Properties

Label 320.6.f.d.289.1
Level $320$
Weight $6$
Character 320.289
Analytic conductor $51.323$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [320,6,Mod(289,320)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(320, 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("320.289");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.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: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 289.1
Character \(\chi\) \(=\) 320.289
Dual form 320.6.f.d.289.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-28.5405 q^{3} +(5.81388 + 55.5985i) q^{5} +92.3750i q^{7} +571.559 q^{9} +O(q^{10})\) \(q-28.5405 q^{3} +(5.81388 + 55.5985i) q^{5} +92.3750i q^{7} +571.559 q^{9} -541.547i q^{11} -782.810 q^{13} +(-165.931 - 1586.81i) q^{15} +1556.72i q^{17} -484.475i q^{19} -2636.43i q^{21} -1096.90i q^{23} +(-3057.40 + 646.487i) q^{25} -9377.22 q^{27} -597.650i q^{29} -8869.25 q^{31} +15456.0i q^{33} +(-5135.92 + 537.058i) q^{35} -13624.1 q^{37} +22341.8 q^{39} +14540.4 q^{41} -1828.39 q^{43} +(3322.98 + 31777.8i) q^{45} -17951.8i q^{47} +8273.86 q^{49} -44429.6i q^{51} +1650.99 q^{53} +(30109.3 - 3148.49i) q^{55} +13827.1i q^{57} +14453.6i q^{59} -24574.4i q^{61} +52797.7i q^{63} +(-4551.17 - 43523.1i) q^{65} +26842.8 q^{67} +31306.0i q^{69} -48050.6 q^{71} -60646.8i q^{73} +(87259.6 - 18451.0i) q^{75} +50025.5 q^{77} +28175.9 q^{79} +128742. q^{81} +24525.8 q^{83} +(-86551.6 + 9050.61i) q^{85} +17057.2i q^{87} +117015. q^{89} -72312.1i q^{91} +253133. q^{93} +(26936.1 - 2816.68i) q^{95} -37703.4i q^{97} -309526. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2944 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2944 q^{9} - 46528 q^{25} - 36768 q^{41} - 113920 q^{49} + 25376 q^{65} + 633472 q^{81} + 968704 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −28.5405 −1.83087 −0.915436 0.402463i \(-0.868154\pi\)
−0.915436 + 0.402463i \(0.868154\pi\)
\(4\) 0 0
\(5\) 5.81388 + 55.5985i 0.104002 + 0.994577i
\(6\) 0 0
\(7\) 92.3750i 0.712540i 0.934383 + 0.356270i \(0.115952\pi\)
−0.934383 + 0.356270i \(0.884048\pi\)
\(8\) 0 0
\(9\) 571.559 2.35209
\(10\) 0 0
\(11\) 541.547i 1.34944i −0.738072 0.674722i \(-0.764264\pi\)
0.738072 0.674722i \(-0.235736\pi\)
\(12\) 0 0
\(13\) −782.810 −1.28469 −0.642345 0.766416i \(-0.722038\pi\)
−0.642345 + 0.766416i \(0.722038\pi\)
\(14\) 0 0
\(15\) −165.931 1586.81i −0.190414 1.82094i
\(16\) 0 0
\(17\) 1556.72i 1.30644i 0.757169 + 0.653219i \(0.226582\pi\)
−0.757169 + 0.653219i \(0.773418\pi\)
\(18\) 0 0
\(19\) 484.475i 0.307884i −0.988080 0.153942i \(-0.950803\pi\)
0.988080 0.153942i \(-0.0491969\pi\)
\(20\) 0 0
\(21\) 2636.43i 1.30457i
\(22\) 0 0
\(23\) 1096.90i 0.432361i −0.976353 0.216181i \(-0.930640\pi\)
0.976353 0.216181i \(-0.0693600\pi\)
\(24\) 0 0
\(25\) −3057.40 + 646.487i −0.978367 + 0.206876i
\(26\) 0 0
\(27\) −9377.22 −2.47551
\(28\) 0 0
\(29\) 597.650i 0.131963i −0.997821 0.0659814i \(-0.978982\pi\)
0.997821 0.0659814i \(-0.0210178\pi\)
\(30\) 0 0
\(31\) −8869.25 −1.65761 −0.828805 0.559537i \(-0.810979\pi\)
−0.828805 + 0.559537i \(0.810979\pi\)
\(32\) 0 0
\(33\) 15456.0i 2.47066i
\(34\) 0 0
\(35\) −5135.92 + 537.058i −0.708676 + 0.0741056i
\(36\) 0 0
\(37\) −13624.1 −1.63608 −0.818039 0.575163i \(-0.804939\pi\)
−0.818039 + 0.575163i \(0.804939\pi\)
\(38\) 0 0
\(39\) 22341.8 2.35210
\(40\) 0 0
\(41\) 14540.4 1.35088 0.675441 0.737414i \(-0.263953\pi\)
0.675441 + 0.737414i \(0.263953\pi\)
\(42\) 0 0
\(43\) −1828.39 −0.150799 −0.0753993 0.997153i \(-0.524023\pi\)
−0.0753993 + 0.997153i \(0.524023\pi\)
\(44\) 0 0
\(45\) 3322.98 + 31777.8i 0.244622 + 2.33934i
\(46\) 0 0
\(47\) 17951.8i 1.18539i −0.805426 0.592697i \(-0.798063\pi\)
0.805426 0.592697i \(-0.201937\pi\)
\(48\) 0 0
\(49\) 8273.86 0.492286
\(50\) 0 0
\(51\) 44429.6i 2.39192i
\(52\) 0 0
\(53\) 1650.99 0.0807337 0.0403669 0.999185i \(-0.487147\pi\)
0.0403669 + 0.999185i \(0.487147\pi\)
\(54\) 0 0
\(55\) 30109.3 3148.49i 1.34213 0.140345i
\(56\) 0 0
\(57\) 13827.1i 0.563697i
\(58\) 0 0
\(59\) 14453.6i 0.540564i 0.962781 + 0.270282i \(0.0871169\pi\)
−0.962781 + 0.270282i \(0.912883\pi\)
\(60\) 0 0
\(61\) 24574.4i 0.845588i −0.906226 0.422794i \(-0.861049\pi\)
0.906226 0.422794i \(-0.138951\pi\)
\(62\) 0 0
\(63\) 52797.7i 1.67596i
\(64\) 0 0
\(65\) −4551.17 43523.1i −0.133610 1.27772i
\(66\) 0 0
\(67\) 26842.8 0.730535 0.365268 0.930903i \(-0.380978\pi\)
0.365268 + 0.930903i \(0.380978\pi\)
\(68\) 0 0
\(69\) 31306.0i 0.791598i
\(70\) 0 0
\(71\) −48050.6 −1.13124 −0.565618 0.824668i \(-0.691362\pi\)
−0.565618 + 0.824668i \(0.691362\pi\)
\(72\) 0 0
\(73\) 60646.8i 1.33199i −0.745957 0.665994i \(-0.768007\pi\)
0.745957 0.665994i \(-0.231993\pi\)
\(74\) 0 0
\(75\) 87259.6 18451.0i 1.79127 0.378763i
\(76\) 0 0
\(77\) 50025.5 0.961533
\(78\) 0 0
\(79\) 28175.9 0.507937 0.253969 0.967212i \(-0.418264\pi\)
0.253969 + 0.967212i \(0.418264\pi\)
\(80\) 0 0
\(81\) 128742. 2.18025
\(82\) 0 0
\(83\) 24525.8 0.390777 0.195388 0.980726i \(-0.437403\pi\)
0.195388 + 0.980726i \(0.437403\pi\)
\(84\) 0 0
\(85\) −86551.6 + 9050.61i −1.29935 + 0.135872i
\(86\) 0 0
\(87\) 17057.2i 0.241607i
\(88\) 0 0
\(89\) 117015. 1.56591 0.782953 0.622081i \(-0.213713\pi\)
0.782953 + 0.622081i \(0.213713\pi\)
\(90\) 0 0
\(91\) 72312.1i 0.915393i
\(92\) 0 0
\(93\) 253133. 3.03487
\(94\) 0 0
\(95\) 26936.1 2816.68i 0.306215 0.0320205i
\(96\) 0 0
\(97\) 37703.4i 0.406865i −0.979089 0.203433i \(-0.934790\pi\)
0.979089 0.203433i \(-0.0652098\pi\)
\(98\) 0 0
\(99\) 309526.i 3.17402i
\(100\) 0 0
\(101\) 106605.i 1.03985i 0.854211 + 0.519927i \(0.174041\pi\)
−0.854211 + 0.519927i \(0.825959\pi\)
\(102\) 0 0
\(103\) 140551.i 1.30539i 0.757619 + 0.652697i \(0.226362\pi\)
−0.757619 + 0.652697i \(0.773638\pi\)
\(104\) 0 0
\(105\) 146581. 15327.9i 1.29750 0.135678i
\(106\) 0 0
\(107\) 78552.8 0.663289 0.331644 0.943405i \(-0.392397\pi\)
0.331644 + 0.943405i \(0.392397\pi\)
\(108\) 0 0
\(109\) 149209.i 1.20290i 0.798910 + 0.601450i \(0.205410\pi\)
−0.798910 + 0.601450i \(0.794590\pi\)
\(110\) 0 0
\(111\) 388839. 2.99545
\(112\) 0 0
\(113\) 190766.i 1.40541i 0.711479 + 0.702707i \(0.248026\pi\)
−0.711479 + 0.702707i \(0.751974\pi\)
\(114\) 0 0
\(115\) 60986.0 6377.24i 0.430017 0.0449664i
\(116\) 0 0
\(117\) −447422. −3.02171
\(118\) 0 0
\(119\) −143802. −0.930890
\(120\) 0 0
\(121\) −132223. −0.820999
\(122\) 0 0
\(123\) −414991. −2.47329
\(124\) 0 0
\(125\) −53719.1 166228.i −0.307506 0.951546i
\(126\) 0 0
\(127\) 257744.i 1.41801i −0.705205 0.709004i \(-0.749145\pi\)
0.705205 0.709004i \(-0.250855\pi\)
\(128\) 0 0
\(129\) 52183.1 0.276093
\(130\) 0 0
\(131\) 165038.i 0.840242i 0.907468 + 0.420121i \(0.138012\pi\)
−0.907468 + 0.420121i \(0.861988\pi\)
\(132\) 0 0
\(133\) 44753.4 0.219380
\(134\) 0 0
\(135\) −54518.1 521360.i −0.257458 2.46209i
\(136\) 0 0
\(137\) 17244.2i 0.0784948i 0.999230 + 0.0392474i \(0.0124960\pi\)
−0.999230 + 0.0392474i \(0.987504\pi\)
\(138\) 0 0
\(139\) 140468.i 0.616654i 0.951280 + 0.308327i \(0.0997692\pi\)
−0.951280 + 0.308327i \(0.900231\pi\)
\(140\) 0 0
\(141\) 512352.i 2.17031i
\(142\) 0 0
\(143\) 423929.i 1.73362i
\(144\) 0 0
\(145\) 33228.5 3474.67i 0.131247 0.0137244i
\(146\) 0 0
\(147\) −236140. −0.901314
\(148\) 0 0
\(149\) 314120.i 1.15913i −0.814928 0.579563i \(-0.803223\pi\)
0.814928 0.579563i \(-0.196777\pi\)
\(150\) 0 0
\(151\) 242427. 0.865242 0.432621 0.901576i \(-0.357589\pi\)
0.432621 + 0.901576i \(0.357589\pi\)
\(152\) 0 0
\(153\) 889759.i 3.07287i
\(154\) 0 0
\(155\) −51564.8 493117.i −0.172395 1.64862i
\(156\) 0 0
\(157\) 343720. 1.11290 0.556450 0.830881i \(-0.312163\pi\)
0.556450 + 0.830881i \(0.312163\pi\)
\(158\) 0 0
\(159\) −47120.1 −0.147813
\(160\) 0 0
\(161\) 101326. 0.308075
\(162\) 0 0
\(163\) −154899. −0.456647 −0.228324 0.973585i \(-0.573324\pi\)
−0.228324 + 0.973585i \(0.573324\pi\)
\(164\) 0 0
\(165\) −859332. + 89859.5i −2.45726 + 0.256953i
\(166\) 0 0
\(167\) 41199.1i 0.114313i 0.998365 + 0.0571567i \(0.0182035\pi\)
−0.998365 + 0.0571567i \(0.981797\pi\)
\(168\) 0 0
\(169\) 241499. 0.650427
\(170\) 0 0
\(171\) 276906.i 0.724172i
\(172\) 0 0
\(173\) 707204. 1.79651 0.898255 0.439475i \(-0.144836\pi\)
0.898255 + 0.439475i \(0.144836\pi\)
\(174\) 0 0
\(175\) −59719.2 282427.i −0.147407 0.697126i
\(176\) 0 0
\(177\) 412513.i 0.989703i
\(178\) 0 0
\(179\) 385923.i 0.900259i −0.892963 0.450130i \(-0.851378\pi\)
0.892963 0.450130i \(-0.148622\pi\)
\(180\) 0 0
\(181\) 283701.i 0.643672i −0.946795 0.321836i \(-0.895700\pi\)
0.946795 0.321836i \(-0.104300\pi\)
\(182\) 0 0
\(183\) 701366.i 1.54816i
\(184\) 0 0
\(185\) −79209.0 757481.i −0.170155 1.62721i
\(186\) 0 0
\(187\) 843040. 1.76297
\(188\) 0 0
\(189\) 866221.i 1.76390i
\(190\) 0 0
\(191\) −749997. −1.48756 −0.743782 0.668422i \(-0.766970\pi\)
−0.743782 + 0.668422i \(0.766970\pi\)
\(192\) 0 0
\(193\) 232810.i 0.449892i −0.974371 0.224946i \(-0.927779\pi\)
0.974371 0.224946i \(-0.0722206\pi\)
\(194\) 0 0
\(195\) 129893. + 1.24217e6i 0.244623 + 2.33935i
\(196\) 0 0
\(197\) −88921.6 −0.163246 −0.0816228 0.996663i \(-0.526010\pi\)
−0.0816228 + 0.996663i \(0.526010\pi\)
\(198\) 0 0
\(199\) −194624. −0.348388 −0.174194 0.984711i \(-0.555732\pi\)
−0.174194 + 0.984711i \(0.555732\pi\)
\(200\) 0 0
\(201\) −766107. −1.33752
\(202\) 0 0
\(203\) 55207.9 0.0940288
\(204\) 0 0
\(205\) 84536.4 + 808427.i 0.140494 + 1.34356i
\(206\) 0 0
\(207\) 626942.i 1.01695i
\(208\) 0 0
\(209\) −262366. −0.415472
\(210\) 0 0
\(211\) 932681.i 1.44220i 0.692828 + 0.721102i \(0.256364\pi\)
−0.692828 + 0.721102i \(0.743636\pi\)
\(212\) 0 0
\(213\) 1.37139e6 2.07115
\(214\) 0 0
\(215\) −10630.0 101656.i −0.0156833 0.149981i
\(216\) 0 0
\(217\) 819297.i 1.18111i
\(218\) 0 0
\(219\) 1.73089e6i 2.43870i
\(220\) 0 0
\(221\) 1.21862e6i 1.67837i
\(222\) 0 0
\(223\) 1.37279e6i 1.84860i 0.381666 + 0.924300i \(0.375351\pi\)
−0.381666 + 0.924300i \(0.624649\pi\)
\(224\) 0 0
\(225\) −1.74748e6 + 369505.i −2.30121 + 0.486591i
\(226\) 0 0
\(227\) 1.38224e6 1.78040 0.890200 0.455569i \(-0.150564\pi\)
0.890200 + 0.455569i \(0.150564\pi\)
\(228\) 0 0
\(229\) 330003.i 0.415843i 0.978146 + 0.207922i \(0.0666699\pi\)
−0.978146 + 0.207922i \(0.933330\pi\)
\(230\) 0 0
\(231\) −1.42775e6 −1.76044
\(232\) 0 0
\(233\) 1.14254e6i 1.37874i −0.724409 0.689370i \(-0.757887\pi\)
0.724409 0.689370i \(-0.242113\pi\)
\(234\) 0 0
\(235\) 998093. 104370.i 1.17897 0.123283i
\(236\) 0 0
\(237\) −804154. −0.929969
\(238\) 0 0
\(239\) 441560. 0.500029 0.250015 0.968242i \(-0.419565\pi\)
0.250015 + 0.968242i \(0.419565\pi\)
\(240\) 0 0
\(241\) 509548. 0.565122 0.282561 0.959249i \(-0.408816\pi\)
0.282561 + 0.959249i \(0.408816\pi\)
\(242\) 0 0
\(243\) −1.39568e6 −1.51625
\(244\) 0 0
\(245\) 48103.3 + 460015.i 0.0511987 + 0.489617i
\(246\) 0 0
\(247\) 379252.i 0.395536i
\(248\) 0 0
\(249\) −699979. −0.715462
\(250\) 0 0
\(251\) 253562.i 0.254039i −0.991900 0.127019i \(-0.959459\pi\)
0.991900 0.127019i \(-0.0405411\pi\)
\(252\) 0 0
\(253\) −594023. −0.583447
\(254\) 0 0
\(255\) 2.47022e6 258309.i 2.37895 0.248765i
\(256\) 0 0
\(257\) 203987.i 0.192650i −0.995350 0.0963252i \(-0.969291\pi\)
0.995350 0.0963252i \(-0.0307089\pi\)
\(258\) 0 0
\(259\) 1.25853e6i 1.16577i
\(260\) 0 0
\(261\) 341592.i 0.310389i
\(262\) 0 0
\(263\) 1.49608e6i 1.33372i −0.745181 0.666862i \(-0.767637\pi\)
0.745181 0.666862i \(-0.232363\pi\)
\(264\) 0 0
\(265\) 9598.67 + 91792.7i 0.00839646 + 0.0802959i
\(266\) 0 0
\(267\) −3.33966e6 −2.86697
\(268\) 0 0
\(269\) 522744.i 0.440462i −0.975448 0.220231i \(-0.929319\pi\)
0.975448 0.220231i \(-0.0706811\pi\)
\(270\) 0 0
\(271\) 1.43490e6 1.18686 0.593429 0.804886i \(-0.297774\pi\)
0.593429 + 0.804886i \(0.297774\pi\)
\(272\) 0 0
\(273\) 2.06382e6i 1.67597i
\(274\) 0 0
\(275\) 350103. + 1.65573e6i 0.279167 + 1.32025i
\(276\) 0 0
\(277\) 360298. 0.282139 0.141069 0.990000i \(-0.454946\pi\)
0.141069 + 0.990000i \(0.454946\pi\)
\(278\) 0 0
\(279\) −5.06930e6 −3.89886
\(280\) 0 0
\(281\) −982971. −0.742634 −0.371317 0.928506i \(-0.621094\pi\)
−0.371317 + 0.928506i \(0.621094\pi\)
\(282\) 0 0
\(283\) 597953. 0.443814 0.221907 0.975068i \(-0.428772\pi\)
0.221907 + 0.975068i \(0.428772\pi\)
\(284\) 0 0
\(285\) −768769. + 80389.4i −0.560640 + 0.0586255i
\(286\) 0 0
\(287\) 1.34317e6i 0.962558i
\(288\) 0 0
\(289\) −1.00353e6 −0.706783
\(290\) 0 0
\(291\) 1.07607e6i 0.744919i
\(292\) 0 0
\(293\) 1.14992e6 0.782529 0.391264 0.920278i \(-0.372038\pi\)
0.391264 + 0.920278i \(0.372038\pi\)
\(294\) 0 0
\(295\) −803601. + 84031.7i −0.537632 + 0.0562197i
\(296\) 0 0
\(297\) 5.07821e6i 3.34056i
\(298\) 0 0
\(299\) 858663.i 0.555450i
\(300\) 0 0
\(301\) 168897.i 0.107450i
\(302\) 0 0
\(303\) 3.04255e6i 1.90384i
\(304\) 0 0
\(305\) 1.36630e6 142873.i 0.841003 0.0879428i
\(306\) 0 0
\(307\) −1.78536e6 −1.08114 −0.540568 0.841300i \(-0.681791\pi\)
−0.540568 + 0.841300i \(0.681791\pi\)
\(308\) 0 0
\(309\) 4.01140e6i 2.39001i
\(310\) 0 0
\(311\) −669162. −0.392311 −0.196155 0.980573i \(-0.562846\pi\)
−0.196155 + 0.980573i \(0.562846\pi\)
\(312\) 0 0
\(313\) 1.22019e6i 0.703989i −0.936002 0.351994i \(-0.885504\pi\)
0.936002 0.351994i \(-0.114496\pi\)
\(314\) 0 0
\(315\) −2.93548e6 + 306960.i −1.66687 + 0.174303i
\(316\) 0 0
\(317\) −1.63087e6 −0.911529 −0.455764 0.890101i \(-0.650634\pi\)
−0.455764 + 0.890101i \(0.650634\pi\)
\(318\) 0 0
\(319\) −323656. −0.178076
\(320\) 0 0
\(321\) −2.24194e6 −1.21440
\(322\) 0 0
\(323\) 754194. 0.402232
\(324\) 0 0
\(325\) 2.39336e6 506077.i 1.25690 0.265771i
\(326\) 0 0
\(327\) 4.25851e6i 2.20236i
\(328\) 0 0
\(329\) 1.65830e6 0.844641
\(330\) 0 0
\(331\) 1.47491e6i 0.739936i 0.929044 + 0.369968i \(0.120631\pi\)
−0.929044 + 0.369968i \(0.879369\pi\)
\(332\) 0 0
\(333\) −7.78698e6 −3.84821
\(334\) 0 0
\(335\) 156061. + 1.49242e6i 0.0759771 + 0.726573i
\(336\) 0 0
\(337\) 3.04284e6i 1.45950i −0.683713 0.729751i \(-0.739636\pi\)
0.683713 0.729751i \(-0.260364\pi\)
\(338\) 0 0
\(339\) 5.44455e6i 2.57314i
\(340\) 0 0
\(341\) 4.80312e6i 2.23685i
\(342\) 0 0
\(343\) 2.31684e6i 1.06331i
\(344\) 0 0
\(345\) −1.74057e6 + 182009.i −0.787306 + 0.0823277i
\(346\) 0 0
\(347\) 3.03217e6 1.35185 0.675927 0.736968i \(-0.263743\pi\)
0.675927 + 0.736968i \(0.263743\pi\)
\(348\) 0 0
\(349\) 142845.i 0.0627773i −0.999507 0.0313887i \(-0.990007\pi\)
0.999507 0.0313887i \(-0.00999296\pi\)
\(350\) 0 0
\(351\) 7.34059e6 3.18026
\(352\) 0 0
\(353\) 955673.i 0.408200i −0.978950 0.204100i \(-0.934573\pi\)
0.978950 0.204100i \(-0.0654267\pi\)
\(354\) 0 0
\(355\) −279361. 2.67154e6i −0.117651 1.12510i
\(356\) 0 0
\(357\) 4.10419e6 1.70434
\(358\) 0 0
\(359\) −1.33046e6 −0.544837 −0.272418 0.962179i \(-0.587823\pi\)
−0.272418 + 0.962179i \(0.587823\pi\)
\(360\) 0 0
\(361\) 2.24138e6 0.905207
\(362\) 0 0
\(363\) 3.77370e6 1.50314
\(364\) 0 0
\(365\) 3.37187e6 352593.i 1.32477 0.138529i
\(366\) 0 0
\(367\) 1.97269e6i 0.764527i 0.924053 + 0.382263i \(0.124855\pi\)
−0.924053 + 0.382263i \(0.875145\pi\)
\(368\) 0 0
\(369\) 8.31071e6 3.17740
\(370\) 0 0
\(371\) 152510.i 0.0575260i
\(372\) 0 0
\(373\) 386597. 0.143875 0.0719377 0.997409i \(-0.477082\pi\)
0.0719377 + 0.997409i \(0.477082\pi\)
\(374\) 0 0
\(375\) 1.53317e6 + 4.74423e6i 0.563004 + 1.74216i
\(376\) 0 0
\(377\) 467846.i 0.169531i
\(378\) 0 0
\(379\) 3.21349e6i 1.14915i −0.818450 0.574577i \(-0.805167\pi\)
0.818450 0.574577i \(-0.194833\pi\)
\(380\) 0 0
\(381\) 7.35612e6i 2.59619i
\(382\) 0 0
\(383\) 2.09419e6i 0.729488i −0.931108 0.364744i \(-0.881156\pi\)
0.931108 0.364744i \(-0.118844\pi\)
\(384\) 0 0
\(385\) 290842. + 2.78134e6i 0.100001 + 0.956319i
\(386\) 0 0
\(387\) −1.04503e6 −0.354692
\(388\) 0 0
\(389\) 944090.i 0.316329i −0.987413 0.158165i \(-0.949442\pi\)
0.987413 0.158165i \(-0.0505577\pi\)
\(390\) 0 0
\(391\) 1.70757e6 0.564854
\(392\) 0 0
\(393\) 4.71025e6i 1.53838i
\(394\) 0 0
\(395\) 163811. + 1.56654e6i 0.0528265 + 0.505183i
\(396\) 0 0
\(397\) 3.62777e6 1.15522 0.577608 0.816314i \(-0.303986\pi\)
0.577608 + 0.816314i \(0.303986\pi\)
\(398\) 0 0
\(399\) −1.27728e6 −0.401657
\(400\) 0 0
\(401\) −3.56035e6 −1.10569 −0.552843 0.833285i \(-0.686457\pi\)
−0.552843 + 0.833285i \(0.686457\pi\)
\(402\) 0 0
\(403\) 6.94294e6 2.12952
\(404\) 0 0
\(405\) 748489. + 7.15785e6i 0.226750 + 2.16843i
\(406\) 0 0
\(407\) 7.37811e6i 2.20780i
\(408\) 0 0
\(409\) 4.04814e6 1.19660 0.598298 0.801273i \(-0.295844\pi\)
0.598298 + 0.801273i \(0.295844\pi\)
\(410\) 0 0
\(411\) 492157.i 0.143714i
\(412\) 0 0
\(413\) −1.33515e6 −0.385173
\(414\) 0 0
\(415\) 142590. + 1.36360e6i 0.0406415 + 0.388657i
\(416\) 0 0
\(417\) 4.00904e6i 1.12902i
\(418\) 0 0
\(419\) 4.13360e6i 1.15025i 0.818064 + 0.575127i \(0.195047\pi\)
−0.818064 + 0.575127i \(0.804953\pi\)
\(420\) 0 0
\(421\) 1.98891e6i 0.546902i −0.961886 0.273451i \(-0.911835\pi\)
0.961886 0.273451i \(-0.0881651\pi\)
\(422\) 0 0
\(423\) 1.02605e7i 2.78816i
\(424\) 0 0
\(425\) −1.00640e6 4.75952e6i −0.270271 1.27818i
\(426\) 0 0
\(427\) 2.27006e6 0.602516
\(428\) 0 0
\(429\) 1.20991e7i 3.17403i
\(430\) 0 0
\(431\) 2.17585e6 0.564203 0.282101 0.959385i \(-0.408969\pi\)
0.282101 + 0.959385i \(0.408969\pi\)
\(432\) 0 0
\(433\) 3.97546e6i 1.01899i −0.860475 0.509493i \(-0.829833\pi\)
0.860475 0.509493i \(-0.170167\pi\)
\(434\) 0 0
\(435\) −948356. + 99168.6i −0.240297 + 0.0251276i
\(436\) 0 0
\(437\) −531420. −0.133117
\(438\) 0 0
\(439\) −2.62877e6 −0.651017 −0.325508 0.945539i \(-0.605535\pi\)
−0.325508 + 0.945539i \(0.605535\pi\)
\(440\) 0 0
\(441\) 4.72900e6 1.15790
\(442\) 0 0
\(443\) −3.63413e6 −0.879814 −0.439907 0.898043i \(-0.644989\pi\)
−0.439907 + 0.898043i \(0.644989\pi\)
\(444\) 0 0
\(445\) 680310. + 6.50585e6i 0.162857 + 1.55741i
\(446\) 0 0
\(447\) 8.96515e6i 2.12221i
\(448\) 0 0
\(449\) −1.40882e6 −0.329792 −0.164896 0.986311i \(-0.552729\pi\)
−0.164896 + 0.986311i \(0.552729\pi\)
\(450\) 0 0
\(451\) 7.87433e6i 1.82294i
\(452\) 0 0
\(453\) −6.91897e6 −1.58415
\(454\) 0 0
\(455\) 4.02045e6 420414.i 0.910429 0.0952026i
\(456\) 0 0
\(457\) 7.07341e6i 1.58430i 0.610325 + 0.792151i \(0.291039\pi\)
−0.610325 + 0.792151i \(0.708961\pi\)
\(458\) 0 0
\(459\) 1.45977e7i 3.23410i
\(460\) 0 0
\(461\) 1.57690e6i 0.345582i −0.984958 0.172791i \(-0.944721\pi\)
0.984958 0.172791i \(-0.0552786\pi\)
\(462\) 0 0
\(463\) 5.38641e6i 1.16774i −0.811847 0.583871i \(-0.801537\pi\)
0.811847 0.583871i \(-0.198463\pi\)
\(464\) 0 0
\(465\) 1.47168e6 + 1.40738e7i 0.315633 + 3.01842i
\(466\) 0 0
\(467\) 1.22575e6 0.260082 0.130041 0.991509i \(-0.458489\pi\)
0.130041 + 0.991509i \(0.458489\pi\)
\(468\) 0 0
\(469\) 2.47961e6i 0.520536i
\(470\) 0 0
\(471\) −9.80994e6 −2.03758
\(472\) 0 0
\(473\) 990159.i 0.203494i
\(474\) 0 0
\(475\) 313207. + 1.48123e6i 0.0636938 + 0.301224i
\(476\) 0 0
\(477\) 943638. 0.189893
\(478\) 0 0
\(479\) 2.58563e6 0.514906 0.257453 0.966291i \(-0.417117\pi\)
0.257453 + 0.966291i \(0.417117\pi\)
\(480\) 0 0
\(481\) 1.06651e7 2.10185
\(482\) 0 0
\(483\) −2.89189e6 −0.564046
\(484\) 0 0
\(485\) 2.09625e6 219203.i 0.404659 0.0423148i
\(486\) 0 0
\(487\) 8.96610e6i 1.71309i −0.516069 0.856547i \(-0.672605\pi\)
0.516069 0.856547i \(-0.327395\pi\)
\(488\) 0 0
\(489\) 4.42090e6 0.836063
\(490\) 0 0
\(491\) 2.48071e6i 0.464378i −0.972671 0.232189i \(-0.925411\pi\)
0.972671 0.232189i \(-0.0745889\pi\)
\(492\) 0 0
\(493\) 930375. 0.172401
\(494\) 0 0
\(495\) 1.72092e7 1.79955e6i 3.15681 0.330104i
\(496\) 0 0
\(497\) 4.43867e6i 0.806051i
\(498\) 0 0
\(499\) 2.82421e6i 0.507744i 0.967238 + 0.253872i \(0.0817043\pi\)
−0.967238 + 0.253872i \(0.918296\pi\)
\(500\) 0 0
\(501\) 1.17584e6i 0.209293i
\(502\) 0 0
\(503\) 1.47261e6i 0.259517i 0.991546 + 0.129759i \(0.0414203\pi\)
−0.991546 + 0.129759i \(0.958580\pi\)
\(504\) 0 0
\(505\) −5.92706e6 + 619787.i −1.03422 + 0.108147i
\(506\) 0 0
\(507\) −6.89250e6 −1.19085
\(508\) 0 0
\(509\) 5.12155e6i 0.876207i 0.898924 + 0.438104i \(0.144350\pi\)
−0.898924 + 0.438104i \(0.855650\pi\)
\(510\) 0 0
\(511\) 5.60225e6 0.949096
\(512\) 0 0
\(513\) 4.54303e6i 0.762171i
\(514\) 0 0
\(515\) −7.81444e6 + 817148.i −1.29831 + 0.135763i
\(516\) 0 0
\(517\) −9.72174e6 −1.59962
\(518\) 0 0
\(519\) −2.01839e7 −3.28918
\(520\) 0 0
\(521\) −2.85592e6 −0.460948 −0.230474 0.973078i \(-0.574028\pi\)
−0.230474 + 0.973078i \(0.574028\pi\)
\(522\) 0 0
\(523\) −5.00538e6 −0.800171 −0.400086 0.916478i \(-0.631020\pi\)
−0.400086 + 0.916478i \(0.631020\pi\)
\(524\) 0 0
\(525\) 1.70442e6 + 8.06060e6i 0.269884 + 1.27635i
\(526\) 0 0
\(527\) 1.38070e7i 2.16557i
\(528\) 0 0
\(529\) 5.23316e6 0.813064
\(530\) 0 0
\(531\) 8.26110e6i 1.27146i
\(532\) 0 0
\(533\) −1.13824e7 −1.73547
\(534\) 0 0
\(535\) 456697. + 4.36742e6i 0.0689833 + 0.659692i
\(536\) 0 0
\(537\) 1.10144e7i 1.64826i
\(538\) 0 0
\(539\) 4.48069e6i 0.664313i
\(540\) 0 0
\(541\) 6.29808e6i 0.925157i −0.886578 0.462578i \(-0.846924\pi\)
0.886578 0.462578i \(-0.153076\pi\)
\(542\) 0 0
\(543\) 8.09696e6i 1.17848i
\(544\) 0 0
\(545\) −8.29582e6 + 867486.i −1.19638 + 0.125104i
\(546\) 0 0
\(547\) −1.56773e6 −0.224029 −0.112014 0.993707i \(-0.535730\pi\)
−0.112014 + 0.993707i \(0.535730\pi\)
\(548\) 0 0
\(549\) 1.40457e7i 1.98890i
\(550\) 0 0
\(551\) −289546. −0.0406293
\(552\) 0 0
\(553\) 2.60275e6i 0.361926i
\(554\) 0 0
\(555\) 2.26066e6 + 2.16189e7i 0.311533 + 2.97921i
\(556\) 0 0
\(557\) 8.52468e6 1.16423 0.582117 0.813105i \(-0.302225\pi\)
0.582117 + 0.813105i \(0.302225\pi\)
\(558\) 0 0
\(559\) 1.43128e6 0.193729
\(560\) 0 0
\(561\) −2.40608e7 −3.22777
\(562\) 0 0
\(563\) −935676. −0.124410 −0.0622049 0.998063i \(-0.519813\pi\)
−0.0622049 + 0.998063i \(0.519813\pi\)
\(564\) 0 0
\(565\) −1.06063e7 + 1.10909e6i −1.39779 + 0.146166i
\(566\) 0 0
\(567\) 1.18925e7i 1.55352i
\(568\) 0 0
\(569\) −9.09876e6 −1.17815 −0.589076 0.808077i \(-0.700508\pi\)
−0.589076 + 0.808077i \(0.700508\pi\)
\(570\) 0 0
\(571\) 1.41349e6i 0.181427i 0.995877 + 0.0907136i \(0.0289148\pi\)
−0.995877 + 0.0907136i \(0.971085\pi\)
\(572\) 0 0
\(573\) 2.14053e7 2.72354
\(574\) 0 0
\(575\) 709131. + 3.35365e6i 0.0894451 + 0.423008i
\(576\) 0 0
\(577\) 1.18400e7i 1.48052i −0.672322 0.740259i \(-0.734703\pi\)
0.672322 0.740259i \(-0.265297\pi\)
\(578\) 0 0
\(579\) 6.64451e6i 0.823695i
\(580\) 0 0
\(581\) 2.26557e6i 0.278444i
\(582\) 0 0
\(583\) 894090.i 0.108946i
\(584\) 0 0
\(585\) −2.60126e6 2.48760e7i −0.314264 3.00532i
\(586\) 0 0
\(587\) 3.37505e6 0.404283 0.202141 0.979356i \(-0.435210\pi\)
0.202141 + 0.979356i \(0.435210\pi\)
\(588\) 0 0
\(589\) 4.29693e6i 0.510352i
\(590\) 0 0
\(591\) 2.53786e6 0.298882
\(592\) 0 0
\(593\) 1.32900e7i 1.55199i 0.630737 + 0.775997i \(0.282753\pi\)
−0.630737 + 0.775997i \(0.717247\pi\)
\(594\) 0 0
\(595\) −836050. 7.99520e6i −0.0968144 0.925842i
\(596\) 0 0
\(597\) 5.55466e6 0.637855
\(598\) 0 0
\(599\) −8.21563e6 −0.935565 −0.467783 0.883844i \(-0.654947\pi\)
−0.467783 + 0.883844i \(0.654947\pi\)
\(600\) 0 0
\(601\) 4.66795e6 0.527157 0.263579 0.964638i \(-0.415097\pi\)
0.263579 + 0.964638i \(0.415097\pi\)
\(602\) 0 0
\(603\) 1.53422e7 1.71829
\(604\) 0 0
\(605\) −768727. 7.35139e6i −0.0853855 0.816547i
\(606\) 0 0
\(607\) 280377.i 0.0308867i −0.999881 0.0154433i \(-0.995084\pi\)
0.999881 0.0154433i \(-0.00491596\pi\)
\(608\) 0 0
\(609\) −1.57566e6 −0.172155
\(610\) 0 0
\(611\) 1.40528e7i 1.52286i
\(612\) 0 0
\(613\) 963624. 0.103575 0.0517877 0.998658i \(-0.483508\pi\)
0.0517877 + 0.998658i \(0.483508\pi\)
\(614\) 0 0
\(615\) −2.41271e6 2.30729e7i −0.257227 2.45988i
\(616\) 0 0
\(617\) 1.00959e7i 1.06766i 0.845593 + 0.533829i \(0.179247\pi\)
−0.845593 + 0.533829i \(0.820753\pi\)
\(618\) 0 0
\(619\) 1.57741e7i 1.65469i −0.561691 0.827347i \(-0.689849\pi\)
0.561691 0.827347i \(-0.310151\pi\)
\(620\) 0 0
\(621\) 1.02859e7i 1.07031i
\(622\) 0 0
\(623\) 1.08092e7i 1.11577i
\(624\) 0 0
\(625\) 8.92973e6 3.95314e6i 0.914405 0.404801i
\(626\) 0 0
\(627\) 7.48806e6 0.760677
\(628\) 0 0
\(629\) 2.12090e7i 2.13744i
\(630\) 0 0
\(631\) 1.60364e7 1.60337 0.801685 0.597747i \(-0.203937\pi\)
0.801685 + 0.597747i \(0.203937\pi\)
\(632\) 0 0
\(633\) 2.66192e7i 2.64049i
\(634\) 0 0
\(635\) 1.43302e7 1.49849e6i 1.41032 0.147475i
\(636\) 0 0
\(637\) −6.47686e6 −0.632435
\(638\) 0 0
\(639\) −2.74637e7 −2.66077
\(640\) 0 0
\(641\) 9.42961e6 0.906460 0.453230 0.891394i \(-0.350272\pi\)
0.453230 + 0.891394i \(0.350272\pi\)
\(642\) 0 0
\(643\) 102240. 0.00975200 0.00487600 0.999988i \(-0.498448\pi\)
0.00487600 + 0.999988i \(0.498448\pi\)
\(644\) 0 0
\(645\) 303386. + 2.90130e6i 0.0287142 + 0.274596i
\(646\) 0 0
\(647\) 7.52613e6i 0.706824i −0.935468 0.353412i \(-0.885021\pi\)
0.935468 0.353412i \(-0.114979\pi\)
\(648\) 0 0
\(649\) 7.82733e6 0.729460
\(650\) 0 0
\(651\) 2.33831e7i 2.16247i
\(652\) 0 0
\(653\) 1.11241e7 1.02090 0.510450 0.859907i \(-0.329479\pi\)
0.510450 + 0.859907i \(0.329479\pi\)
\(654\) 0 0
\(655\) −9.17585e6 + 959509.i −0.835686 + 0.0873868i
\(656\) 0 0
\(657\) 3.46632e7i 3.13296i
\(658\) 0 0
\(659\) 9.90902e6i 0.888827i 0.895822 + 0.444413i \(0.146588\pi\)
−0.895822 + 0.444413i \(0.853412\pi\)
\(660\) 0 0
\(661\) 1.94571e7i 1.73211i 0.499950 + 0.866054i \(0.333352\pi\)
−0.499950 + 0.866054i \(0.666648\pi\)
\(662\) 0 0
\(663\) 3.47800e7i 3.07288i
\(664\) 0 0
\(665\) 260191. + 2.48822e6i 0.0228159 + 0.218190i
\(666\) 0 0
\(667\) −655561. −0.0570556
\(668\) 0 0
\(669\) 3.91802e7i 3.38455i
\(670\) 0 0
\(671\) −1.33082e7 −1.14107
\(672\) 0 0
\(673\) 1.66792e7i 1.41951i 0.704450 + 0.709754i \(0.251194\pi\)
−0.704450 + 0.709754i \(0.748806\pi\)
\(674\) 0 0
\(675\) 2.86699e7 6.06225e6i 2.42196 0.512123i
\(676\) 0 0
\(677\) −1.43143e7 −1.20033 −0.600163 0.799878i \(-0.704898\pi\)
−0.600163 + 0.799878i \(0.704898\pi\)
\(678\) 0 0
\(679\) 3.48285e6 0.289908
\(680\) 0 0
\(681\) −3.94497e7 −3.25969
\(682\) 0 0
\(683\) −2.35057e7 −1.92806 −0.964032 0.265786i \(-0.914369\pi\)
−0.964032 + 0.265786i \(0.914369\pi\)
\(684\) 0 0
\(685\) −958751. + 100256.i −0.0780691 + 0.00816361i
\(686\) 0 0
\(687\) 9.41845e6i 0.761355i
\(688\) 0 0
\(689\) −1.29241e6 −0.103718
\(690\) 0 0
\(691\) 9.02428e6i 0.718981i −0.933149 0.359490i \(-0.882951\pi\)
0.933149 0.359490i \(-0.117049\pi\)
\(692\) 0 0
\(693\) 2.85925e7 2.26162
\(694\) 0 0
\(695\) −7.80984e6 + 816667.i −0.613310 + 0.0641332i
\(696\) 0 0
\(697\) 2.26354e7i 1.76485i
\(698\) 0 0
\(699\) 3.26087e7i 2.52430i
\(700\) 0 0
\(701\) 2.56364e6i 0.197044i −0.995135 0.0985218i \(-0.968589\pi\)
0.995135 0.0985218i \(-0.0314114\pi\)
\(702\) 0 0
\(703\) 6.60054e6i 0.503723i
\(704\) 0 0
\(705\) −2.84860e7 + 2.97876e6i −2.15854 + 0.225716i
\(706\) 0 0
\(707\) −9.84760e6 −0.740938
\(708\) 0 0
\(709\) 1.83762e6i 0.137290i −0.997641 0.0686450i \(-0.978132\pi\)
0.997641 0.0686450i \(-0.0218676\pi\)
\(710\) 0 0
\(711\) 1.61042e7 1.19472
\(712\) 0 0
\(713\) 9.72866e6i 0.716687i
\(714\) 0 0
\(715\) −2.35698e7 + 2.46467e6i −1.72422 + 0.180299i
\(716\) 0 0
\(717\) −1.26023e7 −0.915489
\(718\) 0 0
\(719\) −9.48236e6 −0.684060 −0.342030 0.939689i \(-0.611115\pi\)
−0.342030 + 0.939689i \(0.611115\pi\)
\(720\) 0 0
\(721\) −1.29834e7 −0.930145
\(722\) 0 0
\(723\) −1.45427e7 −1.03467
\(724\) 0 0
\(725\) 386373. + 1.82725e6i 0.0272999 + 0.129108i
\(726\) 0 0
\(727\) 2.49674e6i 0.175201i −0.996156 0.0876007i \(-0.972080\pi\)
0.996156 0.0876007i \(-0.0279200\pi\)
\(728\) 0 0
\(729\) 8.54920e6 0.595809
\(730\) 0 0
\(731\) 2.84629e6i 0.197009i
\(732\) 0 0
\(733\) 2.33505e7 1.60522 0.802612 0.596502i \(-0.203443\pi\)
0.802612 + 0.596502i \(0.203443\pi\)
\(734\) 0 0
\(735\) −1.37289e6 1.31290e7i −0.0937384 0.896426i
\(736\) 0 0
\(737\) 1.45367e7i 0.985816i
\(738\) 0 0
\(739\) 2.42153e7i 1.63109i −0.578692 0.815546i \(-0.696437\pi\)
0.578692 0.815546i \(-0.303563\pi\)
\(740\) 0 0
\(741\) 1.08240e7i 0.724175i
\(742\) 0 0
\(743\) 1.99899e7i 1.32843i −0.747542 0.664214i \(-0.768766\pi\)
0.747542 0.664214i \(-0.231234\pi\)
\(744\) 0 0
\(745\) 1.74646e7 1.82626e6i 1.15284 0.120551i
\(746\) 0 0
\(747\) 1.40180e7 0.919143
\(748\) 0 0
\(749\) 7.25632e6i 0.472620i
\(750\) 0 0
\(751\) 4.33613e6 0.280545 0.140272 0.990113i \(-0.455202\pi\)
0.140272 + 0.990113i \(0.455202\pi\)
\(752\) 0 0
\(753\) 7.23679e6i 0.465113i
\(754\) 0 0
\(755\) 1.40944e6 + 1.34786e7i 0.0899869 + 0.860550i
\(756\) 0 0
\(757\) −1.47258e7 −0.933984 −0.466992 0.884262i \(-0.654662\pi\)
−0.466992 + 0.884262i \(0.654662\pi\)
\(758\) 0 0
\(759\) 1.69537e7 1.06822
\(760\) 0 0
\(761\) −366653. −0.0229506 −0.0114753 0.999934i \(-0.503653\pi\)
−0.0114753 + 0.999934i \(0.503653\pi\)
\(762\) 0 0
\(763\) −1.37832e7 −0.857115
\(764\) 0 0
\(765\) −4.94693e7 + 5.17295e6i −3.05620 + 0.319584i
\(766\) 0 0
\(767\) 1.13145e7i 0.694457i
\(768\) 0 0
\(769\) 5.25862e6 0.320668 0.160334 0.987063i \(-0.448743\pi\)
0.160334 + 0.987063i \(0.448743\pi\)
\(770\) 0 0
\(771\) 5.82189e6i 0.352718i
\(772\) 0 0
\(773\) −249509. −0.0150189 −0.00750943 0.999972i \(-0.502390\pi\)
−0.00750943 + 0.999972i \(0.502390\pi\)
\(774\) 0 0
\(775\) 2.71168e7 5.73385e6i 1.62175 0.342920i
\(776\) 0 0
\(777\) 3.59190e7i 2.13438i
\(778\) 0 0
\(779\) 7.04448e6i 0.415915i
\(780\) 0 0
\(781\) 2.60217e7i 1.52654i
\(782\) 0 0
\(783\) 5.60429e6i 0.326675i
\(784\) 0 0
\(785\) 1.99835e6 + 1.91104e7i 0.115744 + 1.10686i
\(786\) 0 0
\(787\) −1.94586e6 −0.111989 −0.0559945 0.998431i \(-0.517833\pi\)
−0.0559945 + 0.998431i \(0.517833\pi\)
\(788\) 0 0
\(789\) 4.26989e7i 2.44188i
\(790\) 0 0
\(791\) −1.76220e7 −1.00141
\(792\) 0 0
\(793\) 1.92371e7i 1.08632i
\(794\) 0 0
\(795\) −273951. 2.61981e6i −0.0153729 0.147012i
\(796\) 0 0
\(797\) −1.32215e7 −0.737286 −0.368643 0.929571i \(-0.620177\pi\)
−0.368643 + 0.929571i \(0.620177\pi\)
\(798\) 0 0
\(799\) 2.79459e7 1.54864
\(800\) 0 0
\(801\) 6.68808e7 3.68316
\(802\) 0 0
\(803\) −3.28431e7 −1.79744
\(804\) 0 0
\(805\) 589098. + 5.63358e6i 0.0320404 + 0.306404i
\(806\) 0 0
\(807\) 1.49194e7i 0.806430i
\(808\) 0 0
\(809\) −4.37501e6 −0.235022 −0.117511 0.993072i \(-0.537491\pi\)
−0.117511 + 0.993072i \(0.537491\pi\)
\(810\) 0 0
\(811\) 3.36426e7i 1.79613i −0.439863 0.898065i \(-0.644973\pi\)
0.439863 0.898065i \(-0.355027\pi\)
\(812\) 0 0
\(813\) −4.09528e7 −2.17299
\(814\) 0 0
\(815\) −900568. 8.61219e6i −0.0474922 0.454171i
\(816\) 0 0
\(817\) 885808.i 0.0464285i
\(818\) 0 0
\(819\) 4.13306e7i 2.15309i
\(820\) 0 0
\(821\) 3.51821e7i 1.82164i −0.412799 0.910822i \(-0.635449\pi\)
0.412799 0.910822i \(-0.364551\pi\)
\(822\) 0 0
\(823\) 8.11861e6i 0.417813i 0.977936 + 0.208907i \(0.0669905\pi\)
−0.977936 + 0.208907i \(0.933010\pi\)
\(824\) 0 0
\(825\) −9.99212e6 4.72552e7i −0.511120 2.41721i
\(826\) 0 0
\(827\) −1.82572e7 −0.928263 −0.464132 0.885766i \(-0.653634\pi\)
−0.464132 + 0.885766i \(0.653634\pi\)
\(828\) 0 0
\(829\) 3.65919e6i 0.184926i 0.995716 + 0.0924632i \(0.0294740\pi\)
−0.995716 + 0.0924632i \(0.970526\pi\)
\(830\) 0 0
\(831\) −1.02831e7 −0.516560
\(832\) 0 0
\(833\) 1.28801e7i 0.643142i
\(834\) 0 0
\(835\) −2.29061e6 + 239527.i −0.113693 + 0.0118888i
\(836\) 0 0
\(837\) 8.31689e7 4.10343
\(838\) 0 0
\(839\) −86068.5 −0.00422123 −0.00211062 0.999998i \(-0.500672\pi\)
−0.00211062 + 0.999998i \(0.500672\pi\)
\(840\) 0 0
\(841\) 2.01540e7 0.982586
\(842\) 0 0
\(843\) 2.80545e7 1.35967
\(844\) 0 0
\(845\) 1.40405e6 + 1.34270e7i 0.0676457 + 0.646900i
\(846\) 0 0
\(847\) 1.22141e7i 0.584995i
\(848\) 0 0
\(849\) −1.70659e7 −0.812567
\(850\) 0 0
\(851\) 1.49443e7i 0.707377i
\(852\) 0 0
\(853\) 3.70986e6 0.174576 0.0872880 0.996183i \(-0.472180\pi\)
0.0872880 + 0.996183i \(0.472180\pi\)
\(854\) 0 0
\(855\) 1.53956e7 1.60990e6i 0.720245 0.0753153i
\(856\) 0 0
\(857\) 2.77130e7i 1.28893i −0.764632 0.644467i \(-0.777079\pi\)
0.764632 0.644467i \(-0.222921\pi\)
\(858\) 0 0
\(859\) 1.79861e7i 0.831677i 0.909439 + 0.415838i \(0.136512\pi\)
−0.909439 + 0.415838i \(0.863488\pi\)
\(860\) 0 0
\(861\) 3.83348e7i 1.76232i
\(862\) 0 0
\(863\) 1.53944e7i 0.703615i 0.936072 + 0.351807i \(0.114433\pi\)
−0.936072 + 0.351807i \(0.885567\pi\)
\(864\) 0 0
\(865\) 4.11160e6 + 3.93195e7i 0.186840 + 1.78677i
\(866\) 0 0
\(867\) 2.86412e7 1.29403
\(868\) 0 0
\(869\) 1.52586e7i 0.685433i
\(870\) 0 0
\(871\) −2.10128e7 −0.938511
\(872\) 0 0
\(873\) 2.15497e7i 0.956985i
\(874\) 0 0
\(875\) 1.53553e7 4.96230e6i 0.678015 0.219110i
\(876\) 0 0
\(877\) −2.20053e7 −0.966114 −0.483057 0.875589i \(-0.660474\pi\)
−0.483057 + 0.875589i \(0.660474\pi\)
\(878\) 0 0
\(879\) −3.28194e7 −1.43271
\(880\) 0 0
\(881\) −3.35282e7 −1.45536 −0.727680 0.685916i \(-0.759402\pi\)
−0.727680 + 0.685916i \(0.759402\pi\)
\(882\) 0 0
\(883\) 2.51274e7 1.08454 0.542271 0.840203i \(-0.317565\pi\)
0.542271 + 0.840203i \(0.317565\pi\)
\(884\) 0 0
\(885\) 2.29351e7 2.39831e6i 0.984336 0.102931i
\(886\) 0 0
\(887\) 2.68037e7i 1.14389i −0.820291 0.571947i \(-0.806188\pi\)
0.820291 0.571947i \(-0.193812\pi\)
\(888\) 0 0
\(889\) 2.38091e7 1.01039
\(890\) 0 0
\(891\) 6.97197e7i 2.94213i
\(892\) 0 0
\(893\) −8.69719e6 −0.364964
\(894\) 0 0
\(895\) 2.14567e7 2.24371e6i 0.895377 0.0936287i
\(896\) 0 0
\(897\) 2.45067e7i 1.01696i
\(898\) 0 0
\(899\) 5.30070e6i 0.218743i
\(900\) 0 0
\(901\) 2.57014e6i 0.105474i
\(902\) 0 0
\(903\) 4.82041e6i 0.196727i
\(904\) 0 0
\(905\) 1.57734e7 1.64941e6i 0.640181 0.0669431i
\(906\) 0 0
\(907\) 2.72736e7 1.10084 0.550420 0.834888i \(-0.314468\pi\)
0.550420 + 0.834888i \(0.314468\pi\)
\(908\) 0 0
\(909\) 6.09308e7i 2.44584i
\(910\) 0 0
\(911\) 5.24856e6 0.209529 0.104765 0.994497i \(-0.466591\pi\)
0.104765 + 0.994497i \(0.466591\pi\)
\(912\) 0 0
\(913\) 1.32819e7i 0.527331i
\(914\) 0 0
\(915\) −3.89949e7 + 4.07766e6i −1.53977 + 0.161012i
\(916\) 0 0
\(917\) −1.52453e7 −0.598706
\(918\) 0 0
\(919\) 2.33248e7 0.911024 0.455512 0.890230i \(-0.349456\pi\)
0.455512 + 0.890230i \(0.349456\pi\)
\(920\) 0 0
\(921\) 5.09551e7 1.97942
\(922\) 0 0
\(923\) 3.76145e7 1.45329
\(924\) 0 0
\(925\) 4.16543e7 8.80782e6i 1.60069 0.338465i
\(926\) 0 0
\(927\) 8.03333e7i 3.07041i
\(928\) 0 0
\(929\) 3.98540e6 0.151507 0.0757536 0.997127i \(-0.475864\pi\)
0.0757536 + 0.997127i \(0.475864\pi\)
\(930\) 0 0
\(931\) 4.00848e6i 0.151567i
\(932\) 0 0
\(933\) 1.90982e7 0.718271
\(934\) 0 0
\(935\) 4.90133e6 + 4.68718e7i 0.183352 + 1.75341i
\(936\) 0 0
\(937\) 2.33906e7i 0.870347i −0.900347 0.435174i \(-0.856687\pi\)
0.900347 0.435174i \(-0.143313\pi\)
\(938\) 0 0
\(939\) 3.48247e7i 1.28891i
\(940\) 0 0
\(941\) 1.77697e7i 0.654192i −0.944991 0.327096i \(-0.893930\pi\)
0.944991 0.327096i \(-0.106070\pi\)
\(942\) 0 0
\(943\) 1.59494e7i 0.584069i
\(944\) 0 0
\(945\) 4.81606e7 5.03611e6i 1.75434 0.183449i
\(946\) 0 0
\(947\) 1.60461e7 0.581426 0.290713 0.956810i \(-0.406107\pi\)
0.290713 + 0.956810i \(0.406107\pi\)
\(948\) 0 0
\(949\) 4.74749e7i 1.71119i
\(950\) 0 0
\(951\) 4.65457e7 1.66889
\(952\) 0 0
\(953\) 8.96733e6i 0.319839i 0.987130 + 0.159919i \(0.0511234\pi\)
−0.987130 + 0.159919i \(0.948877\pi\)
\(954\) 0 0
\(955\) −4.36039e6 4.16987e7i −0.154710 1.47950i
\(956\) 0 0
\(957\) 9.23729e6 0.326035
\(958\) 0 0
\(959\) −1.59293e6 −0.0559307
\(960\) 0 0
\(961\) 5.00344e7 1.74767
\(962\) 0 0
\(963\) 4.48976e7 1.56012
\(964\) 0 0
\(965\) 1.29439e7 1.35353e6i 0.447453 0.0467897i
\(966\) 0 0
\(967\) 1.42347e7i 0.489532i 0.969582 + 0.244766i \(0.0787111\pi\)
−0.969582 + 0.244766i \(0.921289\pi\)
\(968\) 0 0
\(969\) −2.15250e7 −0.736435
\(970\) 0 0
\(971\) 1.83592e7i 0.624893i −0.949935 0.312447i \(-0.898851\pi\)
0.949935 0.312447i \(-0.101149\pi\)
\(972\) 0 0
\(973\) −1.29758e7 −0.439391
\(974\) 0 0
\(975\) −6.83077e7 + 1.44437e7i −2.30122 + 0.486593i
\(976\) 0 0
\(977\) 2.23259e7i 0.748294i −0.927370 0.374147i \(-0.877936\pi\)
0.927370 0.374147i \(-0.122064\pi\)
\(978\) 0 0
\(979\) 6.33690e7i 2.11310i
\(980\) 0 0
\(981\) 8.52819e7i 2.82933i
\(982\) 0 0
\(983\) 2.90678e7i 0.959463i −0.877415 0.479732i \(-0.840734\pi\)
0.877415 0.479732i \(-0.159266\pi\)
\(984\) 0 0
\(985\) −516980. 4.94391e6i −0.0169779 0.162360i
\(986\) 0 0
\(987\) −4.73285e7 −1.54643
\(988\) 0 0
\(989\) 2.00556e6i 0.0651995i
\(990\) 0 0
\(991\) −3.44761e7 −1.11515 −0.557575 0.830126i \(-0.688268\pi\)
−0.557575 + 0.830126i \(0.688268\pi\)
\(992\) 0 0
\(993\) 4.20945e7i 1.35473i
\(994\) 0 0
\(995\) −1.13152e6 1.08208e7i −0.0362331 0.346499i
\(996\) 0 0
\(997\) −2.87402e7 −0.915696 −0.457848 0.889031i \(-0.651380\pi\)
−0.457848 + 0.889031i \(0.651380\pi\)
\(998\) 0 0
\(999\) 1.27756e8 4.05013
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 320.6.f.d.289.1 32
4.3 odd 2 inner 320.6.f.d.289.32 yes 32
5.4 even 2 inner 320.6.f.d.289.30 yes 32
8.3 odd 2 inner 320.6.f.d.289.2 yes 32
8.5 even 2 inner 320.6.f.d.289.31 yes 32
20.19 odd 2 inner 320.6.f.d.289.3 yes 32
40.19 odd 2 inner 320.6.f.d.289.29 yes 32
40.29 even 2 inner 320.6.f.d.289.4 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
320.6.f.d.289.1 32 1.1 even 1 trivial
320.6.f.d.289.2 yes 32 8.3 odd 2 inner
320.6.f.d.289.3 yes 32 20.19 odd 2 inner
320.6.f.d.289.4 yes 32 40.29 even 2 inner
320.6.f.d.289.29 yes 32 40.19 odd 2 inner
320.6.f.d.289.30 yes 32 5.4 even 2 inner
320.6.f.d.289.31 yes 32 8.5 even 2 inner
320.6.f.d.289.32 yes 32 4.3 odd 2 inner