Properties

Label 162.3.d.a.107.2
Level $162$
Weight $3$
Character 162.107
Analytic conductor $4.414$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,3,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.2
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.3.d.a.53.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-7.34847 + 4.24264i) q^{5} +(-2.50000 + 4.33013i) q^{7} +2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-7.34847 + 4.24264i) q^{5} +(-2.50000 + 4.33013i) q^{7} +2.82843i q^{8} -12.0000 q^{10} +(-7.34847 - 4.24264i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-6.12372 + 3.53553i) q^{14} +(-2.00000 + 3.46410i) q^{16} +25.4558i q^{17} +29.0000 q^{19} +(-14.6969 - 8.48528i) q^{20} +(-6.00000 - 10.3923i) q^{22} +(-7.34847 + 4.24264i) q^{23} +(23.5000 - 40.7032i) q^{25} +1.41421i q^{26} -10.0000 q^{28} +(14.6969 + 8.48528i) q^{29} +(5.00000 + 8.66025i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-18.0000 + 31.1769i) q^{34} -42.4264i q^{35} -25.0000 q^{37} +(35.5176 + 20.5061i) q^{38} +(-12.0000 - 20.7846i) q^{40} +(14.6969 - 8.48528i) q^{41} +(-7.00000 + 12.1244i) q^{43} -16.9706i q^{44} -12.0000 q^{46} +(-7.34847 - 4.24264i) q^{47} +(12.0000 + 20.7846i) q^{49} +(57.5630 - 33.2340i) q^{50} +(-1.00000 + 1.73205i) q^{52} -50.9117i q^{53} +72.0000 q^{55} +(-12.2474 - 7.07107i) q^{56} +(12.0000 + 20.7846i) q^{58} +(80.8332 - 46.6690i) q^{59} +(-11.5000 + 19.9186i) q^{61} +14.1421i q^{62} -8.00000 q^{64} +(-7.34847 - 4.24264i) q^{65} +(9.50000 + 16.4545i) q^{67} +(-44.0908 + 25.4558i) q^{68} +(30.0000 - 51.9615i) q^{70} +101.823i q^{71} -97.0000 q^{73} +(-30.6186 - 17.6777i) q^{74} +(29.0000 + 50.2295i) q^{76} +(36.7423 - 21.2132i) q^{77} +(-38.5000 + 66.6840i) q^{79} -33.9411i q^{80} +24.0000 q^{82} +(102.879 + 59.3970i) q^{83} +(-108.000 - 187.061i) q^{85} +(-17.1464 + 9.89949i) q^{86} +(12.0000 - 20.7846i) q^{88} -76.3675i q^{89} -5.00000 q^{91} +(-14.6969 - 8.48528i) q^{92} +(-6.00000 - 10.3923i) q^{94} +(-213.106 + 123.037i) q^{95} +(24.5000 - 42.4352i) q^{97} +33.9411i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} - 10 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} - 10 q^{7} - 48 q^{10} + 2 q^{13} - 8 q^{16} + 116 q^{19} - 24 q^{22} + 94 q^{25} - 40 q^{28} + 20 q^{31} - 72 q^{34} - 100 q^{37} - 48 q^{40} - 28 q^{43} - 48 q^{46} + 48 q^{49} - 4 q^{52} + 288 q^{55} + 48 q^{58} - 46 q^{61} - 32 q^{64} + 38 q^{67} + 120 q^{70} - 388 q^{73} + 116 q^{76} - 154 q^{79} + 96 q^{82} - 432 q^{85} + 48 q^{88} - 20 q^{91} - 24 q^{94} + 98 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) −7.34847 + 4.24264i −1.46969 + 0.848528i −0.999422 0.0339935i \(-0.989177\pi\)
−0.470272 + 0.882522i \(0.655844\pi\)
\(6\) 0 0
\(7\) −2.50000 + 4.33013i −0.357143 + 0.618590i −0.987482 0.157730i \(-0.949582\pi\)
0.630339 + 0.776320i \(0.282916\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −12.0000 −1.20000
\(11\) −7.34847 4.24264i −0.668043 0.385695i 0.127292 0.991865i \(-0.459371\pi\)
−0.795335 + 0.606171i \(0.792705\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.0384615 + 0.0666173i 0.884615 0.466321i \(-0.154421\pi\)
−0.846154 + 0.532939i \(0.821088\pi\)
\(14\) −6.12372 + 3.53553i −0.437409 + 0.252538i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 25.4558i 1.49740i 0.662908 + 0.748701i \(0.269322\pi\)
−0.662908 + 0.748701i \(0.730678\pi\)
\(18\) 0 0
\(19\) 29.0000 1.52632 0.763158 0.646212i \(-0.223648\pi\)
0.763158 + 0.646212i \(0.223648\pi\)
\(20\) −14.6969 8.48528i −0.734847 0.424264i
\(21\) 0 0
\(22\) −6.00000 10.3923i −0.272727 0.472377i
\(23\) −7.34847 + 4.24264i −0.319499 + 0.184463i −0.651169 0.758933i \(-0.725721\pi\)
0.331670 + 0.943395i \(0.392388\pi\)
\(24\) 0 0
\(25\) 23.5000 40.7032i 0.940000 1.62813i
\(26\) 1.41421i 0.0543928i
\(27\) 0 0
\(28\) −10.0000 −0.357143
\(29\) 14.6969 + 8.48528i 0.506791 + 0.292596i 0.731514 0.681827i \(-0.238814\pi\)
−0.224723 + 0.974423i \(0.572148\pi\)
\(30\) 0 0
\(31\) 5.00000 + 8.66025i 0.161290 + 0.279363i 0.935332 0.353772i \(-0.115101\pi\)
−0.774041 + 0.633135i \(0.781768\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −18.0000 + 31.1769i −0.529412 + 0.916968i
\(35\) 42.4264i 1.21218i
\(36\) 0 0
\(37\) −25.0000 −0.675676 −0.337838 0.941204i \(-0.609696\pi\)
−0.337838 + 0.941204i \(0.609696\pi\)
\(38\) 35.5176 + 20.5061i 0.934674 + 0.539634i
\(39\) 0 0
\(40\) −12.0000 20.7846i −0.300000 0.519615i
\(41\) 14.6969 8.48528i 0.358462 0.206958i −0.309944 0.950755i \(-0.600310\pi\)
0.668406 + 0.743797i \(0.266977\pi\)
\(42\) 0 0
\(43\) −7.00000 + 12.1244i −0.162791 + 0.281962i −0.935869 0.352349i \(-0.885383\pi\)
0.773078 + 0.634311i \(0.218716\pi\)
\(44\) 16.9706i 0.385695i
\(45\) 0 0
\(46\) −12.0000 −0.260870
\(47\) −7.34847 4.24264i −0.156350 0.0902690i 0.419784 0.907624i \(-0.362106\pi\)
−0.576134 + 0.817355i \(0.695439\pi\)
\(48\) 0 0
\(49\) 12.0000 + 20.7846i 0.244898 + 0.424176i
\(50\) 57.5630 33.2340i 1.15126 0.664680i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.0192308 + 0.0333087i
\(53\) 50.9117i 0.960598i −0.877105 0.480299i \(-0.840528\pi\)
0.877105 0.480299i \(-0.159472\pi\)
\(54\) 0 0
\(55\) 72.0000 1.30909
\(56\) −12.2474 7.07107i −0.218704 0.126269i
\(57\) 0 0
\(58\) 12.0000 + 20.7846i 0.206897 + 0.358355i
\(59\) 80.8332 46.6690i 1.37005 0.791001i 0.379119 0.925348i \(-0.376227\pi\)
0.990934 + 0.134347i \(0.0428937\pi\)
\(60\) 0 0
\(61\) −11.5000 + 19.9186i −0.188525 + 0.326534i −0.944759 0.327767i \(-0.893704\pi\)
0.756234 + 0.654301i \(0.227037\pi\)
\(62\) 14.1421i 0.228099i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) −7.34847 4.24264i −0.113053 0.0652714i
\(66\) 0 0
\(67\) 9.50000 + 16.4545i 0.141791 + 0.245589i 0.928171 0.372154i \(-0.121381\pi\)
−0.786380 + 0.617743i \(0.788047\pi\)
\(68\) −44.0908 + 25.4558i −0.648394 + 0.374351i
\(69\) 0 0
\(70\) 30.0000 51.9615i 0.428571 0.742307i
\(71\) 101.823i 1.43413i 0.697005 + 0.717066i \(0.254515\pi\)
−0.697005 + 0.717066i \(0.745485\pi\)
\(72\) 0 0
\(73\) −97.0000 −1.32877 −0.664384 0.747392i \(-0.731306\pi\)
−0.664384 + 0.747392i \(0.731306\pi\)
\(74\) −30.6186 17.6777i −0.413765 0.238887i
\(75\) 0 0
\(76\) 29.0000 + 50.2295i 0.381579 + 0.660914i
\(77\) 36.7423 21.2132i 0.477173 0.275496i
\(78\) 0 0
\(79\) −38.5000 + 66.6840i −0.487342 + 0.844101i −0.999894 0.0145553i \(-0.995367\pi\)
0.512552 + 0.858656i \(0.328700\pi\)
\(80\) 33.9411i 0.424264i
\(81\) 0 0
\(82\) 24.0000 0.292683
\(83\) 102.879 + 59.3970i 1.23950 + 0.715626i 0.968992 0.247091i \(-0.0794748\pi\)
0.270509 + 0.962718i \(0.412808\pi\)
\(84\) 0 0
\(85\) −108.000 187.061i −1.27059 2.20072i
\(86\) −17.1464 + 9.89949i −0.199377 + 0.115110i
\(87\) 0 0
\(88\) 12.0000 20.7846i 0.136364 0.236189i
\(89\) 76.3675i 0.858062i −0.903290 0.429031i \(-0.858855\pi\)
0.903290 0.429031i \(-0.141145\pi\)
\(90\) 0 0
\(91\) −5.00000 −0.0549451
\(92\) −14.6969 8.48528i −0.159749 0.0922313i
\(93\) 0 0
\(94\) −6.00000 10.3923i −0.0638298 0.110556i
\(95\) −213.106 + 123.037i −2.24322 + 1.29512i
\(96\) 0 0
\(97\) 24.5000 42.4352i 0.252577 0.437477i −0.711657 0.702527i \(-0.752055\pi\)
0.964235 + 0.265050i \(0.0853885\pi\)
\(98\) 33.9411i 0.346338i
\(99\) 0 0
\(100\) 94.0000 0.940000
\(101\) −117.576 67.8823i −1.16411 0.672101i −0.211827 0.977307i \(-0.567941\pi\)
−0.952286 + 0.305206i \(0.901275\pi\)
\(102\) 0 0
\(103\) 81.5000 + 141.162i 0.791262 + 1.37051i 0.925186 + 0.379515i \(0.123909\pi\)
−0.133924 + 0.990992i \(0.542758\pi\)
\(104\) −2.44949 + 1.41421i −0.0235528 + 0.0135982i
\(105\) 0 0
\(106\) 36.0000 62.3538i 0.339623 0.588244i
\(107\) 25.4558i 0.237905i 0.992900 + 0.118953i \(0.0379536\pi\)
−0.992900 + 0.118953i \(0.962046\pi\)
\(108\) 0 0
\(109\) 2.00000 0.0183486 0.00917431 0.999958i \(-0.497080\pi\)
0.00917431 + 0.999958i \(0.497080\pi\)
\(110\) 88.1816 + 50.9117i 0.801651 + 0.462834i
\(111\) 0 0
\(112\) −10.0000 17.3205i −0.0892857 0.154647i
\(113\) −95.5301 + 55.1543i −0.845399 + 0.488091i −0.859096 0.511815i \(-0.828973\pi\)
0.0136967 + 0.999906i \(0.495640\pi\)
\(114\) 0 0
\(115\) 36.0000 62.3538i 0.313043 0.542207i
\(116\) 33.9411i 0.292596i
\(117\) 0 0
\(118\) 132.000 1.11864
\(119\) −110.227 63.6396i −0.926278 0.534787i
\(120\) 0 0
\(121\) −24.5000 42.4352i −0.202479 0.350705i
\(122\) −28.1691 + 16.2635i −0.230895 + 0.133307i
\(123\) 0 0
\(124\) −10.0000 + 17.3205i −0.0806452 + 0.139682i
\(125\) 186.676i 1.49341i
\(126\) 0 0
\(127\) −178.000 −1.40157 −0.700787 0.713370i \(-0.747168\pi\)
−0.700787 + 0.713370i \(0.747168\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −6.00000 10.3923i −0.0461538 0.0799408i
\(131\) 102.879 59.3970i 0.785333 0.453412i −0.0529842 0.998595i \(-0.516873\pi\)
0.838317 + 0.545183i \(0.183540\pi\)
\(132\) 0 0
\(133\) −72.5000 + 125.574i −0.545113 + 0.944163i
\(134\) 26.8701i 0.200523i
\(135\) 0 0
\(136\) −72.0000 −0.529412
\(137\) 80.8332 + 46.6690i 0.590023 + 0.340650i 0.765107 0.643904i \(-0.222686\pi\)
−0.175084 + 0.984554i \(0.556020\pi\)
\(138\) 0 0
\(139\) 81.5000 + 141.162i 0.586331 + 1.01555i 0.994708 + 0.102742i \(0.0327615\pi\)
−0.408377 + 0.912813i \(0.633905\pi\)
\(140\) 73.4847 42.4264i 0.524891 0.303046i
\(141\) 0 0
\(142\) −72.0000 + 124.708i −0.507042 + 0.878223i
\(143\) 8.48528i 0.0593376i
\(144\) 0 0
\(145\) −144.000 −0.993103
\(146\) −118.800 68.5894i −0.813700 0.469790i
\(147\) 0 0
\(148\) −25.0000 43.3013i −0.168919 0.292576i
\(149\) −29.3939 + 16.9706i −0.197274 + 0.113896i −0.595383 0.803442i \(-0.703000\pi\)
0.398109 + 0.917338i \(0.369667\pi\)
\(150\) 0 0
\(151\) −74.5000 + 129.038i −0.493377 + 0.854555i −0.999971 0.00763022i \(-0.997571\pi\)
0.506593 + 0.862185i \(0.330905\pi\)
\(152\) 82.0244i 0.539634i
\(153\) 0 0
\(154\) 60.0000 0.389610
\(155\) −73.4847 42.4264i −0.474095 0.273719i
\(156\) 0 0
\(157\) −121.000 209.578i −0.770701 1.33489i −0.937179 0.348848i \(-0.886573\pi\)
0.166479 0.986045i \(-0.446760\pi\)
\(158\) −94.3054 + 54.4472i −0.596869 + 0.344603i
\(159\) 0 0
\(160\) 24.0000 41.5692i 0.150000 0.259808i
\(161\) 42.4264i 0.263518i
\(162\) 0 0
\(163\) 173.000 1.06135 0.530675 0.847575i \(-0.321939\pi\)
0.530675 + 0.847575i \(0.321939\pi\)
\(164\) 29.3939 + 16.9706i 0.179231 + 0.103479i
\(165\) 0 0
\(166\) 84.0000 + 145.492i 0.506024 + 0.876459i
\(167\) 169.015 97.5807i 1.01206 0.584316i 0.100269 0.994960i \(-0.468030\pi\)
0.911796 + 0.410645i \(0.134696\pi\)
\(168\) 0 0
\(169\) 84.0000 145.492i 0.497041 0.860901i
\(170\) 305.470i 1.79688i
\(171\) 0 0
\(172\) −28.0000 −0.162791
\(173\) 279.242 + 161.220i 1.61411 + 0.931910i 0.988403 + 0.151855i \(0.0485248\pi\)
0.625712 + 0.780054i \(0.284809\pi\)
\(174\) 0 0
\(175\) 117.500 + 203.516i 0.671429 + 1.16295i
\(176\) 29.3939 16.9706i 0.167011 0.0964237i
\(177\) 0 0
\(178\) 54.0000 93.5307i 0.303371 0.525454i
\(179\) 305.470i 1.70654i −0.521472 0.853269i \(-0.674617\pi\)
0.521472 0.853269i \(-0.325383\pi\)
\(180\) 0 0
\(181\) 263.000 1.45304 0.726519 0.687146i \(-0.241137\pi\)
0.726519 + 0.687146i \(0.241137\pi\)
\(182\) −6.12372 3.53553i −0.0336468 0.0194260i
\(183\) 0 0
\(184\) −12.0000 20.7846i −0.0652174 0.112960i
\(185\) 183.712 106.066i 0.993036 0.573330i
\(186\) 0 0
\(187\) 108.000 187.061i 0.577540 1.00033i
\(188\) 16.9706i 0.0902690i
\(189\) 0 0
\(190\) −348.000 −1.83158
\(191\) 124.924 + 72.1249i 0.654052 + 0.377617i 0.790007 0.613098i \(-0.210077\pi\)
−0.135955 + 0.990715i \(0.543410\pi\)
\(192\) 0 0
\(193\) −35.5000 61.4878i −0.183938 0.318590i 0.759280 0.650764i \(-0.225551\pi\)
−0.943218 + 0.332174i \(0.892218\pi\)
\(194\) 60.0125 34.6482i 0.309343 0.178599i
\(195\) 0 0
\(196\) −24.0000 + 41.5692i −0.122449 + 0.212088i
\(197\) 76.3675i 0.387652i −0.981036 0.193826i \(-0.937910\pi\)
0.981036 0.193826i \(-0.0620898\pi\)
\(198\) 0 0
\(199\) 173.000 0.869347 0.434673 0.900588i \(-0.356864\pi\)
0.434673 + 0.900588i \(0.356864\pi\)
\(200\) 115.126 + 66.4680i 0.575630 + 0.332340i
\(201\) 0 0
\(202\) −96.0000 166.277i −0.475248 0.823153i
\(203\) −73.4847 + 42.4264i −0.361994 + 0.208997i
\(204\) 0 0
\(205\) −72.0000 + 124.708i −0.351220 + 0.608330i
\(206\) 230.517i 1.11901i
\(207\) 0 0
\(208\) −4.00000 −0.0192308
\(209\) −213.106 123.037i −1.01964 0.588692i
\(210\) 0 0
\(211\) −170.500 295.315i −0.808057 1.39960i −0.914208 0.405246i \(-0.867186\pi\)
0.106151 0.994350i \(-0.466147\pi\)
\(212\) 88.1816 50.9117i 0.415951 0.240149i
\(213\) 0 0
\(214\) −18.0000 + 31.1769i −0.0841121 + 0.145687i
\(215\) 118.794i 0.552530i
\(216\) 0 0
\(217\) −50.0000 −0.230415
\(218\) 2.44949 + 1.41421i 0.0112362 + 0.00648722i
\(219\) 0 0
\(220\) 72.0000 + 124.708i 0.327273 + 0.566853i
\(221\) −22.0454 + 12.7279i −0.0997530 + 0.0575924i
\(222\) 0 0
\(223\) 29.0000 50.2295i 0.130045 0.225244i −0.793649 0.608376i \(-0.791821\pi\)
0.923694 + 0.383132i \(0.125155\pi\)
\(224\) 28.2843i 0.126269i
\(225\) 0 0
\(226\) −156.000 −0.690265
\(227\) −117.576 67.8823i −0.517954 0.299041i 0.218143 0.975917i \(-0.430000\pi\)
−0.736097 + 0.676876i \(0.763333\pi\)
\(228\) 0 0
\(229\) 131.000 + 226.899i 0.572052 + 0.990824i 0.996355 + 0.0853034i \(0.0271859\pi\)
−0.424303 + 0.905520i \(0.639481\pi\)
\(230\) 88.1816 50.9117i 0.383398 0.221355i
\(231\) 0 0
\(232\) −24.0000 + 41.5692i −0.103448 + 0.179178i
\(233\) 305.470i 1.31103i 0.755182 + 0.655515i \(0.227549\pi\)
−0.755182 + 0.655515i \(0.772451\pi\)
\(234\) 0 0
\(235\) 72.0000 0.306383
\(236\) 161.666 + 93.3381i 0.685027 + 0.395500i
\(237\) 0 0
\(238\) −90.0000 155.885i −0.378151 0.654977i
\(239\) 146.969 84.8528i 0.614935 0.355033i −0.159960 0.987124i \(-0.551136\pi\)
0.774894 + 0.632091i \(0.217803\pi\)
\(240\) 0 0
\(241\) 60.5000 104.789i 0.251037 0.434809i −0.712774 0.701393i \(-0.752562\pi\)
0.963812 + 0.266584i \(0.0858950\pi\)
\(242\) 69.2965i 0.286349i
\(243\) 0 0
\(244\) −46.0000 −0.188525
\(245\) −176.363 101.823i −0.719850 0.415606i
\(246\) 0 0
\(247\) 14.5000 + 25.1147i 0.0587045 + 0.101679i
\(248\) −24.4949 + 14.1421i −0.0987697 + 0.0570247i
\(249\) 0 0
\(250\) −132.000 + 228.631i −0.528000 + 0.914523i
\(251\) 356.382i 1.41985i 0.704278 + 0.709924i \(0.251271\pi\)
−0.704278 + 0.709924i \(0.748729\pi\)
\(252\) 0 0
\(253\) 72.0000 0.284585
\(254\) −218.005 125.865i −0.858286 0.495532i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −73.4847 + 42.4264i −0.285933 + 0.165083i −0.636106 0.771602i \(-0.719456\pi\)
0.350173 + 0.936685i \(0.386123\pi\)
\(258\) 0 0
\(259\) 62.5000 108.253i 0.241313 0.417966i
\(260\) 16.9706i 0.0652714i
\(261\) 0 0
\(262\) 168.000 0.641221
\(263\) 146.969 + 84.8528i 0.558819 + 0.322634i 0.752671 0.658396i \(-0.228765\pi\)
−0.193852 + 0.981031i \(0.562098\pi\)
\(264\) 0 0
\(265\) 216.000 + 374.123i 0.815094 + 1.41178i
\(266\) −177.588 + 102.530i −0.667624 + 0.385453i
\(267\) 0 0
\(268\) −19.0000 + 32.9090i −0.0708955 + 0.122795i
\(269\) 280.014i 1.04095i −0.853878 0.520473i \(-0.825756\pi\)
0.853878 0.520473i \(-0.174244\pi\)
\(270\) 0 0
\(271\) 29.0000 0.107011 0.0535055 0.998568i \(-0.482961\pi\)
0.0535055 + 0.998568i \(0.482961\pi\)
\(272\) −88.1816 50.9117i −0.324197 0.187175i
\(273\) 0 0
\(274\) 66.0000 + 114.315i 0.240876 + 0.417209i
\(275\) −345.378 + 199.404i −1.25592 + 0.725106i
\(276\) 0 0
\(277\) 191.000 330.822i 0.689531 1.19430i −0.282459 0.959279i \(-0.591150\pi\)
0.971990 0.235023i \(-0.0755165\pi\)
\(278\) 230.517i 0.829197i
\(279\) 0 0
\(280\) 120.000 0.428571
\(281\) 191.060 + 110.309i 0.679930 + 0.392558i 0.799829 0.600229i \(-0.204924\pi\)
−0.119899 + 0.992786i \(0.538257\pi\)
\(282\) 0 0
\(283\) −31.0000 53.6936i −0.109541 0.189730i 0.806044 0.591856i \(-0.201605\pi\)
−0.915584 + 0.402126i \(0.868271\pi\)
\(284\) −176.363 + 101.823i −0.620997 + 0.358533i
\(285\) 0 0
\(286\) 6.00000 10.3923i 0.0209790 0.0363367i
\(287\) 84.8528i 0.295654i
\(288\) 0 0
\(289\) −359.000 −1.24221
\(290\) −176.363 101.823i −0.608149 0.351115i
\(291\) 0 0
\(292\) −97.0000 168.009i −0.332192 0.575373i
\(293\) −271.893 + 156.978i −0.927964 + 0.535760i −0.886167 0.463366i \(-0.846642\pi\)
−0.0417967 + 0.999126i \(0.513308\pi\)
\(294\) 0 0
\(295\) −396.000 + 685.892i −1.34237 + 2.32506i
\(296\) 70.7107i 0.238887i
\(297\) 0 0
\(298\) −48.0000 −0.161074
\(299\) −7.34847 4.24264i −0.0245768 0.0141894i
\(300\) 0 0
\(301\) −35.0000 60.6218i −0.116279 0.201401i
\(302\) −182.487 + 105.359i −0.604262 + 0.348871i
\(303\) 0 0
\(304\) −58.0000 + 100.459i −0.190789 + 0.330457i
\(305\) 195.161i 0.639874i
\(306\) 0 0
\(307\) −34.0000 −0.110749 −0.0553746 0.998466i \(-0.517635\pi\)
−0.0553746 + 0.998466i \(0.517635\pi\)
\(308\) 73.4847 + 42.4264i 0.238587 + 0.137748i
\(309\) 0 0
\(310\) −60.0000 103.923i −0.193548 0.335236i
\(311\) −51.4393 + 29.6985i −0.165400 + 0.0954935i −0.580415 0.814321i \(-0.697110\pi\)
0.415015 + 0.909814i \(0.363776\pi\)
\(312\) 0 0
\(313\) −119.500 + 206.980i −0.381789 + 0.661278i −0.991318 0.131486i \(-0.958025\pi\)
0.609529 + 0.792764i \(0.291359\pi\)
\(314\) 342.240i 1.08994i
\(315\) 0 0
\(316\) −154.000 −0.487342
\(317\) 14.6969 + 8.48528i 0.0463626 + 0.0267674i 0.523002 0.852331i \(-0.324812\pi\)
−0.476640 + 0.879099i \(0.658145\pi\)
\(318\) 0 0
\(319\) −72.0000 124.708i −0.225705 0.390933i
\(320\) 58.7878 33.9411i 0.183712 0.106066i
\(321\) 0 0
\(322\) 30.0000 51.9615i 0.0931677 0.161371i
\(323\) 738.219i 2.28551i
\(324\) 0 0
\(325\) 47.0000 0.144615
\(326\) 211.881 + 122.329i 0.649941 + 0.375244i
\(327\) 0 0
\(328\) 24.0000 + 41.5692i 0.0731707 + 0.126735i
\(329\) 36.7423 21.2132i 0.111679 0.0644778i
\(330\) 0 0
\(331\) 249.500 432.147i 0.753776 1.30558i −0.192204 0.981355i \(-0.561563\pi\)
0.945980 0.324224i \(-0.105103\pi\)
\(332\) 237.588i 0.715626i
\(333\) 0 0
\(334\) 276.000 0.826347
\(335\) −139.621 80.6102i −0.416779 0.240627i
\(336\) 0 0
\(337\) 72.5000 + 125.574i 0.215134 + 0.372622i 0.953314 0.301981i \(-0.0976480\pi\)
−0.738180 + 0.674603i \(0.764315\pi\)
\(338\) 205.757 118.794i 0.608749 0.351461i
\(339\) 0 0
\(340\) 216.000 374.123i 0.635294 1.10036i
\(341\) 84.8528i 0.248835i
\(342\) 0 0
\(343\) −365.000 −1.06414
\(344\) −34.2929 19.7990i −0.0996885 0.0575552i
\(345\) 0 0
\(346\) 228.000 + 394.908i 0.658960 + 1.14135i
\(347\) −382.120 + 220.617i −1.10121 + 0.635785i −0.936539 0.350564i \(-0.885990\pi\)
−0.164673 + 0.986348i \(0.552657\pi\)
\(348\) 0 0
\(349\) 60.5000 104.789i 0.173352 0.300255i −0.766237 0.642558i \(-0.777873\pi\)
0.939590 + 0.342302i \(0.111207\pi\)
\(350\) 332.340i 0.949543i
\(351\) 0 0
\(352\) 48.0000 0.136364
\(353\) −382.120 220.617i −1.08249 0.624978i −0.150926 0.988545i \(-0.548225\pi\)
−0.931568 + 0.363567i \(0.881559\pi\)
\(354\) 0 0
\(355\) −432.000 748.246i −1.21690 2.10774i
\(356\) 132.272 76.3675i 0.371552 0.214516i
\(357\) 0 0
\(358\) 216.000 374.123i 0.603352 1.04504i
\(359\) 432.749i 1.20543i −0.797957 0.602715i \(-0.794086\pi\)
0.797957 0.602715i \(-0.205914\pi\)
\(360\) 0 0
\(361\) 480.000 1.32964
\(362\) 322.108 + 185.969i 0.889801 + 0.513727i
\(363\) 0 0
\(364\) −5.00000 8.66025i −0.0137363 0.0237919i
\(365\) 712.802 411.536i 1.95288 1.12750i
\(366\) 0 0
\(367\) −74.5000 + 129.038i −0.202997 + 0.351602i −0.949493 0.313789i \(-0.898402\pi\)
0.746496 + 0.665390i \(0.231735\pi\)
\(368\) 33.9411i 0.0922313i
\(369\) 0 0
\(370\) 300.000 0.810811
\(371\) 220.454 + 127.279i 0.594216 + 0.343071i
\(372\) 0 0
\(373\) 180.500 + 312.635i 0.483914 + 0.838164i 0.999829 0.0184757i \(-0.00588134\pi\)
−0.515915 + 0.856640i \(0.672548\pi\)
\(374\) 264.545 152.735i 0.707339 0.408383i
\(375\) 0 0
\(376\) 12.0000 20.7846i 0.0319149 0.0552782i
\(377\) 16.9706i 0.0450148i
\(378\) 0 0
\(379\) 173.000 0.456464 0.228232 0.973607i \(-0.426705\pi\)
0.228232 + 0.973607i \(0.426705\pi\)
\(380\) −426.211 246.073i −1.12161 0.647561i
\(381\) 0 0
\(382\) 102.000 + 176.669i 0.267016 + 0.462485i
\(383\) 587.878 339.411i 1.53493 0.886191i 0.535804 0.844342i \(-0.320008\pi\)
0.999124 0.0418491i \(-0.0133249\pi\)
\(384\) 0 0
\(385\) −180.000 + 311.769i −0.467532 + 0.809790i
\(386\) 100.409i 0.260127i
\(387\) 0 0
\(388\) 98.0000 0.252577
\(389\) −360.075 207.889i −0.925643 0.534420i −0.0402118 0.999191i \(-0.512803\pi\)
−0.885431 + 0.464771i \(0.846137\pi\)
\(390\) 0 0
\(391\) −108.000 187.061i −0.276215 0.478418i
\(392\) −58.7878 + 33.9411i −0.149969 + 0.0865845i
\(393\) 0 0
\(394\) 54.0000 93.5307i 0.137056 0.237388i
\(395\) 653.367i 1.65409i
\(396\) 0 0
\(397\) −286.000 −0.720403 −0.360202 0.932875i \(-0.617292\pi\)
−0.360202 + 0.932875i \(0.617292\pi\)
\(398\) 211.881 + 122.329i 0.532364 + 0.307360i
\(399\) 0 0
\(400\) 94.0000 + 162.813i 0.235000 + 0.407032i
\(401\) −293.939 + 169.706i −0.733014 + 0.423206i −0.819524 0.573045i \(-0.805762\pi\)
0.0865095 + 0.996251i \(0.472429\pi\)
\(402\) 0 0
\(403\) −5.00000 + 8.66025i −0.0124069 + 0.0214895i
\(404\) 271.529i 0.672101i
\(405\) 0 0
\(406\) −120.000 −0.295567
\(407\) 183.712 + 106.066i 0.451380 + 0.260604i
\(408\) 0 0
\(409\) −107.500 186.195i −0.262836 0.455246i 0.704158 0.710043i \(-0.251325\pi\)
−0.966994 + 0.254797i \(0.917991\pi\)
\(410\) −176.363 + 101.823i −0.430154 + 0.248350i
\(411\) 0 0
\(412\) −163.000 + 282.324i −0.395631 + 0.685253i
\(413\) 466.690i 1.13000i
\(414\) 0 0
\(415\) −1008.00 −2.42892
\(416\) −4.89898 2.82843i −0.0117764 0.00679910i
\(417\) 0 0
\(418\) −174.000 301.377i −0.416268 0.720997i
\(419\) 521.741 301.227i 1.24521 0.718920i 0.275057 0.961428i \(-0.411303\pi\)
0.970149 + 0.242508i \(0.0779701\pi\)
\(420\) 0 0
\(421\) −227.500 + 394.042i −0.540380 + 0.935966i 0.458502 + 0.888693i \(0.348386\pi\)
−0.998882 + 0.0472723i \(0.984947\pi\)
\(422\) 482.247i 1.14276i
\(423\) 0 0
\(424\) 144.000 0.339623
\(425\) 1036.13 + 598.212i 2.43796 + 1.40756i
\(426\) 0 0
\(427\) −57.5000 99.5929i −0.134660 0.233239i
\(428\) −44.0908 + 25.4558i −0.103016 + 0.0594763i
\(429\) 0 0
\(430\) 84.0000 145.492i 0.195349 0.338354i
\(431\) 330.926i 0.767810i −0.923373 0.383905i \(-0.874579\pi\)
0.923373 0.383905i \(-0.125421\pi\)
\(432\) 0 0
\(433\) 218.000 0.503464 0.251732 0.967797i \(-0.419000\pi\)
0.251732 + 0.967797i \(0.419000\pi\)
\(434\) −61.2372 35.3553i −0.141100 0.0814639i
\(435\) 0 0
\(436\) 2.00000 + 3.46410i 0.00458716 + 0.00794519i
\(437\) −213.106 + 123.037i −0.487656 + 0.281548i
\(438\) 0 0
\(439\) −187.000 + 323.894i −0.425968 + 0.737798i −0.996510 0.0834699i \(-0.973400\pi\)
0.570542 + 0.821268i \(0.306733\pi\)
\(440\) 203.647i 0.462834i
\(441\) 0 0
\(442\) −36.0000 −0.0814480
\(443\) 14.6969 + 8.48528i 0.0331759 + 0.0191541i 0.516496 0.856289i \(-0.327236\pi\)
−0.483320 + 0.875444i \(0.660569\pi\)
\(444\) 0 0
\(445\) 324.000 + 561.184i 0.728090 + 1.26109i
\(446\) 71.0352 41.0122i 0.159272 0.0919556i
\(447\) 0 0
\(448\) 20.0000 34.6410i 0.0446429 0.0773237i
\(449\) 483.661i 1.07720i −0.842563 0.538598i \(-0.818954\pi\)
0.842563 0.538598i \(-0.181046\pi\)
\(450\) 0 0
\(451\) −144.000 −0.319290
\(452\) −191.060 110.309i −0.422700 0.244046i
\(453\) 0 0
\(454\) −96.0000 166.277i −0.211454 0.366249i
\(455\) 36.7423 21.2132i 0.0807524 0.0466224i
\(456\) 0 0
\(457\) 11.0000 19.0526i 0.0240700 0.0416905i −0.853739 0.520700i \(-0.825671\pi\)
0.877810 + 0.479010i \(0.159004\pi\)
\(458\) 370.524i 0.809004i
\(459\) 0 0
\(460\) 144.000 0.313043
\(461\) 345.378 + 199.404i 0.749193 + 0.432547i 0.825402 0.564545i \(-0.190948\pi\)
−0.0762091 + 0.997092i \(0.524282\pi\)
\(462\) 0 0
\(463\) 441.500 + 764.700i 0.953564 + 1.65162i 0.737621 + 0.675215i \(0.235949\pi\)
0.215942 + 0.976406i \(0.430718\pi\)
\(464\) −58.7878 + 33.9411i −0.126698 + 0.0731490i
\(465\) 0 0
\(466\) −216.000 + 374.123i −0.463519 + 0.802839i
\(467\) 127.279i 0.272547i 0.990671 + 0.136273i \(0.0435125\pi\)
−0.990671 + 0.136273i \(0.956487\pi\)
\(468\) 0 0
\(469\) −95.0000 −0.202559
\(470\) 88.1816 + 50.9117i 0.187620 + 0.108323i
\(471\) 0 0
\(472\) 132.000 + 228.631i 0.279661 + 0.484387i
\(473\) 102.879 59.3970i 0.217502 0.125575i
\(474\) 0 0
\(475\) 681.500 1180.39i 1.43474 2.48504i
\(476\) 254.558i 0.534787i
\(477\) 0 0
\(478\) 240.000 0.502092
\(479\) −338.030 195.161i −0.705699 0.407435i 0.103768 0.994602i \(-0.466910\pi\)
−0.809466 + 0.587166i \(0.800243\pi\)
\(480\) 0 0
\(481\) −12.5000 21.6506i −0.0259875 0.0450117i
\(482\) 148.194 85.5599i 0.307457 0.177510i
\(483\) 0 0
\(484\) 49.0000 84.8705i 0.101240 0.175352i
\(485\) 415.779i 0.857276i
\(486\) 0 0
\(487\) 317.000 0.650924 0.325462 0.945555i \(-0.394480\pi\)
0.325462 + 0.945555i \(0.394480\pi\)
\(488\) −56.3383 32.5269i −0.115447 0.0666535i
\(489\) 0 0
\(490\) −144.000 249.415i −0.293878 0.509011i
\(491\) −315.984 + 182.434i −0.643552 + 0.371555i −0.785982 0.618250i \(-0.787842\pi\)
0.142429 + 0.989805i \(0.454509\pi\)
\(492\) 0 0
\(493\) −216.000 + 374.123i −0.438134 + 0.758870i
\(494\) 41.0122i 0.0830206i
\(495\) 0 0
\(496\) −40.0000 −0.0806452
\(497\) −440.908 254.558i −0.887139 0.512190i
\(498\) 0 0
\(499\) −355.000 614.878i −0.711423 1.23222i −0.964323 0.264728i \(-0.914718\pi\)
0.252900 0.967492i \(-0.418616\pi\)
\(500\) −323.333 + 186.676i −0.646665 + 0.373352i
\(501\) 0 0
\(502\) −252.000 + 436.477i −0.501992 + 0.869476i
\(503\) 280.014i 0.556688i 0.960481 + 0.278344i \(0.0897856\pi\)
−0.960481 + 0.278344i \(0.910214\pi\)
\(504\) 0 0
\(505\) 1152.00 2.28119
\(506\) 88.1816 + 50.9117i 0.174272 + 0.100616i
\(507\) 0 0
\(508\) −178.000 308.305i −0.350394 0.606900i
\(509\) −227.803 + 131.522i −0.447549 + 0.258393i −0.706795 0.707419i \(-0.749859\pi\)
0.259245 + 0.965811i \(0.416526\pi\)
\(510\) 0 0
\(511\) 242.500 420.022i 0.474560 0.821961i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −120.000 −0.233463
\(515\) −1197.80 691.550i −2.32583 1.34282i
\(516\) 0 0
\(517\) 36.0000 + 62.3538i 0.0696325 + 0.120607i
\(518\) 153.093 88.3883i 0.295547 0.170634i
\(519\) 0 0
\(520\) 12.0000 20.7846i 0.0230769 0.0399704i
\(521\) 687.308i 1.31921i 0.751613 + 0.659604i \(0.229276\pi\)
−0.751613 + 0.659604i \(0.770724\pi\)
\(522\) 0 0
\(523\) −763.000 −1.45889 −0.729446 0.684039i \(-0.760222\pi\)
−0.729446 + 0.684039i \(0.760222\pi\)
\(524\) 205.757 + 118.794i 0.392666 + 0.226706i
\(525\) 0 0
\(526\) 120.000 + 207.846i 0.228137 + 0.395145i
\(527\) −220.454 + 127.279i −0.418319 + 0.241517i
\(528\) 0 0
\(529\) −228.500 + 395.774i −0.431947 + 0.748154i
\(530\) 610.940i 1.15272i
\(531\) 0 0
\(532\) −290.000 −0.545113
\(533\) 14.6969 + 8.48528i 0.0275740 + 0.0159199i
\(534\) 0 0
\(535\) −108.000 187.061i −0.201869 0.349648i
\(536\) −46.5403 + 26.8701i −0.0868289 + 0.0501307i
\(537\) 0 0
\(538\) 198.000 342.946i 0.368030 0.637446i
\(539\) 203.647i 0.377823i
\(540\) 0 0
\(541\) −313.000 −0.578558 −0.289279 0.957245i \(-0.593416\pi\)
−0.289279 + 0.957245i \(0.593416\pi\)
\(542\) 35.5176 + 20.5061i 0.0655306 + 0.0378341i
\(543\) 0 0
\(544\) −72.0000 124.708i −0.132353 0.229242i
\(545\) −14.6969 + 8.48528i −0.0269669 + 0.0155693i
\(546\) 0 0
\(547\) 69.5000 120.378i 0.127057 0.220069i −0.795478 0.605982i \(-0.792780\pi\)
0.922535 + 0.385913i \(0.126114\pi\)
\(548\) 186.676i 0.340650i
\(549\) 0 0
\(550\) −564.000 −1.02545
\(551\) 426.211 + 246.073i 0.773523 + 0.446594i
\(552\) 0 0
\(553\) −192.500 333.420i −0.348101 0.602929i
\(554\) 467.853 270.115i 0.844499 0.487572i
\(555\) 0 0
\(556\) −163.000 + 282.324i −0.293165 + 0.507777i
\(557\) 280.014i 0.502719i −0.967894 0.251359i \(-0.919122\pi\)
0.967894 0.251359i \(-0.0808776\pi\)
\(558\) 0 0
\(559\) −14.0000 −0.0250447
\(560\) 146.969 + 84.8528i 0.262445 + 0.151523i
\(561\) 0 0
\(562\) 156.000 + 270.200i 0.277580 + 0.480783i
\(563\) −514.393 + 296.985i −0.913664 + 0.527504i −0.881608 0.471982i \(-0.843539\pi\)
−0.0320558 + 0.999486i \(0.510205\pi\)
\(564\) 0 0
\(565\) 468.000 810.600i 0.828319 1.43469i
\(566\) 87.6812i 0.154914i
\(567\) 0 0
\(568\) −288.000 −0.507042
\(569\) −536.438 309.713i −0.942774 0.544311i −0.0519450 0.998650i \(-0.516542\pi\)
−0.890829 + 0.454339i \(0.849875\pi\)
\(570\) 0 0
\(571\) 81.5000 + 141.162i 0.142732 + 0.247219i 0.928525 0.371271i \(-0.121078\pi\)
−0.785792 + 0.618490i \(0.787745\pi\)
\(572\) 14.6969 8.48528i 0.0256939 0.0148344i
\(573\) 0 0
\(574\) −60.0000 + 103.923i −0.104530 + 0.181051i
\(575\) 398.808i 0.693580i
\(576\) 0 0
\(577\) 1127.00 1.95321 0.976603 0.215050i \(-0.0689913\pi\)
0.976603 + 0.215050i \(0.0689913\pi\)
\(578\) −439.683 253.851i −0.760698 0.439189i
\(579\) 0 0
\(580\) −144.000 249.415i −0.248276 0.430026i
\(581\) −514.393 + 296.985i −0.885358 + 0.511162i
\(582\) 0 0
\(583\) −216.000 + 374.123i −0.370497 + 0.641720i
\(584\) 274.357i 0.469790i
\(585\) 0 0
\(586\) −444.000 −0.757679
\(587\) 874.468 + 504.874i 1.48972 + 0.860092i 0.999931 0.0117465i \(-0.00373911\pi\)
0.489793 + 0.871839i \(0.337072\pi\)
\(588\) 0 0
\(589\) 145.000 + 251.147i 0.246180 + 0.426396i
\(590\) −969.998 + 560.029i −1.64406 + 0.949201i
\(591\) 0 0
\(592\) 50.0000 86.6025i 0.0844595 0.146288i
\(593\) 356.382i 0.600981i 0.953785 + 0.300491i \(0.0971504\pi\)
−0.953785 + 0.300491i \(0.902850\pi\)
\(594\) 0 0
\(595\) 1080.00 1.81513
\(596\) −58.7878 33.9411i −0.0986372 0.0569482i
\(597\) 0 0
\(598\) −6.00000 10.3923i −0.0100334 0.0173784i
\(599\) −778.938 + 449.720i −1.30040 + 0.750784i −0.980472 0.196658i \(-0.936991\pi\)
−0.319925 + 0.947443i \(0.603658\pi\)
\(600\) 0 0
\(601\) 83.0000 143.760i 0.138103 0.239202i −0.788675 0.614810i \(-0.789233\pi\)
0.926779 + 0.375608i \(0.122566\pi\)
\(602\) 98.9949i 0.164443i
\(603\) 0 0
\(604\) −298.000 −0.493377
\(605\) 360.075 + 207.889i 0.595165 + 0.343619i
\(606\) 0 0
\(607\) 261.500 + 452.931i 0.430807 + 0.746180i 0.996943 0.0781320i \(-0.0248955\pi\)
−0.566136 + 0.824312i \(0.691562\pi\)
\(608\) −142.070 + 82.0244i −0.233668 + 0.134909i
\(609\) 0 0
\(610\) 138.000 239.023i 0.226230 0.391841i
\(611\) 8.48528i 0.0138875i
\(612\) 0 0
\(613\) 335.000 0.546493 0.273246 0.961944i \(-0.411903\pi\)
0.273246 + 0.961944i \(0.411903\pi\)
\(614\) −41.6413 24.0416i −0.0678197 0.0391558i
\(615\) 0 0
\(616\) 60.0000 + 103.923i 0.0974026 + 0.168706i
\(617\) 433.560 250.316i 0.702690 0.405698i −0.105659 0.994402i \(-0.533695\pi\)
0.808349 + 0.588704i \(0.200362\pi\)
\(618\) 0 0
\(619\) −2.50000 + 4.33013i −0.00403877 + 0.00699536i −0.868038 0.496498i \(-0.834619\pi\)
0.863999 + 0.503494i \(0.167952\pi\)
\(620\) 169.706i 0.273719i
\(621\) 0 0
\(622\) −84.0000 −0.135048
\(623\) 330.681 + 190.919i 0.530788 + 0.306451i
\(624\) 0 0
\(625\) −204.500 354.204i −0.327200 0.566727i
\(626\) −292.714 + 168.999i −0.467594 + 0.269966i
\(627\) 0 0
\(628\) 242.000 419.156i 0.385350 0.667446i
\(629\) 636.396i 1.01176i
\(630\) 0 0
\(631\) 245.000 0.388273 0.194136 0.980975i \(-0.437810\pi\)
0.194136 + 0.980975i \(0.437810\pi\)
\(632\) −188.611 108.894i −0.298435 0.172301i
\(633\) 0 0
\(634\) 12.0000 + 20.7846i 0.0189274 + 0.0327833i
\(635\) 1308.03 755.190i 2.05989 1.18928i
\(636\) 0 0
\(637\) −12.0000 + 20.7846i −0.0188383 + 0.0326289i
\(638\) 203.647i 0.319196i
\(639\) 0 0
\(640\) 96.0000 0.150000
\(641\) −558.484 322.441i −0.871269 0.503028i −0.00349951 0.999994i \(-0.501114\pi\)
−0.867770 + 0.496966i \(0.834447\pi\)
\(642\) 0 0
\(643\) 41.0000 + 71.0141i 0.0637636 + 0.110442i 0.896145 0.443762i \(-0.146356\pi\)
−0.832381 + 0.554203i \(0.813023\pi\)
\(644\) 73.4847 42.4264i 0.114107 0.0658795i
\(645\) 0 0
\(646\) −522.000 + 904.131i −0.808050 + 1.39958i
\(647\) 458.205i 0.708200i 0.935208 + 0.354100i \(0.115213\pi\)
−0.935208 + 0.354100i \(0.884787\pi\)
\(648\) 0 0
\(649\) −792.000 −1.22034
\(650\) 57.5630 + 33.2340i 0.0885585 + 0.0511293i
\(651\) 0 0
\(652\) 173.000 + 299.645i 0.265337 + 0.459578i
\(653\) 279.242 161.220i 0.427629 0.246892i −0.270707 0.962662i \(-0.587257\pi\)
0.698336 + 0.715770i \(0.253924\pi\)
\(654\) 0 0
\(655\) −504.000 + 872.954i −0.769466 + 1.33275i
\(656\) 67.8823i 0.103479i
\(657\) 0 0
\(658\) 60.0000 0.0911854
\(659\) 896.513 + 517.602i 1.36041 + 0.785436i 0.989679 0.143303i \(-0.0457722\pi\)
0.370736 + 0.928738i \(0.379106\pi\)
\(660\) 0 0
\(661\) −71.5000 123.842i −0.108169 0.187355i 0.806859 0.590744i \(-0.201166\pi\)
−0.915029 + 0.403389i \(0.867832\pi\)
\(662\) 611.148 352.846i 0.923184 0.533000i
\(663\) 0 0
\(664\) −168.000 + 290.985i −0.253012 + 0.438230i
\(665\) 1230.37i 1.85017i
\(666\) 0 0
\(667\) −144.000 −0.215892
\(668\) 338.030 + 195.161i 0.506032 + 0.292158i
\(669\) 0 0
\(670\) −114.000 197.454i −0.170149 0.294707i
\(671\) 169.015 97.5807i 0.251885 0.145426i
\(672\) 0 0
\(673\) −335.500 + 581.103i −0.498514 + 0.863452i −0.999999 0.00171490i \(-0.999454\pi\)
0.501484 + 0.865167i \(0.332787\pi\)
\(674\) 205.061i 0.304245i
\(675\) 0 0
\(676\) 336.000 0.497041
\(677\) −7.34847 4.24264i −0.0108545 0.00626683i 0.494563 0.869142i \(-0.335328\pi\)
−0.505417 + 0.862875i \(0.668661\pi\)
\(678\) 0 0
\(679\) 122.500 + 212.176i 0.180412 + 0.312483i
\(680\) 529.090 305.470i 0.778073 0.449221i
\(681\) 0 0
\(682\) 60.0000 103.923i 0.0879765 0.152380i
\(683\) 101.823i 0.149083i 0.997218 + 0.0745413i \(0.0237493\pi\)
−0.997218 + 0.0745413i \(0.976251\pi\)
\(684\) 0 0
\(685\) −792.000 −1.15620
\(686\) −447.032 258.094i −0.651650 0.376230i
\(687\) 0 0
\(688\) −28.0000 48.4974i −0.0406977 0.0704904i
\(689\) 44.0908 25.4558i 0.0639925 0.0369461i
\(690\) 0 0
\(691\) 425.000 736.122i 0.615051 1.06530i −0.375325 0.926893i \(-0.622469\pi\)
0.990376 0.138406i \(-0.0441978\pi\)
\(692\) 644.881i 0.931910i
\(693\) 0 0
\(694\) −624.000 −0.899135
\(695\) −1197.80 691.550i −1.72345 0.995037i
\(696\) 0 0
\(697\) 216.000 + 374.123i 0.309900 + 0.536762i
\(698\) 148.194 85.5599i 0.212313 0.122579i
\(699\) 0 0
\(700\) −235.000 + 407.032i −0.335714 + 0.581474i
\(701\) 280.014i 0.399450i −0.979852 0.199725i \(-0.935995\pi\)
0.979852 0.199725i \(-0.0640048\pi\)
\(702\) 0 0
\(703\) −725.000 −1.03129
\(704\) 58.7878 + 33.9411i 0.0835053 + 0.0482118i
\(705\) 0 0
\(706\) −312.000 540.400i −0.441926 0.765439i
\(707\) 587.878 339.411i 0.831510 0.480072i
\(708\) 0 0
\(709\) 600.500 1040.10i 0.846968 1.46699i −0.0369339 0.999318i \(-0.511759\pi\)
0.883901 0.467673i \(-0.154908\pi\)
\(710\) 1221.88i 1.72096i
\(711\) 0 0
\(712\) 216.000 0.303371
\(713\) −73.4847 42.4264i −0.103064 0.0595041i
\(714\) 0 0
\(715\) 36.0000 + 62.3538i 0.0503497 + 0.0872082i
\(716\) 529.090 305.470i 0.738952 0.426634i
\(717\) 0 0
\(718\) 306.000 530.008i 0.426184 0.738172i
\(719\) 967.322i 1.34537i 0.739928 + 0.672686i \(0.234859\pi\)
−0.739928 + 0.672686i \(0.765141\pi\)
\(720\) 0 0
\(721\) −815.000 −1.13037
\(722\) 587.878 + 339.411i 0.814235 + 0.470099i
\(723\) 0 0
\(724\) 263.000 + 455.529i 0.363260 + 0.629184i
\(725\) 690.756 398.808i 0.952767 0.550080i
\(726\) 0 0
\(727\) −475.000 + 822.724i −0.653370 + 1.13167i 0.328930 + 0.944354i \(0.393312\pi\)
−0.982300 + 0.187316i \(0.940021\pi\)
\(728\) 14.1421i 0.0194260i
\(729\) 0 0
\(730\) 1164.00 1.59452
\(731\) −308.636 178.191i −0.422210 0.243763i
\(732\) 0 0
\(733\) −49.0000 84.8705i −0.0668486 0.115785i 0.830664 0.556774i \(-0.187961\pi\)
−0.897513 + 0.440989i \(0.854628\pi\)
\(734\) −182.487 + 105.359i −0.248620 + 0.143541i
\(735\) 0 0
\(736\) 24.0000 41.5692i 0.0326087 0.0564799i
\(737\) 161.220i 0.218752i
\(738\) 0 0
\(739\) 1262.00 1.70771 0.853857 0.520508i \(-0.174258\pi\)
0.853857 + 0.520508i \(0.174258\pi\)
\(740\) 367.423 + 212.132i 0.496518 + 0.286665i
\(741\) 0 0
\(742\) 180.000 + 311.769i 0.242588 + 0.420174i
\(743\) −668.711 + 386.080i −0.900014 + 0.519624i −0.877205 0.480116i \(-0.840594\pi\)
−0.0228095 + 0.999740i \(0.507261\pi\)
\(744\) 0 0
\(745\) 144.000 249.415i 0.193289 0.334786i
\(746\) 510.531i 0.684358i
\(747\) 0 0
\(748\) 432.000 0.577540
\(749\) −110.227 63.6396i −0.147166 0.0849661i
\(750\) 0 0
\(751\) −98.5000 170.607i −0.131158 0.227173i 0.792965 0.609267i \(-0.208536\pi\)
−0.924123 + 0.382094i \(0.875203\pi\)
\(752\) 29.3939 16.9706i 0.0390876 0.0225672i
\(753\) 0 0
\(754\) −12.0000 + 20.7846i −0.0159151 + 0.0275658i
\(755\) 1264.31i 1.67458i
\(756\) 0 0
\(757\) −241.000 −0.318362 −0.159181 0.987249i \(-0.550885\pi\)
−0.159181 + 0.987249i \(0.550885\pi\)
\(758\) 211.881 + 122.329i 0.279526 + 0.161385i
\(759\) 0 0
\(760\) −348.000 602.754i −0.457895 0.793097i
\(761\) 433.560 250.316i 0.569724 0.328930i −0.187315 0.982300i \(-0.559979\pi\)
0.757039 + 0.653370i \(0.226645\pi\)
\(762\) 0 0
\(763\) −5.00000 + 8.66025i −0.00655308 + 0.0113503i
\(764\) 288.500i 0.377617i
\(765\) 0 0
\(766\) 960.000 1.25326
\(767\) 80.8332 + 46.6690i 0.105389 + 0.0608462i
\(768\) 0 0
\(769\) −215.500 373.257i −0.280234 0.485380i 0.691208 0.722656i \(-0.257079\pi\)
−0.971442 + 0.237276i \(0.923745\pi\)
\(770\) −440.908 + 254.558i −0.572608 + 0.330595i
\(771\) 0 0
\(772\) 71.0000 122.976i 0.0919689 0.159295i
\(773\) 254.558i 0.329312i −0.986351 0.164656i \(-0.947349\pi\)
0.986351 0.164656i \(-0.0526515\pi\)
\(774\) 0 0
\(775\) 470.000 0.606452
\(776\) 120.025 + 69.2965i 0.154671 + 0.0892996i
\(777\) 0 0
\(778\) −294.000 509.223i −0.377892 0.654528i
\(779\) 426.211 246.073i 0.547126 0.315883i
\(780\) 0 0
\(781\) 432.000 748.246i 0.553137 0.958061i
\(782\) 305.470i 0.390627i
\(783\) 0 0
\(784\) −96.0000 −0.122449
\(785\) 1778.33 + 1026.72i 2.26539 + 1.30792i
\(786\) 0 0
\(787\) −62.5000 108.253i −0.0794155 0.137552i 0.823582 0.567197i \(-0.191972\pi\)
−0.902998 + 0.429645i \(0.858639\pi\)
\(788\) 132.272 76.3675i 0.167858 0.0969131i
\(789\) 0 0
\(790\) 462.000 800.207i 0.584810 1.01292i
\(791\) 551.543i 0.697273i
\(792\) 0 0
\(793\) −23.0000 −0.0290038
\(794\) −350.277 202.233i −0.441155 0.254701i
\(795\) 0 0
\(796\) 173.000 + 299.645i 0.217337 + 0.376438i
\(797\) −734.847 + 424.264i −0.922016 + 0.532326i −0.884278 0.466961i \(-0.845349\pi\)
−0.0377385 + 0.999288i \(0.512015\pi\)
\(798\) 0 0
\(799\) 108.000 187.061i 0.135169 0.234120i
\(800\) 265.872i 0.332340i
\(801\) 0 0
\(802\) −480.000 −0.598504
\(803\) 712.802 + 411.536i 0.887673 + 0.512498i
\(804\) 0 0
\(805\) 180.000 + 311.769i 0.223602 + 0.387291i
\(806\) −12.2474 + 7.07107i −0.0151953 + 0.00877304i
\(807\) 0 0
\(808\) 192.000 332.554i 0.237624 0.411576i
\(809\) 1120.06i 1.38450i 0.721660 + 0.692248i \(0.243380\pi\)
−0.721660 + 0.692248i \(0.756620\pi\)
\(810\) 0 0
\(811\) −322.000 −0.397041 −0.198520 0.980097i \(-0.563614\pi\)
−0.198520 + 0.980097i \(0.563614\pi\)
\(812\) −146.969 84.8528i −0.180997 0.104499i
\(813\) 0 0
\(814\) 150.000 + 259.808i 0.184275 + 0.319174i
\(815\) −1271.29 + 733.977i −1.55986 + 0.900585i
\(816\) 0 0
\(817\) −203.000 + 351.606i −0.248470 + 0.430363i
\(818\) 304.056i 0.371706i
\(819\) 0 0
\(820\) −288.000 −0.351220
\(821\) −756.892 436.992i −0.921915 0.532268i −0.0376696 0.999290i \(-0.511993\pi\)
−0.884246 + 0.467022i \(0.845327\pi\)
\(822\) 0 0
\(823\) −134.500 232.961i −0.163426 0.283063i 0.772669 0.634809i \(-0.218921\pi\)
−0.936095 + 0.351746i \(0.885588\pi\)
\(824\) −399.267 + 230.517i −0.484547 + 0.279753i
\(825\) 0 0
\(826\) −330.000 + 571.577i −0.399516 + 0.691982i
\(827\) 25.4558i 0.0307809i 0.999882 + 0.0153905i \(0.00489913\pi\)
−0.999882 + 0.0153905i \(0.995101\pi\)
\(828\) 0 0
\(829\) −1105.00 −1.33293 −0.666466 0.745536i \(-0.732194\pi\)
−0.666466 + 0.745536i \(0.732194\pi\)
\(830\) −1234.54 712.764i −1.48740 0.858751i
\(831\) 0 0
\(832\) −4.00000 6.92820i −0.00480769 0.00832717i
\(833\) −529.090 + 305.470i −0.635162 + 0.366711i
\(834\) 0 0
\(835\) −828.000 + 1434.14i −0.991617 + 1.71753i
\(836\) 492.146i 0.588692i
\(837\) 0 0
\(838\) 852.000 1.01671
\(839\) 102.879 + 59.3970i 0.122620 + 0.0707950i 0.560056 0.828455i \(-0.310780\pi\)
−0.437435 + 0.899250i \(0.644113\pi\)
\(840\) 0 0
\(841\) −276.500 478.912i −0.328775 0.569455i
\(842\) −557.259 + 321.734i −0.661828 + 0.382106i
\(843\) 0 0
\(844\) 341.000 590.629i 0.404028 0.699798i
\(845\) 1425.53i 1.68701i
\(846\) 0 0
\(847\) 245.000 0.289256
\(848\) 176.363 + 101.823i 0.207976 + 0.120075i
\(849\) 0 0
\(850\) 846.000 + 1465.31i 0.995294 + 1.72390i
\(851\) 183.712 106.066i 0.215877 0.124637i
\(852\) 0 0
\(853\) −695.500 + 1204.64i −0.815358 + 1.41224i 0.0937133 + 0.995599i \(0.470126\pi\)
−0.909071 + 0.416641i \(0.863207\pi\)
\(854\) 162.635i 0.190439i
\(855\) 0 0
\(856\) −72.0000 −0.0841121
\(857\) −470.302 271.529i −0.548777 0.316837i 0.199851 0.979826i \(-0.435954\pi\)
−0.748629 + 0.662990i \(0.769287\pi\)
\(858\) 0 0
\(859\) −422.500 731.791i −0.491851 0.851911i 0.508105 0.861295i \(-0.330346\pi\)
−0.999956 + 0.00938424i \(0.997013\pi\)
\(860\) 205.757 118.794i 0.239252 0.138132i
\(861\) 0 0
\(862\) 234.000 405.300i 0.271462 0.470185i
\(863\) 1247.34i 1.44535i −0.691188 0.722675i \(-0.742913\pi\)
0.691188 0.722675i \(-0.257087\pi\)
\(864\) 0 0
\(865\) −2736.00 −3.16301
\(866\) 266.994 + 154.149i 0.308308 + 0.178001i
\(867\) 0 0
\(868\) −50.0000 86.6025i −0.0576037 0.0997725i
\(869\) 565.832 326.683i 0.651130 0.375930i
\(870\) 0 0
\(871\) −9.50000 + 16.4545i −0.0109070 + 0.0188915i
\(872\) 5.65685i 0.00648722i
\(873\) 0 0
\(874\) −348.000 −0.398169
\(875\) −808.332 466.690i −0.923808 0.533361i
\(876\) 0 0
\(877\) −575.500 996.795i −0.656214 1.13660i −0.981588 0.191011i \(-0.938823\pi\)
0.325374 0.945586i \(-0.394510\pi\)
\(878\) −458.055 + 264.458i −0.521702 + 0.301205i
\(879\) 0 0
\(880\) −144.000 + 249.415i −0.163636 + 0.283426i
\(881\) 1298.25i 1.47361i 0.676107 + 0.736804i \(0.263666\pi\)
−0.676107 + 0.736804i \(0.736334\pi\)
\(882\) 0 0
\(883\) 677.000 0.766704 0.383352 0.923602i \(-0.374770\pi\)
0.383352 + 0.923602i \(0.374770\pi\)
\(884\) −44.0908 25.4558i −0.0498765 0.0287962i
\(885\) 0 0
\(886\) 12.0000 + 20.7846i 0.0135440 + 0.0234589i
\(887\) 896.513 517.602i 1.01073 0.583542i 0.0993213 0.995055i \(-0.468333\pi\)
0.911404 + 0.411513i \(0.135000\pi\)
\(888\) 0 0
\(889\) 445.000 770.763i 0.500562 0.867000i
\(890\) 916.410i 1.02967i
\(891\) 0 0
\(892\) 116.000 0.130045
\(893\) −213.106 123.037i −0.238640 0.137779i
\(894\) 0 0
\(895\) 1296.00 + 2244.74i 1.44804 + 2.50809i
\(896\) 48.9898 28.2843i 0.0546761 0.0315673i
\(897\) 0 0
\(898\) 342.000 592.361i 0.380846 0.659645i
\(899\) 169.706i 0.188772i
\(900\) 0 0
\(901\) 1296.00 1.43840
\(902\) −176.363 101.823i −0.195525 0.112886i
\(903\) 0 0
\(904\) −156.000 270.200i −0.172566 0.298894i
\(905\) −1932.65 + 1115.81i −2.13552 + 1.23294i
\(906\) 0 0
\(907\) −2.50000 + 4.33013i −0.00275634 + 0.00477412i −0.867400 0.497611i \(-0.834211\pi\)
0.864644 + 0.502385i \(0.167544\pi\)
\(908\) 271.529i 0.299041i
\(909\) 0 0
\(910\) 60.0000 0.0659341
\(911\) −867.119 500.632i −0.951832 0.549541i −0.0581828 0.998306i \(-0.518531\pi\)
−0.893650 + 0.448765i \(0.851864\pi\)
\(912\) 0 0
\(913\) −504.000 872.954i −0.552026 0.956138i
\(914\) 26.9444 15.5563i 0.0294796 0.0170201i
\(915\) 0 0
\(916\) −262.000 + 453.797i −0.286026 + 0.495412i
\(917\) 593.970i 0.647731i
\(918\) 0 0
\(919\) 1190.00 1.29489 0.647443 0.762114i \(-0.275838\pi\)
0.647443 + 0.762114i \(0.275838\pi\)
\(920\) 176.363 + 101.823i 0.191699 + 0.110678i
\(921\) 0 0
\(922\) 282.000 + 488.438i 0.305857 + 0.529760i
\(923\) −88.1816 + 50.9117i −0.0955381 + 0.0551589i
\(924\) 0 0
\(925\) −587.500 + 1017.58i −0.635135 + 1.10009i
\(926\) 1248.75i 1.34854i
\(927\) 0 0
\(928\) −96.0000 −0.103448
\(929\) 411.514 + 237.588i 0.442965 + 0.255746i 0.704854 0.709352i \(-0.251012\pi\)
−0.261890 + 0.965098i \(0.584346\pi\)
\(930\) 0 0
\(931\) 348.000 + 602.754i 0.373792 + 0.647426i
\(932\) −529.090 + 305.470i −0.567693 + 0.327758i
\(933\) 0 0
\(934\) −90.0000 + 155.885i −0.0963597 + 0.166900i
\(935\) 1832.82i 1.96024i
\(936\) 0 0
\(937\) 1775.00 1.89434 0.947172 0.320727i \(-0.103927\pi\)
0.947172 + 0.320727i \(0.103927\pi\)
\(938\) −116.351 67.1751i −0.124041 0.0716153i
\(939\) 0 0
\(940\) 72.0000 + 124.708i 0.0765957 + 0.132668i
\(941\) −139.621 + 80.6102i −0.148375 + 0.0856644i −0.572350 0.820010i \(-0.693968\pi\)
0.423975 + 0.905674i \(0.360635\pi\)
\(942\) 0 0
\(943\) −72.0000 + 124.708i −0.0763521 + 0.132246i
\(944\) 373.352i 0.395500i
\(945\) 0 0
\(946\) 168.000 0.177590
\(947\) −492.347 284.257i −0.519902 0.300166i 0.216992 0.976173i \(-0.430375\pi\)
−0.736895 + 0.676008i \(0.763709\pi\)
\(948\) 0 0
\(949\) −48.5000 84.0045i −0.0511064 0.0885189i
\(950\) 1669.33 963.787i 1.75719 1.01451i
\(951\) 0 0
\(952\) 180.000 311.769i 0.189076 0.327489i
\(953\) 1807.36i 1.89650i −0.317524 0.948250i \(-0.602851\pi\)
0.317524 0.948250i \(-0.397149\pi\)
\(954\) 0 0
\(955\) −1224.00 −1.28168
\(956\) 293.939 + 169.706i 0.307467 + 0.177516i
\(957\) 0 0
\(958\) −276.000 478.046i −0.288100 0.499004i
\(959\) −404.166 + 233.345i −0.421445 + 0.243321i
\(960\) 0 0
\(961\) 430.500 745.648i 0.447971 0.775908i
\(962\) 35.3553i 0.0367519i
\(963\) 0 0
\(964\) 242.000 0.251037
\(965\) 521.741 + 301.227i 0.540665 + 0.312153i
\(966\) 0 0
\(967\) −350.500 607.084i −0.362461 0.627801i 0.625904 0.779900i \(-0.284730\pi\)
−0.988365 + 0.152099i \(0.951397\pi\)
\(968\) 120.025 69.2965i 0.123993 0.0715873i
\(969\) 0 0
\(970\) −294.000 + 509.223i −0.303093 + 0.524972i
\(971\) 381.838i 0.393242i 0.980480 + 0.196621i \(0.0629968\pi\)
−0.980480 + 0.196621i \(0.937003\pi\)
\(972\) 0 0
\(973\) −815.000 −0.837616
\(974\) 388.244 + 224.153i 0.398608 + 0.230136i
\(975\) 0 0
\(976\) −46.0000 79.6743i −0.0471311 0.0816335i
\(977\) 279.242 161.220i 0.285816 0.165016i −0.350238 0.936661i \(-0.613899\pi\)
0.636053 + 0.771645i \(0.280566\pi\)
\(978\) 0 0
\(979\) −324.000 + 561.184i −0.330950 + 0.573222i
\(980\) 407.294i 0.415606i
\(981\) 0 0
\(982\) −516.000 −0.525458
\(983\) 36.7423 + 21.2132i 0.0373778 + 0.0215801i 0.518572 0.855034i \(-0.326464\pi\)
−0.481195 + 0.876614i \(0.659797\pi\)
\(984\) 0 0
\(985\) 324.000 + 561.184i 0.328934 + 0.569730i
\(986\) −529.090 + 305.470i −0.536602 + 0.309807i
\(987\) 0 0
\(988\) −29.0000 + 50.2295i −0.0293522 + 0.0508395i
\(989\) 118.794i 0.120115i
\(990\) 0 0
\(991\) −475.000 −0.479314 −0.239657 0.970858i \(-0.577035\pi\)
−0.239657 + 0.970858i \(0.577035\pi\)
\(992\) −48.9898 28.2843i −0.0493849 0.0285124i
\(993\) 0 0
\(994\) −360.000 623.538i −0.362173 0.627302i
\(995\) −1271.29 + 733.977i −1.27767 + 0.737665i
\(996\) 0 0
\(997\) 767.000 1328.48i 0.769308 1.33248i −0.168631 0.985679i \(-0.553935\pi\)
0.937939 0.346801i \(-0.112732\pi\)
\(998\) 1004.09i 1.00610i
\(999\) 0 0
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 162.3.d.a.107.2 4
3.2 odd 2 inner 162.3.d.a.107.1 4
4.3 odd 2 1296.3.q.i.593.1 4
9.2 odd 6 54.3.b.a.53.2 yes 2
9.4 even 3 inner 162.3.d.a.53.1 4
9.5 odd 6 inner 162.3.d.a.53.2 4
9.7 even 3 54.3.b.a.53.1 2
12.11 even 2 1296.3.q.i.593.2 4
36.7 odd 6 432.3.e.d.161.1 2
36.11 even 6 432.3.e.d.161.2 2
36.23 even 6 1296.3.q.i.1025.1 4
36.31 odd 6 1296.3.q.i.1025.2 4
45.2 even 12 1350.3.b.b.1349.2 4
45.7 odd 12 1350.3.b.b.1349.4 4
45.29 odd 6 1350.3.d.d.701.1 2
45.34 even 6 1350.3.d.d.701.2 2
45.38 even 12 1350.3.b.b.1349.3 4
45.43 odd 12 1350.3.b.b.1349.1 4
72.11 even 6 1728.3.e.f.1025.1 2
72.29 odd 6 1728.3.e.l.1025.1 2
72.43 odd 6 1728.3.e.f.1025.2 2
72.61 even 6 1728.3.e.l.1025.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.b.a.53.1 2 9.7 even 3
54.3.b.a.53.2 yes 2 9.2 odd 6
162.3.d.a.53.1 4 9.4 even 3 inner
162.3.d.a.53.2 4 9.5 odd 6 inner
162.3.d.a.107.1 4 3.2 odd 2 inner
162.3.d.a.107.2 4 1.1 even 1 trivial
432.3.e.d.161.1 2 36.7 odd 6
432.3.e.d.161.2 2 36.11 even 6
1296.3.q.i.593.1 4 4.3 odd 2
1296.3.q.i.593.2 4 12.11 even 2
1296.3.q.i.1025.1 4 36.23 even 6
1296.3.q.i.1025.2 4 36.31 odd 6
1350.3.b.b.1349.1 4 45.43 odd 12
1350.3.b.b.1349.2 4 45.2 even 12
1350.3.b.b.1349.3 4 45.38 even 12
1350.3.b.b.1349.4 4 45.7 odd 12
1350.3.d.d.701.1 2 45.29 odd 6
1350.3.d.d.701.2 2 45.34 even 6
1728.3.e.f.1025.1 2 72.11 even 6
1728.3.e.f.1025.2 2 72.43 odd 6
1728.3.e.l.1025.1 2 72.29 odd 6
1728.3.e.l.1025.2 2 72.61 even 6