Properties

Label 828.2.q.c.577.2
Level $828$
Weight $2$
Character 828.577
Analytic conductor $6.612$
Analytic rank $0$
Dimension $20$
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] = [828,2,Mod(73,828)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(828, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("828.73");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 828.q (of order \(11\), degree \(10\), 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: \(6.61161328736\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + 15500 x^{12} - 28190 x^{11} + 41920 x^{10} - 33520 x^{9} - 13837 x^{8} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 276)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 577.2
Root \(-1.54238 - 1.78001i\) of defining polynomial
Character \(\chi\) \(=\) 828.577
Dual form 828.2.q.c.541.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.38954 + 0.701632i) q^{5} +(2.64891 - 3.05701i) q^{7} +O(q^{10})\) \(q+(2.38954 + 0.701632i) q^{5} +(2.64891 - 3.05701i) q^{7} +(4.05943 - 2.60884i) q^{11} +(-2.81278 - 3.24612i) q^{13} +(-1.87409 + 4.10368i) q^{17} +(-1.84032 - 4.02974i) q^{19} +(-4.75085 + 0.655317i) q^{23} +(1.01134 + 0.649950i) q^{25} +(0.207351 - 0.454036i) q^{29} +(-0.727870 + 5.06245i) q^{31} +(8.47457 - 5.44627i) q^{35} +(10.2392 - 3.00650i) q^{37} +(-7.29593 - 2.14228i) q^{41} +(1.07935 + 7.50707i) q^{43} +7.67725 q^{47} +(-1.33235 - 9.26672i) q^{49} +(-5.00164 + 5.77220i) q^{53} +(11.5306 - 3.38569i) q^{55} +(1.85219 + 2.13754i) q^{59} +(-0.225996 + 1.57184i) q^{61} +(-4.44366 - 9.73025i) q^{65} +(10.1121 + 6.49867i) q^{67} +(-3.18977 - 2.04994i) q^{71} +(-3.09627 - 6.77988i) q^{73} +(2.77784 - 19.3203i) q^{77} +(7.62471 + 8.79938i) q^{79} +(5.09163 - 1.49504i) q^{83} +(-7.35747 + 8.49098i) q^{85} +(1.58627 + 11.0327i) q^{89} -17.3742 q^{91} +(-1.57012 - 10.9204i) q^{95} +(-6.84457 - 2.00975i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/828\mathbb{Z}\right)^\times\).

\(n\) \(415\) \(461\) \(649\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 2.38954 + 0.701632i 1.06863 + 0.313779i 0.768323 0.640062i \(-0.221091\pi\)
0.300311 + 0.953841i \(0.402910\pi\)
\(6\) 0 0
\(7\) 2.64891 3.05701i 1.00119 1.15544i 0.0133629 0.999911i \(-0.495746\pi\)
0.987831 0.155529i \(-0.0497082\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.05943 2.60884i 1.22396 0.786594i 0.241024 0.970519i \(-0.422517\pi\)
0.982940 + 0.183925i \(0.0588804\pi\)
\(12\) 0 0
\(13\) −2.81278 3.24612i −0.780123 0.900310i 0.216995 0.976173i \(-0.430375\pi\)
−0.997118 + 0.0758623i \(0.975829\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.87409 + 4.10368i −0.454533 + 0.995288i 0.534167 + 0.845379i \(0.320625\pi\)
−0.988700 + 0.149909i \(0.952102\pi\)
\(18\) 0 0
\(19\) −1.84032 4.02974i −0.422198 0.924485i −0.994529 0.104462i \(-0.966688\pi\)
0.572331 0.820023i \(-0.306039\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.75085 + 0.655317i −0.990620 + 0.136643i
\(24\) 0 0
\(25\) 1.01134 + 0.649950i 0.202268 + 0.129990i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.207351 0.454036i 0.0385042 0.0843124i −0.889403 0.457125i \(-0.848879\pi\)
0.927907 + 0.372812i \(0.121607\pi\)
\(30\) 0 0
\(31\) −0.727870 + 5.06245i −0.130729 + 0.909243i 0.813877 + 0.581037i \(0.197353\pi\)
−0.944606 + 0.328206i \(0.893556\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 8.47457 5.44627i 1.43246 0.920588i
\(36\) 0 0
\(37\) 10.2392 3.00650i 1.68331 0.494265i 0.706384 0.707829i \(-0.250325\pi\)
0.976929 + 0.213564i \(0.0685071\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.29593 2.14228i −1.13943 0.334568i −0.343024 0.939327i \(-0.611451\pi\)
−0.796409 + 0.604759i \(0.793269\pi\)
\(42\) 0 0
\(43\) 1.07935 + 7.50707i 0.164600 + 1.14482i 0.889824 + 0.456305i \(0.150827\pi\)
−0.725224 + 0.688513i \(0.758264\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.67725 1.11984 0.559921 0.828546i \(-0.310831\pi\)
0.559921 + 0.828546i \(0.310831\pi\)
\(48\) 0 0
\(49\) −1.33235 9.26672i −0.190336 1.32382i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.00164 + 5.77220i −0.687028 + 0.792873i −0.986939 0.161095i \(-0.948498\pi\)
0.299911 + 0.953967i \(0.403043\pi\)
\(54\) 0 0
\(55\) 11.5306 3.38569i 1.55479 0.456527i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.85219 + 2.13754i 0.241134 + 0.278284i 0.863397 0.504524i \(-0.168332\pi\)
−0.622263 + 0.782808i \(0.713787\pi\)
\(60\) 0 0
\(61\) −0.225996 + 1.57184i −0.0289358 + 0.201253i −0.999161 0.0409511i \(-0.986961\pi\)
0.970225 + 0.242204i \(0.0778703\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.44366 9.73025i −0.551168 1.20689i
\(66\) 0 0
\(67\) 10.1121 + 6.49867i 1.23539 + 0.793939i 0.984722 0.174134i \(-0.0557124\pi\)
0.250671 + 0.968072i \(0.419349\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.18977 2.04994i −0.378556 0.243283i 0.337501 0.941325i \(-0.390418\pi\)
−0.716057 + 0.698042i \(0.754055\pi\)
\(72\) 0 0
\(73\) −3.09627 6.77988i −0.362391 0.793525i −0.999737 0.0229473i \(-0.992695\pi\)
0.637346 0.770578i \(-0.280032\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.77784 19.3203i 0.316564 2.20175i
\(78\) 0 0
\(79\) 7.62471 + 8.79938i 0.857847 + 0.990008i 1.00000 0.000163051i \(5.19009e-5\pi\)
−0.142153 + 0.989845i \(0.545403\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.09163 1.49504i 0.558879 0.164102i 0.00991953 0.999951i \(-0.496842\pi\)
0.548959 + 0.835849i \(0.315024\pi\)
\(84\) 0 0
\(85\) −7.35747 + 8.49098i −0.798030 + 0.920976i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.58627 + 11.0327i 0.168144 + 1.16947i 0.882717 + 0.469905i \(0.155712\pi\)
−0.714573 + 0.699561i \(0.753379\pi\)
\(90\) 0 0
\(91\) −17.3742 −1.82131
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.57012 10.9204i −0.161091 1.12041i
\(96\) 0 0
\(97\) −6.84457 2.00975i −0.694961 0.204059i −0.0848721 0.996392i \(-0.527048\pi\)
−0.610089 + 0.792333i \(0.708866\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.07150 + 1.48913i −0.504633 + 0.148174i −0.524133 0.851636i \(-0.675611\pi\)
0.0195002 + 0.999810i \(0.493792\pi\)
\(102\) 0 0
\(103\) 16.1144 10.3561i 1.58780 1.02042i 0.615074 0.788470i \(-0.289126\pi\)
0.972728 0.231949i \(-0.0745102\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.56999 + 10.9195i −0.151777 + 1.05563i 0.761463 + 0.648209i \(0.224482\pi\)
−0.913240 + 0.407423i \(0.866428\pi\)
\(108\) 0 0
\(109\) −0.724276 + 1.58594i −0.0693731 + 0.151906i −0.941142 0.338011i \(-0.890246\pi\)
0.871769 + 0.489917i \(0.162973\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.5328 + 9.33966i 1.36713 + 0.878601i 0.998696 0.0510528i \(-0.0162577\pi\)
0.368434 + 0.929654i \(0.379894\pi\)
\(114\) 0 0
\(115\) −11.8121 1.76744i −1.10149 0.164815i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.58068 + 16.5994i 0.694920 + 1.52166i
\(120\) 0 0
\(121\) 5.10337 11.1748i 0.463943 1.01589i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −6.19377 7.14799i −0.553988 0.639336i
\(126\) 0 0
\(127\) −12.0209 + 7.72538i −1.06668 + 0.685516i −0.951444 0.307821i \(-0.900400\pi\)
−0.115240 + 0.993338i \(0.536764\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.51189 + 7.51512i −0.568946 + 0.656599i −0.965191 0.261546i \(-0.915768\pi\)
0.396245 + 0.918145i \(0.370313\pi\)
\(132\) 0 0
\(133\) −17.1938 5.04854i −1.49089 0.437764i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.14309 0.695711 0.347855 0.937548i \(-0.386910\pi\)
0.347855 + 0.937548i \(0.386910\pi\)
\(138\) 0 0
\(139\) −10.1303 −0.859242 −0.429621 0.903009i \(-0.641353\pi\)
−0.429621 + 0.903009i \(0.641353\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −19.8869 5.83931i −1.66302 0.488307i
\(144\) 0 0
\(145\) 0.814041 0.939453i 0.0676024 0.0780173i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.58068 + 3.58648i −0.457187 + 0.293816i −0.748892 0.662692i \(-0.769414\pi\)
0.291705 + 0.956508i \(0.405777\pi\)
\(150\) 0 0
\(151\) 5.56561 + 6.42306i 0.452923 + 0.522701i 0.935583 0.353107i \(-0.114875\pi\)
−0.482660 + 0.875808i \(0.660329\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.29125 + 11.5862i −0.425004 + 0.930628i
\(156\) 0 0
\(157\) 3.89510 + 8.52909i 0.310863 + 0.680695i 0.998992 0.0448934i \(-0.0142948\pi\)
−0.688129 + 0.725589i \(0.741568\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −10.5813 + 16.2592i −0.833921 + 1.28141i
\(162\) 0 0
\(163\) −4.07886 2.62132i −0.319481 0.205318i 0.371064 0.928607i \(-0.378993\pi\)
−0.690545 + 0.723289i \(0.742629\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.54815 12.1488i 0.429329 0.940099i −0.564107 0.825702i \(-0.690779\pi\)
0.993435 0.114397i \(-0.0364934\pi\)
\(168\) 0 0
\(169\) −0.775469 + 5.39351i −0.0596515 + 0.414885i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.57692 + 5.51205i −0.652091 + 0.419073i −0.824430 0.565964i \(-0.808504\pi\)
0.172339 + 0.985038i \(0.444868\pi\)
\(174\) 0 0
\(175\) 4.66585 1.37002i 0.352705 0.103564i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.83694 + 1.71388i 0.436274 + 0.128102i 0.492492 0.870317i \(-0.336086\pi\)
−0.0562183 + 0.998419i \(0.517904\pi\)
\(180\) 0 0
\(181\) 0.660855 + 4.59635i 0.0491209 + 0.341644i 0.999530 + 0.0306423i \(0.00975529\pi\)
−0.950409 + 0.311001i \(0.899336\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 26.5764 1.95394
\(186\) 0 0
\(187\) 3.09810 + 21.5478i 0.226556 + 1.57573i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.73126 + 8.92235i −0.559414 + 0.645599i −0.963050 0.269321i \(-0.913201\pi\)
0.403636 + 0.914920i \(0.367746\pi\)
\(192\) 0 0
\(193\) −21.4550 + 6.29975i −1.54436 + 0.453466i −0.939410 0.342795i \(-0.888626\pi\)
−0.604953 + 0.796261i \(0.706808\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.93139 + 6.84519i 0.422594 + 0.487699i 0.926625 0.375986i \(-0.122696\pi\)
−0.504031 + 0.863685i \(0.668150\pi\)
\(198\) 0 0
\(199\) 0.513726 3.57304i 0.0364171 0.253286i −0.963478 0.267788i \(-0.913707\pi\)
0.999895 + 0.0145021i \(0.00461632\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.838736 1.83658i −0.0588677 0.128902i
\(204\) 0 0
\(205\) −15.9308 10.2381i −1.11266 0.715061i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −17.9836 11.5573i −1.24395 0.799438i
\(210\) 0 0
\(211\) −1.02026 2.23405i −0.0702374 0.153798i 0.871257 0.490827i \(-0.163305\pi\)
−0.941494 + 0.337029i \(0.890578\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.68804 + 18.6958i −0.183323 + 1.27504i
\(216\) 0 0
\(217\) 13.5479 + 15.6351i 0.919690 + 1.06138i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 18.5924 5.45922i 1.25066 0.367227i
\(222\) 0 0
\(223\) 10.9606 12.6492i 0.733976 0.847053i −0.258938 0.965894i \(-0.583372\pi\)
0.992913 + 0.118841i \(0.0379179\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.94100 13.5000i −0.128829 0.896024i −0.947042 0.321109i \(-0.895944\pi\)
0.818213 0.574915i \(-0.194965\pi\)
\(228\) 0 0
\(229\) −6.76866 −0.447286 −0.223643 0.974671i \(-0.571795\pi\)
−0.223643 + 0.974671i \(0.571795\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.54002 10.7111i −0.100890 0.701705i −0.975998 0.217778i \(-0.930119\pi\)
0.875108 0.483927i \(-0.160790\pi\)
\(234\) 0 0
\(235\) 18.3451 + 5.38661i 1.19670 + 0.351383i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 18.3881 5.39923i 1.18943 0.349247i 0.373625 0.927580i \(-0.378115\pi\)
0.815801 + 0.578333i \(0.196296\pi\)
\(240\) 0 0
\(241\) −8.37372 + 5.38147i −0.539399 + 0.346651i −0.781804 0.623525i \(-0.785700\pi\)
0.242405 + 0.970175i \(0.422064\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.31812 23.0780i 0.211987 1.47440i
\(246\) 0 0
\(247\) −7.90458 + 17.3086i −0.502957 + 1.10132i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −9.59137 6.16400i −0.605402 0.389068i 0.201728 0.979442i \(-0.435344\pi\)
−0.807130 + 0.590373i \(0.798981\pi\)
\(252\) 0 0
\(253\) −17.5761 + 15.0544i −1.10500 + 0.946462i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −10.8691 23.8000i −0.677995 1.48460i −0.864754 0.502196i \(-0.832526\pi\)
0.186759 0.982406i \(-0.440202\pi\)
\(258\) 0 0
\(259\) 17.9318 39.2652i 1.11423 2.43982i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −19.2160 22.1764i −1.18491 1.36746i −0.914438 0.404727i \(-0.867367\pi\)
−0.270469 0.962729i \(-0.587179\pi\)
\(264\) 0 0
\(265\) −16.0016 + 10.2836i −0.982969 + 0.631716i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18.5100 + 21.3616i −1.12857 + 1.30244i −0.180790 + 0.983522i \(0.557866\pi\)
−0.947782 + 0.318920i \(0.896680\pi\)
\(270\) 0 0
\(271\) 0.108543 + 0.0318710i 0.00659349 + 0.00193602i 0.285028 0.958519i \(-0.407997\pi\)
−0.278434 + 0.960455i \(0.589815\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.80108 0.349818
\(276\) 0 0
\(277\) −3.96519 −0.238245 −0.119123 0.992880i \(-0.538008\pi\)
−0.119123 + 0.992880i \(0.538008\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.9629 4.68713i −0.952267 0.279611i −0.231536 0.972826i \(-0.574375\pi\)
−0.720730 + 0.693215i \(0.756193\pi\)
\(282\) 0 0
\(283\) 11.0836 12.7911i 0.658851 0.760354i −0.323738 0.946147i \(-0.604940\pi\)
0.982589 + 0.185792i \(0.0594852\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −25.8752 + 16.6290i −1.52737 + 0.981579i
\(288\) 0 0
\(289\) −2.19534 2.53355i −0.129137 0.149032i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8.50419 + 18.6216i −0.496820 + 1.08788i 0.480670 + 0.876902i \(0.340393\pi\)
−0.977490 + 0.210982i \(0.932334\pi\)
\(294\) 0 0
\(295\) 2.92611 + 6.40728i 0.170365 + 0.373046i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 15.4903 + 13.5785i 0.895827 + 0.785267i
\(300\) 0 0
\(301\) 25.8083 + 16.5860i 1.48756 + 0.956000i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.64288 + 3.59740i −0.0940708 + 0.205986i
\(306\) 0 0
\(307\) −2.39426 + 16.6525i −0.136648 + 0.950407i 0.799967 + 0.600045i \(0.204851\pi\)
−0.936614 + 0.350362i \(0.886059\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 25.0518 16.0998i 1.42055 0.912935i 0.420571 0.907260i \(-0.361830\pi\)
0.999984 0.00567544i \(-0.00180656\pi\)
\(312\) 0 0
\(313\) 28.9943 8.51351i 1.63886 0.481212i 0.672861 0.739769i \(-0.265065\pi\)
0.965996 + 0.258557i \(0.0832470\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.02982 1.47689i −0.282503 0.0829504i 0.137411 0.990514i \(-0.456122\pi\)
−0.419914 + 0.907564i \(0.637940\pi\)
\(318\) 0 0
\(319\) −0.342778 2.38407i −0.0191919 0.133483i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 19.9856 1.11203
\(324\) 0 0
\(325\) −0.734864 5.11109i −0.0407629 0.283512i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 20.3364 23.4694i 1.12118 1.29391i
\(330\) 0 0
\(331\) −18.1389 + 5.32606i −0.997003 + 0.292747i −0.739226 0.673458i \(-0.764808\pi\)
−0.257778 + 0.966204i \(0.582990\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 19.6036 + 22.6238i 1.07106 + 1.23607i
\(336\) 0 0
\(337\) 1.73565 12.0717i 0.0945470 0.657589i −0.886344 0.463028i \(-0.846763\pi\)
0.980891 0.194560i \(-0.0623280\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 10.2524 + 22.4496i 0.555197 + 1.21571i
\(342\) 0 0
\(343\) −8.03763 5.16547i −0.433991 0.278909i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7.06027 4.53736i −0.379015 0.243578i 0.337237 0.941420i \(-0.390508\pi\)
−0.716252 + 0.697842i \(0.754144\pi\)
\(348\) 0 0
\(349\) 9.08565 + 19.8948i 0.486344 + 1.06494i 0.980670 + 0.195668i \(0.0626875\pi\)
−0.494326 + 0.869276i \(0.664585\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.92984 20.3775i 0.155940 1.08459i −0.750079 0.661348i \(-0.769985\pi\)
0.906019 0.423237i \(-0.139106\pi\)
\(354\) 0 0
\(355\) −6.18378 7.13646i −0.328201 0.378764i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.5158 + 6.02397i −1.08278 + 0.317933i −0.773991 0.633197i \(-0.781742\pi\)
−0.308790 + 0.951130i \(0.599924\pi\)
\(360\) 0 0
\(361\) −0.409640 + 0.472749i −0.0215600 + 0.0248815i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.64167 18.3732i −0.138271 0.961699i
\(366\) 0 0
\(367\) 11.1339 0.581182 0.290591 0.956847i \(-0.406148\pi\)
0.290591 + 0.956847i \(0.406148\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.39675 + 30.5801i 0.228268 + 1.58764i
\(372\) 0 0
\(373\) −12.8571 3.77518i −0.665714 0.195471i −0.0686206 0.997643i \(-0.521860\pi\)
−0.597094 + 0.802171i \(0.703678\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.05709 + 0.604015i −0.105945 + 0.0311084i
\(378\) 0 0
\(379\) −0.457570 + 0.294062i −0.0235038 + 0.0151050i −0.552340 0.833619i \(-0.686265\pi\)
0.528836 + 0.848724i \(0.322629\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.358061 + 2.49037i −0.0182961 + 0.127252i −0.996922 0.0783945i \(-0.975021\pi\)
0.978626 + 0.205646i \(0.0659297\pi\)
\(384\) 0 0
\(385\) 20.1935 44.2175i 1.02915 2.25353i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.5193 + 6.76037i 0.533352 + 0.342764i 0.779434 0.626485i \(-0.215507\pi\)
−0.246082 + 0.969249i \(0.579143\pi\)
\(390\) 0 0
\(391\) 6.21429 20.7241i 0.314270 1.04806i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.0456 + 26.3762i 0.606080 + 1.32713i
\(396\) 0 0
\(397\) 9.36806 20.5132i 0.470169 1.02953i −0.514881 0.857262i \(-0.672164\pi\)
0.985051 0.172266i \(-0.0551087\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.939019 1.08369i −0.0468924 0.0541167i 0.731819 0.681499i \(-0.238672\pi\)
−0.778711 + 0.627383i \(0.784126\pi\)
\(402\) 0 0
\(403\) 18.4806 11.8768i 0.920586 0.591625i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 33.7218 38.9171i 1.67153 1.92905i
\(408\) 0 0
\(409\) −2.01920 0.592891i −0.0998430 0.0293166i 0.231429 0.972852i \(-0.425660\pi\)
−0.331272 + 0.943535i \(0.607478\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.4407 0.562962
\(414\) 0 0
\(415\) 13.2156 0.648729
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −14.1544 4.15610i −0.691486 0.203039i −0.0829368 0.996555i \(-0.526430\pi\)
−0.608549 + 0.793516i \(0.708248\pi\)
\(420\) 0 0
\(421\) 1.55784 1.79785i 0.0759246 0.0876216i −0.716516 0.697570i \(-0.754264\pi\)
0.792441 + 0.609949i \(0.208810\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.56252 + 2.93216i −0.221315 + 0.142230i
\(426\) 0 0
\(427\) 4.20647 + 4.85452i 0.203565 + 0.234927i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7.23072 + 15.8331i −0.348291 + 0.762652i 0.651700 + 0.758477i \(0.274056\pi\)
−0.999991 + 0.00417490i \(0.998671\pi\)
\(432\) 0 0
\(433\) −8.20769 17.9723i −0.394436 0.863695i −0.997804 0.0662322i \(-0.978902\pi\)
0.603368 0.797463i \(-0.293825\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 11.3838 + 17.9387i 0.544562 + 0.858123i
\(438\) 0 0
\(439\) −15.4395 9.92238i −0.736888 0.473569i 0.117586 0.993063i \(-0.462484\pi\)
−0.854474 + 0.519493i \(0.826121\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.532229 1.16542i 0.0252869 0.0553707i −0.896567 0.442908i \(-0.853947\pi\)
0.921854 + 0.387537i \(0.126674\pi\)
\(444\) 0 0
\(445\) −3.95047 + 27.4761i −0.187270 + 1.30249i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7.96730 + 5.12027i −0.376000 + 0.241641i −0.714968 0.699157i \(-0.753559\pi\)
0.338968 + 0.940798i \(0.389922\pi\)
\(450\) 0 0
\(451\) −35.2062 + 10.3375i −1.65779 + 0.486772i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −41.5163 12.1903i −1.94631 0.571489i
\(456\) 0 0
\(457\) −2.98099 20.7333i −0.139445 0.969861i −0.932618 0.360865i \(-0.882482\pi\)
0.793173 0.608996i \(-0.208428\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.43095 −0.346094 −0.173047 0.984914i \(-0.555361\pi\)
−0.173047 + 0.984914i \(0.555361\pi\)
\(462\) 0 0
\(463\) 3.90134 + 27.1344i 0.181310 + 1.26104i 0.853669 + 0.520816i \(0.174372\pi\)
−0.672358 + 0.740226i \(0.734719\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 24.5015 28.2762i 1.13379 1.30847i 0.188563 0.982061i \(-0.439617\pi\)
0.945230 0.326405i \(-0.105837\pi\)
\(468\) 0 0
\(469\) 46.6526 13.6984i 2.15422 0.632535i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 23.9663 + 27.6586i 1.10197 + 1.27174i
\(474\) 0 0
\(475\) 0.757935 5.27155i 0.0347764 0.241875i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.62333 14.5031i −0.302628 0.662662i 0.695829 0.718208i \(-0.255037\pi\)
−0.998456 + 0.0555460i \(0.982310\pi\)
\(480\) 0 0
\(481\) −38.5600 24.7810i −1.75818 1.12992i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −14.9453 9.60474i −0.678630 0.436129i
\(486\) 0 0
\(487\) 6.29565 + 13.7855i 0.285283 + 0.624683i 0.996968 0.0778164i \(-0.0247948\pi\)
−0.711685 + 0.702499i \(0.752068\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.02270 34.9336i 0.226671 1.57653i −0.485315 0.874340i \(-0.661295\pi\)
0.711986 0.702194i \(-0.247796\pi\)
\(492\) 0 0
\(493\) 1.47462 + 1.70181i 0.0664137 + 0.0766455i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −14.7161 + 4.32104i −0.660107 + 0.193825i
\(498\) 0 0
\(499\) 15.9697 18.4300i 0.714902 0.825041i −0.275782 0.961220i \(-0.588937\pi\)
0.990684 + 0.136179i \(0.0434824\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.74046 + 32.9706i 0.211367 + 1.47009i 0.768599 + 0.639731i \(0.220954\pi\)
−0.557232 + 0.830357i \(0.688137\pi\)
\(504\) 0 0
\(505\) −13.1634 −0.585762
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.84114 + 19.7605i 0.125931 + 0.875870i 0.950636 + 0.310307i \(0.100432\pi\)
−0.824705 + 0.565563i \(0.808659\pi\)
\(510\) 0 0
\(511\) −28.9279 8.49399i −1.27969 0.375752i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 45.7722 13.4399i 2.01697 0.592235i
\(516\) 0 0
\(517\) 31.1653 20.0287i 1.37065 0.880861i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.86877 40.8182i 0.257116 1.78828i −0.296014 0.955184i \(-0.595657\pi\)
0.553130 0.833095i \(-0.313433\pi\)
\(522\) 0 0
\(523\) 4.28867 9.39088i 0.187530 0.410634i −0.792392 0.610012i \(-0.791165\pi\)
0.979923 + 0.199377i \(0.0638920\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −19.4106 12.4744i −0.845538 0.543394i
\(528\) 0 0
\(529\) 22.1411 6.22662i 0.962657 0.270723i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 13.5677 + 29.7092i 0.587683 + 1.28685i
\(534\) 0 0
\(535\) −11.4131 + 24.9911i −0.493429 + 1.08046i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −29.5840 34.1417i −1.27427 1.47059i
\(540\) 0 0
\(541\) −29.0203 + 18.6502i −1.24768 + 0.801834i −0.986548 0.163469i \(-0.947732\pi\)
−0.261130 + 0.965304i \(0.584095\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.84343 + 3.28150i −0.121799 + 0.140564i
\(546\) 0 0
\(547\) 9.85374 + 2.89332i 0.421315 + 0.123709i 0.485516 0.874228i \(-0.338632\pi\)
−0.0642009 + 0.997937i \(0.520450\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.21124 −0.0942019
\(552\) 0 0
\(553\) 47.0969 2.00277
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 29.0734 + 8.53672i 1.23188 + 0.361712i 0.831959 0.554837i \(-0.187220\pi\)
0.399921 + 0.916550i \(0.369038\pi\)
\(558\) 0 0
\(559\) 21.3329 24.6194i 0.902283 1.04129i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 26.7756 17.2076i 1.12846 0.725214i 0.163218 0.986590i \(-0.447813\pi\)
0.965237 + 0.261376i \(0.0841763\pi\)
\(564\) 0 0
\(565\) 28.1737 + 32.5141i 1.18528 + 1.36788i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.827716 1.81245i 0.0346997 0.0759817i −0.891488 0.453043i \(-0.850338\pi\)
0.926188 + 0.377062i \(0.123066\pi\)
\(570\) 0 0
\(571\) −4.19617 9.18833i −0.175604 0.384520i 0.801280 0.598290i \(-0.204153\pi\)
−0.976884 + 0.213770i \(0.931426\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.23065 2.42506i −0.218133 0.101132i
\(576\) 0 0
\(577\) 9.09996 + 5.84819i 0.378836 + 0.243463i 0.716176 0.697920i \(-0.245891\pi\)
−0.337340 + 0.941383i \(0.609527\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.91693 19.5254i 0.369937 0.810048i
\(582\) 0 0
\(583\) −5.24508 + 36.4803i −0.217229 + 1.51086i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.2092 + 12.3450i −0.792848 + 0.509532i −0.873275 0.487228i \(-0.838008\pi\)
0.0804270 + 0.996761i \(0.474372\pi\)
\(588\) 0 0
\(589\) 21.7398 6.38340i 0.895775 0.263023i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12.7448 3.74220i −0.523365 0.153674i 0.00936967 0.999956i \(-0.497017\pi\)
−0.532735 + 0.846282i \(0.678836\pi\)
\(594\) 0 0
\(595\) 6.46768 + 44.9837i 0.265149 + 1.84415i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −15.3103 −0.625563 −0.312781 0.949825i \(-0.601261\pi\)
−0.312781 + 0.949825i \(0.601261\pi\)
\(600\) 0 0
\(601\) 3.13065 + 21.7741i 0.127702 + 0.888185i 0.948457 + 0.316905i \(0.102644\pi\)
−0.820755 + 0.571280i \(0.806447\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 20.0353 23.1220i 0.814552 0.940043i
\(606\) 0 0
\(607\) −1.82069 + 0.534602i −0.0738994 + 0.0216988i −0.318473 0.947932i \(-0.603170\pi\)
0.244574 + 0.969631i \(0.421352\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −21.5944 24.9212i −0.873615 1.00821i
\(612\) 0 0
\(613\) −2.90508 + 20.2052i −0.117335 + 0.816082i 0.843136 + 0.537701i \(0.180707\pi\)
−0.960471 + 0.278381i \(0.910202\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.44479 18.4915i −0.339975 0.744440i 0.660002 0.751264i \(-0.270555\pi\)
−0.999977 + 0.00682330i \(0.997828\pi\)
\(618\) 0 0
\(619\) −29.4504 18.9266i −1.18371 0.760725i −0.207647 0.978204i \(-0.566580\pi\)
−0.976065 + 0.217479i \(0.930217\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 37.9290 + 24.3755i 1.51959 + 0.976583i
\(624\) 0 0
\(625\) −12.2820 26.8939i −0.491281 1.07576i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.85144 + 47.6528i −0.273185 + 1.90004i
\(630\) 0 0
\(631\) −20.2459 23.3650i −0.805976 0.930146i 0.192717 0.981254i \(-0.438270\pi\)
−0.998693 + 0.0511081i \(0.983725\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −34.1448 + 10.0258i −1.35500 + 0.397863i
\(636\) 0 0
\(637\) −26.3332 + 30.3902i −1.04336 + 1.20410i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7.05443 + 49.0646i 0.278633 + 1.93794i 0.341422 + 0.939910i \(0.389092\pi\)
−0.0627883 + 0.998027i \(0.519999\pi\)
\(642\) 0 0
\(643\) 36.1135 1.42418 0.712089 0.702089i \(-0.247749\pi\)
0.712089 + 0.702089i \(0.247749\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.05843 + 14.3167i 0.0809251 + 0.562846i 0.989434 + 0.144982i \(0.0463123\pi\)
−0.908509 + 0.417865i \(0.862779\pi\)
\(648\) 0 0
\(649\) 13.0953 + 3.84513i 0.514036 + 0.150935i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −39.8195 + 11.6921i −1.55826 + 0.457545i −0.943555 0.331215i \(-0.892542\pi\)
−0.614701 + 0.788760i \(0.710723\pi\)
\(654\) 0 0
\(655\) −20.8333 + 13.3887i −0.814023 + 0.523141i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 3.38046 23.5116i 0.131684 0.915881i −0.811675 0.584109i \(-0.801444\pi\)
0.943359 0.331773i \(-0.107647\pi\)
\(660\) 0 0
\(661\) −18.6367 + 40.8086i −0.724882 + 1.58727i 0.0820519 + 0.996628i \(0.473853\pi\)
−0.806934 + 0.590642i \(0.798875\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −37.5429 24.1274i −1.45585 0.935620i
\(666\) 0 0
\(667\) −0.687558 + 2.29294i −0.0266223 + 0.0887829i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.18325 + 6.97034i 0.122888 + 0.269087i
\(672\) 0 0
\(673\) −18.4662 + 40.4353i −0.711819 + 1.55867i 0.113207 + 0.993571i \(0.463888\pi\)
−0.825026 + 0.565095i \(0.808840\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.0916 18.5707i −0.618451 0.713731i 0.356961 0.934119i \(-0.383813\pi\)
−0.975412 + 0.220389i \(0.929267\pi\)
\(678\) 0 0
\(679\) −24.2745 + 15.6003i −0.931569 + 0.598683i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −23.6796 + 27.3277i −0.906076 + 1.04567i 0.0926750 + 0.995696i \(0.470458\pi\)
−0.998751 + 0.0499707i \(0.984087\pi\)
\(684\) 0 0
\(685\) 19.4582 + 5.71345i 0.743461 + 0.218300i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 32.8057 1.24980
\(690\) 0 0
\(691\) −29.9939 −1.14102 −0.570511 0.821290i \(-0.693255\pi\)
−0.570511 + 0.821290i \(0.693255\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −24.2068 7.10776i −0.918216 0.269613i
\(696\) 0 0
\(697\) 22.4644 25.9253i 0.850901 0.981992i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −38.9924 + 25.0589i −1.47272 + 0.946462i −0.474934 + 0.880022i \(0.657528\pi\)
−0.997790 + 0.0664406i \(0.978836\pi\)
\(702\) 0 0
\(703\) −30.9588 35.7283i −1.16763 1.34752i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.88168 + 19.4482i −0.334030 + 0.731424i
\(708\) 0 0
\(709\) −0.678476 1.48565i −0.0254807 0.0557949i 0.896464 0.443117i \(-0.146127\pi\)
−0.921944 + 0.387322i \(0.873400\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.140495 24.5279i 0.00526157 0.918578i
\(714\) 0 0
\(715\) −43.4234 27.9065i −1.62394 1.04364i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.86499 + 4.08377i −0.0695525 + 0.152299i −0.941215 0.337807i \(-0.890315\pi\)
0.871663 + 0.490106i \(0.163042\pi\)
\(720\) 0 0
\(721\) 11.0270 76.6943i 0.410666 2.85625i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.504804 0.324418i 0.0187479 0.0120486i
\(726\) 0 0
\(727\) −25.1042 + 7.37125i −0.931062 + 0.273384i −0.711881 0.702300i \(-0.752157\pi\)
−0.219181 + 0.975684i \(0.570338\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −32.8294 9.63959i −1.21424 0.356533i
\(732\) 0 0
\(733\) 4.67175 + 32.4927i 0.172555 + 1.20015i 0.873461 + 0.486894i \(0.161870\pi\)
−0.700906 + 0.713253i \(0.747221\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 58.0034 2.13658
\(738\) 0 0
\(739\) 1.53138 + 10.6510i 0.0563328 + 0.391803i 0.998408 + 0.0564017i \(0.0179628\pi\)
−0.942075 + 0.335401i \(0.891128\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.99673 10.3828i 0.330058 0.380907i −0.566329 0.824179i \(-0.691637\pi\)
0.896387 + 0.443272i \(0.146182\pi\)
\(744\) 0 0
\(745\) −15.8516 + 4.65446i −0.580759 + 0.170526i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 29.2223 + 33.7244i 1.06776 + 1.23226i
\(750\) 0 0
\(751\) 1.35281 9.40898i 0.0493646 0.343338i −0.950139 0.311827i \(-0.899059\pi\)
0.999503 0.0315111i \(-0.0100319\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.79262 + 19.2532i 0.319996 + 0.700694i
\(756\) 0 0
\(757\) 34.4271 + 22.1249i 1.25127 + 0.804144i 0.987065 0.160322i \(-0.0512531\pi\)
0.264208 + 0.964466i \(0.414889\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −17.7600 11.4136i −0.643798 0.413744i 0.177597 0.984103i \(-0.443168\pi\)
−0.821395 + 0.570359i \(0.806804\pi\)
\(762\) 0 0
\(763\) 2.92970 + 6.41514i 0.106062 + 0.232244i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.72891 12.0248i 0.0624273 0.434191i
\(768\) 0 0
\(769\) −16.4272 18.9580i −0.592380 0.683643i 0.377839 0.925871i \(-0.376667\pi\)
−0.970219 + 0.242228i \(0.922122\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 25.5088 7.49005i 0.917487 0.269399i 0.211298 0.977422i \(-0.432231\pi\)
0.706189 + 0.708023i \(0.250413\pi\)
\(774\) 0 0
\(775\) −4.02646 + 4.64679i −0.144635 + 0.166917i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.79402 + 33.3431i 0.171764 + 1.19464i
\(780\) 0 0
\(781\) −18.2966 −0.654704
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.32322 + 23.1135i 0.118611 + 0.824957i
\(786\) 0 0
\(787\) 22.4544 + 6.59320i 0.800412 + 0.235022i 0.656262 0.754534i \(-0.272137\pi\)
0.144151 + 0.989556i \(0.453955\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 67.0475 19.6869i 2.38393 0.699986i
\(792\) 0 0
\(793\) 5.73803 3.68761i 0.203764 0.130951i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.60649 11.1734i 0.0569047 0.395781i −0.941386 0.337332i \(-0.890475\pi\)
0.998290 0.0584489i \(-0.0186155\pi\)
\(798\) 0 0
\(799\) −14.3878 + 31.5050i −0.509005 + 1.11457i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −30.2567 19.4448i −1.06774 0.686192i
\(804\) 0 0
\(805\) −36.6924 + 31.4280i −1.29324 + 1.10769i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −14.3175 31.3510i −0.503377 1.10224i −0.975357 0.220633i \(-0.929188\pi\)
0.471980 0.881609i \(-0.343540\pi\)
\(810\) 0 0
\(811\) −9.81825 + 21.4990i −0.344765 + 0.754931i −1.00000 0.000494599i \(-0.999843\pi\)
0.655234 + 0.755426i \(0.272570\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −7.90739 9.12562i −0.276984 0.319656i
\(816\) 0 0
\(817\) 28.2652 18.1649i 0.988873 0.635510i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7.23368 + 8.34811i −0.252457 + 0.291351i −0.867805 0.496904i \(-0.834470\pi\)
0.615348 + 0.788255i \(0.289015\pi\)
\(822\) 0 0
\(823\) −39.7025 11.6577i −1.38394 0.406362i −0.496802 0.867864i \(-0.665493\pi\)
−0.887139 + 0.461502i \(0.847311\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 33.3095 1.15828 0.579142 0.815227i \(-0.303388\pi\)
0.579142 + 0.815227i \(0.303388\pi\)
\(828\) 0 0
\(829\) −26.7169 −0.927917 −0.463959 0.885857i \(-0.653571\pi\)
−0.463959 + 0.885857i \(0.653571\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 40.5246 + 11.8991i 1.40409 + 0.412279i
\(834\) 0 0
\(835\) 21.7815 25.1372i 0.753779 0.869907i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 7.30959 4.69759i 0.252355 0.162179i −0.408348 0.912827i \(-0.633895\pi\)
0.660703 + 0.750648i \(0.270258\pi\)
\(840\) 0 0
\(841\) 18.8278 + 21.7284i 0.649235 + 0.749257i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −5.63727 + 12.3439i −0.193928 + 0.424643i
\(846\) 0 0
\(847\) −20.6431 45.2022i −0.709307 1.55317i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −46.6746 + 20.9933i −1.59999 + 0.719642i
\(852\) 0 0
\(853\) 21.0828 + 13.5491i 0.721861 + 0.463912i 0.849284 0.527937i \(-0.177034\pi\)
−0.127423 + 0.991848i \(0.540671\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.96621 + 21.8230i −0.340439 + 0.745458i −0.999981 0.00621000i \(-0.998023\pi\)
0.659541 + 0.751668i \(0.270751\pi\)
\(858\) 0 0
\(859\) 1.08109 7.51915i 0.0368863 0.256550i −0.963031 0.269390i \(-0.913178\pi\)
0.999918 + 0.0128397i \(0.00408711\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.12515 + 2.00841i −0.106381 + 0.0683672i −0.592750 0.805387i \(-0.701958\pi\)
0.486368 + 0.873754i \(0.338321\pi\)
\(864\) 0 0
\(865\) −24.3623 + 7.15342i −0.828343 + 0.243224i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 53.9081 + 15.8289i 1.82871 + 0.536957i
\(870\) 0 0
\(871\) −7.34771 51.1044i −0.248968 1.73161i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −38.2582 −1.29336
\(876\) 0 0
\(877\) −4.74616 33.0103i −0.160266 1.11468i −0.898131 0.439729i \(-0.855075\pi\)
0.737864 0.674949i \(-0.235834\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −15.9310 + 18.3853i −0.536728 + 0.619417i −0.957739 0.287638i \(-0.907130\pi\)
0.421011 + 0.907056i \(0.361675\pi\)
\(882\) 0 0
\(883\) 26.9814 7.92247i 0.907998 0.266612i 0.205800 0.978594i \(-0.434020\pi\)
0.702198 + 0.711982i \(0.252202\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 16.0130 + 18.4800i 0.537665 + 0.620498i 0.957964 0.286887i \(-0.0926204\pi\)
−0.420299 + 0.907385i \(0.638075\pi\)
\(888\) 0 0
\(889\) −8.22583 + 57.2119i −0.275885 + 1.91882i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −14.1286 30.9373i −0.472795 1.03528i
\(894\) 0 0
\(895\) 12.7451 + 8.19077i 0.426021 + 0.273787i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.14761 + 1.38019i 0.0716268 + 0.0460318i
\(900\) 0 0
\(901\) −14.3137 31.3427i −0.476860 1.04418i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.64580 + 11.4468i −0.0547084 + 0.380505i
\(906\) 0 0
\(907\) −5.09587 5.88095i −0.169206 0.195274i 0.664813 0.747010i \(-0.268511\pi\)
−0.834019 + 0.551736i \(0.813966\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 33.4926 9.83430i 1.10966 0.325825i 0.324975 0.945723i \(-0.394644\pi\)
0.784683 + 0.619897i \(0.212826\pi\)
\(912\) 0 0
\(913\) 16.7688 19.3522i 0.554966 0.640465i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5.72435 + 39.8138i 0.189035 + 1.31477i
\(918\) 0 0
\(919\) 17.9522 0.592187 0.296093 0.955159i \(-0.404316\pi\)
0.296093 + 0.955159i \(0.404316\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.31776 + 16.1204i 0.0762900 + 0.530609i
\(924\) 0 0
\(925\) 12.3094 + 3.61436i 0.404730 + 0.118840i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 20.1532 5.91751i 0.661205 0.194147i 0.0661220 0.997812i \(-0.478937\pi\)
0.595083 + 0.803664i \(0.297119\pi\)
\(930\) 0 0
\(931\) −34.8905 + 22.4228i −1.14349 + 0.734876i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −7.71557 + 53.6630i −0.252326 + 1.75497i
\(936\) 0 0
\(937\) −10.2393 + 22.4210i −0.334504 + 0.732462i −0.999902 0.0140270i \(-0.995535\pi\)
0.665397 + 0.746489i \(0.268262\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −39.2493 25.2240i −1.27949 0.822279i −0.288666 0.957430i \(-0.593212\pi\)
−0.990825 + 0.135151i \(0.956848\pi\)
\(942\) 0 0
\(943\) 36.0657 + 5.39649i 1.17446 + 0.175734i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −10.3997 22.7721i −0.337944 0.739995i 0.662010 0.749495i \(-0.269703\pi\)
−0.999955 + 0.00949957i \(0.996976\pi\)
\(948\) 0 0
\(949\) −13.2992 + 29.1211i −0.431709 + 0.945312i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −21.6866 25.0277i −0.702499 0.810727i 0.286589 0.958054i \(-0.407479\pi\)
−0.989088 + 0.147326i \(0.952933\pi\)
\(954\) 0 0
\(955\) −24.7344 + 15.8958i −0.800385 + 0.514376i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 21.5703 24.8935i 0.696542 0.803852i
\(960\) 0 0
\(961\) 4.64567 + 1.36409i 0.149860 + 0.0440030i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −55.6876 −1.79265
\(966\) 0 0
\(967\) 12.0764 0.388352 0.194176 0.980967i \(-0.437797\pi\)
0.194176 + 0.980967i \(0.437797\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −47.4911 13.9446i −1.52406 0.447505i −0.590834 0.806793i \(-0.701201\pi\)
−0.933227 + 0.359288i \(0.883020\pi\)
\(972\) 0 0
\(973\) −26.8343 + 30.9684i −0.860269 + 0.992803i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 18.3854 11.8156i 0.588200 0.378013i −0.212427 0.977177i \(-0.568137\pi\)
0.800626 + 0.599164i \(0.204500\pi\)
\(978\) 0 0
\(979\) 35.2219 + 40.6483i 1.12570 + 1.29912i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −3.00858 + 6.58788i −0.0959589 + 0.210121i −0.951524 0.307575i \(-0.900483\pi\)
0.855565 + 0.517695i \(0.173210\pi\)
\(984\) 0 0
\(985\) 9.37048 + 20.5185i 0.298568 + 0.653774i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −10.0474 34.9577i −0.319487 1.11159i
\(990\) 0 0
\(991\) 47.3042 + 30.4005i 1.50267 + 0.965705i 0.994533 + 0.104427i \(0.0333008\pi\)
0.508134 + 0.861278i \(0.330336\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.73453 8.17747i 0.118392 0.259243i
\(996\) 0 0
\(997\) 8.91121 61.9788i 0.282221 1.96289i 0.0126093 0.999920i \(-0.495986\pi\)
0.269612 0.962969i \(-0.413105\pi\)
\(998\) 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 828.2.q.c.577.2 20
3.2 odd 2 276.2.i.a.25.1 20
23.12 even 11 inner 828.2.q.c.541.2 20
69.14 even 22 6348.2.a.t.1.3 10
69.32 odd 22 6348.2.a.s.1.8 10
69.35 odd 22 276.2.i.a.265.1 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
276.2.i.a.25.1 20 3.2 odd 2
276.2.i.a.265.1 yes 20 69.35 odd 22
828.2.q.c.541.2 20 23.12 even 11 inner
828.2.q.c.577.2 20 1.1 even 1 trivial
6348.2.a.s.1.8 10 69.32 odd 22
6348.2.a.t.1.3 10 69.14 even 22