Properties

Label 588.4.i.a.361.1
Level $588$
Weight $4$
Character 588.361
Analytic conductor $34.693$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,4,Mod(361,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.361");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.i (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: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 588.361
Dual form 588.4.i.a.373.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{3} +(-7.00000 - 12.1244i) q^{5} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{3} +(-7.00000 - 12.1244i) q^{5} +(-4.50000 - 7.79423i) q^{9} +(-2.00000 + 3.46410i) q^{11} +54.0000 q^{13} +42.0000 q^{15} +(7.00000 - 12.1244i) q^{17} +(-46.0000 - 79.6743i) q^{19} +(76.0000 + 131.636i) q^{23} +(-35.5000 + 61.4878i) q^{25} +27.0000 q^{27} -106.000 q^{29} +(72.0000 - 124.708i) q^{31} +(-6.00000 - 10.3923i) q^{33} +(-79.0000 - 136.832i) q^{37} +(-81.0000 + 140.296i) q^{39} -390.000 q^{41} -508.000 q^{43} +(-63.0000 + 109.119i) q^{45} +(264.000 + 457.261i) q^{47} +(21.0000 + 36.3731i) q^{51} +(-303.000 + 524.811i) q^{53} +56.0000 q^{55} +276.000 q^{57} +(182.000 - 315.233i) q^{59} +(-339.000 - 587.165i) q^{61} +(-378.000 - 654.715i) q^{65} +(-422.000 + 730.925i) q^{67} -456.000 q^{69} -8.00000 q^{71} +(211.000 - 365.463i) q^{73} +(-106.500 - 184.463i) q^{75} +(-192.000 - 332.554i) q^{79} +(-40.5000 + 70.1481i) q^{81} -548.000 q^{83} -196.000 q^{85} +(159.000 - 275.396i) q^{87} +(-597.000 - 1034.03i) q^{89} +(216.000 + 374.123i) q^{93} +(-644.000 + 1115.44i) q^{95} -1502.00 q^{97} +36.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} - 14 q^{5} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{3} - 14 q^{5} - 9 q^{9} - 4 q^{11} + 108 q^{13} + 84 q^{15} + 14 q^{17} - 92 q^{19} + 152 q^{23} - 71 q^{25} + 54 q^{27} - 212 q^{29} + 144 q^{31} - 12 q^{33} - 158 q^{37} - 162 q^{39} - 780 q^{41} - 1016 q^{43} - 126 q^{45} + 528 q^{47} + 42 q^{51} - 606 q^{53} + 112 q^{55} + 552 q^{57} + 364 q^{59} - 678 q^{61} - 756 q^{65} - 844 q^{67} - 912 q^{69} - 16 q^{71} + 422 q^{73} - 213 q^{75} - 384 q^{79} - 81 q^{81} - 1096 q^{83} - 392 q^{85} + 318 q^{87} - 1194 q^{89} + 432 q^{93} - 1288 q^{95} - 3004 q^{97} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −7.00000 12.1244i −0.626099 1.08444i −0.988327 0.152346i \(-0.951317\pi\)
0.362228 0.932089i \(-0.382016\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) −2.00000 + 3.46410i −0.0548202 + 0.0949514i −0.892133 0.451772i \(-0.850792\pi\)
0.837313 + 0.546724i \(0.184125\pi\)
\(12\) 0 0
\(13\) 54.0000 1.15207 0.576035 0.817425i \(-0.304599\pi\)
0.576035 + 0.817425i \(0.304599\pi\)
\(14\) 0 0
\(15\) 42.0000 0.722957
\(16\) 0 0
\(17\) 7.00000 12.1244i 0.0998676 0.172976i −0.811762 0.583988i \(-0.801491\pi\)
0.911630 + 0.411012i \(0.134825\pi\)
\(18\) 0 0
\(19\) −46.0000 79.6743i −0.555428 0.962029i −0.997870 0.0652319i \(-0.979221\pi\)
0.442443 0.896797i \(-0.354112\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 76.0000 + 131.636i 0.689004 + 1.19339i 0.972160 + 0.234316i \(0.0752852\pi\)
−0.283156 + 0.959074i \(0.591381\pi\)
\(24\) 0 0
\(25\) −35.5000 + 61.4878i −0.284000 + 0.491902i
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −106.000 −0.678748 −0.339374 0.940651i \(-0.610215\pi\)
−0.339374 + 0.940651i \(0.610215\pi\)
\(30\) 0 0
\(31\) 72.0000 124.708i 0.417148 0.722521i −0.578503 0.815680i \(-0.696363\pi\)
0.995651 + 0.0931587i \(0.0296964\pi\)
\(32\) 0 0
\(33\) −6.00000 10.3923i −0.0316505 0.0548202i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −79.0000 136.832i −0.351014 0.607974i 0.635413 0.772172i \(-0.280830\pi\)
−0.986427 + 0.164198i \(0.947496\pi\)
\(38\) 0 0
\(39\) −81.0000 + 140.296i −0.332574 + 0.576035i
\(40\) 0 0
\(41\) −390.000 −1.48556 −0.742778 0.669538i \(-0.766492\pi\)
−0.742778 + 0.669538i \(0.766492\pi\)
\(42\) 0 0
\(43\) −508.000 −1.80161 −0.900806 0.434223i \(-0.857023\pi\)
−0.900806 + 0.434223i \(0.857023\pi\)
\(44\) 0 0
\(45\) −63.0000 + 109.119i −0.208700 + 0.361478i
\(46\) 0 0
\(47\) 264.000 + 457.261i 0.819327 + 1.41912i 0.906179 + 0.422894i \(0.138986\pi\)
−0.0868522 + 0.996221i \(0.527681\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 21.0000 + 36.3731i 0.0576586 + 0.0998676i
\(52\) 0 0
\(53\) −303.000 + 524.811i −0.785288 + 1.36016i 0.143539 + 0.989645i \(0.454152\pi\)
−0.928827 + 0.370514i \(0.879182\pi\)
\(54\) 0 0
\(55\) 56.0000 0.137292
\(56\) 0 0
\(57\) 276.000 0.641353
\(58\) 0 0
\(59\) 182.000 315.233i 0.401600 0.695591i −0.592319 0.805703i \(-0.701788\pi\)
0.993919 + 0.110112i \(0.0351210\pi\)
\(60\) 0 0
\(61\) −339.000 587.165i −0.711549 1.23244i −0.964275 0.264902i \(-0.914661\pi\)
0.252726 0.967538i \(-0.418673\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −378.000 654.715i −0.721310 1.24935i
\(66\) 0 0
\(67\) −422.000 + 730.925i −0.769485 + 1.33279i 0.168357 + 0.985726i \(0.446154\pi\)
−0.937842 + 0.347061i \(0.887180\pi\)
\(68\) 0 0
\(69\) −456.000 −0.795593
\(70\) 0 0
\(71\) −8.00000 −0.0133722 −0.00668609 0.999978i \(-0.502128\pi\)
−0.00668609 + 0.999978i \(0.502128\pi\)
\(72\) 0 0
\(73\) 211.000 365.463i 0.338297 0.585948i −0.645816 0.763494i \(-0.723482\pi\)
0.984113 + 0.177546i \(0.0568158\pi\)
\(74\) 0 0
\(75\) −106.500 184.463i −0.163967 0.284000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −192.000 332.554i −0.273439 0.473610i 0.696301 0.717750i \(-0.254828\pi\)
−0.969740 + 0.244139i \(0.921495\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −548.000 −0.724709 −0.362354 0.932040i \(-0.618027\pi\)
−0.362354 + 0.932040i \(0.618027\pi\)
\(84\) 0 0
\(85\) −196.000 −0.250108
\(86\) 0 0
\(87\) 159.000 275.396i 0.195938 0.339374i
\(88\) 0 0
\(89\) −597.000 1034.03i −0.711032 1.23154i −0.964470 0.264192i \(-0.914895\pi\)
0.253438 0.967352i \(-0.418439\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 216.000 + 374.123i 0.240840 + 0.417148i
\(94\) 0 0
\(95\) −644.000 + 1115.44i −0.695505 + 1.20465i
\(96\) 0 0
\(97\) −1502.00 −1.57222 −0.786108 0.618089i \(-0.787907\pi\)
−0.786108 + 0.618089i \(0.787907\pi\)
\(98\) 0 0
\(99\) 36.0000 0.0365468
\(100\) 0 0
\(101\) −199.000 + 344.678i −0.196052 + 0.339572i −0.947245 0.320511i \(-0.896145\pi\)
0.751193 + 0.660083i \(0.229479\pi\)
\(102\) 0 0
\(103\) −580.000 1004.59i −0.554846 0.961021i −0.997916 0.0645337i \(-0.979444\pi\)
0.443070 0.896487i \(-0.353889\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −162.000 280.592i −0.146366 0.253513i 0.783516 0.621372i \(-0.213424\pi\)
−0.929882 + 0.367859i \(0.880091\pi\)
\(108\) 0 0
\(109\) 469.000 812.332i 0.412129 0.713828i −0.582993 0.812477i \(-0.698119\pi\)
0.995122 + 0.0986487i \(0.0314520\pi\)
\(110\) 0 0
\(111\) 474.000 0.405316
\(112\) 0 0
\(113\) −622.000 −0.517813 −0.258906 0.965902i \(-0.583362\pi\)
−0.258906 + 0.965902i \(0.583362\pi\)
\(114\) 0 0
\(115\) 1064.00 1842.90i 0.862770 1.49436i
\(116\) 0 0
\(117\) −243.000 420.888i −0.192012 0.332574i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 657.500 + 1138.82i 0.493989 + 0.855615i
\(122\) 0 0
\(123\) 585.000 1013.25i 0.428843 0.742778i
\(124\) 0 0
\(125\) −756.000 −0.540950
\(126\) 0 0
\(127\) 1200.00 0.838447 0.419224 0.907883i \(-0.362302\pi\)
0.419224 + 0.907883i \(0.362302\pi\)
\(128\) 0 0
\(129\) 762.000 1319.82i 0.520080 0.900806i
\(130\) 0 0
\(131\) 698.000 + 1208.97i 0.465531 + 0.806323i 0.999225 0.0393543i \(-0.0125301\pi\)
−0.533694 + 0.845677i \(0.679197\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −189.000 327.358i −0.120493 0.208700i
\(136\) 0 0
\(137\) −1405.00 + 2433.53i −0.876184 + 1.51760i −0.0206885 + 0.999786i \(0.506586\pi\)
−0.855496 + 0.517810i \(0.826747\pi\)
\(138\) 0 0
\(139\) 4.00000 0.00244083 0.00122042 0.999999i \(-0.499612\pi\)
0.00122042 + 0.999999i \(0.499612\pi\)
\(140\) 0 0
\(141\) −1584.00 −0.946077
\(142\) 0 0
\(143\) −108.000 + 187.061i −0.0631567 + 0.109391i
\(144\) 0 0
\(145\) 742.000 + 1285.18i 0.424964 + 0.736059i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −687.000 1189.92i −0.377726 0.654241i 0.613005 0.790079i \(-0.289961\pi\)
−0.990731 + 0.135838i \(0.956627\pi\)
\(150\) 0 0
\(151\) −1052.00 + 1822.12i −0.566957 + 0.981999i 0.429907 + 0.902873i \(0.358546\pi\)
−0.996865 + 0.0791258i \(0.974787\pi\)
\(152\) 0 0
\(153\) −126.000 −0.0665784
\(154\) 0 0
\(155\) −2016.00 −1.04470
\(156\) 0 0
\(157\) −1603.00 + 2776.48i −0.814862 + 1.41138i 0.0945650 + 0.995519i \(0.469854\pi\)
−0.909427 + 0.415864i \(0.863479\pi\)
\(158\) 0 0
\(159\) −909.000 1574.43i −0.453386 0.785288i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −166.000 287.520i −0.0797676 0.138162i 0.823382 0.567488i \(-0.192084\pi\)
−0.903150 + 0.429326i \(0.858751\pi\)
\(164\) 0 0
\(165\) −84.0000 + 145.492i −0.0396327 + 0.0686458i
\(166\) 0 0
\(167\) 1496.00 0.693197 0.346599 0.938014i \(-0.387337\pi\)
0.346599 + 0.938014i \(0.387337\pi\)
\(168\) 0 0
\(169\) 719.000 0.327264
\(170\) 0 0
\(171\) −414.000 + 717.069i −0.185143 + 0.320676i
\(172\) 0 0
\(173\) 1661.00 + 2876.94i 0.729962 + 1.26433i 0.956899 + 0.290422i \(0.0937958\pi\)
−0.226936 + 0.973910i \(0.572871\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 546.000 + 945.700i 0.231864 + 0.401600i
\(178\) 0 0
\(179\) 450.000 779.423i 0.187903 0.325457i −0.756648 0.653822i \(-0.773164\pi\)
0.944551 + 0.328365i \(0.106498\pi\)
\(180\) 0 0
\(181\) 1902.00 0.781075 0.390537 0.920587i \(-0.372289\pi\)
0.390537 + 0.920587i \(0.372289\pi\)
\(182\) 0 0
\(183\) 2034.00 0.821626
\(184\) 0 0
\(185\) −1106.00 + 1915.65i −0.439539 + 0.761304i
\(186\) 0 0
\(187\) 28.0000 + 48.4974i 0.0109495 + 0.0189651i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2064.00 3574.95i −0.781915 1.35432i −0.930825 0.365466i \(-0.880910\pi\)
0.148910 0.988851i \(-0.452424\pi\)
\(192\) 0 0
\(193\) 671.000 1162.21i 0.250257 0.433458i −0.713339 0.700819i \(-0.752818\pi\)
0.963597 + 0.267361i \(0.0861515\pi\)
\(194\) 0 0
\(195\) 2268.00 0.832897
\(196\) 0 0
\(197\) −3506.00 −1.26798 −0.633990 0.773341i \(-0.718584\pi\)
−0.633990 + 0.773341i \(0.718584\pi\)
\(198\) 0 0
\(199\) −340.000 + 588.897i −0.121115 + 0.209778i −0.920208 0.391430i \(-0.871980\pi\)
0.799092 + 0.601208i \(0.205314\pi\)
\(200\) 0 0
\(201\) −1266.00 2192.78i −0.444262 0.769485i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2730.00 + 4728.50i 0.930105 + 1.61099i
\(206\) 0 0
\(207\) 684.000 1184.72i 0.229668 0.397797i
\(208\) 0 0
\(209\) 368.000 0.121795
\(210\) 0 0
\(211\) 5372.00 1.75272 0.876360 0.481657i \(-0.159965\pi\)
0.876360 + 0.481657i \(0.159965\pi\)
\(212\) 0 0
\(213\) 12.0000 20.7846i 0.00386022 0.00668609i
\(214\) 0 0
\(215\) 3556.00 + 6159.17i 1.12799 + 1.95373i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 633.000 + 1096.39i 0.195316 + 0.338297i
\(220\) 0 0
\(221\) 378.000 654.715i 0.115054 0.199280i
\(222\) 0 0
\(223\) −1072.00 −0.321912 −0.160956 0.986962i \(-0.551458\pi\)
−0.160956 + 0.986962i \(0.551458\pi\)
\(224\) 0 0
\(225\) 639.000 0.189333
\(226\) 0 0
\(227\) 1434.00 2483.76i 0.419286 0.726225i −0.576582 0.817039i \(-0.695614\pi\)
0.995868 + 0.0908148i \(0.0289471\pi\)
\(228\) 0 0
\(229\) −2399.00 4155.19i −0.692272 1.19905i −0.971092 0.238707i \(-0.923276\pi\)
0.278819 0.960344i \(-0.410057\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2563.00 + 4439.25i 0.720634 + 1.24817i 0.960746 + 0.277429i \(0.0894825\pi\)
−0.240112 + 0.970745i \(0.577184\pi\)
\(234\) 0 0
\(235\) 3696.00 6401.66i 1.02596 1.77701i
\(236\) 0 0
\(237\) 1152.00 0.315740
\(238\) 0 0
\(239\) −528.000 −0.142902 −0.0714508 0.997444i \(-0.522763\pi\)
−0.0714508 + 0.997444i \(0.522763\pi\)
\(240\) 0 0
\(241\) 407.000 704.945i 0.108785 0.188421i −0.806493 0.591243i \(-0.798637\pi\)
0.915278 + 0.402822i \(0.131971\pi\)
\(242\) 0 0
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2484.00 4302.41i −0.639891 1.10832i
\(248\) 0 0
\(249\) 822.000 1423.75i 0.209205 0.362354i
\(250\) 0 0
\(251\) −1932.00 −0.485844 −0.242922 0.970046i \(-0.578106\pi\)
−0.242922 + 0.970046i \(0.578106\pi\)
\(252\) 0 0
\(253\) −608.000 −0.151086
\(254\) 0 0
\(255\) 294.000 509.223i 0.0722000 0.125054i
\(256\) 0 0
\(257\) 1647.00 + 2852.69i 0.399755 + 0.692396i 0.993695 0.112113i \(-0.0357619\pi\)
−0.593940 + 0.804509i \(0.702429\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 477.000 + 826.188i 0.113125 + 0.195938i
\(262\) 0 0
\(263\) 3540.00 6131.46i 0.829984 1.43757i −0.0680662 0.997681i \(-0.521683\pi\)
0.898050 0.439893i \(-0.144984\pi\)
\(264\) 0 0
\(265\) 8484.00 1.96667
\(266\) 0 0
\(267\) 3582.00 0.821029
\(268\) 0 0
\(269\) −3907.00 + 6767.12i −0.885554 + 1.53382i −0.0404764 + 0.999180i \(0.512888\pi\)
−0.845078 + 0.534644i \(0.820446\pi\)
\(270\) 0 0
\(271\) −1584.00 2743.57i −0.355060 0.614981i 0.632069 0.774912i \(-0.282206\pi\)
−0.987128 + 0.159931i \(0.948873\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −142.000 245.951i −0.0311379 0.0539324i
\(276\) 0 0
\(277\) 3929.00 6805.23i 0.852241 1.47612i −0.0269403 0.999637i \(-0.508576\pi\)
0.879181 0.476488i \(-0.158090\pi\)
\(278\) 0 0
\(279\) −1296.00 −0.278099
\(280\) 0 0
\(281\) 6730.00 1.42875 0.714374 0.699764i \(-0.246712\pi\)
0.714374 + 0.699764i \(0.246712\pi\)
\(282\) 0 0
\(283\) 1510.00 2615.40i 0.317174 0.549361i −0.662723 0.748864i \(-0.730599\pi\)
0.979897 + 0.199503i \(0.0639328\pi\)
\(284\) 0 0
\(285\) −1932.00 3346.32i −0.401550 0.695505i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2358.50 + 4085.04i 0.480053 + 0.831476i
\(290\) 0 0
\(291\) 2253.00 3902.31i 0.453860 0.786108i
\(292\) 0 0
\(293\) −6834.00 −1.36262 −0.681308 0.731997i \(-0.738589\pi\)
−0.681308 + 0.731997i \(0.738589\pi\)
\(294\) 0 0
\(295\) −5096.00 −1.00576
\(296\) 0 0
\(297\) −54.0000 + 93.5307i −0.0105502 + 0.0182734i
\(298\) 0 0
\(299\) 4104.00 + 7108.34i 0.793781 + 1.37487i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −597.000 1034.03i −0.113191 0.196052i
\(304\) 0 0
\(305\) −4746.00 + 8220.31i −0.891001 + 1.54326i
\(306\) 0 0
\(307\) 2332.00 0.433532 0.216766 0.976224i \(-0.430449\pi\)
0.216766 + 0.976224i \(0.430449\pi\)
\(308\) 0 0
\(309\) 3480.00 0.640681
\(310\) 0 0
\(311\) −4420.00 + 7655.66i −0.805901 + 1.39586i 0.109780 + 0.993956i \(0.464985\pi\)
−0.915681 + 0.401906i \(0.868348\pi\)
\(312\) 0 0
\(313\) 523.000 + 905.863i 0.0944464 + 0.163586i 0.909377 0.415972i \(-0.136559\pi\)
−0.814931 + 0.579558i \(0.803225\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3771.00 6531.56i −0.668140 1.15725i −0.978424 0.206609i \(-0.933757\pi\)
0.310283 0.950644i \(-0.399576\pi\)
\(318\) 0 0
\(319\) 212.000 367.195i 0.0372092 0.0644482i
\(320\) 0 0
\(321\) 972.000 0.169009
\(322\) 0 0
\(323\) −1288.00 −0.221877
\(324\) 0 0
\(325\) −1917.00 + 3320.34i −0.327188 + 0.566706i
\(326\) 0 0
\(327\) 1407.00 + 2437.00i 0.237943 + 0.412129i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1378.00 2386.77i −0.228827 0.396340i 0.728634 0.684904i \(-0.240156\pi\)
−0.957461 + 0.288564i \(0.906822\pi\)
\(332\) 0 0
\(333\) −711.000 + 1231.49i −0.117005 + 0.202658i
\(334\) 0 0
\(335\) 11816.0 1.92710
\(336\) 0 0
\(337\) 3954.00 0.639134 0.319567 0.947564i \(-0.396463\pi\)
0.319567 + 0.947564i \(0.396463\pi\)
\(338\) 0 0
\(339\) 933.000 1616.00i 0.149480 0.258906i
\(340\) 0 0
\(341\) 288.000 + 498.831i 0.0457363 + 0.0792176i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 3192.00 + 5528.71i 0.498120 + 0.862770i
\(346\) 0 0
\(347\) −3450.00 + 5975.58i −0.533734 + 0.924454i 0.465489 + 0.885053i \(0.345878\pi\)
−0.999223 + 0.0394010i \(0.987455\pi\)
\(348\) 0 0
\(349\) −2426.00 −0.372094 −0.186047 0.982541i \(-0.559568\pi\)
−0.186047 + 0.982541i \(0.559568\pi\)
\(350\) 0 0
\(351\) 1458.00 0.221716
\(352\) 0 0
\(353\) 735.000 1273.06i 0.110822 0.191949i −0.805280 0.592895i \(-0.797985\pi\)
0.916102 + 0.400946i \(0.131318\pi\)
\(354\) 0 0
\(355\) 56.0000 + 96.9948i 0.00837231 + 0.0145013i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3436.00 5951.33i −0.505140 0.874928i −0.999982 0.00594499i \(-0.998108\pi\)
0.494843 0.868983i \(-0.335226\pi\)
\(360\) 0 0
\(361\) −802.500 + 1389.97i −0.117000 + 0.202649i
\(362\) 0 0
\(363\) −3945.00 −0.570410
\(364\) 0 0
\(365\) −5908.00 −0.847230
\(366\) 0 0
\(367\) 3536.00 6124.53i 0.502937 0.871112i −0.497058 0.867717i \(-0.665586\pi\)
0.999994 0.00339411i \(-0.00108038\pi\)
\(368\) 0 0
\(369\) 1755.00 + 3039.75i 0.247593 + 0.428843i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 409.000 + 708.409i 0.0567754 + 0.0983378i 0.893016 0.450025i \(-0.148585\pi\)
−0.836241 + 0.548362i \(0.815251\pi\)
\(374\) 0 0
\(375\) 1134.00 1964.15i 0.156159 0.270475i
\(376\) 0 0
\(377\) −5724.00 −0.781966
\(378\) 0 0
\(379\) −5132.00 −0.695549 −0.347775 0.937578i \(-0.613063\pi\)
−0.347775 + 0.937578i \(0.613063\pi\)
\(380\) 0 0
\(381\) −1800.00 + 3117.69i −0.242039 + 0.419224i
\(382\) 0 0
\(383\) 4288.00 + 7427.03i 0.572080 + 0.990871i 0.996352 + 0.0853367i \(0.0271966\pi\)
−0.424272 + 0.905535i \(0.639470\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2286.00 + 3959.47i 0.300269 + 0.520080i
\(388\) 0 0
\(389\) 1865.00 3230.27i 0.243083 0.421032i −0.718508 0.695519i \(-0.755175\pi\)
0.961591 + 0.274487i \(0.0885080\pi\)
\(390\) 0 0
\(391\) 2128.00 0.275237
\(392\) 0 0
\(393\) −4188.00 −0.537549
\(394\) 0 0
\(395\) −2688.00 + 4655.75i −0.342400 + 0.593054i
\(396\) 0 0
\(397\) −3339.00 5783.32i −0.422115 0.731124i 0.574031 0.818833i \(-0.305379\pi\)
−0.996146 + 0.0877090i \(0.972045\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1527.00 + 2644.84i 0.190161 + 0.329369i 0.945304 0.326192i \(-0.105766\pi\)
−0.755142 + 0.655561i \(0.772432\pi\)
\(402\) 0 0
\(403\) 3888.00 6734.21i 0.480583 0.832395i
\(404\) 0 0
\(405\) 1134.00 0.139133
\(406\) 0 0
\(407\) 632.000 0.0769707
\(408\) 0 0
\(409\) −133.000 + 230.363i −0.0160793 + 0.0278501i −0.873953 0.486010i \(-0.838452\pi\)
0.857874 + 0.513860i \(0.171785\pi\)
\(410\) 0 0
\(411\) −4215.00 7300.59i −0.505865 0.876184i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 3836.00 + 6644.15i 0.453739 + 0.785900i
\(416\) 0 0
\(417\) −6.00000 + 10.3923i −0.000704607 + 0.00122042i
\(418\) 0 0
\(419\) 8844.00 1.03116 0.515582 0.856840i \(-0.327576\pi\)
0.515582 + 0.856840i \(0.327576\pi\)
\(420\) 0 0
\(421\) −4482.00 −0.518858 −0.259429 0.965762i \(-0.583534\pi\)
−0.259429 + 0.965762i \(0.583534\pi\)
\(422\) 0 0
\(423\) 2376.00 4115.35i 0.273109 0.473039i
\(424\) 0 0
\(425\) 497.000 + 860.829i 0.0567248 + 0.0982502i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −324.000 561.184i −0.0364636 0.0631567i
\(430\) 0 0
\(431\) −4968.00 + 8604.83i −0.555221 + 0.961671i 0.442666 + 0.896687i \(0.354033\pi\)
−0.997886 + 0.0649838i \(0.979300\pi\)
\(432\) 0 0
\(433\) −11758.0 −1.30497 −0.652487 0.757800i \(-0.726274\pi\)
−0.652487 + 0.757800i \(0.726274\pi\)
\(434\) 0 0
\(435\) −4452.00 −0.490706
\(436\) 0 0
\(437\) 6992.00 12110.5i 0.765384 1.32568i
\(438\) 0 0
\(439\) 2052.00 + 3554.17i 0.223090 + 0.386404i 0.955745 0.294197i \(-0.0950522\pi\)
−0.732655 + 0.680601i \(0.761719\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4874.00 8442.02i −0.522733 0.905400i −0.999650 0.0264519i \(-0.991579\pi\)
0.476917 0.878948i \(-0.341754\pi\)
\(444\) 0 0
\(445\) −8358.00 + 14476.5i −0.890353 + 1.54214i
\(446\) 0 0
\(447\) 4122.00 0.436161
\(448\) 0 0
\(449\) −478.000 −0.0502410 −0.0251205 0.999684i \(-0.507997\pi\)
−0.0251205 + 0.999684i \(0.507997\pi\)
\(450\) 0 0
\(451\) 780.000 1351.00i 0.0814385 0.141056i
\(452\) 0 0
\(453\) −3156.00 5466.35i −0.327333 0.566957i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5587.00 + 9676.97i 0.571879 + 0.990524i 0.996373 + 0.0850931i \(0.0271188\pi\)
−0.424494 + 0.905431i \(0.639548\pi\)
\(458\) 0 0
\(459\) 189.000 327.358i 0.0192195 0.0332892i
\(460\) 0 0
\(461\) −11674.0 −1.17942 −0.589710 0.807615i \(-0.700758\pi\)
−0.589710 + 0.807615i \(0.700758\pi\)
\(462\) 0 0
\(463\) 10528.0 1.05676 0.528378 0.849009i \(-0.322801\pi\)
0.528378 + 0.849009i \(0.322801\pi\)
\(464\) 0 0
\(465\) 3024.00 5237.72i 0.301580 0.522352i
\(466\) 0 0
\(467\) −8302.00 14379.5i −0.822635 1.42485i −0.903713 0.428139i \(-0.859170\pi\)
0.0810777 0.996708i \(-0.474164\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −4809.00 8329.43i −0.470461 0.814862i
\(472\) 0 0
\(473\) 1016.00 1759.76i 0.0987648 0.171066i
\(474\) 0 0
\(475\) 6532.00 0.630966
\(476\) 0 0
\(477\) 5454.00 0.523525
\(478\) 0 0
\(479\) 4288.00 7427.03i 0.409027 0.708455i −0.585754 0.810489i \(-0.699202\pi\)
0.994781 + 0.102034i \(0.0325350\pi\)
\(480\) 0 0
\(481\) −4266.00 7388.93i −0.404393 0.700429i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10514.0 + 18210.8i 0.984363 + 1.70497i
\(486\) 0 0
\(487\) −4852.00 + 8403.91i −0.451468 + 0.781966i −0.998478 0.0551605i \(-0.982433\pi\)
0.547009 + 0.837127i \(0.315766\pi\)
\(488\) 0 0
\(489\) 996.000 0.0921077
\(490\) 0 0
\(491\) −4092.00 −0.376109 −0.188054 0.982159i \(-0.560218\pi\)
−0.188054 + 0.982159i \(0.560218\pi\)
\(492\) 0 0
\(493\) −742.000 + 1285.18i −0.0677850 + 0.117407i
\(494\) 0 0
\(495\) −252.000 436.477i −0.0228819 0.0396327i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −8942.00 15488.0i −0.802202 1.38945i −0.918164 0.396201i \(-0.870328\pi\)
0.115961 0.993254i \(-0.463005\pi\)
\(500\) 0 0
\(501\) −2244.00 + 3886.72i −0.200109 + 0.346599i
\(502\) 0 0
\(503\) −7704.00 −0.682911 −0.341456 0.939898i \(-0.610920\pi\)
−0.341456 + 0.939898i \(0.610920\pi\)
\(504\) 0 0
\(505\) 5572.00 0.490992
\(506\) 0 0
\(507\) −1078.50 + 1868.02i −0.0944731 + 0.163632i
\(508\) 0 0
\(509\) −7179.00 12434.4i −0.625154 1.08280i −0.988511 0.151149i \(-0.951703\pi\)
0.363357 0.931650i \(-0.381631\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1242.00 2151.21i −0.106892 0.185143i
\(514\) 0 0
\(515\) −8120.00 + 14064.3i −0.694777 + 1.20339i
\(516\) 0 0
\(517\) −2112.00 −0.179663
\(518\) 0 0
\(519\) −9966.00 −0.842888
\(520\) 0 0
\(521\) −2541.00 + 4401.14i −0.213672 + 0.370091i −0.952861 0.303407i \(-0.901876\pi\)
0.739189 + 0.673498i \(0.235209\pi\)
\(522\) 0 0
\(523\) 878.000 + 1520.74i 0.0734078 + 0.127146i 0.900393 0.435078i \(-0.143279\pi\)
−0.826985 + 0.562224i \(0.809946\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1008.00 1745.91i −0.0833191 0.144313i
\(528\) 0 0
\(529\) −5468.50 + 9471.72i −0.449453 + 0.778476i
\(530\) 0 0
\(531\) −3276.00 −0.267733
\(532\) 0 0
\(533\) −21060.0 −1.71146
\(534\) 0 0
\(535\) −2268.00 + 3928.29i −0.183279 + 0.317448i
\(536\) 0 0
\(537\) 1350.00 + 2338.27i 0.108486 + 0.187903i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −8115.00 14055.6i −0.644900 1.11700i −0.984325 0.176367i \(-0.943566\pi\)
0.339424 0.940633i \(-0.389768\pi\)
\(542\) 0 0
\(543\) −2853.00 + 4941.54i −0.225477 + 0.390537i
\(544\) 0 0
\(545\) −13132.0 −1.03213
\(546\) 0 0
\(547\) 17676.0 1.38167 0.690833 0.723014i \(-0.257244\pi\)
0.690833 + 0.723014i \(0.257244\pi\)
\(548\) 0 0
\(549\) −3051.00 + 5284.49i −0.237183 + 0.410813i
\(550\) 0 0
\(551\) 4876.00 + 8445.48i 0.376996 + 0.652976i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −3318.00 5746.94i −0.253768 0.439539i
\(556\) 0 0
\(557\) 6125.00 10608.8i 0.465933 0.807019i −0.533310 0.845920i \(-0.679052\pi\)
0.999243 + 0.0389004i \(0.0123855\pi\)
\(558\) 0 0
\(559\) −27432.0 −2.07558
\(560\) 0 0
\(561\) −168.000 −0.0126434
\(562\) 0 0
\(563\) 5026.00 8705.29i 0.376236 0.651659i −0.614276 0.789092i \(-0.710552\pi\)
0.990511 + 0.137432i \(0.0438850\pi\)
\(564\) 0 0
\(565\) 4354.00 + 7541.35i 0.324202 + 0.561534i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12837.0 22234.3i −0.945791 1.63816i −0.754160 0.656691i \(-0.771956\pi\)
−0.191631 0.981467i \(-0.561378\pi\)
\(570\) 0 0
\(571\) −1866.00 + 3232.01i −0.136759 + 0.236874i −0.926268 0.376865i \(-0.877002\pi\)
0.789509 + 0.613739i \(0.210335\pi\)
\(572\) 0 0
\(573\) 12384.0 0.902878
\(574\) 0 0
\(575\) −10792.0 −0.782709
\(576\) 0 0
\(577\) 607.000 1051.35i 0.0437950 0.0758552i −0.843297 0.537448i \(-0.819388\pi\)
0.887092 + 0.461593i \(0.152722\pi\)
\(578\) 0 0
\(579\) 2013.00 + 3486.62i 0.144486 + 0.250257i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1212.00 2099.25i −0.0860993 0.149128i
\(584\) 0 0
\(585\) −3402.00 + 5892.44i −0.240437 + 0.416448i
\(586\) 0 0
\(587\) 7108.00 0.499793 0.249897 0.968273i \(-0.419603\pi\)
0.249897 + 0.968273i \(0.419603\pi\)
\(588\) 0 0
\(589\) −13248.0 −0.926782
\(590\) 0 0
\(591\) 5259.00 9108.86i 0.366034 0.633990i
\(592\) 0 0
\(593\) −3081.00 5336.45i −0.213358 0.369548i 0.739405 0.673261i \(-0.235107\pi\)
−0.952763 + 0.303713i \(0.901774\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1020.00 1766.69i −0.0699260 0.121115i
\(598\) 0 0
\(599\) −1236.00 + 2140.81i −0.0843098 + 0.146029i −0.905097 0.425205i \(-0.860202\pi\)
0.820787 + 0.571234i \(0.193535\pi\)
\(600\) 0 0
\(601\) −13750.0 −0.933235 −0.466617 0.884459i \(-0.654528\pi\)
−0.466617 + 0.884459i \(0.654528\pi\)
\(602\) 0 0
\(603\) 7596.00 0.512990
\(604\) 0 0
\(605\) 9205.00 15943.5i 0.618573 1.07140i
\(606\) 0 0
\(607\) 5688.00 + 9851.90i 0.380344 + 0.658775i 0.991111 0.133035i \(-0.0424723\pi\)
−0.610767 + 0.791810i \(0.709139\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 14256.0 + 24692.1i 0.943921 + 1.63492i
\(612\) 0 0
\(613\) −10191.0 + 17651.3i −0.671469 + 1.16302i 0.306018 + 0.952026i \(0.401003\pi\)
−0.977488 + 0.210993i \(0.932330\pi\)
\(614\) 0 0
\(615\) −16380.0 −1.07399
\(616\) 0 0
\(617\) 21178.0 1.38184 0.690919 0.722932i \(-0.257206\pi\)
0.690919 + 0.722932i \(0.257206\pi\)
\(618\) 0 0
\(619\) 2350.00 4070.32i 0.152592 0.264297i −0.779588 0.626293i \(-0.784571\pi\)
0.932180 + 0.361996i \(0.117905\pi\)
\(620\) 0 0
\(621\) 2052.00 + 3554.17i 0.132599 + 0.229668i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9729.50 + 16852.0i 0.622688 + 1.07853i
\(626\) 0 0
\(627\) −552.000 + 956.092i −0.0351591 + 0.0608973i
\(628\) 0 0
\(629\) −2212.00 −0.140220
\(630\) 0 0
\(631\) −21736.0 −1.37131 −0.685655 0.727927i \(-0.740484\pi\)
−0.685655 + 0.727927i \(0.740484\pi\)
\(632\) 0 0
\(633\) −8058.00 + 13956.9i −0.505966 + 0.876360i
\(634\) 0 0
\(635\) −8400.00 14549.2i −0.524951 0.909242i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 36.0000 + 62.3538i 0.00222870 + 0.00386022i
\(640\) 0 0
\(641\) 6511.00 11277.4i 0.401200 0.694898i −0.592671 0.805444i \(-0.701927\pi\)
0.993871 + 0.110546i \(0.0352600\pi\)
\(642\) 0 0
\(643\) 3308.00 0.202885 0.101442 0.994841i \(-0.467654\pi\)
0.101442 + 0.994841i \(0.467654\pi\)
\(644\) 0 0
\(645\) −21336.0 −1.30249
\(646\) 0 0
\(647\) 6900.00 11951.2i 0.419269 0.726195i −0.576597 0.817029i \(-0.695620\pi\)
0.995866 + 0.0908335i \(0.0289531\pi\)
\(648\) 0 0
\(649\) 728.000 + 1260.93i 0.0440316 + 0.0762649i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1341.00 + 2322.68i 0.0803635 + 0.139194i 0.903406 0.428786i \(-0.141059\pi\)
−0.823043 + 0.567980i \(0.807725\pi\)
\(654\) 0 0
\(655\) 9772.00 16925.6i 0.582937 1.00968i
\(656\) 0 0
\(657\) −3798.00 −0.225531
\(658\) 0 0
\(659\) 23836.0 1.40898 0.704491 0.709713i \(-0.251175\pi\)
0.704491 + 0.709713i \(0.251175\pi\)
\(660\) 0 0
\(661\) 5641.00 9770.50i 0.331936 0.574929i −0.650956 0.759116i \(-0.725632\pi\)
0.982891 + 0.184186i \(0.0589650\pi\)
\(662\) 0 0
\(663\) 1134.00 + 1964.15i 0.0664267 + 0.115054i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8056.00 13953.4i −0.467661 0.810012i
\(668\) 0 0
\(669\) 1608.00 2785.14i 0.0929281 0.160956i
\(670\) 0 0
\(671\) 2712.00 0.156029
\(672\) 0 0
\(673\) −13726.0 −0.786179 −0.393089 0.919500i \(-0.628594\pi\)
−0.393089 + 0.919500i \(0.628594\pi\)
\(674\) 0 0
\(675\) −958.500 + 1660.17i −0.0546558 + 0.0946667i
\(676\) 0 0
\(677\) −2487.00 4307.61i −0.141186 0.244542i 0.786757 0.617263i \(-0.211758\pi\)
−0.927944 + 0.372721i \(0.878425\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 4302.00 + 7451.28i 0.242075 + 0.419286i
\(682\) 0 0
\(683\) 4494.00 7783.84i 0.251769 0.436076i −0.712244 0.701932i \(-0.752321\pi\)
0.964013 + 0.265855i \(0.0856544\pi\)
\(684\) 0 0
\(685\) 39340.0 2.19431
\(686\) 0 0
\(687\) 14394.0 0.799367
\(688\) 0 0
\(689\) −16362.0 + 28339.8i −0.904706 + 1.56700i
\(690\) 0 0
\(691\) −5086.00 8809.21i −0.280001 0.484976i 0.691384 0.722488i \(-0.257001\pi\)
−0.971385 + 0.237512i \(0.923668\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −28.0000 48.4974i −0.00152820 0.00264692i
\(696\) 0 0
\(697\) −2730.00 + 4728.50i −0.148359 + 0.256965i
\(698\) 0 0
\(699\) −15378.0 −0.832116
\(700\) 0 0
\(701\) 27446.0 1.47877 0.739387 0.673280i \(-0.235115\pi\)
0.739387 + 0.673280i \(0.235115\pi\)
\(702\) 0 0
\(703\) −7268.00 + 12588.5i −0.389926 + 0.675371i
\(704\) 0 0
\(705\) 11088.0 + 19205.0i 0.592338 + 1.02596i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1999.00 3462.37i −0.105887 0.183402i 0.808213 0.588890i \(-0.200435\pi\)
−0.914100 + 0.405488i \(0.867102\pi\)
\(710\) 0 0
\(711\) −1728.00 + 2992.98i −0.0911464 + 0.157870i
\(712\) 0 0
\(713\) 21888.0 1.14967
\(714\) 0 0
\(715\) 3024.00 0.158169
\(716\) 0 0
\(717\) 792.000 1371.78i 0.0412521 0.0714508i
\(718\) 0 0
\(719\) −12936.0 22405.8i −0.670976 1.16216i −0.977628 0.210342i \(-0.932542\pi\)
0.306652 0.951822i \(-0.400791\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1221.00 + 2114.83i 0.0628070 + 0.108785i
\(724\) 0 0
\(725\) 3763.00 6517.71i 0.192765 0.333878i
\(726\) 0 0
\(727\) 12088.0 0.616670 0.308335 0.951278i \(-0.400228\pi\)
0.308335 + 0.951278i \(0.400228\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −3556.00 + 6159.17i −0.179923 + 0.311635i
\(732\) 0 0
\(733\) −3987.00 6905.69i −0.200905 0.347977i 0.747915 0.663794i \(-0.231055\pi\)
−0.948820 + 0.315817i \(0.897722\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1688.00 2923.70i −0.0843667 0.146127i
\(738\) 0 0
\(739\) 15882.0 27508.4i 0.790567 1.36930i −0.135050 0.990839i \(-0.543119\pi\)
0.925616 0.378463i \(-0.123547\pi\)
\(740\) 0 0
\(741\) 14904.0 0.738883
\(742\) 0 0
\(743\) 888.000 0.0438460 0.0219230 0.999760i \(-0.493021\pi\)
0.0219230 + 0.999760i \(0.493021\pi\)
\(744\) 0 0
\(745\) −9618.00 + 16658.9i −0.472988 + 0.819240i
\(746\) 0 0
\(747\) 2466.00 + 4271.24i 0.120785 + 0.209205i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 17328.0 + 30013.0i 0.841954 + 1.45831i 0.888240 + 0.459379i \(0.151928\pi\)
−0.0462858 + 0.998928i \(0.514738\pi\)
\(752\) 0 0
\(753\) 2898.00 5019.48i 0.140251 0.242922i
\(754\) 0 0
\(755\) 29456.0 1.41989
\(756\) 0 0
\(757\) −22866.0 −1.09786 −0.548929 0.835869i \(-0.684964\pi\)
−0.548929 + 0.835869i \(0.684964\pi\)
\(758\) 0 0
\(759\) 912.000 1579.63i 0.0436146 0.0755428i
\(760\) 0 0
\(761\) −11285.0 19546.2i −0.537557 0.931076i −0.999035 0.0439244i \(-0.986014\pi\)
0.461478 0.887152i \(-0.347319\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 882.000 + 1527.67i 0.0416847 + 0.0722000i
\(766\) 0 0
\(767\) 9828.00 17022.6i 0.462671 0.801369i
\(768\) 0 0
\(769\) −1790.00 −0.0839389 −0.0419695 0.999119i \(-0.513363\pi\)
−0.0419695 + 0.999119i \(0.513363\pi\)
\(770\) 0 0
\(771\) −9882.00 −0.461597
\(772\) 0 0
\(773\) −1495.00 + 2589.42i −0.0695620 + 0.120485i −0.898709 0.438546i \(-0.855493\pi\)
0.829147 + 0.559031i \(0.188827\pi\)
\(774\) 0 0
\(775\) 5112.00 + 8854.24i 0.236940 + 0.410392i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 17940.0 + 31073.0i 0.825118 + 1.42915i
\(780\) 0 0
\(781\) 16.0000 27.7128i 0.000733067 0.00126971i
\(782\) 0 0
\(783\) −2862.00 −0.130625
\(784\) 0 0
\(785\) 44884.0 2.04074
\(786\) 0 0
\(787\) 15378.0 26635.5i 0.696527 1.20642i −0.273137 0.961975i \(-0.588061\pi\)
0.969663 0.244444i \(-0.0786056\pi\)
\(788\) 0 0
\(789\) 10620.0 + 18394.4i 0.479191 + 0.829984i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −18306.0 31706.9i −0.819754 1.41986i
\(794\) 0 0
\(795\) −12726.0 + 22042.1i −0.567729 + 0.983336i
\(796\) 0 0
\(797\) 15126.0 0.672259 0.336129 0.941816i \(-0.390882\pi\)
0.336129 + 0.941816i \(0.390882\pi\)
\(798\) 0 0
\(799\) 7392.00 0.327297
\(800\) 0 0
\(801\) −5373.00 + 9306.31i −0.237011 + 0.410515i
\(802\) 0 0
\(803\) 844.000 + 1461.85i 0.0370911 + 0.0642436i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −11721.0 20301.4i −0.511275 0.885554i
\(808\) 0 0
\(809\) 3251.00 5630.90i 0.141284 0.244712i −0.786696 0.617340i \(-0.788210\pi\)
0.927981 + 0.372629i \(0.121543\pi\)
\(810\) 0 0
\(811\) −8252.00 −0.357296 −0.178648 0.983913i \(-0.557172\pi\)
−0.178648 + 0.983913i \(0.557172\pi\)
\(812\) 0 0
\(813\) 9504.00 0.409987
\(814\) 0 0
\(815\) −2324.00 + 4025.29i −0.0998849 + 0.173006i
\(816\) 0 0
\(817\) 23368.0 + 40474.6i 1.00066 + 1.73320i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 10993.0 + 19040.4i 0.467306 + 0.809398i 0.999302 0.0373488i \(-0.0118913\pi\)
−0.531996 + 0.846747i \(0.678558\pi\)
\(822\) 0 0
\(823\) −1868.00 + 3235.47i −0.0791183 + 0.137037i −0.902870 0.429914i \(-0.858544\pi\)
0.823751 + 0.566951i \(0.191877\pi\)
\(824\) 0 0
\(825\) 852.000 0.0359549
\(826\) 0 0
\(827\) −23820.0 −1.00158 −0.500788 0.865570i \(-0.666956\pi\)
−0.500788 + 0.865570i \(0.666956\pi\)
\(828\) 0 0
\(829\) −3971.00 + 6877.97i −0.166367 + 0.288157i −0.937140 0.348954i \(-0.886537\pi\)
0.770773 + 0.637110i \(0.219870\pi\)
\(830\) 0 0
\(831\) 11787.0 + 20415.7i 0.492042 + 0.852241i
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −10472.0 18138.0i −0.434010 0.751728i
\(836\) 0 0
\(837\) 1944.00 3367.11i 0.0802801 0.139049i
\(838\) 0 0
\(839\) 21016.0 0.864783 0.432391 0.901686i \(-0.357670\pi\)
0.432391 + 0.901686i \(0.357670\pi\)
\(840\) 0 0
\(841\) −13153.0 −0.539301
\(842\) 0 0
\(843\) −10095.0 + 17485.1i −0.412444 + 0.714374i
\(844\) 0 0
\(845\) −5033.00 8717.41i −0.204900 0.354897i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 4530.00 + 7846.19i 0.183120 + 0.317174i
\(850\) 0 0
\(851\) 12008.0 20798.5i 0.483700 0.837793i
\(852\) 0 0
\(853\) 24878.0 0.998601 0.499300 0.866429i \(-0.333590\pi\)
0.499300 + 0.866429i \(0.333590\pi\)
\(854\) 0 0
\(855\) 11592.0 0.463670
\(856\) 0 0
\(857\) 3195.00 5533.90i 0.127350 0.220577i −0.795299 0.606217i \(-0.792686\pi\)
0.922649 + 0.385640i \(0.126019\pi\)
\(858\) 0 0
\(859\) 23222.0 + 40221.7i 0.922380 + 1.59761i 0.795722 + 0.605663i \(0.207092\pi\)
0.126658 + 0.991946i \(0.459575\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 12704.0 + 22004.0i 0.501100 + 0.867930i 0.999999 + 0.00127049i \(0.000404409\pi\)
−0.498899 + 0.866660i \(0.666262\pi\)
\(864\) 0 0
\(865\) 23254.0 40277.1i 0.914057 1.58319i
\(866\) 0 0
\(867\) −14151.0 −0.554317
\(868\) 0 0
\(869\) 1536.00 0.0599600
\(870\) 0 0
\(871\) −22788.0 + 39470.0i −0.886500 + 1.53546i
\(872\) 0 0
\(873\) 6759.00 + 11706.9i 0.262036 + 0.453860i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −539.000 933.575i −0.0207534 0.0359460i 0.855462 0.517865i \(-0.173273\pi\)
−0.876216 + 0.481919i \(0.839940\pi\)
\(878\) 0 0
\(879\) 10251.0 17755.3i 0.393353 0.681308i
\(880\) 0 0
\(881\) −45006.0 −1.72110 −0.860551 0.509364i \(-0.829881\pi\)
−0.860551 + 0.509364i \(0.829881\pi\)
\(882\) 0 0
\(883\) 4028.00 0.153514 0.0767571 0.997050i \(-0.475543\pi\)
0.0767571 + 0.997050i \(0.475543\pi\)
\(884\) 0 0
\(885\) 7644.00 13239.8i 0.290339 0.502882i
\(886\) 0 0
\(887\) 14652.0 + 25378.0i 0.554640 + 0.960665i 0.997931 + 0.0642876i \(0.0204775\pi\)
−0.443291 + 0.896378i \(0.646189\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −162.000 280.592i −0.00609114 0.0105502i
\(892\) 0 0
\(893\) 24288.0 42068.1i 0.910153 1.57643i
\(894\) 0 0
\(895\) −12600.0 −0.470583
\(896\) 0 0
\(897\) −24624.0 −0.916579
\(898\) 0 0
\(899\) −7632.00 + 13219.0i −0.283138 + 0.490410i
\(900\) 0 0
\(901\) 4242.00 + 7347.36i 0.156850 + 0.271672i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −13314.0 23060.5i −0.489030 0.847025i
\(906\) 0 0
\(907\) −25458.0 + 44094.5i −0.931995 + 1.61426i −0.152087 + 0.988367i \(0.548599\pi\)
−0.779908 + 0.625895i \(0.784734\pi\)
\(908\) 0 0
\(909\) 3582.00 0.130701
\(910\) 0 0
\(911\) −24432.0 −0.888549 −0.444275 0.895891i \(-0.646539\pi\)
−0.444275 + 0.895891i \(0.646539\pi\)
\(912\) 0 0
\(913\) 1096.00 1898.33i 0.0397287 0.0688121i
\(914\) 0 0
\(915\) −14238.0 24660.9i −0.514419 0.891001i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 10180.0 + 17632.3i 0.365405 + 0.632900i 0.988841 0.148974i \(-0.0475972\pi\)
−0.623436 + 0.781874i \(0.714264\pi\)
\(920\) 0 0
\(921\) −3498.00 + 6058.71i −0.125150 + 0.216766i
\(922\) 0 0
\(923\) −432.000 −0.0154057
\(924\) 0 0
\(925\) 11218.0 0.398752
\(926\) 0 0
\(927\) −5220.00 + 9041.31i −0.184949 + 0.320340i
\(928\) 0 0
\(929\) −11601.0 20093.5i −0.409706 0.709631i 0.585151 0.810924i \(-0.301035\pi\)
−0.994857 + 0.101293i \(0.967702\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −13260.0 22967.0i −0.465287 0.805901i
\(934\) 0 0
\(935\) 392.000 678.964i 0.0137110 0.0237481i
\(936\) 0 0
\(937\) −1990.00 −0.0693815 −0.0346908 0.999398i \(-0.511045\pi\)
−0.0346908 + 0.999398i \(0.511045\pi\)
\(938\) 0 0
\(939\) −3138.00 −0.109057
\(940\) 0 0
\(941\) 25565.0 44279.9i 0.885648 1.53399i 0.0406798 0.999172i \(-0.487048\pi\)
0.844969 0.534816i \(-0.179619\pi\)
\(942\) 0 0
\(943\) −29640.0 51338.0i −1.02355 1.77285i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 23522.0 + 40741.3i 0.807141 + 1.39801i 0.914836 + 0.403825i \(0.132319\pi\)
−0.107696 + 0.994184i \(0.534347\pi\)
\(948\) 0 0
\(949\) 11394.0 19735.0i 0.389742 0.675052i
\(950\) 0 0
\(951\) 22626.0 0.771502
\(952\) 0 0
\(953\) 46858.0 1.59274 0.796369 0.604811i \(-0.206751\pi\)
0.796369 + 0.604811i \(0.206751\pi\)
\(954\) 0 0
\(955\) −28896.0 + 50049.3i −0.979113 + 1.69587i
\(956\) 0 0
\(957\) 636.000 + 1101.58i 0.0214827 + 0.0372092i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 4527.50 + 7841.86i 0.151975 + 0.263229i
\(962\) 0 0
\(963\) −1458.00 + 2525.33i −0.0487886 + 0.0845043i
\(964\) 0 0
\(965\) −18788.0 −0.626743
\(966\) 0 0
\(967\) 30632.0 1.01867 0.509337 0.860567i \(-0.329890\pi\)
0.509337 + 0.860567i \(0.329890\pi\)
\(968\) 0 0
\(969\) 1932.00 3346.32i 0.0640503 0.110938i
\(970\) 0 0
\(971\) 1902.00 + 3294.36i 0.0628611 + 0.108879i 0.895743 0.444572i \(-0.146644\pi\)
−0.832882 + 0.553450i \(0.813311\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −5751.00 9961.02i −0.188902 0.327188i
\(976\) 0 0
\(977\) 24663.0 42717.6i 0.807614 1.39883i −0.106897 0.994270i \(-0.534092\pi\)
0.914512 0.404559i \(-0.132575\pi\)
\(978\) 0 0
\(979\) 4776.00 0.155916
\(980\) 0 0
\(981\) −8442.00 −0.274753
\(982\) 0 0
\(983\) −5556.00 + 9623.27i −0.180274 + 0.312243i −0.941974 0.335687i \(-0.891032\pi\)
0.761700 + 0.647930i \(0.224365\pi\)
\(984\) 0 0
\(985\) 24542.0 + 42508.0i 0.793881 + 1.37504i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −38608.0 66871.0i −1.24132 2.15002i
\(990\) 0 0
\(991\) −6808.00 + 11791.8i −0.218227 + 0.377981i −0.954266 0.298959i \(-0.903361\pi\)
0.736039 + 0.676939i \(0.236694\pi\)
\(992\) 0 0
\(993\) 8268.00 0.264227
\(994\) 0 0
\(995\) 9520.00 0.303321
\(996\) 0 0
\(997\) 28337.0 49081.1i 0.900142 1.55909i 0.0728338 0.997344i \(-0.476796\pi\)
0.827308 0.561748i \(-0.189871\pi\)
\(998\) 0 0
\(999\) −2133.00 3694.46i −0.0675527 0.117005i
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 588.4.i.a.361.1 2
3.2 odd 2 1764.4.k.n.361.1 2
7.2 even 3 inner 588.4.i.a.373.1 2
7.3 odd 6 588.4.a.a.1.1 1
7.4 even 3 84.4.a.b.1.1 1
7.5 odd 6 588.4.i.h.373.1 2
7.6 odd 2 588.4.i.h.361.1 2
21.2 odd 6 1764.4.k.n.1549.1 2
21.5 even 6 1764.4.k.c.1549.1 2
21.11 odd 6 252.4.a.a.1.1 1
21.17 even 6 1764.4.a.l.1.1 1
21.20 even 2 1764.4.k.c.361.1 2
28.3 even 6 2352.4.a.v.1.1 1
28.11 odd 6 336.4.a.e.1.1 1
35.4 even 6 2100.4.a.g.1.1 1
35.18 odd 12 2100.4.k.g.1849.2 2
35.32 odd 12 2100.4.k.g.1849.1 2
56.11 odd 6 1344.4.a.p.1.1 1
56.53 even 6 1344.4.a.b.1.1 1
84.11 even 6 1008.4.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.4.a.b.1.1 1 7.4 even 3
252.4.a.a.1.1 1 21.11 odd 6
336.4.a.e.1.1 1 28.11 odd 6
588.4.a.a.1.1 1 7.3 odd 6
588.4.i.a.361.1 2 1.1 even 1 trivial
588.4.i.a.373.1 2 7.2 even 3 inner
588.4.i.h.361.1 2 7.6 odd 2
588.4.i.h.373.1 2 7.5 odd 6
1008.4.a.d.1.1 1 84.11 even 6
1344.4.a.b.1.1 1 56.53 even 6
1344.4.a.p.1.1 1 56.11 odd 6
1764.4.a.l.1.1 1 21.17 even 6
1764.4.k.c.361.1 2 21.20 even 2
1764.4.k.c.1549.1 2 21.5 even 6
1764.4.k.n.361.1 2 3.2 odd 2
1764.4.k.n.1549.1 2 21.2 odd 6
2100.4.a.g.1.1 1 35.4 even 6
2100.4.k.g.1849.1 2 35.32 odd 12
2100.4.k.g.1849.2 2 35.18 odd 12
2352.4.a.v.1.1 1 28.3 even 6