Properties

Label 3528.1.fb.a.1333.1
Level $3528$
Weight $1$
Character 3528.1333
Analytic conductor $1.761$
Analytic rank $0$
Dimension $24$
Projective image $D_{42}$
CM discriminant -24
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3528,1,Mod(397,3528)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3528, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 21, 0, 29]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3528.397");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3528.fb (of order \(42\), degree \(12\), 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: \(1.76070136457\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(2\) over \(\Q(\zeta_{42})\)
Coefficient field: \(\Q(\zeta_{84})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{42}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{42} - \cdots)\)

Embedding invariants

Embedding label 1333.1
Root \(-0.294755 - 0.955573i\) of defining polynomial
Character \(\chi\) \(=\) 3528.1333
Dual form 3528.1.fb.a.397.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.149042 + 0.988831i) q^{2} +(-0.955573 - 0.294755i) q^{4} +(-0.139129 - 1.85654i) q^{5} +(0.0747301 - 0.997204i) q^{7} +(0.433884 - 0.900969i) q^{8} +O(q^{10})\) \(q+(-0.149042 + 0.988831i) q^{2} +(-0.955573 - 0.294755i) q^{4} +(-0.139129 - 1.85654i) q^{5} +(0.0747301 - 0.997204i) q^{7} +(0.433884 - 0.900969i) q^{8} +(1.85654 + 0.139129i) q^{10} +(1.77904 - 0.698220i) q^{11} +(0.974928 + 0.222521i) q^{14} +(0.826239 + 0.563320i) q^{16} +(-0.414278 + 1.81507i) q^{20} +(0.425270 + 1.86323i) q^{22} +(-2.43856 + 0.367554i) q^{25} +(-0.365341 + 0.930874i) q^{28} +(1.92808 + 0.440071i) q^{29} +(-0.975699 - 0.563320i) q^{31} +(-0.680173 + 0.733052i) q^{32} -1.86175 q^{35} +(-1.73305 - 0.680173i) q^{40} +(-1.90580 + 0.142820i) q^{44} +(-0.988831 - 0.149042i) q^{49} -2.46610i q^{50} +(0.294755 - 0.955573i) q^{53} +(-1.54379 - 3.20571i) q^{55} +(-0.866025 - 0.500000i) q^{56} +(-0.722521 + 1.84095i) q^{58} +(-0.129436 + 1.72721i) q^{59} +(0.702449 - 0.880843i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(0.277479 - 1.84095i) q^{70} +(0.129334 + 0.858075i) q^{73} +(-0.563320 - 1.82624i) q^{77} +(0.0747301 + 0.129436i) q^{79} +(0.930874 - 1.61232i) q^{80} +(0.185853 + 0.233052i) q^{83} +(0.142820 - 1.90580i) q^{88} +1.36035i q^{97} +(0.294755 - 0.955573i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{4} + 2 q^{7} + 6 q^{10} + 2 q^{16} + 10 q^{22} + 4 q^{25} - 2 q^{28} - 6 q^{31} - 22 q^{40} + 2 q^{49} - 14 q^{55} - 16 q^{58} + 4 q^{64} + 8 q^{70} + 2 q^{79} - 2 q^{88}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\) \(1765\) \(2647\)
\(\chi(n)\) \(1\) \(e\left(\frac{13}{42}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.149042 + 0.988831i −0.149042 + 0.988831i
\(3\) 0 0
\(4\) −0.955573 0.294755i −0.955573 0.294755i
\(5\) −0.139129 1.85654i −0.139129 1.85654i −0.433884 0.900969i \(-0.642857\pi\)
0.294755 0.955573i \(-0.404762\pi\)
\(6\) 0 0
\(7\) 0.0747301 0.997204i 0.0747301 0.997204i
\(8\) 0.433884 0.900969i 0.433884 0.900969i
\(9\) 0 0
\(10\) 1.85654 + 0.139129i 1.85654 + 0.139129i
\(11\) 1.77904 0.698220i 1.77904 0.698220i 0.781831 0.623490i \(-0.214286\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(12\) 0 0
\(13\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(14\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(15\) 0 0
\(16\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(17\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(18\) 0 0
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) −0.414278 + 1.81507i −0.414278 + 1.81507i
\(21\) 0 0
\(22\) 0.425270 + 1.86323i 0.425270 + 1.86323i
\(23\) 0 0 −0.680173 0.733052i \(-0.738095\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(24\) 0 0
\(25\) −2.43856 + 0.367554i −2.43856 + 0.367554i
\(26\) 0 0
\(27\) 0 0
\(28\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(29\) 1.92808 + 0.440071i 1.92808 + 0.440071i 0.997204 + 0.0747301i \(0.0238095\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(30\) 0 0
\(31\) −0.975699 0.563320i −0.975699 0.563320i −0.0747301 0.997204i \(-0.523810\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(32\) −0.680173 + 0.733052i −0.680173 + 0.733052i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.86175 −1.86175
\(36\) 0 0
\(37\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −1.73305 0.680173i −1.73305 0.680173i
\(41\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(42\) 0 0
\(43\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(44\) −1.90580 + 0.142820i −1.90580 + 0.142820i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(48\) 0 0
\(49\) −0.988831 0.149042i −0.988831 0.149042i
\(50\) 2.46610i 2.46610i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.294755 0.955573i 0.294755 0.955573i −0.680173 0.733052i \(-0.738095\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(54\) 0 0
\(55\) −1.54379 3.20571i −1.54379 3.20571i
\(56\) −0.866025 0.500000i −0.866025 0.500000i
\(57\) 0 0
\(58\) −0.722521 + 1.84095i −0.722521 + 1.84095i
\(59\) −0.129436 + 1.72721i −0.129436 + 1.72721i 0.433884 + 0.900969i \(0.357143\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(60\) 0 0
\(61\) 0 0 −0.294755 0.955573i \(-0.595238\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(62\) 0.702449 0.880843i 0.702449 0.880843i
\(63\) 0 0
\(64\) −0.623490 0.781831i −0.623490 0.781831i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0.277479 1.84095i 0.277479 1.84095i
\(71\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(72\) 0 0
\(73\) 0.129334 + 0.858075i 0.129334 + 0.858075i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.563320 1.82624i −0.563320 1.82624i
\(78\) 0 0
\(79\) 0.0747301 + 0.129436i 0.0747301 + 0.129436i 0.900969 0.433884i \(-0.142857\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(80\) 0.930874 1.61232i 0.930874 1.61232i
\(81\) 0 0
\(82\) 0 0
\(83\) 0.185853 + 0.233052i 0.185853 + 0.233052i 0.866025 0.500000i \(-0.166667\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0.142820 1.90580i 0.142820 1.90580i
\(89\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.36035i 1.36035i 0.733052 + 0.680173i \(0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(98\) 0.294755 0.955573i 0.294755 0.955573i
\(99\) 0 0
\(100\) 2.43856 + 0.367554i 2.43856 + 0.367554i
\(101\) 1.61105 1.09839i 1.61105 1.09839i 0.680173 0.733052i \(-0.261905\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(102\) 0 0
\(103\) −1.94440 + 0.145713i −1.94440 + 0.145713i −0.988831 0.149042i \(-0.952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(107\) 0.139129 + 0.0546039i 0.139129 + 0.0546039i 0.433884 0.900969i \(-0.357143\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(108\) 0 0
\(109\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(110\) 3.40000 1.04876i 3.40000 1.04876i
\(111\) 0 0
\(112\) 0.623490 0.781831i 0.623490 0.781831i
\(113\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.71271 0.988831i −1.71271 0.988831i
\(117\) 0 0
\(118\) −1.68862 0.385418i −1.68862 0.385418i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.94440 1.80414i 1.94440 1.80414i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.766310 + 0.825886i 0.766310 + 0.825886i
\(125\) 0.607374 + 2.66108i 0.607374 + 2.66108i
\(126\) 0 0
\(127\) −0.367711 + 1.61105i −0.367711 + 1.61105i 0.365341 + 0.930874i \(0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(128\) 0.866025 0.500000i 0.866025 0.500000i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.64786 1.12349i −1.64786 1.12349i −0.866025 0.500000i \(-0.833333\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.997204 0.0747301i \(-0.976190\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(138\) 0 0
\(139\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(140\) 1.77904 + 0.548760i 1.77904 + 0.548760i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0.548760 3.64078i 0.548760 3.64078i
\(146\) −0.867767 −0.867767
\(147\) 0 0
\(148\) 0 0
\(149\) 0.268565 1.78181i 0.268565 1.78181i −0.294755 0.955573i \(-0.595238\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(150\) 0 0
\(151\) 0.955573 + 0.294755i 0.955573 + 0.294755i 0.733052 0.680173i \(-0.238095\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 1.88980 0.284841i 1.88980 0.284841i
\(155\) −0.910080 + 1.88980i −0.910080 + 1.88980i
\(156\) 0 0
\(157\) 0 0 −0.997204 0.0747301i \(-0.976190\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(158\) −0.139129 + 0.0546039i −0.139129 + 0.0546039i
\(159\) 0 0
\(160\) 1.45557 + 1.16078i 1.45557 + 1.16078i
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.258149 + 0.149042i −0.258149 + 0.149042i
\(167\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(168\) 0 0
\(169\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.14625 + 1.06356i −1.14625 + 1.06356i −0.149042 + 0.988831i \(0.547619\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(174\) 0 0
\(175\) 0.184292 + 2.45921i 0.184292 + 2.45921i
\(176\) 1.86323 + 0.425270i 1.86323 + 0.425270i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.848162 + 0.914101i −0.848162 + 0.914101i −0.997204 0.0747301i \(-0.976190\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(180\) 0 0
\(181\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.997204 0.0747301i \(-0.0238095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(192\) 0 0
\(193\) 0.123490 0.0841939i 0.123490 0.0841939i −0.500000 0.866025i \(-0.666667\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(194\) −1.34515 0.202749i −1.34515 0.202749i
\(195\) 0 0
\(196\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(197\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(198\) 0 0
\(199\) −0.488831 0.716983i −0.488831 0.716983i 0.500000 0.866025i \(-0.333333\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(200\) −0.726897 + 2.35654i −0.726897 + 2.35654i
\(201\) 0 0
\(202\) 0.846011 + 1.75676i 0.846011 + 1.75676i
\(203\) 0.582926 1.88980i 0.582926 1.88980i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.145713 1.94440i 0.145713 1.94440i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(212\) −0.563320 + 0.826239i −0.563320 + 0.826239i
\(213\) 0 0
\(214\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(215\) 0 0
\(216\) 0 0
\(217\) −0.634659 + 0.930874i −0.634659 + 0.930874i
\(218\) 0 0
\(219\) 0 0
\(220\) 0.530303 + 3.51833i 0.530303 + 3.51833i
\(221\) 0 0
\(222\) 0 0
\(223\) −1.32624 + 0.302705i −1.32624 + 0.302705i −0.826239 0.563320i \(-0.809524\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) 0.680173 + 0.733052i 0.680173 + 0.733052i
\(225\) 0 0
\(226\) 0 0
\(227\) −0.294755 + 0.510531i −0.294755 + 0.510531i −0.974928 0.222521i \(-0.928571\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(228\) 0 0
\(229\) 0 0 0.563320 0.826239i \(-0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.23305 1.54620i 1.23305 1.54620i
\(233\) 0 0 −0.294755 0.955573i \(-0.595238\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.632789 1.61232i 0.632789 1.61232i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(240\) 0 0
\(241\) 0.0878620 0.284841i 0.0878620 0.284841i −0.900969 0.433884i \(-0.857143\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(242\) 1.49419 + 2.19158i 1.49419 + 2.19158i
\(243\) 0 0
\(244\) 0 0
\(245\) −0.139129 + 1.85654i −0.139129 + 1.85654i
\(246\) 0 0
\(247\) 0 0
\(248\) −0.930874 + 0.634659i −0.930874 + 0.634659i
\(249\) 0 0
\(250\) −2.72188 + 0.203977i −2.72188 + 0.203977i
\(251\) 1.01507 0.488831i 1.01507 0.488831i 0.149042 0.988831i \(-0.452381\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.53825 0.603718i −1.53825 0.603718i
\(255\) 0 0
\(256\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(257\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.35654 1.46200i 1.35654 1.46200i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) −1.81507 0.414278i −1.81507 0.414278i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.294755 + 0.0444272i −0.294755 + 0.0444272i −0.294755 0.955573i \(-0.595238\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0.925270 + 0.997204i 0.925270 + 0.997204i 1.00000 \(0\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.08165 + 2.35654i −4.08165 + 2.35654i
\(276\) 0 0
\(277\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −0.807782 + 1.67738i −0.807782 + 1.67738i
\(281\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(282\) 0 0
\(283\) 0 0 0.930874 0.365341i \(-0.119048\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(290\) 3.51833 + 1.08526i 3.51833 + 1.08526i
\(291\) 0 0
\(292\) 0.129334 0.858075i 0.129334 0.858075i
\(293\) 1.36035 1.36035 0.680173 0.733052i \(-0.261905\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(294\) 0 0
\(295\) 3.22464 3.22464
\(296\) 0 0
\(297\) 0 0
\(298\) 1.72188 + 0.531130i 1.72188 + 0.531130i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(308\) 1.91115i 1.91115i
\(309\) 0 0
\(310\) −1.73305 1.18157i −1.73305 1.18157i
\(311\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(312\) 0 0
\(313\) 1.72721 0.997204i 1.72721 0.997204i 0.826239 0.563320i \(-0.190476\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.0332580 0.145713i −0.0332580 0.145713i
\(317\) −0.997204 1.07473i −0.997204 1.07473i −0.997204 0.0747301i \(-0.976190\pi\)
1.00000i \(-0.5\pi\)
\(318\) 0 0
\(319\) 3.73738 0.563320i 3.73738 0.563320i
\(320\) −1.36476 + 1.26631i −1.36476 + 1.26631i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(332\) −0.108903 0.277479i −0.108903 0.277479i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.900969 0.433884i 0.900969 0.433884i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(338\) −0.997204 + 0.0747301i −0.997204 + 0.0747301i
\(339\) 0 0
\(340\) 0 0
\(341\) −2.12912 0.320914i −2.12912 0.320914i
\(342\) 0 0
\(343\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(344\) 0 0
\(345\) 0 0
\(346\) −0.880843 1.29196i −0.880843 1.29196i
\(347\) −0.367554 + 1.19158i −0.367554 + 1.19158i 0.563320 + 0.826239i \(0.309524\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(348\) 0 0
\(349\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(350\) −2.45921 0.184292i −2.45921 0.184292i
\(351\) 0 0
\(352\) −0.698220 + 1.77904i −0.698220 + 1.77904i
\(353\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.777479 0.974928i −0.777479 0.974928i
\(359\) 0 0 0.563320 0.826239i \(-0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(360\) 0 0
\(361\) 0.500000 0.866025i 0.500000 0.866025i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.57506 0.359497i 1.57506 0.359497i
\(366\) 0 0
\(367\) −0.258149 1.71271i −0.258149 1.71271i −0.623490 0.781831i \(-0.714286\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.930874 0.365341i −0.930874 0.365341i
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(384\) 0 0
\(385\) −3.31211 + 1.29991i −3.31211 + 1.29991i
\(386\) 0.0648483 + 0.134659i 0.0648483 + 0.134659i
\(387\) 0 0
\(388\) 0.400969 1.29991i 0.400969 1.29991i
\(389\) 0.702449 + 1.03030i 0.702449 + 1.03030i 0.997204 + 0.0747301i \(0.0238095\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.563320 + 0.826239i −0.563320 + 0.826239i
\(393\) 0 0
\(394\) −0.440071 0.0663300i −0.440071 0.0663300i
\(395\) 0.229907 0.156748i 0.229907 0.156748i
\(396\) 0 0
\(397\) 0 0 0.997204 0.0747301i \(-0.0238095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(398\) 0.781831 0.376510i 0.781831 0.376510i
\(399\) 0 0
\(400\) −2.22188 1.07000i −2.22188 1.07000i
\(401\) 0 0 −0.930874 0.365341i \(-0.880952\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −1.86323 + 0.574730i −1.86323 + 0.574730i
\(405\) 0 0
\(406\) 1.78181 + 0.858075i 1.78181 + 0.858075i
\(407\) 0 0
\(408\) 0 0
\(409\) −1.17809 + 1.26968i −1.17809 + 1.26968i −0.222521 + 0.974928i \(0.571429\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.90097 + 0.433884i 1.90097 + 0.433884i
\(413\) 1.71271 + 0.258149i 1.71271 + 0.258149i
\(414\) 0 0
\(415\) 0.406813 0.377467i 0.406813 0.377467i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.347948 + 1.52446i 0.347948 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(420\) 0 0
\(421\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.733052 0.680173i −0.733052 0.680173i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.116853 0.0931869i −0.116853 0.0931869i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.997204 0.0747301i \(-0.976190\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(432\) 0 0
\(433\) 0.678448 1.40881i 0.678448 1.40881i −0.222521 0.974928i \(-0.571429\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(434\) −0.825886 0.766310i −0.825886 0.766310i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −0.0878620 + 0.582926i −0.0878620 + 0.582926i 0.900969 + 0.433884i \(0.142857\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(440\) −3.55807 −3.55807
\(441\) 0 0
\(442\) 0 0
\(443\) 0.218511 1.44973i 0.218511 1.44973i −0.563320 0.826239i \(-0.690476\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.101659 1.35654i −0.101659 1.35654i
\(447\) 0 0
\(448\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(449\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.460898 0.367554i −0.460898 0.367554i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.63402 1.11406i −1.63402 1.11406i −0.900969 0.433884i \(-0.857143\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.193096 0.846011i 0.193096 0.846011i −0.781831 0.623490i \(-0.785714\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(462\) 0 0
\(463\) 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(464\) 1.34515 + 1.44973i 1.34515 + 1.44973i
\(465\) 0 0
\(466\) 0 0
\(467\) 1.42935 1.32624i 1.42935 1.32624i 0.563320 0.826239i \(-0.309524\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.268565 + 0.129334i 0.268565 + 0.129334i
\(483\) 0 0
\(484\) −2.38980 + 1.15087i −2.38980 + 1.15087i
\(485\) 2.52554 0.189263i 2.52554 0.189263i
\(486\) 0 0
\(487\) −1.36534 + 0.930874i −1.36534 + 0.930874i −0.365341 + 0.930874i \(0.619048\pi\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.81507 0.414278i −1.81507 0.414278i
\(491\) 0.730682i 0.730682i −0.930874 0.365341i \(-0.880952\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.488831 1.01507i −0.488831 1.01507i
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(500\) 0.203977 2.72188i 0.203977 2.72188i
\(501\) 0 0
\(502\) 0.332083 + 1.07659i 0.332083 + 1.07659i
\(503\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(504\) 0 0
\(505\) −2.26335 2.83816i −2.26335 2.83816i
\(506\) 0 0
\(507\) 0 0
\(508\) 0.826239 1.43109i 0.826239 1.43109i
\(509\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0.865341 0.0648483i 0.865341 0.0648483i
\(512\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.541044 + 3.58959i 0.541044 + 3.58959i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 0.563320 0.826239i \(-0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(524\) 1.24349 + 1.55929i 1.24349 + 1.55929i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(530\) 0.680173 1.73305i 0.680173 1.73305i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0.0820177 0.265895i 0.0820177 0.265895i
\(536\) 0 0
\(537\) 0 0
\(538\) 0.298085i 0.298085i
\(539\) −1.86323 + 0.425270i −1.86323 + 0.425270i
\(540\) 0 0
\(541\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(542\) −1.12397 + 0.766310i −1.12397 + 0.766310i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −1.72188 4.38729i −1.72188 4.38729i
\(551\) 0 0
\(552\) 0 0
\(553\) 0.134659 0.0648483i 0.134659 0.0648483i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −0.632789 0.365341i −0.632789 0.365341i 0.149042 0.988831i \(-0.452381\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −1.53825 1.04876i −1.53825 1.04876i
\(561\) 0 0
\(562\) 0 0
\(563\) 1.97213 0.297251i 1.97213 0.297251i 0.974928 0.222521i \(-0.0714286\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) 0 0
\(571\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.04876 0.411608i 1.04876 0.411608i 0.222521 0.974928i \(-0.428571\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(578\) −0.997204 0.0747301i −0.997204 0.0747301i
\(579\) 0 0
\(580\) −1.59752 + 3.31728i −1.59752 + 3.31728i
\(581\) 0.246289 0.167917i 0.246289 0.167917i
\(582\) 0 0
\(583\) −0.142820 1.90580i −0.142820 1.90580i
\(584\) 0.829215 + 0.255779i 0.829215 + 0.255779i
\(585\) 0 0
\(586\) −0.202749 + 1.34515i −0.202749 + 1.34515i
\(587\) −0.589510 −0.589510 −0.294755 0.955573i \(-0.595238\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −0.480608 + 3.18862i −0.480608 + 3.18862i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.781831 + 1.62349i −0.781831 + 1.62349i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.930874 0.365341i \(-0.119048\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(600\) 0 0
\(601\) 0.880843 + 0.702449i 0.880843 + 0.702449i 0.955573 0.294755i \(-0.0952381\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.826239 0.563320i −0.826239 0.563320i
\(605\) −3.61999 3.35886i −3.61999 3.35886i
\(606\) 0 0
\(607\) 0.510531 0.294755i 0.510531 0.294755i −0.222521 0.974928i \(-0.571429\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.88980 0.284841i −1.88980 0.284841i
\(617\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(618\) 0 0
\(619\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(620\) 1.42668 1.53759i 1.42668 1.53759i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 2.49936 0.770951i 2.49936 0.770951i
\(626\) 0.728639 + 1.85654i 0.728639 + 1.85654i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −1.32091 + 0.636119i −1.32091 + 0.636119i −0.955573 0.294755i \(-0.904762\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(632\) 0.149042 0.0111692i 0.149042 0.0111692i
\(633\) 0 0
\(634\) 1.21135 0.825886i 1.21135 0.825886i
\(635\) 3.04213 + 0.458528i 3.04213 + 0.458528i
\(636\) 0 0
\(637\) 0 0
\(638\) 3.77960i 3.77960i
\(639\) 0 0
\(640\) −1.04876 1.53825i −1.04876 1.53825i
\(641\) 0 0 0.294755 0.955573i \(-0.404762\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(642\) 0 0
\(643\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(648\) 0 0
\(649\) 0.975699 + 3.16314i 0.975699 + 3.16314i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.411608 + 0.603718i −0.411608 + 0.603718i −0.974928 0.222521i \(-0.928571\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(654\) 0 0
\(655\) −1.85654 + 3.21562i −1.85654 + 3.21562i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.433884 0.0990311i 0.433884 0.0990311i 1.00000i \(-0.5\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(660\) 0 0
\(661\) 0 0 −0.149042 0.988831i \(-0.547619\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.290611 0.0663300i 0.290611 0.0663300i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.19158 + 1.49419i −1.19158 + 1.49419i −0.365341 + 0.930874i \(0.619048\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(674\) 0.294755 + 0.955573i 0.294755 + 0.955573i
\(675\) 0 0
\(676\) 0.0747301 0.997204i 0.0747301 0.997204i
\(677\) −0.215372 + 0.548760i −0.215372 + 0.548760i −0.997204 0.0747301i \(-0.976190\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(678\) 0 0
\(679\) 1.35654 + 0.101659i 1.35654 + 0.101659i
\(680\) 0 0
\(681\) 0 0
\(682\) 0.634659 2.05751i 0.634659 2.05751i
\(683\) −0.411608 0.603718i −0.411608 0.603718i 0.563320 0.826239i \(-0.309524\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.930874 0.365341i −0.930874 0.365341i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.997204 0.0747301i \(-0.0238095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(692\) 1.40881 0.678448i 1.40881 0.678448i
\(693\) 0 0
\(694\) −1.12349 0.541044i −1.12349 0.541044i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.548760 2.40427i 0.548760 2.40427i
\(701\) 1.29196 1.03030i 1.29196 1.03030i 0.294755 0.955573i \(-0.404762\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.65510 0.955573i −1.65510 0.955573i
\(705\) 0 0
\(706\) 0 0
\(707\) −0.974928 1.68862i −0.974928 1.68862i
\(708\) 0 0
\(709\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.07992 0.623490i 1.07992 0.623490i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(720\) 0 0
\(721\) 1.94986i 1.94986i
\(722\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(723\) 0 0
\(724\) 0 0
\(725\) −4.86348 0.364468i −4.86348 0.364468i
\(726\) 0 0
\(727\) −0.129334 + 0.268565i −0.129334 + 0.268565i −0.955573 0.294755i \(-0.904762\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.120731 + 1.61105i 0.120731 + 1.61105i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.149042 0.988831i \(-0.452381\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(734\) 1.73205 1.73205
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.500000 0.866025i 0.500000 0.866025i
\(743\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(744\) 0 0
\(745\) −3.34537 0.250701i −3.34537 0.250701i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.0648483 0.134659i 0.0648483 0.134659i
\(750\) 0 0
\(751\) −1.57906 1.07659i −1.57906 1.07659i −0.955573 0.294755i \(-0.904762\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.414278 1.81507i 0.414278 1.81507i
\(756\) 0 0
\(757\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1.55929 1.24349i 1.55929 1.24349i 0.733052 0.680173i \(-0.238095\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(770\) −0.791745 3.46886i −0.791745 3.46886i
\(771\) 0 0
\(772\) −0.142820 + 0.0440542i −0.142820 + 0.0440542i
\(773\) 0.712362 + 1.81507i 0.712362 + 1.81507i 0.563320 + 0.826239i \(0.309524\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(774\) 0 0
\(775\) 2.58635 + 1.01507i 2.58635 + 1.01507i
\(776\) 1.22563 + 0.590232i 1.22563 + 0.590232i
\(777\) 0 0
\(778\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.733052 0.680173i −0.733052 0.680173i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.563320 0.826239i \(-0.690476\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(788\) 0.131178 0.425270i 0.131178 0.425270i
\(789\) 0 0
\(790\) 0.120731 + 0.250701i 0.120731 + 0.250701i
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0.255779 + 0.829215i 0.255779 + 0.829215i
\(797\) −0.848162 + 1.06356i −0.848162 + 1.06356i 0.149042 + 0.988831i \(0.452381\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.38921 2.03759i 1.38921 2.03759i
\(801\) 0 0
\(802\) 0 0
\(803\) 0.829215 + 1.43624i 0.829215 + 1.43624i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −0.290611 1.92808i −0.290611 1.92808i
\(809\) 0 0 −0.149042 0.988831i \(-0.547619\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(810\) 0 0
\(811\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(812\) −1.11406 + 1.63402i −1.11406 + 1.63402i
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −1.07992 1.35417i −1.07992 1.35417i
\(819\) 0 0
\(820\) 0 0
\(821\) 0.0440542 + 0.142820i 0.0440542 + 0.142820i 0.974928 0.222521i \(-0.0714286\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(822\) 0 0
\(823\) 0.134659 1.79690i 0.134659 1.79690i −0.365341 0.930874i \(-0.619048\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(824\) −0.712362 + 1.81507i −0.712362 + 1.81507i
\(825\) 0 0
\(826\) −0.510531 + 1.65510i −0.510531 + 1.65510i
\(827\) −0.317031 0.658322i −0.317031 0.658322i 0.680173 0.733052i \(-0.261905\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(828\) 0 0
\(829\) 0 0 0.294755 0.955573i \(-0.404762\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(830\) 0.312619 + 0.458528i 0.312619 + 0.458528i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) −1.55929 + 0.116853i −1.55929 + 0.116853i
\(839\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(840\) 0 0
\(841\) 2.62285 + 1.26310i 2.62285 + 1.26310i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.77904 0.548760i 1.77904 0.548760i
\(846\) 0 0
\(847\) −1.65379 2.07379i −1.65379 2.07379i
\(848\) 0.781831 0.623490i 0.781831 0.623490i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.109562 0.101659i 0.109562 0.101659i
\(857\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(858\) 0 0
\(859\) 0 0 −0.680173 0.733052i \(-0.738095\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(864\) 0 0
\(865\) 2.13402 + 1.98008i 2.13402 + 1.98008i
\(866\) 1.29196 + 0.880843i 1.29196 + 0.880843i
\(867\) 0 0
\(868\) 0.880843 0.702449i 0.880843 0.702449i
\(869\) 0.223322 + 0.178094i 0.223322 + 0.178094i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.69903 0.406813i 2.69903 0.406813i
\(876\) 0 0
\(877\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(878\) −0.563320 0.173761i −0.563320 0.173761i
\(879\) 0 0
\(880\) 0.530303 3.51833i 0.530303 3.51833i
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.40097 + 0.432142i 1.40097 + 0.432142i
\(887\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(888\) 0 0
\(889\) 1.57906 + 0.487076i 1.57906 + 0.487076i
\(890\) 0 0
\(891\) 0 0
\(892\) 1.35654 + 0.101659i 1.35654 + 0.101659i
\(893\) 0 0
\(894\) 0 0
\(895\) 1.81507 + 1.44747i 1.81507 + 1.44747i
\(896\) −0.433884 0.900969i −0.433884 0.900969i
\(897\) 0 0
\(898\) 0 0
\(899\) −1.63332 1.51550i −1.63332 1.51550i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(908\) 0.432142 0.400969i 0.432142 0.400969i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(912\) 0 0
\(913\) 0.493360 + 0.284841i 0.493360 + 0.284841i
\(914\) 1.34515 1.44973i 1.34515 1.44973i
\(915\) 0 0
\(916\) 0 0
\(917\) −1.24349 + 1.55929i −1.24349 + 1.55929i
\(918\) 0 0
\(919\) −0.425270 + 0.131178i −0.425270 + 0.131178i −0.500000 0.866025i \(-0.666667\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.807782 + 0.317031i 0.807782 + 0.317031i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −1.24349 + 0.0931869i −1.24349 + 0.0931869i
\(927\) 0 0
\(928\) −1.63402 + 1.11406i −1.63402 + 1.11406i
\(929\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 1.09839 + 1.61105i 1.09839 + 1.61105i
\(935\) 0 0
\(936\) 0 0
\(937\) 0.488831 + 1.01507i 0.488831 + 1.01507i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0.101659 1.35654i 0.101659 1.35654i −0.680173 0.733052i \(-0.738095\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.07992 + 1.35417i −1.07992 + 1.35417i
\(945\) 0 0
\(946\) 0 0
\(947\) −1.01507 + 1.48883i −1.01507 + 1.48883i −0.149042 + 0.988831i \(0.547619\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.134659 + 0.233236i 0.134659 + 0.233236i
\(962\) 0 0
\(963\) 0 0
\(964\) −0.167917 + 0.246289i −0.167917 + 0.246289i
\(965\) −0.173490 0.217550i −0.173490 0.217550i
\(966\) 0 0
\(967\) 0.0931869 0.116853i 0.0931869 0.116853i −0.733052 0.680173i \(-0.761905\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(968\) −0.781831 2.53464i −0.781831 2.53464i
\(969\) 0 0
\(970\) −0.189263 + 2.52554i −0.189263 + 2.52554i
\(971\) 0.411608 1.04876i 0.411608 1.04876i −0.563320 0.826239i \(-0.690476\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −0.716983 1.48883i −0.716983 1.48883i
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 −0.563320 0.826239i \(-0.690476\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.680173 1.73305i 0.680173 1.73305i
\(981\) 0 0
\(982\) 0.722521 + 0.108903i 0.722521 + 0.108903i
\(983\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(984\) 0 0
\(985\) 0.826239 0.0619180i 0.826239 0.0619180i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.698220 + 1.77904i 0.698220 + 1.77904i 0.623490 + 0.781831i \(0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(992\) 1.07659 0.332083i 1.07659 0.332083i
\(993\) 0 0
\(994\) 0 0
\(995\) −1.26310 + 1.00729i −1.26310 + 1.00729i
\(996\) 0 0
\(997\) 0 0 0.680173 0.733052i \(-0.261905\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3528.1.fb.a.1333.1 yes 24
3.2 odd 2 inner 3528.1.fb.a.1333.2 yes 24
8.5 even 2 inner 3528.1.fb.a.1333.2 yes 24
24.5 odd 2 CM 3528.1.fb.a.1333.1 yes 24
49.5 odd 42 inner 3528.1.fb.a.397.2 yes 24
147.5 even 42 inner 3528.1.fb.a.397.1 24
392.5 odd 42 inner 3528.1.fb.a.397.1 24
1176.5 even 42 inner 3528.1.fb.a.397.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3528.1.fb.a.397.1 24 147.5 even 42 inner
3528.1.fb.a.397.1 24 392.5 odd 42 inner
3528.1.fb.a.397.2 yes 24 49.5 odd 42 inner
3528.1.fb.a.397.2 yes 24 1176.5 even 42 inner
3528.1.fb.a.1333.1 yes 24 1.1 even 1 trivial
3528.1.fb.a.1333.1 yes 24 24.5 odd 2 CM
3528.1.fb.a.1333.2 yes 24 3.2 odd 2 inner
3528.1.fb.a.1333.2 yes 24 8.5 even 2 inner