Properties

Label 3024.2.cc.b.2897.4
Level $3024$
Weight $2$
Character 3024.2897
Analytic conductor $24.147$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3024,2,Mod(881,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.cc (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2897.4
Root \(0.0967785 - 1.72934i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2897
Dual form 3024.2.cc.b.881.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.183299 - 0.317483i) q^{5} +(0.624224 + 2.57106i) q^{7} +O(q^{10})\) \(q+(-0.183299 - 0.317483i) q^{5} +(0.624224 + 2.57106i) q^{7} +(0.579764 + 0.334727i) q^{11} +(0.867380 - 0.500782i) q^{13} -4.98906 q^{17} +6.35722i q^{19} +(-6.66371 + 3.84729i) q^{23} +(2.43280 - 4.21374i) q^{25} +(-1.58394 - 0.914490i) q^{29} +(5.47837 - 3.16294i) q^{31} +(0.701849 - 0.669453i) q^{35} -5.16789 q^{37} +(-2.15928 - 3.73998i) q^{41} +(-2.24922 + 3.89576i) q^{43} +(-4.16450 + 7.21313i) q^{47} +(-6.22069 + 3.20983i) q^{49} -0.245420i q^{55} +(-4.36348 - 7.55776i) q^{59} +(4.29351 + 2.47886i) q^{61} +(-0.317980 - 0.183586i) q^{65} +(-5.44537 - 9.43166i) q^{67} -5.49843i q^{71} +4.07314i q^{73} +(-0.498700 + 1.69955i) q^{77} +(4.17784 - 7.23623i) q^{79} +(-8.50712 + 14.7348i) q^{83} +(0.914490 + 1.58394i) q^{85} +10.7113 q^{89} +(1.82898 + 1.91749i) q^{91} +(2.01831 - 1.16527i) q^{95} +(14.9093 + 8.60787i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.183299 0.317483i −0.0819738 0.141983i 0.822124 0.569309i \(-0.192789\pi\)
−0.904098 + 0.427326i \(0.859456\pi\)
\(6\) 0 0
\(7\) 0.624224 + 2.57106i 0.235935 + 0.971769i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.579764 + 0.334727i 0.174805 + 0.100924i 0.584850 0.811142i \(-0.301153\pi\)
−0.410044 + 0.912066i \(0.634487\pi\)
\(12\) 0 0
\(13\) 0.867380 0.500782i 0.240568 0.138892i −0.374870 0.927077i \(-0.622313\pi\)
0.615438 + 0.788185i \(0.288979\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.98906 −1.21003 −0.605013 0.796216i \(-0.706832\pi\)
−0.605013 + 0.796216i \(0.706832\pi\)
\(18\) 0 0
\(19\) 6.35722i 1.45845i 0.684275 + 0.729224i \(0.260119\pi\)
−0.684275 + 0.729224i \(0.739881\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.66371 + 3.84729i −1.38948 + 0.802216i −0.993256 0.115938i \(-0.963012\pi\)
−0.396223 + 0.918154i \(0.629679\pi\)
\(24\) 0 0
\(25\) 2.43280 4.21374i 0.486561 0.842748i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.58394 0.914490i −0.294131 0.169817i 0.345672 0.938355i \(-0.387651\pi\)
−0.639803 + 0.768539i \(0.720984\pi\)
\(30\) 0 0
\(31\) 5.47837 3.16294i 0.983944 0.568081i 0.0804857 0.996756i \(-0.474353\pi\)
0.903459 + 0.428675i \(0.141020\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.701849 0.669453i 0.118634 0.113158i
\(36\) 0 0
\(37\) −5.16789 −0.849595 −0.424798 0.905288i \(-0.639655\pi\)
−0.424798 + 0.905288i \(0.639655\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.15928 3.73998i −0.337223 0.584087i 0.646686 0.762756i \(-0.276154\pi\)
−0.983909 + 0.178669i \(0.942821\pi\)
\(42\) 0 0
\(43\) −2.24922 + 3.89576i −0.343002 + 0.594098i −0.984989 0.172618i \(-0.944777\pi\)
0.641986 + 0.766716i \(0.278111\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.16450 + 7.21313i −0.607455 + 1.05214i 0.384203 + 0.923249i \(0.374476\pi\)
−0.991658 + 0.128895i \(0.958857\pi\)
\(48\) 0 0
\(49\) −6.22069 + 3.20983i −0.888670 + 0.458548i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0.245420i 0.0330925i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.36348 7.55776i −0.568076 0.983937i −0.996756 0.0804804i \(-0.974355\pi\)
0.428680 0.903456i \(-0.358979\pi\)
\(60\) 0 0
\(61\) 4.29351 + 2.47886i 0.549727 + 0.317385i 0.749012 0.662556i \(-0.230529\pi\)
−0.199285 + 0.979942i \(0.563862\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.317980 0.183586i −0.0394406 0.0227710i
\(66\) 0 0
\(67\) −5.44537 9.43166i −0.665258 1.15226i −0.979215 0.202823i \(-0.934988\pi\)
0.313958 0.949437i \(-0.398345\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.49843i 0.652544i −0.945276 0.326272i \(-0.894207\pi\)
0.945276 0.326272i \(-0.105793\pi\)
\(72\) 0 0
\(73\) 4.07314i 0.476725i 0.971176 + 0.238363i \(0.0766106\pi\)
−0.971176 + 0.238363i \(0.923389\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.498700 + 1.69955i −0.0568321 + 0.193682i
\(78\) 0 0
\(79\) 4.17784 7.23623i 0.470044 0.814140i −0.529370 0.848391i \(-0.677571\pi\)
0.999413 + 0.0342518i \(0.0109048\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −8.50712 + 14.7348i −0.933778 + 1.61735i −0.156980 + 0.987602i \(0.550176\pi\)
−0.776798 + 0.629750i \(0.783158\pi\)
\(84\) 0 0
\(85\) 0.914490 + 1.58394i 0.0991904 + 0.171803i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.7113 1.13540 0.567699 0.823236i \(-0.307834\pi\)
0.567699 + 0.823236i \(0.307834\pi\)
\(90\) 0 0
\(91\) 1.82898 + 1.91749i 0.191729 + 0.201007i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.01831 1.16527i 0.207074 0.119555i
\(96\) 0 0
\(97\) 14.9093 + 8.60787i 1.51381 + 0.873997i 0.999869 + 0.0161687i \(0.00514689\pi\)
0.513937 + 0.857828i \(0.328186\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.86586 + 13.6241i −0.782683 + 1.35565i 0.147691 + 0.989034i \(0.452816\pi\)
−0.930374 + 0.366613i \(0.880517\pi\)
\(102\) 0 0
\(103\) −9.91124 + 5.72226i −0.976584 + 0.563831i −0.901237 0.433327i \(-0.857340\pi\)
−0.0753467 + 0.997157i \(0.524006\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.0618i 1.06938i −0.845048 0.534690i \(-0.820428\pi\)
0.845048 0.534690i \(-0.179572\pi\)
\(108\) 0 0
\(109\) −10.5633 −1.01178 −0.505891 0.862597i \(-0.668836\pi\)
−0.505891 + 0.862597i \(0.668836\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.60226 + 2.07976i −0.338872 + 0.195648i −0.659773 0.751465i \(-0.729348\pi\)
0.320901 + 0.947113i \(0.396014\pi\)
\(114\) 0 0
\(115\) 2.44290 + 1.41041i 0.227802 + 0.131521i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.11429 12.8272i −0.285487 1.17586i
\(120\) 0 0
\(121\) −5.27592 9.13815i −0.479629 0.830741i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.61671 −0.323489
\(126\) 0 0
\(127\) 1.66945 0.148140 0.0740700 0.997253i \(-0.476401\pi\)
0.0740700 + 0.997253i \(0.476401\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.76607 11.7192i −0.591154 1.02391i −0.994077 0.108675i \(-0.965339\pi\)
0.402923 0.915234i \(-0.367994\pi\)
\(132\) 0 0
\(133\) −16.3448 + 3.96833i −1.41727 + 0.344098i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.78428 4.49425i −0.665056 0.383970i 0.129145 0.991626i \(-0.458777\pi\)
−0.794201 + 0.607656i \(0.792110\pi\)
\(138\) 0 0
\(139\) −8.05336 + 4.64961i −0.683077 + 0.394375i −0.801014 0.598646i \(-0.795706\pi\)
0.117936 + 0.993021i \(0.462372\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.670501 0.0560701
\(144\) 0 0
\(145\) 0.670501i 0.0556821i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.45268 1.41606i 0.200931 0.116008i −0.396158 0.918182i \(-0.629657\pi\)
0.597090 + 0.802174i \(0.296324\pi\)
\(150\) 0 0
\(151\) −8.27592 + 14.3343i −0.673484 + 1.16651i 0.303425 + 0.952855i \(0.401870\pi\)
−0.976909 + 0.213654i \(0.931463\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00836 1.15953i −0.161315 0.0931355i
\(156\) 0 0
\(157\) −2.45480 + 1.41728i −0.195914 + 0.113111i −0.594748 0.803912i \(-0.702748\pi\)
0.398834 + 0.917023i \(0.369415\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −14.0513 14.7312i −1.10739 1.16098i
\(162\) 0 0
\(163\) −24.7281 −1.93685 −0.968426 0.249300i \(-0.919800\pi\)
−0.968426 + 0.249300i \(0.919800\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.67422 + 16.7562i 0.748614 + 1.29664i 0.948487 + 0.316815i \(0.102614\pi\)
−0.199874 + 0.979822i \(0.564053\pi\)
\(168\) 0 0
\(169\) −5.99843 + 10.3896i −0.461418 + 0.799199i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.41827 + 4.18856i −0.183858 + 0.318451i −0.943191 0.332251i \(-0.892192\pi\)
0.759333 + 0.650702i \(0.225525\pi\)
\(174\) 0 0
\(175\) 12.3524 + 3.62456i 0.933752 + 0.273991i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.65796i 0.273409i −0.990612 0.136704i \(-0.956349\pi\)
0.990612 0.136704i \(-0.0436511\pi\)
\(180\) 0 0
\(181\) 5.66796i 0.421296i 0.977562 + 0.210648i \(0.0675574\pi\)
−0.977562 + 0.210648i \(0.932443\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.947269 + 1.64072i 0.0696446 + 0.120628i
\(186\) 0 0
\(187\) −2.89248 1.66997i −0.211519 0.122120i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 23.7098 + 13.6888i 1.71558 + 0.990490i 0.926583 + 0.376091i \(0.122732\pi\)
0.788996 + 0.614398i \(0.210601\pi\)
\(192\) 0 0
\(193\) 5.01413 + 8.68473i 0.360925 + 0.625141i 0.988113 0.153727i \(-0.0491276\pi\)
−0.627188 + 0.778868i \(0.715794\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.8258i 1.34129i −0.741780 0.670643i \(-0.766018\pi\)
0.741780 0.670643i \(-0.233982\pi\)
\(198\) 0 0
\(199\) 5.36406i 0.380248i 0.981760 + 0.190124i \(0.0608890\pi\)
−0.981760 + 0.190124i \(0.939111\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.36247 4.64326i 0.0956268 0.325893i
\(204\) 0 0
\(205\) −0.791588 + 1.37107i −0.0552869 + 0.0957597i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.12793 + 3.68569i −0.147192 + 0.254944i
\(210\) 0 0
\(211\) 0.828981 + 1.43584i 0.0570694 + 0.0988471i 0.893149 0.449762i \(-0.148491\pi\)
−0.836079 + 0.548609i \(0.815158\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.64912 0.112469
\(216\) 0 0
\(217\) 11.5518 + 12.1108i 0.784189 + 0.822137i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.32741 + 2.49843i −0.291093 + 0.168063i
\(222\) 0 0
\(223\) 14.7546 + 8.51860i 0.988044 + 0.570448i 0.904689 0.426072i \(-0.140103\pi\)
0.0833551 + 0.996520i \(0.473436\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.55512 + 4.42560i −0.169589 + 0.293737i −0.938276 0.345889i \(-0.887577\pi\)
0.768686 + 0.639626i \(0.220911\pi\)
\(228\) 0 0
\(229\) 13.2215 7.63345i 0.873703 0.504433i 0.00512595 0.999987i \(-0.498368\pi\)
0.868577 + 0.495554i \(0.165035\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.1930i 0.667767i 0.942614 + 0.333883i \(0.108359\pi\)
−0.942614 + 0.333883i \(0.891641\pi\)
\(234\) 0 0
\(235\) 3.05340 0.199182
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −16.6117 + 9.59076i −1.07452 + 0.620375i −0.929413 0.369041i \(-0.879686\pi\)
−0.145108 + 0.989416i \(0.546353\pi\)
\(240\) 0 0
\(241\) −17.9140 10.3426i −1.15394 0.666227i −0.204095 0.978951i \(-0.565425\pi\)
−0.949844 + 0.312724i \(0.898759\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.15931 + 1.38661i 0.137954 + 0.0885869i
\(246\) 0 0
\(247\) 3.18359 + 5.51413i 0.202567 + 0.350856i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.81200 0.114373 0.0571864 0.998364i \(-0.481787\pi\)
0.0571864 + 0.998364i \(0.481787\pi\)
\(252\) 0 0
\(253\) −5.15117 −0.323851
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.22773 + 5.59059i 0.201340 + 0.348731i 0.948960 0.315395i \(-0.102137\pi\)
−0.747620 + 0.664126i \(0.768804\pi\)
\(258\) 0 0
\(259\) −3.22592 13.2869i −0.200449 0.825611i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7.63888 4.41031i −0.471034 0.271951i 0.245639 0.969361i \(-0.421002\pi\)
−0.716672 + 0.697410i \(0.754336\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 14.2653 0.869773 0.434886 0.900485i \(-0.356788\pi\)
0.434886 + 0.900485i \(0.356788\pi\)
\(270\) 0 0
\(271\) 3.05281i 0.185445i −0.995692 0.0927226i \(-0.970443\pi\)
0.995692 0.0927226i \(-0.0295570\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.82090 1.62865i 0.170107 0.0982112i
\(276\) 0 0
\(277\) −0.632828 + 1.09609i −0.0380230 + 0.0658577i −0.884411 0.466710i \(-0.845439\pi\)
0.846388 + 0.532567i \(0.178773\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −9.11639 5.26335i −0.543838 0.313985i 0.202795 0.979221i \(-0.434998\pi\)
−0.746633 + 0.665236i \(0.768331\pi\)
\(282\) 0 0
\(283\) −17.2094 + 9.93588i −1.02300 + 0.590627i −0.914970 0.403522i \(-0.867786\pi\)
−0.108025 + 0.994148i \(0.534453\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.26784 7.88623i 0.488035 0.465509i
\(288\) 0 0
\(289\) 7.89074 0.464161
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.70606 + 11.6152i 0.391772 + 0.678569i 0.992683 0.120747i \(-0.0385289\pi\)
−0.600911 + 0.799316i \(0.705196\pi\)
\(294\) 0 0
\(295\) −1.59964 + 2.77066i −0.0931348 + 0.161314i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.85331 + 6.67413i −0.222843 + 0.385975i
\(300\) 0 0
\(301\) −11.4202 3.35104i −0.658252 0.193151i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.81749i 0.104069i
\(306\) 0 0
\(307\) 0.653728i 0.0373102i −0.999826 0.0186551i \(-0.994062\pi\)
0.999826 0.0186551i \(-0.00593845\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.62246 8.00634i −0.262116 0.453998i 0.704688 0.709517i \(-0.251087\pi\)
−0.966804 + 0.255519i \(0.917754\pi\)
\(312\) 0 0
\(313\) 5.33830 + 3.08207i 0.301739 + 0.174209i 0.643224 0.765678i \(-0.277597\pi\)
−0.341485 + 0.939887i \(0.610930\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.8876 + 10.3274i 1.00467 + 0.580045i 0.909626 0.415428i \(-0.136368\pi\)
0.0950420 + 0.995473i \(0.469701\pi\)
\(318\) 0 0
\(319\) −0.612209 1.06038i −0.0342771 0.0593697i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 31.7166i 1.76476i
\(324\) 0 0
\(325\) 4.87322i 0.270318i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −21.1450 6.20457i −1.16576 0.342069i
\(330\) 0 0
\(331\) 5.35568 9.27631i 0.294375 0.509872i −0.680464 0.732781i \(-0.738222\pi\)
0.974839 + 0.222909i \(0.0715553\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.99626 + 3.45763i −0.109067 + 0.188910i
\(336\) 0 0
\(337\) 3.77592 + 6.54008i 0.205687 + 0.356261i 0.950351 0.311179i \(-0.100724\pi\)
−0.744664 + 0.667439i \(0.767390\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.23488 0.229332
\(342\) 0 0
\(343\) −12.1358 13.9901i −0.655270 0.755394i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9.46737 + 5.46599i −0.508235 + 0.293430i −0.732108 0.681189i \(-0.761463\pi\)
0.223873 + 0.974618i \(0.428130\pi\)
\(348\) 0 0
\(349\) −1.02562 0.592145i −0.0549004 0.0316968i 0.472299 0.881439i \(-0.343424\pi\)
−0.527199 + 0.849742i \(0.676758\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.7912 29.0832i 0.893706 1.54794i 0.0583086 0.998299i \(-0.481429\pi\)
0.835398 0.549646i \(-0.185237\pi\)
\(354\) 0 0
\(355\) −1.74566 + 1.00786i −0.0926501 + 0.0534915i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.1281i 0.534542i 0.963621 + 0.267271i \(0.0861219\pi\)
−0.963621 + 0.267271i \(0.913878\pi\)
\(360\) 0 0
\(361\) −21.4143 −1.12707
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.29315 0.746603i 0.0676868 0.0390790i
\(366\) 0 0
\(367\) −15.5903 9.00104i −0.813805 0.469850i 0.0344706 0.999406i \(-0.489025\pi\)
−0.848275 + 0.529555i \(0.822359\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −8.20451 14.2106i −0.424814 0.735799i 0.571589 0.820540i \(-0.306327\pi\)
−0.996403 + 0.0847411i \(0.972994\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.83184 −0.0943447
\(378\) 0 0
\(379\) 2.91372 0.149668 0.0748339 0.997196i \(-0.476157\pi\)
0.0748339 + 0.997196i \(0.476157\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.28721 + 7.42567i 0.219066 + 0.379434i 0.954523 0.298138i \(-0.0963655\pi\)
−0.735456 + 0.677572i \(0.763032\pi\)
\(384\) 0 0
\(385\) 0.630990 0.153197i 0.0321582 0.00780766i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 30.7906 + 17.7770i 1.56115 + 0.901328i 0.997142 + 0.0755559i \(0.0240731\pi\)
0.564004 + 0.825772i \(0.309260\pi\)
\(390\) 0 0
\(391\) 33.2456 19.1944i 1.68130 0.970702i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.06318 −0.154125
\(396\) 0 0
\(397\) 3.58034i 0.179692i −0.995956 0.0898460i \(-0.971363\pi\)
0.995956 0.0898460i \(-0.0286375\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.165300 + 0.0954357i −0.00825467 + 0.00476583i −0.504122 0.863633i \(-0.668184\pi\)
0.495867 + 0.868398i \(0.334850\pi\)
\(402\) 0 0
\(403\) 3.16789 5.48694i 0.157804 0.273324i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.99615 1.72983i −0.148514 0.0857445i
\(408\) 0 0
\(409\) 3.00832 1.73685i 0.148752 0.0858819i −0.423777 0.905767i \(-0.639296\pi\)
0.572529 + 0.819885i \(0.305963\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.7077 15.9365i 0.822130 0.784183i
\(414\) 0 0
\(415\) 6.23739 0.306182
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.703955 1.21929i −0.0343905 0.0595660i 0.848318 0.529487i \(-0.177616\pi\)
−0.882708 + 0.469921i \(0.844282\pi\)
\(420\) 0 0
\(421\) 15.1930 26.3151i 0.740463 1.28252i −0.211822 0.977308i \(-0.567940\pi\)
0.952285 0.305211i \(-0.0987268\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.1374 + 21.0226i −0.588751 + 1.01975i
\(426\) 0 0
\(427\) −3.69318 + 12.5862i −0.178725 + 0.609090i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.2747i 1.31378i 0.753988 + 0.656888i \(0.228127\pi\)
−0.753988 + 0.656888i \(0.771873\pi\)
\(432\) 0 0
\(433\) 8.15047i 0.391686i 0.980635 + 0.195843i \(0.0627444\pi\)
−0.980635 + 0.195843i \(0.937256\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −24.4581 42.3627i −1.16999 2.02648i
\(438\) 0 0
\(439\) 10.6005 + 6.12020i 0.505934 + 0.292101i 0.731161 0.682205i \(-0.238979\pi\)
−0.225226 + 0.974306i \(0.572312\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.93544 + 4.00418i 0.329513 + 0.190244i 0.655625 0.755087i \(-0.272405\pi\)
−0.326112 + 0.945331i \(0.605739\pi\)
\(444\) 0 0
\(445\) −1.96337 3.40067i −0.0930729 0.161207i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14.5183i 0.685163i 0.939488 + 0.342581i \(0.111301\pi\)
−0.939488 + 0.342581i \(0.888699\pi\)
\(450\) 0 0
\(451\) 2.89108i 0.136135i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.273519 0.932144i 0.0128228 0.0436996i
\(456\) 0 0
\(457\) −4.97751 + 8.62130i −0.232838 + 0.403287i −0.958642 0.284614i \(-0.908135\pi\)
0.725804 + 0.687901i \(0.241468\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16.1635 + 27.9960i −0.752810 + 1.30391i 0.193645 + 0.981072i \(0.437969\pi\)
−0.946456 + 0.322834i \(0.895364\pi\)
\(462\) 0 0
\(463\) 4.72516 + 8.18421i 0.219597 + 0.380353i 0.954685 0.297619i \(-0.0961925\pi\)
−0.735088 + 0.677972i \(0.762859\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.6623 −0.956138 −0.478069 0.878322i \(-0.658663\pi\)
−0.478069 + 0.878322i \(0.658663\pi\)
\(468\) 0 0
\(469\) 20.8502 19.8878i 0.962773 0.918335i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.60803 + 1.50575i −0.119917 + 0.0692343i
\(474\) 0 0
\(475\) 26.7877 + 15.4659i 1.22910 + 0.709623i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.08042 8.79955i 0.232131 0.402062i −0.726304 0.687373i \(-0.758764\pi\)
0.958435 + 0.285311i \(0.0920970\pi\)
\(480\) 0 0
\(481\) −4.48252 + 2.58799i −0.204386 + 0.118002i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6.31126i 0.286579i
\(486\) 0 0
\(487\) 31.2296 1.41515 0.707575 0.706638i \(-0.249789\pi\)
0.707575 + 0.706638i \(0.249789\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.8314 10.2950i 0.804720 0.464605i −0.0403987 0.999184i \(-0.512863\pi\)
0.845119 + 0.534578i \(0.179529\pi\)
\(492\) 0 0
\(493\) 7.90239 + 4.56245i 0.355906 + 0.205482i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 14.1368 3.43226i 0.634122 0.153958i
\(498\) 0 0
\(499\) −12.5766 21.7834i −0.563007 0.975157i −0.997232 0.0743527i \(-0.976311\pi\)
0.434225 0.900805i \(-0.357022\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.1553 1.38915 0.694574 0.719421i \(-0.255593\pi\)
0.694574 + 0.719421i \(0.255593\pi\)
\(504\) 0 0
\(505\) 5.76722 0.256638
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.41674 4.18591i −0.107120 0.185537i 0.807482 0.589892i \(-0.200830\pi\)
−0.914602 + 0.404354i \(0.867496\pi\)
\(510\) 0 0
\(511\) −10.4723 + 2.54255i −0.463267 + 0.112476i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3.63344 + 2.09777i 0.160109 + 0.0924387i
\(516\) 0 0
\(517\) −4.82886 + 2.78794i −0.212373 + 0.122613i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.5322 0.768101 0.384050 0.923312i \(-0.374529\pi\)
0.384050 + 0.923312i \(0.374529\pi\)
\(522\) 0 0
\(523\) 19.1019i 0.835267i 0.908616 + 0.417633i \(0.137140\pi\)
−0.908616 + 0.417633i \(0.862860\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −27.3319 + 15.7801i −1.19060 + 0.687392i
\(528\) 0 0
\(529\) 18.1033 31.3559i 0.787101 1.36330i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.74584 2.16266i −0.162250 0.0936752i
\(534\) 0 0
\(535\) −3.51192 + 2.02761i −0.151834 + 0.0876612i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.68095 0.221286i −0.201623 0.00953144i
\(540\) 0 0
\(541\) 13.6642 0.587471 0.293735 0.955887i \(-0.405102\pi\)
0.293735 + 0.955887i \(0.405102\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.93625 + 3.35368i 0.0829397 + 0.143656i
\(546\) 0 0
\(547\) −4.94380 + 8.56292i −0.211382 + 0.366124i −0.952147 0.305640i \(-0.901130\pi\)
0.740765 + 0.671764i \(0.234463\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5.81362 10.0695i 0.247669 0.428975i
\(552\) 0 0
\(553\) 21.2127 + 6.22444i 0.902055 + 0.264690i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.5800i 0.533034i −0.963830 0.266517i \(-0.914127\pi\)
0.963830 0.266517i \(-0.0858728\pi\)
\(558\) 0 0
\(559\) 4.50547i 0.190561i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.1666 21.0732i −0.512763 0.888132i −0.999890 0.0148007i \(-0.995289\pi\)
0.487127 0.873331i \(-0.338045\pi\)
\(564\) 0 0
\(565\) 1.32058 + 0.762437i 0.0555572 + 0.0320760i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.18746 + 4.72703i 0.343236 + 0.198167i 0.661702 0.749767i \(-0.269834\pi\)
−0.318466 + 0.947934i \(0.603168\pi\)
\(570\) 0 0
\(571\) −15.7843 27.3392i −0.660551 1.14411i −0.980471 0.196664i \(-0.936989\pi\)
0.319920 0.947445i \(-0.396344\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 37.4388i 1.56131i
\(576\) 0 0
\(577\) 33.5794i 1.39793i −0.715157 0.698964i \(-0.753645\pi\)
0.715157 0.698964i \(-0.246355\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −43.1943 12.6745i −1.79200 0.525828i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.65855 16.7291i 0.398651 0.690484i −0.594909 0.803793i \(-0.702812\pi\)
0.993560 + 0.113310i \(0.0361452\pi\)
\(588\) 0 0
\(589\) 20.1075 + 34.8272i 0.828516 + 1.43503i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.733196 0.0301088 0.0150544 0.999887i \(-0.495208\pi\)
0.0150544 + 0.999887i \(0.495208\pi\)
\(594\) 0 0
\(595\) −3.50157 + 3.33994i −0.143550 + 0.136924i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 26.6548 15.3892i 1.08909 0.628785i 0.155754 0.987796i \(-0.450219\pi\)
0.933333 + 0.359011i \(0.116886\pi\)
\(600\) 0 0
\(601\) 0.786931 + 0.454335i 0.0320996 + 0.0185327i 0.515964 0.856610i \(-0.327434\pi\)
−0.483864 + 0.875143i \(0.660767\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.93414 + 3.35003i −0.0786340 + 0.136198i
\(606\) 0 0
\(607\) 38.7783 22.3887i 1.57396 0.908728i 0.578287 0.815833i \(-0.303721\pi\)
0.995676 0.0928949i \(-0.0296121\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8.34204i 0.337483i
\(612\) 0 0
\(613\) 18.1480 0.732992 0.366496 0.930420i \(-0.380557\pi\)
0.366496 + 0.930420i \(0.380557\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19.7393 11.3965i 0.794674 0.458805i −0.0469315 0.998898i \(-0.514944\pi\)
0.841605 + 0.540093i \(0.181611\pi\)
\(618\) 0 0
\(619\) −38.4228 22.1834i −1.54434 0.891626i −0.998557 0.0537011i \(-0.982898\pi\)
−0.545785 0.837925i \(-0.683768\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.68626 + 27.5394i 0.267880 + 1.10334i
\(624\) 0 0
\(625\) −11.5011 19.9204i −0.460043 0.796818i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 25.7829 1.02803
\(630\) 0 0
\(631\) 32.5707 1.29662 0.648310 0.761377i \(-0.275476\pi\)
0.648310 + 0.761377i \(0.275476\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.306009 0.530024i −0.0121436 0.0210333i
\(636\) 0 0
\(637\) −3.78828 + 5.89936i −0.150097 + 0.233741i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10.2270 + 5.90456i 0.403942 + 0.233216i 0.688184 0.725537i \(-0.258408\pi\)
−0.284241 + 0.958753i \(0.591742\pi\)
\(642\) 0 0
\(643\) 25.3714 14.6482i 1.00055 0.577668i 0.0921392 0.995746i \(-0.470630\pi\)
0.908411 + 0.418078i \(0.137296\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 28.1683 1.10741 0.553705 0.832713i \(-0.313214\pi\)
0.553705 + 0.832713i \(0.313214\pi\)
\(648\) 0 0
\(649\) 5.84229i 0.229330i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −39.0555 + 22.5487i −1.52836 + 0.882399i −0.528929 + 0.848666i \(0.677406\pi\)
−0.999431 + 0.0337326i \(0.989261\pi\)
\(654\) 0 0
\(655\) −2.48043 + 4.29623i −0.0969184 + 0.167868i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 27.5435 + 15.9022i 1.07294 + 0.619463i 0.928984 0.370121i \(-0.120684\pi\)
0.143958 + 0.989584i \(0.454017\pi\)
\(660\) 0 0
\(661\) −17.1234 + 9.88619i −0.666022 + 0.384528i −0.794568 0.607175i \(-0.792302\pi\)
0.128546 + 0.991704i \(0.458969\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.25587 + 4.46181i 0.165035 + 0.173022i
\(666\) 0 0
\(667\) 14.0733 0.544918
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.65948 + 2.87430i 0.0640635 + 0.110961i
\(672\) 0 0
\(673\) −0.945369 + 1.63743i −0.0364413 + 0.0631182i −0.883671 0.468109i \(-0.844936\pi\)
0.847230 + 0.531227i \(0.178269\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.5661 18.3010i 0.406088 0.703364i −0.588360 0.808599i \(-0.700226\pi\)
0.994447 + 0.105235i \(0.0335595\pi\)
\(678\) 0 0
\(679\) −12.8246 + 43.7058i −0.492164 + 1.67728i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8.71972i 0.333651i 0.985986 + 0.166825i \(0.0533516\pi\)
−0.985986 + 0.166825i \(0.946648\pi\)
\(684\) 0 0
\(685\) 3.29517i 0.125902i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −15.7071 9.06850i −0.597526 0.344982i 0.170542 0.985350i \(-0.445448\pi\)
−0.768068 + 0.640369i \(0.778782\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.95235 + 1.70454i 0.111989 + 0.0646568i
\(696\) 0 0
\(697\) 10.7728 + 18.6590i 0.408048 + 0.706760i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 35.6167i 1.34523i 0.739995 + 0.672613i \(0.234828\pi\)
−0.739995 + 0.672613i \(0.765172\pi\)
\(702\) 0 0
\(703\) 32.8534i 1.23909i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −39.9384 11.7191i −1.50204 0.440743i
\(708\) 0 0
\(709\) 1.80385 3.12436i 0.0677449 0.117338i −0.830163 0.557520i \(-0.811753\pi\)
0.897908 + 0.440183i \(0.145086\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −24.3375 + 42.1538i −0.911447 + 1.57867i
\(714\) 0 0
\(715\) −0.122902 0.212873i −0.00459628 0.00796099i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 25.7829 0.961540 0.480770 0.876847i \(-0.340357\pi\)
0.480770 + 0.876847i \(0.340357\pi\)
\(720\) 0 0
\(721\) −20.8991 21.9104i −0.778323 0.815987i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.70685 + 4.44955i −0.286225 + 0.165252i
\(726\) 0 0
\(727\) 1.32423 + 0.764544i 0.0491129 + 0.0283554i 0.524355 0.851499i \(-0.324306\pi\)
−0.475242 + 0.879855i \(0.657640\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11.2215 19.4362i 0.415042 0.718873i
\(732\) 0 0
\(733\) 17.9908 10.3870i 0.664504 0.383651i −0.129487 0.991581i \(-0.541333\pi\)
0.793991 + 0.607930i \(0.208000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.29084i 0.268562i
\(738\) 0 0
\(739\) 11.8709 0.436678 0.218339 0.975873i \(-0.429936\pi\)
0.218339 + 0.975873i \(0.429936\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −37.5906 + 21.7029i −1.37907 + 0.796204i −0.992047 0.125868i \(-0.959828\pi\)
−0.387019 + 0.922072i \(0.626495\pi\)
\(744\) 0 0
\(745\) −0.899148 0.519124i −0.0329422 0.0190192i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 28.4404 6.90502i 1.03919 0.252304i
\(750\) 0 0
\(751\) 1.15691 + 2.00383i 0.0422164 + 0.0731209i 0.886362 0.462994i \(-0.153225\pi\)
−0.844145 + 0.536115i \(0.819891\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6.06787 0.220832
\(756\) 0 0
\(757\) −15.0946 −0.548624 −0.274312 0.961641i \(-0.588450\pi\)
−0.274312 + 0.961641i \(0.588450\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.6690 + 20.2112i 0.422999 + 0.732656i 0.996231 0.0867370i \(-0.0276440\pi\)
−0.573232 + 0.819393i \(0.694311\pi\)
\(762\) 0 0
\(763\) −6.59388 27.1589i −0.238715 0.983219i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.56959 4.37030i −0.273322 0.157803i
\(768\) 0 0
\(769\) 15.8266 9.13748i 0.570721 0.329506i −0.186716 0.982414i \(-0.559784\pi\)
0.757437 + 0.652908i \(0.226451\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.438507 −0.0157720 −0.00788600 0.999969i \(-0.502510\pi\)
−0.00788600 + 0.999969i \(0.502510\pi\)
\(774\) 0 0
\(775\) 30.7792i 1.10562i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 23.7759 13.7270i 0.851861 0.491822i
\(780\) 0 0
\(781\) 1.84047 3.18779i 0.0658573 0.114068i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.899924 + 0.519571i 0.0321197 + 0.0185443i
\(786\) 0 0
\(787\) −33.1317 + 19.1286i −1.18102 + 0.681861i −0.956250 0.292551i \(-0.905496\pi\)
−0.224769 + 0.974412i \(0.572163\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.59581 7.96337i −0.270076 0.283145i
\(792\) 0 0
\(793\) 4.96547 0.176329
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17.6613 + 30.5902i 0.625594 + 1.08356i 0.988426 + 0.151706i \(0.0484767\pi\)
−0.362832 + 0.931855i \(0.618190\pi\)
\(798\) 0 0
\(799\) 20.7770 35.9868i 0.735036 1.27312i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.36339 + 2.36146i −0.0481130 + 0.0833341i
\(804\) 0 0
\(805\) −2.10133 + 7.16126i −0.0740621 + 0.252401i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 21.7669i 0.765282i 0.923897 + 0.382641i \(0.124985\pi\)
−0.923897 + 0.382641i \(0.875015\pi\)
\(810\) 0 0
\(811\) 17.0184i 0.597598i 0.954316 + 0.298799i \(0.0965860\pi\)
−0.954316 + 0.298799i \(0.903414\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.53263 + 7.85075i 0.158771 + 0.275000i
\(816\) 0 0
\(817\) −24.7662 14.2988i −0.866460 0.500251i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 21.4786 + 12.4007i 0.749608 + 0.432786i 0.825552 0.564326i \(-0.190864\pi\)
−0.0759445 + 0.997112i \(0.524197\pi\)
\(822\) 0 0
\(823\) 10.6572 + 18.4588i 0.371486 + 0.643433i 0.989794 0.142503i \(-0.0455149\pi\)
−0.618308 + 0.785936i \(0.712182\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 49.7585i 1.73027i −0.501537 0.865136i \(-0.667232\pi\)
0.501537 0.865136i \(-0.332768\pi\)
\(828\) 0 0
\(829\) 43.1190i 1.49759i 0.662804 + 0.748793i \(0.269366\pi\)
−0.662804 + 0.748793i \(0.730634\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 31.0354 16.0141i 1.07531 0.554854i
\(834\) 0 0
\(835\) 3.54655 6.14281i 0.122733 0.212581i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −14.9985 + 25.9782i −0.517807 + 0.896868i 0.481979 + 0.876183i \(0.339918\pi\)
−0.999786 + 0.0206851i \(0.993415\pi\)
\(840\) 0 0
\(841\) −12.8274 22.2177i −0.442325 0.766129i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 4.39803 0.151297
\(846\) 0 0
\(847\) 20.2014 19.2689i 0.694128 0.662089i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 34.4373 19.8824i 1.18050 0.681559i
\(852\) 0 0
\(853\) 25.7693 + 14.8779i 0.882325 + 0.509411i 0.871424 0.490530i \(-0.163197\pi\)
0.0109007 + 0.999941i \(0.496530\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 22.9296 39.7152i 0.783260 1.35665i −0.146773 0.989170i \(-0.546889\pi\)
0.930033 0.367476i \(-0.119778\pi\)
\(858\) 0 0
\(859\) −3.24073 + 1.87104i −0.110572 + 0.0638390i −0.554266 0.832339i \(-0.687001\pi\)
0.443694 + 0.896178i \(0.353668\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 31.3944i 1.06868i −0.845270 0.534339i \(-0.820561\pi\)
0.845270 0.534339i \(-0.179439\pi\)
\(864\) 0 0
\(865\) 1.77307 0.0602860
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.84432 2.79687i 0.164332 0.0948773i
\(870\) 0 0
\(871\) −9.44641 5.45389i −0.320080 0.184798i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.25764 9.29878i −0.0763221 0.314356i
\(876\) 0 0
\(877\) 10.1962 + 17.6603i 0.344300 + 0.596344i 0.985226 0.171258i \(-0.0547831\pi\)
−0.640927 + 0.767602i \(0.721450\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 21.2010 0.714280 0.357140 0.934051i \(-0.383752\pi\)
0.357140 + 0.934051i \(0.383752\pi\)
\(882\) 0 0
\(883\) −38.6157 −1.29952 −0.649761 0.760139i \(-0.725131\pi\)
−0.649761 + 0.760139i \(0.725131\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 3.09606 + 5.36253i 0.103955 + 0.180056i 0.913311 0.407263i \(-0.133517\pi\)
−0.809356 + 0.587319i \(0.800183\pi\)
\(888\) 0 0
\(889\) 1.04211 + 4.29226i 0.0349513 + 0.143958i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −45.8555 26.4747i −1.53450 0.885941i
\(894\) 0 0
\(895\) −1.16134 + 0.670501i −0.0388194 + 0.0224124i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −11.5699 −0.385878
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.79948 1.03893i 0.0598168 0.0345353i
\(906\) 0 0
\(907\) −0.0645566 + 0.111815i −0.00214357 + 0.00371277i −0.867095 0.498142i \(-0.834016\pi\)
0.864952 + 0.501855i \(0.167349\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 29.6682 + 17.1290i 0.982952 + 0.567508i 0.903160 0.429304i \(-0.141241\pi\)
0.0797919 + 0.996812i \(0.474574\pi\)
\(912\) 0 0
\(913\) −9.86424 + 5.69512i −0.326459 + 0.188481i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 25.9072 24.7114i 0.855530 0.816041i
\(918\) 0 0
\(919\) −14.3054 −0.471892 −0.235946 0.971766i \(-0.575819\pi\)
−0.235946 + 0.971766i \(0.575819\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.75352 4.76923i −0.0906332 0.156981i
\(924\) 0 0
\(925\) −12.5725 + 21.7761i −0.413380 + 0.715995i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 5.87364 10.1734i 0.192708 0.333780i −0.753439 0.657518i \(-0.771606\pi\)
0.946147 + 0.323738i \(0.104940\pi\)
\(930\) 0 0
\(931\) −20.4056 39.5463i −0.668768 1.29608i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.22442i 0.0400427i
\(936\) 0 0
\(937\) 2.63611i 0.0861179i 0.999073 + 0.0430589i \(0.0137103\pi\)
−0.999073 + 0.0430589i \(0.986290\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −5.96557 10.3327i −0.194472 0.336836i 0.752255 0.658872i \(-0.228966\pi\)
−0.946727 + 0.322036i \(0.895633\pi\)
\(942\) 0 0
\(943\) 28.7776 + 16.6148i 0.937128 + 0.541051i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6.70267 + 3.86979i 0.217807 + 0.125751i 0.604935 0.796275i \(-0.293199\pi\)
−0.387127 + 0.922026i \(0.626533\pi\)
\(948\) 0 0
\(949\) 2.03976 + 3.53296i 0.0662133 + 0.114685i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.76685i 0.122020i 0.998137 + 0.0610102i \(0.0194322\pi\)
−0.998137 + 0.0610102i \(0.980568\pi\)
\(954\) 0 0
\(955\) 10.0366i 0.324777i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6.69586 22.8193i 0.216221 0.736872i
\(960\) 0 0
\(961\) 4.50836 7.80871i 0.145431 0.251894i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.83817 3.18381i 0.0591728 0.102490i
\(966\) 0 0
\(967\) 2.28741 + 3.96191i 0.0735581 + 0.127406i 0.900458 0.434942i \(-0.143231\pi\)
−0.826900 + 0.562349i \(0.809898\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 25.8445 0.829388 0.414694 0.909961i \(-0.363889\pi\)
0.414694 + 0.909961i \(0.363889\pi\)
\(972\) 0 0
\(973\) −16.9815 17.8033i −0.544403 0.570747i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 26.0950 15.0659i 0.834852 0.482002i −0.0206590 0.999787i \(-0.506576\pi\)
0.855511 + 0.517785i \(0.173243\pi\)
\(978\) 0 0
\(979\) 6.21003 + 3.58536i 0.198474 + 0.114589i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 6.30293 10.9170i 0.201032 0.348198i −0.747829 0.663891i \(-0.768904\pi\)
0.948861 + 0.315693i \(0.102237\pi\)
\(984\) 0 0
\(985\) −5.97689 + 3.45076i −0.190440 + 0.109950i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 34.6136i 1.10065i
\(990\) 0 0
\(991\) −51.6852 −1.64184 −0.820918 0.571046i \(-0.806538\pi\)
−0.820918 + 0.571046i \(0.806538\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.70300 0.983227i 0.0539887 0.0311704i
\(996\) 0 0
\(997\) −35.1469 20.2921i −1.11311 0.642656i −0.173479 0.984837i \(-0.555501\pi\)
−0.939634 + 0.342181i \(0.888834\pi\)
\(998\) 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 3024.2.cc.b.2897.4 16
3.2 odd 2 1008.2.cc.b.209.4 16
4.3 odd 2 378.2.m.a.251.2 16
7.6 odd 2 inner 3024.2.cc.b.2897.5 16
9.4 even 3 1008.2.cc.b.545.5 16
9.5 odd 6 inner 3024.2.cc.b.881.5 16
12.11 even 2 126.2.m.a.83.7 yes 16
21.20 even 2 1008.2.cc.b.209.5 16
28.3 even 6 2646.2.t.a.1979.6 16
28.11 odd 6 2646.2.t.a.1979.7 16
28.19 even 6 2646.2.l.b.521.7 16
28.23 odd 6 2646.2.l.b.521.6 16
28.27 even 2 378.2.m.a.251.3 16
36.7 odd 6 1134.2.d.a.1133.13 16
36.11 even 6 1134.2.d.a.1133.4 16
36.23 even 6 378.2.m.a.125.3 16
36.31 odd 6 126.2.m.a.41.6 16
63.13 odd 6 1008.2.cc.b.545.4 16
63.41 even 6 inner 3024.2.cc.b.881.4 16
84.11 even 6 882.2.t.b.803.4 16
84.23 even 6 882.2.l.a.227.1 16
84.47 odd 6 882.2.l.a.227.4 16
84.59 odd 6 882.2.t.b.803.1 16
84.83 odd 2 126.2.m.a.83.6 yes 16
252.23 even 6 2646.2.t.a.2285.6 16
252.31 even 6 882.2.l.a.509.5 16
252.59 odd 6 2646.2.l.b.1097.2 16
252.67 odd 6 882.2.l.a.509.8 16
252.83 odd 6 1134.2.d.a.1133.5 16
252.95 even 6 2646.2.l.b.1097.3 16
252.103 even 6 882.2.t.b.815.4 16
252.131 odd 6 2646.2.t.a.2285.7 16
252.139 even 6 126.2.m.a.41.7 yes 16
252.167 odd 6 378.2.m.a.125.2 16
252.223 even 6 1134.2.d.a.1133.12 16
252.247 odd 6 882.2.t.b.815.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.m.a.41.6 16 36.31 odd 6
126.2.m.a.41.7 yes 16 252.139 even 6
126.2.m.a.83.6 yes 16 84.83 odd 2
126.2.m.a.83.7 yes 16 12.11 even 2
378.2.m.a.125.2 16 252.167 odd 6
378.2.m.a.125.3 16 36.23 even 6
378.2.m.a.251.2 16 4.3 odd 2
378.2.m.a.251.3 16 28.27 even 2
882.2.l.a.227.1 16 84.23 even 6
882.2.l.a.227.4 16 84.47 odd 6
882.2.l.a.509.5 16 252.31 even 6
882.2.l.a.509.8 16 252.67 odd 6
882.2.t.b.803.1 16 84.59 odd 6
882.2.t.b.803.4 16 84.11 even 6
882.2.t.b.815.1 16 252.247 odd 6
882.2.t.b.815.4 16 252.103 even 6
1008.2.cc.b.209.4 16 3.2 odd 2
1008.2.cc.b.209.5 16 21.20 even 2
1008.2.cc.b.545.4 16 63.13 odd 6
1008.2.cc.b.545.5 16 9.4 even 3
1134.2.d.a.1133.4 16 36.11 even 6
1134.2.d.a.1133.5 16 252.83 odd 6
1134.2.d.a.1133.12 16 252.223 even 6
1134.2.d.a.1133.13 16 36.7 odd 6
2646.2.l.b.521.6 16 28.23 odd 6
2646.2.l.b.521.7 16 28.19 even 6
2646.2.l.b.1097.2 16 252.59 odd 6
2646.2.l.b.1097.3 16 252.95 even 6
2646.2.t.a.1979.6 16 28.3 even 6
2646.2.t.a.1979.7 16 28.11 odd 6
2646.2.t.a.2285.6 16 252.23 even 6
2646.2.t.a.2285.7 16 252.131 odd 6
3024.2.cc.b.881.4 16 63.41 even 6 inner
3024.2.cc.b.881.5 16 9.5 odd 6 inner
3024.2.cc.b.2897.4 16 1.1 even 1 trivial
3024.2.cc.b.2897.5 16 7.6 odd 2 inner