Properties

Label 1008.3.cg.q.577.7
Level $1008$
Weight $3$
Character 1008.577
Analytic conductor $27.466$
Analytic rank $0$
Dimension $16$
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] = [1008,3,Mod(145,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.145");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.cg (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: \(27.4660106475\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 81 x^{14} - 118 x^{13} + 1960 x^{12} - 366 x^{11} + 37625 x^{10} - 83714 x^{9} + 623931 x^{8} + 289492 x^{7} + 241286 x^{6} - 4777608 x^{5} + \cdots + 1148023744 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{18} \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 577.7
Root \(-3.20903 - 1.64043i\) of defining polynomial
Character \(\chi\) \(=\) 1008.577
Dual form 1008.3.cg.q.145.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.51611 - 2.60738i) q^{5} +(-6.91807 + 1.06788i) q^{7} +O(q^{10})\) \(q+(4.51611 - 2.60738i) q^{5} +(-6.91807 + 1.06788i) q^{7} +(-4.56040 + 7.89885i) q^{11} -3.43129i q^{13} +(4.73709 + 2.73496i) q^{17} +(9.45229 - 5.45728i) q^{19} +(9.95199 + 17.2374i) q^{23} +(1.09685 - 1.89981i) q^{25} +36.7480 q^{29} +(17.8110 + 10.2832i) q^{31} +(-28.4584 + 22.8607i) q^{35} +(23.5754 + 40.8338i) q^{37} -41.5146i q^{41} +73.9986 q^{43} +(-51.2578 + 29.5937i) q^{47} +(46.7193 - 14.7754i) q^{49} +(31.7014 - 54.9084i) q^{53} +47.5628i q^{55} +(-44.8630 - 25.9017i) q^{59} +(21.2053 - 12.2429i) q^{61} +(-8.94668 - 15.4961i) q^{65} +(9.58916 - 16.6089i) q^{67} -2.54627 q^{71} +(102.444 + 59.1459i) q^{73} +(23.1141 - 59.5147i) q^{77} +(5.67414 + 9.82791i) q^{79} -30.4340i q^{83} +28.5243 q^{85} +(-139.698 + 80.6547i) q^{89} +(3.66422 + 23.7379i) q^{91} +(28.4584 - 49.2914i) q^{95} -101.257i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{7} + 24 q^{19} + 36 q^{25} + 84 q^{31} - 68 q^{37} - 80 q^{43} - 184 q^{49} + 216 q^{61} - 56 q^{67} + 156 q^{73} - 28 q^{79} + 448 q^{85} - 48 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 4.51611 2.60738i 0.903223 0.521476i 0.0249783 0.999688i \(-0.492048\pi\)
0.878244 + 0.478212i \(0.158715\pi\)
\(6\) 0 0
\(7\) −6.91807 + 1.06788i −0.988295 + 0.152555i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.56040 + 7.89885i −0.414582 + 0.718077i −0.995384 0.0959675i \(-0.969406\pi\)
0.580802 + 0.814045i \(0.302739\pi\)
\(12\) 0 0
\(13\) 3.43129i 0.263946i −0.991253 0.131973i \(-0.957869\pi\)
0.991253 0.131973i \(-0.0421312\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.73709 + 2.73496i 0.278652 + 0.160880i 0.632813 0.774305i \(-0.281900\pi\)
−0.354161 + 0.935184i \(0.615233\pi\)
\(18\) 0 0
\(19\) 9.45229 5.45728i 0.497489 0.287225i −0.230187 0.973146i \(-0.573934\pi\)
0.727676 + 0.685921i \(0.240601\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 9.95199 + 17.2374i 0.432695 + 0.749450i 0.997104 0.0760449i \(-0.0242292\pi\)
−0.564409 + 0.825495i \(0.690896\pi\)
\(24\) 0 0
\(25\) 1.09685 1.89981i 0.0438741 0.0759922i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 36.7480 1.26717 0.633586 0.773672i \(-0.281582\pi\)
0.633586 + 0.773672i \(0.281582\pi\)
\(30\) 0 0
\(31\) 17.8110 + 10.2832i 0.574549 + 0.331716i 0.758964 0.651132i \(-0.225706\pi\)
−0.184415 + 0.982848i \(0.559039\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −28.4584 + 22.8607i −0.813097 + 0.653163i
\(36\) 0 0
\(37\) 23.5754 + 40.8338i 0.637173 + 1.10362i 0.986050 + 0.166448i \(0.0532297\pi\)
−0.348877 + 0.937168i \(0.613437\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 41.5146i 1.01255i −0.862372 0.506276i \(-0.831022\pi\)
0.862372 0.506276i \(-0.168978\pi\)
\(42\) 0 0
\(43\) 73.9986 1.72090 0.860448 0.509538i \(-0.170184\pi\)
0.860448 + 0.509538i \(0.170184\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −51.2578 + 29.5937i −1.09059 + 0.629654i −0.933734 0.357967i \(-0.883470\pi\)
−0.156858 + 0.987621i \(0.550137\pi\)
\(48\) 0 0
\(49\) 46.7193 14.7754i 0.953454 0.301538i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 31.7014 54.9084i 0.598139 1.03601i −0.394957 0.918700i \(-0.629240\pi\)
0.993096 0.117307i \(-0.0374263\pi\)
\(54\) 0 0
\(55\) 47.5628i 0.864778i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −44.8630 25.9017i −0.760390 0.439012i 0.0690456 0.997614i \(-0.478005\pi\)
−0.829436 + 0.558602i \(0.811338\pi\)
\(60\) 0 0
\(61\) 21.2053 12.2429i 0.347628 0.200703i −0.316012 0.948755i \(-0.602344\pi\)
0.663640 + 0.748052i \(0.269011\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.94668 15.4961i −0.137641 0.238402i
\(66\) 0 0
\(67\) 9.58916 16.6089i 0.143122 0.247894i −0.785549 0.618800i \(-0.787619\pi\)
0.928671 + 0.370905i \(0.120953\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.54627 −0.0358630 −0.0179315 0.999839i \(-0.505708\pi\)
−0.0179315 + 0.999839i \(0.505708\pi\)
\(72\) 0 0
\(73\) 102.444 + 59.1459i 1.40334 + 0.810218i 0.994734 0.102494i \(-0.0326821\pi\)
0.408605 + 0.912711i \(0.366015\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 23.1141 59.5147i 0.300183 0.772918i
\(78\) 0 0
\(79\) 5.67414 + 9.82791i 0.0718246 + 0.124404i 0.899701 0.436507i \(-0.143784\pi\)
−0.827876 + 0.560911i \(0.810451\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 30.4340i 0.366675i −0.983050 0.183337i \(-0.941310\pi\)
0.983050 0.183337i \(-0.0586901\pi\)
\(84\) 0 0
\(85\) 28.5243 0.335580
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −139.698 + 80.6547i −1.56964 + 0.906233i −0.573432 + 0.819253i \(0.694388\pi\)
−0.996210 + 0.0869797i \(0.972278\pi\)
\(90\) 0 0
\(91\) 3.66422 + 23.7379i 0.0402661 + 0.260856i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 28.4584 49.2914i 0.299562 0.518857i
\(96\) 0 0
\(97\) 101.257i 1.04389i −0.852979 0.521945i \(-0.825207\pi\)
0.852979 0.521945i \(-0.174793\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 58.1423 + 33.5685i 0.575667 + 0.332361i 0.759409 0.650613i \(-0.225488\pi\)
−0.183743 + 0.982974i \(0.558821\pi\)
\(102\) 0 0
\(103\) 96.0523 55.4558i 0.932547 0.538406i 0.0449308 0.998990i \(-0.485693\pi\)
0.887616 + 0.460584i \(0.152360\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 76.4341 + 132.388i 0.714337 + 1.23727i 0.963215 + 0.268734i \(0.0866051\pi\)
−0.248877 + 0.968535i \(0.580062\pi\)
\(108\) 0 0
\(109\) −57.1676 + 99.0172i −0.524474 + 0.908415i 0.475120 + 0.879921i \(0.342405\pi\)
−0.999594 + 0.0284941i \(0.990929\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 71.0257 0.628546 0.314273 0.949333i \(-0.398239\pi\)
0.314273 + 0.949333i \(0.398239\pi\)
\(114\) 0 0
\(115\) 89.8887 + 51.8972i 0.781641 + 0.451280i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −35.6921 13.8620i −0.299933 0.116487i
\(120\) 0 0
\(121\) 18.9055 + 32.7452i 0.156244 + 0.270622i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 118.929i 0.951435i
\(126\) 0 0
\(127\) 73.4312 0.578198 0.289099 0.957299i \(-0.406644\pi\)
0.289099 + 0.957299i \(0.406644\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 116.654 67.3503i 0.890490 0.514125i 0.0163873 0.999866i \(-0.494784\pi\)
0.874103 + 0.485741i \(0.161450\pi\)
\(132\) 0 0
\(133\) −59.5638 + 47.8477i −0.447848 + 0.359757i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −59.1992 + 102.536i −0.432111 + 0.748438i −0.997055 0.0766911i \(-0.975564\pi\)
0.564944 + 0.825129i \(0.308898\pi\)
\(138\) 0 0
\(139\) 24.3343i 0.175067i −0.996162 0.0875336i \(-0.972101\pi\)
0.996162 0.0875336i \(-0.0278985\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 27.1033 + 15.6481i 0.189533 + 0.109427i
\(144\) 0 0
\(145\) 165.958 95.8160i 1.14454 0.660800i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.19935 + 7.27348i 0.0281835 + 0.0488153i 0.879773 0.475394i \(-0.157694\pi\)
−0.851590 + 0.524209i \(0.824361\pi\)
\(150\) 0 0
\(151\) −31.4658 + 54.5003i −0.208383 + 0.360929i −0.951205 0.308559i \(-0.900153\pi\)
0.742823 + 0.669488i \(0.233487\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 107.249 0.691928
\(156\) 0 0
\(157\) 63.0893 + 36.4246i 0.401843 + 0.232004i 0.687279 0.726394i \(-0.258805\pi\)
−0.285436 + 0.958398i \(0.592138\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −87.2560 108.622i −0.541963 0.674669i
\(162\) 0 0
\(163\) 15.2579 + 26.4274i 0.0936065 + 0.162131i 0.909026 0.416739i \(-0.136827\pi\)
−0.815420 + 0.578870i \(0.803494\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 259.382i 1.55319i −0.630003 0.776593i \(-0.716946\pi\)
0.630003 0.776593i \(-0.283054\pi\)
\(168\) 0 0
\(169\) 157.226 0.930333
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −295.907 + 170.842i −1.71044 + 0.987525i −0.776491 + 0.630129i \(0.783002\pi\)
−0.933953 + 0.357397i \(0.883664\pi\)
\(174\) 0 0
\(175\) −5.55933 + 14.3143i −0.0317676 + 0.0817959i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 140.437 243.243i 0.784562 1.35890i −0.144699 0.989476i \(-0.546221\pi\)
0.929261 0.369425i \(-0.120445\pi\)
\(180\) 0 0
\(181\) 213.356i 1.17876i 0.807855 + 0.589382i \(0.200629\pi\)
−0.807855 + 0.589382i \(0.799371\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 212.938 + 122.940i 1.15102 + 0.664541i
\(186\) 0 0
\(187\) −43.2060 + 24.9450i −0.231048 + 0.133396i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 166.145 + 287.771i 0.869869 + 1.50666i 0.862130 + 0.506687i \(0.169130\pi\)
0.00773872 + 0.999970i \(0.497537\pi\)
\(192\) 0 0
\(193\) 82.6792 143.205i 0.428390 0.741993i −0.568341 0.822793i \(-0.692414\pi\)
0.996730 + 0.0808007i \(0.0257477\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −200.474 −1.01764 −0.508818 0.860874i \(-0.669918\pi\)
−0.508818 + 0.860874i \(0.669918\pi\)
\(198\) 0 0
\(199\) 127.958 + 73.8764i 0.643003 + 0.371238i 0.785770 0.618518i \(-0.212267\pi\)
−0.142767 + 0.989756i \(0.545600\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −254.225 + 39.2425i −1.25234 + 0.193313i
\(204\) 0 0
\(205\) −108.244 187.485i −0.528021 0.914559i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 99.5495i 0.476314i
\(210\) 0 0
\(211\) −208.573 −0.988495 −0.494248 0.869321i \(-0.664556\pi\)
−0.494248 + 0.869321i \(0.664556\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 334.186 192.942i 1.55435 0.897406i
\(216\) 0 0
\(217\) −134.199 52.1198i −0.618429 0.240183i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9.38444 16.2543i 0.0424635 0.0735490i
\(222\) 0 0
\(223\) 413.973i 1.85638i −0.372104 0.928191i \(-0.621364\pi\)
0.372104 0.928191i \(-0.378636\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −234.861 135.597i −1.03463 0.597344i −0.116322 0.993212i \(-0.537111\pi\)
−0.918308 + 0.395868i \(0.870444\pi\)
\(228\) 0 0
\(229\) −306.643 + 177.040i −1.33905 + 0.773101i −0.986667 0.162754i \(-0.947962\pi\)
−0.352384 + 0.935856i \(0.614629\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −136.823 236.984i −0.587221 1.01710i −0.994595 0.103835i \(-0.966889\pi\)
0.407373 0.913262i \(-0.366445\pi\)
\(234\) 0 0
\(235\) −154.324 + 267.297i −0.656698 + 1.13744i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −362.362 −1.51616 −0.758080 0.652162i \(-0.773862\pi\)
−0.758080 + 0.652162i \(0.773862\pi\)
\(240\) 0 0
\(241\) −42.4378 24.5015i −0.176090 0.101666i 0.409364 0.912371i \(-0.365751\pi\)
−0.585454 + 0.810705i \(0.699084\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 172.465 188.542i 0.703937 0.769559i
\(246\) 0 0
\(247\) −18.7255 32.4336i −0.0758118 0.131310i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 189.207i 0.753813i 0.926251 + 0.376907i \(0.123012\pi\)
−0.926251 + 0.376907i \(0.876988\pi\)
\(252\) 0 0
\(253\) −181.540 −0.717551
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.7505 10.8256i 0.0729591 0.0421229i −0.463077 0.886318i \(-0.653255\pi\)
0.536036 + 0.844195i \(0.319921\pi\)
\(258\) 0 0
\(259\) −206.702 257.315i −0.798077 0.993495i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −27.9586 + 48.4258i −0.106307 + 0.184128i −0.914271 0.405103i \(-0.867236\pi\)
0.807965 + 0.589231i \(0.200569\pi\)
\(264\) 0 0
\(265\) 330.630i 1.24766i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −54.8437 31.6640i −0.203880 0.117710i 0.394584 0.918860i \(-0.370889\pi\)
−0.598464 + 0.801150i \(0.704222\pi\)
\(270\) 0 0
\(271\) −58.2356 + 33.6223i −0.214891 + 0.124068i −0.603583 0.797300i \(-0.706261\pi\)
0.388691 + 0.921368i \(0.372927\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.0042 + 17.3277i 0.0363788 + 0.0630100i
\(276\) 0 0
\(277\) −220.081 + 381.191i −0.794515 + 1.37614i 0.128632 + 0.991692i \(0.458941\pi\)
−0.923147 + 0.384447i \(0.874392\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 265.924 0.946350 0.473175 0.880969i \(-0.343108\pi\)
0.473175 + 0.880969i \(0.343108\pi\)
\(282\) 0 0
\(283\) 108.996 + 62.9289i 0.385145 + 0.222364i 0.680054 0.733162i \(-0.261956\pi\)
−0.294909 + 0.955525i \(0.595289\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 44.3327 + 287.201i 0.154469 + 1.00070i
\(288\) 0 0
\(289\) −129.540 224.370i −0.448235 0.776366i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 219.939i 0.750646i 0.926894 + 0.375323i \(0.122468\pi\)
−0.926894 + 0.375323i \(0.877532\pi\)
\(294\) 0 0
\(295\) −270.142 −0.915736
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 59.1464 34.1482i 0.197814 0.114208i
\(300\) 0 0
\(301\) −511.927 + 79.0217i −1.70075 + 0.262531i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 63.8437 110.581i 0.209324 0.362559i
\(306\) 0 0
\(307\) 233.059i 0.759150i −0.925161 0.379575i \(-0.876070\pi\)
0.925161 0.379575i \(-0.123930\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −358.462 206.958i −1.15261 0.665461i −0.203089 0.979160i \(-0.565098\pi\)
−0.949522 + 0.313699i \(0.898432\pi\)
\(312\) 0 0
\(313\) 360.041 207.870i 1.15029 0.664121i 0.201333 0.979523i \(-0.435473\pi\)
0.948958 + 0.315402i \(0.102139\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −251.731 436.011i −0.794105 1.37543i −0.923406 0.383825i \(-0.874607\pi\)
0.129301 0.991605i \(-0.458727\pi\)
\(318\) 0 0
\(319\) −167.586 + 290.267i −0.525347 + 0.909928i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 59.7017 0.184835
\(324\) 0 0
\(325\) −6.51879 3.76362i −0.0200578 0.0115804i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 323.002 259.469i 0.981770 0.788659i
\(330\) 0 0
\(331\) −120.274 208.321i −0.363366 0.629368i 0.625147 0.780507i \(-0.285039\pi\)
−0.988513 + 0.151139i \(0.951706\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 100.010i 0.298538i
\(336\) 0 0
\(337\) 202.444 0.600725 0.300362 0.953825i \(-0.402892\pi\)
0.300362 + 0.953825i \(0.402892\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −162.451 + 93.7910i −0.476395 + 0.275047i
\(342\) 0 0
\(343\) −307.429 + 152.108i −0.896293 + 0.443462i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −210.502 + 364.601i −0.606635 + 1.05072i 0.385156 + 0.922852i \(0.374148\pi\)
−0.991791 + 0.127871i \(0.959186\pi\)
\(348\) 0 0
\(349\) 214.402i 0.614332i −0.951656 0.307166i \(-0.900619\pi\)
0.951656 0.307166i \(-0.0993807\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 540.855 + 312.263i 1.53217 + 0.884597i 0.999262 + 0.0384229i \(0.0122334\pi\)
0.532906 + 0.846174i \(0.321100\pi\)
\(354\) 0 0
\(355\) −11.4993 + 6.63910i −0.0323923 + 0.0187017i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 290.906 + 503.864i 0.810323 + 1.40352i 0.912638 + 0.408768i \(0.134041\pi\)
−0.102316 + 0.994752i \(0.532625\pi\)
\(360\) 0 0
\(361\) −120.936 + 209.468i −0.335003 + 0.580243i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 616.863 1.69004
\(366\) 0 0
\(367\) −311.562 179.880i −0.848942 0.490137i 0.0113519 0.999936i \(-0.496387\pi\)
−0.860294 + 0.509799i \(0.829720\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −160.676 + 413.713i −0.433090 + 1.11513i
\(372\) 0 0
\(373\) 67.2930 + 116.555i 0.180410 + 0.312480i 0.942020 0.335556i \(-0.108924\pi\)
−0.761610 + 0.648036i \(0.775591\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 126.093i 0.334465i
\(378\) 0 0
\(379\) 229.181 0.604699 0.302349 0.953197i \(-0.402229\pi\)
0.302349 + 0.953197i \(0.402229\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 29.8010 17.2056i 0.0778093 0.0449232i −0.460591 0.887613i \(-0.652362\pi\)
0.538400 + 0.842689i \(0.319029\pi\)
\(384\) 0 0
\(385\) −50.7914 329.042i −0.131926 0.854656i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −44.9912 + 77.9270i −0.115659 + 0.200327i −0.918043 0.396481i \(-0.870231\pi\)
0.802384 + 0.596808i \(0.203565\pi\)
\(390\) 0 0
\(391\) 108.873i 0.278448i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 51.2502 + 29.5893i 0.129747 + 0.0749096i
\(396\) 0 0
\(397\) −197.880 + 114.246i −0.498439 + 0.287774i −0.728069 0.685504i \(-0.759582\pi\)
0.229629 + 0.973278i \(0.426249\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −214.759 371.974i −0.535559 0.927616i −0.999136 0.0415591i \(-0.986768\pi\)
0.463577 0.886057i \(-0.346566\pi\)
\(402\) 0 0
\(403\) 35.2847 61.1148i 0.0875550 0.151650i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −430.053 −1.05664
\(408\) 0 0
\(409\) 373.831 + 215.831i 0.914011 + 0.527705i 0.881720 0.471774i \(-0.156386\pi\)
0.0322917 + 0.999478i \(0.489719\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 338.025 + 131.281i 0.818463 + 0.317872i
\(414\) 0 0
\(415\) −79.3530 137.443i −0.191212 0.331189i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 144.735i 0.345430i 0.984972 + 0.172715i \(0.0552540\pi\)
−0.984972 + 0.172715i \(0.944746\pi\)
\(420\) 0 0
\(421\) −730.197 −1.73444 −0.867218 0.497929i \(-0.834094\pi\)
−0.867218 + 0.497929i \(0.834094\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 10.3918 5.99969i 0.0244512 0.0141169i
\(426\) 0 0
\(427\) −133.626 + 107.342i −0.312941 + 0.251386i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −145.116 + 251.348i −0.336695 + 0.583173i −0.983809 0.179220i \(-0.942643\pi\)
0.647114 + 0.762394i \(0.275976\pi\)
\(432\) 0 0
\(433\) 439.027i 1.01392i −0.861970 0.506960i \(-0.830769\pi\)
0.861970 0.506960i \(-0.169231\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 188.138 + 108.622i 0.430522 + 0.248562i
\(438\) 0 0
\(439\) 252.777 145.941i 0.575802 0.332439i −0.183662 0.982990i \(-0.558795\pi\)
0.759463 + 0.650550i \(0.225462\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −268.639 465.297i −0.606410 1.05033i −0.991827 0.127590i \(-0.959276\pi\)
0.385417 0.922742i \(-0.374057\pi\)
\(444\) 0 0
\(445\) −420.595 + 728.492i −0.945157 + 1.63706i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −577.008 −1.28509 −0.642547 0.766246i \(-0.722122\pi\)
−0.642547 + 0.766246i \(0.722122\pi\)
\(450\) 0 0
\(451\) 327.917 + 189.323i 0.727090 + 0.419785i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 78.4417 + 97.6491i 0.172399 + 0.214613i
\(456\) 0 0
\(457\) −294.230 509.621i −0.643830 1.11515i −0.984571 0.174988i \(-0.944011\pi\)
0.340741 0.940157i \(-0.389322\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 216.419i 0.469455i −0.972061 0.234728i \(-0.924580\pi\)
0.972061 0.234728i \(-0.0754198\pi\)
\(462\) 0 0
\(463\) 135.169 0.291941 0.145971 0.989289i \(-0.453370\pi\)
0.145971 + 0.989289i \(0.453370\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 676.706 390.696i 1.44905 0.836609i 0.450624 0.892714i \(-0.351202\pi\)
0.998425 + 0.0561055i \(0.0178683\pi\)
\(468\) 0 0
\(469\) −48.6021 + 125.142i −0.103629 + 0.266827i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −337.463 + 584.503i −0.713453 + 1.23574i
\(474\) 0 0
\(475\) 23.9433i 0.0504070i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −200.349 115.672i −0.418266 0.241486i 0.276069 0.961138i \(-0.410968\pi\)
−0.694335 + 0.719652i \(0.744301\pi\)
\(480\) 0 0
\(481\) 140.113 80.8941i 0.291295 0.168179i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −264.016 457.289i −0.544363 0.942865i
\(486\) 0 0
\(487\) −213.293 + 369.434i −0.437973 + 0.758592i −0.997533 0.0701980i \(-0.977637\pi\)
0.559560 + 0.828790i \(0.310970\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 259.716 0.528952 0.264476 0.964392i \(-0.414801\pi\)
0.264476 + 0.964392i \(0.414801\pi\)
\(492\) 0 0
\(493\) 174.078 + 100.504i 0.353100 + 0.203863i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.6153 2.71912i 0.0354432 0.00547107i
\(498\) 0 0
\(499\) −452.741 784.170i −0.907296 1.57148i −0.817805 0.575495i \(-0.804809\pi\)
−0.0894906 0.995988i \(-0.528524\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 981.208i 1.95071i −0.220636 0.975356i \(-0.570813\pi\)
0.220636 0.975356i \(-0.429187\pi\)
\(504\) 0 0
\(505\) 350.103 0.693274
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 48.8362 28.1956i 0.0959453 0.0553940i −0.451260 0.892393i \(-0.649025\pi\)
0.547205 + 0.836999i \(0.315692\pi\)
\(510\) 0 0
\(511\) −771.873 299.777i −1.51051 0.586649i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 289.189 500.890i 0.561532 0.972601i
\(516\) 0 0
\(517\) 539.837i 1.04417i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −634.605 366.389i −1.21805 0.703242i −0.253550 0.967322i \(-0.581598\pi\)
−0.964501 + 0.264080i \(0.914932\pi\)
\(522\) 0 0
\(523\) 9.83785 5.67988i 0.0188104 0.0108602i −0.490565 0.871404i \(-0.663210\pi\)
0.509376 + 0.860544i \(0.329876\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 56.2482 + 97.4248i 0.106733 + 0.184867i
\(528\) 0 0
\(529\) 66.4156 115.035i 0.125549 0.217458i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −142.449 −0.267258
\(534\) 0 0
\(535\) 690.370 + 398.585i 1.29041 + 0.745019i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −96.3503 + 436.410i −0.178758 + 0.809666i
\(540\) 0 0
\(541\) 312.987 + 542.109i 0.578534 + 1.00205i 0.995648 + 0.0931960i \(0.0297083\pi\)
−0.417114 + 0.908854i \(0.636958\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 596.231i 1.09400i
\(546\) 0 0
\(547\) 528.430 0.966051 0.483026 0.875606i \(-0.339538\pi\)
0.483026 + 0.875606i \(0.339538\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 347.353 200.544i 0.630404 0.363964i
\(552\) 0 0
\(553\) −49.7491 61.9308i −0.0899623 0.111991i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −133.581 + 231.369i −0.239822 + 0.415384i −0.960663 0.277716i \(-0.910422\pi\)
0.720841 + 0.693100i \(0.243756\pi\)
\(558\) 0 0
\(559\) 253.911i 0.454223i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −718.302 414.712i −1.27585 0.736610i −0.299765 0.954013i \(-0.596908\pi\)
−0.976082 + 0.217403i \(0.930241\pi\)
\(564\) 0 0
\(565\) 320.760 185.191i 0.567717 0.327771i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12.3916 21.4628i −0.0217778 0.0377203i 0.854931 0.518742i \(-0.173599\pi\)
−0.876709 + 0.481021i \(0.840266\pi\)
\(570\) 0 0
\(571\) −548.479 + 949.994i −0.960559 + 1.66374i −0.239459 + 0.970907i \(0.576970\pi\)
−0.721100 + 0.692831i \(0.756363\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 43.6635 0.0759365
\(576\) 0 0
\(577\) 883.145 + 509.884i 1.53058 + 0.883681i 0.999335 + 0.0364622i \(0.0116089\pi\)
0.531245 + 0.847218i \(0.321724\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 32.4999 + 210.544i 0.0559379 + 0.362383i
\(582\) 0 0
\(583\) 289.142 + 500.809i 0.495955 + 0.859020i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 351.405i 0.598646i 0.954152 + 0.299323i \(0.0967609\pi\)
−0.954152 + 0.299323i \(0.903239\pi\)
\(588\) 0 0
\(589\) 224.473 0.381109
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −624.862 + 360.764i −1.05373 + 0.608371i −0.923691 0.383138i \(-0.874844\pi\)
−0.130039 + 0.991509i \(0.541510\pi\)
\(594\) 0 0
\(595\) −197.333 + 30.4606i −0.331652 + 0.0511942i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −70.5809 + 122.250i −0.117831 + 0.204090i −0.918908 0.394472i \(-0.870928\pi\)
0.801077 + 0.598562i \(0.204261\pi\)
\(600\) 0 0
\(601\) 478.176i 0.795634i −0.917465 0.397817i \(-0.869768\pi\)
0.917465 0.397817i \(-0.130232\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 170.759 + 98.5875i 0.282245 + 0.162954i
\(606\) 0 0
\(607\) 961.350 555.036i 1.58377 0.914391i 0.589471 0.807790i \(-0.299336\pi\)
0.994302 0.106602i \(-0.0339970\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 101.545 + 175.881i 0.166194 + 0.287857i
\(612\) 0 0
\(613\) −298.361 + 516.777i −0.486723 + 0.843029i −0.999884 0.0152634i \(-0.995141\pi\)
0.513160 + 0.858293i \(0.328475\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20.9891 0.0340181 0.0170090 0.999855i \(-0.494586\pi\)
0.0170090 + 0.999855i \(0.494586\pi\)
\(618\) 0 0
\(619\) 867.158 + 500.654i 1.40090 + 0.808811i 0.994485 0.104877i \(-0.0334450\pi\)
0.406416 + 0.913688i \(0.366778\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 880.311 707.156i 1.41302 1.13508i
\(624\) 0 0
\(625\) 337.515 + 584.593i 0.540024 + 0.935349i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 257.911i 0.410033i
\(630\) 0 0
\(631\) 442.571 0.701381 0.350691 0.936491i \(-0.385947\pi\)
0.350691 + 0.936491i \(0.385947\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 331.624 191.463i 0.522242 0.301516i
\(636\) 0 0
\(637\) −50.6986 160.307i −0.0795896 0.251660i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 24.9968 43.2958i 0.0389966 0.0675441i −0.845868 0.533392i \(-0.820917\pi\)
0.884865 + 0.465848i \(0.154251\pi\)
\(642\) 0 0
\(643\) 603.575i 0.938687i −0.883016 0.469343i \(-0.844491\pi\)
0.883016 0.469343i \(-0.155509\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 922.823 + 532.792i 1.42631 + 0.823481i 0.996827 0.0795944i \(-0.0253625\pi\)
0.429483 + 0.903075i \(0.358696\pi\)
\(648\) 0 0
\(649\) 409.187 236.244i 0.630488 0.364013i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 437.990 + 758.620i 0.670734 + 1.16175i 0.977696 + 0.210024i \(0.0673543\pi\)
−0.306962 + 0.951722i \(0.599312\pi\)
\(654\) 0 0
\(655\) 351.216 608.323i 0.536207 0.928738i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 229.670 0.348513 0.174256 0.984700i \(-0.444248\pi\)
0.174256 + 0.984700i \(0.444248\pi\)
\(660\) 0 0
\(661\) 649.011 + 374.707i 0.981863 + 0.566879i 0.902832 0.429994i \(-0.141484\pi\)
0.0790306 + 0.996872i \(0.474818\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −144.240 + 371.391i −0.216902 + 0.558483i
\(666\) 0 0
\(667\) 365.716 + 633.439i 0.548300 + 0.949683i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 223.330i 0.332832i
\(672\) 0 0
\(673\) 229.438 0.340919 0.170459 0.985365i \(-0.445475\pi\)
0.170459 + 0.985365i \(0.445475\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 239.778 138.436i 0.354177 0.204484i −0.312347 0.949968i \(-0.601115\pi\)
0.666523 + 0.745484i \(0.267782\pi\)
\(678\) 0 0
\(679\) 108.131 + 700.504i 0.159250 + 1.03167i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 328.026 568.157i 0.480272 0.831855i −0.519472 0.854487i \(-0.673871\pi\)
0.999744 + 0.0226323i \(0.00720470\pi\)
\(684\) 0 0
\(685\) 617.419i 0.901342i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −188.407 108.777i −0.273450 0.157876i
\(690\) 0 0
\(691\) −185.761 + 107.249i −0.268829 + 0.155208i −0.628355 0.777926i \(-0.716272\pi\)
0.359526 + 0.933135i \(0.382938\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −63.4489 109.897i −0.0912933 0.158125i
\(696\) 0 0
\(697\) 113.541 196.658i 0.162899 0.282150i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −492.902 −0.703142 −0.351571 0.936161i \(-0.614352\pi\)
−0.351571 + 0.936161i \(0.614352\pi\)
\(702\) 0 0
\(703\) 445.683 + 257.315i 0.633973 + 0.366024i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −438.080 170.140i −0.619632 0.240651i
\(708\) 0 0
\(709\) −418.012 724.018i −0.589580 1.02118i −0.994287 0.106736i \(-0.965960\pi\)
0.404708 0.914446i \(-0.367373\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 409.353i 0.574128i
\(714\) 0 0
\(715\) 163.202 0.228254
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −363.072 + 209.620i −0.504968 + 0.291544i −0.730763 0.682631i \(-0.760836\pi\)
0.225795 + 0.974175i \(0.427502\pi\)
\(720\) 0 0
\(721\) −605.276 + 486.220i −0.839495 + 0.674369i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 40.3072 69.8141i 0.0555961 0.0962952i
\(726\) 0 0
\(727\) 872.570i 1.20023i −0.799912 0.600117i \(-0.795121\pi\)
0.799912 0.600117i \(-0.204879\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 350.538 + 202.383i 0.479532 + 0.276858i
\(732\) 0 0
\(733\) 81.7339 47.1891i 0.111506 0.0643780i −0.443210 0.896418i \(-0.646160\pi\)
0.554716 + 0.832040i \(0.312827\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 87.4609 + 151.487i 0.118671 + 0.205545i
\(738\) 0 0
\(739\) −91.8991 + 159.174i −0.124356 + 0.215391i −0.921481 0.388423i \(-0.873020\pi\)
0.797125 + 0.603814i \(0.206353\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −243.953 −0.328335 −0.164167 0.986432i \(-0.552494\pi\)
−0.164167 + 0.986432i \(0.552494\pi\)
\(744\) 0 0
\(745\) 37.9295 + 21.8986i 0.0509120 + 0.0293941i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −670.151 834.244i −0.894727 1.11381i
\(750\) 0 0
\(751\) 120.946 + 209.484i 0.161046 + 0.278940i 0.935244 0.354003i \(-0.115180\pi\)
−0.774198 + 0.632943i \(0.781847\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 328.173i 0.434666i
\(756\) 0 0
\(757\) 1368.88 1.80829 0.904147 0.427221i \(-0.140508\pi\)
0.904147 + 0.427221i \(0.140508\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 402.629 232.458i 0.529079 0.305464i −0.211562 0.977365i \(-0.567855\pi\)
0.740641 + 0.671900i \(0.234522\pi\)
\(762\) 0 0
\(763\) 289.751 746.056i 0.379752 0.977793i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −88.8762 + 153.938i −0.115875 + 0.200702i
\(768\) 0 0
\(769\) 2.47014i 0.00321215i 0.999999 + 0.00160608i \(0.000511230\pi\)
−0.999999 + 0.00160608i \(0.999489\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 667.371 + 385.307i 0.863352 + 0.498456i 0.865133 0.501542i \(-0.167234\pi\)
−0.00178154 + 0.999998i \(0.500567\pi\)
\(774\) 0 0
\(775\) 39.0721 22.5583i 0.0504157 0.0291075i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −226.557 392.408i −0.290830 0.503733i
\(780\) 0 0
\(781\) 11.6120 20.1126i 0.0148682 0.0257524i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 379.891 0.483938
\(786\) 0 0
\(787\) 404.529 + 233.555i 0.514014 + 0.296766i 0.734482 0.678628i \(-0.237425\pi\)
−0.220468 + 0.975394i \(0.570758\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −491.360 + 75.8470i −0.621189 + 0.0958875i
\(792\) 0 0
\(793\) −42.0090 72.7617i −0.0529747 0.0917549i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 511.558i 0.641855i −0.947104 0.320927i \(-0.896005\pi\)
0.947104 0.320927i \(-0.103995\pi\)
\(798\) 0 0
\(799\) −323.750 −0.405195
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −934.369 + 539.458i −1.16360 + 0.671803i
\(804\) 0 0
\(805\) −677.276 263.038i −0.841336 0.326755i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 695.722 1205.03i 0.859978 1.48953i −0.0119703 0.999928i \(-0.503810\pi\)
0.871949 0.489598i \(-0.162856\pi\)
\(810\) 0 0
\(811\) 1203.34i 1.48377i 0.670527 + 0.741885i \(0.266068\pi\)
−0.670527 + 0.741885i \(0.733932\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 137.812 + 79.5660i 0.169095 + 0.0976271i
\(816\) 0 0
\(817\) 699.455 403.831i 0.856127 0.494285i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −134.906 233.663i −0.164319 0.284608i 0.772094 0.635508i \(-0.219209\pi\)
−0.936413 + 0.350900i \(0.885876\pi\)
\(822\) 0 0
\(823\) −568.375 + 984.454i −0.690613 + 1.19618i 0.281024 + 0.959701i \(0.409326\pi\)
−0.971637 + 0.236476i \(0.924007\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 39.3524 0.0475845 0.0237922 0.999717i \(-0.492426\pi\)
0.0237922 + 0.999717i \(0.492426\pi\)
\(828\) 0 0
\(829\) 896.538 + 517.616i 1.08147 + 0.624386i 0.931292 0.364273i \(-0.118682\pi\)
0.150177 + 0.988659i \(0.452016\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 261.723 + 57.7831i 0.314193 + 0.0693674i
\(834\) 0 0
\(835\) −676.307 1171.40i −0.809949 1.40287i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 836.458i 0.996970i 0.866898 + 0.498485i \(0.166110\pi\)
−0.866898 + 0.498485i \(0.833890\pi\)
\(840\) 0 0
\(841\) 509.416 0.605726
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 710.051 409.948i 0.840298 0.485146i
\(846\) 0 0
\(847\) −165.757 206.345i −0.195699 0.243619i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −469.245 + 812.756i −0.551404 + 0.955059i
\(852\) 0 0
\(853\) 782.794i 0.917695i −0.888515 0.458847i \(-0.848262\pi\)
0.888515 0.458847i \(-0.151738\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −236.681 136.648i −0.276174 0.159449i 0.355516 0.934670i \(-0.384305\pi\)
−0.631690 + 0.775221i \(0.717638\pi\)
\(858\) 0 0
\(859\) −8.26065 + 4.76929i −0.00961659 + 0.00555214i −0.504801 0.863236i \(-0.668434\pi\)
0.495184 + 0.868788i \(0.335101\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −496.338 859.683i −0.575131 0.996156i −0.996027 0.0890475i \(-0.971618\pi\)
0.420896 0.907109i \(-0.361716\pi\)
\(864\) 0 0
\(865\) −890.899 + 1543.08i −1.02994 + 1.78391i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −103.506 −0.119109
\(870\) 0 0
\(871\) −56.9901 32.9032i −0.0654306 0.0377764i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −127.002 822.761i −0.145146 0.940298i
\(876\) 0 0
\(877\) −347.810 602.425i −0.396591 0.686915i 0.596712 0.802455i \(-0.296473\pi\)
−0.993303 + 0.115540i \(0.963140\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1431.80i 1.62520i −0.582819 0.812602i \(-0.698051\pi\)
0.582819 0.812602i \(-0.301949\pi\)
\(882\) 0 0
\(883\) −455.669 −0.516046 −0.258023 0.966139i \(-0.583071\pi\)
−0.258023 + 0.966139i \(0.583071\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1133.60 + 654.482i −1.27801 + 0.737860i −0.976482 0.215597i \(-0.930830\pi\)
−0.301529 + 0.953457i \(0.597497\pi\)
\(888\) 0 0
\(889\) −508.002 + 78.4158i −0.571431 + 0.0882068i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −323.002 + 559.457i −0.361705 + 0.626491i
\(894\) 0 0
\(895\) 1464.69i 1.63652i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 654.520 + 377.887i 0.728053 + 0.420342i
\(900\) 0 0
\(901\) 300.344 173.404i 0.333345 0.192457i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 556.301 + 963.541i 0.614697 + 1.06469i
\(906\) 0 0
\(907\) −233.845 + 405.031i −0.257822 + 0.446561i −0.965658 0.259816i \(-0.916338\pi\)
0.707836 + 0.706377i \(0.249672\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −260.111 −0.285522 −0.142761 0.989757i \(-0.545598\pi\)
−0.142761 + 0.989757i \(0.545598\pi\)
\(912\) 0 0
\(913\) 240.394 + 138.791i 0.263301 + 0.152017i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −735.099 + 590.507i −0.801635 + 0.643955i
\(918\) 0 0
\(919\) 848.620 + 1469.85i 0.923417 + 1.59940i 0.794088 + 0.607803i \(0.207949\pi\)
0.129329 + 0.991602i \(0.458718\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 8.73701i 0.00946588i
\(924\) 0 0
\(925\) 103.435 0.111822
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 645.941 372.934i 0.695308 0.401436i −0.110289 0.993900i \(-0.535178\pi\)
0.805598 + 0.592463i \(0.201844\pi\)
\(930\) 0 0
\(931\) 360.970 394.621i 0.387723 0.423868i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −130.082 + 225.309i −0.139125 + 0.240972i
\(936\) 0 0
\(937\) 404.967i 0.432195i 0.976372 + 0.216098i \(0.0693330\pi\)
−0.976372 + 0.216098i \(0.930667\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1420.33 820.028i −1.50938 0.871443i −0.999940 0.0109394i \(-0.996518\pi\)
−0.509444 0.860504i \(-0.670149\pi\)
\(942\) 0 0
\(943\) 715.602 413.153i 0.758857 0.438126i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 332.389 + 575.715i 0.350992 + 0.607935i 0.986423 0.164222i \(-0.0525112\pi\)
−0.635432 + 0.772157i \(0.719178\pi\)
\(948\) 0 0
\(949\) 202.947 351.514i 0.213853 0.370405i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 671.848 0.704982 0.352491 0.935815i \(-0.385335\pi\)
0.352491 + 0.935815i \(0.385335\pi\)
\(954\) 0 0
\(955\) 1500.66 + 866.406i 1.57137 + 0.907231i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 300.048 772.569i 0.312875 0.805598i
\(960\) 0 0
\(961\) −269.012 465.942i −0.279929 0.484851i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 862.304i 0.893580i
\(966\) 0 0
\(967\) 333.134 0.344503 0.172252 0.985053i \(-0.444896\pi\)
0.172252 + 0.985053i \(0.444896\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1536.10 + 886.865i −1.58197 + 0.913353i −0.587402 + 0.809296i \(0.699849\pi\)
−0.994571 + 0.104057i \(0.966818\pi\)
\(972\) 0 0
\(973\) 25.9862 + 168.347i 0.0267073 + 0.173018i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 727.729 1260.46i 0.744860 1.29014i −0.205400 0.978678i \(-0.565849\pi\)
0.950260 0.311458i \(-0.100817\pi\)
\(978\) 0 0
\(979\) 1471.27i 1.50283i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −721.681 416.663i −0.734162 0.423868i 0.0857811 0.996314i \(-0.472661\pi\)
−0.819943 + 0.572446i \(0.805995\pi\)
\(984\) 0 0
\(985\) −905.365 + 522.713i −0.919153 + 0.530673i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 736.433 + 1275.54i 0.744624 + 1.28973i
\(990\) 0 0
\(991\) −381.647 + 661.032i −0.385113 + 0.667036i −0.991785 0.127917i \(-0.959171\pi\)
0.606672 + 0.794953i \(0.292504\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 770.495 0.774367
\(996\) 0 0
\(997\) −232.890 134.459i −0.233591 0.134864i 0.378637 0.925545i \(-0.376393\pi\)
−0.612228 + 0.790682i \(0.709726\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1008.3.cg.q.577.7 16
3.2 odd 2 inner 1008.3.cg.q.577.2 16
4.3 odd 2 504.3.by.d.73.7 yes 16
7.5 odd 6 inner 1008.3.cg.q.145.7 16
12.11 even 2 504.3.by.d.73.2 16
21.5 even 6 inner 1008.3.cg.q.145.2 16
28.3 even 6 3528.3.f.i.2449.3 16
28.11 odd 6 3528.3.f.i.2449.13 16
28.19 even 6 504.3.by.d.145.7 yes 16
84.11 even 6 3528.3.f.i.2449.4 16
84.47 odd 6 504.3.by.d.145.2 yes 16
84.59 odd 6 3528.3.f.i.2449.14 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.3.by.d.73.2 16 12.11 even 2
504.3.by.d.73.7 yes 16 4.3 odd 2
504.3.by.d.145.2 yes 16 84.47 odd 6
504.3.by.d.145.7 yes 16 28.19 even 6
1008.3.cg.q.145.2 16 21.5 even 6 inner
1008.3.cg.q.145.7 16 7.5 odd 6 inner
1008.3.cg.q.577.2 16 3.2 odd 2 inner
1008.3.cg.q.577.7 16 1.1 even 1 trivial
3528.3.f.i.2449.3 16 28.3 even 6
3528.3.f.i.2449.4 16 84.11 even 6
3528.3.f.i.2449.13 16 28.11 odd 6
3528.3.f.i.2449.14 16 84.59 odd 6