Properties

Label 126.3.s.a.107.1
Level $126$
Weight $3$
Character 126.107
Analytic conductor $3.433$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,3,Mod(53,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.53");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.s (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.43325133094\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.1
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 126.107
Dual form 126.3.s.a.53.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-3.67423 - 2.12132i) q^{5} +(-3.50000 + 6.06218i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-3.67423 - 2.12132i) q^{5} +(-3.50000 + 6.06218i) q^{7} -2.82843i q^{8} +(3.00000 + 5.19615i) q^{10} +(-11.0227 + 6.36396i) q^{11} -1.00000 q^{13} +(8.57321 - 4.94975i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-14.6969 + 8.48528i) q^{17} +(-11.5000 + 19.9186i) q^{19} -8.48528i q^{20} +18.0000 q^{22} +(14.6969 + 8.48528i) q^{23} +(-3.50000 - 6.06218i) q^{25} +(1.22474 + 0.707107i) q^{26} -14.0000 q^{28} +33.9411i q^{29} +(-23.5000 - 40.7032i) q^{31} +(4.89898 - 2.82843i) q^{32} +24.0000 q^{34} +(25.7196 - 14.8492i) q^{35} +(27.5000 - 47.6314i) q^{37} +(28.1691 - 16.2635i) q^{38} +(-6.00000 + 10.3923i) q^{40} -46.6690i q^{41} +23.0000 q^{43} +(-22.0454 - 12.7279i) q^{44} +(-12.0000 - 20.7846i) q^{46} +(3.67423 + 2.12132i) q^{47} +(-24.5000 - 42.4352i) q^{49} +9.89949i q^{50} +(-1.00000 - 1.73205i) q^{52} +(-44.0908 + 25.4558i) q^{53} +54.0000 q^{55} +(17.1464 + 9.89949i) q^{56} +(24.0000 - 41.5692i) q^{58} +(73.4847 - 42.4264i) q^{59} +(-52.0000 + 90.0666i) q^{61} +66.4680i q^{62} -8.00000 q^{64} +(3.67423 + 2.12132i) q^{65} +(48.5000 + 84.0045i) q^{67} +(-29.3939 - 16.9706i) q^{68} -42.0000 q^{70} +97.5807i q^{71} +(-32.5000 - 56.2917i) q^{73} +(-67.3610 + 38.8909i) q^{74} -46.0000 q^{76} -89.0955i q^{77} +(-56.5000 + 97.8609i) q^{79} +(14.6969 - 8.48528i) q^{80} +(-33.0000 + 57.1577i) q^{82} -29.6985i q^{83} +72.0000 q^{85} +(-28.1691 - 16.2635i) q^{86} +(18.0000 + 31.1769i) q^{88} +(-117.576 - 67.8823i) q^{89} +(3.50000 - 6.06218i) q^{91} +33.9411i q^{92} +(-3.00000 - 5.19615i) q^{94} +(84.5074 - 48.7904i) q^{95} +104.000 q^{97} +69.2965i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} - 14 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} - 14 q^{7} + 12 q^{10} - 4 q^{13} - 8 q^{16} - 46 q^{19} + 72 q^{22} - 14 q^{25} - 56 q^{28} - 94 q^{31} + 96 q^{34} + 110 q^{37} - 24 q^{40} + 92 q^{43} - 48 q^{46} - 98 q^{49} - 4 q^{52} + 216 q^{55} + 96 q^{58} - 208 q^{61} - 32 q^{64} + 194 q^{67} - 168 q^{70} - 130 q^{73} - 184 q^{76} - 226 q^{79} - 132 q^{82} + 288 q^{85} + 72 q^{88} + 14 q^{91} - 12 q^{94} + 416 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) −3.67423 2.12132i −0.734847 0.424264i 0.0853458 0.996351i \(-0.472801\pi\)
−0.820193 + 0.572087i \(0.806134\pi\)
\(6\) 0 0
\(7\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) 3.00000 + 5.19615i 0.300000 + 0.519615i
\(11\) −11.0227 + 6.36396i −1.00206 + 0.578542i −0.908858 0.417105i \(-0.863045\pi\)
−0.0932057 + 0.995647i \(0.529711\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.0769231 −0.0384615 0.999260i \(-0.512246\pi\)
−0.0384615 + 0.999260i \(0.512246\pi\)
\(14\) 8.57321 4.94975i 0.612372 0.353553i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −14.6969 + 8.48528i −0.864526 + 0.499134i −0.865525 0.500865i \(-0.833015\pi\)
0.000999453 1.00000i \(0.499682\pi\)
\(18\) 0 0
\(19\) −11.5000 + 19.9186i −0.605263 + 1.04835i 0.386747 + 0.922186i \(0.373599\pi\)
−0.992010 + 0.126161i \(0.959735\pi\)
\(20\) 8.48528i 0.424264i
\(21\) 0 0
\(22\) 18.0000 0.818182
\(23\) 14.6969 + 8.48528i 0.638997 + 0.368925i 0.784228 0.620473i \(-0.213059\pi\)
−0.145231 + 0.989398i \(0.546392\pi\)
\(24\) 0 0
\(25\) −3.50000 6.06218i −0.140000 0.242487i
\(26\) 1.22474 + 0.707107i 0.0471056 + 0.0271964i
\(27\) 0 0
\(28\) −14.0000 −0.500000
\(29\) 33.9411i 1.17038i 0.810895 + 0.585192i \(0.198981\pi\)
−0.810895 + 0.585192i \(0.801019\pi\)
\(30\) 0 0
\(31\) −23.5000 40.7032i −0.758065 1.31301i −0.943836 0.330413i \(-0.892812\pi\)
0.185772 0.982593i \(-0.440521\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 24.0000 0.705882
\(35\) 25.7196 14.8492i 0.734847 0.424264i
\(36\) 0 0
\(37\) 27.5000 47.6314i 0.743243 1.28734i −0.207768 0.978178i \(-0.566620\pi\)
0.951011 0.309157i \(-0.100047\pi\)
\(38\) 28.1691 16.2635i 0.741293 0.427986i
\(39\) 0 0
\(40\) −6.00000 + 10.3923i −0.150000 + 0.259808i
\(41\) 46.6690i 1.13827i −0.822244 0.569135i \(-0.807278\pi\)
0.822244 0.569135i \(-0.192722\pi\)
\(42\) 0 0
\(43\) 23.0000 0.534884 0.267442 0.963574i \(-0.413822\pi\)
0.267442 + 0.963574i \(0.413822\pi\)
\(44\) −22.0454 12.7279i −0.501032 0.289271i
\(45\) 0 0
\(46\) −12.0000 20.7846i −0.260870 0.451839i
\(47\) 3.67423 + 2.12132i 0.0781752 + 0.0451345i 0.538578 0.842576i \(-0.318962\pi\)
−0.460403 + 0.887710i \(0.652295\pi\)
\(48\) 0 0
\(49\) −24.5000 42.4352i −0.500000 0.866025i
\(50\) 9.89949i 0.197990i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.0192308 0.0333087i
\(53\) −44.0908 + 25.4558i −0.831902 + 0.480299i −0.854504 0.519446i \(-0.826138\pi\)
0.0226013 + 0.999745i \(0.492805\pi\)
\(54\) 0 0
\(55\) 54.0000 0.981818
\(56\) 17.1464 + 9.89949i 0.306186 + 0.176777i
\(57\) 0 0
\(58\) 24.0000 41.5692i 0.413793 0.716711i
\(59\) 73.4847 42.4264i 1.24550 0.719092i 0.275294 0.961360i \(-0.411225\pi\)
0.970209 + 0.242268i \(0.0778915\pi\)
\(60\) 0 0
\(61\) −52.0000 + 90.0666i −0.852459 + 1.47650i 0.0265234 + 0.999648i \(0.491556\pi\)
−0.878982 + 0.476854i \(0.841777\pi\)
\(62\) 66.4680i 1.07207i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 3.67423 + 2.12132i 0.0565267 + 0.0326357i
\(66\) 0 0
\(67\) 48.5000 + 84.0045i 0.723881 + 1.25380i 0.959433 + 0.281936i \(0.0909767\pi\)
−0.235553 + 0.971862i \(0.575690\pi\)
\(68\) −29.3939 16.9706i −0.432263 0.249567i
\(69\) 0 0
\(70\) −42.0000 −0.600000
\(71\) 97.5807i 1.37438i 0.726479 + 0.687188i \(0.241155\pi\)
−0.726479 + 0.687188i \(0.758845\pi\)
\(72\) 0 0
\(73\) −32.5000 56.2917i −0.445205 0.771119i 0.552861 0.833273i \(-0.313536\pi\)
−0.998067 + 0.0621550i \(0.980203\pi\)
\(74\) −67.3610 + 38.8909i −0.910283 + 0.525552i
\(75\) 0 0
\(76\) −46.0000 −0.605263
\(77\) 89.0955i 1.15708i
\(78\) 0 0
\(79\) −56.5000 + 97.8609i −0.715190 + 1.23875i 0.247696 + 0.968838i \(0.420326\pi\)
−0.962886 + 0.269907i \(0.913007\pi\)
\(80\) 14.6969 8.48528i 0.183712 0.106066i
\(81\) 0 0
\(82\) −33.0000 + 57.1577i −0.402439 + 0.697045i
\(83\) 29.6985i 0.357813i −0.983866 0.178907i \(-0.942744\pi\)
0.983866 0.178907i \(-0.0572560\pi\)
\(84\) 0 0
\(85\) 72.0000 0.847059
\(86\) −28.1691 16.2635i −0.327548 0.189110i
\(87\) 0 0
\(88\) 18.0000 + 31.1769i 0.204545 + 0.354283i
\(89\) −117.576 67.8823i −1.32107 0.762722i −0.337173 0.941443i \(-0.609471\pi\)
−0.983900 + 0.178721i \(0.942804\pi\)
\(90\) 0 0
\(91\) 3.50000 6.06218i 0.0384615 0.0666173i
\(92\) 33.9411i 0.368925i
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.0319149 0.0552782i
\(95\) 84.5074 48.7904i 0.889552 0.513583i
\(96\) 0 0
\(97\) 104.000 1.07216 0.536082 0.844166i \(-0.319904\pi\)
0.536082 + 0.844166i \(0.319904\pi\)
\(98\) 69.2965i 0.707107i
\(99\) 0 0
\(100\) 7.00000 12.1244i 0.0700000 0.121244i
\(101\) −128.598 + 74.2462i −1.27325 + 0.735111i −0.975598 0.219564i \(-0.929537\pi\)
−0.297651 + 0.954675i \(0.596203\pi\)
\(102\) 0 0
\(103\) −59.5000 + 103.057i −0.577670 + 1.00055i 0.418076 + 0.908412i \(0.362705\pi\)
−0.995746 + 0.0921416i \(0.970629\pi\)
\(104\) 2.82843i 0.0271964i
\(105\) 0 0
\(106\) 72.0000 0.679245
\(107\) 102.879 + 59.3970i 0.961482 + 0.555112i 0.896629 0.442783i \(-0.146009\pi\)
0.0648531 + 0.997895i \(0.479342\pi\)
\(108\) 0 0
\(109\) 24.5000 + 42.4352i 0.224771 + 0.389314i 0.956251 0.292549i \(-0.0945034\pi\)
−0.731480 + 0.681863i \(0.761170\pi\)
\(110\) −66.1362 38.1838i −0.601238 0.347125i
\(111\) 0 0
\(112\) −14.0000 24.2487i −0.125000 0.216506i
\(113\) 97.5807i 0.863546i −0.901982 0.431773i \(-0.857888\pi\)
0.901982 0.431773i \(-0.142112\pi\)
\(114\) 0 0
\(115\) −36.0000 62.3538i −0.313043 0.542207i
\(116\) −58.7878 + 33.9411i −0.506791 + 0.292596i
\(117\) 0 0
\(118\) −120.000 −1.01695
\(119\) 118.794i 0.998268i
\(120\) 0 0
\(121\) 20.5000 35.5070i 0.169421 0.293447i
\(122\) 127.373 73.5391i 1.04404 0.602780i
\(123\) 0 0
\(124\) 47.0000 81.4064i 0.379032 0.656503i
\(125\) 135.765i 1.08612i
\(126\) 0 0
\(127\) 113.000 0.889764 0.444882 0.895589i \(-0.353246\pi\)
0.444882 + 0.895589i \(0.353246\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −3.00000 5.19615i −0.0230769 0.0399704i
\(131\) −18.3712 10.6066i −0.140238 0.0809664i 0.428239 0.903665i \(-0.359134\pi\)
−0.568477 + 0.822699i \(0.692467\pi\)
\(132\) 0 0
\(133\) −80.5000 139.430i −0.605263 1.04835i
\(134\) 137.179i 1.02372i
\(135\) 0 0
\(136\) 24.0000 + 41.5692i 0.176471 + 0.305656i
\(137\) 58.7878 33.9411i 0.429108 0.247745i −0.269859 0.962900i \(-0.586977\pi\)
0.698966 + 0.715154i \(0.253644\pi\)
\(138\) 0 0
\(139\) −103.000 −0.741007 −0.370504 0.928831i \(-0.620815\pi\)
−0.370504 + 0.928831i \(0.620815\pi\)
\(140\) 51.4393 + 29.6985i 0.367423 + 0.212132i
\(141\) 0 0
\(142\) 69.0000 119.512i 0.485915 0.841630i
\(143\) 11.0227 6.36396i 0.0770818 0.0445032i
\(144\) 0 0
\(145\) 72.0000 124.708i 0.496552 0.860053i
\(146\) 91.9239i 0.629616i
\(147\) 0 0
\(148\) 110.000 0.743243
\(149\) 146.969 + 84.8528i 0.986372 + 0.569482i 0.904188 0.427135i \(-0.140477\pi\)
0.0821839 + 0.996617i \(0.473811\pi\)
\(150\) 0 0
\(151\) −52.0000 90.0666i −0.344371 0.596468i 0.640868 0.767651i \(-0.278574\pi\)
−0.985239 + 0.171183i \(0.945241\pi\)
\(152\) 56.3383 + 32.5269i 0.370646 + 0.213993i
\(153\) 0 0
\(154\) −63.0000 + 109.119i −0.409091 + 0.708566i
\(155\) 199.404i 1.28648i
\(156\) 0 0
\(157\) −76.0000 131.636i −0.484076 0.838445i 0.515756 0.856735i \(-0.327511\pi\)
−0.999833 + 0.0182904i \(0.994178\pi\)
\(158\) 138.396 79.9031i 0.875925 0.505716i
\(159\) 0 0
\(160\) −24.0000 −0.150000
\(161\) −102.879 + 59.3970i −0.638997 + 0.368925i
\(162\) 0 0
\(163\) −28.0000 + 48.4974i −0.171779 + 0.297530i −0.939042 0.343803i \(-0.888285\pi\)
0.767263 + 0.641333i \(0.221618\pi\)
\(164\) 80.8332 46.6690i 0.492885 0.284567i
\(165\) 0 0
\(166\) −21.0000 + 36.3731i −0.126506 + 0.219115i
\(167\) 4.24264i 0.0254050i −0.999919 0.0127025i \(-0.995957\pi\)
0.999919 0.0127025i \(-0.00404345\pi\)
\(168\) 0 0
\(169\) −168.000 −0.994083
\(170\) −88.1816 50.9117i −0.518715 0.299481i
\(171\) 0 0
\(172\) 23.0000 + 39.8372i 0.133721 + 0.231611i
\(173\) 132.272 + 76.3675i 0.764581 + 0.441431i 0.830938 0.556365i \(-0.187804\pi\)
−0.0663573 + 0.997796i \(0.521138\pi\)
\(174\) 0 0
\(175\) 49.0000 0.280000
\(176\) 50.9117i 0.289271i
\(177\) 0 0
\(178\) 96.0000 + 166.277i 0.539326 + 0.934140i
\(179\) 3.67423 2.12132i 0.0205265 0.0118510i −0.489702 0.871890i \(-0.662894\pi\)
0.510228 + 0.860039i \(0.329561\pi\)
\(180\) 0 0
\(181\) −55.0000 −0.303867 −0.151934 0.988391i \(-0.548550\pi\)
−0.151934 + 0.988391i \(0.548550\pi\)
\(182\) −8.57321 + 4.94975i −0.0471056 + 0.0271964i
\(183\) 0 0
\(184\) 24.0000 41.5692i 0.130435 0.225920i
\(185\) −202.083 + 116.673i −1.09234 + 0.630663i
\(186\) 0 0
\(187\) 108.000 187.061i 0.577540 1.00033i
\(188\) 8.48528i 0.0451345i
\(189\) 0 0
\(190\) −138.000 −0.726316
\(191\) 55.1135 + 31.8198i 0.288552 + 0.166596i 0.637289 0.770625i \(-0.280056\pi\)
−0.348736 + 0.937221i \(0.613389\pi\)
\(192\) 0 0
\(193\) 75.5000 + 130.770i 0.391192 + 0.677564i 0.992607 0.121373i \(-0.0387296\pi\)
−0.601415 + 0.798937i \(0.705396\pi\)
\(194\) −127.373 73.5391i −0.656564 0.379068i
\(195\) 0 0
\(196\) 49.0000 84.8705i 0.250000 0.433013i
\(197\) 16.9706i 0.0861450i 0.999072 + 0.0430725i \(0.0137146\pi\)
−0.999072 + 0.0430725i \(0.986285\pi\)
\(198\) 0 0
\(199\) 80.0000 + 138.564i 0.402010 + 0.696302i 0.993968 0.109667i \(-0.0349784\pi\)
−0.591958 + 0.805969i \(0.701645\pi\)
\(200\) −17.1464 + 9.89949i −0.0857321 + 0.0494975i
\(201\) 0 0
\(202\) 210.000 1.03960
\(203\) −205.757 118.794i −1.01358 0.585192i
\(204\) 0 0
\(205\) −99.0000 + 171.473i −0.482927 + 0.836454i
\(206\) 145.745 84.1457i 0.707498 0.408474i
\(207\) 0 0
\(208\) 2.00000 3.46410i 0.00961538 0.0166543i
\(209\) 292.742i 1.40068i
\(210\) 0 0
\(211\) −208.000 −0.985782 −0.492891 0.870091i \(-0.664060\pi\)
−0.492891 + 0.870091i \(0.664060\pi\)
\(212\) −88.1816 50.9117i −0.415951 0.240149i
\(213\) 0 0
\(214\) −84.0000 145.492i −0.392523 0.679870i
\(215\) −84.5074 48.7904i −0.393058 0.226932i
\(216\) 0 0
\(217\) 329.000 1.51613
\(218\) 69.2965i 0.317874i
\(219\) 0 0
\(220\) 54.0000 + 93.5307i 0.245455 + 0.425140i
\(221\) 14.6969 8.48528i 0.0665020 0.0383949i
\(222\) 0 0
\(223\) −40.0000 −0.179372 −0.0896861 0.995970i \(-0.528586\pi\)
−0.0896861 + 0.995970i \(0.528586\pi\)
\(224\) 39.5980i 0.176777i
\(225\) 0 0
\(226\) −69.0000 + 119.512i −0.305310 + 0.528812i
\(227\) −194.734 + 112.430i −0.857861 + 0.495286i −0.863295 0.504699i \(-0.831603\pi\)
0.00543445 + 0.999985i \(0.498270\pi\)
\(228\) 0 0
\(229\) −188.500 + 326.492i −0.823144 + 1.42573i 0.0801853 + 0.996780i \(0.474449\pi\)
−0.903329 + 0.428947i \(0.858885\pi\)
\(230\) 101.823i 0.442710i
\(231\) 0 0
\(232\) 96.0000 0.413793
\(233\) −297.613 171.827i −1.27731 0.737455i −0.300956 0.953638i \(-0.597306\pi\)
−0.976353 + 0.216183i \(0.930639\pi\)
\(234\) 0 0
\(235\) −9.00000 15.5885i −0.0382979 0.0663339i
\(236\) 146.969 + 84.8528i 0.622752 + 0.359546i
\(237\) 0 0
\(238\) −84.0000 + 145.492i −0.352941 + 0.611312i
\(239\) 12.7279i 0.0532549i −0.999645 0.0266275i \(-0.991523\pi\)
0.999645 0.0266275i \(-0.00847678\pi\)
\(240\) 0 0
\(241\) 65.0000 + 112.583i 0.269710 + 0.467151i 0.968787 0.247896i \(-0.0797390\pi\)
−0.699077 + 0.715046i \(0.746406\pi\)
\(242\) −50.2145 + 28.9914i −0.207498 + 0.119799i
\(243\) 0 0
\(244\) −208.000 −0.852459
\(245\) 207.889i 0.848528i
\(246\) 0 0
\(247\) 11.5000 19.9186i 0.0465587 0.0806420i
\(248\) −115.126 + 66.4680i −0.464218 + 0.268016i
\(249\) 0 0
\(250\) 96.0000 166.277i 0.384000 0.665108i
\(251\) 50.9117i 0.202835i −0.994844 0.101418i \(-0.967662\pi\)
0.994844 0.101418i \(-0.0323379\pi\)
\(252\) 0 0
\(253\) −216.000 −0.853755
\(254\) −138.396 79.9031i −0.544867 0.314579i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 407.840 + 235.467i 1.58693 + 0.916212i 0.993810 + 0.111096i \(0.0354360\pi\)
0.593117 + 0.805117i \(0.297897\pi\)
\(258\) 0 0
\(259\) 192.500 + 333.420i 0.743243 + 1.28734i
\(260\) 8.48528i 0.0326357i
\(261\) 0 0
\(262\) 15.0000 + 25.9808i 0.0572519 + 0.0991632i
\(263\) −88.1816 + 50.9117i −0.335291 + 0.193581i −0.658188 0.752854i \(-0.728677\pi\)
0.322897 + 0.946434i \(0.395343\pi\)
\(264\) 0 0
\(265\) 216.000 0.815094
\(266\) 227.688i 0.855971i
\(267\) 0 0
\(268\) −97.0000 + 168.009i −0.361940 + 0.626899i
\(269\) 246.174 142.128i 0.915144 0.528359i 0.0330613 0.999453i \(-0.489474\pi\)
0.882083 + 0.471095i \(0.156141\pi\)
\(270\) 0 0
\(271\) 260.000 450.333i 0.959410 1.66175i 0.235471 0.971881i \(-0.424337\pi\)
0.723938 0.689865i \(-0.242330\pi\)
\(272\) 67.8823i 0.249567i
\(273\) 0 0
\(274\) −96.0000 −0.350365
\(275\) 77.1589 + 44.5477i 0.280578 + 0.161992i
\(276\) 0 0
\(277\) −56.5000 97.8609i −0.203971 0.353288i 0.745833 0.666133i \(-0.232052\pi\)
−0.949804 + 0.312844i \(0.898718\pi\)
\(278\) 126.149 + 72.8320i 0.453772 + 0.261986i
\(279\) 0 0
\(280\) −42.0000 72.7461i −0.150000 0.259808i
\(281\) 458.205i 1.63062i −0.579022 0.815312i \(-0.696566\pi\)
0.579022 0.815312i \(-0.303434\pi\)
\(282\) 0 0
\(283\) −44.5000 77.0763i −0.157244 0.272354i 0.776630 0.629957i \(-0.216928\pi\)
−0.933874 + 0.357603i \(0.883594\pi\)
\(284\) −169.015 + 97.5807i −0.595123 + 0.343594i
\(285\) 0 0
\(286\) −18.0000 −0.0629371
\(287\) 282.916 + 163.342i 0.985770 + 0.569135i
\(288\) 0 0
\(289\) −0.500000 + 0.866025i −0.00173010 + 0.00299663i
\(290\) −176.363 + 101.823i −0.608149 + 0.351115i
\(291\) 0 0
\(292\) 65.0000 112.583i 0.222603 0.385559i
\(293\) 67.8823i 0.231680i −0.993268 0.115840i \(-0.963044\pi\)
0.993268 0.115840i \(-0.0369560\pi\)
\(294\) 0 0
\(295\) −360.000 −1.22034
\(296\) −134.722 77.7817i −0.455142 0.262776i
\(297\) 0 0
\(298\) −120.000 207.846i −0.402685 0.697470i
\(299\) −14.6969 8.48528i −0.0491536 0.0283789i
\(300\) 0 0
\(301\) −80.5000 + 139.430i −0.267442 + 0.463223i
\(302\) 147.078i 0.487014i
\(303\) 0 0
\(304\) −46.0000 79.6743i −0.151316 0.262087i
\(305\) 382.120 220.617i 1.25285 0.723335i
\(306\) 0 0
\(307\) 233.000 0.758958 0.379479 0.925200i \(-0.376103\pi\)
0.379479 + 0.925200i \(0.376103\pi\)
\(308\) 154.318 89.0955i 0.501032 0.289271i
\(309\) 0 0
\(310\) 141.000 244.219i 0.454839 0.787804i
\(311\) −216.780 + 125.158i −0.697041 + 0.402437i −0.806244 0.591582i \(-0.798503\pi\)
0.109203 + 0.994019i \(0.465170\pi\)
\(312\) 0 0
\(313\) 75.5000 130.770i 0.241214 0.417795i −0.719846 0.694133i \(-0.755788\pi\)
0.961060 + 0.276338i \(0.0891211\pi\)
\(314\) 214.960i 0.684587i
\(315\) 0 0
\(316\) −226.000 −0.715190
\(317\) 352.727 + 203.647i 1.11270 + 0.642419i 0.939528 0.342472i \(-0.111264\pi\)
0.173174 + 0.984891i \(0.444598\pi\)
\(318\) 0 0
\(319\) −216.000 374.123i −0.677116 1.17280i
\(320\) 29.3939 + 16.9706i 0.0918559 + 0.0530330i
\(321\) 0 0
\(322\) 168.000 0.521739
\(323\) 390.323i 1.20843i
\(324\) 0 0
\(325\) 3.50000 + 6.06218i 0.0107692 + 0.0186529i
\(326\) 68.5857 39.5980i 0.210386 0.121466i
\(327\) 0 0
\(328\) −132.000 −0.402439
\(329\) −25.7196 + 14.8492i −0.0781752 + 0.0451345i
\(330\) 0 0
\(331\) 36.5000 63.2199i 0.110272 0.190997i −0.805608 0.592449i \(-0.798161\pi\)
0.915880 + 0.401452i \(0.131495\pi\)
\(332\) 51.4393 29.6985i 0.154938 0.0894533i
\(333\) 0 0
\(334\) −3.00000 + 5.19615i −0.00898204 + 0.0155573i
\(335\) 411.536i 1.22847i
\(336\) 0 0
\(337\) 527.000 1.56380 0.781899 0.623405i \(-0.214251\pi\)
0.781899 + 0.623405i \(0.214251\pi\)
\(338\) 205.757 + 118.794i 0.608749 + 0.351461i
\(339\) 0 0
\(340\) 72.0000 + 124.708i 0.211765 + 0.366787i
\(341\) 518.067 + 299.106i 1.51926 + 0.877144i
\(342\) 0 0
\(343\) 343.000 1.00000
\(344\) 65.0538i 0.189110i
\(345\) 0 0
\(346\) −108.000 187.061i −0.312139 0.540640i
\(347\) −367.423 + 212.132i −1.05886 + 0.611332i −0.925116 0.379685i \(-0.876032\pi\)
−0.133741 + 0.991016i \(0.542699\pi\)
\(348\) 0 0
\(349\) −112.000 −0.320917 −0.160458 0.987043i \(-0.551297\pi\)
−0.160458 + 0.987043i \(0.551297\pi\)
\(350\) −60.0125 34.6482i −0.171464 0.0989949i
\(351\) 0 0
\(352\) −36.0000 + 62.3538i −0.102273 + 0.177142i
\(353\) −268.219 + 154.856i −0.759828 + 0.438687i −0.829234 0.558902i \(-0.811223\pi\)
0.0694063 + 0.997588i \(0.477890\pi\)
\(354\) 0 0
\(355\) 207.000 358.535i 0.583099 1.00996i
\(356\) 271.529i 0.762722i
\(357\) 0 0
\(358\) −6.00000 −0.0167598
\(359\) −440.908 254.558i −1.22816 0.709076i −0.261512 0.965200i \(-0.584221\pi\)
−0.966644 + 0.256124i \(0.917555\pi\)
\(360\) 0 0
\(361\) −84.0000 145.492i −0.232687 0.403026i
\(362\) 67.3610 + 38.8909i 0.186080 + 0.107433i
\(363\) 0 0
\(364\) 14.0000 0.0384615
\(365\) 275.772i 0.755539i
\(366\) 0 0
\(367\) 159.500 + 276.262i 0.434605 + 0.752758i 0.997263 0.0739317i \(-0.0235547\pi\)
−0.562658 + 0.826689i \(0.690221\pi\)
\(368\) −58.7878 + 33.9411i −0.159749 + 0.0922313i
\(369\) 0 0
\(370\) 330.000 0.891892
\(371\) 356.382i 0.960598i
\(372\) 0 0
\(373\) −104.500 + 180.999i −0.280161 + 0.485253i −0.971424 0.237350i \(-0.923721\pi\)
0.691263 + 0.722603i \(0.257054\pi\)
\(374\) −264.545 + 152.735i −0.707339 + 0.408383i
\(375\) 0 0
\(376\) 6.00000 10.3923i 0.0159574 0.0276391i
\(377\) 33.9411i 0.0900295i
\(378\) 0 0
\(379\) −433.000 −1.14248 −0.571240 0.820783i \(-0.693537\pi\)
−0.571240 + 0.820783i \(0.693537\pi\)
\(380\) 169.015 + 97.5807i 0.444776 + 0.256791i
\(381\) 0 0
\(382\) −45.0000 77.9423i −0.117801 0.204037i
\(383\) −338.030 195.161i −0.882584 0.509560i −0.0110743 0.999939i \(-0.503525\pi\)
−0.871509 + 0.490379i \(0.836858\pi\)
\(384\) 0 0
\(385\) −189.000 + 327.358i −0.490909 + 0.850279i
\(386\) 213.546i 0.553229i
\(387\) 0 0
\(388\) 104.000 + 180.133i 0.268041 + 0.464261i
\(389\) 319.658 184.555i 0.821744 0.474434i −0.0292735 0.999571i \(-0.509319\pi\)
0.851018 + 0.525137i \(0.175986\pi\)
\(390\) 0 0
\(391\) −288.000 −0.736573
\(392\) −120.025 + 69.2965i −0.306186 + 0.176777i
\(393\) 0 0
\(394\) 12.0000 20.7846i 0.0304569 0.0527528i
\(395\) 415.189 239.709i 1.05111 0.606859i
\(396\) 0 0
\(397\) −56.5000 + 97.8609i −0.142317 + 0.246501i −0.928369 0.371660i \(-0.878789\pi\)
0.786052 + 0.618161i \(0.212122\pi\)
\(398\) 226.274i 0.568528i
\(399\) 0 0
\(400\) 28.0000 0.0700000
\(401\) −308.636 178.191i −0.769665 0.444366i 0.0630900 0.998008i \(-0.479904\pi\)
−0.832755 + 0.553641i \(0.813238\pi\)
\(402\) 0 0
\(403\) 23.5000 + 40.7032i 0.0583127 + 0.101000i
\(404\) −257.196 148.492i −0.636625 0.367556i
\(405\) 0 0
\(406\) 168.000 + 290.985i 0.413793 + 0.716711i
\(407\) 700.036i 1.71999i
\(408\) 0 0
\(409\) 159.500 + 276.262i 0.389976 + 0.675457i 0.992446 0.122684i \(-0.0391501\pi\)
−0.602470 + 0.798141i \(0.705817\pi\)
\(410\) 242.499 140.007i 0.591462 0.341481i
\(411\) 0 0
\(412\) −238.000 −0.577670
\(413\) 593.970i 1.43818i
\(414\) 0 0
\(415\) −63.0000 + 109.119i −0.151807 + 0.262938i
\(416\) −4.89898 + 2.82843i −0.0117764 + 0.00679910i
\(417\) 0 0
\(418\) −207.000 + 358.535i −0.495215 + 0.857738i
\(419\) 767.918i 1.83274i 0.400333 + 0.916370i \(0.368895\pi\)
−0.400333 + 0.916370i \(0.631105\pi\)
\(420\) 0 0
\(421\) 65.0000 0.154394 0.0771971 0.997016i \(-0.475403\pi\)
0.0771971 + 0.997016i \(0.475403\pi\)
\(422\) 254.747 + 147.078i 0.603666 + 0.348527i
\(423\) 0 0
\(424\) 72.0000 + 124.708i 0.169811 + 0.294122i
\(425\) 102.879 + 59.3970i 0.242067 + 0.139758i
\(426\) 0 0
\(427\) −364.000 630.466i −0.852459 1.47650i
\(428\) 237.588i 0.555112i
\(429\) 0 0
\(430\) 69.0000 + 119.512i 0.160465 + 0.277934i
\(431\) −415.189 + 239.709i −0.963314 + 0.556170i −0.897192 0.441642i \(-0.854396\pi\)
−0.0661229 + 0.997811i \(0.521063\pi\)
\(432\) 0 0
\(433\) −367.000 −0.847575 −0.423788 0.905762i \(-0.639300\pi\)
−0.423788 + 0.905762i \(0.639300\pi\)
\(434\) −402.941 232.638i −0.928436 0.536033i
\(435\) 0 0
\(436\) −49.0000 + 84.8705i −0.112385 + 0.194657i
\(437\) −338.030 + 195.161i −0.773523 + 0.446594i
\(438\) 0 0
\(439\) −268.000 + 464.190i −0.610478 + 1.05738i 0.380681 + 0.924706i \(0.375689\pi\)
−0.991160 + 0.132673i \(0.957644\pi\)
\(440\) 152.735i 0.347125i
\(441\) 0 0
\(442\) −24.0000 −0.0542986
\(443\) −73.4847 42.4264i −0.165880 0.0957707i 0.414762 0.909930i \(-0.363865\pi\)
−0.580642 + 0.814159i \(0.697198\pi\)
\(444\) 0 0
\(445\) 288.000 + 498.831i 0.647191 + 1.12097i
\(446\) 48.9898 + 28.2843i 0.109843 + 0.0634176i
\(447\) 0 0
\(448\) 28.0000 48.4974i 0.0625000 0.108253i
\(449\) 615.183i 1.37012i −0.728488 0.685059i \(-0.759776\pi\)
0.728488 0.685059i \(-0.240224\pi\)
\(450\) 0 0
\(451\) 297.000 + 514.419i 0.658537 + 1.14062i
\(452\) 169.015 97.5807i 0.373927 0.215887i
\(453\) 0 0
\(454\) 318.000 0.700441
\(455\) −25.7196 + 14.8492i −0.0565267 + 0.0326357i
\(456\) 0 0
\(457\) 231.500 400.970i 0.506565 0.877396i −0.493407 0.869799i \(-0.664249\pi\)
0.999971 0.00759675i \(-0.00241814\pi\)
\(458\) 461.729 266.579i 1.00814 0.582051i
\(459\) 0 0
\(460\) 72.0000 124.708i 0.156522 0.271104i
\(461\) 271.529i 0.589000i 0.955651 + 0.294500i \(0.0951531\pi\)
−0.955651 + 0.294500i \(0.904847\pi\)
\(462\) 0 0
\(463\) 47.0000 0.101512 0.0507559 0.998711i \(-0.483837\pi\)
0.0507559 + 0.998711i \(0.483837\pi\)
\(464\) −117.576 67.8823i −0.253395 0.146298i
\(465\) 0 0
\(466\) 243.000 + 420.888i 0.521459 + 0.903194i
\(467\) −642.991 371.231i −1.37685 0.794927i −0.385075 0.922885i \(-0.625824\pi\)
−0.991780 + 0.127958i \(0.959158\pi\)
\(468\) 0 0
\(469\) −679.000 −1.44776
\(470\) 25.4558i 0.0541614i
\(471\) 0 0
\(472\) −120.000 207.846i −0.254237 0.440352i
\(473\) −253.522 + 146.371i −0.535988 + 0.309453i
\(474\) 0 0
\(475\) 161.000 0.338947
\(476\) 205.757 118.794i 0.432263 0.249567i
\(477\) 0 0
\(478\) −9.00000 + 15.5885i −0.0188285 + 0.0326118i
\(479\) 367.423 212.132i 0.767064 0.442864i −0.0647625 0.997901i \(-0.520629\pi\)
0.831826 + 0.555036i \(0.187296\pi\)
\(480\) 0 0
\(481\) −27.5000 + 47.6314i −0.0571726 + 0.0990258i
\(482\) 183.848i 0.381427i
\(483\) 0 0
\(484\) 82.0000 0.169421
\(485\) −382.120 220.617i −0.787877 0.454881i
\(486\) 0 0
\(487\) −119.500 206.980i −0.245380 0.425010i 0.716858 0.697219i \(-0.245579\pi\)
−0.962238 + 0.272208i \(0.912246\pi\)
\(488\) 254.747 + 147.078i 0.522022 + 0.301390i
\(489\) 0 0
\(490\) 147.000 254.611i 0.300000 0.519615i
\(491\) 203.647i 0.414759i 0.978261 + 0.207380i \(0.0664935\pi\)
−0.978261 + 0.207380i \(0.933506\pi\)
\(492\) 0 0
\(493\) −288.000 498.831i −0.584178 1.01183i
\(494\) −28.1691 + 16.2635i −0.0570225 + 0.0329220i
\(495\) 0 0
\(496\) 188.000 0.379032
\(497\) −591.552 341.533i −1.19025 0.687188i
\(498\) 0 0
\(499\) 24.5000 42.4352i 0.0490982 0.0850406i −0.840432 0.541917i \(-0.817699\pi\)
0.889530 + 0.456877i \(0.151032\pi\)
\(500\) −235.151 + 135.765i −0.470302 + 0.271529i
\(501\) 0 0
\(502\) −36.0000 + 62.3538i −0.0717131 + 0.124211i
\(503\) 589.727i 1.17242i 0.810159 + 0.586210i \(0.199381\pi\)
−0.810159 + 0.586210i \(0.800619\pi\)
\(504\) 0 0
\(505\) 630.000 1.24752
\(506\) 264.545 + 152.735i 0.522816 + 0.301848i
\(507\) 0 0
\(508\) 113.000 + 195.722i 0.222441 + 0.385279i
\(509\) 209.431 + 120.915i 0.411457 + 0.237555i 0.691415 0.722457i \(-0.256987\pi\)
−0.279959 + 0.960012i \(0.590321\pi\)
\(510\) 0 0
\(511\) 455.000 0.890411
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −333.000 576.773i −0.647860 1.12213i
\(515\) 437.234 252.437i 0.848998 0.490169i
\(516\) 0 0
\(517\) −54.0000 −0.104449
\(518\) 544.472i 1.05110i
\(519\) 0 0
\(520\) 6.00000 10.3923i 0.0115385 0.0199852i
\(521\) 734.847 424.264i 1.41045 0.814326i 0.415024 0.909811i \(-0.363773\pi\)
0.995431 + 0.0954841i \(0.0304399\pi\)
\(522\) 0 0
\(523\) 195.500 338.616i 0.373805 0.647449i −0.616342 0.787478i \(-0.711386\pi\)
0.990147 + 0.140029i \(0.0447196\pi\)
\(524\) 42.4264i 0.0809664i
\(525\) 0 0
\(526\) 144.000 0.273764
\(527\) 690.756 + 398.808i 1.31073 + 0.756752i
\(528\) 0 0
\(529\) −120.500 208.712i −0.227788 0.394541i
\(530\) −264.545 152.735i −0.499141 0.288179i
\(531\) 0 0
\(532\) 161.000 278.860i 0.302632 0.524173i
\(533\) 46.6690i 0.0875592i
\(534\) 0 0
\(535\) −252.000 436.477i −0.471028 0.815844i
\(536\) 237.601 137.179i 0.443285 0.255930i
\(537\) 0 0
\(538\) −402.000 −0.747212
\(539\) 540.112 + 311.834i 1.00206 + 0.578542i
\(540\) 0 0
\(541\) 36.5000 63.2199i 0.0674677 0.116857i −0.830318 0.557289i \(-0.811841\pi\)
0.897786 + 0.440432i \(0.145175\pi\)
\(542\) −636.867 + 367.696i −1.17503 + 0.678405i
\(543\) 0 0
\(544\) −48.0000 + 83.1384i −0.0882353 + 0.152828i
\(545\) 207.889i 0.381448i
\(546\) 0 0
\(547\) 32.0000 0.0585009 0.0292505 0.999572i \(-0.490688\pi\)
0.0292505 + 0.999572i \(0.490688\pi\)
\(548\) 117.576 + 67.8823i 0.214554 + 0.123873i
\(549\) 0 0
\(550\) −63.0000 109.119i −0.114545 0.198399i
\(551\) −676.059 390.323i −1.22697 0.708390i
\(552\) 0 0
\(553\) −395.500 685.026i −0.715190 1.23875i
\(554\) 159.806i 0.288459i
\(555\) 0 0
\(556\) −103.000 178.401i −0.185252 0.320866i
\(557\) −40.4166 + 23.3345i −0.0725612 + 0.0418932i −0.535842 0.844319i \(-0.680006\pi\)
0.463280 + 0.886212i \(0.346672\pi\)
\(558\) 0 0
\(559\) −23.0000 −0.0411449
\(560\) 118.794i 0.212132i
\(561\) 0 0
\(562\) −324.000 + 561.184i −0.576512 + 0.998549i
\(563\) 767.915 443.356i 1.36397 0.787488i 0.373820 0.927501i \(-0.378048\pi\)
0.990150 + 0.140013i \(0.0447144\pi\)
\(564\) 0 0
\(565\) −207.000 + 358.535i −0.366372 + 0.634574i
\(566\) 125.865i 0.222376i
\(567\) 0 0
\(568\) 276.000 0.485915
\(569\) 275.568 + 159.099i 0.484302 + 0.279612i 0.722207 0.691677i \(-0.243128\pi\)
−0.237906 + 0.971288i \(0.576461\pi\)
\(570\) 0 0
\(571\) 267.500 + 463.324i 0.468476 + 0.811425i 0.999351 0.0360256i \(-0.0114698\pi\)
−0.530875 + 0.847450i \(0.678136\pi\)
\(572\) 22.0454 + 12.7279i 0.0385409 + 0.0222516i
\(573\) 0 0
\(574\) −231.000 400.104i −0.402439 0.697045i
\(575\) 118.794i 0.206598i
\(576\) 0 0
\(577\) −452.500 783.753i −0.784229 1.35832i −0.929459 0.368926i \(-0.879726\pi\)
0.145230 0.989398i \(-0.453608\pi\)
\(578\) 1.22474 0.707107i 0.00211894 0.00122337i
\(579\) 0 0
\(580\) 288.000 0.496552
\(581\) 180.037 + 103.945i 0.309875 + 0.178907i
\(582\) 0 0
\(583\) 324.000 561.184i 0.555746 0.962581i
\(584\) −159.217 + 91.9239i −0.272632 + 0.157404i
\(585\) 0 0
\(586\) −48.0000 + 83.1384i −0.0819113 + 0.141874i
\(587\) 576.999i 0.982963i 0.870888 + 0.491481i \(0.163544\pi\)
−0.870888 + 0.491481i \(0.836456\pi\)
\(588\) 0 0
\(589\) 1081.00 1.83531
\(590\) 440.908 + 254.558i 0.747302 + 0.431455i
\(591\) 0 0
\(592\) 110.000 + 190.526i 0.185811 + 0.321834i
\(593\) −481.325 277.893i −0.811677 0.468622i 0.0358606 0.999357i \(-0.488583\pi\)
−0.847538 + 0.530735i \(0.821916\pi\)
\(594\) 0 0
\(595\) −252.000 + 436.477i −0.423529 + 0.733574i
\(596\) 339.411i 0.569482i
\(597\) 0 0
\(598\) 12.0000 + 20.7846i 0.0200669 + 0.0347569i
\(599\) 176.363 101.823i 0.294429 0.169989i −0.345508 0.938416i \(-0.612293\pi\)
0.639938 + 0.768427i \(0.278960\pi\)
\(600\) 0 0
\(601\) 143.000 0.237937 0.118968 0.992898i \(-0.462041\pi\)
0.118968 + 0.992898i \(0.462041\pi\)
\(602\) 197.184 113.844i 0.327548 0.189110i
\(603\) 0 0
\(604\) 104.000 180.133i 0.172185 0.298234i
\(605\) −150.644 + 86.9741i −0.248998 + 0.143759i
\(606\) 0 0
\(607\) −299.500 + 518.749i −0.493410 + 0.854612i −0.999971 0.00759259i \(-0.997583\pi\)
0.506561 + 0.862204i \(0.330917\pi\)
\(608\) 130.108i 0.213993i
\(609\) 0 0
\(610\) −624.000 −1.02295
\(611\) −3.67423 2.12132i −0.00601348 0.00347188i
\(612\) 0 0
\(613\) 152.000 + 263.272i 0.247961 + 0.429481i 0.962960 0.269645i \(-0.0869062\pi\)
−0.714999 + 0.699125i \(0.753573\pi\)
\(614\) −285.366 164.756i −0.464765 0.268332i
\(615\) 0 0
\(616\) −252.000 −0.409091
\(617\) 292.742i 0.474461i −0.971453 0.237230i \(-0.923760\pi\)
0.971453 0.237230i \(-0.0762396\pi\)
\(618\) 0 0
\(619\) 171.500 + 297.047i 0.277060 + 0.479882i 0.970653 0.240486i \(-0.0773067\pi\)
−0.693593 + 0.720367i \(0.743973\pi\)
\(620\) −345.378 + 199.404i −0.557061 + 0.321620i
\(621\) 0 0
\(622\) 354.000 0.569132
\(623\) 823.029 475.176i 1.32107 0.762722i
\(624\) 0 0
\(625\) 200.500 347.276i 0.320800 0.555642i
\(626\) −184.936 + 106.773i −0.295426 + 0.170564i
\(627\) 0 0
\(628\) 152.000 263.272i 0.242038 0.419222i
\(629\) 933.381i 1.48391i
\(630\) 0 0
\(631\) 272.000 0.431062 0.215531 0.976497i \(-0.430852\pi\)
0.215531 + 0.976497i \(0.430852\pi\)
\(632\) 276.792 + 159.806i 0.437963 + 0.252858i
\(633\) 0 0
\(634\) −288.000 498.831i −0.454259 0.786799i
\(635\) −415.189 239.709i −0.653840 0.377495i
\(636\) 0 0
\(637\) 24.5000 + 42.4352i 0.0384615 + 0.0666173i
\(638\) 610.940i 0.957587i
\(639\) 0 0
\(640\) −24.0000 41.5692i −0.0375000 0.0649519i
\(641\) −367.423 + 212.132i −0.573204 + 0.330939i −0.758428 0.651757i \(-0.774032\pi\)
0.185224 + 0.982696i \(0.440699\pi\)
\(642\) 0 0
\(643\) −679.000 −1.05599 −0.527994 0.849248i \(-0.677056\pi\)
−0.527994 + 0.849248i \(0.677056\pi\)
\(644\) −205.757 118.794i −0.319499 0.184463i
\(645\) 0 0
\(646\) −276.000 + 478.046i −0.427245 + 0.740009i
\(647\) 834.051 481.540i 1.28911 0.744265i 0.310611 0.950537i \(-0.399466\pi\)
0.978495 + 0.206272i \(0.0661331\pi\)
\(648\) 0 0
\(649\) −540.000 + 935.307i −0.832049 + 1.44115i
\(650\) 9.89949i 0.0152300i
\(651\) 0 0
\(652\) −112.000 −0.171779
\(653\) −775.264 447.599i −1.18723 0.685450i −0.229557 0.973295i \(-0.573728\pi\)
−0.957677 + 0.287846i \(0.907061\pi\)
\(654\) 0 0
\(655\) 45.0000 + 77.9423i 0.0687023 + 0.118996i
\(656\) 161.666 + 93.3381i 0.246443 + 0.142284i
\(657\) 0 0
\(658\) 42.0000 0.0638298
\(659\) 16.9706i 0.0257520i 0.999917 + 0.0128760i \(0.00409867\pi\)
−0.999917 + 0.0128760i \(0.995901\pi\)
\(660\) 0 0
\(661\) 216.500 + 374.989i 0.327534 + 0.567306i 0.982022 0.188767i \(-0.0604491\pi\)
−0.654488 + 0.756072i \(0.727116\pi\)
\(662\) −89.4064 + 51.6188i −0.135055 + 0.0779740i
\(663\) 0 0
\(664\) −84.0000 −0.126506
\(665\) 683.065i 1.02717i
\(666\) 0 0
\(667\) −288.000 + 498.831i −0.431784 + 0.747872i
\(668\) 7.34847 4.24264i 0.0110007 0.00635126i
\(669\) 0 0
\(670\) −291.000 + 504.027i −0.434328 + 0.752279i
\(671\) 1323.70i 1.97273i
\(672\) 0 0
\(673\) 737.000 1.09510 0.547548 0.836774i \(-0.315561\pi\)
0.547548 + 0.836774i \(0.315561\pi\)
\(674\) −645.441 372.645i −0.957627 0.552886i
\(675\) 0 0
\(676\) −168.000 290.985i −0.248521 0.430450i
\(677\) −117.576 67.8823i −0.173671 0.100269i 0.410644 0.911796i \(-0.365304\pi\)
−0.584316 + 0.811526i \(0.698637\pi\)
\(678\) 0 0
\(679\) −364.000 + 630.466i −0.536082 + 0.928522i
\(680\) 203.647i 0.299481i
\(681\) 0 0
\(682\) −423.000 732.657i −0.620235 1.07428i
\(683\) −1102.27 + 636.396i −1.61387 + 0.931766i −0.625403 + 0.780302i \(0.715065\pi\)
−0.988463 + 0.151464i \(0.951601\pi\)
\(684\) 0 0
\(685\) −288.000 −0.420438
\(686\) −420.087 242.538i −0.612372 0.353553i
\(687\) 0 0
\(688\) −46.0000 + 79.6743i −0.0668605 + 0.115806i
\(689\) 44.0908 25.4558i 0.0639925 0.0369461i
\(690\) 0 0
\(691\) 123.500 213.908i 0.178726 0.309563i −0.762718 0.646731i \(-0.776136\pi\)
0.941445 + 0.337168i \(0.109469\pi\)
\(692\) 305.470i 0.441431i
\(693\) 0 0
\(694\) 600.000 0.864553
\(695\) 378.446 + 218.496i 0.544527 + 0.314383i
\(696\) 0 0
\(697\) 396.000 + 685.892i 0.568149 + 0.984063i
\(698\) 137.171 + 79.1960i 0.196521 + 0.113461i
\(699\) 0 0
\(700\) 49.0000 + 84.8705i 0.0700000 + 0.121244i
\(701\) 322.441i 0.459972i −0.973194 0.229986i \(-0.926132\pi\)
0.973194 0.229986i \(-0.0738681\pi\)
\(702\) 0 0
\(703\) 632.500 + 1095.52i 0.899716 + 1.55835i
\(704\) 88.1816 50.9117i 0.125258 0.0723177i
\(705\) 0 0
\(706\) 438.000 0.620397
\(707\) 1039.45i 1.47022i
\(708\) 0 0
\(709\) 524.000 907.595i 0.739069 1.28011i −0.213846 0.976867i \(-0.568599\pi\)
0.952915 0.303238i \(-0.0980677\pi\)
\(710\) −507.044 + 292.742i −0.714147 + 0.412313i
\(711\) 0 0
\(712\) −192.000 + 332.554i −0.269663 + 0.467070i
\(713\) 797.616i 1.11868i
\(714\) 0 0
\(715\) −54.0000 −0.0755245
\(716\) 7.34847 + 4.24264i 0.0102632 + 0.00592548i
\(717\) 0 0
\(718\) 360.000 + 623.538i 0.501393 + 0.868438i
\(719\) 216.780 + 125.158i 0.301502 + 0.174072i 0.643117 0.765768i \(-0.277641\pi\)
−0.341616 + 0.939840i \(0.610974\pi\)
\(720\) 0 0
\(721\) −416.500 721.399i −0.577670 1.00055i
\(722\) 237.588i 0.329069i
\(723\) 0 0
\(724\) −55.0000 95.2628i −0.0759669 0.131578i
\(725\) 205.757 118.794i 0.283803 0.163854i
\(726\) 0 0
\(727\) 641.000 0.881706 0.440853 0.897579i \(-0.354676\pi\)
0.440853 + 0.897579i \(0.354676\pi\)
\(728\) −17.1464 9.89949i −0.0235528 0.0135982i
\(729\) 0 0
\(730\) 195.000 337.750i 0.267123 0.462671i
\(731\) −338.030 + 195.161i −0.462421 + 0.266979i
\(732\) 0 0
\(733\) 12.5000 21.6506i 0.0170532 0.0295370i −0.857373 0.514696i \(-0.827905\pi\)
0.874426 + 0.485159i \(0.161238\pi\)
\(734\) 451.134i 0.614624i
\(735\) 0 0
\(736\) 96.0000 0.130435
\(737\) −1069.20 617.304i −1.45075 0.837591i
\(738\) 0 0
\(739\) 267.500 + 463.324i 0.361976 + 0.626960i 0.988286 0.152614i \(-0.0487690\pi\)
−0.626310 + 0.779574i \(0.715436\pi\)
\(740\) −404.166 233.345i −0.546170 0.315331i
\(741\) 0 0
\(742\) −252.000 + 436.477i −0.339623 + 0.588244i
\(743\) 937.624i 1.26194i 0.775806 + 0.630971i \(0.217344\pi\)
−0.775806 + 0.630971i \(0.782656\pi\)
\(744\) 0 0
\(745\) −360.000 623.538i −0.483221 0.836964i
\(746\) 255.972 147.785i 0.343126 0.198104i
\(747\) 0 0
\(748\) 432.000 0.577540
\(749\) −720.150 + 415.779i −0.961482 + 0.555112i
\(750\) 0 0
\(751\) −20.5000 + 35.5070i −0.0272969 + 0.0472797i −0.879351 0.476174i \(-0.842023\pi\)
0.852054 + 0.523454i \(0.175357\pi\)
\(752\) −14.6969 + 8.48528i −0.0195438 + 0.0112836i
\(753\) 0 0
\(754\) −24.0000 + 41.5692i −0.0318302 + 0.0551316i
\(755\) 441.235i 0.584417i
\(756\) 0 0
\(757\) −1114.00 −1.47160 −0.735799 0.677200i \(-0.763193\pi\)
−0.735799 + 0.677200i \(0.763193\pi\)
\(758\) 530.315 + 306.177i 0.699623 + 0.403928i
\(759\) 0 0
\(760\) −138.000 239.023i −0.181579 0.314504i
\(761\) 249.848 + 144.250i 0.328315 + 0.189553i 0.655093 0.755548i \(-0.272629\pi\)
−0.326778 + 0.945101i \(0.605963\pi\)
\(762\) 0 0
\(763\) −343.000 −0.449541
\(764\) 127.279i 0.166596i
\(765\) 0 0
\(766\) 276.000 + 478.046i 0.360313 + 0.624081i
\(767\) −73.4847 + 42.4264i −0.0958079 + 0.0553147i
\(768\) 0 0
\(769\) 1127.00 1.46554 0.732770 0.680477i \(-0.238227\pi\)
0.732770 + 0.680477i \(0.238227\pi\)
\(770\) 462.954 267.286i 0.601238 0.347125i
\(771\) 0 0
\(772\) −151.000 + 261.540i −0.195596 + 0.338782i
\(773\) −187.386 + 108.187i −0.242414 + 0.139958i −0.616286 0.787523i \(-0.711363\pi\)
0.373872 + 0.927480i \(0.378030\pi\)
\(774\) 0 0
\(775\) −164.500 + 284.922i −0.212258 + 0.367642i
\(776\) 294.156i 0.379068i
\(777\) 0 0
\(778\) −522.000 −0.670951
\(779\) 929.581 + 536.694i 1.19330 + 0.688953i
\(780\) 0 0
\(781\) −621.000 1075.60i −0.795134 1.37721i
\(782\) 352.727 + 203.647i 0.451057 + 0.260418i
\(783\) 0 0
\(784\) 196.000 0.250000
\(785\) 644.881i 0.821505i
\(786\) 0 0
\(787\) −85.0000 147.224i −0.108005 0.187070i 0.806957 0.590610i \(-0.201113\pi\)
−0.914962 + 0.403540i \(0.867780\pi\)
\(788\) −29.3939 + 16.9706i −0.0373019 + 0.0215362i
\(789\) 0 0
\(790\) −678.000 −0.858228
\(791\) 591.552 + 341.533i 0.747853 + 0.431773i
\(792\) 0 0
\(793\) 52.0000 90.0666i 0.0655738 0.113577i
\(794\) 138.396 79.9031i 0.174302 0.100634i
\(795\) 0 0
\(796\) −160.000 + 277.128i −0.201005 + 0.348151i
\(797\) 1170.97i 1.46922i −0.678489 0.734610i \(-0.737365\pi\)
0.678489 0.734610i \(-0.262635\pi\)
\(798\) 0 0
\(799\) −72.0000 −0.0901126
\(800\) −34.2929 19.7990i −0.0428661 0.0247487i
\(801\) 0 0
\(802\) 252.000 + 436.477i 0.314214 + 0.544235i
\(803\) 716.476 + 413.657i 0.892249 + 0.515140i
\(804\) 0 0
\(805\) 504.000 0.626087
\(806\) 66.4680i 0.0824665i
\(807\) 0 0
\(808\) 210.000 + 363.731i 0.259901 + 0.450162i
\(809\) −290.265 + 167.584i −0.358794 + 0.207150i −0.668552 0.743666i \(-0.733085\pi\)
0.309757 + 0.950816i \(0.399752\pi\)
\(810\) 0 0
\(811\) −1114.00 −1.37361 −0.686806 0.726840i \(-0.740988\pi\)
−0.686806 + 0.726840i \(0.740988\pi\)
\(812\) 475.176i 0.585192i
\(813\) 0 0
\(814\) 495.000 857.365i 0.608108 1.05327i
\(815\) 205.757 118.794i 0.252463 0.145759i
\(816\) 0 0
\(817\) −264.500 + 458.127i −0.323745 + 0.560743i
\(818\) 451.134i 0.551509i
\(819\) 0 0
\(820\) −396.000 −0.482927
\(821\) 84.5074 + 48.7904i 0.102932 + 0.0594280i 0.550582 0.834781i \(-0.314406\pi\)
−0.447650 + 0.894209i \(0.647739\pi\)
\(822\) 0 0
\(823\) −796.000 1378.71i −0.967193 1.67523i −0.703603 0.710593i \(-0.748427\pi\)
−0.263590 0.964635i \(-0.584907\pi\)
\(824\) 291.489 + 168.291i 0.353749 + 0.204237i
\(825\) 0 0
\(826\) 420.000 727.461i 0.508475 0.880704i
\(827\) 1022.48i 1.23637i 0.786033 + 0.618184i \(0.212131\pi\)
−0.786033 + 0.618184i \(0.787869\pi\)
\(828\) 0 0
\(829\) −191.500 331.688i −0.231001 0.400106i 0.727102 0.686530i \(-0.240867\pi\)
−0.958103 + 0.286424i \(0.907533\pi\)
\(830\) 154.318 89.0955i 0.185925 0.107344i
\(831\) 0 0
\(832\) 8.00000 0.00961538
\(833\) 720.150 + 415.779i 0.864526 + 0.499134i
\(834\) 0 0
\(835\) −9.00000 + 15.5885i −0.0107784 + 0.0186688i
\(836\) 507.044 292.742i 0.606512 0.350170i
\(837\) 0 0
\(838\) 543.000 940.504i 0.647971 1.12232i
\(839\) 576.999i 0.687722i 0.939020 + 0.343861i \(0.111735\pi\)
−0.939020 + 0.343861i \(0.888265\pi\)
\(840\) 0 0
\(841\) −311.000 −0.369798
\(842\) −79.6084 45.9619i −0.0945468 0.0545866i
\(843\) 0 0
\(844\) −208.000 360.267i −0.246445 0.426856i
\(845\) 617.271 + 356.382i 0.730499 + 0.421754i
\(846\) 0 0
\(847\) 143.500 + 248.549i 0.169421 + 0.293447i
\(848\) 203.647i 0.240149i
\(849\) 0 0
\(850\) −84.0000 145.492i −0.0988235 0.171167i
\(851\) 808.332 466.690i 0.949861 0.548402i
\(852\) 0 0
\(853\) 527.000 0.617819 0.308910 0.951091i \(-0.400036\pi\)
0.308910 + 0.951091i \(0.400036\pi\)
\(854\) 1029.55i 1.20556i
\(855\) 0 0
\(856\) 168.000 290.985i 0.196262 0.339935i
\(857\) −1146.36 + 661.852i −1.33764 + 0.772289i −0.986458 0.164016i \(-0.947555\pi\)
−0.351187 + 0.936305i \(0.614222\pi\)
\(858\) 0 0
\(859\) 707.000 1224.56i 0.823050 1.42556i −0.0803504 0.996767i \(-0.525604\pi\)
0.903400 0.428798i \(-0.141063\pi\)
\(860\) 195.161i 0.226932i
\(861\) 0 0
\(862\) 678.000 0.786543
\(863\) −1186.78 685.186i −1.37518 0.793959i −0.383603 0.923498i \(-0.625317\pi\)
−0.991574 + 0.129539i \(0.958650\pi\)
\(864\) 0 0
\(865\) −324.000 561.184i −0.374566 0.648768i
\(866\) 449.481 + 259.508i 0.519032 + 0.299663i
\(867\) 0 0
\(868\) 329.000 + 569.845i 0.379032 + 0.656503i
\(869\) 1438.26i 1.65507i
\(870\) 0 0
\(871\) −48.5000 84.0045i −0.0556831 0.0964460i
\(872\) 120.025 69.2965i 0.137643 0.0794684i
\(873\) 0 0
\(874\) 552.000 0.631579
\(875\) −823.029 475.176i −0.940604 0.543058i
\(876\) 0 0
\(877\) −112.000 + 193.990i −0.127708 + 0.221197i −0.922788 0.385307i \(-0.874095\pi\)
0.795080 + 0.606504i \(0.207429\pi\)
\(878\) 656.463 379.009i 0.747680 0.431673i
\(879\) 0 0
\(880\) −108.000 + 187.061i −0.122727 + 0.212570i
\(881\) 1612.20i 1.82997i 0.403488 + 0.914985i \(0.367798\pi\)
−0.403488 + 0.914985i \(0.632202\pi\)
\(882\) 0 0
\(883\) 329.000 0.372593 0.186297 0.982494i \(-0.440351\pi\)
0.186297 + 0.982494i \(0.440351\pi\)
\(884\) 29.3939 + 16.9706i 0.0332510 + 0.0191975i
\(885\) 0 0
\(886\) 60.0000 + 103.923i 0.0677201 + 0.117295i
\(887\) −47.7650 27.5772i −0.0538501 0.0310904i 0.472833 0.881152i \(-0.343231\pi\)
−0.526683 + 0.850062i \(0.676565\pi\)
\(888\) 0 0
\(889\) −395.500 + 685.026i −0.444882 + 0.770558i
\(890\) 814.587i 0.915266i
\(891\) 0 0
\(892\) −40.0000 69.2820i −0.0448430 0.0776704i
\(893\) −84.5074 + 48.7904i −0.0946331 + 0.0546365i
\(894\) 0 0
\(895\) −18.0000 −0.0201117
\(896\) −68.5857 + 39.5980i −0.0765466 + 0.0441942i
\(897\) 0 0
\(898\) −435.000 + 753.442i −0.484410 + 0.839022i
\(899\) 1381.51 797.616i 1.53672 0.887226i
\(900\) 0 0
\(901\) 432.000 748.246i 0.479467 0.830462i
\(902\) 840.043i 0.931311i
\(903\) 0 0
\(904\) −276.000 −0.305310
\(905\) 202.083 + 116.673i 0.223296 + 0.128920i
\(906\) 0 0
\(907\) −155.500 269.334i −0.171444 0.296950i 0.767481 0.641072i \(-0.221510\pi\)
−0.938925 + 0.344122i \(0.888177\pi\)
\(908\) −389.469 224.860i −0.428930 0.247643i
\(909\) 0 0
\(910\) 42.0000 0.0461538
\(911\) 356.382i 0.391198i 0.980684 + 0.195599i \(0.0626652\pi\)
−0.980684 + 0.195599i \(0.937335\pi\)
\(912\) 0 0
\(913\) 189.000 + 327.358i 0.207010 + 0.358552i
\(914\) −567.057 + 327.390i −0.620412 + 0.358195i
\(915\) 0 0
\(916\) −754.000 −0.823144
\(917\) 128.598 74.2462i 0.140238 0.0809664i
\(918\) 0 0
\(919\) 72.5000 125.574i 0.0788901 0.136642i −0.823881 0.566762i \(-0.808196\pi\)
0.902771 + 0.430121i \(0.141529\pi\)
\(920\) −176.363 + 101.823i −0.191699 + 0.110678i
\(921\) 0 0
\(922\) 192.000 332.554i 0.208243 0.360687i
\(923\) 97.5807i 0.105721i
\(924\) 0 0
\(925\) −385.000 −0.416216
\(926\) −57.5630 33.2340i −0.0621631 0.0358899i
\(927\) 0 0
\(928\) 96.0000 + 166.277i 0.103448 + 0.179178i
\(929\) 268.219 + 154.856i 0.288718 + 0.166691i 0.637364 0.770563i \(-0.280025\pi\)
−0.348645 + 0.937255i \(0.613358\pi\)
\(930\) 0 0
\(931\) 1127.00 1.21053
\(932\) 687.308i 0.737455i
\(933\) 0 0
\(934\) 525.000 + 909.327i 0.562099 + 0.973583i
\(935\) −793.635 + 458.205i −0.848807 + 0.490059i
\(936\) 0 0
\(937\) −487.000 −0.519744 −0.259872 0.965643i \(-0.583680\pi\)
−0.259872 + 0.965643i \(0.583680\pi\)
\(938\) 831.602 + 480.126i 0.886569 + 0.511861i
\(939\) 0 0
\(940\) 18.0000 31.1769i 0.0191489 0.0331669i
\(941\) −1190.45 + 687.308i −1.26509 + 0.730401i −0.974055 0.226310i \(-0.927334\pi\)
−0.291037 + 0.956712i \(0.594000\pi\)
\(942\) 0 0
\(943\) 396.000 685.892i 0.419936 0.727351i
\(944\) 339.411i 0.359546i
\(945\) 0 0
\(946\) 414.000 0.437632
\(947\) 165.341 + 95.4594i 0.174594 + 0.100802i 0.584750 0.811213i \(-0.301192\pi\)
−0.410156 + 0.912015i \(0.634526\pi\)
\(948\) 0 0
\(949\) 32.5000 + 56.2917i 0.0342466 + 0.0593168i
\(950\) −197.184 113.844i −0.207562 0.119836i
\(951\) 0 0
\(952\) −336.000 −0.352941
\(953\) 1035.20i 1.08626i −0.839649 0.543129i \(-0.817239\pi\)
0.839649 0.543129i \(-0.182761\pi\)
\(954\) 0 0
\(955\) −135.000 233.827i −0.141361 0.244845i
\(956\) 22.0454 12.7279i 0.0230600 0.0133137i
\(957\) 0 0
\(958\) −600.000 −0.626305
\(959\) 475.176i 0.495491i
\(960\) 0 0
\(961\) −624.000 + 1080.80i −0.649324 + 1.12466i
\(962\) 67.3610 38.8909i 0.0700218 0.0404271i
\(963\) 0 0
\(964\) −130.000 + 225.167i −0.134855 + 0.233575i
\(965\) 640.639i 0.663874i
\(966\) 0 0
\(967\) −1681.00 −1.73837 −0.869183 0.494490i \(-0.835355\pi\)
−0.869183 + 0.494490i \(0.835355\pi\)
\(968\) −100.429 57.9828i −0.103749 0.0598995i
\(969\) 0 0
\(970\) 312.000 + 540.400i 0.321649 + 0.557113i
\(971\) −1043.48 602.455i −1.07465 0.620448i −0.145200 0.989402i \(-0.546383\pi\)
−0.929448 + 0.368954i \(0.879716\pi\)
\(972\) 0 0
\(973\) 360.500 624.404i 0.370504 0.641731i
\(974\) 337.997i 0.347020i
\(975\) 0 0
\(976\) −208.000 360.267i −0.213115 0.369126i
\(977\) 1017.76 587.606i 1.04172 0.601439i 0.121402 0.992603i \(-0.461261\pi\)
0.920321 + 0.391165i \(0.127928\pi\)
\(978\) 0 0
\(979\) 1728.00 1.76507
\(980\) −360.075 + 207.889i −0.367423 + 0.212132i
\(981\) 0 0
\(982\) 144.000 249.415i 0.146640 0.253987i
\(983\) −1660.75 + 958.837i −1.68948 + 0.975419i −0.734558 + 0.678546i \(0.762611\pi\)
−0.954917 + 0.296873i \(0.904056\pi\)
\(984\) 0 0
\(985\) 36.0000 62.3538i 0.0365482 0.0633034i
\(986\) 814.587i 0.826153i
\(987\) 0 0
\(988\) 46.0000 0.0465587
\(989\) 338.030 + 195.161i 0.341789 + 0.197332i
\(990\) 0 0
\(991\) 312.500 + 541.266i 0.315338 + 0.546182i 0.979509 0.201399i \(-0.0645488\pi\)
−0.664171 + 0.747580i \(0.731215\pi\)
\(992\) −230.252 132.936i −0.232109 0.134008i
\(993\) 0 0
\(994\) 483.000 + 836.581i 0.485915 + 0.841630i
\(995\) 678.823i 0.682234i
\(996\) 0 0
\(997\) 471.500 + 816.662i 0.472919 + 0.819119i 0.999520 0.0309934i \(-0.00986707\pi\)
−0.526601 + 0.850113i \(0.676534\pi\)
\(998\) −60.0125 + 34.6482i −0.0601328 + 0.0347177i
\(999\) 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 126.3.s.a.107.1 yes 4
3.2 odd 2 inner 126.3.s.a.107.2 yes 4
4.3 odd 2 1008.3.dc.b.737.1 4
7.2 even 3 882.3.b.b.197.2 2
7.3 odd 6 882.3.s.a.557.2 4
7.4 even 3 inner 126.3.s.a.53.2 yes 4
7.5 odd 6 882.3.b.e.197.2 2
7.6 odd 2 882.3.s.a.863.1 4
12.11 even 2 1008.3.dc.b.737.2 4
21.2 odd 6 882.3.b.b.197.1 2
21.5 even 6 882.3.b.e.197.1 2
21.11 odd 6 inner 126.3.s.a.53.1 4
21.17 even 6 882.3.s.a.557.1 4
21.20 even 2 882.3.s.a.863.2 4
28.11 odd 6 1008.3.dc.b.305.2 4
84.11 even 6 1008.3.dc.b.305.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.3.s.a.53.1 4 21.11 odd 6 inner
126.3.s.a.53.2 yes 4 7.4 even 3 inner
126.3.s.a.107.1 yes 4 1.1 even 1 trivial
126.3.s.a.107.2 yes 4 3.2 odd 2 inner
882.3.b.b.197.1 2 21.2 odd 6
882.3.b.b.197.2 2 7.2 even 3
882.3.b.e.197.1 2 21.5 even 6
882.3.b.e.197.2 2 7.5 odd 6
882.3.s.a.557.1 4 21.17 even 6
882.3.s.a.557.2 4 7.3 odd 6
882.3.s.a.863.1 4 7.6 odd 2
882.3.s.a.863.2 4 21.20 even 2
1008.3.dc.b.305.1 4 84.11 even 6
1008.3.dc.b.305.2 4 28.11 odd 6
1008.3.dc.b.737.1 4 4.3 odd 2
1008.3.dc.b.737.2 4 12.11 even 2