Properties

Label 3997.1.cz.a.342.1
Level $3997$
Weight $1$
Character 3997.342
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 342.1
Root \(-0.761300 - 0.648400i\) of defining polynomial
Character \(\chi\) \(=\) 3997.342
Dual form 3997.1.cz.a.2092.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.70487 + 0.188695i) q^{2} +(1.89518 - 0.424719i) q^{4} +(-0.934564 + 0.355794i) q^{7} +(-1.52855 + 0.524751i) q^{8} +(0.0715891 - 0.997434i) q^{9} +O(q^{10})\) \(q+(-1.70487 + 0.188695i) q^{2} +(1.89518 - 0.424719i) q^{4} +(-0.934564 + 0.355794i) q^{7} +(-1.52855 + 0.524751i) q^{8} +(0.0715891 - 0.997434i) q^{9} +(-0.710680 - 0.126659i) q^{11} +(1.52617 - 0.782930i) q^{14} +(0.750526 - 0.354182i) q^{16} +(0.0661607 + 1.71400i) q^{18} +(1.23552 + 0.0818350i) q^{22} +(-0.00633087 - 0.00902376i) q^{23} +(-0.381410 + 0.924406i) q^{25} +(-1.62005 + 1.07122i) q^{28} +(-0.752996 - 0.914313i) q^{29} +(0.164081 - 0.100860i) q^{32} +(-0.287956 - 1.92072i) q^{36} +(1.20227 - 0.957234i) q^{37} +(-0.918045 + 1.47520i) q^{43} +(-1.40066 + 0.0617987i) q^{44} +(0.0124960 + 0.0141897i) q^{46} +(0.746821 - 0.665025i) q^{49} +(0.475824 - 1.64796i) q^{50} +(-0.740847 + 1.63959i) q^{53} +(1.24182 - 1.03426i) q^{56} +(1.45629 + 1.41670i) q^{58} +(0.287976 + 0.957638i) q^{63} +(-0.915613 + 0.712650i) q^{64} +(1.15955 + 1.61463i) q^{67} +(-0.506840 + 0.225660i) q^{71} +(0.413977 + 1.56219i) q^{72} +(-1.86910 + 1.85882i) q^{74} +(0.709241 - 0.134485i) q^{77} +(-0.143163 + 0.424627i) q^{79} +(-0.989750 - 0.142811i) q^{81} +(1.28678 - 2.68826i) q^{86} +(1.15277 - 0.179326i) q^{88} +(-0.0158307 - 0.0144128i) q^{92} +(-1.14775 + 1.27470i) q^{98} +(-0.177211 + 0.699789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + q^{2} + 5 q^{4} + 2 q^{7} + 21 q^{8} - q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times\).

\(n\) \(1716\) \(2285\)
\(\chi(n)\) \(e\left(\frac{217}{285}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70487 + 0.188695i −1.70487 + 0.188695i −0.909007 0.416782i \(-0.863158\pi\)
−0.795863 + 0.605477i \(0.792982\pi\)
\(3\) 0 0 0.731980 0.681326i \(-0.238596\pi\)
−0.731980 + 0.681326i \(0.761404\pi\)
\(4\) 1.89518 0.424719i 1.89518 0.424719i
\(5\) 0 0 −0.556143 0.831087i \(-0.687719\pi\)
0.556143 + 0.831087i \(0.312281\pi\)
\(6\) 0 0
\(7\) −0.934564 + 0.355794i −0.934564 + 0.355794i
\(8\) −1.52855 + 0.524751i −1.52855 + 0.524751i
\(9\) 0.0715891 0.997434i 0.0715891 0.997434i
\(10\) 0 0
\(11\) −0.710680 0.126659i −0.710680 0.126659i −0.191711 0.981451i \(-0.561404\pi\)
−0.518970 + 0.854793i \(0.673684\pi\)
\(12\) 0 0
\(13\) 0 0 −0.999028 0.0440782i \(-0.985965\pi\)
0.999028 + 0.0440782i \(0.0140351\pi\)
\(14\) 1.52617 0.782930i 1.52617 0.782930i
\(15\) 0 0
\(16\) 0.750526 0.354182i 0.750526 0.354182i
\(17\) 0 0 −0.126427 0.991976i \(-0.540351\pi\)
0.126427 + 0.991976i \(0.459649\pi\)
\(18\) 0.0661607 + 1.71400i 0.0661607 + 1.71400i
\(19\) 0 0 0.992658 0.120958i \(-0.0385965\pi\)
−0.992658 + 0.120958i \(0.961404\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.23552 + 0.0818350i 1.23552 + 0.0818350i
\(23\) −0.00633087 0.00902376i −0.00633087 0.00902376i 0.815447 0.578832i \(-0.196491\pi\)
−0.821778 + 0.569808i \(0.807018\pi\)
\(24\) 0 0
\(25\) −0.381410 + 0.924406i −0.381410 + 0.924406i
\(26\) 0 0
\(27\) 0 0
\(28\) −1.62005 + 1.07122i −1.62005 + 1.07122i
\(29\) −0.752996 0.914313i −0.752996 0.914313i 0.245485 0.969400i \(-0.421053\pi\)
−0.998482 + 0.0550878i \(0.982456\pi\)
\(30\) 0 0
\(31\) 0 0 0.0825793 0.996584i \(-0.473684\pi\)
−0.0825793 + 0.996584i \(0.526316\pi\)
\(32\) 0.164081 0.100860i 0.164081 0.100860i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.287956 1.92072i −0.287956 1.92072i
\(37\) 1.20227 0.957234i 1.20227 0.957234i 0.202517 0.979279i \(-0.435088\pi\)
0.999757 + 0.0220445i \(0.00701754\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.962268 0.272103i \(-0.0877193\pi\)
−0.962268 + 0.272103i \(0.912281\pi\)
\(42\) 0 0
\(43\) −0.918045 + 1.47520i −0.918045 + 1.47520i −0.0385714 + 0.999256i \(0.512281\pi\)
−0.879474 + 0.475947i \(0.842105\pi\)
\(44\) −1.40066 + 0.0617987i −1.40066 + 0.0617987i
\(45\) 0 0
\(46\) 0.0124960 + 0.0141897i 0.0124960 + 0.0141897i
\(47\) 0 0 −0.821778 0.569808i \(-0.807018\pi\)
0.821778 + 0.569808i \(0.192982\pi\)
\(48\) 0 0
\(49\) 0.746821 0.665025i 0.746821 0.665025i
\(50\) 0.475824 1.64796i 0.475824 1.64796i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.740847 + 1.63959i −0.740847 + 1.63959i 0.0275543 + 0.999620i \(0.491228\pi\)
−0.768401 + 0.639969i \(0.778947\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.24182 1.03426i 1.24182 1.03426i
\(57\) 0 0
\(58\) 1.45629 + 1.41670i 1.45629 + 1.41670i
\(59\) 0 0 0.546948 0.837166i \(-0.315789\pi\)
−0.546948 + 0.837166i \(0.684211\pi\)
\(60\) 0 0
\(61\) 0 0 −0.00551154 0.999985i \(-0.501754\pi\)
0.00551154 + 0.999985i \(0.498246\pi\)
\(62\) 0 0
\(63\) 0.287976 + 0.957638i 0.287976 + 0.957638i
\(64\) −0.915613 + 0.712650i −0.915613 + 0.712650i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.15955 + 1.61463i 1.15955 + 1.61463i 0.669131 + 0.743145i \(0.266667\pi\)
0.490424 + 0.871484i \(0.336842\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.506840 + 0.225660i −0.506840 + 0.225660i −0.644194 0.764862i \(-0.722807\pi\)
0.137354 + 0.990522i \(0.456140\pi\)
\(72\) 0.413977 + 1.56219i 0.413977 + 1.56219i
\(73\) 0 0 −0.930586 0.366074i \(-0.880702\pi\)
0.930586 + 0.366074i \(0.119298\pi\)
\(74\) −1.86910 + 1.85882i −1.86910 + 1.85882i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.709241 0.134485i 0.709241 0.134485i
\(78\) 0 0
\(79\) −0.143163 + 0.424627i −0.143163 + 0.424627i −0.995083 0.0990455i \(-0.968421\pi\)
0.851919 + 0.523673i \(0.175439\pi\)
\(80\) 0 0
\(81\) −0.989750 0.142811i −0.989750 0.142811i
\(82\) 0 0
\(83\) 0 0 −0.329907 0.944013i \(-0.607018\pi\)
0.329907 + 0.944013i \(0.392982\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.28678 2.68826i 1.28678 2.68826i
\(87\) 0 0
\(88\) 1.15277 0.179326i 1.15277 0.179326i
\(89\) 0 0 −0.982493 0.186298i \(-0.940351\pi\)
0.982493 + 0.186298i \(0.0596491\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.0158307 0.0144128i −0.0158307 0.0144128i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.509516 0.860461i \(-0.670175\pi\)
0.509516 + 0.860461i \(0.329825\pi\)
\(98\) −1.14775 + 1.27470i −1.14775 + 1.27470i
\(99\) −0.177211 + 0.699789i −0.177211 + 0.699789i
\(100\) −0.330227 + 1.91391i −0.330227 + 1.91391i
\(101\) 0 0 −0.0935596 0.995614i \(-0.529825\pi\)
0.0935596 + 0.995614i \(0.470175\pi\)
\(102\) 0 0
\(103\) 0 0 −0.104528 0.994522i \(-0.533333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.953665 2.93508i 0.953665 2.93508i
\(107\) −1.13438 0.535328i −1.13438 0.535328i −0.234785 0.972047i \(-0.575439\pi\)
−0.899598 + 0.436719i \(0.856140\pi\)
\(108\) 0 0
\(109\) −0.863256 + 1.49520i −0.863256 + 1.49520i 0.00551154 + 0.999985i \(0.498246\pi\)
−0.868768 + 0.495219i \(0.835088\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.575399 + 0.598038i −0.575399 + 0.598038i
\(113\) −0.0674603 0.243688i −0.0674603 0.243688i 0.922290 0.386499i \(-0.126316\pi\)
−0.989750 + 0.142811i \(0.954386\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.81539 1.41297i −1.81539 1.41297i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.449406 0.165443i −0.449406 0.165443i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.671663 1.57831i −0.671663 1.57831i
\(127\) 0.141927 + 1.97744i 0.141927 + 1.97744i 0.202517 + 0.979279i \(0.435088\pi\)
−0.0605901 + 0.998163i \(0.519298\pi\)
\(128\) 1.28847 1.25345i 1.28847 1.25345i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.677282 0.735724i \(-0.736842\pi\)
0.677282 + 0.735724i \(0.263158\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −2.28156 2.53393i −2.28156 2.53393i
\(135\) 0 0
\(136\) 0 0
\(137\) 0.678721 + 1.64498i 0.678721 + 1.64498i 0.761300 + 0.648400i \(0.224561\pi\)
−0.0825793 + 0.996584i \(0.526316\pi\)
\(138\) 0 0
\(139\) 0 0 −0.899598 0.436719i \(-0.856140\pi\)
0.899598 + 0.436719i \(0.143860\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.821516 0.480359i 0.821516 0.480359i
\(143\) 0 0
\(144\) −0.299544 0.773956i −0.299544 0.773956i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 1.87197 2.32476i 1.87197 2.32476i
\(149\) 0.943941 1.34546i 0.943941 1.34546i 0.00551154 0.999985i \(-0.498246\pi\)
0.938430 0.345471i \(-0.112281\pi\)
\(150\) 0 0
\(151\) 1.25586 0.462330i 1.25586 0.462330i 0.371197 0.928554i \(-0.378947\pi\)
0.884667 + 0.466224i \(0.154386\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −1.18379 + 0.363109i −1.18379 + 0.363109i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.795863 0.605477i \(-0.207018\pi\)
−0.795863 + 0.605477i \(0.792982\pi\)
\(158\) 0.163950 0.750949i 0.163950 0.750949i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.00912720 + 0.00618080i 0.00912720 + 0.00618080i
\(162\) 1.71434 + 0.0567129i 1.71434 + 0.0567129i
\(163\) 1.86811 + 0.711199i 1.86811 + 0.711199i 0.945817 + 0.324699i \(0.105263\pi\)
0.922290 + 0.386499i \(0.126316\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(168\) 0 0
\(169\) 0.996114 + 0.0880708i 0.996114 + 0.0880708i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.11331 + 3.18568i −1.11331 + 3.18568i
\(173\) 0 0 −0.840168 0.542326i \(-0.817544\pi\)
0.840168 + 0.542326i \(0.182456\pi\)
\(174\) 0 0
\(175\) 0.0275543 0.999620i 0.0275543 0.999620i
\(176\) −0.578244 + 0.156649i −0.578244 + 0.156649i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.949492 + 1.68725i −0.949492 + 1.68725i −0.256156 + 0.966635i \(0.582456\pi\)
−0.693336 + 0.720615i \(0.743860\pi\)
\(180\) 0 0
\(181\) 0 0 −0.986361 0.164595i \(-0.947368\pi\)
0.986361 + 0.164595i \(0.0526316\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.0144123 + 0.0104711i 0.0144123 + 0.0104711i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.978802 0.727760i −0.978802 0.727760i −0.0165339 0.999863i \(-0.505263\pi\)
−0.962268 + 0.272103i \(0.912281\pi\)
\(192\) 0 0
\(193\) −1.79510 0.799232i −1.79510 0.799232i −0.973327 0.229424i \(-0.926316\pi\)
−0.821778 0.569808i \(-0.807018\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.13291 1.57753i 1.13291 1.57753i
\(197\) −0.0706865 1.16449i −0.0706865 1.16449i −0.846095 0.533032i \(-0.821053\pi\)
0.775409 0.631460i \(-0.217544\pi\)
\(198\) 0.170074 1.22649i 0.170074 1.22649i
\(199\) 0 0 −0.775409 0.631460i \(-0.782456\pi\)
0.775409 + 0.631460i \(0.217544\pi\)
\(200\) 0.0979204 1.61314i 0.0979204 1.61314i
\(201\) 0 0
\(202\) 0 0
\(203\) 1.02903 + 0.586573i 1.02903 + 0.586573i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.00945383 + 0.00566862i −0.00945383 + 0.00566862i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −1.07786 + 1.22395i −1.07786 + 1.22395i −0.104528 + 0.994522i \(0.533333\pi\)
−0.973327 + 0.229424i \(0.926316\pi\)
\(212\) −0.707671 + 3.42196i −0.707671 + 3.42196i
\(213\) 0 0
\(214\) 2.03499 + 0.698612i 2.03499 + 0.698612i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 1.18960 2.71202i 1.18960 2.71202i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.996114 0.0880708i \(-0.0280702\pi\)
−0.996114 + 0.0880708i \(0.971930\pi\)
\(224\) −0.117459 + 0.152640i −0.117459 + 0.152640i
\(225\) 0.894729 + 0.446609i 0.894729 + 0.446609i
\(226\) 0.160994 + 0.402728i 0.160994 + 0.402728i
\(227\) 0 0 0.224056 0.974576i \(-0.428070\pi\)
−0.224056 + 0.974576i \(0.571930\pi\)
\(228\) 0 0
\(229\) 0 0 −0.159156 0.987253i \(-0.550877\pi\)
0.159156 + 0.987253i \(0.449123\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.63078 + 1.00243i 1.63078 + 1.00243i
\(233\) −1.44850 + 0.0319392i −1.44850 + 0.0319392i −0.739446 0.673216i \(-0.764912\pi\)
−0.709053 + 0.705155i \(0.750877\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.370526 + 0.595397i 0.370526 + 0.595397i 0.980380 0.197117i \(-0.0631579\pi\)
−0.609854 + 0.792514i \(0.708772\pi\)
\(240\) 0 0
\(241\) 0 0 −0.956036 0.293250i \(-0.905263\pi\)
0.956036 + 0.293250i \(0.0947368\pi\)
\(242\) 0.797396 + 0.197258i 0.797396 + 0.197258i
\(243\) 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 −0.949339 0.314254i \(-0.898246\pi\)
0.949339 + 0.314254i \(0.101754\pi\)
\(252\) 0.952494 + 1.69258i 0.952494 + 1.69258i
\(253\) 0.00335628 + 0.00721487i 0.00335628 + 0.00721487i
\(254\) −0.615101 3.34450i −0.615101 3.34450i
\(255\) 0 0
\(256\) −1.22255 + 1.48446i −1.22255 + 1.48446i
\(257\) 0 0 0.724425 0.689353i \(-0.242105\pi\)
−0.724425 + 0.689353i \(0.757895\pi\)
\(258\) 0 0
\(259\) −0.783025 + 1.32236i −0.783025 + 1.32236i
\(260\) 0 0
\(261\) −0.965873 + 0.685609i −0.965873 + 0.685609i
\(262\) 0 0
\(263\) −1.28743 + 0.556280i −1.28743 + 0.556280i −0.926494 0.376309i \(-0.877193\pi\)
−0.360939 + 0.932589i \(0.617544\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 2.88333 + 2.56752i 2.88333 + 2.56752i
\(269\) 0 0 0.894729 0.446609i \(-0.147368\pi\)
−0.894729 + 0.446609i \(0.852632\pi\)
\(270\) 0 0
\(271\) 0 0 −0.546948 0.837166i \(-0.684211\pi\)
0.546948 + 0.837166i \(0.315789\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −1.46753 2.67641i −1.46753 2.67641i
\(275\) 0.388145 0.608648i 0.388145 0.608648i
\(276\) 0 0
\(277\) 0.0316141 + 1.91181i 0.0316141 + 1.91181i 0.309017 + 0.951057i \(0.400000\pi\)
−0.277403 + 0.960754i \(0.589474\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.239087 + 1.29999i −0.239087 + 1.29999i 0.618553 + 0.785743i \(0.287719\pi\)
−0.857640 + 0.514250i \(0.828070\pi\)
\(282\) 0 0
\(283\) 0 0 −0.461341 0.887223i \(-0.652632\pi\)
0.461341 + 0.887223i \(0.347368\pi\)
\(284\) −0.864711 + 0.642930i −0.864711 + 0.642930i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.0888551 0.170881i −0.0888551 0.170881i
\(289\) −0.968033 + 0.250825i −0.968033 + 0.250825i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.942181 0.335105i \(-0.891228\pi\)
0.942181 + 0.335105i \(0.108772\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.33542 + 2.09407i −1.33542 + 2.09407i
\(297\) 0 0
\(298\) −1.35542 + 2.47194i −1.35542 + 2.47194i
\(299\) 0 0
\(300\) 0 0
\(301\) 0.333104 1.70531i 0.333104 1.70531i
\(302\) −2.05384 + 1.02519i −2.05384 + 1.02519i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.618553 0.785743i \(-0.287719\pi\)
−0.618553 + 0.785743i \(0.712281\pi\)
\(308\) 1.28702 0.556101i 1.28702 0.556101i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.693336 0.720615i \(-0.743860\pi\)
0.693336 + 0.720615i \(0.256140\pi\)
\(312\) 0 0
\(313\) 0 0 −0.298515 0.954405i \(-0.596491\pi\)
0.298515 + 0.954405i \(0.403509\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.0909728 + 0.865549i −0.0909728 + 0.865549i
\(317\) 0.344666 + 1.87406i 0.344666 + 1.87406i 0.471093 + 0.882084i \(0.343860\pi\)
−0.126427 + 0.991976i \(0.540351\pi\)
\(318\) 0 0
\(319\) 0.419334 + 0.745157i 0.419334 + 0.745157i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.0167270 0.00881521i −0.0167270 0.00881521i
\(323\) 0 0
\(324\) −1.93641 + 0.149714i −1.93641 + 0.149714i
\(325\) 0 0
\(326\) −3.31908 0.859999i −3.31908 0.859999i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.17589 + 0.249944i −1.17589 + 0.249944i −0.754107 0.656752i \(-0.771930\pi\)
−0.421786 + 0.906696i \(0.638596\pi\)
\(332\) 0 0
\(333\) −0.868708 1.26772i −0.868708 1.26772i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.00317439 0.575944i 0.00317439 0.575944i −0.956036 0.293250i \(-0.905263\pi\)
0.959210 0.282694i \(-0.0912281\pi\)
\(338\) −1.71486 + 0.0378125i −1.71486 + 0.0378125i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.461341 + 0.887223i −0.461341 + 0.887223i
\(344\) 0.629161 2.73666i 0.629161 2.73666i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.15362 + 1.49915i −1.15362 + 1.49915i −0.319482 + 0.947592i \(0.603509\pi\)
−0.834139 + 0.551554i \(0.814035\pi\)
\(348\) 0 0
\(349\) 0 0 0.0385714 0.999256i \(-0.487719\pi\)
−0.0385714 + 0.999256i \(0.512281\pi\)
\(350\) 0.141647 + 1.70942i 0.141647 + 1.70942i
\(351\) 0 0
\(352\) −0.129384 + 0.0508971i −0.129384 + 0.0508971i
\(353\) 0 0 0.401695 0.915773i \(-0.368421\pi\)
−0.401695 + 0.915773i \(0.631579\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.30038 3.05571i 1.30038 3.05571i
\(359\) −0.0863938 + 0.417760i −0.0863938 + 0.417760i 0.913545 + 0.406737i \(0.133333\pi\)
−0.999939 + 0.0110229i \(0.996491\pi\)
\(360\) 0 0
\(361\) 0.970739 0.240139i 0.970739 0.240139i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.889752 0.456444i \(-0.849123\pi\)
0.889752 + 0.456444i \(0.150877\pi\)
\(368\) −0.00794753 0.00453029i −0.00794753 0.00453029i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.109013 1.79589i 0.109013 1.79589i
\(372\) 0 0
\(373\) −0.00454199 + 0.0327545i −0.00454199 + 0.0327545i −0.992658 0.120958i \(-0.961404\pi\)
0.988116 + 0.153712i \(0.0491228\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.267435 1.65892i 0.267435 1.65892i −0.401695 0.915773i \(-0.631579\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.80605 + 1.05604i 1.80605 + 1.05604i
\(383\) 0 0 −0.926494 0.376309i \(-0.877193\pi\)
0.926494 + 0.376309i \(0.122807\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3.21123 + 1.02386i 3.21123 + 1.02386i
\(387\) 1.40570 + 1.02130i 1.40570 + 1.02130i
\(388\) 0 0
\(389\) 1.71290 0.785368i 1.71290 0.785368i 0.716783 0.697297i \(-0.245614\pi\)
0.996114 0.0880708i \(-0.0280702\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.792580 + 1.40842i −0.792580 + 1.40842i
\(393\) 0 0
\(394\) 0.340245 + 1.97197i 0.340245 + 1.97197i
\(395\) 0 0
\(396\) −0.0386318 + 1.40149i −0.0386318 + 1.40149i
\(397\) 0 0 −0.999757 0.0220445i \(-0.992982\pi\)
0.999757 + 0.0220445i \(0.00701754\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.0411496 + 0.828879i 0.0411496 + 0.828879i
\(401\) 0.404357 0.439249i 0.404357 0.439249i −0.500000 0.866025i \(-0.666667\pi\)
0.904357 + 0.426776i \(0.140351\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −1.86505 0.805857i −1.86505 0.805857i
\(407\) −0.975675 + 0.528009i −0.975675 + 0.528009i
\(408\) 0 0
\(409\) 0 0 −0.999453 0.0330634i \(-0.989474\pi\)
0.999453 + 0.0330634i \(0.0105263\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.0150479 0.0114482i 0.0150479 0.0114482i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.899598 0.436719i \(-0.143860\pi\)
−0.899598 + 0.436719i \(0.856140\pi\)
\(420\) 0 0
\(421\) −0.0547169 0.108124i −0.0547169 0.108124i 0.863256 0.504766i \(-0.168421\pi\)
−0.917973 + 0.396642i \(0.870175\pi\)
\(422\) 1.60665 2.29005i 1.60665 2.29005i
\(423\) 0 0
\(424\) 0.272043 2.89495i 0.272043 2.89495i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −2.37722 0.532748i −2.37722 0.532748i
\(429\) 0 0
\(430\) 0 0
\(431\) −0.778017 0.326040i −0.778017 0.326040i −0.0385714 0.999256i \(-0.512281\pi\)
−0.739446 + 0.673216i \(0.764912\pi\)
\(432\) 0 0
\(433\) 0 0 −0.995083 0.0990455i \(-0.968421\pi\)
0.995083 + 0.0990455i \(0.0315789\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.00098 + 3.20032i −1.00098 + 3.20032i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.701237 0.712928i \(-0.252632\pi\)
−0.701237 + 0.712928i \(0.747368\pi\)
\(440\) 0 0
\(441\) −0.609854 0.792514i −0.609854 0.792514i
\(442\) 0 0
\(443\) −1.43139 + 1.39248i −1.43139 + 1.39248i −0.677282 + 0.735724i \(0.736842\pi\)
−0.754107 + 0.656752i \(0.771930\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.602143 0.991787i 0.602143 0.991787i
\(449\) 0.158295 + 1.36153i 0.158295 + 1.36153i 0.802489 + 0.596667i \(0.203509\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(450\) −1.60967 0.592579i −1.60967 0.592579i
\(451\) 0 0
\(452\) −0.231348 0.433181i −0.231348 0.433181i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.412877 + 0.616994i −0.412877 + 0.616994i −0.978148 0.207912i \(-0.933333\pi\)
0.565270 + 0.824906i \(0.308772\pi\)
\(458\) 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
\(463\) −1.12151 0.892930i −1.12151 0.892930i −0.126427 0.991976i \(-0.540351\pi\)
−0.995083 + 0.0990455i \(0.968421\pi\)
\(464\) −0.888976 0.419518i −0.888976 0.419518i
\(465\) 0 0
\(466\) 2.46347 0.327776i 2.46347 0.327776i
\(467\) 0 0 0.959210 0.282694i \(-0.0912281\pi\)
−0.959210 + 0.282694i \(0.908772\pi\)
\(468\) 0 0
\(469\) −1.65815 1.09641i −1.65815 1.09641i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.839284 0.932119i 0.839284 0.932119i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.58235 + 0.856323i 1.58235 + 0.856323i
\(478\) −0.744047 0.945157i −0.744047 0.945157i
\(479\) 0 0 −0.739446 0.673216i \(-0.764912\pi\)
0.739446 + 0.673216i \(0.235088\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.921970 0.122672i −0.921970 0.122672i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.269687 1.11655i 0.269687 1.11655i −0.660898 0.750475i \(-0.729825\pi\)
0.930586 0.366074i \(-0.119298\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.45129 + 0.870210i 1.45129 + 0.870210i 0.999757 0.0220445i \(-0.00701754\pi\)
0.451533 + 0.892254i \(0.350877\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.393387 0.391224i 0.393387 0.391224i
\(498\) 0 0
\(499\) 0.363256 + 1.37079i 0.363256 + 1.37079i 0.863256 + 0.504766i \(0.168421\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.340293 0.940319i \(-0.610526\pi\)
0.340293 + 0.940319i \(0.389474\pi\)
\(504\) −0.942707 1.31268i −0.942707 1.31268i
\(505\) 0 0
\(506\) −0.00708344 0.0116671i −0.00708344 0.0116671i
\(507\) 0 0
\(508\) 1.10884 + 3.68732i 1.10884 + 3.68732i
\(509\) 0 0 −0.0275543 0.999620i \(-0.508772\pi\)
0.0275543 + 0.999620i \(0.491228\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.820998 1.25663i 0.820998 1.25663i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.08543 2.40220i 1.08543 2.40220i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.277403 0.960754i \(-0.410526\pi\)
−0.277403 + 0.960754i \(0.589474\pi\)
\(522\) 1.51732 1.35113i 1.51732 1.35113i
\(523\) 0 0 0.371197 0.928554i \(-0.378947\pi\)
−0.371197 + 0.928554i \(0.621053\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 2.08994 1.19132i 2.08994 1.19132i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.340252 0.940205i 0.340252 0.940205i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −2.61971 1.85956i −2.61971 1.85956i
\(537\) 0 0
\(538\) 0 0
\(539\) −0.614982 + 0.378028i −0.614982 + 0.378028i
\(540\) 0 0
\(541\) −1.69133 0.206092i −1.69133 0.206092i −0.782322 0.622874i \(-0.785965\pi\)
−0.909007 + 0.416782i \(0.863158\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.291151 0.545158i 0.291151 0.545158i −0.693336 0.720615i \(-0.743860\pi\)
0.984487 + 0.175457i \(0.0561404\pi\)
\(548\) 1.98495 + 2.82927i 1.98495 + 2.82927i
\(549\) 0 0
\(550\) −0.546887 + 1.11091i −0.546887 + 1.11091i
\(551\) 0 0
\(552\) 0 0
\(553\) −0.0172843 0.447778i −0.0172843 0.447778i
\(554\) −0.414647 3.25342i −0.414647 3.25342i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.360381 + 0.184876i −0.360381 + 0.184876i −0.627176 0.778877i \(-0.715789\pi\)
0.266796 + 0.963753i \(0.414035\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.162310 2.26143i 0.162310 2.26143i
\(563\) 0 0 0.945817 0.324699i \(-0.105263\pi\)
−0.945817 + 0.324699i \(0.894737\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.975796 0.218681i 0.975796 0.218681i
\(568\) 0.656314 0.610897i 0.656314 0.610897i
\(569\) 1.51336 0.167499i 1.51336 0.167499i 0.685350 0.728214i \(-0.259649\pi\)
0.828009 + 0.560715i \(0.189474\pi\)
\(570\) 0 0
\(571\) 0.904357 0.426776i 0.904357 0.426776i
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.0107563 0.00241054i 0.0107563 0.00241054i
\(576\) 0.645274 + 0.964281i 0.645274 + 0.964281i
\(577\) 0 0 0.652586 0.757715i \(-0.273684\pi\)
−0.652586 + 0.757715i \(0.726316\pi\)
\(578\) 1.60304 0.610286i 1.60304 0.610286i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.734173 1.07139i 0.734173 1.07139i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.904357 0.426776i \(-0.140351\pi\)
−0.904357 + 0.426776i \(0.859649\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.563303 1.14425i 0.563303 1.14425i
\(593\) 0 0 −0.997814 0.0660906i \(-0.978947\pi\)
0.997814 + 0.0660906i \(0.0210526\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.21750 2.95079i 1.21750 2.95079i
\(597\) 0 0
\(598\) 0 0
\(599\) 1.07469 0.710615i 1.07469 0.710615i 0.115485 0.993309i \(-0.463158\pi\)
0.959210 + 0.282694i \(0.0912281\pi\)
\(600\) 0 0
\(601\) 0 0 −0.992658 0.120958i \(-0.961404\pi\)
0.992658 + 0.120958i \(0.0385965\pi\)
\(602\) −0.246116 + 2.97018i −0.246116 + 2.97018i
\(603\) 1.69350 1.04099i 1.69350 1.04099i
\(604\) 2.18373 1.40959i 2.18373 1.40959i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.148264 0.988948i \(-0.547368\pi\)
0.148264 + 0.988948i \(0.452632\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.618657 1.70951i 0.618657 1.70951i −0.0825793 0.996584i \(-0.526316\pi\)
0.701237 0.712928i \(-0.252632\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.01354 + 0.577741i −1.01354 + 0.577741i
\(617\) 0.504147 + 0.572478i 0.504147 + 0.572478i 0.945817 0.324699i \(-0.105263\pi\)
−0.441671 + 0.897177i \(0.645614\pi\)
\(618\) 0 0
\(619\) 0 0 0.371197 0.928554i \(-0.378947\pi\)
−0.371197 + 0.928554i \(0.621053\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.709053 0.705155i −0.709053 0.705155i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.318292 0.00350872i −0.318292 0.00350872i −0.148264 0.988948i \(-0.547368\pi\)
−0.170028 + 0.985439i \(0.554386\pi\)
\(632\) −0.00399145 0.724188i −0.00399145 0.724188i
\(633\) 0 0
\(634\) −0.941236 3.12999i −0.941236 3.12999i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.855517 1.19127i −0.855517 1.19127i
\(639\) 0.188797 + 0.521695i 0.188797 + 0.521695i
\(640\) 0 0
\(641\) −1.31844 0.732408i −1.31844 0.732408i −0.340293 0.940319i \(-0.610526\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(642\) 0 0
\(643\) 0 0 −0.256156 0.966635i \(-0.582456\pi\)
0.256156 + 0.966635i \(0.417544\pi\)
\(644\) 0.0199228 + 0.00783722i 0.0199228 + 0.00783722i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.942181 0.335105i \(-0.108772\pi\)
−0.942181 + 0.335105i \(0.891228\pi\)
\(648\) 1.58782 0.301079i 1.58782 0.301079i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 3.84245 + 0.554427i 3.84245 + 0.554427i
\(653\) 1.84747 0.750379i 1.84747 0.750379i 0.894729 0.446609i \(-0.147368\pi\)
0.952745 0.303771i \(-0.0982456\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.40125 + 0.217980i −1.40125 + 0.217980i −0.809017 0.587785i \(-0.800000\pi\)
−0.592235 + 0.805765i \(0.701754\pi\)
\(660\) 0 0
\(661\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(662\) 1.95758 0.648006i 1.95758 0.648006i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.72025 + 1.99737i 1.72025 + 1.99737i
\(667\) −0.00348342 + 0.0125833i −0.00348342 + 0.0125833i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.229144 0.151516i −0.229144 0.151516i 0.431754 0.901991i \(-0.357895\pi\)
−0.660898 + 0.750475i \(0.729825\pi\)
\(674\) 0.103266 + 0.982508i 0.103266 + 0.982508i
\(675\) 0 0
\(676\) 1.92522 0.256159i 1.92522 0.256159i
\(677\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.265840 0.276299i 0.265840 0.276299i −0.574329 0.818625i \(-0.694737\pi\)
0.840168 + 0.542326i \(0.182456\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.619112 1.59965i 0.619112 1.59965i
\(687\) 0 0
\(688\) −0.166527 + 1.43233i −0.166527 + 1.43233i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.995083 0.0990455i \(-0.0315789\pi\)
−0.995083 + 0.0990455i \(0.968421\pi\)
\(692\) 0 0
\(693\) −0.0833659 0.717049i −0.0833659 0.717049i
\(694\) 1.68389 2.77353i 1.68389 2.77353i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.372338 1.90616i −0.372338 1.90616i
\(701\) −0.928564 1.20668i −0.928564 1.20668i −0.978148 0.207912i \(-0.933333\pi\)
0.0495838 0.998770i \(-0.484211\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.740971 0.390496i 0.740971 0.390496i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.12498 0.111975i −1.12498 0.111975i −0.480787 0.876837i \(-0.659649\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(710\) 0 0
\(711\) 0.413289 + 0.173195i 0.413289 + 0.173195i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.08285 + 3.60091i −1.08285 + 3.60091i
\(717\) 0 0
\(718\) 0.0684610 0.728528i 0.0684610 0.728528i
\(719\) 0 0 0.627176 0.778877i \(-0.284211\pi\)
−0.627176 + 0.778877i \(0.715789\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.60967 + 0.592579i −1.60967 + 0.592579i
\(723\) 0 0
\(724\) 0 0
\(725\) 1.13240 0.347346i 1.13240 0.347346i
\(726\) 0 0
\(727\) 0 0 0.601081 0.799188i \(-0.294737\pi\)
−0.601081 + 0.799188i \(0.705263\pi\)
\(728\) 0 0
\(729\) −0.213300 + 0.976987i −0.213300 + 0.976987i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.999453 0.0330634i \(-0.989474\pi\)
0.999453 + 0.0330634i \(0.0105263\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.00194892 0.000842096i −0.00194892 0.000842096i
\(737\) −0.619565 1.29435i −0.619565 1.29435i
\(738\) 0 0
\(739\) −0.160745 + 1.26125i −0.160745 + 1.26125i 0.685350 + 0.728214i \(0.259649\pi\)
−0.846095 + 0.533032i \(0.821053\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.153022 + 3.08233i 0.153022 + 3.08233i
\(743\) 0.646869 1.85098i 0.646869 1.85098i 0.137354 0.990522i \(-0.456140\pi\)
0.509516 0.860461i \(-0.329825\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.00156290 0.0566992i 0.00156290 0.0566992i
\(747\) 0 0
\(748\) 0 0
\(749\) 1.25062 + 0.0966923i 1.25062 + 0.0966923i
\(750\) 0 0
\(751\) 1.45872 1.32807i 1.45872 1.32807i 0.618553 0.785743i \(-0.287719\pi\)
0.840168 0.542326i \(-0.182456\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.647019 0.657806i −0.647019 0.657806i 0.309017 0.951057i \(-0.400000\pi\)
−0.956036 + 0.293250i \(0.905263\pi\)
\(758\) −0.142913 + 2.87870i −0.142913 + 2.87870i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.731980 0.681326i \(-0.761404\pi\)
0.731980 + 0.681326i \(0.238596\pi\)
\(762\) 0 0
\(763\) 0.274784 1.70451i 0.274784 1.70451i
\(764\) −2.16410 0.963518i −2.16410 0.963518i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 0.137354 0.990522i \(-0.456140\pi\)
−0.137354 + 0.990522i \(0.543860\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.74149 0.752271i −3.74149 0.752271i
\(773\) 0 0 −0.202517 0.979279i \(-0.564912\pi\)
0.202517 + 0.979279i \(0.435088\pi\)
\(774\) −2.58924 1.47593i −2.58924 1.47593i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −2.77207 + 1.66216i −2.77207 + 1.66216i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.388783 0.0961762i 0.388783 0.0961762i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.324969 0.763629i 0.324969 0.763629i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.846095 0.533032i \(-0.821053\pi\)
0.846095 + 0.533032i \(0.178947\pi\)
\(788\) −0.628545 2.17690i −0.628545 2.17690i
\(789\) 0 0
\(790\) 0 0
\(791\) 0.149749 + 0.203741i 0.149749 + 0.203741i
\(792\) −0.0963401 1.16265i −0.0963401 1.16265i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.371197 0.928554i \(-0.621053\pi\)
0.371197 + 0.928554i \(0.378947\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.0306537 + 0.190147i 0.0306537 + 0.190147i
\(801\) 0 0
\(802\) −0.606492 + 0.825162i −0.606492 + 0.825162i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0.597333 + 0.871695i 0.597333 + 0.871695i 0.999028 0.0440782i \(-0.0140351\pi\)
−0.401695 + 0.915773i \(0.631579\pi\)
\(810\) 0 0
\(811\) 0 0 0.978148 0.207912i \(-0.0666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(812\) 2.19932 + 0.674611i 2.19932 + 0.674611i
\(813\) 0 0
\(814\) 1.56377 1.08429i 1.56377 1.08429i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.30593 0.416378i 1.30593 0.416378i 0.431754 0.901991i \(-0.357895\pi\)
0.874174 + 0.485613i \(0.161404\pi\)
\(822\) 0 0
\(823\) −0.413707 0.735159i −0.413707 0.735159i 0.583317 0.812244i \(-0.301754\pi\)
−0.997024 + 0.0770854i \(0.975439\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0.523538 0.635697i 0.523538 0.635697i −0.441671 0.897177i \(-0.645614\pi\)
0.965209 + 0.261480i \(0.0842105\pi\)
\(828\) −0.0155091 + 0.0147583i −0.0155091 + 0.0147583i
\(829\) 0 0 −0.298515 0.954405i \(-0.596491\pi\)
0.298515 + 0.954405i \(0.403509\pi\)
\(830\) 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 −0.746821 0.665025i \(-0.768421\pi\)
0.746821 + 0.665025i \(0.231579\pi\)
\(840\) 0 0
\(841\) −0.0772537 + 0.395496i −0.0772537 + 0.395496i
\(842\) 0.113688 + 0.174012i 0.113688 + 0.174012i
\(843\) 0 0
\(844\) −1.52289 + 2.77738i −1.52289 + 2.77738i
\(845\) 0 0
\(846\) 0 0
\(847\) 0.478862 0.00527877i 0.478862 0.00527877i
\(848\) 0.0246877 + 1.49295i 0.0246877 + 1.49295i
\(849\) 0 0
\(850\) 0 0
\(851\) −0.0162493 0.00478892i −0.0162493 0.00478892i
\(852\) 0 0
\(853\) 0 0 0.968033 0.250825i \(-0.0807018\pi\)
−0.968033 + 0.250825i \(0.919298\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 2.01487 + 0.223006i 2.01487 + 0.223006i
\(857\) 0 0 −0.993931 0.110008i \(-0.964912\pi\)
0.993931 + 0.110008i \(0.0350877\pi\)
\(858\) 0 0
\(859\) 0 0 −0.461341 0.887223i \(-0.652632\pi\)
0.461341 + 0.887223i \(0.347368\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.38794 + 0.409047i 1.38794 + 0.409047i
\(863\) −0.631370 0.0982163i −0.631370 0.0982163i −0.170028 0.985439i \(-0.554386\pi\)
−0.461341 + 0.887223i \(0.652632\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.155526 0.283641i 0.155526 0.283641i
\(870\) 0 0
\(871\) 0 0
\(872\) 0.534919 2.73848i 0.534919 2.73848i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.33609 0.222954i 1.33609 0.222954i 0.546948 0.837166i \(-0.315789\pi\)
0.789141 + 0.614213i \(0.210526\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.815447 0.578832i \(-0.196491\pi\)
−0.815447 + 0.578832i \(0.803509\pi\)
\(882\) 1.18926 + 1.23606i 1.18926 + 1.23606i
\(883\) −0.996763 + 1.68332i −0.996763 + 1.68332i −0.319482 + 0.947592i \(0.603509\pi\)
−0.677282 + 0.735724i \(0.736842\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 2.17758 2.64409i 2.17758 2.64409i
\(887\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(888\) 0 0
\(889\) −0.836202 1.79755i −0.836202 1.79755i
\(890\) 0 0
\(891\) 0.685308 + 0.226853i 0.685308 + 0.226853i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −0.758193 + 1.62986i −0.758193 + 1.62986i
\(897\) 0 0
\(898\) −0.526786 2.29136i −0.526786 2.29136i
\(899\) 0 0
\(900\) 1.88535 + 0.466394i 1.88535 + 0.466394i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0.230992 + 0.337089i 0.230992 + 0.337089i
\(905\) 0 0
\(906\) 0 0
\(907\) 0.0318202 1.92427i 0.0318202 1.92427i −0.256156 0.966635i \(-0.582456\pi\)
0.287976 0.957638i \(-0.407018\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.252647 0.343739i 0.252647 0.343739i −0.660898 0.750475i \(-0.729825\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.587479 1.12980i 0.587479 1.12980i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.78251 0.157599i 1.78251 0.157599i 0.851919 0.523673i \(-0.175439\pi\)
0.930586 + 0.366074i \(0.119298\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0.426313 + 1.47649i 0.426313 + 1.47649i
\(926\) 2.08052 + 1.31071i 2.08052 + 1.31071i
\(927\) 0 0
\(928\) −0.215770 0.0740740i −0.215770 0.0740740i
\(929\) 0 0 0.391577 0.920146i \(-0.371930\pi\)
−0.391577 + 0.920146i \(0.628070\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −2.73160 + 0.675736i −2.73160 + 0.675736i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.761300 0.648400i \(-0.775439\pi\)
0.761300 + 0.648400i \(0.224561\pi\)
\(938\) 3.03382 + 1.55636i 3.03382 + 1.55636i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.980380 0.197117i \(-0.936842\pi\)
0.980380 + 0.197117i \(0.0631579\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −1.25498 + 1.74751i −1.25498 + 1.74751i
\(947\) 0.850011 + 0.240360i 0.850011 + 0.240360i 0.669131 0.743145i \(-0.266667\pi\)
0.180881 + 0.983505i \(0.442105\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.0475729 + 0.0278170i 0.0475729 + 0.0278170i 0.528360 0.849020i \(-0.322807\pi\)
−0.480787 + 0.876837i \(0.659649\pi\)
\(954\) −2.85928 1.16134i −2.85928 1.16134i
\(955\) 0 0
\(956\) 0.955089 + 0.971013i 0.955089 + 0.971013i
\(957\) 0 0
\(958\) 0 0
\(959\) −1.21958 1.29586i −1.21958 1.29586i
\(960\) 0 0
\(961\) −0.986361 0.164595i −0.986361 0.164595i
\(962\) 0 0
\(963\) −0.615164 + 1.09315i −0.615164 + 1.09315i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −0.00576043 + 0.208978i −0.00576043 + 0.208978i 0.991264 + 0.131892i \(0.0421053\pi\)
−0.997024 + 0.0770854i \(0.975439\pi\)
\(968\) 0.773754 + 0.0170611i 0.773754 + 0.0170611i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.0495838 0.998770i \(-0.515789\pi\)
0.0495838 + 0.998770i \(0.484211\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −0.249095 + 1.95446i −0.249095 + 1.95446i
\(975\) 0 0
\(976\) 0 0
\(977\) −1.37112 0.592442i −1.37112 0.592442i −0.421786 0.906696i \(-0.638596\pi\)
−0.949339 + 0.314254i \(0.898246\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1.42957 + 0.968082i 1.42957 + 0.968082i
\(982\) −2.63846 1.20974i −2.63846 1.20974i
\(983\) 0 0 −0.319482 0.947592i \(-0.603509\pi\)
0.319482 + 0.947592i \(0.396491\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.0191239 0.00105510i 0.0191239 0.00105510i
\(990\) 0 0
\(991\) 0.847465 0.311983i 0.847465 0.311983i 0.115485 0.993309i \(-0.463158\pi\)
0.731980 + 0.681326i \(0.238596\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −0.596851 + 0.741217i −0.596851 + 0.741217i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.287976 0.957638i \(-0.407018\pi\)
−0.287976 + 0.957638i \(0.592982\pi\)
\(998\) −0.877966 2.26848i −0.877966 2.26848i
\(999\) 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.342.1 144
7.6 odd 2 CM 3997.1.cz.a.342.1 144
571.379 even 285 inner 3997.1.cz.a.2092.1 yes 144
3997.2092 odd 570 inner 3997.1.cz.a.2092.1 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3997.1.cz.a.342.1 144 1.1 even 1 trivial
3997.1.cz.a.342.1 144 7.6 odd 2 CM
3997.1.cz.a.2092.1 yes 144 571.379 even 285 inner
3997.1.cz.a.2092.1 yes 144 3997.2092 odd 570 inner