Properties

Label 76.6.i.a.9.5
Level $76$
Weight $6$
Character 76.9
Analytic conductor $12.189$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,6,Mod(5,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 16]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\), degree \(6\), 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: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.5
Character \(\chi\) \(=\) 76.9
Dual form 76.6.i.a.17.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6.23353 - 5.23055i) q^{3} +(-51.5730 - 18.7710i) q^{5} +(-28.9937 + 50.2186i) q^{7} +(-30.6983 + 174.099i) q^{9} +O(q^{10})\) \(q+(6.23353 - 5.23055i) q^{3} +(-51.5730 - 18.7710i) q^{5} +(-28.9937 + 50.2186i) q^{7} +(-30.6983 + 174.099i) q^{9} +(274.013 + 474.604i) q^{11} +(-42.6757 - 35.8092i) q^{13} +(-419.664 + 152.745i) q^{15} +(38.5884 + 218.846i) q^{17} +(1008.29 + 1208.08i) q^{19} +(81.9378 + 464.692i) q^{21} +(-1368.59 + 498.127i) q^{23} +(-86.4698 - 72.5568i) q^{25} +(1707.96 + 2958.27i) q^{27} +(-879.600 + 4988.46i) q^{29} +(-2849.24 + 4935.03i) q^{31} +(4190.51 + 1525.22i) q^{33} +(2437.95 - 2045.68i) q^{35} -7901.20 q^{37} -453.322 q^{39} +(6030.90 - 5060.53i) q^{41} +(-13086.3 - 4763.04i) q^{43} +(4851.21 - 8402.54i) q^{45} +(3726.61 - 21134.6i) q^{47} +(6722.23 + 11643.2i) q^{49} +(1385.23 + 1162.34i) q^{51} +(7952.22 - 2894.37i) q^{53} +(-5222.85 - 29620.2i) q^{55} +(12604.1 + 2256.65i) q^{57} +(-1789.95 - 10151.3i) q^{59} +(-17924.4 + 6523.94i) q^{61} +(-7852.93 - 6589.39i) q^{63} +(1528.74 + 2647.85i) q^{65} +(7697.37 - 43653.9i) q^{67} +(-5925.68 + 10263.6i) q^{69} +(6445.09 + 2345.82i) q^{71} +(-16171.8 + 13569.8i) q^{73} -918.525 q^{75} -31778.6 q^{77} +(42246.1 - 35448.7i) q^{79} +(-14247.9 - 5185.82i) q^{81} +(-35556.3 + 61585.3i) q^{83} +(2117.84 - 12010.9i) q^{85} +(20609.4 + 35696.5i) q^{87} +(98367.6 + 82540.2i) q^{89} +(3035.62 - 1104.87i) q^{91} +(8052.11 + 45665.8i) q^{93} +(-29323.8 - 81230.7i) q^{95} +(31642.3 + 179452. i) q^{97} +(-91039.7 + 33135.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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 0
\(3\) 6.23353 5.23055i 0.399881 0.335540i −0.420567 0.907262i \(-0.638169\pi\)
0.820448 + 0.571722i \(0.193724\pi\)
\(4\) 0 0
\(5\) −51.5730 18.7710i −0.922565 0.335786i −0.163307 0.986575i \(-0.552216\pi\)
−0.759259 + 0.650789i \(0.774438\pi\)
\(6\) 0 0
\(7\) −28.9937 + 50.2186i −0.223645 + 0.387364i −0.955912 0.293653i \(-0.905129\pi\)
0.732267 + 0.681017i \(0.238462\pi\)
\(8\) 0 0
\(9\) −30.6983 + 174.099i −0.126330 + 0.716455i
\(10\) 0 0
\(11\) 274.013 + 474.604i 0.682793 + 1.18263i 0.974125 + 0.226010i \(0.0725683\pi\)
−0.291332 + 0.956622i \(0.594098\pi\)
\(12\) 0 0
\(13\) −42.6757 35.8092i −0.0700362 0.0587674i 0.607098 0.794627i \(-0.292334\pi\)
−0.677134 + 0.735860i \(0.736778\pi\)
\(14\) 0 0
\(15\) −419.664 + 152.745i −0.481586 + 0.175283i
\(16\) 0 0
\(17\) 38.5884 + 218.846i 0.0323843 + 0.183661i 0.996709 0.0810613i \(-0.0258309\pi\)
−0.964325 + 0.264722i \(0.914720\pi\)
\(18\) 0 0
\(19\) 1008.29 + 1208.08i 0.640770 + 0.767733i
\(20\) 0 0
\(21\) 81.9378 + 464.692i 0.0405449 + 0.229941i
\(22\) 0 0
\(23\) −1368.59 + 498.127i −0.539454 + 0.196345i −0.597355 0.801977i \(-0.703782\pi\)
0.0579007 + 0.998322i \(0.481559\pi\)
\(24\) 0 0
\(25\) −86.4698 72.5568i −0.0276703 0.0232182i
\(26\) 0 0
\(27\) 1707.96 + 2958.27i 0.450886 + 0.780958i
\(28\) 0 0
\(29\) −879.600 + 4988.46i −0.194218 + 1.10147i 0.719309 + 0.694690i \(0.244459\pi\)
−0.913527 + 0.406777i \(0.866653\pi\)
\(30\) 0 0
\(31\) −2849.24 + 4935.03i −0.532507 + 0.922329i 0.466773 + 0.884377i \(0.345417\pi\)
−0.999280 + 0.0379518i \(0.987917\pi\)
\(32\) 0 0
\(33\) 4190.51 + 1525.22i 0.669857 + 0.243808i
\(34\) 0 0
\(35\) 2437.95 2045.68i 0.336398 0.282272i
\(36\) 0 0
\(37\) −7901.20 −0.948831 −0.474415 0.880301i \(-0.657340\pi\)
−0.474415 + 0.880301i \(0.657340\pi\)
\(38\) 0 0
\(39\) −453.322 −0.0477250
\(40\) 0 0
\(41\) 6030.90 5060.53i 0.560302 0.470150i −0.318109 0.948054i \(-0.603048\pi\)
0.878412 + 0.477904i \(0.158603\pi\)
\(42\) 0 0
\(43\) −13086.3 4763.04i −1.07931 0.392838i −0.259661 0.965700i \(-0.583611\pi\)
−0.819652 + 0.572862i \(0.805833\pi\)
\(44\) 0 0
\(45\) 4851.21 8402.54i 0.357124 0.618557i
\(46\) 0 0
\(47\) 3726.61 21134.6i 0.246076 1.39556i −0.571905 0.820320i \(-0.693796\pi\)
0.817981 0.575245i \(-0.195093\pi\)
\(48\) 0 0
\(49\) 6722.23 + 11643.2i 0.399966 + 0.692762i
\(50\) 0 0
\(51\) 1385.23 + 1162.34i 0.0745754 + 0.0625762i
\(52\) 0 0
\(53\) 7952.22 2894.37i 0.388865 0.141535i −0.140186 0.990125i \(-0.544770\pi\)
0.529051 + 0.848590i \(0.322548\pi\)
\(54\) 0 0
\(55\) −5222.85 29620.2i −0.232809 1.32033i
\(56\) 0 0
\(57\) 12604.1 + 2256.65i 0.513837 + 0.0919978i
\(58\) 0 0
\(59\) −1789.95 10151.3i −0.0669437 0.379657i −0.999811 0.0194366i \(-0.993813\pi\)
0.932867 0.360220i \(-0.117298\pi\)
\(60\) 0 0
\(61\) −17924.4 + 6523.94i −0.616764 + 0.224484i −0.631460 0.775408i \(-0.717544\pi\)
0.0146961 + 0.999892i \(0.495322\pi\)
\(62\) 0 0
\(63\) −7852.93 6589.39i −0.249276 0.209167i
\(64\) 0 0
\(65\) 1528.74 + 2647.85i 0.0448797 + 0.0777339i
\(66\) 0 0
\(67\) 7697.37 43653.9i 0.209486 1.18805i −0.680736 0.732528i \(-0.738340\pi\)
0.890222 0.455526i \(-0.150549\pi\)
\(68\) 0 0
\(69\) −5925.68 + 10263.6i −0.149836 + 0.259523i
\(70\) 0 0
\(71\) 6445.09 + 2345.82i 0.151734 + 0.0552267i 0.416771 0.909012i \(-0.363162\pi\)
−0.265037 + 0.964238i \(0.585384\pi\)
\(72\) 0 0
\(73\) −16171.8 + 13569.8i −0.355183 + 0.298034i −0.802867 0.596158i \(-0.796693\pi\)
0.447684 + 0.894192i \(0.352249\pi\)
\(74\) 0 0
\(75\) −918.525 −0.0188555
\(76\) 0 0
\(77\) −31778.6 −0.610812
\(78\) 0 0
\(79\) 42246.1 35448.7i 0.761586 0.639047i −0.176953 0.984219i \(-0.556624\pi\)
0.938539 + 0.345173i \(0.112180\pi\)
\(80\) 0 0
\(81\) −14247.9 5185.82i −0.241290 0.0878224i
\(82\) 0 0
\(83\) −35556.3 + 61585.3i −0.566528 + 0.981255i 0.430378 + 0.902649i \(0.358380\pi\)
−0.996906 + 0.0786064i \(0.974953\pi\)
\(84\) 0 0
\(85\) 2117.84 12010.9i 0.0317941 0.180313i
\(86\) 0 0
\(87\) 20609.4 + 35696.5i 0.291922 + 0.505624i
\(88\) 0 0
\(89\) 98367.6 + 82540.2i 1.31637 + 1.10456i 0.987062 + 0.160339i \(0.0512589\pi\)
0.329305 + 0.944224i \(0.393186\pi\)
\(90\) 0 0
\(91\) 3035.62 1104.87i 0.0384276 0.0139865i
\(92\) 0 0
\(93\) 8052.11 + 45665.8i 0.0965390 + 0.547500i
\(94\) 0 0
\(95\) −29323.8 81230.7i −0.333358 0.923445i
\(96\) 0 0
\(97\) 31642.3 + 179452.i 0.341459 + 1.93651i 0.350529 + 0.936552i \(0.386002\pi\)
−0.00906989 + 0.999959i \(0.502887\pi\)
\(98\) 0 0
\(99\) −91039.7 + 33135.7i −0.933561 + 0.339788i
\(100\) 0 0
\(101\) 37866.4 + 31773.7i 0.369361 + 0.309931i 0.808509 0.588484i \(-0.200275\pi\)
−0.439148 + 0.898415i \(0.644720\pi\)
\(102\) 0 0
\(103\) −35793.4 61996.0i −0.332437 0.575799i 0.650552 0.759462i \(-0.274538\pi\)
−0.982989 + 0.183663i \(0.941204\pi\)
\(104\) 0 0
\(105\) 4496.97 25503.6i 0.0398059 0.225750i
\(106\) 0 0
\(107\) 2218.09 3841.84i 0.0187292 0.0324399i −0.856509 0.516132i \(-0.827371\pi\)
0.875238 + 0.483692i \(0.160705\pi\)
\(108\) 0 0
\(109\) −39598.8 14412.8i −0.319239 0.116193i 0.177430 0.984133i \(-0.443222\pi\)
−0.496669 + 0.867940i \(0.665444\pi\)
\(110\) 0 0
\(111\) −49252.4 + 41327.6i −0.379419 + 0.318371i
\(112\) 0 0
\(113\) 40076.5 0.295252 0.147626 0.989043i \(-0.452837\pi\)
0.147626 + 0.989043i \(0.452837\pi\)
\(114\) 0 0
\(115\) 79932.7 0.563612
\(116\) 0 0
\(117\) 7544.41 6330.51i 0.0509519 0.0427537i
\(118\) 0 0
\(119\) −12109.0 4407.30i −0.0783861 0.0285302i
\(120\) 0 0
\(121\) −69640.6 + 120621.i −0.432413 + 0.748962i
\(122\) 0 0
\(123\) 11124.5 63089.9i 0.0663004 0.376008i
\(124\) 0 0
\(125\) 88851.9 + 153896.i 0.508618 + 0.880952i
\(126\) 0 0
\(127\) 15593.3 + 13084.3i 0.0857884 + 0.0719850i 0.684673 0.728850i \(-0.259945\pi\)
−0.598885 + 0.800835i \(0.704389\pi\)
\(128\) 0 0
\(129\) −106487. + 38758.3i −0.563410 + 0.205064i
\(130\) 0 0
\(131\) −9012.64 51113.2i −0.0458853 0.260229i 0.953232 0.302240i \(-0.0977345\pi\)
−0.999117 + 0.0420116i \(0.986623\pi\)
\(132\) 0 0
\(133\) −89902.0 + 15608.4i −0.440697 + 0.0765119i
\(134\) 0 0
\(135\) −32554.6 184627.i −0.153737 0.871886i
\(136\) 0 0
\(137\) 97870.4 35621.9i 0.445502 0.162150i −0.109521 0.993985i \(-0.534932\pi\)
0.555023 + 0.831835i \(0.312709\pi\)
\(138\) 0 0
\(139\) −76180.7 63923.2i −0.334432 0.280622i 0.460071 0.887882i \(-0.347824\pi\)
−0.794503 + 0.607261i \(0.792268\pi\)
\(140\) 0 0
\(141\) −87315.9 151236.i −0.369867 0.640628i
\(142\) 0 0
\(143\) 5301.49 30066.3i 0.0216799 0.122953i
\(144\) 0 0
\(145\) 139002. 240759.i 0.549037 0.950959i
\(146\) 0 0
\(147\) 102804. + 37417.5i 0.392388 + 0.142818i
\(148\) 0 0
\(149\) 402329. 337594.i 1.48462 1.24574i 0.583547 0.812079i \(-0.301664\pi\)
0.901074 0.433666i \(-0.142780\pi\)
\(150\) 0 0
\(151\) −166773. −0.595227 −0.297614 0.954686i \(-0.596191\pi\)
−0.297614 + 0.954686i \(0.596191\pi\)
\(152\) 0 0
\(153\) −39285.4 −0.135676
\(154\) 0 0
\(155\) 239580. 201031.i 0.800978 0.672100i
\(156\) 0 0
\(157\) −209840. 76375.5i −0.679421 0.247289i −0.0208219 0.999783i \(-0.506628\pi\)
−0.658599 + 0.752494i \(0.728851\pi\)
\(158\) 0 0
\(159\) 34431.2 59636.7i 0.108009 0.187077i
\(160\) 0 0
\(161\) 14665.3 83171.3i 0.0445890 0.252877i
\(162\) 0 0
\(163\) −42579.0 73749.0i −0.125524 0.217414i 0.796414 0.604752i \(-0.206728\pi\)
−0.921938 + 0.387338i \(0.873395\pi\)
\(164\) 0 0
\(165\) −187487. 157320.i −0.536119 0.449857i
\(166\) 0 0
\(167\) −196481. + 71513.2i −0.545166 + 0.198424i −0.599898 0.800077i \(-0.704792\pi\)
0.0547312 + 0.998501i \(0.482570\pi\)
\(168\) 0 0
\(169\) −63935.4 362596.i −0.172197 0.976576i
\(170\) 0 0
\(171\) −241277. + 138456.i −0.630995 + 0.362095i
\(172\) 0 0
\(173\) 59197.6 + 335726.i 0.150380 + 0.852845i 0.962889 + 0.269897i \(0.0869897\pi\)
−0.812510 + 0.582948i \(0.801899\pi\)
\(174\) 0 0
\(175\) 6150.78 2238.70i 0.0151822 0.00552587i
\(176\) 0 0
\(177\) −64254.5 53915.9i −0.154160 0.129355i
\(178\) 0 0
\(179\) 383209. + 663737.i 0.893928 + 1.54833i 0.835126 + 0.550059i \(0.185395\pi\)
0.0588023 + 0.998270i \(0.481272\pi\)
\(180\) 0 0
\(181\) −19109.4 + 108375.i −0.0433562 + 0.245885i −0.998782 0.0493472i \(-0.984286\pi\)
0.955426 + 0.295232i \(0.0953970\pi\)
\(182\) 0 0
\(183\) −77608.3 + 134422.i −0.171309 + 0.296716i
\(184\) 0 0
\(185\) 407488. + 148314.i 0.875358 + 0.318604i
\(186\) 0 0
\(187\) −93291.4 + 78280.8i −0.195091 + 0.163701i
\(188\) 0 0
\(189\) −198080. −0.403353
\(190\) 0 0
\(191\) 764355. 1.51604 0.758022 0.652229i \(-0.226166\pi\)
0.758022 + 0.652229i \(0.226166\pi\)
\(192\) 0 0
\(193\) −471126. + 395322.i −0.910425 + 0.763937i −0.972200 0.234153i \(-0.924768\pi\)
0.0617751 + 0.998090i \(0.480324\pi\)
\(194\) 0 0
\(195\) 23379.2 + 8509.33i 0.0440294 + 0.0160254i
\(196\) 0 0
\(197\) 114320. 198008.i 0.209873 0.363511i −0.741801 0.670620i \(-0.766028\pi\)
0.951674 + 0.307109i \(0.0993616\pi\)
\(198\) 0 0
\(199\) −55113.9 + 312566.i −0.0986571 + 0.559512i 0.894908 + 0.446250i \(0.147241\pi\)
−0.993565 + 0.113262i \(0.963870\pi\)
\(200\) 0 0
\(201\) −180352. 312380.i −0.314870 0.545372i
\(202\) 0 0
\(203\) −225011. 188806.i −0.383233 0.321571i
\(204\) 0 0
\(205\) −406023. + 147780.i −0.674785 + 0.245602i
\(206\) 0 0
\(207\) −44709.8 253562.i −0.0725231 0.411299i
\(208\) 0 0
\(209\) −297073. + 809568.i −0.470432 + 1.28200i
\(210\) 0 0
\(211\) 21986.2 + 124690.i 0.0339972 + 0.192808i 0.997076 0.0764102i \(-0.0243459\pi\)
−0.963079 + 0.269218i \(0.913235\pi\)
\(212\) 0 0
\(213\) 52445.6 19088.7i 0.0792064 0.0288288i
\(214\) 0 0
\(215\) 585494. + 491288.i 0.863827 + 0.724837i
\(216\) 0 0
\(217\) −165220. 286170.i −0.238185 0.412548i
\(218\) 0 0
\(219\) −29830.2 + 169175.i −0.0420287 + 0.238356i
\(220\) 0 0
\(221\) 6189.91 10721.2i 0.00852518 0.0147660i
\(222\) 0 0
\(223\) 83606.6 + 30430.3i 0.112584 + 0.0409774i 0.397698 0.917516i \(-0.369809\pi\)
−0.285114 + 0.958494i \(0.592031\pi\)
\(224\) 0 0
\(225\) 15286.5 12826.9i 0.0201304 0.0168914i
\(226\) 0 0
\(227\) 489797. 0.630887 0.315443 0.948944i \(-0.397847\pi\)
0.315443 + 0.948944i \(0.397847\pi\)
\(228\) 0 0
\(229\) 228119. 0.287456 0.143728 0.989617i \(-0.454091\pi\)
0.143728 + 0.989617i \(0.454091\pi\)
\(230\) 0 0
\(231\) −198093. + 166220.i −0.244252 + 0.204952i
\(232\) 0 0
\(233\) 1.40400e6 + 511014.i 1.69425 + 0.616656i 0.995150 0.0983701i \(-0.0313629\pi\)
0.699098 + 0.715026i \(0.253585\pi\)
\(234\) 0 0
\(235\) −588911. + 1.02002e6i −0.695632 + 1.20487i
\(236\) 0 0
\(237\) 77926.2 441941.i 0.0901182 0.511086i
\(238\) 0 0
\(239\) −45481.2 78775.7i −0.0515035 0.0892067i 0.839124 0.543940i \(-0.183068\pi\)
−0.890628 + 0.454733i \(0.849735\pi\)
\(240\) 0 0
\(241\) 116320. + 97603.7i 0.129006 + 0.108249i 0.705008 0.709199i \(-0.250943\pi\)
−0.576002 + 0.817448i \(0.695388\pi\)
\(242\) 0 0
\(243\) −895947. + 326098.i −0.973344 + 0.354268i
\(244\) 0 0
\(245\) −128130. 726660.i −0.136375 0.773421i
\(246\) 0 0
\(247\) 230.624 87661.6i 0.000240526 0.0914255i
\(248\) 0 0
\(249\) 100484. + 569873.i 0.102707 + 0.582478i
\(250\) 0 0
\(251\) −446089. + 162363.i −0.446927 + 0.162668i −0.555672 0.831401i \(-0.687539\pi\)
0.108745 + 0.994070i \(0.465317\pi\)
\(252\) 0 0
\(253\) −611425. 513046.i −0.600540 0.503913i
\(254\) 0 0
\(255\) −49621.9 85947.6i −0.0477884 0.0827720i
\(256\) 0 0
\(257\) 235146. 1.33358e6i 0.222078 1.25947i −0.646116 0.763239i \(-0.723608\pi\)
0.868193 0.496226i \(-0.165281\pi\)
\(258\) 0 0
\(259\) 229085. 396787.i 0.212201 0.367543i
\(260\) 0 0
\(261\) −841482. 306274.i −0.764616 0.278298i
\(262\) 0 0
\(263\) −542040. + 454825.i −0.483216 + 0.405467i −0.851588 0.524212i \(-0.824360\pi\)
0.368371 + 0.929679i \(0.379915\pi\)
\(264\) 0 0
\(265\) −464450. −0.406279
\(266\) 0 0
\(267\) 1.04491e6 0.897016
\(268\) 0 0
\(269\) 796656. 668474.i 0.671259 0.563253i −0.242179 0.970232i \(-0.577862\pi\)
0.913438 + 0.406978i \(0.133418\pi\)
\(270\) 0 0
\(271\) 1.62320e6 + 590795.i 1.34260 + 0.488668i 0.910631 0.413220i \(-0.135596\pi\)
0.431972 + 0.901887i \(0.357818\pi\)
\(272\) 0 0
\(273\) 13143.5 22765.2i 0.0106734 0.0184869i
\(274\) 0 0
\(275\) 10741.9 60920.4i 0.00856545 0.0485771i
\(276\) 0 0
\(277\) −1.06622e6 1.84675e6i −0.834928 1.44614i −0.894089 0.447889i \(-0.852176\pi\)
0.0591610 0.998248i \(-0.481157\pi\)
\(278\) 0 0
\(279\) −771716. 647547.i −0.593536 0.498036i
\(280\) 0 0
\(281\) −114867. + 41808.2i −0.0867821 + 0.0315861i −0.385046 0.922897i \(-0.625815\pi\)
0.298264 + 0.954483i \(0.403592\pi\)
\(282\) 0 0
\(283\) −353629. 2.00553e6i −0.262471 1.48855i −0.776141 0.630559i \(-0.782826\pi\)
0.513670 0.857988i \(-0.328285\pi\)
\(284\) 0 0
\(285\) −607672. 352975.i −0.443157 0.257413i
\(286\) 0 0
\(287\) 79274.3 + 449587.i 0.0568104 + 0.322188i
\(288\) 0 0
\(289\) 1.28782e6 468730.i 0.907010 0.330125i
\(290\) 0 0
\(291\) 1.13588e6 + 953115.i 0.786320 + 0.659801i
\(292\) 0 0
\(293\) −1.14587e6 1.98471e6i −0.779770 1.35060i −0.932074 0.362267i \(-0.882003\pi\)
0.152305 0.988334i \(-0.451331\pi\)
\(294\) 0 0
\(295\) −98237.2 + 557131.i −0.0657235 + 0.372737i
\(296\) 0 0
\(297\) −936003. + 1.62121e6i −0.615724 + 1.06647i
\(298\) 0 0
\(299\) 76243.2 + 27750.3i 0.0493200 + 0.0179510i
\(300\) 0 0
\(301\) 618615. 519079.i 0.393554 0.330231i
\(302\) 0 0
\(303\) 402236. 0.251695
\(304\) 0 0
\(305\) 1.04687e6 0.644384
\(306\) 0 0
\(307\) 1.86619e6 1.56592e6i 1.13008 0.948254i 0.131015 0.991380i \(-0.458176\pi\)
0.999070 + 0.0431267i \(0.0137319\pi\)
\(308\) 0 0
\(309\) −547393. 199235.i −0.326139 0.118705i
\(310\) 0 0
\(311\) 349201. 604834.i 0.204727 0.354597i −0.745319 0.666708i \(-0.767703\pi\)
0.950046 + 0.312111i \(0.101036\pi\)
\(312\) 0 0
\(313\) −249321. + 1.41397e6i −0.143846 + 0.815792i 0.824440 + 0.565949i \(0.191490\pi\)
−0.968286 + 0.249843i \(0.919621\pi\)
\(314\) 0 0
\(315\) 281309. + 487242.i 0.159738 + 0.276674i
\(316\) 0 0
\(317\) 694313. + 582598.i 0.388067 + 0.325627i 0.815860 0.578250i \(-0.196264\pi\)
−0.427792 + 0.903877i \(0.640709\pi\)
\(318\) 0 0
\(319\) −2.60857e6 + 949440.i −1.43524 + 0.522385i
\(320\) 0 0
\(321\) −6268.43 35550.0i −0.00339544 0.0192565i
\(322\) 0 0
\(323\) −225474. + 267278.i −0.120251 + 0.142547i
\(324\) 0 0
\(325\) 1091.96 + 6192.83i 0.000573455 + 0.00325223i
\(326\) 0 0
\(327\) −322227. + 117281.i −0.166645 + 0.0606539i
\(328\) 0 0
\(329\) 953303. + 799916.i 0.485558 + 0.407432i
\(330\) 0 0
\(331\) −1.76318e6 3.05392e6i −0.884560 1.53210i −0.846217 0.532838i \(-0.821125\pi\)
−0.0383427 0.999265i \(-0.512208\pi\)
\(332\) 0 0
\(333\) 242553. 1.37559e6i 0.119866 0.679795i
\(334\) 0 0
\(335\) −1.21640e6 + 2.10687e6i −0.592197 + 1.02572i
\(336\) 0 0
\(337\) 3.49626e6 + 1.27253e6i 1.67698 + 0.610372i 0.992892 0.119022i \(-0.0379760\pi\)
0.684093 + 0.729395i \(0.260198\pi\)
\(338\) 0 0
\(339\) 249818. 209622.i 0.118066 0.0990690i
\(340\) 0 0
\(341\) −3.12292e6 −1.45437
\(342\) 0 0
\(343\) −1.75420e6 −0.805091
\(344\) 0 0
\(345\) 498263. 418092.i 0.225378 0.189114i
\(346\) 0 0
\(347\) 1.20176e6 + 437406.i 0.535790 + 0.195012i 0.595722 0.803191i \(-0.296866\pi\)
−0.0599317 + 0.998202i \(0.519088\pi\)
\(348\) 0 0
\(349\) −1.95602e6 + 3.38792e6i −0.859625 + 1.48891i 0.0126622 + 0.999920i \(0.495969\pi\)
−0.872287 + 0.488994i \(0.837364\pi\)
\(350\) 0 0
\(351\) 33044.8 187407.i 0.0143165 0.0811927i
\(352\) 0 0
\(353\) 2.03793e6 + 3.52980e6i 0.870468 + 1.50769i 0.861513 + 0.507735i \(0.169517\pi\)
0.00895472 + 0.999960i \(0.497150\pi\)
\(354\) 0 0
\(355\) −288359. 241962.i −0.121440 0.101901i
\(356\) 0 0
\(357\) −98534.1 + 35863.5i −0.0409182 + 0.0148930i
\(358\) 0 0
\(359\) −424380. 2.40678e6i −0.173788 0.985599i −0.939534 0.342456i \(-0.888741\pi\)
0.765746 0.643143i \(-0.222370\pi\)
\(360\) 0 0
\(361\) −442795. + 2.43619e6i −0.178827 + 0.983880i
\(362\) 0 0
\(363\) 196808. + 1.11615e6i 0.0783928 + 0.444588i
\(364\) 0 0
\(365\) 1.08875e6 396272.i 0.427755 0.155690i
\(366\) 0 0
\(367\) 2.40089e6 + 2.01459e6i 0.930481 + 0.780767i 0.975904 0.218201i \(-0.0700189\pi\)
−0.0454224 + 0.998968i \(0.514463\pi\)
\(368\) 0 0
\(369\) 695893. + 1.20532e6i 0.266058 + 0.460826i
\(370\) 0 0
\(371\) −85213.1 + 483268.i −0.0321419 + 0.182286i
\(372\) 0 0
\(373\) −2.32324e6 + 4.02398e6i −0.864615 + 1.49756i 0.00281439 + 0.999996i \(0.499104\pi\)
−0.867429 + 0.497561i \(0.834229\pi\)
\(374\) 0 0
\(375\) 1.35882e6 + 494571.i 0.498982 + 0.181614i
\(376\) 0 0
\(377\) 216170. 181388.i 0.0783326 0.0657289i
\(378\) 0 0
\(379\) −4.39435e6 −1.57144 −0.785718 0.618585i \(-0.787706\pi\)
−0.785718 + 0.618585i \(0.787706\pi\)
\(380\) 0 0
\(381\) 165640. 0.0584590
\(382\) 0 0
\(383\) 3.16232e6 2.65350e6i 1.10156 0.924319i 0.104032 0.994574i \(-0.466826\pi\)
0.997529 + 0.0702547i \(0.0223812\pi\)
\(384\) 0 0
\(385\) 1.63892e6 + 596517.i 0.563514 + 0.205102i
\(386\) 0 0
\(387\) 1.23097e6 2.13210e6i 0.417801 0.723652i
\(388\) 0 0
\(389\) −120666. + 684333.i −0.0404308 + 0.229295i −0.998327 0.0578202i \(-0.981585\pi\)
0.957896 + 0.287115i \(0.0926961\pi\)
\(390\) 0 0
\(391\) −161825. 280289.i −0.0535307 0.0927180i
\(392\) 0 0
\(393\) −323531. 271475.i −0.105666 0.0886641i
\(394\) 0 0
\(395\) −2.84417e6 + 1.03519e6i −0.917196 + 0.333832i
\(396\) 0 0
\(397\) −700660. 3.97364e6i −0.223116 1.26535i −0.866254 0.499604i \(-0.833479\pi\)
0.643138 0.765750i \(-0.277632\pi\)
\(398\) 0 0
\(399\) −478766. + 567532.i −0.150554 + 0.178467i
\(400\) 0 0
\(401\) 601652. + 3.41214e6i 0.186846 + 1.05966i 0.923560 + 0.383453i \(0.125265\pi\)
−0.736714 + 0.676204i \(0.763624\pi\)
\(402\) 0 0
\(403\) 298313. 108577.i 0.0914976 0.0333024i
\(404\) 0 0
\(405\) 637465. + 534897.i 0.193116 + 0.162044i
\(406\) 0 0
\(407\) −2.16503e6 3.74994e6i −0.647855 1.12212i
\(408\) 0 0
\(409\) 165554. 938903.i 0.0489363 0.277532i −0.950514 0.310682i \(-0.899443\pi\)
0.999450 + 0.0331498i \(0.0105539\pi\)
\(410\) 0 0
\(411\) 423756. 733967.i 0.123740 0.214325i
\(412\) 0 0
\(413\) 561680. + 204435.i 0.162037 + 0.0589766i
\(414\) 0 0
\(415\) 2.98976e6 2.50871e6i 0.852151 0.715040i
\(416\) 0 0
\(417\) −809228. −0.227893
\(418\) 0 0
\(419\) −1.67305e6 −0.465559 −0.232780 0.972530i \(-0.574782\pi\)
−0.232780 + 0.972530i \(0.574782\pi\)
\(420\) 0 0
\(421\) 2.44937e6 2.05526e6i 0.673517 0.565148i −0.240587 0.970628i \(-0.577340\pi\)
0.914104 + 0.405479i \(0.132895\pi\)
\(422\) 0 0
\(423\) 3.56511e6 + 1.29759e6i 0.968773 + 0.352605i
\(424\) 0 0
\(425\) 12542.0 21723.4i 0.00336818 0.00583386i
\(426\) 0 0
\(427\) 192071. 1.08929e6i 0.0509791 0.289117i
\(428\) 0 0
\(429\) −124216. 215149.i −0.0325863 0.0564411i
\(430\) 0 0
\(431\) −4.98412e6 4.18217e6i −1.29239 1.08445i −0.991406 0.130820i \(-0.958239\pi\)
−0.300989 0.953628i \(-0.597317\pi\)
\(432\) 0 0
\(433\) 631885. 229987.i 0.161964 0.0589501i −0.259766 0.965672i \(-0.583645\pi\)
0.421730 + 0.906722i \(0.361423\pi\)
\(434\) 0 0
\(435\) −392827. 2.22783e6i −0.0995356 0.564495i
\(436\) 0 0
\(437\) −1.98172e6 1.15111e6i −0.496407 0.288344i
\(438\) 0 0
\(439\) 584926. + 3.31728e6i 0.144857 + 0.821525i 0.967482 + 0.252941i \(0.0813978\pi\)
−0.822625 + 0.568585i \(0.807491\pi\)
\(440\) 0 0
\(441\) −2.23343e6 + 812903.i −0.546861 + 0.199041i
\(442\) 0 0
\(443\) 875761. + 734851.i 0.212020 + 0.177906i 0.742613 0.669721i \(-0.233586\pi\)
−0.530593 + 0.847627i \(0.678031\pi\)
\(444\) 0 0
\(445\) −3.52374e6 6.10330e6i −0.843537 1.46105i
\(446\) 0 0
\(447\) 742126. 4.20881e6i 0.175675 0.996300i
\(448\) 0 0
\(449\) −3.32175e6 + 5.75344e6i −0.777591 + 1.34683i 0.155736 + 0.987799i \(0.450225\pi\)
−0.933327 + 0.359028i \(0.883108\pi\)
\(450\) 0 0
\(451\) 4.05429e6 + 1.47564e6i 0.938585 + 0.341617i
\(452\) 0 0
\(453\) −1.03958e6 + 872314.i −0.238020 + 0.199723i
\(454\) 0 0
\(455\) −177295. −0.0401484
\(456\) 0 0
\(457\) 7.19460e6 1.61145 0.805723 0.592292i \(-0.201777\pi\)
0.805723 + 0.592292i \(0.201777\pi\)
\(458\) 0 0
\(459\) −581497. + 487934.i −0.128830 + 0.108101i
\(460\) 0 0
\(461\) 3.84545e6 + 1.39963e6i 0.842742 + 0.306733i 0.727078 0.686555i \(-0.240878\pi\)
0.115664 + 0.993288i \(0.463100\pi\)
\(462\) 0 0
\(463\) −2.24350e6 + 3.88586e6i −0.486378 + 0.842431i −0.999877 0.0156588i \(-0.995015\pi\)
0.513500 + 0.858090i \(0.328349\pi\)
\(464\) 0 0
\(465\) 441923. 2.50627e6i 0.0947794 0.537521i
\(466\) 0 0
\(467\) −1.95647e6 3.38870e6i −0.415126 0.719020i 0.580315 0.814392i \(-0.302929\pi\)
−0.995442 + 0.0953718i \(0.969596\pi\)
\(468\) 0 0
\(469\) 1.96906e6 + 1.65224e6i 0.413359 + 0.346849i
\(470\) 0 0
\(471\) −1.70753e6 + 621490.i −0.354663 + 0.129087i
\(472\) 0 0
\(473\) −1.32527e6 7.51597e6i −0.272365 1.54466i
\(474\) 0 0
\(475\) 467.291 177621.i 9.50284e−5 0.0361209i
\(476\) 0 0
\(477\) 259787. + 1.47332e6i 0.0522782 + 0.296484i
\(478\) 0 0
\(479\) −7.70914e6 + 2.80590e6i −1.53521 + 0.558770i −0.964890 0.262654i \(-0.915402\pi\)
−0.570318 + 0.821424i \(0.693180\pi\)
\(480\) 0 0
\(481\) 337189. + 282936.i 0.0664525 + 0.0557603i
\(482\) 0 0
\(483\) −343615. 595159.i −0.0670200 0.116082i
\(484\) 0 0
\(485\) 1.73662e6 9.84885e6i 0.335235 1.90121i
\(486\) 0 0
\(487\) 3.05649e6 5.29399e6i 0.583983 1.01149i −0.411019 0.911627i \(-0.634827\pi\)
0.995001 0.0998607i \(-0.0318397\pi\)
\(488\) 0 0
\(489\) −651166. 237005.i −0.123146 0.0448214i
\(490\) 0 0
\(491\) 574415. 481992.i 0.107528 0.0902268i −0.587438 0.809269i \(-0.699864\pi\)
0.694967 + 0.719042i \(0.255419\pi\)
\(492\) 0 0
\(493\) −1.12565e6 −0.208586
\(494\) 0 0
\(495\) 5.31718e6 0.975367
\(496\) 0 0
\(497\) −304671. + 255649.i −0.0553274 + 0.0464252i
\(498\) 0 0
\(499\) 6.50875e6 + 2.36899e6i 1.17016 + 0.425905i 0.852718 0.522372i \(-0.174953\pi\)
0.317446 + 0.948276i \(0.397175\pi\)
\(500\) 0 0
\(501\) −850716. + 1.47348e6i −0.151422 + 0.262271i
\(502\) 0 0
\(503\) 310961. 1.76355e6i 0.0548007 0.310790i −0.945070 0.326868i \(-0.894007\pi\)
0.999871 + 0.0160776i \(0.00511788\pi\)
\(504\) 0 0
\(505\) −1.35646e6 2.34946e6i −0.236689 0.409958i
\(506\) 0 0
\(507\) −2.29512e6 1.92583e6i −0.396539 0.332735i
\(508\) 0 0
\(509\) −9.57557e6 + 3.48522e6i −1.63821 + 0.596260i −0.986725 0.162400i \(-0.948077\pi\)
−0.651487 + 0.758660i \(0.725854\pi\)
\(510\) 0 0
\(511\) −212574. 1.20557e6i −0.0360128 0.204239i
\(512\) 0 0
\(513\) −1.85169e6 + 5.04613e6i −0.310653 + 0.846575i
\(514\) 0 0
\(515\) 682244. + 3.86920e6i 0.113350 + 0.642840i
\(516\) 0 0
\(517\) 1.10517e7 4.02250e6i 1.81846 0.661865i
\(518\) 0 0
\(519\) 2.12504e6 + 1.78312e6i 0.346298 + 0.290578i
\(520\) 0 0
\(521\) 1.39630e6 + 2.41846e6i 0.225364 + 0.390342i 0.956429 0.291966i \(-0.0943095\pi\)
−0.731065 + 0.682308i \(0.760976\pi\)
\(522\) 0 0
\(523\) −1.49781e6 + 8.49448e6i −0.239443 + 1.35795i 0.593610 + 0.804753i \(0.297702\pi\)
−0.833053 + 0.553194i \(0.813409\pi\)
\(524\) 0 0
\(525\) 26631.4 46127.0i 0.00421693 0.00730394i
\(526\) 0 0
\(527\) −1.18996e6 433110.i −0.186640 0.0679316i
\(528\) 0 0
\(529\) −3.30561e6 + 2.77374e6i −0.513585 + 0.430949i
\(530\) 0 0
\(531\) 1.82227e6 0.280464
\(532\) 0 0
\(533\) −438587. −0.0668709
\(534\) 0 0
\(535\) −186508. + 156499.i −0.0281718 + 0.0236389i
\(536\) 0 0
\(537\) 5.86045e6 + 2.13303e6i 0.876991 + 0.319199i
\(538\) 0 0
\(539\) −3.68395e6 + 6.38080e6i −0.546188 + 0.946026i
\(540\) 0 0
\(541\) −1.51343e6 + 8.58309e6i −0.222315 + 1.26081i 0.645436 + 0.763814i \(0.276676\pi\)
−0.867752 + 0.496998i \(0.834436\pi\)
\(542\) 0 0
\(543\) 447741. + 775511.i 0.0651670 + 0.112873i
\(544\) 0 0
\(545\) 1.77168e6 + 1.48662e6i 0.255503 + 0.214392i
\(546\) 0 0
\(547\) −8.03856e6 + 2.92580e6i −1.14871 + 0.418096i −0.845051 0.534685i \(-0.820430\pi\)
−0.303658 + 0.952781i \(0.598208\pi\)
\(548\) 0 0
\(549\) −585561. 3.32088e6i −0.0829166 0.470243i
\(550\) 0 0
\(551\) −6.91333e6 + 3.96720e6i −0.970082 + 0.556679i
\(552\) 0 0
\(553\) 555312. + 3.14933e6i 0.0772190 + 0.437931i
\(554\) 0 0
\(555\) 3.31585e6 1.20687e6i 0.456944 0.166314i
\(556\) 0 0
\(557\) 2.60451e6 + 2.18544e6i 0.355703 + 0.298471i 0.803075 0.595877i \(-0.203196\pi\)
−0.447372 + 0.894348i \(0.647640\pi\)
\(558\) 0 0
\(559\) 387909. + 671878.i 0.0525049 + 0.0909412i
\(560\) 0 0
\(561\) −172083. + 975932.i −0.0230851 + 0.130922i
\(562\) 0 0
\(563\) −2.56746e6 + 4.44697e6i −0.341375 + 0.591280i −0.984688 0.174324i \(-0.944226\pi\)
0.643313 + 0.765603i \(0.277559\pi\)
\(564\) 0 0
\(565\) −2.06686e6 752276.i −0.272390 0.0991417i
\(566\) 0 0
\(567\) 673525. 565155.i 0.0879825 0.0738261i
\(568\) 0 0
\(569\) −5.24402e6 −0.679022 −0.339511 0.940602i \(-0.610262\pi\)
−0.339511 + 0.940602i \(0.610262\pi\)
\(570\) 0 0
\(571\) 1.24825e7 1.60218 0.801088 0.598547i \(-0.204255\pi\)
0.801088 + 0.598547i \(0.204255\pi\)
\(572\) 0 0
\(573\) 4.76463e6 3.99800e6i 0.606237 0.508693i
\(574\) 0 0
\(575\) 154484. + 56227.7i 0.0194857 + 0.00709220i
\(576\) 0 0
\(577\) 1.40693e6 2.43688e6i 0.175928 0.304715i −0.764554 0.644559i \(-0.777041\pi\)
0.940482 + 0.339844i \(0.110374\pi\)
\(578\) 0 0
\(579\) −869028. + 4.92850e6i −0.107730 + 0.610968i
\(580\) 0 0
\(581\) −2.06182e6 3.57117e6i −0.253402 0.438905i
\(582\) 0 0
\(583\) 3.55269e6 + 2.98106e6i 0.432898 + 0.363245i
\(584\) 0 0
\(585\) −507917. + 184867.i −0.0613626 + 0.0223341i
\(586\) 0 0
\(587\) −1.40702e6 7.97961e6i −0.168541 0.955842i −0.945338 0.326092i \(-0.894268\pi\)
0.776797 0.629751i \(-0.216843\pi\)
\(588\) 0 0
\(589\) −8.83476e6 + 1.53385e6i −1.04932 + 0.182178i
\(590\) 0 0
\(591\) −323075. 1.83225e6i −0.0380482 0.215782i
\(592\) 0 0
\(593\) −6.90589e6 + 2.51354e6i −0.806460 + 0.293528i −0.712161 0.702016i \(-0.752283\pi\)
−0.0942994 + 0.995544i \(0.530061\pi\)
\(594\) 0 0
\(595\) 541765. + 454595.i 0.0627362 + 0.0526420i
\(596\) 0 0
\(597\) 1.29134e6 + 2.23667e6i 0.148288 + 0.256842i
\(598\) 0 0
\(599\) −874115. + 4.95735e6i −0.0995409 + 0.564524i 0.893720 + 0.448625i \(0.148086\pi\)
−0.993261 + 0.115899i \(0.963025\pi\)
\(600\) 0 0
\(601\) 2.09419e6 3.62725e6i 0.236500 0.409630i −0.723208 0.690631i \(-0.757333\pi\)
0.959708 + 0.281001i \(0.0906664\pi\)
\(602\) 0 0
\(603\) 7.36379e6 + 2.68020e6i 0.824723 + 0.300175i
\(604\) 0 0
\(605\) 5.85575e6 4.91356e6i 0.650420 0.545767i
\(606\) 0 0
\(607\) 5.66875e6 0.624476 0.312238 0.950004i \(-0.398921\pi\)
0.312238 + 0.950004i \(0.398921\pi\)
\(608\) 0 0
\(609\) −2.39017e6 −0.261147
\(610\) 0 0
\(611\) −915850. + 768489.i −0.0992479 + 0.0832789i
\(612\) 0 0
\(613\) −1.42908e7 5.20142e6i −1.53605 0.559076i −0.570955 0.820981i \(-0.693427\pi\)
−0.965093 + 0.261906i \(0.915649\pi\)
\(614\) 0 0
\(615\) −1.75798e6 + 3.04492e6i −0.187425 + 0.324629i
\(616\) 0 0
\(617\) 2.36523e6 1.34139e7i 0.250127 1.41854i −0.558150 0.829740i \(-0.688489\pi\)
0.808277 0.588802i \(-0.200400\pi\)
\(618\) 0 0
\(619\) −1.22728e6 2.12572e6i −0.128741 0.222987i 0.794448 0.607332i \(-0.207760\pi\)
−0.923189 + 0.384346i \(0.874427\pi\)
\(620\) 0 0
\(621\) −3.81109e6 3.19788e6i −0.396570 0.332762i
\(622\) 0 0
\(623\) −6.99709e6 + 2.54673e6i −0.722267 + 0.262884i
\(624\) 0 0
\(625\) −1.63232e6 9.25733e6i −0.167149 0.947951i
\(626\) 0 0
\(627\) 2.38267e6 + 6.60032e6i 0.242045 + 0.670496i
\(628\) 0 0
\(629\) −304895. 1.72914e6i −0.0307272 0.174263i
\(630\) 0 0
\(631\) 1.33848e7 4.87167e6i 1.33825 0.487084i 0.428991 0.903309i \(-0.358869\pi\)
0.909262 + 0.416224i \(0.136647\pi\)
\(632\) 0 0
\(633\) 789248. + 662258.i 0.0782896 + 0.0656928i
\(634\) 0 0
\(635\) −558586. 967499.i −0.0549738 0.0952174i
\(636\) 0 0
\(637\) 130059. 737602.i 0.0126997 0.0720233i
\(638\) 0 0
\(639\) −606258. + 1.05007e6i −0.0587361 + 0.101734i
\(640\) 0 0
\(641\) 7.43998e6 + 2.70793e6i 0.715198 + 0.260311i 0.673886 0.738835i \(-0.264624\pi\)
0.0413124 + 0.999146i \(0.486846\pi\)
\(642\) 0 0
\(643\) 6.49275e6 5.44806e6i 0.619300 0.519654i −0.278284 0.960499i \(-0.589765\pi\)
0.897583 + 0.440845i \(0.145321\pi\)
\(644\) 0 0
\(645\) 6.21941e6 0.588640
\(646\) 0 0
\(647\) 1.43995e7 1.35234 0.676169 0.736746i \(-0.263639\pi\)
0.676169 + 0.736746i \(0.263639\pi\)
\(648\) 0 0
\(649\) 4.32737e6 3.63110e6i 0.403286 0.338397i
\(650\) 0 0
\(651\) −2.52673e6 919656.i −0.233672 0.0850497i
\(652\) 0 0
\(653\) 2.57952e6 4.46785e6i 0.236731 0.410030i −0.723043 0.690803i \(-0.757257\pi\)
0.959774 + 0.280772i \(0.0905906\pi\)
\(654\) 0 0
\(655\) −494639. + 2.80524e6i −0.0450490 + 0.255485i
\(656\) 0 0
\(657\) −1.86603e6 3.23207e6i −0.168658 0.292124i
\(658\) 0 0
\(659\) −4.93040e6 4.13709e6i −0.442251 0.371092i 0.394300 0.918982i \(-0.370987\pi\)
−0.836551 + 0.547889i \(0.815431\pi\)
\(660\) 0 0
\(661\) −1.91519e7 + 6.97073e6i −1.70494 + 0.620547i −0.996373 0.0850983i \(-0.972880\pi\)
−0.708566 + 0.705645i \(0.750657\pi\)
\(662\) 0 0
\(663\) −17493.0 99207.8i −0.00154554 0.00876520i
\(664\) 0 0
\(665\) 4.92950e6 + 882581.i 0.432263 + 0.0773928i
\(666\) 0 0
\(667\) −1.28107e6 7.26532e6i −0.111496 0.632325i
\(668\) 0 0
\(669\) 680332. 247621.i 0.0587700 0.0213905i
\(670\) 0 0
\(671\) −8.00779e6 6.71934e6i −0.686604 0.576129i
\(672\) 0 0
\(673\) −4.15315e6 7.19347e6i −0.353460 0.612211i 0.633393 0.773830i \(-0.281662\pi\)
−0.986853 + 0.161619i \(0.948328\pi\)
\(674\) 0 0
\(675\) 66955.7 379724.i 0.00565624 0.0320781i
\(676\) 0 0
\(677\) 5.48034e6 9.49222e6i 0.459553 0.795969i −0.539384 0.842060i \(-0.681343\pi\)
0.998937 + 0.0460906i \(0.0146763\pi\)
\(678\) 0 0
\(679\) −9.92927e6 3.61396e6i −0.826500 0.300821i
\(680\) 0 0
\(681\) 3.05316e6 2.56191e6i 0.252280 0.211688i
\(682\) 0 0
\(683\) −1.88927e7 −1.54968 −0.774838 0.632159i \(-0.782169\pi\)
−0.774838 + 0.632159i \(0.782169\pi\)
\(684\) 0 0
\(685\) −5.71613e6 −0.465453
\(686\) 0 0
\(687\) 1.42198e6 1.19319e6i 0.114948 0.0964532i
\(688\) 0 0
\(689\) −443012. 161243.i −0.0355523 0.0129400i
\(690\) 0 0
\(691\) −2.75357e6 + 4.76933e6i −0.219382 + 0.379981i −0.954619 0.297829i \(-0.903737\pi\)
0.735237 + 0.677810i \(0.237071\pi\)
\(692\) 0 0
\(693\) 975549. 5.53261e6i 0.0771642 0.437620i
\(694\) 0 0
\(695\) 2.72896e6 + 4.72670e6i 0.214306 + 0.371189i
\(696\) 0 0
\(697\) 1.34020e6 + 1.12456e6i 0.104493 + 0.0876800i
\(698\) 0 0
\(699\) 1.14248e7 4.15827e6i 0.884411 0.321899i
\(700\) 0 0
\(701\) 228643. + 1.29670e6i 0.0175736 + 0.0996651i 0.992333 0.123593i \(-0.0394418\pi\)
−0.974759 + 0.223258i \(0.928331\pi\)
\(702\) 0 0
\(703\) −7.96671e6 9.54525e6i −0.607982 0.728448i
\(704\) 0 0
\(705\) 1.66429e6 + 9.43868e6i 0.126112 + 0.715218i
\(706\) 0 0
\(707\) −2.69352e6 + 980361.i −0.202662 + 0.0737628i
\(708\) 0 0
\(709\) 7.11882e6 + 5.97340e6i 0.531854 + 0.446278i 0.868741 0.495267i \(-0.164930\pi\)
−0.336887 + 0.941545i \(0.609374\pi\)
\(710\) 0 0
\(711\) 4.87469e6 + 8.44321e6i 0.361637 + 0.626374i
\(712\) 0 0
\(713\) 1.44118e6 8.17334e6i 0.106168 0.602110i
\(714\) 0 0
\(715\) −837788. + 1.45109e6i −0.0612871 + 0.106152i
\(716\) 0 0
\(717\) −695549. 253159.i −0.0505277 0.0183906i
\(718\) 0 0
\(719\) −6.70837e6 + 5.62899e6i −0.483944 + 0.406077i −0.851850 0.523786i \(-0.824519\pi\)
0.367906 + 0.929863i \(0.380075\pi\)
\(720\) 0 0
\(721\) 4.15113e6 0.297392
\(722\) 0 0
\(723\) 1.23560e6 0.0879089
\(724\) 0 0
\(725\) 438006. 367530.i 0.0309481 0.0259686i
\(726\) 0 0
\(727\) 1.75800e7 + 6.39860e6i 1.23363 + 0.449003i 0.874838 0.484416i \(-0.160968\pi\)
0.358788 + 0.933419i \(0.383190\pi\)
\(728\) 0 0
\(729\) −2.03702e6 + 3.52821e6i −0.141963 + 0.245887i
\(730\) 0 0
\(731\) 537390. 3.04769e6i 0.0371960 0.210949i
\(732\) 0 0
\(733\) 1.12351e7 + 1.94597e7i 0.772352 + 1.33775i 0.936271 + 0.351280i \(0.114253\pi\)
−0.163918 + 0.986474i \(0.552413\pi\)
\(734\) 0 0
\(735\) −4.59953e6 3.85947e6i −0.314048 0.263517i
\(736\) 0 0
\(737\) 2.28275e7 8.30854e6i 1.54807 0.563450i
\(738\) 0 0
\(739\) 2.15804e6 + 1.22389e7i 0.145361 + 0.824384i 0.967076 + 0.254486i \(0.0819062\pi\)
−0.821715 + 0.569898i \(0.806983\pi\)
\(740\) 0 0
\(741\) −457081. 547648.i −0.0305807 0.0366400i
\(742\) 0 0
\(743\) 3.21380e6 + 1.82264e7i 0.213573 + 1.21123i 0.883365 + 0.468686i \(0.155272\pi\)
−0.669792 + 0.742549i \(0.733617\pi\)
\(744\) 0 0
\(745\) −2.70863e7 + 9.85860e6i −1.78796 + 0.650766i
\(746\) 0 0
\(747\) −9.63040e6 8.08087e6i −0.631456 0.529854i
\(748\) 0 0
\(749\) 128621. + 222778.i 0.00837737 + 0.0145100i
\(750\) 0 0
\(751\) 1.82373e6 1.03429e7i 0.117995 0.669180i −0.867229 0.497909i \(-0.834101\pi\)
0.985224 0.171271i \(-0.0547875\pi\)
\(752\) 0 0
\(753\) −1.93146e6 + 3.34539e6i −0.124136 + 0.215010i
\(754\) 0 0
\(755\) 8.60096e6 + 3.13049e6i 0.549136 + 0.199869i
\(756\) 0 0
\(757\) −4.07683e6 + 3.42087e6i −0.258573 + 0.216968i −0.762853 0.646572i \(-0.776202\pi\)
0.504281 + 0.863540i \(0.331758\pi\)
\(758\) 0 0
\(759\) −6.49485e6 −0.409228
\(760\) 0 0
\(761\) −2.04886e7 −1.28248 −0.641241 0.767340i \(-0.721580\pi\)
−0.641241 + 0.767340i \(0.721580\pi\)
\(762\) 0 0
\(763\) 1.87191e6 1.57072e6i 0.116405 0.0976756i
\(764\) 0 0
\(765\) 2.02606e6 + 737427.i 0.125170 + 0.0455581i
\(766\) 0 0
\(767\) −287122. + 497310.i −0.0176229 + 0.0305238i
\(768\) 0 0
\(769\) −609711. + 3.45784e6i −0.0371799 + 0.210858i −0.997738 0.0672214i \(-0.978587\pi\)
0.960558 + 0.278079i \(0.0896977\pi\)
\(770\) 0 0
\(771\) −5.50957e6 9.54286e6i −0.333797 0.578153i
\(772\) 0 0
\(773\) 2.02804e7 + 1.70173e7i 1.22075 + 1.02433i 0.998785 + 0.0492803i \(0.0156928\pi\)
0.221969 + 0.975054i \(0.428752\pi\)
\(774\) 0 0
\(775\) 604444. 220000.i 0.0361495 0.0131573i
\(776\) 0 0
\(777\) −647407. 3.67163e6i −0.0384702 0.218175i
\(778\) 0 0
\(779\) 1.21944e7 + 2.18330e6i 0.719974 + 0.128905i
\(780\) 0 0
\(781\) 652702. + 3.70165e6i 0.0382901 + 0.217154i
\(782\) 0 0
\(783\) −1.62595e7 + 5.91798e6i −0.947770 + 0.344960i
\(784\) 0 0
\(785\) 9.38842e6 + 7.87782e6i 0.543774 + 0.456280i
\(786\) 0 0
\(787\) −2.75399e6 4.77005e6i −0.158499 0.274528i 0.775829 0.630943i \(-0.217332\pi\)
−0.934327 + 0.356416i \(0.883999\pi\)
\(788\) 0 0
\(789\) −999833. + 5.67033e6i −0.0571788 + 0.324277i
\(790\) 0 0
\(791\) −1.16197e6 + 2.01258e6i −0.0660316 + 0.114370i
\(792\) 0 0
\(793\) 998553. + 363443.i 0.0563882 + 0.0205236i
\(794\) 0 0
\(795\) −2.89516e6 + 2.42933e6i −0.162463 + 0.136323i
\(796\) 0 0
\(797\) 1.43780e7 0.801776 0.400888 0.916127i \(-0.368702\pi\)
0.400888 + 0.916127i \(0.368702\pi\)
\(798\) 0 0
\(799\) 4.76903e6 0.264279
\(800\) 0 0
\(801\) −1.73899e7 + 1.45918e7i −0.957667 + 0.803578i
\(802\) 0 0
\(803\) −1.08716e7 3.95693e6i −0.594981 0.216556i
\(804\) 0 0
\(805\) −2.31755e6 + 4.01411e6i −0.126049 + 0.218323i
\(806\) 0 0
\(807\) 1.46949e6 8.33391e6i 0.0794298 0.450469i
\(808\) 0 0
\(809\) 9.85184e6 + 1.70639e7i 0.529232 + 0.916656i 0.999419 + 0.0340896i \(0.0108532\pi\)
−0.470187 + 0.882567i \(0.655814\pi\)
\(810\) 0 0
\(811\) 4.67971e6 + 3.92674e6i 0.249843 + 0.209643i 0.759105 0.650969i \(-0.225637\pi\)
−0.509262 + 0.860612i \(0.670082\pi\)
\(812\) 0 0
\(813\) 1.32084e7 4.80747e6i 0.700849 0.255088i
\(814\) 0 0
\(815\) 811581. + 4.60271e6i 0.0427994 + 0.242728i
\(816\) 0 0
\(817\) −7.44074e6 2.06118e7i −0.389997 1.08034i
\(818\) 0 0
\(819\) 99168.8 + 562414.i 0.00516613 + 0.0292986i
\(820\) 0 0
\(821\) 3.87272e6 1.40955e6i 0.200520 0.0729833i −0.239808 0.970820i \(-0.577084\pi\)
0.440328 + 0.897837i \(0.354862\pi\)
\(822\) 0 0
\(823\) −285331. 239421.i −0.0146842 0.0123215i 0.635416 0.772170i \(-0.280829\pi\)
−0.650100 + 0.759849i \(0.725273\pi\)
\(824\) 0 0
\(825\) −251688. 435936.i −0.0128744 0.0222991i
\(826\) 0 0
\(827\) 271216. 1.53814e6i 0.0137896 0.0782047i −0.977136 0.212614i \(-0.931802\pi\)
0.990926 + 0.134409i \(0.0429136\pi\)
\(828\) 0 0
\(829\) −6.34675e6 + 1.09929e7i −0.320749 + 0.555554i −0.980643 0.195805i \(-0.937268\pi\)
0.659894 + 0.751359i \(0.270601\pi\)
\(830\) 0 0
\(831\) −1.63059e7 5.93486e6i −0.819109 0.298131i
\(832\) 0 0
\(833\) −2.28868e6 + 1.92043e6i −0.114280 + 0.0958926i
\(834\) 0 0
\(835\) 1.14755e7 0.569580
\(836\) 0 0
\(837\) −1.94655e7 −0.960401
\(838\) 0 0
\(839\) −1.14530e7 + 9.61020e6i −0.561713 + 0.471333i −0.878884 0.477035i \(-0.841711\pi\)
0.317171 + 0.948368i \(0.397267\pi\)
\(840\) 0 0
\(841\) −4.83687e6 1.76048e6i −0.235817 0.0858303i
\(842\) 0 0
\(843\) −497348. + 861431.i −0.0241041 + 0.0417495i
\(844\) 0 0
\(845\) −3.50896e6 + 1.99003e7i −0.169058 + 0.958776i
\(846\) 0 0
\(847\) −4.03828e6 6.99450e6i −0.193414 0.335003i
\(848\) 0 0
\(849\) −1.26944e7 1.06518e7i −0.604424 0.507172i
\(850\) 0 0
\(851\) 1.08135e7 3.93580e6i 0.511851 0.186298i
\(852\) 0 0
\(853\) 6.03106e6 + 3.42039e7i 0.283806 + 1.60954i 0.709520 + 0.704685i \(0.248912\pi\)
−0.425714 + 0.904858i \(0.639977\pi\)
\(854\) 0 0
\(855\) 1.50423e7 2.61159e6i 0.703721 0.122177i
\(856\) 0 0
\(857\) −1.31012e6 7.43004e6i −0.0609337 0.345572i −0.999998 0.00183155i \(-0.999417\pi\)
0.939065 0.343741i \(-0.111694\pi\)
\(858\) 0 0
\(859\) 2.55252e7 9.29041e6i 1.18028 0.429588i 0.323981 0.946064i \(-0.394979\pi\)
0.856302 + 0.516476i \(0.172756\pi\)
\(860\) 0 0
\(861\) 2.84575e6 + 2.38786e6i 0.130824 + 0.109775i
\(862\) 0 0
\(863\) −3.16468e6 5.48138e6i −0.144645 0.250532i 0.784596 0.620008i \(-0.212871\pi\)
−0.929240 + 0.369476i \(0.879537\pi\)
\(864\) 0 0
\(865\) 3.24893e6 1.84256e7i 0.147639 0.837301i
\(866\) 0 0
\(867\) 5.57598e6 9.65788e6i 0.251926 0.436349i
\(868\) 0 0
\(869\) 2.84001e7 + 1.03368e7i 1.27576 + 0.464340i
\(870\) 0 0
\(871\) −1.89170e6 + 1.58733e6i −0.0844904 + 0.0708959i
\(872\) 0 0
\(873\) −3.22138e7 −1.43056
\(874\) 0 0
\(875\) −1.03046e7 −0.454999
\(876\) 0 0
\(877\) 2.06978e7 1.73675e7i 0.908712 0.762500i −0.0631619 0.998003i \(-0.520118\pi\)
0.971873 + 0.235504i \(0.0756740\pi\)
\(878\) 0 0
\(879\) −1.75239e7 6.37819e6i −0.764996 0.278436i
\(880\) 0 0
\(881\) 1.17187e7 2.02974e7i 0.508675 0.881052i −0.491274 0.871005i \(-0.663469\pi\)
0.999950 0.0100467i \(-0.00319801\pi\)
\(882\) 0 0
\(883\) 1.38716e6 7.86699e6i 0.0598722 0.339552i −0.940127 0.340824i \(-0.889294\pi\)
0.999999 + 0.00127210i \(0.000404923\pi\)
\(884\) 0 0
\(885\) 2.30174e6 + 3.98673e6i 0.0987865 + 0.171103i
\(886\) 0 0
\(887\) 5.42289e6 + 4.55035e6i 0.231431 + 0.194194i 0.751127 0.660157i \(-0.229510\pi\)
−0.519696 + 0.854351i \(0.673955\pi\)
\(888\) 0 0
\(889\) −1.10918e6 + 403710.i −0.0470705 + 0.0171323i
\(890\) 0 0
\(891\) −1.44290e6 8.18311e6i −0.0608896 0.345322i
\(892\) 0 0
\(893\) 2.92897e7 1.68079e7i 1.22910 0.705316i
\(894\) 0 0
\(895\) −7.30418e6 4.14241e7i −0.304799 1.72860i
\(896\) 0 0
\(897\) 620414. 225812.i 0.0257454 0.00937057i
\(898\) 0 0
\(899\) −2.21120e7 1.85542e7i −0.912493 0.765672i
\(900\) 0 0
\(901\) 940285. + 1.62862e6i 0.0385876 + 0.0668356i
\(902\) 0 0
\(903\) 1.14108e6 6.47139e6i 0.0465690 0.264106i
\(904\) 0 0
\(905\) 3.01984e6 5.23051e6i 0.122564 0.212287i
\(906\) 0 0
\(907\) −4.22883e7 1.53917e7i −1.70687 0.621251i −0.710296 0.703903i \(-0.751439\pi\)
−0.996578 + 0.0826519i \(0.973661\pi\)
\(908\) 0 0
\(909\) −6.69420e6 + 5.61710e6i −0.268713 + 0.225477i
\(910\) 0 0
\(911\) 2.75563e7 1.10008 0.550040 0.835138i \(-0.314612\pi\)
0.550040 + 0.835138i \(0.314612\pi\)
\(912\) 0 0
\(913\) −3.89715e7 −1.54729
\(914\) 0 0
\(915\) 6.52572e6 5.47573e6i 0.257677 0.216217i
\(916\) 0 0
\(917\) 2.82814e6 + 1.02936e6i 0.111065 + 0.0404244i
\(918\) 0 0
\(919\) 2.34089e7 4.05453e7i 0.914306 1.58362i 0.106391 0.994324i \(-0.466070\pi\)
0.807915 0.589300i \(-0.200596\pi\)
\(920\) 0 0
\(921\) 3.44234e6 1.95225e7i 0.133722 0.758378i
\(922\) 0 0
\(923\) −191047. 330903.i −0.00738136 0.0127849i
\(924\) 0 0
\(925\) 683215. + 573286.i 0.0262545 + 0.0220301i
\(926\) 0 0
\(927\) 1.18922e7 4.32841e6i 0.454531 0.165436i
\(928\) 0 0
\(929\) 407827. + 2.31290e6i 0.0155037 + 0.0879261i 0.991578 0.129512i \(-0.0413411\pi\)
−0.976074 + 0.217438i \(0.930230\pi\)
\(930\) 0 0
\(931\) −7.28795e6 + 1.98607e7i −0.275570 + 0.750968i
\(932\) 0 0
\(933\) −986862. 5.59677e6i −0.0371152 0.210491i
\(934\) 0 0
\(935\) 6.28073e6 2.28600e6i 0.234953 0.0855159i
\(936\) 0 0
\(937\) −4.23241e6 3.55141e6i −0.157485 0.132145i 0.560640 0.828059i \(-0.310555\pi\)
−0.718125 + 0.695914i \(0.754999\pi\)
\(938\) 0 0
\(939\) 5.84169e6 + 1.01181e7i 0.216210 + 0.374486i
\(940\) 0 0
\(941\) −8.57824e6 + 4.86496e7i −0.315809 + 1.79104i 0.251839 + 0.967769i \(0.418965\pi\)
−0.567648 + 0.823272i \(0.692146\pi\)
\(942\) 0 0
\(943\) −5.73306e6 + 9.92995e6i −0.209946 + 0.363637i
\(944\) 0 0
\(945\) 1.02156e7 + 3.71816e6i 0.372120 + 0.135441i
\(946\) 0 0
\(947\) 1.82651e7 1.53262e7i 0.661830 0.555341i −0.248805 0.968554i \(-0.580038\pi\)
0.910635 + 0.413212i \(0.135593\pi\)
\(948\) 0 0
\(949\) 1.17607e6 0.0423904
\(950\) 0 0
\(951\) 7.37533e6 0.264442
\(952\) 0 0
\(953\) 1.47639e7 1.23884e7i 0.526585 0.441858i −0.340335 0.940304i \(-0.610540\pi\)
0.866920 + 0.498447i \(0.166096\pi\)
\(954\) 0 0
\(955\) −3.94200e7 1.43477e7i −1.39865 0.509067i
\(956\) 0 0
\(957\) −1.12945e7 + 1.95626e7i −0.398645 + 0.690473i
\(958\) 0 0
\(959\) −1.04874e6 + 5.94773e6i −0.0368233 + 0.208836i
\(960\) 0 0
\(961\) −1.92180e6 3.32866e6i −0.0671275 0.116268i
\(962\) 0 0
\(963\) 600767. + 504103.i 0.0208757 + 0.0175168i
\(964\) 0 0
\(965\) 3.17180e7 1.15444e7i 1.09645 0.399074i
\(966\) 0 0
\(967\) 8.07102e6 + 4.57730e7i 0.277563 + 1.57414i 0.730700 + 0.682699i \(0.239194\pi\)
−0.453136 + 0.891441i \(0.649695\pi\)
\(968\) 0 0
\(969\) −7485.90 + 2.84544e6i −0.000256115 + 0.0973509i
\(970\) 0 0
\(971\) −5.76725e6 3.27077e7i −0.196300 1.11327i −0.910555 0.413388i \(-0.864345\pi\)
0.714255 0.699885i \(-0.246766\pi\)
\(972\) 0 0
\(973\) 5.41889e6 1.97231e6i 0.183497 0.0667873i
\(974\) 0 0
\(975\) 39198.7 + 32891.6i 0.00132057 + 0.00110809i
\(976\) 0 0
\(977\) 1.02870e7 + 1.78177e7i 0.344789 + 0.597192i 0.985315 0.170744i \(-0.0546171\pi\)
−0.640526 + 0.767936i \(0.721284\pi\)
\(978\) 0 0
\(979\) −1.22199e7 + 6.93027e7i −0.407486 + 2.31097i
\(980\) 0 0
\(981\) 3.72486e6 6.45165e6i 0.123577 0.214042i
\(982\) 0 0
\(983\) −3.02333e7 1.10040e7i −0.997933 0.363218i −0.209146 0.977884i \(-0.567068\pi\)
−0.788787 + 0.614666i \(0.789291\pi\)
\(984\) 0 0
\(985\) −9.61264e6 + 8.06596e6i −0.315684 + 0.264890i
\(986\) 0 0
\(987\) 1.01264e7 0.330875
\(988\) 0 0
\(989\) 2.02825e7 0.659371
\(990\) 0 0
\(991\) −3.72919e7 + 3.12916e7i −1.20623 + 1.01215i −0.206801 + 0.978383i \(0.566305\pi\)
−0.999430 + 0.0337652i \(0.989250\pi\)
\(992\) 0 0
\(993\) −2.69646e7 9.81429e6i −0.867801 0.315854i
\(994\) 0 0
\(995\) 8.70957e6 1.50854e7i 0.278894 0.483059i
\(996\) 0 0
\(997\) −9.67241e6 + 5.48549e7i −0.308174 + 1.74774i 0.299998 + 0.953940i \(0.403014\pi\)
−0.608173 + 0.793805i \(0.708097\pi\)
\(998\) 0 0
\(999\) −1.34949e7 2.33738e7i −0.427815 0.740997i
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 76.6.i.a.9.5 48
19.17 even 9 inner 76.6.i.a.17.5 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.6.i.a.9.5 48 1.1 even 1 trivial
76.6.i.a.17.5 yes 48 19.17 even 9 inner