Properties

Label 810.3.j.d.539.1
Level $810$
Weight $3$
Character 810.539
Analytic conductor $22.071$
Analytic rank $0$
Dimension $8$
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] = [810,3,Mod(269,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.269");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.j (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: \(22.0709014132\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 539.1
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 810.539
Dual form 810.3.j.d.269.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-4.82963 + 1.29410i) q^{5} +(-3.46410 + 2.00000i) q^{7} +2.82843 q^{8} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-4.82963 + 1.29410i) q^{5} +(-3.46410 + 2.00000i) q^{7} +2.82843 q^{8} +(5.00000 + 5.00000i) q^{10} +(9.79796 - 5.65685i) q^{11} +(15.5885 + 9.00000i) q^{13} +(4.89898 + 2.82843i) q^{14} +(-2.00000 - 3.46410i) q^{16} +1.41421 q^{17} -24.0000 q^{19} +(2.58819 - 9.65926i) q^{20} +(-13.8564 - 8.00000i) q^{22} +(19.7990 - 34.2929i) q^{23} +(21.6506 - 12.5000i) q^{25} -25.4558i q^{26} -8.00000i q^{28} +(-33.0681 + 19.0919i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-1.00000 - 1.73205i) q^{34} +(14.1421 - 14.1421i) q^{35} +56.0000i q^{37} +(16.9706 + 29.3939i) q^{38} +(-13.6603 + 3.66025i) q^{40} +(-20.8207 - 12.0208i) q^{41} +(-69.2820 + 40.0000i) q^{43} +22.6274i q^{44} -56.0000 q^{46} +(-14.1421 - 24.4949i) q^{47} +(-16.5000 + 28.5788i) q^{49} +(-30.6186 - 17.6777i) q^{50} +(-31.1769 + 18.0000i) q^{52} +4.24264 q^{53} +(-40.0000 + 40.0000i) q^{55} +(-9.79796 + 5.65685i) q^{56} +(46.7654 + 27.0000i) q^{58} +(-53.8888 - 31.1127i) q^{59} +(-55.0000 - 95.2628i) q^{61} +5.65685 q^{62} +8.00000 q^{64} +(-86.9333 - 23.2937i) q^{65} +(27.7128 + 16.0000i) q^{67} +(-1.41421 + 2.44949i) q^{68} +(-27.3205 - 7.32051i) q^{70} +50.9117i q^{71} +46.0000i q^{73} +(68.5857 - 39.5980i) q^{74} +(24.0000 - 41.5692i) q^{76} +(-22.6274 + 39.1918i) q^{77} +(-18.0000 - 31.1769i) q^{79} +(14.1421 + 14.1421i) q^{80} +34.0000i q^{82} +(2.82843 + 4.89898i) q^{83} +(-6.83013 + 1.83013i) q^{85} +(97.9796 + 56.5685i) q^{86} +(27.7128 - 16.0000i) q^{88} -57.9828i q^{89} -72.0000 q^{91} +(39.5980 + 68.5857i) q^{92} +(-20.0000 + 34.6410i) q^{94} +(115.911 - 31.0583i) q^{95} +(-12.1244 + 7.00000i) q^{97} +46.6690 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 40 q^{10} - 16 q^{16} - 192 q^{19} - 16 q^{31} - 8 q^{34} - 40 q^{40} - 448 q^{46} - 132 q^{49} - 320 q^{55} - 440 q^{61} + 64 q^{64} - 80 q^{70} + 192 q^{76} - 144 q^{79} - 20 q^{85} - 576 q^{91} - 160 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) −4.82963 + 1.29410i −0.965926 + 0.258819i
\(6\) 0 0
\(7\) −3.46410 + 2.00000i −0.494872 + 0.285714i −0.726593 0.687068i \(-0.758897\pi\)
0.231722 + 0.972782i \(0.425564\pi\)
\(8\) 2.82843 0.353553
\(9\) 0 0
\(10\) 5.00000 + 5.00000i 0.500000 + 0.500000i
\(11\) 9.79796 5.65685i 0.890724 0.514259i 0.0165444 0.999863i \(-0.494733\pi\)
0.874179 + 0.485604i \(0.161400\pi\)
\(12\) 0 0
\(13\) 15.5885 + 9.00000i 1.19911 + 0.692308i 0.960357 0.278772i \(-0.0899274\pi\)
0.238755 + 0.971080i \(0.423261\pi\)
\(14\) 4.89898 + 2.82843i 0.349927 + 0.202031i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 1.41421 0.0831890 0.0415945 0.999135i \(-0.486756\pi\)
0.0415945 + 0.999135i \(0.486756\pi\)
\(18\) 0 0
\(19\) −24.0000 −1.26316 −0.631579 0.775312i \(-0.717593\pi\)
−0.631579 + 0.775312i \(0.717593\pi\)
\(20\) 2.58819 9.65926i 0.129410 0.482963i
\(21\) 0 0
\(22\) −13.8564 8.00000i −0.629837 0.363636i
\(23\) 19.7990 34.2929i 0.860826 1.49099i −0.0103075 0.999947i \(-0.503281\pi\)
0.871133 0.491047i \(-0.163386\pi\)
\(24\) 0 0
\(25\) 21.6506 12.5000i 0.866025 0.500000i
\(26\) 25.4558i 0.979071i
\(27\) 0 0
\(28\) 8.00000i 0.285714i
\(29\) −33.0681 + 19.0919i −1.14028 + 0.658341i −0.946500 0.322704i \(-0.895408\pi\)
−0.193780 + 0.981045i \(0.562075\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.0645161 + 0.111745i −0.896479 0.443086i \(-0.853884\pi\)
0.831963 + 0.554831i \(0.187217\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −1.00000 1.73205i −0.0294118 0.0509427i
\(35\) 14.1421 14.1421i 0.404061 0.404061i
\(36\) 0 0
\(37\) 56.0000i 1.51351i 0.653697 + 0.756757i \(0.273217\pi\)
−0.653697 + 0.756757i \(0.726783\pi\)
\(38\) 16.9706 + 29.3939i 0.446594 + 0.773523i
\(39\) 0 0
\(40\) −13.6603 + 3.66025i −0.341506 + 0.0915064i
\(41\) −20.8207 12.0208i −0.507821 0.293191i 0.224116 0.974562i \(-0.428050\pi\)
−0.731938 + 0.681372i \(0.761384\pi\)
\(42\) 0 0
\(43\) −69.2820 + 40.0000i −1.61121 + 0.930233i −0.622120 + 0.782922i \(0.713728\pi\)
−0.989090 + 0.147310i \(0.952938\pi\)
\(44\) 22.6274i 0.514259i
\(45\) 0 0
\(46\) −56.0000 −1.21739
\(47\) −14.1421 24.4949i −0.300897 0.521168i 0.675443 0.737412i \(-0.263953\pi\)
−0.976339 + 0.216244i \(0.930619\pi\)
\(48\) 0 0
\(49\) −16.5000 + 28.5788i −0.336735 + 0.583242i
\(50\) −30.6186 17.6777i −0.612372 0.353553i
\(51\) 0 0
\(52\) −31.1769 + 18.0000i −0.599556 + 0.346154i
\(53\) 4.24264 0.0800498 0.0400249 0.999199i \(-0.487256\pi\)
0.0400249 + 0.999199i \(0.487256\pi\)
\(54\) 0 0
\(55\) −40.0000 + 40.0000i −0.727273 + 0.727273i
\(56\) −9.79796 + 5.65685i −0.174964 + 0.101015i
\(57\) 0 0
\(58\) 46.7654 + 27.0000i 0.806300 + 0.465517i
\(59\) −53.8888 31.1127i −0.913369 0.527334i −0.0318554 0.999492i \(-0.510142\pi\)
−0.881514 + 0.472159i \(0.843475\pi\)
\(60\) 0 0
\(61\) −55.0000 95.2628i −0.901639 1.56169i −0.825366 0.564598i \(-0.809031\pi\)
−0.0762735 0.997087i \(-0.524302\pi\)
\(62\) 5.65685 0.0912396
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −86.9333 23.2937i −1.33744 0.358365i
\(66\) 0 0
\(67\) 27.7128 + 16.0000i 0.413624 + 0.238806i 0.692346 0.721566i \(-0.256577\pi\)
−0.278722 + 0.960372i \(0.589911\pi\)
\(68\) −1.41421 + 2.44949i −0.0207973 + 0.0360219i
\(69\) 0 0
\(70\) −27.3205 7.32051i −0.390293 0.104579i
\(71\) 50.9117i 0.717066i 0.933517 + 0.358533i \(0.116723\pi\)
−0.933517 + 0.358533i \(0.883277\pi\)
\(72\) 0 0
\(73\) 46.0000i 0.630137i 0.949069 + 0.315068i \(0.102027\pi\)
−0.949069 + 0.315068i \(0.897973\pi\)
\(74\) 68.5857 39.5980i 0.926834 0.535108i
\(75\) 0 0
\(76\) 24.0000 41.5692i 0.315789 0.546963i
\(77\) −22.6274 + 39.1918i −0.293863 + 0.508985i
\(78\) 0 0
\(79\) −18.0000 31.1769i −0.227848 0.394644i 0.729322 0.684171i \(-0.239836\pi\)
−0.957170 + 0.289526i \(0.906502\pi\)
\(80\) 14.1421 + 14.1421i 0.176777 + 0.176777i
\(81\) 0 0
\(82\) 34.0000i 0.414634i
\(83\) 2.82843 + 4.89898i 0.0340774 + 0.0590238i 0.882561 0.470198i \(-0.155817\pi\)
−0.848484 + 0.529222i \(0.822484\pi\)
\(84\) 0 0
\(85\) −6.83013 + 1.83013i −0.0803544 + 0.0215309i
\(86\) 97.9796 + 56.5685i 1.13930 + 0.657774i
\(87\) 0 0
\(88\) 27.7128 16.0000i 0.314918 0.181818i
\(89\) 57.9828i 0.651492i −0.945457 0.325746i \(-0.894385\pi\)
0.945457 0.325746i \(-0.105615\pi\)
\(90\) 0 0
\(91\) −72.0000 −0.791209
\(92\) 39.5980 + 68.5857i 0.430413 + 0.745497i
\(93\) 0 0
\(94\) −20.0000 + 34.6410i −0.212766 + 0.368521i
\(95\) 115.911 31.0583i 1.22012 0.326929i
\(96\) 0 0
\(97\) −12.1244 + 7.00000i −0.124993 + 0.0721649i −0.561193 0.827685i \(-0.689657\pi\)
0.436200 + 0.899850i \(0.356324\pi\)
\(98\) 46.6690 0.476215
\(99\) 0 0
\(100\) 50.0000i 0.500000i
\(101\) 23.2702 13.4350i 0.230398 0.133020i −0.380358 0.924839i \(-0.624199\pi\)
0.610755 + 0.791819i \(0.290866\pi\)
\(102\) 0 0
\(103\) −58.8897 34.0000i −0.571745 0.330097i 0.186101 0.982531i \(-0.440415\pi\)
−0.757846 + 0.652434i \(0.773748\pi\)
\(104\) 44.0908 + 25.4558i 0.423950 + 0.244768i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.0283019 0.0490203i
\(107\) −169.706 −1.58603 −0.793017 0.609200i \(-0.791491\pi\)
−0.793017 + 0.609200i \(0.791491\pi\)
\(108\) 0 0
\(109\) −136.000 −1.24771 −0.623853 0.781542i \(-0.714434\pi\)
−0.623853 + 0.781542i \(0.714434\pi\)
\(110\) 77.2741 + 20.7055i 0.702492 + 0.188232i
\(111\) 0 0
\(112\) 13.8564 + 8.00000i 0.123718 + 0.0714286i
\(113\) 6.36396 11.0227i 0.0563182 0.0975461i −0.836492 0.547979i \(-0.815397\pi\)
0.892810 + 0.450433i \(0.148731\pi\)
\(114\) 0 0
\(115\) −51.2436 + 191.244i −0.445596 + 1.66299i
\(116\) 76.3675i 0.658341i
\(117\) 0 0
\(118\) 88.0000i 0.745763i
\(119\) −4.89898 + 2.82843i −0.0411679 + 0.0237683i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.0289256 0.0501006i
\(122\) −77.7817 + 134.722i −0.637555 + 1.10428i
\(123\) 0 0
\(124\) −4.00000 6.92820i −0.0322581 0.0558726i
\(125\) −88.3883 + 88.3883i −0.707107 + 0.707107i
\(126\) 0 0
\(127\) 28.0000i 0.220472i −0.993905 0.110236i \(-0.964839\pi\)
0.993905 0.110236i \(-0.0351607\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 32.9423 + 122.942i 0.253402 + 0.945710i
\(131\) −73.4847 42.4264i −0.560952 0.323866i 0.192576 0.981282i \(-0.438316\pi\)
−0.753527 + 0.657416i \(0.771649\pi\)
\(132\) 0 0
\(133\) 83.1384 48.0000i 0.625101 0.360902i
\(134\) 45.2548i 0.337723i
\(135\) 0 0
\(136\) 4.00000 0.0294118
\(137\) 6.36396 + 11.0227i 0.0464523 + 0.0804577i 0.888317 0.459231i \(-0.151875\pi\)
−0.841864 + 0.539689i \(0.818542\pi\)
\(138\) 0 0
\(139\) −4.00000 + 6.92820i −0.0287770 + 0.0498432i −0.880055 0.474871i \(-0.842495\pi\)
0.851278 + 0.524715i \(0.175828\pi\)
\(140\) 10.3528 + 38.6370i 0.0739483 + 0.275979i
\(141\) 0 0
\(142\) 62.3538 36.0000i 0.439111 0.253521i
\(143\) 203.647 1.42410
\(144\) 0 0
\(145\) 135.000 135.000i 0.931034 0.931034i
\(146\) 56.3383 32.5269i 0.385879 0.222787i
\(147\) 0 0
\(148\) −96.9948 56.0000i −0.655371 0.378378i
\(149\) 104.103 + 60.1041i 0.698680 + 0.403383i 0.806856 0.590749i \(-0.201168\pi\)
−0.108176 + 0.994132i \(0.534501\pi\)
\(150\) 0 0
\(151\) −86.0000 148.956i −0.569536 0.986466i −0.996612 0.0822500i \(-0.973789\pi\)
0.427075 0.904216i \(-0.359544\pi\)
\(152\) −67.8823 −0.446594
\(153\) 0 0
\(154\) 64.0000 0.415584
\(155\) 5.17638 19.3185i 0.0333960 0.124636i
\(156\) 0 0
\(157\) 131.636 + 76.0000i 0.838445 + 0.484076i 0.856735 0.515756i \(-0.172489\pi\)
−0.0182904 + 0.999833i \(0.505822\pi\)
\(158\) −25.4558 + 44.0908i −0.161113 + 0.279056i
\(159\) 0 0
\(160\) 7.32051 27.3205i 0.0457532 0.170753i
\(161\) 158.392i 0.983801i
\(162\) 0 0
\(163\) 104.000i 0.638037i 0.947749 + 0.319018i \(0.103353\pi\)
−0.947749 + 0.319018i \(0.896647\pi\)
\(164\) 41.6413 24.0416i 0.253911 0.146595i
\(165\) 0 0
\(166\) 4.00000 6.92820i 0.0240964 0.0417362i
\(167\) −101.823 + 176.363i −0.609721 + 1.05607i 0.381565 + 0.924342i \(0.375385\pi\)
−0.991286 + 0.131726i \(0.957948\pi\)
\(168\) 0 0
\(169\) 77.5000 + 134.234i 0.458580 + 0.794284i
\(170\) 7.07107 + 7.07107i 0.0415945 + 0.0415945i
\(171\) 0 0
\(172\) 160.000i 0.930233i
\(173\) −115.258 199.633i −0.666234 1.15395i −0.978949 0.204104i \(-0.934572\pi\)
0.312716 0.949847i \(-0.398761\pi\)
\(174\) 0 0
\(175\) −50.0000 + 86.6025i −0.285714 + 0.494872i
\(176\) −39.1918 22.6274i −0.222681 0.128565i
\(177\) 0 0
\(178\) −71.0141 + 41.0000i −0.398956 + 0.230337i
\(179\) 164.049i 0.916474i 0.888830 + 0.458237i \(0.151519\pi\)
−0.888830 + 0.458237i \(0.848481\pi\)
\(180\) 0 0
\(181\) 8.00000 0.0441989 0.0220994 0.999756i \(-0.492965\pi\)
0.0220994 + 0.999756i \(0.492965\pi\)
\(182\) 50.9117 + 88.1816i 0.279735 + 0.484514i
\(183\) 0 0
\(184\) 56.0000 96.9948i 0.304348 0.527146i
\(185\) −72.4693 270.459i −0.391726 1.46194i
\(186\) 0 0
\(187\) 13.8564 8.00000i 0.0740984 0.0427807i
\(188\) 56.5685 0.300897
\(189\) 0 0
\(190\) −120.000 120.000i −0.631579 0.631579i
\(191\) −264.545 + 152.735i −1.38505 + 0.799660i −0.992752 0.120178i \(-0.961654\pi\)
−0.392299 + 0.919838i \(0.628320\pi\)
\(192\) 0 0
\(193\) −55.4256 32.0000i −0.287179 0.165803i 0.349490 0.936940i \(-0.386355\pi\)
−0.636669 + 0.771137i \(0.719688\pi\)
\(194\) 17.1464 + 9.89949i 0.0883837 + 0.0510283i
\(195\) 0 0
\(196\) −33.0000 57.1577i −0.168367 0.291621i
\(197\) −230.517 −1.17014 −0.585068 0.810984i \(-0.698932\pi\)
−0.585068 + 0.810984i \(0.698932\pi\)
\(198\) 0 0
\(199\) 300.000 1.50754 0.753769 0.657140i \(-0.228234\pi\)
0.753769 + 0.657140i \(0.228234\pi\)
\(200\) 61.2372 35.3553i 0.306186 0.176777i
\(201\) 0 0
\(202\) −32.9090 19.0000i −0.162916 0.0940594i
\(203\) 76.3675 132.272i 0.376195 0.651588i
\(204\) 0 0
\(205\) 116.112 + 31.1122i 0.566401 + 0.151767i
\(206\) 96.1665i 0.466828i
\(207\) 0 0
\(208\) 72.0000i 0.346154i
\(209\) −235.151 + 135.765i −1.12512 + 0.649591i
\(210\) 0 0
\(211\) 132.000 228.631i 0.625592 1.08356i −0.362834 0.931854i \(-0.618191\pi\)
0.988426 0.151704i \(-0.0484760\pi\)
\(212\) −4.24264 + 7.34847i −0.0200125 + 0.0346626i
\(213\) 0 0
\(214\) 120.000 + 207.846i 0.560748 + 0.971243i
\(215\) 282.843 282.843i 1.31555 1.31555i
\(216\) 0 0
\(217\) 16.0000i 0.0737327i
\(218\) 96.1665 + 166.565i 0.441131 + 0.764061i
\(219\) 0 0
\(220\) −29.2820 109.282i −0.133100 0.496737i
\(221\) 22.0454 + 12.7279i 0.0997530 + 0.0575924i
\(222\) 0 0
\(223\) 273.664 158.000i 1.22719 0.708520i 0.260751 0.965406i \(-0.416030\pi\)
0.966442 + 0.256886i \(0.0826964\pi\)
\(224\) 22.6274i 0.101015i
\(225\) 0 0
\(226\) −18.0000 −0.0796460
\(227\) 48.0833 + 83.2827i 0.211821 + 0.366884i 0.952284 0.305212i \(-0.0987274\pi\)
−0.740464 + 0.672096i \(0.765394\pi\)
\(228\) 0 0
\(229\) 4.00000 6.92820i 0.0174672 0.0302542i −0.857160 0.515051i \(-0.827773\pi\)
0.874627 + 0.484797i \(0.161106\pi\)
\(230\) 270.459 72.4693i 1.17591 0.315084i
\(231\) 0 0
\(232\) −93.5307 + 54.0000i −0.403150 + 0.232759i
\(233\) −227.688 −0.977203 −0.488602 0.872507i \(-0.662493\pi\)
−0.488602 + 0.872507i \(0.662493\pi\)
\(234\) 0 0
\(235\) 100.000 + 100.000i 0.425532 + 0.425532i
\(236\) 107.778 62.2254i 0.456685 0.263667i
\(237\) 0 0
\(238\) 6.92820 + 4.00000i 0.0291101 + 0.0168067i
\(239\) −166.565 96.1665i −0.696926 0.402370i 0.109276 0.994012i \(-0.465147\pi\)
−0.806201 + 0.591641i \(0.798480\pi\)
\(240\) 0 0
\(241\) 64.0000 + 110.851i 0.265560 + 0.459964i 0.967710 0.252065i \(-0.0811098\pi\)
−0.702150 + 0.712029i \(0.747776\pi\)
\(242\) −9.89949 −0.0409070
\(243\) 0 0
\(244\) 220.000 0.901639
\(245\) 42.7051 159.378i 0.174307 0.650521i
\(246\) 0 0
\(247\) −374.123 216.000i −1.51467 0.874494i
\(248\) −5.65685 + 9.79796i −0.0228099 + 0.0395079i
\(249\) 0 0
\(250\) 170.753 + 45.7532i 0.683013 + 0.183013i
\(251\) 475.176i 1.89313i −0.322512 0.946565i \(-0.604527\pi\)
0.322512 0.946565i \(-0.395473\pi\)
\(252\) 0 0
\(253\) 448.000i 1.77075i
\(254\) −34.2929 + 19.7990i −0.135011 + 0.0779488i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −163.342 + 282.916i −0.635571 + 1.10084i 0.350823 + 0.936442i \(0.385902\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(258\) 0 0
\(259\) −112.000 193.990i −0.432432 0.748995i
\(260\) 127.279 127.279i 0.489535 0.489535i
\(261\) 0 0
\(262\) 120.000i 0.458015i
\(263\) −39.5980 68.5857i −0.150563 0.260782i 0.780872 0.624691i \(-0.214775\pi\)
−0.931434 + 0.363909i \(0.881442\pi\)
\(264\) 0 0
\(265\) −20.4904 + 5.49038i −0.0773222 + 0.0207184i
\(266\) −117.576 67.8823i −0.442013 0.255196i
\(267\) 0 0
\(268\) −55.4256 + 32.0000i −0.206812 + 0.119403i
\(269\) 165.463i 0.615104i 0.951531 + 0.307552i \(0.0995098\pi\)
−0.951531 + 0.307552i \(0.900490\pi\)
\(270\) 0 0
\(271\) 220.000 0.811808 0.405904 0.913916i \(-0.366957\pi\)
0.405904 + 0.913916i \(0.366957\pi\)
\(272\) −2.82843 4.89898i −0.0103986 0.0180110i
\(273\) 0 0
\(274\) 9.00000 15.5885i 0.0328467 0.0568922i
\(275\) 141.421 244.949i 0.514259 0.890724i
\(276\) 0 0
\(277\) 1.73205 1.00000i 0.00625289 0.00361011i −0.496870 0.867825i \(-0.665518\pi\)
0.503123 + 0.864215i \(0.332184\pi\)
\(278\) 11.3137 0.0406968
\(279\) 0 0
\(280\) 40.0000 40.0000i 0.142857 0.142857i
\(281\) 11.0227 6.36396i 0.0392267 0.0226475i −0.480258 0.877127i \(-0.659457\pi\)
0.519485 + 0.854480i \(0.326124\pi\)
\(282\) 0 0
\(283\) 408.764 + 236.000i 1.44440 + 0.833922i 0.998139 0.0609826i \(-0.0194234\pi\)
0.446257 + 0.894905i \(0.352757\pi\)
\(284\) −88.1816 50.9117i −0.310499 0.179267i
\(285\) 0 0
\(286\) −144.000 249.415i −0.503497 0.872082i
\(287\) 96.1665 0.335075
\(288\) 0 0
\(289\) −287.000 −0.993080
\(290\) −260.800 69.8811i −0.899310 0.240969i
\(291\) 0 0
\(292\) −79.6743 46.0000i −0.272857 0.157534i
\(293\) 205.768 356.401i 0.702280 1.21638i −0.265384 0.964143i \(-0.585499\pi\)
0.967664 0.252242i \(-0.0811679\pi\)
\(294\) 0 0
\(295\) 300.526 + 80.5256i 1.01873 + 0.272968i
\(296\) 158.392i 0.535108i
\(297\) 0 0
\(298\) 170.000i 0.570470i
\(299\) 617.271 356.382i 2.06445 1.19191i
\(300\) 0 0
\(301\) 160.000 277.128i 0.531561 0.920691i
\(302\) −121.622 + 210.656i −0.402723 + 0.697537i
\(303\) 0 0
\(304\) 48.0000 + 83.1384i 0.157895 + 0.273482i
\(305\) 388.909 + 388.909i 1.27511 + 1.27511i
\(306\) 0 0
\(307\) 360.000i 1.17264i −0.810080 0.586319i \(-0.800576\pi\)
0.810080 0.586319i \(-0.199424\pi\)
\(308\) −45.2548 78.3837i −0.146931 0.254492i
\(309\) 0 0
\(310\) −27.3205 + 7.32051i −0.0881307 + 0.0236145i
\(311\) −29.3939 16.9706i −0.0945141 0.0545677i 0.451998 0.892019i \(-0.350711\pi\)
−0.546512 + 0.837451i \(0.684045\pi\)
\(312\) 0 0
\(313\) −360.267 + 208.000i −1.15101 + 0.664537i −0.949133 0.314874i \(-0.898038\pi\)
−0.201878 + 0.979411i \(0.564704\pi\)
\(314\) 214.960i 0.684587i
\(315\) 0 0
\(316\) 72.0000 0.227848
\(317\) 37.4767 + 64.9115i 0.118223 + 0.204768i 0.919063 0.394110i \(-0.128947\pi\)
−0.800841 + 0.598878i \(0.795614\pi\)
\(318\) 0 0
\(319\) −216.000 + 374.123i −0.677116 + 1.17280i
\(320\) −38.6370 + 10.3528i −0.120741 + 0.0323524i
\(321\) 0 0
\(322\) 193.990 112.000i 0.602452 0.347826i
\(323\) −33.9411 −0.105081
\(324\) 0 0
\(325\) 450.000 1.38462
\(326\) 127.373 73.5391i 0.390716 0.225580i
\(327\) 0 0
\(328\) −58.8897 34.0000i −0.179542 0.103659i
\(329\) 97.9796 + 56.5685i 0.297810 + 0.171941i
\(330\) 0 0
\(331\) 232.000 + 401.836i 0.700906 + 1.21401i 0.968149 + 0.250376i \(0.0805543\pi\)
−0.267242 + 0.963629i \(0.586112\pi\)
\(332\) −11.3137 −0.0340774
\(333\) 0 0
\(334\) 288.000 0.862275
\(335\) −154.548 41.4110i −0.461338 0.123615i
\(336\) 0 0
\(337\) −53.6936 31.0000i −0.159328 0.0919881i 0.418216 0.908348i \(-0.362656\pi\)
−0.577544 + 0.816359i \(0.695989\pi\)
\(338\) 109.602 189.835i 0.324265 0.561643i
\(339\) 0 0
\(340\) 3.66025 13.6603i 0.0107655 0.0401772i
\(341\) 45.2548i 0.132712i
\(342\) 0 0
\(343\) 328.000i 0.956268i
\(344\) −195.959 + 113.137i −0.569649 + 0.328887i
\(345\) 0 0
\(346\) −163.000 + 282.324i −0.471098 + 0.815966i
\(347\) −229.103 + 396.817i −0.660238 + 1.14357i 0.320315 + 0.947311i \(0.396211\pi\)
−0.980553 + 0.196255i \(0.937122\pi\)
\(348\) 0 0
\(349\) 71.0000 + 122.976i 0.203438 + 0.352366i 0.949634 0.313361i \(-0.101455\pi\)
−0.746196 + 0.665727i \(0.768122\pi\)
\(350\) 141.421 0.404061
\(351\) 0 0
\(352\) 64.0000i 0.181818i
\(353\) 50.2046 + 86.9569i 0.142223 + 0.246337i 0.928333 0.371749i \(-0.121242\pi\)
−0.786111 + 0.618086i \(0.787908\pi\)
\(354\) 0 0
\(355\) −65.8846 245.885i −0.185590 0.692633i
\(356\) 100.429 + 57.9828i 0.282104 + 0.162873i
\(357\) 0 0
\(358\) 200.918 116.000i 0.561223 0.324022i
\(359\) 390.323i 1.08725i −0.839328 0.543625i \(-0.817051\pi\)
0.839328 0.543625i \(-0.182949\pi\)
\(360\) 0 0
\(361\) 215.000 0.595568
\(362\) −5.65685 9.79796i −0.0156267 0.0270662i
\(363\) 0 0
\(364\) 72.0000 124.708i 0.197802 0.342603i
\(365\) −59.5284 222.163i −0.163091 0.608666i
\(366\) 0 0
\(367\) 245.951 142.000i 0.670167 0.386921i −0.125973 0.992034i \(-0.540205\pi\)
0.796140 + 0.605113i \(0.206872\pi\)
\(368\) −158.392 −0.430413
\(369\) 0 0
\(370\) −280.000 + 280.000i −0.756757 + 0.756757i
\(371\) −14.6969 + 8.48528i −0.0396144 + 0.0228714i
\(372\) 0 0
\(373\) −311.769 180.000i −0.835842 0.482574i 0.0200066 0.999800i \(-0.493631\pi\)
−0.855849 + 0.517226i \(0.826965\pi\)
\(374\) −19.5959 11.3137i −0.0523955 0.0302506i
\(375\) 0 0
\(376\) −40.0000 69.2820i −0.106383 0.184261i
\(377\) −687.308 −1.82310
\(378\) 0 0
\(379\) −320.000 −0.844327 −0.422164 0.906520i \(-0.638729\pi\)
−0.422164 + 0.906520i \(0.638729\pi\)
\(380\) −62.1166 + 231.822i −0.163465 + 0.610058i
\(381\) 0 0
\(382\) 374.123 + 216.000i 0.979380 + 0.565445i
\(383\) 90.5097 156.767i 0.236318 0.409314i −0.723337 0.690495i \(-0.757393\pi\)
0.959655 + 0.281181i \(0.0907261\pi\)
\(384\) 0 0
\(385\) 58.5641 218.564i 0.152114 0.567699i
\(386\) 90.5097i 0.234481i
\(387\) 0 0
\(388\) 28.0000i 0.0721649i
\(389\) −594.001 + 342.947i −1.52700 + 0.881611i −0.527510 + 0.849549i \(0.676874\pi\)
−0.999486 + 0.0320622i \(0.989793\pi\)
\(390\) 0 0
\(391\) 28.0000 48.4974i 0.0716113 0.124034i
\(392\) −46.6690 + 80.8332i −0.119054 + 0.206207i
\(393\) 0 0
\(394\) 163.000 + 282.324i 0.413706 + 0.716559i
\(395\) 127.279 + 127.279i 0.322226 + 0.322226i
\(396\) 0 0
\(397\) 296.000i 0.745592i 0.927913 + 0.372796i \(0.121601\pi\)
−0.927913 + 0.372796i \(0.878399\pi\)
\(398\) −212.132 367.423i −0.532995 0.923175i
\(399\) 0 0
\(400\) −86.6025 50.0000i −0.216506 0.125000i
\(401\) 380.896 + 219.910i 0.949864 + 0.548405i 0.893039 0.449980i \(-0.148569\pi\)
0.0568256 + 0.998384i \(0.481902\pi\)
\(402\) 0 0
\(403\) −62.3538 + 36.0000i −0.154724 + 0.0893300i
\(404\) 53.7401i 0.133020i
\(405\) 0 0
\(406\) −216.000 −0.532020
\(407\) 316.784 + 548.686i 0.778339 + 1.34812i
\(408\) 0 0
\(409\) 184.000 318.697i 0.449878 0.779211i −0.548500 0.836151i \(-0.684801\pi\)
0.998378 + 0.0569395i \(0.0181342\pi\)
\(410\) −43.9992 164.207i −0.107315 0.400506i
\(411\) 0 0
\(412\) 117.779 68.0000i 0.285872 0.165049i
\(413\) 248.902 0.602667
\(414\) 0 0
\(415\) −20.0000 20.0000i −0.0481928 0.0481928i
\(416\) −88.1816 + 50.9117i −0.211975 + 0.122384i
\(417\) 0 0
\(418\) 332.554 + 192.000i 0.795583 + 0.459330i
\(419\) −166.565 96.1665i −0.397531 0.229514i 0.287887 0.957664i \(-0.407047\pi\)
−0.685418 + 0.728150i \(0.740380\pi\)
\(420\) 0 0
\(421\) −140.000 242.487i −0.332542 0.575979i 0.650468 0.759534i \(-0.274573\pi\)
−0.983009 + 0.183555i \(0.941240\pi\)
\(422\) −373.352 −0.884721
\(423\) 0 0
\(424\) 12.0000 0.0283019
\(425\) 30.6186 17.6777i 0.0720438 0.0415945i
\(426\) 0 0
\(427\) 381.051 + 220.000i 0.892392 + 0.515222i
\(428\) 169.706 293.939i 0.396508 0.686773i
\(429\) 0 0
\(430\) −546.410 146.410i −1.27072 0.340489i
\(431\) 96.1665i 0.223124i 0.993757 + 0.111562i \(0.0355854\pi\)
−0.993757 + 0.111562i \(0.964415\pi\)
\(432\) 0 0
\(433\) 688.000i 1.58891i 0.607320 + 0.794457i \(0.292245\pi\)
−0.607320 + 0.794457i \(0.707755\pi\)
\(434\) −19.5959 + 11.3137i −0.0451519 + 0.0260685i
\(435\) 0 0
\(436\) 136.000 235.559i 0.311927 0.540273i
\(437\) −475.176 + 823.029i −1.08736 + 1.88336i
\(438\) 0 0
\(439\) −162.000 280.592i −0.369021 0.639162i 0.620392 0.784292i \(-0.286973\pi\)
−0.989413 + 0.145129i \(0.953640\pi\)
\(440\) −113.137 + 113.137i −0.257130 + 0.257130i
\(441\) 0 0
\(442\) 36.0000i 0.0814480i
\(443\) 161.220 + 279.242i 0.363929 + 0.630343i 0.988604 0.150542i \(-0.0481019\pi\)
−0.624675 + 0.780885i \(0.714769\pi\)
\(444\) 0 0
\(445\) 75.0352 + 280.035i 0.168618 + 0.629293i
\(446\) −387.019 223.446i −0.867756 0.500999i
\(447\) 0 0
\(448\) −27.7128 + 16.0000i −0.0618590 + 0.0357143i
\(449\) 123.037i 0.274024i −0.990569 0.137012i \(-0.956250\pi\)
0.990569 0.137012i \(-0.0437498\pi\)
\(450\) 0 0
\(451\) −272.000 −0.603104
\(452\) 12.7279 + 22.0454i 0.0281591 + 0.0487730i
\(453\) 0 0
\(454\) 68.0000 117.779i 0.149780 0.259426i
\(455\) 347.733 93.1749i 0.764249 0.204780i
\(456\) 0 0
\(457\) −112.583 + 65.0000i −0.246353 + 0.142232i −0.618093 0.786105i \(-0.712095\pi\)
0.371740 + 0.928337i \(0.378761\pi\)
\(458\) −11.3137 −0.0247024
\(459\) 0 0
\(460\) −280.000 280.000i −0.608696 0.608696i
\(461\) 407.840 235.467i 0.884686 0.510773i 0.0124851 0.999922i \(-0.496026\pi\)
0.872200 + 0.489149i \(0.162692\pi\)
\(462\) 0 0
\(463\) −384.515 222.000i −0.830487 0.479482i 0.0235327 0.999723i \(-0.492509\pi\)
−0.854019 + 0.520241i \(0.825842\pi\)
\(464\) 132.272 + 76.3675i 0.285070 + 0.164585i
\(465\) 0 0
\(466\) 161.000 + 278.860i 0.345494 + 0.598412i
\(467\) 186.676 0.399735 0.199867 0.979823i \(-0.435949\pi\)
0.199867 + 0.979823i \(0.435949\pi\)
\(468\) 0 0
\(469\) −128.000 −0.272921
\(470\) 51.7638 193.185i 0.110136 0.411032i
\(471\) 0 0
\(472\) −152.420 88.0000i −0.322925 0.186441i
\(473\) −452.548 + 783.837i −0.956762 + 1.65716i
\(474\) 0 0
\(475\) −519.615 + 300.000i −1.09393 + 0.631579i
\(476\) 11.3137i 0.0237683i
\(477\) 0 0
\(478\) 272.000i 0.569038i
\(479\) 504.595 291.328i 1.05343 0.608200i 0.129825 0.991537i \(-0.458558\pi\)
0.923609 + 0.383336i \(0.125225\pi\)
\(480\) 0 0
\(481\) −504.000 + 872.954i −1.04782 + 1.81487i
\(482\) 90.5097 156.767i 0.187779 0.325243i
\(483\) 0 0
\(484\) 7.00000 + 12.1244i 0.0144628 + 0.0250503i
\(485\) 49.4975 49.4975i 0.102057 0.102057i
\(486\) 0 0
\(487\) 84.0000i 0.172485i −0.996274 0.0862423i \(-0.972514\pi\)
0.996274 0.0862423i \(-0.0274859\pi\)
\(488\) −155.563 269.444i −0.318778 0.552139i
\(489\) 0 0
\(490\) −225.394 + 60.3942i −0.459988 + 0.123253i
\(491\) 279.242 + 161.220i 0.568721 + 0.328351i 0.756638 0.653834i \(-0.226840\pi\)
−0.187918 + 0.982185i \(0.560174\pi\)
\(492\) 0 0
\(493\) −46.7654 + 27.0000i −0.0948588 + 0.0547667i
\(494\) 610.940i 1.23672i
\(495\) 0 0
\(496\) 16.0000 0.0322581
\(497\) −101.823 176.363i −0.204876 0.354856i
\(498\) 0 0
\(499\) −228.000 + 394.908i −0.456914 + 0.791398i −0.998796 0.0490565i \(-0.984379\pi\)
0.541882 + 0.840454i \(0.317712\pi\)
\(500\) −64.7048 241.481i −0.129410 0.482963i
\(501\) 0 0
\(502\) −581.969 + 336.000i −1.15930 + 0.669323i
\(503\) 492.146 0.978422 0.489211 0.872165i \(-0.337285\pi\)
0.489211 + 0.872165i \(0.337285\pi\)
\(504\) 0 0
\(505\) −95.0000 + 95.0000i −0.188119 + 0.188119i
\(506\) −548.686 + 316.784i −1.08436 + 0.626055i
\(507\) 0 0
\(508\) 48.4974 + 28.0000i 0.0954674 + 0.0551181i
\(509\) 503.370 + 290.621i 0.988939 + 0.570964i 0.904957 0.425503i \(-0.139903\pi\)
0.0839823 + 0.996467i \(0.473236\pi\)
\(510\) 0 0
\(511\) −92.0000 159.349i −0.180039 0.311837i
\(512\) 22.6274 0.0441942
\(513\) 0 0
\(514\) 462.000 0.898833
\(515\) 328.415 + 87.9985i 0.637699 + 0.170871i
\(516\) 0 0
\(517\) −277.128 160.000i −0.536031 0.309478i
\(518\) −158.392 + 274.343i −0.305776 + 0.529619i
\(519\) 0 0
\(520\) −245.885 65.8846i −0.472855 0.126701i
\(521\) 408.708i 0.784468i 0.919866 + 0.392234i \(0.128298\pi\)
−0.919866 + 0.392234i \(0.871702\pi\)
\(522\) 0 0
\(523\) 656.000i 1.25430i 0.778898 + 0.627151i \(0.215779\pi\)
−0.778898 + 0.627151i \(0.784221\pi\)
\(524\) 146.969 84.8528i 0.280476 0.161933i
\(525\) 0 0
\(526\) −56.0000 + 96.9948i −0.106464 + 0.184401i
\(527\) −2.82843 + 4.89898i −0.00536703 + 0.00929598i
\(528\) 0 0
\(529\) −519.500 899.800i −0.982042 1.70095i
\(530\) 21.2132 + 21.2132i 0.0400249 + 0.0400249i
\(531\) 0 0
\(532\) 192.000i 0.360902i
\(533\) −216.375 374.772i −0.405956 0.703137i
\(534\) 0 0
\(535\) 819.615 219.615i 1.53199 0.410496i
\(536\) 78.3837 + 45.2548i 0.146238 + 0.0844307i
\(537\) 0 0
\(538\) 202.650 117.000i 0.376673 0.217472i
\(539\) 373.352i 0.692676i
\(540\) 0 0
\(541\) −248.000 −0.458410 −0.229205 0.973378i \(-0.573613\pi\)
−0.229205 + 0.973378i \(0.573613\pi\)
\(542\) −155.563 269.444i −0.287018 0.497129i
\(543\) 0 0
\(544\) −4.00000 + 6.92820i −0.00735294 + 0.0127357i
\(545\) 656.830 175.997i 1.20519 0.322930i
\(546\) 0 0
\(547\) −263.272 + 152.000i −0.481301 + 0.277879i −0.720959 0.692978i \(-0.756298\pi\)
0.239657 + 0.970858i \(0.422965\pi\)
\(548\) −25.4558 −0.0464523
\(549\) 0 0
\(550\) −400.000 −0.727273
\(551\) 793.635 458.205i 1.44035 0.831588i
\(552\) 0 0
\(553\) 124.708 + 72.0000i 0.225511 + 0.130199i
\(554\) −2.44949 1.41421i −0.00442146 0.00255273i
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.0143885 0.0249216i
\(557\) −886.712 −1.59194 −0.795971 0.605335i \(-0.793039\pi\)
−0.795971 + 0.605335i \(0.793039\pi\)
\(558\) 0 0
\(559\) −1440.00 −2.57603
\(560\) −77.2741 20.7055i −0.137989 0.0369741i
\(561\) 0 0
\(562\) −15.5885 9.00000i −0.0277375 0.0160142i
\(563\) −19.7990 + 34.2929i −0.0351669 + 0.0609109i −0.883073 0.469235i \(-0.844530\pi\)
0.847906 + 0.530146i \(0.177863\pi\)
\(564\) 0 0
\(565\) −16.4711 + 61.4711i −0.0291525 + 0.108798i
\(566\) 667.509i 1.17934i
\(567\) 0 0
\(568\) 144.000i 0.253521i
\(569\) 37.9671 21.9203i 0.0667260 0.0385243i −0.466266 0.884645i \(-0.654401\pi\)
0.532992 + 0.846120i \(0.321068\pi\)
\(570\) 0 0
\(571\) 196.000 339.482i 0.343257 0.594539i −0.641778 0.766890i \(-0.721803\pi\)
0.985036 + 0.172351i \(0.0551363\pi\)
\(572\) −203.647 + 352.727i −0.356026 + 0.616655i
\(573\) 0 0
\(574\) −68.0000 117.779i −0.118467 0.205191i
\(575\) 989.949i 1.72165i
\(576\) 0 0
\(577\) 112.000i 0.194107i −0.995279 0.0970537i \(-0.969058\pi\)
0.995279 0.0970537i \(-0.0309419\pi\)
\(578\) 202.940 + 351.502i 0.351107 + 0.608135i
\(579\) 0 0
\(580\) 98.8269 + 368.827i 0.170391 + 0.635908i
\(581\) −19.5959 11.3137i −0.0337279 0.0194728i
\(582\) 0 0
\(583\) 41.5692 24.0000i 0.0713023 0.0411664i
\(584\) 130.108i 0.222787i
\(585\) 0 0
\(586\) −582.000 −0.993174
\(587\) 576.999 + 999.392i 0.982963 + 1.70254i 0.650661 + 0.759368i \(0.274492\pi\)
0.332302 + 0.943173i \(0.392175\pi\)
\(588\) 0 0
\(589\) 48.0000 83.1384i 0.0814941 0.141152i
\(590\) −113.880 425.007i −0.193018 0.720351i
\(591\) 0 0
\(592\) 193.990 112.000i 0.327685 0.189189i
\(593\) −258.801 −0.436427 −0.218213 0.975901i \(-0.570023\pi\)
−0.218213 + 0.975901i \(0.570023\pi\)
\(594\) 0 0
\(595\) 20.0000 20.0000i 0.0336134 0.0336134i
\(596\) −208.207 + 120.208i −0.349340 + 0.201692i
\(597\) 0 0
\(598\) −872.954 504.000i −1.45979 0.842809i
\(599\) −249.848 144.250i −0.417108 0.240818i 0.276731 0.960947i \(-0.410749\pi\)
−0.693839 + 0.720130i \(0.744082\pi\)
\(600\) 0 0
\(601\) 431.000 + 746.514i 0.717138 + 1.24212i 0.962129 + 0.272594i \(0.0878817\pi\)
−0.244991 + 0.969525i \(0.578785\pi\)
\(602\) −452.548 −0.751741
\(603\) 0 0
\(604\) 344.000 0.569536
\(605\) −9.05867 + 33.8074i −0.0149730 + 0.0558800i
\(606\) 0 0
\(607\) 682.428 + 394.000i 1.12426 + 0.649094i 0.942486 0.334246i \(-0.108482\pi\)
0.181778 + 0.983340i \(0.441815\pi\)
\(608\) 67.8823 117.576i 0.111648 0.193381i
\(609\) 0 0
\(610\) 201.314 751.314i 0.330023 1.23166i
\(611\) 509.117i 0.833252i
\(612\) 0 0
\(613\) 952.000i 1.55302i 0.630106 + 0.776509i \(0.283011\pi\)
−0.630106 + 0.776509i \(0.716989\pi\)
\(614\) −440.908 + 254.558i −0.718091 + 0.414590i
\(615\) 0 0
\(616\) −64.0000 + 110.851i −0.103896 + 0.179953i
\(617\) −191.626 + 331.906i −0.310577 + 0.537935i −0.978487 0.206307i \(-0.933856\pi\)
0.667911 + 0.744242i \(0.267189\pi\)
\(618\) 0 0
\(619\) −152.000 263.272i −0.245557 0.425318i 0.716731 0.697350i \(-0.245638\pi\)
−0.962288 + 0.272032i \(0.912304\pi\)
\(620\) 28.2843 + 28.2843i 0.0456198 + 0.0456198i
\(621\) 0 0
\(622\) 48.0000i 0.0771704i
\(623\) 115.966 + 200.858i 0.186140 + 0.322405i
\(624\) 0 0
\(625\) 312.500 541.266i 0.500000 0.866025i
\(626\) 509.494 + 294.156i 0.813888 + 0.469898i
\(627\) 0 0
\(628\) −263.272 + 152.000i −0.419222 + 0.242038i
\(629\) 79.1960i 0.125908i
\(630\) 0 0
\(631\) 860.000 1.36292 0.681458 0.731857i \(-0.261346\pi\)
0.681458 + 0.731857i \(0.261346\pi\)
\(632\) −50.9117 88.1816i −0.0805565 0.139528i
\(633\) 0 0
\(634\) 53.0000 91.7987i 0.0835962 0.144793i
\(635\) 36.2347 + 135.230i 0.0570625 + 0.212960i
\(636\) 0 0
\(637\) −514.419 + 297.000i −0.807565 + 0.466248i
\(638\) 610.940 0.957587
\(639\) 0 0
\(640\) 40.0000 + 40.0000i 0.0625000 + 0.0625000i
\(641\) −383.345 + 221.324i −0.598042 + 0.345280i −0.768271 0.640125i \(-0.778883\pi\)
0.170229 + 0.985405i \(0.445549\pi\)
\(642\) 0 0
\(643\) 561.184 + 324.000i 0.872760 + 0.503888i 0.868264 0.496102i \(-0.165236\pi\)
0.00449534 + 0.999990i \(0.498569\pi\)
\(644\) −274.343 158.392i −0.425998 0.245950i
\(645\) 0 0
\(646\) 24.0000 + 41.5692i 0.0371517 + 0.0643486i
\(647\) 390.323 0.603281 0.301641 0.953422i \(-0.402466\pi\)
0.301641 + 0.953422i \(0.402466\pi\)
\(648\) 0 0
\(649\) −704.000 −1.08475
\(650\) −318.198 551.135i −0.489535 0.847900i
\(651\) 0 0
\(652\) −180.133 104.000i −0.276278 0.159509i
\(653\) 454.670 787.511i 0.696278 1.20599i −0.273470 0.961881i \(-0.588171\pi\)
0.969748 0.244109i \(-0.0784953\pi\)
\(654\) 0 0
\(655\) 409.808 + 109.808i 0.625660 + 0.167645i
\(656\) 96.1665i 0.146595i
\(657\) 0 0
\(658\) 160.000i 0.243161i
\(659\) −298.838 + 172.534i −0.453472 + 0.261812i −0.709295 0.704912i \(-0.750987\pi\)
0.255824 + 0.966723i \(0.417653\pi\)
\(660\) 0 0
\(661\) −481.000 + 833.116i −0.727685 + 1.26039i 0.230174 + 0.973150i \(0.426071\pi\)
−0.957859 + 0.287238i \(0.907263\pi\)
\(662\) 328.098 568.282i 0.495616 0.858431i
\(663\) 0 0
\(664\) 8.00000 + 13.8564i 0.0120482 + 0.0208681i
\(665\) −339.411 + 339.411i −0.510393 + 0.510393i
\(666\) 0 0
\(667\) 1512.00i 2.26687i
\(668\) −203.647 352.727i −0.304860 0.528034i
\(669\) 0 0
\(670\) 58.5641 + 218.564i 0.0874091 + 0.326215i
\(671\) −1077.78 622.254i −1.60622 0.927353i
\(672\) 0 0
\(673\) 207.846 120.000i 0.308835 0.178306i −0.337570 0.941300i \(-0.609605\pi\)
0.646405 + 0.762994i \(0.276272\pi\)
\(674\) 87.6812i 0.130091i
\(675\) 0 0
\(676\) −310.000 −0.458580
\(677\) −166.170 287.815i −0.245451 0.425133i 0.716808 0.697271i \(-0.245603\pi\)
−0.962258 + 0.272138i \(0.912269\pi\)
\(678\) 0 0
\(679\) 28.0000 48.4974i 0.0412371 0.0714248i
\(680\) −19.3185 + 5.17638i −0.0284096 + 0.00761232i
\(681\) 0 0
\(682\) 55.4256 32.0000i 0.0812692 0.0469208i
\(683\) 1012.58 1.48254 0.741272 0.671205i \(-0.234223\pi\)
0.741272 + 0.671205i \(0.234223\pi\)
\(684\) 0 0
\(685\) −45.0000 45.0000i −0.0656934 0.0656934i
\(686\) −401.716 + 231.931i −0.585592 + 0.338092i
\(687\) 0 0
\(688\) 277.128 + 160.000i 0.402803 + 0.232558i
\(689\) 66.1362 + 38.1838i 0.0959887 + 0.0554191i
\(690\) 0 0
\(691\) 40.0000 + 69.2820i 0.0578871 + 0.100263i 0.893517 0.449030i \(-0.148230\pi\)
−0.835630 + 0.549293i \(0.814897\pi\)
\(692\) 461.034 0.666234
\(693\) 0 0
\(694\) 648.000 0.933718
\(695\) 10.3528 38.6370i 0.0148961 0.0555929i
\(696\) 0 0
\(697\) −29.4449 17.0000i −0.0422451 0.0243902i
\(698\) 100.409 173.914i 0.143853 0.249160i
\(699\) 0 0
\(700\) −100.000 173.205i −0.142857 0.247436i
\(701\) 558.614i 0.796882i 0.917194 + 0.398441i \(0.130449\pi\)
−0.917194 + 0.398441i \(0.869551\pi\)
\(702\) 0 0
\(703\) 1344.00i 1.91181i
\(704\) 78.3837 45.2548i 0.111340 0.0642824i
\(705\) 0 0
\(706\) 71.0000 122.976i 0.100567 0.174186i
\(707\) −53.7401 + 93.0806i −0.0760115 + 0.131656i
\(708\) 0 0
\(709\) −156.000 270.200i −0.220028 0.381100i 0.734788 0.678297i \(-0.237282\pi\)
−0.954816 + 0.297197i \(0.903948\pi\)
\(710\) −254.558 + 254.558i −0.358533 + 0.358533i
\(711\) 0 0
\(712\) 164.000i 0.230337i
\(713\) 79.1960 + 137.171i 0.111074 + 0.192386i
\(714\) 0 0
\(715\) −983.538 + 263.538i −1.37558 + 0.368585i
\(716\) −284.141 164.049i −0.396845 0.229118i
\(717\) 0 0
\(718\) −478.046 + 276.000i −0.665802 + 0.384401i
\(719\) 1148.34i 1.59714i −0.601904 0.798568i \(-0.705591\pi\)
0.601904 0.798568i \(-0.294409\pi\)
\(720\) 0 0
\(721\) 272.000 0.377254
\(722\) −152.028 263.320i −0.210565 0.364709i
\(723\) 0 0
\(724\) −8.00000 + 13.8564i −0.0110497 + 0.0191387i
\(725\) −477.297 + 826.703i −0.658341 + 1.14028i
\(726\) 0 0
\(727\) −405.300 + 234.000i −0.557496 + 0.321871i −0.752140 0.659003i \(-0.770978\pi\)
0.194644 + 0.980874i \(0.437645\pi\)
\(728\) −203.647 −0.279735
\(729\) 0 0
\(730\) −230.000 + 230.000i −0.315068 + 0.315068i
\(731\) −97.9796 + 56.5685i −0.134035 + 0.0773851i
\(732\) 0 0
\(733\) 455.529 + 263.000i 0.621459 + 0.358799i 0.777437 0.628961i \(-0.216520\pi\)
−0.155978 + 0.987761i \(0.549853\pi\)
\(734\) −347.828 200.818i −0.473879 0.273594i
\(735\) 0 0
\(736\) 112.000 + 193.990i 0.152174 + 0.263573i
\(737\) 362.039 0.491233
\(738\) 0 0
\(739\) 344.000 0.465494 0.232747 0.972537i \(-0.425229\pi\)
0.232747 + 0.972537i \(0.425229\pi\)
\(740\) 540.918 + 144.939i 0.730971 + 0.195863i
\(741\) 0 0
\(742\) 20.7846 + 12.0000i 0.0280116 + 0.0161725i
\(743\) 339.411 587.878i 0.456812 0.791221i −0.541978 0.840392i \(-0.682325\pi\)
0.998790 + 0.0491709i \(0.0156579\pi\)
\(744\) 0 0
\(745\) −580.561 155.561i −0.779276 0.208806i
\(746\) 509.117i 0.682462i
\(747\) 0 0
\(748\) 32.0000i 0.0427807i
\(749\) 587.878 339.411i 0.784883 0.453153i
\(750\) 0 0
\(751\) −154.000 + 266.736i −0.205060 + 0.355174i −0.950152 0.311788i \(-0.899072\pi\)
0.745092 + 0.666962i \(0.232406\pi\)
\(752\) −56.5685 + 97.9796i −0.0752241 + 0.130292i
\(753\) 0 0
\(754\) 486.000 + 841.777i 0.644562 + 1.11641i
\(755\) 608.112 + 608.112i 0.805446 + 0.805446i
\(756\) 0 0
\(757\) 610.000i 0.805812i −0.915241 0.402906i \(-0.868000\pi\)
0.915241 0.402906i \(-0.132000\pi\)
\(758\) 226.274 + 391.918i 0.298515 + 0.517043i
\(759\) 0 0
\(760\) 327.846 87.8461i 0.431376 0.115587i
\(761\) −1017.76 587.606i −1.33740 0.772149i −0.350981 0.936383i \(-0.614152\pi\)
−0.986422 + 0.164233i \(0.947485\pi\)
\(762\) 0 0
\(763\) 471.118 272.000i 0.617455 0.356488i
\(764\) 610.940i 0.799660i
\(765\) 0 0
\(766\) −256.000 −0.334204
\(767\) −560.029 969.998i −0.730155 1.26466i
\(768\) 0 0
\(769\) 135.000 233.827i 0.175553 0.304066i −0.764800 0.644268i \(-0.777162\pi\)
0.940352 + 0.340202i \(0.110495\pi\)
\(770\) −309.096 + 82.8221i −0.401424 + 0.107561i
\(771\) 0 0
\(772\) 110.851 64.0000i 0.143590 0.0829016i
\(773\) −267.286 −0.345778 −0.172889 0.984941i \(-0.555310\pi\)
−0.172889 + 0.984941i \(0.555310\pi\)
\(774\) 0 0
\(775\) 100.000i 0.129032i
\(776\) −34.2929 + 19.7990i −0.0441918 + 0.0255142i
\(777\) 0 0
\(778\) 840.045 + 485.000i 1.07975 + 0.623393i
\(779\) 499.696 + 288.500i 0.641458 + 0.370346i
\(780\) 0 0
\(781\) 288.000 + 498.831i 0.368758 + 0.638708i
\(782\) −79.1960 −0.101274
\(783\) 0 0
\(784\) 132.000 0.168367
\(785\) −734.104 196.702i −0.935164 0.250576i
\(786\) 0 0
\(787\) −1316.36 760.000i −1.67263 0.965693i −0.966158 0.257950i \(-0.916953\pi\)
−0.706470 0.707743i \(-0.749714\pi\)
\(788\) 230.517 399.267i 0.292534 0.506684i
\(789\) 0 0
\(790\) 65.8846 245.885i 0.0833982 0.311246i
\(791\) 50.9117i 0.0643637i
\(792\) 0 0
\(793\) 1980.00i 2.49685i
\(794\) 362.524 209.304i 0.456580 0.263607i
\(795\) 0 0
\(796\) −300.000 + 519.615i −0.376884 + 0.652783i
\(797\) 194.454 336.805i 0.243983 0.422591i −0.717862 0.696185i \(-0.754879\pi\)
0.961845 + 0.273594i \(0.0882126\pi\)
\(798\) 0 0
\(799\) −20.0000 34.6410i −0.0250313 0.0433555i
\(800\) 141.421i 0.176777i
\(801\) 0 0
\(802\) 622.000i 0.775561i
\(803\) 260.215 + 450.706i 0.324054 + 0.561278i
\(804\) 0 0
\(805\) −204.974 764.974i −0.254626 0.950279i
\(806\) 88.1816 + 50.9117i 0.109406 + 0.0631659i
\(807\) 0 0
\(808\) 65.8179 38.0000i 0.0814578 0.0470297i
\(809\) 46.6690i 0.0576873i −0.999584 0.0288437i \(-0.990818\pi\)
0.999584 0.0288437i \(-0.00918250\pi\)
\(810\) 0 0
\(811\) 1120.00 1.38101 0.690506 0.723327i \(-0.257388\pi\)
0.690506 + 0.723327i \(0.257388\pi\)
\(812\) 152.735 + 264.545i 0.188097 + 0.325794i
\(813\) 0 0
\(814\) 448.000 775.959i 0.550369 0.953266i
\(815\) −134.586 502.281i −0.165136 0.616296i
\(816\) 0 0
\(817\) 1662.77 960.000i 2.03521 1.17503i
\(818\) −520.431 −0.636223
\(819\) 0 0
\(820\) −170.000 + 170.000i −0.207317 + 0.207317i
\(821\) −1101.05 + 635.689i −1.34110 + 0.774286i −0.986969 0.160909i \(-0.948558\pi\)
−0.354134 + 0.935195i \(0.615224\pi\)
\(822\) 0 0
\(823\) −717.069 414.000i −0.871287 0.503038i −0.00351115 0.999994i \(-0.501118\pi\)
−0.867776 + 0.496956i \(0.834451\pi\)
\(824\) −166.565 96.1665i −0.202142 0.116707i
\(825\) 0 0
\(826\) −176.000 304.841i −0.213075 0.369057i
\(827\) 158.392 0.191526 0.0957629 0.995404i \(-0.469471\pi\)
0.0957629 + 0.995404i \(0.469471\pi\)
\(828\) 0 0
\(829\) −552.000 −0.665862 −0.332931 0.942951i \(-0.608038\pi\)
−0.332931 + 0.942951i \(0.608038\pi\)
\(830\) −10.3528 + 38.6370i −0.0124732 + 0.0465506i
\(831\) 0 0
\(832\) 124.708 + 72.0000i 0.149889 + 0.0865385i
\(833\) −23.3345 + 40.4166i −0.0280126 + 0.0485193i
\(834\) 0 0
\(835\) 263.538 983.538i 0.315615 1.17789i
\(836\) 543.058i 0.649591i
\(837\) 0 0
\(838\) 272.000i 0.324582i
\(839\) −739.746 + 427.092i −0.881700 + 0.509049i −0.871218 0.490896i \(-0.836670\pi\)
−0.0104811 + 0.999945i \(0.503336\pi\)
\(840\) 0 0
\(841\) 308.500 534.338i 0.366825 0.635360i
\(842\) −197.990 + 342.929i −0.235142 + 0.407279i
\(843\) 0 0
\(844\) 264.000 + 457.261i 0.312796 + 0.541779i
\(845\) −548.008 548.008i −0.648530 0.648530i
\(846\) 0 0
\(847\) 28.0000i 0.0330579i
\(848\) −8.48528 14.6969i −0.0100062 0.0173313i
\(849\) 0 0
\(850\) −43.3013 25.0000i −0.0509427 0.0294118i
\(851\) 1920.40 + 1108.74i 2.25664 + 1.30287i
\(852\) 0 0
\(853\) −741.318 + 428.000i −0.869071 + 0.501758i −0.867039 0.498239i \(-0.833980\pi\)
−0.00203173 + 0.999998i \(0.500647\pi\)
\(854\) 622.254i 0.728635i
\(855\) 0 0
\(856\) −480.000 −0.560748
\(857\) 277.893 + 481.325i 0.324263 + 0.561639i 0.981363 0.192164i \(-0.0615506\pi\)
−0.657100 + 0.753803i \(0.728217\pi\)
\(858\) 0 0
\(859\) −236.000 + 408.764i −0.274738 + 0.475860i −0.970069 0.242829i \(-0.921924\pi\)
0.695331 + 0.718690i \(0.255258\pi\)
\(860\) 207.055 + 772.741i 0.240762 + 0.898536i
\(861\) 0 0
\(862\) 117.779 68.0000i 0.136635 0.0788863i
\(863\) −441.235 −0.511280 −0.255640 0.966772i \(-0.582286\pi\)
−0.255640 + 0.966772i \(0.582286\pi\)
\(864\) 0 0
\(865\) 815.000 + 815.000i 0.942197 + 0.942197i
\(866\) 842.624 486.489i 0.973007 0.561766i
\(867\) 0 0
\(868\) 27.7128 + 16.0000i 0.0319272 + 0.0184332i
\(869\) −352.727 203.647i −0.405899 0.234346i
\(870\) 0 0
\(871\) 288.000 + 498.831i 0.330654 + 0.572710i
\(872\) −384.666 −0.441131
\(873\) 0 0
\(874\) 1344.00 1.53776
\(875\) 129.410 482.963i 0.147897 0.551958i
\(876\) 0 0
\(877\) 588.897 + 340.000i 0.671491 + 0.387685i 0.796641 0.604452i \(-0.206608\pi\)
−0.125151 + 0.992138i \(0.539941\pi\)
\(878\) −229.103 + 396.817i −0.260937 + 0.451956i
\(879\) 0 0
\(880\) 218.564 + 58.5641i 0.248368 + 0.0665501i
\(881\) 292.742i 0.332284i 0.986102 + 0.166142i \(0.0531310\pi\)
−0.986102 + 0.166142i \(0.946869\pi\)
\(882\) 0 0
\(883\) 696.000i 0.788222i 0.919063 + 0.394111i \(0.128947\pi\)
−0.919063 + 0.394111i \(0.871053\pi\)
\(884\) −44.0908 + 25.4558i −0.0498765 + 0.0287962i
\(885\) 0 0
\(886\) 228.000 394.908i 0.257336 0.445720i
\(887\) 441.235 764.241i 0.497446 0.861602i −0.502550 0.864548i \(-0.667605\pi\)
0.999996 + 0.00294656i \(0.000937921\pi\)
\(888\) 0 0
\(889\) 56.0000 + 96.9948i 0.0629921 + 0.109106i
\(890\) 289.914 289.914i 0.325746 0.325746i
\(891\) 0 0
\(892\) 632.000i 0.708520i
\(893\) 339.411 + 587.878i 0.380080 + 0.658318i
\(894\) 0 0
\(895\) −212.295 792.295i −0.237201 0.885246i
\(896\) 39.1918 + 22.6274i 0.0437409 + 0.0252538i
\(897\) 0 0
\(898\) −150.688 + 87.0000i −0.167804 + 0.0968820i
\(899\) 152.735i 0.169894i
\(900\) 0 0
\(901\) 6.00000 0.00665927
\(902\) 192.333 + 333.131i 0.213230 + 0.369324i
\(903\) 0 0
\(904\) 18.0000 31.1769i 0.0199115 0.0344877i
\(905\) −38.6370 + 10.3528i −0.0426929 + 0.0114395i
\(906\) 0 0
\(907\) −457.261 + 264.000i −0.504147 + 0.291069i −0.730425 0.682993i \(-0.760678\pi\)
0.226277 + 0.974063i \(0.427344\pi\)
\(908\) −192.333 −0.211821
\(909\) 0 0
\(910\) −360.000 360.000i −0.395604 0.395604i
\(911\) 1381.51 797.616i 1.51648 0.875539i 0.516666 0.856187i \(-0.327173\pi\)
0.999813 0.0193525i \(-0.00616047\pi\)
\(912\) 0 0
\(913\) 55.4256 + 32.0000i 0.0607071 + 0.0350493i
\(914\) 159.217 + 91.9239i 0.174198 + 0.100573i
\(915\) 0 0
\(916\) 8.00000 + 13.8564i 0.00873362 + 0.0151271i
\(917\) 339.411 0.370132
\(918\) 0 0
\(919\) −660.000 −0.718172 −0.359086 0.933304i \(-0.616912\pi\)
−0.359086 + 0.933304i \(0.616912\pi\)
\(920\) −144.939 + 540.918i −0.157542 + 0.587955i
\(921\) 0 0
\(922\) −576.773 333.000i −0.625567 0.361171i
\(923\) −458.205 + 793.635i −0.496430 + 0.859843i
\(924\) 0 0
\(925\) 700.000 + 1212.44i 0.756757 + 1.31074i
\(926\) 627.911i 0.678089i
\(927\) 0 0
\(928\) 216.000i 0.232759i
\(929\) 870.794 502.753i 0.937345 0.541176i 0.0482180 0.998837i \(-0.484646\pi\)
0.889127 + 0.457660i \(0.151312\pi\)
\(930\) 0 0
\(931\) 396.000 685.892i 0.425349 0.736726i
\(932\) 227.688 394.368i 0.244301 0.423141i
\(933\) 0 0
\(934\) −132.000 228.631i −0.141328 0.244787i
\(935\) −56.5685 + 56.5685i −0.0605011 + 0.0605011i
\(936\) 0 0
\(937\) 1568.00i 1.67343i −0.547642 0.836713i \(-0.684474\pi\)
0.547642 0.836713i \(-0.315526\pi\)
\(938\) 90.5097 + 156.767i 0.0964922 + 0.167129i
\(939\) 0 0
\(940\) −273.205 + 73.2051i −0.290644 + 0.0778777i
\(941\) 552.360 + 318.905i 0.586992 + 0.338900i 0.763907 0.645326i \(-0.223278\pi\)
−0.176915 + 0.984226i \(0.556612\pi\)
\(942\) 0 0
\(943\) −824.456 + 476.000i −0.874291 + 0.504772i
\(944\) 248.902i 0.263667i
\(945\) 0 0
\(946\) 1280.00 1.35307
\(947\) −814.587 1410.91i −0.860176 1.48987i −0.871758 0.489936i \(-0.837020\pi\)
0.0115819 0.999933i \(-0.496313\pi\)
\(948\) 0 0
\(949\) −414.000 + 717.069i −0.436249 + 0.755605i
\(950\) 734.847 + 424.264i 0.773523 + 0.446594i
\(951\) 0 0
\(952\) −13.8564 + 8.00000i −0.0145550 + 0.00840336i
\(953\) −914.996 −0.960122 −0.480061 0.877235i \(-0.659385\pi\)
−0.480061 + 0.877235i \(0.659385\pi\)
\(954\) 0 0
\(955\) 1080.00 1080.00i 1.13089 1.13089i
\(956\) 333.131 192.333i 0.348463 0.201185i
\(957\) 0 0
\(958\) −713.605 412.000i −0.744890 0.430063i
\(959\) −44.0908 25.4558i −0.0459758 0.0265442i
\(960\) 0 0
\(961\) 472.500 + 818.394i 0.491675 + 0.851607i
\(962\) 1425.53 1.48184
\(963\) 0 0
\(964\) −256.000 −0.265560
\(965\) 309.096 + 82.8221i 0.320307 + 0.0858260i
\(966\) 0 0
\(967\) 433.013 + 250.000i 0.447790 + 0.258532i 0.706896 0.707317i \(-0.250095\pi\)
−0.259107 + 0.965849i \(0.583428\pi\)
\(968\) 9.89949 17.1464i 0.0102268 0.0177133i
\(969\) 0 0
\(970\) −95.6218 25.6218i −0.0985792 0.0264142i
\(971\) 1221.88i 1.25837i −0.777254 0.629187i \(-0.783388\pi\)
0.777254 0.629187i \(-0.216612\pi\)
\(972\) 0 0
\(973\) 32.0000i 0.0328880i
\(974\) −102.879 + 59.3970i −0.105625 + 0.0609825i
\(975\) 0 0
\(976\) −220.000 + 381.051i −0.225410 + 0.390421i
\(977\) 871.863 1510.11i 0.892388 1.54566i 0.0553827 0.998465i \(-0.482362\pi\)
0.837005 0.547195i \(-0.184305\pi\)
\(978\) 0 0
\(979\) −328.000 568.113i −0.335036 0.580299i
\(980\) 233.345 + 233.345i 0.238107 + 0.238107i
\(981\) 0 0
\(982\) 456.000i 0.464358i
\(983\) 39.5980 + 68.5857i 0.0402828 + 0.0697718i 0.885464 0.464708i \(-0.153841\pi\)
−0.845181 + 0.534480i \(0.820507\pi\)
\(984\) 0 0
\(985\) 1113.31 298.311i 1.13026 0.302854i
\(986\) 66.1362 + 38.1838i 0.0670753 + 0.0387259i
\(987\) 0 0
\(988\) 748.246 432.000i 0.757334 0.437247i
\(989\) 3167.84i 3.20307i
\(990\) 0 0
\(991\) 748.000 0.754793 0.377397 0.926052i \(-0.376819\pi\)
0.377397 + 0.926052i \(0.376819\pi\)
\(992\) −11.3137 19.5959i −0.0114049 0.0197539i
\(993\) 0 0
\(994\) −144.000 + 249.415i −0.144869 + 0.250921i
\(995\) −1448.89 + 388.229i −1.45617 + 0.390179i
\(996\) 0 0
\(997\) 1267.86 732.000i 1.27168 0.734203i 0.296373 0.955072i \(-0.404223\pi\)
0.975303 + 0.220870i \(0.0708896\pi\)
\(998\) 644.881 0.646174
\(999\) 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 810.3.j.d.539.1 8
3.2 odd 2 inner 810.3.j.d.539.4 8
5.4 even 2 inner 810.3.j.d.539.3 8
9.2 odd 6 inner 810.3.j.d.269.3 8
9.4 even 3 90.3.b.a.89.4 yes 4
9.5 odd 6 90.3.b.a.89.1 4
9.7 even 3 inner 810.3.j.d.269.2 8
15.14 odd 2 inner 810.3.j.d.539.2 8
36.23 even 6 720.3.c.c.449.1 4
36.31 odd 6 720.3.c.c.449.4 4
45.4 even 6 90.3.b.a.89.2 yes 4
45.13 odd 12 450.3.d.b.251.1 2
45.14 odd 6 90.3.b.a.89.3 yes 4
45.22 odd 12 450.3.d.e.251.2 2
45.23 even 12 450.3.d.b.251.2 2
45.29 odd 6 inner 810.3.j.d.269.1 8
45.32 even 12 450.3.d.e.251.1 2
45.34 even 6 inner 810.3.j.d.269.4 8
72.5 odd 6 2880.3.c.h.449.4 4
72.13 even 6 2880.3.c.h.449.1 4
72.59 even 6 2880.3.c.a.449.4 4
72.67 odd 6 2880.3.c.a.449.1 4
180.23 odd 12 3600.3.l.i.1601.2 2
180.59 even 6 720.3.c.c.449.3 4
180.67 even 12 3600.3.l.c.1601.1 2
180.103 even 12 3600.3.l.i.1601.1 2
180.139 odd 6 720.3.c.c.449.2 4
180.167 odd 12 3600.3.l.c.1601.2 2
360.59 even 6 2880.3.c.a.449.2 4
360.139 odd 6 2880.3.c.a.449.3 4
360.149 odd 6 2880.3.c.h.449.2 4
360.229 even 6 2880.3.c.h.449.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.3.b.a.89.1 4 9.5 odd 6
90.3.b.a.89.2 yes 4 45.4 even 6
90.3.b.a.89.3 yes 4 45.14 odd 6
90.3.b.a.89.4 yes 4 9.4 even 3
450.3.d.b.251.1 2 45.13 odd 12
450.3.d.b.251.2 2 45.23 even 12
450.3.d.e.251.1 2 45.32 even 12
450.3.d.e.251.2 2 45.22 odd 12
720.3.c.c.449.1 4 36.23 even 6
720.3.c.c.449.2 4 180.139 odd 6
720.3.c.c.449.3 4 180.59 even 6
720.3.c.c.449.4 4 36.31 odd 6
810.3.j.d.269.1 8 45.29 odd 6 inner
810.3.j.d.269.2 8 9.7 even 3 inner
810.3.j.d.269.3 8 9.2 odd 6 inner
810.3.j.d.269.4 8 45.34 even 6 inner
810.3.j.d.539.1 8 1.1 even 1 trivial
810.3.j.d.539.2 8 15.14 odd 2 inner
810.3.j.d.539.3 8 5.4 even 2 inner
810.3.j.d.539.4 8 3.2 odd 2 inner
2880.3.c.a.449.1 4 72.67 odd 6
2880.3.c.a.449.2 4 360.59 even 6
2880.3.c.a.449.3 4 360.139 odd 6
2880.3.c.a.449.4 4 72.59 even 6
2880.3.c.h.449.1 4 72.13 even 6
2880.3.c.h.449.2 4 360.149 odd 6
2880.3.c.h.449.3 4 360.229 even 6
2880.3.c.h.449.4 4 72.5 odd 6
3600.3.l.c.1601.1 2 180.67 even 12
3600.3.l.c.1601.2 2 180.167 odd 12
3600.3.l.i.1601.1 2 180.103 even 12
3600.3.l.i.1601.2 2 180.23 odd 12