Properties

Label 900.3.l.a.757.1
Level $900$
Weight $3$
Character 900.757
Analytic conductor $24.523$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [900,3,Mod(757,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("900.757");
 
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.l (of order \(4\), degree \(2\), 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: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 757.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 900.757
Dual form 900.3.l.a.793.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.00000 + 7.00000i) q^{7} +O(q^{10})\) \(q+(7.00000 + 7.00000i) q^{7} -10.0000 q^{11} +(-9.00000 + 9.00000i) q^{13} +(1.00000 + 1.00000i) q^{17} -8.00000i q^{19} +(-23.0000 + 23.0000i) q^{23} +8.00000i q^{29} -14.0000 q^{31} +(-33.0000 - 33.0000i) q^{37} +14.0000 q^{41} +(15.0000 - 15.0000i) q^{43} +(-39.0000 - 39.0000i) q^{47} +49.0000i q^{49} +(-7.00000 + 7.00000i) q^{53} +56.0000i q^{59} +42.0000 q^{61} +(7.00000 + 7.00000i) q^{67} -98.0000 q^{71} +(-49.0000 + 49.0000i) q^{73} +(-70.0000 - 70.0000i) q^{77} +96.0000i q^{79} +(-63.0000 + 63.0000i) q^{83} +112.000i q^{89} -126.000 q^{91} +(-33.0000 - 33.0000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 14 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 14 q^{7} - 20 q^{11} - 18 q^{13} + 2 q^{17} - 46 q^{23} - 28 q^{31} - 66 q^{37} + 28 q^{41} + 30 q^{43} - 78 q^{47} - 14 q^{53} + 84 q^{61} + 14 q^{67} - 196 q^{71} - 98 q^{73} - 140 q^{77} - 126 q^{83} - 252 q^{91} - 66 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(5\) 0 0
\(6\) 0 0
\(7\) 7.00000 + 7.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −10.0000 −0.909091 −0.454545 0.890724i \(-0.650198\pi\)
−0.454545 + 0.890724i \(0.650198\pi\)
\(12\) 0 0
\(13\) −9.00000 + 9.00000i −0.692308 + 0.692308i −0.962739 0.270432i \(-0.912834\pi\)
0.270432 + 0.962739i \(0.412834\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 + 1.00000i 0.0588235 + 0.0588235i 0.735907 0.677083i \(-0.236756\pi\)
−0.677083 + 0.735907i \(0.736756\pi\)
\(18\) 0 0
\(19\) 8.00000i 0.421053i −0.977588 0.210526i \(-0.932482\pi\)
0.977588 0.210526i \(-0.0675178\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −23.0000 + 23.0000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.00000i 0.275862i 0.990442 + 0.137931i \(0.0440452\pi\)
−0.990442 + 0.137931i \(0.955955\pi\)
\(30\) 0 0
\(31\) −14.0000 −0.451613 −0.225806 0.974172i \(-0.572502\pi\)
−0.225806 + 0.974172i \(0.572502\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −33.0000 33.0000i −0.891892 0.891892i 0.102809 0.994701i \(-0.467217\pi\)
−0.994701 + 0.102809i \(0.967217\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 14.0000 0.341463 0.170732 0.985318i \(-0.445387\pi\)
0.170732 + 0.985318i \(0.445387\pi\)
\(42\) 0 0
\(43\) 15.0000 15.0000i 0.348837 0.348837i −0.510839 0.859676i \(-0.670665\pi\)
0.859676 + 0.510839i \(0.170665\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −39.0000 39.0000i −0.829787 0.829787i 0.157700 0.987487i \(-0.449592\pi\)
−0.987487 + 0.157700i \(0.949592\pi\)
\(48\) 0 0
\(49\) 49.0000i 1.00000i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −7.00000 + 7.00000i −0.132075 + 0.132075i −0.770054 0.637979i \(-0.779771\pi\)
0.637979 + 0.770054i \(0.279771\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 56.0000i 0.949153i 0.880214 + 0.474576i \(0.157399\pi\)
−0.880214 + 0.474576i \(0.842601\pi\)
\(60\) 0 0
\(61\) 42.0000 0.688525 0.344262 0.938874i \(-0.388129\pi\)
0.344262 + 0.938874i \(0.388129\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.00000 + 7.00000i 0.104478 + 0.104478i 0.757413 0.652936i \(-0.226463\pi\)
−0.652936 + 0.757413i \(0.726463\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −98.0000 −1.38028 −0.690141 0.723675i \(-0.742451\pi\)
−0.690141 + 0.723675i \(0.742451\pi\)
\(72\) 0 0
\(73\) −49.0000 + 49.0000i −0.671233 + 0.671233i −0.958000 0.286767i \(-0.907419\pi\)
0.286767 + 0.958000i \(0.407419\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −70.0000 70.0000i −0.909091 0.909091i
\(78\) 0 0
\(79\) 96.0000i 1.21519i 0.794247 + 0.607595i \(0.207866\pi\)
−0.794247 + 0.607595i \(0.792134\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −63.0000 + 63.0000i −0.759036 + 0.759036i −0.976147 0.217111i \(-0.930337\pi\)
0.217111 + 0.976147i \(0.430337\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 112.000i 1.25843i 0.777233 + 0.629213i \(0.216623\pi\)
−0.777233 + 0.629213i \(0.783377\pi\)
\(90\) 0 0
\(91\) −126.000 −1.38462
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −33.0000 33.0000i −0.340206 0.340206i 0.516239 0.856445i \(-0.327332\pi\)
−0.856445 + 0.516239i \(0.827332\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −26.0000 −0.257426 −0.128713 0.991682i \(-0.541085\pi\)
−0.128713 + 0.991682i \(0.541085\pi\)
\(102\) 0 0
\(103\) −73.0000 + 73.0000i −0.708738 + 0.708738i −0.966270 0.257532i \(-0.917091\pi\)
0.257532 + 0.966270i \(0.417091\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 121.000 + 121.000i 1.13084 + 1.13084i 0.990038 + 0.140804i \(0.0449686\pi\)
0.140804 + 0.990038i \(0.455031\pi\)
\(108\) 0 0
\(109\) 136.000i 1.24771i −0.781542 0.623853i \(-0.785566\pi\)
0.781542 0.623853i \(-0.214434\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −127.000 + 127.000i −1.12389 + 1.12389i −0.132743 + 0.991150i \(0.542379\pi\)
−0.991150 + 0.132743i \(0.957621\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 14.0000i 0.117647i
\(120\) 0 0
\(121\) −21.0000 −0.173554
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 7.00000 + 7.00000i 0.0551181 + 0.0551181i 0.734129 0.679010i \(-0.237591\pi\)
−0.679010 + 0.734129i \(0.737591\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 230.000 1.75573 0.877863 0.478913i \(-0.158969\pi\)
0.877863 + 0.478913i \(0.158969\pi\)
\(132\) 0 0
\(133\) 56.0000 56.0000i 0.421053 0.421053i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −63.0000 63.0000i −0.459854 0.459854i 0.438753 0.898607i \(-0.355420\pi\)
−0.898607 + 0.438753i \(0.855420\pi\)
\(138\) 0 0
\(139\) 88.0000i 0.633094i −0.948577 0.316547i \(-0.897477\pi\)
0.948577 0.316547i \(-0.102523\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 90.0000 90.0000i 0.629371 0.629371i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 168.000i 1.12752i −0.825940 0.563758i \(-0.809355\pi\)
0.825940 0.563758i \(-0.190645\pi\)
\(150\) 0 0
\(151\) 130.000 0.860927 0.430464 0.902608i \(-0.358350\pi\)
0.430464 + 0.902608i \(0.358350\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 63.0000 + 63.0000i 0.401274 + 0.401274i 0.878682 0.477408i \(-0.158424\pi\)
−0.477408 + 0.878682i \(0.658424\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −322.000 −2.00000
\(162\) 0 0
\(163\) −65.0000 + 65.0000i −0.398773 + 0.398773i −0.877800 0.479027i \(-0.840990\pi\)
0.479027 + 0.877800i \(0.340990\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −103.000 103.000i −0.616766 0.616766i 0.327934 0.944701i \(-0.393648\pi\)
−0.944701 + 0.327934i \(0.893648\pi\)
\(168\) 0 0
\(169\) 7.00000i 0.0414201i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 73.0000 73.0000i 0.421965 0.421965i −0.463915 0.885880i \(-0.653556\pi\)
0.885880 + 0.463915i \(0.153556\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 56.0000i 0.312849i −0.987690 0.156425i \(-0.950003\pi\)
0.987690 0.156425i \(-0.0499968\pi\)
\(180\) 0 0
\(181\) −70.0000 −0.386740 −0.193370 0.981126i \(-0.561942\pi\)
−0.193370 + 0.981126i \(0.561942\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −10.0000 10.0000i −0.0534759 0.0534759i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 142.000 0.743455 0.371728 0.928342i \(-0.378765\pi\)
0.371728 + 0.928342i \(0.378765\pi\)
\(192\) 0 0
\(193\) 63.0000 63.0000i 0.326425 0.326425i −0.524800 0.851225i \(-0.675860\pi\)
0.851225 + 0.524800i \(0.175860\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −63.0000 63.0000i −0.319797 0.319797i 0.528892 0.848689i \(-0.322608\pi\)
−0.848689 + 0.528892i \(0.822608\pi\)
\(198\) 0 0
\(199\) 336.000i 1.68844i 0.535995 + 0.844221i \(0.319937\pi\)
−0.535995 + 0.844221i \(0.680063\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −56.0000 + 56.0000i −0.275862 + 0.275862i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 80.0000i 0.382775i
\(210\) 0 0
\(211\) 314.000 1.48815 0.744076 0.668095i \(-0.232890\pi\)
0.744076 + 0.668095i \(0.232890\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −98.0000 98.0000i −0.451613 0.451613i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −18.0000 −0.0814480
\(222\) 0 0
\(223\) 135.000 135.000i 0.605381 0.605381i −0.336354 0.941736i \(-0.609194\pi\)
0.941736 + 0.336354i \(0.109194\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 281.000 + 281.000i 1.23789 + 1.23789i 0.960864 + 0.277022i \(0.0893474\pi\)
0.277022 + 0.960864i \(0.410653\pi\)
\(228\) 0 0
\(229\) 168.000i 0.733624i 0.930295 + 0.366812i \(0.119551\pi\)
−0.930295 + 0.366812i \(0.880449\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 273.000 273.000i 1.17167 1.17167i 0.189863 0.981811i \(-0.439196\pi\)
0.981811 0.189863i \(-0.0608045\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 288.000i 1.20502i 0.798111 + 0.602510i \(0.205833\pi\)
−0.798111 + 0.602510i \(0.794167\pi\)
\(240\) 0 0
\(241\) −446.000 −1.85062 −0.925311 0.379209i \(-0.876196\pi\)
−0.925311 + 0.379209i \(0.876196\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 72.0000 + 72.0000i 0.291498 + 0.291498i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 150.000 0.597610 0.298805 0.954314i \(-0.403412\pi\)
0.298805 + 0.954314i \(0.403412\pi\)
\(252\) 0 0
\(253\) 230.000 230.000i 0.909091 0.909091i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 161.000 + 161.000i 0.626459 + 0.626459i 0.947175 0.320716i \(-0.103924\pi\)
−0.320716 + 0.947175i \(0.603924\pi\)
\(258\) 0 0
\(259\) 462.000i 1.78378i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −151.000 + 151.000i −0.574144 + 0.574144i −0.933284 0.359139i \(-0.883070\pi\)
0.359139 + 0.933284i \(0.383070\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 376.000i 1.39777i −0.715234 0.698885i \(-0.753680\pi\)
0.715234 0.698885i \(-0.246320\pi\)
\(270\) 0 0
\(271\) 210.000 0.774908 0.387454 0.921889i \(-0.373355\pi\)
0.387454 + 0.921889i \(0.373355\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −129.000 129.000i −0.465704 0.465704i 0.434816 0.900520i \(-0.356814\pi\)
−0.900520 + 0.434816i \(0.856814\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 174.000 0.619217 0.309609 0.950864i \(-0.399802\pi\)
0.309609 + 0.950864i \(0.399802\pi\)
\(282\) 0 0
\(283\) −113.000 + 113.000i −0.399293 + 0.399293i −0.877984 0.478690i \(-0.841112\pi\)
0.478690 + 0.877984i \(0.341112\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 98.0000 + 98.0000i 0.341463 + 0.341463i
\(288\) 0 0
\(289\) 287.000i 0.993080i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 345.000 345.000i 1.17747 1.17747i 0.197089 0.980386i \(-0.436851\pi\)
0.980386 0.197089i \(-0.0631487\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 414.000i 1.38462i
\(300\) 0 0
\(301\) 210.000 0.697674
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 327.000 + 327.000i 1.06515 + 1.06515i 0.997725 + 0.0674220i \(0.0214774\pi\)
0.0674220 + 0.997725i \(0.478523\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.00000 −0.00643087 −0.00321543 0.999995i \(-0.501024\pi\)
−0.00321543 + 0.999995i \(0.501024\pi\)
\(312\) 0 0
\(313\) −81.0000 + 81.0000i −0.258786 + 0.258786i −0.824560 0.565774i \(-0.808577\pi\)
0.565774 + 0.824560i \(0.308577\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −159.000 159.000i −0.501577 0.501577i 0.410351 0.911928i \(-0.365406\pi\)
−0.911928 + 0.410351i \(0.865406\pi\)
\(318\) 0 0
\(319\) 80.0000i 0.250784i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000 8.00000i 0.0247678 0.0247678i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 546.000i 1.65957i
\(330\) 0 0
\(331\) −182.000 −0.549849 −0.274924 0.961466i \(-0.588653\pi\)
−0.274924 + 0.961466i \(0.588653\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 447.000 + 447.000i 1.32641 + 1.32641i 0.908479 + 0.417930i \(0.137244\pi\)
0.417930 + 0.908479i \(0.362756\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 140.000 0.410557
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 25.0000 + 25.0000i 0.0720461 + 0.0720461i 0.742212 0.670166i \(-0.233777\pi\)
−0.670166 + 0.742212i \(0.733777\pi\)
\(348\) 0 0
\(349\) 200.000i 0.573066i −0.958070 0.286533i \(-0.907497\pi\)
0.958070 0.286533i \(-0.0925028\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 321.000 321.000i 0.909348 0.909348i −0.0868711 0.996220i \(-0.527687\pi\)
0.996220 + 0.0868711i \(0.0276868\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 112.000i 0.311978i 0.987759 + 0.155989i \(0.0498564\pi\)
−0.987759 + 0.155989i \(0.950144\pi\)
\(360\) 0 0
\(361\) 297.000 0.822715
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −377.000 377.000i −1.02725 1.02725i −0.999618 0.0276297i \(-0.991204\pi\)
−0.0276297 0.999618i \(-0.508796\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −98.0000 −0.264151
\(372\) 0 0
\(373\) −217.000 + 217.000i −0.581769 + 0.581769i −0.935389 0.353620i \(-0.884951\pi\)
0.353620 + 0.935389i \(0.384951\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −72.0000 72.0000i −0.190981 0.190981i
\(378\) 0 0
\(379\) 56.0000i 0.147757i −0.997267 0.0738786i \(-0.976462\pi\)
0.997267 0.0738786i \(-0.0235377\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 57.0000 57.0000i 0.148825 0.148825i −0.628768 0.777593i \(-0.716440\pi\)
0.777593 + 0.628768i \(0.216440\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 312.000i 0.802057i 0.916066 + 0.401028i \(0.131347\pi\)
−0.916066 + 0.401028i \(0.868653\pi\)
\(390\) 0 0
\(391\) −46.0000 −0.117647
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −193.000 193.000i −0.486146 0.486146i 0.420942 0.907088i \(-0.361700\pi\)
−0.907088 + 0.420942i \(0.861700\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 30.0000 0.0748130 0.0374065 0.999300i \(-0.488090\pi\)
0.0374065 + 0.999300i \(0.488090\pi\)
\(402\) 0 0
\(403\) 126.000 126.000i 0.312655 0.312655i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 330.000 + 330.000i 0.810811 + 0.810811i
\(408\) 0 0
\(409\) 432.000i 1.05623i 0.849171 + 0.528117i \(0.177102\pi\)
−0.849171 + 0.528117i \(0.822898\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −392.000 + 392.000i −0.949153 + 0.949153i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 168.000i 0.400955i 0.979698 + 0.200477i \(0.0642493\pi\)
−0.979698 + 0.200477i \(0.935751\pi\)
\(420\) 0 0
\(421\) −454.000 −1.07838 −0.539192 0.842183i \(-0.681270\pi\)
−0.539192 + 0.842183i \(0.681270\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 294.000 + 294.000i 0.688525 + 0.688525i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 494.000 1.14617 0.573086 0.819495i \(-0.305746\pi\)
0.573086 + 0.819495i \(0.305746\pi\)
\(432\) 0 0
\(433\) 511.000 511.000i 1.18014 1.18014i 0.200431 0.979708i \(-0.435766\pi\)
0.979708 0.200431i \(-0.0642341\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 184.000 + 184.000i 0.421053 + 0.421053i
\(438\) 0 0
\(439\) 176.000i 0.400911i 0.979703 + 0.200456i \(0.0642422\pi\)
−0.979703 + 0.200456i \(0.935758\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 177.000 177.000i 0.399549 0.399549i −0.478525 0.878074i \(-0.658828\pi\)
0.878074 + 0.478525i \(0.158828\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 608.000i 1.35412i 0.735928 + 0.677060i \(0.236746\pi\)
−0.735928 + 0.677060i \(0.763254\pi\)
\(450\) 0 0
\(451\) −140.000 −0.310421
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −609.000 609.000i −1.33260 1.33260i −0.903033 0.429571i \(-0.858665\pi\)
−0.429571 0.903033i \(-0.641335\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −490.000 −1.06291 −0.531453 0.847088i \(-0.678354\pi\)
−0.531453 + 0.847088i \(0.678354\pi\)
\(462\) 0 0
\(463\) 7.00000 7.00000i 0.0151188 0.0151188i −0.699507 0.714626i \(-0.746597\pi\)
0.714626 + 0.699507i \(0.246597\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.0000 + 25.0000i 0.0535332 + 0.0535332i 0.733367 0.679833i \(-0.237948\pi\)
−0.679833 + 0.733367i \(0.737948\pi\)
\(468\) 0 0
\(469\) 98.0000i 0.208955i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −150.000 + 150.000i −0.317125 + 0.317125i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 128.000i 0.267223i 0.991034 + 0.133612i \(0.0426575\pi\)
−0.991034 + 0.133612i \(0.957343\pi\)
\(480\) 0 0
\(481\) 594.000 1.23493
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −249.000 249.000i −0.511294 0.511294i 0.403629 0.914923i \(-0.367749\pi\)
−0.914923 + 0.403629i \(0.867749\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −650.000 −1.32383 −0.661914 0.749579i \(-0.730256\pi\)
−0.661914 + 0.749579i \(0.730256\pi\)
\(492\) 0 0
\(493\) −8.00000 + 8.00000i −0.0162272 + 0.0162272i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −686.000 686.000i −1.38028 1.38028i
\(498\) 0 0
\(499\) 632.000i 1.26653i 0.773934 + 0.633267i \(0.218286\pi\)
−0.773934 + 0.633267i \(0.781714\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −471.000 + 471.000i −0.936382 + 0.936382i −0.998094 0.0617123i \(-0.980344\pi\)
0.0617123 + 0.998094i \(0.480344\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.00000i 0.0157171i 0.999969 + 0.00785855i \(0.00250148\pi\)
−0.999969 + 0.00785855i \(0.997499\pi\)
\(510\) 0 0
\(511\) −686.000 −1.34247
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 390.000 + 390.000i 0.754352 + 0.754352i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 366.000 0.702495 0.351248 0.936283i \(-0.385758\pi\)
0.351248 + 0.936283i \(0.385758\pi\)
\(522\) 0 0
\(523\) −273.000 + 273.000i −0.521989 + 0.521989i −0.918172 0.396183i \(-0.870335\pi\)
0.396183 + 0.918172i \(0.370335\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.0000 14.0000i −0.0265655 0.0265655i
\(528\) 0 0
\(529\) 529.000i 1.00000i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −126.000 + 126.000i −0.236398 + 0.236398i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 490.000i 0.909091i
\(540\) 0 0
\(541\) 394.000 0.728281 0.364140 0.931344i \(-0.381363\pi\)
0.364140 + 0.931344i \(0.381363\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 231.000 + 231.000i 0.422303 + 0.422303i 0.885996 0.463693i \(-0.153476\pi\)
−0.463693 + 0.885996i \(0.653476\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 64.0000 0.116152
\(552\) 0 0
\(553\) −672.000 + 672.000i −1.21519 + 1.21519i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −735.000 735.000i −1.31957 1.31957i −0.914116 0.405453i \(-0.867114\pi\)
−0.405453 0.914116i \(-0.632886\pi\)
\(558\) 0 0
\(559\) 270.000i 0.483005i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 609.000 609.000i 1.08171 1.08171i 0.0853545 0.996351i \(-0.472798\pi\)
0.996351 0.0853545i \(-0.0272023\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 560.000i 0.984183i −0.870544 0.492091i \(-0.836233\pi\)
0.870544 0.492091i \(-0.163767\pi\)
\(570\) 0 0
\(571\) 938.000 1.64273 0.821366 0.570401i \(-0.193212\pi\)
0.821366 + 0.570401i \(0.193212\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −97.0000 97.0000i −0.168111 0.168111i 0.618038 0.786149i \(-0.287928\pi\)
−0.786149 + 0.618038i \(0.787928\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −882.000 −1.51807
\(582\) 0 0
\(583\) 70.0000 70.0000i 0.120069 0.120069i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −39.0000 39.0000i −0.0664395 0.0664395i 0.673106 0.739546i \(-0.264960\pi\)
−0.739546 + 0.673106i \(0.764960\pi\)
\(588\) 0 0
\(589\) 112.000i 0.190153i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −479.000 + 479.000i −0.807757 + 0.807757i −0.984294 0.176537i \(-0.943511\pi\)
0.176537 + 0.984294i \(0.443511\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1040.00i 1.73623i 0.496366 + 0.868114i \(0.334668\pi\)
−0.496366 + 0.868114i \(0.665332\pi\)
\(600\) 0 0
\(601\) −430.000 −0.715474 −0.357737 0.933822i \(-0.616452\pi\)
−0.357737 + 0.933822i \(0.616452\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 423.000 + 423.000i 0.696870 + 0.696870i 0.963734 0.266864i \(-0.0859875\pi\)
−0.266864 + 0.963734i \(0.585988\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 702.000 1.14894
\(612\) 0 0
\(613\) −249.000 + 249.000i −0.406199 + 0.406199i −0.880411 0.474212i \(-0.842733\pi\)
0.474212 + 0.880411i \(0.342733\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 321.000 + 321.000i 0.520259 + 0.520259i 0.917650 0.397390i \(-0.130084\pi\)
−0.397390 + 0.917650i \(0.630084\pi\)
\(618\) 0 0
\(619\) 600.000i 0.969305i −0.874707 0.484653i \(-0.838946\pi\)
0.874707 0.484653i \(-0.161054\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −784.000 + 784.000i −1.25843 + 1.25843i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 66.0000i 0.104928i
\(630\) 0 0
\(631\) −638.000 −1.01109 −0.505547 0.862799i \(-0.668709\pi\)
−0.505547 + 0.862799i \(0.668709\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −441.000 441.000i −0.692308 0.692308i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −482.000 −0.751950 −0.375975 0.926630i \(-0.622692\pi\)
−0.375975 + 0.926630i \(0.622692\pi\)
\(642\) 0 0
\(643\) −33.0000 + 33.0000i −0.0513219 + 0.0513219i −0.732302 0.680980i \(-0.761554\pi\)
0.680980 + 0.732302i \(0.261554\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.00000 7.00000i −0.0108192 0.0108192i 0.701677 0.712496i \(-0.252435\pi\)
−0.712496 + 0.701677i \(0.752435\pi\)
\(648\) 0 0
\(649\) 560.000i 0.862866i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −471.000 + 471.000i −0.721286 + 0.721286i −0.968867 0.247581i \(-0.920364\pi\)
0.247581 + 0.968867i \(0.420364\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 328.000i 0.497724i 0.968539 + 0.248862i \(0.0800565\pi\)
−0.968539 + 0.248862i \(0.919943\pi\)
\(660\) 0 0
\(661\) −742.000 −1.12254 −0.561271 0.827632i \(-0.689687\pi\)
−0.561271 + 0.827632i \(0.689687\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −184.000 184.000i −0.275862 0.275862i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −420.000 −0.625931
\(672\) 0 0
\(673\) 287.000 287.000i 0.426449 0.426449i −0.460968 0.887417i \(-0.652498\pi\)
0.887417 + 0.460968i \(0.152498\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 577.000 + 577.000i 0.852290 + 0.852290i 0.990415 0.138125i \(-0.0441077\pi\)
−0.138125 + 0.990415i \(0.544108\pi\)
\(678\) 0 0
\(679\) 462.000i 0.680412i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −399.000 + 399.000i −0.584187 + 0.584187i −0.936051 0.351864i \(-0.885548\pi\)
0.351864 + 0.936051i \(0.385548\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 126.000i 0.182874i
\(690\) 0 0
\(691\) 378.000 0.547033 0.273517 0.961867i \(-0.411813\pi\)
0.273517 + 0.961867i \(0.411813\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 14.0000 + 14.0000i 0.0200861 + 0.0200861i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 470.000 0.670471 0.335235 0.942134i \(-0.391184\pi\)
0.335235 + 0.942134i \(0.391184\pi\)
\(702\) 0 0
\(703\) −264.000 + 264.000i −0.375533 + 0.375533i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −182.000 182.000i −0.257426 0.257426i
\(708\) 0 0
\(709\) 1192.00i 1.68124i 0.541624 + 0.840621i \(0.317810\pi\)
−0.541624 + 0.840621i \(0.682190\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 322.000 322.000i 0.451613 0.451613i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 608.000i 0.845619i 0.906219 + 0.422809i \(0.138956\pi\)
−0.906219 + 0.422809i \(0.861044\pi\)
\(720\) 0 0
\(721\) −1022.00 −1.41748
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −441.000 441.000i −0.606602 0.606602i 0.335454 0.942057i \(-0.391110\pi\)
−0.942057 + 0.335454i \(0.891110\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 30.0000 0.0410397
\(732\) 0 0
\(733\) −361.000 + 361.000i −0.492497 + 0.492497i −0.909092 0.416595i \(-0.863223\pi\)
0.416595 + 0.909092i \(0.363223\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −70.0000 70.0000i −0.0949796 0.0949796i
\(738\) 0 0
\(739\) 920.000i 1.24493i 0.782649 + 0.622463i \(0.213868\pi\)
−0.782649 + 0.622463i \(0.786132\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −343.000 + 343.000i −0.461642 + 0.461642i −0.899193 0.437551i \(-0.855846\pi\)
0.437551 + 0.899193i \(0.355846\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1694.00i 2.26168i
\(750\) 0 0
\(751\) 786.000 1.04660 0.523302 0.852147i \(-0.324700\pi\)
0.523302 + 0.852147i \(0.324700\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 63.0000 + 63.0000i 0.0832232 + 0.0832232i 0.747493 0.664270i \(-0.231257\pi\)
−0.664270 + 0.747493i \(0.731257\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 398.000 0.522996 0.261498 0.965204i \(-0.415784\pi\)
0.261498 + 0.965204i \(0.415784\pi\)
\(762\) 0 0
\(763\) 952.000 952.000i 1.24771 1.24771i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −504.000 504.000i −0.657106 0.657106i
\(768\) 0 0
\(769\) 704.000i 0.915475i 0.889087 + 0.457737i \(0.151340\pi\)
−0.889087 + 0.457737i \(0.848660\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 825.000 825.000i 1.06727 1.06727i 0.0697026 0.997568i \(-0.477795\pi\)
0.997568 0.0697026i \(-0.0222050\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 112.000i 0.143774i
\(780\) 0 0
\(781\) 980.000 1.25480
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 71.0000 + 71.0000i 0.0902160 + 0.0902160i 0.750775 0.660559i \(-0.229680\pi\)
−0.660559 + 0.750775i \(0.729680\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1778.00 −2.24779
\(792\) 0 0
\(793\) −378.000 + 378.000i −0.476671 + 0.476671i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 33.0000 + 33.0000i 0.0414053 + 0.0414053i 0.727506 0.686101i \(-0.240679\pi\)
−0.686101 + 0.727506i \(0.740679\pi\)
\(798\) 0 0
\(799\) 78.0000i 0.0976220i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 490.000 490.000i 0.610212 0.610212i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 368.000i 0.454883i −0.973792 0.227441i \(-0.926964\pi\)
0.973792 0.227441i \(-0.0730360\pi\)
\(810\) 0 0
\(811\) −886.000 −1.09248 −0.546239 0.837629i \(-0.683941\pi\)
−0.546239 + 0.837629i \(0.683941\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −120.000 120.000i −0.146879 0.146879i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 614.000 0.747868 0.373934 0.927455i \(-0.378009\pi\)
0.373934 + 0.927455i \(0.378009\pi\)
\(822\) 0 0
\(823\) −1001.00 + 1001.00i −1.21628 + 1.21628i −0.247358 + 0.968924i \(0.579562\pi\)
−0.968924 + 0.247358i \(0.920438\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −615.000 615.000i −0.743652 0.743652i 0.229627 0.973279i \(-0.426249\pi\)
−0.973279 + 0.229627i \(0.926249\pi\)
\(828\) 0 0
\(829\) 616.000i 0.743064i −0.928420 0.371532i \(-0.878833\pi\)
0.928420 0.371532i \(-0.121167\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −49.0000 + 49.0000i −0.0588235 + 0.0588235i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1424.00i 1.69726i −0.528988 0.848629i \(-0.677428\pi\)
0.528988 0.848629i \(-0.322572\pi\)
\(840\) 0 0
\(841\) 777.000 0.923900
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −147.000 147.000i −0.173554 0.173554i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1518.00 1.78378
\(852\) 0 0
\(853\) 935.000 935.000i 1.09613 1.09613i 0.101273 0.994859i \(-0.467709\pi\)
0.994859 0.101273i \(-0.0322914\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −63.0000 63.0000i −0.0735123 0.0735123i 0.669395 0.742907i \(-0.266554\pi\)
−0.742907 + 0.669395i \(0.766554\pi\)
\(858\) 0 0
\(859\) 392.000i 0.456345i 0.973621 + 0.228172i \(0.0732749\pi\)
−0.973621 + 0.228172i \(0.926725\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 217.000 217.000i 0.251448 0.251448i −0.570116 0.821564i \(-0.693102\pi\)
0.821564 + 0.570116i \(0.193102\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 960.000i 1.10472i
\(870\) 0 0
\(871\) −126.000 −0.144661
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 831.000 + 831.000i 0.947548 + 0.947548i 0.998691 0.0511429i \(-0.0162864\pi\)
−0.0511429 + 0.998691i \(0.516286\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −322.000 −0.365494 −0.182747 0.983160i \(-0.558499\pi\)
−0.182747 + 0.983160i \(0.558499\pi\)
\(882\) 0 0
\(883\) 287.000 287.000i 0.325028 0.325028i −0.525664 0.850692i \(-0.676183\pi\)
0.850692 + 0.525664i \(0.176183\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −903.000 903.000i −1.01804 1.01804i −0.999834 0.0182040i \(-0.994205\pi\)
−0.0182040 0.999834i \(-0.505795\pi\)
\(888\) 0 0
\(889\) 98.0000i 0.110236i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −312.000 + 312.000i −0.349384 + 0.349384i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 112.000i 0.124583i
\(900\) 0 0
\(901\) −14.0000 −0.0155383
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1081.00 1081.00i −1.19184 1.19184i −0.976550 0.215291i \(-0.930930\pi\)
−0.215291 0.976550i \(-0.569070\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 238.000 0.261251 0.130626 0.991432i \(-0.458301\pi\)
0.130626 + 0.991432i \(0.458301\pi\)
\(912\) 0 0
\(913\) 630.000 630.000i 0.690033 0.690033i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1610.00 + 1610.00i 1.75573 + 1.75573i
\(918\) 0 0
\(919\) 1552.00i 1.68879i −0.535719 0.844396i \(-0.679960\pi\)
0.535719 0.844396i \(-0.320040\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 882.000 882.000i 0.955580 0.955580i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 224.000i 0.241119i 0.992706 + 0.120560i \(0.0384689\pi\)
−0.992706 + 0.120560i \(0.961531\pi\)
\(930\) 0 0
\(931\) 392.000 0.421053
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 383.000 + 383.000i 0.408751 + 0.408751i 0.881303 0.472552i \(-0.156667\pi\)
−0.472552 + 0.881303i \(0.656667\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −42.0000 −0.0446334 −0.0223167 0.999751i \(-0.507104\pi\)
−0.0223167 + 0.999751i \(0.507104\pi\)
\(942\) 0 0
\(943\) −322.000 + 322.000i −0.341463 + 0.341463i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1337.00 + 1337.00i 1.41183 + 1.41183i 0.746977 + 0.664849i \(0.231504\pi\)
0.664849 + 0.746977i \(0.268496\pi\)
\(948\) 0 0
\(949\) 882.000i 0.929399i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 273.000 273.000i 0.286464 0.286464i −0.549216 0.835680i \(-0.685074\pi\)
0.835680 + 0.549216i \(0.185074\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 882.000i 0.919708i
\(960\) 0 0
\(961\) −765.000 −0.796046
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 743.000 + 743.000i 0.768356 + 0.768356i 0.977817 0.209461i \(-0.0671710\pi\)
−0.209461 + 0.977817i \(0.567171\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −266.000 −0.273944 −0.136972 0.990575i \(-0.543737\pi\)
−0.136972 + 0.990575i \(0.543737\pi\)
\(972\) 0 0
\(973\) 616.000 616.000i 0.633094 0.633094i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 417.000 + 417.000i 0.426817 + 0.426817i 0.887543 0.460726i \(-0.152411\pi\)
−0.460726 + 0.887543i \(0.652411\pi\)
\(978\) 0 0
\(979\) 1120.00i 1.14402i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −631.000 + 631.000i −0.641913 + 0.641913i −0.951025 0.309113i \(-0.899968\pi\)
0.309113 + 0.951025i \(0.399968\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 690.000i 0.697674i
\(990\) 0 0
\(991\) −14.0000 −0.0141271 −0.00706357 0.999975i \(-0.502248\pi\)
−0.00706357 + 0.999975i \(0.502248\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 671.000 + 671.000i 0.673019 + 0.673019i 0.958411 0.285392i \(-0.0921237\pi\)
−0.285392 + 0.958411i \(0.592124\pi\)
\(998\) 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.l.a.757.1 2
3.2 odd 2 100.3.f.a.57.1 2
5.2 odd 4 180.3.l.a.73.1 2
5.3 odd 4 inner 900.3.l.a.793.1 2
5.4 even 2 180.3.l.a.37.1 2
12.11 even 2 400.3.p.d.257.1 2
15.2 even 4 20.3.f.a.13.1 2
15.8 even 4 100.3.f.a.93.1 2
15.14 odd 2 20.3.f.a.17.1 yes 2
20.7 even 4 720.3.bh.e.433.1 2
20.19 odd 2 720.3.bh.e.577.1 2
60.23 odd 4 400.3.p.d.193.1 2
60.47 odd 4 80.3.p.a.33.1 2
60.59 even 2 80.3.p.a.17.1 2
105.62 odd 4 980.3.l.a.393.1 2
105.104 even 2 980.3.l.a.197.1 2
120.29 odd 2 320.3.p.c.257.1 2
120.59 even 2 320.3.p.g.257.1 2
120.77 even 4 320.3.p.c.193.1 2
120.107 odd 4 320.3.p.g.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.3.f.a.13.1 2 15.2 even 4
20.3.f.a.17.1 yes 2 15.14 odd 2
80.3.p.a.17.1 2 60.59 even 2
80.3.p.a.33.1 2 60.47 odd 4
100.3.f.a.57.1 2 3.2 odd 2
100.3.f.a.93.1 2 15.8 even 4
180.3.l.a.37.1 2 5.4 even 2
180.3.l.a.73.1 2 5.2 odd 4
320.3.p.c.193.1 2 120.77 even 4
320.3.p.c.257.1 2 120.29 odd 2
320.3.p.g.193.1 2 120.107 odd 4
320.3.p.g.257.1 2 120.59 even 2
400.3.p.d.193.1 2 60.23 odd 4
400.3.p.d.257.1 2 12.11 even 2
720.3.bh.e.433.1 2 20.7 even 4
720.3.bh.e.577.1 2 20.19 odd 2
900.3.l.a.757.1 2 1.1 even 1 trivial
900.3.l.a.793.1 2 5.3 odd 4 inner
980.3.l.a.197.1 2 105.104 even 2
980.3.l.a.393.1 2 105.62 odd 4