Properties

Label 1512.2.t.d.289.11
Level $1512$
Weight $2$
Character 1512.289
Analytic conductor $12.073$
Analytic rank $0$
Dimension $22$
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] = [1512,2,Mod(289,1512)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1512.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.t (of order \(3\), 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: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.11
Character \(\chi\) \(=\) 1512.289
Dual form 1512.2.t.d.361.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.52959 q^{5} +(1.16715 + 2.37440i) q^{7} +O(q^{10})\) \(q+3.52959 q^{5} +(1.16715 + 2.37440i) q^{7} +2.32073 q^{11} +(-2.35884 - 4.08563i) q^{13} +(0.636946 + 1.10322i) q^{17} +(2.78386 - 4.82178i) q^{19} +3.29710 q^{23} +7.45798 q^{25} +(4.32116 - 7.48447i) q^{29} +(-4.25821 + 7.37543i) q^{31} +(4.11956 + 8.38064i) q^{35} +(-2.84024 + 4.91943i) q^{37} +(-1.66553 - 2.88478i) q^{41} +(0.0444165 - 0.0769317i) q^{43} +(3.52607 + 6.10733i) q^{47} +(-4.27552 + 5.54256i) q^{49} +(-3.41816 - 5.92042i) q^{53} +8.19121 q^{55} +(-3.99745 + 6.92378i) q^{59} +(-6.67764 - 11.5660i) q^{61} +(-8.32572 - 14.4206i) q^{65} +(-3.06402 + 5.30704i) q^{67} -1.30202 q^{71} +(6.64529 + 11.5100i) q^{73} +(2.70864 + 5.51033i) q^{77} +(5.01403 + 8.68455i) q^{79} +(5.90243 - 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(-0.561496 + 0.972540i) q^{89} +(6.94778 - 10.3694i) q^{91} +(9.82586 - 17.0189i) q^{95} +(-3.50818 + 6.07635i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 6 q^{5} + 7 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 6 q^{5} + 7 q^{7} - 6 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} + 4 q^{23} + 20 q^{25} - 9 q^{29} - 4 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} - 5 q^{47} - 15 q^{49} - 11 q^{53} + 22 q^{55} + 19 q^{59} - 13 q^{61} - 13 q^{65} + 26 q^{67} + 48 q^{71} - 35 q^{73} + 4 q^{77} + 10 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} - 12 q^{95} - 29 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 3.52959 1.57848 0.789239 0.614086i \(-0.210475\pi\)
0.789239 + 0.614086i \(0.210475\pi\)
\(6\) 0 0
\(7\) 1.16715 + 2.37440i 0.441141 + 0.897438i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.32073 0.699726 0.349863 0.936801i \(-0.386228\pi\)
0.349863 + 0.936801i \(0.386228\pi\)
\(12\) 0 0
\(13\) −2.35884 4.08563i −0.654224 1.13315i −0.982088 0.188424i \(-0.939662\pi\)
0.327864 0.944725i \(-0.393671\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.636946 + 1.10322i 0.154482 + 0.267571i 0.932870 0.360212i \(-0.117296\pi\)
−0.778388 + 0.627783i \(0.783962\pi\)
\(18\) 0 0
\(19\) 2.78386 4.82178i 0.638661 1.10619i −0.347066 0.937841i \(-0.612822\pi\)
0.985727 0.168352i \(-0.0538445\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.29710 0.687492 0.343746 0.939063i \(-0.388304\pi\)
0.343746 + 0.939063i \(0.388304\pi\)
\(24\) 0 0
\(25\) 7.45798 1.49160
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.32116 7.48447i 0.802419 1.38983i −0.115601 0.993296i \(-0.536879\pi\)
0.918020 0.396535i \(-0.129787\pi\)
\(30\) 0 0
\(31\) −4.25821 + 7.37543i −0.764797 + 1.32467i 0.175557 + 0.984469i \(0.443827\pi\)
−0.940354 + 0.340197i \(0.889506\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.11956 + 8.38064i 0.696332 + 1.41659i
\(36\) 0 0
\(37\) −2.84024 + 4.91943i −0.466932 + 0.808750i −0.999286 0.0377716i \(-0.987974\pi\)
0.532354 + 0.846522i \(0.321307\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.66553 2.88478i −0.260112 0.450528i 0.706159 0.708053i \(-0.250426\pi\)
−0.966272 + 0.257525i \(0.917093\pi\)
\(42\) 0 0
\(43\) 0.0444165 0.0769317i 0.00677346 0.0117320i −0.862619 0.505855i \(-0.831177\pi\)
0.869392 + 0.494123i \(0.164511\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.52607 + 6.10733i 0.514330 + 0.890845i 0.999862 + 0.0166264i \(0.00529258\pi\)
−0.485532 + 0.874219i \(0.661374\pi\)
\(48\) 0 0
\(49\) −4.27552 + 5.54256i −0.610789 + 0.791794i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.41816 5.92042i −0.469520 0.813233i 0.529873 0.848077i \(-0.322240\pi\)
−0.999393 + 0.0348444i \(0.988906\pi\)
\(54\) 0 0
\(55\) 8.19121 1.10450
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.99745 + 6.92378i −0.520423 + 0.901400i 0.479295 + 0.877654i \(0.340893\pi\)
−0.999718 + 0.0237457i \(0.992441\pi\)
\(60\) 0 0
\(61\) −6.67764 11.5660i −0.854985 1.48088i −0.876659 0.481112i \(-0.840233\pi\)
0.0216747 0.999765i \(-0.493100\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.32572 14.4206i −1.03268 1.78865i
\(66\) 0 0
\(67\) −3.06402 + 5.30704i −0.374330 + 0.648358i −0.990226 0.139469i \(-0.955461\pi\)
0.615897 + 0.787827i \(0.288794\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.30202 −0.154522 −0.0772609 0.997011i \(-0.524617\pi\)
−0.0772609 + 0.997011i \(0.524617\pi\)
\(72\) 0 0
\(73\) 6.64529 + 11.5100i 0.777772 + 1.34714i 0.933223 + 0.359297i \(0.116984\pi\)
−0.155451 + 0.987844i \(0.549683\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.70864 + 5.51033i 0.308678 + 0.627961i
\(78\) 0 0
\(79\) 5.01403 + 8.68455i 0.564122 + 0.977088i 0.997131 + 0.0756985i \(0.0241187\pi\)
−0.433009 + 0.901390i \(0.642548\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.90243 10.2233i 0.647876 1.12215i −0.335753 0.941950i \(-0.608991\pi\)
0.983629 0.180204i \(-0.0576758\pi\)
\(84\) 0 0
\(85\) 2.24815 + 3.89392i 0.243847 + 0.422355i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.561496 + 0.972540i −0.0595185 + 0.103089i −0.894249 0.447569i \(-0.852290\pi\)
0.834731 + 0.550658i \(0.185623\pi\)
\(90\) 0 0
\(91\) 6.94778 10.3694i 0.728325 1.08700i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 9.82586 17.0189i 1.00811 1.74610i
\(96\) 0 0
\(97\) −3.50818 + 6.07635i −0.356202 + 0.616960i −0.987323 0.158724i \(-0.949262\pi\)
0.631121 + 0.775685i \(0.282595\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.74111 0.969277 0.484638 0.874715i \(-0.338951\pi\)
0.484638 + 0.874715i \(0.338951\pi\)
\(102\) 0 0
\(103\) 10.2856 1.01347 0.506734 0.862103i \(-0.330853\pi\)
0.506734 + 0.862103i \(0.330853\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.72201 + 4.71465i −0.263146 + 0.455783i −0.967076 0.254487i \(-0.918094\pi\)
0.703930 + 0.710269i \(0.251427\pi\)
\(108\) 0 0
\(109\) 0.417404 + 0.722965i 0.0399800 + 0.0692475i 0.885323 0.464977i \(-0.153937\pi\)
−0.845343 + 0.534224i \(0.820604\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.44881 9.43761i −0.512581 0.887815i −0.999894 0.0145882i \(-0.995356\pi\)
0.487313 0.873227i \(-0.337977\pi\)
\(114\) 0 0
\(115\) 11.6374 1.08519
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.87608 + 2.79999i −0.171980 + 0.256674i
\(120\) 0 0
\(121\) −5.61421 −0.510383
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 8.67565 0.775974
\(126\) 0 0
\(127\) −9.90354 −0.878797 −0.439399 0.898292i \(-0.644808\pi\)
−0.439399 + 0.898292i \(0.644808\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −17.1844 −1.50141 −0.750704 0.660639i \(-0.770285\pi\)
−0.750704 + 0.660639i \(0.770285\pi\)
\(132\) 0 0
\(133\) 14.6980 + 0.982238i 1.27448 + 0.0851708i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.0939 1.37500 0.687498 0.726186i \(-0.258709\pi\)
0.687498 + 0.726186i \(0.258709\pi\)
\(138\) 0 0
\(139\) 1.11151 + 1.92519i 0.0942768 + 0.163292i 0.909307 0.416127i \(-0.136613\pi\)
−0.815030 + 0.579419i \(0.803279\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −5.47422 9.48163i −0.457778 0.792894i
\(144\) 0 0
\(145\) 15.2519 26.4171i 1.26660 2.19382i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.93692 −0.568295 −0.284147 0.958781i \(-0.591710\pi\)
−0.284147 + 0.958781i \(0.591710\pi\)
\(150\) 0 0
\(151\) 15.5167 1.26273 0.631365 0.775486i \(-0.282495\pi\)
0.631365 + 0.775486i \(0.282495\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −15.0297 + 26.0322i −1.20722 + 2.09096i
\(156\) 0 0
\(157\) −0.401055 + 0.694648i −0.0320077 + 0.0554389i −0.881586 0.472024i \(-0.843523\pi\)
0.849578 + 0.527463i \(0.176857\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.84821 + 7.82862i 0.303281 + 0.616982i
\(162\) 0 0
\(163\) 1.77500 3.07438i 0.139028 0.240804i −0.788101 0.615546i \(-0.788935\pi\)
0.927129 + 0.374742i \(0.122269\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.865131 1.49845i −0.0669459 0.115954i 0.830610 0.556855i \(-0.187992\pi\)
−0.897556 + 0.440901i \(0.854659\pi\)
\(168\) 0 0
\(169\) −4.62823 + 8.01633i −0.356018 + 0.616641i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.11729 + 1.93521i 0.0849462 + 0.147131i 0.905368 0.424627i \(-0.139595\pi\)
−0.820422 + 0.571758i \(0.806262\pi\)
\(174\) 0 0
\(175\) 8.70458 + 17.7082i 0.658005 + 1.33861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.350412 + 0.606931i 0.0261910 + 0.0453641i 0.878824 0.477146i \(-0.158329\pi\)
−0.852633 + 0.522511i \(0.824996\pi\)
\(180\) 0 0
\(181\) −19.6339 −1.45938 −0.729688 0.683780i \(-0.760335\pi\)
−0.729688 + 0.683780i \(0.760335\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −10.0249 + 17.3636i −0.737042 + 1.27659i
\(186\) 0 0
\(187\) 1.47818 + 2.56028i 0.108095 + 0.187226i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.04289 + 13.9307i 0.581963 + 1.00799i 0.995247 + 0.0973872i \(0.0310485\pi\)
−0.413284 + 0.910602i \(0.635618\pi\)
\(192\) 0 0
\(193\) 0.292732 0.507026i 0.0210713 0.0364965i −0.855297 0.518137i \(-0.826626\pi\)
0.876369 + 0.481641i \(0.159959\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.2923 1.23203 0.616014 0.787735i \(-0.288746\pi\)
0.616014 + 0.787735i \(0.288746\pi\)
\(198\) 0 0
\(199\) −12.2119 21.1517i −0.865681 1.49940i −0.866369 0.499404i \(-0.833552\pi\)
0.000687656 1.00000i \(-0.499781\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 22.8145 + 1.52465i 1.60127 + 0.107009i
\(204\) 0 0
\(205\) −5.87864 10.1821i −0.410582 0.711149i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6.46058 11.1900i 0.446888 0.774032i
\(210\) 0 0
\(211\) −5.58733 9.67754i −0.384648 0.666230i 0.607072 0.794647i \(-0.292344\pi\)
−0.991720 + 0.128417i \(0.959010\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.156772 0.271537i 0.0106918 0.0185187i
\(216\) 0 0
\(217\) −22.4822 1.50244i −1.52619 0.101992i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.00490 5.20464i 0.202132 0.350102i
\(222\) 0 0
\(223\) −1.32951 + 2.30277i −0.0890303 + 0.154205i −0.907101 0.420912i \(-0.861710\pi\)
0.818071 + 0.575117i \(0.195043\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.9157 −0.790874 −0.395437 0.918493i \(-0.629407\pi\)
−0.395437 + 0.918493i \(0.629407\pi\)
\(228\) 0 0
\(229\) −29.6128 −1.95687 −0.978434 0.206561i \(-0.933773\pi\)
−0.978434 + 0.206561i \(0.933773\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.84417 + 3.19420i −0.120816 + 0.209259i −0.920090 0.391708i \(-0.871884\pi\)
0.799274 + 0.600967i \(0.205218\pi\)
\(234\) 0 0
\(235\) 12.4456 + 21.5563i 0.811859 + 1.40618i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.03590 13.9186i −0.519799 0.900319i −0.999735 0.0230153i \(-0.992673\pi\)
0.479936 0.877304i \(-0.340660\pi\)
\(240\) 0 0
\(241\) 4.49867 0.289785 0.144892 0.989447i \(-0.453716\pi\)
0.144892 + 0.989447i \(0.453716\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −15.0908 + 19.5629i −0.964117 + 1.24983i
\(246\) 0 0
\(247\) −26.2667 −1.67131
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 17.2696 1.09005 0.545023 0.838421i \(-0.316521\pi\)
0.545023 + 0.838421i \(0.316521\pi\)
\(252\) 0 0
\(253\) 7.65167 0.481057
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.82173 −0.300771 −0.150386 0.988627i \(-0.548052\pi\)
−0.150386 + 0.988627i \(0.548052\pi\)
\(258\) 0 0
\(259\) −14.9957 1.00213i −0.931786 0.0622693i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −28.0903 −1.73212 −0.866062 0.499936i \(-0.833357\pi\)
−0.866062 + 0.499936i \(0.833357\pi\)
\(264\) 0 0
\(265\) −12.0647 20.8966i −0.741128 1.28367i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.4126 21.4993i −0.756810 1.31083i −0.944469 0.328599i \(-0.893423\pi\)
0.187659 0.982234i \(-0.439910\pi\)
\(270\) 0 0
\(271\) −4.79671 + 8.30815i −0.291379 + 0.504684i −0.974136 0.225962i \(-0.927448\pi\)
0.682757 + 0.730646i \(0.260781\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 17.3080 1.04371
\(276\) 0 0
\(277\) 16.9383 1.01772 0.508862 0.860848i \(-0.330067\pi\)
0.508862 + 0.860848i \(0.330067\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.4291 + 19.7958i −0.681805 + 1.18092i 0.292625 + 0.956227i \(0.405471\pi\)
−0.974430 + 0.224693i \(0.927862\pi\)
\(282\) 0 0
\(283\) −4.17811 + 7.23669i −0.248363 + 0.430177i −0.963072 0.269245i \(-0.913226\pi\)
0.714709 + 0.699422i \(0.246559\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.90570 7.32161i 0.289574 0.432181i
\(288\) 0 0
\(289\) 7.68860 13.3170i 0.452271 0.783356i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.16141 + 3.74368i 0.126271 + 0.218708i 0.922229 0.386644i \(-0.126366\pi\)
−0.795958 + 0.605352i \(0.793032\pi\)
\(294\) 0 0
\(295\) −14.1093 + 24.4381i −0.821477 + 1.42284i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −7.77732 13.4707i −0.449774 0.779031i
\(300\) 0 0
\(301\) 0.234507 + 0.0156716i 0.0135168 + 0.000903298i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −23.5693 40.8233i −1.34958 2.33753i
\(306\) 0 0
\(307\) −9.22888 −0.526720 −0.263360 0.964698i \(-0.584831\pi\)
−0.263360 + 0.964698i \(0.584831\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.55365 + 16.5474i −0.541738 + 0.938317i 0.457067 + 0.889432i \(0.348900\pi\)
−0.998804 + 0.0488847i \(0.984433\pi\)
\(312\) 0 0
\(313\) −2.83951 4.91818i −0.160499 0.277992i 0.774549 0.632514i \(-0.217977\pi\)
−0.935048 + 0.354522i \(0.884644\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.1341 24.4809i −0.793848 1.37499i −0.923568 0.383434i \(-0.874741\pi\)
0.129720 0.991551i \(-0.458592\pi\)
\(318\) 0 0
\(319\) 10.0282 17.3694i 0.561474 0.972501i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7.09266 0.394646
\(324\) 0 0
\(325\) −17.5922 30.4705i −0.975838 1.69020i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −10.3858 + 15.5005i −0.572586 + 0.854568i
\(330\) 0 0
\(331\) 3.34045 + 5.78584i 0.183608 + 0.318018i 0.943107 0.332491i \(-0.107889\pi\)
−0.759499 + 0.650509i \(0.774556\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10.8147 + 18.7317i −0.590872 + 1.02342i
\(336\) 0 0
\(337\) −3.49421 6.05215i −0.190342 0.329681i 0.755022 0.655700i \(-0.227626\pi\)
−0.945363 + 0.326018i \(0.894293\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −9.88215 + 17.1164i −0.535148 + 0.926904i
\(342\) 0 0
\(343\) −18.1504 3.68279i −0.980030 0.198852i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.14410 7.17780i 0.222467 0.385324i −0.733089 0.680132i \(-0.761922\pi\)
0.955557 + 0.294808i \(0.0952557\pi\)
\(348\) 0 0
\(349\) 3.05373 5.28921i 0.163462 0.283125i −0.772646 0.634837i \(-0.781067\pi\)
0.936108 + 0.351712i \(0.114400\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 26.7208 1.42221 0.711104 0.703087i \(-0.248196\pi\)
0.711104 + 0.703087i \(0.248196\pi\)
\(354\) 0 0
\(355\) −4.59561 −0.243909
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.45603 + 4.25397i −0.129624 + 0.224516i −0.923531 0.383523i \(-0.874711\pi\)
0.793907 + 0.608040i \(0.208044\pi\)
\(360\) 0 0
\(361\) −5.99972 10.3918i −0.315775 0.546938i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 23.4551 + 40.6255i 1.22770 + 2.12643i
\(366\) 0 0
\(367\) −30.7064 −1.60286 −0.801430 0.598089i \(-0.795927\pi\)
−0.801430 + 0.598089i \(0.795927\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.0679 15.0261i 0.522701 0.780116i
\(372\) 0 0
\(373\) 16.5838 0.858676 0.429338 0.903144i \(-0.358747\pi\)
0.429338 + 0.903144i \(0.358747\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −40.7716 −2.09985
\(378\) 0 0
\(379\) 4.08857 0.210016 0.105008 0.994471i \(-0.466513\pi\)
0.105008 + 0.994471i \(0.466513\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −30.3538 −1.55101 −0.775503 0.631344i \(-0.782504\pi\)
−0.775503 + 0.631344i \(0.782504\pi\)
\(384\) 0 0
\(385\) 9.56038 + 19.4492i 0.487242 + 0.991223i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.46764 0.175816 0.0879082 0.996129i \(-0.471982\pi\)
0.0879082 + 0.996129i \(0.471982\pi\)
\(390\) 0 0
\(391\) 2.10007 + 3.63743i 0.106205 + 0.183953i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 17.6974 + 30.6529i 0.890455 + 1.54231i
\(396\) 0 0
\(397\) −7.04243 + 12.1979i −0.353450 + 0.612193i −0.986851 0.161630i \(-0.948325\pi\)
0.633402 + 0.773823i \(0.281658\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.9319 0.545911 0.272955 0.962027i \(-0.411999\pi\)
0.272955 + 0.962027i \(0.411999\pi\)
\(402\) 0 0
\(403\) 40.1777 2.00139
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6.59142 + 11.4167i −0.326725 + 0.565904i
\(408\) 0 0
\(409\) −7.99397 + 13.8460i −0.395276 + 0.684639i −0.993136 0.116962i \(-0.962685\pi\)
0.597860 + 0.801600i \(0.296018\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −21.1054 1.41043i −1.03853 0.0694029i
\(414\) 0 0
\(415\) 20.8331 36.0841i 1.02266 1.77130i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.56197 + 6.16951i 0.174014 + 0.301400i 0.939819 0.341671i \(-0.110993\pi\)
−0.765806 + 0.643072i \(0.777660\pi\)
\(420\) 0 0
\(421\) −16.6326 + 28.8086i −0.810625 + 1.40404i 0.101802 + 0.994805i \(0.467539\pi\)
−0.912427 + 0.409239i \(0.865794\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.75033 + 8.22781i 0.230425 + 0.399107i
\(426\) 0 0
\(427\) 19.6685 29.3547i 0.951826 1.42057i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.62382 + 4.54459i 0.126385 + 0.218905i 0.922273 0.386538i \(-0.126329\pi\)
−0.795889 + 0.605443i \(0.792996\pi\)
\(432\) 0 0
\(433\) 22.1053 1.06231 0.531156 0.847274i \(-0.321758\pi\)
0.531156 + 0.847274i \(0.321758\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9.17865 15.8979i 0.439074 0.760499i
\(438\) 0 0
\(439\) −17.3083 29.9788i −0.826079 1.43081i −0.901092 0.433628i \(-0.857233\pi\)
0.0750132 0.997183i \(-0.476100\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.20461 3.81850i −0.104744 0.181423i 0.808889 0.587961i \(-0.200069\pi\)
−0.913634 + 0.406538i \(0.866736\pi\)
\(444\) 0 0
\(445\) −1.98185 + 3.43266i −0.0939486 + 0.162724i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 19.6336 0.926568 0.463284 0.886210i \(-0.346671\pi\)
0.463284 + 0.886210i \(0.346671\pi\)
\(450\) 0 0
\(451\) −3.86525 6.69481i −0.182007 0.315246i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 24.5228 36.5995i 1.14965 1.71581i
\(456\) 0 0
\(457\) 15.4196 + 26.7075i 0.721297 + 1.24932i 0.960480 + 0.278349i \(0.0897872\pi\)
−0.239183 + 0.970975i \(0.576879\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.6297 23.6074i 0.634800 1.09951i −0.351757 0.936091i \(-0.614416\pi\)
0.986557 0.163415i \(-0.0522510\pi\)
\(462\) 0 0
\(463\) −0.959750 1.66234i −0.0446034 0.0772553i 0.842862 0.538130i \(-0.180869\pi\)
−0.887465 + 0.460875i \(0.847536\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.88655 + 8.46376i −0.226123 + 0.391656i −0.956656 0.291221i \(-0.905938\pi\)
0.730533 + 0.682877i \(0.239272\pi\)
\(468\) 0 0
\(469\) −16.1772 1.08109i −0.746994 0.0499201i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.103079 0.178538i 0.00473957 0.00820917i
\(474\) 0 0
\(475\) 20.7619 35.9607i 0.952623 1.64999i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15.3762 −0.702556 −0.351278 0.936271i \(-0.614253\pi\)
−0.351278 + 0.936271i \(0.614253\pi\)
\(480\) 0 0
\(481\) 26.7986 1.22191
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −12.3824 + 21.4470i −0.562258 + 0.973859i
\(486\) 0 0
\(487\) 5.18342 + 8.97794i 0.234883 + 0.406829i 0.959239 0.282597i \(-0.0911959\pi\)
−0.724356 + 0.689427i \(0.757863\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.94718 + 12.0329i 0.313522 + 0.543035i 0.979122 0.203273i \(-0.0651578\pi\)
−0.665600 + 0.746308i \(0.731825\pi\)
\(492\) 0 0
\(493\) 11.0094 0.495837
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.51966 3.09152i −0.0681660 0.138674i
\(498\) 0 0
\(499\) −3.40977 −0.152642 −0.0763210 0.997083i \(-0.524317\pi\)
−0.0763210 + 0.997083i \(0.524317\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −43.8911 −1.95701 −0.978504 0.206227i \(-0.933881\pi\)
−0.978504 + 0.206227i \(0.933881\pi\)
\(504\) 0 0
\(505\) 34.3821 1.52998
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −39.3348 −1.74348 −0.871742 0.489966i \(-0.837009\pi\)
−0.871742 + 0.489966i \(0.837009\pi\)
\(510\) 0 0
\(511\) −19.5732 + 29.2124i −0.865868 + 1.29228i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 36.3038 1.59974
\(516\) 0 0
\(517\) 8.18305 + 14.1735i 0.359890 + 0.623348i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12.4779 21.6124i −0.546669 0.946858i −0.998500 0.0547547i \(-0.982562\pi\)
0.451831 0.892104i \(-0.350771\pi\)
\(522\) 0 0
\(523\) −15.1575 + 26.2536i −0.662792 + 1.14799i 0.317086 + 0.948397i \(0.397296\pi\)
−0.979879 + 0.199594i \(0.936038\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.8490 −0.472589
\(528\) 0 0
\(529\) −12.1291 −0.527354
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7.85744 + 13.6095i −0.340343 + 0.589492i
\(534\) 0 0
\(535\) −9.60755 + 16.6408i −0.415371 + 0.719443i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9.92233 + 12.8628i −0.427385 + 0.554039i
\(540\) 0 0
\(541\) −14.2812 + 24.7357i −0.613996 + 1.06347i 0.376563 + 0.926391i \(0.377106\pi\)
−0.990560 + 0.137082i \(0.956228\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.47326 + 2.55177i 0.0631077 + 0.109306i
\(546\) 0 0
\(547\) 3.89233 6.74171i 0.166424 0.288255i −0.770736 0.637154i \(-0.780111\pi\)
0.937160 + 0.348900i \(0.113445\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −24.0590 41.6714i −1.02495 1.77526i
\(552\) 0 0
\(553\) −14.7684 + 22.0415i −0.628018 + 0.937299i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 23.2470 + 40.2650i 0.985008 + 1.70608i 0.641900 + 0.766788i \(0.278146\pi\)
0.343108 + 0.939296i \(0.388520\pi\)
\(558\) 0 0
\(559\) −0.419086 −0.0177254
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 13.9913 24.2336i 0.589663 1.02133i −0.404614 0.914488i \(-0.632594\pi\)
0.994276 0.106838i \(-0.0340726\pi\)
\(564\) 0 0
\(565\) −19.2320 33.3109i −0.809098 1.40140i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.44979 + 7.70726i 0.186545 + 0.323105i 0.944096 0.329671i \(-0.106938\pi\)
−0.757551 + 0.652776i \(0.773604\pi\)
\(570\) 0 0
\(571\) 16.1652 27.9989i 0.676492 1.17172i −0.299539 0.954084i \(-0.596833\pi\)
0.976031 0.217634i \(-0.0698338\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 24.5897 1.02546
\(576\) 0 0
\(577\) −16.8414 29.1701i −0.701115 1.21437i −0.968075 0.250659i \(-0.919353\pi\)
0.266960 0.963707i \(-0.413981\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 31.1632 + 2.08257i 1.29287 + 0.0863997i
\(582\) 0 0
\(583\) −7.93262 13.7397i −0.328536 0.569040i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.24076 2.14907i 0.0512118 0.0887015i −0.839283 0.543695i \(-0.817025\pi\)
0.890495 + 0.454993i \(0.150358\pi\)
\(588\) 0 0
\(589\) 23.7085 + 41.0643i 0.976891 + 1.69202i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15.0903 26.1371i 0.619684 1.07332i −0.369859 0.929088i \(-0.620594\pi\)
0.989543 0.144236i \(-0.0460725\pi\)
\(594\) 0 0
\(595\) −6.62177 + 9.88280i −0.271466 + 0.405155i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.20414 + 14.2100i −0.335212 + 0.580604i −0.983526 0.180769i \(-0.942141\pi\)
0.648314 + 0.761373i \(0.275475\pi\)
\(600\) 0 0
\(601\) −2.96998 + 5.14416i −0.121148 + 0.209835i −0.920221 0.391400i \(-0.871991\pi\)
0.799073 + 0.601235i \(0.205324\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −19.8159 −0.805629
\(606\) 0 0
\(607\) −5.95146 −0.241563 −0.120781 0.992679i \(-0.538540\pi\)
−0.120781 + 0.992679i \(0.538540\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16.6348 28.8124i 0.672974 1.16562i
\(612\) 0 0
\(613\) 15.5920 + 27.0062i 0.629756 + 1.09077i 0.987601 + 0.156988i \(0.0501783\pi\)
−0.357845 + 0.933781i \(0.616488\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.1437 + 19.3014i 0.448627 + 0.777045i 0.998297 0.0583367i \(-0.0185797\pi\)
−0.549670 + 0.835382i \(0.685246\pi\)
\(618\) 0 0
\(619\) 34.5887 1.39024 0.695118 0.718895i \(-0.255352\pi\)
0.695118 + 0.718895i \(0.255352\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.96454 0.198115i −0.118772 0.00793729i
\(624\) 0 0
\(625\) −6.66844 −0.266738
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.23631 −0.288530
\(630\) 0 0
\(631\) −26.2933 −1.04672 −0.523360 0.852112i \(-0.675322\pi\)
−0.523360 + 0.852112i \(0.675322\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −34.9554 −1.38716
\(636\) 0 0
\(637\) 32.7301 + 4.39419i 1.29681 + 0.174104i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 32.5346 1.28504 0.642519 0.766269i \(-0.277889\pi\)
0.642519 + 0.766269i \(0.277889\pi\)
\(642\) 0 0
\(643\) 5.21987 + 9.04107i 0.205851 + 0.356545i 0.950404 0.311019i \(-0.100670\pi\)
−0.744552 + 0.667564i \(0.767337\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.685824 1.18788i −0.0269625 0.0467005i 0.852229 0.523168i \(-0.175250\pi\)
−0.879192 + 0.476468i \(0.841917\pi\)
\(648\) 0 0
\(649\) −9.27699 + 16.0682i −0.364154 + 0.630733i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.25134 0.283767 0.141883 0.989883i \(-0.454684\pi\)
0.141883 + 0.989883i \(0.454684\pi\)
\(654\) 0 0
\(655\) −60.6538 −2.36994
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.3187 23.0686i 0.518822 0.898626i −0.480939 0.876754i \(-0.659704\pi\)
0.999761 0.0218722i \(-0.00696268\pi\)
\(660\) 0 0
\(661\) 17.4099 30.1549i 0.677168 1.17289i −0.298662 0.954359i \(-0.596540\pi\)
0.975830 0.218531i \(-0.0701265\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 51.8779 + 3.46689i 2.01174 + 0.134440i
\(666\) 0 0
\(667\) 14.2473 24.6770i 0.551657 0.955498i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −15.4970 26.8416i −0.598255 1.03621i
\(672\) 0 0
\(673\) 8.23841 14.2693i 0.317567 0.550043i −0.662412 0.749139i \(-0.730467\pi\)
0.979980 + 0.199096i \(0.0638007\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.5827 18.3297i −0.406725 0.704469i 0.587795 0.809010i \(-0.299996\pi\)
−0.994521 + 0.104541i \(0.966663\pi\)
\(678\) 0 0
\(679\) −18.5223 1.23780i −0.710819 0.0475026i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −14.0756 24.3796i −0.538587 0.932859i −0.998980 0.0451447i \(-0.985625\pi\)
0.460394 0.887715i \(-0.347708\pi\)
\(684\) 0 0
\(685\) 56.8049 2.17040
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −16.1258 + 27.9306i −0.614343 + 1.06407i
\(690\) 0 0
\(691\) −9.53980 16.5234i −0.362911 0.628580i 0.625528 0.780202i \(-0.284884\pi\)
−0.988439 + 0.151622i \(0.951550\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.92316 + 6.79511i 0.148814 + 0.257753i
\(696\) 0 0
\(697\) 2.12171 3.67490i 0.0803653 0.139197i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −23.8508 −0.900834 −0.450417 0.892818i \(-0.648725\pi\)
−0.450417 + 0.892818i \(0.648725\pi\)
\(702\) 0 0
\(703\) 15.8136 + 27.3900i 0.596422 + 1.03303i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 11.3693 + 23.1293i 0.427588 + 0.869865i
\(708\) 0 0
\(709\) −10.0493 17.4059i −0.377409 0.653691i 0.613276 0.789869i \(-0.289851\pi\)
−0.990684 + 0.136178i \(0.956518\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −14.0397 + 24.3175i −0.525792 + 0.910698i
\(714\) 0 0
\(715\) −19.3217 33.4662i −0.722592 1.25157i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3.29246 5.70270i 0.122788 0.212675i −0.798078 0.602554i \(-0.794150\pi\)
0.920866 + 0.389879i \(0.127483\pi\)
\(720\) 0 0
\(721\) 12.0048 + 24.4220i 0.447082 + 0.909524i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 32.2271 55.8190i 1.19688 2.07307i
\(726\) 0 0
\(727\) 18.2342 31.5826i 0.676269 1.17133i −0.299827 0.953994i \(-0.596929\pi\)
0.976096 0.217339i \(-0.0697376\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.113164 0.00418551
\(732\) 0 0
\(733\) 23.3647 0.862997 0.431498 0.902114i \(-0.357985\pi\)
0.431498 + 0.902114i \(0.357985\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.11077 + 12.3162i −0.261928 + 0.453673i
\(738\) 0 0
\(739\) 14.4596 + 25.0448i 0.531906 + 0.921288i 0.999306 + 0.0372422i \(0.0118573\pi\)
−0.467400 + 0.884046i \(0.654809\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −11.6794 20.2292i −0.428474 0.742139i 0.568264 0.822847i \(-0.307615\pi\)
−0.996738 + 0.0807074i \(0.974282\pi\)
\(744\) 0 0
\(745\) −24.4845 −0.897041
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −14.3714 0.960415i −0.525121 0.0350928i
\(750\) 0 0
\(751\) −1.71323 −0.0625167 −0.0312584 0.999511i \(-0.509951\pi\)
−0.0312584 + 0.999511i \(0.509951\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 54.7675 1.99319
\(756\) 0 0
\(757\) 28.4587 1.03435 0.517175 0.855880i \(-0.326984\pi\)
0.517175 + 0.855880i \(0.326984\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 34.1051 1.23631 0.618154 0.786057i \(-0.287881\pi\)
0.618154 + 0.786057i \(0.287881\pi\)
\(762\) 0 0
\(763\) −1.22943 + 1.83489i −0.0445084 + 0.0664275i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 37.7173 1.36189
\(768\) 0 0
\(769\) 2.48467 + 4.30357i 0.0895995 + 0.155191i 0.907342 0.420394i \(-0.138108\pi\)
−0.817742 + 0.575584i \(0.804775\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5.74814 + 9.95607i 0.206746 + 0.358095i 0.950688 0.310150i \(-0.100379\pi\)
−0.743941 + 0.668245i \(0.767046\pi\)
\(774\) 0 0
\(775\) −31.7576 + 55.0058i −1.14077 + 1.97587i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −18.5464 −0.664494
\(780\) 0 0
\(781\) −3.02165 −0.108123
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.41556 + 2.45182i −0.0505235 + 0.0875092i
\(786\) 0 0
\(787\) −24.3005 + 42.0898i −0.866221 + 1.50034i −0.000391003 1.00000i \(0.500124\pi\)
−0.865830 + 0.500339i \(0.833209\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 16.0491 23.9527i 0.570639 0.851661i
\(792\) 0 0
\(793\) −31.5030 + 54.5647i −1.11870 + 1.93765i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −16.8556 29.1947i −0.597056 1.03413i −0.993253 0.115965i \(-0.963004\pi\)
0.396198 0.918165i \(-0.370330\pi\)
\(798\) 0 0
\(799\) −4.49183 + 7.78007i −0.158909 + 0.275239i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 15.4219 + 26.7115i 0.544228 + 0.942630i
\(804\) 0 0
\(805\) 13.5826 + 27.6318i 0.478723 + 0.973892i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 7.93617 + 13.7459i 0.279021 + 0.483278i 0.971142 0.238503i \(-0.0766568\pi\)
−0.692121 + 0.721782i \(0.743323\pi\)
\(810\) 0 0
\(811\) 27.2524 0.956963 0.478481 0.878098i \(-0.341187\pi\)
0.478481 + 0.878098i \(0.341187\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6.26500 10.8513i 0.219454 0.380105i
\(816\) 0 0
\(817\) −0.247299 0.428334i −0.00865188 0.0149855i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 12.1694 + 21.0781i 0.424717 + 0.735631i 0.996394 0.0848477i \(-0.0270404\pi\)
−0.571677 + 0.820479i \(0.693707\pi\)
\(822\) 0 0
\(823\) 5.76898 9.99217i 0.201094 0.348305i −0.747787 0.663939i \(-0.768884\pi\)
0.948881 + 0.315633i \(0.102217\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 34.8582 1.21214 0.606069 0.795412i \(-0.292745\pi\)
0.606069 + 0.795412i \(0.292745\pi\)
\(828\) 0 0
\(829\) −7.64018 13.2332i −0.265354 0.459607i 0.702302 0.711879i \(-0.252156\pi\)
−0.967656 + 0.252272i \(0.918822\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −8.83795 1.18654i −0.306217 0.0411113i
\(834\) 0 0
\(835\) −3.05356 5.28891i −0.105673 0.183030i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 8.39990 14.5490i 0.289997 0.502289i −0.683812 0.729658i \(-0.739679\pi\)
0.973809 + 0.227369i \(0.0730125\pi\)
\(840\) 0 0
\(841\) −22.8448 39.5684i −0.787753 1.36443i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −16.3357 + 28.2943i −0.561967 + 0.973355i
\(846\) 0 0
\(847\) −6.55263 13.3304i −0.225151 0.458037i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9.36454 + 16.2199i −0.321012 + 0.556009i
\(852\) 0 0
\(853\) −11.4270 + 19.7921i −0.391253 + 0.677670i −0.992615 0.121306i \(-0.961292\pi\)
0.601362 + 0.798977i \(0.294625\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 35.1743 1.20153 0.600765 0.799426i \(-0.294863\pi\)
0.600765 + 0.799426i \(0.294863\pi\)
\(858\) 0 0
\(859\) 10.5704 0.360658 0.180329 0.983606i \(-0.442284\pi\)
0.180329 + 0.983606i \(0.442284\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 7.29326 12.6323i 0.248265 0.430008i −0.714779 0.699350i \(-0.753473\pi\)
0.963045 + 0.269342i \(0.0868061\pi\)
\(864\) 0 0
\(865\) 3.94358 + 6.83048i 0.134086 + 0.232243i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 11.6362 + 20.1545i 0.394731 + 0.683694i
\(870\) 0 0
\(871\) 28.9101 0.979582
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 10.1258 + 20.5994i 0.342314 + 0.696388i
\(876\) 0 0
\(877\) 11.3183 0.382191 0.191096 0.981571i \(-0.438796\pi\)
0.191096 + 0.981571i \(0.438796\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0.733220 0.0247028 0.0123514 0.999924i \(-0.496068\pi\)
0.0123514 + 0.999924i \(0.496068\pi\)
\(882\) 0 0
\(883\) −14.1726 −0.476944 −0.238472 0.971149i \(-0.576647\pi\)
−0.238472 + 0.971149i \(0.576647\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 33.6325 1.12927 0.564634 0.825341i \(-0.309017\pi\)
0.564634 + 0.825341i \(0.309017\pi\)
\(888\) 0 0
\(889\) −11.5589 23.5149i −0.387674 0.788666i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 39.2643 1.31393
\(894\) 0 0
\(895\) 1.23681 + 2.14221i 0.0413419 + 0.0716063i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 36.8008 + 63.7408i 1.22737 + 2.12588i
\(900\) 0 0
\(901\) 4.35436 7.54198i 0.145065 0.251260i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −69.2996 −2.30360
\(906\) 0 0
\(907\) 9.58510 0.318268 0.159134 0.987257i \(-0.449130\pi\)
0.159134 + 0.987257i \(0.449130\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 9.37499 16.2380i 0.310607 0.537988i −0.667887 0.744263i \(-0.732801\pi\)
0.978494 + 0.206275i \(0.0661342\pi\)
\(912\) 0 0
\(913\) 13.6979 23.7255i 0.453336 0.785201i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −20.0568 40.8026i −0.662333 1.34742i
\(918\) 0 0
\(919\) 21.2895 36.8745i 0.702276 1.21638i −0.265390 0.964141i \(-0.585501\pi\)
0.967666 0.252236i \(-0.0811661\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 3.07126 + 5.31958i 0.101092 + 0.175096i
\(924\) 0 0
\(925\) −21.1824 + 36.6890i −0.696474 + 1.20633i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 19.0762 + 33.0409i 0.625869 + 1.08404i 0.988372 + 0.152054i \(0.0485889\pi\)
−0.362503 + 0.931983i \(0.618078\pi\)
\(930\) 0 0
\(931\) 14.8226 + 36.0453i 0.485790 + 1.18134i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 5.21736 + 9.03673i 0.170626 + 0.295533i
\(936\) 0 0
\(937\) 6.48960 0.212006 0.106003 0.994366i \(-0.466195\pi\)
0.106003 + 0.994366i \(0.466195\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −0.233235 + 0.403976i −0.00760326 + 0.0131692i −0.869802 0.493401i \(-0.835754\pi\)
0.862199 + 0.506570i \(0.169087\pi\)
\(942\) 0 0
\(943\) −5.49142 9.51142i −0.178825 0.309734i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −7.55575 13.0869i −0.245529 0.425268i 0.716751 0.697329i \(-0.245628\pi\)
−0.962280 + 0.272060i \(0.912295\pi\)
\(948\) 0 0
\(949\) 31.3503 54.3003i 1.01767 1.76266i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −19.6802 −0.637503 −0.318751 0.947838i \(-0.603264\pi\)
−0.318751 + 0.947838i \(0.603264\pi\)
\(954\) 0 0
\(955\) 28.3881 + 49.1696i 0.918616 + 1.59109i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 18.7840 + 38.2133i 0.606568 + 1.23397i
\(960\) 0 0
\(961\) −20.7647 35.9655i −0.669828 1.16018i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.03322 1.78959i 0.0332606 0.0576090i
\(966\) 0 0
\(967\) 8.83228 + 15.2980i 0.284027 + 0.491949i 0.972373 0.233433i \(-0.0749961\pi\)
−0.688346 + 0.725383i \(0.741663\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 11.7523 20.3555i 0.377148 0.653240i −0.613498 0.789697i \(-0.710238\pi\)
0.990646 + 0.136456i \(0.0435713\pi\)
\(972\) 0 0
\(973\) −3.27386 + 4.88614i −0.104955 + 0.156642i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.71689 + 4.70580i −0.0869211 + 0.150552i −0.906208 0.422832i \(-0.861036\pi\)
0.819287 + 0.573384i \(0.194369\pi\)
\(978\) 0 0
\(979\) −1.30308 + 2.25700i −0.0416466 + 0.0721341i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.10690 0.0671997 0.0335998 0.999435i \(-0.489303\pi\)
0.0335998 + 0.999435i \(0.489303\pi\)
\(984\) 0 0
\(985\) 61.0348 1.94473
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.146446 0.253651i 0.00465670 0.00806564i
\(990\) 0 0
\(991\) 8.91172 + 15.4356i 0.283090 + 0.490327i 0.972144 0.234383i \(-0.0753071\pi\)
−0.689054 + 0.724710i \(0.741974\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −43.1031 74.6567i −1.36646 2.36678i
\(996\) 0 0
\(997\) −36.4954 −1.15582 −0.577911 0.816100i \(-0.696132\pi\)
−0.577911 + 0.816100i \(0.696132\pi\)
\(998\) 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 1512.2.t.d.289.11 22
3.2 odd 2 504.2.t.d.457.7 yes 22
4.3 odd 2 3024.2.t.l.289.11 22
7.4 even 3 1512.2.q.c.1369.1 22
9.4 even 3 1512.2.q.c.793.1 22
9.5 odd 6 504.2.q.d.121.8 yes 22
12.11 even 2 1008.2.t.k.961.5 22
21.11 odd 6 504.2.q.d.25.8 22
28.11 odd 6 3024.2.q.k.2881.1 22
36.23 even 6 1008.2.q.k.625.4 22
36.31 odd 6 3024.2.q.k.2305.1 22
63.4 even 3 inner 1512.2.t.d.361.11 22
63.32 odd 6 504.2.t.d.193.7 yes 22
84.11 even 6 1008.2.q.k.529.4 22
252.67 odd 6 3024.2.t.l.1873.11 22
252.95 even 6 1008.2.t.k.193.5 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.q.d.25.8 22 21.11 odd 6
504.2.q.d.121.8 yes 22 9.5 odd 6
504.2.t.d.193.7 yes 22 63.32 odd 6
504.2.t.d.457.7 yes 22 3.2 odd 2
1008.2.q.k.529.4 22 84.11 even 6
1008.2.q.k.625.4 22 36.23 even 6
1008.2.t.k.193.5 22 252.95 even 6
1008.2.t.k.961.5 22 12.11 even 2
1512.2.q.c.793.1 22 9.4 even 3
1512.2.q.c.1369.1 22 7.4 even 3
1512.2.t.d.289.11 22 1.1 even 1 trivial
1512.2.t.d.361.11 22 63.4 even 3 inner
3024.2.q.k.2305.1 22 36.31 odd 6
3024.2.q.k.2881.1 22 28.11 odd 6
3024.2.t.l.289.11 22 4.3 odd 2
3024.2.t.l.1873.11 22 252.67 odd 6