Properties

Label 404.1.o.a.79.1
Level $404$
Weight $1$
Character 404.79
Analytic conductor $0.202$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -4
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [404,1,Mod(19,404)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(404, base_ring=CyclotomicField(50))
 
chi = DirichletCharacter(H, H._module([25, 48]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("404.19");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 404 = 2^{2} \cdot 101 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 404.o (of order \(50\), degree \(20\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.201622265104\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{50})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{15} + x^{10} - x^{5} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{25}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{25} - \cdots)\)

Embedding invariants

Embedding label 79.1
Root \(-0.876307 - 0.481754i\) of defining polynomial
Character \(\chi\) \(=\) 404.79
Dual form 404.1.o.a.179.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.425779 + 0.904827i) q^{2} +(-0.637424 - 0.770513i) q^{4} +(-0.0534698 - 0.113629i) q^{5} +(0.968583 - 0.248690i) q^{8} +(0.535827 + 0.844328i) q^{9} +O(q^{10})\) \(q+(-0.425779 + 0.904827i) q^{2} +(-0.637424 - 0.770513i) q^{4} +(-0.0534698 - 0.113629i) q^{5} +(0.968583 - 0.248690i) q^{8} +(0.535827 + 0.844328i) q^{9} +0.125581 q^{10} +(1.27760 + 1.19975i) q^{13} +(-0.187381 + 0.982287i) q^{16} +(-0.500000 - 0.363271i) q^{17} +(-0.992115 + 0.125333i) q^{18} +(-0.0534698 + 0.113629i) q^{20} +(0.627371 - 0.758362i) q^{25} +(-1.62954 + 0.645180i) q^{26} +(-1.17950 - 1.10762i) q^{29} +(-0.809017 - 0.587785i) q^{32} +(0.541587 - 0.297740i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-1.11716 + 0.614163i) q^{37} +(-0.0800484 - 0.0967619i) q^{40} +(0.303189 - 0.220280i) q^{41} +(0.0672897 - 0.106032i) q^{45} +(0.0627905 - 0.998027i) q^{49} +(0.419064 + 0.890557i) q^{50} +(0.110048 - 1.74915i) q^{52} +(-0.929324 + 1.12336i) q^{53} +(1.50441 - 0.595638i) q^{58} +(-1.23480 - 1.49261i) q^{61} +(0.876307 - 0.481754i) q^{64} +(0.0680131 - 0.209323i) q^{65} +(0.0388067 + 0.616814i) q^{68} +(0.728969 + 0.684547i) q^{72} +(1.84489 + 0.233064i) q^{73} +(-0.0800484 - 1.27233i) q^{74} +(0.121636 - 0.0312307i) q^{80} +(-0.425779 + 0.904827i) q^{81} +(0.0702235 + 0.368125i) q^{82} +(-0.0145433 + 0.0762386i) q^{85} +(-0.200808 - 1.05267i) q^{89} +(0.0672897 + 0.106032i) q^{90} +(-0.929324 - 1.12336i) q^{97} +(0.876307 + 0.481754i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 5 q^{13} - 10 q^{17} - 5 q^{32} - 5 q^{36} - 5 q^{40} - 5 q^{45} - 5 q^{50} - 5 q^{61} - 5 q^{74} - 5 q^{80} + 20 q^{82} - 5 q^{90}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/404\mathbb{Z}\right)^\times\).

\(n\) \(203\) \(305\)
\(\chi(n)\) \(-1\) \(e\left(\frac{16}{25}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(3\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(4\) −0.637424 0.770513i −0.637424 0.770513i
\(5\) −0.0534698 0.113629i −0.0534698 0.113629i 0.876307 0.481754i \(-0.160000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(6\) 0 0
\(7\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(8\) 0.968583 0.248690i 0.968583 0.248690i
\(9\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(10\) 0.125581 0.125581
\(11\) 0 0 −0.535827 0.844328i \(-0.680000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(12\) 0 0
\(13\) 1.27760 + 1.19975i 1.27760 + 1.19975i 0.968583 + 0.248690i \(0.0800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(17\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(19\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(20\) −0.0534698 + 0.113629i −0.0534698 + 0.113629i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(24\) 0 0
\(25\) 0.627371 0.758362i 0.627371 0.758362i
\(26\) −1.62954 + 0.645180i −1.62954 + 0.645180i
\(27\) 0 0
\(28\) 0 0
\(29\) −1.17950 1.10762i −1.17950 1.10762i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(30\) 0 0
\(31\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(32\) −0.809017 0.587785i −0.809017 0.587785i
\(33\) 0 0
\(34\) 0.541587 0.297740i 0.541587 0.297740i
\(35\) 0 0
\(36\) 0.309017 0.951057i 0.309017 0.951057i
\(37\) −1.11716 + 0.614163i −1.11716 + 0.614163i −0.929776 0.368125i \(-0.880000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.0800484 0.0967619i −0.0800484 0.0967619i
\(41\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(42\) 0 0
\(43\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(44\) 0 0
\(45\) 0.0672897 0.106032i 0.0672897 0.106032i
\(46\) 0 0
\(47\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(48\) 0 0
\(49\) 0.0627905 0.998027i 0.0627905 0.998027i
\(50\) 0.419064 + 0.890557i 0.419064 + 0.890557i
\(51\) 0 0
\(52\) 0.110048 1.74915i 0.110048 1.74915i
\(53\) −0.929324 + 1.12336i −0.929324 + 1.12336i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 1.50441 0.595638i 1.50441 0.595638i
\(59\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(60\) 0 0
\(61\) −1.23480 1.49261i −1.23480 1.49261i −0.809017 0.587785i \(-0.800000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.876307 0.481754i 0.876307 0.481754i
\(65\) 0.0680131 0.209323i 0.0680131 0.209323i
\(66\) 0 0
\(67\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(68\) 0.0388067 + 0.616814i 0.0388067 + 0.616814i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(72\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(73\) 1.84489 + 0.233064i 1.84489 + 0.233064i 0.968583 0.248690i \(-0.0800000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(74\) −0.0800484 1.27233i −0.0800484 1.27233i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(80\) 0.121636 0.0312307i 0.121636 0.0312307i
\(81\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(82\) 0.0702235 + 0.368125i 0.0702235 + 0.368125i
\(83\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(84\) 0 0
\(85\) −0.0145433 + 0.0762386i −0.0145433 + 0.0762386i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.200808 1.05267i −0.200808 1.05267i −0.929776 0.368125i \(-0.880000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(90\) 0.0672897 + 0.106032i 0.0672897 + 0.106032i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.929324 1.12336i −0.929324 1.12336i −0.992115 0.125333i \(-0.960000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(98\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(99\) 0 0
\(100\) −0.984229 −0.984229
\(101\) −0.637424 0.770513i −0.637424 0.770513i
\(102\) 0 0
\(103\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(104\) 1.53583 + 0.844328i 1.53583 + 0.844328i
\(105\) 0 0
\(106\) −0.620759 1.31918i −0.620759 1.31918i
\(107\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) 0 0
\(109\) −0.824805 + 0.211774i −0.824805 + 0.211774i −0.637424 0.770513i \(-0.720000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.159566 + 0.836475i 0.159566 + 0.836475i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.101597 + 1.61484i −0.101597 + 1.61484i
\(117\) −0.328407 + 1.72157i −0.328407 + 1.72157i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(122\) 1.87631 0.481754i 1.87631 0.481754i
\(123\) 0 0
\(124\) 0 0
\(125\) −0.241353 0.0619689i −0.241353 0.0619689i
\(126\) 0 0
\(127\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(128\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(129\) 0 0
\(130\) 0.160442 + 0.150665i 0.160442 + 0.150665i
\(131\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.574633 0.227513i −0.574633 0.227513i
\(137\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(145\) −0.0627905 + 0.193249i −0.0627905 + 0.193249i
\(146\) −0.996398 + 1.57007i −0.996398 + 1.57007i
\(147\) 0 0
\(148\) 1.18532 + 0.469303i 1.18532 + 0.469303i
\(149\) 1.18532 1.43281i 1.18532 1.43281i 0.309017 0.951057i \(-0.400000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(150\) 0 0
\(151\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(152\) 0 0
\(153\) 0.0388067 0.616814i 0.0388067 0.616814i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.456288 + 0.718995i −0.456288 + 0.718995i −0.992115 0.125333i \(-0.960000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.0235315 + 0.123357i −0.0235315 + 0.123357i
\(161\) 0 0
\(162\) −0.637424 0.770513i −0.637424 0.770513i
\(163\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(164\) −0.362989 0.0931997i −0.362989 0.0931997i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(168\) 0 0
\(169\) 0.130080 + 2.06757i 0.130080 + 2.06757i
\(170\) −0.0627905 0.0456200i −0.0627905 0.0456200i
\(171\) 0 0
\(172\) 0 0
\(173\) −0.929324 0.872693i −0.929324 0.872693i 0.0627905 0.998027i \(-0.480000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 1.03799 + 0.266509i 1.03799 + 0.266509i
\(179\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(180\) −0.124591 + 0.0157395i −0.124591 + 0.0157395i
\(181\) 1.87631 0.481754i 1.87631 0.481754i 0.876307 0.481754i \(-0.160000\pi\)
1.00000 \(0\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.129521 + 0.0941025i 0.129521 + 0.0941025i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.535827 0.844328i \(-0.680000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(192\) 0 0
\(193\) −0.200808 0.316423i −0.200808 0.316423i 0.728969 0.684547i \(-0.240000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(194\) 1.41213 0.362574i 1.41213 0.362574i
\(195\) 0 0
\(196\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(197\) 0.688925 + 1.46404i 0.688925 + 1.46404i 0.876307 + 0.481754i \(0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(198\) 0 0
\(199\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(200\) 0.419064 0.890557i 0.419064 0.890557i
\(201\) 0 0
\(202\) 0.968583 0.248690i 0.968583 0.248690i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.0412417 0.0226728i −0.0412417 0.0226728i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.535827 0.844328i \(-0.680000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(212\) 1.45794 1.45794
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.159566 0.836475i 0.159566 0.836475i
\(219\) 0 0
\(220\) 0 0
\(221\) −0.202967 1.06399i −0.202967 1.06399i
\(222\) 0 0
\(223\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(224\) 0 0
\(225\) 0.976468 + 0.123357i 0.976468 + 0.123357i
\(226\) −0.824805 0.211774i −0.824805 0.211774i
\(227\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(228\) 0 0
\(229\) 0.0915446 + 1.45506i 0.0915446 + 1.45506i 0.728969 + 0.684547i \(0.240000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.41789 0.779494i −1.41789 0.779494i
\(233\) 1.41213 1.32608i 1.41213 1.32608i 0.535827 0.844328i \(-0.320000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(234\) −1.41789 1.03016i −1.41789 1.03016i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(240\) 0 0
\(241\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(242\) −0.637424 0.770513i −0.637424 0.770513i
\(243\) 0 0
\(244\) −0.362989 + 1.90285i −0.362989 + 1.90285i
\(245\) −0.116762 + 0.0462295i −0.116762 + 0.0462295i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0.158834 0.191998i 0.158834 0.191998i
\(251\) 0 0 0.0627905 0.998027i \(-0.480000\pi\)
−0.0627905 + 0.998027i \(0.520000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.929776 0.368125i −0.929776 0.368125i
\(257\) 1.03799 1.63560i 1.03799 1.63560i 0.309017 0.951057i \(-0.400000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.204639 + 0.0810224i −0.204639 + 0.0810224i
\(261\) 0.303189 1.58937i 0.303189 1.58937i
\(262\) 0 0
\(263\) 0 0 −0.637424 0.770513i \(-0.720000\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(264\) 0 0
\(265\) 0.177337 + 0.0455325i 0.177337 + 0.0455325i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.73879 + 0.955910i −1.73879 + 0.955910i −0.809017 + 0.587785i \(0.800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0.450527 0.423073i 0.450527 0.423073i
\(273\) 0 0
\(274\) −1.35556 1.27295i −1.35556 1.27295i
\(275\) 0 0
\(276\) 0 0
\(277\) 0.348445 0.137959i 0.348445 0.137959i −0.187381 0.982287i \(-0.560000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.26480 0.159781i 1.26480 0.159781i 0.535827 0.844328i \(-0.320000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(282\) 0 0
\(283\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.0627905 0.998027i 0.0627905 0.998027i
\(289\) −0.190983 0.587785i −0.190983 0.587785i
\(290\) −0.148122 0.139096i −0.148122 0.139096i
\(291\) 0 0
\(292\) −0.996398 1.57007i −0.996398 1.57007i
\(293\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.929324 + 0.872693i −0.929324 + 0.872693i
\(297\) 0 0
\(298\) 0.791759 + 1.68257i 0.791759 + 1.68257i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.103580 + 0.220119i −0.103580 + 0.220119i
\(306\) 0.541587 + 0.297740i 0.541587 + 0.297740i
\(307\) 0 0 −0.637424 0.770513i \(-0.720000\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(312\) 0 0
\(313\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) −0.456288 0.718995i −0.456288 0.718995i
\(315\) 0 0
\(316\) 0 0
\(317\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.101597 0.0738147i −0.101597 0.0738147i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.968583 0.248690i 0.968583 0.248690i
\(325\) 1.71137 0.216197i 1.71137 0.216197i
\(326\) 0 0
\(327\) 0 0
\(328\) 0.238883 0.288760i 0.238883 0.288760i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(332\) 0 0
\(333\) −1.11716 0.614163i −1.11716 0.614163i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.62954 + 0.895846i −1.62954 + 0.895846i −0.637424 + 0.770513i \(0.720000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(338\) −1.92617 0.762627i −1.92617 0.762627i
\(339\) 0 0
\(340\) 0.0680131 0.0373905i 0.0680131 0.0373905i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 1.18532 0.469303i 1.18532 0.469303i
\(347\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(348\) 0 0
\(349\) −0.683098 + 1.07639i −0.683098 + 1.07639i 0.309017 + 0.951057i \(0.400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.688925 + 1.46404i 0.688925 + 1.46404i 0.876307 + 0.481754i \(0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.683098 + 0.825723i −0.683098 + 0.825723i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(360\) 0.0388067 0.119435i 0.0388067 0.119435i
\(361\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(362\) −0.362989 + 1.90285i −0.362989 + 1.90285i
\(363\) 0 0
\(364\) 0 0
\(365\) −0.0721631 0.222095i −0.0721631 0.222095i
\(366\) 0 0
\(367\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(368\) 0 0
\(369\) 0.348445 + 0.137959i 0.348445 + 0.137959i
\(370\) −0.140294 + 0.0771272i −0.140294 + 0.0771272i
\(371\) 0 0
\(372\) 0 0
\(373\) −0.929324 + 0.872693i −0.929324 + 0.872693i −0.992115 0.125333i \(-0.960000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.178061 2.83019i −0.178061 2.83019i
\(378\) 0 0
\(379\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.371808 0.0469702i 0.371808 0.0469702i
\(387\) 0 0
\(388\) −0.273190 + 1.43211i −0.273190 + 1.43211i
\(389\) 0.0388067 0.616814i 0.0388067 0.616814i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.187381 0.982287i −0.187381 0.982287i
\(393\) 0 0
\(394\) −1.61803 −1.61803
\(395\) 0 0
\(396\) 0 0
\(397\) 1.27760 1.19975i 1.27760 1.19975i 0.309017 0.951057i \(-0.400000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.627371 + 0.758362i 0.627371 + 0.758362i
\(401\) 1.53583 + 0.844328i 1.53583 + 0.844328i 1.00000 \(0\)
0.535827 + 0.844328i \(0.320000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(405\) 0.125581 0.125581
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.362576 + 0.770513i 0.362576 + 0.770513i 1.00000 \(0\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(410\) 0.0380748 0.0276630i 0.0380748 0.0276630i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −0.328407 1.72157i −0.328407 1.72157i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.0627905 0.998027i \(-0.480000\pi\)
−0.0627905 + 0.998027i \(0.520000\pi\)
\(420\) 0 0
\(421\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.620759 + 1.31918i −0.620759 + 1.31918i
\(425\) −0.589177 + 0.151275i −0.589177 + 0.151275i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(432\) 0 0
\(433\) −1.44644 1.35830i −1.44644 1.35830i −0.809017 0.587785i \(-0.800000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(440\) 0 0
\(441\) 0.876307 0.481754i 0.876307 0.481754i
\(442\) 1.04914 + 0.269375i 1.04914 + 0.269375i
\(443\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(444\) 0 0
\(445\) −0.108877 + 0.0791038i −0.108877 + 0.0791038i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.06320 + 1.67534i −1.06320 + 1.67534i −0.425779 + 0.904827i \(0.640000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(450\) −0.527376 + 0.831012i −0.527376 + 0.831012i
\(451\) 0 0
\(452\) 0.542804 0.656137i 0.542804 0.656137i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.11716 + 1.35041i −1.11716 + 1.35041i −0.187381 + 0.982287i \(0.560000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(458\) −1.35556 0.536702i −1.35556 0.536702i
\(459\) 0 0
\(460\) 0 0
\(461\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(462\) 0 0
\(463\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(464\) 1.30902 0.951057i 1.30902 0.951057i
\(465\) 0 0
\(466\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(467\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(468\) 1.53583 0.844328i 1.53583 0.844328i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.44644 0.182728i −1.44644 0.182728i
\(478\) 0 0
\(479\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(480\) 0 0
\(481\) −2.16412 0.555652i −2.16412 0.555652i
\(482\) 1.96858 + 0.248690i 1.96858 + 0.248690i
\(483\) 0 0
\(484\) 0.968583 0.248690i 0.968583 0.248690i
\(485\) −0.0779556 + 0.165664i −0.0779556 + 0.165664i
\(486\) 0 0
\(487\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(488\) −1.56720 1.13864i −1.56720 1.13864i
\(489\) 0 0
\(490\) 0.00788530 0.125333i 0.00788530 0.125333i
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0.187381 + 0.982287i 0.187381 + 0.982287i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(500\) 0.106096 + 0.225466i 0.106096 + 0.225466i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(504\) 0 0
\(505\) −0.0534698 + 0.113629i −0.0534698 + 0.113629i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.03137 + 1.24672i 1.03137 + 1.24672i 0.968583 + 0.248690i \(0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.728969 0.684547i 0.728969 0.684547i
\(513\) 0 0
\(514\) 1.03799 + 1.63560i 1.03799 + 1.63560i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.0138199 0.219661i 0.0138199 0.219661i
\(521\) −0.362989 + 1.90285i −0.362989 + 1.90285i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(522\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(523\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(530\) −0.116705 + 0.141073i −0.116705 + 0.141073i
\(531\) 0 0
\(532\) 0 0
\(533\) 0.651635 + 0.0823206i 0.651635 + 0.0823206i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.124591 1.98031i −0.124591 1.98031i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(545\) 0.0681659 + 0.0823984i 0.0681659 + 0.0823984i
\(546\) 0 0
\(547\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(548\) 1.72897 0.684547i 1.72897 0.684547i
\(549\) 0.598617 1.84235i 0.598617 1.84235i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −0.0235315 + 0.374023i −0.0235315 + 0.374023i
\(555\) 0 0
\(556\) 0 0
\(557\) 0.0915446 1.45506i 0.0915446 1.45506i −0.637424 0.770513i \(-0.720000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(563\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(564\) 0 0
\(565\) 0.0865160 0.0628575i 0.0865160 0.0628575i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.41789 + 0.779494i −1.41789 + 0.779494i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(570\) 0 0
\(571\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(577\) −0.273190 0.256543i −0.273190 0.256543i 0.535827 0.844328i \(-0.320000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) 0.613161 + 0.0774602i 0.613161 + 0.0774602i
\(579\) 0 0
\(580\) 0.188925 0.0748008i 0.188925 0.0748008i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 1.84489 0.233064i 1.84489 0.233064i
\(585\) 0.213180 0.0547354i 0.213180 0.0547354i
\(586\) −0.456288 + 0.969661i −0.456288 + 0.969661i
\(587\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.393950 1.21245i −0.393950 1.21245i
\(593\) −1.44644 1.35830i −1.44644 1.35830i −0.809017 0.587785i \(-0.800000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.85955 −1.85955
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(600\) 0 0
\(601\) −0.263146 0.559214i −0.263146 0.559214i 0.728969 0.684547i \(-0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.125581 0.125581
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −0.155067 0.187444i −0.155067 0.187444i
\(611\) 0 0
\(612\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(613\) −1.44644 + 1.35830i −1.44644 + 1.35830i −0.637424 + 0.770513i \(0.720000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.781202 + 1.23098i 0.781202 + 1.23098i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.178563 0.936058i −0.178563 0.936058i
\(626\) −0.263146 + 0.559214i −0.263146 + 0.559214i
\(627\) 0 0
\(628\) 0.844844 0.106729i 0.844844 0.106729i
\(629\) 0.781687 + 0.0987500i 0.781687 + 0.0987500i
\(630\) 0 0
\(631\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −1.06320 0.134314i −1.06320 0.134314i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.27760 1.19975i 1.27760 1.19975i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.110048 0.0604991i 0.110048 0.0604991i
\(641\) −1.80113 0.713118i −1.80113 0.713118i −0.992115 0.125333i \(-0.960000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(642\) 0 0
\(643\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(648\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(649\) 0 0
\(650\) −0.533046 + 1.64055i −0.533046 + 1.64055i
\(651\) 0 0
\(652\) 0 0
\(653\) −0.574633 0.227513i −0.574633 0.227513i 0.0627905 0.998027i \(-0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.159566 + 0.339095i 0.159566 + 0.339095i
\(657\) 0.791759 + 1.68257i 0.791759 + 1.68257i
\(658\) 0 0
\(659\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(660\) 0 0
\(661\) −0.200808 + 0.316423i −0.200808 + 0.316423i −0.929776 0.368125i \(-0.880000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.03137 0.749337i 1.03137 0.749337i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.11716 + 0.614163i −1.11716 + 0.614163i −0.929776 0.368125i \(-0.880000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(674\) −0.116762 1.85588i −0.116762 1.85588i
\(675\) 0 0
\(676\) 1.51017 1.41814i 1.51017 1.41814i
\(677\) −1.73879 0.955910i −1.73879 0.955910i −0.929776 0.368125i \(-0.880000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.00487338 + 0.0774602i 0.00487338 + 0.0774602i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(684\) 0 0
\(685\) 0.231683 0.0292684i 0.231683 0.0292684i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.53505 + 0.320252i −2.53505 + 0.320252i
\(690\) 0 0
\(691\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(692\) −0.0800484 + 1.27233i −0.0800484 + 1.27233i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.231616 −0.231616
\(698\) −0.683098 1.07639i −0.683098 1.07639i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.61803 −1.61803
\(707\) 0 0
\(708\) 0 0
\(709\) −0.456288 + 0.969661i −0.456288 + 0.969661i 0.535827 + 0.844328i \(0.320000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.456288 0.969661i −0.456288 0.969661i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(720\) 0.0915446 + 0.0859661i 0.0915446 + 0.0859661i
\(721\) 0 0
\(722\) 0.0627905 0.998027i 0.0627905 0.998027i
\(723\) 0 0
\(724\) −1.56720 1.13864i −1.56720 1.13864i
\(725\) −1.57996 + 0.199595i −1.57996 + 0.199595i
\(726\) 0 0
\(727\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(728\) 0 0
\(729\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(730\) 0.231683 + 0.0292684i 0.231683 + 0.0292684i
\(731\) 0 0
\(732\) 0 0
\(733\) 0.791759 0.313480i 0.791759 0.313480i 0.0627905 0.998027i \(-0.480000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −0.273190 + 0.256543i −0.273190 + 0.256543i
\(739\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) −0.0100526 0.159781i −0.0100526 0.159781i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(744\) 0 0
\(745\) −0.226188 0.0580752i −0.226188 0.0580752i
\(746\) −0.393950 1.21245i −0.393950 1.21245i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 2.63665 + 1.04392i 2.63665 + 1.04392i
\(755\) 0 0
\(756\) 0 0
\(757\) −0.456288 0.969661i −0.456288 0.969661i −0.992115 0.125333i \(-0.960000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.18532 + 0.469303i 1.18532 + 0.469303i 0.876307 0.481754i \(-0.160000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.0721631 + 0.0285714i −0.0721631 + 0.0285714i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(773\) 1.72897 + 0.684547i 1.72897 + 0.684547i 1.00000 \(0\)
0.728969 + 0.684547i \(0.240000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.17950 0.856954i −1.17950 0.856954i
\(777\) 0 0
\(778\) 0.541587 + 0.297740i 0.541587 + 0.297740i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(785\) 0.106096 + 0.0134031i 0.106096 + 0.0134031i
\(786\) 0 0
\(787\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(788\) 0.688925 1.46404i 0.688925 1.46404i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.213180 3.38840i 0.213180 3.38840i
\(794\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(795\) 0 0
\(796\) 0 0
\(797\) 1.03799 + 1.63560i 1.03799 + 1.63560i 0.728969 + 0.684547i \(0.240000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.953308 + 0.244768i −0.953308 + 0.244768i
\(801\) 0.781202 0.733597i 0.781202 0.733597i
\(802\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −0.809017 0.587785i −0.809017 0.587785i
\(809\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(810\) −0.0534698 + 0.113629i −0.0534698 + 0.113629i
\(811\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −0.851559 −0.851559
\(819\) 0 0
\(820\) 0.00881874 + 0.0462295i 0.00881874 + 0.0462295i
\(821\) −0.273190 0.256543i −0.273190 0.256543i 0.535827 0.844328i \(-0.320000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(822\) 0 0
\(823\) 0 0 0.0627905 0.998027i \(-0.480000\pi\)
−0.0627905 + 0.998027i \(0.520000\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(828\) 0 0
\(829\) 1.69755 0.435857i 1.69755 0.435857i 0.728969 0.684547i \(-0.240000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.69755 + 0.435857i 1.69755 + 0.435857i
\(833\) −0.393950 + 0.476203i −0.393950 + 0.476203i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(840\) 0 0
\(841\) 0.101597 + 1.61484i 0.101597 + 1.61484i
\(842\) −1.73879 + 0.955910i −1.73879 + 0.955910i
\(843\) 0 0
\(844\) 0 0
\(845\) 0.227980 0.125333i 0.227980 0.125333i
\(846\) 0 0
\(847\) 0 0
\(848\) −0.929324 1.12336i −0.929324 1.12336i
\(849\) 0 0
\(850\) 0.113982 0.597513i 0.113982 0.597513i
\(851\) 0 0
\(852\) 0 0
\(853\) 0.574221 0.904827i 0.574221 0.904827i −0.425779 0.904827i \(-0.640000\pi\)
1.00000 \(0\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −0.116762 + 1.85588i −0.116762 + 1.85588i 0.309017 + 0.951057i \(0.400000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(858\) 0 0
\(859\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(864\) 0 0
\(865\) −0.0494726 + 0.152261i −0.0494726 + 0.152261i
\(866\) 1.84489 0.730444i 1.84489 0.730444i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −0.746226 + 0.410241i −0.746226 + 0.410241i
\(873\) 0.450527 1.38658i 0.450527 1.38658i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0.844844 + 0.106729i 0.844844 + 0.106729i 0.535827 0.844328i \(-0.320000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(882\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(883\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(884\) −0.690441 + 0.834600i −0.690441 + 0.834600i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −0.0252177 0.132196i −0.0252177 0.132196i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1.06320 1.67534i −1.06320 1.67534i
\(899\) 0 0
\(900\) −0.527376 0.831012i −0.527376 0.831012i
\(901\) 0.872746 0.224083i 0.872746 0.224083i
\(902\) 0 0
\(903\) 0 0
\(904\) 0.362576 + 0.770513i 0.362576 + 0.770513i
\(905\) −0.155067 0.187444i −0.155067 0.187444i
\(906\) 0 0
\(907\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(908\) 0 0
\(909\) 0.309017 0.951057i 0.309017 0.951057i
\(910\) 0 0
\(911\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.746226 1.58581i −0.746226 1.58581i
\(915\) 0 0
\(916\) 1.06279 0.998027i 1.06279 0.998027i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.781202 + 0.733597i 0.781202 + 0.733597i
\(923\) 0 0
\(924\) 0 0
\(925\) −0.235115 + 1.23252i −0.235115 + 1.23252i
\(926\) 0 0
\(927\) 0 0
\(928\) 0.303189 + 1.58937i 0.303189 + 1.58937i
\(929\) 0.688925 1.46404i 0.688925 1.46404i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −1.92189 0.242791i −1.92189 0.242791i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0.110048 + 1.74915i 0.110048 + 1.74915i
\(937\) −1.73879 0.219661i −1.73879 0.219661i −0.809017 0.587785i \(-0.800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(948\) 0 0
\(949\) 2.07741 + 2.51116i 2.07741 + 2.51116i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(954\) 0.781202 1.23098i 0.781202 1.23098i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.0627905 0.998027i 0.0627905 0.998027i
\(962\) 1.42421 1.72157i 1.42421 1.72157i
\(963\) 0 0
\(964\) −1.06320 + 1.67534i −1.06320 + 1.67534i
\(965\) −0.0252177 + 0.0397367i −0.0252177 + 0.0397367i
\(966\) 0 0
\(967\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(968\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(969\) 0 0
\(970\) −0.116705 0.141073i −0.116705 0.141073i
\(971\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 1.69755 0.933237i 1.69755 0.933237i
\(977\) 0.110048 + 1.74915i 0.110048 + 1.74915i 0.535827 + 0.844328i \(0.320000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.110048 + 0.0604991i 0.110048 + 0.0604991i
\(981\) −0.620759 0.582932i −0.620759 0.582932i
\(982\) 0 0
\(983\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(984\) 0 0
\(985\) 0.129521 0.156564i 0.129521 0.156564i
\(986\) −0.968583 0.248690i −0.968583 0.248690i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.06279 + 0.998027i 1.06279 + 0.998027i 1.00000 \(0\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(998\) 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 404.1.o.a.79.1 20
3.2 odd 2 3636.1.bt.a.2503.1 20
4.3 odd 2 CM 404.1.o.a.79.1 20
12.11 even 2 3636.1.bt.a.2503.1 20
101.78 even 25 inner 404.1.o.a.179.1 yes 20
303.179 odd 50 3636.1.bt.a.3007.1 20
404.179 odd 50 inner 404.1.o.a.179.1 yes 20
1212.179 even 50 3636.1.bt.a.3007.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
404.1.o.a.79.1 20 1.1 even 1 trivial
404.1.o.a.79.1 20 4.3 odd 2 CM
404.1.o.a.179.1 yes 20 101.78 even 25 inner
404.1.o.a.179.1 yes 20 404.179 odd 50 inner
3636.1.bt.a.2503.1 20 3.2 odd 2
3636.1.bt.a.2503.1 20 12.11 even 2
3636.1.bt.a.3007.1 20 303.179 odd 50
3636.1.bt.a.3007.1 20 1212.179 even 50