7050 + 63.5749i 1.30508 + 2.26046i
\(792\) 37.8610 1.34533
\(793\) −0.200415 −0.00711694
\(794\) −7.78500 + 13.4840i −0.276279 + 0.478530i
\(795\) 0.314161 + 0.544143i 0.0111421 + 0.0192988i
\(796\) 11.8306 + 20.4912i 0.419324 + 0.726290i
\(797\) 0.574141 + 0.994441i 0.0203371 + 0.0352249i 0.876015 0.482284i \(-0.160193\pi\)
−0.855678 + 0.517509i \(0.826859\pi\)
\(798\) −28.6323 + 49.5926i −1.01357 + 1.75556i
\(799\) 19.7202 0.697650
\(800\) 55.6250 96.3454i 1.96664 3.40632i
\(801\) −5.53901 −0.195711
\(802\) −9.40704 16.2935i −0.332174 0.575343i
\(803\) 26.1585 45.3079i 0.923115 1.59888i
\(804\) 5.72151 + 9.90995i 0.201782 + 0.349497i
\(805\) 1.47070 + 2.54733i 0.0518353 + 0.0897814i
\(806\) 2.97546 + 5.15365i 0.104806 + 0.181529i
\(807\) −2.65602 4.60036i −0.0934963 0.161940i
\(808\) −59.2095 −2.08298
\(809\) −23.7265 41.0954i −0.834178 1.44484i −0.894698 0.446671i \(-0.852609\pi\)
0.0605206 0.998167i \(-0.480724\pi\)
\(810\) 0.763851 1.32303i 0.0268390 0.0464865i
\(811\) −11.2672 + 19.5154i −0.395646 + 0.685279i −0.993183 0.116562i \(-0.962813\pi\)
0.597537 + 0.801841i \(0.296146\pi\)
\(812\) 254.016 8.91422
\(813\) −20.4959 −0.718821
\(814\) −27.0142 −0.946848
\(815\) −4.02744 + 6.97572i −0.141075 + 0.244349i
\(816\) −45.4051 + 78.6440i −1.58950 + 2.75309i
\(817\) 47.5171 1.66241
\(818\) −31.0747 + 53.8230i −1.08650 + 1.88188i
\(819\) −1.26690 2.19433i −0.0442690 0.0766761i
\(820\) 13.2947 + 23.0271i 0.464270 + 0.804140i
\(821\) −15.4423 + 26.7469i −0.538941 + 0.933474i 0.460020 + 0.887908i \(0.347842\pi\)
−0.998961 + 0.0455651i \(0.985491\pi\)
\(822\) 15.5586 26.9482i 0.542668 0.939928i
\(823\) 5.83220 + 10.1017i 0.203298 + 0.352122i 0.949589 0.313498i \(-0.101501\pi\)
−0.746291 + 0.665619i \(0.768167\pi\)
\(824\) 81.9816 2.85596
\(825\) −9.09220 15.7482i −0.316550 0.548280i
\(826\) −23.1695 −0.806170
\(827\) 15.8961 + 27.5329i 0.552762 + 0.957411i 0.998074 + 0.0620358i \(0.0197593\pi\)
−0.445312 + 0.895375i \(0.646907\pi\)
\(828\) 3.31819 5.74727i 0.115315 0.199732i
\(829\) −18.2199 31.5578i −0.632803 1.09605i −0.986976 0.160867i \(-0.948571\pi\)
0.354173 0.935180i \(-0.384762\pi\)
\(830\) −10.4325 −0.362119
\(831\) −8.71576 −0.302346
\(832\) 9.64309 16.7023i 0.334314 0.579049i
\(833\) 36.3869 + 63.0240i 1.26073 + 2.18365i
\(834\) −6.68828 −0.231596
\(835\) 0.852768 1.47704i 0.0295113 0.0511150i
\(836\) −50.6457 + 87.7209i −1.75162 + 3.03389i
\(837\) 1.89212 3.27726i 0.0654014 0.113279i
\(838\) −38.4889 + 66.6648i −1.32958 + 2.30290i
\(839\) 13.3836 0.462052 0.231026 0.972948i \(-0.425792\pi\)
0.231026 + 0.972948i \(0.425792\pi\)
\(840\) 12.0209 20.8208i 0.414761 0.718387i
\(841\) 77.6750 2.67845
\(842\) 15.5280 26.8953i 0.535130 0.926873i
\(843\) 11.2743 0.388307
\(844\) −95.9415 −3.30244
\(845\) −3.52205 + 6.10036i −0.121162 + 0.209859i
\(846\) 4.69599 + 8.13369i 0.161451 + 0.279642i
\(847\) 8.91579 15.4426i 0.306350 0.530614i
\(848\) 8.89396 15.4048i 0.305420 0.529002i
\(849\) −4.87931 −0.167457
\(850\) 74.4016 2.55195
\(851\) −1.51496 + 2.62398i −0.0519320 + 0.0899489i
\(852\) 51.9914 1.78120
\(853\) 17.7724 + 30.7827i 0.608516 + 1.05398i 0.991485 + 0.130219i \(0.0415681\pi\)
−0.382969 + 0.923761i \(0.625099\pi\)
\(854\) 2.13159 + 3.69202i 0.0729414 + 0.126338i
\(855\) 1.30764 + 2.26489i 0.0447202 + 0.0774577i
\(856\) −21.9148 + 37.9576i −0.749033 + 1.29736i
\(857\) 23.0527 39.9284i 0.787464 1.36393i −0.140052 0.990144i \(-0.544727\pi\)
0.927516 0.373784i \(-0.121940\pi\)
\(858\) −3.04793 5.27917i −0.104055 0.180228i
\(859\) −8.85858 + 15.3435i −0.302251 + 0.523514i −0.976645 0.214857i \(-0.931071\pi\)
0.674395 + 0.738371i \(0.264405\pi\)
\(860\) −31.1769 −1.06312
\(861\) −19.0714 33.0327i −0.649953 1.12575i
\(862\) −47.8253 82.8359i −1.62894 2.82140i
\(863\) 31.5711 1.07469 0.537346 0.843362i \(-0.319427\pi\)
0.537346 + 0.843362i \(0.319427\pi\)
\(864\) −23.7155 −0.806817
\(865\) −1.51702 2.62756i −0.0515802 0.0893396i
\(866\) −38.5282 66.7328i −1.30924 2.26767i
\(867\) −16.3018 −0.553639
\(868\) 46.5350 80.6010i 1.57950 2.73578i
\(869\) 13.7061 + 23.7397i 0.464948 + 0.805314i
\(870\) 7.88933 13.6647i 0.267473 0.463277i
\(871\) 0.589457 1.02097i 0.0199730 0.0345942i
\(872\) −3.37763 5.85023i −0.114381 0.198114i
\(873\) −8.40042 14.5500i −0.284311 0.492441i
\(874\) 7.72604 + 13.3819i 0.261337 + 0.452649i
\(875\) −23.8548 −0.806439
\(876\) −37.4771 + 64.9122i −1.26623 + 2.19318i
\(877\) −51.1839 −1.72836 −0.864178 0.503186i \(-0.832161\pi\)
−0.864178 + 0.503186i \(0.832161\pi\)
\(878\) −69.8281 −2.35659
\(879\) −3.23932 + 5.61067i −0.109260 + 0.189243i
\(880\) 16.9535 29.3644i 0.571504 0.989874i
\(881\) −4.55283 7.88573i −0.153389 0.265677i 0.779082 0.626921i \(-0.215685\pi\)
−0.932471 + 0.361244i \(0.882352\pi\)
\(882\) −17.3297 + 30.0159i −0.583521 + 1.01069i
\(883\) 21.0563 0.708602 0.354301 0.935131i \(-0.384719\pi\)
0.354301 + 0.935131i \(0.384719\pi\)
\(884\) 18.3375 0.616758
\(885\) −0.529076 + 0.916386i −0.0177847 + 0.0308040i
\(886\) −28.9962 −0.974148
\(887\) 10.5389 18.2539i 0.353862 0.612907i −0.633061 0.774102i \(-0.718202\pi\)
0.986923 + 0.161195i \(0.0515349\pi\)
\(888\) 24.7653 0.831068
\(889\) −3.37841 + 5.85157i −0.113308 + 0.196255i
\(890\) −4.23098 + 7.32826i −0.141823 + 0.245644i
\(891\) −1.93821 + 3.35708i −0.0649325 + 0.112466i
\(892\) 76.1015 131.812i 2.54807 4.41338i
\(893\) −16.0781 −0.538034
\(894\) 13.1596 + 22.7931i 0.440124 + 0.762317i
\(895\) 2.79333 4.83819i 0.0933707 0.161723i
\(896\) −200.207 −6.68846
\(897\) −0.683711 −0.0228284
\(898\) 3.20746 + 5.55549i 0.107034 + 0.185389i
\(899\) 19.5425 33.8487i 0.651780 1.12892i
\(900\) 13.0263 + 22.5622i 0.434210 + 0.752074i
\(901\) 6.52316 0.217318
\(902\) −45.8825 79.4709i −1.52772 2.64609i
\(903\) 44.7237 1.48831
\(904\) −80.9542 140.217i −2.69250 4.66354i
\(905\) 4.41528 7.64748i 0.146769 0.254211i
\(906\) −22.0276 + 38.1528i −0.731816 + 1.26754i
\(907\) 6.28390 + 10.8840i 0.208653 + 0.361398i 0.951291 0.308296i \(-0.0997586\pi\)
−0.742637 + 0.669694i \(0.766425\pi\)
\(908\) −10.2958 17.8328i −0.341677 0.591801i
\(909\) 3.03110 5.25002i 0.100535 0.174132i
\(910\) −3.87088 −0.128318
\(911\) 10.0571 17.4193i 0.333205 0.577128i −0.649933 0.759991i \(-0.725203\pi\)
0.983138 + 0.182863i \(0.0585365\pi\)
\(912\) 37.0194 64.1195i 1.22584 2.12321i
\(913\) 26.4717 0.876086
\(914\) 102.413 3.38750
\(915\) 0.194699 0.00643656
\(916\) −14.8455 + 25.7132i −0.490510 + 0.849588i
\(917\) −41.9467 + 72.6538i −1.38520 + 2.39924i
\(918\) −7.93020 13.7355i −0.261736 0.453339i
\(919\) 44.3075 1.46157 0.730785 0.682608i \(-0.239154\pi\)
0.730785 + 0.682608i \(0.239154\pi\)
\(920\) −3.24368 5.61822i −0.106941 0.185227i
\(921\) 4.40751 + 7.63403i 0.145232 + 0.251550i
\(922\) 14.2380 + 24.6609i 0.468902 + 0.812162i
\(923\) −2.67820 4.63877i −0.0881540 0.152687i
\(924\) −47.6684 + 82.5642i −1.56818 + 2.71616i
\(925\) −5.94730 10.3010i −0.195546 0.338696i
\(926\) −26.4391 −0.868843
\(927\) −4.19686 + 7.26918i −0.137843 + 0.238751i
\(928\) −244.942 −8.04062
\(929\) −12.5366 + 21.7140i −0.411311 + 0.712412i −0.995033 0.0995413i \(-0.968262\pi\)
0.583722 + 0.811954i \(0.301596\pi\)
\(930\) −2.89060 5.00667i −0.0947866 0.164175i
\(931\) −29.6667 51.3843i −0.972288 1.68405i
\(932\) 35.9835 + 62.3253i 1.17868 + 2.04153i
\(933\) −3.01535 + 5.22275i −0.0987182 + 0.170985i
\(934\) −103.386 −3.38289
\(935\) 12.4344 0.406647
\(936\) 2.79419 + 4.83968i 0.0913309 + 0.158190i
\(937\) 18.1986 + 31.5209i 0.594523 + 1.02974i 0.993614 + 0.112832i \(0.0359922\pi\)
−0.399092 + 0.916911i \(0.630674\pi\)
\(938\) −25.0776 −0.818811
\(939\) −0.900591 1.55987i −0.0293897 0.0509044i
\(940\) 10.5492 0.344076
\(941\) −8.00495 −0.260954 −0.130477 0.991451i \(-0.541651\pi\)
−0.130477 + 0.991451i \(0.541651\pi\)
\(942\) −34.2597 + 3.49394i −1.11624 + 0.113839i
\(943\) −10.2924 −0.335165
\(944\) 29.9564 0.974999
\(945\) 1.23077 + 2.13175i 0.0400368 + 0.0693458i
\(946\) 107.597 3.49829
\(947\) 5.66048 + 9.80424i 0.183941 + 0.318595i 0.943219 0.332171i \(-0.107781\pi\)
−0.759278 + 0.650766i \(0.774448\pi\)
\(948\) −19.6366 34.0116i −0.637767 1.10465i
\(949\) 7.72212 0.250671
\(950\) −60.6606 −1.96809
\(951\) 9.54975 16.5406i 0.309672 0.536367i
\(952\) −124.799 216.159i −4.04477 7.00575i
\(953\) 0.0397597 + 0.0688658i 0.00128794 + 0.00223078i 0.866669 0.498884i \(-0.166257\pi\)
−0.865381 + 0.501115i \(0.832923\pi\)
\(954\) 1.55337 + 2.69051i 0.0502921 + 0.0871085i
\(955\) −0.720635 + 1.24818i −0.0233192 + 0.0403901i
\(956\) −149.524 −4.83596
\(957\) −20.0185 + 34.6731i −0.647107 + 1.12082i
\(958\) −54.7587 −1.76917
\(959\) 25.0690 + 43.4208i 0.809520 + 1.40213i
\(960\) −9.36809 + 16.2260i −0.302354 + 0.523692i
\(961\) 8.33973 + 14.4448i 0.269023 + 0.465962i
\(962\) −1.99368 3.45316i −0.0642789 0.111334i
\(963\) −2.24376 3.88630i −0.0723041 0.125234i
\(964\) 36.8535 + 63.8322i 1.18697 + 2.05590i
\(965\) 8.39531 0.270255
\(966\) 7.27186 + 12.5952i 0.233968 + 0.405245i
\(967\) −21.3744 + 37.0215i −0.687353 + 1.19053i 0.285338 + 0.958427i \(0.407894\pi\)
−0.972691 + 0.232103i \(0.925439\pi\)
\(968\) −19.6641 + 34.0592i −0.632028 + 1.09470i
\(969\) 27.1514 0.872230
\(970\) −25.6667 −0.824107
\(971\) 21.3792 0.686091 0.343046 0.939319i \(-0.388541\pi\)
0.343046 + 0.939319i \(0.388541\pi\)
\(972\) 2.77685 4.80965i 0.0890676 0.154270i
\(973\) 5.38830 9.33280i 0.172741 0.299196i
\(974\) −89.9003 −2.88059
\(975\) 1.34203 2.32446i 0.0429794 0.0744424i
\(976\) −2.75599 4.77351i −0.0882170 0.152796i
\(977\) 8.08335 + 14.0008i 0.258609 + 0.447925i 0.965870 0.259029i \(-0.0834024\pi\)
−0.707260 + 0.706953i \(0.750069\pi\)
\(978\) −19.9136 + 34.4914i −0.636767 + 1.10291i
\(979\) 10.7358 18.5949i 0.343116 0.594295i
\(980\) 19.4649 + 33.7142i 0.621784 + 1.07696i
\(981\) 0.691641 0.0220824
\(982\) 3.29216 + 5.70219i 0.105057 + 0.181964i
\(983\) 22.6666 0.722952 0.361476 0.932381i \(-0.382273\pi\)
0.361476 + 0.932381i \(0.382273\pi\)
\(984\) 42.0628 + 72.8549i 1.34091 + 2.32253i
\(985\) −3.11267 + 5.39131i −0.0991780 + 0.171781i
\(986\) −81.9059 141.865i −2.60842 4.51791i
\(987\) −15.1330 −0.481688
\(988\) −14.9508 −0.475650
\(989\) 6.03406 10.4513i 0.191872 0.332332i
\(990\) 2.96101 + 5.12862i 0.0941070 + 0.162998i
\(991\) 8.70427 0.276500 0.138250 0.990397i \(-0.455852\pi\)
0.138250 + 0.990397i \(0.455852\pi\)
\(992\) −44.8727 + 77.7217i −1.42471 + 2.46767i
\(993\) 3.27008 5.66394i 0.103773 0.179740i
\(994\) −56.9699 + 98.6748i −1.80698 + 3.12978i
\(995\) −1.18408 + 2.05089i −0.0375379 + 0.0650176i
\(996\) −37.9258 −1.20172
\(997\) −28.5071 + 49.3757i −0.902827 + 1.56374i −0.0790202 + 0.996873i \(0.525179\pi\)
−0.823807 + 0.566870i \(0.808154\pi\)
\(998\) 19.7755 0.625982
\(999\) −1.26780 + 2.19590i −0.0401115 + 0.0694751i
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 471.2.e.b.169.11 22
157.144 even 3 inner 471.2.e.b.301.11 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.e.b.169.11 22 1.1 even 1 trivial
471.2.e.b.301.11 yes 22 157.144 even 3 inner