Properties

Label 900.3.y.a.89.3
Level $900$
Weight $3$
Character 900.89
Analytic conductor $24.523$
Analytic rank $0$
Dimension $80$
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] = [900,3,Mod(89,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("900.89");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.y (of order \(10\), degree \(4\), 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: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 89.3
Character \(\chi\) \(=\) 900.89
Dual form 900.3.y.a.809.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.98271 - 0.415486i) q^{5} +3.91927i q^{7} +O(q^{10})\) \(q+(-4.98271 - 0.415486i) q^{5} +3.91927i q^{7} +(-1.92910 - 2.65518i) q^{11} +(11.5122 - 15.8451i) q^{13} +(6.71776 + 20.6751i) q^{17} +(-7.10679 - 21.8724i) q^{19} +(-5.27008 + 3.82894i) q^{23} +(24.6547 + 4.14049i) q^{25} +(-20.7268 - 6.73453i) q^{29} +(12.6700 + 38.9943i) q^{31} +(1.62840 - 19.5286i) q^{35} +(-19.7719 + 27.2137i) q^{37} +(-25.6093 + 35.2482i) q^{41} +31.4782i q^{43} +(-6.51163 + 20.0408i) q^{47} +33.6393 q^{49} +(-17.8194 + 54.8425i) q^{53} +(8.50895 + 14.0315i) q^{55} +(-31.1679 + 42.8990i) q^{59} +(-41.6382 + 30.2519i) q^{61} +(-63.9451 + 74.1685i) q^{65} +(73.5135 - 23.8860i) q^{67} +(93.7744 + 30.4691i) q^{71} +(31.0857 + 42.7858i) q^{73} +(10.4064 - 7.56067i) q^{77} +(-18.3643 + 56.5197i) q^{79} +(-34.6261 - 106.568i) q^{83} +(-24.8824 - 105.809i) q^{85} +(56.4115 + 77.6438i) q^{89} +(62.1013 + 45.1193i) q^{91} +(26.3233 + 111.937i) q^{95} +(-15.4495 - 5.01984i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\)

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
\(5\) −4.98271 0.415486i −0.996541 0.0830972i
\(6\) 0 0
\(7\) 3.91927i 0.559896i 0.960015 + 0.279948i \(0.0903172\pi\)
−0.960015 + 0.279948i \(0.909683\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.92910 2.65518i −0.175373 0.241380i 0.712278 0.701898i \(-0.247664\pi\)
−0.887650 + 0.460518i \(0.847664\pi\)
\(12\) 0 0
\(13\) 11.5122 15.8451i 0.885550 1.21886i −0.0893023 0.996005i \(-0.528464\pi\)
0.974853 0.222851i \(-0.0715363\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.71776 + 20.6751i 0.395162 + 1.21618i 0.928835 + 0.370493i \(0.120811\pi\)
−0.533673 + 0.845691i \(0.679189\pi\)
\(18\) 0 0
\(19\) −7.10679 21.8724i −0.374041 1.15118i −0.944123 0.329593i \(-0.893088\pi\)
0.570082 0.821588i \(-0.306912\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.27008 + 3.82894i −0.229134 + 0.166476i −0.696429 0.717626i \(-0.745229\pi\)
0.467295 + 0.884102i \(0.345229\pi\)
\(24\) 0 0
\(25\) 24.6547 + 4.14049i 0.986190 + 0.165620i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −20.7268 6.73453i −0.714716 0.232225i −0.0709851 0.997477i \(-0.522614\pi\)
−0.643731 + 0.765252i \(0.722614\pi\)
\(30\) 0 0
\(31\) 12.6700 + 38.9943i 0.408710 + 1.25788i 0.917757 + 0.397141i \(0.129998\pi\)
−0.509048 + 0.860738i \(0.670002\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.62840 19.5286i 0.0465258 0.557960i
\(36\) 0 0
\(37\) −19.7719 + 27.2137i −0.534375 + 0.735505i −0.987789 0.155796i \(-0.950206\pi\)
0.453414 + 0.891300i \(0.350206\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −25.6093 + 35.2482i −0.624618 + 0.859712i −0.997679 0.0680944i \(-0.978308\pi\)
0.373061 + 0.927807i \(0.378308\pi\)
\(42\) 0 0
\(43\) 31.4782i 0.732050i 0.930605 + 0.366025i \(0.119282\pi\)
−0.930605 + 0.366025i \(0.880718\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.51163 + 20.0408i −0.138545 + 0.426399i −0.996125 0.0879530i \(-0.971967\pi\)
0.857579 + 0.514352i \(0.171967\pi\)
\(48\) 0 0
\(49\) 33.6393 0.686516
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −17.8194 + 54.8425i −0.336215 + 1.03476i 0.629905 + 0.776672i \(0.283094\pi\)
−0.966120 + 0.258092i \(0.916906\pi\)
\(54\) 0 0
\(55\) 8.50895 + 14.0315i 0.154708 + 0.255118i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −31.1679 + 42.8990i −0.528270 + 0.727101i −0.986866 0.161544i \(-0.948353\pi\)
0.458596 + 0.888645i \(0.348353\pi\)
\(60\) 0 0
\(61\) −41.6382 + 30.2519i −0.682593 + 0.495933i −0.874217 0.485536i \(-0.838625\pi\)
0.191624 + 0.981468i \(0.438625\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −63.9451 + 74.1685i −0.983771 + 1.14105i
\(66\) 0 0
\(67\) 73.5135 23.8860i 1.09722 0.356507i 0.296186 0.955130i \(-0.404285\pi\)
0.801031 + 0.598623i \(0.204285\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 93.7744 + 30.4691i 1.32077 + 0.429143i 0.882758 0.469828i \(-0.155684\pi\)
0.438008 + 0.898971i \(0.355684\pi\)
\(72\) 0 0
\(73\) 31.0857 + 42.7858i 0.425831 + 0.586107i 0.966990 0.254814i \(-0.0820142\pi\)
−0.541159 + 0.840920i \(0.682014\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.4064 7.56067i 0.135148 0.0981905i
\(78\) 0 0
\(79\) −18.3643 + 56.5197i −0.232460 + 0.715439i 0.764988 + 0.644044i \(0.222745\pi\)
−0.997448 + 0.0713942i \(0.977255\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −34.6261 106.568i −0.417182 1.28396i −0.910284 0.413984i \(-0.864137\pi\)
0.493102 0.869971i \(-0.335863\pi\)
\(84\) 0 0
\(85\) −24.8824 105.809i −0.292734 1.24482i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 56.4115 + 77.6438i 0.633837 + 0.872402i 0.998268 0.0588286i \(-0.0187365\pi\)
−0.364431 + 0.931230i \(0.618737\pi\)
\(90\) 0 0
\(91\) 62.1013 + 45.1193i 0.682432 + 0.495816i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 26.3233 + 111.937i 0.277088 + 1.17828i
\(96\) 0 0
\(97\) −15.4495 5.01984i −0.159273 0.0517510i 0.228295 0.973592i \(-0.426685\pi\)
−0.387568 + 0.921841i \(0.626685\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.92444i 0.0586578i 0.999570 + 0.0293289i \(0.00933702\pi\)
−0.999570 + 0.0293289i \(0.990663\pi\)
\(102\) 0 0
\(103\) 139.464 + 45.3146i 1.35402 + 0.439948i 0.894042 0.447982i \(-0.147857\pi\)
0.459978 + 0.887930i \(0.347857\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −209.615 −1.95902 −0.979509 0.201403i \(-0.935450\pi\)
−0.979509 + 0.201403i \(0.935450\pi\)
\(108\) 0 0
\(109\) 71.6458 + 52.0538i 0.657301 + 0.477557i 0.865751 0.500476i \(-0.166842\pi\)
−0.208449 + 0.978033i \(0.566842\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 56.5402 + 41.0789i 0.500356 + 0.363530i 0.809153 0.587598i \(-0.199926\pi\)
−0.308797 + 0.951128i \(0.599926\pi\)
\(114\) 0 0
\(115\) 27.8501 16.8888i 0.242175 0.146859i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −81.0315 + 26.3287i −0.680937 + 0.221250i
\(120\) 0 0
\(121\) 34.0625 104.834i 0.281508 0.866394i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −121.127 30.8746i −0.969016 0.246997i
\(126\) 0 0
\(127\) −46.7583 64.3573i −0.368176 0.506750i 0.584228 0.811589i \(-0.301397\pi\)
−0.952404 + 0.304839i \(0.901397\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −111.634 + 36.2721i −0.852167 + 0.276886i −0.702354 0.711828i \(-0.747867\pi\)
−0.149814 + 0.988714i \(0.547867\pi\)
\(132\) 0 0
\(133\) 85.7240 27.8534i 0.644542 0.209424i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 44.3045 + 32.1891i 0.323391 + 0.234957i 0.737621 0.675215i \(-0.235949\pi\)
−0.414230 + 0.910172i \(0.635949\pi\)
\(138\) 0 0
\(139\) −195.185 + 141.810i −1.40421 + 1.02022i −0.410074 + 0.912052i \(0.634497\pi\)
−0.994133 + 0.108164i \(0.965503\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −64.2797 −0.449509
\(144\) 0 0
\(145\) 100.477 + 42.1679i 0.692947 + 0.290813i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 67.3024i 0.451694i 0.974163 + 0.225847i \(0.0725150\pi\)
−0.974163 + 0.225847i \(0.927485\pi\)
\(150\) 0 0
\(151\) −86.9606 −0.575898 −0.287949 0.957646i \(-0.592973\pi\)
−0.287949 + 0.957646i \(0.592973\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −46.9294 199.561i −0.302770 1.28749i
\(156\) 0 0
\(157\) 113.116i 0.720483i −0.932859 0.360242i \(-0.882694\pi\)
0.932859 0.360242i \(-0.117306\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −15.0067 20.6549i −0.0932090 0.128291i
\(162\) 0 0
\(163\) 19.5822 26.9526i 0.120136 0.165354i −0.744713 0.667385i \(-0.767414\pi\)
0.864850 + 0.502031i \(0.167414\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.98196 + 15.3329i 0.0298321 + 0.0918137i 0.964864 0.262750i \(-0.0846294\pi\)
−0.935032 + 0.354564i \(0.884629\pi\)
\(168\) 0 0
\(169\) −66.3143 204.094i −0.392392 1.20766i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 210.342 152.822i 1.21585 0.883365i 0.220099 0.975477i \(-0.429362\pi\)
0.995749 + 0.0921123i \(0.0293619\pi\)
\(174\) 0 0
\(175\) −16.2277 + 96.6286i −0.0927298 + 0.552164i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 248.594 + 80.7731i 1.38879 + 0.451247i 0.905550 0.424239i \(-0.139458\pi\)
0.483244 + 0.875486i \(0.339458\pi\)
\(180\) 0 0
\(181\) 90.6204 + 278.901i 0.500665 + 1.54089i 0.807938 + 0.589267i \(0.200584\pi\)
−0.307273 + 0.951621i \(0.599416\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 109.824 127.383i 0.593646 0.688556i
\(186\) 0 0
\(187\) 41.9369 57.7213i 0.224262 0.308670i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.1808 30.5293i 0.116130 0.159839i −0.746995 0.664830i \(-0.768504\pi\)
0.863125 + 0.504991i \(0.168504\pi\)
\(192\) 0 0
\(193\) 152.054i 0.787847i 0.919143 + 0.393924i \(0.128883\pi\)
−0.919143 + 0.393924i \(0.871117\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −84.6500 + 260.526i −0.429696 + 1.32247i 0.468730 + 0.883342i \(0.344712\pi\)
−0.898426 + 0.439126i \(0.855288\pi\)
\(198\) 0 0
\(199\) −246.402 −1.23820 −0.619101 0.785311i \(-0.712503\pi\)
−0.619101 + 0.785311i \(0.712503\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 26.3945 81.2338i 0.130022 0.400166i
\(204\) 0 0
\(205\) 142.249 164.991i 0.693897 0.804835i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −44.3655 + 61.0639i −0.212275 + 0.292172i
\(210\) 0 0
\(211\) −84.7429 + 61.5693i −0.401625 + 0.291798i −0.770203 0.637799i \(-0.779845\pi\)
0.368577 + 0.929597i \(0.379845\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 13.0787 156.846i 0.0608313 0.729518i
\(216\) 0 0
\(217\) −152.829 + 49.6572i −0.704282 + 0.228835i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 404.936 + 131.572i 1.83229 + 0.595347i
\(222\) 0 0
\(223\) −110.794 152.495i −0.496833 0.683833i 0.484797 0.874627i \(-0.338894\pi\)
−0.981630 + 0.190794i \(0.938894\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 28.5710 20.7581i 0.125864 0.0914452i −0.523072 0.852288i \(-0.675214\pi\)
0.648936 + 0.760843i \(0.275214\pi\)
\(228\) 0 0
\(229\) −32.5334 + 100.128i −0.142067 + 0.437238i −0.996622 0.0821229i \(-0.973830\pi\)
0.854555 + 0.519361i \(0.173830\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 36.0883 + 111.068i 0.154885 + 0.476688i 0.998149 0.0608116i \(-0.0193689\pi\)
−0.843264 + 0.537500i \(0.819369\pi\)
\(234\) 0 0
\(235\) 40.7722 97.1517i 0.173499 0.413411i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −117.529 161.765i −0.491753 0.676840i 0.488957 0.872308i \(-0.337377\pi\)
−0.980710 + 0.195468i \(0.937377\pi\)
\(240\) 0 0
\(241\) 193.762 + 140.776i 0.803992 + 0.584135i 0.912083 0.410006i \(-0.134474\pi\)
−0.108090 + 0.994141i \(0.534474\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −167.615 13.9767i −0.684142 0.0570476i
\(246\) 0 0
\(247\) −428.386 139.191i −1.73436 0.563526i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 413.644i 1.64798i −0.566601 0.823992i \(-0.691742\pi\)
0.566601 0.823992i \(-0.308258\pi\)
\(252\) 0 0
\(253\) 20.3330 + 6.60660i 0.0803677 + 0.0261131i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.9908 0.0427660 0.0213830 0.999771i \(-0.493193\pi\)
0.0213830 + 0.999771i \(0.493193\pi\)
\(258\) 0 0
\(259\) −106.658 77.4914i −0.411806 0.299195i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −203.928 148.162i −0.775391 0.563354i 0.128201 0.991748i \(-0.459080\pi\)
−0.903592 + 0.428394i \(0.859080\pi\)
\(264\) 0 0
\(265\) 111.575 265.860i 0.421038 1.00325i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 305.833 99.3712i 1.13693 0.369410i 0.320722 0.947173i \(-0.396075\pi\)
0.816204 + 0.577764i \(0.196075\pi\)
\(270\) 0 0
\(271\) −138.402 + 425.957i −0.510707 + 1.57180i 0.280252 + 0.959927i \(0.409582\pi\)
−0.790959 + 0.611869i \(0.790418\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −36.5677 73.4502i −0.132974 0.267092i
\(276\) 0 0
\(277\) −266.645 367.006i −0.962619 1.32493i −0.945688 0.325074i \(-0.894611\pi\)
−0.0169303 0.999857i \(-0.505389\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 493.513 160.352i 1.75628 0.570648i 0.759472 0.650540i \(-0.225457\pi\)
0.996804 + 0.0798916i \(0.0254574\pi\)
\(282\) 0 0
\(283\) 183.224 59.5330i 0.647434 0.210364i 0.0331515 0.999450i \(-0.489446\pi\)
0.614282 + 0.789086i \(0.289446\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −138.147 100.370i −0.481349 0.349721i
\(288\) 0 0
\(289\) −148.527 + 107.911i −0.513934 + 0.373395i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −37.9439 −0.129501 −0.0647507 0.997901i \(-0.520625\pi\)
−0.0647507 + 0.997901i \(0.520625\pi\)
\(294\) 0 0
\(295\) 173.125 200.803i 0.586863 0.680689i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 127.584i 0.426704i
\(300\) 0 0
\(301\) −123.371 −0.409872
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 220.040 133.436i 0.721443 0.437496i
\(306\) 0 0
\(307\) 182.514i 0.594507i −0.954799 0.297253i \(-0.903929\pi\)
0.954799 0.297253i \(-0.0960706\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 80.1499 + 110.317i 0.257717 + 0.354716i 0.918195 0.396129i \(-0.129647\pi\)
−0.660478 + 0.750845i \(0.729647\pi\)
\(312\) 0 0
\(313\) 4.71068 6.48370i 0.0150501 0.0207147i −0.801426 0.598094i \(-0.795925\pi\)
0.816476 + 0.577380i \(0.195925\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −98.9966 304.680i −0.312292 0.961137i −0.976855 0.213904i \(-0.931382\pi\)
0.664562 0.747233i \(-0.268618\pi\)
\(318\) 0 0
\(319\) 22.1026 + 68.0248i 0.0692872 + 0.213244i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 404.474 293.868i 1.25224 0.909807i
\(324\) 0 0
\(325\) 349.436 342.991i 1.07519 1.05536i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −78.5452 25.5209i −0.238739 0.0775710i
\(330\) 0 0
\(331\) −83.1059 255.774i −0.251075 0.772730i −0.994578 0.103997i \(-0.966837\pi\)
0.743502 0.668733i \(-0.233163\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −376.221 + 88.4731i −1.12305 + 0.264099i
\(336\) 0 0
\(337\) 338.343 465.689i 1.00398 1.38187i 0.0811363 0.996703i \(-0.474145\pi\)
0.922848 0.385163i \(-0.125855\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 79.0950 108.865i 0.231950 0.319252i
\(342\) 0 0
\(343\) 323.886i 0.944274i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 41.5770 127.961i 0.119818 0.368763i −0.873103 0.487536i \(-0.837896\pi\)
0.992921 + 0.118773i \(0.0378959\pi\)
\(348\) 0 0
\(349\) −446.343 −1.27892 −0.639461 0.768824i \(-0.720842\pi\)
−0.639461 + 0.768824i \(0.720842\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 107.030 329.405i 0.303202 0.933159i −0.677140 0.735854i \(-0.736781\pi\)
0.980342 0.197305i \(-0.0632189\pi\)
\(354\) 0 0
\(355\) −454.591 190.781i −1.28054 0.537411i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −233.133 + 320.880i −0.649395 + 0.893815i −0.999073 0.0430546i \(-0.986291\pi\)
0.349678 + 0.936870i \(0.386291\pi\)
\(360\) 0 0
\(361\) −135.842 + 98.6950i −0.376294 + 0.273393i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −137.114 226.105i −0.375655 0.619465i
\(366\) 0 0
\(367\) −506.808 + 164.672i −1.38095 + 0.448697i −0.902981 0.429681i \(-0.858626\pi\)
−0.477967 + 0.878378i \(0.658626\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −214.943 69.8391i −0.579360 0.188246i
\(372\) 0 0
\(373\) 173.642 + 238.997i 0.465527 + 0.640743i 0.975643 0.219362i \(-0.0703977\pi\)
−0.510116 + 0.860105i \(0.670398\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −345.319 + 250.889i −0.915966 + 0.665488i
\(378\) 0 0
\(379\) −29.1751 + 89.7918i −0.0769792 + 0.236918i −0.982140 0.188152i \(-0.939750\pi\)
0.905161 + 0.425069i \(0.139750\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −175.807 541.077i −0.459025 1.41273i −0.866344 0.499448i \(-0.833536\pi\)
0.407319 0.913286i \(-0.366464\pi\)
\(384\) 0 0
\(385\) −54.9932 + 33.3489i −0.142840 + 0.0866205i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 289.468 + 398.419i 0.744135 + 1.02421i 0.998370 + 0.0570713i \(0.0181762\pi\)
−0.254235 + 0.967142i \(0.581824\pi\)
\(390\) 0 0
\(391\) −114.567 83.2378i −0.293010 0.212884i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 114.987 273.991i 0.291107 0.693647i
\(396\) 0 0
\(397\) 354.512 + 115.188i 0.892977 + 0.290146i 0.719335 0.694663i \(-0.244447\pi\)
0.173642 + 0.984809i \(0.444447\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 410.370i 1.02337i 0.859174 + 0.511683i \(0.170978\pi\)
−0.859174 + 0.511683i \(0.829022\pi\)
\(402\) 0 0
\(403\) 763.728 + 248.150i 1.89511 + 0.615758i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 110.399 0.271251
\(408\) 0 0
\(409\) −446.694 324.542i −1.09216 0.793502i −0.112398 0.993663i \(-0.535853\pi\)
−0.979763 + 0.200162i \(0.935853\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −168.133 122.156i −0.407101 0.295776i
\(414\) 0 0
\(415\) 128.254 + 545.385i 0.309046 + 1.31418i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 471.125 153.078i 1.12440 0.365341i 0.312957 0.949767i \(-0.398681\pi\)
0.811447 + 0.584427i \(0.198681\pi\)
\(420\) 0 0
\(421\) −148.946 + 458.410i −0.353792 + 1.08886i 0.602914 + 0.797806i \(0.294006\pi\)
−0.956707 + 0.291054i \(0.905994\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 80.0194 + 537.555i 0.188281 + 1.26484i
\(426\) 0 0
\(427\) −118.565 163.191i −0.277671 0.382181i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 187.019 60.7663i 0.433920 0.140989i −0.0839090 0.996473i \(-0.526741\pi\)
0.517829 + 0.855484i \(0.326741\pi\)
\(432\) 0 0
\(433\) 666.372 216.518i 1.53897 0.500040i 0.587875 0.808952i \(-0.299965\pi\)
0.951091 + 0.308911i \(0.0999646\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 121.202 + 88.0581i 0.277349 + 0.201506i
\(438\) 0 0
\(439\) −205.621 + 149.393i −0.468385 + 0.340302i −0.796812 0.604228i \(-0.793482\pi\)
0.328426 + 0.944530i \(0.393482\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 735.899 1.66117 0.830586 0.556890i \(-0.188006\pi\)
0.830586 + 0.556890i \(0.188006\pi\)
\(444\) 0 0
\(445\) −248.822 410.314i −0.559151 0.922055i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 320.333i 0.713436i 0.934212 + 0.356718i \(0.116104\pi\)
−0.934212 + 0.356718i \(0.883896\pi\)
\(450\) 0 0
\(451\) 142.993 0.317058
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −290.686 250.618i −0.638871 0.550809i
\(456\) 0 0
\(457\) 371.347i 0.812577i −0.913745 0.406288i \(-0.866823\pi\)
0.913745 0.406288i \(-0.133177\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 287.569 + 395.805i 0.623794 + 0.858578i 0.997622 0.0689195i \(-0.0219552\pi\)
−0.373829 + 0.927498i \(0.621955\pi\)
\(462\) 0 0
\(463\) 55.0271 75.7382i 0.118849 0.163582i −0.745447 0.666564i \(-0.767764\pi\)
0.864296 + 0.502983i \(0.167764\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 88.5517 + 272.534i 0.189618 + 0.583585i 0.999997 0.00232117i \(-0.000738851\pi\)
−0.810379 + 0.585906i \(0.800739\pi\)
\(468\) 0 0
\(469\) 93.6157 + 288.120i 0.199607 + 0.614327i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 83.5801 60.7245i 0.176702 0.128382i
\(474\) 0 0
\(475\) −84.6533 568.685i −0.178218 1.19723i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −143.020 46.4699i −0.298580 0.0970144i 0.155896 0.987773i \(-0.450173\pi\)
−0.454476 + 0.890759i \(0.650173\pi\)
\(480\) 0 0
\(481\) 203.587 + 626.576i 0.423257 + 1.30265i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 74.8946 + 31.4315i 0.154422 + 0.0648071i
\(486\) 0 0
\(487\) −276.674 + 380.809i −0.568119 + 0.781948i −0.992330 0.123615i \(-0.960551\pi\)
0.424212 + 0.905563i \(0.360551\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 89.7565 123.539i 0.182804 0.251607i −0.707774 0.706439i \(-0.750300\pi\)
0.890578 + 0.454831i \(0.150300\pi\)
\(492\) 0 0
\(493\) 473.769i 0.960993i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −119.417 + 367.527i −0.240275 + 0.739491i
\(498\) 0 0
\(499\) −708.670 −1.42018 −0.710090 0.704110i \(-0.751346\pi\)
−0.710090 + 0.704110i \(0.751346\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 57.1391 175.856i 0.113597 0.349614i −0.878055 0.478559i \(-0.841159\pi\)
0.991652 + 0.128945i \(0.0411591\pi\)
\(504\) 0 0
\(505\) 2.46152 29.5197i 0.00487430 0.0584549i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −246.414 + 339.160i −0.484115 + 0.666327i −0.979289 0.202467i \(-0.935104\pi\)
0.495174 + 0.868794i \(0.335104\pi\)
\(510\) 0 0
\(511\) −167.689 + 121.833i −0.328159 + 0.238421i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −676.081 283.735i −1.31278 0.550942i
\(516\) 0 0
\(517\) 65.7734 21.3711i 0.127221 0.0413367i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −338.109 109.858i −0.648961 0.210860i −0.0340051 0.999422i \(-0.510826\pi\)
−0.614956 + 0.788561i \(0.710826\pi\)
\(522\) 0 0
\(523\) 481.758 + 663.083i 0.921144 + 1.26785i 0.963215 + 0.268731i \(0.0866042\pi\)
−0.0420716 + 0.999115i \(0.513396\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −721.098 + 523.908i −1.36831 + 0.994133i
\(528\) 0 0
\(529\) −150.357 + 462.751i −0.284229 + 0.874766i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 263.694 + 811.565i 0.494735 + 1.52264i
\(534\) 0 0
\(535\) 1044.45 + 87.0921i 1.95224 + 0.162789i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −64.8936 89.3184i −0.120396 0.165711i
\(540\) 0 0
\(541\) 356.350 + 258.904i 0.658688 + 0.478565i 0.866220 0.499663i \(-0.166543\pi\)
−0.207532 + 0.978228i \(0.566543\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −335.363 289.136i −0.615344 0.530526i
\(546\) 0 0
\(547\) −5.72191 1.85916i −0.0104605 0.00339883i 0.303782 0.952742i \(-0.401751\pi\)
−0.314243 + 0.949343i \(0.601751\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 501.206i 0.909629i
\(552\) 0 0
\(553\) −221.516 71.9749i −0.400571 0.130153i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −511.337 −0.918020 −0.459010 0.888431i \(-0.651796\pi\)
−0.459010 + 0.888431i \(0.651796\pi\)
\(558\) 0 0
\(559\) 498.775 + 362.381i 0.892263 + 0.648267i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −677.355 492.127i −1.20312 0.874116i −0.208529 0.978016i \(-0.566868\pi\)
−0.994588 + 0.103901i \(0.966868\pi\)
\(564\) 0 0
\(565\) −264.656 228.176i −0.468417 0.403851i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 178.776 58.0878i 0.314193 0.102088i −0.147676 0.989036i \(-0.547179\pi\)
0.461869 + 0.886948i \(0.347179\pi\)
\(570\) 0 0
\(571\) −142.570 + 438.785i −0.249685 + 0.768451i 0.745146 + 0.666902i \(0.232380\pi\)
−0.994831 + 0.101549i \(0.967620\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −145.786 + 72.5808i −0.253541 + 0.126227i
\(576\) 0 0
\(577\) −144.165 198.426i −0.249852 0.343892i 0.665607 0.746302i \(-0.268173\pi\)
−0.915460 + 0.402410i \(0.868173\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 417.670 135.709i 0.718881 0.233579i
\(582\) 0 0
\(583\) 179.992 58.4830i 0.308734 0.100314i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −40.9156 29.7269i −0.0697029 0.0506421i 0.552388 0.833587i \(-0.313717\pi\)
−0.622091 + 0.782945i \(0.713717\pi\)
\(588\) 0 0
\(589\) 762.857 554.248i 1.29517 0.940998i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −373.871 −0.630473 −0.315237 0.949013i \(-0.602084\pi\)
−0.315237 + 0.949013i \(0.602084\pi\)
\(594\) 0 0
\(595\) 414.695 97.5209i 0.696967 0.163901i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 152.760i 0.255025i 0.991837 + 0.127513i \(0.0406993\pi\)
−0.991837 + 0.127513i \(0.959301\pi\)
\(600\) 0 0
\(601\) 442.462 0.736210 0.368105 0.929784i \(-0.380007\pi\)
0.368105 + 0.929784i \(0.380007\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −213.280 + 508.203i −0.352530 + 0.840005i
\(606\) 0 0
\(607\) 66.9050i 0.110222i 0.998480 + 0.0551112i \(0.0175513\pi\)
−0.998480 + 0.0551112i \(0.982449\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 242.585 + 333.890i 0.397030 + 0.546465i
\(612\) 0 0
\(613\) −610.239 + 839.923i −0.995497 + 1.37018i −0.0674487 + 0.997723i \(0.521486\pi\)
−0.928048 + 0.372461i \(0.878514\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.2157 65.2952i −0.0343852 0.105827i 0.932391 0.361452i \(-0.117719\pi\)
−0.966776 + 0.255625i \(0.917719\pi\)
\(618\) 0 0
\(619\) −279.981 861.692i −0.452311 1.39207i −0.874263 0.485452i \(-0.838655\pi\)
0.421952 0.906618i \(-0.361345\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −304.307 + 221.092i −0.488454 + 0.354883i
\(624\) 0 0
\(625\) 590.713 + 204.166i 0.945140 + 0.326665i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −695.469 225.972i −1.10567 0.359255i
\(630\) 0 0
\(631\) 173.326 + 533.442i 0.274685 + 0.845392i 0.989303 + 0.145877i \(0.0466005\pi\)
−0.714618 + 0.699515i \(0.753400\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 206.243 + 340.101i 0.324793 + 0.535592i
\(636\) 0 0
\(637\) 387.261 533.019i 0.607945 0.836764i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 500.539 688.933i 0.780873 1.07478i −0.214312 0.976765i \(-0.568751\pi\)
0.995185 0.0980139i \(-0.0312490\pi\)
\(642\) 0 0
\(643\) 279.237i 0.434272i −0.976141 0.217136i \(-0.930328\pi\)
0.976141 0.217136i \(-0.0696716\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −54.2292 + 166.900i −0.0838164 + 0.257960i −0.984178 0.177182i \(-0.943302\pi\)
0.900362 + 0.435142i \(0.143302\pi\)
\(648\) 0 0
\(649\) 174.030 0.268152
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −58.0638 + 178.702i −0.0889185 + 0.273663i −0.985621 0.168971i \(-0.945956\pi\)
0.896703 + 0.442633i \(0.145956\pi\)
\(654\) 0 0
\(655\) 571.310 134.351i 0.872229 0.205116i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −733.416 + 1009.46i −1.11292 + 1.53181i −0.295885 + 0.955224i \(0.595615\pi\)
−0.817038 + 0.576584i \(0.804385\pi\)
\(660\) 0 0
\(661\) −65.0567 + 47.2665i −0.0984217 + 0.0715076i −0.635908 0.771765i \(-0.719374\pi\)
0.537486 + 0.843273i \(0.319374\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −438.710 + 103.168i −0.659715 + 0.155140i
\(666\) 0 0
\(667\) 135.018 43.8699i 0.202425 0.0657720i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 160.648 + 52.1978i 0.239416 + 0.0777911i
\(672\) 0 0
\(673\) −310.068 426.772i −0.460725 0.634133i 0.513934 0.857830i \(-0.328188\pi\)
−0.974659 + 0.223696i \(0.928188\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 345.000 250.657i 0.509601 0.370247i −0.303071 0.952968i \(-0.598012\pi\)
0.812672 + 0.582721i \(0.198012\pi\)
\(678\) 0 0
\(679\) 19.6741 60.5507i 0.0289752 0.0891764i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 268.621 + 826.730i 0.393296 + 1.21044i 0.930281 + 0.366848i \(0.119563\pi\)
−0.536985 + 0.843592i \(0.680437\pi\)
\(684\) 0 0
\(685\) −207.382 178.797i −0.302748 0.261017i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 663.846 + 913.706i 0.963492 + 1.32613i
\(690\) 0 0
\(691\) −424.247 308.234i −0.613961 0.446069i 0.236846 0.971547i \(-0.423886\pi\)
−0.850807 + 0.525478i \(0.823886\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1031.47 625.502i 1.48413 0.900002i
\(696\) 0 0
\(697\) −900.799 292.687i −1.29239 0.419924i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 465.185i 0.663602i 0.943349 + 0.331801i \(0.107656\pi\)
−0.943349 + 0.331801i \(0.892344\pi\)
\(702\) 0 0
\(703\) 735.744 + 239.058i 1.04658 + 0.340054i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −23.2195 −0.0328423
\(708\) 0 0
\(709\) 562.969 + 409.021i 0.794032 + 0.576898i 0.909157 0.416453i \(-0.136727\pi\)
−0.115125 + 0.993351i \(0.536727\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −216.079 156.990i −0.303056 0.220183i
\(714\) 0 0
\(715\) 320.287 + 26.7073i 0.447954 + 0.0373529i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −638.711 + 207.530i −0.888332 + 0.288637i −0.717413 0.696648i \(-0.754674\pi\)
−0.170919 + 0.985285i \(0.554674\pi\)
\(720\) 0 0
\(721\) −177.600 + 546.598i −0.246325 + 0.758111i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −483.129 251.857i −0.666384 0.347389i
\(726\) 0 0
\(727\) −191.108 263.037i −0.262871 0.361812i 0.657096 0.753807i \(-0.271785\pi\)
−0.919967 + 0.391996i \(0.871785\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −650.815 + 211.463i −0.890308 + 0.289279i
\(732\) 0 0
\(733\) 516.306 167.758i 0.704374 0.228865i 0.0651386 0.997876i \(-0.479251\pi\)
0.639235 + 0.769011i \(0.279251\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −205.237 149.113i −0.278476 0.202324i
\(738\) 0 0
\(739\) −1085.93 + 788.976i −1.46946 + 1.06763i −0.488693 + 0.872456i \(0.662526\pi\)
−0.980769 + 0.195171i \(0.937474\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −983.917 −1.32425 −0.662125 0.749394i \(-0.730345\pi\)
−0.662125 + 0.749394i \(0.730345\pi\)
\(744\) 0 0
\(745\) 27.9632 335.348i 0.0375345 0.450132i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 821.538i 1.09685i
\(750\) 0 0
\(751\) 841.325 1.12027 0.560137 0.828400i \(-0.310749\pi\)
0.560137 + 0.828400i \(0.310749\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 433.299 + 36.1309i 0.573906 + 0.0478555i
\(756\) 0 0
\(757\) 337.631i 0.446012i 0.974817 + 0.223006i \(0.0715870\pi\)
−0.974817 + 0.223006i \(0.928413\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −216.485 297.966i −0.284475 0.391546i 0.642735 0.766089i \(-0.277800\pi\)
−0.927210 + 0.374543i \(0.877800\pi\)
\(762\) 0 0
\(763\) −204.013 + 280.800i −0.267382 + 0.368020i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 320.929 + 987.719i 0.418422 + 1.28777i
\(768\) 0 0
\(769\) 263.712 + 811.621i 0.342928 + 1.05542i 0.962684 + 0.270629i \(0.0872316\pi\)
−0.619756 + 0.784795i \(0.712768\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1016.04 738.200i 1.31442 0.954980i 0.314433 0.949280i \(-0.398185\pi\)
0.999984 0.00570041i \(-0.00181451\pi\)
\(774\) 0 0
\(775\) 150.920 + 1013.85i 0.194736 + 1.30820i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 952.964 + 309.637i 1.22332 + 0.397480i
\(780\) 0 0
\(781\) −99.9991 307.766i −0.128040 0.394066i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −46.9981 + 563.623i −0.0598702 + 0.717991i
\(786\) 0 0
\(787\) −514.243 + 707.795i −0.653422 + 0.899358i −0.999241 0.0389430i \(-0.987601\pi\)
0.345820 + 0.938301i \(0.387601\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −160.999 + 221.597i −0.203539 + 0.280147i
\(792\) 0 0
\(793\) 1008.03i 1.27116i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −82.5788 + 254.151i −0.103612 + 0.318885i −0.989402 0.145201i \(-0.953617\pi\)
0.885790 + 0.464086i \(0.153617\pi\)
\(798\) 0 0
\(799\) −458.089 −0.573328
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 53.6365 165.076i 0.0667951 0.205574i
\(804\) 0 0
\(805\) 66.1919 + 109.152i 0.0822260 + 0.135593i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 787.718 1084.20i 0.973694 1.34017i 0.0335353 0.999438i \(-0.489323\pi\)
0.940159 0.340737i \(-0.110677\pi\)
\(810\) 0 0
\(811\) 611.355 444.175i 0.753829 0.547689i −0.143183 0.989696i \(-0.545734\pi\)
0.897011 + 0.442008i \(0.145734\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −108.771 + 126.161i −0.133461 + 0.154799i
\(816\) 0 0
\(817\) 688.504 223.708i 0.842722 0.273817i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −755.137 245.359i −0.919778 0.298854i −0.189402 0.981900i \(-0.560655\pi\)
−0.730376 + 0.683046i \(0.760655\pi\)
\(822\) 0 0
\(823\) −643.168 885.245i −0.781492 1.07563i −0.995116 0.0987156i \(-0.968527\pi\)
0.213624 0.976916i \(-0.431473\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 516.929 375.571i 0.625065 0.454137i −0.229622 0.973280i \(-0.573749\pi\)
0.854687 + 0.519143i \(0.173749\pi\)
\(828\) 0 0
\(829\) −248.173 + 763.798i −0.299364 + 0.921348i 0.682356 + 0.731020i \(0.260955\pi\)
−0.981720 + 0.190328i \(0.939045\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 225.981 + 695.497i 0.271285 + 0.834931i
\(834\) 0 0
\(835\) −18.4530 78.4692i −0.0220994 0.0939751i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 500.862 + 689.377i 0.596975 + 0.821666i 0.995427 0.0955235i \(-0.0304525\pi\)
−0.398452 + 0.917189i \(0.630452\pi\)
\(840\) 0 0
\(841\) −296.139 215.157i −0.352127 0.255835i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 245.626 + 1044.50i 0.290682 + 1.23609i
\(846\) 0 0
\(847\) 410.872 + 133.500i 0.485090 + 0.157615i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 219.124i 0.257490i
\(852\) 0 0
\(853\) 358.654 + 116.534i 0.420462 + 0.136616i 0.511604 0.859222i \(-0.329052\pi\)
−0.0911417 + 0.995838i \(0.529052\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1224.38 −1.42868 −0.714340 0.699799i \(-0.753273\pi\)
−0.714340 + 0.699799i \(0.753273\pi\)
\(858\) 0 0
\(859\) −1243.79 903.670i −1.44796 1.05200i −0.986303 0.164941i \(-0.947257\pi\)
−0.461653 0.887061i \(-0.652743\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −439.239 319.126i −0.508968 0.369787i 0.303464 0.952843i \(-0.401857\pi\)
−0.812432 + 0.583056i \(0.801857\pi\)
\(864\) 0 0
\(865\) −1111.57 + 674.074i −1.28505 + 0.779276i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 185.496 60.2714i 0.213460 0.0693572i
\(870\) 0 0
\(871\) 467.823 1439.81i 0.537110 1.65305i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 121.006 474.730i 0.138292 0.542548i
\(876\) 0 0
\(877\) 210.629 + 289.906i 0.240170 + 0.330565i 0.912038 0.410105i \(-0.134508\pi\)
−0.671869 + 0.740670i \(0.734508\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 461.872 150.071i 0.524258 0.170342i −0.0349186 0.999390i \(-0.511117\pi\)
0.559177 + 0.829048i \(0.311117\pi\)
\(882\) 0 0
\(883\) 768.885 249.826i 0.870765 0.282929i 0.160647 0.987012i \(-0.448642\pi\)
0.710117 + 0.704083i \(0.248642\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −39.2028 28.4825i −0.0441971 0.0321111i 0.565467 0.824771i \(-0.308696\pi\)
−0.609664 + 0.792660i \(0.708696\pi\)
\(888\) 0 0
\(889\) 252.234 183.259i 0.283728 0.206140i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 484.617 0.542684
\(894\) 0 0
\(895\) −1205.11 505.756i −1.34649 0.565091i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 893.551i 0.993939i
\(900\) 0 0
\(901\) −1253.58 −1.39132
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −335.655 1427.33i −0.370890 1.57716i
\(906\) 0 0
\(907\) 669.083i 0.737688i −0.929491 0.368844i \(-0.879754\pi\)
0.929491 0.368844i \(-0.120246\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −873.093 1201.71i −0.958390 1.31911i −0.947698 0.319168i \(-0.896597\pi\)
−0.0106915 0.999943i \(-0.503403\pi\)
\(912\) 0 0
\(913\) −216.161 + 297.519i −0.236758 + 0.325870i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −142.160 437.524i −0.155027 0.477125i
\(918\) 0 0
\(919\) −169.678 522.215i −0.184633 0.568242i 0.815309 0.579026i \(-0.196567\pi\)
−0.999942 + 0.0107842i \(0.996567\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1562.33 1135.10i 1.69267 1.22979i
\(924\) 0 0
\(925\) −600.149 + 589.081i −0.648809 + 0.636844i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −589.067 191.400i −0.634088 0.206028i −0.0257026 0.999670i \(-0.508182\pi\)
−0.608385 + 0.793642i \(0.708182\pi\)
\(930\) 0 0
\(931\) −239.067 735.774i −0.256786 0.790305i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −232.942 + 270.184i −0.249136 + 0.288967i
\(936\) 0 0
\(937\) 293.703 404.247i 0.313450 0.431427i −0.623003 0.782219i \(-0.714088\pi\)
0.936453 + 0.350792i \(0.114088\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −648.463 + 892.532i −0.689121 + 0.948493i −0.999998 0.00195660i \(-0.999377\pi\)
0.310877 + 0.950450i \(0.399377\pi\)
\(942\) 0 0
\(943\) 283.817i 0.300973i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 159.120 489.721i 0.168025 0.517129i −0.831221 0.555942i \(-0.812358\pi\)
0.999246 + 0.0388130i \(0.0123577\pi\)
\(948\) 0 0
\(949\) 1035.81 1.09147
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −215.793 + 664.143i −0.226436 + 0.696898i 0.771707 + 0.635978i \(0.219403\pi\)
−0.998143 + 0.0609193i \(0.980597\pi\)
\(954\) 0 0
\(955\) −123.205 + 142.903i −0.129010 + 0.149636i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −126.158 + 173.642i −0.131552 + 0.181065i
\(960\) 0 0
\(961\) −582.559 + 423.254i −0.606201 + 0.440431i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 63.1765 757.643i 0.0654679 0.785122i
\(966\) 0 0
\(967\) 926.107 300.910i 0.957712 0.311179i 0.211866 0.977299i \(-0.432046\pi\)
0.745845 + 0.666119i \(0.232046\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1633.95 + 530.903i 1.68275 + 0.546759i 0.985442 0.170010i \(-0.0543801\pi\)
0.697310 + 0.716770i \(0.254380\pi\)
\(972\) 0 0
\(973\) −555.792 764.982i −0.571215 0.786210i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 962.183 699.067i 0.984834 0.715524i 0.0260503 0.999661i \(-0.491707\pi\)
0.958784 + 0.284137i \(0.0917070\pi\)
\(978\) 0 0
\(979\) 97.3346 299.565i 0.0994225 0.305991i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 161.024 + 495.580i 0.163808 + 0.504150i 0.998946 0.0458900i \(-0.0146124\pi\)
−0.835138 + 0.550040i \(0.814612\pi\)
\(984\) 0 0
\(985\) 530.031 1262.95i 0.538103 1.28219i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −120.528 165.892i −0.121868 0.167738i
\(990\) 0 0
\(991\) 641.848 + 466.330i 0.647677 + 0.470565i 0.862479 0.506093i \(-0.168911\pi\)
−0.214802 + 0.976658i \(0.568911\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1227.75 + 102.377i 1.23392 + 0.102891i
\(996\) 0 0
\(997\) −138.298 44.9356i −0.138714 0.0450708i 0.238837 0.971060i \(-0.423234\pi\)
−0.377551 + 0.925989i \(0.623234\pi\)
\(998\) 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 900.3.y.a.89.3 80
3.2 odd 2 inner 900.3.y.a.89.18 yes 80
25.9 even 10 inner 900.3.y.a.809.18 yes 80
75.59 odd 10 inner 900.3.y.a.809.3 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
900.3.y.a.89.3 80 1.1 even 1 trivial
900.3.y.a.89.18 yes 80 3.2 odd 2 inner
900.3.y.a.809.3 yes 80 75.59 odd 10 inner
900.3.y.a.809.18 yes 80 25.9 even 10 inner