Properties

Label 2736.2.f.c.1025.2
Level $2736$
Weight $2$
Character 2736.1025
Analytic conductor $21.847$
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] = [2736,2,Mod(1025,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.1025");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.f (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: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1368)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1025.2
Root \(1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 2736.1025
Dual form 2736.2.f.c.1025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421i q^{5} -2.00000 q^{7} +O(q^{10})\) \(q+1.41421i q^{5} -2.00000 q^{7} +4.24264i q^{11} -2.82843i q^{13} -7.07107i q^{17} +(1.00000 - 4.24264i) q^{19} +1.41421i q^{23} +3.00000 q^{25} -10.0000 q^{29} +2.82843i q^{31} -2.82843i q^{35} -5.65685i q^{37} +10.0000 q^{41} -12.0000 q^{43} -1.41421i q^{47} -3.00000 q^{49} +10.0000 q^{53} -6.00000 q^{55} +12.0000 q^{59} +8.00000 q^{61} +4.00000 q^{65} -14.1421i q^{67} +8.00000 q^{71} +6.00000 q^{73} -8.48528i q^{77} +11.3137i q^{79} +4.24264i q^{83} +10.0000 q^{85} +6.00000 q^{89} +5.65685i q^{91} +(6.00000 + 1.41421i) q^{95} -8.48528i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{7} + 2 q^{19} + 6 q^{25} - 20 q^{29} + 20 q^{41} - 24 q^{43} - 6 q^{49} + 20 q^{53} - 12 q^{55} + 24 q^{59} + 16 q^{61} + 8 q^{65} + 16 q^{71} + 12 q^{73} + 20 q^{85} + 12 q^{89} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(1\)

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
\(5\) 1.41421i 0.632456i 0.948683 + 0.316228i \(0.102416\pi\)
−0.948683 + 0.316228i \(0.897584\pi\)
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.24264i 1.27920i 0.768706 + 0.639602i \(0.220901\pi\)
−0.768706 + 0.639602i \(0.779099\pi\)
\(12\) 0 0
\(13\) 2.82843i 0.784465i −0.919866 0.392232i \(-0.871703\pi\)
0.919866 0.392232i \(-0.128297\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.07107i 1.71499i −0.514496 0.857493i \(-0.672021\pi\)
0.514496 0.857493i \(-0.327979\pi\)
\(18\) 0 0
\(19\) 1.00000 4.24264i 0.229416 0.973329i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.41421i 0.294884i 0.989071 + 0.147442i \(0.0471040\pi\)
−0.989071 + 0.147442i \(0.952896\pi\)
\(24\) 0 0
\(25\) 3.00000 0.600000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) 2.82843i 0.508001i 0.967204 + 0.254000i \(0.0817464\pi\)
−0.967204 + 0.254000i \(0.918254\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.82843i 0.478091i
\(36\) 0 0
\(37\) 5.65685i 0.929981i −0.885316 0.464991i \(-0.846058\pi\)
0.885316 0.464991i \(-0.153942\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.41421i 0.206284i −0.994667 0.103142i \(-0.967110\pi\)
0.994667 0.103142i \(-0.0328896\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) 14.1421i 1.72774i −0.503718 0.863868i \(-0.668035\pi\)
0.503718 0.863868i \(-0.331965\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8.48528i 0.966988i
\(78\) 0 0
\(79\) 11.3137i 1.27289i 0.771321 + 0.636446i \(0.219596\pi\)
−0.771321 + 0.636446i \(0.780404\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.24264i 0.465690i 0.972514 + 0.232845i \(0.0748035\pi\)
−0.972514 + 0.232845i \(0.925196\pi\)
\(84\) 0 0
\(85\) 10.0000 1.08465
\(86\) 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
\(91\) 5.65685i 0.592999i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.00000 + 1.41421i 0.615587 + 0.145095i
\(96\) 0 0
\(97\) 8.48528i 0.861550i −0.902459 0.430775i \(-0.858240\pi\)
0.902459 0.430775i \(-0.141760\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.89949i 0.985037i −0.870302 0.492518i \(-0.836076\pi\)
0.870302 0.492518i \(-0.163924\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 0 0
\(109\) 8.48528i 0.812743i −0.913708 0.406371i \(-0.866794\pi\)
0.913708 0.406371i \(-0.133206\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −2.00000 −0.186501
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 14.1421i 1.29641i
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) 19.7990i 1.75688i −0.477856 0.878438i \(-0.658586\pi\)
0.477856 0.878438i \(-0.341414\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.89949i 0.864923i −0.901652 0.432461i \(-0.857645\pi\)
0.901652 0.432461i \(-0.142355\pi\)
\(132\) 0 0
\(133\) −2.00000 + 8.48528i −0.173422 + 0.735767i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.89949i 0.845771i −0.906183 0.422885i \(-0.861017\pi\)
0.906183 0.422885i \(-0.138983\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) 14.1421i 1.17444i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.24264i 0.347571i −0.984784 0.173785i \(-0.944400\pi\)
0.984784 0.173785i \(-0.0555999\pi\)
\(150\) 0 0
\(151\) 11.3137i 0.920697i −0.887738 0.460348i \(-0.847725\pi\)
0.887738 0.460348i \(-0.152275\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −24.0000 −1.91541 −0.957704 0.287754i \(-0.907091\pi\)
−0.957704 + 0.287754i \(0.907091\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.82843i 0.222911i
\(162\) 0 0
\(163\) −14.0000 −1.09656 −0.548282 0.836293i \(-0.684718\pi\)
−0.548282 + 0.836293i \(0.684718\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −16.0000 −1.23812 −0.619059 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 0 0
\(175\) −6.00000 −0.453557
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.00000 −0.597948 −0.298974 0.954261i \(-0.596644\pi\)
−0.298974 + 0.954261i \(0.596644\pi\)
\(180\) 0 0
\(181\) 14.1421i 1.05118i 0.850739 + 0.525588i \(0.176155\pi\)
−0.850739 + 0.525588i \(0.823845\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.00000 0.588172
\(186\) 0 0
\(187\) 30.0000 2.19382
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.5563i 1.12562i −0.826587 0.562809i \(-0.809721\pi\)
0.826587 0.562809i \(-0.190279\pi\)
\(192\) 0 0
\(193\) 16.9706i 1.22157i −0.791797 0.610784i \(-0.790854\pi\)
0.791797 0.610784i \(-0.209146\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.2132i 1.51138i 0.654931 + 0.755689i \(0.272698\pi\)
−0.654931 + 0.755689i \(0.727302\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 20.0000 1.40372
\(204\) 0 0
\(205\) 14.1421i 0.987730i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 18.0000 + 4.24264i 1.24509 + 0.293470i
\(210\) 0 0
\(211\) 14.1421i 0.973585i 0.873518 + 0.486792i \(0.161833\pi\)
−0.873518 + 0.486792i \(0.838167\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 16.9706i 1.15738i
\(216\) 0 0
\(217\) 5.65685i 0.384012i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −20.0000 −1.34535
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 0 0
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.7279i 0.833834i 0.908945 + 0.416917i \(0.136889\pi\)
−0.908945 + 0.416917i \(0.863111\pi\)
\(234\) 0 0
\(235\) 2.00000 0.130466
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.24264i 0.274434i −0.990541 0.137217i \(-0.956184\pi\)
0.990541 0.137217i \(-0.0438157\pi\)
\(240\) 0 0
\(241\) 8.48528i 0.546585i 0.961931 + 0.273293i \(0.0881127\pi\)
−0.961931 + 0.273293i \(0.911887\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.24264i 0.271052i
\(246\) 0 0
\(247\) −12.0000 2.82843i −0.763542 0.179969i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.5563i 0.981908i −0.871185 0.490954i \(-0.836648\pi\)
0.871185 0.490954i \(-0.163352\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 11.3137i 0.703000i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7.07107i 0.436021i 0.975946 + 0.218010i \(0.0699567\pi\)
−0.975946 + 0.218010i \(0.930043\pi\)
\(264\) 0 0
\(265\) 14.1421i 0.868744i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.7279i 0.767523i
\(276\) 0 0
\(277\) −20.0000 −1.20168 −0.600842 0.799368i \(-0.705168\pi\)
−0.600842 + 0.799368i \(0.705168\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) 20.0000 1.18888 0.594438 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −20.0000 −1.18056
\(288\) 0 0
\(289\) −33.0000 −1.94118
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 16.9706i 0.988064i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.00000 0.231326
\(300\) 0 0
\(301\) 24.0000 1.38334
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 11.3137i 0.647821i
\(306\) 0 0
\(307\) 33.9411i 1.93712i −0.248776 0.968561i \(-0.580028\pi\)
0.248776 0.968561i \(-0.419972\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 15.5563i 0.882120i 0.897478 + 0.441060i \(0.145397\pi\)
−0.897478 + 0.441060i \(0.854603\pi\)
\(312\) 0 0
\(313\) −4.00000 −0.226093 −0.113047 0.993590i \(-0.536061\pi\)
−0.113047 + 0.993590i \(0.536061\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 0 0
\(319\) 42.4264i 2.37542i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −30.0000 7.07107i −1.66924 0.393445i
\(324\) 0 0
\(325\) 8.48528i 0.470679i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.82843i 0.155936i
\(330\) 0 0
\(331\) 5.65685i 0.310929i 0.987841 + 0.155464i \(0.0496874\pi\)
−0.987841 + 0.155464i \(0.950313\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 20.0000 1.09272
\(336\) 0 0
\(337\) 25.4558i 1.38667i −0.720616 0.693334i \(-0.756141\pi\)
0.720616 0.693334i \(-0.243859\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.07107i 0.379595i −0.981823 0.189797i \(-0.939217\pi\)
0.981823 0.189797i \(-0.0607831\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.3848i 0.978523i −0.872137 0.489261i \(-0.837266\pi\)
0.872137 0.489261i \(-0.162734\pi\)
\(354\) 0 0
\(355\) 11.3137i 0.600469i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 32.5269i 1.71670i −0.513061 0.858352i \(-0.671488\pi\)
0.513061 0.858352i \(-0.328512\pi\)
\(360\) 0 0
\(361\) −17.0000 8.48528i −0.894737 0.446594i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8.48528i 0.444140i
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −20.0000 −1.03835
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 28.2843i 1.45671i
\(378\) 0 0
\(379\) 11.3137i 0.581146i −0.956853 0.290573i \(-0.906154\pi\)
0.956853 0.290573i \(-0.0938459\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 12.0000 0.611577
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 24.0416i 1.21896i 0.792802 + 0.609480i \(0.208622\pi\)
−0.792802 + 0.609480i \(0.791378\pi\)
\(390\) 0 0
\(391\) 10.0000 0.505722
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −16.0000 −0.805047
\(396\) 0 0
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) 8.48528i 0.419570i 0.977748 + 0.209785i \(0.0672764\pi\)
−0.977748 + 0.209785i \(0.932724\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −24.0000 −1.18096
\(414\) 0 0
\(415\) −6.00000 −0.294528
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15.5563i 0.759977i 0.924991 + 0.379989i \(0.124072\pi\)
−0.924991 + 0.379989i \(0.875928\pi\)
\(420\) 0 0
\(421\) 8.48528i 0.413547i 0.978389 + 0.206774i \(0.0662964\pi\)
−0.978389 + 0.206774i \(0.933704\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 21.2132i 1.02899i
\(426\) 0 0
\(427\) −16.0000 −0.774294
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000 + 1.41421i 0.287019 + 0.0676510i
\(438\) 0 0
\(439\) 16.9706i 0.809961i 0.914325 + 0.404980i \(0.132722\pi\)
−0.914325 + 0.404980i \(0.867278\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.07107i 0.335957i 0.985791 + 0.167978i \(0.0537239\pi\)
−0.985791 + 0.167978i \(0.946276\pi\)
\(444\) 0 0
\(445\) 8.48528i 0.402241i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 0 0
\(451\) 42.4264i 1.99778i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.00000 −0.375046
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 18.3848i 0.856264i 0.903716 + 0.428132i \(0.140828\pi\)
−0.903716 + 0.428132i \(0.859172\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.41421i 0.0654420i −0.999465 0.0327210i \(-0.989583\pi\)
0.999465 0.0327210i \(-0.0104173\pi\)
\(468\) 0 0
\(469\) 28.2843i 1.30605i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 50.9117i 2.34092i
\(474\) 0 0
\(475\) 3.00000 12.7279i 0.137649 0.583997i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.5563i 0.710788i 0.934717 + 0.355394i \(0.115653\pi\)
−0.934717 + 0.355394i \(0.884347\pi\)
\(480\) 0 0
\(481\) −16.0000 −0.729537
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.0000 0.544892
\(486\) 0 0
\(487\) 31.1127i 1.40985i 0.709281 + 0.704925i \(0.249020\pi\)
−0.709281 + 0.704925i \(0.750980\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.7279i 0.574403i 0.957870 + 0.287202i \(0.0927249\pi\)
−0.957870 + 0.287202i \(0.907275\pi\)
\(492\) 0 0
\(493\) 70.7107i 3.18465i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.0000 −0.717698
\(498\) 0 0
\(499\) 30.0000 1.34298 0.671492 0.741012i \(-0.265654\pi\)
0.671492 + 0.741012i \(0.265654\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15.5563i 0.693623i −0.937935 0.346812i \(-0.887264\pi\)
0.937935 0.346812i \(-0.112736\pi\)
\(504\) 0 0
\(505\) 14.0000 0.622992
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) −12.0000 −0.530849
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −22.0000 −0.963837 −0.481919 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) 14.1421i 0.618392i −0.950998 0.309196i \(-0.899940\pi\)
0.950998 0.309196i \(-0.100060\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20.0000 0.871214
\(528\) 0 0
\(529\) 21.0000 0.913043
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 28.2843i 1.22513i
\(534\) 0 0
\(535\) 11.3137i 0.489134i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 12.7279i 0.548230i
\(540\) 0 0
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.0000 0.514024
\(546\) 0 0
\(547\) 16.9706i 0.725609i 0.931865 + 0.362804i \(0.118181\pi\)
−0.931865 + 0.362804i \(0.881819\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −10.0000 + 42.4264i −0.426014 + 1.80743i
\(552\) 0 0
\(553\) 22.6274i 0.962216i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18.3848i 0.778988i 0.921029 + 0.389494i \(0.127350\pi\)
−0.921029 + 0.389494i \(0.872650\pi\)
\(558\) 0 0
\(559\) 33.9411i 1.43556i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) 8.48528i 0.356978i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) −44.0000 −1.84134 −0.920671 0.390339i \(-0.872358\pi\)
−0.920671 + 0.390339i \(0.872358\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.24264i 0.176930i
\(576\) 0 0
\(577\) 44.0000 1.83174 0.915872 0.401470i \(-0.131501\pi\)
0.915872 + 0.401470i \(0.131501\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.48528i 0.352029i
\(582\) 0 0
\(583\) 42.4264i 1.75712i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.3848i 0.758821i −0.925228 0.379410i \(-0.876127\pi\)
0.925228 0.379410i \(-0.123873\pi\)
\(588\) 0 0
\(589\) 12.0000 + 2.82843i 0.494451 + 0.116543i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 43.8406i 1.80032i 0.435561 + 0.900159i \(0.356550\pi\)
−0.435561 + 0.900159i \(0.643450\pi\)
\(594\) 0 0
\(595\) −20.0000 −0.819920
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −44.0000 −1.79779 −0.898896 0.438163i \(-0.855629\pi\)
−0.898896 + 0.438163i \(0.855629\pi\)
\(600\) 0 0
\(601\) 33.9411i 1.38449i −0.721664 0.692244i \(-0.756622\pi\)
0.721664 0.692244i \(-0.243378\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.89949i 0.402472i
\(606\) 0 0
\(607\) 31.1127i 1.26283i −0.775447 0.631413i \(-0.782475\pi\)
0.775447 0.631413i \(-0.217525\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.00000 −0.161823
\(612\) 0 0
\(613\) 24.0000 0.969351 0.484675 0.874694i \(-0.338938\pi\)
0.484675 + 0.874694i \(0.338938\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.7279i 0.512407i 0.966623 + 0.256203i \(0.0824717\pi\)
−0.966623 + 0.256203i \(0.917528\pi\)
\(618\) 0 0
\(619\) −34.0000 −1.36658 −0.683288 0.730149i \(-0.739451\pi\)
−0.683288 + 0.730149i \(0.739451\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −40.0000 −1.59490
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 28.0000 1.11115
\(636\) 0 0
\(637\) 8.48528i 0.336199i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −46.0000 −1.81689 −0.908445 0.418004i \(-0.862730\pi\)
−0.908445 + 0.418004i \(0.862730\pi\)
\(642\) 0 0
\(643\) 12.0000 0.473234 0.236617 0.971603i \(-0.423961\pi\)
0.236617 + 0.971603i \(0.423961\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18.3848i 0.722780i −0.932415 0.361390i \(-0.882302\pi\)
0.932415 0.361390i \(-0.117698\pi\)
\(648\) 0 0
\(649\) 50.9117i 1.99846i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.24264i 0.166027i 0.996548 + 0.0830137i \(0.0264545\pi\)
−0.996548 + 0.0830137i \(0.973545\pi\)
\(654\) 0 0
\(655\) 14.0000 0.547025
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 22.6274i 0.880105i 0.897972 + 0.440052i \(0.145040\pi\)
−0.897972 + 0.440052i \(0.854960\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −12.0000 2.82843i −0.465340 0.109682i
\(666\) 0 0
\(667\) 14.1421i 0.547586i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 33.9411i 1.31028i
\(672\) 0 0
\(673\) 22.6274i 0.872223i −0.899893 0.436111i \(-0.856355\pi\)
0.899893 0.436111i \(-0.143645\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) 16.9706i 0.651270i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −44.0000 −1.68361 −0.841807 0.539779i \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) 0 0
\(685\) 14.0000 0.534913
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 28.2843i 1.07754i
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.82843i 0.107288i
\(696\) 0 0
\(697\) 70.7107i 2.67836i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12.7279i 0.480727i −0.970683 0.240363i \(-0.922733\pi\)
0.970683 0.240363i \(-0.0772666\pi\)
\(702\) 0 0
\(703\) −24.0000 5.65685i −0.905177 0.213352i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 19.7990i 0.744618i
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) 16.9706i 0.634663i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 41.0122i 1.52950i 0.644329 + 0.764748i \(0.277137\pi\)
−0.644329 + 0.764748i \(0.722863\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −30.0000 −1.11417
\(726\) 0 0
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 84.8528i 3.13839i
\(732\) 0 0
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 60.0000 2.21013
\(738\) 0 0
\(739\) −10.0000 −0.367856 −0.183928 0.982940i \(-0.558881\pi\)
−0.183928 + 0.982940i \(0.558881\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 12.0000 0.440237 0.220119 0.975473i \(-0.429356\pi\)
0.220119 + 0.975473i \(0.429356\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −16.0000 −0.584627
\(750\) 0 0
\(751\) 45.2548i 1.65137i −0.564130 0.825686i \(-0.690788\pi\)
0.564130 0.825686i \(-0.309212\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) −20.0000 −0.726912 −0.363456 0.931611i \(-0.618403\pi\)
−0.363456 + 0.931611i \(0.618403\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.41421i 0.0512652i −0.999671 0.0256326i \(-0.991840\pi\)
0.999671 0.0256326i \(-0.00816000\pi\)
\(762\) 0 0
\(763\) 16.9706i 0.614376i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 33.9411i 1.22554i
\(768\) 0 0
\(769\) −20.0000 −0.721218 −0.360609 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) 8.48528i 0.304800i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.0000 42.4264i 0.358287 1.52008i
\(780\) 0 0
\(781\) 33.9411i 1.21451i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 33.9411i 1.21141i
\(786\) 0 0
\(787\) 8.48528i 0.302468i 0.988498 + 0.151234i \(0.0483246\pi\)
−0.988498 + 0.151234i \(0.951675\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 22.6274i 0.803523i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) −10.0000 −0.353775
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 25.4558i 0.898317i
\(804\) 0 0
\(805\) 4.00000 0.140981
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 15.5563i 0.546932i 0.961882 + 0.273466i \(0.0881701\pi\)
−0.961882 + 0.273466i \(0.911830\pi\)
\(810\) 0 0
\(811\) 16.9706i 0.595917i −0.954579 0.297959i \(-0.903694\pi\)
0.954579 0.297959i \(-0.0963057\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 19.7990i 0.693528i
\(816\) 0 0
\(817\) −12.0000 + 50.9117i −0.419827 + 1.78117i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 46.6690i 1.62876i −0.580331 0.814380i \(-0.697077\pi\)
0.580331 0.814380i \(-0.302923\pi\)
\(822\) 0 0
\(823\) −26.0000 −0.906303 −0.453152 0.891434i \(-0.649700\pi\)
−0.453152 + 0.891434i \(0.649700\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) 48.0833i 1.67000i −0.550249 0.835000i \(-0.685467\pi\)
0.550249 0.835000i \(-0.314533\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 21.2132i 0.734994i
\(834\) 0 0
\(835\) 22.6274i 0.783054i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −32.0000 −1.10476 −0.552381 0.833592i \(-0.686281\pi\)
−0.552381 + 0.833592i \(0.686281\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7.07107i 0.243252i
\(846\) 0 0
\(847\) 14.0000 0.481046
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 8.00000 0.274236
\(852\) 0 0
\(853\) 2.00000 0.0684787 0.0342393 0.999414i \(-0.489099\pi\)
0.0342393 + 0.999414i \(0.489099\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −6.00000 −0.204717 −0.102359 0.994748i \(-0.532639\pi\)
−0.102359 + 0.994748i \(0.532639\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 20.0000 0.680808 0.340404 0.940279i \(-0.389436\pi\)
0.340404 + 0.940279i \(0.389436\pi\)
\(864\) 0 0
\(865\) 2.82843i 0.0961694i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −48.0000 −1.62829
\(870\) 0 0
\(871\) −40.0000 −1.35535
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 22.6274i 0.764946i
\(876\) 0 0
\(877\) 28.2843i 0.955092i 0.878607 + 0.477546i \(0.158474\pi\)
−0.878607 + 0.477546i \(0.841526\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 49.4975i 1.66761i −0.552057 0.833806i \(-0.686157\pi\)
0.552057 0.833806i \(-0.313843\pi\)
\(882\) 0 0
\(883\) −2.00000 −0.0673054 −0.0336527 0.999434i \(-0.510714\pi\)
−0.0336527 + 0.999434i \(0.510714\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −36.0000 −1.20876 −0.604381 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) 0 0
\(889\) 39.5980i 1.32807i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −6.00000 1.41421i −0.200782 0.0473249i
\(894\) 0 0
\(895\) 11.3137i 0.378176i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 28.2843i 0.943333i
\(900\) 0 0
\(901\) 70.7107i 2.35571i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −20.0000 −0.664822
\(906\) 0 0
\(907\) 42.4264i 1.40875i 0.709830 + 0.704373i \(0.248772\pi\)
−0.709830 + 0.704373i \(0.751228\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −20.0000 −0.662630 −0.331315 0.943520i \(-0.607492\pi\)
−0.331315 + 0.943520i \(0.607492\pi\)
\(912\) 0 0
\(913\) −18.0000 −0.595713
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 19.7990i 0.653820i
\(918\) 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
\(923\) 22.6274i 0.744791i
\(924\) 0 0
\(925\) 16.9706i 0.557989i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 18.3848i 0.603185i 0.953437 + 0.301592i \(0.0975182\pi\)
−0.953437 + 0.301592i \(0.902482\pi\)
\(930\) 0 0
\(931\) −3.00000 + 12.7279i −0.0983210 + 0.417141i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 42.4264i 1.38749i
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −10.0000 −0.325991 −0.162995 0.986627i \(-0.552116\pi\)
−0.162995 + 0.986627i \(0.552116\pi\)
\(942\) 0 0
\(943\) 14.1421i 0.460531i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.41421i 0.0459558i 0.999736 + 0.0229779i \(0.00731473\pi\)
−0.999736 + 0.0229779i \(0.992685\pi\)
\(948\) 0 0
\(949\) 16.9706i 0.550888i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 46.0000 1.49009 0.745043 0.667016i \(-0.232429\pi\)
0.745043 + 0.667016i \(0.232429\pi\)
\(954\) 0 0
\(955\) 22.0000 0.711903
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 19.7990i 0.639343i
\(960\) 0 0
\(961\) 23.0000 0.741935
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 24.0000 0.772587
\(966\) 0 0
\(967\) −50.0000 −1.60789 −0.803946 0.594703i \(-0.797270\pi\)
−0.803946 + 0.594703i \(0.797270\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 0 0
\(973\) 4.00000 0.128234
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 6.00000 0.191957 0.0959785 0.995383i \(-0.469402\pi\)
0.0959785 + 0.995383i \(0.469402\pi\)
\(978\) 0 0
\(979\) 25.4558i 0.813572i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.00000 0.127580 0.0637901 0.997963i \(-0.479681\pi\)
0.0637901 + 0.997963i \(0.479681\pi\)
\(984\) 0 0
\(985\) −30.0000 −0.955879
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 16.9706i 0.539633i
\(990\) 0 0
\(991\) 31.1127i 0.988327i −0.869369 0.494164i \(-0.835474\pi\)
0.869369 0.494164i \(-0.164526\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 33.9411i 1.07601i
\(996\) 0 0
\(997\) 16.0000 0.506725 0.253363 0.967371i \(-0.418463\pi\)
0.253363 + 0.967371i \(0.418463\pi\)
\(998\) 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 2736.2.f.c.1025.2 2
3.2 odd 2 2736.2.f.d.1025.1 2
4.3 odd 2 1368.2.f.a.1025.2 yes 2
12.11 even 2 1368.2.f.b.1025.1 yes 2
19.18 odd 2 2736.2.f.d.1025.2 2
57.56 even 2 inner 2736.2.f.c.1025.1 2
76.75 even 2 1368.2.f.b.1025.2 yes 2
228.227 odd 2 1368.2.f.a.1025.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1368.2.f.a.1025.1 2 228.227 odd 2
1368.2.f.a.1025.2 yes 2 4.3 odd 2
1368.2.f.b.1025.1 yes 2 12.11 even 2
1368.2.f.b.1025.2 yes 2 76.75 even 2
2736.2.f.c.1025.1 2 57.56 even 2 inner
2736.2.f.c.1025.2 2 1.1 even 1 trivial
2736.2.f.d.1025.1 2 3.2 odd 2
2736.2.f.d.1025.2 2 19.18 odd 2