Properties

Label 200.6.f.d.149.38
Level $200$
Weight $6$
Character 200.149
Analytic conductor $32.077$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [200,6,Mod(149,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.149");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 200.f (of order \(2\), degree \(1\), 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: \(32.0767639626\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.38
Character \(\chi\) \(=\) 200.149
Dual form 200.6.f.d.149.37

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.36768 + 1.78549i) q^{2} -29.6034 q^{3} +(25.6240 + 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} +90.3364i q^{7} +(103.318 + 148.639i) q^{8} +633.360 q^{9} +O(q^{10})\) \(q+(5.36768 + 1.78549i) q^{2} -29.6034 q^{3} +(25.6240 + 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} +90.3364i q^{7} +(103.318 + 148.639i) q^{8} +633.360 q^{9} -181.932i q^{11} +(-758.558 - 567.435i) q^{12} +455.237 q^{13} +(-161.295 + 484.897i) q^{14} +(289.182 + 982.319i) q^{16} +615.967i q^{17} +(3399.68 + 1130.86i) q^{18} -2493.63i q^{19} -2674.26i q^{21} +(324.839 - 976.555i) q^{22} +4427.05i q^{23} +(-3058.55 - 4400.21i) q^{24} +(2443.57 + 812.823i) q^{26} -11556.0 q^{27} +(-1731.56 + 2314.78i) q^{28} +7659.34i q^{29} -6767.72 q^{31} +(-201.685 + 5789.11i) q^{32} +5385.81i q^{33} +(-1099.80 + 3306.31i) q^{34} +(16229.2 + 12140.2i) q^{36} -4808.64 q^{37} +(4452.35 - 13385.0i) q^{38} -13476.6 q^{39} +1885.99 q^{41} +(4774.88 - 14354.6i) q^{42} -8262.94 q^{43} +(3487.26 - 4661.84i) q^{44} +(-7904.46 + 23763.0i) q^{46} -5728.44i q^{47} +(-8560.77 - 29080.0i) q^{48} +8646.33 q^{49} -18234.7i q^{51} +(11665.0 + 8725.95i) q^{52} -32364.5 q^{53} +(-62028.9 - 20633.1i) q^{54} +(-13427.5 + 9333.33i) q^{56} +73819.8i q^{57} +(-13675.7 + 41112.9i) q^{58} +20848.8i q^{59} -13265.1i q^{61} +(-36327.0 - 12083.7i) q^{62} +57215.5i q^{63} +(-11419.0 + 30714.0i) q^{64} +(-9616.33 + 28909.3i) q^{66} -9642.36 q^{67} +(-11806.8 + 15783.6i) q^{68} -131056. i q^{69} -33088.4 q^{71} +(65437.2 + 94141.9i) q^{72} +18595.6i q^{73} +(-25811.2 - 8585.79i) q^{74} +(47797.6 - 63896.7i) q^{76} +16435.1 q^{77} +(-72337.9 - 24062.3i) q^{78} -44201.2 q^{79} +188190. q^{81} +(10123.4 + 3367.42i) q^{82} +80063.0 q^{83} +(51260.1 - 68525.4i) q^{84} +(-44352.8 - 14753.4i) q^{86} -226742. i q^{87} +(27042.2 - 18796.8i) q^{88} +81639.3 q^{89} +41124.5i q^{91} +(-84857.3 + 113439. i) q^{92} +200348. q^{93} +(10228.1 - 30748.4i) q^{94} +(5970.56 - 171377. i) q^{96} +22224.8i q^{97} +(46410.7 + 15438.0i) q^{98} -115229. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(177\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.36768 + 1.78549i 0.948881 + 0.315633i
\(3\) −29.6034 −1.89906 −0.949529 0.313679i \(-0.898438\pi\)
−0.949529 + 0.313679i \(0.898438\pi\)
\(4\) 25.6240 + 19.1679i 0.800751 + 0.598997i
\(5\) 0 0
\(6\) −158.902 52.8566i −1.80198 0.599406i
\(7\) 90.3364i 0.696816i 0.937343 + 0.348408i \(0.113278\pi\)
−0.937343 + 0.348408i \(0.886722\pi\)
\(8\) 103.318 + 148.639i 0.570754 + 0.821121i
\(9\) 633.360 2.60642
\(10\) 0 0
\(11\) 181.932i 0.453344i −0.973971 0.226672i \(-0.927215\pi\)
0.973971 0.226672i \(-0.0727846\pi\)
\(12\) −758.558 567.435i −1.52067 1.13753i
\(13\) 455.237 0.747101 0.373551 0.927610i \(-0.378140\pi\)
0.373551 + 0.927610i \(0.378140\pi\)
\(14\) −161.295 + 484.897i −0.219938 + 0.661195i
\(15\) 0 0
\(16\) 289.182 + 982.319i 0.282404 + 0.959295i
\(17\) 615.967i 0.516934i 0.966020 + 0.258467i \(0.0832173\pi\)
−0.966020 + 0.258467i \(0.916783\pi\)
\(18\) 3399.68 + 1130.86i 2.47318 + 0.822674i
\(19\) 2493.63i 1.58470i −0.610067 0.792350i \(-0.708857\pi\)
0.610067 0.792350i \(-0.291143\pi\)
\(20\) 0 0
\(21\) 2674.26i 1.32329i
\(22\) 324.839 976.555i 0.143091 0.430170i
\(23\) 4427.05i 1.74500i 0.488616 + 0.872499i \(0.337502\pi\)
−0.488616 + 0.872499i \(0.662498\pi\)
\(24\) −3058.55 4400.21i −1.08389 1.55936i
\(25\) 0 0
\(26\) 2443.57 + 812.823i 0.708910 + 0.235810i
\(27\) −11556.0 −3.05069
\(28\) −1731.56 + 2314.78i −0.417391 + 0.557976i
\(29\) 7659.34i 1.69121i 0.533813 + 0.845603i \(0.320759\pi\)
−0.533813 + 0.845603i \(0.679241\pi\)
\(30\) 0 0
\(31\) −6767.72 −1.26485 −0.632424 0.774622i \(-0.717940\pi\)
−0.632424 + 0.774622i \(0.717940\pi\)
\(32\) −201.685 + 5789.11i −0.0348176 + 0.999394i
\(33\) 5385.81i 0.860927i
\(34\) −1099.80 + 3306.31i −0.163162 + 0.490509i
\(35\) 0 0
\(36\) 16229.2 + 12140.2i 2.08709 + 1.56124i
\(37\) −4808.64 −0.577455 −0.288727 0.957411i \(-0.593232\pi\)
−0.288727 + 0.957411i \(0.593232\pi\)
\(38\) 4452.35 13385.0i 0.500185 1.50369i
\(39\) −13476.6 −1.41879
\(40\) 0 0
\(41\) 1885.99 0.175218 0.0876092 0.996155i \(-0.472077\pi\)
0.0876092 + 0.996155i \(0.472077\pi\)
\(42\) 4774.88 14354.6i 0.417676 1.25565i
\(43\) −8262.94 −0.681496 −0.340748 0.940155i \(-0.610680\pi\)
−0.340748 + 0.940155i \(0.610680\pi\)
\(44\) 3487.26 4661.84i 0.271552 0.363016i
\(45\) 0 0
\(46\) −7904.46 + 23763.0i −0.550780 + 1.65580i
\(47\) 5728.44i 0.378261i −0.981952 0.189130i \(-0.939433\pi\)
0.981952 0.189130i \(-0.0605669\pi\)
\(48\) −8560.77 29080.0i −0.536302 1.82176i
\(49\) 8646.33 0.514448
\(50\) 0 0
\(51\) 18234.7i 0.981687i
\(52\) 11665.0 + 8725.95i 0.598242 + 0.447512i
\(53\) −32364.5 −1.58263 −0.791316 0.611408i \(-0.790604\pi\)
−0.791316 + 0.611408i \(0.790604\pi\)
\(54\) −62028.9 20633.1i −2.89474 0.962899i
\(55\) 0 0
\(56\) −13427.5 + 9333.33i −0.572170 + 0.397710i
\(57\) 73819.8i 3.00944i
\(58\) −13675.7 + 41112.9i −0.533801 + 1.60475i
\(59\) 20848.8i 0.779740i 0.920870 + 0.389870i \(0.127480\pi\)
−0.920870 + 0.389870i \(0.872520\pi\)
\(60\) 0 0
\(61\) 13265.1i 0.456442i −0.973609 0.228221i \(-0.926709\pi\)
0.973609 0.228221i \(-0.0732909\pi\)
\(62\) −36327.0 12083.7i −1.20019 0.399228i
\(63\) 57215.5i 1.81620i
\(64\) −11419.0 + 30714.0i −0.348480 + 0.937316i
\(65\) 0 0
\(66\) −9616.33 + 28909.3i −0.271737 + 0.816918i
\(67\) −9642.36 −0.262420 −0.131210 0.991355i \(-0.541886\pi\)
−0.131210 + 0.991355i \(0.541886\pi\)
\(68\) −11806.8 + 15783.6i −0.309642 + 0.413935i
\(69\) 131056.i 3.31385i
\(70\) 0 0
\(71\) −33088.4 −0.778986 −0.389493 0.921029i \(-0.627350\pi\)
−0.389493 + 0.921029i \(0.627350\pi\)
\(72\) 65437.2 + 94141.9i 1.48763 + 2.14019i
\(73\) 18595.6i 0.408417i 0.978927 + 0.204208i \(0.0654620\pi\)
−0.978927 + 0.204208i \(0.934538\pi\)
\(74\) −25811.2 8585.79i −0.547936 0.182264i
\(75\) 0 0
\(76\) 47797.6 63896.7i 0.949231 1.26895i
\(77\) 16435.1 0.315897
\(78\) −72337.9 24062.3i −1.34626 0.447817i
\(79\) −44201.2 −0.796831 −0.398415 0.917205i \(-0.630440\pi\)
−0.398415 + 0.917205i \(0.630440\pi\)
\(80\) 0 0
\(81\) 188190. 3.18701
\(82\) 10123.4 + 3367.42i 0.166261 + 0.0553048i
\(83\) 80063.0 1.27567 0.637833 0.770175i \(-0.279831\pi\)
0.637833 + 0.770175i \(0.279831\pi\)
\(84\) 51260.1 68525.4i 0.792649 1.05963i
\(85\) 0 0
\(86\) −44352.8 14753.4i −0.646659 0.215103i
\(87\) 226742.i 3.21170i
\(88\) 27042.2 18796.8i 0.372251 0.258748i
\(89\) 81639.3 1.09251 0.546254 0.837620i \(-0.316053\pi\)
0.546254 + 0.837620i \(0.316053\pi\)
\(90\) 0 0
\(91\) 41124.5i 0.520592i
\(92\) −84857.3 + 113439.i −1.04525 + 1.39731i
\(93\) 200348. 2.40202
\(94\) 10228.1 30748.4i 0.119392 0.358925i
\(95\) 0 0
\(96\) 5970.56 171377.i 0.0661206 1.89791i
\(97\) 22224.8i 0.239833i 0.992784 + 0.119917i \(0.0382627\pi\)
−0.992784 + 0.119917i \(0.961737\pi\)
\(98\) 46410.7 + 15438.0i 0.488150 + 0.162377i
\(99\) 115229.i 1.18161i
\(100\) 0 0
\(101\) 38894.0i 0.379384i 0.981844 + 0.189692i \(0.0607489\pi\)
−0.981844 + 0.189692i \(0.939251\pi\)
\(102\) 32557.9 97878.1i 0.309853 0.931505i
\(103\) 175773.i 1.63253i 0.577681 + 0.816263i \(0.303958\pi\)
−0.577681 + 0.816263i \(0.696042\pi\)
\(104\) 47034.0 + 67665.9i 0.426411 + 0.613461i
\(105\) 0 0
\(106\) −173723. 57786.6i −1.50173 0.499531i
\(107\) −128182. −1.08235 −0.541175 0.840910i \(-0.682020\pi\)
−0.541175 + 0.840910i \(0.682020\pi\)
\(108\) −296111. 221504.i −2.44284 1.82735i
\(109\) 49566.1i 0.399594i 0.979837 + 0.199797i \(0.0640283\pi\)
−0.979837 + 0.199797i \(0.935972\pi\)
\(110\) 0 0
\(111\) 142352. 1.09662
\(112\) −88739.2 + 26123.7i −0.668452 + 0.196784i
\(113\) 92377.7i 0.680567i −0.940323 0.340283i \(-0.889477\pi\)
0.940323 0.340283i \(-0.110523\pi\)
\(114\) −131805. + 396241.i −0.949879 + 2.85560i
\(115\) 0 0
\(116\) −146814. + 196263.i −1.01303 + 1.35423i
\(117\) 288329. 1.94726
\(118\) −37225.3 + 111909.i −0.246112 + 0.739881i
\(119\) −55644.2 −0.360208
\(120\) 0 0
\(121\) 127952. 0.794479
\(122\) 23684.7 71202.9i 0.144069 0.433110i
\(123\) −55831.7 −0.332750
\(124\) −173416. 129723.i −1.01283 0.757641i
\(125\) 0 0
\(126\) −102158. + 307115.i −0.573252 + 1.72335i
\(127\) 137192.i 0.754778i 0.926055 + 0.377389i \(0.123178\pi\)
−0.926055 + 0.377389i \(0.876822\pi\)
\(128\) −116133. + 144474.i −0.626514 + 0.779410i
\(129\) 244611. 1.29420
\(130\) 0 0
\(131\) 91906.6i 0.467917i −0.972247 0.233958i \(-0.924832\pi\)
0.972247 0.233958i \(-0.0751679\pi\)
\(132\) −103235. + 138006.i −0.515693 + 0.689388i
\(133\) 225265. 1.10424
\(134\) −51757.1 17216.4i −0.249005 0.0828284i
\(135\) 0 0
\(136\) −91556.6 + 63640.1i −0.424465 + 0.295042i
\(137\) 220709.i 1.00466i −0.864676 0.502330i \(-0.832476\pi\)
0.864676 0.502330i \(-0.167524\pi\)
\(138\) 233999. 703465.i 1.04596 3.14445i
\(139\) 154375.i 0.677706i 0.940839 + 0.338853i \(0.110039\pi\)
−0.940839 + 0.338853i \(0.889961\pi\)
\(140\) 0 0
\(141\) 169581.i 0.718339i
\(142\) −177608. 59079.1i −0.739165 0.245874i
\(143\) 82822.4i 0.338694i
\(144\) 183157. + 622162.i 0.736065 + 2.50033i
\(145\) 0 0
\(146\) −33202.4 + 99815.4i −0.128910 + 0.387539i
\(147\) −255961. −0.976967
\(148\) −123217. 92171.6i −0.462397 0.345894i
\(149\) 152976.i 0.564492i 0.959342 + 0.282246i \(0.0910794\pi\)
−0.959342 + 0.282246i \(0.908921\pi\)
\(150\) 0 0
\(151\) −440485. −1.57213 −0.786066 0.618143i \(-0.787885\pi\)
−0.786066 + 0.618143i \(0.787885\pi\)
\(152\) 370649. 257635.i 1.30123 0.904474i
\(153\) 390129.i 1.34735i
\(154\) 88218.5 + 29344.8i 0.299749 + 0.0997078i
\(155\) 0 0
\(156\) −345324. 258318.i −1.13610 0.849851i
\(157\) −433381. −1.40320 −0.701601 0.712570i \(-0.747531\pi\)
−0.701601 + 0.712570i \(0.747531\pi\)
\(158\) −237258. 78920.9i −0.756098 0.251507i
\(159\) 958100. 3.00551
\(160\) 0 0
\(161\) −399924. −1.21594
\(162\) 1.01014e6 + 336012.i 3.02410 + 1.00593i
\(163\) 201943. 0.595333 0.297666 0.954670i \(-0.403792\pi\)
0.297666 + 0.954670i \(0.403792\pi\)
\(164\) 48326.6 + 36150.5i 0.140306 + 0.104955i
\(165\) 0 0
\(166\) 429753. + 142952.i 1.21046 + 0.402643i
\(167\) 300699.i 0.834337i −0.908829 0.417168i \(-0.863023\pi\)
0.908829 0.417168i \(-0.136977\pi\)
\(168\) 397499. 276298.i 1.08658 0.755275i
\(169\) −164052. −0.441840
\(170\) 0 0
\(171\) 1.57936e6i 4.13040i
\(172\) −211730. 158383.i −0.545709 0.408214i
\(173\) −100504. −0.255311 −0.127656 0.991819i \(-0.540745\pi\)
−0.127656 + 0.991819i \(0.540745\pi\)
\(174\) 404847. 1.21708e6i 1.01372 3.04752i
\(175\) 0 0
\(176\) 178715. 52611.6i 0.434891 0.128026i
\(177\) 617194.i 1.48077i
\(178\) 438214. + 145766.i 1.03666 + 0.344832i
\(179\) 554078.i 1.29252i 0.763116 + 0.646262i \(0.223669\pi\)
−0.763116 + 0.646262i \(0.776331\pi\)
\(180\) 0 0
\(181\) 227592.i 0.516368i 0.966096 + 0.258184i \(0.0831241\pi\)
−0.966096 + 0.258184i \(0.916876\pi\)
\(182\) −73427.5 + 220743.i −0.164316 + 0.493980i
\(183\) 392692.i 0.866811i
\(184\) −658031. + 457392.i −1.43285 + 0.995964i
\(185\) 0 0
\(186\) 1.07540e6 + 357719.i 2.27923 + 0.758158i
\(187\) 112064. 0.234349
\(188\) 109802. 146786.i 0.226577 0.302893i
\(189\) 1.04393e6i 2.12577i
\(190\) 0 0
\(191\) 796597. 1.57999 0.789997 0.613111i \(-0.210082\pi\)
0.789997 + 0.613111i \(0.210082\pi\)
\(192\) 338041. 909238.i 0.661783 1.78002i
\(193\) 356611.i 0.689131i 0.938762 + 0.344565i \(0.111974\pi\)
−0.938762 + 0.344565i \(0.888026\pi\)
\(194\) −39682.3 + 119296.i −0.0756994 + 0.227573i
\(195\) 0 0
\(196\) 221554. + 165732.i 0.411945 + 0.308153i
\(197\) 226534. 0.415880 0.207940 0.978142i \(-0.433324\pi\)
0.207940 + 0.978142i \(0.433324\pi\)
\(198\) 205740. 618511.i 0.372955 1.12120i
\(199\) 177886. 0.318427 0.159213 0.987244i \(-0.449104\pi\)
0.159213 + 0.987244i \(0.449104\pi\)
\(200\) 0 0
\(201\) 285447. 0.498350
\(202\) −69444.9 + 208770.i −0.119746 + 0.359990i
\(203\) −691917. −1.17846
\(204\) 349521. 467247.i 0.588028 0.786087i
\(205\) 0 0
\(206\) −313842. + 943495.i −0.515280 + 1.54907i
\(207\) 2.80392e6i 4.54820i
\(208\) 131646. + 447188.i 0.210985 + 0.716691i
\(209\) −453671. −0.718415
\(210\) 0 0
\(211\) 525263.i 0.812215i −0.913825 0.406107i \(-0.866886\pi\)
0.913825 0.406107i \(-0.133114\pi\)
\(212\) −829310. 620361.i −1.26729 0.947992i
\(213\) 979528. 1.47934
\(214\) −688041. 228868.i −1.02702 0.341626i
\(215\) 0 0
\(216\) −1.19394e6 1.71767e6i −1.74119 2.50498i
\(217\) 611372.i 0.881366i
\(218\) −88500.0 + 266055.i −0.126125 + 0.379167i
\(219\) 550494.i 0.775607i
\(220\) 0 0
\(221\) 280411.i 0.386202i
\(222\) 764100. + 254168.i 1.04056 + 0.346130i
\(223\) 711308.i 0.957846i −0.877857 0.478923i \(-0.841027\pi\)
0.877857 0.478923i \(-0.158973\pi\)
\(224\) −522967. 18219.5i −0.696393 0.0242614i
\(225\) 0 0
\(226\) 164940. 495854.i 0.214810 0.645777i
\(227\) 216347. 0.278668 0.139334 0.990245i \(-0.455504\pi\)
0.139334 + 0.990245i \(0.455504\pi\)
\(228\) −1.41497e6 + 1.89156e6i −1.80265 + 2.40981i
\(229\) 759408.i 0.956944i 0.878103 + 0.478472i \(0.158809\pi\)
−0.878103 + 0.478472i \(0.841191\pi\)
\(230\) 0 0
\(231\) −486535. −0.599907
\(232\) −1.13848e6 + 791344.i −1.38868 + 0.965262i
\(233\) 860736.i 1.03868i −0.854569 0.519338i \(-0.826179\pi\)
0.854569 0.519338i \(-0.173821\pi\)
\(234\) 1.54766e6 + 514810.i 1.84772 + 0.614621i
\(235\) 0 0
\(236\) −399627. + 534229.i −0.467062 + 0.624378i
\(237\) 1.30850e6 1.51323
\(238\) −298681. 99352.4i −0.341794 0.113694i
\(239\) 348130. 0.394228 0.197114 0.980381i \(-0.436843\pi\)
0.197114 + 0.980381i \(0.436843\pi\)
\(240\) 0 0
\(241\) −844167. −0.936237 −0.468119 0.883666i \(-0.655068\pi\)
−0.468119 + 0.883666i \(0.655068\pi\)
\(242\) 686804. + 228457.i 0.753866 + 0.250764i
\(243\) −2.76295e6 −3.00163
\(244\) 254264. 339905.i 0.273408 0.365497i
\(245\) 0 0
\(246\) −299687. 99687.0i −0.315740 0.105027i
\(247\) 1.13519e6i 1.18393i
\(248\) −699224. 1.00595e6i −0.721917 1.03859i
\(249\) −2.37014e6 −2.42256
\(250\) 0 0
\(251\) 1.52042e6i 1.52328i 0.648000 + 0.761640i \(0.275606\pi\)
−0.648000 + 0.761640i \(0.724394\pi\)
\(252\) −1.09670e6 + 1.46609e6i −1.08790 + 1.45432i
\(253\) 805423. 0.791085
\(254\) −244955. + 736403.i −0.238233 + 0.716195i
\(255\) 0 0
\(256\) −881323. + 568138.i −0.840496 + 0.541818i
\(257\) 682391.i 0.644466i −0.946660 0.322233i \(-0.895566\pi\)
0.946660 0.322233i \(-0.104434\pi\)
\(258\) 1.31299e6 + 436751.i 1.22804 + 0.408493i
\(259\) 434395.i 0.402379i
\(260\) 0 0
\(261\) 4.85112e6i 4.40799i
\(262\) 164099. 493326.i 0.147690 0.443997i
\(263\) 91394.4i 0.0814761i 0.999170 + 0.0407381i \(0.0129709\pi\)
−0.999170 + 0.0407381i \(0.987029\pi\)
\(264\) −800541. + 556449.i −0.706925 + 0.491378i
\(265\) 0 0
\(266\) 1.20915e6 + 402209.i 1.04780 + 0.348536i
\(267\) −2.41680e6 −2.07474
\(268\) −247076. 184824.i −0.210133 0.157189i
\(269\) 935475.i 0.788227i 0.919062 + 0.394114i \(0.128948\pi\)
−0.919062 + 0.394114i \(0.871052\pi\)
\(270\) 0 0
\(271\) 512294. 0.423737 0.211868 0.977298i \(-0.432045\pi\)
0.211868 + 0.977298i \(0.432045\pi\)
\(272\) −605076. + 178127.i −0.495892 + 0.145984i
\(273\) 1.21742e6i 0.988634i
\(274\) 394075. 1.18470e6i 0.317105 0.953304i
\(275\) 0 0
\(276\) 2.51206e6 3.35817e6i 1.98499 2.65357i
\(277\) 615832. 0.482239 0.241120 0.970495i \(-0.422485\pi\)
0.241120 + 0.970495i \(0.422485\pi\)
\(278\) −275636. + 828638.i −0.213907 + 0.643062i
\(279\) −4.28641e6 −3.29673
\(280\) 0 0
\(281\) 1.22082e6 0.922330 0.461165 0.887314i \(-0.347432\pi\)
0.461165 + 0.887314i \(0.347432\pi\)
\(282\) −302786. + 910258.i −0.226732 + 0.681619i
\(283\) 696315. 0.516820 0.258410 0.966035i \(-0.416801\pi\)
0.258410 + 0.966035i \(0.416801\pi\)
\(284\) −847858. 634235.i −0.623774 0.466611i
\(285\) 0 0
\(286\) 147879. 444564.i 0.106903 0.321380i
\(287\) 170374.i 0.122095i
\(288\) −127739. + 3.66659e6i −0.0907493 + 2.60484i
\(289\) 1.04044e6 0.732779
\(290\) 0 0
\(291\) 657931.i 0.455457i
\(292\) −356439. + 476495.i −0.244641 + 0.327040i
\(293\) −134741. −0.0916922 −0.0458461 0.998949i \(-0.514598\pi\)
−0.0458461 + 0.998949i \(0.514598\pi\)
\(294\) −1.37392e6 457016.i −0.927025 0.308363i
\(295\) 0 0
\(296\) −496817. 714750.i −0.329584 0.474160i
\(297\) 2.10241e6i 1.38301i
\(298\) −273137. + 821126.i −0.178172 + 0.535636i
\(299\) 2.01536e6i 1.30369i
\(300\) 0 0
\(301\) 746444.i 0.474877i
\(302\) −2.36438e6 786483.i −1.49177 0.496217i
\(303\) 1.15139e6i 0.720472i
\(304\) 2.44953e6 721112.i 1.52020 0.447526i
\(305\) 0 0
\(306\) −696572. + 2.09409e6i −0.425268 + 1.27847i
\(307\) −280871. −0.170083 −0.0850414 0.996377i \(-0.527102\pi\)
−0.0850414 + 0.996377i \(0.527102\pi\)
\(308\) 421134. + 315027.i 0.252955 + 0.189222i
\(309\) 5.20348e6i 3.10026i
\(310\) 0 0
\(311\) −2.40348e6 −1.40909 −0.704547 0.709657i \(-0.748850\pi\)
−0.704547 + 0.709657i \(0.748850\pi\)
\(312\) −1.39236e6 2.00314e6i −0.809779 1.16500i
\(313\) 619525.i 0.357436i −0.983900 0.178718i \(-0.942805\pi\)
0.983900 0.178718i \(-0.0571949\pi\)
\(314\) −2.32625e6 773798.i −1.33147 0.442898i
\(315\) 0 0
\(316\) −1.13261e6 847245.i −0.638063 0.477300i
\(317\) 913021. 0.510308 0.255154 0.966900i \(-0.417874\pi\)
0.255154 + 0.966900i \(0.417874\pi\)
\(318\) 5.14278e6 + 1.71068e6i 2.85187 + 0.948639i
\(319\) 1.39348e6 0.766698
\(320\) 0 0
\(321\) 3.79462e6 2.05545
\(322\) −2.14666e6 714061.i −1.15378 0.383792i
\(323\) 1.53599e6 0.819185
\(324\) 4.82218e6 + 3.60721e6i 2.55200 + 1.90901i
\(325\) 0 0
\(326\) 1.08397e6 + 360568.i 0.564900 + 0.187907i
\(327\) 1.46733e6i 0.758852i
\(328\) 194856. + 280331.i 0.100007 + 0.143875i
\(329\) 517487. 0.263578
\(330\) 0 0
\(331\) 3.37863e6i 1.69500i −0.530793 0.847502i \(-0.678106\pi\)
0.530793 0.847502i \(-0.321894\pi\)
\(332\) 2.05154e6 + 1.53464e6i 1.02149 + 0.764120i
\(333\) −3.04560e6 −1.50509
\(334\) 536896. 1.61406e6i 0.263345 0.791686i
\(335\) 0 0
\(336\) 2.62698e6 773349.i 1.26943 0.373704i
\(337\) 3.19536e6i 1.53266i 0.642448 + 0.766329i \(0.277919\pi\)
−0.642448 + 0.766329i \(0.722081\pi\)
\(338\) −880579. 292914.i −0.419254 0.139459i
\(339\) 2.73469e6i 1.29244i
\(340\) 0 0
\(341\) 1.23127e6i 0.573412i
\(342\) 2.81994e6 8.47752e6i 1.30369 3.91926i
\(343\) 2.29936e6i 1.05529i
\(344\) −853706. 1.22819e6i −0.388966 0.559591i
\(345\) 0 0
\(346\) −539476. 179450.i −0.242260 0.0805847i
\(347\) 2.15234e6 0.959592 0.479796 0.877380i \(-0.340711\pi\)
0.479796 + 0.877380i \(0.340711\pi\)
\(348\) 4.34618e6 5.81006e6i 1.92380 2.57177i
\(349\) 2.78827e6i 1.22538i 0.790322 + 0.612692i \(0.209913\pi\)
−0.790322 + 0.612692i \(0.790087\pi\)
\(350\) 0 0
\(351\) −5.26072e6 −2.27917
\(352\) 1.05323e6 + 36693.0i 0.453069 + 0.0157843i
\(353\) 3.23259e6i 1.38075i −0.723453 0.690373i \(-0.757446\pi\)
0.723453 0.690373i \(-0.242554\pi\)
\(354\) 1.10199e6 3.31290e6i 0.467381 1.40508i
\(355\) 0 0
\(356\) 2.09193e6 + 1.56486e6i 0.874826 + 0.654409i
\(357\) 1.64726e6 0.684055
\(358\) −989303. + 2.97412e6i −0.407964 + 1.22645i
\(359\) 2.02100e6 0.827620 0.413810 0.910363i \(-0.364198\pi\)
0.413810 + 0.910363i \(0.364198\pi\)
\(360\) 0 0
\(361\) −3.74207e6 −1.51128
\(362\) −406363. + 1.22164e6i −0.162983 + 0.489972i
\(363\) −3.78780e6 −1.50876
\(364\) −788271. + 1.05378e6i −0.311833 + 0.416864i
\(365\) 0 0
\(366\) −701149. + 2.10785e6i −0.273595 + 0.822500i
\(367\) 2.50488e6i 0.970781i −0.874297 0.485391i \(-0.838677\pi\)
0.874297 0.485391i \(-0.161323\pi\)
\(368\) −4.34877e6 + 1.28022e6i −1.67397 + 0.492795i
\(369\) 1.19451e6 0.456693
\(370\) 0 0
\(371\) 2.92370e6i 1.10280i
\(372\) 5.13371e6 + 3.84024e6i 1.92342 + 1.43880i
\(373\) 495172. 0.184283 0.0921413 0.995746i \(-0.470629\pi\)
0.0921413 + 0.995746i \(0.470629\pi\)
\(374\) 601525. + 200090.i 0.222369 + 0.0739684i
\(375\) 0 0
\(376\) 851468. 591848.i 0.310598 0.215894i
\(377\) 3.48682e6i 1.26350i
\(378\) 1.86392e6 5.60347e6i 0.670963 2.01710i
\(379\) 2.19040e6i 0.783294i 0.920116 + 0.391647i \(0.128095\pi\)
−0.920116 + 0.391647i \(0.871905\pi\)
\(380\) 0 0
\(381\) 4.06135e6i 1.43337i
\(382\) 4.27588e6 + 1.42232e6i 1.49923 + 0.498699i
\(383\) 289759.i 0.100935i −0.998726 0.0504674i \(-0.983929\pi\)
0.998726 0.0504674i \(-0.0160711\pi\)
\(384\) 3.43793e6 4.27693e6i 1.18979 1.48014i
\(385\) 0 0
\(386\) −636726. + 1.91417e6i −0.217513 + 0.653903i
\(387\) −5.23342e6 −1.77627
\(388\) −426004. + 569490.i −0.143659 + 0.192047i
\(389\) 2.11554e6i 0.708839i 0.935087 + 0.354420i \(0.115322\pi\)
−0.935087 + 0.354420i \(0.884678\pi\)
\(390\) 0 0
\(391\) −2.72692e6 −0.902048
\(392\) 893317. + 1.28518e6i 0.293623 + 0.422424i
\(393\) 2.72075e6i 0.888601i
\(394\) 1.21596e6 + 404475.i 0.394621 + 0.131266i
\(395\) 0 0
\(396\) 2.20869e6 2.95263e6i 0.707779 0.946173i
\(397\) −1.80742e6 −0.575549 −0.287774 0.957698i \(-0.592915\pi\)
−0.287774 + 0.957698i \(0.592915\pi\)
\(398\) 954837. + 317615.i 0.302149 + 0.100506i
\(399\) −6.66861e6 −2.09702
\(400\) 0 0
\(401\) −2.59111e6 −0.804683 −0.402342 0.915490i \(-0.631804\pi\)
−0.402342 + 0.915490i \(0.631804\pi\)
\(402\) 1.53219e6 + 509663.i 0.472875 + 0.157296i
\(403\) −3.08092e6 −0.944969
\(404\) −745516. + 996620.i −0.227250 + 0.303792i
\(405\) 0 0
\(406\) −3.71399e6 1.23541e6i −1.11822 0.371961i
\(407\) 874847.i 0.261786i
\(408\) 2.71038e6 1.88396e6i 0.806084 0.560302i
\(409\) 5.00884e6 1.48057 0.740285 0.672293i \(-0.234690\pi\)
0.740285 + 0.672293i \(0.234690\pi\)
\(410\) 0 0
\(411\) 6.53375e6i 1.90791i
\(412\) −3.36921e6 + 4.50402e6i −0.977878 + 1.30725i
\(413\) −1.88340e6 −0.543335
\(414\) −5.00638e6 + 1.50505e7i −1.43556 + 4.31570i
\(415\) 0 0
\(416\) −91814.5 + 2.63542e6i −0.0260122 + 0.746648i
\(417\) 4.57003e6i 1.28700i
\(418\) −2.43516e6 810026.i −0.681690 0.226756i
\(419\) 2.27862e6i 0.634071i −0.948414 0.317035i \(-0.897313\pi\)
0.948414 0.317035i \(-0.102687\pi\)
\(420\) 0 0
\(421\) 1.30407e6i 0.358587i −0.983796 0.179293i \(-0.942619\pi\)
0.983796 0.179293i \(-0.0573811\pi\)
\(422\) 937853. 2.81945e6i 0.256362 0.770695i
\(423\) 3.62817e6i 0.985907i
\(424\) −3.34382e6 4.81063e6i −0.903293 1.29953i
\(425\) 0 0
\(426\) 5.25780e6 + 1.74894e6i 1.40372 + 0.466929i
\(427\) 1.19832e6 0.318056
\(428\) −3.28454e6 2.45698e6i −0.866693 0.648325i
\(429\) 2.45182e6i 0.643200i
\(430\) 0 0
\(431\) 3.93997e6 1.02164 0.510822 0.859687i \(-0.329341\pi\)
0.510822 + 0.859687i \(0.329341\pi\)
\(432\) −3.34179e6 1.13517e7i −0.861528 2.92651i
\(433\) 5.84454e6i 1.49806i −0.662534 0.749032i \(-0.730519\pi\)
0.662534 0.749032i \(-0.269481\pi\)
\(434\) 1.09160e6 3.28165e6i 0.278189 0.836311i
\(435\) 0 0
\(436\) −950080. + 1.27008e6i −0.239356 + 0.319975i
\(437\) 1.10394e7 2.76530
\(438\) 982902. 2.95487e6i 0.244808 0.735959i
\(439\) 7.63016e6 1.88961 0.944805 0.327634i \(-0.106251\pi\)
0.944805 + 0.327634i \(0.106251\pi\)
\(440\) 0 0
\(441\) 5.47624e6 1.34087
\(442\) −500672. + 1.50516e6i −0.121898 + 0.366460i
\(443\) 1.99010e6 0.481798 0.240899 0.970550i \(-0.422558\pi\)
0.240899 + 0.970550i \(0.422558\pi\)
\(444\) 3.64763e6 + 2.72859e6i 0.878119 + 0.656872i
\(445\) 0 0
\(446\) 1.27004e6 3.81808e6i 0.302328 0.908882i
\(447\) 4.52861e6i 1.07200i
\(448\) −2.77459e6 1.03155e6i −0.653137 0.242826i
\(449\) 2.05507e6 0.481074 0.240537 0.970640i \(-0.422676\pi\)
0.240537 + 0.970640i \(0.422676\pi\)
\(450\) 0 0
\(451\) 343122.i 0.0794342i
\(452\) 1.77069e6 2.36709e6i 0.407658 0.544965i
\(453\) 1.30398e7 2.98557
\(454\) 1.16128e6 + 386287.i 0.264423 + 0.0879569i
\(455\) 0 0
\(456\) −1.09725e7 + 7.62687e6i −2.47111 + 1.71765i
\(457\) 2.74689e6i 0.615250i −0.951508 0.307625i \(-0.900466\pi\)
0.951508 0.307625i \(-0.0995342\pi\)
\(458\) −1.35592e6 + 4.07626e6i −0.302044 + 0.908026i
\(459\) 7.11811e6i 1.57700i
\(460\) 0 0
\(461\) 4.01666e6i 0.880264i −0.897933 0.440132i \(-0.854932\pi\)
0.897933 0.440132i \(-0.145068\pi\)
\(462\) −2.61157e6 868705.i −0.569241 0.189351i
\(463\) 7.77791e6i 1.68620i 0.537753 + 0.843102i \(0.319273\pi\)
−0.537753 + 0.843102i \(0.680727\pi\)
\(464\) −7.52391e6 + 2.21494e6i −1.62237 + 0.477604i
\(465\) 0 0
\(466\) 1.53684e6 4.62015e6i 0.327841 0.985580i
\(467\) 3.81432e6 0.809329 0.404664 0.914465i \(-0.367388\pi\)
0.404664 + 0.914465i \(0.367388\pi\)
\(468\) 7.38816e6 + 5.52667e6i 1.55927 + 1.16640i
\(469\) 871056.i 0.182858i
\(470\) 0 0
\(471\) 1.28295e7 2.66476
\(472\) −3.09893e6 + 2.15404e6i −0.640261 + 0.445040i
\(473\) 1.50330e6i 0.308952i
\(474\) 7.02364e6 + 2.33633e6i 1.43587 + 0.477625i
\(475\) 0 0
\(476\) −1.42583e6 1.06658e6i −0.288437 0.215763i
\(477\) −2.04984e7 −4.12500
\(478\) 1.86865e6 + 621584.i 0.374075 + 0.124431i
\(479\) 2.44255e6 0.486413 0.243206 0.969975i \(-0.421801\pi\)
0.243206 + 0.969975i \(0.421801\pi\)
\(480\) 0 0
\(481\) −2.18907e6 −0.431417
\(482\) −4.53122e6 1.50725e6i −0.888378 0.295508i
\(483\) 1.18391e7 2.30914
\(484\) 3.27864e6 + 2.45257e6i 0.636180 + 0.475891i
\(485\) 0 0
\(486\) −1.48307e7 4.93323e6i −2.84819 0.947416i
\(487\) 8.35163e6i 1.59569i 0.602862 + 0.797846i \(0.294027\pi\)
−0.602862 + 0.797846i \(0.705973\pi\)
\(488\) 1.97171e6 1.37052e6i 0.374795 0.260516i
\(489\) −5.97820e6 −1.13057
\(490\) 0 0
\(491\) 340069.i 0.0636595i 0.999493 + 0.0318298i \(0.0101334\pi\)
−0.999493 + 0.0318298i \(0.989867\pi\)
\(492\) −1.43063e6 1.07018e6i −0.266450 0.199316i
\(493\) −4.71790e6 −0.874241
\(494\) 2.02688e6 6.09335e6i 0.373688 1.12341i
\(495\) 0 0
\(496\) −1.95710e6 6.64806e6i −0.357199 1.21336i
\(497\) 2.98909e6i 0.542810i
\(498\) −1.27221e7 4.23186e6i −2.29872 0.764642i
\(499\) 648994.i 0.116678i 0.998297 + 0.0583391i \(0.0185805\pi\)
−0.998297 + 0.0583391i \(0.981420\pi\)
\(500\) 0 0
\(501\) 8.90172e6i 1.58445i
\(502\) −2.71470e6 + 8.16114e6i −0.480798 + 1.44541i
\(503\) 3.13514e6i 0.552506i −0.961085 0.276253i \(-0.910907\pi\)
0.961085 0.276253i \(-0.0890928\pi\)
\(504\) −8.50445e6 + 5.91137e6i −1.49132 + 1.03660i
\(505\) 0 0
\(506\) 4.32326e6 + 1.43808e6i 0.750645 + 0.249693i
\(507\) 4.85650e6 0.839080
\(508\) −2.62968e6 + 3.51541e6i −0.452110 + 0.604390i
\(509\) 5.04542e6i 0.863183i −0.902069 0.431591i \(-0.857952\pi\)
0.902069 0.431591i \(-0.142048\pi\)
\(510\) 0 0
\(511\) −1.67986e6 −0.284591
\(512\) −5.74507e6 + 1.47599e6i −0.968546 + 0.248833i
\(513\) 2.88163e7i 4.83443i
\(514\) 1.21840e6 3.66286e6i 0.203415 0.611522i
\(515\) 0 0
\(516\) 6.26792e6 + 4.68868e6i 1.03633 + 0.775223i
\(517\) −1.04219e6 −0.171482
\(518\) 775610. 2.33170e6i 0.127004 0.381810i
\(519\) 2.97527e6 0.484851
\(520\) 0 0
\(521\) 598792. 0.0966456 0.0483228 0.998832i \(-0.484612\pi\)
0.0483228 + 0.998832i \(0.484612\pi\)
\(522\) −8.66165e6 + 2.60393e7i −1.39131 + 4.18266i
\(523\) 1.12334e7 1.79580 0.897901 0.440197i \(-0.145091\pi\)
0.897901 + 0.440197i \(0.145091\pi\)
\(524\) 1.76166e6 2.35502e6i 0.280281 0.374685i
\(525\) 0 0
\(526\) −163184. + 490576.i −0.0257166 + 0.0773111i
\(527\) 4.16869e6i 0.653843i
\(528\) −5.29058e6 + 1.55748e6i −0.825884 + 0.243130i
\(529\) −1.31624e7 −2.04502
\(530\) 0 0
\(531\) 1.32048e7i 2.03233i
\(532\) 5.77220e6 + 4.31786e6i 0.884224 + 0.661439i
\(533\) 858572. 0.130906
\(534\) −1.29726e7 4.31518e6i −1.96868 0.654856i
\(535\) 0 0
\(536\) −996225. 1.43323e6i −0.149777 0.215478i
\(537\) 1.64026e7i 2.45458i
\(538\) −1.67028e6 + 5.02133e6i −0.248791 + 0.747934i
\(539\) 1.57305e6i 0.233222i
\(540\) 0 0
\(541\) 8.05017e6i 1.18253i −0.806478 0.591264i \(-0.798629\pi\)
0.806478 0.591264i \(-0.201371\pi\)
\(542\) 2.74983e6 + 914697.i 0.402076 + 0.133746i
\(543\) 6.73748e6i 0.980614i
\(544\) −3.56590e6 124231.i −0.516620 0.0179984i
\(545\) 0 0
\(546\) 2.17370e6 6.53475e6i 0.312046 0.938096i
\(547\) 6.14990e6 0.878819 0.439410 0.898287i \(-0.355188\pi\)
0.439410 + 0.898287i \(0.355188\pi\)
\(548\) 4.23054e6 5.65547e6i 0.601789 0.804483i
\(549\) 8.40159e6i 1.18968i
\(550\) 0 0
\(551\) 1.90995e7 2.68005
\(552\) 1.94800e7 1.35403e7i 2.72107 1.89139i
\(553\) 3.99298e6i 0.555244i
\(554\) 3.30559e6 + 1.09956e6i 0.457588 + 0.152211i
\(555\) 0 0
\(556\) −2.95905e6 + 3.95572e6i −0.405944 + 0.542673i
\(557\) −6.26714e6 −0.855917 −0.427959 0.903798i \(-0.640767\pi\)
−0.427959 + 0.903798i \(0.640767\pi\)
\(558\) −2.30081e7 7.65335e6i −3.12820 1.04056i
\(559\) −3.76160e6 −0.509146
\(560\) 0 0
\(561\) −3.31748e6 −0.445042
\(562\) 6.55298e6 + 2.17977e6i 0.875182 + 0.291118i
\(563\) −149874. −0.0199276 −0.00996378 0.999950i \(-0.503172\pi\)
−0.00996378 + 0.999950i \(0.503172\pi\)
\(564\) −3.25052e6 + 4.34535e6i −0.430283 + 0.575211i
\(565\) 0 0
\(566\) 3.73760e6 + 1.24327e6i 0.490401 + 0.163126i
\(567\) 1.70004e7i 2.22076i
\(568\) −3.41861e6 4.91822e6i −0.444609 0.639642i
\(569\) −2.10351e6 −0.272373 −0.136186 0.990683i \(-0.543485\pi\)
−0.136186 + 0.990683i \(0.543485\pi\)
\(570\) 0 0
\(571\) 8.72030e6i 1.11929i −0.828734 0.559643i \(-0.810938\pi\)
0.828734 0.559643i \(-0.189062\pi\)
\(572\) 1.58753e6 2.12224e6i 0.202877 0.271210i
\(573\) −2.35820e7 −3.00050
\(574\) −304201. + 914511.i −0.0385372 + 0.115854i
\(575\) 0 0
\(576\) −7.23234e6 + 1.94530e7i −0.908285 + 2.44304i
\(577\) 5.44606e6i 0.680993i 0.940246 + 0.340497i \(0.110595\pi\)
−0.940246 + 0.340497i \(0.889405\pi\)
\(578\) 5.58476e6 + 1.85770e6i 0.695321 + 0.231290i
\(579\) 1.05569e7i 1.30870i
\(580\) 0 0
\(581\) 7.23261e6i 0.888904i
\(582\) 1.17473e6 3.53156e6i 0.143758 0.432175i
\(583\) 5.88816e6i 0.717477i
\(584\) −2.76403e6 + 1.92125e6i −0.335360 + 0.233106i
\(585\) 0 0
\(586\) −723249. 240580.i −0.0870050 0.0289411i
\(587\) 1.53801e6 0.184232 0.0921158 0.995748i \(-0.470637\pi\)
0.0921158 + 0.995748i \(0.470637\pi\)
\(588\) −6.55874e6 4.90623e6i −0.782307 0.585201i
\(589\) 1.68762e7i 2.00441i
\(590\) 0 0
\(591\) −6.70618e6 −0.789781
\(592\) −1.39057e6 4.72361e6i −0.163076 0.553950i
\(593\) 1.23546e7i 1.44275i −0.692542 0.721377i \(-0.743509\pi\)
0.692542 0.721377i \(-0.256491\pi\)
\(594\) −3.75383e6 + 1.12851e7i −0.436525 + 1.31231i
\(595\) 0 0
\(596\) −2.93223e6 + 3.91986e6i −0.338129 + 0.452017i
\(597\) −5.26604e6 −0.604711
\(598\) −3.59841e6 + 1.08178e7i −0.411488 + 1.23705i
\(599\) 1.46319e7 1.66622 0.833112 0.553105i \(-0.186557\pi\)
0.833112 + 0.553105i \(0.186557\pi\)
\(600\) 0 0
\(601\) −1.08262e7 −1.22261 −0.611306 0.791394i \(-0.709356\pi\)
−0.611306 + 0.791394i \(0.709356\pi\)
\(602\) 1.33277e6 4.00668e6i 0.149887 0.450602i
\(603\) −6.10709e6 −0.683976
\(604\) −1.12870e7 8.44318e6i −1.25889 0.941702i
\(605\) 0 0
\(606\) 2.05580e6 6.18031e6i 0.227405 0.683642i
\(607\) 722652.i 0.0796082i −0.999208 0.0398041i \(-0.987327\pi\)
0.999208 0.0398041i \(-0.0126734\pi\)
\(608\) 1.44359e7 + 502927.i 1.58374 + 0.0551754i
\(609\) 2.04831e7 2.23796
\(610\) 0 0
\(611\) 2.60780e6i 0.282599i
\(612\) −7.47796e6 + 9.99668e6i −0.807058 + 1.07889i
\(613\) 1.19951e6 0.128930 0.0644648 0.997920i \(-0.479466\pi\)
0.0644648 + 0.997920i \(0.479466\pi\)
\(614\) −1.50762e6 501492.i −0.161388 0.0536838i
\(615\) 0 0
\(616\) 1.69804e6 + 2.44290e6i 0.180300 + 0.259390i
\(617\) 1.26945e7i 1.34246i 0.741249 + 0.671230i \(0.234234\pi\)
−0.741249 + 0.671230i \(0.765766\pi\)
\(618\) 9.29078e6 2.79307e7i 0.978546 2.94178i
\(619\) 9.69565e6i 1.01707i −0.861042 0.508534i \(-0.830187\pi\)
0.861042 0.508534i \(-0.169813\pi\)
\(620\) 0 0
\(621\) 5.11590e7i 5.32344i
\(622\) −1.29011e7 4.29140e6i −1.33706 0.444757i
\(623\) 7.37501e6i 0.761276i
\(624\) −3.89718e6 1.32383e7i −0.400672 1.36104i
\(625\) 0 0
\(626\) 1.10616e6 3.32541e6i 0.112819 0.339164i
\(627\) 1.34302e7 1.36431
\(628\) −1.11050e7 8.30700e6i −1.12362 0.840515i
\(629\) 2.96196e6i 0.298506i
\(630\) 0 0
\(631\) 2.38091e6 0.238051 0.119025 0.992891i \(-0.462023\pi\)
0.119025 + 0.992891i \(0.462023\pi\)
\(632\) −4.56676e6 6.57001e6i −0.454794 0.654295i
\(633\) 1.55496e7i 1.54244i
\(634\) 4.90081e6 + 1.63019e6i 0.484222 + 0.161070i
\(635\) 0 0
\(636\) 2.45504e7 + 1.83648e7i 2.40666 + 1.80029i
\(637\) 3.93613e6 0.384345
\(638\) 7.47977e6 + 2.48805e6i 0.727506 + 0.241996i
\(639\) −2.09569e7 −2.03037
\(640\) 0 0
\(641\) 6.37112e6 0.612450 0.306225 0.951959i \(-0.400934\pi\)
0.306225 + 0.951959i \(0.400934\pi\)
\(642\) 2.03683e7 + 6.77527e6i 1.95037 + 0.648768i
\(643\) −1.64996e7 −1.57379 −0.786896 0.617086i \(-0.788313\pi\)
−0.786896 + 0.617086i \(0.788313\pi\)
\(644\) −1.02477e7 7.66571e6i −0.973666 0.728346i
\(645\) 0 0
\(646\) 8.24471e6 + 2.74250e6i 0.777310 + 0.258562i
\(647\) 2.94843e6i 0.276905i −0.990369 0.138452i \(-0.955787\pi\)
0.990369 0.138452i \(-0.0442128\pi\)
\(648\) 1.94433e7 + 2.79723e7i 1.81900 + 2.61692i
\(649\) 3.79306e6 0.353491
\(650\) 0 0
\(651\) 1.80987e7i 1.67376i
\(652\) 5.17460e6 + 3.87083e6i 0.476713 + 0.356603i
\(653\) 1.02662e7 0.942167 0.471083 0.882089i \(-0.343863\pi\)
0.471083 + 0.882089i \(0.343863\pi\)
\(654\) 2.61990e6 7.87614e6i 0.239519 0.720061i
\(655\) 0 0
\(656\) 545394. + 1.85264e6i 0.0494824 + 0.168086i
\(657\) 1.17777e7i 1.06451i
\(658\) 2.77770e6 + 923968.i 0.250104 + 0.0831941i
\(659\) 7.94727e6i 0.712860i −0.934322 0.356430i \(-0.883994\pi\)
0.934322 0.356430i \(-0.116006\pi\)
\(660\) 0 0
\(661\) 9.79140e6i 0.871648i 0.900032 + 0.435824i \(0.143543\pi\)
−0.900032 + 0.435824i \(0.856457\pi\)
\(662\) 6.03252e6 1.81354e7i 0.535000 1.60836i
\(663\) 8.30112e6i 0.733420i
\(664\) 8.27191e6 + 1.19005e7i 0.728091 + 1.04748i
\(665\) 0 0
\(666\) −1.63478e7 5.43790e6i −1.42815 0.475057i
\(667\) −3.39083e7 −2.95115
\(668\) 5.76378e6 7.70513e6i 0.499765 0.668096i
\(669\) 2.10571e7i 1.81901i
\(670\) 0 0
\(671\) −2.41335e6 −0.206926
\(672\) 1.54816e7 + 539359.i 1.32249 + 0.0460739i
\(673\) 1.64861e7i 1.40307i 0.712635 + 0.701535i \(0.247502\pi\)
−0.712635 + 0.701535i \(0.752498\pi\)
\(674\) −5.70530e6 + 1.71517e7i −0.483758 + 1.45431i
\(675\) 0 0
\(676\) −4.20368e6 3.14454e6i −0.353804 0.264661i
\(677\) −2.81251e6 −0.235843 −0.117922 0.993023i \(-0.537623\pi\)
−0.117922 + 0.993023i \(0.537623\pi\)
\(678\) −4.88277e6 + 1.46790e7i −0.407936 + 1.22637i
\(679\) −2.00771e6 −0.167120
\(680\) 0 0
\(681\) −6.40461e6 −0.529206
\(682\) −2.19842e6 + 6.60905e6i −0.180988 + 0.544100i
\(683\) 1.56071e7 1.28018 0.640090 0.768300i \(-0.278897\pi\)
0.640090 + 0.768300i \(0.278897\pi\)
\(684\) 3.02731e7 4.04697e7i 2.47410 3.30742i
\(685\) 0 0
\(686\) −4.10550e6 + 1.23423e7i −0.333085 + 1.00135i
\(687\) 2.24811e7i 1.81729i
\(688\) −2.38949e6 8.11684e6i −0.192457 0.653756i
\(689\) −1.47335e7 −1.18239
\(690\) 0 0
\(691\) 1.32611e7i 1.05654i 0.849077 + 0.528269i \(0.177159\pi\)
−0.849077 + 0.528269i \(0.822841\pi\)
\(692\) −2.57533e6 1.92646e6i −0.204441 0.152931i
\(693\) 1.04094e7 0.823362
\(694\) 1.15531e7 + 3.84298e6i 0.910539 + 0.302879i
\(695\) 0 0
\(696\) 3.37027e7 2.34265e7i 2.63719 1.83309i
\(697\) 1.16171e6i 0.0905763i
\(698\) −4.97844e6 + 1.49666e7i −0.386772 + 1.16274i
\(699\) 2.54807e7i 1.97251i
\(700\) 0 0
\(701\) 2.41803e7i 1.85852i −0.369432 0.929258i \(-0.620448\pi\)
0.369432 0.929258i \(-0.379552\pi\)
\(702\) −2.82379e7 9.39297e6i −2.16266 0.719383i
\(703\) 1.19909e7i 0.915093i
\(704\) 5.58787e6 + 2.07748e6i 0.424927 + 0.157981i
\(705\) 0 0
\(706\) 5.77177e6 1.73515e7i 0.435810 1.31016i
\(707\) −3.51354e6 −0.264361
\(708\) 1.18303e7 1.58150e7i 0.886979 1.18573i
\(709\) 3.10586e6i 0.232042i −0.993247 0.116021i \(-0.962986\pi\)
0.993247 0.116021i \(-0.0370140\pi\)
\(710\) 0 0
\(711\) −2.79953e7 −2.07688
\(712\) 8.43477e6 + 1.21348e7i 0.623553 + 0.897081i
\(713\) 2.99610e7i 2.20716i
\(714\) 8.84196e6 + 2.94117e6i 0.649087 + 0.215911i
\(715\) 0 0
\(716\) −1.06205e7 + 1.41977e7i −0.774219 + 1.03499i
\(717\) −1.03058e7 −0.748661
\(718\) 1.08481e7 + 3.60849e6i 0.785313 + 0.261225i
\(719\) 7.95560e6 0.573919 0.286960 0.957943i \(-0.407355\pi\)
0.286960 + 0.957943i \(0.407355\pi\)
\(720\) 0 0
\(721\) −1.58787e7 −1.13757
\(722\) −2.00862e7 6.68143e6i −1.43402 0.477009i
\(723\) 2.49902e7 1.77797
\(724\) −4.36246e6 + 5.83181e6i −0.309303 + 0.413483i
\(725\) 0 0
\(726\) −2.03317e7 6.76309e6i −1.43164 0.476216i
\(727\) 2.50891e7i 1.76055i −0.474463 0.880276i \(-0.657358\pi\)
0.474463 0.880276i \(-0.342642\pi\)
\(728\) −6.11270e6 + 4.24888e6i −0.427469 + 0.297130i
\(729\) 3.60626e7 2.51327
\(730\) 0 0
\(731\) 5.08969e6i 0.352288i
\(732\) −7.52709e6 + 1.00624e7i −0.519217 + 0.694100i
\(733\) −2.58258e7 −1.77539 −0.887694 0.460434i \(-0.847694\pi\)
−0.887694 + 0.460434i \(0.847694\pi\)
\(734\) 4.47244e6 1.34454e7i 0.306411 0.921156i
\(735\) 0 0
\(736\) −2.56287e7 892869.i −1.74394 0.0607566i
\(737\) 1.75426e6i 0.118966i
\(738\) 6.41176e6 + 2.13279e6i 0.433347 + 0.144148i
\(739\) 2.15950e7i 1.45459i 0.686323 + 0.727297i \(0.259224\pi\)
−0.686323 + 0.727297i \(0.740776\pi\)
\(740\) 0 0
\(741\) 3.36055e7i 2.24835i
\(742\) 5.22024e6 1.56935e7i 0.348081 1.04643i
\(743\) 1.25570e7i 0.834479i 0.908797 + 0.417239i \(0.137002\pi\)
−0.908797 + 0.417239i \(0.862998\pi\)
\(744\) 2.06994e7 + 2.97794e7i 1.37096 + 1.97235i
\(745\) 0 0
\(746\) 2.65793e6 + 884126.i 0.174862 + 0.0581657i
\(747\) 5.07088e7 3.32492
\(748\) 2.87154e6 + 2.14804e6i 0.187655 + 0.140374i
\(749\) 1.15795e7i 0.754199i
\(750\) 0 0
\(751\) −5.43894e6 −0.351896 −0.175948 0.984399i \(-0.556299\pi\)
−0.175948 + 0.984399i \(0.556299\pi\)
\(752\) 5.62715e6 1.65656e6i 0.362864 0.106823i
\(753\) 4.50097e7i 2.89280i
\(754\) −6.22569e6 + 1.87161e7i −0.398803 + 1.19891i
\(755\) 0 0
\(756\) 2.00099e7 2.67496e7i 1.27333 1.70221i
\(757\) 1.06247e7 0.673873 0.336937 0.941527i \(-0.390609\pi\)
0.336937 + 0.941527i \(0.390609\pi\)
\(758\) −3.91094e6 + 1.17574e7i −0.247234 + 0.743253i
\(759\) −2.38433e7 −1.50232
\(760\) 0 0
\(761\) 2.31511e7 1.44914 0.724570 0.689201i \(-0.242038\pi\)
0.724570 + 0.689201i \(0.242038\pi\)
\(762\) 7.25151e6 2.18000e7i 0.452419 1.36010i
\(763\) −4.47763e6 −0.278443
\(764\) 2.04120e7 + 1.52691e7i 1.26518 + 0.946412i
\(765\) 0 0
\(766\) 517363. 1.55534e6i 0.0318584 0.0957751i
\(767\) 9.49113e6i 0.582545i
\(768\) 2.60902e7 1.68188e7i 1.59615 1.02894i
\(769\) −9.09958e6 −0.554888 −0.277444 0.960742i \(-0.589487\pi\)
−0.277444 + 0.960742i \(0.589487\pi\)
\(770\) 0 0
\(771\) 2.02011e7i 1.22388i
\(772\) −6.83549e6 + 9.13781e6i −0.412787 + 0.551822i
\(773\) −1.82799e7 −1.10034 −0.550169 0.835053i \(-0.685437\pi\)
−0.550169 + 0.835053i \(0.685437\pi\)
\(774\) −2.80913e7 9.34423e6i −1.68547 0.560649i
\(775\) 0 0
\(776\) −3.30347e6 + 2.29622e6i −0.196932 + 0.136886i
\(777\) 1.28596e7i 0.764142i
\(778\) −3.77728e6 + 1.13556e7i −0.223733 + 0.672604i
\(779\) 4.70295e6i 0.277669i
\(780\) 0 0
\(781\) 6.01985e6i 0.353149i
\(782\) −1.46372e7 4.86889e6i −0.855937 0.284717i
\(783\) 8.85113e7i 5.15934i
\(784\) 2.50036e6 + 8.49345e6i 0.145282 + 0.493508i
\(785\) 0 0
\(786\) −4.85787e6 + 1.46041e7i −0.280472 + 0.843177i
\(787\) −3.07594e6 −0.177028 −0.0885139 0.996075i \(-0.528212\pi\)
−0.0885139 + 0.996075i \(0.528212\pi\)
\(788\) 5.80472e6 + 4.34219e6i 0.333017 + 0.249111i
\(789\) 2.70558e6i 0.154728i
\(790\) 0 0
\(791\) 8.34507e6 0.474230
\(792\) 1.71275e7 1.19051e7i 0.970242 0.674407i
\(793\) 6.03877e6i 0.341009i
\(794\) −9.70164e6 3.22713e6i −0.546127 0.181662i
\(795\) 0 0
\(796\) 4.55816e6 + 3.40971e6i 0.254981 + 0.190737i
\(797\) −2.64996e6 −0.147772 −0.0738861 0.997267i \(-0.523540\pi\)
−0.0738861 + 0.997267i \(0.523540\pi\)
\(798\) −3.57950e7 1.19068e7i −1.98983 0.661891i
\(799\) 3.52853e6 0.195536
\(800\) 0 0
\(801\) 5.17071e7 2.84754
\(802\) −1.39083e7 4.62641e6i −0.763549 0.253985i
\(803\) 3.38315e6 0.185153
\(804\) 7.31429e6 + 5.47141e6i 0.399054 + 0.298510i
\(805\) 0 0
\(806\) −1.65374e7 5.50096e6i −0.896664 0.298264i
\(807\) 2.76932e7i 1.49689i
\(808\) −5.78115e6 + 4.01843e6i −0.311520 + 0.216535i
\(809\) −4.52804e6 −0.243242 −0.121621 0.992577i \(-0.538809\pi\)
−0.121621 + 0.992577i \(0.538809\pi\)
\(810\) 0 0
\(811\) 2.45669e7i 1.31159i 0.754939 + 0.655795i \(0.227666\pi\)
−0.754939 + 0.655795i \(0.772334\pi\)
\(812\) −1.77297e7 1.32626e7i −0.943652 0.705893i
\(813\) −1.51656e7 −0.804701
\(814\) −1.56203e6 + 4.69590e6i −0.0826283 + 0.248404i
\(815\) 0 0
\(816\) 1.79123e7 5.27315e6i 0.941728 0.277233i
\(817\) 2.06047e7i 1.07997i
\(818\) 2.68859e7 + 8.94325e6i 1.40489 + 0.467318i
\(819\) 2.60466e7i 1.35688i
\(820\) 0 0
\(821\) 3.38228e7i 1.75126i 0.482981 + 0.875631i \(0.339554\pi\)
−0.482981 + 0.875631i \(0.660446\pi\)
\(822\) −1.16660e7 + 3.50711e7i −0.602200 + 1.81038i
\(823\) 1.50699e7i 0.775554i 0.921753 + 0.387777i \(0.126757\pi\)
−0.921753 + 0.387777i \(0.873243\pi\)
\(824\) −2.61267e7 + 1.81605e7i −1.34050 + 0.931770i
\(825\) 0 0
\(826\) −1.01095e7 3.36280e6i −0.515561 0.171495i
\(827\) 1.25312e7 0.637132 0.318566 0.947901i \(-0.396799\pi\)
0.318566 + 0.947901i \(0.396799\pi\)
\(828\) −5.37453e7 + 7.18477e7i −2.72436 + 3.64198i
\(829\) 6.28073e6i 0.317412i −0.987326 0.158706i \(-0.949268\pi\)
0.987326 0.158706i \(-0.0507323\pi\)
\(830\) 0 0
\(831\) −1.82307e7 −0.915801
\(832\) −5.19835e6 + 1.39821e7i −0.260350 + 0.700270i
\(833\) 5.32585e6i 0.265936i
\(834\) 8.15976e6 2.45305e7i 0.406221 1.22121i
\(835\) 0 0
\(836\) −1.16249e7 8.69593e6i −0.575271 0.430329i
\(837\) 7.82078e7 3.85866
\(838\) 4.06847e6 1.22309e7i 0.200134 0.601658i
\(839\) −2.04326e7 −1.00212 −0.501058 0.865414i \(-0.667056\pi\)
−0.501058 + 0.865414i \(0.667056\pi\)
\(840\) 0 0
\(841\) −3.81543e7 −1.86018
\(842\) 2.32840e6 6.99981e6i 0.113182 0.340256i
\(843\) −3.61404e7 −1.75156
\(844\) 1.00682e7 1.34594e7i 0.486514 0.650382i
\(845\) 0 0
\(846\) 6.47806e6 1.94748e7i 0.311185 0.935509i
\(847\) 1.15587e7i 0.553605i
\(848\) −9.35924e6 3.17923e7i −0.446942 1.51821i
\(849\) −2.06133e7 −0.981472
\(850\) 0 0
\(851\) 2.12881e7i 1.00766i
\(852\) 2.50995e7 + 1.87755e7i 1.18458 + 0.886121i
\(853\) 2.97962e7 1.40213 0.701066 0.713097i \(-0.252708\pi\)
0.701066 + 0.713097i \(0.252708\pi\)
\(854\) 6.43221e6 + 2.13960e6i 0.301798 + 0.100389i
\(855\) 0 0
\(856\) −1.32435e7 1.90528e7i −0.617756 0.888741i
\(857\) 2.06770e7i 0.961690i 0.876806 + 0.480845i \(0.159670\pi\)
−0.876806 + 0.480845i \(0.840330\pi\)
\(858\) −4.37771e6 + 1.31606e7i −0.203015 + 0.610320i
\(859\) 2.17795e7i 1.00708i −0.863971 0.503542i \(-0.832030\pi\)
0.863971 0.503542i \(-0.167970\pi\)
\(860\) 0 0
\(861\) 5.04363e6i 0.231865i
\(862\) 2.11485e7 + 7.03478e6i 0.969419 + 0.322465i
\(863\) 2.24327e7i 1.02531i 0.858596 + 0.512654i \(0.171337\pi\)
−0.858596 + 0.512654i \(0.828663\pi\)
\(864\) 2.33067e6 6.68989e7i 0.106218 3.04884i
\(865\) 0 0
\(866\) 1.04354e7 3.13716e7i 0.472839 1.42148i
\(867\) −3.08006e7 −1.39159
\(868\) 1.17187e7 1.56658e7i 0.527936 0.705755i
\(869\) 8.04162e6i 0.361239i
\(870\) 0 0
\(871\) −4.38956e6 −0.196054
\(872\) −7.36745e6 + 5.12105e6i −0.328115 + 0.228070i
\(873\) 1.40763e7i 0.625107i
\(874\) 5.92560e7 + 1.97108e7i 2.62394 + 0.872821i
\(875\) 0 0
\(876\) 1.05518e7 1.41059e7i 0.464587 0.621068i
\(877\) −3.66024e7 −1.60698 −0.803491 0.595317i \(-0.797027\pi\)
−0.803491 + 0.595317i \(0.797027\pi\)
\(878\) 4.09563e7 + 1.36236e7i 1.79302 + 0.596424i
\(879\) 3.98880e6 0.174129
\(880\) 0 0
\(881\) −4.27422e7 −1.85531 −0.927656 0.373436i \(-0.878179\pi\)
−0.927656 + 0.373436i \(0.878179\pi\)
\(882\) 2.93947e7 + 9.77779e6i 1.27233 + 0.423223i
\(883\) 1.39684e7 0.602901 0.301451 0.953482i \(-0.402529\pi\)
0.301451 + 0.953482i \(0.402529\pi\)
\(884\) −5.37489e6 + 7.18526e6i −0.231334 + 0.309252i
\(885\) 0 0
\(886\) 1.06822e7 + 3.55330e6i 0.457169 + 0.152071i
\(887\) 8.75249e6i 0.373528i −0.982405 0.186764i \(-0.940200\pi\)
0.982405 0.186764i \(-0.0597999\pi\)
\(888\) 1.47075e7 + 2.11590e7i 0.625900 + 0.900458i
\(889\) −1.23934e7 −0.525941
\(890\) 0 0
\(891\) 3.42378e7i 1.44481i
\(892\) 1.36343e7 1.82266e7i 0.573747 0.766996i
\(893\) −1.42846e7 −0.599430
\(894\) 8.08579e6 2.43081e7i 0.338360 1.01720i
\(895\) 0 0
\(896\) −1.30513e7 1.04910e7i −0.543105 0.436565i
\(897\) 5.96614e7i 2.47578i
\(898\) 1.10310e7 + 3.66932e6i 0.456482 + 0.151843i
\(899\) 5.18363e7i 2.13912i
\(900\) 0 0
\(901\) 1.99355e7i 0.818116i
\(902\) 612642. 1.84177e6i 0.0250721 0.0753736i
\(903\) 2.20973e7i 0.901819i
\(904\) 1.37309e7 9.54423e6i 0.558828 0.388436i
\(905\) 0 0
\(906\) 6.99938e7 + 2.32826e7i 2.83295 + 0.942345i
\(907\) −4.22342e7 −1.70469 −0.852345 0.522979i \(-0.824820\pi\)
−0.852345 + 0.522979i \(0.824820\pi\)
\(908\) 5.54369e6 + 4.14693e6i 0.223144 + 0.166921i
\(909\) 2.46339e7i 0.988834i
\(910\) 0 0
\(911\) 3.59551e7 1.43537 0.717686 0.696367i \(-0.245201\pi\)
0.717686 + 0.696367i \(0.245201\pi\)
\(912\) −7.25145e7 + 2.13473e7i −2.88694 + 0.849878i
\(913\) 1.45661e7i 0.578316i
\(914\) 4.90456e6 1.47445e7i 0.194193 0.583799i
\(915\) 0 0
\(916\) −1.45563e7 + 1.94591e7i −0.573207 + 0.766274i
\(917\) 8.30252e6 0.326052
\(918\) 1.27093e7 3.82077e7i 0.497755 1.49639i
\(919\) −4.72565e6 −0.184575 −0.0922875 0.995732i \(-0.529418\pi\)
−0.0922875 + 0.995732i \(0.529418\pi\)
\(920\) 0 0
\(921\) 8.31472e6 0.322997
\(922\) 7.17172e6 2.15602e7i 0.277841 0.835266i
\(923\) −1.50631e7 −0.581981
\(924\) −1.24670e7 9.32586e6i −0.480376 0.359343i
\(925\) 0 0
\(926\) −1.38874e7 + 4.17493e7i −0.532223 + 1.60001i
\(927\) 1.11328e8i 4.25505i
\(928\) −4.43407e7 1.54477e6i −1.69018 0.0588837i
\(929\) 3.52534e7 1.34018 0.670088 0.742282i \(-0.266256\pi\)
0.670088 + 0.742282i \(0.266256\pi\)
\(930\) 0 0
\(931\) 2.15607e7i 0.815246i
\(932\) 1.64985e7 2.20555e7i 0.622164 0.831721i
\(933\) 7.11513e7 2.67595
\(934\) 2.04741e7 + 6.81044e6i 0.767957 + 0.255451i
\(935\) 0 0
\(936\) 2.97895e7 + 4.28569e7i 1.11141 + 1.59894i
\(937\) 4.46076e7i 1.65982i −0.557899 0.829909i \(-0.688393\pi\)
0.557899 0.829909i \(-0.311607\pi\)
\(938\) 1.55526e6 4.67555e6i 0.0577161 0.173511i
\(939\) 1.83400e7i 0.678791i
\(940\) 0 0
\(941\) 901496.i 0.0331886i 0.999862 + 0.0165943i \(0.00528238\pi\)
−0.999862 + 0.0165943i \(0.994718\pi\)
\(942\) 6.88649e7 + 2.29070e7i 2.52854 + 0.841089i
\(943\) 8.34937e6i 0.305756i
\(944\) −2.04801e7 + 6.02909e6i −0.748001 + 0.220202i
\(945\) 0 0
\(946\) −2.68412e6 + 8.06921e6i −0.0975157 + 0.293159i
\(947\) 1.66417e7 0.603006 0.301503 0.953465i \(-0.402512\pi\)
0.301503 + 0.953465i \(0.402512\pi\)
\(948\) 3.35292e7 + 2.50813e7i 1.21172 + 0.906420i
\(949\) 8.46542e6i 0.305129i
\(950\) 0 0
\(951\) −2.70285e7 −0.969105
\(952\) −5.74902e6 8.27089e6i −0.205590 0.295774i
\(953\) 1.76926e7i 0.631043i 0.948918 + 0.315522i \(0.102179\pi\)
−0.948918 + 0.315522i \(0.897821\pi\)
\(954\) −1.10029e8 3.65998e7i −3.91414 1.30199i
\(955\) 0 0
\(956\) 8.92050e6 + 6.67293e6i 0.315678 + 0.236141i
\(957\) −4.12518e7 −1.45600
\(958\) 1.31108e7 + 4.36116e6i 0.461548 + 0.153528i
\(959\) 1.99381e7 0.700063
\(960\) 0 0
\(961\) 1.71729e7 0.599841
\(962\) −1.17502e7 3.90857e6i −0.409363 0.136170i
\(963\) −8.11855e7 −2.82106
\(964\) −2.16310e7 1.61809e7i −0.749693 0.560804i
\(965\) 0 0
\(966\) 6.35485e7 + 2.11386e7i 2.19110 + 0.728843i
\(967\) 1.08926e7i 0.374598i 0.982303 + 0.187299i \(0.0599733\pi\)
−0.982303 + 0.187299i \(0.940027\pi\)
\(968\) 1.32196e7 + 1.90186e7i 0.453452 + 0.652363i
\(969\) −4.54705e7 −1.55568
\(970\) 0 0
\(971\) 1.33282e7i 0.453654i −0.973935 0.226827i \(-0.927165\pi\)
0.973935 0.226827i \(-0.0728351\pi\)
\(972\) −7.07980e7 5.29600e7i −2.40356 1.79797i
\(973\) −1.39457e7 −0.472236
\(974\) −1.49118e7 + 4.48289e7i −0.503654 + 1.51412i
\(975\) 0 0
\(976\) 1.30306e7 3.83603e6i 0.437863 0.128901i
\(977\) 5.24537e7i 1.75808i 0.476745 + 0.879042i \(0.341816\pi\)
−0.476745 + 0.879042i \(0.658184\pi\)
\(978\) −3.20891e7 1.06740e7i −1.07278 0.356846i
\(979\) 1.48528e7i 0.495282i
\(980\) 0 0
\(981\) 3.13932e7i 1.04151i
\(982\) −607191. + 1.82538e6i −0.0200931 + 0.0604053i
\(983\) 9.86355e6i 0.325574i 0.986661 + 0.162787i \(0.0520483\pi\)
−0.986661 + 0.162787i \(0.947952\pi\)
\(984\) −5.76839e6 8.29875e6i −0.189918 0.273228i
\(985\) 0 0
\(986\) −2.53242e7 8.42377e6i −0.829551 0.275940i
\(987\) −1.53194e7 −0.500550
\(988\) 2.17592e7 2.90882e7i 0.709172 0.948034i
\(989\) 3.65804e7i 1.18921i
\(990\) 0 0
\(991\) 2.89033e7 0.934897 0.467448 0.884020i \(-0.345173\pi\)
0.467448 + 0.884020i \(0.345173\pi\)
\(992\) 1.36495e6 3.91791e7i 0.0440389 1.26408i
\(993\) 1.00019e8i 3.21891i
\(994\) 5.33699e6 1.60445e7i 0.171329 0.515062i
\(995\) 0 0
\(996\) −6.07325e7 4.54306e7i −1.93987 1.45111i
\(997\) −4.81768e6 −0.153497 −0.0767485 0.997050i \(-0.524454\pi\)
−0.0767485 + 0.997050i \(0.524454\pi\)
\(998\) −1.15877e6 + 3.48360e6i −0.0368275 + 0.110714i
\(999\) 5.55686e7 1.76163
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 200.6.f.d.149.38 40
4.3 odd 2 800.6.f.d.49.39 40
5.2 odd 4 200.6.d.d.101.10 yes 20
5.3 odd 4 200.6.d.c.101.11 20
5.4 even 2 inner 200.6.f.d.149.3 40
8.3 odd 2 800.6.f.d.49.1 40
8.5 even 2 inner 200.6.f.d.149.4 40
20.3 even 4 800.6.d.d.401.20 20
20.7 even 4 800.6.d.b.401.1 20
20.19 odd 2 800.6.f.d.49.2 40
40.3 even 4 800.6.d.d.401.1 20
40.13 odd 4 200.6.d.c.101.12 yes 20
40.19 odd 2 800.6.f.d.49.40 40
40.27 even 4 800.6.d.b.401.20 20
40.29 even 2 inner 200.6.f.d.149.37 40
40.37 odd 4 200.6.d.d.101.9 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.6.d.c.101.11 20 5.3 odd 4
200.6.d.c.101.12 yes 20 40.13 odd 4
200.6.d.d.101.9 yes 20 40.37 odd 4
200.6.d.d.101.10 yes 20 5.2 odd 4
200.6.f.d.149.3 40 5.4 even 2 inner
200.6.f.d.149.4 40 8.5 even 2 inner
200.6.f.d.149.37 40 40.29 even 2 inner
200.6.f.d.149.38 40 1.1 even 1 trivial
800.6.d.b.401.1 20 20.7 even 4
800.6.d.b.401.20 20 40.27 even 4
800.6.d.d.401.1 20 40.3 even 4
800.6.d.d.401.20 20 20.3 even 4
800.6.f.d.49.1 40 8.3 odd 2
800.6.f.d.49.2 40 20.19 odd 2
800.6.f.d.49.39 40 4.3 odd 2
800.6.f.d.49.40 40 40.19 odd 2