Properties

Label 592.3.k.c.401.1
Level $592$
Weight $3$
Character 592.401
Analytic conductor $16.131$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [592,3,Mod(401,592)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(592, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("592.401");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 592 = 2^{4} \cdot 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 592.k (of order \(4\), degree \(2\), not 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: \(16.1308316501\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 74)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 592.401
Dual form 592.3.k.c.561.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000i q^{3} +(3.00000 - 3.00000i) q^{5} +4.00000 q^{7} -7.00000 q^{9} +O(q^{10})\) \(q-4.00000i q^{3} +(3.00000 - 3.00000i) q^{5} +4.00000 q^{7} -7.00000 q^{9} -4.00000i q^{11} +(3.00000 - 3.00000i) q^{13} +(-12.0000 - 12.0000i) q^{15} +(23.0000 - 23.0000i) q^{17} +(-10.0000 + 10.0000i) q^{19} -16.0000i q^{21} +(10.0000 - 10.0000i) q^{23} +7.00000i q^{25} -8.00000i q^{27} +(-19.0000 - 19.0000i) q^{29} +(18.0000 + 18.0000i) q^{31} -16.0000 q^{33} +(12.0000 - 12.0000i) q^{35} -37.0000i q^{37} +(-12.0000 - 12.0000i) q^{39} +74.0000i q^{41} +(-42.0000 + 42.0000i) q^{43} +(-21.0000 + 21.0000i) q^{45} +44.0000 q^{47} -33.0000 q^{49} +(-92.0000 - 92.0000i) q^{51} -80.0000 q^{53} +(-12.0000 - 12.0000i) q^{55} +(40.0000 + 40.0000i) q^{57} +(54.0000 - 54.0000i) q^{59} +(-3.00000 - 3.00000i) q^{61} -28.0000 q^{63} -18.0000i q^{65} +12.0000i q^{67} +(-40.0000 - 40.0000i) q^{69} -124.000 q^{71} -10.0000i q^{73} +28.0000 q^{75} -16.0000i q^{77} +(-14.0000 + 14.0000i) q^{79} -95.0000 q^{81} +64.0000 q^{83} -138.000i q^{85} +(-76.0000 + 76.0000i) q^{87} +(17.0000 + 17.0000i) q^{89} +(12.0000 - 12.0000i) q^{91} +(72.0000 - 72.0000i) q^{93} +60.0000i q^{95} +(129.000 - 129.000i) q^{97} +28.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{5} + 8 q^{7} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{5} + 8 q^{7} - 14 q^{9} + 6 q^{13} - 24 q^{15} + 46 q^{17} - 20 q^{19} + 20 q^{23} - 38 q^{29} + 36 q^{31} - 32 q^{33} + 24 q^{35} - 24 q^{39} - 84 q^{43} - 42 q^{45} + 88 q^{47} - 66 q^{49} - 184 q^{51} - 160 q^{53} - 24 q^{55} + 80 q^{57} + 108 q^{59} - 6 q^{61} - 56 q^{63} - 80 q^{69} - 248 q^{71} + 56 q^{75} - 28 q^{79} - 190 q^{81} + 128 q^{83} - 152 q^{87} + 34 q^{89} + 24 q^{91} + 144 q^{93} + 258 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/592\mathbb{Z}\right)^\times\).

\(n\) \(113\) \(149\) \(223\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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 0
\(3\) 4.00000i 1.33333i −0.745356 0.666667i \(-0.767720\pi\)
0.745356 0.666667i \(-0.232280\pi\)
\(4\) 0 0
\(5\) 3.00000 3.00000i 0.600000 0.600000i −0.340312 0.940312i \(-0.610533\pi\)
0.940312 + 0.340312i \(0.110533\pi\)
\(6\) 0 0
\(7\) 4.00000 0.571429 0.285714 0.958315i \(-0.407769\pi\)
0.285714 + 0.958315i \(0.407769\pi\)
\(8\) 0 0
\(9\) −7.00000 −0.777778
\(10\) 0 0
\(11\) 4.00000i 0.363636i −0.983332 0.181818i \(-0.941802\pi\)
0.983332 0.181818i \(-0.0581982\pi\)
\(12\) 0 0
\(13\) 3.00000 3.00000i 0.230769 0.230769i −0.582245 0.813014i \(-0.697825\pi\)
0.813014 + 0.582245i \(0.197825\pi\)
\(14\) 0 0
\(15\) −12.0000 12.0000i −0.800000 0.800000i
\(16\) 0 0
\(17\) 23.0000 23.0000i 1.35294 1.35294i 0.470588 0.882353i \(-0.344042\pi\)
0.882353 0.470588i \(-0.155958\pi\)
\(18\) 0 0
\(19\) −10.0000 + 10.0000i −0.526316 + 0.526316i −0.919472 0.393156i \(-0.871383\pi\)
0.393156 + 0.919472i \(0.371383\pi\)
\(20\) 0 0
\(21\) 16.0000i 0.761905i
\(22\) 0 0
\(23\) 10.0000 10.0000i 0.434783 0.434783i −0.455469 0.890252i \(-0.650528\pi\)
0.890252 + 0.455469i \(0.150528\pi\)
\(24\) 0 0
\(25\) 7.00000i 0.280000i
\(26\) 0 0
\(27\) 8.00000i 0.296296i
\(28\) 0 0
\(29\) −19.0000 19.0000i −0.655172 0.655172i 0.299061 0.954234i \(-0.403326\pi\)
−0.954234 + 0.299061i \(0.903326\pi\)
\(30\) 0 0
\(31\) 18.0000 + 18.0000i 0.580645 + 0.580645i 0.935081 0.354435i \(-0.115327\pi\)
−0.354435 + 0.935081i \(0.615327\pi\)
\(32\) 0 0
\(33\) −16.0000 −0.484848
\(34\) 0 0
\(35\) 12.0000 12.0000i 0.342857 0.342857i
\(36\) 0 0
\(37\) 37.0000i 1.00000i
\(38\) 0 0
\(39\) −12.0000 12.0000i −0.307692 0.307692i
\(40\) 0 0
\(41\) 74.0000i 1.80488i 0.430818 + 0.902439i \(0.358225\pi\)
−0.430818 + 0.902439i \(0.641775\pi\)
\(42\) 0 0
\(43\) −42.0000 + 42.0000i −0.976744 + 0.976744i −0.999736 0.0229915i \(-0.992681\pi\)
0.0229915 + 0.999736i \(0.492681\pi\)
\(44\) 0 0
\(45\) −21.0000 + 21.0000i −0.466667 + 0.466667i
\(46\) 0 0
\(47\) 44.0000 0.936170 0.468085 0.883683i \(-0.344944\pi\)
0.468085 + 0.883683i \(0.344944\pi\)
\(48\) 0 0
\(49\) −33.0000 −0.673469
\(50\) 0 0
\(51\) −92.0000 92.0000i −1.80392 1.80392i
\(52\) 0 0
\(53\) −80.0000 −1.50943 −0.754717 0.656051i \(-0.772226\pi\)
−0.754717 + 0.656051i \(0.772226\pi\)
\(54\) 0 0
\(55\) −12.0000 12.0000i −0.218182 0.218182i
\(56\) 0 0
\(57\) 40.0000 + 40.0000i 0.701754 + 0.701754i
\(58\) 0 0
\(59\) 54.0000 54.0000i 0.915254 0.915254i −0.0814252 0.996679i \(-0.525947\pi\)
0.996679 + 0.0814252i \(0.0259472\pi\)
\(60\) 0 0
\(61\) −3.00000 3.00000i −0.0491803 0.0491803i 0.682089 0.731269i \(-0.261072\pi\)
−0.731269 + 0.682089i \(0.761072\pi\)
\(62\) 0 0
\(63\) −28.0000 −0.444444
\(64\) 0 0
\(65\) 18.0000i 0.276923i
\(66\) 0 0
\(67\) 12.0000i 0.179104i 0.995982 + 0.0895522i \(0.0285436\pi\)
−0.995982 + 0.0895522i \(0.971456\pi\)
\(68\) 0 0
\(69\) −40.0000 40.0000i −0.579710 0.579710i
\(70\) 0 0
\(71\) −124.000 −1.74648 −0.873239 0.487291i \(-0.837985\pi\)
−0.873239 + 0.487291i \(0.837985\pi\)
\(72\) 0 0
\(73\) 10.0000i 0.136986i −0.997652 0.0684932i \(-0.978181\pi\)
0.997652 0.0684932i \(-0.0218191\pi\)
\(74\) 0 0
\(75\) 28.0000 0.373333
\(76\) 0 0
\(77\) 16.0000i 0.207792i
\(78\) 0 0
\(79\) −14.0000 + 14.0000i −0.177215 + 0.177215i −0.790141 0.612926i \(-0.789993\pi\)
0.612926 + 0.790141i \(0.289993\pi\)
\(80\) 0 0
\(81\) −95.0000 −1.17284
\(82\) 0 0
\(83\) 64.0000 0.771084 0.385542 0.922690i \(-0.374014\pi\)
0.385542 + 0.922690i \(0.374014\pi\)
\(84\) 0 0
\(85\) 138.000i 1.62353i
\(86\) 0 0
\(87\) −76.0000 + 76.0000i −0.873563 + 0.873563i
\(88\) 0 0
\(89\) 17.0000 + 17.0000i 0.191011 + 0.191011i 0.796133 0.605122i \(-0.206876\pi\)
−0.605122 + 0.796133i \(0.706876\pi\)
\(90\) 0 0
\(91\) 12.0000 12.0000i 0.131868 0.131868i
\(92\) 0 0
\(93\) 72.0000 72.0000i 0.774194 0.774194i
\(94\) 0 0
\(95\) 60.0000i 0.631579i
\(96\) 0 0
\(97\) 129.000 129.000i 1.32990 1.32990i 0.424442 0.905455i \(-0.360470\pi\)
0.905455 0.424442i \(-0.139530\pi\)
\(98\) 0 0
\(99\) 28.0000i 0.282828i
\(100\) 0 0
\(101\) 118.000i 1.16832i 0.811640 + 0.584158i \(0.198575\pi\)
−0.811640 + 0.584158i \(0.801425\pi\)
\(102\) 0 0
\(103\) 42.0000 + 42.0000i 0.407767 + 0.407767i 0.880959 0.473192i \(-0.156898\pi\)
−0.473192 + 0.880959i \(0.656898\pi\)
\(104\) 0 0
\(105\) −48.0000 48.0000i −0.457143 0.457143i
\(106\) 0 0
\(107\) 24.0000 0.224299 0.112150 0.993691i \(-0.464226\pi\)
0.112150 + 0.993691i \(0.464226\pi\)
\(108\) 0 0
\(109\) −91.0000 + 91.0000i −0.834862 + 0.834862i −0.988177 0.153315i \(-0.951005\pi\)
0.153315 + 0.988177i \(0.451005\pi\)
\(110\) 0 0
\(111\) −148.000 −1.33333
\(112\) 0 0
\(113\) 7.00000 + 7.00000i 0.0619469 + 0.0619469i 0.737402 0.675455i \(-0.236053\pi\)
−0.675455 + 0.737402i \(0.736053\pi\)
\(114\) 0 0
\(115\) 60.0000i 0.521739i
\(116\) 0 0
\(117\) −21.0000 + 21.0000i −0.179487 + 0.179487i
\(118\) 0 0
\(119\) 92.0000 92.0000i 0.773109 0.773109i
\(120\) 0 0
\(121\) 105.000 0.867769
\(122\) 0 0
\(123\) 296.000 2.40650
\(124\) 0 0
\(125\) 96.0000 + 96.0000i 0.768000 + 0.768000i
\(126\) 0 0
\(127\) −76.0000 −0.598425 −0.299213 0.954186i \(-0.596724\pi\)
−0.299213 + 0.954186i \(0.596724\pi\)
\(128\) 0 0
\(129\) 168.000 + 168.000i 1.30233 + 1.30233i
\(130\) 0 0
\(131\) −70.0000 70.0000i −0.534351 0.534351i 0.387513 0.921864i \(-0.373334\pi\)
−0.921864 + 0.387513i \(0.873334\pi\)
\(132\) 0 0
\(133\) −40.0000 + 40.0000i −0.300752 + 0.300752i
\(134\) 0 0
\(135\) −24.0000 24.0000i −0.177778 0.177778i
\(136\) 0 0
\(137\) 216.000 1.57664 0.788321 0.615264i \(-0.210951\pi\)
0.788321 + 0.615264i \(0.210951\pi\)
\(138\) 0 0
\(139\) 180.000i 1.29496i −0.762081 0.647482i \(-0.775822\pi\)
0.762081 0.647482i \(-0.224178\pi\)
\(140\) 0 0
\(141\) 176.000i 1.24823i
\(142\) 0 0
\(143\) −12.0000 12.0000i −0.0839161 0.0839161i
\(144\) 0 0
\(145\) −114.000 −0.786207
\(146\) 0 0
\(147\) 132.000i 0.897959i
\(148\) 0 0
\(149\) −34.0000 −0.228188 −0.114094 0.993470i \(-0.536396\pi\)
−0.114094 + 0.993470i \(0.536396\pi\)
\(150\) 0 0
\(151\) 72.0000i 0.476821i 0.971164 + 0.238411i \(0.0766264\pi\)
−0.971164 + 0.238411i \(0.923374\pi\)
\(152\) 0 0
\(153\) −161.000 + 161.000i −1.05229 + 1.05229i
\(154\) 0 0
\(155\) 108.000 0.696774
\(156\) 0 0
\(157\) −14.0000 −0.0891720 −0.0445860 0.999006i \(-0.514197\pi\)
−0.0445860 + 0.999006i \(0.514197\pi\)
\(158\) 0 0
\(159\) 320.000i 2.01258i
\(160\) 0 0
\(161\) 40.0000 40.0000i 0.248447 0.248447i
\(162\) 0 0
\(163\) 66.0000 + 66.0000i 0.404908 + 0.404908i 0.879959 0.475051i \(-0.157570\pi\)
−0.475051 + 0.879959i \(0.657570\pi\)
\(164\) 0 0
\(165\) −48.0000 + 48.0000i −0.290909 + 0.290909i
\(166\) 0 0
\(167\) 230.000 230.000i 1.37725 1.37725i 0.528003 0.849242i \(-0.322941\pi\)
0.849242 0.528003i \(-0.177059\pi\)
\(168\) 0 0
\(169\) 151.000i 0.893491i
\(170\) 0 0
\(171\) 70.0000 70.0000i 0.409357 0.409357i
\(172\) 0 0
\(173\) 88.0000i 0.508671i −0.967116 0.254335i \(-0.918143\pi\)
0.967116 0.254335i \(-0.0818567\pi\)
\(174\) 0 0
\(175\) 28.0000i 0.160000i
\(176\) 0 0
\(177\) −216.000 216.000i −1.22034 1.22034i
\(178\) 0 0
\(179\) 166.000 + 166.000i 0.927374 + 0.927374i 0.997536 0.0701614i \(-0.0223514\pi\)
−0.0701614 + 0.997536i \(0.522351\pi\)
\(180\) 0 0
\(181\) 304.000 1.67956 0.839779 0.542928i \(-0.182684\pi\)
0.839779 + 0.542928i \(0.182684\pi\)
\(182\) 0 0
\(183\) −12.0000 + 12.0000i −0.0655738 + 0.0655738i
\(184\) 0 0
\(185\) −111.000 111.000i −0.600000 0.600000i
\(186\) 0 0
\(187\) −92.0000 92.0000i −0.491979 0.491979i
\(188\) 0 0
\(189\) 32.0000i 0.169312i
\(190\) 0 0
\(191\) −186.000 + 186.000i −0.973822 + 0.973822i −0.999666 0.0258440i \(-0.991773\pi\)
0.0258440 + 0.999666i \(0.491773\pi\)
\(192\) 0 0
\(193\) −9.00000 + 9.00000i −0.0466321 + 0.0466321i −0.730038 0.683406i \(-0.760498\pi\)
0.683406 + 0.730038i \(0.260498\pi\)
\(194\) 0 0
\(195\) −72.0000 −0.369231
\(196\) 0 0
\(197\) 34.0000 0.172589 0.0862944 0.996270i \(-0.472497\pi\)
0.0862944 + 0.996270i \(0.472497\pi\)
\(198\) 0 0
\(199\) −46.0000 46.0000i −0.231156 0.231156i 0.582019 0.813175i \(-0.302263\pi\)
−0.813175 + 0.582019i \(0.802263\pi\)
\(200\) 0 0
\(201\) 48.0000 0.238806
\(202\) 0 0
\(203\) −76.0000 76.0000i −0.374384 0.374384i
\(204\) 0 0
\(205\) 222.000 + 222.000i 1.08293 + 1.08293i
\(206\) 0 0
\(207\) −70.0000 + 70.0000i −0.338164 + 0.338164i
\(208\) 0 0
\(209\) 40.0000 + 40.0000i 0.191388 + 0.191388i
\(210\) 0 0
\(211\) 208.000 0.985782 0.492891 0.870091i \(-0.335940\pi\)
0.492891 + 0.870091i \(0.335940\pi\)
\(212\) 0 0
\(213\) 496.000i 2.32864i
\(214\) 0 0
\(215\) 252.000i 1.17209i
\(216\) 0 0
\(217\) 72.0000 + 72.0000i 0.331797 + 0.331797i
\(218\) 0 0
\(219\) −40.0000 −0.182648
\(220\) 0 0
\(221\) 138.000i 0.624434i
\(222\) 0 0
\(223\) 124.000 0.556054 0.278027 0.960573i \(-0.410320\pi\)
0.278027 + 0.960573i \(0.410320\pi\)
\(224\) 0 0
\(225\) 49.0000i 0.217778i
\(226\) 0 0
\(227\) 90.0000 90.0000i 0.396476 0.396476i −0.480512 0.876988i \(-0.659549\pi\)
0.876988 + 0.480512i \(0.159549\pi\)
\(228\) 0 0
\(229\) −2.00000 −0.00873362 −0.00436681 0.999990i \(-0.501390\pi\)
−0.00436681 + 0.999990i \(0.501390\pi\)
\(230\) 0 0
\(231\) −64.0000 −0.277056
\(232\) 0 0
\(233\) 42.0000i 0.180258i 0.995930 + 0.0901288i \(0.0287279\pi\)
−0.995930 + 0.0901288i \(0.971272\pi\)
\(234\) 0 0
\(235\) 132.000 132.000i 0.561702 0.561702i
\(236\) 0 0
\(237\) 56.0000 + 56.0000i 0.236287 + 0.236287i
\(238\) 0 0
\(239\) −22.0000 + 22.0000i −0.0920502 + 0.0920502i −0.751632 0.659582i \(-0.770733\pi\)
0.659582 + 0.751632i \(0.270733\pi\)
\(240\) 0 0
\(241\) −175.000 + 175.000i −0.726141 + 0.726141i −0.969849 0.243708i \(-0.921636\pi\)
0.243708 + 0.969849i \(0.421636\pi\)
\(242\) 0 0
\(243\) 308.000i 1.26749i
\(244\) 0 0
\(245\) −99.0000 + 99.0000i −0.404082 + 0.404082i
\(246\) 0 0
\(247\) 60.0000i 0.242915i
\(248\) 0 0
\(249\) 256.000i 1.02811i
\(250\) 0 0
\(251\) 198.000 + 198.000i 0.788845 + 0.788845i 0.981305 0.192460i \(-0.0616466\pi\)
−0.192460 + 0.981305i \(0.561647\pi\)
\(252\) 0 0
\(253\) −40.0000 40.0000i −0.158103 0.158103i
\(254\) 0 0
\(255\) −552.000 −2.16471
\(256\) 0 0
\(257\) −159.000 + 159.000i −0.618677 + 0.618677i −0.945192 0.326515i \(-0.894126\pi\)
0.326515 + 0.945192i \(0.394126\pi\)
\(258\) 0 0
\(259\) 148.000i 0.571429i
\(260\) 0 0
\(261\) 133.000 + 133.000i 0.509579 + 0.509579i
\(262\) 0 0
\(263\) 88.0000i 0.334601i 0.985906 + 0.167300i \(0.0535050\pi\)
−0.985906 + 0.167300i \(0.946495\pi\)
\(264\) 0 0
\(265\) −240.000 + 240.000i −0.905660 + 0.905660i
\(266\) 0 0
\(267\) 68.0000 68.0000i 0.254682 0.254682i
\(268\) 0 0
\(269\) 178.000 0.661710 0.330855 0.943682i \(-0.392663\pi\)
0.330855 + 0.943682i \(0.392663\pi\)
\(270\) 0 0
\(271\) −404.000 −1.49077 −0.745387 0.666631i \(-0.767735\pi\)
−0.745387 + 0.666631i \(0.767735\pi\)
\(272\) 0 0
\(273\) −48.0000 48.0000i −0.175824 0.175824i
\(274\) 0 0
\(275\) 28.0000 0.101818
\(276\) 0 0
\(277\) −147.000 147.000i −0.530686 0.530686i 0.390091 0.920776i \(-0.372444\pi\)
−0.920776 + 0.390091i \(0.872444\pi\)
\(278\) 0 0
\(279\) −126.000 126.000i −0.451613 0.451613i
\(280\) 0 0
\(281\) 135.000 135.000i 0.480427 0.480427i −0.424841 0.905268i \(-0.639670\pi\)
0.905268 + 0.424841i \(0.139670\pi\)
\(282\) 0 0
\(283\) 258.000 + 258.000i 0.911661 + 0.911661i 0.996403 0.0847421i \(-0.0270066\pi\)
−0.0847421 + 0.996403i \(0.527007\pi\)
\(284\) 0 0
\(285\) 240.000 0.842105
\(286\) 0 0
\(287\) 296.000i 1.03136i
\(288\) 0 0
\(289\) 769.000i 2.66090i
\(290\) 0 0
\(291\) −516.000 516.000i −1.77320 1.77320i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 324.000i 1.09831i
\(296\) 0 0
\(297\) −32.0000 −0.107744
\(298\) 0 0
\(299\) 60.0000i 0.200669i
\(300\) 0 0
\(301\) −168.000 + 168.000i −0.558140 + 0.558140i
\(302\) 0 0
\(303\) 472.000 1.55776
\(304\) 0 0
\(305\) −18.0000 −0.0590164
\(306\) 0 0
\(307\) 364.000i 1.18567i −0.805325 0.592834i \(-0.798009\pi\)
0.805325 0.592834i \(-0.201991\pi\)
\(308\) 0 0
\(309\) 168.000 168.000i 0.543689 0.543689i
\(310\) 0 0
\(311\) 238.000 + 238.000i 0.765273 + 0.765273i 0.977270 0.211997i \(-0.0679967\pi\)
−0.211997 + 0.977270i \(0.567997\pi\)
\(312\) 0 0
\(313\) 87.0000 87.0000i 0.277955 0.277955i −0.554337 0.832292i \(-0.687028\pi\)
0.832292 + 0.554337i \(0.187028\pi\)
\(314\) 0 0
\(315\) −84.0000 + 84.0000i −0.266667 + 0.266667i
\(316\) 0 0
\(317\) 264.000i 0.832808i 0.909180 + 0.416404i \(0.136710\pi\)
−0.909180 + 0.416404i \(0.863290\pi\)
\(318\) 0 0
\(319\) −76.0000 + 76.0000i −0.238245 + 0.238245i
\(320\) 0 0
\(321\) 96.0000i 0.299065i
\(322\) 0 0
\(323\) 460.000i 1.42415i
\(324\) 0 0
\(325\) 21.0000 + 21.0000i 0.0646154 + 0.0646154i
\(326\) 0 0
\(327\) 364.000 + 364.000i 1.11315 + 1.11315i
\(328\) 0 0
\(329\) 176.000 0.534954
\(330\) 0 0
\(331\) 326.000 326.000i 0.984894 0.984894i −0.0149933 0.999888i \(-0.504773\pi\)
0.999888 + 0.0149933i \(0.00477271\pi\)
\(332\) 0 0
\(333\) 259.000i 0.777778i
\(334\) 0 0
\(335\) 36.0000 + 36.0000i 0.107463 + 0.107463i
\(336\) 0 0
\(337\) 230.000i 0.682493i −0.939974 0.341246i \(-0.889151\pi\)
0.939974 0.341246i \(-0.110849\pi\)
\(338\) 0 0
\(339\) 28.0000 28.0000i 0.0825959 0.0825959i
\(340\) 0 0
\(341\) 72.0000 72.0000i 0.211144 0.211144i
\(342\) 0 0
\(343\) −328.000 −0.956268
\(344\) 0 0
\(345\) −240.000 −0.695652
\(346\) 0 0
\(347\) −362.000 362.000i −1.04323 1.04323i −0.999022 0.0442052i \(-0.985924\pi\)
−0.0442052 0.999022i \(-0.514076\pi\)
\(348\) 0 0
\(349\) −48.0000 −0.137536 −0.0687679 0.997633i \(-0.521907\pi\)
−0.0687679 + 0.997633i \(0.521907\pi\)
\(350\) 0 0
\(351\) −24.0000 24.0000i −0.0683761 0.0683761i
\(352\) 0 0
\(353\) 343.000 + 343.000i 0.971671 + 0.971671i 0.999610 0.0279383i \(-0.00889418\pi\)
−0.0279383 + 0.999610i \(0.508894\pi\)
\(354\) 0 0
\(355\) −372.000 + 372.000i −1.04789 + 1.04789i
\(356\) 0 0
\(357\) −368.000 368.000i −1.03081 1.03081i
\(358\) 0 0
\(359\) 404.000 1.12535 0.562674 0.826679i \(-0.309773\pi\)
0.562674 + 0.826679i \(0.309773\pi\)
\(360\) 0 0
\(361\) 161.000i 0.445983i
\(362\) 0 0
\(363\) 420.000i 1.15702i
\(364\) 0 0
\(365\) −30.0000 30.0000i −0.0821918 0.0821918i
\(366\) 0 0
\(367\) −492.000 −1.34060 −0.670300 0.742090i \(-0.733834\pi\)
−0.670300 + 0.742090i \(0.733834\pi\)
\(368\) 0 0
\(369\) 518.000i 1.40379i
\(370\) 0 0
\(371\) −320.000 −0.862534
\(372\) 0 0
\(373\) 488.000i 1.30831i −0.756360 0.654155i \(-0.773024\pi\)
0.756360 0.654155i \(-0.226976\pi\)
\(374\) 0 0
\(375\) 384.000 384.000i 1.02400 1.02400i
\(376\) 0 0
\(377\) −114.000 −0.302387
\(378\) 0 0
\(379\) 440.000 1.16095 0.580475 0.814278i \(-0.302867\pi\)
0.580475 + 0.814278i \(0.302867\pi\)
\(380\) 0 0
\(381\) 304.000i 0.797900i
\(382\) 0 0
\(383\) 450.000 450.000i 1.17493 1.17493i 0.193917 0.981018i \(-0.437881\pi\)
0.981018 0.193917i \(-0.0621192\pi\)
\(384\) 0 0
\(385\) −48.0000 48.0000i −0.124675 0.124675i
\(386\) 0 0
\(387\) 294.000 294.000i 0.759690 0.759690i
\(388\) 0 0
\(389\) 21.0000 21.0000i 0.0539846 0.0539846i −0.679599 0.733584i \(-0.737846\pi\)
0.733584 + 0.679599i \(0.237846\pi\)
\(390\) 0 0
\(391\) 460.000i 1.17647i
\(392\) 0 0
\(393\) −280.000 + 280.000i −0.712468 + 0.712468i
\(394\) 0 0
\(395\) 84.0000i 0.212658i
\(396\) 0 0
\(397\) 646.000i 1.62720i −0.581422 0.813602i \(-0.697504\pi\)
0.581422 0.813602i \(-0.302496\pi\)
\(398\) 0 0
\(399\) 160.000 + 160.000i 0.401003 + 0.401003i
\(400\) 0 0
\(401\) 273.000 + 273.000i 0.680798 + 0.680798i 0.960180 0.279382i \(-0.0901296\pi\)
−0.279382 + 0.960180i \(0.590130\pi\)
\(402\) 0 0
\(403\) 108.000 0.267990
\(404\) 0 0
\(405\) −285.000 + 285.000i −0.703704 + 0.703704i
\(406\) 0 0
\(407\) −148.000 −0.363636
\(408\) 0 0
\(409\) 39.0000 + 39.0000i 0.0953545 + 0.0953545i 0.753175 0.657820i \(-0.228521\pi\)
−0.657820 + 0.753175i \(0.728521\pi\)
\(410\) 0 0
\(411\) 864.000i 2.10219i
\(412\) 0 0
\(413\) 216.000 216.000i 0.523002 0.523002i
\(414\) 0 0
\(415\) 192.000 192.000i 0.462651 0.462651i
\(416\) 0 0
\(417\) −720.000 −1.72662
\(418\) 0 0
\(419\) −464.000 −1.10740 −0.553699 0.832717i \(-0.686784\pi\)
−0.553699 + 0.832717i \(0.686784\pi\)
\(420\) 0 0
\(421\) −469.000 469.000i −1.11401 1.11401i −0.992602 0.121412i \(-0.961258\pi\)
−0.121412 0.992602i \(-0.538742\pi\)
\(422\) 0 0
\(423\) −308.000 −0.728132
\(424\) 0 0
\(425\) 161.000 + 161.000i 0.378824 + 0.378824i
\(426\) 0 0
\(427\) −12.0000 12.0000i −0.0281030 0.0281030i
\(428\) 0 0
\(429\) −48.0000 + 48.0000i −0.111888 + 0.111888i
\(430\) 0 0
\(431\) −450.000 450.000i −1.04408 1.04408i −0.998982 0.0451011i \(-0.985639\pi\)
−0.0451011 0.998982i \(-0.514361\pi\)
\(432\) 0 0
\(433\) 200.000 0.461894 0.230947 0.972966i \(-0.425818\pi\)
0.230947 + 0.972966i \(0.425818\pi\)
\(434\) 0 0
\(435\) 456.000i 1.04828i
\(436\) 0 0
\(437\) 200.000i 0.457666i
\(438\) 0 0
\(439\) −246.000 246.000i −0.560364 0.560364i 0.369046 0.929411i \(-0.379684\pi\)
−0.929411 + 0.369046i \(0.879684\pi\)
\(440\) 0 0
\(441\) 231.000 0.523810
\(442\) 0 0
\(443\) 668.000i 1.50790i 0.656931 + 0.753950i \(0.271854\pi\)
−0.656931 + 0.753950i \(0.728146\pi\)
\(444\) 0 0
\(445\) 102.000 0.229213
\(446\) 0 0
\(447\) 136.000i 0.304251i
\(448\) 0 0
\(449\) 199.000 199.000i 0.443207 0.443207i −0.449881 0.893088i \(-0.648534\pi\)
0.893088 + 0.449881i \(0.148534\pi\)
\(450\) 0 0
\(451\) 296.000 0.656319
\(452\) 0 0
\(453\) 288.000 0.635762
\(454\) 0 0
\(455\) 72.0000i 0.158242i
\(456\) 0 0
\(457\) −255.000 + 255.000i −0.557987 + 0.557987i −0.928734 0.370747i \(-0.879102\pi\)
0.370747 + 0.928734i \(0.379102\pi\)
\(458\) 0 0
\(459\) −184.000 184.000i −0.400871 0.400871i
\(460\) 0 0
\(461\) −555.000 + 555.000i −1.20390 + 1.20390i −0.230935 + 0.972969i \(0.574179\pi\)
−0.972969 + 0.230935i \(0.925821\pi\)
\(462\) 0 0
\(463\) −554.000 + 554.000i −1.19654 + 1.19654i −0.221350 + 0.975194i \(0.571046\pi\)
−0.975194 + 0.221350i \(0.928954\pi\)
\(464\) 0 0
\(465\) 432.000i 0.929032i
\(466\) 0 0
\(467\) −158.000 + 158.000i −0.338330 + 0.338330i −0.855738 0.517409i \(-0.826897\pi\)
0.517409 + 0.855738i \(0.326897\pi\)
\(468\) 0 0
\(469\) 48.0000i 0.102345i
\(470\) 0 0
\(471\) 56.0000i 0.118896i
\(472\) 0 0
\(473\) 168.000 + 168.000i 0.355180 + 0.355180i
\(474\) 0 0
\(475\) −70.0000 70.0000i −0.147368 0.147368i
\(476\) 0 0
\(477\) 560.000 1.17400
\(478\) 0 0
\(479\) −290.000 + 290.000i −0.605428 + 0.605428i −0.941748 0.336320i \(-0.890818\pi\)
0.336320 + 0.941748i \(0.390818\pi\)
\(480\) 0 0
\(481\) −111.000 111.000i −0.230769 0.230769i
\(482\) 0 0
\(483\) −160.000 160.000i −0.331263 0.331263i
\(484\) 0 0
\(485\) 774.000i 1.59588i
\(486\) 0 0
\(487\) −266.000 + 266.000i −0.546201 + 0.546201i −0.925340 0.379139i \(-0.876220\pi\)
0.379139 + 0.925340i \(0.376220\pi\)
\(488\) 0 0
\(489\) 264.000 264.000i 0.539877 0.539877i
\(490\) 0 0
\(491\) −312.000 −0.635438 −0.317719 0.948185i \(-0.602917\pi\)
−0.317719 + 0.948185i \(0.602917\pi\)
\(492\) 0 0
\(493\) −874.000 −1.77282
\(494\) 0 0
\(495\) 84.0000 + 84.0000i 0.169697 + 0.169697i
\(496\) 0 0
\(497\) −496.000 −0.997988
\(498\) 0 0
\(499\) 210.000 + 210.000i 0.420842 + 0.420842i 0.885493 0.464652i \(-0.153820\pi\)
−0.464652 + 0.885493i \(0.653820\pi\)
\(500\) 0 0
\(501\) −920.000 920.000i −1.83633 1.83633i
\(502\) 0 0
\(503\) −298.000 + 298.000i −0.592445 + 0.592445i −0.938291 0.345846i \(-0.887592\pi\)
0.345846 + 0.938291i \(0.387592\pi\)
\(504\) 0 0
\(505\) 354.000 + 354.000i 0.700990 + 0.700990i
\(506\) 0 0
\(507\) 604.000 1.19132
\(508\) 0 0
\(509\) 808.000i 1.58743i 0.608292 + 0.793713i \(0.291855\pi\)
−0.608292 + 0.793713i \(0.708145\pi\)
\(510\) 0 0
\(511\) 40.0000i 0.0782779i
\(512\) 0 0
\(513\) 80.0000 + 80.0000i 0.155945 + 0.155945i
\(514\) 0 0
\(515\) 252.000 0.489320
\(516\) 0 0
\(517\) 176.000i 0.340426i
\(518\) 0 0
\(519\) −352.000 −0.678227
\(520\) 0 0
\(521\) 170.000i 0.326296i −0.986602 0.163148i \(-0.947835\pi\)
0.986602 0.163148i \(-0.0521647\pi\)
\(522\) 0 0
\(523\) −654.000 + 654.000i −1.25048 + 1.25048i −0.294972 + 0.955506i \(0.595310\pi\)
−0.955506 + 0.294972i \(0.904690\pi\)
\(524\) 0 0
\(525\) 112.000 0.213333
\(526\) 0 0
\(527\) 828.000 1.57116
\(528\) 0 0
\(529\) 329.000i 0.621928i
\(530\) 0 0
\(531\) −378.000 + 378.000i −0.711864 + 0.711864i
\(532\) 0 0
\(533\) 222.000 + 222.000i 0.416510 + 0.416510i
\(534\) 0 0
\(535\) 72.0000 72.0000i 0.134579 0.134579i
\(536\) 0 0
\(537\) 664.000 664.000i 1.23650 1.23650i
\(538\) 0 0
\(539\) 132.000i 0.244898i
\(540\) 0 0
\(541\) 147.000 147.000i 0.271719 0.271719i −0.558073 0.829792i \(-0.688459\pi\)
0.829792 + 0.558073i \(0.188459\pi\)
\(542\) 0 0
\(543\) 1216.00i 2.23941i
\(544\) 0 0
\(545\) 546.000i 1.00183i
\(546\) 0 0
\(547\) 294.000 + 294.000i 0.537477 + 0.537477i 0.922787 0.385310i \(-0.125905\pi\)
−0.385310 + 0.922787i \(0.625905\pi\)
\(548\) 0 0
\(549\) 21.0000 + 21.0000i 0.0382514 + 0.0382514i
\(550\) 0 0
\(551\) 380.000 0.689655
\(552\) 0 0
\(553\) −56.0000 + 56.0000i −0.101266 + 0.101266i
\(554\) 0 0
\(555\) −444.000 + 444.000i −0.800000 + 0.800000i
\(556\) 0 0
\(557\) −179.000 179.000i −0.321364 0.321364i 0.527926 0.849290i \(-0.322970\pi\)
−0.849290 + 0.527926i \(0.822970\pi\)
\(558\) 0 0
\(559\) 252.000i 0.450805i
\(560\) 0 0
\(561\) −368.000 + 368.000i −0.655971 + 0.655971i
\(562\) 0 0
\(563\) −282.000 + 282.000i −0.500888 + 0.500888i −0.911714 0.410826i \(-0.865240\pi\)
0.410826 + 0.911714i \(0.365240\pi\)
\(564\) 0 0
\(565\) 42.0000 0.0743363
\(566\) 0 0
\(567\) −380.000 −0.670194
\(568\) 0 0
\(569\) 375.000 + 375.000i 0.659051 + 0.659051i 0.955156 0.296105i \(-0.0956877\pi\)
−0.296105 + 0.955156i \(0.595688\pi\)
\(570\) 0 0
\(571\) 184.000 0.322242 0.161121 0.986935i \(-0.448489\pi\)
0.161121 + 0.986935i \(0.448489\pi\)
\(572\) 0 0
\(573\) 744.000 + 744.000i 1.29843 + 1.29843i
\(574\) 0 0
\(575\) 70.0000 + 70.0000i 0.121739 + 0.121739i
\(576\) 0 0
\(577\) −623.000 + 623.000i −1.07972 + 1.07972i −0.0831889 + 0.996534i \(0.526510\pi\)
−0.996534 + 0.0831889i \(0.973490\pi\)
\(578\) 0 0
\(579\) 36.0000 + 36.0000i 0.0621762 + 0.0621762i
\(580\) 0 0
\(581\) 256.000 0.440620
\(582\) 0 0
\(583\) 320.000i 0.548885i
\(584\) 0 0
\(585\) 126.000i 0.215385i
\(586\) 0 0
\(587\) 382.000 + 382.000i 0.650767 + 0.650767i 0.953178 0.302411i \(-0.0977915\pi\)
−0.302411 + 0.953178i \(0.597792\pi\)
\(588\) 0 0
\(589\) −360.000 −0.611205
\(590\) 0 0
\(591\) 136.000i 0.230118i
\(592\) 0 0
\(593\) 734.000 1.23777 0.618887 0.785480i \(-0.287584\pi\)
0.618887 + 0.785480i \(0.287584\pi\)
\(594\) 0 0
\(595\) 552.000i 0.927731i
\(596\) 0 0
\(597\) −184.000 + 184.000i −0.308208 + 0.308208i
\(598\) 0 0
\(599\) 1004.00 1.67613 0.838063 0.545573i \(-0.183688\pi\)
0.838063 + 0.545573i \(0.183688\pi\)
\(600\) 0 0
\(601\) 306.000 0.509151 0.254576 0.967053i \(-0.418064\pi\)
0.254576 + 0.967053i \(0.418064\pi\)
\(602\) 0 0
\(603\) 84.0000i 0.139303i
\(604\) 0 0
\(605\) 315.000 315.000i 0.520661 0.520661i
\(606\) 0 0
\(607\) −298.000 298.000i −0.490939 0.490939i 0.417663 0.908602i \(-0.362849\pi\)
−0.908602 + 0.417663i \(0.862849\pi\)
\(608\) 0 0
\(609\) −304.000 + 304.000i −0.499179 + 0.499179i
\(610\) 0 0
\(611\) 132.000 132.000i 0.216039 0.216039i
\(612\) 0 0
\(613\) 470.000i 0.766721i 0.923599 + 0.383361i \(0.125233\pi\)
−0.923599 + 0.383361i \(0.874767\pi\)
\(614\) 0 0
\(615\) 888.000 888.000i 1.44390 1.44390i
\(616\) 0 0
\(617\) 304.000i 0.492707i 0.969180 + 0.246353i \(0.0792324\pi\)
−0.969180 + 0.246353i \(0.920768\pi\)
\(618\) 0 0
\(619\) 956.000i 1.54443i −0.635363 0.772213i \(-0.719150\pi\)
0.635363 0.772213i \(-0.280850\pi\)
\(620\) 0 0
\(621\) −80.0000 80.0000i −0.128824 0.128824i
\(622\) 0 0
\(623\) 68.0000 + 68.0000i 0.109149 + 0.109149i
\(624\) 0 0
\(625\) 401.000 0.641600
\(626\) 0 0
\(627\) 160.000 160.000i 0.255183 0.255183i
\(628\) 0 0
\(629\) −851.000 851.000i −1.35294 1.35294i
\(630\) 0 0
\(631\) 362.000 + 362.000i 0.573693 + 0.573693i 0.933158 0.359466i \(-0.117041\pi\)
−0.359466 + 0.933158i \(0.617041\pi\)
\(632\) 0 0
\(633\) 832.000i 1.31438i
\(634\) 0 0
\(635\) −228.000 + 228.000i −0.359055 + 0.359055i
\(636\) 0 0
\(637\) −99.0000 + 99.0000i −0.155416 + 0.155416i
\(638\) 0 0
\(639\) 868.000 1.35837
\(640\) 0 0
\(641\) −398.000 −0.620905 −0.310452 0.950589i \(-0.600481\pi\)
−0.310452 + 0.950589i \(0.600481\pi\)
\(642\) 0 0
\(643\) −218.000 218.000i −0.339036 0.339036i 0.516969 0.856004i \(-0.327060\pi\)
−0.856004 + 0.516969i \(0.827060\pi\)
\(644\) 0 0
\(645\) 1008.00 1.56279
\(646\) 0 0
\(647\) 358.000 + 358.000i 0.553323 + 0.553323i 0.927398 0.374075i \(-0.122040\pi\)
−0.374075 + 0.927398i \(0.622040\pi\)
\(648\) 0 0
\(649\) −216.000 216.000i −0.332820 0.332820i
\(650\) 0 0
\(651\) 288.000 288.000i 0.442396 0.442396i
\(652\) 0 0
\(653\) 555.000 + 555.000i 0.849923 + 0.849923i 0.990123 0.140200i \(-0.0447745\pi\)
−0.140200 + 0.990123i \(0.544774\pi\)
\(654\) 0 0
\(655\) −420.000 −0.641221
\(656\) 0 0
\(657\) 70.0000i 0.106545i
\(658\) 0 0
\(659\) 788.000i 1.19575i −0.801589 0.597876i \(-0.796012\pi\)
0.801589 0.597876i \(-0.203988\pi\)
\(660\) 0 0
\(661\) −661.000 661.000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) −552.000 −0.832579
\(664\) 0 0
\(665\) 240.000i 0.360902i
\(666\) 0 0
\(667\) −380.000 −0.569715
\(668\) 0 0
\(669\) 496.000i 0.741405i
\(670\) 0 0
\(671\) −12.0000 + 12.0000i −0.0178838 + 0.0178838i
\(672\) 0 0
\(673\) 50.0000 0.0742942 0.0371471 0.999310i \(-0.488173\pi\)
0.0371471 + 0.999310i \(0.488173\pi\)
\(674\) 0 0
\(675\) 56.0000 0.0829630
\(676\) 0 0
\(677\) 296.000i 0.437223i −0.975812 0.218612i \(-0.929847\pi\)
0.975812 0.218612i \(-0.0701527\pi\)
\(678\) 0 0
\(679\) 516.000 516.000i 0.759941 0.759941i
\(680\) 0 0
\(681\) −360.000 360.000i −0.528634 0.528634i
\(682\) 0 0
\(683\) −6.00000 + 6.00000i −0.00878477 + 0.00878477i −0.711486 0.702701i \(-0.751977\pi\)
0.702701 + 0.711486i \(0.251977\pi\)
\(684\) 0 0
\(685\) 648.000 648.000i 0.945985 0.945985i
\(686\) 0 0
\(687\) 8.00000i 0.0116448i
\(688\) 0 0
\(689\) −240.000 + 240.000i −0.348331 + 0.348331i
\(690\) 0 0
\(691\) 708.000i 1.02460i 0.858806 + 0.512301i \(0.171207\pi\)
−0.858806 + 0.512301i \(0.828793\pi\)
\(692\) 0 0
\(693\) 112.000i 0.161616i
\(694\) 0 0
\(695\) −540.000 540.000i −0.776978 0.776978i
\(696\) 0 0
\(697\) 1702.00 + 1702.00i 2.44189 + 2.44189i
\(698\) 0 0
\(699\) 168.000 0.240343
\(700\) 0 0
\(701\) 291.000 291.000i 0.415121 0.415121i −0.468397 0.883518i \(-0.655168\pi\)
0.883518 + 0.468397i \(0.155168\pi\)
\(702\) 0 0
\(703\) 370.000 + 370.000i 0.526316 + 0.526316i
\(704\) 0 0
\(705\) −528.000 528.000i −0.748936 0.748936i
\(706\) 0 0
\(707\) 472.000i 0.667610i
\(708\) 0 0
\(709\) −77.0000 + 77.0000i −0.108604 + 0.108604i −0.759320 0.650717i \(-0.774469\pi\)
0.650717 + 0.759320i \(0.274469\pi\)
\(710\) 0 0
\(711\) 98.0000 98.0000i 0.137834 0.137834i
\(712\) 0 0
\(713\) 360.000 0.504909
\(714\) 0 0
\(715\) −72.0000 −0.100699
\(716\) 0 0
\(717\) 88.0000 + 88.0000i 0.122734 + 0.122734i
\(718\) 0 0
\(719\) 412.000 0.573018 0.286509 0.958078i \(-0.407505\pi\)
0.286509 + 0.958078i \(0.407505\pi\)
\(720\) 0 0
\(721\) 168.000 + 168.000i 0.233010 + 0.233010i
\(722\) 0 0
\(723\) 700.000 + 700.000i 0.968188 + 0.968188i
\(724\) 0 0
\(725\) 133.000 133.000i 0.183448 0.183448i
\(726\) 0 0
\(727\) 262.000 + 262.000i 0.360385 + 0.360385i 0.863955 0.503570i \(-0.167980\pi\)
−0.503570 + 0.863955i \(0.667980\pi\)
\(728\) 0 0
\(729\) 377.000 0.517147
\(730\) 0 0
\(731\) 1932.00i 2.64295i
\(732\) 0 0
\(733\) 682.000i 0.930423i 0.885200 + 0.465211i \(0.154022\pi\)
−0.885200 + 0.465211i \(0.845978\pi\)
\(734\) 0 0
\(735\) 396.000 + 396.000i 0.538776 + 0.538776i
\(736\) 0 0
\(737\) 48.0000 0.0651289
\(738\) 0 0
\(739\) 100.000i 0.135318i −0.997709 0.0676590i \(-0.978447\pi\)
0.997709 0.0676590i \(-0.0215530\pi\)
\(740\) 0 0
\(741\) 240.000 0.323887
\(742\) 0 0
\(743\) 800.000i 1.07672i 0.842716 + 0.538358i \(0.180955\pi\)
−0.842716 + 0.538358i \(0.819045\pi\)
\(744\) 0 0
\(745\) −102.000 + 102.000i −0.136913 + 0.136913i
\(746\) 0 0
\(747\) −448.000 −0.599732
\(748\) 0 0
\(749\) 96.0000 0.128171
\(750\) 0 0
\(751\) 536.000i 0.713715i −0.934159 0.356858i \(-0.883848\pi\)
0.934159 0.356858i \(-0.116152\pi\)
\(752\) 0 0
\(753\) 792.000 792.000i 1.05179 1.05179i
\(754\) 0 0
\(755\) 216.000 + 216.000i 0.286093 + 0.286093i
\(756\) 0 0
\(757\) −157.000 + 157.000i −0.207398 + 0.207398i −0.803160 0.595763i \(-0.796850\pi\)
0.595763 + 0.803160i \(0.296850\pi\)
\(758\) 0 0
\(759\) −160.000 + 160.000i −0.210804 + 0.210804i
\(760\) 0 0
\(761\) 272.000i 0.357424i 0.983901 + 0.178712i \(0.0571931\pi\)
−0.983901 + 0.178712i \(0.942807\pi\)
\(762\) 0 0
\(763\) −364.000 + 364.000i −0.477064 + 0.477064i
\(764\) 0 0
\(765\) 966.000i 1.26275i
\(766\) 0 0
\(767\) 324.000i 0.422425i
\(768\) 0 0
\(769\) −761.000 761.000i −0.989597 0.989597i 0.0103496 0.999946i \(-0.496706\pi\)
−0.999946 + 0.0103496i \(0.996706\pi\)
\(770\) 0 0
\(771\) 636.000 + 636.000i 0.824903 + 0.824903i
\(772\) 0 0
\(773\) −1282.00 −1.65847 −0.829237 0.558898i \(-0.811225\pi\)
−0.829237 + 0.558898i \(0.811225\pi\)
\(774\) 0 0
\(775\) −126.000 + 126.000i −0.162581 + 0.162581i
\(776\) 0 0
\(777\) −592.000 −0.761905
\(778\) 0 0
\(779\) −740.000 740.000i −0.949936 0.949936i
\(780\) 0 0
\(781\) 496.000i 0.635083i
\(782\) 0 0
\(783\) −152.000 + 152.000i −0.194125 + 0.194125i
\(784\) 0 0
\(785\) −42.0000 + 42.0000i −0.0535032 + 0.0535032i
\(786\) 0 0
\(787\) 376.000 0.477764 0.238882 0.971049i \(-0.423219\pi\)
0.238882 + 0.971049i \(0.423219\pi\)
\(788\) 0 0
\(789\) 352.000 0.446134
\(790\) 0 0
\(791\) 28.0000 + 28.0000i 0.0353982 + 0.0353982i
\(792\) 0 0
\(793\) −18.0000 −0.0226986
\(794\) 0 0
\(795\) 960.000 + 960.000i 1.20755 + 1.20755i
\(796\) 0 0
\(797\) −69.0000 69.0000i −0.0865747 0.0865747i 0.662493 0.749068i \(-0.269498\pi\)
−0.749068 + 0.662493i \(0.769498\pi\)
\(798\) 0 0
\(799\) 1012.00 1012.00i 1.26658 1.26658i
\(800\) 0 0
\(801\) −119.000 119.000i −0.148564 0.148564i
\(802\) 0 0
\(803\) −40.0000 −0.0498132
\(804\) 0 0
\(805\) 240.000i 0.298137i
\(806\) 0 0
\(807\) 712.000i 0.882280i
\(808\) 0 0
\(809\) 631.000 + 631.000i 0.779975 + 0.779975i 0.979826 0.199851i \(-0.0640458\pi\)
−0.199851 + 0.979826i \(0.564046\pi\)
\(810\) 0 0
\(811\) −1184.00 −1.45993 −0.729963 0.683487i \(-0.760463\pi\)
−0.729963 + 0.683487i \(0.760463\pi\)
\(812\) 0 0
\(813\) 1616.00i 1.98770i
\(814\) 0 0
\(815\) 396.000 0.485890
\(816\) 0 0
\(817\) 840.000i 1.02815i
\(818\) 0 0
\(819\) −84.0000 + 84.0000i −0.102564 + 0.102564i
\(820\) 0 0
\(821\) 784.000 0.954933 0.477467 0.878650i \(-0.341555\pi\)
0.477467 + 0.878650i \(0.341555\pi\)
\(822\) 0 0
\(823\) −1116.00 −1.35601 −0.678007 0.735055i \(-0.737156\pi\)
−0.678007 + 0.735055i \(0.737156\pi\)
\(824\) 0 0
\(825\) 112.000i 0.135758i
\(826\) 0 0
\(827\) −382.000 + 382.000i −0.461911 + 0.461911i −0.899281 0.437371i \(-0.855910\pi\)
0.437371 + 0.899281i \(0.355910\pi\)
\(828\) 0 0
\(829\) 603.000 + 603.000i 0.727382 + 0.727382i 0.970098 0.242715i \(-0.0780381\pi\)
−0.242715 + 0.970098i \(0.578038\pi\)
\(830\) 0 0
\(831\) −588.000 + 588.000i −0.707581 + 0.707581i
\(832\) 0 0
\(833\) −759.000 + 759.000i −0.911164 + 0.911164i
\(834\) 0 0
\(835\) 1380.00i 1.65269i
\(836\) 0 0
\(837\) 144.000 144.000i 0.172043 0.172043i
\(838\) 0 0
\(839\) 48.0000i 0.0572110i 0.999591 + 0.0286055i \(0.00910665\pi\)
−0.999591 + 0.0286055i \(0.990893\pi\)
\(840\) 0 0
\(841\) 119.000i 0.141498i
\(842\) 0 0
\(843\) −540.000 540.000i −0.640569 0.640569i
\(844\) 0 0
\(845\) 453.000 + 453.000i 0.536095 + 0.536095i
\(846\) 0 0
\(847\) 420.000 0.495868
\(848\) 0 0
\(849\) 1032.00 1032.00i 1.21555 1.21555i
\(850\) 0 0
\(851\) −370.000 370.000i −0.434783 0.434783i
\(852\) 0 0
\(853\) −163.000 163.000i −0.191090 0.191090i 0.605077 0.796167i \(-0.293142\pi\)
−0.796167 + 0.605077i \(0.793142\pi\)
\(854\) 0 0
\(855\) 420.000i 0.491228i
\(856\) 0 0
\(857\) −815.000 + 815.000i −0.950992 + 0.950992i −0.998854 0.0478621i \(-0.984759\pi\)
0.0478621 + 0.998854i \(0.484759\pi\)
\(858\) 0 0
\(859\) −962.000 + 962.000i −1.11991 + 1.11991i −0.128152 + 0.991754i \(0.540905\pi\)
−0.991754 + 0.128152i \(0.959095\pi\)
\(860\) 0 0
\(861\) 1184.00 1.37515
\(862\) 0 0
\(863\) −156.000 −0.180765 −0.0903824 0.995907i \(-0.528809\pi\)
−0.0903824 + 0.995907i \(0.528809\pi\)
\(864\) 0 0
\(865\) −264.000 264.000i −0.305202 0.305202i
\(866\) 0 0
\(867\) −3076.00 −3.54787
\(868\) 0 0
\(869\) 56.0000 + 56.0000i 0.0644419 + 0.0644419i
\(870\) 0 0
\(871\) 36.0000 + 36.0000i 0.0413318 + 0.0413318i
\(872\) 0 0
\(873\) −903.000 + 903.000i −1.03436 + 1.03436i
\(874\) 0 0
\(875\) 384.000 + 384.000i 0.438857 + 0.438857i
\(876\) 0 0
\(877\) 210.000 0.239453 0.119726 0.992807i \(-0.461798\pi\)
0.119726 + 0.992807i \(0.461798\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 720.000i 0.817253i −0.912702 0.408627i \(-0.866008\pi\)
0.912702 0.408627i \(-0.133992\pi\)
\(882\) 0 0
\(883\) 294.000 + 294.000i 0.332956 + 0.332956i 0.853708 0.520752i \(-0.174348\pi\)
−0.520752 + 0.853708i \(0.674348\pi\)
\(884\) 0 0
\(885\) −1296.00 −1.46441
\(886\) 0 0
\(887\) 904.000i 1.01917i −0.860422 0.509583i \(-0.829800\pi\)
0.860422 0.509583i \(-0.170200\pi\)
\(888\) 0 0
\(889\) −304.000 −0.341957
\(890\) 0 0
\(891\) 380.000i 0.426487i
\(892\) 0 0
\(893\) −440.000 + 440.000i −0.492721 + 0.492721i
\(894\) 0 0
\(895\) 996.000 1.11285
\(896\) 0 0
\(897\) −240.000 −0.267559
\(898\) 0 0
\(899\) 684.000i 0.760845i
\(900\) 0 0
\(901\) −1840.00 + 1840.00i −2.04218 + 2.04218i
\(902\) 0 0
\(903\) 672.000 + 672.000i 0.744186 + 0.744186i
\(904\) 0 0
\(905\) 912.000 912.000i 1.00773 1.00773i
\(906\) 0 0
\(907\) −618.000 + 618.000i −0.681367 + 0.681367i −0.960308 0.278941i \(-0.910017\pi\)
0.278941 + 0.960308i \(0.410017\pi\)
\(908\) 0 0
\(909\) 826.000i 0.908691i
\(910\) 0 0
\(911\) 882.000 882.000i 0.968167 0.968167i −0.0313419 0.999509i \(-0.509978\pi\)
0.999509 + 0.0313419i \(0.00997806\pi\)
\(912\) 0 0
\(913\) 256.000i 0.280394i
\(914\) 0 0
\(915\) 72.0000i 0.0786885i
\(916\) 0 0
\(917\) −280.000 280.000i −0.305344 0.305344i
\(918\) 0 0
\(919\) 1218.00 + 1218.00i 1.32535 + 1.32535i 0.909374 + 0.415980i \(0.136561\pi\)
0.415980 + 0.909374i \(0.363439\pi\)
\(920\) 0 0
\(921\) −1456.00 −1.58089
\(922\) 0 0
\(923\) −372.000 + 372.000i −0.403034 + 0.403034i
\(924\) 0 0
\(925\) 259.000 0.280000
\(926\) 0 0
\(927\) −294.000 294.000i −0.317152 0.317152i
\(928\) 0 0
\(929\) 666.000i 0.716900i −0.933549 0.358450i \(-0.883305\pi\)
0.933549 0.358450i \(-0.116695\pi\)
\(930\) 0 0
\(931\) 330.000 330.000i 0.354458 0.354458i
\(932\) 0 0
\(933\) 952.000 952.000i 1.02036 1.02036i
\(934\) 0 0
\(935\) −552.000 −0.590374
\(936\) 0 0
\(937\) −424.000 −0.452508 −0.226254 0.974068i \(-0.572648\pi\)
−0.226254 + 0.974068i \(0.572648\pi\)
\(938\) 0 0
\(939\) −348.000 348.000i −0.370607 0.370607i
\(940\) 0 0
\(941\) −912.000 −0.969182 −0.484591 0.874741i \(-0.661032\pi\)
−0.484591 + 0.874741i \(0.661032\pi\)
\(942\) 0 0
\(943\) 740.000 + 740.000i 0.784730 + 0.784730i
\(944\) 0 0
\(945\) −96.0000 96.0000i −0.101587 0.101587i
\(946\) 0 0
\(947\) 134.000 134.000i 0.141499 0.141499i −0.632809 0.774308i \(-0.718098\pi\)
0.774308 + 0.632809i \(0.218098\pi\)
\(948\) 0 0
\(949\) −30.0000 30.0000i −0.0316122 0.0316122i
\(950\) 0 0
\(951\) 1056.00 1.11041
\(952\) 0 0
\(953\) 1264.00i 1.32634i −0.748470 0.663169i \(-0.769211\pi\)
0.748470 0.663169i \(-0.230789\pi\)
\(954\) 0 0
\(955\) 1116.00i 1.16859i
\(956\) 0 0
\(957\) 304.000 + 304.000i 0.317659 + 0.317659i
\(958\) 0 0
\(959\) 864.000 0.900938
\(960\) 0 0
\(961\) 313.000i 0.325702i
\(962\) 0 0
\(963\) −168.000 −0.174455
\(964\) 0 0
\(965\) 54.0000i 0.0559585i
\(966\) 0 0
\(967\) −1006.00 + 1006.00i −1.04033 + 1.04033i −0.0411791 + 0.999152i \(0.513111\pi\)
−0.999152 + 0.0411791i \(0.986889\pi\)
\(968\) 0 0
\(969\) 1840.00 1.89886
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 720.000i 0.739979i
\(974\) 0 0
\(975\) 84.0000 84.0000i 0.0861538 0.0861538i
\(976\) 0 0
\(977\) −921.000 921.000i −0.942682 0.942682i 0.0557624 0.998444i \(-0.482241\pi\)
−0.998444 + 0.0557624i \(0.982241\pi\)
\(978\) 0 0
\(979\) 68.0000 68.0000i 0.0694586 0.0694586i
\(980\) 0 0
\(981\) 637.000 637.000i 0.649337 0.649337i
\(982\) 0 0
\(983\) 1480.00i 1.50560i −0.658252 0.752798i \(-0.728704\pi\)
0.658252 0.752798i \(-0.271296\pi\)
\(984\) 0 0
\(985\) 102.000 102.000i 0.103553 0.103553i
\(986\) 0 0
\(987\) 704.000i 0.713273i
\(988\) 0 0
\(989\) 840.000i 0.849343i
\(990\) 0 0
\(991\) −1038.00 1038.00i −1.04743 1.04743i −0.998818 0.0486090i \(-0.984521\pi\)
−0.0486090 0.998818i \(-0.515479\pi\)
\(992\) 0 0
\(993\) −1304.00 1304.00i −1.31319 1.31319i
\(994\) 0 0
\(995\) −276.000 −0.277387
\(996\) 0 0
\(997\) 355.000 355.000i 0.356068 0.356068i −0.506293 0.862361i \(-0.668985\pi\)
0.862361 + 0.506293i \(0.168985\pi\)
\(998\) 0 0
\(999\) −296.000 −0.296296
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 592.3.k.c.401.1 2
4.3 odd 2 74.3.d.b.31.1 2
12.11 even 2 666.3.i.a.253.1 2
37.6 odd 4 inner 592.3.k.c.561.1 2
148.43 even 4 74.3.d.b.43.1 yes 2
444.191 odd 4 666.3.i.a.487.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.3.d.b.31.1 2 4.3 odd 2
74.3.d.b.43.1 yes 2 148.43 even 4
592.3.k.c.401.1 2 1.1 even 1 trivial
592.3.k.c.561.1 2 37.6 odd 4 inner
666.3.i.a.253.1 2 12.11 even 2
666.3.i.a.487.1 2 444.191 odd 4