Properties

Label 847.1.bb.a.174.1
Level $847$
Weight $1$
Character 847.174
Analytic conductor $0.423$
Analytic rank $0$
Dimension $40$
Projective image $D_{55}$
CM discriminant -7
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,1,Mod(20,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(110))
 
chi = DirichletCharacter(H, H._module([55, 76]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.20");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 847.bb (of order \(110\), degree \(40\), 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: \(0.422708065700\)
Analytic rank: \(0\)
Dimension: \(40\)
Coefficient field: \(\Q(\zeta_{55})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} - x^{12} + x^{10} - x^{6} + x^{5} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{55}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{55} - \cdots)\)

Embedding invariants

Embedding label 174.1
Root \(0.993482 - 0.113991i\) of defining polynomial
Character \(\chi\) \(=\) 847.174
Dual form 847.1.bb.a.258.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.38479 - 0.158890i) q^{2} +(0.918384 - 0.213561i) q^{4} +(0.696938 - 0.717132i) q^{7} +(-0.0749775 + 0.0267519i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(1.38479 - 0.158890i) q^{2} +(0.918384 - 0.213561i) q^{4} +(0.696938 - 0.717132i) q^{7} +(-0.0749775 + 0.0267519i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.736741 + 0.676175i) q^{11} +(0.851167 - 1.10381i) q^{14} +(-0.945724 + 0.464981i) q^{16} +(0.276810 - 1.36611i) q^{18} +(-0.912794 + 1.05342i) q^{22} +(0.132827 + 0.923835i) q^{23} +(-0.362808 + 0.931864i) q^{25} +(0.486905 - 0.807441i) q^{28} +(0.409569 + 1.05197i) q^{29} +(-1.16878 + 0.751128i) q^{32} +(0.0806876 - 0.939429i) q^{36} +(-0.138463 - 1.61210i) q^{37} +(-1.72209 - 0.505653i) q^{43} +(-0.532207 + 0.778327i) q^{44} +(0.330726 + 1.25821i) q^{46} +(-0.0285561 - 0.999592i) q^{49} +(-0.354349 + 1.34808i) q^{50} +(-0.456270 - 0.224333i) q^{53} +(-0.0330700 + 0.0724132i) q^{56} +(0.734314 + 1.39168i) q^{58} +(-0.466667 - 0.884433i) q^{63} +(-0.683335 + 0.558760i) q^{64} +(0.643180 + 1.40837i) q^{67} +(-0.262555 + 0.998864i) q^{71} +(0.00227327 + 0.0795747i) q^{72} +(-0.447888 - 2.21042i) q^{74} +(-0.0285561 + 0.999592i) q^{77} +(0.0526073 - 1.84150i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-2.46508 - 0.426599i) q^{86} +(0.0371501 - 0.0704072i) q^{88} +(0.319282 + 0.820068i) q^{92} +(-0.198369 - 1.37969i) q^{98} +(0.415415 + 0.909632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{55}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38479 0.158890i 1.38479 0.158890i 0.610648 0.791902i \(-0.290909\pi\)
0.774142 + 0.633012i \(0.218182\pi\)
\(3\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) 0.918384 0.213561i 0.918384 0.213561i
\(5\) 0 0 −0.564443 0.825472i \(-0.690909\pi\)
0.564443 + 0.825472i \(0.309091\pi\)
\(6\) 0 0
\(7\) 0.696938 0.717132i 0.696938 0.717132i
\(8\) −0.0749775 + 0.0267519i −0.0749775 + 0.0267519i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) 0 0
\(11\) −0.736741 + 0.676175i −0.736741 + 0.676175i
\(12\) 0 0
\(13\) 0 0 −0.516397 0.856349i \(-0.672727\pi\)
0.516397 + 0.856349i \(0.327273\pi\)
\(14\) 0.851167 1.10381i 0.851167 1.10381i
\(15\) 0 0
\(16\) −0.945724 + 0.464981i −0.945724 + 0.464981i
\(17\) 0 0 −0.774142 0.633012i \(-0.781818\pi\)
0.774142 + 0.633012i \(0.218182\pi\)
\(18\) 0.276810 1.36611i 0.276810 1.36611i
\(19\) 0 0 0.998369 0.0570888i \(-0.0181818\pi\)
−0.998369 + 0.0570888i \(0.981818\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.912794 + 1.05342i −0.912794 + 1.05342i
\(23\) 0.132827 + 0.923835i 0.132827 + 0.923835i 0.941844 + 0.336049i \(0.109091\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) 0 0
\(25\) −0.362808 + 0.931864i −0.362808 + 0.931864i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.486905 0.807441i 0.486905 0.807441i
\(29\) 0.409569 + 1.05197i 0.409569 + 1.05197i 0.974012 + 0.226497i \(0.0727273\pi\)
−0.564443 + 0.825472i \(0.690909\pi\)
\(30\) 0 0
\(31\) 0 0 0.921124 0.389270i \(-0.127273\pi\)
−0.921124 + 0.389270i \(0.872727\pi\)
\(32\) −1.16878 + 0.751128i −1.16878 + 0.751128i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.0806876 0.939429i 0.0806876 0.939429i
\(37\) −0.138463 1.61210i −0.138463 1.61210i −0.654861 0.755750i \(-0.727273\pi\)
0.516397 0.856349i \(-0.327273\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.870746 0.491733i \(-0.836364\pi\)
0.870746 + 0.491733i \(0.163636\pi\)
\(42\) 0 0
\(43\) −1.72209 0.505653i −1.72209 0.505653i −0.736741 0.676175i \(-0.763636\pi\)
−0.985354 + 0.170522i \(0.945455\pi\)
\(44\) −0.532207 + 0.778327i −0.532207 + 0.778327i
\(45\) 0 0
\(46\) 0.330726 + 1.25821i 0.330726 + 1.25821i
\(47\) 0 0 −0.198590 0.980083i \(-0.563636\pi\)
0.198590 + 0.980083i \(0.436364\pi\)
\(48\) 0 0
\(49\) −0.0285561 0.999592i −0.0285561 0.999592i
\(50\) −0.354349 + 1.34808i −0.354349 + 1.34808i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.456270 0.224333i −0.456270 0.224333i 0.198590 0.980083i \(-0.436364\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.0330700 + 0.0724132i −0.0330700 + 0.0724132i
\(57\) 0 0
\(58\) 0.734314 + 1.39168i 0.734314 + 1.39168i
\(59\) 0 0 0.870746 0.491733i \(-0.163636\pi\)
−0.870746 + 0.491733i \(0.836364\pi\)
\(60\) 0 0
\(61\) 0 0 −0.993482 0.113991i \(-0.963636\pi\)
0.993482 + 0.113991i \(0.0363636\pi\)
\(62\) 0 0
\(63\) −0.466667 0.884433i −0.466667 0.884433i
\(64\) −0.683335 + 0.558760i −0.683335 + 0.558760i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.643180 + 1.40837i 0.643180 + 1.40837i 0.897398 + 0.441221i \(0.145455\pi\)
−0.254218 + 0.967147i \(0.581818\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.262555 + 0.998864i −0.262555 + 0.998864i 0.696938 + 0.717132i \(0.254545\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(72\) 0.00227327 + 0.0795747i 0.00227327 + 0.0795747i
\(73\) 0 0 0.466667 0.884433i \(-0.345455\pi\)
−0.466667 + 0.884433i \(0.654545\pi\)
\(74\) −0.447888 2.21042i −0.447888 2.21042i
\(75\) 0 0
\(76\) 0 0
\(77\) −0.0285561 + 0.999592i −0.0285561 + 0.999592i
\(78\) 0 0
\(79\) 0.0526073 1.84150i 0.0526073 1.84150i −0.362808 0.931864i \(-0.618182\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 0 0
\(83\) 0 0 0.985354 0.170522i \(-0.0545455\pi\)
−0.985354 + 0.170522i \(0.945455\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.46508 0.426599i −2.46508 0.426599i
\(87\) 0 0
\(88\) 0.0371501 0.0704072i 0.0371501 0.0704072i
\(89\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.319282 + 0.820068i 0.319282 + 0.820068i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.564443 0.825472i \(-0.309091\pi\)
−0.564443 + 0.825472i \(0.690909\pi\)
\(98\) −0.198369 1.37969i −0.198369 1.37969i
\(99\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(100\) −0.134187 + 0.933291i −0.134187 + 0.933291i
\(101\) 0 0 −0.736741 0.676175i \(-0.763636\pi\)
0.736741 + 0.676175i \(0.236364\pi\)
\(102\) 0 0
\(103\) 0 0 0.198590 0.980083i \(-0.436364\pi\)
−0.198590 + 0.980083i \(0.563636\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.667482 0.238157i −0.667482 0.238157i
\(107\) −0.443096 + 0.574616i −0.443096 + 0.574616i −0.959493 0.281733i \(-0.909091\pi\)
0.516397 + 0.856349i \(0.327273\pi\)
\(108\) 0 0
\(109\) −0.260098 + 0.300169i −0.260098 + 0.300169i −0.870746 0.491733i \(-0.836364\pi\)
0.610648 + 0.791902i \(0.290909\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.325658 + 1.00227i −0.325658 + 1.00227i
\(113\) 1.87141 0.667718i 1.87141 0.667718i 0.897398 0.441221i \(-0.145455\pi\)
0.974012 0.226497i \(-0.0727273\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.600801 + 0.878643i 0.600801 + 0.878643i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0855750 0.996332i 0.0855750 0.996332i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.786763 1.15060i −0.786763 1.15060i
\(127\) −0.899779 + 0.825810i −0.899779 + 0.825810i −0.985354 0.170522i \(-0.945455\pi\)
0.0855750 + 0.996332i \(0.472727\pi\)
\(128\) 0.110781 0.113991i 0.110781 0.113991i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.11444 + 1.84810i 1.11444 + 1.84810i
\(135\) 0 0
\(136\) 0 0
\(137\) 1.74815 0.859509i 1.74815 0.859509i 0.774142 0.633012i \(-0.218182\pi\)
0.974012 0.226497i \(-0.0727273\pi\)
\(138\) 0 0
\(139\) 0 0 0.198590 0.980083i \(-0.436364\pi\)
−0.198590 + 0.980083i \(0.563636\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.204875 + 1.42493i −0.204875 + 1.42493i
\(143\) 0 0
\(144\) 0.149979 + 1.04312i 0.149979 + 1.04312i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −0.471444 1.45096i −0.471444 1.45096i
\(149\) 0.429039 0.711480i 0.429039 0.711480i −0.564443 0.825472i \(-0.690909\pi\)
0.993482 + 0.113991i \(0.0363636\pi\)
\(150\) 0 0
\(151\) 1.83474 + 0.426649i 1.83474 + 0.426649i 0.993482 0.113991i \(-0.0363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0.119281 + 1.38876i 0.119281 + 1.38876i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.0855750 0.996332i \(-0.472727\pi\)
−0.0855750 + 0.996332i \(0.527273\pi\)
\(158\) −0.219745 2.55844i −0.219745 2.55844i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.755084 + 0.548600i 0.755084 + 0.548600i
\(162\) −1.21371 0.685414i −1.21371 0.685414i
\(163\) 0.0207207 0.725319i 0.0207207 0.725319i −0.921124 0.389270i \(-0.872727\pi\)
0.941844 0.336049i \(-0.109091\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.254218 0.967147i \(-0.581818\pi\)
0.254218 + 0.967147i \(0.418182\pi\)
\(168\) 0 0
\(169\) −0.466667 + 0.884433i −0.466667 + 0.884433i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.68953 0.0966110i −1.68953 0.0966110i
\(173\) 0 0 −0.696938 0.717132i \(-0.745455\pi\)
0.696938 + 0.717132i \(0.254545\pi\)
\(174\) 0 0
\(175\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(176\) 0.382345 0.982045i 0.382345 0.982045i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.569939 1.08015i −0.569939 1.08015i −0.985354 0.170522i \(-0.945455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(180\) 0 0
\(181\) 0 0 −0.993482 0.113991i \(-0.963636\pi\)
0.993482 + 0.113991i \(0.0363636\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.0346734 0.0657135i −0.0346734 0.0657135i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.83924 + 0.105172i 1.83924 + 0.105172i 0.941844 0.336049i \(-0.109091\pi\)
0.897398 + 0.441221i \(0.145455\pi\)
\(192\) 0 0
\(193\) −0.0567398 1.98615i −0.0567398 1.98615i −0.142315 0.989821i \(-0.545455\pi\)
0.0855750 0.996332i \(-0.472727\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.239699 0.911911i −0.239699 0.911911i
\(197\) −1.86912 + 0.548822i −1.86912 + 0.548822i −0.870746 + 0.491733i \(0.836364\pi\)
−0.998369 + 0.0570888i \(0.981818\pi\)
\(198\) 0.719794 + 1.19364i 0.719794 + 1.19364i
\(199\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(200\) 0.00227327 0.0795747i 0.00227327 0.0795747i
\(201\) 0 0
\(202\) 0 0
\(203\) 1.03984 + 0.439442i 1.03984 + 0.439442i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.919665 + 0.159154i 0.919665 + 0.159154i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.157650 + 0.0666236i −0.157650 + 0.0666236i −0.466667 0.884433i \(-0.654545\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(212\) −0.466940 0.108582i −0.466940 0.108582i
\(213\) 0 0
\(214\) −0.522293 + 0.866126i −0.522293 + 0.866126i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −0.312487 + 0.456998i −0.312487 + 0.456998i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.998369 0.0570888i \(-0.0181818\pi\)
−0.998369 + 0.0570888i \(0.981818\pi\)
\(224\) −0.275907 + 1.36166i −0.275907 + 1.36166i
\(225\) 0.774142 + 0.633012i 0.774142 + 0.633012i
\(226\) 2.48542 1.22200i 2.48542 1.22200i
\(227\) 0 0 −0.941844 0.336049i \(-0.890909\pi\)
0.941844 + 0.336049i \(0.109091\pi\)
\(228\) 0 0
\(229\) 0 0 −0.516397 0.856349i \(-0.672727\pi\)
0.516397 + 0.856349i \(0.327273\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.0588506 0.0679173i −0.0588506 0.0679173i
\(233\) 0.519923 1.60016i 0.519923 1.60016i −0.254218 0.967147i \(-0.581818\pi\)
0.774142 0.633012i \(-0.218182\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.25259 + 0.910058i −1.25259 + 0.910058i −0.998369 0.0570888i \(-0.981818\pi\)
−0.254218 + 0.967147i \(0.581818\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.0398036 1.39331i −0.0398036 1.39331i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) −0.617460 0.712587i −0.617460 0.712587i
\(253\) −0.722533 0.590812i −0.722533 0.590812i
\(254\) −1.11479 + 1.28654i −1.11479 + 1.28654i
\(255\) 0 0
\(256\) 0.674316 0.874468i 0.674316 0.874468i
\(257\) 0 0 −0.941844 0.336049i \(-0.890909\pi\)
0.941844 + 0.336049i \(0.109091\pi\)
\(258\) 0 0
\(259\) −1.25259 1.02424i −1.25259 1.02424i
\(260\) 0 0
\(261\) 1.12705 0.0644468i 1.12705 0.0644468i
\(262\) 0 0
\(263\) −0.146982 + 1.02228i −0.146982 + 1.02228i 0.774142 + 0.633012i \(0.218182\pi\)
−0.921124 + 0.389270i \(0.872727\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.891459 + 1.15606i 0.891459 + 1.15606i
\(269\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.362808 0.931864i \(-0.618182\pi\)
0.362808 + 0.931864i \(0.381818\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 2.28426 1.46800i 2.28426 1.46800i
\(275\) −0.362808 0.931864i −0.362808 0.931864i
\(276\) 0 0
\(277\) 1.96749 + 0.340488i 1.96749 + 0.340488i 0.993482 + 0.113991i \(0.0363636\pi\)
0.974012 + 0.226497i \(0.0727273\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.468333 + 0.197919i 0.468333 + 0.197919i 0.610648 0.791902i \(-0.290909\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(282\) 0 0
\(283\) 0 0 −0.870746 0.491733i \(-0.836364\pi\)
0.870746 + 0.491733i \(0.163636\pi\)
\(284\) −0.0278082 + 0.973413i −0.0278082 + 0.973413i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.353193 + 1.34368i 0.353193 + 1.34368i
\(289\) 0.198590 + 0.980083i 0.198590 + 0.980083i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.998369 0.0570888i \(-0.981818\pi\)
0.998369 + 0.0570888i \(0.0181818\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.0535084 + 0.117167i 0.0535084 + 0.117167i
\(297\) 0 0
\(298\) 0.481081 1.05342i 0.481081 1.05342i
\(299\) 0 0
\(300\) 0 0
\(301\) −1.56281 + 0.882561i −1.56281 + 0.882561i
\(302\) 2.60851 + 0.299299i 2.60851 + 0.299299i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(308\) 0.187249 + 0.924108i 0.187249 + 0.924108i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.696938 0.717132i \(-0.745455\pi\)
0.696938 + 0.717132i \(0.254545\pi\)
\(312\) 0 0
\(313\) 0 0 0.254218 0.967147i \(-0.418182\pi\)
−0.254218 + 0.967147i \(0.581818\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.344958 1.70244i −0.344958 1.70244i
\(317\) −0.157116 0.597730i −0.157116 0.597730i −0.998369 0.0570888i \(-0.981818\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(318\) 0 0
\(319\) −1.01306 0.498089i −1.01306 0.498089i
\(320\) 0 0
\(321\) 0 0
\(322\) 1.13280 + 0.639721i 1.13280 + 0.639721i
\(323\) 0 0
\(324\) −0.868516 0.367038i −0.868516 0.367038i
\(325\) 0 0
\(326\) −0.0865520 1.00771i −0.0865520 1.00771i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.46504 + 0.941522i −1.46504 + 0.941522i −0.466667 + 0.884433i \(0.654545\pi\)
−0.998369 + 0.0570888i \(0.981818\pi\)
\(332\) 0 0
\(333\) −1.57598 0.366479i −1.57598 0.366479i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.06344 1.37909i −1.06344 1.37909i −0.921124 0.389270i \(-0.872727\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(338\) −0.505709 + 1.29890i −0.505709 + 1.29890i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.736741 0.676175i −0.736741 0.676175i
\(344\) 0.142646 0.00815677i 0.142646 0.00815677i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.76851 + 0.869518i −1.76851 + 0.869518i −0.809017 + 0.587785i \(0.800000\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(348\) 0 0
\(349\) 0 0 0.610648 0.791902i \(-0.290909\pi\)
−0.610648 + 0.791902i \(0.709091\pi\)
\(350\) 0.719794 + 1.19364i 0.719794 + 1.19364i
\(351\) 0 0
\(352\) 0.353193 1.34368i 0.353193 1.34368i
\(353\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.960871 1.40523i −0.960871 1.40523i
\(359\) −1.69623 + 0.394442i −1.69623 + 0.394442i −0.959493 0.281733i \(-0.909091\pi\)
−0.736741 + 0.676175i \(0.763636\pi\)
\(360\) 0 0
\(361\) 0.993482 0.113991i 0.993482 0.113991i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.974012 0.226497i \(-0.0727273\pi\)
−0.974012 + 0.226497i \(0.927273\pi\)
\(368\) −0.555184 0.811930i −0.555184 0.811930i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.478868 + 0.170860i −0.478868 + 0.170860i
\(372\) 0 0
\(373\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.69042 0.831123i 1.69042 0.831123i 0.696938 0.717132i \(-0.254545\pi\)
0.993482 0.113991i \(-0.0363636\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 2.56367 0.146596i 2.56367 0.146596i
\(383\) 0 0 −0.736741 0.676175i \(-0.763636\pi\)
0.736741 + 0.676175i \(0.236364\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.394152 2.74139i −0.394152 2.74139i
\(387\) −1.01306 + 1.48155i −1.01306 + 1.48155i
\(388\) 0 0
\(389\) 1.15027 + 1.49170i 1.15027 + 1.49170i 0.841254 + 0.540641i \(0.181818\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.0288821 + 0.0741830i 0.0288821 + 0.0741830i
\(393\) 0 0
\(394\) −2.50113 + 1.05699i −2.50113 + 1.05699i
\(395\) 0 0
\(396\) 0.575772 + 0.746675i 0.575772 + 0.746675i
\(397\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.0901832 1.04998i −0.0901832 1.04998i
\(401\) −0.168643 + 0.0291849i −0.168643 + 0.0291849i −0.254218 0.967147i \(-0.581818\pi\)
0.0855750 + 0.996332i \(0.472727\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 1.50979 + 0.443314i 1.50979 + 0.443314i
\(407\) 1.19207 + 1.09407i 1.19207 + 1.09407i
\(408\) 0 0
\(409\) 0 0 −0.254218 0.967147i \(-0.581818\pi\)
0.254218 + 0.967147i \(0.418182\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 1.29883 + 0.0742698i 1.29883 + 0.0742698i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(420\) 0 0
\(421\) 0.812697 + 1.54023i 0.812697 + 1.54023i 0.841254 + 0.540641i \(0.181818\pi\)
−0.0285561 + 0.999592i \(0.509091\pi\)
\(422\) −0.207727 + 0.117309i −0.207727 + 0.117309i
\(423\) 0 0
\(424\) 0.0402114 + 0.00461382i 0.0402114 + 0.00461382i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.284216 + 0.622347i −0.284216 + 0.622347i
\(429\) 0 0
\(430\) 0 0
\(431\) −1.79187 0.881003i −1.79187 0.881003i −0.921124 0.389270i \(-0.872727\pi\)
−0.870746 0.491733i \(-0.836364\pi\)
\(432\) 0 0
\(433\) 0 0 −0.998369 0.0570888i \(-0.981818\pi\)
0.998369 + 0.0570888i \(0.0181818\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.174766 + 0.331218i −0.174766 + 0.331218i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(440\) 0 0
\(441\) −0.959493 0.281733i −0.959493 0.281733i
\(442\) 0 0
\(443\) 1.71599 + 0.969062i 1.71599 + 0.969062i 0.941844 + 0.336049i \(0.109091\pi\)
0.774142 + 0.633012i \(0.218182\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.0755371 + 0.879462i −0.0755371 + 0.879462i
\(449\) −0.391364 0.0677282i −0.391364 0.0677282i −0.0285561 0.999592i \(-0.509091\pi\)
−0.362808 + 0.931864i \(0.618182\pi\)
\(450\) 1.17260 + 0.753586i 1.17260 + 0.753586i
\(451\) 0 0
\(452\) 1.57607 1.01288i 1.57607 1.01288i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(462\) 0 0
\(463\) 0.209698 1.45848i 0.209698 1.45848i −0.564443 0.825472i \(-0.690909\pi\)
0.774142 0.633012i \(-0.218182\pi\)
\(464\) −0.876484 0.804430i −0.876484 0.804430i
\(465\) 0 0
\(466\) 0.465735 2.29849i 0.465735 2.29849i
\(467\) 0 0 −0.774142 0.633012i \(-0.781818\pi\)
0.774142 + 0.633012i \(0.218182\pi\)
\(468\) 0 0
\(469\) 1.45824 + 0.520300i 1.45824 + 0.520300i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.61065 0.791902i 1.61065 0.791902i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.354349 + 0.364616i −0.354349 + 0.364616i
\(478\) −1.58997 + 1.45926i −1.58997 + 1.45926i
\(479\) 0 0 −0.564443 0.825472i \(-0.690909\pi\)
0.564443 + 0.825472i \(0.309091\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.134187 0.933291i −0.134187 0.933291i
\(485\) 0 0
\(486\) 0 0
\(487\) −1.45202 + 1.05496i −1.45202 + 1.05496i −0.466667 + 0.884433i \(0.654545\pi\)
−0.985354 + 0.170522i \(0.945455\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.198369 + 0.204117i −0.198369 + 0.204117i −0.809017 0.587785i \(-0.800000\pi\)
0.610648 + 0.791902i \(0.290909\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.533333 + 0.884433i 0.533333 + 0.884433i
\(498\) 0 0
\(499\) 0.582092 + 0.207690i 0.582092 + 0.207690i 0.610648 0.791902i \(-0.290909\pi\)
−0.0285561 + 0.999592i \(0.509091\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.998369 0.0570888i \(-0.0181818\pi\)
−0.998369 + 0.0570888i \(0.981818\pi\)
\(504\) 0.0586499 + 0.0538283i 0.0586499 + 0.0538283i
\(505\) 0 0
\(506\) −1.09443 0.703348i −1.09443 0.703348i
\(507\) 0 0
\(508\) −0.649982 + 0.950568i −0.649982 + 0.950568i
\(509\) 0 0 0.362808 0.931864i \(-0.381818\pi\)
−0.362808 + 0.931864i \(0.618182\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.712758 1.18198i 0.712758 1.18198i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −1.89731 1.21933i −1.89731 1.21933i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.0855750 0.996332i \(-0.527273\pi\)
0.0855750 + 0.996332i \(0.472727\pi\)
\(522\) 1.55048 0.268321i 1.55048 0.268321i
\(523\) 0 0 −0.921124 0.389270i \(-0.872727\pi\)
0.921124 + 0.389270i \(0.127273\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −0.0411089 + 1.43900i −0.0411089 + 1.43900i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.123666 0.0363115i 0.123666 0.0363115i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.0859006 0.0883896i −0.0859006 0.0883896i
\(537\) 0 0
\(538\) 0 0
\(539\) 0.696938 + 0.717132i 0.696938 + 0.717132i
\(540\) 0 0
\(541\) 0.132494 0.108340i 0.132494 0.108340i −0.564443 0.825472i \(-0.690909\pi\)
0.696938 + 0.717132i \(0.254545\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.785171 1.48806i −0.785171 1.48806i −0.870746 0.491733i \(-0.836364\pi\)
0.0855750 0.996332i \(-0.472727\pi\)
\(548\) 1.42192 1.16270i 1.42192 1.16270i
\(549\) 0 0
\(550\) −0.650476 1.23279i −0.650476 1.23279i
\(551\) 0 0
\(552\) 0 0
\(553\) −1.28393 1.32113i −1.28393 1.32113i
\(554\) 2.77866 + 0.158890i 2.77866 + 0.158890i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.288416 + 0.546610i −0.288416 + 0.546610i −0.985354 0.170522i \(-0.945455\pi\)
0.696938 + 0.717132i \(0.254545\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.679990 + 0.199663i 0.679990 + 0.199663i
\(563\) 0 0 0.0285561 0.999592i \(-0.490909\pi\)
−0.0285561 + 0.999592i \(0.509091\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.985354 + 0.170522i −0.985354 + 0.170522i
\(568\) −0.00703579 0.0819163i −0.00703579 0.0819163i
\(569\) −0.164217 + 1.91195i −0.164217 + 1.91195i 0.198590 + 0.980083i \(0.436364\pi\)
−0.362808 + 0.931864i \(0.618182\pi\)
\(570\) 0 0
\(571\) 1.63878 + 1.05318i 1.63878 + 1.05318i 0.941844 + 0.336049i \(0.109091\pi\)
0.696938 + 0.717132i \(0.254545\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.909079 0.211397i −0.909079 0.211397i
\(576\) 0.320250 + 0.822557i 0.320250 + 0.822557i
\(577\) 0 0 0.516397 0.856349i \(-0.327273\pi\)
−0.516397 + 0.856349i \(0.672727\pi\)
\(578\) 0.430731 + 1.32565i 0.430731 + 1.32565i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.487841 0.143243i 0.487841 0.143243i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.198590 0.980083i \(-0.436364\pi\)
−0.198590 + 0.980083i \(0.563636\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.880543 + 1.46022i 0.880543 + 1.46022i
\(593\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.242078 0.745038i 0.242078 0.745038i
\(597\) 0 0
\(598\) 0 0
\(599\) −0.292620 + 0.268564i −0.292620 + 0.268564i −0.809017 0.587785i \(-0.800000\pi\)
0.516397 + 0.856349i \(0.327273\pi\)
\(600\) 0 0
\(601\) 0 0 0.974012 0.226497i \(-0.0727273\pi\)
−0.974012 + 0.226497i \(0.927273\pi\)
\(602\) −2.02394 + 1.47048i −2.02394 + 1.47048i
\(603\) 1.53819 0.176491i 1.53819 0.176491i
\(604\) 1.77611 1.77611
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.993482 0.113991i \(-0.0363636\pi\)
−0.993482 + 0.113991i \(0.963636\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.85610 + 0.662255i −1.85610 + 0.662255i −0.870746 + 0.491733i \(0.836364\pi\)
−0.985354 + 0.170522i \(0.945455\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.0246000 0.0757109i −0.0246000 0.0757109i
\(617\) 0.964926 1.11358i 0.964926 1.11358i −0.0285561 0.999592i \(-0.509091\pi\)
0.993482 0.113991i \(-0.0363636\pi\)
\(618\) 0 0
\(619\) 0 0 0.610648 0.791902i \(-0.290909\pi\)
−0.610648 + 0.791902i \(0.709091\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.736741 0.676175i −0.736741 0.676175i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.104512 + 0.135534i 0.104512 + 0.135534i 0.841254 0.540641i \(-0.181818\pi\)
−0.736741 + 0.676175i \(0.763636\pi\)
\(632\) 0.0453192 + 0.139478i 0.0453192 + 0.139478i
\(633\) 0 0
\(634\) −0.312545 0.802766i −0.312545 0.802766i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −1.48202 0.528783i −1.48202 0.528783i
\(639\) 0.868842 + 0.558371i 0.868842 + 0.558371i
\(640\) 0 0
\(641\) −0.168643 + 1.96348i −0.168643 + 1.96348i 0.0855750 + 0.996332i \(0.472727\pi\)
−0.254218 + 0.967147i \(0.581818\pi\)
\(642\) 0 0
\(643\) 0 0 0.985354 0.170522i \(-0.0545455\pi\)
−0.985354 + 0.170522i \(0.945455\pi\)
\(644\) 0.810616 + 0.342569i 0.810616 + 0.342569i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.0285561 0.999592i \(-0.490909\pi\)
−0.0285561 + 0.999592i \(0.509091\pi\)
\(648\) 0.0763825 + 0.0224279i 0.0763825 + 0.0224279i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.135870 0.670547i −0.135870 0.670547i
\(653\) −0.569939 + 1.08015i −0.569939 + 1.08015i 0.415415 + 0.909632i \(0.363636\pi\)
−0.985354 + 0.170522i \(0.945455\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(660\) 0 0
\(661\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(662\) −1.87917 + 1.53659i −1.87917 + 1.53659i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −2.24064 0.257089i −2.24064 0.257089i
\(667\) −0.917443 + 0.518104i −0.917443 + 0.518104i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.76851 0.869518i −1.76851 0.869518i −0.959493 0.281733i \(-0.909091\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(674\) −1.69176 1.74078i −1.69176 1.74078i
\(675\) 0 0
\(676\) −0.239699 + 0.911911i −0.239699 + 0.911911i
\(677\) 0 0 −0.0285561 0.999592i \(-0.509091\pi\)
0.0285561 + 0.999592i \(0.490909\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.164217 0.0482185i −0.164217 0.0482185i 0.198590 0.980083i \(-0.436364\pi\)
−0.362808 + 0.931864i \(0.618182\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.12767 0.819299i −1.12767 0.819299i
\(687\) 0 0
\(688\) 1.86374 0.322534i 1.86374 0.322534i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.985354 0.170522i \(-0.945455\pi\)
0.985354 + 0.170522i \(0.0545455\pi\)
\(692\) 0 0
\(693\) 0.941844 + 0.336049i 0.941844 + 0.336049i
\(694\) −2.31086 + 1.48510i −2.31086 + 1.48510i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.575772 + 0.746675i 0.575772 + 0.746675i
\(701\) −0.683417 + 1.75534i −0.683417 + 1.75534i −0.0285561 + 0.999592i \(0.509091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.125621 0.873716i 0.125621 0.873716i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.52561 1.24748i −1.52561 1.24748i −0.870746 0.491733i \(-0.836364\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(710\) 0 0
\(711\) −1.73511 0.619086i −1.73511 0.619086i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.754102 0.870280i −0.754102 0.870280i
\(717\) 0 0
\(718\) −2.28625 + 0.815734i −2.28625 + 0.815734i
\(719\) 0 0 0.696938 0.717132i \(-0.254545\pi\)
−0.696938 + 0.717132i \(0.745455\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.35765 0.315708i 1.35765 0.315708i
\(723\) 0 0
\(724\) 0 0
\(725\) −1.12889 −1.12889
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.696938 0.717132i \(-0.254545\pi\)
−0.696938 + 0.717132i \(0.745455\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.849163 0.979987i −0.849163 0.979987i
\(737\) −1.42616 0.602700i −1.42616 0.602700i
\(738\) 0 0
\(739\) 0.319151 + 0.529253i 0.319151 + 0.529253i 0.974012 0.226497i \(-0.0727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.635984 + 0.312692i −0.635984 + 0.312692i
\(743\) 0.478446 + 0.391223i 0.478446 + 0.391223i 0.841254 0.540641i \(-0.181818\pi\)
−0.362808 + 0.931864i \(0.618182\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.292293 + 0.268264i 0.292293 + 0.268264i
\(747\) 0 0
\(748\) 0 0
\(749\) 0.103266 + 0.718230i 0.103266 + 0.718230i
\(750\) 0 0
\(751\) −0.706758 + 1.81529i −0.706758 + 1.81529i −0.142315 + 0.989821i \(0.545455\pi\)
−0.564443 + 0.825472i \(0.690909\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.35726 0.573583i 1.35726 0.573583i 0.415415 0.909632i \(-0.363636\pi\)
0.941844 + 0.336049i \(0.109091\pi\)
\(758\) 2.20882 1.41952i 2.20882 1.41952i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.985354 0.170522i \(-0.945455\pi\)
0.985354 + 0.170522i \(0.0545455\pi\)
\(762\) 0 0
\(763\) 0.0339888 + 0.395724i 0.0339888 + 0.395724i
\(764\) 1.71159 0.296203i 1.71159 0.296203i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.476274 1.81193i −0.476274 1.81193i
\(773\) 0 0 −0.198590 0.980083i \(-0.563636\pi\)
0.198590 + 0.980083i \(0.436364\pi\)
\(774\) −1.16747 + 2.21261i −1.16747 + 2.21261i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1.82990 + 1.88292i 1.82990 + 1.88292i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.481972 0.913438i −0.481972 0.913438i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.491798 + 0.932060i 0.491798 + 0.932060i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.993482 0.113991i \(-0.963636\pi\)
0.993482 + 0.113991i \(0.0363636\pi\)
\(788\) −1.59936 + 0.903199i −1.59936 + 0.903199i
\(789\) 0 0
\(790\) 0 0
\(791\) 0.825414 1.80741i 0.825414 1.80741i
\(792\) −0.0554812 0.0570888i −0.0554812 0.0570888i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.254218 0.967147i \(-0.418182\pi\)
−0.254218 + 0.967147i \(0.581818\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.275907 1.36166i −0.275907 1.36166i
\(801\) 0 0
\(802\) −0.228898 + 0.0672106i −0.228898 + 0.0672106i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.20341 + 0.208258i −1.20341 + 0.208258i −0.736741 0.676175i \(-0.763636\pi\)
−0.466667 + 0.884433i \(0.654545\pi\)
\(810\) 0 0
\(811\) 0 0 0.0855750 0.996332i \(-0.472727\pi\)
−0.0855750 + 0.996332i \(0.527273\pi\)
\(812\) 1.04882 + 0.181506i 1.04882 + 0.181506i
\(813\) 0 0
\(814\) 1.82461 + 1.32565i 1.82461 + 1.32565i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −0.799779 1.03717i −0.799779 1.03717i −0.998369 0.0570888i \(-0.981818\pi\)
0.198590 0.980083i \(-0.436364\pi\)
\(822\) 0 0
\(823\) −0.348845 + 0.510170i −0.348845 + 0.510170i −0.959493 0.281733i \(-0.909091\pi\)
0.610648 + 0.791902i \(0.290909\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −0.612107 0.561786i −0.612107 0.561786i 0.309017 0.951057i \(-0.400000\pi\)
−0.921124 + 0.389270i \(0.872727\pi\)
\(828\) 0.878595 0.0502399i 0.878595 0.0502399i
\(829\) 0 0 0.198590 0.980083i \(-0.436364\pi\)
−0.198590 + 0.980083i \(0.563636\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.941844 0.336049i \(-0.109091\pi\)
−0.941844 + 0.336049i \(0.890909\pi\)
\(840\) 0 0
\(841\) −0.202150 + 0.185532i −0.202150 + 0.185532i
\(842\) 1.37014 + 2.00377i 1.37014 + 2.00377i
\(843\) 0 0
\(844\) −0.130555 + 0.0948540i −0.130555 + 0.0948540i
\(845\) 0 0
\(846\) 0 0
\(847\) −0.654861 0.755750i −0.654861 0.755750i
\(848\) 0.535816 0.535816
\(849\) 0 0
\(850\) 0 0
\(851\) 1.47092 0.342048i 1.47092 0.342048i
\(852\) 0 0
\(853\) 0 0 0.736741 0.676175i \(-0.236364\pi\)
−0.736741 + 0.676175i \(0.763636\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.0178501 0.0549370i 0.0178501 0.0549370i
\(857\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(858\) 0 0
\(859\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −2.62134 0.935294i −2.62134 0.935294i
\(863\) −1.17534 + 0.577877i −1.17534 + 0.577877i −0.921124 0.389270i \(-0.872727\pi\)
−0.254218 + 0.967147i \(0.581818\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.20642 + 1.39228i 1.20642 + 1.39228i
\(870\) 0 0
\(871\) 0 0
\(872\) 0.0114714 0.0294641i 0.0114714 0.0294641i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.00595 + 0.233925i 1.00595 + 0.233925i 0.696938 0.717132i \(-0.254545\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(882\) −1.37346 0.237687i −1.37346 0.237687i
\(883\) 0.143981 1.67634i 0.143981 1.67634i −0.466667 0.884433i \(-0.654545\pi\)
0.610648 0.791902i \(-0.290909\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 2.53025 + 1.06929i 2.53025 + 1.06929i
\(887\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(888\) 0 0
\(889\) −0.0348754 + 1.22080i −0.0348754 + 1.22080i
\(890\) 0 0
\(891\) 0.993482 0.113991i 0.993482 0.113991i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −0.00453912 0.158890i −0.00453912 0.158890i
\(897\) 0 0
\(898\) −0.552718 0.0316055i −0.552718 0.0316055i
\(899\) 0 0
\(900\) 0.846146 + 0.416022i 0.846146 + 0.416022i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −0.122451 + 0.100128i −0.122451 + 0.100128i
\(905\) 0 0
\(906\) 0 0
\(907\) 1.97401 + 0.226497i 1.97401 + 0.226497i 1.00000 \(0\)
0.974012 + 0.226497i \(0.0727273\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.643180 0.525926i 0.643180 0.525926i −0.254218 0.967147i \(-0.581818\pi\)
0.897398 + 0.441221i \(0.145455\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.936901 2.05153i −0.936901 2.05153i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0.00163090 + 0.0570888i 0.00163090 + 0.0570888i 1.00000 \(0\)
−0.998369 + 0.0570888i \(0.981818\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.55249 + 0.455853i 1.55249 + 0.455853i
\(926\) 0.0586499 2.05301i 0.0586499 2.05301i
\(927\) 0 0
\(928\) −1.26886 0.921879i −1.26886 0.921879i
\(929\) 0 0 −0.921124 0.389270i \(-0.872727\pi\)
0.921124 + 0.389270i \(0.127273\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0.135758 1.58060i 0.135758 1.58060i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.921124 0.389270i \(-0.127273\pi\)
−0.921124 + 0.389270i \(0.872727\pi\)
\(938\) 2.10203 + 0.488806i 2.10203 + 0.488806i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 2.10458 1.35253i 2.10458 1.35253i
\(947\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.161197 + 0.0575149i 0.161197 + 0.0575149i 0.415415 0.909632i \(-0.363636\pi\)
−0.254218 + 0.967147i \(0.581818\pi\)
\(954\) −0.432764 + 0.561219i −0.432764 + 0.561219i
\(955\) 0 0
\(956\) −0.956003 + 1.10329i −0.956003 + 1.10329i
\(957\) 0 0
\(958\) 0 0
\(959\) 0.601972 1.85268i 0.601972 1.85268i
\(960\) 0 0
\(961\) 0.696938 0.717132i 0.696938 0.717132i
\(962\) 0 0
\(963\) 0.409569 + 0.598975i 0.409569 + 0.598975i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0.397181 0.397181 0.198590 0.980083i \(-0.436364\pi\)
0.198590 + 0.980083i \(0.436364\pi\)
\(968\) 0.0202376 + 0.0769918i 0.0202376 + 0.0769918i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −1.84312 + 1.69160i −1.84312 + 1.69160i
\(975\) 0 0
\(976\) 0 0
\(977\) −0.538151 + 1.65626i −0.538151 + 1.65626i 0.198590 + 0.980083i \(0.436364\pi\)
−0.736741 + 0.676175i \(0.763636\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0.205103 + 0.340126i 0.205103 + 0.340126i
\(982\) −0.242267 + 0.314178i −0.242267 + 0.314178i
\(983\) 0 0 −0.941844 0.336049i \(-0.890909\pi\)
0.941844 + 0.336049i \(0.109091\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.238398 1.65810i 0.238398 1.65810i
\(990\) 0 0
\(991\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0.879081 + 1.14001i 0.879081 + 1.14001i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.362808 0.931864i \(-0.618182\pi\)
0.362808 + 0.931864i \(0.381818\pi\)
\(998\) 0.839074 + 0.195118i 0.839074 + 0.195118i
\(999\) 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 847.1.bb.a.174.1 40
7.6 odd 2 CM 847.1.bb.a.174.1 40
121.16 even 55 inner 847.1.bb.a.258.1 yes 40
847.258 odd 110 inner 847.1.bb.a.258.1 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.1.bb.a.174.1 40 1.1 even 1 trivial
847.1.bb.a.174.1 40 7.6 odd 2 CM
847.1.bb.a.258.1 yes 40 121.16 even 55 inner
847.1.bb.a.258.1 yes 40 847.258 odd 110 inner