Properties

Label 3997.1.cz.a.237.1
Level $3997$
Weight $1$
Character 3997.237
Analytic conductor $1.995$
Analytic rank $0$
Dimension $144$
Projective image $D_{285}$
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] = [3997,1,Mod(13,3997)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3997, base_ring=CyclotomicField(570))
 
chi = DirichletCharacter(H, H._module([285, 352]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3997.13");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3997 = 7 \cdot 571 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3997.cz (of order \(570\), degree \(144\), 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: \(1.99476285549\)
Analytic rank: \(0\)
Dimension: \(144\)
Coefficient field: \(\Q(\zeta_{570})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{144} - x^{143} + x^{142} + x^{139} - x^{138} + x^{137} - x^{129} + x^{128} - x^{127} + x^{125} - 2 x^{124} + 2 x^{123} - x^{122} + x^{120} - x^{119} + x^{118} + x^{114} - x^{113} + x^{112} - x^{110} + 2 x^{109} - 2 x^{108} + x^{107} - x^{105} + x^{104} - x^{103} - x^{99} + x^{98} - x^{97} + x^{95} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{285}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{285} - \cdots)\)

Embedding invariants

Embedding label 237.1
Root \(-0.840168 - 0.542326i\) of defining polynomial
Character \(\chi\) \(=\) 3997.237
Dual form 3997.1.cz.a.3373.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.579560 + 1.85296i) q^{2} +(-2.27578 - 1.57799i) q^{4} +(-0.995083 + 0.0990455i) q^{7} +(2.71079 - 2.10989i) q^{8} +(0.938430 + 0.345471i) q^{9} +O(q^{10})\) \(q+(-0.579560 + 1.85296i) q^{2} +(-2.27578 - 1.57799i) q^{4} +(-0.995083 + 0.0990455i) q^{7} +(2.71079 - 2.10989i) q^{8} +(0.938430 + 0.345471i) q^{9} +(-0.0109101 - 0.00157421i) q^{11} +(0.393183 - 1.90125i) q^{14} +(1.36744 + 3.65228i) q^{16} +(-1.18402 + 1.53865i) q^{18} +(0.00924000 - 0.0193036i) q^{22} +(0.154936 - 0.104921i) q^{23} +(-0.360939 - 0.932589i) q^{25} +(2.42088 + 1.34482i) q^{28} +(-1.47171 - 1.28171i) q^{29} +(-4.13011 + 0.227865i) q^{32} +(-1.59051 - 2.26704i) q^{36} +(0.611104 - 1.31367i) q^{37} +(-0.0629058 - 1.62968i) q^{43} +(0.0223448 + 0.0207986i) q^{44} +(0.104618 + 0.347898i) q^{46} +(0.980380 - 0.197117i) q^{49} +(1.93723 - 0.128313i) q^{50} +(-0.272892 - 0.202901i) q^{53} +(-2.48849 + 2.36801i) q^{56} +(3.22790 - 1.98418i) q^{58} +(-0.968033 - 0.250825i) q^{63} +(1.01406 - 4.00444i) q^{64} +(0.548057 - 0.236807i) q^{67} +(1.33534 + 1.48304i) q^{71} +(3.27279 - 1.04349i) q^{72} +(2.07999 + 1.89370i) q^{74} +(0.0110124 + 0.000485878i) q^{77} +(-0.882997 + 0.938222i) q^{79} +(0.761300 + 0.648400i) q^{81} +(3.05618 + 0.827935i) q^{86} +(-0.0328964 + 0.0187518i) q^{88} +(-0.518164 - 0.00571202i) q^{92} +(-0.202940 + 1.93084i) q^{98} +(-0.00969451 - 0.00524640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9} + 6 q^{11} + q^{14} + 6 q^{16} - 9 q^{18} + 21 q^{22} + 3 q^{23} - q^{25} - 10 q^{28} - 4 q^{29} - 5 q^{32} - 2 q^{37} - 9 q^{43} - 20 q^{44} - 34 q^{46} + 2 q^{49} - 2 q^{50} + 6 q^{53} - 8 q^{56} - q^{58} - q^{63} + 11 q^{64} + 20 q^{67} + 3 q^{71} + 23 q^{72} - 31 q^{74} + q^{77} + 6 q^{79} - q^{81} + 7 q^{86} - 9 q^{88} + 9 q^{92} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times\).

\(n\) \(1716\) \(2285\)
\(\chi(n)\) \(e\left(\frac{16}{285}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.579560 + 1.85296i −0.579560 + 1.85296i −0.0605901 + 0.998163i \(0.519298\pi\)
−0.518970 + 0.854793i \(0.673684\pi\)
\(3\) 0 0 −0.984487 0.175457i \(-0.943860\pi\)
0.984487 + 0.175457i \(0.0561404\pi\)
\(4\) −2.27578 1.57799i −2.27578 1.57799i
\(5\) 0 0 0.565270 0.824906i \(-0.308772\pi\)
−0.565270 + 0.824906i \(0.691228\pi\)
\(6\) 0 0
\(7\) −0.995083 + 0.0990455i −0.995083 + 0.0990455i
\(8\) 2.71079 2.10989i 2.71079 2.10989i
\(9\) 0.938430 + 0.345471i 0.938430 + 0.345471i
\(10\) 0 0
\(11\) −0.0109101 0.00157421i −0.0109101 0.00157421i 0.137354 0.990522i \(-0.456140\pi\)
−0.148264 + 0.988948i \(0.547368\pi\)
\(12\) 0 0
\(13\) 0 0 0.731980 0.681326i \(-0.238596\pi\)
−0.731980 + 0.681326i \(0.761404\pi\)
\(14\) 0.393183 1.90125i 0.393183 1.90125i
\(15\) 0 0
\(16\) 1.36744 + 3.65228i 1.36744 + 3.65228i
\(17\) 0 0 −0.834139 0.551554i \(-0.814035\pi\)
0.834139 + 0.551554i \(0.185965\pi\)
\(18\) −1.18402 + 1.53865i −1.18402 + 1.53865i
\(19\) 0 0 0.471093 0.882084i \(-0.343860\pi\)
−0.471093 + 0.882084i \(0.656140\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.00924000 0.0193036i 0.00924000 0.0193036i
\(23\) 0.154936 0.104921i 0.154936 0.104921i −0.480787 0.876837i \(-0.659649\pi\)
0.635724 + 0.771917i \(0.280702\pi\)
\(24\) 0 0
\(25\) −0.360939 0.932589i −0.360939 0.932589i
\(26\) 0 0
\(27\) 0 0
\(28\) 2.42088 + 1.34482i 2.42088 + 1.34482i
\(29\) −1.47171 1.28171i −1.47171 1.28171i −0.879474 0.475947i \(-0.842105\pi\)
−0.592235 0.805765i \(-0.701754\pi\)
\(30\) 0 0
\(31\) 0 0 −0.986361 0.164595i \(-0.947368\pi\)
0.986361 + 0.164595i \(0.0526316\pi\)
\(32\) −4.13011 + 0.227865i −4.13011 + 0.227865i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1.59051 2.26704i −1.59051 2.26704i
\(37\) 0.611104 1.31367i 0.611104 1.31367i −0.319482 0.947592i \(-0.603509\pi\)
0.930586 0.366074i \(-0.119298\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.0275543 0.999620i \(-0.508772\pi\)
0.0275543 + 0.999620i \(0.491228\pi\)
\(42\) 0 0
\(43\) −0.0629058 1.62968i −0.0629058 1.62968i −0.609854 0.792514i \(-0.708772\pi\)
0.546948 0.837166i \(-0.315789\pi\)
\(44\) 0.0223448 + 0.0207986i 0.0223448 + 0.0207986i
\(45\) 0 0
\(46\) 0.104618 + 0.347898i 0.104618 + 0.347898i
\(47\) 0 0 0.635724 0.771917i \(-0.280702\pi\)
−0.635724 + 0.771917i \(0.719298\pi\)
\(48\) 0 0
\(49\) 0.980380 0.197117i 0.980380 0.197117i
\(50\) 1.93723 0.128313i 1.93723 0.128313i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.272892 0.202901i −0.272892 0.202901i 0.451533 0.892254i \(-0.350877\pi\)
−0.724425 + 0.689353i \(0.757895\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.48849 + 2.36801i −2.48849 + 2.36801i
\(57\) 0 0
\(58\) 3.22790 1.98418i 3.22790 1.98418i
\(59\) 0 0 −0.401695 0.915773i \(-0.631579\pi\)
0.401695 + 0.915773i \(0.368421\pi\)
\(60\) 0 0
\(61\) 0 0 0.0935596 0.995614i \(-0.470175\pi\)
−0.0935596 + 0.995614i \(0.529825\pi\)
\(62\) 0 0
\(63\) −0.968033 0.250825i −0.968033 0.250825i
\(64\) 1.01406 4.00444i 1.01406 4.00444i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.548057 0.236807i 0.548057 0.236807i −0.104528 0.994522i \(-0.533333\pi\)
0.652586 + 0.757715i \(0.273684\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.33534 + 1.48304i 1.33534 + 1.48304i 0.716783 + 0.697297i \(0.245614\pi\)
0.618553 + 0.785743i \(0.287719\pi\)
\(72\) 3.27279 1.04349i 3.27279 1.04349i
\(73\) 0 0 0.996114 0.0880708i \(-0.0280702\pi\)
−0.996114 + 0.0880708i \(0.971930\pi\)
\(74\) 2.07999 + 1.89370i 2.07999 + 1.89370i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.0110124 0.000485878i 0.0110124 0.000485878i
\(78\) 0 0
\(79\) −0.882997 + 0.938222i −0.882997 + 0.938222i −0.998482 0.0550878i \(-0.982456\pi\)
0.115485 + 0.993309i \(0.463158\pi\)
\(80\) 0 0
\(81\) 0.761300 + 0.648400i 0.761300 + 0.648400i
\(82\) 0 0
\(83\) 0 0 −0.537687 0.843145i \(-0.680702\pi\)
0.537687 + 0.843145i \(0.319298\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 3.05618 + 0.827935i 3.05618 + 0.827935i
\(87\) 0 0
\(88\) −0.0328964 + 0.0187518i −0.0328964 + 0.0187518i
\(89\) 0 0 0.999028 0.0440782i \(-0.0140351\pi\)
−0.999028 + 0.0440782i \(0.985965\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.518164 0.00571202i −0.518164 0.00571202i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.329907 0.944013i \(-0.607018\pi\)
0.329907 + 0.944013i \(0.392982\pi\)
\(98\) −0.202940 + 1.93084i −0.202940 + 1.93084i
\(99\) −0.00969451 0.00524640i −0.00969451 0.00524640i
\(100\) −0.650198 + 2.69192i −0.650198 + 2.69192i
\(101\) 0 0 −0.999757 0.0220445i \(-0.992982\pi\)
0.999757 + 0.0220445i \(0.00701754\pi\)
\(102\) 0 0
\(103\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.534123 0.388063i 0.534123 0.388063i
\(107\) 0.605380 1.61690i 0.605380 1.61690i −0.170028 0.985439i \(-0.554386\pi\)
0.775409 0.631460i \(-0.217544\pi\)
\(108\) 0 0
\(109\) 0.909007 1.57445i 0.909007 1.57445i 0.0935596 0.995614i \(-0.470175\pi\)
0.815447 0.578832i \(-0.196491\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.72246 3.49888i −1.72246 3.49888i
\(113\) 1.65603 0.201791i 1.65603 0.201791i 0.761300 0.648400i \(-0.224561\pi\)
0.894729 + 0.446609i \(0.147368\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.32675 + 5.23923i 1.32675 + 5.23923i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.959094 0.282660i −0.959094 0.282660i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 1.02580 1.64835i 1.02580 1.64835i
\(127\) −1.17712 + 0.433342i −1.17712 + 0.433342i −0.857640 0.514250i \(-0.828070\pi\)
−0.319482 + 0.947592i \(0.603509\pi\)
\(128\) 3.30846 + 2.03371i 3.30846 + 2.03371i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.0825793 0.996584i \(-0.473684\pi\)
−0.0825793 + 0.996584i \(0.526316\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.121161 + 1.15277i 0.121161 + 1.15277i
\(135\) 0 0
\(136\) 0 0
\(137\) −0.146193 + 0.377731i −0.146193 + 0.377731i −0.986361 0.164595i \(-0.947368\pi\)
0.840168 + 0.542326i \(0.182456\pi\)
\(138\) 0 0
\(139\) 0 0 0.170028 0.985439i \(-0.445614\pi\)
−0.170028 + 0.985439i \(0.554386\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.52191 + 1.61481i −3.52191 + 1.61481i
\(143\) 0 0
\(144\) 0.0214943 + 3.89981i 0.0214943 + 3.89981i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −3.46369 + 2.02530i −3.46369 + 2.02530i
\(149\) 1.05277 + 0.712920i 1.05277 + 0.712920i 0.959210 0.282694i \(-0.0912281\pi\)
0.0935596 + 0.995614i \(0.470175\pi\)
\(150\) 0 0
\(151\) −0.200530 + 0.0590991i −0.200530 + 0.0590991i −0.381410 0.924406i \(-0.624561\pi\)
0.180881 + 0.983505i \(0.442105\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.00728263 + 0.0201238i −0.00728263 + 0.0201238i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.0605901 0.998163i \(-0.480702\pi\)
−0.0605901 + 0.998163i \(0.519298\pi\)
\(158\) −1.22673 2.17991i −1.22673 2.17991i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.143783 + 0.119750i −0.143783 + 0.119750i
\(162\) −1.64267 + 1.03487i −1.64267 + 1.03487i
\(163\) 1.68387 + 0.167604i 1.68387 + 0.167604i 0.894729 0.446609i \(-0.147368\pi\)
0.789141 + 0.614213i \(0.210526\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(168\) 0 0
\(169\) 0.0715891 0.997434i 0.0715891 0.997434i
\(170\) 0 0
\(171\) 0 0
\(172\) −2.42846 + 3.80805i −2.42846 + 3.80805i
\(173\) 0 0 0.949339 0.314254i \(-0.101754\pi\)
−0.949339 + 0.314254i \(0.898246\pi\)
\(174\) 0 0
\(175\) 0.451533 + 0.892254i 0.451533 + 0.892254i
\(176\) −0.00916945 0.0419993i −0.00916945 0.0419993i
\(177\) 0 0
\(178\) 0 0
\(179\) 0.511075 0.593407i 0.511075 0.593407i −0.441671 0.897177i \(-0.645614\pi\)
0.952745 + 0.303771i \(0.0982456\pi\)
\(180\) 0 0
\(181\) 0 0 −0.945817 0.324699i \(-0.894737\pi\)
0.945817 + 0.324699i \(0.105263\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.198629 0.611317i 0.198629 0.611317i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.249849 + 1.96037i −0.249849 + 1.96037i 0.0275543 + 0.999620i \(0.491228\pi\)
−0.277403 + 0.960754i \(0.589474\pi\)
\(192\) 0 0
\(193\) 1.33696 1.48485i 1.33696 1.48485i 0.635724 0.771917i \(-0.280702\pi\)
0.701237 0.712928i \(-0.252632\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −2.54217 1.09843i −2.54217 1.09843i
\(197\) 1.57458 0.944136i 1.57458 0.944136i 0.583317 0.812244i \(-0.301754\pi\)
0.991264 0.131892i \(-0.0421053\pi\)
\(198\) 0.0153399 0.0149229i 0.0153399 0.0149229i
\(199\) 0 0 −0.583317 0.812244i \(-0.698246\pi\)
0.583317 + 0.812244i \(0.301754\pi\)
\(200\) −2.94610 1.76651i −2.94610 1.76651i
\(201\) 0 0
\(202\) 0 0
\(203\) 1.59142 + 1.12964i 1.59142 + 1.12964i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.181644 0.0449346i 0.181644 0.0449346i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.276911 + 0.920840i −0.276911 + 0.920840i 0.701237 + 0.712928i \(0.252632\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(212\) 0.300866 + 0.892377i 0.300866 + 0.892377i
\(213\) 0 0
\(214\) 2.64519 + 2.05883i 2.64519 + 2.05883i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 2.39055 + 2.59683i 2.39055 + 2.59683i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.0715891 0.997434i \(-0.522807\pi\)
0.0715891 + 0.997434i \(0.477193\pi\)
\(224\) 4.08724 0.635814i 4.08724 0.635814i
\(225\) −0.0165339 0.999863i −0.0165339 0.999863i
\(226\) −0.585858 + 3.18550i −0.585858 + 3.18550i
\(227\) 0 0 −0.644194 0.764862i \(-0.722807\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(228\) 0 0
\(229\) 0 0 −0.411766 0.911290i \(-0.635088\pi\)
0.411766 + 0.911290i \(0.364912\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.69378 0.369306i −6.69378 0.369306i
\(233\) −1.73938 0.684239i −1.73938 0.684239i −0.999939 0.0110229i \(-0.996491\pi\)
−0.739446 0.673216i \(-0.764912\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.0147891 0.383136i 0.0147891 0.383136i −0.973327 0.229424i \(-0.926316\pi\)
0.988116 0.153712i \(-0.0491228\pi\)
\(240\) 0 0
\(241\) 0 0 −0.340293 0.940319i \(-0.610526\pi\)
0.340293 + 0.940319i \(0.389474\pi\)
\(242\) 1.07961 1.61334i 1.07961 1.61334i
\(243\) 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 −0.660898 0.750475i \(-0.729825\pi\)
0.660898 + 0.750475i \(0.270175\pi\)
\(252\) 1.80723 + 2.09837i 1.80723 + 2.09837i
\(253\) −0.00185554 0.000900790i −0.00185554 0.000900790i
\(254\) −0.120751 2.43230i −0.120751 2.43230i
\(255\) 0 0
\(256\) −2.57072 + 2.23884i −2.57072 + 2.23884i
\(257\) 0 0 −0.934564 0.355794i \(-0.884211\pi\)
0.934564 + 0.355794i \(0.115789\pi\)
\(258\) 0 0
\(259\) −0.477987 + 1.36773i −0.477987 + 1.36773i
\(260\) 0 0
\(261\) −0.938301 1.71123i −0.938301 1.71123i
\(262\) 0 0
\(263\) −0.956756 0.727881i −0.956756 0.727881i 0.00551154 0.999985i \(-0.498246\pi\)
−0.962268 + 0.272103i \(0.912281\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −1.62093 0.325908i −1.62093 0.325908i
\(269\) 0 0 0.0165339 0.999863i \(-0.494737\pi\)
−0.0165339 + 0.999863i \(0.505263\pi\)
\(270\) 0 0
\(271\) 0 0 0.401695 0.915773i \(-0.368421\pi\)
−0.401695 + 0.915773i \(0.631579\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.615191 0.489807i −0.615191 0.489807i
\(275\) 0.00246979 + 0.0107428i 0.00246979 + 0.0107428i
\(276\) 0 0
\(277\) 0.188797 0.653876i 0.188797 0.653876i −0.809017 0.587785i \(-0.800000\pi\)
0.997814 0.0660906i \(-0.0210526\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.0285579 0.575244i 0.0285579 0.575244i −0.942181 0.335105i \(-0.891228\pi\)
0.970739 0.240139i \(-0.0771930\pi\)
\(282\) 0 0
\(283\) 0 0 −0.956036 0.293250i \(-0.905263\pi\)
0.956036 + 0.293250i \(0.0947368\pi\)
\(284\) −0.698705 5.48221i −0.698705 5.48221i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −3.95454 1.21300i −3.95454 1.21300i
\(289\) 0.391577 + 0.920146i 0.391577 + 0.920146i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.889752 0.456444i \(-0.849123\pi\)
0.889752 + 0.456444i \(0.150877\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.11512 4.85044i −1.11512 4.85044i
\(297\) 0 0
\(298\) −1.93115 + 1.53756i −1.93115 + 1.53756i
\(299\) 0 0
\(300\) 0 0
\(301\) 0.224009 + 1.61544i 0.224009 + 1.61544i
\(302\) 0.00671078 0.405824i 0.00671078 0.405824i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.942181 0.335105i \(-0.108772\pi\)
−0.942181 + 0.335105i \(0.891228\pi\)
\(308\) −0.0242950 0.0184831i −0.0242950 0.0184831i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.441671 0.897177i \(-0.354386\pi\)
−0.441671 + 0.897177i \(0.645614\pi\)
\(312\) 0 0
\(313\) 0 0 −0.904357 0.426776i \(-0.859649\pi\)
0.904357 + 0.426776i \(0.140351\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 3.49001 0.741824i 3.49001 0.741824i
\(317\) 0.0505274 + 1.01778i 0.0505274 + 1.01778i 0.884667 + 0.466224i \(0.154386\pi\)
−0.834139 + 0.551554i \(0.814035\pi\)
\(318\) 0 0
\(319\) 0.0140388 + 0.0163004i 0.0140388 + 0.0163004i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.138562 0.335825i −0.138562 0.335825i
\(323\) 0 0
\(324\) −0.709382 2.67694i −0.709382 2.67694i
\(325\) 0 0
\(326\) −1.28647 + 3.02300i −1.28647 + 3.02300i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.82609 0.813029i −1.82609 0.813029i −0.926494 0.376309i \(-0.877193\pi\)
−0.899598 0.436719i \(-0.856140\pi\)
\(332\) 0 0
\(333\) 1.02731 1.02166i 1.02731 1.02166i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.181137 1.92757i −0.181137 1.92757i −0.340293 0.940319i \(-0.610526\pi\)
0.159156 0.987253i \(-0.449123\pi\)
\(338\) 1.80671 + 0.710724i 1.80671 + 0.710724i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.956036 + 0.293250i −0.956036 + 0.293250i
\(344\) −3.60898 4.28500i −3.60898 4.28500i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.55952 0.242601i 1.55952 0.242601i 0.685350 0.728214i \(-0.259649\pi\)
0.874174 + 0.485613i \(0.161404\pi\)
\(348\) 0 0
\(349\) 0 0 −0.609854 0.792514i \(-0.708772\pi\)
0.609854 + 0.792514i \(0.291228\pi\)
\(350\) −1.91500 + 0.319557i −1.91500 + 0.319557i
\(351\) 0 0
\(352\) 0.0454186 + 0.00401566i 0.0454186 + 0.00401566i
\(353\) 0 0 −0.677282 0.735724i \(-0.736842\pi\)
0.677282 + 0.735724i \(0.263158\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.803358 + 1.29091i 0.803358 + 1.29091i
\(359\) −0.313363 0.929443i −0.313363 0.929443i −0.982493 0.186298i \(-0.940351\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(360\) 0 0
\(361\) −0.556143 0.831087i −0.556143 0.831087i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.202517 0.979279i \(-0.564912\pi\)
0.202517 + 0.979279i \(0.435088\pi\)
\(368\) 0.595065 + 0.422397i 0.595065 + 0.422397i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.291646 + 0.174874i 0.291646 + 0.174874i
\(372\) 0 0
\(373\) −0.397675 + 0.386864i −0.397675 + 0.386864i −0.868768 0.495219i \(-0.835088\pi\)
0.471093 + 0.882084i \(0.343860\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.781810 + 1.73025i −0.781810 + 1.73025i −0.104528 + 0.994522i \(0.533333\pi\)
−0.677282 + 0.735724i \(0.736842\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −3.48768 1.59911i −3.48768 1.59911i
\(383\) 0 0 0.962268 0.272103i \(-0.0877193\pi\)
−0.962268 + 0.272103i \(0.912281\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.97650 + 3.33788i 1.97650 + 3.33788i
\(387\) 0.503974 1.55107i 0.503974 1.55107i
\(388\) 0 0
\(389\) 0.923508 + 1.52111i 0.923508 + 1.52111i 0.851919 + 0.523673i \(0.175439\pi\)
0.0715891 + 0.997434i \(0.477193\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 2.24171 2.60284i 2.24171 2.60284i
\(393\) 0 0
\(394\) 0.836879 + 3.46481i 0.836879 + 3.46481i
\(395\) 0 0
\(396\) 0.0137838 + 0.0272375i 0.0137838 + 0.0272375i
\(397\) 0 0 0.930586 0.366074i \(-0.119298\pi\)
−0.930586 + 0.366074i \(0.880702\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 2.91251 2.59351i 2.91251 2.59351i
\(401\) −0.149362 1.80254i −0.149362 1.80254i −0.500000 0.866025i \(-0.666667\pi\)
0.350638 0.936511i \(-0.385965\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −3.01550 + 2.29413i −3.01550 + 2.29413i
\(407\) −0.00873519 + 0.0133702i −0.00873519 + 0.0133702i
\(408\) 0 0
\(409\) 0 0 0.846095 0.533032i \(-0.178947\pi\)
−0.846095 + 0.533032i \(0.821053\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.0220116 + 0.362620i −0.0220116 + 0.362620i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.170028 0.985439i \(-0.554386\pi\)
0.170028 + 0.985439i \(0.445614\pi\)
\(420\) 0 0
\(421\) −1.70487 0.188695i −1.70487 0.188695i −0.795863 0.605477i \(-0.792982\pi\)
−0.909007 + 0.416782i \(0.863158\pi\)
\(422\) −1.54579 1.04679i −1.54579 1.04679i
\(423\) 0 0
\(424\) −1.16785 + 0.0257510i −1.16785 + 0.0257510i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −3.92916 + 2.72442i −3.92916 + 2.72442i
\(429\) 0 0
\(430\) 0 0
\(431\) −1.60979 + 0.803537i −1.60979 + 0.803537i −0.609854 + 0.792514i \(0.708772\pi\)
−0.999939 + 0.0110229i \(0.996491\pi\)
\(432\) 0 0
\(433\) 0 0 −0.115485 0.993309i \(-0.536842\pi\)
0.115485 + 0.993309i \(0.463158\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.55315 + 2.14868i −4.55315 + 2.14868i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.601081 0.799188i \(-0.705263\pi\)
0.601081 + 0.799188i \(0.294737\pi\)
\(440\) 0 0
\(441\) 0.988116 + 0.153712i 0.988116 + 0.153712i
\(442\) 0 0
\(443\) −1.00907 0.620275i −1.00907 0.620275i −0.0825793 0.996584i \(-0.526316\pi\)
−0.926494 + 0.376309i \(0.877193\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.612454 + 4.08519i −0.612454 + 4.08519i
\(449\) 0.492126 + 0.206233i 0.492126 + 0.206233i 0.618553 0.785743i \(-0.287719\pi\)
−0.126427 + 0.991976i \(0.540351\pi\)
\(450\) 1.86228 + 0.548844i 1.86228 + 0.548844i
\(451\) 0 0
\(452\) −4.08718 2.15396i −4.08718 2.15396i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.204493 + 0.298419i 0.204493 + 0.298419i 0.913545 0.406737i \(-0.133333\pi\)
−0.709053 + 0.705155i \(0.750877\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) −0.718655 1.54486i −0.718655 1.54486i −0.834139 0.551554i \(-0.814035\pi\)
0.115485 0.993309i \(-0.463158\pi\)
\(464\) 2.66869 7.12775i 2.66869 7.12775i
\(465\) 0 0
\(466\) 2.27594 2.82645i 2.27594 2.82645i
\(467\) 0 0 0.159156 0.987253i \(-0.449123\pi\)
−0.159156 + 0.987253i \(0.550877\pi\)
\(468\) 0 0
\(469\) −0.521908 + 0.289925i −0.521908 + 0.289925i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.00187916 + 0.0178790i −0.00187916 + 0.0178790i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.185994 0.284684i −0.185994 0.284684i
\(478\) 0.701363 + 0.249454i 0.701363 + 0.249454i
\(479\) 0 0 −0.999939 0.0110229i \(-0.996491\pi\)
0.999939 + 0.0110229i \(0.00350877\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.73665 + 2.15671i 1.73665 + 2.15671i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.28409 + 1.04571i 1.28409 + 1.04571i 0.996114 + 0.0880708i \(0.0280702\pi\)
0.287976 + 0.957638i \(0.407018\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.92452 + 0.476082i 1.92452 + 0.476082i 0.993931 + 0.110008i \(0.0350877\pi\)
0.930586 + 0.366074i \(0.119298\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.47566 1.34349i −1.47566 1.34349i
\(498\) 0 0
\(499\) −1.40901 + 0.449244i −1.40901 + 0.449244i −0.909007 0.416782i \(-0.863158\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.371197 0.928554i \(-0.621053\pi\)
0.371197 + 0.928554i \(0.378947\pi\)
\(504\) −3.15335 + 1.36251i −3.15335 + 1.36251i
\(505\) 0 0
\(506\) −0.000593729 0.00396029i −0.000593729 0.00396029i
\(507\) 0 0
\(508\) 3.36267 + 0.871295i 3.36267 + 0.871295i
\(509\) 0 0 0.451533 0.892254i \(-0.350877\pi\)
−0.451533 + 0.892254i \(0.649123\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.09859 2.50453i −1.09859 2.50453i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −2.25733 1.67837i −2.25733 1.67837i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.997814 0.0660906i \(-0.0210526\pi\)
−0.997814 + 0.0660906i \(0.978947\pi\)
\(522\) 3.71463 0.746871i 3.71463 0.746871i
\(523\) 0 0 −0.180881 0.983505i \(-0.557895\pi\)
0.180881 + 0.983505i \(0.442105\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.90323 1.35098i 1.90323 1.35098i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.358200 + 0.896042i −0.358200 + 0.896042i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.986032 1.79828i 0.986032 1.79828i
\(537\) 0 0
\(538\) 0 0
\(539\) −0.0110063 0.000607237i −0.0110063 0.000607237i
\(540\) 0 0
\(541\) −0.940755 1.76149i −0.940755 1.76149i −0.518970 0.854793i \(-0.673684\pi\)
−0.421786 0.906696i \(-0.638596\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.43142 + 0.754366i −1.43142 + 0.754366i −0.989750 0.142811i \(-0.954386\pi\)
−0.441671 + 0.897177i \(0.645614\pi\)
\(548\) 0.928758 0.628941i 0.928758 0.628941i
\(549\) 0 0
\(550\) −0.0213374 0.00164971i −0.0213374 0.00164971i
\(551\) 0 0
\(552\) 0 0
\(553\) 0.785728 1.02107i 0.785728 1.02107i
\(554\) 1.10218 + 0.728792i 1.10218 + 0.728792i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.129401 + 0.625723i −0.129401 + 0.625723i 0.863256 + 0.504766i \(0.168421\pi\)
−0.992658 + 0.120958i \(0.961404\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 1.04935 + 0.386305i 1.04935 + 0.386305i
\(563\) 0 0 0.789141 0.614213i \(-0.210526\pi\)
−0.789141 + 0.614213i \(0.789474\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.821778 0.569808i −0.821778 0.569808i
\(568\) 6.74887 + 1.20280i 6.74887 + 1.20280i
\(569\) −0.501605 + 1.60372i −0.501605 + 1.60372i 0.266796 + 0.963753i \(0.414035\pi\)
−0.768401 + 0.639969i \(0.778947\pi\)
\(570\) 0 0
\(571\) 0.350638 + 0.936511i 0.350638 + 0.936511i
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.153770 0.106622i −0.153770 0.106622i
\(576\) 2.33504 3.40756i 2.33504 3.40756i
\(577\) 0 0 0.461341 0.887223i \(-0.347368\pi\)
−0.461341 + 0.887223i \(0.652632\pi\)
\(578\) −1.93193 + 0.192295i −1.93193 + 0.192295i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.00265787 + 0.00264326i 0.00265787 + 0.00264326i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.350638 0.936511i \(-0.614035\pi\)
0.350638 + 0.936511i \(0.385965\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 5.63352 + 0.435558i 5.63352 + 0.435558i
\(593\) 0 0 0.431754 0.901991i \(-0.357895\pi\)
−0.431754 + 0.901991i \(0.642105\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.27089 3.28370i −1.27089 3.28370i
\(597\) 0 0
\(598\) 0 0
\(599\) 1.08145 + 0.600754i 1.08145 + 0.600754i 0.922290 0.386499i \(-0.126316\pi\)
0.159156 + 0.987253i \(0.449123\pi\)
\(600\) 0 0
\(601\) 0 0 −0.471093 0.882084i \(-0.656140\pi\)
0.471093 + 0.882084i \(0.343860\pi\)
\(602\) −3.12316 0.521163i −3.12316 0.521163i
\(603\) 0.596123 0.0328890i 0.596123 0.0328890i
\(604\) 0.549618 + 0.181937i 0.549618 + 0.181937i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.574329 0.818625i \(-0.694737\pi\)
0.574329 + 0.818625i \(0.305263\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.385280 + 0.963783i −0.385280 + 0.963783i 0.601081 + 0.799188i \(0.294737\pi\)
−0.986361 + 0.164595i \(0.947368\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.0308774 0.0219178i 0.0308774 0.0219178i
\(617\) −0.207884 0.691298i −0.207884 0.691298i −0.997024 0.0770854i \(-0.975439\pi\)
0.789141 0.614213i \(-0.210526\pi\)
\(618\) 0 0
\(619\) 0 0 −0.180881 0.983505i \(-0.557895\pi\)
0.180881 + 0.983505i \(0.442105\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.739446 + 0.673216i −0.739446 + 0.673216i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.809114 + 0.153423i −0.809114 + 0.153423i −0.574329 0.818625i \(-0.694737\pi\)
−0.234785 + 0.972047i \(0.575439\pi\)
\(632\) −0.414073 + 4.40635i −0.414073 + 4.40635i
\(633\) 0 0
\(634\) −1.91518 0.496238i −1.91518 0.496238i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.0383402 + 0.0165662i −0.0383402 + 0.0165662i
\(639\) 0.740771 + 1.85305i 0.740771 + 1.85305i
\(640\) 0 0
\(641\) 1.28474 + 1.33529i 1.28474 + 1.33529i 0.913545 + 0.406737i \(0.133333\pi\)
0.371197 + 0.928554i \(0.378947\pi\)
\(642\) 0 0
\(643\) 0 0 0.952745 0.303771i \(-0.0982456\pi\)
−0.952745 + 0.303771i \(0.901754\pi\)
\(644\) 0.516182 0.0456379i 0.516182 0.0456379i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.889752 0.456444i \(-0.150877\pi\)
−0.889752 + 0.456444i \(0.849123\pi\)
\(648\) 3.43178 + 0.151414i 3.43178 + 0.151414i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −3.56763 3.03856i −3.56763 3.03856i
\(653\) 0.492982 + 0.139402i 0.492982 + 0.139402i 0.509516 0.860461i \(-0.329825\pi\)
−0.0165339 + 0.999863i \(0.505263\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.28481 0.732375i 1.28481 0.732375i 0.309017 0.951057i \(-0.400000\pi\)
0.975796 + 0.218681i \(0.0701754\pi\)
\(660\) 0 0
\(661\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(662\) 2.56483 2.91247i 2.56483 2.91247i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.29771 + 2.49568i 1.29771 + 2.49568i
\(667\) −0.362499 0.0441713i −0.362499 0.0441713i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.25319 0.696158i 1.25319 0.696158i 0.287976 0.957638i \(-0.407018\pi\)
0.965209 + 0.261480i \(0.0842105\pi\)
\(674\) 3.67669 + 0.781504i 3.67669 + 0.781504i
\(675\) 0 0
\(676\) −1.73686 + 2.15697i −1.73686 + 2.15697i
\(677\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.121330 0.246461i −0.121330 0.246461i 0.828009 0.560715i \(-0.189474\pi\)
−0.949339 + 0.314254i \(0.898246\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.0107005 1.94145i 0.0107005 1.94145i
\(687\) 0 0
\(688\) 5.86602 2.45824i 5.86602 2.45824i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.115485 0.993309i \(-0.463158\pi\)
−0.115485 + 0.993309i \(0.536842\pi\)
\(692\) 0 0
\(693\) 0.0101665 + 0.00426041i 0.0101665 + 0.00426041i
\(694\) −0.454309 + 3.03033i −0.454309 + 3.03033i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.380378 2.74309i 0.380378 2.74309i
\(701\) 1.66037 + 0.258288i 1.66037 + 0.258288i 0.913545 0.406737i \(-0.133333\pi\)
0.746821 + 0.665025i \(0.231579\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.0173674 + 0.0420925i −0.0173674 + 0.0420925i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.163769 1.40862i −0.163769 1.40862i −0.782322 0.622874i \(-0.785965\pi\)
0.618553 0.785743i \(-0.287719\pi\)
\(710\) 0 0
\(711\) −1.15276 + 0.575405i −1.15276 + 0.575405i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −2.09948 + 0.543991i −2.09948 + 0.543991i
\(717\) 0 0
\(718\) 1.90383 0.0419791i 1.90383 0.0419791i
\(719\) 0 0 0.863256 0.504766i \(-0.168421\pi\)
−0.863256 + 0.504766i \(0.831579\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.86228 0.548844i 1.86228 0.548844i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.664114 + 1.83512i −0.664114 + 1.83512i
\(726\) 0 0
\(727\) 0 0 −0.999453 0.0330634i \(-0.989474\pi\)
0.999453 + 0.0330634i \(0.0105263\pi\)
\(728\) 0 0
\(729\) 0.490424 + 0.871484i 0.490424 + 0.871484i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.846095 0.533032i \(-0.178947\pi\)
−0.846095 + 0.533032i \(0.821053\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.615997 + 0.468638i −0.615997 + 0.468638i
\(737\) −0.00635214 + 0.00172083i −0.00635214 + 0.00172083i
\(738\) 0 0
\(739\) 1.25806 0.831861i 1.25806 0.831861i 0.266796 0.963753i \(-0.414035\pi\)
0.991264 + 0.131892i \(0.0421053\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.493061 + 0.439058i −0.493061 + 0.439058i
\(743\) 1.04669 1.64131i 1.04669 1.64131i 0.329907 0.944013i \(-0.392982\pi\)
0.716783 0.697297i \(-0.245614\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.486366 0.961085i −0.486366 0.961085i
\(747\) 0 0
\(748\) 0 0
\(749\) −0.442257 + 1.66891i −0.442257 + 1.66891i
\(750\) 0 0
\(751\) −1.89152 + 0.0208513i −1.89152 + 0.0208513i −0.949339 0.314254i \(-0.898246\pi\)
−0.942181 + 0.335105i \(0.891228\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.14931 + 1.52810i −1.14931 + 1.52810i −0.340293 + 0.940319i \(0.610526\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) −2.75296 2.45144i −2.75296 2.45144i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.984487 0.175457i \(-0.0561404\pi\)
−0.984487 + 0.175457i \(0.943860\pi\)
\(762\) 0 0
\(763\) −0.748595 + 1.65674i −0.748595 + 1.65674i
\(764\) 3.66205 4.06712i 3.66205 4.06712i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 0.716783 0.697297i \(-0.245614\pi\)
−0.716783 + 0.697297i \(0.754386\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.38569 + 1.26947i −5.38569 + 1.26947i
\(773\) 0 0 0.319482 0.947592i \(-0.396491\pi\)
−0.319482 + 0.947592i \(0.603509\pi\)
\(774\) 2.58198 + 1.83278i 2.58198 + 1.83278i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −3.35377 + 0.829648i −3.35377 + 0.829648i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.0122340 0.0182822i −0.0122340 0.0182822i
\(782\) 0 0
\(783\) 0 0
\(784\) 2.06054 + 3.31107i 2.06054 + 3.31107i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.991264 0.131892i \(-0.0421053\pi\)
−0.991264 + 0.131892i \(0.957895\pi\)
\(788\) −5.07323 0.336028i −5.07323 0.336028i
\(789\) 0 0
\(790\) 0 0
\(791\) −1.62790 + 0.364821i −1.62790 + 0.364821i
\(792\) −0.0373492 + 0.00623247i −0.0373492 + 0.00623247i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.180881 0.983505i \(-0.442105\pi\)
−0.180881 + 0.983505i \(0.557895\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.70322 + 3.76945i 1.70322 + 3.76945i
\(801\) 0 0
\(802\) 3.42658 + 0.767916i 3.42658 + 0.767916i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0.0546983 0.0543977i 0.0546983 0.0543977i −0.677282 0.735724i \(-0.736842\pi\)
0.731980 + 0.681326i \(0.238596\pi\)
\(810\) 0 0
\(811\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(812\) −1.83915 5.08206i −1.83915 5.08206i
\(813\) 0 0
\(814\) −0.0197118 0.0239348i −0.0197118 0.0239348i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0.271873 0.459135i 0.271873 0.459135i −0.693336 0.720615i \(-0.743860\pi\)
0.965209 + 0.261480i \(0.0842105\pi\)
\(822\) 0 0
\(823\) −1.17413 1.36328i −1.17413 1.36328i −0.917973 0.396642i \(-0.870175\pi\)
−0.256156 0.966635i \(-0.582456\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.21032 + 1.05407i −1.21032 + 1.05407i −0.213300 + 0.976987i \(0.568421\pi\)
−0.997024 + 0.0770854i \(0.975439\pi\)
\(828\) −0.484287 0.184371i −0.484287 0.184371i
\(829\) 0 0 −0.904357 0.426776i \(-0.859649\pi\)
0.904357 + 0.426776i \(0.140351\pi\)
\(830\) 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 −0.980380 0.197117i \(-0.936842\pi\)
0.980380 + 0.197117i \(0.0631579\pi\)
\(840\) 0 0
\(841\) 0.385787 + 2.78209i 0.385787 + 2.78209i
\(842\) 1.33772 3.04969i 1.33772 3.04969i
\(843\) 0 0
\(844\) 2.08326 1.65866i 2.08326 1.65866i
\(845\) 0 0
\(846\) 0 0
\(847\) 0.982374 + 0.186276i 0.982374 + 0.186276i
\(848\) 0.367886 1.27413i 0.367886 1.27413i
\(849\) 0 0
\(850\) 0 0
\(851\) −0.0431483 0.267652i −0.0431483 0.267652i
\(852\) 0 0
\(853\) 0 0 −0.391577 0.920146i \(-0.628070\pi\)
0.391577 + 0.920146i \(0.371930\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.77043 5.66037i −1.77043 5.66037i
\(857\) 0 0 −0.298515 0.954405i \(-0.596491\pi\)
0.298515 + 0.954405i \(0.403509\pi\)
\(858\) 0 0
\(859\) 0 0 −0.956036 0.293250i \(-0.905263\pi\)
0.956036 + 0.293250i \(0.0947368\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −0.555946 3.44857i −0.555946 3.44857i
\(863\) −1.19082 0.678797i −1.19082 0.678797i −0.234785 0.972047i \(-0.575439\pi\)
−0.956036 + 0.293250i \(0.905263\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.0111105 0.00884605i 0.0111105 0.00884605i
\(870\) 0 0
\(871\) 0 0
\(872\) −0.857786 6.18590i −0.857786 6.18590i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.156210 + 0.0536269i −0.156210 + 0.0536269i −0.401695 0.915773i \(-0.631579\pi\)
0.245485 + 0.969400i \(0.421053\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.480787 0.876837i \(-0.659649\pi\)
0.480787 + 0.876837i \(0.340351\pi\)
\(882\) −0.857494 + 1.74185i −0.857494 + 1.74185i
\(883\) 0.602771 1.72480i 0.602771 1.72480i −0.0825793 0.996584i \(-0.526316\pi\)
0.685350 0.728214i \(-0.259649\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.73416 1.51028i 1.73416 1.51028i
\(887\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(888\) 0 0
\(889\) 1.12841 0.547800i 1.12841 0.547800i
\(890\) 0 0
\(891\) −0.00728513 0.00827255i −0.00728513 0.00827255i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −3.49363 1.69602i −3.49363 1.69602i
\(897\) 0 0
\(898\) −0.667356 + 0.792363i −0.667356 + 0.792363i
\(899\) 0 0
\(900\) −1.54015 + 2.30156i −1.54015 + 2.30156i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 4.06339 4.04106i 4.06339 4.04106i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.0152873 0.0529459i −0.0152873 0.0529459i 0.952745 0.303771i \(-0.0982456\pi\)
−0.968033 + 0.250825i \(0.919298\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.957107 + 0.214493i 0.957107 + 0.214493i 0.669131 0.743145i \(-0.266667\pi\)
0.287976 + 0.957638i \(0.407018\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.671473 + 0.205964i −0.671473 + 0.205964i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −0.00236730 0.0329830i −0.00236730 0.0329830i 0.996114 0.0880708i \(-0.0280702\pi\)
−0.998482 + 0.0550878i \(0.982456\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.44568 0.0957554i −1.44568 0.0957554i
\(926\) 3.27907 0.436295i 3.27907 0.436295i
\(927\) 0 0
\(928\) 6.37038 + 4.95827i 6.37038 + 4.95827i
\(929\) 0 0 −0.528360 0.849020i \(-0.677193\pi\)
0.528360 + 0.849020i \(0.322807\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 2.87873 + 4.30190i 2.87873 + 4.30190i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.840168 0.542326i \(-0.817544\pi\)
0.840168 + 0.542326i \(0.182456\pi\)
\(938\) −0.234742 1.13510i −0.234742 1.13510i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.973327 0.229424i \(-0.0736842\pi\)
−0.973327 + 0.229424i \(0.926316\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −0.0320399 0.0138439i −0.0320399 0.0138439i
\(947\) −0.0549447 + 1.99329i −0.0549447 + 1.99329i 0.0495838 + 0.998770i \(0.484211\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −0.820894 0.376382i −0.820894 0.376382i −0.0385714 0.999256i \(-0.512281\pi\)
−0.782322 + 0.622874i \(0.785965\pi\)
\(954\) 0.635302 0.179646i 0.635302 0.179646i
\(955\) 0 0
\(956\) −0.638241 + 0.848595i −0.638241 + 0.848595i
\(957\) 0 0
\(958\) 0 0
\(959\) 0.108062 0.390354i 0.108062 0.390354i
\(960\) 0 0
\(961\) 0.945817 + 0.324699i 0.945817 + 0.324699i
\(962\) 0 0
\(963\) 1.12670 1.30820i 1.12670 1.30820i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −0.883333 1.74551i −0.883333 1.74551i −0.627176 0.778877i \(-0.715789\pi\)
−0.256156 0.966635i \(-0.582456\pi\)
\(968\) −3.19629 + 1.25735i −3.19629 + 1.25735i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.746821 0.665025i \(-0.231579\pi\)
−0.746821 + 0.665025i \(0.768421\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −2.68186 + 1.77331i −2.68186 + 1.77331i
\(975\) 0 0
\(976\) 0 0
\(977\) −1.56050 + 1.18719i −1.56050 + 1.18719i −0.660898 + 0.750475i \(0.729825\pi\)
−0.899598 + 0.436719i \(0.856140\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1.39696 1.16347i 1.39696 1.16347i
\(982\) −1.99753 + 3.29013i −1.99753 + 3.29013i
\(983\) 0 0 −0.685350 0.728214i \(-0.740351\pi\)
0.685350 + 0.728214i \(0.259649\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.180733 0.245897i −0.180733 0.245897i
\(990\) 0 0
\(991\) 1.90678 0.561956i 1.90678 0.561956i 0.922290 0.386499i \(-0.126316\pi\)
0.984487 0.175457i \(-0.0561404\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 3.34466 1.95570i 3.34466 1.95570i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.968033 0.250825i \(-0.0807018\pi\)
−0.968033 + 0.250825i \(0.919298\pi\)
\(998\) −0.0158249 2.87119i −0.0158249 2.87119i
\(999\) 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 3997.1.cz.a.237.1 144
7.6 odd 2 CM 3997.1.cz.a.237.1 144
571.518 even 285 inner 3997.1.cz.a.3373.1 yes 144
3997.3373 odd 570 inner 3997.1.cz.a.3373.1 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3997.1.cz.a.237.1 144 1.1 even 1 trivial
3997.1.cz.a.237.1 144 7.6 odd 2 CM
3997.1.cz.a.3373.1 yes 144 571.518 even 285 inner
3997.1.cz.a.3373.1 yes 144 3997.3373 odd 570 inner