Properties

Label 350.5.i.a.199.3
Level $350$
Weight $5$
Character 350.199
Analytic conductor $36.179$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,5,Mod(199,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.199");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 350.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(36.1794870793\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.3
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 350.199
Dual form 350.5.i.a.299.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.44949 - 1.41421i) q^{2} +(-7.49706 + 12.9853i) q^{3} +(4.00000 - 6.92820i) q^{4} +42.4098i q^{6} +(48.4974 - 7.00000i) q^{7} -22.6274i q^{8} +(-71.9117 - 124.555i) q^{9} +O(q^{10})\) \(q+(2.44949 - 1.41421i) q^{2} +(-7.49706 + 12.9853i) q^{3} +(4.00000 - 6.92820i) q^{4} +42.4098i q^{6} +(48.4974 - 7.00000i) q^{7} -22.6274i q^{8} +(-71.9117 - 124.555i) q^{9} +(-21.9853 + 38.0796i) q^{11} +(59.9764 + 103.882i) q^{12} -162.507 q^{13} +(108.894 - 85.7321i) q^{14} +(-32.0000 - 55.4256i) q^{16} +(-54.1182 + 93.7355i) q^{17} +(-352.294 - 203.397i) q^{18} +(-389.338 + 224.784i) q^{19} +(-272.691 + 682.232i) q^{21} +124.368i q^{22} +(377.433 - 217.911i) q^{23} +(293.823 + 169.639i) q^{24} +(-398.059 + 229.819i) q^{26} +941.981 q^{27} +(145.492 - 364.000i) q^{28} -742.118 q^{29} +(-900.175 - 519.716i) q^{31} +(-156.767 - 90.5097i) q^{32} +(-329.650 - 570.970i) q^{33} +306.139i q^{34} -1150.59 q^{36} +(854.486 - 493.338i) q^{37} +(-635.786 + 1101.21i) q^{38} +(1218.32 - 2110.20i) q^{39} +1143.70i q^{41} +(296.868 + 2056.76i) q^{42} -2418.82i q^{43} +(175.882 + 304.637i) q^{44} +(616.346 - 1067.54i) q^{46} +(-672.714 - 1165.17i) q^{47} +959.623 q^{48} +(2303.00 - 678.964i) q^{49} +(-811.455 - 1405.48i) q^{51} +(-650.027 + 1125.88i) q^{52} +(-3088.42 - 1783.10i) q^{53} +(2307.37 - 1332.16i) q^{54} +(-158.392 - 1097.37i) q^{56} -6740.88i q^{57} +(-1817.81 + 1049.51i) q^{58} +(-3710.93 - 2142.50i) q^{59} +(-1209.57 + 698.345i) q^{61} -2939.96 q^{62} +(-4359.41 - 5537.20i) q^{63} -512.000 q^{64} +(-1614.95 - 932.390i) q^{66} +(-6292.36 - 3632.89i) q^{67} +(432.946 + 749.884i) q^{68} +6534.77i q^{69} +5987.76 q^{71} +(-2818.35 + 1627.18i) q^{72} +(-288.746 + 500.123i) q^{73} +(1395.37 - 2416.85i) q^{74} +3596.55i q^{76} +(-799.672 + 2000.66i) q^{77} -6891.88i q^{78} +(-1573.12 - 2724.72i) q^{79} +(-1237.24 + 2142.95i) q^{81} +(1617.43 + 2801.47i) q^{82} +4729.96 q^{83} +(3635.88 + 4618.19i) q^{84} +(-3420.73 - 5924.88i) q^{86} +(5563.70 - 9636.61i) q^{87} +(861.644 + 497.470i) q^{88} +(725.651 - 418.955i) q^{89} +(-7881.16 + 1137.55i) q^{91} -3486.58i q^{92} +(13497.3 - 7792.69i) q^{93} +(-3295.61 - 1902.72i) q^{94} +(2350.59 - 1357.11i) q^{96} +5622.23 q^{97} +(4680.97 - 4920.05i) q^{98} +6323.99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 32 q^{4} - 168 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 32 q^{4} - 168 q^{9} - 108 q^{11} - 256 q^{16} - 60 q^{19} - 756 q^{21} + 1536 q^{24} - 3456 q^{26} - 6480 q^{29} - 1092 q^{31} - 2688 q^{36} + 6624 q^{39} + 864 q^{44} + 7680 q^{46} + 18424 q^{49} + 636 q^{51} + 2880 q^{54} - 24732 q^{59} + 15372 q^{61} - 4096 q^{64} - 6912 q^{66} + 37584 q^{71} + 8640 q^{74} - 1588 q^{79} - 8676 q^{81} + 10080 q^{84} - 20736 q^{86} + 24948 q^{89} + 5376 q^{91} - 30336 q^{94} + 12288 q^{96} + 22896 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.44949 1.41421i 0.612372 0.353553i
\(3\) −7.49706 + 12.9853i −0.833006 + 1.44281i 0.0626373 + 0.998036i \(0.480049\pi\)
−0.895643 + 0.444773i \(0.853284\pi\)
\(4\) 4.00000 6.92820i 0.250000 0.433013i
\(5\) 0 0
\(6\) 42.4098i 1.17805i
\(7\) 48.4974 7.00000i 0.989743 0.142857i
\(8\) 22.6274i 0.353553i
\(9\) −71.9117 124.555i −0.887799 1.53771i
\(10\) 0 0
\(11\) −21.9853 + 38.0796i −0.181697 + 0.314708i −0.942458 0.334324i \(-0.891492\pi\)
0.760762 + 0.649031i \(0.224826\pi\)
\(12\) 59.9764 + 103.882i 0.416503 + 0.721405i
\(13\) −162.507 −0.961579 −0.480790 0.876836i \(-0.659650\pi\)
−0.480790 + 0.876836i \(0.659650\pi\)
\(14\) 108.894 85.7321i 0.555584 0.437409i
\(15\) 0 0
\(16\) −32.0000 55.4256i −0.125000 0.216506i
\(17\) −54.1182 + 93.7355i −0.187260 + 0.324344i −0.944336 0.328983i \(-0.893294\pi\)
0.757076 + 0.653327i \(0.226627\pi\)
\(18\) −352.294 203.397i −1.08733 0.627768i
\(19\) −389.338 + 224.784i −1.07850 + 0.622671i −0.930491 0.366315i \(-0.880619\pi\)
−0.148007 + 0.988986i \(0.547286\pi\)
\(20\) 0 0
\(21\) −272.691 + 682.232i −0.618347 + 1.54701i
\(22\) 124.368i 0.256958i
\(23\) 377.433 217.911i 0.713485 0.411931i −0.0988653 0.995101i \(-0.531521\pi\)
0.812350 + 0.583170i \(0.198188\pi\)
\(24\) 293.823 + 169.639i 0.510110 + 0.294512i
\(25\) 0 0
\(26\) −398.059 + 229.819i −0.588844 + 0.339970i
\(27\) 941.981 1.29215
\(28\) 145.492 364.000i 0.185577 0.464286i
\(29\) −742.118 −0.882423 −0.441212 0.897403i \(-0.645451\pi\)
−0.441212 + 0.897403i \(0.645451\pi\)
\(30\) 0 0
\(31\) −900.175 519.716i −0.936707 0.540808i −0.0477804 0.998858i \(-0.515215\pi\)
−0.888926 + 0.458050i \(0.848548\pi\)
\(32\) −156.767 90.5097i −0.153093 0.0883883i
\(33\) −329.650 570.970i −0.302709 0.524307i
\(34\) 306.139i 0.264826i
\(35\) 0 0
\(36\) −1150.59 −0.887799
\(37\) 854.486 493.338i 0.624168 0.360364i −0.154322 0.988021i \(-0.549319\pi\)
0.778490 + 0.627657i \(0.215986\pi\)
\(38\) −635.786 + 1101.21i −0.440295 + 0.762613i
\(39\) 1218.32 2110.20i 0.801001 1.38737i
\(40\) 0 0
\(41\) 1143.70i 0.680366i 0.940359 + 0.340183i \(0.110489\pi\)
−0.940359 + 0.340183i \(0.889511\pi\)
\(42\) 296.868 + 2056.76i 0.168293 + 1.16597i
\(43\) 2418.82i 1.30818i −0.756418 0.654089i \(-0.773052\pi\)
0.756418 0.654089i \(-0.226948\pi\)
\(44\) 175.882 + 304.637i 0.0908483 + 0.157354i
\(45\) 0 0
\(46\) 616.346 1067.54i 0.291279 0.504510i
\(47\) −672.714 1165.17i −0.304533 0.527467i 0.672624 0.739984i \(-0.265167\pi\)
−0.977157 + 0.212517i \(0.931834\pi\)
\(48\) 959.623 0.416503
\(49\) 2303.00 678.964i 0.959184 0.282784i
\(50\) 0 0
\(51\) −811.455 1405.48i −0.311978 0.540362i
\(52\) −650.027 + 1125.88i −0.240395 + 0.416376i
\(53\) −3088.42 1783.10i −1.09947 0.634782i −0.163391 0.986561i \(-0.552243\pi\)
−0.936083 + 0.351780i \(0.885577\pi\)
\(54\) 2307.37 1332.16i 0.791280 0.456846i
\(55\) 0 0
\(56\) −158.392 1097.37i −0.0505076 0.349927i
\(57\) 6740.88i 2.07475i
\(58\) −1817.81 + 1049.51i −0.540372 + 0.311984i
\(59\) −3710.93 2142.50i −1.06605 0.615485i −0.138952 0.990299i \(-0.544373\pi\)
−0.927100 + 0.374814i \(0.877707\pi\)
\(60\) 0 0
\(61\) −1209.57 + 698.345i −0.325066 + 0.187677i −0.653648 0.756799i \(-0.726762\pi\)
0.328583 + 0.944475i \(0.393429\pi\)
\(62\) −2939.96 −0.764818
\(63\) −4359.41 5537.20i −1.09837 1.39511i
\(64\) −512.000 −0.125000
\(65\) 0 0
\(66\) −1614.95 932.390i −0.370741 0.214047i
\(67\) −6292.36 3632.89i −1.40173 0.809288i −0.407158 0.913358i \(-0.633480\pi\)
−0.994570 + 0.104070i \(0.966813\pi\)
\(68\) 432.946 + 749.884i 0.0936301 + 0.162172i
\(69\) 6534.77i 1.37256i
\(70\) 0 0
\(71\) 5987.76 1.18781 0.593906 0.804534i \(-0.297585\pi\)
0.593906 + 0.804534i \(0.297585\pi\)
\(72\) −2818.35 + 1627.18i −0.543663 + 0.313884i
\(73\) −288.746 + 500.123i −0.0541840 + 0.0938494i −0.891845 0.452341i \(-0.850589\pi\)
0.837661 + 0.546190i \(0.183922\pi\)
\(74\) 1395.37 2416.85i 0.254815 0.441353i
\(75\) 0 0
\(76\) 3596.55i 0.622671i
\(77\) −799.672 + 2000.66i −0.134875 + 0.337436i
\(78\) 6891.88i 1.13279i
\(79\) −1573.12 2724.72i −0.252061 0.436583i 0.712032 0.702147i \(-0.247775\pi\)
−0.964093 + 0.265564i \(0.914442\pi\)
\(80\) 0 0
\(81\) −1237.24 + 2142.95i −0.188574 + 0.326620i
\(82\) 1617.43 + 2801.47i 0.240546 + 0.416637i
\(83\) 4729.96 0.686596 0.343298 0.939227i \(-0.388456\pi\)
0.343298 + 0.939227i \(0.388456\pi\)
\(84\) 3635.88 + 4618.19i 0.515289 + 0.654505i
\(85\) 0 0
\(86\) −3420.73 5924.88i −0.462511 0.801092i
\(87\) 5563.70 9636.61i 0.735064 1.27317i
\(88\) 861.644 + 497.470i 0.111266 + 0.0642394i
\(89\) 725.651 418.955i 0.0916110 0.0528916i −0.453495 0.891259i \(-0.649823\pi\)
0.545106 + 0.838367i \(0.316490\pi\)
\(90\) 0 0
\(91\) −7881.16 + 1137.55i −0.951716 + 0.137368i
\(92\) 3486.58i 0.411931i
\(93\) 13497.3 7792.69i 1.56057 0.900993i
\(94\) −3295.61 1902.72i −0.372975 0.215337i
\(95\) 0 0
\(96\) 2350.59 1357.11i 0.255055 0.147256i
\(97\) 5622.23 0.597537 0.298769 0.954326i \(-0.403424\pi\)
0.298769 + 0.954326i \(0.403424\pi\)
\(98\) 4680.97 4920.05i 0.487398 0.512292i
\(99\) 6323.99 0.645240
\(100\) 0 0
\(101\) −5703.21 3292.75i −0.559083 0.322787i 0.193694 0.981062i \(-0.437953\pi\)
−0.752778 + 0.658275i \(0.771286\pi\)
\(102\) −3975.30 2295.14i −0.382093 0.220602i
\(103\) −762.249 1320.25i −0.0718492 0.124447i 0.827863 0.560931i \(-0.189557\pi\)
−0.899712 + 0.436484i \(0.856223\pi\)
\(104\) 3677.11i 0.339970i
\(105\) 0 0
\(106\) −10086.7 −0.897717
\(107\) 9185.61 5303.31i 0.802306 0.463212i −0.0419706 0.999119i \(-0.513364\pi\)
0.844277 + 0.535907i \(0.180030\pi\)
\(108\) 3767.92 6526.23i 0.323039 0.559519i
\(109\) −6976.13 + 12083.0i −0.587167 + 1.01700i 0.407434 + 0.913235i \(0.366424\pi\)
−0.994601 + 0.103769i \(0.966910\pi\)
\(110\) 0 0
\(111\) 14794.3i 1.20074i
\(112\) −1939.90 2464.00i −0.154647 0.196429i
\(113\) 8811.30i 0.690054i 0.938593 + 0.345027i \(0.112130\pi\)
−0.938593 + 0.345027i \(0.887870\pi\)
\(114\) −9533.04 16511.7i −0.733537 1.27052i
\(115\) 0 0
\(116\) −2968.47 + 5141.54i −0.220606 + 0.382100i
\(117\) 11686.1 + 20241.0i 0.853689 + 1.47863i
\(118\) −12119.8 −0.870427
\(119\) −1968.45 + 4924.76i −0.139005 + 0.347769i
\(120\) 0 0
\(121\) 6353.79 + 11005.1i 0.433973 + 0.751663i
\(122\) −1975.22 + 3421.18i −0.132707 + 0.229856i
\(123\) −14851.2 8574.35i −0.981638 0.566749i
\(124\) −7201.40 + 4157.73i −0.468353 + 0.270404i
\(125\) 0 0
\(126\) −18509.1 7398.17i −1.16586 0.465997i
\(127\) 3992.70i 0.247548i 0.992310 + 0.123774i \(0.0394998\pi\)
−0.992310 + 0.123774i \(0.960500\pi\)
\(128\) −1254.14 + 724.077i −0.0765466 + 0.0441942i
\(129\) 31409.1 + 18134.0i 1.88745 + 1.08972i
\(130\) 0 0
\(131\) −17515.4 + 10112.5i −1.02065 + 0.589272i −0.914292 0.405056i \(-0.867252\pi\)
−0.106357 + 0.994328i \(0.533919\pi\)
\(132\) −5274.40 −0.302709
\(133\) −17308.4 + 13626.8i −0.978483 + 0.770355i
\(134\) −20550.7 −1.14451
\(135\) 0 0
\(136\) 2120.99 + 1224.56i 0.114673 + 0.0662065i
\(137\) −21700.6 12528.9i −1.15620 0.667530i −0.205807 0.978593i \(-0.565982\pi\)
−0.950389 + 0.311062i \(0.899315\pi\)
\(138\) 9241.56 + 16006.9i 0.485274 + 0.840520i
\(139\) 20070.1i 1.03877i 0.854541 + 0.519385i \(0.173839\pi\)
−0.854541 + 0.519385i \(0.826161\pi\)
\(140\) 0 0
\(141\) 20173.5 1.01471
\(142\) 14667.0 8467.98i 0.727384 0.419955i
\(143\) 3572.76 6188.20i 0.174716 0.302616i
\(144\) −4602.35 + 7971.50i −0.221950 + 0.384428i
\(145\) 0 0
\(146\) 1633.40i 0.0766277i
\(147\) −8449.18 + 34995.3i −0.391003 + 1.61948i
\(148\) 7893.40i 0.360364i
\(149\) −21353.9 36986.1i −0.961846 1.66597i −0.717860 0.696188i \(-0.754878\pi\)
−0.243986 0.969779i \(-0.578455\pi\)
\(150\) 0 0
\(151\) −14803.7 + 25640.8i −0.649258 + 1.12455i 0.334043 + 0.942558i \(0.391587\pi\)
−0.983301 + 0.181989i \(0.941746\pi\)
\(152\) 5086.29 + 8809.71i 0.220147 + 0.381307i
\(153\) 15566.9 0.664998
\(154\) 870.573 + 6031.50i 0.0367082 + 0.254322i
\(155\) 0 0
\(156\) −9746.58 16881.6i −0.400501 0.693687i
\(157\) −6118.53 + 10597.6i −0.248226 + 0.429940i −0.963034 0.269381i \(-0.913181\pi\)
0.714808 + 0.699321i \(0.246514\pi\)
\(158\) −7706.66 4449.44i −0.308711 0.178234i
\(159\) 46308.1 26736.0i 1.83174 1.05755i
\(160\) 0 0
\(161\) 16779.2 13210.2i 0.647319 0.509632i
\(162\) 6998.86i 0.266684i
\(163\) −18646.5 + 10765.6i −0.701814 + 0.405193i −0.808023 0.589151i \(-0.799462\pi\)
0.106209 + 0.994344i \(0.466129\pi\)
\(164\) 7923.75 + 4574.78i 0.294607 + 0.170092i
\(165\) 0 0
\(166\) 11586.0 6689.17i 0.420452 0.242748i
\(167\) 16578.9 0.594461 0.297230 0.954806i \(-0.403937\pi\)
0.297230 + 0.954806i \(0.403937\pi\)
\(168\) 15437.1 + 6170.29i 0.546951 + 0.218619i
\(169\) −2152.52 −0.0753658
\(170\) 0 0
\(171\) 55995.9 + 32329.2i 1.91498 + 1.10561i
\(172\) −16758.1 9675.28i −0.566458 0.327044i
\(173\) 20191.5 + 34972.8i 0.674648 + 1.16852i 0.976572 + 0.215192i \(0.0690377\pi\)
−0.301924 + 0.953332i \(0.597629\pi\)
\(174\) 31473.0i 1.03954i
\(175\) 0 0
\(176\) 2814.12 0.0908483
\(177\) 55642.0 32124.9i 1.77606 1.02541i
\(178\) 1184.98 2052.45i 0.0374000 0.0647788i
\(179\) −26747.2 + 46327.5i −0.834780 + 1.44588i 0.0594290 + 0.998233i \(0.481072\pi\)
−0.894209 + 0.447649i \(0.852261\pi\)
\(180\) 0 0
\(181\) 54202.1i 1.65447i −0.561857 0.827235i \(-0.689913\pi\)
0.561857 0.827235i \(-0.310087\pi\)
\(182\) −17696.1 + 13932.1i −0.534238 + 0.420603i
\(183\) 20942.1i 0.625343i
\(184\) −4930.77 8540.34i −0.145639 0.252255i
\(185\) 0 0
\(186\) 22041.0 38176.2i 0.637098 1.10349i
\(187\) −2379.61 4121.60i −0.0680491 0.117864i
\(188\) −10763.4 −0.304533
\(189\) 45683.6 6593.86i 1.27890 0.184594i
\(190\) 0 0
\(191\) 601.936 + 1042.58i 0.0165000 + 0.0285788i 0.874158 0.485643i \(-0.161414\pi\)
−0.857658 + 0.514221i \(0.828081\pi\)
\(192\) 3838.49 6648.46i 0.104126 0.180351i
\(193\) 44438.3 + 25656.5i 1.19301 + 0.688783i 0.958987 0.283449i \(-0.0914788\pi\)
0.234019 + 0.972232i \(0.424812\pi\)
\(194\) 13771.6 7951.03i 0.365915 0.211261i
\(195\) 0 0
\(196\) 4508.00 18671.5i 0.117347 0.486035i
\(197\) 1456.28i 0.0375242i −0.999824 0.0187621i \(-0.994027\pi\)
0.999824 0.0187621i \(-0.00597251\pi\)
\(198\) 15490.6 8943.48i 0.395127 0.228127i
\(199\) −59546.3 34379.1i −1.50366 0.868137i −0.999991 0.00423890i \(-0.998651\pi\)
−0.503667 0.863898i \(-0.668016\pi\)
\(200\) 0 0
\(201\) 94348.3 54472.0i 2.33530 1.34828i
\(202\) −18626.6 −0.456490
\(203\) −35990.8 + 5194.82i −0.873372 + 0.126060i
\(204\) −12983.3 −0.311978
\(205\) 0 0
\(206\) −3734.24 2155.96i −0.0879970 0.0508051i
\(207\) −54283.7 31340.7i −1.26686 0.731423i
\(208\) 5200.22 + 9007.04i 0.120197 + 0.208188i
\(209\) 19767.8i 0.452549i
\(210\) 0 0
\(211\) −622.821 −0.0139894 −0.00699469 0.999976i \(-0.502226\pi\)
−0.00699469 + 0.999976i \(0.502226\pi\)
\(212\) −24707.4 + 14264.8i −0.549737 + 0.317391i
\(213\) −44890.6 + 77752.8i −0.989455 + 1.71379i
\(214\) 15000.0 25980.8i 0.327540 0.567316i
\(215\) 0 0
\(216\) 21314.6i 0.456846i
\(217\) −47294.2 18903.7i −1.00436 0.401446i
\(218\) 39463.0i 0.830380i
\(219\) −4329.50 7498.91i −0.0902712 0.156354i
\(220\) 0 0
\(221\) 8794.58 15232.7i 0.180066 0.311883i
\(222\) 20922.3 + 36238.5i 0.424526 + 0.735300i
\(223\) −11509.7 −0.231449 −0.115725 0.993281i \(-0.536919\pi\)
−0.115725 + 0.993281i \(0.536919\pi\)
\(224\) −8236.38 3292.11i −0.164150 0.0656113i
\(225\) 0 0
\(226\) 12461.1 + 21583.2i 0.243971 + 0.422570i
\(227\) 28183.6 48815.4i 0.546946 0.947339i −0.451535 0.892253i \(-0.649124\pi\)
0.998482 0.0550855i \(-0.0175431\pi\)
\(228\) −46702.2 26963.5i −0.898395 0.518689i
\(229\) 36484.4 21064.3i 0.695722 0.401675i −0.110030 0.993928i \(-0.535095\pi\)
0.805752 + 0.592253i \(0.201761\pi\)
\(230\) 0 0
\(231\) −19984.0 25383.0i −0.374505 0.475685i
\(232\) 16792.2i 0.311984i
\(233\) 47719.6 27550.9i 0.878992 0.507486i 0.00866633 0.999962i \(-0.497241\pi\)
0.870326 + 0.492476i \(0.163908\pi\)
\(234\) 57250.2 + 33053.4i 1.04555 + 0.603649i
\(235\) 0 0
\(236\) −29687.4 + 17140.0i −0.533026 + 0.307743i
\(237\) 47174.9 0.839875
\(238\) 2142.97 + 14846.9i 0.0378323 + 0.262110i
\(239\) −23082.5 −0.404098 −0.202049 0.979375i \(-0.564760\pi\)
−0.202049 + 0.979375i \(0.564760\pi\)
\(240\) 0 0
\(241\) 70643.9 + 40786.3i 1.21630 + 0.702231i 0.964124 0.265451i \(-0.0855209\pi\)
0.252175 + 0.967682i \(0.418854\pi\)
\(242\) 31127.1 + 17971.2i 0.531506 + 0.306865i
\(243\) 19599.0 + 33946.4i 0.331910 + 0.574886i
\(244\) 11173.5i 0.187677i
\(245\) 0 0
\(246\) −48503.8 −0.801504
\(247\) 63270.0 36529.0i 1.03706 0.598747i
\(248\) −11759.8 + 20368.6i −0.191204 + 0.331176i
\(249\) −35460.8 + 61419.8i −0.571939 + 0.990627i
\(250\) 0 0
\(251\) 27207.6i 0.431859i 0.976409 + 0.215930i \(0.0692782\pi\)
−0.976409 + 0.215930i \(0.930722\pi\)
\(252\) −55800.5 + 8054.11i −0.878693 + 0.126828i
\(253\) 19163.4i 0.299385i
\(254\) 5646.53 + 9780.08i 0.0875214 + 0.151592i
\(255\) 0 0
\(256\) −2048.00 + 3547.24i −0.0312500 + 0.0541266i
\(257\) 53964.5 + 93469.3i 0.817038 + 1.41515i 0.907856 + 0.419283i \(0.137719\pi\)
−0.0908179 + 0.995868i \(0.528948\pi\)
\(258\) 102582. 1.54110
\(259\) 37987.0 29907.0i 0.566286 0.445834i
\(260\) 0 0
\(261\) 53366.9 + 92434.3i 0.783414 + 1.35691i
\(262\) −28602.5 + 49540.9i −0.416678 + 0.721708i
\(263\) −34765.8 20072.0i −0.502621 0.290188i 0.227174 0.973854i \(-0.427051\pi\)
−0.729795 + 0.683666i \(0.760385\pi\)
\(264\) −12919.6 + 7459.12i −0.185370 + 0.107024i
\(265\) 0 0
\(266\) −23125.5 + 57856.5i −0.326834 + 0.817690i
\(267\) 12563.7i 0.176236i
\(268\) −50338.8 + 29063.1i −0.700864 + 0.404644i
\(269\) −91239.0 52676.9i −1.26089 0.727973i −0.287641 0.957738i \(-0.592871\pi\)
−0.973246 + 0.229765i \(0.926204\pi\)
\(270\) 0 0
\(271\) −13189.3 + 7614.84i −0.179590 + 0.103687i −0.587100 0.809514i \(-0.699731\pi\)
0.407510 + 0.913201i \(0.366397\pi\)
\(272\) 6927.13 0.0936301
\(273\) 44314.1 110867.i 0.594589 1.48757i
\(274\) −70874.0 −0.944030
\(275\) 0 0
\(276\) 45274.2 + 26139.1i 0.594337 + 0.343141i
\(277\) 8549.07 + 4935.81i 0.111419 + 0.0643278i 0.554674 0.832068i \(-0.312843\pi\)
−0.443255 + 0.896396i \(0.646176\pi\)
\(278\) 28383.4 + 49161.4i 0.367260 + 0.636114i
\(279\) 149495.i 1.92051i
\(280\) 0 0
\(281\) −155117. −1.96448 −0.982240 0.187631i \(-0.939919\pi\)
−0.982240 + 0.187631i \(0.939919\pi\)
\(282\) 49414.8 28529.6i 0.621382 0.358755i
\(283\) −54831.0 + 94970.0i −0.684626 + 1.18581i 0.288929 + 0.957351i \(0.406701\pi\)
−0.973554 + 0.228456i \(0.926632\pi\)
\(284\) 23951.1 41484.4i 0.296953 0.514338i
\(285\) 0 0
\(286\) 20210.6i 0.247085i
\(287\) 8005.87 + 55466.3i 0.0971952 + 0.673388i
\(288\) 26034.8i 0.313884i
\(289\) 35902.9 + 62185.7i 0.429867 + 0.744552i
\(290\) 0 0
\(291\) −42150.2 + 73006.2i −0.497752 + 0.862132i
\(292\) 2309.97 + 4000.99i 0.0270920 + 0.0469247i
\(293\) 89912.4 1.04733 0.523666 0.851924i \(-0.324564\pi\)
0.523666 + 0.851924i \(0.324564\pi\)
\(294\) 28794.7 + 97669.7i 0.333133 + 1.12997i
\(295\) 0 0
\(296\) −11163.0 19334.8i −0.127408 0.220677i
\(297\) −20709.7 + 35870.3i −0.234780 + 0.406651i
\(298\) −104613. 60398.1i −1.17802 0.680128i
\(299\) −61335.5 + 35412.1i −0.686072 + 0.396104i
\(300\) 0 0
\(301\) −16931.7 117307.i −0.186883 1.29476i
\(302\) 83742.5i 0.918189i
\(303\) 85514.6 49371.9i 0.931440 0.537767i
\(304\) 24917.6 + 14386.2i 0.269624 + 0.155668i
\(305\) 0 0
\(306\) 38131.0 22015.0i 0.407226 0.235112i
\(307\) −141681. −1.50327 −0.751633 0.659582i \(-0.770733\pi\)
−0.751633 + 0.659582i \(0.770733\pi\)
\(308\) 10662.3 + 13542.9i 0.112396 + 0.142762i
\(309\) 22858.5 0.239403
\(310\) 0 0
\(311\) −74171.3 42822.8i −0.766858 0.442746i 0.0648948 0.997892i \(-0.479329\pi\)
−0.831753 + 0.555147i \(0.812662\pi\)
\(312\) −47748.3 27567.5i −0.490511 0.283197i
\(313\) −8915.78 15442.6i −0.0910061 0.157627i 0.816929 0.576739i \(-0.195675\pi\)
−0.907935 + 0.419112i \(0.862342\pi\)
\(314\) 34611.6i 0.351045i
\(315\) 0 0
\(316\) −25169.8 −0.252061
\(317\) 69979.4 40402.6i 0.696388 0.402060i −0.109613 0.993974i \(-0.534961\pi\)
0.806001 + 0.591914i \(0.201628\pi\)
\(318\) 75620.9 130979.i 0.747804 1.29523i
\(319\) 16315.7 28259.6i 0.160333 0.277705i
\(320\) 0 0
\(321\) 159037.i 1.54343i
\(322\) 22418.4 56087.5i 0.216218 0.540946i
\(323\) 48659.7i 0.466406i
\(324\) 9897.88 + 17143.6i 0.0942871 + 0.163310i
\(325\) 0 0
\(326\) −30449.6 + 52740.3i −0.286514 + 0.496258i
\(327\) −104601. 181174.i −0.978228 1.69434i
\(328\) 25878.9 0.240546
\(329\) −40781.1 51799.0i −0.376762 0.478552i
\(330\) 0 0
\(331\) −36402.1 63050.3i −0.332254 0.575482i 0.650699 0.759336i \(-0.274476\pi\)
−0.982954 + 0.183854i \(0.941143\pi\)
\(332\) 18919.8 32770.1i 0.171649 0.297305i
\(333\) −122895. 70953.5i −1.10827 0.639860i
\(334\) 40609.9 23446.1i 0.364031 0.210174i
\(335\) 0 0
\(336\) 46539.2 6717.36i 0.412231 0.0595004i
\(337\) 126538.i 1.11419i 0.830449 + 0.557095i \(0.188084\pi\)
−0.830449 + 0.557095i \(0.811916\pi\)
\(338\) −5272.58 + 3044.13i −0.0461519 + 0.0266458i
\(339\) −114417. 66058.8i −0.995616 0.574819i
\(340\) 0 0
\(341\) 39581.2 22852.2i 0.340393 0.196526i
\(342\) 182882. 1.56357
\(343\) 106937. 49049.0i 0.908948 0.416910i
\(344\) −54731.7 −0.462511
\(345\) 0 0
\(346\) 98917.9 + 57110.3i 0.826271 + 0.477048i
\(347\) 57979.8 + 33474.6i 0.481524 + 0.278008i 0.721051 0.692882i \(-0.243659\pi\)
−0.239528 + 0.970890i \(0.576993\pi\)
\(348\) −44509.6 77092.9i −0.367532 0.636584i
\(349\) 25527.5i 0.209583i 0.994494 + 0.104792i \(0.0334176\pi\)
−0.994494 + 0.104792i \(0.966582\pi\)
\(350\) 0 0
\(351\) −153078. −1.24251
\(352\) 6893.15 3979.76i 0.0556330 0.0321197i
\(353\) −28287.8 + 48995.9i −0.227013 + 0.393197i −0.956921 0.290347i \(-0.906229\pi\)
0.729909 + 0.683545i \(0.239563\pi\)
\(354\) 90863.1 157379.i 0.725071 1.25586i
\(355\) 0 0
\(356\) 6703.27i 0.0528916i
\(357\) −49191.8 62482.0i −0.385973 0.490251i
\(358\) 151305.i 1.18056i
\(359\) 18902.4 + 32739.9i 0.146665 + 0.254032i 0.929993 0.367577i \(-0.119813\pi\)
−0.783328 + 0.621609i \(0.786479\pi\)
\(360\) 0 0
\(361\) 35895.4 62172.6i 0.275438 0.477073i
\(362\) −76653.3 132767.i −0.584943 1.01315i
\(363\) −190539. −1.44601
\(364\) −23643.5 + 59152.5i −0.178447 + 0.446447i
\(365\) 0 0
\(366\) −29616.6 51297.5i −0.221092 0.382943i
\(367\) −5408.20 + 9367.27i −0.0401532 + 0.0695474i −0.885404 0.464823i \(-0.846118\pi\)
0.845250 + 0.534370i \(0.179451\pi\)
\(368\) −24155.7 13946.3i −0.178371 0.102983i
\(369\) 142453. 82245.1i 1.04621 0.604028i
\(370\) 0 0
\(371\) −162262. 64856.9i −1.17888 0.471203i
\(372\) 124683.i 0.900993i
\(373\) 26867.0 15511.7i 0.193109 0.111491i −0.400328 0.916372i \(-0.631104\pi\)
0.593437 + 0.804880i \(0.297771\pi\)
\(374\) −11657.7 6730.55i −0.0833428 0.0481180i
\(375\) 0 0
\(376\) −26364.9 + 15221.8i −0.186488 + 0.107669i
\(377\) 120599. 0.848519
\(378\) 102576. 80758.0i 0.717900 0.565200i
\(379\) 98527.5 0.685929 0.342964 0.939348i \(-0.388569\pi\)
0.342964 + 0.939348i \(0.388569\pi\)
\(380\) 0 0
\(381\) −51846.3 29933.5i −0.357164 0.206209i
\(382\) 2948.87 + 1702.53i 0.0202083 + 0.0116673i
\(383\) 2571.67 + 4454.26i 0.0175314 + 0.0303653i 0.874658 0.484741i \(-0.161086\pi\)
−0.857127 + 0.515106i \(0.827753\pi\)
\(384\) 21713.8i 0.147256i
\(385\) 0 0
\(386\) 145135. 0.974086
\(387\) −301275. + 173941.i −2.01160 + 1.16140i
\(388\) 22488.9 38951.9i 0.149384 0.258741i
\(389\) 43141.0 74722.4i 0.285096 0.493801i −0.687537 0.726150i \(-0.741308\pi\)
0.972632 + 0.232349i \(0.0746412\pi\)
\(390\) 0 0
\(391\) 47171.9i 0.308553i
\(392\) −15363.2 52110.9i −0.0999792 0.339123i
\(393\) 303256.i 1.96347i
\(394\) −2059.48 3567.13i −0.0132668 0.0229788i
\(395\) 0 0
\(396\) 25296.0 43813.9i 0.161310 0.279397i
\(397\) −77963.1 135036.i −0.494661 0.856778i 0.505320 0.862932i \(-0.331375\pi\)
−0.999981 + 0.00615368i \(0.998041\pi\)
\(398\) −194478. −1.22773
\(399\) −47186.2 326915.i −0.296394 2.05347i
\(400\) 0 0
\(401\) −17307.2 29977.0i −0.107631 0.186423i 0.807179 0.590307i \(-0.200993\pi\)
−0.914810 + 0.403884i \(0.867660\pi\)
\(402\) 154070. 266857.i 0.953381 1.65130i
\(403\) 146285. + 84457.5i 0.900718 + 0.520030i
\(404\) −45625.7 + 26342.0i −0.279542 + 0.161393i
\(405\) 0 0
\(406\) −80812.5 + 63623.3i −0.490260 + 0.385980i
\(407\) 43384.7i 0.261907i
\(408\) −31802.4 + 18361.1i −0.191047 + 0.110301i
\(409\) 271749. + 156894.i 1.62450 + 0.937907i 0.985695 + 0.168542i \(0.0539058\pi\)
0.638809 + 0.769366i \(0.279428\pi\)
\(410\) 0 0
\(411\) 325382. 187859.i 1.92624 1.11211i
\(412\) −12196.0 −0.0718492
\(413\) −194968. 77929.4i −1.14304 0.456879i
\(414\) −177290. −1.03439
\(415\) 0 0
\(416\) 25475.8 + 14708.4i 0.147211 + 0.0849924i
\(417\) −260615. 150466.i −1.49875 0.865301i
\(418\) −27955.9 48421.0i −0.160000 0.277128i
\(419\) 7324.74i 0.0417219i −0.999782 0.0208609i \(-0.993359\pi\)
0.999782 0.0208609i \(-0.00664073\pi\)
\(420\) 0 0
\(421\) −25178.3 −0.142057 −0.0710285 0.997474i \(-0.522628\pi\)
−0.0710285 + 0.997474i \(0.522628\pi\)
\(422\) −1525.59 + 880.802i −0.00856671 + 0.00494599i
\(423\) −96752.0 + 167579.i −0.540728 + 0.936569i
\(424\) −40347.0 + 69883.0i −0.224429 + 0.388723i
\(425\) 0 0
\(426\) 253940.i 1.39930i
\(427\) −53772.6 + 42334.9i −0.294920 + 0.232190i
\(428\) 84853.0i 0.463212i
\(429\) 53570.3 + 92786.6i 0.291078 + 0.504162i
\(430\) 0 0
\(431\) −6913.59 + 11974.7i −0.0372176 + 0.0644629i −0.884034 0.467422i \(-0.845183\pi\)
0.846817 + 0.531885i \(0.178516\pi\)
\(432\) −30143.4 52209.9i −0.161519 0.279760i
\(433\) 47438.8 0.253022 0.126511 0.991965i \(-0.459622\pi\)
0.126511 + 0.991965i \(0.459622\pi\)
\(434\) −142580. + 20579.7i −0.756973 + 0.109260i
\(435\) 0 0
\(436\) 55809.1 + 96664.1i 0.293584 + 0.508502i
\(437\) −97966.0 + 169682.i −0.512994 + 0.888532i
\(438\) −21210.1 12245.7i −0.110559 0.0638314i
\(439\) −95101.7 + 54907.0i −0.493469 + 0.284904i −0.726012 0.687682i \(-0.758628\pi\)
0.232544 + 0.972586i \(0.425295\pi\)
\(440\) 0 0
\(441\) −250181. 238024.i −1.28640 1.22389i
\(442\) 49749.7i 0.254651i
\(443\) 71499.7 41280.4i 0.364331 0.210347i −0.306648 0.951823i \(-0.599207\pi\)
0.670979 + 0.741476i \(0.265874\pi\)
\(444\) 102498. + 59177.3i 0.519936 + 0.300185i
\(445\) 0 0
\(446\) −28193.0 + 16277.2i −0.141733 + 0.0818297i
\(447\) 640367. 3.20490
\(448\) −24830.7 + 3584.00i −0.123718 + 0.0178571i
\(449\) 330438. 1.63907 0.819534 0.573030i \(-0.194232\pi\)
0.819534 + 0.573030i \(0.194232\pi\)
\(450\) 0 0
\(451\) −43551.5 25144.5i −0.214116 0.123620i
\(452\) 61046.4 + 35245.2i 0.298802 + 0.172513i
\(453\) −221969. 384461.i −1.08167 1.87351i
\(454\) 159430.i 0.773499i
\(455\) 0 0
\(456\) −152529. −0.733537
\(457\) −323276. + 186644.i −1.54789 + 0.893677i −0.549591 + 0.835434i \(0.685217\pi\)
−0.998302 + 0.0582431i \(0.981450\pi\)
\(458\) 59578.7 103193.i 0.284027 0.491950i
\(459\) −50978.3 + 88297.0i −0.241969 + 0.419103i
\(460\) 0 0
\(461\) 20355.2i 0.0957798i 0.998853 + 0.0478899i \(0.0152497\pi\)
−0.998853 + 0.0478899i \(0.984750\pi\)
\(462\) −84847.5 33913.9i −0.397517 0.158889i
\(463\) 31552.7i 0.147189i 0.997288 + 0.0735944i \(0.0234470\pi\)
−0.997288 + 0.0735944i \(0.976553\pi\)
\(464\) 23747.8 + 41132.3i 0.110303 + 0.191050i
\(465\) 0 0
\(466\) 77925.8 134971.i 0.358847 0.621541i
\(467\) −120927. 209452.i −0.554486 0.960397i −0.997943 0.0641019i \(-0.979582\pi\)
0.443458 0.896295i \(-0.353752\pi\)
\(468\) 186978. 0.853689
\(469\) −330593. 132139.i −1.50296 0.600740i
\(470\) 0 0
\(471\) −91741.9 158902.i −0.413548 0.716286i
\(472\) −48479.3 + 83968.7i −0.217607 + 0.376906i
\(473\) 92107.8 + 53178.5i 0.411694 + 0.237691i
\(474\) 115555. 66715.4i 0.514316 0.296941i
\(475\) 0 0
\(476\) 26245.9 + 33336.8i 0.115837 + 0.147133i
\(477\) 512903.i 2.25423i
\(478\) −56540.3 + 32643.5i −0.247458 + 0.142870i
\(479\) −235631. 136042.i −1.02698 0.592926i −0.110861 0.993836i \(-0.535361\pi\)
−0.916117 + 0.400910i \(0.868694\pi\)
\(480\) 0 0
\(481\) −138860. + 80170.8i −0.600187 + 0.346518i
\(482\) 230722. 0.993104
\(483\) 45743.4 + 316920.i 0.196080 + 1.35848i
\(484\) 101661. 0.433973
\(485\) 0 0
\(486\) 96015.0 + 55434.3i 0.406506 + 0.234696i
\(487\) 353119. + 203873.i 1.48889 + 0.859611i 0.999919 0.0126891i \(-0.00403916\pi\)
0.488971 + 0.872300i \(0.337372\pi\)
\(488\) 15801.7 + 27369.4i 0.0663537 + 0.114928i
\(489\) 322840.i 1.35011i
\(490\) 0 0
\(491\) −286772. −1.18953 −0.594763 0.803901i \(-0.702754\pi\)
−0.594763 + 0.803901i \(0.702754\pi\)
\(492\) −118810. + 68594.8i −0.490819 + 0.283375i
\(493\) 40162.1 69562.8i 0.165243 0.286209i
\(494\) 103320. 178955.i 0.423378 0.733313i
\(495\) 0 0
\(496\) 66523.7i 0.270404i
\(497\) 290391. 41914.3i 1.17563 0.169687i
\(498\) 200596.i 0.808843i
\(499\) 175718. + 304352.i 0.705690 + 1.22229i 0.966442 + 0.256886i \(0.0826964\pi\)
−0.260751 + 0.965406i \(0.583970\pi\)
\(500\) 0 0
\(501\) −124293. + 215282.i −0.495189 + 0.857693i
\(502\) 38477.3 + 66644.7i 0.152685 + 0.264459i
\(503\) 116045. 0.458660 0.229330 0.973349i \(-0.426347\pi\)
0.229330 + 0.973349i \(0.426347\pi\)
\(504\) −125293. + 98642.3i −0.493247 + 0.388331i
\(505\) 0 0
\(506\) 27101.1 + 46940.5i 0.105849 + 0.183335i
\(507\) 16137.6 27951.1i 0.0627802 0.108738i
\(508\) 27662.2 + 15970.8i 0.107191 + 0.0618870i
\(509\) −72030.7 + 41586.9i −0.278024 + 0.160517i −0.632528 0.774537i \(-0.717983\pi\)
0.354505 + 0.935054i \(0.384649\pi\)
\(510\) 0 0
\(511\) −10502.6 + 26275.9i −0.0402212 + 0.100627i
\(512\) 11585.2i 0.0441942i
\(513\) −366749. + 211742.i −1.39359 + 0.804587i
\(514\) 264371. + 152635.i 1.00066 + 0.577733i
\(515\) 0 0
\(516\) 251273. 145072.i 0.943725 0.544860i
\(517\) 59159.2 0.221330
\(518\) 50753.9 126979.i 0.189151 0.473229i
\(519\) −605508. −2.24794
\(520\) 0 0
\(521\) 174948. + 101006.i 0.644517 + 0.372112i 0.786352 0.617778i \(-0.211967\pi\)
−0.141835 + 0.989890i \(0.545300\pi\)
\(522\) 261444. + 150945.i 0.959482 + 0.553957i
\(523\) 13933.8 + 24134.0i 0.0509408 + 0.0882321i 0.890371 0.455235i \(-0.150445\pi\)
−0.839431 + 0.543467i \(0.817111\pi\)
\(524\) 161800.i 0.589272i
\(525\) 0 0
\(526\) −113545. −0.410389
\(527\) 97431.8 56252.3i 0.350816 0.202544i
\(528\) −21097.6 + 36542.1i −0.0756772 + 0.131077i
\(529\) −44949.9 + 77855.5i −0.160626 + 0.278213i
\(530\) 0 0
\(531\) 616284.i 2.18571i
\(532\) 25175.8 + 174423.i 0.0889530 + 0.616284i
\(533\) 185858.i 0.654226i
\(534\) 17767.8 + 30774.7i 0.0623089 + 0.107922i
\(535\) 0 0
\(536\) −82203.0 + 142380.i −0.286126 + 0.495586i
\(537\) −401050. 694640.i −1.39075 2.40886i
\(538\) −297985. −1.02951
\(539\) −24777.4 + 102625.i −0.0852861 + 0.353243i
\(540\) 0 0
\(541\) 18996.8 + 32903.4i 0.0649062 + 0.112421i 0.896652 0.442735i \(-0.145992\pi\)
−0.831746 + 0.555156i \(0.812659\pi\)
\(542\) −21538.0 + 37305.0i −0.0733175 + 0.126990i
\(543\) 703829. + 406356.i 2.38708 + 1.37818i
\(544\) 16967.9 9796.44i 0.0573365 0.0331032i
\(545\) 0 0
\(546\) −48243.1 334238.i −0.161827 1.12117i
\(547\) 360160.i 1.20371i 0.798606 + 0.601854i \(0.205571\pi\)
−0.798606 + 0.601854i \(0.794429\pi\)
\(548\) −173605. + 100231.i −0.578098 + 0.333765i
\(549\) 173964. + 100438.i 0.577185 + 0.333238i
\(550\) 0 0
\(551\) 288934. 166816.i 0.951691 0.549459i
\(552\) 147865. 0.485274
\(553\) −95365.1 121130.i −0.311845 0.396097i
\(554\) 27921.1 0.0909732
\(555\) 0 0
\(556\) 139049. + 80280.2i 0.449800 + 0.259692i
\(557\) −268938. 155272.i −0.866847 0.500474i −0.000547960 1.00000i \(-0.500174\pi\)
−0.866299 + 0.499525i \(0.833508\pi\)
\(558\) 211418. + 366186.i 0.679004 + 1.17607i
\(559\) 393075.i 1.25792i
\(560\) 0 0
\(561\) 71360.2 0.226741
\(562\) −379958. + 219369.i −1.20299 + 0.694548i
\(563\) 8344.68 14453.4i 0.0263265 0.0455988i −0.852562 0.522626i \(-0.824952\pi\)
0.878888 + 0.477027i \(0.158286\pi\)
\(564\) 80694.0 139766.i 0.253678 0.439383i
\(565\) 0 0
\(566\) 310171.i 0.968207i
\(567\) −45002.0 + 112588.i −0.139980 + 0.350209i
\(568\) 135488.i 0.419955i
\(569\) −65131.1 112810.i −0.201170 0.348437i 0.747736 0.663997i \(-0.231141\pi\)
−0.948906 + 0.315560i \(0.897808\pi\)
\(570\) 0 0
\(571\) 249119. 431487.i 0.764073 1.32341i −0.176662 0.984272i \(-0.556530\pi\)
0.940735 0.339142i \(-0.110137\pi\)
\(572\) −28582.1 49505.6i −0.0873578 0.151308i
\(573\) −18051.0 −0.0549784
\(574\) 98051.5 + 124542.i 0.297598 + 0.378000i
\(575\) 0 0
\(576\) 36818.8 + 63772.0i 0.110975 + 0.192214i
\(577\) 16858.1 29199.1i 0.0506357 0.0877035i −0.839597 0.543210i \(-0.817209\pi\)
0.890232 + 0.455507i \(0.150542\pi\)
\(578\) 175888. + 101549.i 0.526478 + 0.303962i
\(579\) −666313. + 384696.i −1.98756 + 1.14752i
\(580\) 0 0
\(581\) 229391. 33109.7i 0.679554 0.0980851i
\(582\) 238437.i 0.703928i
\(583\) 135800. 78404.0i 0.399541 0.230675i
\(584\) 11316.5 + 6533.58i 0.0331808 + 0.0191569i
\(585\) 0 0
\(586\) 220240. 127155.i 0.641357 0.370288i
\(587\) −356809. −1.03552 −0.517762 0.855525i \(-0.673235\pi\)
−0.517762 + 0.855525i \(0.673235\pi\)
\(588\) 208658. + 198519.i 0.603504 + 0.574179i
\(589\) 467296. 1.34698
\(590\) 0 0
\(591\) 18910.1 + 10917.8i 0.0541402 + 0.0312579i
\(592\) −54687.1 31573.6i −0.156042 0.0900909i
\(593\) 16669.6 + 28872.6i 0.0474041 + 0.0821063i 0.888754 0.458385i \(-0.151572\pi\)
−0.841350 + 0.540491i \(0.818238\pi\)
\(594\) 117152.i 0.332029i
\(595\) 0 0
\(596\) −341663. −0.961846
\(597\) 892844. 515484.i 2.50511 1.44633i
\(598\) −100160. + 173483.i −0.280088 + 0.485126i
\(599\) 162165. 280878.i 0.451963 0.782824i −0.546545 0.837430i \(-0.684057\pi\)
0.998508 + 0.0546064i \(0.0173904\pi\)
\(600\) 0 0
\(601\) 66322.0i 0.183615i 0.995777 + 0.0918076i \(0.0292645\pi\)
−0.995777 + 0.0918076i \(0.970736\pi\)
\(602\) −207371. 263396.i −0.572209 0.726803i
\(603\) 1.04499e6i 2.87394i
\(604\) 118430. + 205126.i 0.324629 + 0.562274i
\(605\) 0 0
\(606\) 139645. 241872.i 0.380259 0.658628i
\(607\) −243828. 422322.i −0.661768 1.14622i −0.980151 0.198253i \(-0.936473\pi\)
0.318383 0.947962i \(-0.396860\pi\)
\(608\) 81380.6 0.220147
\(609\) 202369. 506297.i 0.545643 1.36512i
\(610\) 0 0
\(611\) 109321. + 189349.i 0.292833 + 0.507201i
\(612\) 62267.7 107851.i 0.166249 0.287952i
\(613\) −295757. 170755.i −0.787070 0.454415i 0.0518597 0.998654i \(-0.483485\pi\)
−0.838930 + 0.544239i \(0.816818\pi\)
\(614\) −347047. + 200368.i −0.920558 + 0.531484i
\(615\) 0 0
\(616\) 45269.8 + 18094.5i 0.119302 + 0.0476854i
\(617\) 240873.i 0.632728i 0.948638 + 0.316364i \(0.102462\pi\)
−0.948638 + 0.316364i \(0.897538\pi\)
\(618\) 55991.6 32326.8i 0.146604 0.0846419i
\(619\) 133658. + 77167.4i 0.348830 + 0.201397i 0.664170 0.747582i \(-0.268785\pi\)
−0.315340 + 0.948979i \(0.602119\pi\)
\(620\) 0 0
\(621\) 355535. 205268.i 0.921932 0.532278i
\(622\) −242242. −0.626137
\(623\) 32259.5 25397.8i 0.0831154 0.0654364i
\(624\) −155945. −0.400501
\(625\) 0 0
\(626\) −43678.2 25217.6i −0.111459 0.0643510i
\(627\) 256690. + 148200.i 0.652941 + 0.376976i
\(628\) 48948.2 + 84780.8i 0.124113 + 0.214970i
\(629\) 106794.i 0.269927i
\(630\) 0 0
\(631\) 220248. 0.553164 0.276582 0.960990i \(-0.410798\pi\)
0.276582 + 0.960990i \(0.410798\pi\)
\(632\) −61653.3 + 35595.5i −0.154355 + 0.0891172i
\(633\) 4669.32 8087.50i 0.0116532 0.0201840i
\(634\) 114276. 197932.i 0.284299 0.492421i
\(635\) 0 0
\(636\) 427776.i 1.05755i
\(637\) −374253. + 110336.i −0.922331 + 0.271919i
\(638\) 92295.4i 0.226745i
\(639\) −430590. 745804.i −1.05454 1.82651i
\(640\) 0 0
\(641\) 340604. 589943.i 0.828960 1.43580i −0.0698947 0.997554i \(-0.522266\pi\)
0.898855 0.438247i \(-0.144400\pi\)
\(642\) 224912. + 389559.i 0.545686 + 0.945156i
\(643\) 572102. 1.38373 0.691865 0.722027i \(-0.256789\pi\)
0.691865 + 0.722027i \(0.256789\pi\)
\(644\) −24406.1 169090.i −0.0588472 0.407705i
\(645\) 0 0
\(646\) −68815.2 119191.i −0.164899 0.285614i
\(647\) 303637. 525915.i 0.725348 1.25634i −0.233482 0.972361i \(-0.575012\pi\)
0.958830 0.283979i \(-0.0916547\pi\)
\(648\) 48489.5 + 27995.4i 0.115478 + 0.0666710i
\(649\) 163171. 94207.1i 0.387396 0.223663i
\(650\) 0 0
\(651\) 600037. 472407.i 1.41585 1.11469i
\(652\) 172249.i 0.405193i
\(653\) 419737. 242335.i 0.984353 0.568316i 0.0807713 0.996733i \(-0.474262\pi\)
0.903581 + 0.428416i \(0.140928\pi\)
\(654\) −512438. 295856.i −1.19808 0.691711i
\(655\) 0 0
\(656\) 63390.0 36598.3i 0.147304 0.0850458i
\(657\) 83057.0 0.192418
\(658\) −173148. 69207.8i −0.399912 0.159847i
\(659\) −329627. −0.759017 −0.379509 0.925188i \(-0.623907\pi\)
−0.379509 + 0.925188i \(0.623907\pi\)
\(660\) 0 0
\(661\) −182392. 105304.i −0.417449 0.241014i 0.276536 0.961003i \(-0.410813\pi\)
−0.693985 + 0.719989i \(0.744147\pi\)
\(662\) −178333. 102961.i −0.406927 0.234939i
\(663\) 131867. + 228400.i 0.299991 + 0.519600i
\(664\) 107027.i 0.242748i
\(665\) 0 0
\(666\) −401374. −0.904899
\(667\) −280100. + 161716.i −0.629595 + 0.363497i
\(668\) 66315.7 114862.i 0.148615 0.257409i
\(669\) 86289.2 149457.i 0.192799 0.333937i
\(670\) 0 0
\(671\) 61413.2i 0.136401i
\(672\) 104498. 82270.5i 0.231402 0.182182i
\(673\) 94709.8i 0.209105i −0.994519 0.104553i \(-0.966659\pi\)
0.994519 0.104553i \(-0.0333411\pi\)
\(674\) 178951. + 309952.i 0.393926 + 0.682300i
\(675\) 0 0
\(676\) −8610.09 + 14913.1i −0.0188414 + 0.0326343i
\(677\) 269276. + 466400.i 0.587517 + 1.01761i 0.994556 + 0.104199i \(0.0332278\pi\)
−0.407039 + 0.913411i \(0.633439\pi\)
\(678\) −373685. −0.812917
\(679\) 272664. 39355.6i 0.591408 0.0853625i
\(680\) 0 0
\(681\) 422588. + 731944.i 0.911219 + 1.57828i
\(682\) 64635.9 111953.i 0.138965 0.240694i
\(683\) −111779. 64535.9i −0.239618 0.138344i 0.375383 0.926870i \(-0.377511\pi\)
−0.615001 + 0.788526i \(0.710845\pi\)
\(684\) 447967. 258634.i 0.957489 0.552806i
\(685\) 0 0
\(686\) 192575. 271377.i 0.409215 0.576666i
\(687\) 631680.i 1.33839i
\(688\) −134065. + 77402.3i −0.283229 + 0.163522i
\(689\) 501890. + 289766.i 1.05723 + 0.610393i
\(690\) 0 0
\(691\) 113201. 65356.6i 0.237079 0.136878i −0.376754 0.926313i \(-0.622960\pi\)
0.613834 + 0.789435i \(0.289627\pi\)
\(692\) 323064. 0.674648
\(693\) 306697. 44268.0i 0.638622 0.0921771i
\(694\) 189361. 0.393162
\(695\) 0 0
\(696\) −218052. 125892.i −0.450133 0.259884i
\(697\) −107205. 61894.8i −0.220673 0.127406i
\(698\) 36101.3 + 62529.3i 0.0740989 + 0.128343i
\(699\) 826204.i 1.69096i
\(700\) 0 0
\(701\) −182501. −0.371389 −0.185694 0.982608i \(-0.559453\pi\)
−0.185694 + 0.982608i \(0.559453\pi\)
\(702\) −374964. + 216485.i −0.760878 + 0.439293i
\(703\) −221789. + 384150.i −0.448776 + 0.777302i
\(704\) 11256.5 19496.8i 0.0227121 0.0393385i
\(705\) 0 0
\(706\) 160020.i 0.321044i
\(707\) −299640. 119767.i −0.599462 0.239607i
\(708\) 513999.i 1.02541i
\(709\) 406899. + 704770.i 0.809458 + 1.40202i 0.913240 + 0.407422i \(0.133572\pi\)
−0.103783 + 0.994600i \(0.533095\pi\)
\(710\) 0 0
\(711\) −226251. + 391878.i −0.447560 + 0.775196i
\(712\) −9479.86 16419.6i −0.0187000 0.0323894i
\(713\) −453008. −0.891101
\(714\) −208858. 83481.3i −0.409689 0.163754i
\(715\) 0 0
\(716\) 213978. + 370620.i 0.417390 + 0.722941i
\(717\) 173051. 299732.i 0.336616 0.583036i
\(718\) 92602.4 + 53464.0i 0.179628 + 0.103708i
\(719\) 364222. 210283.i 0.704544 0.406769i −0.104494 0.994526i \(-0.533322\pi\)
0.809038 + 0.587757i \(0.199989\pi\)
\(720\) 0 0
\(721\) −46208.9 58693.1i −0.0888904 0.112906i
\(722\) 203055.i 0.389528i
\(723\) −1.05924e6 + 611554.i −2.02637 + 1.16992i
\(724\) −375523. 216808.i −0.716406 0.413617i
\(725\) 0 0
\(726\) −466723. + 269463.i −0.885495 + 0.511241i
\(727\) −172948. −0.327225 −0.163613 0.986525i \(-0.552315\pi\)
−0.163613 + 0.986525i \(0.552315\pi\)
\(728\) 25739.8 + 178330.i 0.0485671 + 0.336483i
\(729\) −788171. −1.48308
\(730\) 0 0
\(731\) 226729. + 130902.i 0.424300 + 0.244970i
\(732\) −145091. 83768.5i −0.270782 0.156336i
\(733\) −65780.9 113936.i −0.122431 0.212057i 0.798295 0.602267i \(-0.205736\pi\)
−0.920726 + 0.390210i \(0.872402\pi\)
\(734\) 30593.4i 0.0567852i
\(735\) 0 0
\(736\) −78892.3 −0.145639
\(737\) 276678. 159740.i 0.509378 0.294090i
\(738\) 232624. 402917.i 0.427112 0.739780i
\(739\) −244884. + 424151.i −0.448406 + 0.776662i −0.998282 0.0585842i \(-0.981341\pi\)
0.549877 + 0.835246i \(0.314675\pi\)
\(740\) 0 0
\(741\) 1.09544e6i 1.99504i
\(742\) −489181. + 70607.2i −0.888509 + 0.128245i
\(743\) 580258.i 1.05110i −0.850763 0.525549i \(-0.823860\pi\)
0.850763 0.525549i \(-0.176140\pi\)
\(744\) −176328. 305410.i −0.318549 0.551743i
\(745\) 0 0
\(746\) 43873.7 75991.5i 0.0788364 0.136549i
\(747\) −340139. 589139.i −0.609559 1.05579i
\(748\) −38073.7 −0.0680491
\(749\) 408355. 321496.i 0.727904 0.573076i
\(750\) 0 0
\(751\) −218698. 378797.i −0.387763 0.671624i 0.604386 0.796692i \(-0.293419\pi\)
−0.992148 + 0.125067i \(0.960085\pi\)
\(752\) −43053.7 + 74571.2i −0.0761333 + 0.131867i
\(753\) −353298. 203977.i −0.623091 0.359742i
\(754\) 295407. 170553.i 0.519610 0.299997i
\(755\) 0 0
\(756\) 137051. 342881.i 0.239794 0.599929i
\(757\) 24171.7i 0.0421809i −0.999778 0.0210905i \(-0.993286\pi\)
0.999778 0.0210905i \(-0.00671380\pi\)
\(758\) 241342. 139339.i 0.420044 0.242512i
\(759\) −248842. 143669.i −0.431956 0.249390i
\(760\) 0 0
\(761\) −561376. + 324111.i −0.969359 + 0.559659i −0.899041 0.437865i \(-0.855735\pi\)
−0.0703180 + 0.997525i \(0.522401\pi\)
\(762\) −169329. −0.291624
\(763\) −253743. + 634828.i −0.435859 + 1.09045i
\(764\) 9630.98 0.0165000
\(765\) 0 0
\(766\) 12598.5 + 7273.77i 0.0214715 + 0.0123966i
\(767\) 603051. + 348172.i 1.02509 + 0.591838i
\(768\) −30707.9 53187.7i −0.0520629 0.0901756i
\(769\) 179564.i 0.303646i 0.988408 + 0.151823i \(0.0485143\pi\)
−0.988408 + 0.151823i \(0.951486\pi\)
\(770\) 0 0
\(771\) −1.61830e6 −2.72239
\(772\) 355506. 205252.i 0.596503 0.344391i
\(773\) 305457. 529068.i 0.511201 0.885426i −0.488715 0.872444i \(-0.662534\pi\)
0.999916 0.0129823i \(-0.00413252\pi\)
\(774\) −491981. + 852136.i −0.821233 + 1.42242i
\(775\) 0 0
\(776\) 127216.i 0.211261i
\(777\) 103560. + 717486.i 0.171534 + 1.18842i
\(778\) 244042.i 0.403186i
\(779\) −257085. 445284.i −0.423644 0.733773i
\(780\) 0 0
\(781\) −131643. + 228012.i −0.215821 + 0.373814i
\(782\) 66711.1 + 115547.i 0.109090 + 0.188949i
\(783\) −699061. −1.14023
\(784\) −111328. 105918.i −0.181122 0.172321i
\(785\) 0 0
\(786\) −428868. 742822.i −0.694191 1.20237i
\(787\) −595774. + 1.03191e6i −0.961905 + 1.66607i −0.244195 + 0.969726i \(0.578524\pi\)
−0.717710 + 0.696342i \(0.754810\pi\)
\(788\) −10089.4 5825.10i −0.0162484 0.00938104i
\(789\) 521282. 300963.i 0.837373 0.483458i
\(790\) 0 0
\(791\) 61679.1 + 427325.i 0.0985791 + 0.682976i
\(792\) 143096.i 0.228127i
\(793\) 196563. 113486.i 0.312576 0.180466i
\(794\) −381939. 220513.i −0.605834 0.349778i
\(795\) 0 0
\(796\) −476371. + 275033.i −0.751829 + 0.434069i
\(797\) 900495. 1.41764 0.708818 0.705392i \(-0.249229\pi\)
0.708818 + 0.705392i \(0.249229\pi\)
\(798\) −577910. 734044.i −0.907516 1.15270i
\(799\) 145624. 0.228108
\(800\) 0 0
\(801\) −104366. 60255.5i −0.162664 0.0939142i
\(802\) −84787.8 48952.2i −0.131821 0.0761069i
\(803\) −12696.3 21990.7i −0.0196901 0.0341042i
\(804\) 871552.i 1.34828i
\(805\) 0 0
\(806\) 477764. 0.735433
\(807\) 1.36805e6 789843.i 2.10065 1.21281i
\(808\) −74506.4 + 129049.i −0.114122 + 0.197666i
\(809\) 277882. 481306.i 0.424584 0.735401i −0.571798 0.820395i \(-0.693754\pi\)
0.996381 + 0.0849939i \(0.0270871\pi\)
\(810\) 0 0
\(811\) 70954.2i 0.107879i 0.998544 + 0.0539395i \(0.0171778\pi\)
−0.998544 + 0.0539395i \(0.982822\pi\)
\(812\) −107972. + 270131.i −0.163757 + 0.409696i
\(813\) 228356.i 0.345486i
\(814\) 61355.2 + 106270.i 0.0925982 + 0.160385i
\(815\) 0 0
\(816\) −51933.1 + 89950.8i −0.0779945 + 0.135090i
\(817\) 543713. + 941738.i 0.814564 + 1.41087i
\(818\) 887527. 1.32640
\(819\) 708435. + 899833.i 1.05617 + 1.34151i
\(820\) 0 0
\(821\) 312356. + 541016.i 0.463408 + 0.802646i 0.999128 0.0417495i \(-0.0132931\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(822\) 531346. 920319.i 0.786383 1.36206i
\(823\) −181916. 105029.i −0.268579 0.155064i 0.359663 0.933082i \(-0.382892\pi\)
−0.628242 + 0.778018i \(0.716225\pi\)
\(824\) −29873.9 + 17247.7i −0.0439985 + 0.0254025i
\(825\) 0 0
\(826\) −587781. + 84838.8i −0.861500 + 0.124347i
\(827\) 880910.i 1.28801i −0.765020 0.644007i \(-0.777271\pi\)
0.765020 0.644007i \(-0.222729\pi\)
\(828\) −434270. + 250726.i −0.633431 + 0.365711i
\(829\) 1.11951e6 + 646349.i 1.62899 + 0.940498i 0.984395 + 0.175974i \(0.0563075\pi\)
0.644595 + 0.764524i \(0.277026\pi\)
\(830\) 0 0
\(831\) −128186. + 74008.1i −0.185625 + 0.107171i
\(832\) 83203.5 0.120197
\(833\) −60991.2 + 252617.i −0.0878977 + 0.364060i
\(834\) −851166. −1.22372
\(835\) 0 0
\(836\) −136955. 79071.1i −0.195959 0.113137i
\(837\) −847948. 489563.i −1.21037 0.698808i
\(838\) −10358.7 17941.9i −0.0147509 0.0255493i
\(839\) 1.11586e6i 1.58520i −0.609741 0.792601i \(-0.708726\pi\)
0.609741 0.792601i \(-0.291274\pi\)
\(840\) 0 0
\(841\) −156542. −0.221330
\(842\) −61674.1 + 35607.5i −0.0869918 + 0.0502247i
\(843\) 1.16292e6 2.01424e6i 1.63642 2.83437i
\(844\) −2491.28 + 4315.03i −0.00349734 + 0.00605758i
\(845\) 0 0
\(846\) 547312.i 0.764705i
\(847\) 385178. + 489242.i 0.536902 + 0.681957i
\(848\) 228237.i 0.317391i
\(849\) −822142. 1.42399e6i −1.14059 1.97557i
\(850\) 0 0
\(851\) 215008. 372404.i 0.296889 0.514228i
\(852\) 359125. + 622022.i 0.494728 + 0.856893i
\(853\) −1.28959e6 −1.77236 −0.886180 0.463341i \(-0.846650\pi\)
−0.886180 + 0.463341i \(0.846650\pi\)
\(854\) −71844.7 + 179745.i −0.0985097 + 0.246457i
\(855\) 0 0
\(856\) −120000. 207847.i −0.163770 0.283658i
\(857\) 327273. 566854.i 0.445604 0.771809i −0.552490 0.833519i \(-0.686322\pi\)
0.998094 + 0.0617109i \(0.0196557\pi\)
\(858\) 262440. + 151520.i 0.356497 + 0.205823i
\(859\) −211796. + 122281.i −0.287033 + 0.165718i −0.636603 0.771192i \(-0.719661\pi\)
0.349570 + 0.936910i \(0.386328\pi\)
\(860\) 0 0
\(861\) −780266. 311875.i −1.05253 0.420702i
\(862\) 39109.2i 0.0526337i
\(863\) 402942. 232638.i 0.541029 0.312363i −0.204467 0.978873i \(-0.565546\pi\)
0.745496 + 0.666510i \(0.232213\pi\)
\(864\) −147672. 85258.4i −0.197820 0.114211i
\(865\) 0 0
\(866\) 116201. 67088.6i 0.154944 0.0894567i
\(867\) −1.07667e6 −1.43233
\(868\) −320145. + 252049.i −0.424921 + 0.334538i
\(869\) 138342. 0.183195
\(870\) 0 0
\(871\) 1.02255e6 + 590370.i 1.34787 + 0.778194i
\(872\) 273407. + 157852.i 0.359565 + 0.207595i
\(873\) −404304. 700275.i −0.530493 0.918840i
\(874\) 554179.i 0.725484i
\(875\) 0 0
\(876\) −69271.9 −0.0902712
\(877\) 263420. 152086.i 0.342492 0.197738i −0.318882 0.947795i \(-0.603307\pi\)
0.661373 + 0.750057i \(0.269974\pi\)
\(878\) −155301. + 268988.i −0.201458 + 0.348935i
\(879\) −674078. + 1.16754e6i −0.872434 + 1.51110i
\(880\) 0 0
\(881\) 697876.i 0.899138i −0.893246 0.449569i \(-0.851578\pi\)
0.893246 0.449569i \(-0.148422\pi\)
\(882\) −949432. 229228.i −1.22047 0.294667i
\(883\) 891773.i 1.14375i −0.820339 0.571877i \(-0.806215\pi\)
0.820339 0.571877i \(-0.193785\pi\)
\(884\) −70356.6 121861.i −0.0900328 0.155941i
\(885\) 0 0
\(886\) 116758. 202232.i 0.148738 0.257621i
\(887\) −631278. 1.09340e6i −0.802367 1.38974i −0.918054 0.396455i \(-0.870240\pi\)
0.115687 0.993286i \(-0.463093\pi\)
\(888\) 334757. 0.424526
\(889\) 27948.9 + 193636.i 0.0353640 + 0.245009i
\(890\) 0 0
\(891\) −54401.9 94226.9i −0.0685265 0.118691i
\(892\) −46039.0 + 79741.8i −0.0578623 + 0.100220i
\(893\) 523826. + 302431.i 0.656877 + 0.379248i
\(894\) 1.56857e6 905616.i 1.96259 1.13310i
\(895\) 0 0
\(896\) −55754.0 + 43894.9i −0.0694480 + 0.0546761i
\(897\) 1.06195e6i 1.31983i
\(898\) 809404. 467310.i 1.00372 0.579498i
\(899\) 668036. + 385691.i 0.826572 + 0.477221i
\(900\) 0 0
\(901\) 334280. 192997.i 0.411776 0.237739i
\(902\) −142239. −0.174825
\(903\) 1.65020e6 + 659590.i 2.02377 + 0.808907i
\(904\) 199377. 0.243971
\(905\) 0 0
\(906\) −1.08742e6 627822.i −1.32477 0.764857i
\(907\) −824439. 475990.i −1.00218 0.578607i −0.0932848 0.995639i \(-0.529737\pi\)
−0.908891 + 0.417033i \(0.863070\pi\)
\(908\) −225469. 390523.i −0.273473 0.473669i
\(909\) 947149.i 1.14628i
\(910\) 0 0
\(911\) −743243. −0.895559 −0.447779 0.894144i \(-0.647785\pi\)
−0.447779 + 0.894144i \(0.647785\pi\)
\(912\) −373617. + 215708.i −0.449198 + 0.259344i
\(913\) −103989. + 180115.i −0.124752 + 0.216077i
\(914\) −527908. + 914363.i −0.631925 + 1.09453i
\(915\) 0 0
\(916\) 337028.i 0.401675i
\(917\) −778662. + 613038.i −0.925999 + 0.729035i
\(918\) 288377.i 0.342196i
\(919\) −262150. 454057.i −0.310398 0.537625i 0.668050 0.744116i \(-0.267129\pi\)
−0.978449 + 0.206491i \(0.933796\pi\)
\(920\) 0 0
\(921\) 1.06219e6 1.83977e6i 1.25223 2.16892i
\(922\) 28786.6 + 49859.9i 0.0338633 + 0.0586529i
\(923\) −973052. −1.14218
\(924\) −255795. + 36920.8i −0.299604 + 0.0432441i
\(925\) 0 0
\(926\) 44622.3 + 77288.1i 0.0520391 + 0.0901344i
\(927\) −109629. + 189883.i −0.127575 + 0.220967i
\(928\) 116340. + 67168.8i 0.135093 + 0.0779959i
\(929\) −848178. + 489696.i −0.982779 + 0.567408i −0.903108 0.429414i \(-0.858720\pi\)
−0.0796709 + 0.996821i \(0.525387\pi\)
\(930\) 0 0
\(931\) −744024. + 782024.i −0.858396 + 0.902237i
\(932\) 440815.i 0.507486i
\(933\) 1.11213e6 642090.i 1.27759 0.737620i
\(934\) −592420. 342034.i −0.679103 0.392081i
\(935\) 0 0
\(936\) 458001. 264427.i 0.522775 0.301824i
\(937\) −1.13988e6 −1.29831 −0.649155 0.760656i \(-0.724877\pi\)
−0.649155 + 0.760656i \(0.724877\pi\)
\(938\) −996658. + 143855.i −1.13277 + 0.163501i
\(939\) 267368. 0.303235
\(940\) 0 0
\(941\) 693791. + 400561.i 0.783519 + 0.452365i 0.837676 0.546167i \(-0.183914\pi\)
−0.0541569 + 0.998532i \(0.517247\pi\)
\(942\) −449441. 259485.i −0.506491 0.292422i
\(943\) 249224. + 431669.i 0.280264 + 0.485431i
\(944\) 274240.i 0.307743i
\(945\) 0 0
\(946\) 300823. 0.336146
\(947\) 589145. 340143.i 0.656935 0.379282i −0.134173 0.990958i \(-0.542838\pi\)
0.791108 + 0.611676i \(0.209504\pi\)
\(948\) 188700. 326838.i 0.209969 0.363677i
\(949\) 46923.3 81273.5i 0.0521022 0.0902436i
\(950\) 0 0
\(951\) 1.21160e6i 1.33967i
\(952\) 111435. + 44540.8i 0.122955 + 0.0491456i
\(953\) 394774.i 0.434673i 0.976097 + 0.217337i \(0.0697369\pi\)
−0.976097 + 0.217337i \(0.930263\pi\)
\(954\) 725355. + 1.25635e6i 0.796992 + 1.38043i
\(955\) 0 0
\(956\) −92329.9 + 159920.i −0.101024 + 0.174979i
\(957\) 244639. + 423727.i 0.267117 + 0.462660i
\(958\) −769567. −0.838524
\(959\) −1.14013e6 455714.i −1.23970 0.495513i
\(960\) 0 0
\(961\) 78449.9 + 135879.i 0.0849465 + 0.147132i
\(962\) −226757. + 392755.i −0.245025 + 0.424396i
\(963\) −1.32110e6 762740.i −1.42457 0.822478i
\(964\) 565151. 326290.i 0.608150 0.351115i
\(965\) 0 0
\(966\) 560240. + 711600.i 0.600371 + 0.762574i
\(967\) 604328.i 0.646279i −0.946351 0.323140i \(-0.895262\pi\)
0.946351 0.323140i \(-0.104738\pi\)
\(968\) 249017. 143770.i 0.265753 0.153433i
\(969\) 631860. + 364804.i 0.672935 + 0.388519i
\(970\) 0 0
\(971\) 657301. 379493.i 0.697149 0.402499i −0.109136 0.994027i \(-0.534808\pi\)
0.806285 + 0.591528i \(0.201475\pi\)
\(972\) 313584. 0.331910
\(973\) 140490. + 973346.i 0.148396 + 1.02811i
\(974\) 1.15328e6 1.21567
\(975\) 0 0
\(976\) 77412.4 + 44694.1i 0.0812664 + 0.0469192i
\(977\) −1.06104e6 612591.i −1.11158 0.641773i −0.172345 0.985037i \(-0.555134\pi\)
−0.939239 + 0.343263i \(0.888468\pi\)
\(978\) −456565. 790793.i −0.477337 0.826771i
\(979\) 36843.3i 0.0384409i
\(980\) 0 0
\(981\) 2.00666e6 2.08514
\(982\) −702446. + 405557.i −0.728434 + 0.420561i
\(983\) −600236. + 1.03964e6i −0.621177 + 1.07591i 0.368090 + 0.929790i \(0.380012\pi\)
−0.989267 + 0.146120i \(0.953322\pi\)
\(984\) −194015. + 336044.i −0.200376 + 0.347062i
\(985\) 0 0
\(986\) 227191.i 0.233689i
\(987\) 978362. 141214.i 1.00430 0.144959i
\(988\) 584464.i 0.598747i
\(989\) −527088. 912944.i −0.538878 0.933365i
\(990\) 0 0
\(991\) −904963. + 1.56744e6i −0.921475 + 1.59604i −0.124340 + 0.992240i \(0.539682\pi\)
−0.797134 + 0.603802i \(0.793652\pi\)
\(992\) 94078.7 + 162949.i 0.0956022 + 0.165588i
\(993\) 1.09164e6 1.10708
\(994\) 652034. 513344.i 0.659929 0.519560i
\(995\) 0 0
\(996\) 283686. + 491359.i 0.285969 + 0.495313i
\(997\) −374644. + 648903.i −0.376902 + 0.652814i −0.990610 0.136719i \(-0.956344\pi\)
0.613707 + 0.789534i \(0.289677\pi\)
\(998\) 860837. + 497004.i 0.864291 + 0.498998i
\(999\) 804909. 464715.i 0.806521 0.465645i
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 350.5.i.a.199.3 8
5.2 odd 4 350.5.k.a.101.2 4
5.3 odd 4 14.5.d.a.3.1 4
5.4 even 2 inner 350.5.i.a.199.2 8
7.5 odd 6 inner 350.5.i.a.299.2 8
15.8 even 4 126.5.n.a.73.2 4
20.3 even 4 112.5.s.b.17.2 4
35.3 even 12 98.5.b.b.97.3 4
35.12 even 12 350.5.k.a.201.2 4
35.13 even 4 98.5.d.a.31.1 4
35.18 odd 12 98.5.b.b.97.4 4
35.19 odd 6 inner 350.5.i.a.299.3 8
35.23 odd 12 98.5.d.a.19.1 4
35.33 even 12 14.5.d.a.5.1 yes 4
105.38 odd 12 882.5.c.b.685.2 4
105.53 even 12 882.5.c.b.685.1 4
105.68 odd 12 126.5.n.a.19.2 4
140.3 odd 12 784.5.c.b.97.4 4
140.103 odd 12 112.5.s.b.33.2 4
140.123 even 12 784.5.c.b.97.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.5.d.a.3.1 4 5.3 odd 4
14.5.d.a.5.1 yes 4 35.33 even 12
98.5.b.b.97.3 4 35.3 even 12
98.5.b.b.97.4 4 35.18 odd 12
98.5.d.a.19.1 4 35.23 odd 12
98.5.d.a.31.1 4 35.13 even 4
112.5.s.b.17.2 4 20.3 even 4
112.5.s.b.33.2 4 140.103 odd 12
126.5.n.a.19.2 4 105.68 odd 12
126.5.n.a.73.2 4 15.8 even 4
350.5.i.a.199.2 8 5.4 even 2 inner
350.5.i.a.199.3 8 1.1 even 1 trivial
350.5.i.a.299.2 8 7.5 odd 6 inner
350.5.i.a.299.3 8 35.19 odd 6 inner
350.5.k.a.101.2 4 5.2 odd 4
350.5.k.a.201.2 4 35.12 even 12
784.5.c.b.97.1 4 140.123 even 12
784.5.c.b.97.4 4 140.3 odd 12
882.5.c.b.685.1 4 105.53 even 12
882.5.c.b.685.2 4 105.38 odd 12