Properties

Label 260.2.p.d.207.20
Level $260$
Weight $2$
Character 260.207
Analytic conductor $2.076$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [260,2,Mod(103,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.103");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.p (of order \(4\), 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: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 207.20
Character \(\chi\) \(=\) 260.207
Dual form 260.2.p.d.103.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.528615 + 1.31170i) q^{2} +(0.834468 + 0.834468i) q^{3} +(-1.44113 + 1.38677i) q^{4} +(-0.462357 + 2.18774i) q^{5} +(-0.653463 + 1.53569i) q^{6} +(1.21162 + 1.21162i) q^{7} +(-2.58084 - 1.15727i) q^{8} -1.60733i q^{9} +O(q^{10})\) \(q+(0.528615 + 1.31170i) q^{2} +(0.834468 + 0.834468i) q^{3} +(-1.44113 + 1.38677i) q^{4} +(-0.462357 + 2.18774i) q^{5} +(-0.653463 + 1.53569i) q^{6} +(1.21162 + 1.21162i) q^{7} +(-2.58084 - 1.15727i) q^{8} -1.60733i q^{9} +(-3.11408 + 0.549999i) q^{10} -0.135866 q^{11} +(-2.35980 - 0.0453632i) q^{12} +(1.01757 - 3.45898i) q^{13} +(-0.948804 + 2.22976i) q^{14} +(-2.21142 + 1.43978i) q^{15} +(0.153730 - 3.99704i) q^{16} +(-1.10965 - 1.10965i) q^{17} +(2.10834 - 0.849657i) q^{18} +6.12150i q^{19} +(-2.36758 - 3.79401i) q^{20} +2.02211i q^{21} +(-0.0718210 - 0.178217i) q^{22} +(4.72792 + 4.72792i) q^{23} +(-1.18792 - 3.11933i) q^{24} +(-4.57245 - 2.02304i) q^{25} +(5.07506 - 0.493718i) q^{26} +(3.84467 - 3.84467i) q^{27} +(-3.42634 - 0.0658656i) q^{28} +4.39615i q^{29} +(-3.05756 - 2.13964i) q^{30} +3.12087 q^{31} +(5.32420 - 1.91125i) q^{32} +(-0.113376 - 0.113376i) q^{33} +(0.868956 - 2.04211i) q^{34} +(-3.21091 + 2.09051i) q^{35} +(2.22900 + 2.31637i) q^{36} +(6.39942 - 6.39942i) q^{37} +(-8.02960 + 3.23592i) q^{38} +(3.73554 - 2.03728i) q^{39} +(3.72508 - 5.11114i) q^{40} -2.92506i q^{41} +(-2.65241 + 1.06892i) q^{42} +(1.51561 + 1.51561i) q^{43} +(0.195802 - 0.188416i) q^{44} +(3.51642 + 0.743158i) q^{45} +(-3.70239 + 8.70089i) q^{46} +(-8.14297 - 8.14297i) q^{47} +(3.46369 - 3.20712i) q^{48} -4.06397i q^{49} +(0.236559 - 7.06711i) q^{50} -1.85194i q^{51} +(3.33036 + 6.39599i) q^{52} +(-5.39849 + 5.39849i) q^{53} +(7.07541 + 3.01072i) q^{54} +(0.0628188 - 0.297241i) q^{55} +(-1.72481 - 4.52915i) q^{56} +(-5.10820 + 5.10820i) q^{57} +(-5.76645 + 2.32387i) q^{58} +5.47588i q^{59} +(1.19031 - 5.14166i) q^{60} +11.7875 q^{61} +(1.64974 + 4.09366i) q^{62} +(1.94746 - 1.94746i) q^{63} +(5.32144 + 5.97346i) q^{64} +(7.09689 + 3.82547i) q^{65} +(0.0887836 - 0.208648i) q^{66} +(-7.10562 - 7.10562i) q^{67} +(3.13799 + 0.0603226i) q^{68} +7.89060i q^{69} +(-4.43946 - 3.10668i) q^{70} +4.49049 q^{71} +(-1.86011 + 4.14825i) q^{72} +(-6.04423 - 6.04423i) q^{73} +(11.7770 + 5.01132i) q^{74} +(-2.12741 - 5.50372i) q^{75} +(-8.48913 - 8.82190i) q^{76} +(-0.164618 - 0.164618i) q^{77} +(4.64697 + 3.82298i) q^{78} +0.944179 q^{79} +(8.67344 + 2.18438i) q^{80} +1.59452 q^{81} +(3.83681 - 1.54623i) q^{82} +(4.61273 - 4.61273i) q^{83} +(-2.80420 - 2.91413i) q^{84} +(2.94069 - 1.91458i) q^{85} +(-1.18686 + 2.78920i) q^{86} +(-3.66845 + 3.66845i) q^{87} +(0.350649 + 0.157234i) q^{88} -3.22796 q^{89} +(0.884028 + 5.00535i) q^{90} +(5.42386 - 2.95805i) q^{91} +(-13.3701 - 0.257018i) q^{92} +(2.60427 + 2.60427i) q^{93} +(6.37667 - 14.9857i) q^{94} +(-13.3923 - 2.83032i) q^{95} +(6.03775 + 2.84800i) q^{96} +(-2.31733 + 2.31733i) q^{97} +(5.33073 - 2.14827i) q^{98} +0.218382i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.528615 + 1.31170i 0.373787 + 0.927515i
\(3\) 0.834468 + 0.834468i 0.481780 + 0.481780i 0.905700 0.423920i \(-0.139346\pi\)
−0.423920 + 0.905700i \(0.639346\pi\)
\(4\) −1.44113 + 1.38677i −0.720567 + 0.693386i
\(5\) −0.462357 + 2.18774i −0.206772 + 0.978389i
\(6\) −0.653463 + 1.53569i −0.266775 + 0.626941i
\(7\) 1.21162 + 1.21162i 0.457948 + 0.457948i 0.897981 0.440033i \(-0.145033\pi\)
−0.440033 + 0.897981i \(0.645033\pi\)
\(8\) −2.58084 1.15727i −0.912464 0.409158i
\(9\) 1.60733i 0.535776i
\(10\) −3.11408 + 0.549999i −0.984759 + 0.173925i
\(11\) −0.135866 −0.0409653 −0.0204826 0.999790i \(-0.506520\pi\)
−0.0204826 + 0.999790i \(0.506520\pi\)
\(12\) −2.35980 0.0453632i −0.681214 0.0130952i
\(13\) 1.01757 3.45898i 0.282223 0.959349i
\(14\) −0.948804 + 2.22976i −0.253578 + 0.595928i
\(15\) −2.21142 + 1.43978i −0.570987 + 0.371750i
\(16\) 0.153730 3.99704i 0.0384325 0.999261i
\(17\) −1.10965 1.10965i −0.269130 0.269130i 0.559620 0.828750i \(-0.310947\pi\)
−0.828750 + 0.559620i \(0.810947\pi\)
\(18\) 2.10834 0.849657i 0.496940 0.200266i
\(19\) 6.12150i 1.40437i 0.711995 + 0.702185i \(0.247792\pi\)
−0.711995 + 0.702185i \(0.752208\pi\)
\(20\) −2.36758 3.79401i −0.529408 0.848367i
\(21\) 2.02211i 0.441261i
\(22\) −0.0718210 0.178217i −0.0153123 0.0379959i
\(23\) 4.72792 + 4.72792i 0.985840 + 0.985840i 0.999901 0.0140607i \(-0.00447582\pi\)
−0.0140607 + 0.999901i \(0.504476\pi\)
\(24\) −1.18792 3.11933i −0.242483 0.636731i
\(25\) −4.57245 2.02304i −0.914491 0.404607i
\(26\) 5.07506 0.493718i 0.995301 0.0968261i
\(27\) 3.84467 3.84467i 0.739906 0.739906i
\(28\) −3.42634 0.0658656i −0.647517 0.0124474i
\(29\) 4.39615i 0.816345i 0.912905 + 0.408172i \(0.133834\pi\)
−0.912905 + 0.408172i \(0.866166\pi\)
\(30\) −3.05756 2.13964i −0.558231 0.390644i
\(31\) 3.12087 0.560525 0.280263 0.959923i \(-0.409578\pi\)
0.280263 + 0.959923i \(0.409578\pi\)
\(32\) 5.32420 1.91125i 0.941195 0.337864i
\(33\) −0.113376 0.113376i −0.0197363 0.0197363i
\(34\) 0.868956 2.04211i 0.149025 0.350219i
\(35\) −3.21091 + 2.09051i −0.542742 + 0.353360i
\(36\) 2.22900 + 2.31637i 0.371499 + 0.386062i
\(37\) 6.39942 6.39942i 1.05206 1.05206i 0.0534895 0.998568i \(-0.482966\pi\)
0.998568 0.0534895i \(-0.0170344\pi\)
\(38\) −8.02960 + 3.23592i −1.30257 + 0.524935i
\(39\) 3.73554 2.03728i 0.598165 0.326226i
\(40\) 3.72508 5.11114i 0.588987 0.808142i
\(41\) 2.92506i 0.456817i −0.973565 0.228409i \(-0.926648\pi\)
0.973565 0.228409i \(-0.0733522\pi\)
\(42\) −2.65241 + 1.06892i −0.409276 + 0.164937i
\(43\) 1.51561 + 1.51561i 0.231128 + 0.231128i 0.813163 0.582035i \(-0.197744\pi\)
−0.582035 + 0.813163i \(0.697744\pi\)
\(44\) 0.195802 0.188416i 0.0295182 0.0284047i
\(45\) 3.51642 + 0.743158i 0.524197 + 0.110784i
\(46\) −3.70239 + 8.70089i −0.545887 + 1.28288i
\(47\) −8.14297 8.14297i −1.18777 1.18777i −0.977681 0.210093i \(-0.932623\pi\)
−0.210093 0.977681i \(-0.567377\pi\)
\(48\) 3.46369 3.20712i 0.499940 0.462908i
\(49\) 4.06397i 0.580567i
\(50\) 0.236559 7.06711i 0.0334545 0.999440i
\(51\) 1.85194i 0.259323i
\(52\) 3.33036 + 6.39599i 0.461838 + 0.886964i
\(53\) −5.39849 + 5.39849i −0.741540 + 0.741540i −0.972874 0.231334i \(-0.925691\pi\)
0.231334 + 0.972874i \(0.425691\pi\)
\(54\) 7.07541 + 3.01072i 0.962841 + 0.409707i
\(55\) 0.0628188 0.297241i 0.00847048 0.0400800i
\(56\) −1.72481 4.52915i −0.230488 0.605234i
\(57\) −5.10820 + 5.10820i −0.676597 + 0.676597i
\(58\) −5.76645 + 2.32387i −0.757172 + 0.305139i
\(59\) 5.47588i 0.712899i 0.934315 + 0.356449i \(0.116013\pi\)
−0.934315 + 0.356449i \(0.883987\pi\)
\(60\) 1.19031 5.14166i 0.153668 0.663785i
\(61\) 11.7875 1.50923 0.754616 0.656167i \(-0.227823\pi\)
0.754616 + 0.656167i \(0.227823\pi\)
\(62\) 1.64974 + 4.09366i 0.209517 + 0.519895i
\(63\) 1.94746 1.94746i 0.245357 0.245357i
\(64\) 5.32144 + 5.97346i 0.665180 + 0.746683i
\(65\) 7.09689 + 3.82547i 0.880261 + 0.474491i
\(66\) 0.0887836 0.208648i 0.0109285 0.0256828i
\(67\) −7.10562 7.10562i −0.868089 0.868089i 0.124172 0.992261i \(-0.460373\pi\)
−0.992261 + 0.124172i \(0.960373\pi\)
\(68\) 3.13799 + 0.0603226i 0.380537 + 0.00731519i
\(69\) 7.89060i 0.949917i
\(70\) −4.43946 3.10668i −0.530617 0.371320i
\(71\) 4.49049 0.532923 0.266461 0.963846i \(-0.414146\pi\)
0.266461 + 0.963846i \(0.414146\pi\)
\(72\) −1.86011 + 4.14825i −0.219217 + 0.488876i
\(73\) −6.04423 6.04423i −0.707424 0.707424i 0.258569 0.965993i \(-0.416749\pi\)
−0.965993 + 0.258569i \(0.916749\pi\)
\(74\) 11.7770 + 5.01132i 1.36904 + 0.582554i
\(75\) −2.12741 5.50372i −0.245652 0.635515i
\(76\) −8.48913 8.82190i −0.973769 1.01194i
\(77\) −0.164618 0.164618i −0.0187600 0.0187600i
\(78\) 4.64697 + 3.82298i 0.526165 + 0.432868i
\(79\) 0.944179 0.106228 0.0531142 0.998588i \(-0.483085\pi\)
0.0531142 + 0.998588i \(0.483085\pi\)
\(80\) 8.67344 + 2.18438i 0.969720 + 0.244221i
\(81\) 1.59452 0.177169
\(82\) 3.83681 1.54623i 0.423705 0.170752i
\(83\) 4.61273 4.61273i 0.506313 0.506313i −0.407079 0.913393i \(-0.633453\pi\)
0.913393 + 0.407079i \(0.133453\pi\)
\(84\) −2.80420 2.91413i −0.305964 0.317958i
\(85\) 2.94069 1.91458i 0.318962 0.207665i
\(86\) −1.18686 + 2.78920i −0.127982 + 0.300767i
\(87\) −3.66845 + 3.66845i −0.393299 + 0.393299i
\(88\) 0.350649 + 0.157234i 0.0373793 + 0.0167613i
\(89\) −3.22796 −0.342163 −0.171082 0.985257i \(-0.554726\pi\)
−0.171082 + 0.985257i \(0.554726\pi\)
\(90\) 0.884028 + 5.00535i 0.0931847 + 0.527610i
\(91\) 5.42386 2.95805i 0.568575 0.310088i
\(92\) −13.3701 0.257018i −1.39393 0.0267960i
\(93\) 2.60427 + 2.60427i 0.270050 + 0.270050i
\(94\) 6.37667 14.9857i 0.657703 1.54565i
\(95\) −13.3923 2.83032i −1.37402 0.290384i
\(96\) 6.03775 + 2.84800i 0.616225 + 0.290673i
\(97\) −2.31733 + 2.31733i −0.235289 + 0.235289i −0.814896 0.579607i \(-0.803206\pi\)
0.579607 + 0.814896i \(0.303206\pi\)
\(98\) 5.33073 2.14827i 0.538485 0.217009i
\(99\) 0.218382i 0.0219482i
\(100\) 9.39500 3.42548i 0.939500 0.342548i
\(101\) 2.63267 0.261960 0.130980 0.991385i \(-0.458188\pi\)
0.130980 + 0.991385i \(0.458188\pi\)
\(102\) 2.42919 0.978961i 0.240526 0.0969316i
\(103\) −7.36490 7.36490i −0.725685 0.725685i 0.244072 0.969757i \(-0.421517\pi\)
−0.969757 + 0.244072i \(0.921517\pi\)
\(104\) −6.62916 + 7.74946i −0.650043 + 0.759897i
\(105\) −4.42386 0.934936i −0.431724 0.0912404i
\(106\) −9.93494 4.22750i −0.964967 0.410611i
\(107\) −11.9158 + 11.9158i −1.15194 + 1.15194i −0.165780 + 0.986163i \(0.553014\pi\)
−0.986163 + 0.165780i \(0.946986\pi\)
\(108\) −0.209003 + 10.8723i −0.0201113 + 1.04619i
\(109\) 1.57023 0.150401 0.0752004 0.997168i \(-0.476040\pi\)
0.0752004 + 0.997168i \(0.476040\pi\)
\(110\) 0.423099 0.0747264i 0.0403409 0.00712488i
\(111\) 10.6802 1.01372
\(112\) 5.02915 4.65662i 0.475210 0.440010i
\(113\) 0.755135 0.755135i 0.0710371 0.0710371i −0.670696 0.741733i \(-0.734004\pi\)
0.741733 + 0.670696i \(0.234004\pi\)
\(114\) −9.40071 4.00017i −0.880457 0.374651i
\(115\) −12.5295 + 8.15750i −1.16838 + 0.760691i
\(116\) −6.09646 6.33544i −0.566042 0.588231i
\(117\) −5.55971 1.63557i −0.513996 0.151208i
\(118\) −7.18273 + 2.89463i −0.661224 + 0.266472i
\(119\) 2.68894i 0.246495i
\(120\) 7.37354 1.15662i 0.673109 0.105584i
\(121\) −10.9815 −0.998322
\(122\) 6.23103 + 15.4617i 0.564131 + 1.39983i
\(123\) 2.44087 2.44087i 0.220085 0.220085i
\(124\) −4.49759 + 4.32794i −0.403896 + 0.388660i
\(125\) 6.53999 9.06799i 0.584955 0.811066i
\(126\) 3.58395 + 1.52504i 0.319284 + 0.135861i
\(127\) 15.1631 15.1631i 1.34551 1.34551i 0.455037 0.890472i \(-0.349626\pi\)
0.890472 0.455037i \(-0.150374\pi\)
\(128\) −5.02242 + 10.1378i −0.443923 + 0.896065i
\(129\) 2.52945i 0.222706i
\(130\) −1.26636 + 11.3312i −0.111067 + 0.993813i
\(131\) 0.235056i 0.0205370i 0.999947 + 0.0102685i \(0.00326862\pi\)
−0.999947 + 0.0102685i \(0.996731\pi\)
\(132\) 0.320617 + 0.00616333i 0.0279061 + 0.000536449i
\(133\) −7.41691 + 7.41691i −0.643128 + 0.643128i
\(134\) 5.56433 13.0766i 0.480685 1.12965i
\(135\) 6.63354 + 10.1888i 0.570924 + 0.876908i
\(136\) 1.57966 + 4.14800i 0.135455 + 0.355688i
\(137\) −12.2710 + 12.2710i −1.04838 + 1.04838i −0.0496147 + 0.998768i \(0.515799\pi\)
−0.998768 + 0.0496147i \(0.984201\pi\)
\(138\) −10.3501 + 4.17109i −0.881062 + 0.355067i
\(139\) −19.6129 −1.66354 −0.831772 0.555117i \(-0.812673\pi\)
−0.831772 + 0.555117i \(0.812673\pi\)
\(140\) 1.72829 7.46549i 0.146067 0.630949i
\(141\) 13.5901i 1.14449i
\(142\) 2.37374 + 5.89019i 0.199200 + 0.494294i
\(143\) −0.138254 + 0.469960i −0.0115613 + 0.0393000i
\(144\) −6.42456 0.247094i −0.535380 0.0205912i
\(145\) −9.61766 2.03259i −0.798703 0.168797i
\(146\) 4.73317 11.1233i 0.391720 0.920572i
\(147\) 3.39125 3.39125i 0.279706 0.279706i
\(148\) −0.347884 + 18.0969i −0.0285959 + 1.48756i
\(149\) −2.39818 −0.196467 −0.0982333 0.995163i \(-0.531319\pi\)
−0.0982333 + 0.995163i \(0.531319\pi\)
\(150\) 6.09468 5.69987i 0.497628 0.465393i
\(151\) −5.63264 −0.458378 −0.229189 0.973382i \(-0.573607\pi\)
−0.229189 + 0.973382i \(0.573607\pi\)
\(152\) 7.08424 15.7986i 0.574608 1.28144i
\(153\) −1.78357 + 1.78357i −0.144193 + 0.144193i
\(154\) 0.128911 0.302950i 0.0103879 0.0244124i
\(155\) −1.44296 + 6.82767i −0.115901 + 0.548412i
\(156\) −2.55817 + 8.11633i −0.204817 + 0.649826i
\(157\) −3.62360 3.62360i −0.289195 0.289195i 0.547567 0.836762i \(-0.315554\pi\)
−0.836762 + 0.547567i \(0.815554\pi\)
\(158\) 0.499107 + 1.23848i 0.0397068 + 0.0985284i
\(159\) −9.00974 −0.714519
\(160\) 1.71964 + 12.5317i 0.135950 + 0.990716i
\(161\) 11.4569i 0.902927i
\(162\) 0.842886 + 2.09154i 0.0662233 + 0.164327i
\(163\) 6.40798 6.40798i 0.501911 0.501911i −0.410120 0.912032i \(-0.634513\pi\)
0.912032 + 0.410120i \(0.134513\pi\)
\(164\) 4.05639 + 4.21540i 0.316751 + 0.329167i
\(165\) 0.300458 0.195618i 0.0233906 0.0152288i
\(166\) 8.48890 + 3.61218i 0.658866 + 0.280360i
\(167\) −5.94641 5.94641i −0.460147 0.460147i 0.438556 0.898704i \(-0.355490\pi\)
−0.898704 + 0.438556i \(0.855490\pi\)
\(168\) 2.34013 5.21874i 0.180545 0.402634i
\(169\) −10.9291 7.03951i −0.840700 0.541501i
\(170\) 4.06585 + 2.84524i 0.311837 + 0.218220i
\(171\) 9.83926 0.752427
\(172\) −4.28599 0.0823911i −0.326804 0.00628226i
\(173\) 8.64623 8.64623i 0.657361 0.657361i −0.297394 0.954755i \(-0.596117\pi\)
0.954755 + 0.297394i \(0.0961175\pi\)
\(174\) −6.75111 2.87272i −0.511800 0.217780i
\(175\) −3.08891 7.99120i −0.233500 0.604078i
\(176\) −0.0208867 + 0.543064i −0.00157440 + 0.0409350i
\(177\) −4.56944 + 4.56944i −0.343460 + 0.343460i
\(178\) −1.70635 4.23413i −0.127896 0.317361i
\(179\) 12.7865 0.955706 0.477853 0.878440i \(-0.341415\pi\)
0.477853 + 0.878440i \(0.341415\pi\)
\(180\) −6.09822 + 3.80548i −0.454535 + 0.283644i
\(181\) −4.48458 −0.333337 −0.166668 0.986013i \(-0.553301\pi\)
−0.166668 + 0.986013i \(0.553301\pi\)
\(182\) 6.74722 + 5.55083i 0.500138 + 0.411455i
\(183\) 9.83627 + 9.83627i 0.727118 + 0.727118i
\(184\) −6.73051 17.6735i −0.496180 1.30291i
\(185\) 11.0415 + 16.9591i 0.811786 + 1.24686i
\(186\) −2.03937 + 4.79268i −0.149534 + 0.351416i
\(187\) 0.150764 + 0.150764i 0.0110250 + 0.0110250i
\(188\) 23.0275 + 0.442666i 1.67946 + 0.0322848i
\(189\) 9.31652 0.677677
\(190\) −3.36682 19.0629i −0.244255 1.38296i
\(191\) 23.2641i 1.68333i 0.540000 + 0.841665i \(0.318424\pi\)
−0.540000 + 0.841665i \(0.681576\pi\)
\(192\) −0.544090 + 9.42523i −0.0392663 + 0.680208i
\(193\) 0.896999 + 0.896999i 0.0645674 + 0.0645674i 0.738653 0.674086i \(-0.235462\pi\)
−0.674086 + 0.738653i \(0.735462\pi\)
\(194\) −4.26463 1.81468i −0.306182 0.130286i
\(195\) 2.72990 + 9.11435i 0.195492 + 0.652692i
\(196\) 5.63580 + 5.85672i 0.402557 + 0.418337i
\(197\) 6.48712 6.48712i 0.462188 0.462188i −0.437184 0.899372i \(-0.644024\pi\)
0.899372 + 0.437184i \(0.144024\pi\)
\(198\) −0.286452 + 0.115440i −0.0203573 + 0.00820395i
\(199\) −6.60481 −0.468203 −0.234101 0.972212i \(-0.575215\pi\)
−0.234101 + 0.972212i \(0.575215\pi\)
\(200\) 9.45955 + 10.5127i 0.668891 + 0.743360i
\(201\) 11.8588i 0.836456i
\(202\) 1.39167 + 3.45328i 0.0979173 + 0.242972i
\(203\) −5.32645 + 5.32645i −0.373843 + 0.373843i
\(204\) 2.56821 + 2.66889i 0.179811 + 0.186859i
\(205\) 6.39928 + 1.35242i 0.446945 + 0.0944571i
\(206\) 5.76737 13.5538i 0.401832 0.944335i
\(207\) 7.59932 7.59932i 0.528189 0.528189i
\(208\) −13.6693 4.59902i −0.947794 0.318885i
\(209\) 0.831707i 0.0575304i
\(210\) −1.11216 6.29701i −0.0767462 0.434535i
\(211\) 6.75732i 0.465193i −0.972573 0.232596i \(-0.925278\pi\)
0.972573 0.232596i \(-0.0747221\pi\)
\(212\) 0.293472 15.2664i 0.0201557 1.04850i
\(213\) 3.74717 + 3.74717i 0.256752 + 0.256752i
\(214\) −21.9288 9.33112i −1.49902 0.637862i
\(215\) −4.01651 + 2.61501i −0.273924 + 0.178342i
\(216\) −14.3718 + 5.47313i −0.977876 + 0.372399i
\(217\) 3.78130 + 3.78130i 0.256691 + 0.256691i
\(218\) 0.830047 + 2.05968i 0.0562179 + 0.139499i
\(219\) 10.0874i 0.681646i
\(220\) 0.321675 + 0.515479i 0.0216873 + 0.0347536i
\(221\) −4.96741 + 2.70912i −0.334144 + 0.182235i
\(222\) 5.64572 + 14.0093i 0.378916 + 0.940241i
\(223\) −4.45155 + 4.45155i −0.298098 + 0.298098i −0.840268 0.542171i \(-0.817603\pi\)
0.542171 + 0.840268i \(0.317603\pi\)
\(224\) 8.76659 + 4.13519i 0.585742 + 0.276294i
\(225\) −3.25168 + 7.34943i −0.216779 + 0.489962i
\(226\) 1.38969 + 0.591338i 0.0924407 + 0.0393352i
\(227\) −8.81803 8.81803i −0.585273 0.585273i 0.351075 0.936348i \(-0.385816\pi\)
−0.936348 + 0.351075i \(0.885816\pi\)
\(228\) 0.277691 14.4455i 0.0183905 0.956676i
\(229\) 29.3112 1.93694 0.968470 0.249129i \(-0.0801442\pi\)
0.968470 + 0.249129i \(0.0801442\pi\)
\(230\) −17.3235 12.1228i −1.14228 0.799353i
\(231\) 0.274737i 0.0180764i
\(232\) 5.08754 11.3458i 0.334014 0.744885i
\(233\) 17.8139 17.8139i 1.16703 1.16703i 0.184122 0.982903i \(-0.441056\pi\)
0.982903 0.184122i \(-0.0589443\pi\)
\(234\) −0.793566 8.15728i −0.0518771 0.533258i
\(235\) 21.5797 14.0498i 1.40770 0.916507i
\(236\) −7.59379 7.89147i −0.494314 0.513691i
\(237\) 0.787887 + 0.787887i 0.0511787 + 0.0511787i
\(238\) 3.52710 1.42141i 0.228628 0.0921366i
\(239\) 15.2637i 0.987328i 0.869653 + 0.493664i \(0.164343\pi\)
−0.869653 + 0.493664i \(0.835657\pi\)
\(240\) 5.41491 + 9.06050i 0.349531 + 0.584853i
\(241\) 12.6676i 0.815990i 0.912984 + 0.407995i \(0.133772\pi\)
−0.912984 + 0.407995i \(0.866228\pi\)
\(242\) −5.80500 14.4045i −0.373160 0.925958i
\(243\) −10.2034 10.2034i −0.654550 0.654550i
\(244\) −16.9873 + 16.3465i −1.08750 + 1.04648i
\(245\) 8.89093 + 1.87900i 0.568021 + 0.120045i
\(246\) 4.49197 + 1.91142i 0.286398 + 0.121867i
\(247\) 21.1742 + 6.22906i 1.34728 + 0.396345i
\(248\) −8.05446 3.61170i −0.511459 0.229343i
\(249\) 7.69836 0.487863
\(250\) 15.3517 + 3.78506i 0.970924 + 0.239388i
\(251\) 16.0887i 1.01551i 0.861501 + 0.507755i \(0.169525\pi\)
−0.861501 + 0.507755i \(0.830475\pi\)
\(252\) −0.105868 + 5.50724i −0.00666903 + 0.346924i
\(253\) −0.642366 0.642366i −0.0403852 0.0403852i
\(254\) 27.9050 + 11.8741i 1.75091 + 0.745046i
\(255\) 4.05156 + 0.856255i 0.253719 + 0.0536208i
\(256\) −15.9527 1.22893i −0.997046 0.0768082i
\(257\) −16.0293 16.0293i −0.999880 0.999880i 0.000120104 1.00000i \(-0.499962\pi\)
−1.00000 0.000120104i \(0.999962\pi\)
\(258\) −3.31789 + 1.33710i −0.206563 + 0.0832445i
\(259\) 15.5073 0.963576
\(260\) −15.5326 + 4.32876i −0.963291 + 0.268458i
\(261\) 7.06605 0.437378
\(262\) −0.308324 + 0.124254i −0.0190483 + 0.00767645i
\(263\) −1.00613 1.00613i −0.0620408 0.0620408i 0.675406 0.737446i \(-0.263969\pi\)
−0.737446 + 0.675406i \(0.763969\pi\)
\(264\) 0.161398 + 0.423813i 0.00993338 + 0.0260839i
\(265\) −9.31449 14.3066i −0.572185 0.878844i
\(266\) −13.6495 5.80810i −0.836903 0.356118i
\(267\) −2.69363 2.69363i −0.164848 0.164848i
\(268\) 20.0940 + 0.386274i 1.22744 + 0.0235954i
\(269\) 19.2720i 1.17504i 0.809211 + 0.587519i \(0.199895\pi\)
−0.809211 + 0.587519i \(0.800105\pi\)
\(270\) −9.85804 + 14.0872i −0.599941 + 0.857317i
\(271\) −28.0613 −1.70460 −0.852301 0.523052i \(-0.824793\pi\)
−0.852301 + 0.523052i \(0.824793\pi\)
\(272\) −4.60591 + 4.26474i −0.279274 + 0.258588i
\(273\) 6.99444 + 2.05764i 0.423323 + 0.124534i
\(274\) −22.5826 9.60929i −1.36426 0.580519i
\(275\) 0.621243 + 0.274863i 0.0374624 + 0.0165748i
\(276\) −10.9425 11.3714i −0.658659 0.684478i
\(277\) 12.7073 + 12.7073i 0.763505 + 0.763505i 0.976954 0.213449i \(-0.0684697\pi\)
−0.213449 + 0.976954i \(0.568470\pi\)
\(278\) −10.3677 25.7263i −0.621811 1.54296i
\(279\) 5.01626i 0.300316i
\(280\) 10.7061 1.67937i 0.639813 0.100362i
\(281\) 17.4196i 1.03917i −0.854420 0.519583i \(-0.826087\pi\)
0.854420 0.519583i \(-0.173913\pi\)
\(282\) 17.8262 7.18392i 1.06153 0.427796i
\(283\) 10.9442 + 10.9442i 0.650568 + 0.650568i 0.953130 0.302562i \(-0.0978420\pi\)
−0.302562 + 0.953130i \(0.597842\pi\)
\(284\) −6.47139 + 6.22728i −0.384006 + 0.369521i
\(285\) −8.81362 13.5372i −0.522074 0.801877i
\(286\) −0.689531 + 0.0670797i −0.0407728 + 0.00396651i
\(287\) 3.54405 3.54405i 0.209199 0.209199i
\(288\) −3.07200 8.55773i −0.181019 0.504269i
\(289\) 14.5373i 0.855138i
\(290\) −2.41788 13.6900i −0.141983 0.803903i
\(291\) −3.86748 −0.226716
\(292\) 17.0925 + 0.328575i 1.00026 + 0.0192284i
\(293\) −1.56341 1.56341i −0.0913353 0.0913353i 0.659963 0.751298i \(-0.270572\pi\)
−0.751298 + 0.659963i \(0.770572\pi\)
\(294\) 6.24099 + 2.65565i 0.363982 + 0.154881i
\(295\) −11.9798 2.53181i −0.697492 0.147408i
\(296\) −23.9217 + 9.10999i −1.39042 + 0.529507i
\(297\) −0.522361 + 0.522361i −0.0303105 + 0.0303105i
\(298\) −1.26771 3.14570i −0.0734366 0.182226i
\(299\) 21.1648 11.5428i 1.22399 0.667538i
\(300\) 10.6983 + 4.98137i 0.617666 + 0.287600i
\(301\) 3.67267i 0.211689i
\(302\) −2.97750 7.38836i −0.171336 0.425152i
\(303\) 2.19688 + 2.19688i 0.126207 + 0.126207i
\(304\) 24.4679 + 0.941058i 1.40333 + 0.0539734i
\(305\) −5.45002 + 25.7880i −0.312067 + 1.47662i
\(306\) −3.28234 1.39670i −0.187639 0.0798438i
\(307\) 12.1227 + 12.1227i 0.691877 + 0.691877i 0.962645 0.270768i \(-0.0872775\pi\)
−0.270768 + 0.962645i \(0.587277\pi\)
\(308\) 0.465524 + 0.00894893i 0.0265257 + 0.000509913i
\(309\) 12.2915i 0.699241i
\(310\) −9.71865 + 1.71648i −0.551982 + 0.0974893i
\(311\) 18.9025i 1.07186i 0.844261 + 0.535932i \(0.180040\pi\)
−0.844261 + 0.535932i \(0.819960\pi\)
\(312\) −11.9985 + 0.934853i −0.679281 + 0.0529256i
\(313\) 5.87564 5.87564i 0.332111 0.332111i −0.521277 0.853388i \(-0.674544\pi\)
0.853388 + 0.521277i \(0.174544\pi\)
\(314\) 2.83760 6.66858i 0.160135 0.376330i
\(315\) 3.36013 + 5.16098i 0.189322 + 0.290788i
\(316\) −1.36069 + 1.30936i −0.0765446 + 0.0736572i
\(317\) 10.2637 10.2637i 0.576467 0.576467i −0.357461 0.933928i \(-0.616357\pi\)
0.933928 + 0.357461i \(0.116357\pi\)
\(318\) −4.76268 11.8181i −0.267078 0.662726i
\(319\) 0.597290i 0.0334418i
\(320\) −15.5288 + 8.88009i −0.868087 + 0.496412i
\(321\) −19.8867 −1.10997
\(322\) −15.0280 + 6.05626i −0.837478 + 0.337502i
\(323\) 6.79273 6.79273i 0.377958 0.377958i
\(324\) −2.29791 + 2.21123i −0.127662 + 0.122846i
\(325\) −11.6504 + 13.7574i −0.646250 + 0.763126i
\(326\) 11.7927 + 5.01802i 0.653138 + 0.277922i
\(327\) 1.31031 + 1.31031i 0.0724602 + 0.0724602i
\(328\) −3.38509 + 7.54910i −0.186910 + 0.416829i
\(329\) 19.7323i 1.08788i
\(330\) 0.415419 + 0.290706i 0.0228681 + 0.0160028i
\(331\) 16.3191 0.896980 0.448490 0.893788i \(-0.351962\pi\)
0.448490 + 0.893788i \(0.351962\pi\)
\(332\) −0.250756 + 13.0444i −0.0137620 + 0.715903i
\(333\) −10.2860 10.2860i −0.563667 0.563667i
\(334\) 4.65657 10.9433i 0.254796 0.598790i
\(335\) 18.8306 12.2599i 1.02883 0.669832i
\(336\) 8.08246 + 0.310859i 0.440934 + 0.0169587i
\(337\) 14.5265 + 14.5265i 0.791309 + 0.791309i 0.981707 0.190398i \(-0.0609779\pi\)
−0.190398 + 0.981707i \(0.560978\pi\)
\(338\) 3.45647 18.0569i 0.188007 0.982168i
\(339\) 1.26027 0.0684485
\(340\) −1.58284 + 6.83723i −0.0858416 + 0.370801i
\(341\) −0.424022 −0.0229621
\(342\) 5.20117 + 12.9062i 0.281247 + 0.697887i
\(343\) 13.4053 13.4053i 0.723818 0.723818i
\(344\) −2.15757 5.66551i −0.116328 0.305464i
\(345\) −17.2626 3.64827i −0.929388 0.196416i
\(346\) 15.9118 + 6.77077i 0.855425 + 0.363999i
\(347\) −7.03773 + 7.03773i −0.377805 + 0.377805i −0.870310 0.492505i \(-0.836081\pi\)
0.492505 + 0.870310i \(0.336081\pi\)
\(348\) 0.199423 10.3740i 0.0106902 0.556106i
\(349\) −19.3224 −1.03430 −0.517152 0.855894i \(-0.673008\pi\)
−0.517152 + 0.855894i \(0.673008\pi\)
\(350\) 8.84925 8.27601i 0.473012 0.442371i
\(351\) −9.38641 17.2108i −0.501010 0.918647i
\(352\) −0.723380 + 0.259674i −0.0385563 + 0.0138407i
\(353\) 1.78993 + 1.78993i 0.0952685 + 0.0952685i 0.753135 0.657866i \(-0.228541\pi\)
−0.657866 + 0.753135i \(0.728541\pi\)
\(354\) −8.40923 3.57828i −0.446946 0.190184i
\(355\) −2.07621 + 9.82404i −0.110194 + 0.521406i
\(356\) 4.65192 4.47645i 0.246551 0.237251i
\(357\) 2.24384 2.24384i 0.118756 0.118756i
\(358\) 6.75912 + 16.7721i 0.357230 + 0.886431i
\(359\) 7.57948i 0.400029i 0.979793 + 0.200015i \(0.0640990\pi\)
−0.979793 + 0.200015i \(0.935901\pi\)
\(360\) −8.21527 5.98743i −0.432983 0.315565i
\(361\) −18.4728 −0.972252
\(362\) −2.37062 5.88245i −0.124597 0.309175i
\(363\) −9.16374 9.16374i −0.480972 0.480972i
\(364\) −3.71436 + 11.7846i −0.194686 + 0.617681i
\(365\) 16.0178 10.4286i 0.838411 0.545860i
\(366\) −7.70268 + 18.1019i −0.402625 + 0.946200i
\(367\) −25.0286 + 25.0286i −1.30648 + 1.30648i −0.382544 + 0.923937i \(0.624952\pi\)
−0.923937 + 0.382544i \(0.875048\pi\)
\(368\) 19.6245 18.1709i 1.02300 0.947224i
\(369\) −4.70152 −0.244752
\(370\) −16.4086 + 23.4480i −0.853044 + 1.21900i
\(371\) −13.0818 −0.679173
\(372\) −7.36462 0.141573i −0.381838 0.00734020i
\(373\) −12.9400 + 12.9400i −0.670007 + 0.670007i −0.957717 0.287711i \(-0.907106\pi\)
0.287711 + 0.957717i \(0.407106\pi\)
\(374\) −0.118062 + 0.277454i −0.00610484 + 0.0143468i
\(375\) 13.0244 2.10954i 0.672575 0.108936i
\(376\) 11.5920 + 30.4393i 0.597814 + 1.56979i
\(377\) 15.2062 + 4.47339i 0.783159 + 0.230391i
\(378\) 4.92485 + 12.2205i 0.253307 + 0.628555i
\(379\) 25.4640i 1.30800i 0.756495 + 0.653999i \(0.226910\pi\)
−0.756495 + 0.653999i \(0.773090\pi\)
\(380\) 23.2251 14.4932i 1.19142 0.743484i
\(381\) 25.3063 1.29648
\(382\) −30.5156 + 12.2977i −1.56131 + 0.629207i
\(383\) −23.7178 + 23.7178i −1.21192 + 1.21192i −0.241528 + 0.970394i \(0.577649\pi\)
−0.970394 + 0.241528i \(0.922351\pi\)
\(384\) −12.6507 + 4.26863i −0.645580 + 0.217833i
\(385\) 0.436254 0.284030i 0.0222336 0.0144755i
\(386\) −0.702430 + 1.65076i −0.0357528 + 0.0840217i
\(387\) 2.43608 2.43608i 0.123833 0.123833i
\(388\) 0.125974 6.55319i 0.00639537 0.332688i
\(389\) 27.0309i 1.37052i 0.728297 + 0.685262i \(0.240312\pi\)
−0.728297 + 0.685262i \(0.759688\pi\)
\(390\) −10.5123 + 8.39879i −0.532309 + 0.425289i
\(391\) 10.4927i 0.530638i
\(392\) −4.70312 + 10.4884i −0.237543 + 0.529747i
\(393\) −0.196147 + 0.196147i −0.00989431 + 0.00989431i
\(394\) 11.9384 + 5.07999i 0.601446 + 0.255926i
\(395\) −0.436547 + 2.06562i −0.0219651 + 0.103933i
\(396\) −0.302846 0.314717i −0.0152186 0.0158151i
\(397\) 9.49107 9.49107i 0.476343 0.476343i −0.427617 0.903960i \(-0.640647\pi\)
0.903960 + 0.427617i \(0.140647\pi\)
\(398\) −3.49140 8.66356i −0.175008 0.434265i
\(399\) −12.3783 −0.619693
\(400\) −8.78909 + 17.9653i −0.439455 + 0.898265i
\(401\) 16.6170i 0.829811i 0.909864 + 0.414906i \(0.136185\pi\)
−0.909864 + 0.414906i \(0.863815\pi\)
\(402\) 15.5553 6.26874i 0.775825 0.312656i
\(403\) 3.17571 10.7950i 0.158193 0.537739i
\(404\) −3.79403 + 3.65091i −0.188760 + 0.181640i
\(405\) −0.737236 + 3.48840i −0.0366336 + 0.173340i
\(406\) −9.80236 4.17108i −0.486483 0.207007i
\(407\) −0.869466 + 0.869466i −0.0430978 + 0.0430978i
\(408\) −2.14319 + 4.77955i −0.106104 + 0.236623i
\(409\) −9.84810 −0.486957 −0.243479 0.969906i \(-0.578289\pi\)
−0.243479 + 0.969906i \(0.578289\pi\)
\(410\) 1.60878 + 9.10887i 0.0794519 + 0.449855i
\(411\) −20.4795 −1.01018
\(412\) 20.8272 + 0.400369i 1.02608 + 0.0197248i
\(413\) −6.63466 + 6.63466i −0.326470 + 0.326470i
\(414\) 13.9852 + 5.95095i 0.687334 + 0.292473i
\(415\) 7.95876 + 12.2242i 0.390680 + 0.600063i
\(416\) −1.19322 20.3611i −0.0585026 0.998287i
\(417\) −16.3663 16.3663i −0.801463 0.801463i
\(418\) 1.09095 0.439652i 0.0533603 0.0215041i
\(419\) −35.8407 −1.75093 −0.875466 0.483279i \(-0.839446\pi\)
−0.875466 + 0.483279i \(0.839446\pi\)
\(420\) 7.67191 4.78751i 0.374351 0.233607i
\(421\) 29.4970i 1.43760i 0.695218 + 0.718799i \(0.255308\pi\)
−0.695218 + 0.718799i \(0.744692\pi\)
\(422\) 8.86360 3.57202i 0.431473 0.173883i
\(423\) −13.0884 + 13.0884i −0.636381 + 0.636381i
\(424\) 20.1802 7.68511i 0.980035 0.373222i
\(425\) 2.82896 + 7.31869i 0.137225 + 0.355009i
\(426\) −2.93437 + 6.89598i −0.142170 + 0.334111i
\(427\) 14.2819 + 14.2819i 0.691150 + 0.691150i
\(428\) 0.647763 33.6967i 0.0313108 1.62879i
\(429\) −0.507534 + 0.276798i −0.0245040 + 0.0133639i
\(430\) −5.55331 3.88614i −0.267804 0.187406i
\(431\) 19.7901 0.953253 0.476627 0.879106i \(-0.341859\pi\)
0.476627 + 0.879106i \(0.341859\pi\)
\(432\) −14.7763 15.9583i −0.710923 0.767796i
\(433\) −2.28416 + 2.28416i −0.109770 + 0.109770i −0.759858 0.650089i \(-0.774732\pi\)
0.650089 + 0.759858i \(0.274732\pi\)
\(434\) −2.96110 + 6.95880i −0.142137 + 0.334033i
\(435\) −6.32949 9.72176i −0.303476 0.466122i
\(436\) −2.26291 + 2.17755i −0.108374 + 0.104286i
\(437\) −28.9420 + 28.9420i −1.38448 + 1.38448i
\(438\) 13.2317 5.33237i 0.632236 0.254790i
\(439\) −6.80513 −0.324791 −0.162396 0.986726i \(-0.551922\pi\)
−0.162396 + 0.986726i \(0.551922\pi\)
\(440\) −0.506114 + 0.694432i −0.0241280 + 0.0331058i
\(441\) −6.53213 −0.311054
\(442\) −6.17940 5.08369i −0.293924 0.241807i
\(443\) −15.2445 15.2445i −0.724286 0.724286i 0.245189 0.969475i \(-0.421150\pi\)
−0.969475 + 0.245189i \(0.921150\pi\)
\(444\) −15.3916 + 14.8110i −0.730454 + 0.702900i
\(445\) 1.49247 7.06196i 0.0707499 0.334769i
\(446\) −8.19227 3.48596i −0.387915 0.165065i
\(447\) −2.00120 2.00120i −0.0946537 0.0946537i
\(448\) −0.789998 + 13.6851i −0.0373239 + 0.646560i
\(449\) 8.62094 0.406847 0.203424 0.979091i \(-0.434793\pi\)
0.203424 + 0.979091i \(0.434793\pi\)
\(450\) −11.3592 0.380228i −0.535476 0.0179241i
\(451\) 0.397417i 0.0187136i
\(452\) −0.0410505 + 2.13545i −0.00193085 + 0.100443i
\(453\) −4.70026 4.70026i −0.220837 0.220837i
\(454\) 6.90530 16.2280i 0.324082 0.761617i
\(455\) 3.96371 + 13.2337i 0.185822 + 0.620406i
\(456\) 19.0950 7.27185i 0.894205 0.340536i
\(457\) 15.8492 15.8492i 0.741395 0.741395i −0.231452 0.972846i \(-0.574347\pi\)
0.972846 + 0.231452i \(0.0743475\pi\)
\(458\) 15.4943 + 38.4477i 0.724003 + 1.79654i
\(459\) −8.53248 −0.398262
\(460\) 6.74405 29.1316i 0.314443 1.35827i
\(461\) 31.2187i 1.45400i −0.686638 0.726999i \(-0.740914\pi\)
0.686638 0.726999i \(-0.259086\pi\)
\(462\) 0.360373 0.145230i 0.0167661 0.00675671i
\(463\) 17.2870 17.2870i 0.803396 0.803396i −0.180229 0.983625i \(-0.557684\pi\)
0.983625 + 0.180229i \(0.0576839\pi\)
\(464\) 17.5716 + 0.675820i 0.815742 + 0.0313742i
\(465\) −6.90157 + 4.49337i −0.320053 + 0.208375i
\(466\) 32.7832 + 13.9499i 1.51865 + 0.646214i
\(467\) −3.44862 + 3.44862i −0.159583 + 0.159583i −0.782382 0.622799i \(-0.785995\pi\)
0.622799 + 0.782382i \(0.285995\pi\)
\(468\) 10.2804 5.35298i 0.475214 0.247442i
\(469\) 17.2186i 0.795079i
\(470\) 29.8365 + 20.8792i 1.37625 + 0.963088i
\(471\) 6.04756i 0.278657i
\(472\) 6.33708 14.1324i 0.291688 0.650494i
\(473\) −0.205920 0.205920i −0.00946822 0.00946822i
\(474\) −0.616985 + 1.44996i −0.0283391 + 0.0665990i
\(475\) 12.3840 27.9903i 0.568218 1.28428i
\(476\) 3.72895 + 3.87513i 0.170916 + 0.177616i
\(477\) 8.67714 + 8.67714i 0.397299 + 0.397299i
\(478\) −20.0215 + 8.06863i −0.915761 + 0.369050i
\(479\) 30.8029i 1.40742i −0.710488 0.703710i \(-0.751526\pi\)
0.710488 0.703710i \(-0.248474\pi\)
\(480\) −9.02229 + 11.8923i −0.411809 + 0.542805i
\(481\) −15.6236 28.6473i −0.712376 1.30621i
\(482\) −16.6161 + 6.69626i −0.756843 + 0.305006i
\(483\) −9.56038 + 9.56038i −0.435012 + 0.435012i
\(484\) 15.8259 15.2289i 0.719357 0.692222i
\(485\) −3.99830 6.14116i −0.181553 0.278856i
\(486\) 7.99019 18.7775i 0.362442 0.851767i
\(487\) 21.5008 + 21.5008i 0.974296 + 0.974296i 0.999678 0.0253815i \(-0.00808004\pi\)
−0.0253815 + 0.999678i \(0.508080\pi\)
\(488\) −30.4216 13.6413i −1.37712 0.617514i
\(489\) 10.6945 0.483622
\(490\) 2.23518 + 12.6555i 0.100975 + 0.571719i
\(491\) 31.4355i 1.41866i −0.704875 0.709332i \(-0.748997\pi\)
0.704875 0.709332i \(-0.251003\pi\)
\(492\) −0.132690 + 6.90254i −0.00598212 + 0.311190i
\(493\) 4.87820 4.87820i 0.219703 0.219703i
\(494\) 3.02230 + 31.0670i 0.135980 + 1.39777i
\(495\) −0.477764 0.100970i −0.0214739 0.00453828i
\(496\) 0.479772 12.4743i 0.0215424 0.560111i
\(497\) 5.44075 + 5.44075i 0.244051 + 0.244051i
\(498\) 4.06946 + 10.0980i 0.182357 + 0.452500i
\(499\) 30.8204i 1.37971i −0.723948 0.689855i \(-0.757674\pi\)
0.723948 0.689855i \(-0.242326\pi\)
\(500\) 3.15024 + 22.1377i 0.140883 + 0.990026i
\(501\) 9.92418i 0.443380i
\(502\) −21.1036 + 8.50473i −0.941901 + 0.379585i
\(503\) −15.7158 15.7158i −0.700733 0.700733i 0.263835 0.964568i \(-0.415013\pi\)
−0.964568 + 0.263835i \(0.915013\pi\)
\(504\) −7.27983 + 2.77234i −0.324270 + 0.123490i
\(505\) −1.21723 + 5.75961i −0.0541661 + 0.256299i
\(506\) 0.503030 1.18216i 0.0223624 0.0525534i
\(507\) −3.24574 14.9942i −0.144148 0.665917i
\(508\) −0.824294 + 42.8799i −0.0365722 + 1.90249i
\(509\) −38.9696 −1.72730 −0.863649 0.504093i \(-0.831827\pi\)
−0.863649 + 0.504093i \(0.831827\pi\)
\(510\) 1.01856 + 5.76708i 0.0451027 + 0.255371i
\(511\) 14.6466i 0.647927i
\(512\) −6.82085 21.5749i −0.301442 0.953485i
\(513\) 23.5351 + 23.5351i 1.03910 + 1.03910i
\(514\) 12.5524 29.4990i 0.553661 1.30115i
\(515\) 19.5177 12.7073i 0.860054 0.559951i
\(516\) −3.50777 3.64528i −0.154421 0.160474i
\(517\) 1.10636 + 1.10636i 0.0486575 + 0.0486575i
\(518\) 8.19738 + 20.3410i 0.360172 + 0.893730i
\(519\) 14.4300 0.633407
\(520\) −13.8888 18.0859i −0.609064 0.793121i
\(521\) 6.74679 0.295582 0.147791 0.989019i \(-0.452784\pi\)
0.147791 + 0.989019i \(0.452784\pi\)
\(522\) 3.73522 + 9.26857i 0.163486 + 0.405674i
\(523\) 17.7325 + 17.7325i 0.775387 + 0.775387i 0.979043 0.203655i \(-0.0652822\pi\)
−0.203655 + 0.979043i \(0.565282\pi\)
\(524\) −0.325970 0.338748i −0.0142400 0.0147983i
\(525\) 4.09080 9.24600i 0.178537 0.403529i
\(526\) 0.787892 1.85161i 0.0343537 0.0807338i
\(527\) −3.46308 3.46308i −0.150854 0.150854i
\(528\) −0.470599 + 0.435740i −0.0204802 + 0.0189632i
\(529\) 21.7065i 0.943763i
\(530\) 13.8422 19.7805i 0.601266 0.859210i
\(531\) 8.80153 0.381954
\(532\) 0.403197 20.9743i 0.0174808 0.909352i
\(533\) −10.1177 2.97645i −0.438247 0.128924i
\(534\) 2.10935 4.95714i 0.0912806 0.214516i
\(535\) −20.5594 31.5780i −0.888858 1.36524i
\(536\) 10.1153 + 26.5616i 0.436915 + 1.14729i
\(537\) 10.6699 + 10.6699i 0.460440 + 0.460440i
\(538\) −25.2792 + 10.1875i −1.08986 + 0.439214i
\(539\) 0.552157i 0.0237831i
\(540\) −23.6893 5.48415i −1.01942 0.236000i
\(541\) 31.9567i 1.37393i 0.726692 + 0.686963i \(0.241057\pi\)
−0.726692 + 0.686963i \(0.758943\pi\)
\(542\) −14.8336 36.8081i −0.637158 1.58104i
\(543\) −3.74224 3.74224i −0.160595 0.160595i
\(544\) −8.02883 3.78719i −0.344233 0.162374i
\(545\) −0.726007 + 3.43527i −0.0310987 + 0.147151i
\(546\) 0.998352 + 10.2623i 0.0427255 + 0.439187i
\(547\) −6.16147 + 6.16147i −0.263445 + 0.263445i −0.826452 0.563007i \(-0.809644\pi\)
0.563007 + 0.826452i \(0.309644\pi\)
\(548\) 0.667074 34.7012i 0.0284960 1.48236i
\(549\) 18.9463i 0.808610i
\(550\) −0.0321405 + 0.960183i −0.00137047 + 0.0409423i
\(551\) −26.9111 −1.14645
\(552\) 9.13157 20.3644i 0.388666 0.866765i
\(553\) 1.14398 + 1.14398i 0.0486471 + 0.0486471i
\(554\) −9.95092 + 23.3854i −0.422774 + 0.993551i
\(555\) −4.93807 + 23.3656i −0.209609 + 0.991814i
\(556\) 28.2648 27.1986i 1.19869 1.15348i
\(557\) 22.6497 22.6497i 0.959697 0.959697i −0.0395221 0.999219i \(-0.512584\pi\)
0.999219 + 0.0395221i \(0.0125835\pi\)
\(558\) 6.57985 2.65167i 0.278547 0.112254i
\(559\) 6.78469 3.70022i 0.286962 0.156503i
\(560\) 7.86224 + 13.1555i 0.332240 + 0.555922i
\(561\) 0.251616i 0.0106232i
\(562\) 22.8493 9.20825i 0.963841 0.388426i
\(563\) −6.24205 6.24205i −0.263071 0.263071i 0.563229 0.826301i \(-0.309559\pi\)
−0.826301 + 0.563229i \(0.809559\pi\)
\(564\) 18.8464 + 19.5851i 0.793575 + 0.824683i
\(565\) 1.30290 + 2.00118i 0.0548134 + 0.0841904i
\(566\) −8.57032 + 20.1409i −0.360237 + 0.846585i
\(567\) 1.93194 + 1.93194i 0.0811340 + 0.0811340i
\(568\) −11.5892 5.19672i −0.486273 0.218049i
\(569\) 10.8680i 0.455611i −0.973707 0.227805i \(-0.926845\pi\)
0.973707 0.227805i \(-0.0731550\pi\)
\(570\) 13.0978 18.7168i 0.548608 0.783962i
\(571\) 19.4497i 0.813943i −0.913441 0.406971i \(-0.866585\pi\)
0.913441 0.406971i \(-0.133415\pi\)
\(572\) −0.452485 0.869000i −0.0189193 0.0363347i
\(573\) −19.4131 + 19.4131i −0.810995 + 0.810995i
\(574\) 6.52218 + 2.77530i 0.272230 + 0.115839i
\(575\) −12.0534 31.1830i −0.502664 1.30042i
\(576\) 9.60131 8.55330i 0.400055 0.356387i
\(577\) 12.4491 12.4491i 0.518263 0.518263i −0.398782 0.917046i \(-0.630567\pi\)
0.917046 + 0.398782i \(0.130567\pi\)
\(578\) 19.0687 7.68465i 0.793153 0.319639i
\(579\) 1.49703i 0.0622146i
\(580\) 16.6791 10.4083i 0.692560 0.432179i
\(581\) 11.1777 0.463730
\(582\) −2.04440 5.07298i −0.0847433 0.210282i
\(583\) 0.733474 0.733474i 0.0303774 0.0303774i
\(584\) 8.60436 + 22.5940i 0.356051 + 0.934947i
\(585\) 6.14877 11.4070i 0.254221 0.471622i
\(586\) 1.22429 2.87717i 0.0505749 0.118855i
\(587\) −0.126933 0.126933i −0.00523910 0.00523910i 0.704482 0.709721i \(-0.251179\pi\)
−0.709721 + 0.704482i \(0.751179\pi\)
\(588\) −0.184355 + 9.59014i −0.00760265 + 0.395491i
\(589\) 19.1044i 0.787184i
\(590\) −3.01173 17.0523i −0.123991 0.702033i
\(591\) 10.8266 0.445346
\(592\) −24.5950 26.5625i −1.01085 1.09171i
\(593\) 2.22865 + 2.22865i 0.0915195 + 0.0915195i 0.751384 0.659865i \(-0.229386\pi\)
−0.659865 + 0.751384i \(0.729386\pi\)
\(594\) −0.961311 0.409055i −0.0394431 0.0167837i
\(595\) 5.88272 + 1.24325i 0.241168 + 0.0509683i
\(596\) 3.45610 3.32573i 0.141567 0.136227i
\(597\) −5.51150 5.51150i −0.225571 0.225571i
\(598\) 26.3288 + 21.6602i 1.07666 + 0.885753i
\(599\) 9.98842 0.408116 0.204058 0.978959i \(-0.434587\pi\)
0.204058 + 0.978959i \(0.434587\pi\)
\(600\) −0.878818 + 16.6662i −0.0358776 + 0.680395i
\(601\) 26.6091 1.08541 0.542705 0.839924i \(-0.317400\pi\)
0.542705 + 0.839924i \(0.317400\pi\)
\(602\) −4.81745 + 1.94143i −0.196345 + 0.0791266i
\(603\) −11.4210 + 11.4210i −0.465101 + 0.465101i
\(604\) 8.11739 7.81119i 0.330292 0.317833i
\(605\) 5.07739 24.0248i 0.206425 0.976747i
\(606\) −1.72035 + 4.04295i −0.0698845 + 0.164234i
\(607\) −7.48637 + 7.48637i −0.303863 + 0.303863i −0.842523 0.538660i \(-0.818931\pi\)
0.538660 + 0.842523i \(0.318931\pi\)
\(608\) 11.6997 + 32.5921i 0.474486 + 1.32178i
\(609\) −8.88950 −0.360221
\(610\) −36.7072 + 6.48310i −1.48623 + 0.262493i
\(611\) −36.4524 + 19.8803i −1.47471 + 0.804273i
\(612\) 0.0969582 5.04377i 0.00391930 0.203882i
\(613\) 25.6786 + 25.6786i 1.03715 + 1.03715i 0.999283 + 0.0378679i \(0.0120566\pi\)
0.0378679 + 0.999283i \(0.487943\pi\)
\(614\) −9.49313 + 22.3096i −0.383112 + 0.900341i
\(615\) 4.21144 + 6.46854i 0.169822 + 0.260837i
\(616\) 0.234344 + 0.615360i 0.00944201 + 0.0247936i
\(617\) 3.95103 3.95103i 0.159062 0.159062i −0.623089 0.782151i \(-0.714122\pi\)
0.782151 + 0.623089i \(0.214122\pi\)
\(618\) 16.1229 6.49749i 0.648557 0.261367i
\(619\) 8.51161i 0.342111i −0.985261 0.171055i \(-0.945282\pi\)
0.985261 0.171055i \(-0.0547177\pi\)
\(620\) −7.38893 11.8406i −0.296747 0.475531i
\(621\) 36.3546 1.45886
\(622\) −24.7945 + 9.99215i −0.994169 + 0.400649i
\(623\) −3.91105 3.91105i −0.156693 0.156693i
\(624\) −7.56883 15.2443i −0.302996 0.610260i
\(625\) 16.8146 + 18.5005i 0.672586 + 0.740019i
\(626\) 10.8130 + 4.60115i 0.432176 + 0.183899i
\(627\) 0.694033 0.694033i 0.0277170 0.0277170i
\(628\) 10.2472 + 0.196986i 0.408908 + 0.00786058i
\(629\) −14.2022 −0.566281
\(630\) −4.99346 + 7.13566i −0.198944 + 0.284292i
\(631\) 7.04210 0.280341 0.140171 0.990127i \(-0.455235\pi\)
0.140171 + 0.990127i \(0.455235\pi\)
\(632\) −2.43677 1.09267i −0.0969296 0.0434641i
\(633\) 5.63876 5.63876i 0.224121 0.224121i
\(634\) 18.8885 + 8.03740i 0.750158 + 0.319206i
\(635\) 26.1623 + 40.1838i 1.03822 + 1.59465i
\(636\) 12.9842 12.4944i 0.514858 0.495437i
\(637\) −14.0572 4.13537i −0.556967 0.163849i
\(638\) 0.783467 0.315736i 0.0310178 0.0125001i
\(639\) 7.21768i 0.285527i
\(640\) −19.8568 15.6751i −0.784909 0.619611i
\(641\) −36.7633 −1.45206 −0.726032 0.687661i \(-0.758638\pi\)
−0.726032 + 0.687661i \(0.758638\pi\)
\(642\) −10.5124 26.0854i −0.414891 1.02951i
\(643\) −20.9784 + 20.9784i −0.827306 + 0.827306i −0.987143 0.159838i \(-0.948903\pi\)
0.159838 + 0.987143i \(0.448903\pi\)
\(644\) −15.8880 16.5109i −0.626077 0.650619i
\(645\) −5.53379 1.16951i −0.217893 0.0460494i
\(646\) 12.5008 + 5.31932i 0.491837 + 0.209286i
\(647\) −8.79846 + 8.79846i −0.345903 + 0.345903i −0.858581 0.512678i \(-0.828654\pi\)
0.512678 + 0.858581i \(0.328654\pi\)
\(648\) −4.11519 1.84529i −0.161660 0.0724899i
\(649\) 0.743988i 0.0292041i
\(650\) −24.2043 8.00953i −0.949370 0.314160i
\(651\) 6.31075i 0.247338i
\(652\) −0.348349 + 18.1211i −0.0136424 + 0.709679i
\(653\) −26.6946 + 26.6946i −1.04464 + 1.04464i −0.0456859 + 0.998956i \(0.514547\pi\)
−0.998956 + 0.0456859i \(0.985453\pi\)
\(654\) −1.02609 + 2.41138i −0.0401232 + 0.0942925i
\(655\) −0.514243 0.108680i −0.0200932 0.00424648i
\(656\) −11.6916 0.449669i −0.456480 0.0175566i
\(657\) −9.71506 + 9.71506i −0.379021 + 0.379021i
\(658\) 25.8829 10.4308i 1.00902 0.406634i
\(659\) 30.2389 1.17794 0.588970 0.808155i \(-0.299534\pi\)
0.588970 + 0.808155i \(0.299534\pi\)
\(660\) −0.161723 + 0.698578i −0.00629507 + 0.0271921i
\(661\) 44.3556i 1.72523i 0.505857 + 0.862617i \(0.331176\pi\)
−0.505857 + 0.862617i \(0.668824\pi\)
\(662\) 8.62653 + 21.4059i 0.335279 + 0.831962i
\(663\) −6.40581 1.88447i −0.248781 0.0731869i
\(664\) −17.2429 + 6.56653i −0.669154 + 0.254831i
\(665\) −12.7971 19.6556i −0.496248 0.762210i
\(666\) 8.05482 18.9294i 0.312118 0.733501i
\(667\) −20.7847 + 20.7847i −0.804786 + 0.804786i
\(668\) 16.8159 + 0.323258i 0.650626 + 0.0125072i
\(669\) −7.42935 −0.287235
\(670\) 26.0355 + 18.2194i 1.00584 + 0.703876i
\(671\) −1.60152 −0.0618261
\(672\) 3.86475 + 10.7661i 0.149086 + 0.415312i
\(673\) 8.50808 8.50808i 0.327962 0.327962i −0.523849 0.851811i \(-0.675504\pi\)
0.851811 + 0.523849i \(0.175504\pi\)
\(674\) −11.3755 + 26.7334i −0.438169 + 1.02973i
\(675\) −25.3575 + 9.80165i −0.976009 + 0.377266i
\(676\) 25.5125 5.01130i 0.981249 0.192742i
\(677\) −9.05251 9.05251i −0.347916 0.347916i 0.511417 0.859333i \(-0.329121\pi\)
−0.859333 + 0.511417i \(0.829121\pi\)
\(678\) 0.666198 + 1.65310i 0.0255852 + 0.0634870i
\(679\) −5.61543 −0.215501
\(680\) −9.80513 + 1.53804i −0.376009 + 0.0589812i
\(681\) 14.7167i 0.563946i
\(682\) −0.224144 0.556191i −0.00858292 0.0212977i
\(683\) −19.2696 + 19.2696i −0.737331 + 0.737331i −0.972061 0.234730i \(-0.924580\pi\)
0.234730 + 0.972061i \(0.424580\pi\)
\(684\) −14.1797 + 13.6448i −0.542174 + 0.521722i
\(685\) −21.1723 32.5194i −0.808950 1.24250i
\(686\) 24.6700 + 10.4975i 0.941905 + 0.400798i
\(687\) 24.4593 + 24.4593i 0.933180 + 0.933180i
\(688\) 6.29095 5.82496i 0.239840 0.222074i
\(689\) 13.1799 + 24.1666i 0.502116 + 0.920675i
\(690\) −4.33982 24.5720i −0.165214 0.935439i
\(691\) 19.1766 0.729511 0.364756 0.931103i \(-0.381153\pi\)
0.364756 + 0.931103i \(0.381153\pi\)
\(692\) −0.470025 + 24.4507i −0.0178677 + 0.929477i
\(693\) −0.264595 + 0.264595i −0.0100511 + 0.0100511i
\(694\) −12.9517 5.51117i −0.491638 0.209201i
\(695\) 9.06815 42.9080i 0.343975 1.62759i
\(696\) 13.7131 5.22227i 0.519792 0.197950i
\(697\) −3.24579 + 3.24579i −0.122943 + 0.122943i
\(698\) −10.2141 25.3453i −0.386609 0.959332i
\(699\) 29.7302 1.12450
\(700\) 15.5335 + 7.23277i 0.587111 + 0.273373i
\(701\) 1.64833 0.0622567 0.0311284 0.999515i \(-0.490090\pi\)
0.0311284 + 0.999515i \(0.490090\pi\)
\(702\) 17.6137 21.4101i 0.664788 0.808072i
\(703\) 39.1741 + 39.1741i 1.47748 + 1.47748i
\(704\) −0.723005 0.811593i −0.0272493 0.0305881i
\(705\) 29.7316 + 6.28347i 1.11976 + 0.236649i
\(706\) −1.40168 + 3.29405i −0.0527528 + 0.123973i
\(707\) 3.18978 + 3.18978i 0.119964 + 0.119964i
\(708\) 0.248403 12.9220i 0.00933556 0.485637i
\(709\) 19.9349 0.748672 0.374336 0.927293i \(-0.377871\pi\)
0.374336 + 0.927293i \(0.377871\pi\)
\(710\) −13.9837 + 2.46976i −0.524801 + 0.0926885i
\(711\) 1.51760i 0.0569146i
\(712\) 8.33085 + 3.73563i 0.312212 + 0.139999i
\(713\) 14.7553 + 14.7553i 0.552588 + 0.552588i
\(714\) 4.12937 + 1.75712i 0.154538 + 0.0657587i
\(715\) −0.964229 0.519752i −0.0360601 0.0194376i
\(716\) −18.4270 + 17.7319i −0.688650 + 0.662673i
\(717\) −12.7371 + 12.7371i −0.475675 + 0.475675i
\(718\) −9.94203 + 4.00662i −0.371033 + 0.149526i
\(719\) 30.5169 1.13809 0.569044 0.822307i \(-0.307313\pi\)
0.569044 + 0.822307i \(0.307313\pi\)
\(720\) 3.51102 13.9410i 0.130848 0.519552i
\(721\) 17.8469i 0.664652i
\(722\) −9.76499 24.2308i −0.363415 0.901778i
\(723\) −10.5707 + 10.5707i −0.393128 + 0.393128i
\(724\) 6.46288 6.21909i 0.240191 0.231131i
\(725\) 8.89357 20.1012i 0.330299 0.746540i
\(726\) 7.17603 16.8642i 0.266327 0.625889i
\(727\) 16.6943 16.6943i 0.619157 0.619157i −0.326159 0.945315i \(-0.605754\pi\)
0.945315 + 0.326159i \(0.105754\pi\)
\(728\) −17.4214 + 1.35737i −0.645679 + 0.0503075i
\(729\) 21.8124i 0.807867i
\(730\) 22.1466 + 15.4979i 0.819681 + 0.573603i
\(731\) 3.36359i 0.124407i
\(732\) −27.8160 0.534717i −1.02811 0.0197637i
\(733\) −24.1094 24.1094i −0.890499 0.890499i 0.104071 0.994570i \(-0.466813\pi\)
−0.994570 + 0.104071i \(0.966813\pi\)
\(734\) −46.0606 19.5996i −1.70013 0.723435i
\(735\) 5.85123 + 8.98716i 0.215826 + 0.331497i
\(736\) 34.2087 + 16.1362i 1.26095 + 0.594788i
\(737\) 0.965415 + 0.965415i 0.0355615 + 0.0355615i
\(738\) −2.48529 6.16701i −0.0914849 0.227011i
\(739\) 38.8417i 1.42881i 0.699731 + 0.714407i \(0.253303\pi\)
−0.699731 + 0.714407i \(0.746697\pi\)
\(740\) −39.4306 9.12832i −1.44950 0.335564i
\(741\) 12.4712 + 22.8671i 0.458141 + 0.840044i
\(742\) −6.91523 17.1595i −0.253866 0.629943i
\(743\) −1.46488 + 1.46488i −0.0537411 + 0.0537411i −0.733467 0.679726i \(-0.762099\pi\)
0.679726 + 0.733467i \(0.262099\pi\)
\(744\) −3.70734 9.73504i −0.135918 0.356904i
\(745\) 1.10881 5.24660i 0.0406238 0.192221i
\(746\) −23.8137 10.1332i −0.871881 0.371001i
\(747\) −7.41417 7.41417i −0.271270 0.271270i
\(748\) −0.426347 0.00819582i −0.0155888 0.000299669i
\(749\) −28.8747 −1.05506
\(750\) 9.65195 + 15.9690i 0.352440 + 0.583104i
\(751\) 3.07742i 0.112297i 0.998422 + 0.0561484i \(0.0178820\pi\)
−0.998422 + 0.0561484i \(0.982118\pi\)
\(752\) −33.7996 + 31.2960i −1.23255 + 1.14125i
\(753\) −13.4255 + 13.4255i −0.489253 + 0.489253i
\(754\) 2.17046 + 22.3107i 0.0790435 + 0.812509i
\(755\) 2.60429 12.3228i 0.0947798 0.448472i
\(756\) −13.4263 + 12.9199i −0.488312 + 0.469892i
\(757\) −31.9991 31.9991i −1.16303 1.16303i −0.983809 0.179219i \(-0.942643\pi\)
−0.179219 0.983809i \(-0.557357\pi\)
\(758\) −33.4012 + 13.4606i −1.21319 + 0.488913i
\(759\) 1.07207i 0.0389136i
\(760\) 31.2879 + 22.8031i 1.13493 + 0.827156i
\(761\) 9.64916i 0.349782i −0.984588 0.174891i \(-0.944043\pi\)
0.984588 0.174891i \(-0.0559572\pi\)
\(762\) 13.3773 + 33.1943i 0.484607 + 1.20250i
\(763\) 1.90252 + 1.90252i 0.0688758 + 0.0688758i
\(764\) −32.2620 33.5267i −1.16720 1.21295i
\(765\) −3.07735 4.72665i −0.111262 0.170892i
\(766\) −43.6483 18.5731i −1.57708 0.671075i
\(767\) 18.9410 + 5.57209i 0.683918 + 0.201196i
\(768\) −12.2865 14.3375i −0.443352 0.517362i
\(769\) 13.2266 0.476963 0.238481 0.971147i \(-0.423350\pi\)
0.238481 + 0.971147i \(0.423350\pi\)
\(770\) 0.603174 + 0.422094i 0.0217369 + 0.0152112i
\(771\) 26.7519i 0.963445i
\(772\) −2.53663 0.0487625i −0.0912952 0.00175500i
\(773\) 0.434455 + 0.434455i 0.0156263 + 0.0156263i 0.714877 0.699250i \(-0.246483\pi\)
−0.699250 + 0.714877i \(0.746483\pi\)
\(774\) 4.48316 + 1.90767i 0.161144 + 0.0685696i
\(775\) −14.2700 6.31364i −0.512595 0.226793i
\(776\) 8.66244 3.29887i 0.310963 0.118423i
\(777\) 12.9403 + 12.9403i 0.464232 + 0.464232i
\(778\) −35.4566 + 14.2889i −1.27118 + 0.512284i
\(779\) 17.9057 0.641540
\(780\) −16.5737 9.34925i −0.593432 0.334757i
\(781\) −0.610107 −0.0218313
\(782\) 13.7633 5.54659i 0.492175 0.198346i
\(783\) 16.9017 + 16.9017i 0.604019 + 0.604019i
\(784\) −16.2439 0.624754i −0.580138 0.0223126i
\(785\) 9.60292 6.25212i 0.342743 0.223148i
\(786\) −0.360973 0.153601i −0.0128755 0.00547875i
\(787\) −5.24534 5.24534i −0.186976 0.186976i 0.607411 0.794388i \(-0.292208\pi\)
−0.794388 + 0.607411i \(0.792208\pi\)
\(788\) −0.352651 + 18.3450i −0.0125627 + 0.653512i
\(789\) 1.67917i 0.0597801i
\(790\) −2.94025 + 0.519297i −0.104609 + 0.0184758i
\(791\) 1.82987 0.0650626
\(792\) 0.252727 0.563608i 0.00898027 0.0200269i
\(793\) 11.9946 40.7727i 0.425940 1.44788i
\(794\) 17.4666 + 7.43235i 0.619866 + 0.263764i
\(795\) 4.16571 19.7110i 0.147743 0.699077i
\(796\) 9.51842 9.15937i 0.337371 0.324645i
\(797\) −31.7432 31.7432i −1.12440 1.12440i −0.991071 0.133332i \(-0.957432\pi\)
−0.133332 0.991071i \(-0.542568\pi\)
\(798\) −6.54338 16.2367i −0.231633 0.574774i
\(799\) 18.0717i 0.639331i
\(800\) −28.2112 2.03196i −0.997416 0.0718408i
\(801\) 5.18839i 0.183323i
\(802\) −21.7965 + 8.78397i −0.769662 + 0.310173i
\(803\) 0.821208 + 0.821208i 0.0289798 + 0.0289798i
\(804\) 16.4455 + 17.0901i 0.579987 + 0.602722i
\(805\) −25.0647 5.29716i −0.883414 0.186700i
\(806\) 15.8386 1.54083i 0.557892 0.0542735i
\(807\) −16.0819 + 16.0819i −0.566110 + 0.566110i
\(808\) −6.79449 3.04671i −0.239029 0.107183i
\(809\) 2.77546i 0.0975801i −0.998809 0.0487900i \(-0.984463\pi\)
0.998809 0.0487900i \(-0.0155365\pi\)
\(810\) −4.96546 + 0.876983i −0.174468 + 0.0308140i
\(811\) −34.9977 −1.22894 −0.614468 0.788942i \(-0.710629\pi\)
−0.614468 + 0.788942i \(0.710629\pi\)
\(812\) 0.289555 15.0627i 0.0101614 0.528597i
\(813\) −23.4162 23.4162i −0.821243 0.821243i
\(814\) −1.60009 0.680870i −0.0560833 0.0238645i
\(815\) 11.0562 + 16.9818i 0.387283 + 0.594846i
\(816\) −7.40227 0.284698i −0.259131 0.00996643i
\(817\) −9.27779 + 9.27779i −0.324589 + 0.324589i
\(818\) −5.20585 12.9178i −0.182018 0.451660i
\(819\) −4.75456 8.71792i −0.166138 0.304629i
\(820\) −11.0977 + 6.92532i −0.387549 + 0.241843i
\(821\) 40.4443i 1.41152i 0.708453 + 0.705758i \(0.249393\pi\)
−0.708453 + 0.705758i \(0.750607\pi\)
\(822\) −10.8258 26.8631i −0.377592 0.936957i
\(823\) −8.51119 8.51119i −0.296681 0.296681i 0.543031 0.839713i \(-0.317277\pi\)
−0.839713 + 0.543031i \(0.817277\pi\)
\(824\) 10.4844 + 27.5308i 0.365242 + 0.959081i
\(825\) 0.289043 + 0.747771i 0.0100632 + 0.0260341i
\(826\) −12.2099 5.19553i −0.424837 0.180776i
\(827\) 24.4440 + 24.4440i 0.850002 + 0.850002i 0.990133 0.140131i \(-0.0447523\pi\)
−0.140131 + 0.990133i \(0.544752\pi\)
\(828\) −0.413113 + 21.4902i −0.0143567 + 0.746835i
\(829\) 3.08143i 0.107023i 0.998567 + 0.0535113i \(0.0170413\pi\)
−0.998567 + 0.0535113i \(0.982959\pi\)
\(830\) −11.8274 + 16.9014i −0.410536 + 0.586657i
\(831\) 21.2076i 0.735683i
\(832\) 26.0770 12.3284i 0.904058 0.427409i
\(833\) −4.50959 + 4.50959i −0.156248 + 0.156248i
\(834\) 12.8163 30.1193i 0.443792 1.04294i
\(835\) 15.7586 10.2599i 0.545349 0.355058i
\(836\) 1.15339 + 1.19860i 0.0398907 + 0.0414545i
\(837\) 11.9987 11.9987i 0.414736 0.414736i
\(838\) −18.9459 47.0124i −0.654476 1.62402i
\(839\) 25.5414i 0.881789i 0.897559 + 0.440894i \(0.145339\pi\)
−0.897559 + 0.440894i \(0.854661\pi\)
\(840\) 10.3353 + 7.53253i 0.356601 + 0.259897i
\(841\) 9.67385 0.333581
\(842\) −38.6914 + 15.5926i −1.33339 + 0.537355i
\(843\) 14.5361 14.5361i 0.500649 0.500649i
\(844\) 9.37085 + 9.73819i 0.322558 + 0.335202i
\(845\) 20.4538 20.6553i 0.703632 0.710565i
\(846\) −24.0869 10.2494i −0.828123 0.352382i
\(847\) −13.3054 13.3054i −0.457179 0.457179i
\(848\) 20.7481 + 22.4079i 0.712493 + 0.769491i
\(849\) 18.2652i 0.626861i
\(850\) −8.10453 + 7.57953i −0.277983 + 0.259976i
\(851\) 60.5119 2.07432
\(852\) −10.5966 0.203703i −0.363035 0.00697874i
\(853\) 7.28569 + 7.28569i 0.249457 + 0.249457i 0.820748 0.571291i \(-0.193557\pi\)
−0.571291 + 0.820748i \(0.693557\pi\)
\(854\) −11.1840 + 26.2832i −0.382709 + 0.899394i
\(855\) −4.54925 + 21.5258i −0.155581 + 0.736166i
\(856\) 44.5425 16.9629i 1.52243 0.579780i
\(857\) 18.1854 + 18.1854i 0.621200 + 0.621200i 0.945838 0.324638i \(-0.105243\pi\)
−0.324638 + 0.945838i \(0.605243\pi\)
\(858\) −0.631367 0.519415i −0.0215545 0.0177325i
\(859\) −47.8646 −1.63312 −0.816559 0.577261i \(-0.804121\pi\)
−0.816559 + 0.577261i \(0.804121\pi\)
\(860\) 2.16191 9.33856i 0.0737205 0.318442i
\(861\) 5.91479 0.201575
\(862\) 10.4613 + 25.9587i 0.356314 + 0.884156i
\(863\) −7.98468 + 7.98468i −0.271802 + 0.271802i −0.829825 0.558023i \(-0.811560\pi\)
0.558023 + 0.829825i \(0.311560\pi\)
\(864\) 13.1217 27.8179i 0.446408 0.946384i
\(865\) 14.9181 + 22.9134i 0.507231 + 0.779079i
\(866\) −4.20358 1.78870i −0.142843 0.0607825i
\(867\) 12.1309 12.1309i 0.411989 0.411989i
\(868\) −10.6932 0.205558i −0.362949 0.00697710i
\(869\) −0.128282 −0.00435168
\(870\) 9.40620 13.4415i 0.318900 0.455709i
\(871\) −31.8087 + 17.3477i −1.07780 + 0.587806i
\(872\) −4.05251 1.81719i −0.137235 0.0615377i
\(873\) 3.72471 + 3.72471i 0.126062 + 0.126062i
\(874\) −53.2625 22.6642i −1.80163 0.766627i
\(875\) 18.9109 3.06297i 0.639305 0.103547i
\(876\) 13.9890 + 14.5373i 0.472643 + 0.491171i
\(877\) −5.81287 + 5.81287i −0.196287 + 0.196287i −0.798406 0.602119i \(-0.794323\pi\)
0.602119 + 0.798406i \(0.294323\pi\)
\(878\) −3.59729 8.92631i −0.121403 0.301248i
\(879\) 2.60923i 0.0880071i
\(880\) −1.17843 0.296784i −0.0397248 0.0100046i
\(881\) −23.0235 −0.775681 −0.387840 0.921727i \(-0.626779\pi\)
−0.387840 + 0.921727i \(0.626779\pi\)
\(882\) −3.45298 8.56822i −0.116268 0.288507i
\(883\) −7.69986 7.69986i −0.259121 0.259121i 0.565576 0.824696i \(-0.308654\pi\)
−0.824696 + 0.565576i \(0.808654\pi\)
\(884\) 3.40178 10.7929i 0.114414 0.363003i
\(885\) −7.88406 12.1095i −0.265020 0.407056i
\(886\) 11.9378 28.0547i 0.401057 0.942514i
\(887\) 18.5646 18.5646i 0.623340 0.623340i −0.323044 0.946384i \(-0.604706\pi\)
0.946384 + 0.323044i \(0.104706\pi\)
\(888\) −27.5639 12.3599i −0.924984 0.414772i
\(889\) 36.7438 1.23235
\(890\) 10.0521 1.77538i 0.336948 0.0595107i
\(891\) −0.216642 −0.00725776
\(892\) 0.241994 12.5886i 0.00810256 0.421496i
\(893\) 49.8472 49.8472i 1.66807 1.66807i
\(894\) 1.56712 3.68285i 0.0524124 0.123173i
\(895\) −5.91191 + 27.9735i −0.197613 + 0.935052i
\(896\) −18.3684 + 6.19790i −0.613645 + 0.207057i
\(897\) 27.2934 + 8.02924i 0.911302 + 0.268088i
\(898\) 4.55715 + 11.3081i 0.152074 + 0.377357i
\(899\) 13.7198i 0.457582i
\(900\) −5.50587 15.1008i −0.183529 0.503361i
\(901\) 11.9809 0.399141
\(902\) −0.521294 + 0.210081i −0.0173572 + 0.00699492i
\(903\) −3.06472 + 3.06472i −0.101988 + 0.101988i
\(904\) −2.82278 + 1.07498i −0.0938841 + 0.0357534i
\(905\) 2.07348 9.81113i 0.0689247 0.326133i
\(906\) 3.68072 8.64997i 0.122284 0.287376i
\(907\) −24.7376 + 24.7376i −0.821398 + 0.821398i −0.986308 0.164911i \(-0.947266\pi\)
0.164911 + 0.986308i \(0.447266\pi\)
\(908\) 24.9365 + 0.479364i 0.827548 + 0.0159082i
\(909\) 4.23156i 0.140352i
\(910\) −15.2634 + 12.1947i −0.505978 + 0.404252i
\(911\) 54.7745i 1.81476i −0.420313 0.907379i \(-0.638080\pi\)
0.420313 0.907379i \(-0.361920\pi\)
\(912\) 19.6324 + 21.2030i 0.650094 + 0.702101i
\(913\) −0.626716 + 0.626716i −0.0207413 + 0.0207413i
\(914\) 29.1676 + 12.4113i 0.964778 + 0.410531i
\(915\) −26.0671 + 16.9714i −0.861752 + 0.561057i
\(916\) −42.2414 + 40.6480i −1.39569 + 1.34305i
\(917\) −0.284798 + 0.284798i −0.00940487 + 0.00940487i
\(918\) −4.51039 11.1921i −0.148865 0.369394i
\(919\) 33.2299 1.09615 0.548076 0.836428i \(-0.315360\pi\)
0.548076 + 0.836428i \(0.315360\pi\)
\(920\) 41.7770 6.55317i 1.37735 0.216052i
\(921\) 20.2320i 0.666665i
\(922\) 40.9496 16.5026i 1.34860 0.543486i
\(923\) 4.56938 15.5325i 0.150403 0.511259i
\(924\) 0.380997 + 0.395932i 0.0125339 + 0.0130252i
\(925\) −42.2073 + 16.3148i −1.38777 + 0.536427i
\(926\) 31.8136 + 13.5373i 1.04546 + 0.444862i
\(927\) −11.8378 + 11.8378i −0.388804 + 0.388804i
\(928\) 8.40214 + 23.4060i 0.275814 + 0.768340i
\(929\) 33.1243 1.08677 0.543386 0.839483i \(-0.317142\pi\)
0.543386 + 0.839483i \(0.317142\pi\)
\(930\) −9.54224 6.67756i −0.312903 0.218966i
\(931\) 24.8776 0.815331
\(932\) −0.968394 + 50.3759i −0.0317208 + 1.65012i
\(933\) −15.7735 + 15.7735i −0.516403 + 0.516403i
\(934\) −6.34655 2.70057i −0.207666 0.0883655i
\(935\) −0.399541 + 0.260127i −0.0130664 + 0.00850706i
\(936\) 12.4559 + 10.6552i 0.407135 + 0.348277i
\(937\) 23.6889 + 23.6889i 0.773882 + 0.773882i 0.978783 0.204901i \(-0.0656872\pi\)
−0.204901 + 0.978783i \(0.565687\pi\)
\(938\) 22.5857 9.10198i 0.737448 0.297190i
\(939\) 9.80606 0.320009
\(940\) −11.6154 + 50.1737i −0.378852 + 1.63649i
\(941\) 12.1245i 0.395247i −0.980278 0.197624i \(-0.936678\pi\)
0.980278 0.197624i \(-0.0633224\pi\)
\(942\) 7.93261 3.19683i 0.258458 0.104158i
\(943\) 13.8295 13.8295i 0.450349 0.450349i
\(944\) 21.8873 + 0.841807i 0.712372 + 0.0273985i
\(945\) −4.30756 + 20.3822i −0.140125 + 0.663032i
\(946\) 0.161254 0.378959i 0.00524282 0.0123210i
\(947\) 4.68453 + 4.68453i 0.152227 + 0.152227i 0.779112 0.626885i \(-0.215670\pi\)
−0.626885 + 0.779112i \(0.715670\pi\)
\(948\) −2.22807 0.0428309i −0.0723643 0.00139108i
\(949\) −27.0573 + 14.7565i −0.878318 + 0.479015i
\(950\) 43.2613 + 1.44810i 1.40358 + 0.0469825i
\(951\) 17.1295 0.555461
\(952\) −3.11184 + 6.93973i −0.100855 + 0.224918i
\(953\) −15.6053 + 15.6053i −0.505504 + 0.505504i −0.913143 0.407639i \(-0.866352\pi\)
0.407639 + 0.913143i \(0.366352\pi\)
\(954\) −6.79498 + 15.9687i −0.219995 + 0.517006i
\(955\) −50.8959 10.7563i −1.64695 0.348066i
\(956\) −21.1673 21.9971i −0.684599 0.711436i
\(957\) 0.498419 0.498419i 0.0161116 0.0161116i
\(958\) 40.4042 16.2828i 1.30540 0.526075i
\(959\) −29.7355 −0.960210
\(960\) −20.3684 5.54815i −0.657389 0.179066i
\(961\) −21.2602 −0.685811
\(962\) 29.3179 35.6369i 0.945248 1.14898i
\(963\) 19.1526 + 19.1526i 0.617183 + 0.617183i
\(964\) −17.5670 18.2557i −0.565796 0.587975i
\(965\) −2.37714 + 1.54767i −0.0765228 + 0.0498213i
\(966\) −17.5941 7.48663i −0.566082 0.240878i
\(967\) 7.06843 + 7.06843i 0.227305 + 0.227305i 0.811566 0.584261i \(-0.198615\pi\)
−0.584261 + 0.811566i \(0.698615\pi\)
\(968\) 28.3416 + 12.7086i 0.910933 + 0.408471i
\(969\) 11.3366 0.364185
\(970\) 5.94183 8.49089i 0.190781 0.272626i
\(971\) 16.4004i 0.526315i −0.964753 0.263158i \(-0.915236\pi\)
0.964753 0.263158i \(-0.0847639\pi\)
\(972\) 28.8543 + 0.554676i 0.925502 + 0.0177913i
\(973\) −23.7633 23.7633i −0.761817 0.761817i
\(974\) −16.8371 + 39.5684i −0.539495 + 1.26785i
\(975\) −21.2021 + 1.75823i −0.679009 + 0.0563086i
\(976\) 1.81209 47.1151i 0.0580035 1.50812i
\(977\) 9.44147 9.44147i 0.302059 0.302059i −0.539760 0.841819i \(-0.681485\pi\)
0.841819 + 0.539760i \(0.181485\pi\)
\(978\) 5.65327 + 14.0280i 0.180772 + 0.448566i
\(979\) 0.438572 0.0140168
\(980\) −15.4188 + 9.62179i −0.492534 + 0.307357i
\(981\) 2.52388i 0.0805811i
\(982\) 41.2340 16.6173i 1.31583 0.530278i
\(983\) 2.87573 2.87573i 0.0917216 0.0917216i −0.659757 0.751479i \(-0.729341\pi\)
0.751479 + 0.659757i \(0.229341\pi\)
\(984\) −9.12422 + 3.47473i −0.290870 + 0.110770i
\(985\) 11.1928 + 17.1915i 0.356632 + 0.547768i
\(986\) 8.97743 + 3.82006i 0.285900 + 0.121656i
\(987\) 16.4660 16.4660i 0.524118 0.524118i
\(988\) −39.1531 + 20.3868i −1.24562 + 0.648591i
\(989\) 14.3314i 0.455711i
\(990\) −0.120110 0.680059i −0.00381734 0.0216137i
\(991\) 12.4832i 0.396541i 0.980147 + 0.198271i \(0.0635325\pi\)
−0.980147 + 0.198271i \(0.936468\pi\)
\(992\) 16.6162 5.96476i 0.527564 0.189381i
\(993\) 13.6178 + 13.6178i 0.432147 + 0.432147i
\(994\) −4.26059 + 10.0127i −0.135138 + 0.317584i
\(995\) 3.05378 14.4496i 0.0968113 0.458085i
\(996\) −11.0944 + 10.6759i −0.351538 + 0.338278i
\(997\) 30.7425 + 30.7425i 0.973625 + 0.973625i 0.999661 0.0260359i \(-0.00828842\pi\)
−0.0260359 + 0.999661i \(0.508288\pi\)
\(998\) 40.4272 16.2921i 1.27970 0.515718i
\(999\) 49.2073i 1.55685i
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 260.2.p.d.207.20 yes 64
4.3 odd 2 inner 260.2.p.d.207.4 yes 64
5.3 odd 4 inner 260.2.p.d.103.29 yes 64
13.12 even 2 inner 260.2.p.d.207.13 yes 64
20.3 even 4 inner 260.2.p.d.103.13 yes 64
52.51 odd 2 inner 260.2.p.d.207.29 yes 64
65.38 odd 4 inner 260.2.p.d.103.4 64
260.103 even 4 inner 260.2.p.d.103.20 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.p.d.103.4 64 65.38 odd 4 inner
260.2.p.d.103.13 yes 64 20.3 even 4 inner
260.2.p.d.103.20 yes 64 260.103 even 4 inner
260.2.p.d.103.29 yes 64 5.3 odd 4 inner
260.2.p.d.207.4 yes 64 4.3 odd 2 inner
260.2.p.d.207.13 yes 64 13.12 even 2 inner
260.2.p.d.207.20 yes 64 1.1 even 1 trivial
260.2.p.d.207.29 yes 64 52.51 odd 2 inner