Properties

Label 162.7.d.f.107.4
Level $162$
Weight $7$
Character 162.107
Analytic conductor $37.269$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,7,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(37.2687615464\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.4
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.7.d.f.53.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(180.591 - 104.264i) q^{5} +(-2.09808 + 3.63397i) q^{7} +181.019i q^{8} +O(q^{10})\) \(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(180.591 - 104.264i) q^{5} +(-2.09808 + 3.63397i) q^{7} +181.019i q^{8} +1179.62 q^{10} +(1958.91 + 1130.98i) q^{11} +(-1420.00 - 2459.52i) q^{13} +(-20.5569 + 11.8685i) q^{14} +(-512.000 + 886.810i) q^{16} +1965.86i q^{17} -281.295 q^{19} +(5778.91 + 3336.46i) q^{20} +(6397.77 + 11081.3i) q^{22} +(14501.0 - 8372.14i) q^{23} +(13929.6 - 24126.7i) q^{25} -16065.5i q^{26} -134.277 q^{28} +(-32141.8 - 18557.1i) q^{29} +(12354.2 + 21398.0i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-5560.29 + 9630.70i) q^{34} +875.017i q^{35} -17016.7 q^{37} +(-1378.06 - 795.623i) q^{38} +(18873.8 + 32690.5i) q^{40} +(100663. - 58117.9i) q^{41} +(15331.4 - 26554.8i) q^{43} +72382.5i q^{44} +94720.0 q^{46} +(67261.3 + 38833.3i) q^{47} +(58815.7 + 101872. i) q^{49} +(136481. - 78797.5i) q^{50} +(45440.1 - 78704.6i) q^{52} +138657. i q^{53} +471682. q^{55} +(-657.820 - 379.792i) q^{56} +(-104975. - 181821. i) q^{58} +(-132465. + 76478.8i) q^{59} +(8069.05 - 13976.0i) q^{61} +139771. i q^{62} -32768.0 q^{64} +(-512880. - 296111. i) q^{65} +(237334. + 411074. i) q^{67} +(-54479.4 + 31453.7i) q^{68} +(-2474.92 + 4286.69i) q^{70} -150338. i q^{71} +331690. q^{73} +(-83364.7 - 48130.6i) q^{74} +(-4500.73 - 7795.49i) q^{76} +(-8219.88 + 4745.75i) q^{77} +(448056. - 776056. i) q^{79} +213533. i q^{80} +657529. q^{82} +(-818472. - 472545. i) q^{83} +(204969. + 355016. i) q^{85} +(150217. - 86727.7i) q^{86} +(-204729. + 354600. i) q^{88} +790302. i q^{89} +11917.1 q^{91} +(464031. + 267909. i) q^{92} +(219674. + 380487. i) q^{94} +(-50799.4 + 29329.0i) q^{95} +(-696338. + 1.20609e6i) q^{97} +665424. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 128 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 128 q^{4} + 4 q^{7} + 5280 q^{10} - 3836 q^{13} - 4096 q^{16} + 20488 q^{19} + 27072 q^{22} + 25700 q^{25} + 256 q^{28} + 40096 q^{31} - 60528 q^{34} - 40400 q^{37} + 84480 q^{40} - 184940 q^{43} + 325440 q^{46} + 470484 q^{49} + 122752 q^{52} + 1899720 q^{55} - 24624 q^{58} - 609056 q^{61} - 262144 q^{64} + 2008972 q^{67} - 8160 q^{70} + 1051648 q^{73} + 327808 q^{76} + 848716 q^{79} + 1411584 q^{82} + 987840 q^{85} - 866304 q^{88} + 70520 q^{91} + 1965408 q^{94} - 3621728 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.89898 + 2.82843i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 16.0000 + 27.7128i 0.250000 + 0.433013i
\(5\) 180.591 104.264i 1.44473 0.834114i 0.446568 0.894750i \(-0.352646\pi\)
0.998160 + 0.0606359i \(0.0193128\pi\)
\(6\) 0 0
\(7\) −2.09808 + 3.63397i −0.00611684 + 0.0105947i −0.869068 0.494693i \(-0.835280\pi\)
0.862951 + 0.505288i \(0.168614\pi\)
\(8\) 181.019i 0.353553i
\(9\) 0 0
\(10\) 1179.62 1.17962
\(11\) 1958.91 + 1130.98i 1.47176 + 0.849719i 0.999496 0.0317396i \(-0.0101047\pi\)
0.472261 + 0.881459i \(0.343438\pi\)
\(12\) 0 0
\(13\) −1420.00 2459.52i −0.646338 1.11949i −0.983991 0.178219i \(-0.942966\pi\)
0.337653 0.941271i \(-0.390367\pi\)
\(14\) −20.5569 + 11.8685i −0.00749157 + 0.00432526i
\(15\) 0 0
\(16\) −512.000 + 886.810i −0.125000 + 0.216506i
\(17\) 1965.86i 0.400134i 0.979782 + 0.200067i \(0.0641160\pi\)
−0.979782 + 0.200067i \(0.935884\pi\)
\(18\) 0 0
\(19\) −281.295 −0.0410111 −0.0205056 0.999790i \(-0.506528\pi\)
−0.0205056 + 0.999790i \(0.506528\pi\)
\(20\) 5778.91 + 3336.46i 0.722364 + 0.417057i
\(21\) 0 0
\(22\) 6397.77 + 11081.3i 0.600842 + 1.04069i
\(23\) 14501.0 8372.14i 1.19183 0.688102i 0.233107 0.972451i \(-0.425111\pi\)
0.958721 + 0.284348i \(0.0917773\pi\)
\(24\) 0 0
\(25\) 13929.6 24126.7i 0.891492 1.54411i
\(26\) 16065.5i 0.914059i
\(27\) 0 0
\(28\) −134.277 −0.00611684
\(29\) −32141.8 18557.1i −1.31788 0.760878i −0.334492 0.942399i \(-0.608565\pi\)
−0.983387 + 0.181520i \(0.941898\pi\)
\(30\) 0 0
\(31\) 12354.2 + 21398.0i 0.414694 + 0.718272i 0.995396 0.0958444i \(-0.0305551\pi\)
−0.580702 + 0.814116i \(0.697222\pi\)
\(32\) −5016.55 + 2896.31i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −5560.29 + 9630.70i −0.141469 + 0.245031i
\(35\) 875.017i 0.0204086i
\(36\) 0 0
\(37\) −17016.7 −0.335947 −0.167974 0.985791i \(-0.553722\pi\)
−0.167974 + 0.985791i \(0.553722\pi\)
\(38\) −1378.06 795.623i −0.0251141 0.0144996i
\(39\) 0 0
\(40\) 18873.8 + 32690.5i 0.294904 + 0.510788i
\(41\) 100663. 58117.9i 1.46056 0.843253i 0.461521 0.887129i \(-0.347304\pi\)
0.999037 + 0.0438761i \(0.0139707\pi\)
\(42\) 0 0
\(43\) 15331.4 26554.8i 0.192831 0.333993i −0.753356 0.657613i \(-0.771566\pi\)
0.946187 + 0.323619i \(0.104900\pi\)
\(44\) 72382.5i 0.849719i
\(45\) 0 0
\(46\) 94720.0 0.973124
\(47\) 67261.3 + 38833.3i 0.647846 + 0.374034i 0.787630 0.616148i \(-0.211308\pi\)
−0.139785 + 0.990182i \(0.544641\pi\)
\(48\) 0 0
\(49\) 58815.7 + 101872.i 0.499925 + 0.865896i
\(50\) 136481. 78797.5i 1.09185 0.630380i
\(51\) 0 0
\(52\) 45440.1 78704.6i 0.323169 0.559745i
\(53\) 138657.i 0.931354i 0.884955 + 0.465677i \(0.154189\pi\)
−0.884955 + 0.465677i \(0.845811\pi\)
\(54\) 0 0
\(55\) 471682. 2.83505
\(56\) −657.820 379.792i −0.00374578 0.00216263i
\(57\) 0 0
\(58\) −104975. 181821.i −0.538022 0.931881i
\(59\) −132465. + 76478.8i −0.644979 + 0.372379i −0.786530 0.617552i \(-0.788124\pi\)
0.141551 + 0.989931i \(0.454791\pi\)
\(60\) 0 0
\(61\) 8069.05 13976.0i 0.0355495 0.0615735i −0.847703 0.530471i \(-0.822015\pi\)
0.883253 + 0.468897i \(0.155349\pi\)
\(62\) 139771.i 0.586467i
\(63\) 0 0
\(64\) −32768.0 −0.125000
\(65\) −512880. 296111.i −1.86756 1.07824i
\(66\) 0 0
\(67\) 237334. + 411074.i 0.789105 + 1.36677i 0.926516 + 0.376255i \(0.122788\pi\)
−0.137411 + 0.990514i \(0.543878\pi\)
\(68\) −54479.4 + 31453.7i −0.173263 + 0.100033i
\(69\) 0 0
\(70\) −2474.92 + 4286.69i −0.00721552 + 0.0124976i
\(71\) 150338.i 0.420043i −0.977697 0.210021i \(-0.932647\pi\)
0.977697 0.210021i \(-0.0673534\pi\)
\(72\) 0 0
\(73\) 331690. 0.852636 0.426318 0.904573i \(-0.359811\pi\)
0.426318 + 0.904573i \(0.359811\pi\)
\(74\) −83364.7 48130.6i −0.205725 0.118775i
\(75\) 0 0
\(76\) −4500.73 7795.49i −0.0102528 0.0177583i
\(77\) −8219.88 + 4745.75i −0.0180050 + 0.0103952i
\(78\) 0 0
\(79\) 448056. 776056.i 0.908764 1.57403i 0.0929805 0.995668i \(-0.470361\pi\)
0.815783 0.578357i \(-0.196306\pi\)
\(80\) 213533.i 0.417057i
\(81\) 0 0
\(82\) 657529. 1.19254
\(83\) −818472. 472545.i −1.43143 0.826435i −0.434198 0.900817i \(-0.642968\pi\)
−0.997230 + 0.0743823i \(0.976301\pi\)
\(84\) 0 0
\(85\) 204969. + 355016.i 0.333757 + 0.578084i
\(86\) 150217. 86727.7i 0.236169 0.136352i
\(87\) 0 0
\(88\) −204729. + 354600.i −0.300421 + 0.520345i
\(89\) 790302.i 1.12105i 0.828139 + 0.560523i \(0.189400\pi\)
−0.828139 + 0.560523i \(0.810600\pi\)
\(90\) 0 0
\(91\) 11917.1 0.0158142
\(92\) 464031. + 267909.i 0.595914 + 0.344051i
\(93\) 0 0
\(94\) 219674. + 380487.i 0.264482 + 0.458096i
\(95\) −50799.4 + 29329.0i −0.0592499 + 0.0342080i
\(96\) 0 0
\(97\) −696338. + 1.20609e6i −0.762965 + 1.32149i 0.178351 + 0.983967i \(0.442924\pi\)
−0.941316 + 0.337527i \(0.890409\pi\)
\(98\) 665424.i 0.707001i
\(99\) 0 0
\(100\) 891492. 0.891492
\(101\) −113927. 65775.9i −0.110577 0.0638414i 0.443692 0.896179i \(-0.353669\pi\)
−0.554268 + 0.832338i \(0.687002\pi\)
\(102\) 0 0
\(103\) −967305. 1.67542e6i −0.885221 1.53325i −0.845460 0.534038i \(-0.820674\pi\)
−0.0397603 0.999209i \(-0.512659\pi\)
\(104\) 445220. 257048.i 0.395799 0.228515i
\(105\) 0 0
\(106\) −392182. + 679279.i −0.329283 + 0.570336i
\(107\) 621916.i 0.507669i −0.967248 0.253834i \(-0.918308\pi\)
0.967248 0.253834i \(-0.0816918\pi\)
\(108\) 0 0
\(109\) −1.34578e6 −1.03919 −0.519594 0.854413i \(-0.673917\pi\)
−0.519594 + 0.854413i \(0.673917\pi\)
\(110\) 2.31076e6 + 1.33412e6i 1.73611 + 1.00234i
\(111\) 0 0
\(112\) −2148.43 3721.19i −0.00152921 0.00264867i
\(113\) 1.07329e6 619662.i 0.743841 0.429457i −0.0796229 0.996825i \(-0.525372\pi\)
0.823464 + 0.567368i \(0.192038\pi\)
\(114\) 0 0
\(115\) 1.74583e6 3.02387e6i 1.14791 1.98824i
\(116\) 1.18765e6i 0.760878i
\(117\) 0 0
\(118\) −865259. −0.526623
\(119\) −7143.88 4124.52i −0.00423929 0.00244755i
\(120\) 0 0
\(121\) 1.67243e6 + 2.89674e6i 0.944046 + 1.63514i
\(122\) 79060.2 45645.5i 0.0435390 0.0251373i
\(123\) 0 0
\(124\) −395333. + 684737.i −0.207347 + 0.359136i
\(125\) 2.55116e6i 1.30620i
\(126\) 0 0
\(127\) −1.65297e6 −0.806962 −0.403481 0.914988i \(-0.632200\pi\)
−0.403481 + 0.914988i \(0.632200\pi\)
\(128\) −160530. 92681.9i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −1.67506e6 2.90129e6i −0.762430 1.32057i
\(131\) −2.30472e6 + 1.33063e6i −1.02519 + 0.591893i −0.915602 0.402085i \(-0.868286\pi\)
−0.109586 + 0.993977i \(0.534952\pi\)
\(132\) 0 0
\(133\) 590.179 1022.22i 0.000250859 0.000434500i
\(134\) 2.68512e6i 1.11596i
\(135\) 0 0
\(136\) −355858. −0.141469
\(137\) −2.26046e6 1.30508e6i −0.879092 0.507544i −0.00873327 0.999962i \(-0.502780\pi\)
−0.870359 + 0.492418i \(0.836113\pi\)
\(138\) 0 0
\(139\) 350661. + 607362.i 0.130570 + 0.226153i 0.923896 0.382643i \(-0.124986\pi\)
−0.793327 + 0.608796i \(0.791653\pi\)
\(140\) −24249.2 + 14000.3i −0.00883717 + 0.00510214i
\(141\) 0 0
\(142\) 425220. 736503.i 0.148508 0.257223i
\(143\) 6.42396e6i 2.19682i
\(144\) 0 0
\(145\) −7.73935e6 −2.53864
\(146\) 1.62494e6 + 938160.i 0.522131 + 0.301452i
\(147\) 0 0
\(148\) −272268. 471582.i −0.0839868 0.145469i
\(149\) −4.09928e6 + 2.36672e6i −1.23922 + 0.715464i −0.968935 0.247316i \(-0.920451\pi\)
−0.270285 + 0.962780i \(0.587118\pi\)
\(150\) 0 0
\(151\) −1.86865e6 + 3.23659e6i −0.542746 + 0.940063i 0.455999 + 0.889980i \(0.349282\pi\)
−0.998745 + 0.0500829i \(0.984051\pi\)
\(152\) 50919.9i 0.0144996i
\(153\) 0 0
\(154\) −53692.0 −0.0147010
\(155\) 4.46210e6 + 2.57619e6i 1.19824 + 0.691805i
\(156\) 0 0
\(157\) −1.60331e6 2.77701e6i −0.414303 0.717594i 0.581052 0.813867i \(-0.302641\pi\)
−0.995355 + 0.0962723i \(0.969308\pi\)
\(158\) 4.39004e6 2.53459e6i 1.11300 0.642593i
\(159\) 0 0
\(160\) −603963. + 1.04609e6i −0.147452 + 0.255394i
\(161\) 70261.6i 0.0168361i
\(162\) 0 0
\(163\) −964418. −0.222691 −0.111345 0.993782i \(-0.535516\pi\)
−0.111345 + 0.993782i \(0.535516\pi\)
\(164\) 3.22122e6 + 1.85977e6i 0.730279 + 0.421627i
\(165\) 0 0
\(166\) −2.67312e6 4.62998e6i −0.584378 1.01217i
\(167\) −896330. + 517496.i −0.192450 + 0.111111i −0.593129 0.805107i \(-0.702108\pi\)
0.400679 + 0.916219i \(0.368774\pi\)
\(168\) 0 0
\(169\) −1.61942e6 + 2.80491e6i −0.335504 + 0.581111i
\(170\) 2.31896e6i 0.472004i
\(171\) 0 0
\(172\) 981212. 0.192831
\(173\) −561701. 324298.i −0.108484 0.0626334i 0.444776 0.895642i \(-0.353283\pi\)
−0.553260 + 0.833008i \(0.686617\pi\)
\(174\) 0 0
\(175\) 58450.6 + 101239.i 0.0109062 + 0.0188901i
\(176\) −2.00592e6 + 1.15812e6i −0.367939 + 0.212430i
\(177\) 0 0
\(178\) −2.23531e6 + 3.87168e6i −0.396349 + 0.686497i
\(179\) 4.65189e6i 0.811092i 0.914075 + 0.405546i \(0.132919\pi\)
−0.914075 + 0.405546i \(0.867081\pi\)
\(180\) 0 0
\(181\) 3.43720e6 0.579654 0.289827 0.957079i \(-0.406402\pi\)
0.289827 + 0.957079i \(0.406402\pi\)
\(182\) 58381.6 + 33706.7i 0.00968416 + 0.00559115i
\(183\) 0 0
\(184\) 1.51552e6 + 2.62496e6i 0.243281 + 0.421375i
\(185\) −3.07307e6 + 1.77424e6i −0.485352 + 0.280218i
\(186\) 0 0
\(187\) −2.22334e6 + 3.85094e6i −0.340001 + 0.588900i
\(188\) 2.48533e6i 0.374034i
\(189\) 0 0
\(190\) −331820. −0.0483774
\(191\) −1.01766e7 5.87547e6i −1.46050 0.843222i −0.461470 0.887156i \(-0.652678\pi\)
−0.999034 + 0.0439335i \(0.986011\pi\)
\(192\) 0 0
\(193\) −3.47800e6 6.02407e6i −0.483790 0.837950i 0.516036 0.856567i \(-0.327407\pi\)
−0.999827 + 0.0186172i \(0.994074\pi\)
\(194\) −6.82269e6 + 3.93908e6i −0.934438 + 0.539498i
\(195\) 0 0
\(196\) −1.88210e6 + 3.25990e6i −0.249963 + 0.432948i
\(197\) 409645.i 0.0535807i 0.999641 + 0.0267904i \(0.00852866\pi\)
−0.999641 + 0.0267904i \(0.991471\pi\)
\(198\) 0 0
\(199\) −3.24847e6 −0.412212 −0.206106 0.978530i \(-0.566079\pi\)
−0.206106 + 0.978530i \(0.566079\pi\)
\(200\) 4.36740e6 + 2.52152e6i 0.545925 + 0.315190i
\(201\) 0 0
\(202\) −372084. 644469.i −0.0451427 0.0781894i
\(203\) 134872. 77868.2i 0.0161225 0.00930834i
\(204\) 0 0
\(205\) 1.21192e7 2.09911e7i 1.40674 2.43654i
\(206\) 1.09438e7i 1.25189i
\(207\) 0 0
\(208\) 2.90817e6 0.323169
\(209\) −551032. 318138.i −0.0603584 0.0348480i
\(210\) 0 0
\(211\) 2.49743e6 + 4.32568e6i 0.265856 + 0.460476i 0.967788 0.251768i \(-0.0810121\pi\)
−0.701932 + 0.712244i \(0.747679\pi\)
\(212\) −3.84258e6 + 2.21852e6i −0.403288 + 0.232839i
\(213\) 0 0
\(214\) 1.75904e6 3.04676e6i 0.179488 0.310882i
\(215\) 6.39408e6i 0.643373i
\(216\) 0 0
\(217\) −103680. −0.0101465
\(218\) −6.59294e6 3.80644e6i −0.636370 0.367408i
\(219\) 0 0
\(220\) 7.54691e6 + 1.30716e7i 0.708763 + 1.22761i
\(221\) 4.83506e6 2.79152e6i 0.447946 0.258622i
\(222\) 0 0
\(223\) −2.84462e6 + 4.92703e6i −0.256513 + 0.444294i −0.965305 0.261123i \(-0.915907\pi\)
0.708792 + 0.705417i \(0.249240\pi\)
\(224\) 24306.7i 0.00216263i
\(225\) 0 0
\(226\) 7.01068e6 0.607344
\(227\) −1.00514e7 5.80319e6i −0.859310 0.496123i 0.00447105 0.999990i \(-0.498577\pi\)
−0.863781 + 0.503867i \(0.831910\pi\)
\(228\) 0 0
\(229\) 1.72845e6 + 2.99376e6i 0.143930 + 0.249294i 0.928973 0.370147i \(-0.120693\pi\)
−0.785043 + 0.619441i \(0.787359\pi\)
\(230\) 1.71056e7 9.87591e6i 1.40590 0.811696i
\(231\) 0 0
\(232\) 3.35919e6 5.81828e6i 0.269011 0.465941i
\(233\) 1.27739e7i 1.00985i 0.863164 + 0.504924i \(0.168480\pi\)
−0.863164 + 0.504924i \(0.831520\pi\)
\(234\) 0 0
\(235\) 1.61957e7 1.24795
\(236\) −4.23889e6 2.44732e6i −0.322490 0.186189i
\(237\) 0 0
\(238\) −23331.8 40411.9i −0.00173068 0.00299763i
\(239\) 1.11918e7 6.46157e6i 0.819795 0.473309i −0.0305510 0.999533i \(-0.509726\pi\)
0.850346 + 0.526225i \(0.176393\pi\)
\(240\) 0 0
\(241\) −3.64016e6 + 6.30494e6i −0.260057 + 0.450433i −0.966257 0.257580i \(-0.917075\pi\)
0.706200 + 0.708013i \(0.250408\pi\)
\(242\) 1.89214e7i 1.33508i
\(243\) 0 0
\(244\) 516419. 0.0355495
\(245\) 2.12432e7 + 1.22647e7i 1.44451 + 0.833989i
\(246\) 0 0
\(247\) 399440. + 691851.i 0.0265070 + 0.0459115i
\(248\) −3.87346e6 + 2.23634e6i −0.253947 + 0.146617i
\(249\) 0 0
\(250\) 7.21578e6 1.24981e7i 0.461810 0.799879i
\(251\) 1.71927e7i 1.08723i 0.839334 + 0.543616i \(0.182945\pi\)
−0.839334 + 0.543616i \(0.817055\pi\)
\(252\) 0 0
\(253\) 3.78748e7 2.33878
\(254\) −8.09785e6 4.67529e6i −0.494161 0.285304i
\(255\) 0 0
\(256\) −524288. 908093.i −0.0312500 0.0541266i
\(257\) 6.93783e6 4.00556e6i 0.408718 0.235974i −0.281521 0.959555i \(-0.590839\pi\)
0.690239 + 0.723582i \(0.257505\pi\)
\(258\) 0 0
\(259\) 35702.4 61838.4i 0.00205494 0.00355925i
\(260\) 1.89511e7i 1.07824i
\(261\) 0 0
\(262\) −1.50543e7 −0.837062
\(263\) 1.45674e7 + 8.41046e6i 0.800780 + 0.462331i 0.843744 0.536746i \(-0.180347\pi\)
−0.0429637 + 0.999077i \(0.513680\pi\)
\(264\) 0 0
\(265\) 1.44570e7 + 2.50402e7i 0.776856 + 1.34555i
\(266\) 5782.55 3338.56i 0.000307238 0.000177384i
\(267\) 0 0
\(268\) −7.59467e6 + 1.31544e7i −0.394552 + 0.683385i
\(269\) 3.33514e6i 0.171339i 0.996324 + 0.0856697i \(0.0273030\pi\)
−0.996324 + 0.0856697i \(0.972697\pi\)
\(270\) 0 0
\(271\) −1.47048e7 −0.738840 −0.369420 0.929263i \(-0.620444\pi\)
−0.369420 + 0.929263i \(0.620444\pi\)
\(272\) −1.74334e6 1.00652e6i −0.0866315 0.0500167i
\(273\) 0 0
\(274\) −7.38262e6 1.27871e7i −0.358888 0.621612i
\(275\) 5.45735e7 3.15080e7i 2.62412 1.51504i
\(276\) 0 0
\(277\) 5.46003e6 9.45705e6i 0.256895 0.444955i −0.708514 0.705697i \(-0.750634\pi\)
0.965408 + 0.260742i \(0.0839672\pi\)
\(278\) 3.96727e6i 0.184653i
\(279\) 0 0
\(280\) −158395. −0.00721552
\(281\) 1.61727e7 + 9.33733e6i 0.728894 + 0.420827i 0.818017 0.575194i \(-0.195073\pi\)
−0.0891235 + 0.996021i \(0.528407\pi\)
\(282\) 0 0
\(283\) 7.31274e6 + 1.26660e7i 0.322642 + 0.558832i 0.981032 0.193845i \(-0.0620957\pi\)
−0.658390 + 0.752677i \(0.728762\pi\)
\(284\) 4.16629e6 2.40541e6i 0.181884 0.105011i
\(285\) 0 0
\(286\) 1.81697e7 3.14709e7i 0.776694 1.34527i
\(287\) 487743.i 0.0206322i
\(288\) 0 0
\(289\) 2.02730e7 0.839893
\(290\) −3.79149e7 2.18902e7i −1.55459 0.897543i
\(291\) 0 0
\(292\) 5.30704e6 + 9.19206e6i 0.213159 + 0.369202i
\(293\) −4.14332e7 + 2.39215e7i −1.64720 + 0.951010i −0.669018 + 0.743247i \(0.733285\pi\)
−0.978179 + 0.207763i \(0.933382\pi\)
\(294\) 0 0
\(295\) −1.59480e7 + 2.76228e7i −0.621213 + 1.07597i
\(296\) 3.08036e6i 0.118775i
\(297\) 0 0
\(298\) −2.67764e7 −1.01182
\(299\) −4.11829e7 2.37769e7i −1.54065 0.889493i
\(300\) 0 0
\(301\) 64333.0 + 111428.i 0.00235904 + 0.00408597i
\(302\) −1.83089e7 + 1.05707e7i −0.664725 + 0.383779i
\(303\) 0 0
\(304\) 144023. 249456.i 0.00512639 0.00887917i
\(305\) 3.36525e6i 0.118609i
\(306\) 0 0
\(307\) 4.24782e7 1.46808 0.734042 0.679104i \(-0.237631\pi\)
0.734042 + 0.679104i \(0.237631\pi\)
\(308\) −263036. 151864.i −0.00900250 0.00519760i
\(309\) 0 0
\(310\) 1.45732e7 + 2.52415e7i 0.489180 + 0.847285i
\(311\) −2.68464e7 + 1.54998e7i −0.892494 + 0.515282i −0.874757 0.484561i \(-0.838979\pi\)
−0.0177365 + 0.999843i \(0.505646\pi\)
\(312\) 0 0
\(313\) 1.48914e7 2.57927e7i 0.485627 0.841131i −0.514237 0.857648i \(-0.671925\pi\)
0.999864 + 0.0165178i \(0.00525800\pi\)
\(314\) 1.81394e7i 0.585913i
\(315\) 0 0
\(316\) 2.86756e7 0.908764
\(317\) −1.88717e6 1.08956e6i −0.0592424 0.0342036i 0.470086 0.882620i \(-0.344223\pi\)
−0.529329 + 0.848417i \(0.677556\pi\)
\(318\) 0 0
\(319\) −4.19752e7 7.27031e7i −1.29307 2.23966i
\(320\) −5.91760e6 + 3.41653e6i −0.180591 + 0.104264i
\(321\) 0 0
\(322\) −198730. + 344210.i −0.00595244 + 0.0103099i
\(323\) 552987.i 0.0164099i
\(324\) 0 0
\(325\) −7.91201e7 −2.30482
\(326\) −4.72466e6 2.72779e6i −0.136370 0.0787331i
\(327\) 0 0
\(328\) 1.05205e7 + 1.82220e7i 0.298135 + 0.516385i
\(329\) −282239. + 162951.i −0.00792554 + 0.00457581i
\(330\) 0 0
\(331\) −6.68355e6 + 1.15762e7i −0.184299 + 0.319215i −0.943340 0.331827i \(-0.892335\pi\)
0.759041 + 0.651043i \(0.225668\pi\)
\(332\) 3.02429e7i 0.826435i
\(333\) 0 0
\(334\) −5.85480e6 −0.157135
\(335\) 8.57206e7 + 4.94908e7i 2.28008 + 1.31641i
\(336\) 0 0
\(337\) −2.22744e7 3.85804e7i −0.581991 1.00804i −0.995243 0.0974216i \(-0.968940\pi\)
0.413252 0.910617i \(-0.364393\pi\)
\(338\) −1.58670e7 + 9.16080e6i −0.410907 + 0.237237i
\(339\) 0 0
\(340\) −6.55900e6 + 1.13605e7i −0.166879 + 0.289042i
\(341\) 5.58891e7i 1.40950i
\(342\) 0 0
\(343\) −987272. −0.0244655
\(344\) 4.80694e6 + 2.77529e6i 0.118085 + 0.0681761i
\(345\) 0 0
\(346\) −1.83451e6 3.17746e6i −0.0442885 0.0767100i
\(347\) −1.80987e7 + 1.04493e7i −0.433170 + 0.250091i −0.700696 0.713460i \(-0.747127\pi\)
0.267526 + 0.963551i \(0.413794\pi\)
\(348\) 0 0
\(349\) −3.22577e7 + 5.58720e7i −0.758852 + 1.31437i 0.184584 + 0.982817i \(0.440906\pi\)
−0.943436 + 0.331554i \(0.892427\pi\)
\(350\) 661293.i 0.0154237i
\(351\) 0 0
\(352\) −1.31026e7 −0.300421
\(353\) 3.64529e6 + 2.10461e6i 0.0828719 + 0.0478461i 0.540863 0.841110i \(-0.318098\pi\)
−0.457991 + 0.888957i \(0.651431\pi\)
\(354\) 0 0
\(355\) −1.56749e7 2.71497e7i −0.350364 0.606848i
\(356\) −2.19015e7 + 1.26448e7i −0.485427 + 0.280261i
\(357\) 0 0
\(358\) −1.31575e7 + 2.27895e7i −0.286764 + 0.496690i
\(359\) 5.61320e7i 1.21319i −0.795012 0.606593i \(-0.792536\pi\)
0.795012 0.606593i \(-0.207464\pi\)
\(360\) 0 0
\(361\) −4.69668e7 −0.998318
\(362\) 1.68388e7 + 9.72186e6i 0.354964 + 0.204939i
\(363\) 0 0
\(364\) 190674. + 330256.i 0.00395354 + 0.00684774i
\(365\) 5.99002e7 3.45834e7i 1.23183 0.711195i
\(366\) 0 0
\(367\) −1.67551e7 + 2.90207e7i −0.338961 + 0.587097i −0.984238 0.176852i \(-0.943409\pi\)
0.645277 + 0.763949i \(0.276742\pi\)
\(368\) 1.71461e7i 0.344051i
\(369\) 0 0
\(370\) −2.00732e7 −0.396289
\(371\) −503877. 290913.i −0.00986740 0.00569695i
\(372\) 0 0
\(373\) −1.11388e7 1.92931e7i −0.214642 0.371770i 0.738520 0.674231i \(-0.235525\pi\)
−0.953162 + 0.302461i \(0.902192\pi\)
\(374\) −2.17842e7 + 1.25771e7i −0.416415 + 0.240417i
\(375\) 0 0
\(376\) −7.02958e6 + 1.21756e7i −0.132241 + 0.229048i
\(377\) 1.05404e8i 1.96714i
\(378\) 0 0
\(379\) 7.72205e7 1.41845 0.709226 0.704981i \(-0.249044\pi\)
0.709226 + 0.704981i \(0.249044\pi\)
\(380\) −1.62558e6 938530.i −0.0296250 0.0171040i
\(381\) 0 0
\(382\) −3.32367e7 5.75676e7i −0.596248 1.03273i
\(383\) −2.88035e7 + 1.66297e7i −0.512683 + 0.295998i −0.733936 0.679219i \(-0.762319\pi\)
0.221253 + 0.975217i \(0.428985\pi\)
\(384\) 0 0
\(385\) −989624. + 1.71408e6i −0.0173416 + 0.0300365i
\(386\) 3.93490e7i 0.684183i
\(387\) 0 0
\(388\) −4.45656e7 −0.762965
\(389\) 1.30734e7 + 7.54793e6i 0.222096 + 0.128227i 0.606920 0.794763i \(-0.292405\pi\)
−0.384825 + 0.922990i \(0.625738\pi\)
\(390\) 0 0
\(391\) 1.64584e7 + 2.85069e7i 0.275333 + 0.476891i
\(392\) −1.84408e7 + 1.06468e7i −0.306140 + 0.176750i
\(393\) 0 0
\(394\) −1.15865e6 + 2.00684e6i −0.0189436 + 0.0328114i
\(395\) 1.86865e8i 3.03205i
\(396\) 0 0
\(397\) −8.91350e7 −1.42455 −0.712273 0.701902i \(-0.752334\pi\)
−0.712273 + 0.701902i \(0.752334\pi\)
\(398\) −1.59142e7 9.18807e6i −0.252427 0.145739i
\(399\) 0 0
\(400\) 1.42639e7 + 2.47058e7i 0.222873 + 0.386027i
\(401\) −9.70320e7 + 5.60214e7i −1.50481 + 0.868803i −0.504826 + 0.863221i \(0.668443\pi\)
−0.999984 + 0.00558177i \(0.998223\pi\)
\(402\) 0 0
\(403\) 3.50859e7 6.07706e7i 0.536065 0.928492i
\(404\) 4.20966e6i 0.0638414i
\(405\) 0 0
\(406\) 880978. 0.0131640
\(407\) −3.33342e7 1.92455e7i −0.494433 0.285461i
\(408\) 0 0
\(409\) 3.33970e7 + 5.78454e7i 0.488133 + 0.845471i 0.999907 0.0136491i \(-0.00434478\pi\)
−0.511774 + 0.859120i \(0.671011\pi\)
\(410\) 1.18744e8 6.85567e7i 1.72290 0.994715i
\(411\) 0 0
\(412\) 3.09537e7 5.36135e7i 0.442610 0.766624i
\(413\) 641833.i 0.00911113i
\(414\) 0 0
\(415\) −1.97078e8 −2.75736
\(416\) 1.42471e7 + 8.22554e6i 0.197900 + 0.114257i
\(417\) 0 0
\(418\) −1.79966e6 3.11711e6i −0.0246412 0.0426799i
\(419\) 4.10125e7 2.36786e7i 0.557537 0.321894i −0.194619 0.980879i \(-0.562347\pi\)
0.752156 + 0.658985i \(0.229014\pi\)
\(420\) 0 0
\(421\) −3.30784e7 + 5.72936e7i −0.443301 + 0.767820i −0.997932 0.0642763i \(-0.979526\pi\)
0.554631 + 0.832096i \(0.312859\pi\)
\(422\) 2.82552e7i 0.375977i
\(423\) 0 0
\(424\) −2.50996e7 −0.329283
\(425\) 4.74297e7 + 2.73835e7i 0.617851 + 0.356716i
\(426\) 0 0
\(427\) 33859.0 + 58645.5i 0.000434901 + 0.000753270i
\(428\) 1.72350e7 9.95066e6i 0.219827 0.126917i
\(429\) 0 0
\(430\) 1.80852e7 3.13245e7i 0.227467 0.393984i
\(431\) 9.06666e7i 1.13244i −0.824254 0.566221i \(-0.808405\pi\)
0.824254 0.566221i \(-0.191595\pi\)
\(432\) 0 0
\(433\) −699414. −0.00861530 −0.00430765 0.999991i \(-0.501371\pi\)
−0.00430765 + 0.999991i \(0.501371\pi\)
\(434\) −507926. 293251.i −0.00621342 0.00358732i
\(435\) 0 0
\(436\) −2.15325e7 3.72953e7i −0.259797 0.449982i
\(437\) −4.07906e6 + 2.35505e6i −0.0488782 + 0.0282199i
\(438\) 0 0
\(439\) 1.28648e7 2.22825e7i 0.152058 0.263372i −0.779926 0.625872i \(-0.784743\pi\)
0.931984 + 0.362500i \(0.118077\pi\)
\(440\) 8.53835e7i 1.00234i
\(441\) 0 0
\(442\) 3.15825e7 0.365746
\(443\) −143395. 82789.0i −0.00164938 0.000952273i 0.499175 0.866501i \(-0.333636\pi\)
−0.500824 + 0.865549i \(0.666970\pi\)
\(444\) 0 0
\(445\) 8.24003e7 + 1.42721e8i 0.935080 + 1.61961i
\(446\) −2.78715e7 + 1.60916e7i −0.314163 + 0.181382i
\(447\) 0 0
\(448\) 68749.8 119078.i 0.000764605 0.00132433i
\(449\) 4.30456e7i 0.475542i −0.971321 0.237771i \(-0.923583\pi\)
0.971321 0.237771i \(-0.0764169\pi\)
\(450\) 0 0
\(451\) 2.62920e8 2.86611
\(452\) 3.43452e7 + 1.98292e7i 0.371921 + 0.214729i
\(453\) 0 0
\(454\) −3.28278e7 5.68594e7i −0.350812 0.607624i
\(455\) 2.15212e6 1.24253e6i 0.0228472 0.0131908i
\(456\) 0 0
\(457\) 6.77455e7 1.17339e8i 0.709793 1.22940i −0.255141 0.966904i \(-0.582122\pi\)
0.964934 0.262493i \(-0.0845448\pi\)
\(458\) 1.95552e7i 0.203547i
\(459\) 0 0
\(460\) 1.11733e8 1.14791
\(461\) −2.77431e7 1.60175e7i −0.283173 0.163490i 0.351686 0.936118i \(-0.385608\pi\)
−0.634859 + 0.772628i \(0.718942\pi\)
\(462\) 0 0
\(463\) −6.46664e7 1.12006e8i −0.651532 1.12849i −0.982751 0.184933i \(-0.940793\pi\)
0.331219 0.943554i \(-0.392540\pi\)
\(464\) 3.29132e7 1.90024e7i 0.329470 0.190220i
\(465\) 0 0
\(466\) −3.61301e7 + 6.25791e7i −0.357035 + 0.618403i
\(467\) 8.49294e7i 0.833887i 0.908932 + 0.416944i \(0.136899\pi\)
−0.908932 + 0.416944i \(0.863101\pi\)
\(468\) 0 0
\(469\) −1.99178e6 −0.0193073
\(470\) 7.93424e7 + 4.58084e7i 0.764209 + 0.441216i
\(471\) 0 0
\(472\) −1.38441e7 2.39788e7i −0.131656 0.228035i
\(473\) 6.00657e7 3.46790e7i 0.567601 0.327705i
\(474\) 0 0
\(475\) −3.91832e6 + 6.78673e6i −0.0365611 + 0.0633257i
\(476\) 263969.i 0.00244755i
\(477\) 0 0
\(478\) 7.31043e7 0.669360
\(479\) −1.00215e8 5.78593e7i −0.911858 0.526461i −0.0308294 0.999525i \(-0.509815\pi\)
−0.881028 + 0.473063i \(0.843148\pi\)
\(480\) 0 0
\(481\) 2.41638e7 + 4.18530e7i 0.217135 + 0.376089i
\(482\) −3.56661e7 + 2.05918e7i −0.318504 + 0.183888i
\(483\) 0 0
\(484\) −5.35179e7 + 9.26957e7i −0.472023 + 0.817568i
\(485\) 2.90412e8i 2.54560i
\(486\) 0 0
\(487\) 4.52839e7 0.392064 0.196032 0.980597i \(-0.437194\pi\)
0.196032 + 0.980597i \(0.437194\pi\)
\(488\) 2.52993e6 + 1.46065e6i 0.0217695 + 0.0125686i
\(489\) 0 0
\(490\) 6.93799e7 + 1.20169e8i 0.589719 + 1.02142i
\(491\) 1.76939e8 1.02156e8i 1.49479 0.863017i 0.494807 0.869003i \(-0.335239\pi\)
0.999982 + 0.00598645i \(0.00190556\pi\)
\(492\) 0 0
\(493\) 3.64805e7 6.31861e7i 0.304453 0.527328i
\(494\) 4.51915e6i 0.0374866i
\(495\) 0 0
\(496\) −2.53013e7 −0.207347
\(497\) 546324. + 315420.i 0.00445022 + 0.00256933i
\(498\) 0 0
\(499\) 1.46495e7 + 2.53736e7i 0.117902 + 0.204212i 0.918936 0.394407i \(-0.129050\pi\)
−0.801034 + 0.598619i \(0.795717\pi\)
\(500\) 7.06999e7 4.08186e7i 0.565600 0.326549i
\(501\) 0 0
\(502\) −4.86282e7 + 8.42265e7i −0.384394 + 0.665790i
\(503\) 1.64834e8i 1.29522i −0.761973 0.647609i \(-0.775769\pi\)
0.761973 0.647609i \(-0.224231\pi\)
\(504\) 0 0
\(505\) −2.74323e7 −0.213004
\(506\) 1.85548e8 + 1.07126e8i 1.43220 + 0.826882i
\(507\) 0 0
\(508\) −2.64475e7 4.58083e7i −0.201740 0.349425i
\(509\) −1.44920e8 + 8.36696e7i −1.09894 + 0.634474i −0.935943 0.352152i \(-0.885450\pi\)
−0.162999 + 0.986626i \(0.552117\pi\)
\(510\) 0 0
\(511\) −695910. + 1.20535e6i −0.00521544 + 0.00903340i
\(512\) 5.93164e6i 0.0441942i
\(513\) 0 0
\(514\) 4.53177e7 0.333717
\(515\) −3.49373e8 2.01711e8i −2.55781 1.47675i
\(516\) 0 0
\(517\) 8.78391e7 + 1.52142e8i 0.635648 + 1.10097i
\(518\) 349811. 201963.i 0.00251677 0.00145306i
\(519\) 0 0
\(520\) 5.36019e7 9.28411e7i 0.381215 0.660283i
\(521\) 6.01419e7i 0.425270i −0.977132 0.212635i \(-0.931796\pi\)
0.977132 0.212635i \(-0.0682045\pi\)
\(522\) 0 0
\(523\) 1.09251e8 0.763698 0.381849 0.924225i \(-0.375287\pi\)
0.381849 + 0.924225i \(0.375287\pi\)
\(524\) −7.37509e7 4.25801e7i −0.512594 0.295946i
\(525\) 0 0
\(526\) 4.75768e7 + 8.24054e7i 0.326917 + 0.566237i
\(527\) −4.20655e7 + 2.42865e7i −0.287405 + 0.165933i
\(528\) 0 0
\(529\) 6.61676e7 1.14606e8i 0.446970 0.774175i
\(530\) 1.63562e8i 1.09864i
\(531\) 0 0
\(532\) 37771.5 0.000250859
\(533\) −2.85884e8 1.65055e8i −1.88803 1.09005i
\(534\) 0 0
\(535\) −6.48436e7 1.12312e8i −0.423454 0.733443i
\(536\) −7.44123e7 + 4.29620e7i −0.483226 + 0.278991i
\(537\) 0 0
\(538\) −9.43320e6 + 1.63388e7i −0.0605776 + 0.104923i
\(539\) 2.66077e8i 1.69918i
\(540\) 0 0
\(541\) 4.52159e7 0.285561 0.142781 0.989754i \(-0.454396\pi\)
0.142781 + 0.989754i \(0.454396\pi\)
\(542\) −7.20383e7 4.15914e7i −0.452445 0.261219i
\(543\) 0 0
\(544\) −5.69373e6 9.86183e6i −0.0353672 0.0612577i
\(545\) −2.43035e8 + 1.40317e8i −1.50134 + 0.866801i
\(546\) 0 0
\(547\) −2.55726e7 + 4.42930e7i −0.156247 + 0.270628i −0.933512 0.358545i \(-0.883273\pi\)
0.777265 + 0.629173i \(0.216606\pi\)
\(548\) 8.35248e7i 0.507544i
\(549\) 0 0
\(550\) 3.56473e8 2.14258
\(551\) 9.04133e6 + 5.22001e6i 0.0540477 + 0.0312045i
\(552\) 0 0
\(553\) 1.88011e6 + 3.25645e6i 0.0111175 + 0.0192561i
\(554\) 5.34971e7 3.08866e7i 0.314631 0.181652i
\(555\) 0 0
\(556\) −1.12211e7 + 1.94356e7i −0.0652849 + 0.113077i
\(557\) 2.43306e7i 0.140795i −0.997519 0.0703974i \(-0.977573\pi\)
0.997519 0.0703974i \(-0.0224267\pi\)
\(558\) 0 0
\(559\) −8.70827e7 −0.498536
\(560\) −775974. 448009.i −0.00441858 0.00255107i
\(561\) 0 0
\(562\) 5.28199e7 + 9.14868e7i 0.297570 + 0.515406i
\(563\) 1.25053e8 7.21992e7i 0.700758 0.404583i −0.106872 0.994273i \(-0.534083\pi\)
0.807630 + 0.589690i \(0.200750\pi\)
\(564\) 0 0
\(565\) 1.29217e8 2.23811e8i 0.716432 1.24090i
\(566\) 8.27342e7i 0.456284i
\(567\) 0 0
\(568\) 2.72141e7 0.148508
\(569\) 7.20146e7 + 4.15777e7i 0.390916 + 0.225696i 0.682557 0.730832i \(-0.260868\pi\)
−0.291641 + 0.956528i \(0.594201\pi\)
\(570\) 0 0
\(571\) 1.13040e8 + 1.95791e8i 0.607188 + 1.05168i 0.991702 + 0.128561i \(0.0410359\pi\)
−0.384513 + 0.923119i \(0.625631\pi\)
\(572\) 1.78026e8 1.02783e8i 0.951252 0.549205i
\(573\) 0 0
\(574\) −1.37955e6 + 2.38944e6i −0.00729458 + 0.0126346i
\(575\) 4.66481e8i 2.45375i
\(576\) 0 0
\(577\) 4.11006e7 0.213954 0.106977 0.994261i \(-0.465883\pi\)
0.106977 + 0.994261i \(0.465883\pi\)
\(578\) 9.93169e7 + 5.73406e7i 0.514327 + 0.296947i
\(579\) 0 0
\(580\) −1.23830e8 2.14479e8i −0.634659 1.09926i
\(581\) 3.43443e6 1.98287e6i 0.0175116 0.0101103i
\(582\) 0 0
\(583\) −1.56818e8 + 2.71617e8i −0.791390 + 1.37073i
\(584\) 6.00423e7i 0.301452i
\(585\) 0 0
\(586\) −2.70640e8 −1.34493
\(587\) 9.93271e7 + 5.73465e7i 0.491081 + 0.283526i 0.725023 0.688725i \(-0.241829\pi\)
−0.233942 + 0.972251i \(0.575162\pi\)
\(588\) 0 0
\(589\) −3.47517e6 6.01917e6i −0.0170071 0.0294571i
\(590\) −1.56258e8 + 9.02156e7i −0.760827 + 0.439264i
\(591\) 0 0
\(592\) 8.71257e6 1.50906e7i 0.0419934 0.0727347i
\(593\) 2.90487e8i 1.39304i 0.717539 + 0.696518i \(0.245269\pi\)
−0.717539 + 0.696518i \(0.754731\pi\)
\(594\) 0 0
\(595\) −1.72016e6 −0.00816616
\(596\) −1.31177e8 7.57350e7i −0.619610 0.357732i
\(597\) 0 0
\(598\) −1.34503e8 2.32966e8i −0.628966 1.08940i
\(599\) 3.09303e8 1.78576e8i 1.43914 0.830888i 0.441351 0.897335i \(-0.354499\pi\)
0.997790 + 0.0664462i \(0.0211661\pi\)
\(600\) 0 0
\(601\) 4.20047e7 7.27542e7i 0.193497 0.335147i −0.752910 0.658124i \(-0.771350\pi\)
0.946407 + 0.322977i \(0.104684\pi\)
\(602\) 727845.i 0.00333618i
\(603\) 0 0
\(604\) −1.19593e8 −0.542746
\(605\) 6.04053e8 + 3.48750e8i 2.72778 + 1.57488i
\(606\) 0 0
\(607\) −2.58143e7 4.47117e7i −0.115424 0.199920i 0.802525 0.596618i \(-0.203489\pi\)
−0.917949 + 0.396698i \(0.870156\pi\)
\(608\) 1.41113e6 814718.i 0.00627852 0.00362491i
\(609\) 0 0
\(610\) 9.51838e6 1.64863e7i 0.0419347 0.0726330i
\(611\) 2.20574e8i 0.967009i
\(612\) 0 0
\(613\) 4.44326e7 0.192895 0.0964473 0.995338i \(-0.469252\pi\)
0.0964473 + 0.995338i \(0.469252\pi\)
\(614\) 2.08100e8 + 1.20147e8i 0.899015 + 0.519046i
\(615\) 0 0
\(616\) −859072. 1.48796e6i −0.00367526 0.00636573i
\(617\) −1.43248e8 + 8.27040e7i −0.609862 + 0.352104i −0.772911 0.634514i \(-0.781200\pi\)
0.163049 + 0.986618i \(0.447867\pi\)
\(618\) 0 0
\(619\) −1.34081e8 + 2.32235e8i −0.565320 + 0.979164i 0.431699 + 0.902018i \(0.357914\pi\)
−0.997020 + 0.0771460i \(0.975419\pi\)
\(620\) 1.64876e8i 0.691805i
\(621\) 0 0
\(622\) −1.75360e8 −0.728718
\(623\) −2.87194e6 1.65811e6i −0.0118771 0.00685726i
\(624\) 0 0
\(625\) −4.83458e7 8.37373e7i −0.198024 0.342988i
\(626\) 1.45905e8 8.42385e7i 0.594769 0.343390i
\(627\) 0 0
\(628\) 5.13059e7 8.88644e7i 0.207152 0.358797i
\(629\) 3.34525e7i 0.134424i
\(630\) 0 0
\(631\) 1.13998e8 0.453741 0.226871 0.973925i \(-0.427151\pi\)
0.226871 + 0.973925i \(0.427151\pi\)
\(632\) 1.40481e8 + 8.11068e7i 0.556502 + 0.321297i
\(633\) 0 0
\(634\) −6.16346e6 1.06754e7i −0.0241856 0.0418907i
\(635\) −2.98511e8 + 1.72345e8i −1.16584 + 0.673098i
\(636\) 0 0
\(637\) 1.67037e8 2.89317e8i 0.646241 1.11932i
\(638\) 4.74895e8i 1.82867i
\(639\) 0 0
\(640\) −3.86536e7 −0.147452
\(641\) −3.16652e7 1.82819e7i −0.120229 0.0694142i 0.438680 0.898644i \(-0.355446\pi\)
−0.558908 + 0.829229i \(0.688780\pi\)
\(642\) 0 0
\(643\) 1.41134e8 + 2.44452e8i 0.530883 + 0.919517i 0.999350 + 0.0360362i \(0.0114732\pi\)
−0.468467 + 0.883481i \(0.655194\pi\)
\(644\) −1.94715e6 + 1.12419e6i −0.00729022 + 0.00420901i
\(645\) 0 0
\(646\) 1.56408e6 2.70907e6i 0.00580179 0.0100490i
\(647\) 1.45187e8i 0.536062i 0.963410 + 0.268031i \(0.0863729\pi\)
−0.963410 + 0.268031i \(0.913627\pi\)
\(648\) 0 0
\(649\) −3.45983e8 −1.26567
\(650\) −3.87608e8 2.23786e8i −1.41141 0.814877i
\(651\) 0 0
\(652\) −1.54307e7 2.67267e7i −0.0556727 0.0964280i
\(653\) 8.59015e7 4.95952e7i 0.308504 0.178115i −0.337753 0.941235i \(-0.609667\pi\)
0.646257 + 0.763120i \(0.276333\pi\)
\(654\) 0 0
\(655\) −2.77474e8 + 4.80599e8i −0.987412 + 1.71025i
\(656\) 1.19025e8i 0.421627i
\(657\) 0 0
\(658\) −1.84357e6 −0.00647117
\(659\) −1.46859e8 8.47892e7i −0.513150 0.296268i 0.220977 0.975279i \(-0.429075\pi\)
−0.734128 + 0.679011i \(0.762409\pi\)
\(660\) 0 0
\(661\) −2.69025e8 4.65965e8i −0.931511 1.61342i −0.780740 0.624856i \(-0.785158\pi\)
−0.150771 0.988569i \(-0.548176\pi\)
\(662\) −6.54851e7 + 3.78079e7i −0.225719 + 0.130319i
\(663\) 0 0
\(664\) 8.55398e7 1.48159e8i 0.292189 0.506086i
\(665\) 246138.i 0.000836978i
\(666\) 0 0
\(667\) −6.21449e8 −2.09425
\(668\) −2.86825e7 1.65599e7i −0.0962251 0.0555556i
\(669\) 0 0
\(670\) 2.79962e8 + 4.84909e8i 0.930840 + 1.61226i
\(671\) 3.16131e7 1.82518e7i 0.104640 0.0604141i
\(672\) 0 0
\(673\) 1.92682e7 3.33736e7i 0.0632116 0.109486i −0.832688 0.553743i \(-0.813199\pi\)
0.895899 + 0.444257i \(0.146532\pi\)
\(674\) 2.52006e8i 0.823060i
\(675\) 0 0
\(676\) −1.03643e8 −0.335504
\(677\) 1.65239e8 + 9.54008e7i 0.532533 + 0.307458i 0.742047 0.670347i \(-0.233855\pi\)
−0.209514 + 0.977806i \(0.567188\pi\)
\(678\) 0 0
\(679\) −2.92194e6 5.06095e6i −0.00933387 0.0161667i
\(680\) −6.42648e7 + 3.71033e7i −0.204384 + 0.118001i
\(681\) 0 0
\(682\) −1.58078e8 + 2.73799e8i −0.498332 + 0.863136i
\(683\) 5.45896e8i 1.71336i −0.515850 0.856679i \(-0.672524\pi\)
0.515850 0.856679i \(-0.327476\pi\)
\(684\) 0 0
\(685\) −5.44291e8 −1.69340
\(686\) −4.83663e6 2.79243e6i −0.0149820 0.00864987i
\(687\) 0 0
\(688\) 1.56994e7 + 2.71921e7i 0.0482078 + 0.0834984i
\(689\) 3.41030e8 1.96894e8i 1.04264 0.601969i
\(690\) 0 0
\(691\) 8.52235e7 1.47611e8i 0.258301 0.447390i −0.707486 0.706727i \(-0.750171\pi\)
0.965787 + 0.259337i \(0.0835042\pi\)
\(692\) 2.07551e7i 0.0626334i
\(693\) 0 0
\(694\) −1.18220e8 −0.353682
\(695\) 1.26652e8 + 7.31227e7i 0.377275 + 0.217820i
\(696\) 0 0
\(697\) 1.14251e8 + 1.97889e8i 0.337414 + 0.584419i
\(698\) −3.16060e8 + 1.82477e8i −0.929400 + 0.536589i
\(699\) 0 0
\(700\) −1.87042e6 + 3.23966e6i −0.00545311 + 0.00944507i
\(701\) 8.02305e7i 0.232909i −0.993196 0.116454i \(-0.962847\pi\)
0.993196 0.116454i \(-0.0371529\pi\)
\(702\) 0 0
\(703\) 4.78673e6 0.0137776
\(704\) −6.41895e7 3.70598e7i −0.183970 0.106215i
\(705\) 0 0
\(706\) 1.19055e7 + 2.06209e7i 0.0338323 + 0.0585993i
\(707\) 478056. 276006.i 0.00135276 0.000781015i
\(708\) 0 0
\(709\) −2.00566e8 + 3.47390e8i −0.562754 + 0.974718i 0.434501 + 0.900671i \(0.356925\pi\)
−0.997255 + 0.0740465i \(0.976409\pi\)
\(710\) 1.77341e8i 0.495489i
\(711\) 0 0
\(712\) −1.43060e8 −0.396349
\(713\) 3.58295e8 + 2.06862e8i 0.988489 + 0.570705i
\(714\) 0 0
\(715\) −6.69790e8 1.16011e9i −1.83240 3.17381i
\(716\) −1.28917e8 + 7.44302e7i −0.351213 + 0.202773i
\(717\) 0 0
\(718\) 1.58765e8 2.74990e8i 0.428926 0.742922i
\(719\) 1.02302e8i 0.275232i −0.990486 0.137616i \(-0.956056\pi\)
0.990486 0.137616i \(-0.0439439\pi\)
\(720\) 0 0
\(721\) 8.11792e6 0.0216590
\(722\) −2.30089e8 1.32842e8i −0.611342 0.352959i
\(723\) 0 0
\(724\) 5.49951e7 + 9.52544e7i 0.144913 + 0.250997i
\(725\) −8.95441e8 + 5.16983e8i −2.34976 + 1.35663i
\(726\) 0 0
\(727\) 2.93837e8 5.08941e8i 0.764722 1.32454i −0.175671 0.984449i \(-0.556209\pi\)
0.940393 0.340089i \(-0.110457\pi\)
\(728\) 2.15723e6i 0.00559115i
\(729\) 0 0
\(730\) 3.91266e8 1.00578
\(731\) 5.22030e7 + 3.01394e7i 0.133642 + 0.0771583i
\(732\) 0 0
\(733\) 5.60077e7 + 9.70083e7i 0.142212 + 0.246318i 0.928329 0.371759i \(-0.121245\pi\)
−0.786117 + 0.618077i \(0.787912\pi\)
\(734\) −1.64166e8 + 9.47813e7i −0.415141 + 0.239682i
\(735\) 0 0
\(736\) −4.84966e7 + 8.39986e7i −0.121640 + 0.210687i
\(737\) 1.07367e9i 2.68207i
\(738\) 0 0
\(739\) 6.86968e8 1.70217 0.851086 0.525027i \(-0.175945\pi\)
0.851086 + 0.525027i \(0.175945\pi\)
\(740\) −9.83382e7 5.67756e7i −0.242676 0.140109i
\(741\) 0 0
\(742\) −1.64565e6 2.85036e6i −0.00402835 0.00697730i
\(743\) 4.82909e8 2.78808e8i 1.17733 0.679732i 0.221936 0.975061i \(-0.428763\pi\)
0.955396 + 0.295329i \(0.0954292\pi\)
\(744\) 0 0
\(745\) −4.93528e8 + 8.54816e8i −1.19356 + 2.06730i
\(746\) 1.26022e8i 0.303549i
\(747\) 0 0
\(748\) −1.42294e8 −0.340001
\(749\) 2.26003e6 + 1.30483e6i 0.00537859 + 0.00310533i
\(750\) 0 0
\(751\) −2.02498e8 3.50737e8i −0.478080 0.828059i 0.521604 0.853188i \(-0.325334\pi\)
−0.999684 + 0.0251288i \(0.992000\pi\)
\(752\) −6.88756e7 + 3.97653e7i −0.161961 + 0.0935085i
\(753\) 0 0
\(754\) −2.98128e8 + 5.16374e8i −0.695488 + 1.20462i
\(755\) 7.79332e8i 1.81085i
\(756\) 0 0
\(757\) 6.51769e8 1.50247 0.751235 0.660035i \(-0.229458\pi\)
0.751235 + 0.660035i \(0.229458\pi\)
\(758\) 3.78301e8 + 2.18412e8i 0.868621 + 0.501499i
\(759\) 0 0
\(760\) −5.30912e6 9.19567e6i −0.0120943 0.0209480i
\(761\) 2.69514e8 1.55604e8i 0.611543 0.353074i −0.162026 0.986786i \(-0.551803\pi\)
0.773569 + 0.633712i \(0.218470\pi\)
\(762\) 0 0
\(763\) 2.82355e6 4.89053e6i 0.00635655 0.0110099i
\(764\) 3.76030e8i 0.843222i
\(765\) 0 0
\(766\) −1.88144e8 −0.418604
\(767\) 3.76202e8 + 2.17200e8i 0.833749 + 0.481365i
\(768\) 0 0
\(769\) 2.18605e8 + 3.78636e8i 0.480708 + 0.832612i 0.999755 0.0221345i \(-0.00704620\pi\)
−0.519047 + 0.854746i \(0.673713\pi\)
\(770\) −9.69629e6 + 5.59816e6i −0.0212390 + 0.0122623i
\(771\) 0 0
\(772\) 1.11296e8 1.92770e8i 0.241895 0.418975i
\(773\) 5.41906e7i 0.117324i −0.998278 0.0586619i \(-0.981317\pi\)
0.998278 0.0586619i \(-0.0186834\pi\)
\(774\) 0 0
\(775\) 6.88352e8 1.47879
\(776\) −2.18326e8 1.26051e8i −0.467219 0.269749i
\(777\) 0 0
\(778\) 4.26976e7 + 7.39543e7i 0.0906701 + 0.157045i
\(779\) −2.83161e7 + 1.63483e7i −0.0598991 + 0.0345828i
\(780\) 0 0
\(781\) 1.70029e8 2.94498e8i 0.356918 0.618201i
\(782\) 1.86206e8i 0.389380i
\(783\) 0 0
\(784\) −1.20455e8 −0.249963
\(785\) −5.79086e8 3.34336e8i −1.19711 0.691152i
\(786\) 0 0
\(787\) 2.01160e7 + 3.48419e7i 0.0412684 + 0.0714789i 0.885922 0.463835i \(-0.153527\pi\)
−0.844653 + 0.535314i \(0.820193\pi\)
\(788\) −1.13524e7 + 6.55431e6i −0.0232011 + 0.0133952i
\(789\) 0 0
\(790\) 5.28534e8 9.15447e8i 1.07199 1.85674i
\(791\) 5.20039e6i 0.0105077i
\(792\) 0 0
\(793\) −4.58323e7 −0.0919078
\(794\) −4.36670e8 2.52112e8i −0.872353 0.503653i
\(795\) 0 0
\(796\) −5.19756e7 9.00244e7i −0.103053 0.178493i
\(797\) 7.74252e7 4.47015e7i 0.152935 0.0882972i −0.421579 0.906791i \(-0.638524\pi\)
0.574515 + 0.818494i \(0.305191\pi\)
\(798\) 0 0
\(799\) −7.63408e7 + 1.32226e8i −0.149664 + 0.259225i
\(800\) 1.61377e8i 0.315190i
\(801\) 0 0
\(802\) −6.33810e8 −1.22867
\(803\) 6.49750e8 + 3.75133e8i 1.25487 + 0.724501i
\(804\) 0 0
\(805\) 7.32577e6 + 1.26886e7i 0.0140432 + 0.0243235i
\(806\) 3.43770e8 1.98476e8i 0.656543 0.379055i
\(807\) 0 0
\(808\) 1.19067e7 2.06230e7i 0.0225713 0.0390947i
\(809\) 7.82985e8i 1.47879i −0.673270 0.739397i \(-0.735111\pi\)
0.673270 0.739397i \(-0.264889\pi\)
\(810\) 0 0
\(811\) −6.76238e6 −0.0126776 −0.00633880 0.999980i \(-0.502018\pi\)
−0.00633880 + 0.999980i \(0.502018\pi\)
\(812\) 4.31590e6 + 2.49178e6i 0.00806126 + 0.00465417i
\(813\) 0 0
\(814\) −1.08869e8 1.88567e8i −0.201851 0.349617i
\(815\) −1.74165e8 + 1.00554e8i −0.321728 + 0.185750i
\(816\) 0 0
\(817\) −4.31266e6 + 7.46975e6i −0.00790823 + 0.0136974i
\(818\) 3.77844e8i 0.690324i
\(819\) 0 0
\(820\) 7.75631e8 1.40674
\(821\) −2.54001e7 1.46648e7i −0.0458993 0.0265000i 0.476875 0.878971i \(-0.341770\pi\)
−0.522774 + 0.852471i \(0.675103\pi\)
\(822\) 0 0
\(823\) 4.45476e8 + 7.71587e8i 0.799144 + 1.38416i 0.920174 + 0.391509i \(0.128047\pi\)
−0.121031 + 0.992649i \(0.538620\pi\)
\(824\) 3.03284e8 1.75101e8i 0.542085 0.312973i
\(825\) 0 0
\(826\) 1.81538e6 3.14433e6i 0.00322127 0.00557940i
\(827\) 4.36886e8i 0.772417i −0.922411 0.386209i \(-0.873784\pi\)
0.922411 0.386209i \(-0.126216\pi\)
\(828\) 0 0
\(829\) 2.08489e8 0.365948 0.182974 0.983118i \(-0.441428\pi\)
0.182974 + 0.983118i \(0.441428\pi\)
\(830\) −9.65482e8 5.57421e8i −1.68853 0.974876i
\(831\) 0 0
\(832\) 4.65307e7 + 8.05935e7i 0.0807922 + 0.139936i
\(833\) −2.00265e8 + 1.15623e8i −0.346474 + 0.200037i
\(834\) 0 0
\(835\) −1.07913e8 + 1.86910e8i −0.185359 + 0.321051i
\(836\) 2.03609e7i 0.0348480i
\(837\) 0 0
\(838\) 2.67892e8 0.455227
\(839\) −9.64994e8 5.57140e8i −1.63395 0.943361i −0.982858 0.184362i \(-0.940978\pi\)
−0.651091 0.758999i \(-0.725689\pi\)
\(840\) 0 0
\(841\) 3.91317e8 + 6.77781e8i 0.657871 + 1.13947i
\(842\) −3.24101e8 + 1.87120e8i −0.542931 + 0.313461i
\(843\) 0 0
\(844\) −7.99178e7 + 1.38422e8i −0.132928 + 0.230238i
\(845\) 6.75389e8i 1.11940i
\(846\) 0 0
\(847\) −1.40356e7 −0.0230983
\(848\) −1.22963e8 7.09925e7i −0.201644 0.116419i
\(849\) 0 0
\(850\) 1.54905e8 + 2.68303e8i 0.252236 + 0.436886i
\(851\) −2.46759e8 + 1.42467e8i −0.400392 + 0.231166i
\(852\) 0 0
\(853\) 3.51904e7 6.09516e7i 0.0566993 0.0982060i −0.836283 0.548299i \(-0.815276\pi\)
0.892982 + 0.450093i \(0.148609\pi\)
\(854\) 383071.i 0.000615043i
\(855\) 0 0
\(856\) 1.12579e8 0.179488
\(857\) −1.37625e8 7.94581e7i −0.218653 0.126240i 0.386673 0.922217i \(-0.373624\pi\)
−0.605327 + 0.795977i \(0.706957\pi\)
\(858\) 0 0
\(859\) −1.57121e8 2.72141e8i −0.247887 0.429353i 0.715052 0.699071i \(-0.246403\pi\)
−0.962939 + 0.269718i \(0.913069\pi\)
\(860\) 1.77198e8 1.02305e8i 0.278589 0.160843i
\(861\) 0 0
\(862\) 2.56444e8 4.44174e8i 0.400378 0.693476i
\(863\) 3.90351e8i 0.607328i 0.952779 + 0.303664i \(0.0982101\pi\)
−0.952779 + 0.303664i \(0.901790\pi\)
\(864\) 0 0
\(865\) −1.35251e8 −0.208974
\(866\) −3.42641e6 1.97824e6i −0.00527577 0.00304597i
\(867\) 0 0
\(868\) −1.65888e6 2.87326e6i −0.00253662 0.00439355i
\(869\) 1.75540e9 1.01348e9i 2.67496 1.54439i
\(870\) 0 0
\(871\) 6.74029e8 1.16745e9i 1.02006 1.76679i
\(872\) 2.43612e8i 0.367408i
\(873\) 0 0
\(874\) −2.66443e7 −0.0399089
\(875\) 9.27087e6 + 5.35254e6i 0.0138387 + 0.00798979i
\(876\) 0 0
\(877\) 5.77897e8 + 1.00095e9i 0.856745 + 1.48393i 0.875017 + 0.484092i \(0.160850\pi\)
−0.0182723 + 0.999833i \(0.505817\pi\)
\(878\) 1.26049e8 7.27743e7i 0.186232 0.107521i
\(879\) 0 0
\(880\) −2.41501e8 + 4.18292e8i −0.354381 + 0.613806i
\(881\) 7.82859e8i 1.14487i 0.819951 + 0.572434i \(0.194001\pi\)
−0.819951 + 0.572434i \(0.805999\pi\)
\(882\) 0 0
\(883\) 1.01047e9 1.46772 0.733860 0.679300i \(-0.237717\pi\)
0.733860 + 0.679300i \(0.237717\pi\)
\(884\) 1.54722e8 + 8.93288e7i 0.223973 + 0.129311i
\(885\) 0 0
\(886\) −468325. 811163.i −0.000673358 0.00116629i
\(887\) 2.84354e8 1.64172e8i 0.407463 0.235249i −0.282236 0.959345i \(-0.591076\pi\)
0.689699 + 0.724096i \(0.257743\pi\)
\(888\) 0 0
\(889\) 3.46805e6 6.00684e6i 0.00493605 0.00854950i
\(890\) 9.32253e8i 1.32240i
\(891\) 0 0
\(892\) −1.82056e8 −0.256513
\(893\) −1.89203e7 1.09236e7i −0.0265689 0.0153396i
\(894\) 0 0
\(895\) 4.85026e8 + 8.40089e8i 0.676543 + 1.17181i
\(896\) 673607. 388907.i 0.000936446 0.000540657i
\(897\) 0 0
\(898\) 1.21751e8 2.10879e8i 0.168130 0.291209i
\(899\) 9.17028e8i 1.26213i
\(900\) 0 0
\(901\) −2.72580e8 −0.372666
\(902\) 1.28804e9 + 7.43649e8i 1.75513 + 1.01332i
\(903\) 0 0
\(904\) 1.12171e8 + 1.94286e8i 0.151836 + 0.262988i
\(905\) 6.20727e8 3.58377e8i 0.837442 0.483497i
\(906\) 0 0
\(907\) −1.07719e8 + 1.86575e8i −0.144368 + 0.250053i −0.929137 0.369736i \(-0.879448\pi\)
0.784769 + 0.619789i \(0.212782\pi\)
\(908\) 3.71404e8i 0.496123i
\(909\) 0 0
\(910\) 1.40576e7 0.0186546
\(911\) 6.51453e8 + 3.76117e8i 0.861645 + 0.497471i 0.864563 0.502525i \(-0.167596\pi\)
−0.00291806 + 0.999996i \(0.500929\pi\)
\(912\) 0 0
\(913\) −1.06887e9 1.85134e9i −1.40448 2.43262i
\(914\) 6.63767e8 3.83226e8i 0.869315 0.501899i
\(915\) 0 0
\(916\) −5.53104e7 + 9.58004e7i −0.0719649 + 0.124647i
\(917\) 1.11670e7i 0.0144820i
\(918\) 0 0
\(919\) 6.81968e8 0.878653 0.439327 0.898327i \(-0.355217\pi\)
0.439327 + 0.898327i \(0.355217\pi\)
\(920\) 5.47378e8 + 3.16029e8i 0.702950 + 0.405848i
\(921\) 0 0
\(922\) −9.06085e7 1.56938e8i −0.115605 0.200233i
\(923\) −3.69759e8 + 2.13480e8i −0.470234 + 0.271489i
\(924\) 0 0
\(925\) −2.37036e8 + 4.10558e8i −0.299494 + 0.518739i
\(926\) 7.31617e8i 0.921406i
\(927\) 0 0
\(928\) 2.14988e8 0.269011
\(929\) 9.66823e7 + 5.58196e7i 0.120587 + 0.0696208i 0.559080 0.829114i \(-0.311154\pi\)
−0.438493 + 0.898734i \(0.644488\pi\)
\(930\) 0 0
\(931\) −1.65446e7 2.86561e7i −0.0205025 0.0355114i
\(932\) −3.54001e8 + 2.04383e8i −0.437277 + 0.252462i
\(933\) 0 0
\(934\) −2.40217e8 + 4.16067e8i −0.294824 + 0.510649i
\(935\) 9.27259e8i 1.13440i
\(936\) 0 0
\(937\) 7.66443e8 0.931668 0.465834 0.884872i \(-0.345754\pi\)
0.465834 + 0.884872i \(0.345754\pi\)
\(938\) −9.75767e6 5.63359e6i −0.0118233 0.00682617i
\(939\) 0 0
\(940\) 2.59131e8 + 4.48829e8i 0.311987 + 0.540377i
\(941\) −4.61588e8 + 2.66498e8i −0.553969 + 0.319834i −0.750721 0.660619i \(-0.770294\pi\)
0.196752 + 0.980453i \(0.436961\pi\)
\(942\) 0 0
\(943\) 9.73142e8 1.68553e9i 1.16049 2.01003i
\(944\) 1.56629e8i 0.186189i
\(945\) 0 0
\(946\) 3.92348e8 0.463445
\(947\) 2.71610e7 + 1.56814e7i 0.0319812 + 0.0184644i 0.515905 0.856646i \(-0.327456\pi\)
−0.483924 + 0.875110i \(0.660789\pi\)
\(948\) 0 0
\(949\) −4.71001e8 8.15797e8i −0.551090 0.954517i
\(950\) −3.83916e7 + 2.21654e7i −0.0447780 + 0.0258526i
\(951\) 0 0
\(952\) 746618. 1.29318e6i 0.000865341 0.00149882i
\(953\) 6.21244e8i 0.717767i −0.933382 0.358883i \(-0.883158\pi\)
0.933382 0.358883i \(-0.116842\pi\)
\(954\) 0 0
\(955\) −2.45040e9 −2.81337
\(956\) 3.58137e8 + 2.06770e8i 0.409897 + 0.236654i
\(957\) 0 0
\(958\) −3.27302e8 5.66903e8i −0.372264 0.644781i
\(959\) 9.48522e6 5.47629e6i 0.0107545 0.00620913i
\(960\) 0 0
\(961\) 1.38501e8 2.39891e8i 0.156057 0.270299i
\(962\) 2.73383e8i 0.307076i
\(963\) 0 0
\(964\) −2.32970e8 −0.260057
\(965\) −1.25619e9 7.25261e8i −1.39789 0.807073i
\(966\) 0 0
\(967\) 3.14992e8 + 5.45583e8i 0.348354 + 0.603366i 0.985957 0.166998i \(-0.0534075\pi\)
−0.637603 + 0.770365i \(0.720074\pi\)
\(968\) −5.24366e8 + 3.02743e8i −0.578108 + 0.333771i
\(969\) 0 0
\(970\) −8.21410e8 + 1.42272e9i −0.900005 + 1.55885i
\(971\) 1.38333e8i 0.151101i −0.997142 0.0755507i \(-0.975929\pi\)
0.997142 0.0755507i \(-0.0240715\pi\)
\(972\) 0 0
\(973\) −2.94285e6 −0.00319470
\(974\) 2.21845e8 + 1.28082e8i 0.240089 + 0.138616i
\(975\) 0 0
\(976\) 8.26271e6 + 1.43114e7i 0.00888736 + 0.0153934i
\(977\) −7.13583e8 + 4.11988e8i −0.765175 + 0.441774i −0.831151 0.556047i \(-0.812317\pi\)
0.0659754 + 0.997821i \(0.478984\pi\)
\(978\) 0 0
\(979\) −8.93813e8 + 1.54813e9i −0.952574 + 1.64991i
\(980\) 7.84944e8i 0.833989i
\(981\) 0 0
\(982\) 1.15576e9 1.22049
\(983\) −1.11372e9 6.43006e8i −1.17251 0.676947i −0.218237 0.975896i \(-0.570031\pi\)
−0.954269 + 0.298949i \(0.903364\pi\)
\(984\) 0 0
\(985\) 4.27113e7 + 7.39781e7i 0.0446924 + 0.0774096i
\(986\) 3.57435e8 2.06365e8i 0.372877 0.215281i
\(987\) 0 0
\(988\) −1.27821e7 + 2.21392e7i −0.0132535 + 0.0229558i
\(989\) 5.13428e8i 0.530751i
\(990\) 0 0
\(991\) −1.70244e8 −0.174924 −0.0874621 0.996168i \(-0.527876\pi\)
−0.0874621 + 0.996168i \(0.527876\pi\)
\(992\) −1.23951e8 7.15630e7i −0.126974 0.0733083i
\(993\) 0 0
\(994\) 1.78429e6 + 3.09048e6i 0.00181679 + 0.00314678i
\(995\) −5.86645e8 + 3.38700e8i −0.595534 + 0.343831i
\(996\) 0 0
\(997\) 3.50539e8 6.07152e8i 0.353713 0.612649i −0.633184 0.774001i \(-0.718252\pi\)
0.986897 + 0.161353i \(0.0515856\pi\)
\(998\) 1.65740e8i 0.166738i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 162.7.d.f.107.4 8
3.2 odd 2 inner 162.7.d.f.107.1 8
9.2 odd 6 162.7.b.a.161.3 yes 4
9.4 even 3 inner 162.7.d.f.53.1 8
9.5 odd 6 inner 162.7.d.f.53.4 8
9.7 even 3 162.7.b.a.161.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.7.b.a.161.2 4 9.7 even 3
162.7.b.a.161.3 yes 4 9.2 odd 6
162.7.d.f.53.1 8 9.4 even 3 inner
162.7.d.f.53.4 8 9.5 odd 6 inner
162.7.d.f.107.1 8 3.2 odd 2 inner
162.7.d.f.107.4 8 1.1 even 1 trivial