Properties

Label 1400.2.x.b.657.4
Level $1400$
Weight $2$
Character 1400.657
Analytic conductor $11.179$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1400,2,Mod(657,1400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1400, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1400.657");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\), degree \(2\), 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: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 657.4
Character \(\chi\) \(=\) 1400.657
Dual form 1400.2.x.b.993.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.03893 - 1.03893i) q^{3} +(-1.58883 - 2.11557i) q^{7} -0.841261i q^{9} +O(q^{10})\) \(q+(-1.03893 - 1.03893i) q^{3} +(-1.58883 - 2.11557i) q^{7} -0.841261i q^{9} -2.34687 q^{11} +(-1.96436 - 1.96436i) q^{13} +(5.15858 - 5.15858i) q^{17} +3.74821 q^{19} +(-0.547244 + 3.84860i) q^{21} +(-6.08007 + 6.08007i) q^{23} +(-3.99079 + 3.99079i) q^{27} +5.89034i q^{29} -1.56648i q^{31} +(2.43823 + 2.43823i) q^{33} +(-1.53441 - 1.53441i) q^{37} +4.08166i q^{39} -9.51977i q^{41} +(-1.86313 + 1.86313i) q^{43} +(-4.59474 + 4.59474i) q^{47} +(-1.95125 + 6.72254i) q^{49} -10.7188 q^{51} +(-3.88128 + 3.88128i) q^{53} +(-3.89412 - 3.89412i) q^{57} -4.62061 q^{59} -2.00065i q^{61} +(-1.77974 + 1.33662i) q^{63} +(-2.69156 - 2.69156i) q^{67} +12.6335 q^{69} -0.392229 q^{71} +(7.08543 + 7.08543i) q^{73} +(3.72878 + 4.96497i) q^{77} -4.98717i q^{79} +5.76850 q^{81} +(9.36651 + 9.36651i) q^{83} +(6.11964 - 6.11964i) q^{87} -9.83200 q^{89} +(-1.03471 + 7.27677i) q^{91} +(-1.62746 + 1.62746i) q^{93} +(-11.8576 + 11.8576i) q^{97} +1.97433i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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 0
\(3\) −1.03893 1.03893i −0.599825 0.599825i 0.340441 0.940266i \(-0.389424\pi\)
−0.940266 + 0.340441i \(0.889424\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.58883 2.11557i −0.600520 0.799609i
\(8\) 0 0
\(9\) 0.841261i 0.280420i
\(10\) 0 0
\(11\) −2.34687 −0.707609 −0.353804 0.935319i \(-0.615112\pi\)
−0.353804 + 0.935319i \(0.615112\pi\)
\(12\) 0 0
\(13\) −1.96436 1.96436i −0.544816 0.544816i 0.380121 0.924937i \(-0.375882\pi\)
−0.924937 + 0.380121i \(0.875882\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.15858 5.15858i 1.25114 1.25114i 0.295929 0.955210i \(-0.404371\pi\)
0.955210 0.295929i \(-0.0956291\pi\)
\(18\) 0 0
\(19\) 3.74821 0.859899 0.429949 0.902853i \(-0.358531\pi\)
0.429949 + 0.902853i \(0.358531\pi\)
\(20\) 0 0
\(21\) −0.547244 + 3.84860i −0.119419 + 0.839833i
\(22\) 0 0
\(23\) −6.08007 + 6.08007i −1.26778 + 1.26778i −0.320550 + 0.947232i \(0.603868\pi\)
−0.947232 + 0.320550i \(0.896132\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.99079 + 3.99079i −0.768028 + 0.768028i
\(28\) 0 0
\(29\) 5.89034i 1.09381i 0.837195 + 0.546905i \(0.184194\pi\)
−0.837195 + 0.546905i \(0.815806\pi\)
\(30\) 0 0
\(31\) 1.56648i 0.281348i −0.990056 0.140674i \(-0.955073\pi\)
0.990056 0.140674i \(-0.0449270\pi\)
\(32\) 0 0
\(33\) 2.43823 + 2.43823i 0.424441 + 0.424441i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.53441 1.53441i −0.252256 0.252256i 0.569639 0.821895i \(-0.307083\pi\)
−0.821895 + 0.569639i \(0.807083\pi\)
\(38\) 0 0
\(39\) 4.08166i 0.653588i
\(40\) 0 0
\(41\) 9.51977i 1.48674i −0.668882 0.743369i \(-0.733227\pi\)
0.668882 0.743369i \(-0.266773\pi\)
\(42\) 0 0
\(43\) −1.86313 + 1.86313i −0.284125 + 0.284125i −0.834752 0.550626i \(-0.814389\pi\)
0.550626 + 0.834752i \(0.314389\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.59474 + 4.59474i −0.670212 + 0.670212i −0.957765 0.287553i \(-0.907158\pi\)
0.287553 + 0.957765i \(0.407158\pi\)
\(48\) 0 0
\(49\) −1.95125 + 6.72254i −0.278750 + 0.960364i
\(50\) 0 0
\(51\) −10.7188 −1.50093
\(52\) 0 0
\(53\) −3.88128 + 3.88128i −0.533135 + 0.533135i −0.921504 0.388369i \(-0.873039\pi\)
0.388369 + 0.921504i \(0.373039\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.89412 3.89412i −0.515789 0.515789i
\(58\) 0 0
\(59\) −4.62061 −0.601552 −0.300776 0.953695i \(-0.597246\pi\)
−0.300776 + 0.953695i \(0.597246\pi\)
\(60\) 0 0
\(61\) 2.00065i 0.256156i −0.991764 0.128078i \(-0.959119\pi\)
0.991764 0.128078i \(-0.0408808\pi\)
\(62\) 0 0
\(63\) −1.77974 + 1.33662i −0.224227 + 0.168398i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.69156 2.69156i −0.328827 0.328827i 0.523314 0.852140i \(-0.324696\pi\)
−0.852140 + 0.523314i \(0.824696\pi\)
\(68\) 0 0
\(69\) 12.6335 1.52089
\(70\) 0 0
\(71\) −0.392229 −0.0465491 −0.0232745 0.999729i \(-0.507409\pi\)
−0.0232745 + 0.999729i \(0.507409\pi\)
\(72\) 0 0
\(73\) 7.08543 + 7.08543i 0.829287 + 0.829287i 0.987418 0.158131i \(-0.0505468\pi\)
−0.158131 + 0.987418i \(0.550547\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.72878 + 4.96497i 0.424934 + 0.565811i
\(78\) 0 0
\(79\) 4.98717i 0.561100i −0.959839 0.280550i \(-0.909483\pi\)
0.959839 0.280550i \(-0.0905169\pi\)
\(80\) 0 0
\(81\) 5.76850 0.640944
\(82\) 0 0
\(83\) 9.36651 + 9.36651i 1.02811 + 1.02811i 0.999593 + 0.0285148i \(0.00907776\pi\)
0.0285148 + 0.999593i \(0.490922\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 6.11964 6.11964i 0.656094 0.656094i
\(88\) 0 0
\(89\) −9.83200 −1.04219 −0.521095 0.853499i \(-0.674476\pi\)
−0.521095 + 0.853499i \(0.674476\pi\)
\(90\) 0 0
\(91\) −1.03471 + 7.27677i −0.108467 + 0.762813i
\(92\) 0 0
\(93\) −1.62746 + 1.62746i −0.168760 + 0.168760i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −11.8576 + 11.8576i −1.20396 + 1.20396i −0.231006 + 0.972952i \(0.574202\pi\)
−0.972952 + 0.231006i \(0.925798\pi\)
\(98\) 0 0
\(99\) 1.97433i 0.198428i
\(100\) 0 0
\(101\) 8.41529i 0.837353i 0.908135 + 0.418676i \(0.137506\pi\)
−0.908135 + 0.418676i \(0.862494\pi\)
\(102\) 0 0
\(103\) −8.77874 8.77874i −0.864995 0.864995i 0.126918 0.991913i \(-0.459491\pi\)
−0.991913 + 0.126918i \(0.959491\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.3741 10.3741i −1.00290 1.00290i −0.999996 0.00290471i \(-0.999075\pi\)
−0.00290471 0.999996i \(-0.500925\pi\)
\(108\) 0 0
\(109\) 4.92724i 0.471944i 0.971760 + 0.235972i \(0.0758273\pi\)
−0.971760 + 0.235972i \(0.924173\pi\)
\(110\) 0 0
\(111\) 3.18828i 0.302618i
\(112\) 0 0
\(113\) 3.79963 3.79963i 0.357439 0.357439i −0.505429 0.862868i \(-0.668666\pi\)
0.862868 + 0.505429i \(0.168666\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.65254 + 1.65254i −0.152777 + 0.152777i
\(118\) 0 0
\(119\) −19.1094 2.71723i −1.75176 0.249088i
\(120\) 0 0
\(121\) −5.49219 −0.499290
\(122\) 0 0
\(123\) −9.89034 + 9.89034i −0.891782 + 0.891782i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.777755 + 0.777755i 0.0690146 + 0.0690146i 0.740772 0.671757i \(-0.234460\pi\)
−0.671757 + 0.740772i \(0.734460\pi\)
\(128\) 0 0
\(129\) 3.87132 0.340851
\(130\) 0 0
\(131\) 11.0373i 0.964336i 0.876079 + 0.482168i \(0.160151\pi\)
−0.876079 + 0.482168i \(0.839849\pi\)
\(132\) 0 0
\(133\) −5.95526 7.92959i −0.516387 0.687583i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.65313 2.65313i −0.226672 0.226672i 0.584629 0.811301i \(-0.301240\pi\)
−0.811301 + 0.584629i \(0.801240\pi\)
\(138\) 0 0
\(139\) 7.15451 0.606838 0.303419 0.952857i \(-0.401872\pi\)
0.303419 + 0.952857i \(0.401872\pi\)
\(140\) 0 0
\(141\) 9.54720 0.804019
\(142\) 0 0
\(143\) 4.61011 + 4.61011i 0.385516 + 0.385516i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 9.01144 4.95702i 0.743251 0.408848i
\(148\) 0 0
\(149\) 12.2552i 1.00399i 0.864872 + 0.501993i \(0.167400\pi\)
−0.864872 + 0.501993i \(0.832600\pi\)
\(150\) 0 0
\(151\) −13.2221 −1.07600 −0.537998 0.842946i \(-0.680819\pi\)
−0.537998 + 0.842946i \(0.680819\pi\)
\(152\) 0 0
\(153\) −4.33971 4.33971i −0.350845 0.350845i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 8.35401 8.35401i 0.666723 0.666723i −0.290233 0.956956i \(-0.593733\pi\)
0.956956 + 0.290233i \(0.0937329\pi\)
\(158\) 0 0
\(159\) 8.06474 0.639576
\(160\) 0 0
\(161\) 22.5230 + 3.20261i 1.77506 + 0.252401i
\(162\) 0 0
\(163\) −2.21768 + 2.21768i −0.173702 + 0.173702i −0.788604 0.614902i \(-0.789196\pi\)
0.614902 + 0.788604i \(0.289196\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.1934 15.1934i 1.17570 1.17570i 0.194871 0.980829i \(-0.437571\pi\)
0.980829 0.194871i \(-0.0624288\pi\)
\(168\) 0 0
\(169\) 5.28257i 0.406352i
\(170\) 0 0
\(171\) 3.15322i 0.241133i
\(172\) 0 0
\(173\) −4.60458 4.60458i −0.350080 0.350080i 0.510059 0.860139i \(-0.329623\pi\)
−0.860139 + 0.510059i \(0.829623\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.80047 + 4.80047i 0.360826 + 0.360826i
\(178\) 0 0
\(179\) 11.5721i 0.864939i −0.901648 0.432470i \(-0.857642\pi\)
0.901648 0.432470i \(-0.142358\pi\)
\(180\) 0 0
\(181\) 5.28640i 0.392935i −0.980510 0.196467i \(-0.937053\pi\)
0.980510 0.196467i \(-0.0629470\pi\)
\(182\) 0 0
\(183\) −2.07852 + 2.07852i −0.153649 + 0.153649i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −12.1065 + 12.1065i −0.885317 + 0.885317i
\(188\) 0 0
\(189\) 14.7835 + 2.10211i 1.07534 + 0.152906i
\(190\) 0 0
\(191\) −11.6115 −0.840179 −0.420089 0.907483i \(-0.638001\pi\)
−0.420089 + 0.907483i \(0.638001\pi\)
\(192\) 0 0
\(193\) 17.6369 17.6369i 1.26954 1.26954i 0.323207 0.946328i \(-0.395239\pi\)
0.946328 0.323207i \(-0.104761\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.2130 + 17.2130i 1.22637 + 1.22637i 0.965325 + 0.261049i \(0.0840685\pi\)
0.261049 + 0.965325i \(0.415931\pi\)
\(198\) 0 0
\(199\) 6.95883 0.493299 0.246649 0.969105i \(-0.420670\pi\)
0.246649 + 0.969105i \(0.420670\pi\)
\(200\) 0 0
\(201\) 5.59267i 0.394477i
\(202\) 0 0
\(203\) 12.4614 9.35874i 0.874620 0.656855i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 5.11492 + 5.11492i 0.355512 + 0.355512i
\(208\) 0 0
\(209\) −8.79658 −0.608472
\(210\) 0 0
\(211\) 9.28431 0.639159 0.319579 0.947560i \(-0.396458\pi\)
0.319579 + 0.947560i \(0.396458\pi\)
\(212\) 0 0
\(213\) 0.407498 + 0.407498i 0.0279213 + 0.0279213i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −3.31400 + 2.48887i −0.224969 + 0.168955i
\(218\) 0 0
\(219\) 14.7225i 0.994854i
\(220\) 0 0
\(221\) −20.2666 −1.36328
\(222\) 0 0
\(223\) −4.77582 4.77582i −0.319813 0.319813i 0.528882 0.848695i \(-0.322611\pi\)
−0.848695 + 0.528882i \(0.822611\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.49990 + 2.49990i −0.165925 + 0.165925i −0.785185 0.619261i \(-0.787432\pi\)
0.619261 + 0.785185i \(0.287432\pi\)
\(228\) 0 0
\(229\) −18.0694 −1.19406 −0.597031 0.802218i \(-0.703653\pi\)
−0.597031 + 0.802218i \(0.703653\pi\)
\(230\) 0 0
\(231\) 1.28431 9.03217i 0.0845016 0.594273i
\(232\) 0 0
\(233\) −9.14278 + 9.14278i −0.598963 + 0.598963i −0.940037 0.341073i \(-0.889210\pi\)
0.341073 + 0.940037i \(0.389210\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.18130 + 5.18130i −0.336562 + 0.336562i
\(238\) 0 0
\(239\) 11.3719i 0.735590i 0.929907 + 0.367795i \(0.119887\pi\)
−0.929907 + 0.367795i \(0.880113\pi\)
\(240\) 0 0
\(241\) 19.6361i 1.26488i −0.774611 0.632438i \(-0.782054\pi\)
0.774611 0.632438i \(-0.217946\pi\)
\(242\) 0 0
\(243\) 5.97932 + 5.97932i 0.383574 + 0.383574i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.36284 7.36284i −0.468486 0.468486i
\(248\) 0 0
\(249\) 19.4622i 1.23337i
\(250\) 0 0
\(251\) 26.2420i 1.65638i −0.560447 0.828190i \(-0.689371\pi\)
0.560447 0.828190i \(-0.310629\pi\)
\(252\) 0 0
\(253\) 14.2691 14.2691i 0.897094 0.897094i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.93157 1.93157i 0.120488 0.120488i −0.644292 0.764780i \(-0.722848\pi\)
0.764780 + 0.644292i \(0.222848\pi\)
\(258\) 0 0
\(259\) −0.808236 + 5.68406i −0.0502213 + 0.353191i
\(260\) 0 0
\(261\) 4.95532 0.306726
\(262\) 0 0
\(263\) −2.64248 + 2.64248i −0.162942 + 0.162942i −0.783869 0.620927i \(-0.786757\pi\)
0.620927 + 0.783869i \(0.286757\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 10.2147 + 10.2147i 0.625131 + 0.625131i
\(268\) 0 0
\(269\) 1.17948 0.0719143 0.0359572 0.999353i \(-0.488552\pi\)
0.0359572 + 0.999353i \(0.488552\pi\)
\(270\) 0 0
\(271\) 14.7880i 0.898306i −0.893455 0.449153i \(-0.851726\pi\)
0.893455 0.449153i \(-0.148274\pi\)
\(272\) 0 0
\(273\) 8.63502 6.48505i 0.522615 0.392493i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −11.6478 11.6478i −0.699848 0.699848i 0.264529 0.964378i \(-0.414783\pi\)
−0.964378 + 0.264529i \(0.914783\pi\)
\(278\) 0 0
\(279\) −1.31782 −0.0788957
\(280\) 0 0
\(281\) 20.2153 1.20594 0.602971 0.797763i \(-0.293983\pi\)
0.602971 + 0.797763i \(0.293983\pi\)
\(282\) 0 0
\(283\) −5.53654 5.53654i −0.329113 0.329113i 0.523136 0.852249i \(-0.324762\pi\)
−0.852249 + 0.523136i \(0.824762\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −20.1397 + 15.1253i −1.18881 + 0.892816i
\(288\) 0 0
\(289\) 36.2218i 2.13070i
\(290\) 0 0
\(291\) 24.6384 1.44433
\(292\) 0 0
\(293\) 1.12050 + 1.12050i 0.0654601 + 0.0654601i 0.739079 0.673619i \(-0.235261\pi\)
−0.673619 + 0.739079i \(0.735261\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 9.36588 9.36588i 0.543463 0.543463i
\(298\) 0 0
\(299\) 23.8869 1.38141
\(300\) 0 0
\(301\) 6.90179 + 0.981388i 0.397812 + 0.0565662i
\(302\) 0 0
\(303\) 8.74288 8.74288i 0.502265 0.502265i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9.43044 9.43044i 0.538224 0.538224i −0.384783 0.923007i \(-0.625724\pi\)
0.923007 + 0.384783i \(0.125724\pi\)
\(308\) 0 0
\(309\) 18.2409i 1.03769i
\(310\) 0 0
\(311\) 14.6035i 0.828090i −0.910256 0.414045i \(-0.864116\pi\)
0.910256 0.414045i \(-0.135884\pi\)
\(312\) 0 0
\(313\) 7.05535 + 7.05535i 0.398792 + 0.398792i 0.877807 0.479015i \(-0.159006\pi\)
−0.479015 + 0.877807i \(0.659006\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.2538 + 11.2538i 0.632075 + 0.632075i 0.948588 0.316513i \(-0.102512\pi\)
−0.316513 + 0.948588i \(0.602512\pi\)
\(318\) 0 0
\(319\) 13.8239i 0.773989i
\(320\) 0 0
\(321\) 21.5558i 1.20313i
\(322\) 0 0
\(323\) 19.3354 19.3354i 1.07585 1.07585i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 5.11904 5.11904i 0.283084 0.283084i
\(328\) 0 0
\(329\) 17.0207 + 2.42023i 0.938383 + 0.133432i
\(330\) 0 0
\(331\) −33.6643 −1.85036 −0.925179 0.379531i \(-0.876085\pi\)
−0.925179 + 0.379531i \(0.876085\pi\)
\(332\) 0 0
\(333\) −1.29084 + 1.29084i −0.0707376 + 0.0707376i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −12.8298 12.8298i −0.698885 0.698885i 0.265285 0.964170i \(-0.414534\pi\)
−0.964170 + 0.265285i \(0.914534\pi\)
\(338\) 0 0
\(339\) −7.89507 −0.428802
\(340\) 0 0
\(341\) 3.67633i 0.199085i
\(342\) 0 0
\(343\) 17.3222 6.55296i 0.935311 0.353826i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.6439 + 20.6439i 1.10822 + 1.10822i 0.993384 + 0.114837i \(0.0366345\pi\)
0.114837 + 0.993384i \(0.463365\pi\)
\(348\) 0 0
\(349\) −29.3356 −1.57030 −0.785150 0.619306i \(-0.787414\pi\)
−0.785150 + 0.619306i \(0.787414\pi\)
\(350\) 0 0
\(351\) 15.6787 0.836867
\(352\) 0 0
\(353\) −16.5837 16.5837i −0.882662 0.882662i 0.111142 0.993805i \(-0.464549\pi\)
−0.993805 + 0.111142i \(0.964549\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 17.0303 + 22.6763i 0.901338 + 1.20016i
\(358\) 0 0
\(359\) 30.4050i 1.60472i −0.596843 0.802358i \(-0.703579\pi\)
0.596843 0.802358i \(-0.296421\pi\)
\(360\) 0 0
\(361\) −4.95092 −0.260575
\(362\) 0 0
\(363\) 5.70598 + 5.70598i 0.299486 + 0.299486i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −13.6007 + 13.6007i −0.709950 + 0.709950i −0.966525 0.256574i \(-0.917406\pi\)
0.256574 + 0.966525i \(0.417406\pi\)
\(368\) 0 0
\(369\) −8.00861 −0.416911
\(370\) 0 0
\(371\) 14.3778 + 2.04443i 0.746459 + 0.106141i
\(372\) 0 0
\(373\) −13.8626 + 13.8626i −0.717776 + 0.717776i −0.968149 0.250373i \(-0.919447\pi\)
0.250373 + 0.968149i \(0.419447\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.5708 11.5708i 0.595925 0.595925i
\(378\) 0 0
\(379\) 11.8896i 0.610727i −0.952236 0.305363i \(-0.901222\pi\)
0.952236 0.305363i \(-0.0987779\pi\)
\(380\) 0 0
\(381\) 1.61606i 0.0827934i
\(382\) 0 0
\(383\) −16.5186 16.5186i −0.844059 0.844059i 0.145325 0.989384i \(-0.453577\pi\)
−0.989384 + 0.145325i \(0.953577\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.56738 + 1.56738i 0.0796745 + 0.0796745i
\(388\) 0 0
\(389\) 9.62098i 0.487803i 0.969800 + 0.243902i \(0.0784274\pi\)
−0.969800 + 0.243902i \(0.921573\pi\)
\(390\) 0 0
\(391\) 62.7290i 3.17234i
\(392\) 0 0
\(393\) 11.4670 11.4670i 0.578433 0.578433i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 17.5393 17.5393i 0.880270 0.880270i −0.113292 0.993562i \(-0.536139\pi\)
0.993562 + 0.113292i \(0.0361394\pi\)
\(398\) 0 0
\(399\) −2.05119 + 14.4254i −0.102688 + 0.722171i
\(400\) 0 0
\(401\) −14.2238 −0.710302 −0.355151 0.934809i \(-0.615571\pi\)
−0.355151 + 0.934809i \(0.615571\pi\)
\(402\) 0 0
\(403\) −3.07713 + 3.07713i −0.153283 + 0.153283i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.60107 + 3.60107i 0.178498 + 0.178498i
\(408\) 0 0
\(409\) 14.2602 0.705123 0.352562 0.935789i \(-0.385311\pi\)
0.352562 + 0.935789i \(0.385311\pi\)
\(410\) 0 0
\(411\) 5.51281i 0.271927i
\(412\) 0 0
\(413\) 7.34135 + 9.77520i 0.361244 + 0.481006i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.43302 7.43302i −0.363996 0.363996i
\(418\) 0 0
\(419\) −13.5802 −0.663434 −0.331717 0.943379i \(-0.607628\pi\)
−0.331717 + 0.943379i \(0.607628\pi\)
\(420\) 0 0
\(421\) −12.7805 −0.622884 −0.311442 0.950265i \(-0.600812\pi\)
−0.311442 + 0.950265i \(0.600812\pi\)
\(422\) 0 0
\(423\) 3.86537 + 3.86537i 0.187941 + 0.187941i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −4.23250 + 3.17868i −0.204825 + 0.153827i
\(428\) 0 0
\(429\) 9.57913i 0.462485i
\(430\) 0 0
\(431\) 37.7947 1.82051 0.910254 0.414049i \(-0.135886\pi\)
0.910254 + 0.414049i \(0.135886\pi\)
\(432\) 0 0
\(433\) −14.2122 14.2122i −0.682996 0.682996i 0.277678 0.960674i \(-0.410435\pi\)
−0.960674 + 0.277678i \(0.910435\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −22.7894 + 22.7894i −1.09016 + 1.09016i
\(438\) 0 0
\(439\) −27.7697 −1.32538 −0.662688 0.748896i \(-0.730584\pi\)
−0.662688 + 0.748896i \(0.730584\pi\)
\(440\) 0 0
\(441\) 5.65541 + 1.64151i 0.269305 + 0.0781673i
\(442\) 0 0
\(443\) −11.8951 + 11.8951i −0.565152 + 0.565152i −0.930766 0.365615i \(-0.880859\pi\)
0.365615 + 0.930766i \(0.380859\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.7323 12.7323i 0.602216 0.602216i
\(448\) 0 0
\(449\) 3.92227i 0.185104i 0.995708 + 0.0925518i \(0.0295024\pi\)
−0.995708 + 0.0925518i \(0.970498\pi\)
\(450\) 0 0
\(451\) 22.3417i 1.05203i
\(452\) 0 0
\(453\) 13.7367 + 13.7367i 0.645409 + 0.645409i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −17.6596 17.6596i −0.826083 0.826083i 0.160889 0.986972i \(-0.448564\pi\)
−0.986972 + 0.160889i \(0.948564\pi\)
\(458\) 0 0
\(459\) 41.1736i 1.92182i
\(460\) 0 0
\(461\) 0.616064i 0.0286930i −0.999897 0.0143465i \(-0.995433\pi\)
0.999897 0.0143465i \(-0.00456678\pi\)
\(462\) 0 0
\(463\) 11.9726 11.9726i 0.556413 0.556413i −0.371871 0.928284i \(-0.621284\pi\)
0.928284 + 0.371871i \(0.121284\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.8767 12.8767i 0.595861 0.595861i −0.343348 0.939208i \(-0.611561\pi\)
0.939208 + 0.343348i \(0.111561\pi\)
\(468\) 0 0
\(469\) −1.41775 + 9.97061i −0.0654658 + 0.460400i
\(470\) 0 0
\(471\) −17.3584 −0.799834
\(472\) 0 0
\(473\) 4.37254 4.37254i 0.201050 0.201050i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 3.26517 + 3.26517i 0.149502 + 0.149502i
\(478\) 0 0
\(479\) 8.34016 0.381072 0.190536 0.981680i \(-0.438977\pi\)
0.190536 + 0.981680i \(0.438977\pi\)
\(480\) 0 0
\(481\) 6.02827i 0.274866i
\(482\) 0 0
\(483\) −20.0724 26.7270i −0.913328 1.21612i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.90541 + 6.90541i 0.312914 + 0.312914i 0.846037 0.533123i \(-0.178982\pi\)
−0.533123 + 0.846037i \(0.678982\pi\)
\(488\) 0 0
\(489\) 4.60801 0.208381
\(490\) 0 0
\(491\) 25.1783 1.13628 0.568140 0.822932i \(-0.307663\pi\)
0.568140 + 0.822932i \(0.307663\pi\)
\(492\) 0 0
\(493\) 30.3858 + 30.3858i 1.36851 + 1.36851i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.623185 + 0.829788i 0.0279537 + 0.0372211i
\(498\) 0 0
\(499\) 20.8907i 0.935197i 0.883941 + 0.467599i \(0.154881\pi\)
−0.883941 + 0.467599i \(0.845119\pi\)
\(500\) 0 0
\(501\) −31.5696 −1.41043
\(502\) 0 0
\(503\) 0.585795 + 0.585795i 0.0261193 + 0.0261193i 0.720046 0.693927i \(-0.244121\pi\)
−0.693927 + 0.720046i \(0.744121\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −5.48821 + 5.48821i −0.243740 + 0.243740i
\(508\) 0 0
\(509\) 38.2153 1.69386 0.846932 0.531701i \(-0.178447\pi\)
0.846932 + 0.531701i \(0.178447\pi\)
\(510\) 0 0
\(511\) 3.73218 26.2472i 0.165102 1.16111i
\(512\) 0 0
\(513\) −14.9583 + 14.9583i −0.660426 + 0.660426i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10.7833 10.7833i 0.474248 0.474248i
\(518\) 0 0
\(519\) 9.56765i 0.419973i
\(520\) 0 0
\(521\) 8.40522i 0.368239i 0.982904 + 0.184120i \(0.0589434\pi\)
−0.982904 + 0.184120i \(0.941057\pi\)
\(522\) 0 0
\(523\) 14.1989 + 14.1989i 0.620876 + 0.620876i 0.945755 0.324879i \(-0.105324\pi\)
−0.324879 + 0.945755i \(0.605324\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.08081 8.08081i −0.352006 0.352006i
\(528\) 0 0
\(529\) 50.9344i 2.21454i
\(530\) 0 0
\(531\) 3.88713i 0.168687i
\(532\) 0 0
\(533\) −18.7003 + 18.7003i −0.809998 + 0.809998i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −12.0226 + 12.0226i −0.518812 + 0.518812i
\(538\) 0 0
\(539\) 4.57934 15.7770i 0.197246 0.679562i
\(540\) 0 0
\(541\) −38.9363 −1.67400 −0.837001 0.547202i \(-0.815693\pi\)
−0.837001 + 0.547202i \(0.815693\pi\)
\(542\) 0 0
\(543\) −5.49218 + 5.49218i −0.235692 + 0.235692i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.30390 2.30390i −0.0985078 0.0985078i 0.656135 0.754643i \(-0.272190\pi\)
−0.754643 + 0.656135i \(0.772190\pi\)
\(548\) 0 0
\(549\) −1.68306 −0.0718314
\(550\) 0 0
\(551\) 22.0783i 0.940565i
\(552\) 0 0
\(553\) −10.5507 + 7.92375i −0.448661 + 0.336952i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.69913 7.69913i −0.326223 0.326223i 0.524926 0.851148i \(-0.324093\pi\)
−0.851148 + 0.524926i \(0.824093\pi\)
\(558\) 0 0
\(559\) 7.31974 0.309592
\(560\) 0 0
\(561\) 25.1556 1.06207
\(562\) 0 0
\(563\) −11.8855 11.8855i −0.500914 0.500914i 0.410808 0.911722i \(-0.365247\pi\)
−0.911722 + 0.410808i \(0.865247\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −9.16515 12.2036i −0.384900 0.512505i
\(568\) 0 0
\(569\) 3.16924i 0.132861i 0.997791 + 0.0664307i \(0.0211611\pi\)
−0.997791 + 0.0664307i \(0.978839\pi\)
\(570\) 0 0
\(571\) −24.8492 −1.03991 −0.519953 0.854195i \(-0.674050\pi\)
−0.519953 + 0.854195i \(0.674050\pi\)
\(572\) 0 0
\(573\) 12.0635 + 12.0635i 0.503960 + 0.503960i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −29.2688 + 29.2688i −1.21848 + 1.21848i −0.250309 + 0.968166i \(0.580532\pi\)
−0.968166 + 0.250309i \(0.919468\pi\)
\(578\) 0 0
\(579\) −36.6470 −1.52300
\(580\) 0 0
\(581\) 4.93372 34.6973i 0.204685 1.43948i
\(582\) 0 0
\(583\) 9.10888 9.10888i 0.377251 0.377251i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.3313 + 16.3313i −0.674065 + 0.674065i −0.958651 0.284586i \(-0.908144\pi\)
0.284586 + 0.958651i \(0.408144\pi\)
\(588\) 0 0
\(589\) 5.87150i 0.241931i
\(590\) 0 0
\(591\) 35.7661i 1.47122i
\(592\) 0 0
\(593\) −17.5540 17.5540i −0.720858 0.720858i 0.247922 0.968780i \(-0.420252\pi\)
−0.968780 + 0.247922i \(0.920252\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.22972 7.22972i −0.295893 0.295893i
\(598\) 0 0
\(599\) 21.4754i 0.877461i 0.898619 + 0.438731i \(0.144572\pi\)
−0.898619 + 0.438731i \(0.855428\pi\)
\(600\) 0 0
\(601\) 32.4373i 1.32314i −0.749882 0.661572i \(-0.769890\pi\)
0.749882 0.661572i \(-0.230110\pi\)
\(602\) 0 0
\(603\) −2.26431 + 2.26431i −0.0922096 + 0.0922096i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 13.4507 13.4507i 0.545947 0.545947i −0.379319 0.925266i \(-0.623842\pi\)
0.925266 + 0.379319i \(0.123842\pi\)
\(608\) 0 0
\(609\) −22.6696 3.22346i −0.918617 0.130621i
\(610\) 0 0
\(611\) 18.0515 0.730284
\(612\) 0 0
\(613\) 1.66986 1.66986i 0.0674449 0.0674449i −0.672580 0.740025i \(-0.734814\pi\)
0.740025 + 0.672580i \(0.234814\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16.0944 + 16.0944i 0.647938 + 0.647938i 0.952494 0.304556i \(-0.0985082\pi\)
−0.304556 + 0.952494i \(0.598508\pi\)
\(618\) 0 0
\(619\) −0.973019 −0.0391089 −0.0195545 0.999809i \(-0.506225\pi\)
−0.0195545 + 0.999809i \(0.506225\pi\)
\(620\) 0 0
\(621\) 48.5285i 1.94738i
\(622\) 0 0
\(623\) 15.6213 + 20.8003i 0.625856 + 0.833345i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 9.13900 + 9.13900i 0.364977 + 0.364977i
\(628\) 0 0
\(629\) −15.8308 −0.631213
\(630\) 0 0
\(631\) 17.4830 0.695987 0.347994 0.937497i \(-0.386863\pi\)
0.347994 + 0.937497i \(0.386863\pi\)
\(632\) 0 0
\(633\) −9.64573 9.64573i −0.383383 0.383383i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 17.0385 9.37254i 0.675089 0.371353i
\(638\) 0 0
\(639\) 0.329967i 0.0130533i
\(640\) 0 0
\(641\) −25.0710 −0.990244 −0.495122 0.868823i \(-0.664877\pi\)
−0.495122 + 0.868823i \(0.664877\pi\)
\(642\) 0 0
\(643\) 3.86619 + 3.86619i 0.152468 + 0.152468i 0.779219 0.626752i \(-0.215616\pi\)
−0.626752 + 0.779219i \(0.715616\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24.4727 + 24.4727i −0.962119 + 0.962119i −0.999308 0.0371889i \(-0.988160\pi\)
0.0371889 + 0.999308i \(0.488160\pi\)
\(648\) 0 0
\(649\) 10.8440 0.425663
\(650\) 0 0
\(651\) 6.02875 + 0.857248i 0.236285 + 0.0335982i
\(652\) 0 0
\(653\) −23.1478 + 23.1478i −0.905845 + 0.905845i −0.995934 0.0900885i \(-0.971285\pi\)
0.0900885 + 0.995934i \(0.471285\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5.96070 5.96070i 0.232549 0.232549i
\(658\) 0 0
\(659\) 36.1548i 1.40839i 0.710006 + 0.704195i \(0.248692\pi\)
−0.710006 + 0.704195i \(0.751308\pi\)
\(660\) 0 0
\(661\) 33.4541i 1.30121i 0.759415 + 0.650606i \(0.225485\pi\)
−0.759415 + 0.650606i \(0.774515\pi\)
\(662\) 0 0
\(663\) 21.0555 + 21.0555i 0.817729 + 0.817729i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −35.8137 35.8137i −1.38671 1.38671i
\(668\) 0 0
\(669\) 9.92347i 0.383663i
\(670\) 0 0
\(671\) 4.69526i 0.181259i
\(672\) 0 0
\(673\) 6.30998 6.30998i 0.243232 0.243232i −0.574954 0.818186i \(-0.694980\pi\)
0.818186 + 0.574954i \(0.194980\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.88730 + 6.88730i −0.264700 + 0.264700i −0.826960 0.562260i \(-0.809932\pi\)
0.562260 + 0.826960i \(0.309932\pi\)
\(678\) 0 0
\(679\) 43.9253 + 6.24588i 1.68570 + 0.239695i
\(680\) 0 0
\(681\) 5.19444 0.199051
\(682\) 0 0
\(683\) −1.06740 + 1.06740i −0.0408430 + 0.0408430i −0.727233 0.686390i \(-0.759194\pi\)
0.686390 + 0.727233i \(0.259194\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 18.7728 + 18.7728i 0.716228 + 0.716228i
\(688\) 0 0
\(689\) 15.2485 0.580921
\(690\) 0 0
\(691\) 43.8638i 1.66866i −0.551267 0.834329i \(-0.685855\pi\)
0.551267 0.834329i \(-0.314145\pi\)
\(692\) 0 0
\(693\) 4.17683 3.13687i 0.158665 0.119160i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −49.1085 49.1085i −1.86012 1.86012i
\(698\) 0 0
\(699\) 18.9974 0.718546
\(700\) 0 0
\(701\) −36.6200 −1.38312 −0.691559 0.722320i \(-0.743076\pi\)
−0.691559 + 0.722320i \(0.743076\pi\)
\(702\) 0 0
\(703\) −5.75130 5.75130i −0.216914 0.216914i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 17.8031 13.3705i 0.669555 0.502848i
\(708\) 0 0
\(709\) 30.7975i 1.15662i 0.815816 + 0.578311i \(0.196288\pi\)
−0.815816 + 0.578311i \(0.803712\pi\)
\(710\) 0 0
\(711\) −4.19551 −0.157344
\(712\) 0 0
\(713\) 9.52431 + 9.52431i 0.356688 + 0.356688i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 11.8146 11.8146i 0.441225 0.441225i
\(718\) 0 0
\(719\) 36.9703 1.37876 0.689379 0.724401i \(-0.257883\pi\)
0.689379 + 0.724401i \(0.257883\pi\)
\(720\) 0 0
\(721\) −4.62411 + 32.5199i −0.172211 + 1.21111i
\(722\) 0 0
\(723\) −20.4005 + 20.4005i −0.758704 + 0.758704i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −4.99011 + 4.99011i −0.185073 + 0.185073i −0.793562 0.608489i \(-0.791776\pi\)
0.608489 + 0.793562i \(0.291776\pi\)
\(728\) 0 0
\(729\) 29.7297i 1.10110i
\(730\) 0 0
\(731\) 19.2222i 0.710960i
\(732\) 0 0
\(733\) −18.9857 18.9857i −0.701252 0.701252i 0.263427 0.964679i \(-0.415147\pi\)
−0.964679 + 0.263427i \(0.915147\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.31675 + 6.31675i 0.232681 + 0.232681i
\(738\) 0 0
\(739\) 4.09135i 0.150503i 0.997165 + 0.0752515i \(0.0239759\pi\)
−0.997165 + 0.0752515i \(0.976024\pi\)
\(740\) 0 0
\(741\) 15.2989i 0.562019i
\(742\) 0 0
\(743\) −37.7330 + 37.7330i −1.38429 + 1.38429i −0.547451 + 0.836838i \(0.684402\pi\)
−0.836838 + 0.547451i \(0.815598\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 7.87968 7.87968i 0.288302 0.288302i
\(748\) 0 0
\(749\) −5.46444 + 38.4297i −0.199666 + 1.40419i
\(750\) 0 0
\(751\) −21.3975 −0.780805 −0.390403 0.920644i \(-0.627664\pi\)
−0.390403 + 0.920644i \(0.627664\pi\)
\(752\) 0 0
\(753\) −27.2635 + 27.2635i −0.993538 + 0.993538i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −24.8160 24.8160i −0.901952 0.901952i 0.0936529 0.995605i \(-0.470146\pi\)
−0.995605 + 0.0936529i \(0.970146\pi\)
\(758\) 0 0
\(759\) −29.6492 −1.07620
\(760\) 0 0
\(761\) 20.4451i 0.741135i 0.928806 + 0.370567i \(0.120837\pi\)
−0.928806 + 0.370567i \(0.879163\pi\)
\(762\) 0 0
\(763\) 10.4239 7.82853i 0.377371 0.283412i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.07654 + 9.07654i 0.327735 + 0.327735i
\(768\) 0 0
\(769\) 6.20785 0.223861 0.111930 0.993716i \(-0.464297\pi\)
0.111930 + 0.993716i \(0.464297\pi\)
\(770\) 0 0
\(771\) −4.01351 −0.144543
\(772\) 0 0
\(773\) −12.7179 12.7179i −0.457430 0.457430i 0.440381 0.897811i \(-0.354843\pi\)
−0.897811 + 0.440381i \(0.854843\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.74503 5.06563i 0.241976 0.181728i
\(778\) 0 0
\(779\) 35.6821i 1.27844i
\(780\) 0 0
\(781\) 0.920513 0.0329385
\(782\) 0 0
\(783\) −23.5071 23.5071i −0.840076 0.840076i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 32.6842 32.6842i 1.16506 1.16506i 0.181713 0.983352i \(-0.441836\pi\)
0.983352 0.181713i \(-0.0581642\pi\)
\(788\) 0 0
\(789\) 5.49068 0.195474
\(790\) 0 0
\(791\) −14.0753 2.00142i −0.500461 0.0711622i
\(792\) 0 0
\(793\) −3.92999 + 3.92999i −0.139558 + 0.139558i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.76878 + 8.76878i −0.310606 + 0.310606i −0.845144 0.534538i \(-0.820486\pi\)
0.534538 + 0.845144i \(0.320486\pi\)
\(798\) 0 0
\(799\) 47.4046i 1.67706i
\(800\) 0 0
\(801\) 8.27127i 0.292251i
\(802\) 0 0
\(803\) −16.6286 16.6286i −0.586811 0.586811i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.22540 1.22540i −0.0431360 0.0431360i
\(808\) 0 0
\(809\) 15.9362i 0.560287i 0.959958 + 0.280144i \(0.0903821\pi\)
−0.959958 + 0.280144i \(0.909618\pi\)
\(810\) 0 0
\(811\) 49.6560i 1.74366i −0.489812 0.871828i \(-0.662935\pi\)
0.489812 0.871828i \(-0.337065\pi\)
\(812\) 0 0
\(813\) −15.3636 + 15.3636i −0.538826 + 0.538826i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −6.98342 + 6.98342i −0.244319 + 0.244319i
\(818\) 0 0
\(819\) 6.12166 + 0.870459i 0.213908 + 0.0304163i
\(820\) 0 0
\(821\) −30.1755 −1.05313 −0.526566 0.850135i \(-0.676521\pi\)
−0.526566 + 0.850135i \(0.676521\pi\)
\(822\) 0 0
\(823\) −17.2900 + 17.2900i −0.602693 + 0.602693i −0.941026 0.338333i \(-0.890137\pi\)
0.338333 + 0.941026i \(0.390137\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.93183 1.93183i −0.0671761 0.0671761i 0.672721 0.739897i \(-0.265126\pi\)
−0.739897 + 0.672721i \(0.765126\pi\)
\(828\) 0 0
\(829\) −31.2032 −1.08373 −0.541865 0.840465i \(-0.682282\pi\)
−0.541865 + 0.840465i \(0.682282\pi\)
\(830\) 0 0
\(831\) 24.2024i 0.839573i
\(832\) 0 0
\(833\) 24.6131 + 44.7445i 0.852793 + 1.55030i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 6.25150 + 6.25150i 0.216083 + 0.216083i
\(838\) 0 0
\(839\) 7.79348 0.269061 0.134530 0.990909i \(-0.457047\pi\)
0.134530 + 0.990909i \(0.457047\pi\)
\(840\) 0 0
\(841\) −5.69616 −0.196419
\(842\) 0 0
\(843\) −21.0022 21.0022i −0.723354 0.723354i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 8.72614 + 11.6191i 0.299834 + 0.399237i
\(848\) 0 0
\(849\) 11.5041i 0.394821i
\(850\) 0 0
\(851\) 18.6586 0.639610
\(852\) 0 0
\(853\) −16.5954 16.5954i −0.568215 0.568215i 0.363413 0.931628i \(-0.381611\pi\)
−0.931628 + 0.363413i \(0.881611\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 29.2133 29.2133i 0.997909 0.997909i −0.00208912 0.999998i \(-0.500665\pi\)
0.999998 + 0.00208912i \(0.000664987\pi\)
\(858\) 0 0
\(859\) −18.3754 −0.626962 −0.313481 0.949594i \(-0.601495\pi\)
−0.313481 + 0.949594i \(0.601495\pi\)
\(860\) 0 0
\(861\) 36.6377 + 5.20964i 1.24861 + 0.177544i
\(862\) 0 0
\(863\) 31.7261 31.7261i 1.07997 1.07997i 0.0834585 0.996511i \(-0.473403\pi\)
0.996511 0.0834585i \(-0.0265966\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −37.6318 + 37.6318i −1.27804 + 1.27804i
\(868\) 0 0
\(869\) 11.7042i 0.397039i
\(870\) 0 0
\(871\) 10.5744i 0.358300i
\(872\) 0 0
\(873\) 9.97534 + 9.97534i 0.337614 + 0.337614i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 32.2606 + 32.2606i 1.08936 + 1.08936i 0.995594 + 0.0937674i \(0.0298910\pi\)
0.0937674 + 0.995594i \(0.470109\pi\)
\(878\) 0 0
\(879\) 2.32823i 0.0785292i
\(880\) 0 0
\(881\) 9.96766i 0.335819i 0.985802 + 0.167909i \(0.0537016\pi\)
−0.985802 + 0.167909i \(0.946298\pi\)
\(882\) 0 0
\(883\) 36.7464 36.7464i 1.23662 1.23662i 0.275239 0.961376i \(-0.411243\pi\)
0.961376 0.275239i \(-0.0887571\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 9.82975 9.82975i 0.330051 0.330051i −0.522555 0.852606i \(-0.675021\pi\)
0.852606 + 0.522555i \(0.175021\pi\)
\(888\) 0 0
\(889\) 0.409675 2.88111i 0.0137401 0.0966294i
\(890\) 0 0
\(891\) −13.5379 −0.453538
\(892\) 0 0
\(893\) −17.2221 + 17.2221i −0.576314 + 0.576314i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −24.8167 24.8167i −0.828607 0.828607i
\(898\) 0 0
\(899\) 9.22711 0.307741
\(900\) 0 0
\(901\) 40.0438i 1.33405i
\(902\) 0 0
\(903\) −6.15086 8.19004i −0.204688 0.272548i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −10.4096 10.4096i −0.345646 0.345646i 0.512839 0.858485i \(-0.328594\pi\)
−0.858485 + 0.512839i \(0.828594\pi\)
\(908\) 0 0
\(909\) 7.07946 0.234811
\(910\) 0 0
\(911\) 16.5150 0.547167 0.273583 0.961848i \(-0.411791\pi\)
0.273583 + 0.961848i \(0.411791\pi\)
\(912\) 0 0
\(913\) −21.9820 21.9820i −0.727498 0.727498i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 23.3502 17.5364i 0.771092 0.579104i
\(918\) 0 0
\(919\) 14.9494i 0.493134i −0.969126 0.246567i \(-0.920697\pi\)
0.969126 0.246567i \(-0.0793026\pi\)
\(920\) 0 0
\(921\) −19.5951 −0.645680
\(922\) 0 0
\(923\) 0.770480 + 0.770480i 0.0253607 + 0.0253607i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −7.38521 + 7.38521i −0.242562 + 0.242562i
\(928\) 0 0
\(929\) −2.36098 −0.0774611 −0.0387306 0.999250i \(-0.512331\pi\)
−0.0387306 + 0.999250i \(0.512331\pi\)
\(930\) 0 0
\(931\) −7.31371 + 25.1975i −0.239697 + 0.825815i
\(932\) 0 0
\(933\) −15.1720 + 15.1720i −0.496709 + 0.496709i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −2.28379 + 2.28379i −0.0746081 + 0.0746081i −0.743426 0.668818i \(-0.766801\pi\)
0.668818 + 0.743426i \(0.266801\pi\)
\(938\) 0 0
\(939\) 14.6600i 0.478410i
\(940\) 0 0
\(941\) 30.1034i 0.981344i 0.871344 + 0.490672i \(0.163249\pi\)
−0.871344 + 0.490672i \(0.836751\pi\)
\(942\) 0 0
\(943\) 57.8808 + 57.8808i 1.88486 + 1.88486i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −9.50072 9.50072i −0.308732 0.308732i 0.535686 0.844417i \(-0.320053\pi\)
−0.844417 + 0.535686i \(0.820053\pi\)
\(948\) 0 0
\(949\) 27.8367i 0.903617i
\(950\) 0 0
\(951\) 23.3837i 0.758269i
\(952\) 0 0
\(953\) 21.9629 21.9629i 0.711448 0.711448i −0.255390 0.966838i \(-0.582204\pi\)
0.966838 + 0.255390i \(0.0822039\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −14.3620 + 14.3620i −0.464258 + 0.464258i
\(958\) 0 0
\(959\) −1.39751 + 9.82823i −0.0451279 + 0.317370i
\(960\) 0 0
\(961\) 28.5461 0.920843
\(962\) 0 0
\(963\) −8.72731 + 8.72731i −0.281234 + 0.281234i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −14.6279 14.6279i −0.470400 0.470400i 0.431644 0.902044i \(-0.357934\pi\)
−0.902044 + 0.431644i \(0.857934\pi\)
\(968\) 0 0
\(969\) −40.1762 −1.29065
\(970\) 0 0
\(971\) 14.5120i 0.465712i −0.972511 0.232856i \(-0.925193\pi\)
0.972511 0.232856i \(-0.0748071\pi\)
\(972\) 0 0
\(973\) −11.3673 15.1359i −0.364419 0.485233i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.07281 3.07281i −0.0983080 0.0983080i 0.656242 0.754550i \(-0.272145\pi\)
−0.754550 + 0.656242i \(0.772145\pi\)
\(978\) 0 0
\(979\) 23.0744 0.737463
\(980\) 0 0
\(981\) 4.14509 0.132343
\(982\) 0 0
\(983\) 38.2010 + 38.2010i 1.21842 + 1.21842i 0.968184 + 0.250238i \(0.0805088\pi\)
0.250238 + 0.968184i \(0.419491\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −15.1689 20.1977i −0.482830 0.642901i
\(988\) 0 0
\(989\) 22.6560i 0.720418i
\(990\) 0 0
\(991\) 42.3300 1.34466 0.672328 0.740253i \(-0.265294\pi\)
0.672328 + 0.740253i \(0.265294\pi\)
\(992\) 0 0
\(993\) 34.9748 + 34.9748i 1.10989 + 1.10989i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −24.3987 + 24.3987i −0.772713 + 0.772713i −0.978580 0.205867i \(-0.933999\pi\)
0.205867 + 0.978580i \(0.433999\pi\)
\(998\) 0 0
\(999\) 12.2470 0.387479
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 1400.2.x.b.657.4 24
5.2 odd 4 280.2.x.a.153.4 yes 24
5.3 odd 4 inner 1400.2.x.b.993.9 24
5.4 even 2 280.2.x.a.97.9 yes 24
7.6 odd 2 inner 1400.2.x.b.657.9 24
20.7 even 4 560.2.bj.d.433.9 24
20.19 odd 2 560.2.bj.d.97.4 24
35.13 even 4 inner 1400.2.x.b.993.4 24
35.27 even 4 280.2.x.a.153.9 yes 24
35.34 odd 2 280.2.x.a.97.4 24
140.27 odd 4 560.2.bj.d.433.4 24
140.139 even 2 560.2.bj.d.97.9 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.x.a.97.4 24 35.34 odd 2
280.2.x.a.97.9 yes 24 5.4 even 2
280.2.x.a.153.4 yes 24 5.2 odd 4
280.2.x.a.153.9 yes 24 35.27 even 4
560.2.bj.d.97.4 24 20.19 odd 2
560.2.bj.d.97.9 24 140.139 even 2
560.2.bj.d.433.4 24 140.27 odd 4
560.2.bj.d.433.9 24 20.7 even 4
1400.2.x.b.657.4 24 1.1 even 1 trivial
1400.2.x.b.657.9 24 7.6 odd 2 inner
1400.2.x.b.993.4 24 35.13 even 4 inner
1400.2.x.b.993.9 24 5.3 odd 4 inner