Properties

Label 40.6.f.a.29.9
Level $40$
Weight $6$
Character 40.29
Analytic conductor $6.415$
Analytic rank $0$
Dimension $28$
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] = [40,6,Mod(29,40)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(40, 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("40.29");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 40.f (of order \(2\), degree \(1\), 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: \(6.41535279252\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.9
Character \(\chi\) \(=\) 40.29
Dual form 40.6.f.a.29.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.25299 - 4.62796i) q^{2} +1.29818 q^{3} +(-10.8361 + 30.1095i) q^{4} +(51.3939 - 21.9924i) q^{5} +(-4.22299 - 6.00795i) q^{6} -170.399i q^{7} +(174.595 - 47.7971i) q^{8} -241.315 q^{9} +O(q^{10})\) \(q+(-3.25299 - 4.62796i) q^{2} +1.29818 q^{3} +(-10.8361 + 30.1095i) q^{4} +(51.3939 - 21.9924i) q^{5} +(-4.22299 - 6.00795i) q^{6} -170.399i q^{7} +(174.595 - 47.7971i) q^{8} -241.315 q^{9} +(-268.964 - 166.308i) q^{10} -39.8166i q^{11} +(-14.0672 + 39.0876i) q^{12} -537.234 q^{13} +(-788.600 + 554.307i) q^{14} +(66.7187 - 28.5502i) q^{15} +(-789.160 - 652.536i) q^{16} -1355.83i q^{17} +(784.995 + 1116.80i) q^{18} -1039.21i q^{19} +(105.274 + 1785.75i) q^{20} -221.209i q^{21} +(-184.270 + 129.523i) q^{22} -1610.62i q^{23} +(226.657 - 62.0494i) q^{24} +(2157.67 - 2260.55i) q^{25} +(1747.62 + 2486.30i) q^{26} -628.730 q^{27} +(5130.62 + 1846.45i) q^{28} +5910.56i q^{29} +(-349.165 - 215.898i) q^{30} +9611.53 q^{31} +(-452.776 + 5774.90i) q^{32} -51.6892i q^{33} +(-6274.71 + 4410.50i) q^{34} +(-3747.49 - 8757.46i) q^{35} +(2614.90 - 7265.86i) q^{36} -5295.85 q^{37} +(-4809.42 + 3380.54i) q^{38} -697.429 q^{39} +(7921.95 - 6296.25i) q^{40} -12105.1 q^{41} +(-1023.75 + 719.592i) q^{42} +19338.2 q^{43} +(1198.86 + 431.455i) q^{44} +(-12402.1 + 5307.10i) q^{45} +(-7453.87 + 5239.32i) q^{46} +7894.36i q^{47} +(-1024.47 - 847.111i) q^{48} -12228.8 q^{49} +(-17480.6 - 2632.02i) q^{50} -1760.11i q^{51} +(5821.50 - 16175.8i) q^{52} +18932.1 q^{53} +(2045.25 + 2909.74i) q^{54} +(-875.664 - 2046.33i) q^{55} +(-8144.57 - 29750.8i) q^{56} -1349.09i q^{57} +(27353.9 - 19227.0i) q^{58} -32322.2i q^{59} +(136.665 + 2318.24i) q^{60} +48808.2i q^{61} +(-31266.2 - 44481.8i) q^{62} +41119.8i q^{63} +(28198.9 - 16690.3i) q^{64} +(-27610.6 + 11815.1i) q^{65} +(-239.216 + 168.145i) q^{66} -882.245 q^{67} +(40823.2 + 14691.8i) q^{68} -2090.88i q^{69} +(-28338.6 + 45831.2i) q^{70} -8818.78 q^{71} +(-42132.4 + 11534.1i) q^{72} +14380.4i q^{73} +(17227.4 + 24509.0i) q^{74} +(2801.05 - 2934.62i) q^{75} +(31290.1 + 11260.9i) q^{76} -6784.70 q^{77} +(2268.73 + 3227.68i) q^{78} +49813.9 q^{79} +(-54908.9 - 16180.8i) q^{80} +57823.3 q^{81} +(39377.9 + 56022.1i) q^{82} +13938.9 q^{83} +(6660.49 + 2397.03i) q^{84} +(-29817.9 - 69681.2i) q^{85} +(-62906.9 - 89496.2i) q^{86} +7673.00i q^{87} +(-1903.12 - 6951.78i) q^{88} +7581.49 q^{89} +(64905.0 + 40132.5i) q^{90} +91544.2i q^{91} +(48494.8 + 17452.7i) q^{92} +12477.5 q^{93} +(36534.8 - 25680.3i) q^{94} +(-22854.8 - 53409.1i) q^{95} +(-587.787 + 7496.88i) q^{96} -66750.3i q^{97} +(39780.2 + 56594.3i) q^{98} +9608.33i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36} + 23360 q^{39} - 22496 q^{40} - 2480 q^{41} + 10712 q^{44} + 58372 q^{46} - 38420 q^{49} + 45624 q^{50} - 3568 q^{54} - 48776 q^{55} + 110944 q^{56} + 111688 q^{60} - 46944 q^{64} + 37200 q^{65} - 136120 q^{66} - 112852 q^{70} - 69232 q^{71} + 34176 q^{74} - 13944 q^{76} - 35984 q^{79} - 47064 q^{80} + 122596 q^{81} - 165688 q^{84} - 73676 q^{86} - 178744 q^{89} + 51496 q^{90} + 314740 q^{94} + 89416 q^{95} - 236176 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.25299 4.62796i −0.575054 0.818116i
\(3\) 1.29818 0.0832785 0.0416393 0.999133i \(-0.486742\pi\)
0.0416393 + 0.999133i \(0.486742\pi\)
\(4\) −10.8361 + 30.1095i −0.338627 + 0.940921i
\(5\) 51.3939 21.9924i 0.919362 0.393413i
\(6\) −4.22299 6.00795i −0.0478896 0.0681315i
\(7\) 170.399i 1.31438i −0.753724 0.657191i \(-0.771744\pi\)
0.753724 0.657191i \(-0.228256\pi\)
\(8\) 174.595 47.7971i 0.964511 0.264044i
\(9\) −241.315 −0.993065
\(10\) −268.964 166.308i −0.850540 0.525911i
\(11\) 39.8166i 0.0992161i −0.998769 0.0496081i \(-0.984203\pi\)
0.998769 0.0496081i \(-0.0157972\pi\)
\(12\) −14.0672 + 39.0876i −0.0282003 + 0.0783585i
\(13\) −537.234 −0.881669 −0.440834 0.897588i \(-0.645317\pi\)
−0.440834 + 0.897588i \(0.645317\pi\)
\(14\) −788.600 + 554.307i −1.07532 + 0.755840i
\(15\) 66.7187 28.5502i 0.0765631 0.0327628i
\(16\) −789.160 652.536i −0.770664 0.637242i
\(17\) 1355.83i 1.13784i −0.822392 0.568921i \(-0.807361\pi\)
0.822392 0.568921i \(-0.192639\pi\)
\(18\) 784.995 + 1116.80i 0.571065 + 0.812442i
\(19\) 1039.21i 0.660419i −0.943908 0.330209i \(-0.892881\pi\)
0.943908 0.330209i \(-0.107119\pi\)
\(20\) 105.274 + 1785.75i 0.0588498 + 0.998267i
\(21\) 221.209i 0.109460i
\(22\) −184.270 + 129.523i −0.0811703 + 0.0570546i
\(23\) 1610.62i 0.634852i −0.948283 0.317426i \(-0.897182\pi\)
0.948283 0.317426i \(-0.102818\pi\)
\(24\) 226.657 62.0494i 0.0803230 0.0219892i
\(25\) 2157.67 2260.55i 0.690453 0.723377i
\(26\) 1747.62 + 2486.30i 0.507007 + 0.721307i
\(27\) −628.730 −0.165980
\(28\) 5130.62 + 1846.45i 1.23673 + 0.445085i
\(29\) 5910.56i 1.30507i 0.757759 + 0.652535i \(0.226294\pi\)
−0.757759 + 0.652535i \(0.773706\pi\)
\(30\) −349.165 215.898i −0.0708317 0.0437971i
\(31\) 9611.53 1.79634 0.898169 0.439650i \(-0.144898\pi\)
0.898169 + 0.439650i \(0.144898\pi\)
\(32\) −452.776 + 5774.90i −0.0781643 + 0.996940i
\(33\) 51.6892i 0.00826257i
\(34\) −6274.71 + 4410.50i −0.930886 + 0.654320i
\(35\) −3747.49 8757.46i −0.517095 1.20839i
\(36\) 2614.90 7265.86i 0.336278 0.934395i
\(37\) −5295.85 −0.635963 −0.317981 0.948097i \(-0.603005\pi\)
−0.317981 + 0.948097i \(0.603005\pi\)
\(38\) −4809.42 + 3380.54i −0.540299 + 0.379776i
\(39\) −697.429 −0.0734241
\(40\) 7921.95 6296.25i 0.782856 0.622203i
\(41\) −12105.1 −1.12463 −0.562315 0.826923i \(-0.690089\pi\)
−0.562315 + 0.826923i \(0.690089\pi\)
\(42\) −1023.75 + 719.592i −0.0895508 + 0.0629453i
\(43\) 19338.2 1.59494 0.797469 0.603360i \(-0.206172\pi\)
0.797469 + 0.603360i \(0.206172\pi\)
\(44\) 1198.86 + 431.455i 0.0933545 + 0.0335972i
\(45\) −12402.1 + 5307.10i −0.912986 + 0.390684i
\(46\) −7453.87 + 5239.32i −0.519382 + 0.365074i
\(47\) 7894.36i 0.521282i 0.965436 + 0.260641i \(0.0839338\pi\)
−0.965436 + 0.260641i \(0.916066\pi\)
\(48\) −1024.47 847.111i −0.0641798 0.0530686i
\(49\) −12228.8 −0.727601
\(50\) −17480.6 2632.02i −0.988854 0.148890i
\(51\) 1760.11i 0.0947578i
\(52\) 5821.50 16175.8i 0.298557 0.829581i
\(53\) 18932.1 0.925783 0.462891 0.886415i \(-0.346812\pi\)
0.462891 + 0.886415i \(0.346812\pi\)
\(54\) 2045.25 + 2909.74i 0.0954471 + 0.135790i
\(55\) −875.664 2046.33i −0.0390329 0.0912155i
\(56\) −8144.57 29750.8i −0.347055 1.26774i
\(57\) 1349.09i 0.0549987i
\(58\) 27353.9 19227.0i 1.06770 0.750485i
\(59\) 32322.2i 1.20885i −0.796663 0.604424i \(-0.793403\pi\)
0.796663 0.604424i \(-0.206597\pi\)
\(60\) 136.665 + 2318.24i 0.00490092 + 0.0831342i
\(61\) 48808.2i 1.67945i 0.543008 + 0.839727i \(0.317285\pi\)
−0.543008 + 0.839727i \(0.682715\pi\)
\(62\) −31266.2 44481.8i −1.03299 1.46961i
\(63\) 41119.8i 1.30527i
\(64\) 28198.9 16690.3i 0.860561 0.509347i
\(65\) −27610.6 + 11815.1i −0.810573 + 0.346860i
\(66\) −239.216 + 168.145i −0.00675974 + 0.00475142i
\(67\) −882.245 −0.0240106 −0.0120053 0.999928i \(-0.503821\pi\)
−0.0120053 + 0.999928i \(0.503821\pi\)
\(68\) 40823.2 + 14691.8i 1.07062 + 0.385304i
\(69\) 2090.88i 0.0528695i
\(70\) −28338.6 + 45831.2i −0.691248 + 1.11793i
\(71\) −8818.78 −0.207617 −0.103808 0.994597i \(-0.533103\pi\)
−0.103808 + 0.994597i \(0.533103\pi\)
\(72\) −42132.4 + 11534.1i −0.957821 + 0.262213i
\(73\) 14380.4i 0.315837i 0.987452 + 0.157919i \(0.0504784\pi\)
−0.987452 + 0.157919i \(0.949522\pi\)
\(74\) 17227.4 + 24509.0i 0.365713 + 0.520291i
\(75\) 2801.05 2934.62i 0.0574999 0.0602418i
\(76\) 31290.1 + 11260.9i 0.621402 + 0.223635i
\(77\) −6784.70 −0.130408
\(78\) 2268.73 + 3227.68i 0.0422228 + 0.0600694i
\(79\) 49813.9 0.898014 0.449007 0.893528i \(-0.351778\pi\)
0.449007 + 0.893528i \(0.351778\pi\)
\(80\) −54908.9 16180.8i −0.959218 0.282667i
\(81\) 57823.3 0.979242
\(82\) 39377.9 + 56022.1i 0.646723 + 0.920078i
\(83\) 13938.9 0.222092 0.111046 0.993815i \(-0.464580\pi\)
0.111046 + 0.993815i \(0.464580\pi\)
\(84\) 6660.49 + 2397.03i 0.102993 + 0.0370660i
\(85\) −29817.9 69681.2i −0.447641 1.04609i
\(86\) −62906.9 89496.2i −0.917175 1.30484i
\(87\) 7673.00i 0.108684i
\(88\) −1903.12 6951.78i −0.0261974 0.0956950i
\(89\) 7581.49 0.101456 0.0507282 0.998712i \(-0.483846\pi\)
0.0507282 + 0.998712i \(0.483846\pi\)
\(90\) 64905.0 + 40132.5i 0.844641 + 0.522264i
\(91\) 91544.2i 1.15885i
\(92\) 48494.8 + 17452.7i 0.597345 + 0.214978i
\(93\) 12477.5 0.149596
\(94\) 36534.8 25680.3i 0.426469 0.299765i
\(95\) −22854.8 53409.1i −0.259817 0.607164i
\(96\) −587.787 + 7496.88i −0.00650941 + 0.0830238i
\(97\) 66750.3i 0.720317i −0.932891 0.360159i \(-0.882723\pi\)
0.932891 0.360159i \(-0.117277\pi\)
\(98\) 39780.2 + 56594.3i 0.418409 + 0.595262i
\(99\) 9608.33i 0.0985280i
\(100\) 44683.5 + 89461.6i 0.446835 + 0.894616i
\(101\) 66492.6i 0.648590i 0.945956 + 0.324295i \(0.105127\pi\)
−0.945956 + 0.324295i \(0.894873\pi\)
\(102\) −8145.73 + 5725.64i −0.0775228 + 0.0544908i
\(103\) 166310.i 1.54463i −0.635237 0.772317i \(-0.719098\pi\)
0.635237 0.772317i \(-0.280902\pi\)
\(104\) −93798.5 + 25678.2i −0.850379 + 0.232800i
\(105\) −4864.93 11368.8i −0.0430629 0.100633i
\(106\) −61586.0 87617.0i −0.532375 0.757398i
\(107\) −121647. −1.02717 −0.513583 0.858040i \(-0.671682\pi\)
−0.513583 + 0.858040i \(0.671682\pi\)
\(108\) 6812.95 18930.7i 0.0562051 0.156174i
\(109\) 170773.i 1.37674i −0.725359 0.688370i \(-0.758326\pi\)
0.725359 0.688370i \(-0.241674\pi\)
\(110\) −6621.80 + 10709.2i −0.0521789 + 0.0843872i
\(111\) −6874.99 −0.0529621
\(112\) −111191. + 134472.i −0.837579 + 1.01295i
\(113\) 3705.12i 0.0272964i −0.999907 0.0136482i \(-0.995656\pi\)
0.999907 0.0136482i \(-0.00434449\pi\)
\(114\) −6243.52 + 4388.57i −0.0449953 + 0.0316272i
\(115\) −35421.4 82775.8i −0.249759 0.583658i
\(116\) −177964. 64047.2i −1.22797 0.441931i
\(117\) 129643. 0.875554
\(118\) −149586. + 105144.i −0.988977 + 0.695152i
\(119\) −231031. −1.49556
\(120\) 10284.1 8173.69i 0.0651951 0.0518162i
\(121\) 159466. 0.990156
\(122\) 225883. 158773.i 1.37399 0.965777i
\(123\) −15714.7 −0.0936576
\(124\) −104151. + 289398.i −0.608288 + 1.69021i
\(125\) 61175.7 163631.i 0.350190 0.936679i
\(126\) 190301. 133762.i 1.06786 0.750598i
\(127\) 77574.6i 0.426786i 0.976966 + 0.213393i \(0.0684515\pi\)
−0.976966 + 0.213393i \(0.931548\pi\)
\(128\) −168973. 76209.9i −0.911574 0.411137i
\(129\) 25104.5 0.132824
\(130\) 144497. + 89346.2i 0.749894 + 0.463679i
\(131\) 330023.i 1.68022i 0.542418 + 0.840109i \(0.317509\pi\)
−0.542418 + 0.840109i \(0.682491\pi\)
\(132\) 1556.34 + 560.107i 0.00777443 + 0.00279793i
\(133\) −177080. −0.868043
\(134\) 2869.94 + 4083.00i 0.0138074 + 0.0196434i
\(135\) −32312.9 + 13827.3i −0.152595 + 0.0652985i
\(136\) −64804.6 236721.i −0.300440 1.09746i
\(137\) 135014.i 0.614578i −0.951616 0.307289i \(-0.900578\pi\)
0.951616 0.307289i \(-0.0994219\pi\)
\(138\) −9676.49 + 6801.61i −0.0432534 + 0.0304028i
\(139\) 130330.i 0.572146i 0.958208 + 0.286073i \(0.0923500\pi\)
−0.958208 + 0.286073i \(0.907650\pi\)
\(140\) 304291. 17938.5i 1.31210 0.0773511i
\(141\) 10248.3i 0.0434116i
\(142\) 28687.5 + 40813.0i 0.119391 + 0.169855i
\(143\) 21390.8i 0.0874758i
\(144\) 190436. + 157466.i 0.765319 + 0.632822i
\(145\) 129988. + 303767.i 0.513431 + 1.19983i
\(146\) 66551.9 46779.3i 0.258392 0.181623i
\(147\) −15875.2 −0.0605935
\(148\) 57386.2 159455.i 0.215354 0.598391i
\(149\) 56728.8i 0.209333i 0.994507 + 0.104667i \(0.0333775\pi\)
−0.994507 + 0.104667i \(0.966622\pi\)
\(150\) −22693.1 3416.85i −0.0823503 0.0123993i
\(151\) 272831. 0.973757 0.486879 0.873470i \(-0.338135\pi\)
0.486879 + 0.873470i \(0.338135\pi\)
\(152\) −49671.2 181441.i −0.174380 0.636981i
\(153\) 327181.i 1.12995i
\(154\) 22070.6 + 31399.3i 0.0749915 + 0.106689i
\(155\) 493974. 211381.i 1.65148 0.706702i
\(156\) 7557.38 20999.2i 0.0248634 0.0690863i
\(157\) 351466. 1.13798 0.568990 0.822345i \(-0.307334\pi\)
0.568990 + 0.822345i \(0.307334\pi\)
\(158\) −162044. 230537.i −0.516406 0.734679i
\(159\) 24577.4 0.0770979
\(160\) 103734. + 306752.i 0.320348 + 0.947300i
\(161\) −274447. −0.834438
\(162\) −188099. 267604.i −0.563117 0.801133i
\(163\) −434277. −1.28026 −0.640129 0.768268i \(-0.721119\pi\)
−0.640129 + 0.768268i \(0.721119\pi\)
\(164\) 131172. 364479.i 0.380830 1.05819i
\(165\) −1136.77 2656.51i −0.00325060 0.00759630i
\(166\) −45343.1 64508.7i −0.127715 0.181697i
\(167\) 580367.i 1.61032i 0.593059 + 0.805159i \(0.297920\pi\)
−0.593059 + 0.805159i \(0.702080\pi\)
\(168\) −10573.2 38622.0i −0.0289022 0.105575i
\(169\) −82672.1 −0.222660
\(170\) −225484. + 364669.i −0.598404 + 0.967779i
\(171\) 250777.i 0.655838i
\(172\) −209549. + 582261.i −0.540089 + 1.50071i
\(173\) −243764. −0.619233 −0.309617 0.950861i \(-0.600201\pi\)
−0.309617 + 0.950861i \(0.600201\pi\)
\(174\) 35510.3 24960.2i 0.0889163 0.0624993i
\(175\) −385196. 367664.i −0.950794 0.907519i
\(176\) −25981.7 + 31421.6i −0.0632246 + 0.0764623i
\(177\) 41960.2i 0.100671i
\(178\) −24662.5 35086.8i −0.0583429 0.0830031i
\(179\) 589838.i 1.37594i −0.725738 0.687971i \(-0.758502\pi\)
0.725738 0.687971i \(-0.241498\pi\)
\(180\) −25404.1 430929.i −0.0584416 0.991344i
\(181\) 306392.i 0.695154i 0.937651 + 0.347577i \(0.112995\pi\)
−0.937651 + 0.347577i \(0.887005\pi\)
\(182\) 423663. 297793.i 0.948073 0.666401i
\(183\) 63362.0i 0.139863i
\(184\) −76982.7 281205.i −0.167629 0.612321i
\(185\) −272175. + 116469.i −0.584680 + 0.250196i
\(186\) −40589.3 57745.5i −0.0860260 0.122387i
\(187\) −53984.4 −0.112892
\(188\) −237695. 85543.7i −0.490485 0.176520i
\(189\) 107135.i 0.218161i
\(190\) −172829. + 279510.i −0.347321 + 0.561712i
\(191\) −123083. −0.244127 −0.122064 0.992522i \(-0.538951\pi\)
−0.122064 + 0.992522i \(0.538951\pi\)
\(192\) 36607.3 21667.0i 0.0716663 0.0424177i
\(193\) 689437.i 1.33230i −0.745819 0.666149i \(-0.767941\pi\)
0.745819 0.666149i \(-0.232059\pi\)
\(194\) −308918. + 217138.i −0.589303 + 0.414221i
\(195\) −35843.6 + 15338.2i −0.0675033 + 0.0288860i
\(196\) 132512. 368202.i 0.246385 0.684615i
\(197\) 70782.9 0.129946 0.0649730 0.997887i \(-0.479304\pi\)
0.0649730 + 0.997887i \(0.479304\pi\)
\(198\) 44467.0 31255.8i 0.0806073 0.0566589i
\(199\) 314584. 0.563123 0.281561 0.959543i \(-0.409148\pi\)
0.281561 + 0.959543i \(0.409148\pi\)
\(200\) 268670. 497812.i 0.474946 0.880015i
\(201\) −1145.32 −0.00199956
\(202\) 307725. 216300.i 0.530622 0.372974i
\(203\) 1.00715e6 1.71536
\(204\) 52996.0 + 19072.7i 0.0891596 + 0.0320875i
\(205\) −622130. + 266221.i −1.03394 + 0.442444i
\(206\) −769677. + 541006.i −1.26369 + 0.888248i
\(207\) 388665.i 0.630449i
\(208\) 423964. + 350565.i 0.679470 + 0.561836i
\(209\) −41377.8 −0.0655242
\(210\) −36788.8 + 59497.3i −0.0575661 + 0.0930999i
\(211\) 1.09357e6i 1.69098i −0.533989 0.845491i \(-0.679308\pi\)
0.533989 0.845491i \(-0.320692\pi\)
\(212\) −205149. + 570035.i −0.313495 + 0.871088i
\(213\) −11448.4 −0.0172900
\(214\) 395716. + 562976.i 0.590675 + 0.840341i
\(215\) 993863. 425293.i 1.46633 0.627469i
\(216\) −109773. + 30051.5i −0.160089 + 0.0438259i
\(217\) 1.63779e6i 2.36107i
\(218\) −790330. + 555523.i −1.12633 + 0.791700i
\(219\) 18668.4i 0.0263025i
\(220\) 71102.6 4191.64i 0.0990442 0.00583885i
\(221\) 728397.i 1.00320i
\(222\) 22364.3 + 31817.2i 0.0304560 + 0.0433291i
\(223\) 917927.i 1.23608i −0.786147 0.618039i \(-0.787927\pi\)
0.786147 0.618039i \(-0.212073\pi\)
\(224\) 984036. + 77152.6i 1.31036 + 0.102738i
\(225\) −520676. + 545505.i −0.685664 + 0.718361i
\(226\) −17147.1 + 12052.7i −0.0223316 + 0.0156969i
\(227\) −1.20791e6 −1.55585 −0.777926 0.628356i \(-0.783728\pi\)
−0.777926 + 0.628356i \(0.783728\pi\)
\(228\) 40620.3 + 14618.8i 0.0517494 + 0.0186240i
\(229\) 323648.i 0.407834i −0.978988 0.203917i \(-0.934633\pi\)
0.978988 0.203917i \(-0.0653673\pi\)
\(230\) −267858. + 433198.i −0.333875 + 0.539966i
\(231\) −8807.79 −0.0108602
\(232\) 282508. + 1.03195e6i 0.344596 + 1.25875i
\(233\) 1.34719e6i 1.62570i 0.582476 + 0.812848i \(0.302084\pi\)
−0.582476 + 0.812848i \(0.697916\pi\)
\(234\) −421727. 599981.i −0.503491 0.716305i
\(235\) 173616. + 405722.i 0.205079 + 0.479247i
\(236\) 973206. + 350246.i 1.13743 + 0.409348i
\(237\) 64667.7 0.0747853
\(238\) 751544. + 1.06920e6i 0.860027 + 1.22354i
\(239\) 997494. 1.12958 0.564788 0.825236i \(-0.308958\pi\)
0.564788 + 0.825236i \(0.308958\pi\)
\(240\) −71281.8 21005.6i −0.0798823 0.0235401i
\(241\) 610095. 0.676636 0.338318 0.941032i \(-0.390142\pi\)
0.338318 + 0.941032i \(0.390142\pi\)
\(242\) −518741. 738001.i −0.569393 0.810062i
\(243\) 227847. 0.247529
\(244\) −1.46959e6 528888.i −1.58023 0.568708i
\(245\) −628485. + 268941.i −0.668928 + 0.286247i
\(246\) 51119.8 + 72727.0i 0.0538581 + 0.0766227i
\(247\) 558300.i 0.582271i
\(248\) 1.67812e6 459403.i 1.73259 0.474313i
\(249\) 18095.2 0.0184955
\(250\) −956282. + 249172.i −0.967690 + 0.252144i
\(251\) 691093.i 0.692392i −0.938162 0.346196i \(-0.887473\pi\)
0.938162 0.346196i \(-0.112527\pi\)
\(252\) −1.23809e6 445576.i −1.22815 0.441998i
\(253\) −64129.2 −0.0629875
\(254\) 359012. 252350.i 0.349161 0.245425i
\(255\) −38709.2 90459.0i −0.0372789 0.0871167i
\(256\) 196971. + 1.02991e6i 0.187846 + 0.982198i
\(257\) 755800.i 0.713796i −0.934143 0.356898i \(-0.883834\pi\)
0.934143 0.356898i \(-0.116166\pi\)
\(258\) −81664.7 116183.i −0.0763810 0.108665i
\(259\) 902408.i 0.835898i
\(260\) −56556.7 959369.i −0.0518860 0.880141i
\(261\) 1.42631e6i 1.29602i
\(262\) 1.52733e6 1.07356e6i 1.37461 0.966215i
\(263\) 316724.i 0.282353i 0.989984 + 0.141176i \(0.0450885\pi\)
−0.989984 + 0.141176i \(0.954912\pi\)
\(264\) −2470.60 9024.69i −0.00218168 0.00796934i
\(265\) 972994. 416363.i 0.851130 0.364215i
\(266\) 576041. + 819521.i 0.499171 + 0.710159i
\(267\) 9842.17 0.00844914
\(268\) 9560.05 26563.9i 0.00813061 0.0225920i
\(269\) 1.50082e6i 1.26458i 0.774731 + 0.632291i \(0.217885\pi\)
−0.774731 + 0.632291i \(0.782115\pi\)
\(270\) 169106. + 104563.i 0.141172 + 0.0872905i
\(271\) −660806. −0.546576 −0.273288 0.961932i \(-0.588111\pi\)
−0.273288 + 0.961932i \(0.588111\pi\)
\(272\) −884725. + 1.06996e6i −0.725080 + 0.876894i
\(273\) 118841.i 0.0965073i
\(274\) −624839. + 439200.i −0.502796 + 0.353415i
\(275\) −90007.5 85910.8i −0.0717707 0.0685040i
\(276\) 62955.1 + 22656.8i 0.0497460 + 0.0179030i
\(277\) 1.57567e6 1.23386 0.616931 0.787017i \(-0.288376\pi\)
0.616931 + 0.787017i \(0.288376\pi\)
\(278\) 603161. 423962.i 0.468082 0.329015i
\(279\) −2.31940e6 −1.78388
\(280\) −1.07287e6 1.34989e6i −0.817812 1.02897i
\(281\) −1.45729e6 −1.10098 −0.550491 0.834841i \(-0.685560\pi\)
−0.550491 + 0.834841i \(0.685560\pi\)
\(282\) 47428.9 33337.8i 0.0355157 0.0249640i
\(283\) 1.38341e6 1.02680 0.513400 0.858149i \(-0.328386\pi\)
0.513400 + 0.858149i \(0.328386\pi\)
\(284\) 95560.8 265529.i 0.0703046 0.195351i
\(285\) −29669.7 69334.8i −0.0216372 0.0505637i
\(286\) 98996.0 69584.3i 0.0715653 0.0503033i
\(287\) 2.06270e6i 1.47819i
\(288\) 109262. 1.39357e6i 0.0776222 0.990026i
\(289\) −418409. −0.294684
\(290\) 982972. 1.58973e6i 0.686351 1.11001i
\(291\) 86654.2i 0.0599870i
\(292\) −432986. 155827.i −0.297178 0.106951i
\(293\) 544523. 0.370551 0.185275 0.982687i \(-0.440682\pi\)
0.185275 + 0.982687i \(0.440682\pi\)
\(294\) 51642.0 + 73469.9i 0.0348445 + 0.0495725i
\(295\) −710845. 1.66117e6i −0.475576 1.11137i
\(296\) −924630. + 253126.i −0.613393 + 0.167922i
\(297\) 25033.9i 0.0164678i
\(298\) 262539. 184538.i 0.171259 0.120378i
\(299\) 865278.i 0.559729i
\(300\) 58007.4 + 116138.i 0.0372118 + 0.0745023i
\(301\) 3.29520e6i 2.09636i
\(302\) −887516. 1.26265e6i −0.559963 0.796646i
\(303\) 86319.7i 0.0540136i
\(304\) −678121. + 820103.i −0.420846 + 0.508961i
\(305\) 1.07341e6 + 2.50844e6i 0.660719 + 1.54403i
\(306\) 1.51418e6 1.06432e6i 0.924430 0.649782i
\(307\) −2.70567e6 −1.63843 −0.819216 0.573485i \(-0.805591\pi\)
−0.819216 + 0.573485i \(0.805591\pi\)
\(308\) 73519.4 204284.i 0.0441596 0.122704i
\(309\) 215901.i 0.128635i
\(310\) −2.58516e6 1.59847e6i −1.52786 0.944714i
\(311\) −309689. −0.181562 −0.0907810 0.995871i \(-0.528936\pi\)
−0.0907810 + 0.995871i \(0.528936\pi\)
\(312\) −121768. + 33335.1i −0.0708183 + 0.0193872i
\(313\) 1.89714e6i 1.09456i 0.836950 + 0.547279i \(0.184336\pi\)
−0.836950 + 0.547279i \(0.815664\pi\)
\(314\) −1.14332e6 1.62657e6i −0.654399 0.930999i
\(315\) 904324. + 2.11330e6i 0.513508 + 1.20001i
\(316\) −539786. + 1.49987e6i −0.304091 + 0.844960i
\(317\) 546064. 0.305207 0.152604 0.988287i \(-0.451234\pi\)
0.152604 + 0.988287i \(0.451234\pi\)
\(318\) −79950.0 113743.i −0.0443354 0.0630750i
\(319\) 235338. 0.129484
\(320\) 1.08219e6 1.47794e6i 0.590784 0.806830i
\(321\) −157920. −0.0855409
\(322\) 892775. + 1.27013e6i 0.479846 + 0.682667i
\(323\) −1.40899e6 −0.751452
\(324\) −626576. + 1.74103e6i −0.331597 + 0.921389i
\(325\) −1.15917e6 + 1.21445e6i −0.608751 + 0.637779i
\(326\) 1.41270e6 + 2.00981e6i 0.736217 + 1.04740i
\(327\) 221694.i 0.114653i
\(328\) −2.11350e6 + 578590.i −1.08472 + 0.296952i
\(329\) 1.34519e6 0.685163
\(330\) −8596.32 + 13902.6i −0.00434538 + 0.00702765i
\(331\) 1.57476e6i 0.790029i 0.918675 + 0.395015i \(0.129260\pi\)
−0.918675 + 0.395015i \(0.870740\pi\)
\(332\) −151043. + 419693.i −0.0752063 + 0.208971i
\(333\) 1.27797e6 0.631552
\(334\) 2.68592e6 1.88793e6i 1.31743 0.926020i
\(335\) −45342.0 + 19402.7i −0.0220744 + 0.00944606i
\(336\) −144347. + 174569.i −0.0697524 + 0.0843568i
\(337\) 77460.4i 0.0371540i 0.999827 + 0.0185770i \(0.00591358\pi\)
−0.999827 + 0.0185770i \(0.994086\pi\)
\(338\) 268932. + 382603.i 0.128041 + 0.182162i
\(339\) 4809.92i 0.00227321i
\(340\) 2.42117e6 142733.i 1.13587 0.0669617i
\(341\) 382698.i 0.178226i
\(342\) 1.16058e6 815775.i 0.536552 0.377142i
\(343\) 780123.i 0.358037i
\(344\) 3.37635e6 924308.i 1.53833 0.421134i
\(345\) −45983.4 107458.i −0.0207995 0.0486062i
\(346\) 792963. + 1.12813e6i 0.356092 + 0.506605i
\(347\) 2.74014e6 1.22165 0.610827 0.791764i \(-0.290837\pi\)
0.610827 + 0.791764i \(0.290837\pi\)
\(348\) −231030. 83145.0i −0.102263 0.0368034i
\(349\) 2.65302e6i 1.16594i −0.812493 0.582972i \(-0.801890\pi\)
0.812493 0.582972i \(-0.198110\pi\)
\(350\) −448493. + 2.97868e6i −0.195698 + 1.29973i
\(351\) 337775. 0.146339
\(352\) 229937. + 18028.0i 0.0989126 + 0.00775516i
\(353\) 2.88565e6i 1.23256i −0.787528 0.616279i \(-0.788640\pi\)
0.787528 0.616279i \(-0.211360\pi\)
\(354\) −194190. + 136496.i −0.0823606 + 0.0578913i
\(355\) −453232. + 193947.i −0.190875 + 0.0816792i
\(356\) −82153.4 + 228275.i −0.0343559 + 0.0954625i
\(357\) −299921. −0.124548
\(358\) −2.72975e6 + 1.91874e6i −1.12568 + 0.791241i
\(359\) 1.66246e6 0.680794 0.340397 0.940282i \(-0.389439\pi\)
0.340397 + 0.940282i \(0.389439\pi\)
\(360\) −1.91168e6 + 1.51938e6i −0.777427 + 0.617888i
\(361\) 1.39614e6 0.563847
\(362\) 1.41797e6 996692.i 0.568716 0.399751i
\(363\) 207016. 0.0824588
\(364\) −2.75635e6 991977.i −1.09039 0.392417i
\(365\) 316260. + 739064.i 0.124254 + 0.290369i
\(366\) 293237. 206116.i 0.114424 0.0804285i
\(367\) 183532.i 0.0711291i −0.999367 0.0355645i \(-0.988677\pi\)
0.999367 0.0355645i \(-0.0113229\pi\)
\(368\) −1.05098e6 + 1.27103e6i −0.404554 + 0.489257i
\(369\) 2.92115e6 1.11683
\(370\) 1.42440e6 + 880741.i 0.540912 + 0.334460i
\(371\) 3.22601e6i 1.21683i
\(372\) −135207. + 375692.i −0.0506573 + 0.140758i
\(373\) −2.57701e6 −0.959056 −0.479528 0.877527i \(-0.659192\pi\)
−0.479528 + 0.877527i \(0.659192\pi\)
\(374\) 175611. + 249838.i 0.0649191 + 0.0923589i
\(375\) 79417.3 212423.i 0.0291633 0.0780052i
\(376\) 377328. + 1.37832e6i 0.137641 + 0.502782i
\(377\) 3.17536e6i 1.15064i
\(378\) 495816. 348509.i 0.178481 0.125454i
\(379\) 1.87753e6i 0.671412i 0.941967 + 0.335706i \(0.108975\pi\)
−0.941967 + 0.335706i \(0.891025\pi\)
\(380\) 1.85577e6 109401.i 0.659274 0.0388655i
\(381\) 100706.i 0.0355421i
\(382\) 400390. + 569625.i 0.140386 + 0.199724i
\(383\) 1.41226e6i 0.491945i −0.969277 0.245973i \(-0.920893\pi\)
0.969277 0.245973i \(-0.0791073\pi\)
\(384\) −219358. 98934.5i −0.0759145 0.0342389i
\(385\) −348692. + 149212.i −0.119892 + 0.0513041i
\(386\) −3.19069e6 + 2.24273e6i −1.08997 + 0.766143i
\(387\) −4.66658e6 −1.58388
\(388\) 2.00982e6 + 723310.i 0.677762 + 0.243919i
\(389\) 2.90646e6i 0.973846i 0.873445 + 0.486923i \(0.161881\pi\)
−0.873445 + 0.486923i \(0.838119\pi\)
\(390\) 187584. + 115988.i 0.0624501 + 0.0386145i
\(391\) −2.18372e6 −0.722361
\(392\) −2.13509e6 + 584500.i −0.701779 + 0.192119i
\(393\) 428430.i 0.139926i
\(394\) −230256. 327581.i −0.0747259 0.106311i
\(395\) 2.56013e6 1.09553e6i 0.825600 0.353290i
\(396\) −289302. 104116.i −0.0927071 0.0333642i
\(397\) 2.30169e6 0.732943 0.366472 0.930429i \(-0.380566\pi\)
0.366472 + 0.930429i \(0.380566\pi\)
\(398\) −1.02334e6 1.45588e6i −0.323826 0.460700i
\(399\) −229883. −0.0722893
\(400\) −3.17783e6 + 375986.i −0.993073 + 0.117496i
\(401\) −2.58744e6 −0.803544 −0.401772 0.915740i \(-0.631606\pi\)
−0.401772 + 0.915740i \(0.631606\pi\)
\(402\) 3725.71 + 5300.48i 0.00114986 + 0.00163587i
\(403\) −5.16364e6 −1.58378
\(404\) −2.00206e6 720518.i −0.610272 0.219630i
\(405\) 2.97176e6 1.27167e6i 0.900278 0.385246i
\(406\) −3.27626e6 4.66107e6i −0.986424 1.40336i
\(407\) 210863.i 0.0630978i
\(408\) −84128.3 307307.i −0.0250202 0.0913949i
\(409\) −3.17301e6 −0.937916 −0.468958 0.883221i \(-0.655370\pi\)
−0.468958 + 0.883221i \(0.655370\pi\)
\(410\) 3.25585e6 + 2.01318e6i 0.956543 + 0.591456i
\(411\) 175273.i 0.0511812i
\(412\) 5.00751e6 + 1.80215e6i 1.45338 + 0.523054i
\(413\) −5.50768e6 −1.58889
\(414\) 1.79873e6 1.26433e6i 0.515780 0.362542i
\(415\) 716374. 306550.i 0.204183 0.0873738i
\(416\) 243247. 3.10247e6i 0.0689151 0.878971i
\(417\) 169192.i 0.0476475i
\(418\) 134602. + 191495.i 0.0376799 + 0.0536064i
\(419\) 6.16028e6i 1.71422i −0.515137 0.857108i \(-0.672259\pi\)
0.515137 0.857108i \(-0.327741\pi\)
\(420\) 395025. 23287.5i 0.109270 0.00644169i
\(421\) 2.93941e6i 0.808268i 0.914700 + 0.404134i \(0.132427\pi\)
−0.914700 + 0.404134i \(0.867573\pi\)
\(422\) −5.06098e6 + 3.55737e6i −1.38342 + 0.972406i
\(423\) 1.90503e6i 0.517666i
\(424\) 3.30545e6 904900.i 0.892927 0.244448i
\(425\) −3.06492e6 2.92542e6i −0.823089 0.785626i
\(426\) 37241.6 + 52982.8i 0.00994270 + 0.0141453i
\(427\) 8.31687e6 2.20745
\(428\) 1.31817e6 3.66271e6i 0.347826 0.966482i
\(429\) 27769.2i 0.00728485i
\(430\) −5.20127e6 3.21608e6i −1.35656 0.838796i
\(431\) 2.60556e6 0.675629 0.337815 0.941213i \(-0.390312\pi\)
0.337815 + 0.941213i \(0.390312\pi\)
\(432\) 496168. + 410268.i 0.127914 + 0.105769i
\(433\) 525118.i 0.134597i 0.997733 + 0.0672987i \(0.0214381\pi\)
−0.997733 + 0.0672987i \(0.978562\pi\)
\(434\) −7.57964e6 + 5.32773e6i −1.93163 + 1.35774i
\(435\) 168748. + 394345.i 0.0427578 + 0.0999202i
\(436\) 5.14188e6 + 1.85050e6i 1.29540 + 0.466201i
\(437\) −1.67377e6 −0.419268
\(438\) 86396.6 60728.2i 0.0215185 0.0151253i
\(439\) 3.48971e6 0.864228 0.432114 0.901819i \(-0.357768\pi\)
0.432114 + 0.901819i \(0.357768\pi\)
\(440\) −250695. 315425.i −0.0617326 0.0776719i
\(441\) 2.95099e6 0.722555
\(442\) 3.37099e6 2.36947e6i 0.820733 0.576894i
\(443\) 5.36353e6 1.29850 0.649250 0.760575i \(-0.275083\pi\)
0.649250 + 0.760575i \(0.275083\pi\)
\(444\) 74497.8 207002.i 0.0179344 0.0498331i
\(445\) 389642. 166735.i 0.0932752 0.0399143i
\(446\) −4.24813e6 + 2.98601e6i −1.01126 + 0.710811i
\(447\) 73644.4i 0.0174330i
\(448\) −2.84400e6 4.80506e6i −0.669476 1.13111i
\(449\) −5.64299e6 −1.32097 −0.660486 0.750838i \(-0.729650\pi\)
−0.660486 + 0.750838i \(0.729650\pi\)
\(450\) 4.21833e6 + 635145.i 0.981996 + 0.147857i
\(451\) 481985.i 0.111581i
\(452\) 111559. + 40148.8i 0.0256838 + 0.00924329i
\(453\) 354184. 0.0810931
\(454\) 3.92931e6 + 5.59014e6i 0.894698 + 1.27287i
\(455\) 2.01328e6 + 4.70481e6i 0.455906 + 1.06540i
\(456\) −64482.4 235544.i −0.0145221 0.0530468i
\(457\) 6.54027e6i 1.46489i 0.680825 + 0.732446i \(0.261621\pi\)
−0.680825 + 0.732446i \(0.738379\pi\)
\(458\) −1.49783e6 + 1.05282e6i −0.333656 + 0.234527i
\(459\) 852448.i 0.188858i
\(460\) 2.87616e6 169555.i 0.633751 0.0373609i
\(461\) 7.92791e6i 1.73743i 0.495315 + 0.868713i \(0.335053\pi\)
−0.495315 + 0.868713i \(0.664947\pi\)
\(462\) 28651.7 + 40762.1i 0.00624519 + 0.00888488i
\(463\) 5.43590e6i 1.17847i 0.807961 + 0.589235i \(0.200571\pi\)
−0.807961 + 0.589235i \(0.799429\pi\)
\(464\) 3.85685e6 4.66438e6i 0.831645 1.00577i
\(465\) 641269. 274411.i 0.137533 0.0588531i
\(466\) 6.23475e6 4.38240e6i 1.33001 0.934862i
\(467\) −1.47407e6 −0.312771 −0.156386 0.987696i \(-0.549984\pi\)
−0.156386 + 0.987696i \(0.549984\pi\)
\(468\) −1.40481e6 + 3.90347e6i −0.296486 + 0.823827i
\(469\) 150334.i 0.0315590i
\(470\) 1.31289e6 2.12330e6i 0.274148 0.443371i
\(471\) 456268. 0.0947692
\(472\) −1.54491e6 5.64330e6i −0.319189 1.16595i
\(473\) 769979.i 0.158244i
\(474\) −210364. 299279.i −0.0430056 0.0611830i
\(475\) −2.34919e6 2.24227e6i −0.477732 0.455988i
\(476\) 2.50347e6 6.95623e6i 0.506436 1.40720i
\(477\) −4.56859e6 −0.919362
\(478\) −3.24484e6 4.61636e6i −0.649567 0.924124i
\(479\) −4.13083e6 −0.822618 −0.411309 0.911496i \(-0.634928\pi\)
−0.411309 + 0.911496i \(0.634928\pi\)
\(480\) 134666. + 398221.i 0.0266781 + 0.0788898i
\(481\) 2.84512e6 0.560709
\(482\) −1.98464e6 2.82350e6i −0.389102 0.553566i
\(483\) −356283. −0.0694908
\(484\) −1.72798e6 + 4.80143e6i −0.335293 + 0.931659i
\(485\) −1.46800e6 3.43056e6i −0.283382 0.662232i
\(486\) −741184. 1.05446e6i −0.142343 0.202508i
\(487\) 2.24605e6i 0.429138i 0.976709 + 0.214569i \(0.0688347\pi\)
−0.976709 + 0.214569i \(0.931165\pi\)
\(488\) 2.33289e6 + 8.52167e6i 0.443450 + 1.61985i
\(489\) −563771. −0.106618
\(490\) 3.28911e6 + 2.03374e6i 0.618853 + 0.382653i
\(491\) 578316.i 0.108258i 0.998534 + 0.0541292i \(0.0172383\pi\)
−0.998534 + 0.0541292i \(0.982762\pi\)
\(492\) 170285. 473161.i 0.0317150 0.0881244i
\(493\) 8.01370e6 1.48496
\(494\) 2.58379e6 1.81615e6i 0.476365 0.334837i
\(495\) 211311. + 493809.i 0.0387622 + 0.0905829i
\(496\) −7.58503e6 6.27186e6i −1.38437 1.14470i
\(497\) 1.50271e6i 0.272888i
\(498\) −58863.7 83744.1i −0.0106359 0.0151315i
\(499\) 307235.i 0.0552357i 0.999619 + 0.0276178i \(0.00879215\pi\)
−0.999619 + 0.0276178i \(0.991208\pi\)
\(500\) 4.26394e6 + 3.61508e6i 0.762757 + 0.646686i
\(501\) 753424.i 0.134105i
\(502\) −3.19835e6 + 2.24812e6i −0.566457 + 0.398162i
\(503\) 3.87678e6i 0.683206i 0.939844 + 0.341603i \(0.110970\pi\)
−0.939844 + 0.341603i \(0.889030\pi\)
\(504\) 1.96541e6 + 7.17931e6i 0.344648 + 1.25894i
\(505\) 1.46234e6 + 3.41732e6i 0.255164 + 0.596289i
\(506\) 208612. + 296787.i 0.0362212 + 0.0515311i
\(507\) −107324. −0.0185428
\(508\) −2.33573e6 840603.i −0.401572 0.144521i
\(509\) 4.90268e6i 0.838762i 0.907810 + 0.419381i \(0.137753\pi\)
−0.907810 + 0.419381i \(0.862247\pi\)
\(510\) −292720. + 473407.i −0.0498342 + 0.0805953i
\(511\) 2.45040e6 0.415131
\(512\) 4.12564e6 4.26186e6i 0.695531 0.718497i
\(513\) 653382.i 0.109616i
\(514\) −3.49781e6 + 2.45861e6i −0.583967 + 0.410471i
\(515\) −3.65757e6 8.54733e6i −0.607679 1.42008i
\(516\) −272033. + 755882.i −0.0449778 + 0.124977i
\(517\) 314327. 0.0517195
\(518\) 4.17631e6 2.93553e6i 0.683862 0.480686i
\(519\) −316451. −0.0515689
\(520\) −4.25594e6 + 3.38256e6i −0.690220 + 0.548577i
\(521\) −5.57462e6 −0.899749 −0.449874 0.893092i \(-0.648531\pi\)
−0.449874 + 0.893092i \(0.648531\pi\)
\(522\) −6.60089e6 + 4.63976e6i −1.06029 + 0.745280i
\(523\) 1.23492e6 0.197417 0.0987087 0.995116i \(-0.468529\pi\)
0.0987087 + 0.995116i \(0.468529\pi\)
\(524\) −9.93681e6 3.57614e6i −1.58095 0.568967i
\(525\) −500055. 477295.i −0.0791808 0.0755769i
\(526\) 1.46579e6 1.03030e6i 0.230997 0.162368i
\(527\) 1.30316e7i 2.04395i
\(528\) −33729.1 + 40791.1i −0.00526526 + 0.00636767i
\(529\) 3.84226e6 0.596963
\(530\) −5.09206e6 3.14855e6i −0.787415 0.486879i
\(531\) 7.79983e6i 1.20046i
\(532\) 1.91885e6 5.33179e6i 0.293942 0.816759i
\(533\) 6.50329e6 0.991552
\(534\) −32016.5 45549.2i −0.00485871 0.00691238i
\(535\) −6.25189e6 + 2.67531e6i −0.944337 + 0.404100i
\(536\) −154036. + 42168.7i −0.0231584 + 0.00633985i
\(537\) 765718.i 0.114586i
\(538\) 6.94572e6 4.88215e6i 1.03457 0.727203i
\(539\) 486908.i 0.0721897i
\(540\) −66188.7 1.12276e6i −0.00976786 0.165692i
\(541\) 2.07857e6i 0.305332i −0.988278 0.152666i \(-0.951214\pi\)
0.988278 0.152666i \(-0.0487858\pi\)
\(542\) 2.14960e6 + 3.05818e6i 0.314310 + 0.447162i
\(543\) 397753.i 0.0578914i
\(544\) 7.82976e6 + 613886.i 1.13436 + 0.0889386i
\(545\) −3.75571e6 8.77668e6i −0.541627 1.26572i
\(546\) 549992. 386590.i 0.0789542 0.0554969i
\(547\) 6.52487e6 0.932403 0.466201 0.884679i \(-0.345622\pi\)
0.466201 + 0.884679i \(0.345622\pi\)
\(548\) 4.06520e6 + 1.46302e6i 0.578269 + 0.208113i
\(549\) 1.17781e7i 1.66781i
\(550\) −104798. + 696019.i −0.0147722 + 0.0981102i
\(551\) 6.14232e6 0.861893
\(552\) −99937.8 365056.i −0.0139599 0.0509932i
\(553\) 8.48824e6i 1.18033i
\(554\) −5.12566e6 7.29216e6i −0.709537 1.00944i
\(555\) −353333. + 151198.i −0.0486913 + 0.0208359i
\(556\) −3.92416e6 1.41226e6i −0.538344 0.193744i
\(557\) −1.09214e7 −1.49156 −0.745778 0.666194i \(-0.767922\pi\)
−0.745778 + 0.666194i \(0.767922\pi\)
\(558\) 7.54500e6 + 1.07341e7i 1.02583 + 1.45942i
\(559\) −1.03891e7 −1.40621
\(560\) −2.75719e6 + 9.35641e6i −0.371532 + 1.26078i
\(561\) −70081.7 −0.00940150
\(562\) 4.74056e6 + 6.74428e6i 0.633124 + 0.900731i
\(563\) −3.64784e6 −0.485025 −0.242513 0.970148i \(-0.577972\pi\)
−0.242513 + 0.970148i \(0.577972\pi\)
\(564\) −308572. 111052.i −0.0408469 0.0147003i
\(565\) −81484.5 190420.i −0.0107388 0.0250953i
\(566\) −4.50024e6 6.40239e6i −0.590466 0.840042i
\(567\) 9.85302e6i 1.28710i
\(568\) −1.53972e6 + 421512.i −0.200249 + 0.0548200i
\(569\) 7.78255e6 1.00772 0.503861 0.863784i \(-0.331912\pi\)
0.503861 + 0.863784i \(0.331912\pi\)
\(570\) −224363. + 362856.i −0.0289244 + 0.0467786i
\(571\) 1.52835e7i 1.96170i 0.194753 + 0.980852i \(0.437609\pi\)
−0.194753 + 0.980852i \(0.562391\pi\)
\(572\) −644067. 231792.i −0.0823078 0.0296216i
\(573\) −159785. −0.0203306
\(574\) 9.54610e6 6.70995e6i 1.20933 0.850041i
\(575\) −3.64088e6 3.47517e6i −0.459237 0.438335i
\(576\) −6.80480e6 + 4.02761e6i −0.854593 + 0.505814i
\(577\) 1.01412e7i 1.26809i 0.773296 + 0.634046i \(0.218607\pi\)
−0.773296 + 0.634046i \(0.781393\pi\)
\(578\) 1.36108e6 + 1.93638e6i 0.169459 + 0.241085i
\(579\) 895016.i 0.110952i
\(580\) −1.05548e7 + 622227.i −1.30281 + 0.0768031i
\(581\) 2.37517e6i 0.291914i
\(582\) −401032. + 281886.i −0.0490763 + 0.0344957i
\(583\) 753811.i 0.0918526i
\(584\) 687341. + 2.51075e6i 0.0833950 + 0.304629i
\(585\) 6.66284e6 2.85116e6i 0.804951 0.344454i
\(586\) −1.77133e6 2.52003e6i −0.213086 0.303153i
\(587\) −3.15239e6 −0.377612 −0.188806 0.982014i \(-0.560462\pi\)
−0.188806 + 0.982014i \(0.560462\pi\)
\(588\) 172025. 477994.i 0.0205186 0.0570137i
\(589\) 9.98839e6i 1.18634i
\(590\) −5.37544e6 + 8.69353e6i −0.635746 + 1.02817i
\(591\) 91889.3 0.0108217
\(592\) 4.17928e6 + 3.45573e6i 0.490114 + 0.405262i
\(593\) 2.82025e6i 0.329345i 0.986348 + 0.164673i \(0.0526568\pi\)
−0.986348 + 0.164673i \(0.947343\pi\)
\(594\) 115856. 81435.0i 0.0134726 0.00946989i
\(595\) −1.18736e7 + 5.08094e6i −1.37496 + 0.588372i
\(596\) −1.70807e6 614716.i −0.196966 0.0708858i
\(597\) 408387. 0.0468961
\(598\) 4.00447e6 2.81475e6i 0.457923 0.321874i
\(599\) 1.25796e7 1.43252 0.716261 0.697833i \(-0.245852\pi\)
0.716261 + 0.697833i \(0.245852\pi\)
\(600\) 348783. 646251.i 0.0395528 0.0732864i
\(601\) 3.63021e6 0.409964 0.204982 0.978766i \(-0.434286\pi\)
0.204982 + 0.978766i \(0.434286\pi\)
\(602\) −1.52501e7 + 1.07193e7i −1.71506 + 1.20552i
\(603\) 212899. 0.0238440
\(604\) −2.95641e6 + 8.21478e6i −0.329740 + 0.916228i
\(605\) 8.19556e6 3.50704e6i 0.910312 0.389540i
\(606\) 399484. 280797.i 0.0441894 0.0310607i
\(607\) 322555.i 0.0355331i −0.999842 0.0177665i \(-0.994344\pi\)
0.999842 0.0177665i \(-0.00565556\pi\)
\(608\) 6.00133e6 + 470530.i 0.658398 + 0.0516212i
\(609\) 1.30747e6 0.142853
\(610\) 8.11718e6 1.31277e7i 0.883244 1.42844i
\(611\) 4.24112e6i 0.459598i
\(612\) −9.85124e6 3.54535e6i −1.06319 0.382631i
\(613\) −1.51954e6 −0.163329 −0.0816643 0.996660i \(-0.526024\pi\)
−0.0816643 + 0.996660i \(0.526024\pi\)
\(614\) 8.80152e6 + 1.25217e7i 0.942187 + 1.34043i
\(615\) −807639. + 345604.i −0.0861052 + 0.0368461i
\(616\) −1.18458e6 + 324289.i −0.125780 + 0.0344334i
\(617\) 8.51821e6i 0.900815i 0.892823 + 0.450408i \(0.148721\pi\)
−0.892823 + 0.450408i \(0.851279\pi\)
\(618\) −999182. + 702325.i −0.105238 + 0.0739720i
\(619\) 6.08130e6i 0.637926i −0.947767 0.318963i \(-0.896665\pi\)
0.947767 0.318963i \(-0.103335\pi\)
\(620\) 1.01184e6 + 1.71638e7i 0.105714 + 1.79322i
\(621\) 1.01264e6i 0.105372i
\(622\) 1.00742e6 + 1.43323e6i 0.104408 + 0.148539i
\(623\) 1.29188e6i 0.133353i
\(624\) 550383. + 455097.i 0.0565853 + 0.0467889i
\(625\) −454587. 9.75504e6i −0.0465497 0.998916i
\(626\) 8.77989e6 6.17139e6i 0.895475 0.629429i
\(627\) −53716.0 −0.00545676
\(628\) −3.80850e6 + 1.05825e7i −0.385350 + 1.07075i
\(629\) 7.18026e6i 0.723625i
\(630\) 6.83853e6 1.10597e7i 0.686454 1.11018i
\(631\) −1.52443e7 −1.52417 −0.762086 0.647476i \(-0.775825\pi\)
−0.762086 + 0.647476i \(0.775825\pi\)
\(632\) 8.69727e6 2.38096e6i 0.866144 0.237115i
\(633\) 1.41965e6i 0.140823i
\(634\) −1.77634e6 2.52716e6i −0.175511 0.249695i
\(635\) 1.70606e6 + 3.98686e6i 0.167903 + 0.392371i
\(636\) −266321. + 740011.i −0.0261074 + 0.0725430i
\(637\) 6.56972e6 0.641503
\(638\) −765554. 1.08914e6i −0.0744602 0.105933i
\(639\) 2.12810e6 0.206177
\(640\) −1.03602e7 200602.i −0.999813 0.0193591i
\(641\) 1.58871e7 1.52722 0.763609 0.645679i \(-0.223426\pi\)
0.763609 + 0.645679i \(0.223426\pi\)
\(642\) 513712. + 730846.i 0.0491906 + 0.0699823i
\(643\) −3.42866e6 −0.327037 −0.163519 0.986540i \(-0.552284\pi\)
−0.163519 + 0.986540i \(0.552284\pi\)
\(644\) 2.97392e6 8.26346e6i 0.282563 0.785140i
\(645\) 1.29022e6 552109.i 0.122113 0.0522547i
\(646\) 4.58343e6 + 6.52075e6i 0.432125 + 0.614775i
\(647\) 3.99640e6i 0.375326i −0.982234 0.187663i \(-0.939909\pi\)
0.982234 0.187663i \(-0.0600912\pi\)
\(648\) 1.00957e7 2.76378e6i 0.944489 0.258563i
\(649\) −1.28696e6 −0.119937
\(650\) 9.39120e6 + 1.41401e6i 0.871842 + 0.131271i
\(651\) 2.12616e6i 0.196627i
\(652\) 4.70584e6 1.30758e7i 0.433529 1.20462i
\(653\) 6.78426e6 0.622615 0.311308 0.950309i \(-0.399233\pi\)
0.311308 + 0.950309i \(0.399233\pi\)
\(654\) −1.02599e6 + 721171.i −0.0937994 + 0.0659316i
\(655\) 7.25801e6 + 1.69612e7i 0.661019 + 1.54473i
\(656\) 9.55288e6 + 7.89903e6i 0.866712 + 0.716661i
\(657\) 3.47020e6i 0.313647i
\(658\) −4.37590e6 6.22549e6i −0.394006 0.560543i
\(659\) 1.38518e7i 1.24249i 0.783617 + 0.621244i \(0.213372\pi\)
−0.783617 + 0.621244i \(0.786628\pi\)
\(660\) 92304.3 5441.52i 0.00824825 0.000486251i
\(661\) 7.99240e6i 0.711498i 0.934582 + 0.355749i \(0.115774\pi\)
−0.934582 + 0.355749i \(0.884226\pi\)
\(662\) 7.28791e6 5.12267e6i 0.646335 0.454309i
\(663\) 945593.i 0.0835450i
\(664\) 2.43366e6 666239.i 0.214210 0.0586421i
\(665\) −9.10084e6 + 3.89443e6i −0.798045 + 0.341499i
\(666\) −4.15722e6 5.91439e6i −0.363176 0.516683i
\(667\) 9.51964e6 0.828526
\(668\) −1.74746e7 6.28889e6i −1.51518 0.545297i
\(669\) 1.19164e6i 0.102939i
\(670\) 237292. + 146724.i 0.0204219 + 0.0126274i
\(671\) 1.94338e6 0.166629
\(672\) 1.27746e6 + 100158.i 0.109125 + 0.00855586i
\(673\) 1.10858e7i 0.943471i 0.881740 + 0.471735i \(0.156372\pi\)
−0.881740 + 0.471735i \(0.843628\pi\)
\(674\) 358484. 251978.i 0.0303962 0.0213655i
\(675\) −1.35659e6 + 1.42128e6i −0.114601 + 0.120066i
\(676\) 895839. 2.48921e6i 0.0753986 0.209505i
\(677\) −1.70523e7 −1.42992 −0.714958 0.699167i \(-0.753554\pi\)
−0.714958 + 0.699167i \(0.753554\pi\)
\(678\) −22260.1 + 15646.6i −0.00185975 + 0.00130722i
\(679\) −1.13742e7 −0.946772
\(680\) −8.53662e6 1.07408e7i −0.707968 0.890766i
\(681\) −1.56808e6 −0.129569
\(682\) −1.77111e6 + 1.24491e6i −0.145809 + 0.102489i
\(683\) 4.24549e6 0.348238 0.174119 0.984725i \(-0.444292\pi\)
0.174119 + 0.984725i \(0.444292\pi\)
\(684\) −7.55075e6 2.71743e6i −0.617092 0.222084i
\(685\) −2.96929e6 6.93889e6i −0.241783 0.565020i
\(686\) −3.61038e6 + 2.53774e6i −0.292916 + 0.205890i
\(687\) 420154.i 0.0339639i
\(688\) −1.52609e7 1.26188e7i −1.22916 1.01636i
\(689\) −1.01710e7 −0.816234
\(690\) −347729. + 562371.i −0.0278047 + 0.0449676i
\(691\) 8.87637e6i 0.707196i −0.935397 0.353598i \(-0.884958\pi\)
0.935397 0.353598i \(-0.115042\pi\)
\(692\) 2.64144e6 7.33961e6i 0.209689 0.582650i
\(693\) 1.63725e6 0.129503
\(694\) −8.91365e6 1.26812e7i −0.702517 0.999455i
\(695\) 2.86627e6 + 6.69816e6i 0.225090 + 0.526009i
\(696\) 366747. + 1.33967e6i 0.0286975 + 0.104827i
\(697\) 1.64125e7i 1.27965i
\(698\) −1.22781e7 + 8.63027e6i −0.953876 + 0.670480i
\(699\) 1.74890e6i 0.135386i
\(700\) 1.52442e7 7.61402e6i 1.17587 0.587312i
\(701\) 1.25460e7i 0.964298i −0.876089 0.482149i \(-0.839856\pi\)
0.876089 0.482149i \(-0.160144\pi\)
\(702\) −1.09878e6 1.56321e6i −0.0841528 0.119722i
\(703\) 5.50351e6i 0.420002i
\(704\) −664550. 1.12278e6i −0.0505354 0.0853816i
\(705\) 225386. + 526702.i 0.0170787 + 0.0399110i
\(706\) −1.33547e7 + 9.38701e6i −1.00837 + 0.708786i
\(707\) 1.13303e7 0.852495
\(708\) 1.26340e6 + 454683.i 0.0947235 + 0.0340899i
\(709\) 6.92792e6i 0.517592i 0.965932 + 0.258796i \(0.0833257\pi\)
−0.965932 + 0.258796i \(0.916674\pi\)
\(710\) 2.37194e6 + 1.46663e6i 0.176586 + 0.109188i
\(711\) −1.20208e7 −0.891786
\(712\) 1.32369e6 362373.i 0.0978558 0.0267890i
\(713\) 1.54805e7i 1.14041i
\(714\) 975642. + 1.38802e6i 0.0716218 + 0.101895i
\(715\) 470437. + 1.09936e6i 0.0344141 + 0.0804219i
\(716\) 1.77597e7 + 6.39152e6i 1.29465 + 0.465931i
\(717\) 1.29493e6 0.0940694
\(718\) −5.40798e6 7.69381e6i −0.391493 0.556968i
\(719\) 5.47581e6 0.395026 0.197513 0.980300i \(-0.436713\pi\)
0.197513 + 0.980300i \(0.436713\pi\)
\(720\) 1.32503e7 + 3.90466e6i 0.952566 + 0.280706i
\(721\) −2.83391e7 −2.03024
\(722\) −4.54164e6 6.46129e6i −0.324242 0.461292i
\(723\) 792016. 0.0563492
\(724\) −9.22530e6 3.32008e6i −0.654085 0.235398i
\(725\) 1.33611e7 + 1.27530e7i 0.944058 + 0.901089i
\(726\) −673421. 958061.i −0.0474182 0.0674608i
\(727\) 1.16133e7i 0.814926i −0.913222 0.407463i \(-0.866414\pi\)
0.913222 0.407463i \(-0.133586\pi\)
\(728\) 4.37555e6 + 1.59832e7i 0.305988 + 1.11772i
\(729\) −1.37553e7 −0.958628
\(730\) 2.39157e6 3.86781e6i 0.166102 0.268632i
\(731\) 2.62192e7i 1.81479i
\(732\) −1.90780e6 686594.i −0.131600 0.0473612i
\(733\) −1.43863e7 −0.988984 −0.494492 0.869182i \(-0.664646\pi\)
−0.494492 + 0.869182i \(0.664646\pi\)
\(734\) −849380. + 597029.i −0.0581918 + 0.0409030i
\(735\) −815889. + 349135.i −0.0557074 + 0.0238383i
\(736\) 9.30114e6 + 729248.i 0.632909 + 0.0496228i
\(737\) 35128.0i 0.00238223i
\(738\) −9.50247e6 1.35190e7i −0.642238 0.913697i
\(739\) 8.91435e6i 0.600452i −0.953868 0.300226i \(-0.902938\pi\)
0.953868 0.300226i \(-0.0970621\pi\)
\(740\) −557514. 9.45709e6i −0.0374263 0.634861i
\(741\) 724775.i 0.0484906i
\(742\) −1.49298e7 + 1.04942e7i −0.995510 + 0.699744i
\(743\) 9.84971e6i 0.654563i 0.944927 + 0.327281i \(0.106133\pi\)
−0.944927 + 0.327281i \(0.893867\pi\)
\(744\) 2.17851e6 596390.i 0.144287 0.0395001i
\(745\) 1.24760e6 + 2.91551e6i 0.0823543 + 0.192453i
\(746\) 8.38300e6 + 1.19263e7i 0.551509 + 0.784619i
\(747\) −3.36366e6 −0.220552
\(748\) 584978. 1.62544e6i 0.0382283 0.106223i
\(749\) 2.07284e7i 1.35009i
\(750\) −1.24143e6 + 323471.i −0.0805878 + 0.0209982i
\(751\) 2.31729e7 1.49928 0.749638 0.661849i \(-0.230228\pi\)
0.749638 + 0.661849i \(0.230228\pi\)
\(752\) 5.15135e6 6.22992e6i 0.332182 0.401733i
\(753\) 897165.i 0.0576614i
\(754\) −1.46954e7 + 1.03294e7i −0.941356 + 0.661679i
\(755\) 1.40218e7 6.00021e6i 0.895235 0.383089i
\(756\) −3.22577e6 1.16092e6i −0.205272 0.0738750i
\(757\) 1.04310e7 0.661586 0.330793 0.943703i \(-0.392684\pi\)
0.330793 + 0.943703i \(0.392684\pi\)
\(758\) 8.68914e6 6.10760e6i 0.549292 0.386098i
\(759\) −83251.5 −0.00524551
\(760\) −6.54313e6 8.23257e6i −0.410914 0.517013i
\(761\) 7.98132e6 0.499589 0.249795 0.968299i \(-0.419637\pi\)
0.249795 + 0.968299i \(0.419637\pi\)
\(762\) 466064. 327597.i 0.0290776 0.0204386i
\(763\) −2.90995e7 −1.80956
\(764\) 1.33374e6 3.70598e6i 0.0826680 0.229704i
\(765\) 7.19551e6 + 1.68151e7i 0.444537 + 1.03883i
\(766\) −6.53587e6 + 4.59406e6i −0.402468 + 0.282895i
\(767\) 1.73646e7i 1.06580i
\(768\) 255704. + 1.33701e6i 0.0156435 + 0.0817961i
\(769\) 1.28302e7 0.782378 0.391189 0.920310i \(-0.372064\pi\)
0.391189 + 0.920310i \(0.372064\pi\)
\(770\) 1.82484e6 + 1.12835e6i 0.110917 + 0.0685830i
\(771\) 981167.i 0.0594439i
\(772\) 2.07586e7 + 7.47078e6i 1.25359 + 0.451152i
\(773\) −1.70361e7 −1.02547 −0.512733 0.858548i \(-0.671367\pi\)
−0.512733 + 0.858548i \(0.671367\pi\)
\(774\) 1.51804e7 + 2.15968e7i 0.910814 + 1.29579i
\(775\) 2.07385e7 2.17274e7i 1.24029 1.29943i
\(776\) −3.19047e6 1.16543e7i −0.190196 0.694754i
\(777\) 1.17149e6i 0.0696124i
\(778\) 1.34510e7 9.45470e6i 0.796719 0.560014i
\(779\) 1.25798e7i 0.742727i
\(780\) −73420.9 1.24544e6i −0.00432099 0.0732968i
\(781\) 351134.i 0.0205989i
\(782\) 7.10361e6 + 1.01061e7i 0.415396 + 0.590975i
\(783\) 3.71615e6i 0.216615i
\(784\) 9.65047e6 + 7.97972e6i 0.560736 + 0.463658i
\(785\) 1.80632e7 7.72960e6i 1.04621 0.447695i
\(786\) 1.98276e6 1.39368e6i 0.114476 0.0804650i
\(787\) 2.17976e7 1.25450 0.627252 0.778817i \(-0.284180\pi\)
0.627252 + 0.778817i \(0.284180\pi\)
\(788\) −767007. + 2.13124e6i −0.0440032 + 0.122269i
\(789\) 411167.i 0.0235139i
\(790\) −1.33982e7 8.28444e6i −0.763797 0.472276i
\(791\) −631348. −0.0358779
\(792\) 459250. + 1.67757e6i 0.0260157 + 0.0950313i
\(793\) 2.62215e7i 1.48072i
\(794\) −7.48738e6 1.06521e7i −0.421482 0.599632i
\(795\) 1.26313e6 540516.i 0.0708808 0.0303313i
\(796\) −3.40884e6 + 9.47194e6i −0.190688 + 0.529854i
\(797\) −7.68922e6 −0.428782 −0.214391 0.976748i \(-0.568777\pi\)
−0.214391 + 0.976748i \(0.568777\pi\)
\(798\) 747807. + 1.06389e6i 0.0415702 + 0.0591410i
\(799\) 1.07034e7 0.593136
\(800\) 1.20775e7 + 1.34838e7i 0.667195 + 0.744883i
\(801\) −1.82953e6 −0.100753
\(802\) 8.41694e6 + 1.19746e7i 0.462081 + 0.657392i
\(803\) 572578. 0.0313362
\(804\) 12410.7 34484.9i 0.000677106 0.00188143i
\(805\) −1.41049e7 + 6.03576e6i −0.767150 + 0.328278i
\(806\) 1.67973e7 + 2.38971e7i 0.910756 + 1.29571i
\(807\) 1.94834e6i 0.105313i
\(808\) 3.17816e6 + 1.16093e7i 0.171256 + 0.625572i
\(809\) 4.70149e6 0.252560 0.126280 0.991995i \(-0.459696\pi\)
0.126280 + 0.991995i \(0.459696\pi\)
\(810\) −1.55524e7 9.61645e6i −0.832884 0.514994i
\(811\) 1.31175e7i 0.700322i −0.936689 0.350161i \(-0.886127\pi\)
0.936689 0.350161i \(-0.113873\pi\)
\(812\) −1.09136e7 + 3.03248e7i −0.580867 + 1.61402i
\(813\) −857847. −0.0455180
\(814\) 975865. 685936.i 0.0516213 0.0362846i
\(815\) −2.23192e7 + 9.55080e6i −1.17702 + 0.503670i
\(816\) −1.14854e6 + 1.38901e6i −0.0603836 + 0.0730264i
\(817\) 2.00964e7i 1.05333i
\(818\) 1.03218e7 + 1.46846e7i 0.539352 + 0.767324i
\(819\) 2.20910e7i 1.15081i
\(820\) −1.27435e6 2.16168e7i −0.0661843 1.12268i
\(821\) 2.69837e7i 1.39715i −0.715537 0.698575i \(-0.753818\pi\)
0.715537 0.698575i \(-0.246182\pi\)
\(822\) −811156. + 570162.i −0.0418721 + 0.0294319i
\(823\) 279830.i 0.0144011i −0.999974 0.00720053i \(-0.997708\pi\)
0.999974 0.00720053i \(-0.00229202\pi\)
\(824\) −7.94914e6 2.90369e7i −0.407852 1.48982i
\(825\) −116846. 111528.i −0.00597696 0.00570492i
\(826\) 1.79164e7 + 2.54893e7i 0.913696 + 1.29989i
\(827\) −2.31889e7 −1.17901 −0.589504 0.807765i \(-0.700677\pi\)
−0.589504 + 0.807765i \(0.700677\pi\)
\(828\) −1.17025e7 4.21160e6i −0.593202 0.213487i
\(829\) 5.30543e6i 0.268123i 0.990973 + 0.134062i \(0.0428020\pi\)
−0.990973 + 0.134062i \(0.957198\pi\)
\(830\) −3.74906e6 2.31814e6i −0.188898 0.116801i
\(831\) 2.04551e6 0.102754
\(832\) −1.51494e7 + 8.96659e6i −0.758730 + 0.449075i
\(833\) 1.65801e7i 0.827894i
\(834\) 783015. 550381.i 0.0389812 0.0273999i
\(835\) 1.27637e7 + 2.98273e7i 0.633520 + 1.48047i
\(836\) 448372. 1.24586e6i 0.0221882 0.0616531i
\(837\) −6.04305e6 −0.298155
\(838\) −2.85095e7 + 2.00394e7i −1.40243 + 0.985766i
\(839\) 1.39887e7 0.686077 0.343039 0.939321i \(-0.388544\pi\)
0.343039 + 0.939321i \(0.388544\pi\)
\(840\) −1.39279e6 1.75241e6i −0.0681062 0.0856913i
\(841\) −1.44236e7 −0.703207
\(842\) 1.36035e7 9.56190e6i 0.661257 0.464798i
\(843\) −1.89183e6 −0.0916882
\(844\) 3.29267e7 + 1.18499e7i 1.59108 + 0.572612i
\(845\) −4.24884e6 + 1.81816e6i −0.204705 + 0.0875973i
\(846\) −8.81639e6 + 6.19704e6i −0.423511 + 0.297686i
\(847\) 2.71728e7i 1.30144i
\(848\) −1.49405e7 1.23539e7i −0.713468 0.589947i
\(849\) 1.79593e6 0.0855105
\(850\) −3.56856e6 + 2.37007e7i −0.169413 + 1.12516i
\(851\) 8.52958e6i 0.403742i
\(852\) 124056. 344705.i 0.00585487 0.0162686i
\(853\) 1.48401e7 0.698335 0.349168 0.937060i \(-0.386464\pi\)
0.349168 + 0.937060i \(0.386464\pi\)
\(854\) −2.70547e7 3.84901e7i −1.26940 1.80595i
\(855\) 5.51519e6 + 1.28884e7i 0.258015 + 0.602953i
\(856\) −2.12389e7 + 5.81435e6i −0.990712 + 0.271217i
\(857\) 8.97091e6i 0.417239i −0.977997 0.208619i \(-0.933103\pi\)
0.977997 0.208619i \(-0.0668970\pi\)
\(858\) 128515. 90333.2i 0.00595985 0.00418918i
\(859\) 2.21880e7i 1.02597i −0.858398 0.512985i \(-0.828540\pi\)
0.858398 0.512985i \(-0.171460\pi\)
\(860\) 2.03580e6 + 3.45332e7i 0.0938617 + 1.59217i
\(861\) 2.67777e6i 0.123102i
\(862\) −8.47588e6 1.20584e7i −0.388523 0.552743i
\(863\) 2.60169e7i 1.18913i −0.804047 0.594565i \(-0.797324\pi\)
0.804047 0.594565i \(-0.202676\pi\)
\(864\) 284674. 3.63085e6i 0.0129737 0.165472i
\(865\) −1.25280e7 + 5.36097e6i −0.569300 + 0.243614i
\(866\) 2.43022e6 1.70820e6i 0.110116 0.0774008i
\(867\) −543172. −0.0245408
\(868\) 4.93131e7 + 1.77472e7i 2.22158 + 0.799523i
\(869\) 1.98342e6i 0.0890975i
\(870\) 1.27608e6 2.06376e6i 0.0571583 0.0924403i
\(871\) 473972. 0.0211694
\(872\) −8.16244e6 2.98161e7i −0.363520 1.32788i
\(873\) 1.61078e7i 0.715322i
\(874\) 5.44476e6 + 7.74613e6i 0.241102 + 0.343010i
\(875\) −2.78825e7 1.04243e7i −1.23115 0.460284i
\(876\) −562095. 202292.i −0.0247485 0.00890672i
\(877\) −5.75323e6 −0.252588 −0.126294 0.991993i \(-0.540308\pi\)
−0.126294 + 0.991993i \(0.540308\pi\)
\(878\) −1.13520e7 1.61503e7i −0.496977 0.707039i
\(879\) 706892. 0.0308589
\(880\) −644264. + 2.18628e6i −0.0280451 + 0.0951699i
\(881\) −1.39231e7 −0.604362 −0.302181 0.953251i \(-0.597715\pi\)
−0.302181 + 0.953251i \(0.597715\pi\)
\(882\) −9.59954e6 1.36570e7i −0.415508 0.591133i
\(883\) 4.47703e7 1.93236 0.966180 0.257867i \(-0.0830197\pi\)
0.966180 + 0.257867i \(0.0830197\pi\)
\(884\) −2.19316e7 7.89295e6i −0.943931 0.339710i
\(885\) −922808. 2.15650e6i −0.0396053 0.0925531i
\(886\) −1.74475e7 2.48222e7i −0.746707 1.06232i
\(887\) 1.25115e7i 0.533949i 0.963704 + 0.266974i \(0.0860239\pi\)
−0.963704 + 0.266974i \(0.913976\pi\)
\(888\) −1.20034e6 + 328605.i −0.0510825 + 0.0139843i
\(889\) 1.32186e7 0.560960
\(890\) −2.03915e6 1.26086e6i −0.0862927 0.0533571i
\(891\) 2.30232e6i 0.0971566i
\(892\) 2.76383e7 + 9.94670e6i 1.16305 + 0.418569i
\(893\) 8.20390e6 0.344264
\(894\) 340824. 239565.i 0.0142622 0.0100249i
\(895\) −1.29720e7 3.03141e7i −0.541313 1.26499i
\(896\) −1.29861e7 + 2.87928e7i −0.540391 + 1.19816i
\(897\) 1.12329e6i 0.0466134i
\(898\) 1.83566e7 + 2.61156e7i 0.759630 + 1.08071i
\(899\) 5.68095e7i 2.34435i
\(900\) −1.07828e7 2.15884e7i −0.443736 0.888412i
\(901\) 2.56686e7i 1.05339i
\(902\) 2.23061e6 1.56789e6i 0.0912865 0.0641653i
\(903\) 4.27778e6i 0.174582i
\(904\) −177094. 646895.i −0.00720746 0.0263277i
\(905\) 6.73831e6 + 1.57467e7i 0.273482 + 0.639098i
\(906\) −1.15216e6 1.63915e6i −0.0466329 0.0663435i
\(907\) −3.38418e7 −1.36595 −0.682975 0.730442i \(-0.739314\pi\)
−0.682975 + 0.730442i \(0.739314\pi\)
\(908\) 1.30889e7 3.63694e7i 0.526853 1.46393i
\(909\) 1.60457e7i 0.644092i
\(910\) 1.52245e7 2.46221e7i 0.609452 0.985648i
\(911\) −3.39018e7 −1.35340 −0.676701 0.736258i \(-0.736591\pi\)
−0.676701 + 0.736258i \(0.736591\pi\)
\(912\) −880326. + 1.06464e6i −0.0350475 + 0.0423855i
\(913\) 554999.i 0.0220351i
\(914\) 3.02681e7 2.12755e7i 1.19845 0.842391i
\(915\) 1.39349e6 + 3.25642e6i 0.0550237 + 0.128584i
\(916\) 9.74486e6 + 3.50706e6i 0.383740 + 0.138104i
\(917\) 5.62355e7 2.20845
\(918\) 3.94510e6 2.77301e6i 0.154508 0.108604i
\(919\) −2.44903e7 −0.956544 −0.478272 0.878212i \(-0.658737\pi\)
−0.478272 + 0.878212i \(0.658737\pi\)
\(920\) −1.01408e7 1.27592e7i −0.395007 0.496997i
\(921\) −3.51245e6 −0.136446
\(922\) 3.66901e7 2.57895e7i 1.42142 0.999113i
\(923\) 4.73776e6 0.183049
\(924\) 95441.7 265198.i 0.00367755 0.0102186i
\(925\) −1.14267e7 + 1.19716e7i −0.439102 + 0.460041i
\(926\) 2.51571e7 1.76829e7i 0.964125 0.677684i
\(927\) 4.01331e7i 1.53392i
\(928\) −3.41329e7 2.67616e6i −1.30108 0.102010i
\(929\) 4.91159e6 0.186717 0.0933583 0.995633i \(-0.470240\pi\)
0.0933583 + 0.995633i \(0.470240\pi\)
\(930\) −3.35601e6 2.07511e6i −0.127238 0.0786744i
\(931\) 1.27083e7i 0.480521i
\(932\) −4.05632e7 1.45982e7i −1.52965 0.550504i
\(933\) −402034. −0.0151202
\(934\) 4.79515e6 + 6.82196e6i 0.179860 + 0.255883i
\(935\) −2.77447e6 + 1.18725e6i −0.103789 + 0.0444132i
\(936\) 2.26350e7 6.19654e6i 0.844481 0.231185i
\(937\) 2.63398e7i 0.980083i −0.871699 0.490042i \(-0.836982\pi\)
0.871699 0.490042i \(-0.163018\pi\)
\(938\) 695738. 489034.i 0.0258190 0.0181481i
\(939\) 2.46284e6i 0.0911532i
\(940\) −1.40974e7 + 831069.i −0.520378 + 0.0306773i
\(941\) 3.47907e6i 0.128082i −0.997947 0.0640411i \(-0.979601\pi\)
0.997947 0.0640411i \(-0.0203989\pi\)
\(942\) −1.48424e6 2.11159e6i −0.0544974 0.0775322i
\(943\) 1.94967e7i 0.713973i
\(944\) −2.10914e7 + 2.55074e7i −0.770328 + 0.931615i
\(945\) 2.35616e6 + 5.50608e6i 0.0858271 + 0.200568i
\(946\) −3.56343e6 + 2.50474e6i −0.129462 + 0.0909985i
\(947\) −1.24338e7 −0.450537 −0.225268 0.974297i \(-0.572326\pi\)
−0.225268 + 0.974297i \(0.572326\pi\)
\(948\) −700742. + 1.94711e6i −0.0253243 + 0.0703670i
\(949\) 7.72564e6i 0.278464i
\(950\) −2.73522e6 + 1.81660e7i −0.0983294 + 0.653058i
\(951\) 708891. 0.0254172
\(952\) −4.03369e7 + 1.10426e7i −1.44248 + 0.394894i
\(953\) 4.64549e7i 1.65691i 0.560056 + 0.828455i \(0.310780\pi\)
−0.560056 + 0.828455i \(0.689220\pi\)
\(954\) 1.48616e7 + 2.11433e7i 0.528683 + 0.752145i
\(955\) −6.32574e6 + 2.70691e6i −0.224441 + 0.0960428i
\(956\) −1.08089e7 + 3.00340e7i −0.382504 + 1.06284i
\(957\) 305512. 0.0107832
\(958\) 1.34376e7 + 1.91173e7i 0.473050 + 0.672997i
\(959\) −2.30062e7 −0.807791
\(960\) 1.40488e6 1.91864e6i 0.0491996 0.0671916i
\(961\) 6.37523e7 2.22683
\(962\) −9.25515e6 1.31671e7i −0.322438 0.458725i
\(963\) 2.93551e7 1.02004
\(964\) −6.61102e6 + 1.83696e7i −0.229127 + 0.636661i
\(965\) −1.51624e7 3.54329e7i −0.524143 1.22486i
\(966\) 1.15899e6 + 1.64886e6i 0.0399609 + 0.0568515i
\(967\) 4.66797e7i 1.60532i 0.596435 + 0.802661i \(0.296583\pi\)
−0.596435 + 0.802661i \(0.703417\pi\)
\(968\) 2.78419e7 7.62199e6i 0.955016 0.261445i
\(969\) −1.82913e6 −0.0625798
\(970\) −1.11011e7 + 1.79534e7i −0.378823 + 0.612658i
\(971\) 1.61987e7i 0.551357i 0.961250 + 0.275678i \(0.0889025\pi\)
−0.961250 + 0.275678i \(0.911098\pi\)
\(972\) −2.46896e6 + 6.86034e6i −0.0838200 + 0.232906i
\(973\) 2.22081e7 0.752019
\(974\) 1.03946e7 7.30639e6i 0.351085 0.246777i
\(975\) −1.50482e6 + 1.57658e6i −0.0506959 + 0.0531133i
\(976\) 3.18491e7 3.85175e7i 1.07022 1.29430i
\(977\) 1.46888e7i 0.492322i 0.969229 + 0.246161i \(0.0791693\pi\)
−0.969229 + 0.246161i \(0.920831\pi\)
\(978\) 1.83394e6 + 2.60911e6i 0.0613111 + 0.0872258i
\(979\) 301869.i 0.0100661i
\(980\) −1.28737e6 2.18376e7i −0.0428191 0.726340i
\(981\) 4.12100e7i 1.36719i
\(982\) 2.67642e6 1.88126e6i 0.0885679 0.0622544i
\(983\) 4.22739e6i 0.139537i −0.997563 0.0697684i \(-0.977774\pi\)
0.997563 0.0697684i \(-0.0222260\pi\)
\(984\) −2.74371e6 + 751116.i −0.0903337 + 0.0247297i
\(985\) 3.63781e6 1.55669e6i 0.119467 0.0511224i
\(986\) −2.60685e7 3.70871e7i −0.853933 1.21487i
\(987\) 1.74631e6 0.0570594
\(988\) −1.68101e7 6.04976e6i −0.547871 0.197172i
\(989\) 3.11463e7i 1.01255i
\(990\) 1.59794e6 2.58430e6i 0.0518170 0.0838020i
\(991\) 1.49618e7 0.483948 0.241974 0.970283i \(-0.422205\pi\)
0.241974 + 0.970283i \(0.422205\pi\)
\(992\) −4.35187e6 + 5.55056e7i −0.140410 + 1.79084i
\(993\) 2.04432e6i 0.0657925i
\(994\) 6.95449e6 4.88831e6i 0.223254 0.156925i
\(995\) 1.61677e7 6.91846e6i 0.517714 0.221540i
\(996\) −196081. + 544838.i −0.00626307 + 0.0174028i
\(997\) −3.45075e7 −1.09945 −0.549724 0.835346i \(-0.685267\pi\)
−0.549724 + 0.835346i \(0.685267\pi\)
\(998\) 1.42187e6 999435.i 0.0451892 0.0317635i
\(999\) 3.32966e6 0.105557
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 40.6.f.a.29.9 28
4.3 odd 2 160.6.f.a.49.13 28
5.2 odd 4 200.6.d.e.101.23 28
5.3 odd 4 200.6.d.e.101.6 28
5.4 even 2 inner 40.6.f.a.29.20 yes 28
8.3 odd 2 160.6.f.a.49.15 28
8.5 even 2 inner 40.6.f.a.29.19 yes 28
20.3 even 4 800.6.d.e.401.3 28
20.7 even 4 800.6.d.e.401.26 28
20.19 odd 2 160.6.f.a.49.16 28
40.3 even 4 800.6.d.e.401.4 28
40.13 odd 4 200.6.d.e.101.5 28
40.19 odd 2 160.6.f.a.49.14 28
40.27 even 4 800.6.d.e.401.25 28
40.29 even 2 inner 40.6.f.a.29.10 yes 28
40.37 odd 4 200.6.d.e.101.24 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.f.a.29.9 28 1.1 even 1 trivial
40.6.f.a.29.10 yes 28 40.29 even 2 inner
40.6.f.a.29.19 yes 28 8.5 even 2 inner
40.6.f.a.29.20 yes 28 5.4 even 2 inner
160.6.f.a.49.13 28 4.3 odd 2
160.6.f.a.49.14 28 40.19 odd 2
160.6.f.a.49.15 28 8.3 odd 2
160.6.f.a.49.16 28 20.19 odd 2
200.6.d.e.101.5 28 40.13 odd 4
200.6.d.e.101.6 28 5.3 odd 4
200.6.d.e.101.23 28 5.2 odd 4
200.6.d.e.101.24 28 40.37 odd 4
800.6.d.e.401.3 28 20.3 even 4
800.6.d.e.401.4 28 40.3 even 4
800.6.d.e.401.25 28 40.27 even 4
800.6.d.e.401.26 28 20.7 even 4