Properties

Label 9900.2.c.q.5149.4
Level $9900$
Weight $2$
Character 9900.5149
Analytic conductor $79.052$
Analytic rank $0$
Dimension $4$
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] = [9900,2,Mod(5149,9900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9900.5149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9900.c (of order \(2\), degree \(1\), 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: \(79.0518980011\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{13})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 7x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 660)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5149.4
Root \(2.30278i\) of defining polynomial
Character \(\chi\) \(=\) 9900.5149
Dual form 9900.2.c.q.5149.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.60555i q^{7} +O(q^{10})\) \(q+4.60555i q^{7} -1.00000 q^{11} +4.60555i q^{13} -6.60555i q^{17} +7.21110 q^{19} +8.00000 q^{29} +9.21110 q^{31} -3.21110i q^{37} -8.00000 q^{41} +3.39445i q^{43} +5.21110i q^{47} -14.2111 q^{49} +2.00000i q^{53} +8.00000 q^{59} +7.21110 q^{61} -4.00000i q^{67} +14.4222 q^{71} -0.605551i q^{73} -4.60555i q^{77} +11.2111 q^{79} -10.6056i q^{83} +6.00000 q^{89} -21.2111 q^{91} -12.4222i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{11} + 32 q^{29} + 8 q^{31} - 32 q^{41} - 28 q^{49} + 32 q^{59} + 16 q^{79} + 24 q^{89} - 56 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/9900\mathbb{Z}\right)^\times\).

\(n\) \(2377\) \(4501\) \(4951\) \(5501\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.60555i 1.74073i 0.492403 + 0.870367i \(0.336119\pi\)
−0.492403 + 0.870367i \(0.663881\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 4.60555i 1.27735i 0.769477 + 0.638675i \(0.220517\pi\)
−0.769477 + 0.638675i \(0.779483\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 6.60555i − 1.60208i −0.598610 0.801041i \(-0.704280\pi\)
0.598610 0.801041i \(-0.295720\pi\)
\(18\) 0 0
\(19\) 7.21110 1.65434 0.827170 0.561951i \(-0.189949\pi\)
0.827170 + 0.561951i \(0.189949\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) 9.21110 1.65436 0.827181 0.561935i \(-0.189943\pi\)
0.827181 + 0.561935i \(0.189943\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) − 3.21110i − 0.527902i −0.964536 0.263951i \(-0.914974\pi\)
0.964536 0.263951i \(-0.0850257\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 3.39445i 0.517649i 0.965924 + 0.258824i \(0.0833351\pi\)
−0.965924 + 0.258824i \(0.916665\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.21110i 0.760117i 0.924962 + 0.380059i \(0.124096\pi\)
−0.924962 + 0.380059i \(0.875904\pi\)
\(48\) 0 0
\(49\) −14.2111 −2.03016
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.00000i 0.274721i 0.990521 + 0.137361i \(0.0438619\pi\)
−0.990521 + 0.137361i \(0.956138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) 7.21110 0.923287 0.461644 0.887066i \(-0.347260\pi\)
0.461644 + 0.887066i \(0.347260\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 4.00000i − 0.488678i −0.969690 0.244339i \(-0.921429\pi\)
0.969690 0.244339i \(-0.0785709\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.4222 1.71160 0.855800 0.517306i \(-0.173065\pi\)
0.855800 + 0.517306i \(0.173065\pi\)
\(72\) 0 0
\(73\) − 0.605551i − 0.0708744i −0.999372 0.0354372i \(-0.988718\pi\)
0.999372 0.0354372i \(-0.0112824\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 4.60555i − 0.524851i
\(78\) 0 0
\(79\) 11.2111 1.26135 0.630674 0.776048i \(-0.282779\pi\)
0.630674 + 0.776048i \(0.282779\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 10.6056i − 1.16411i −0.813149 0.582055i \(-0.802249\pi\)
0.813149 0.582055i \(-0.197751\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −21.2111 −2.22353
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) − 12.4222i − 1.26128i −0.776074 0.630642i \(-0.782792\pi\)
0.776074 0.630642i \(-0.217208\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.21110 −0.518524 −0.259262 0.965807i \(-0.583479\pi\)
−0.259262 + 0.965807i \(0.583479\pi\)
\(102\) 0 0
\(103\) − 1.21110i − 0.119333i −0.998218 0.0596667i \(-0.980996\pi\)
0.998218 0.0596667i \(-0.0190038\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 15.8167i − 1.52905i −0.644592 0.764527i \(-0.722973\pi\)
0.644592 0.764527i \(-0.277027\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 0.788897i − 0.0742132i −0.999311 0.0371066i \(-0.988186\pi\)
0.999311 0.0371066i \(-0.0118141\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 30.4222 2.78880
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 8.60555i − 0.763619i −0.924241 0.381810i \(-0.875301\pi\)
0.924241 0.381810i \(-0.124699\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.78890 0.593149 0.296574 0.955010i \(-0.404156\pi\)
0.296574 + 0.955010i \(0.404156\pi\)
\(132\) 0 0
\(133\) 33.2111i 2.87977i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000i 0.512615i 0.966595 + 0.256307i \(0.0825059\pi\)
−0.966595 + 0.256307i \(0.917494\pi\)
\(138\) 0 0
\(139\) −16.4222 −1.39291 −0.696457 0.717599i \(-0.745241\pi\)
−0.696457 + 0.717599i \(0.745241\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 4.60555i − 0.385136i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.21110 −0.754603 −0.377301 0.926090i \(-0.623148\pi\)
−0.377301 + 0.926090i \(0.623148\pi\)
\(150\) 0 0
\(151\) −19.2111 −1.56338 −0.781689 0.623669i \(-0.785641\pi\)
−0.781689 + 0.623669i \(0.785641\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 3.21110i 0.256274i 0.991756 + 0.128137i \(0.0408997\pi\)
−0.991756 + 0.128137i \(0.959100\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.21110i 0.408165i 0.978954 + 0.204083i \(0.0654211\pi\)
−0.978954 + 0.204083i \(0.934579\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.8167i 1.53346i 0.641970 + 0.766729i \(0.278117\pi\)
−0.641970 + 0.766729i \(0.721883\pi\)
\(168\) 0 0
\(169\) −8.21110 −0.631623
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.183346i 0.0139396i 0.999976 + 0.00696978i \(0.00221857\pi\)
−0.999976 + 0.00696978i \(0.997781\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 23.2111 1.72527 0.862634 0.505829i \(-0.168813\pi\)
0.862634 + 0.505829i \(0.168813\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 6.60555i 0.483046i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −18.4222 −1.33298 −0.666492 0.745512i \(-0.732205\pi\)
−0.666492 + 0.745512i \(0.732205\pi\)
\(192\) 0 0
\(193\) 21.8167i 1.57040i 0.619244 + 0.785199i \(0.287439\pi\)
−0.619244 + 0.785199i \(0.712561\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.3944i 0.954315i 0.878818 + 0.477157i \(0.158333\pi\)
−0.878818 + 0.477157i \(0.841667\pi\)
\(198\) 0 0
\(199\) 10.4222 0.738811 0.369405 0.929268i \(-0.379561\pi\)
0.369405 + 0.929268i \(0.379561\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 36.8444i 2.58597i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.21110 −0.498802
\(210\) 0 0
\(211\) −23.2111 −1.59792 −0.798959 0.601385i \(-0.794616\pi\)
−0.798959 + 0.601385i \(0.794616\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 42.4222i 2.87981i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 30.4222 2.04642
\(222\) 0 0
\(223\) − 9.21110i − 0.616821i −0.951253 0.308411i \(-0.900203\pi\)
0.951253 0.308411i \(-0.0997970\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.8167i 1.04979i 0.851168 + 0.524894i \(0.175895\pi\)
−0.851168 + 0.524894i \(0.824105\pi\)
\(228\) 0 0
\(229\) 8.42221 0.556555 0.278277 0.960501i \(-0.410237\pi\)
0.278277 + 0.960501i \(0.410237\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 10.6056i − 0.694793i −0.937718 0.347396i \(-0.887066\pi\)
0.937718 0.347396i \(-0.112934\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.78890 0.439137 0.219569 0.975597i \(-0.429535\pi\)
0.219569 + 0.975597i \(0.429535\pi\)
\(240\) 0 0
\(241\) −15.2111 −0.979833 −0.489917 0.871769i \(-0.662973\pi\)
−0.489917 + 0.871769i \(0.662973\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 33.2111i 2.11317i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 10.4222 0.657844 0.328922 0.944357i \(-0.393315\pi\)
0.328922 + 0.944357i \(0.393315\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 23.2111i 1.44787i 0.689869 + 0.723934i \(0.257668\pi\)
−0.689869 + 0.723934i \(0.742332\pi\)
\(258\) 0 0
\(259\) 14.7889 0.918937
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 17.0278i − 1.04998i −0.851109 0.524988i \(-0.824070\pi\)
0.851109 0.524988i \(-0.175930\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −20.4222 −1.24516 −0.622582 0.782555i \(-0.713916\pi\)
−0.622582 + 0.782555i \(0.713916\pi\)
\(270\) 0 0
\(271\) −4.78890 −0.290905 −0.145452 0.989365i \(-0.546464\pi\)
−0.145452 + 0.989365i \(0.546464\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 32.2389i 1.93705i 0.248925 + 0.968523i \(0.419923\pi\)
−0.248925 + 0.968523i \(0.580077\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) − 4.60555i − 0.273772i −0.990587 0.136886i \(-0.956291\pi\)
0.990587 0.136886i \(-0.0437093\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 36.8444i − 2.17486i
\(288\) 0 0
\(289\) −26.6333 −1.56667
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 19.8167i 1.15770i 0.815434 + 0.578851i \(0.196499\pi\)
−0.815434 + 0.578851i \(0.803501\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −15.6333 −0.901089
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 8.60555i 0.491145i 0.969378 + 0.245572i \(0.0789759\pi\)
−0.969378 + 0.245572i \(0.921024\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −30.4222 −1.72508 −0.862542 0.505985i \(-0.831129\pi\)
−0.862542 + 0.505985i \(0.831129\pi\)
\(312\) 0 0
\(313\) − 8.78890i − 0.496778i −0.968660 0.248389i \(-0.920099\pi\)
0.968660 0.248389i \(-0.0799011\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 11.2111i − 0.629678i −0.949145 0.314839i \(-0.898049\pi\)
0.949145 0.314839i \(-0.101951\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 47.6333i − 2.65039i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −24.0000 −1.32316
\(330\) 0 0
\(331\) −6.78890 −0.373152 −0.186576 0.982441i \(-0.559739\pi\)
−0.186576 + 0.982441i \(0.559739\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 28.2389i − 1.53827i −0.639087 0.769134i \(-0.720688\pi\)
0.639087 0.769134i \(-0.279312\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −9.21110 −0.498809
\(342\) 0 0
\(343\) − 33.2111i − 1.79323i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 29.0278i 1.55829i 0.626843 + 0.779146i \(0.284347\pi\)
−0.626843 + 0.779146i \(0.715653\pi\)
\(348\) 0 0
\(349\) 8.78890 0.470459 0.235229 0.971940i \(-0.424416\pi\)
0.235229 + 0.971940i \(0.424416\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 26.0000i − 1.38384i −0.721974 0.691920i \(-0.756765\pi\)
0.721974 0.691920i \(-0.243235\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.7889 0.991640 0.495820 0.868425i \(-0.334868\pi\)
0.495820 + 0.868425i \(0.334868\pi\)
\(360\) 0 0
\(361\) 33.0000 1.73684
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 6.78890i 0.354378i 0.984177 + 0.177189i \(0.0567003\pi\)
−0.984177 + 0.177189i \(0.943300\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9.21110 −0.478217
\(372\) 0 0
\(373\) − 4.60555i − 0.238466i −0.992866 0.119233i \(-0.961956\pi\)
0.992866 0.119233i \(-0.0380436\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 36.8444i 1.89758i
\(378\) 0 0
\(379\) 18.4222 0.946285 0.473143 0.880986i \(-0.343120\pi\)
0.473143 + 0.880986i \(0.343120\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 18.7889i 0.960068i 0.877250 + 0.480034i \(0.159376\pi\)
−0.877250 + 0.480034i \(0.840624\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 30.8444 1.56387 0.781937 0.623358i \(-0.214232\pi\)
0.781937 + 0.623358i \(0.214232\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 28.4222i 1.42647i 0.700925 + 0.713235i \(0.252771\pi\)
−0.700925 + 0.713235i \(0.747229\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −20.4222 −1.01984 −0.509918 0.860223i \(-0.670324\pi\)
−0.509918 + 0.860223i \(0.670324\pi\)
\(402\) 0 0
\(403\) 42.4222i 2.11320i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.21110i 0.159168i
\(408\) 0 0
\(409\) 2.00000 0.0988936 0.0494468 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 36.8444i 1.81299i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −19.2111 −0.936292 −0.468146 0.883651i \(-0.655078\pi\)
−0.468146 + 0.883651i \(0.655078\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 33.2111i 1.60720i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.57779 0.0759997 0.0379999 0.999278i \(-0.487901\pi\)
0.0379999 + 0.999278i \(0.487901\pi\)
\(432\) 0 0
\(433\) − 8.42221i − 0.404745i −0.979309 0.202373i \(-0.935135\pi\)
0.979309 0.202373i \(-0.0648652\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 25.2111i 1.19782i 0.800818 + 0.598908i \(0.204398\pi\)
−0.800818 + 0.598908i \(0.795602\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 18.8444 0.889323 0.444661 0.895699i \(-0.353324\pi\)
0.444661 + 0.895699i \(0.353324\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) − 4.60555i − 0.215439i −0.994181 0.107719i \(-0.965645\pi\)
0.994181 0.107719i \(-0.0343548\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9.21110 0.429004 0.214502 0.976724i \(-0.431187\pi\)
0.214502 + 0.976724i \(0.431187\pi\)
\(462\) 0 0
\(463\) − 1.21110i − 0.0562847i −0.999604 0.0281424i \(-0.991041\pi\)
0.999604 0.0281424i \(-0.00895917\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.00000i 0.185098i 0.995708 + 0.0925490i \(0.0295015\pi\)
−0.995708 + 0.0925490i \(0.970499\pi\)
\(468\) 0 0
\(469\) 18.4222 0.850658
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 3.39445i − 0.156077i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14.7889 −0.675722 −0.337861 0.941196i \(-0.609703\pi\)
−0.337861 + 0.941196i \(0.609703\pi\)
\(480\) 0 0
\(481\) 14.7889 0.674316
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 5.57779i 0.252754i 0.991982 + 0.126377i \(0.0403349\pi\)
−0.991982 + 0.126377i \(0.959665\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.57779 0.251722 0.125861 0.992048i \(-0.459831\pi\)
0.125861 + 0.992048i \(0.459831\pi\)
\(492\) 0 0
\(493\) − 52.8444i − 2.37999i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 66.4222i 2.97944i
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.18335i 0.186526i 0.995641 + 0.0932631i \(0.0297298\pi\)
−0.995641 + 0.0932631i \(0.970270\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −28.4222 −1.25979 −0.629896 0.776679i \(-0.716903\pi\)
−0.629896 + 0.776679i \(0.716903\pi\)
\(510\) 0 0
\(511\) 2.78890 0.123374
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) − 5.21110i − 0.229184i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8.42221 0.368984 0.184492 0.982834i \(-0.440936\pi\)
0.184492 + 0.982834i \(0.440936\pi\)
\(522\) 0 0
\(523\) − 28.2389i − 1.23480i −0.786650 0.617400i \(-0.788186\pi\)
0.786650 0.617400i \(-0.211814\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 60.8444i − 2.65042i
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 36.8444i − 1.59591i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14.2111 0.612116
\(540\) 0 0
\(541\) 3.57779 0.153821 0.0769107 0.997038i \(-0.475494\pi\)
0.0769107 + 0.997038i \(0.475494\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 14.1833i − 0.606436i −0.952921 0.303218i \(-0.901939\pi\)
0.952921 0.303218i \(-0.0980611\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 57.6888 2.45763
\(552\) 0 0
\(553\) 51.6333i 2.19567i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.97224i 0.295423i 0.989030 + 0.147712i \(0.0471908\pi\)
−0.989030 + 0.147712i \(0.952809\pi\)
\(558\) 0 0
\(559\) −15.6333 −0.661218
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 19.8167i − 0.835172i −0.908637 0.417586i \(-0.862876\pi\)
0.908637 0.417586i \(-0.137124\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −27.6333 −1.15845 −0.579224 0.815168i \(-0.696644\pi\)
−0.579224 + 0.815168i \(0.696644\pi\)
\(570\) 0 0
\(571\) 12.4222 0.519853 0.259927 0.965628i \(-0.416302\pi\)
0.259927 + 0.965628i \(0.416302\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 28.7889i 1.19850i 0.800563 + 0.599249i \(0.204534\pi\)
−0.800563 + 0.599249i \(0.795466\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 48.8444 2.02641
\(582\) 0 0
\(583\) − 2.00000i − 0.0828315i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 6.42221i − 0.265073i −0.991178 0.132536i \(-0.957688\pi\)
0.991178 0.132536i \(-0.0423121\pi\)
\(588\) 0 0
\(589\) 66.4222 2.73688
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 13.0278i 0.534986i 0.963560 + 0.267493i \(0.0861952\pi\)
−0.963560 + 0.267493i \(0.913805\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −8.78890 −0.358507 −0.179253 0.983803i \(-0.557368\pi\)
−0.179253 + 0.983803i \(0.557368\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 4.97224i 0.201817i 0.994896 + 0.100909i \(0.0321750\pi\)
−0.994896 + 0.100909i \(0.967825\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) 21.8167i 0.881166i 0.897712 + 0.440583i \(0.145228\pi\)
−0.897712 + 0.440583i \(0.854772\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.7889i 0.997963i 0.866613 + 0.498982i \(0.166293\pi\)
−0.866613 + 0.498982i \(0.833707\pi\)
\(618\) 0 0
\(619\) 19.6333 0.789129 0.394565 0.918868i \(-0.370895\pi\)
0.394565 + 0.918868i \(0.370895\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 27.6333i 1.10711i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −21.2111 −0.845742
\(630\) 0 0
\(631\) 36.8444 1.46675 0.733376 0.679823i \(-0.237943\pi\)
0.733376 + 0.679823i \(0.237943\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 65.4500i − 2.59322i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.8444 −0.744309 −0.372155 0.928171i \(-0.621381\pi\)
−0.372155 + 0.928171i \(0.621381\pi\)
\(642\) 0 0
\(643\) − 0.366692i − 0.0144609i −0.999974 0.00723047i \(-0.997698\pi\)
0.999974 0.00723047i \(-0.00230155\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 45.2111i − 1.77743i −0.458458 0.888716i \(-0.651598\pi\)
0.458458 0.888716i \(-0.348402\pi\)
\(648\) 0 0
\(649\) −8.00000 −0.314027
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.78890i 0.187404i 0.995600 + 0.0937020i \(0.0298701\pi\)
−0.995600 + 0.0937020i \(0.970130\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 45.2666 1.76067 0.880334 0.474355i \(-0.157319\pi\)
0.880334 + 0.474355i \(0.157319\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7.21110 −0.278382
\(672\) 0 0
\(673\) 11.3944i 0.439224i 0.975587 + 0.219612i \(0.0704791\pi\)
−0.975587 + 0.219612i \(0.929521\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 5.39445i − 0.207326i −0.994613 0.103663i \(-0.966944\pi\)
0.994613 0.103663i \(-0.0330563\pi\)
\(678\) 0 0
\(679\) 57.2111 2.19556
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 30.7889i − 1.17810i −0.808095 0.589052i \(-0.799501\pi\)
0.808095 0.589052i \(-0.200499\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9.21110 −0.350915
\(690\) 0 0
\(691\) −13.5778 −0.516524 −0.258262 0.966075i \(-0.583150\pi\)
−0.258262 + 0.966075i \(0.583150\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 52.8444i 2.00162i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −46.4222 −1.75334 −0.876671 0.481090i \(-0.840241\pi\)
−0.876671 + 0.481090i \(0.840241\pi\)
\(702\) 0 0
\(703\) − 23.1556i − 0.873330i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 24.0000i − 0.902613i
\(708\) 0 0
\(709\) −5.63331 −0.211563 −0.105782 0.994389i \(-0.533734\pi\)
−0.105782 + 0.994389i \(0.533734\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −26.4222 −0.985382 −0.492691 0.870204i \(-0.663987\pi\)
−0.492691 + 0.870204i \(0.663987\pi\)
\(720\) 0 0
\(721\) 5.57779 0.207728
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 28.8444i − 1.06978i −0.844922 0.534890i \(-0.820353\pi\)
0.844922 0.534890i \(-0.179647\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 22.4222 0.829315
\(732\) 0 0
\(733\) 7.39445i 0.273120i 0.990632 + 0.136560i \(0.0436047\pi\)
−0.990632 + 0.136560i \(0.956395\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.00000i 0.147342i
\(738\) 0 0
\(739\) −41.2666 −1.51802 −0.759008 0.651081i \(-0.774316\pi\)
−0.759008 + 0.651081i \(0.774316\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 37.3944i 1.37187i 0.727663 + 0.685935i \(0.240606\pi\)
−0.727663 + 0.685935i \(0.759394\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 72.8444 2.66168
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 12.7889i − 0.464820i −0.972618 0.232410i \(-0.925339\pi\)
0.972618 0.232410i \(-0.0746612\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −27.6333 −1.00171 −0.500853 0.865532i \(-0.666980\pi\)
−0.500853 + 0.865532i \(0.666980\pi\)
\(762\) 0 0
\(763\) 46.0555i 1.66732i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 36.8444i 1.33037i
\(768\) 0 0
\(769\) 43.2111 1.55823 0.779116 0.626880i \(-0.215668\pi\)
0.779116 + 0.626880i \(0.215668\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 48.0555i − 1.72844i −0.503117 0.864218i \(-0.667814\pi\)
0.503117 0.864218i \(-0.332186\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −57.6888 −2.06692
\(780\) 0 0
\(781\) −14.4222 −0.516067
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 39.0278i 1.39119i 0.718434 + 0.695595i \(0.244859\pi\)
−0.718434 + 0.695595i \(0.755141\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.63331 0.129186
\(792\) 0 0
\(793\) 33.2111i 1.17936i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 40.0555i − 1.41884i −0.704786 0.709420i \(-0.748957\pi\)
0.704786 0.709420i \(-0.251043\pi\)
\(798\) 0 0
\(799\) 34.4222 1.21777
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0.605551i 0.0213694i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −12.0000 −0.421898 −0.210949 0.977497i \(-0.567655\pi\)
−0.210949 + 0.977497i \(0.567655\pi\)
\(810\) 0 0
\(811\) −7.57779 −0.266092 −0.133046 0.991110i \(-0.542476\pi\)
−0.133046 + 0.991110i \(0.542476\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 24.4777i 0.856367i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 12.8444 0.448273 0.224137 0.974558i \(-0.428044\pi\)
0.224137 + 0.974558i \(0.428044\pi\)
\(822\) 0 0
\(823\) − 41.2111i − 1.43653i −0.695770 0.718264i \(-0.744937\pi\)
0.695770 0.718264i \(-0.255063\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.60555i 0.0906039i 0.998973 + 0.0453019i \(0.0144250\pi\)
−0.998973 + 0.0453019i \(0.985575\pi\)
\(828\) 0 0
\(829\) −6.36669 −0.221124 −0.110562 0.993869i \(-0.535265\pi\)
−0.110562 + 0.993869i \(0.535265\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 93.8722i 3.25248i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 30.4222 1.05029 0.525146 0.851012i \(-0.324011\pi\)
0.525146 + 0.851012i \(0.324011\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 4.60555i 0.158249i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 40.2389i 1.37775i 0.724879 + 0.688876i \(0.241896\pi\)
−0.724879 + 0.688876i \(0.758104\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 25.0278i − 0.854932i −0.904031 0.427466i \(-0.859406\pi\)
0.904031 0.427466i \(-0.140594\pi\)
\(858\) 0 0
\(859\) −57.2111 −1.95202 −0.976009 0.217731i \(-0.930134\pi\)
−0.976009 + 0.217731i \(0.930134\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 39.6333i 1.34913i 0.738214 + 0.674567i \(0.235670\pi\)
−0.738214 + 0.674567i \(0.764330\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −11.2111 −0.380311
\(870\) 0 0
\(871\) 18.4222 0.624213
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 24.2389i − 0.818488i −0.912425 0.409244i \(-0.865792\pi\)
0.912425 0.409244i \(-0.134208\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −26.8444 −0.904411 −0.452206 0.891914i \(-0.649363\pi\)
−0.452206 + 0.891914i \(0.649363\pi\)
\(882\) 0 0
\(883\) − 6.42221i − 0.216124i −0.994144 0.108062i \(-0.965535\pi\)
0.994144 0.108062i \(-0.0344646\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 13.0278i − 0.437429i −0.975789 0.218715i \(-0.929814\pi\)
0.975789 0.218715i \(-0.0701864\pi\)
\(888\) 0 0
\(889\) 39.6333 1.32926
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 37.5778i 1.25749i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 73.6888 2.45766
\(900\) 0 0
\(901\) 13.2111 0.440126
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) − 34.0555i − 1.13079i −0.824819 0.565397i \(-0.808723\pi\)
0.824819 0.565397i \(-0.191277\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −18.4222 −0.610355 −0.305177 0.952296i \(-0.598716\pi\)
−0.305177 + 0.952296i \(0.598716\pi\)
\(912\) 0 0
\(913\) 10.6056i 0.350993i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 31.2666i 1.03251i
\(918\) 0 0
\(919\) 26.0000 0.857661 0.428830 0.903385i \(-0.358926\pi\)
0.428830 + 0.903385i \(0.358926\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 66.4222i 2.18631i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 26.8444 0.880737 0.440368 0.897817i \(-0.354848\pi\)
0.440368 + 0.897817i \(0.354848\pi\)
\(930\) 0 0
\(931\) −102.478 −3.35857
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 20.9722i 0.685133i 0.939494 + 0.342567i \(0.111296\pi\)
−0.939494 + 0.342567i \(0.888704\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −53.2111 −1.73463 −0.867316 0.497758i \(-0.834157\pi\)
−0.867316 + 0.497758i \(0.834157\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.63331i 0.118067i 0.998256 + 0.0590333i \(0.0188018\pi\)
−0.998256 + 0.0590333i \(0.981198\pi\)
\(948\) 0 0
\(949\) 2.78890 0.0905314
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 35.4500i − 1.14834i −0.818737 0.574168i \(-0.805325\pi\)
0.818737 0.574168i \(-0.194675\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −27.6333 −0.892326
\(960\) 0 0
\(961\) 53.8444 1.73692
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 25.8167i 0.830208i 0.909774 + 0.415104i \(0.136255\pi\)
−0.909774 + 0.415104i \(0.863745\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 0 0
\(973\) − 75.6333i − 2.42469i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30.0000i 0.959785i 0.877327 + 0.479893i \(0.159324\pi\)
−0.877327 + 0.479893i \(0.840676\pi\)
\(978\) 0 0
\(979\) −6.00000 −0.191761
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 52.4777i 1.67378i 0.547372 + 0.836890i \(0.315628\pi\)
−0.547372 + 0.836890i \(0.684372\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −35.6333 −1.13193 −0.565965 0.824430i \(-0.691496\pi\)
−0.565965 + 0.824430i \(0.691496\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 15.0278i 0.475934i 0.971273 + 0.237967i \(0.0764810\pi\)
−0.971273 + 0.237967i \(0.923519\pi\)
\(998\) 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 9900.2.c.q.5149.4 4
3.2 odd 2 3300.2.c.l.1849.4 4
5.2 odd 4 9900.2.a.bl.1.1 2
5.3 odd 4 1980.2.a.h.1.2 2
5.4 even 2 inner 9900.2.c.q.5149.1 4
15.2 even 4 3300.2.a.w.1.1 2
15.8 even 4 660.2.a.e.1.2 2
15.14 odd 2 3300.2.c.l.1849.1 4
20.3 even 4 7920.2.a.bo.1.1 2
60.23 odd 4 2640.2.a.bc.1.1 2
165.98 odd 4 7260.2.a.w.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
660.2.a.e.1.2 2 15.8 even 4
1980.2.a.h.1.2 2 5.3 odd 4
2640.2.a.bc.1.1 2 60.23 odd 4
3300.2.a.w.1.1 2 15.2 even 4
3300.2.c.l.1849.1 4 15.14 odd 2
3300.2.c.l.1849.4 4 3.2 odd 2
7260.2.a.w.1.1 2 165.98 odd 4
7920.2.a.bo.1.1 2 20.3 even 4
9900.2.a.bl.1.1 2 5.2 odd 4
9900.2.c.q.5149.1 4 5.4 even 2 inner
9900.2.c.q.5149.4 4 1.1 even 1 trivial