Properties

Label 5733.2.a.bl.1.1
Level $5733$
Weight $2$
Character 5733.1
Self dual yes
Analytic conductor $45.778$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5733,2,Mod(1,5733)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5733, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5733.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.a (trivial)

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: yes
Analytic conductor: \(45.7782354788\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.746052.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 7x^{3} + 8x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.72525\) of defining polynomial
Character \(\chi\) \(=\) 5733.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.72525 q^{2} +5.42699 q^{4} -2.18716 q^{5} -9.33940 q^{8} +O(q^{10})\) \(q-2.72525 q^{2} +5.42699 q^{4} -2.18716 q^{5} -9.33940 q^{8} +5.96057 q^{10} +1.04815 q^{11} +1.00000 q^{13} +14.5982 q^{16} +5.29125 q^{17} +0.756906 q^{19} -11.8697 q^{20} -2.85648 q^{22} -0.653584 q^{23} -0.216314 q^{25} -2.72525 q^{26} +3.10408 q^{29} +1.02791 q^{31} -21.1050 q^{32} -14.4200 q^{34} -10.8932 q^{37} -2.06276 q^{38} +20.4268 q^{40} -7.32040 q^{41} +0.887771 q^{43} +5.68833 q^{44} +1.78118 q^{46} -2.33751 q^{47} +0.589510 q^{50} +5.42699 q^{52} -4.88814 q^{53} -2.29249 q^{55} -8.45941 q^{58} +1.04815 q^{59} -12.4998 q^{61} -2.80132 q^{62} +28.3200 q^{64} -2.18716 q^{65} +4.47889 q^{67} +28.7155 q^{68} +6.60274 q^{71} -8.28347 q^{73} +29.6868 q^{74} +4.10772 q^{76} +2.14014 q^{79} -31.9287 q^{80} +19.9499 q^{82} +6.66558 q^{83} -11.5728 q^{85} -2.41940 q^{86} -9.78914 q^{88} +5.76777 q^{89} -3.54699 q^{92} +6.37030 q^{94} -1.65548 q^{95} -2.88777 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8} - 5 q^{10} - 11 q^{11} + 5 q^{13} + 10 q^{16} + 5 q^{17} + 9 q^{19} - q^{20} + 8 q^{22} - 10 q^{23} + 9 q^{25} - 4 q^{26} + 3 q^{29} - 6 q^{31} - 22 q^{32} - 22 q^{34} + 4 q^{37} + 10 q^{38} + 28 q^{40} - 14 q^{41} + 2 q^{43} + 3 q^{46} - q^{47} - 9 q^{50} + 8 q^{52} - 17 q^{53} - 27 q^{58} - 11 q^{59} - 11 q^{61} + 23 q^{62} + 9 q^{64} - 2 q^{65} + 13 q^{67} + 32 q^{68} - 15 q^{71} + 33 q^{74} + 8 q^{76} + 2 q^{79} - 55 q^{80} + 34 q^{82} - 6 q^{83} - 22 q^{85} - 28 q^{86} - 3 q^{88} + 4 q^{89} - 21 q^{92} + 20 q^{94} + 12 q^{95} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72525 −1.92704 −0.963521 0.267631i \(-0.913759\pi\)
−0.963521 + 0.267631i \(0.913759\pi\)
\(3\) 0 0
\(4\) 5.42699 2.71349
\(5\) −2.18716 −0.978129 −0.489065 0.872247i \(-0.662662\pi\)
−0.489065 + 0.872247i \(0.662662\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −9.33940 −3.30198
\(9\) 0 0
\(10\) 5.96057 1.88490
\(11\) 1.04815 0.316031 0.158015 0.987437i \(-0.449490\pi\)
0.158015 + 0.987437i \(0.449490\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 14.5982 3.64956
\(17\) 5.29125 1.28332 0.641658 0.766991i \(-0.278247\pi\)
0.641658 + 0.766991i \(0.278247\pi\)
\(18\) 0 0
\(19\) 0.756906 0.173646 0.0868231 0.996224i \(-0.472329\pi\)
0.0868231 + 0.996224i \(0.472329\pi\)
\(20\) −11.8697 −2.65415
\(21\) 0 0
\(22\) −2.85648 −0.609005
\(23\) −0.653584 −0.136282 −0.0681408 0.997676i \(-0.521707\pi\)
−0.0681408 + 0.997676i \(0.521707\pi\)
\(24\) 0 0
\(25\) −0.216314 −0.0432628
\(26\) −2.72525 −0.534466
\(27\) 0 0
\(28\) 0 0
\(29\) 3.10408 0.576414 0.288207 0.957568i \(-0.406941\pi\)
0.288207 + 0.957568i \(0.406941\pi\)
\(30\) 0 0
\(31\) 1.02791 0.184618 0.0923092 0.995730i \(-0.470575\pi\)
0.0923092 + 0.995730i \(0.470575\pi\)
\(32\) −21.1050 −3.73088
\(33\) 0 0
\(34\) −14.4200 −2.47301
\(35\) 0 0
\(36\) 0 0
\(37\) −10.8932 −1.79084 −0.895418 0.445227i \(-0.853123\pi\)
−0.895418 + 0.445227i \(0.853123\pi\)
\(38\) −2.06276 −0.334624
\(39\) 0 0
\(40\) 20.4268 3.22976
\(41\) −7.32040 −1.14325 −0.571627 0.820514i \(-0.693688\pi\)
−0.571627 + 0.820514i \(0.693688\pi\)
\(42\) 0 0
\(43\) 0.887771 0.135384 0.0676919 0.997706i \(-0.478437\pi\)
0.0676919 + 0.997706i \(0.478437\pi\)
\(44\) 5.68833 0.857547
\(45\) 0 0
\(46\) 1.78118 0.262621
\(47\) −2.33751 −0.340961 −0.170480 0.985361i \(-0.554532\pi\)
−0.170480 + 0.985361i \(0.554532\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.589510 0.0833692
\(51\) 0 0
\(52\) 5.42699 0.752588
\(53\) −4.88814 −0.671438 −0.335719 0.941962i \(-0.608979\pi\)
−0.335719 + 0.941962i \(0.608979\pi\)
\(54\) 0 0
\(55\) −2.29249 −0.309119
\(56\) 0 0
\(57\) 0 0
\(58\) −8.45941 −1.11077
\(59\) 1.04815 0.136458 0.0682291 0.997670i \(-0.478265\pi\)
0.0682291 + 0.997670i \(0.478265\pi\)
\(60\) 0 0
\(61\) −12.4998 −1.60043 −0.800217 0.599711i \(-0.795282\pi\)
−0.800217 + 0.599711i \(0.795282\pi\)
\(62\) −2.80132 −0.355768
\(63\) 0 0
\(64\) 28.3200 3.54000
\(65\) −2.18716 −0.271284
\(66\) 0 0
\(67\) 4.47889 0.547183 0.273592 0.961846i \(-0.411788\pi\)
0.273592 + 0.961846i \(0.411788\pi\)
\(68\) 28.7155 3.48227
\(69\) 0 0
\(70\) 0 0
\(71\) 6.60274 0.783601 0.391801 0.920050i \(-0.371852\pi\)
0.391801 + 0.920050i \(0.371852\pi\)
\(72\) 0 0
\(73\) −8.28347 −0.969507 −0.484754 0.874651i \(-0.661091\pi\)
−0.484754 + 0.874651i \(0.661091\pi\)
\(74\) 29.6868 3.45102
\(75\) 0 0
\(76\) 4.10772 0.471188
\(77\) 0 0
\(78\) 0 0
\(79\) 2.14014 0.240785 0.120392 0.992726i \(-0.461585\pi\)
0.120392 + 0.992726i \(0.461585\pi\)
\(80\) −31.9287 −3.56974
\(81\) 0 0
\(82\) 19.9499 2.20310
\(83\) 6.66558 0.731642 0.365821 0.930685i \(-0.380788\pi\)
0.365821 + 0.930685i \(0.380788\pi\)
\(84\) 0 0
\(85\) −11.5728 −1.25525
\(86\) −2.41940 −0.260890
\(87\) 0 0
\(88\) −9.78914 −1.04353
\(89\) 5.76777 0.611382 0.305691 0.952131i \(-0.401113\pi\)
0.305691 + 0.952131i \(0.401113\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.54699 −0.369800
\(93\) 0 0
\(94\) 6.37030 0.657046
\(95\) −1.65548 −0.169848
\(96\) 0 0
\(97\) −2.88777 −0.293209 −0.146604 0.989195i \(-0.546834\pi\)
−0.146604 + 0.989195i \(0.546834\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.17393 −0.117393
\(101\) 11.2543 1.11985 0.559924 0.828544i \(-0.310830\pi\)
0.559924 + 0.828544i \(0.310830\pi\)
\(102\) 0 0
\(103\) 20.2334 1.99366 0.996828 0.0795900i \(-0.0253611\pi\)
0.996828 + 0.0795900i \(0.0253611\pi\)
\(104\) −9.33940 −0.915804
\(105\) 0 0
\(106\) 13.3214 1.29389
\(107\) −9.05517 −0.875396 −0.437698 0.899122i \(-0.644206\pi\)
−0.437698 + 0.899122i \(0.644206\pi\)
\(108\) 0 0
\(109\) 15.1014 1.44645 0.723226 0.690612i \(-0.242659\pi\)
0.723226 + 0.690612i \(0.242659\pi\)
\(110\) 6.24760 0.595685
\(111\) 0 0
\(112\) 0 0
\(113\) −3.10408 −0.292008 −0.146004 0.989284i \(-0.546641\pi\)
−0.146004 + 0.989284i \(0.546641\pi\)
\(114\) 0 0
\(115\) 1.42950 0.133301
\(116\) 16.8458 1.56410
\(117\) 0 0
\(118\) −2.85648 −0.262961
\(119\) 0 0
\(120\) 0 0
\(121\) −9.90137 −0.900125
\(122\) 34.0651 3.08410
\(123\) 0 0
\(124\) 5.57847 0.500961
\(125\) 11.4089 1.02045
\(126\) 0 0
\(127\) 8.78914 0.779910 0.389955 0.920834i \(-0.372491\pi\)
0.389955 + 0.920834i \(0.372491\pi\)
\(128\) −34.9691 −3.09086
\(129\) 0 0
\(130\) 5.96057 0.522776
\(131\) 10.5145 0.918653 0.459327 0.888267i \(-0.348091\pi\)
0.459327 + 0.888267i \(0.348091\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.2061 −1.05445
\(135\) 0 0
\(136\) −49.4171 −4.23748
\(137\) −8.73165 −0.745995 −0.372998 0.927832i \(-0.621670\pi\)
−0.372998 + 0.927832i \(0.621670\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −17.9941 −1.51003
\(143\) 1.04815 0.0876511
\(144\) 0 0
\(145\) −6.78914 −0.563808
\(146\) 22.5745 1.86828
\(147\) 0 0
\(148\) −59.1174 −4.85942
\(149\) −15.3926 −1.26101 −0.630507 0.776183i \(-0.717153\pi\)
−0.630507 + 0.776183i \(0.717153\pi\)
\(150\) 0 0
\(151\) −13.6757 −1.11291 −0.556457 0.830876i \(-0.687840\pi\)
−0.556457 + 0.830876i \(0.687840\pi\)
\(152\) −7.06905 −0.573376
\(153\) 0 0
\(154\) 0 0
\(155\) −2.24821 −0.180581
\(156\) 0 0
\(157\) 3.38756 0.270357 0.135178 0.990821i \(-0.456839\pi\)
0.135178 + 0.990821i \(0.456839\pi\)
\(158\) −5.83242 −0.464002
\(159\) 0 0
\(160\) 46.1602 3.64928
\(161\) 0 0
\(162\) 0 0
\(163\) −13.8100 −1.08169 −0.540843 0.841124i \(-0.681895\pi\)
−0.540843 + 0.841124i \(0.681895\pi\)
\(164\) −39.7277 −3.10221
\(165\) 0 0
\(166\) −18.1654 −1.40991
\(167\) −16.3783 −1.26739 −0.633695 0.773583i \(-0.718462\pi\)
−0.633695 + 0.773583i \(0.718462\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 31.5389 2.41892
\(171\) 0 0
\(172\) 4.81792 0.367363
\(173\) −4.12546 −0.313653 −0.156826 0.987626i \(-0.550126\pi\)
−0.156826 + 0.987626i \(0.550126\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 15.3012 1.15337
\(177\) 0 0
\(178\) −15.7186 −1.17816
\(179\) −14.4136 −1.07732 −0.538661 0.842523i \(-0.681069\pi\)
−0.538661 + 0.842523i \(0.681069\pi\)
\(180\) 0 0
\(181\) 18.1014 1.34547 0.672733 0.739885i \(-0.265120\pi\)
0.672733 + 0.739885i \(0.265120\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 6.10408 0.449999
\(185\) 23.8253 1.75167
\(186\) 0 0
\(187\) 5.54605 0.405567
\(188\) −12.6856 −0.925195
\(189\) 0 0
\(190\) 4.51159 0.327305
\(191\) −5.54135 −0.400958 −0.200479 0.979698i \(-0.564250\pi\)
−0.200479 + 0.979698i \(0.564250\pi\)
\(192\) 0 0
\(193\) −8.74088 −0.629182 −0.314591 0.949227i \(-0.601867\pi\)
−0.314591 + 0.949227i \(0.601867\pi\)
\(194\) 7.86990 0.565026
\(195\) 0 0
\(196\) 0 0
\(197\) 5.46874 0.389632 0.194816 0.980840i \(-0.437589\pi\)
0.194816 + 0.980840i \(0.437589\pi\)
\(198\) 0 0
\(199\) 19.5368 1.38493 0.692463 0.721454i \(-0.256526\pi\)
0.692463 + 0.721454i \(0.256526\pi\)
\(200\) 2.02024 0.142853
\(201\) 0 0
\(202\) −30.6708 −2.15799
\(203\) 0 0
\(204\) 0 0
\(205\) 16.0109 1.11825
\(206\) −55.1411 −3.84186
\(207\) 0 0
\(208\) 14.5982 1.01221
\(209\) 0.793355 0.0548775
\(210\) 0 0
\(211\) 16.6905 1.14902 0.574511 0.818497i \(-0.305192\pi\)
0.574511 + 0.818497i \(0.305192\pi\)
\(212\) −26.5279 −1.82194
\(213\) 0 0
\(214\) 24.6776 1.68693
\(215\) −1.94170 −0.132423
\(216\) 0 0
\(217\) 0 0
\(218\) −41.1551 −2.78737
\(219\) 0 0
\(220\) −12.4413 −0.838792
\(221\) 5.29125 0.355928
\(222\) 0 0
\(223\) −5.34217 −0.357738 −0.178869 0.983873i \(-0.557244\pi\)
−0.178869 + 0.983873i \(0.557244\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 8.45941 0.562711
\(227\) −20.1215 −1.33551 −0.667757 0.744380i \(-0.732745\pi\)
−0.667757 + 0.744380i \(0.732745\pi\)
\(228\) 0 0
\(229\) 25.2497 1.66855 0.834275 0.551349i \(-0.185887\pi\)
0.834275 + 0.551349i \(0.185887\pi\)
\(230\) −3.89573 −0.256877
\(231\) 0 0
\(232\) −28.9903 −1.90331
\(233\) 0.793355 0.0519744 0.0259872 0.999662i \(-0.491727\pi\)
0.0259872 + 0.999662i \(0.491727\pi\)
\(234\) 0 0
\(235\) 5.11252 0.333504
\(236\) 5.68833 0.370278
\(237\) 0 0
\(238\) 0 0
\(239\) −20.0488 −1.29685 −0.648425 0.761279i \(-0.724572\pi\)
−0.648425 + 0.761279i \(0.724572\pi\)
\(240\) 0 0
\(241\) 13.8120 0.889712 0.444856 0.895602i \(-0.353255\pi\)
0.444856 + 0.895602i \(0.353255\pi\)
\(242\) 26.9837 1.73458
\(243\) 0 0
\(244\) −67.8362 −4.34277
\(245\) 0 0
\(246\) 0 0
\(247\) 0.756906 0.0481608
\(248\) −9.60008 −0.609606
\(249\) 0 0
\(250\) −31.0922 −1.96644
\(251\) 26.1095 1.64802 0.824010 0.566576i \(-0.191732\pi\)
0.824010 + 0.566576i \(0.191732\pi\)
\(252\) 0 0
\(253\) −0.685057 −0.0430692
\(254\) −23.9526 −1.50292
\(255\) 0 0
\(256\) 38.6595 2.41622
\(257\) −10.6198 −0.662444 −0.331222 0.943553i \(-0.607461\pi\)
−0.331222 + 0.943553i \(0.607461\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −11.8697 −0.736128
\(261\) 0 0
\(262\) −28.6546 −1.77028
\(263\) −10.3578 −0.638686 −0.319343 0.947639i \(-0.603462\pi\)
−0.319343 + 0.947639i \(0.603462\pi\)
\(264\) 0 0
\(265\) 10.6912 0.656753
\(266\) 0 0
\(267\) 0 0
\(268\) 24.3069 1.48478
\(269\) −11.9701 −0.729827 −0.364914 0.931041i \(-0.618901\pi\)
−0.364914 + 0.931041i \(0.618901\pi\)
\(270\) 0 0
\(271\) −2.75691 −0.167470 −0.0837351 0.996488i \(-0.526685\pi\)
−0.0837351 + 0.996488i \(0.526685\pi\)
\(272\) 77.2429 4.68354
\(273\) 0 0
\(274\) 23.7959 1.43757
\(275\) −0.226731 −0.0136724
\(276\) 0 0
\(277\) −23.9275 −1.43766 −0.718831 0.695185i \(-0.755322\pi\)
−0.718831 + 0.695185i \(0.755322\pi\)
\(278\) 10.9010 0.653799
\(279\) 0 0
\(280\) 0 0
\(281\) 3.87870 0.231384 0.115692 0.993285i \(-0.463091\pi\)
0.115692 + 0.993285i \(0.463091\pi\)
\(282\) 0 0
\(283\) −6.20999 −0.369146 −0.184573 0.982819i \(-0.559090\pi\)
−0.184573 + 0.982819i \(0.559090\pi\)
\(284\) 35.8330 2.12630
\(285\) 0 0
\(286\) −2.85648 −0.168907
\(287\) 0 0
\(288\) 0 0
\(289\) 10.9973 0.646901
\(290\) 18.5021 1.08648
\(291\) 0 0
\(292\) −44.9543 −2.63075
\(293\) −16.5754 −0.968347 −0.484174 0.874972i \(-0.660880\pi\)
−0.484174 + 0.874972i \(0.660880\pi\)
\(294\) 0 0
\(295\) −2.29249 −0.133474
\(296\) 101.736 5.91330
\(297\) 0 0
\(298\) 41.9488 2.43003
\(299\) −0.653584 −0.0377977
\(300\) 0 0
\(301\) 0 0
\(302\) 37.2698 2.14463
\(303\) 0 0
\(304\) 11.0495 0.633732
\(305\) 27.3391 1.56543
\(306\) 0 0
\(307\) −7.05788 −0.402815 −0.201407 0.979508i \(-0.564551\pi\)
−0.201407 + 0.979508i \(0.564551\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.12694 0.347987
\(311\) −21.1102 −1.19705 −0.598525 0.801104i \(-0.704246\pi\)
−0.598525 + 0.801104i \(0.704246\pi\)
\(312\) 0 0
\(313\) 1.98052 0.111946 0.0559728 0.998432i \(-0.482174\pi\)
0.0559728 + 0.998432i \(0.482174\pi\)
\(314\) −9.23194 −0.520989
\(315\) 0 0
\(316\) 11.6145 0.653368
\(317\) 18.0459 1.01356 0.506781 0.862075i \(-0.330835\pi\)
0.506781 + 0.862075i \(0.330835\pi\)
\(318\) 0 0
\(319\) 3.25356 0.182164
\(320\) −61.9406 −3.46258
\(321\) 0 0
\(322\) 0 0
\(323\) 4.00498 0.222843
\(324\) 0 0
\(325\) −0.216314 −0.0119989
\(326\) 37.6358 2.08446
\(327\) 0 0
\(328\) 68.3682 3.77500
\(329\) 0 0
\(330\) 0 0
\(331\) −14.6738 −0.806544 −0.403272 0.915080i \(-0.632127\pi\)
−0.403272 + 0.915080i \(0.632127\pi\)
\(332\) 36.1740 1.98531
\(333\) 0 0
\(334\) 44.6349 2.44231
\(335\) −9.79606 −0.535216
\(336\) 0 0
\(337\) 12.8080 0.697698 0.348849 0.937179i \(-0.386573\pi\)
0.348849 + 0.937179i \(0.386573\pi\)
\(338\) −2.72525 −0.148234
\(339\) 0 0
\(340\) −62.8056 −3.40611
\(341\) 1.07741 0.0583451
\(342\) 0 0
\(343\) 0 0
\(344\) −8.29125 −0.447034
\(345\) 0 0
\(346\) 11.2429 0.604423
\(347\) −20.2054 −1.08468 −0.542342 0.840158i \(-0.682462\pi\)
−0.542342 + 0.840158i \(0.682462\pi\)
\(348\) 0 0
\(349\) −18.4434 −0.987252 −0.493626 0.869674i \(-0.664329\pi\)
−0.493626 + 0.869674i \(0.664329\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −22.1213 −1.17907
\(353\) 8.14436 0.433480 0.216740 0.976229i \(-0.430458\pi\)
0.216740 + 0.976229i \(0.430458\pi\)
\(354\) 0 0
\(355\) −14.4413 −0.766463
\(356\) 31.3016 1.65898
\(357\) 0 0
\(358\) 39.2806 2.07604
\(359\) 32.6100 1.72109 0.860545 0.509375i \(-0.170123\pi\)
0.860545 + 0.509375i \(0.170123\pi\)
\(360\) 0 0
\(361\) −18.4271 −0.969847
\(362\) −49.3308 −2.59277
\(363\) 0 0
\(364\) 0 0
\(365\) 18.1173 0.948304
\(366\) 0 0
\(367\) −3.16012 −0.164957 −0.0824786 0.996593i \(-0.526284\pi\)
−0.0824786 + 0.996593i \(0.526284\pi\)
\(368\) −9.54117 −0.497368
\(369\) 0 0
\(370\) −64.9298 −3.37554
\(371\) 0 0
\(372\) 0 0
\(373\) −1.47770 −0.0765123 −0.0382561 0.999268i \(-0.512180\pi\)
−0.0382561 + 0.999268i \(0.512180\pi\)
\(374\) −15.1144 −0.781545
\(375\) 0 0
\(376\) 21.8309 1.12584
\(377\) 3.10408 0.159868
\(378\) 0 0
\(379\) 10.7254 0.550927 0.275463 0.961312i \(-0.411169\pi\)
0.275463 + 0.961312i \(0.411169\pi\)
\(380\) −8.98426 −0.460883
\(381\) 0 0
\(382\) 15.1016 0.772664
\(383\) 21.4109 1.09405 0.547023 0.837118i \(-0.315761\pi\)
0.547023 + 0.837118i \(0.315761\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 23.8211 1.21246
\(387\) 0 0
\(388\) −15.6719 −0.795620
\(389\) −34.7819 −1.76351 −0.881755 0.471707i \(-0.843638\pi\)
−0.881755 + 0.471707i \(0.843638\pi\)
\(390\) 0 0
\(391\) −3.45828 −0.174893
\(392\) 0 0
\(393\) 0 0
\(394\) −14.9037 −0.750837
\(395\) −4.68084 −0.235519
\(396\) 0 0
\(397\) 4.45211 0.223445 0.111722 0.993739i \(-0.464363\pi\)
0.111722 + 0.993739i \(0.464363\pi\)
\(398\) −53.2426 −2.66881
\(399\) 0 0
\(400\) −3.15780 −0.157890
\(401\) 13.7537 0.686829 0.343415 0.939184i \(-0.388416\pi\)
0.343415 + 0.939184i \(0.388416\pi\)
\(402\) 0 0
\(403\) 1.02791 0.0512039
\(404\) 61.0771 3.03870
\(405\) 0 0
\(406\) 0 0
\(407\) −11.4178 −0.565959
\(408\) 0 0
\(409\) −3.49207 −0.172672 −0.0863358 0.996266i \(-0.527516\pi\)
−0.0863358 + 0.996266i \(0.527516\pi\)
\(410\) −43.6337 −2.15492
\(411\) 0 0
\(412\) 109.806 5.40977
\(413\) 0 0
\(414\) 0 0
\(415\) −14.5787 −0.715641
\(416\) −21.1050 −1.03476
\(417\) 0 0
\(418\) −2.16209 −0.105751
\(419\) 3.56737 0.174278 0.0871388 0.996196i \(-0.472228\pi\)
0.0871388 + 0.996196i \(0.472228\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −45.4858 −2.21422
\(423\) 0 0
\(424\) 45.6523 2.21707
\(425\) −1.14457 −0.0555198
\(426\) 0 0
\(427\) 0 0
\(428\) −49.1423 −2.37538
\(429\) 0 0
\(430\) 5.29162 0.255185
\(431\) 11.3642 0.547396 0.273698 0.961816i \(-0.411753\pi\)
0.273698 + 0.961816i \(0.411753\pi\)
\(432\) 0 0
\(433\) −21.2136 −1.01946 −0.509731 0.860334i \(-0.670255\pi\)
−0.509731 + 0.860334i \(0.670255\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 81.9551 3.92494
\(437\) −0.494702 −0.0236648
\(438\) 0 0
\(439\) −24.5007 −1.16935 −0.584676 0.811267i \(-0.698778\pi\)
−0.584676 + 0.811267i \(0.698778\pi\)
\(440\) 21.4105 1.02070
\(441\) 0 0
\(442\) −14.4200 −0.685888
\(443\) −40.4688 −1.92273 −0.961366 0.275274i \(-0.911231\pi\)
−0.961366 + 0.275274i \(0.911231\pi\)
\(444\) 0 0
\(445\) −12.6151 −0.598011
\(446\) 14.5587 0.689376
\(447\) 0 0
\(448\) 0 0
\(449\) 27.7638 1.31025 0.655127 0.755519i \(-0.272615\pi\)
0.655127 + 0.755519i \(0.272615\pi\)
\(450\) 0 0
\(451\) −7.67291 −0.361303
\(452\) −16.8458 −0.792361
\(453\) 0 0
\(454\) 54.8362 2.57359
\(455\) 0 0
\(456\) 0 0
\(457\) −11.1939 −0.523629 −0.261815 0.965118i \(-0.584321\pi\)
−0.261815 + 0.965118i \(0.584321\pi\)
\(458\) −68.8119 −3.21537
\(459\) 0 0
\(460\) 7.75786 0.361712
\(461\) 9.29773 0.433038 0.216519 0.976278i \(-0.430530\pi\)
0.216519 + 0.976278i \(0.430530\pi\)
\(462\) 0 0
\(463\) 28.2439 1.31260 0.656302 0.754499i \(-0.272120\pi\)
0.656302 + 0.754499i \(0.272120\pi\)
\(464\) 45.3142 2.10366
\(465\) 0 0
\(466\) −2.16209 −0.100157
\(467\) −22.2606 −1.03010 −0.515050 0.857160i \(-0.672227\pi\)
−0.515050 + 0.857160i \(0.672227\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −13.9329 −0.642676
\(471\) 0 0
\(472\) −9.78914 −0.450582
\(473\) 0.930521 0.0427854
\(474\) 0 0
\(475\) −0.163729 −0.00751242
\(476\) 0 0
\(477\) 0 0
\(478\) 54.6380 2.49909
\(479\) 32.8764 1.50216 0.751081 0.660210i \(-0.229533\pi\)
0.751081 + 0.660210i \(0.229533\pi\)
\(480\) 0 0
\(481\) −10.8932 −0.496688
\(482\) −37.6413 −1.71451
\(483\) 0 0
\(484\) −53.7346 −2.44248
\(485\) 6.31603 0.286796
\(486\) 0 0
\(487\) −27.8924 −1.26392 −0.631962 0.774999i \(-0.717750\pi\)
−0.631962 + 0.774999i \(0.717750\pi\)
\(488\) 116.741 5.28460
\(489\) 0 0
\(490\) 0 0
\(491\) −10.6571 −0.480948 −0.240474 0.970656i \(-0.577303\pi\)
−0.240474 + 0.970656i \(0.577303\pi\)
\(492\) 0 0
\(493\) 16.4245 0.739722
\(494\) −2.06276 −0.0928079
\(495\) 0 0
\(496\) 15.0057 0.673776
\(497\) 0 0
\(498\) 0 0
\(499\) −24.5114 −1.09728 −0.548641 0.836058i \(-0.684854\pi\)
−0.548641 + 0.836058i \(0.684854\pi\)
\(500\) 61.9162 2.76897
\(501\) 0 0
\(502\) −71.1550 −3.17580
\(503\) 38.0054 1.69458 0.847288 0.531134i \(-0.178234\pi\)
0.847288 + 0.531134i \(0.178234\pi\)
\(504\) 0 0
\(505\) −24.6151 −1.09536
\(506\) 1.86695 0.0829962
\(507\) 0 0
\(508\) 47.6986 2.11628
\(509\) −39.8501 −1.76632 −0.883161 0.469070i \(-0.844589\pi\)
−0.883161 + 0.469070i \(0.844589\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −35.4186 −1.56530
\(513\) 0 0
\(514\) 28.9416 1.27656
\(515\) −44.2537 −1.95005
\(516\) 0 0
\(517\) −2.45007 −0.107754
\(518\) 0 0
\(519\) 0 0
\(520\) 20.4268 0.895775
\(521\) 19.6334 0.860155 0.430077 0.902792i \(-0.358486\pi\)
0.430077 + 0.902792i \(0.358486\pi\)
\(522\) 0 0
\(523\) 22.8324 0.998391 0.499195 0.866489i \(-0.333629\pi\)
0.499195 + 0.866489i \(0.333629\pi\)
\(524\) 57.0619 2.49276
\(525\) 0 0
\(526\) 28.2275 1.23078
\(527\) 5.43894 0.236924
\(528\) 0 0
\(529\) −22.5728 −0.981427
\(530\) −29.1361 −1.26559
\(531\) 0 0
\(532\) 0 0
\(533\) −7.32040 −0.317082
\(534\) 0 0
\(535\) 19.8051 0.856251
\(536\) −41.8301 −1.80679
\(537\) 0 0
\(538\) 32.6214 1.40641
\(539\) 0 0
\(540\) 0 0
\(541\) −9.64668 −0.414743 −0.207372 0.978262i \(-0.566491\pi\)
−0.207372 + 0.978262i \(0.566491\pi\)
\(542\) 7.51326 0.322722
\(543\) 0 0
\(544\) −111.672 −4.78790
\(545\) −33.0292 −1.41482
\(546\) 0 0
\(547\) −43.8570 −1.87519 −0.937596 0.347728i \(-0.886953\pi\)
−0.937596 + 0.347728i \(0.886953\pi\)
\(548\) −47.3866 −2.02425
\(549\) 0 0
\(550\) 0.617897 0.0263472
\(551\) 2.34950 0.100092
\(552\) 0 0
\(553\) 0 0
\(554\) 65.2083 2.77044
\(555\) 0 0
\(556\) −21.7080 −0.920622
\(557\) −14.9195 −0.632161 −0.316080 0.948732i \(-0.602367\pi\)
−0.316080 + 0.948732i \(0.602367\pi\)
\(558\) 0 0
\(559\) 0.887771 0.0375487
\(560\) 0 0
\(561\) 0 0
\(562\) −10.5704 −0.445886
\(563\) 17.2697 0.727832 0.363916 0.931432i \(-0.381440\pi\)
0.363916 + 0.931432i \(0.381440\pi\)
\(564\) 0 0
\(565\) 6.78914 0.285621
\(566\) 16.9238 0.711359
\(567\) 0 0
\(568\) −61.6657 −2.58743
\(569\) −26.5324 −1.11230 −0.556148 0.831083i \(-0.687721\pi\)
−0.556148 + 0.831083i \(0.687721\pi\)
\(570\) 0 0
\(571\) −1.98569 −0.0830985 −0.0415492 0.999136i \(-0.513229\pi\)
−0.0415492 + 0.999136i \(0.513229\pi\)
\(572\) 5.68833 0.237841
\(573\) 0 0
\(574\) 0 0
\(575\) 0.141379 0.00589593
\(576\) 0 0
\(577\) 11.8983 0.495333 0.247666 0.968845i \(-0.420336\pi\)
0.247666 + 0.968845i \(0.420336\pi\)
\(578\) −29.9704 −1.24661
\(579\) 0 0
\(580\) −36.8446 −1.52989
\(581\) 0 0
\(582\) 0 0
\(583\) −5.12353 −0.212195
\(584\) 77.3627 3.20129
\(585\) 0 0
\(586\) 45.1722 1.86605
\(587\) −33.5122 −1.38320 −0.691598 0.722283i \(-0.743093\pi\)
−0.691598 + 0.722283i \(0.743093\pi\)
\(588\) 0 0
\(589\) 0.778033 0.0320583
\(590\) 6.24760 0.257210
\(591\) 0 0
\(592\) −159.022 −6.53576
\(593\) −35.2815 −1.44884 −0.724419 0.689360i \(-0.757892\pi\)
−0.724419 + 0.689360i \(0.757892\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −83.5357 −3.42176
\(597\) 0 0
\(598\) 1.78118 0.0728379
\(599\) 25.0068 1.02175 0.510876 0.859655i \(-0.329321\pi\)
0.510876 + 0.859655i \(0.329321\pi\)
\(600\) 0 0
\(601\) −28.4688 −1.16127 −0.580634 0.814165i \(-0.697195\pi\)
−0.580634 + 0.814165i \(0.697195\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −74.2180 −3.01989
\(605\) 21.6559 0.880438
\(606\) 0 0
\(607\) 36.0469 1.46310 0.731549 0.681789i \(-0.238798\pi\)
0.731549 + 0.681789i \(0.238798\pi\)
\(608\) −15.9745 −0.647853
\(609\) 0 0
\(610\) −74.5058 −3.01665
\(611\) −2.33751 −0.0945655
\(612\) 0 0
\(613\) 18.3253 0.740151 0.370075 0.929002i \(-0.379332\pi\)
0.370075 + 0.929002i \(0.379332\pi\)
\(614\) 19.2345 0.776241
\(615\) 0 0
\(616\) 0 0
\(617\) −44.3782 −1.78660 −0.893299 0.449463i \(-0.851615\pi\)
−0.893299 + 0.449463i \(0.851615\pi\)
\(618\) 0 0
\(619\) −25.0085 −1.00518 −0.502588 0.864526i \(-0.667619\pi\)
−0.502588 + 0.864526i \(0.667619\pi\)
\(620\) −12.2010 −0.490005
\(621\) 0 0
\(622\) 57.5306 2.30677
\(623\) 0 0
\(624\) 0 0
\(625\) −23.8716 −0.954866
\(626\) −5.39741 −0.215724
\(627\) 0 0
\(628\) 18.3842 0.733611
\(629\) −57.6388 −2.29821
\(630\) 0 0
\(631\) −18.4638 −0.735032 −0.367516 0.930017i \(-0.619792\pi\)
−0.367516 + 0.930017i \(0.619792\pi\)
\(632\) −19.9876 −0.795066
\(633\) 0 0
\(634\) −49.1797 −1.95318
\(635\) −19.2233 −0.762853
\(636\) 0 0
\(637\) 0 0
\(638\) −8.86677 −0.351039
\(639\) 0 0
\(640\) 76.4832 3.02326
\(641\) 21.2567 0.839589 0.419795 0.907619i \(-0.362102\pi\)
0.419795 + 0.907619i \(0.362102\pi\)
\(642\) 0 0
\(643\) −36.0554 −1.42188 −0.710942 0.703251i \(-0.751731\pi\)
−0.710942 + 0.703251i \(0.751731\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −10.9146 −0.429428
\(647\) −39.8234 −1.56562 −0.782809 0.622262i \(-0.786214\pi\)
−0.782809 + 0.622262i \(0.786214\pi\)
\(648\) 0 0
\(649\) 1.09863 0.0431250
\(650\) 0.589510 0.0231225
\(651\) 0 0
\(652\) −74.9469 −2.93515
\(653\) 32.4669 1.27053 0.635265 0.772295i \(-0.280891\pi\)
0.635265 + 0.772295i \(0.280891\pi\)
\(654\) 0 0
\(655\) −22.9969 −0.898562
\(656\) −106.865 −4.17237
\(657\) 0 0
\(658\) 0 0
\(659\) −23.5230 −0.916327 −0.458164 0.888868i \(-0.651493\pi\)
−0.458164 + 0.888868i \(0.651493\pi\)
\(660\) 0 0
\(661\) 14.0389 0.546049 0.273025 0.962007i \(-0.411976\pi\)
0.273025 + 0.962007i \(0.411976\pi\)
\(662\) 39.9897 1.55424
\(663\) 0 0
\(664\) −62.2525 −2.41587
\(665\) 0 0
\(666\) 0 0
\(667\) −2.02878 −0.0785547
\(668\) −88.8848 −3.43905
\(669\) 0 0
\(670\) 26.6967 1.03138
\(671\) −13.1017 −0.505786
\(672\) 0 0
\(673\) −47.1937 −1.81918 −0.909592 0.415502i \(-0.863606\pi\)
−0.909592 + 0.415502i \(0.863606\pi\)
\(674\) −34.9051 −1.34449
\(675\) 0 0
\(676\) 5.42699 0.208730
\(677\) 9.58876 0.368526 0.184263 0.982877i \(-0.441010\pi\)
0.184263 + 0.982877i \(0.441010\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 108.083 4.14481
\(681\) 0 0
\(682\) −2.93621 −0.112433
\(683\) −47.3161 −1.81050 −0.905250 0.424879i \(-0.860317\pi\)
−0.905250 + 0.424879i \(0.860317\pi\)
\(684\) 0 0
\(685\) 19.0976 0.729680
\(686\) 0 0
\(687\) 0 0
\(688\) 12.9599 0.494091
\(689\) −4.88814 −0.186223
\(690\) 0 0
\(691\) −27.1119 −1.03138 −0.515692 0.856774i \(-0.672465\pi\)
−0.515692 + 0.856774i \(0.672465\pi\)
\(692\) −22.3888 −0.851095
\(693\) 0 0
\(694\) 55.0648 2.09023
\(695\) 8.74866 0.331855
\(696\) 0 0
\(697\) −38.7340 −1.46716
\(698\) 50.2628 1.90248
\(699\) 0 0
\(700\) 0 0
\(701\) 1.79821 0.0679176 0.0339588 0.999423i \(-0.489189\pi\)
0.0339588 + 0.999423i \(0.489189\pi\)
\(702\) 0 0
\(703\) −8.24515 −0.310972
\(704\) 29.6838 1.11875
\(705\) 0 0
\(706\) −22.1954 −0.835336
\(707\) 0 0
\(708\) 0 0
\(709\) −28.3230 −1.06369 −0.531846 0.846841i \(-0.678502\pi\)
−0.531846 + 0.846841i \(0.678502\pi\)
\(710\) 39.3561 1.47701
\(711\) 0 0
\(712\) −53.8675 −2.01877
\(713\) −0.671827 −0.0251601
\(714\) 0 0
\(715\) −2.29249 −0.0857341
\(716\) −78.2223 −2.92331
\(717\) 0 0
\(718\) −88.8704 −3.31661
\(719\) 41.8971 1.56250 0.781249 0.624220i \(-0.214583\pi\)
0.781249 + 0.624220i \(0.214583\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 50.2184 1.86894
\(723\) 0 0
\(724\) 98.2361 3.65092
\(725\) −0.671457 −0.0249373
\(726\) 0 0
\(727\) 19.5123 0.723670 0.361835 0.932242i \(-0.382150\pi\)
0.361835 + 0.932242i \(0.382150\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −49.3742 −1.82742
\(731\) 4.69742 0.173740
\(732\) 0 0
\(733\) 17.7540 0.655757 0.327879 0.944720i \(-0.393666\pi\)
0.327879 + 0.944720i \(0.393666\pi\)
\(734\) 8.61213 0.317880
\(735\) 0 0
\(736\) 13.7939 0.508450
\(737\) 4.69457 0.172927
\(738\) 0 0
\(739\) 44.3142 1.63012 0.815061 0.579375i \(-0.196703\pi\)
0.815061 + 0.579375i \(0.196703\pi\)
\(740\) 129.299 4.75314
\(741\) 0 0
\(742\) 0 0
\(743\) 7.16727 0.262941 0.131471 0.991320i \(-0.458030\pi\)
0.131471 + 0.991320i \(0.458030\pi\)
\(744\) 0 0
\(745\) 33.6662 1.23344
\(746\) 4.02710 0.147442
\(747\) 0 0
\(748\) 30.0983 1.10050
\(749\) 0 0
\(750\) 0 0
\(751\) −33.9065 −1.23726 −0.618632 0.785681i \(-0.712313\pi\)
−0.618632 + 0.785681i \(0.712313\pi\)
\(752\) −34.1235 −1.24436
\(753\) 0 0
\(754\) −8.45941 −0.308073
\(755\) 29.9110 1.08857
\(756\) 0 0
\(757\) −0.906670 −0.0329535 −0.0164767 0.999864i \(-0.505245\pi\)
−0.0164767 + 0.999864i \(0.505245\pi\)
\(758\) −29.2294 −1.06166
\(759\) 0 0
\(760\) 15.4612 0.560836
\(761\) −20.2494 −0.734039 −0.367020 0.930213i \(-0.619622\pi\)
−0.367020 + 0.930213i \(0.619622\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −30.0729 −1.08800
\(765\) 0 0
\(766\) −58.3500 −2.10827
\(767\) 1.04815 0.0378467
\(768\) 0 0
\(769\) −36.9094 −1.33099 −0.665494 0.746403i \(-0.731779\pi\)
−0.665494 + 0.746403i \(0.731779\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −47.4367 −1.70728
\(773\) 9.88037 0.355372 0.177686 0.984087i \(-0.443139\pi\)
0.177686 + 0.984087i \(0.443139\pi\)
\(774\) 0 0
\(775\) −0.222352 −0.00798711
\(776\) 26.9701 0.968169
\(777\) 0 0
\(778\) 94.7893 3.39836
\(779\) −5.54086 −0.198522
\(780\) 0 0
\(781\) 6.92069 0.247642
\(782\) 9.42467 0.337025
\(783\) 0 0
\(784\) 0 0
\(785\) −7.40915 −0.264444
\(786\) 0 0
\(787\) 37.6821 1.34322 0.671611 0.740904i \(-0.265603\pi\)
0.671611 + 0.740904i \(0.265603\pi\)
\(788\) 29.6788 1.05726
\(789\) 0 0
\(790\) 12.7565 0.453854
\(791\) 0 0
\(792\) 0 0
\(793\) −12.4998 −0.443880
\(794\) −12.1331 −0.430588
\(795\) 0 0
\(796\) 106.026 3.75799
\(797\) −28.3837 −1.00540 −0.502701 0.864460i \(-0.667660\pi\)
−0.502701 + 0.864460i \(0.667660\pi\)
\(798\) 0 0
\(799\) −12.3683 −0.437560
\(800\) 4.56531 0.161408
\(801\) 0 0
\(802\) −37.4824 −1.32355
\(803\) −8.68236 −0.306394
\(804\) 0 0
\(805\) 0 0
\(806\) −2.80132 −0.0986722
\(807\) 0 0
\(808\) −105.109 −3.69771
\(809\) 11.7465 0.412987 0.206493 0.978448i \(-0.433795\pi\)
0.206493 + 0.978448i \(0.433795\pi\)
\(810\) 0 0
\(811\) 2.01940 0.0709108 0.0354554 0.999371i \(-0.488712\pi\)
0.0354554 + 0.999371i \(0.488712\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 31.1163 1.09063
\(815\) 30.2048 1.05803
\(816\) 0 0
\(817\) 0.671959 0.0235089
\(818\) 9.51676 0.332746
\(819\) 0 0
\(820\) 86.8910 3.03437
\(821\) 15.0842 0.526441 0.263220 0.964736i \(-0.415215\pi\)
0.263220 + 0.964736i \(0.415215\pi\)
\(822\) 0 0
\(823\) −14.7766 −0.515079 −0.257539 0.966268i \(-0.582912\pi\)
−0.257539 + 0.966268i \(0.582912\pi\)
\(824\) −188.968 −6.58301
\(825\) 0 0
\(826\) 0 0
\(827\) −13.0407 −0.453471 −0.226736 0.973956i \(-0.572805\pi\)
−0.226736 + 0.973956i \(0.572805\pi\)
\(828\) 0 0
\(829\) −25.4581 −0.884198 −0.442099 0.896966i \(-0.645766\pi\)
−0.442099 + 0.896966i \(0.645766\pi\)
\(830\) 39.7306 1.37907
\(831\) 0 0
\(832\) 28.3200 0.981820
\(833\) 0 0
\(834\) 0 0
\(835\) 35.8220 1.23967
\(836\) 4.30553 0.148910
\(837\) 0 0
\(838\) −9.72198 −0.335840
\(839\) −32.1703 −1.11064 −0.555321 0.831636i \(-0.687404\pi\)
−0.555321 + 0.831636i \(0.687404\pi\)
\(840\) 0 0
\(841\) −19.3647 −0.667747
\(842\) 27.2525 0.939183
\(843\) 0 0
\(844\) 90.5792 3.11787
\(845\) −2.18716 −0.0752407
\(846\) 0 0
\(847\) 0 0
\(848\) −71.3582 −2.45045
\(849\) 0 0
\(850\) 3.11924 0.106989
\(851\) 7.11964 0.244058
\(852\) 0 0
\(853\) −19.3910 −0.663934 −0.331967 0.943291i \(-0.607712\pi\)
−0.331967 + 0.943291i \(0.607712\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 84.5699 2.89054
\(857\) −17.4242 −0.595199 −0.297600 0.954691i \(-0.596186\pi\)
−0.297600 + 0.954691i \(0.596186\pi\)
\(858\) 0 0
\(859\) −35.4917 −1.21096 −0.605481 0.795860i \(-0.707019\pi\)
−0.605481 + 0.795860i \(0.707019\pi\)
\(860\) −10.5376 −0.359329
\(861\) 0 0
\(862\) −30.9704 −1.05486
\(863\) −56.0019 −1.90633 −0.953164 0.302455i \(-0.902194\pi\)
−0.953164 + 0.302455i \(0.902194\pi\)
\(864\) 0 0
\(865\) 9.02306 0.306793
\(866\) 57.8124 1.96455
\(867\) 0 0
\(868\) 0 0
\(869\) 2.24320 0.0760953
\(870\) 0 0
\(871\) 4.47889 0.151761
\(872\) −141.038 −4.77615
\(873\) 0 0
\(874\) 1.34819 0.0456031
\(875\) 0 0
\(876\) 0 0
\(877\) 25.2062 0.851153 0.425577 0.904922i \(-0.360071\pi\)
0.425577 + 0.904922i \(0.360071\pi\)
\(878\) 66.7704 2.25339
\(879\) 0 0
\(880\) −33.4663 −1.12815
\(881\) 18.6082 0.626925 0.313463 0.949601i \(-0.398511\pi\)
0.313463 + 0.949601i \(0.398511\pi\)
\(882\) 0 0
\(883\) −11.2552 −0.378768 −0.189384 0.981903i \(-0.560649\pi\)
−0.189384 + 0.981903i \(0.560649\pi\)
\(884\) 28.7155 0.965808
\(885\) 0 0
\(886\) 110.288 3.70519
\(887\) 39.2112 1.31658 0.658292 0.752762i \(-0.271279\pi\)
0.658292 + 0.752762i \(0.271279\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 34.3792 1.15239
\(891\) 0 0
\(892\) −28.9919 −0.970720
\(893\) −1.76928 −0.0592066
\(894\) 0 0
\(895\) 31.5249 1.05376
\(896\) 0 0
\(897\) 0 0
\(898\) −75.6633 −2.52492
\(899\) 3.19073 0.106417
\(900\) 0 0
\(901\) −25.8644 −0.861667
\(902\) 20.9106 0.696247
\(903\) 0 0
\(904\) 28.9903 0.964203
\(905\) −39.5907 −1.31604
\(906\) 0 0
\(907\) 21.5970 0.717116 0.358558 0.933508i \(-0.383269\pi\)
0.358558 + 0.933508i \(0.383269\pi\)
\(908\) −109.199 −3.62391
\(909\) 0 0
\(910\) 0 0
\(911\) 32.4434 1.07490 0.537449 0.843297i \(-0.319388\pi\)
0.537449 + 0.843297i \(0.319388\pi\)
\(912\) 0 0
\(913\) 6.98656 0.231221
\(914\) 30.5062 1.00906
\(915\) 0 0
\(916\) 137.030 4.52760
\(917\) 0 0
\(918\) 0 0
\(919\) 35.7372 1.17886 0.589430 0.807819i \(-0.299352\pi\)
0.589430 + 0.807819i \(0.299352\pi\)
\(920\) −13.3506 −0.440157
\(921\) 0 0
\(922\) −25.3386 −0.834483
\(923\) 6.60274 0.217332
\(924\) 0 0
\(925\) 2.35636 0.0774765
\(926\) −76.9716 −2.52944
\(927\) 0 0
\(928\) −65.5118 −2.15053
\(929\) −11.7769 −0.386389 −0.193194 0.981161i \(-0.561885\pi\)
−0.193194 + 0.981161i \(0.561885\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 4.30553 0.141032
\(933\) 0 0
\(934\) 60.6658 1.98505
\(935\) −12.1301 −0.396697
\(936\) 0 0
\(937\) 18.9937 0.620497 0.310248 0.950655i \(-0.399588\pi\)
0.310248 + 0.950655i \(0.399588\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 27.7456 0.904961
\(941\) −6.81864 −0.222281 −0.111141 0.993805i \(-0.535450\pi\)
−0.111141 + 0.993805i \(0.535450\pi\)
\(942\) 0 0
\(943\) 4.78450 0.155805
\(944\) 15.3012 0.498012
\(945\) 0 0
\(946\) −2.53590 −0.0824493
\(947\) −1.05992 −0.0344426 −0.0172213 0.999852i \(-0.505482\pi\)
−0.0172213 + 0.999852i \(0.505482\pi\)
\(948\) 0 0
\(949\) −8.28347 −0.268893
\(950\) 0.446204 0.0144768
\(951\) 0 0
\(952\) 0 0
\(953\) 40.4127 1.30910 0.654548 0.756020i \(-0.272859\pi\)
0.654548 + 0.756020i \(0.272859\pi\)
\(954\) 0 0
\(955\) 12.1199 0.392189
\(956\) −108.805 −3.51899
\(957\) 0 0
\(958\) −89.5964 −2.89473
\(959\) 0 0
\(960\) 0 0
\(961\) −29.9434 −0.965916
\(962\) 29.6868 0.957140
\(963\) 0 0
\(964\) 74.9578 2.41423
\(965\) 19.1177 0.615422
\(966\) 0 0
\(967\) −36.2949 −1.16717 −0.583583 0.812053i \(-0.698350\pi\)
−0.583583 + 0.812053i \(0.698350\pi\)
\(968\) 92.4729 2.97219
\(969\) 0 0
\(970\) −17.2128 −0.552668
\(971\) 21.4437 0.688160 0.344080 0.938940i \(-0.388191\pi\)
0.344080 + 0.938940i \(0.388191\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 76.0137 2.43564
\(975\) 0 0
\(976\) −182.475 −5.84088
\(977\) 39.8277 1.27420 0.637100 0.770781i \(-0.280134\pi\)
0.637100 + 0.770781i \(0.280134\pi\)
\(978\) 0 0
\(979\) 6.04551 0.193215
\(980\) 0 0
\(981\) 0 0
\(982\) 29.0432 0.926807
\(983\) −15.8814 −0.506538 −0.253269 0.967396i \(-0.581506\pi\)
−0.253269 + 0.967396i \(0.581506\pi\)
\(984\) 0 0
\(985\) −11.9610 −0.381110
\(986\) −44.7608 −1.42548
\(987\) 0 0
\(988\) 4.10772 0.130684
\(989\) −0.580233 −0.0184503
\(990\) 0 0
\(991\) −17.6687 −0.561265 −0.280633 0.959815i \(-0.590544\pi\)
−0.280633 + 0.959815i \(0.590544\pi\)
\(992\) −21.6941 −0.688789
\(993\) 0 0
\(994\) 0 0
\(995\) −42.7301 −1.35464
\(996\) 0 0
\(997\) −24.8608 −0.787350 −0.393675 0.919250i \(-0.628797\pi\)
−0.393675 + 0.919250i \(0.628797\pi\)
\(998\) 66.7997 2.11451
\(999\) 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 5733.2.a.bl.1.1 5
3.2 odd 2 637.2.a.l.1.5 5
7.2 even 3 819.2.j.h.235.5 10
7.4 even 3 819.2.j.h.352.5 10
7.6 odd 2 5733.2.a.bm.1.1 5
21.2 odd 6 91.2.e.c.53.1 10
21.5 even 6 637.2.e.m.508.1 10
21.11 odd 6 91.2.e.c.79.1 yes 10
21.17 even 6 637.2.e.m.79.1 10
21.20 even 2 637.2.a.k.1.5 5
39.38 odd 2 8281.2.a.bw.1.1 5
84.11 even 6 1456.2.r.p.625.2 10
84.23 even 6 1456.2.r.p.417.2 10
273.116 odd 6 1183.2.e.f.170.5 10
273.233 odd 6 1183.2.e.f.508.5 10
273.272 even 2 8281.2.a.bx.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.1 10 21.2 odd 6
91.2.e.c.79.1 yes 10 21.11 odd 6
637.2.a.k.1.5 5 21.20 even 2
637.2.a.l.1.5 5 3.2 odd 2
637.2.e.m.79.1 10 21.17 even 6
637.2.e.m.508.1 10 21.5 even 6
819.2.j.h.235.5 10 7.2 even 3
819.2.j.h.352.5 10 7.4 even 3
1183.2.e.f.170.5 10 273.116 odd 6
1183.2.e.f.508.5 10 273.233 odd 6
1456.2.r.p.417.2 10 84.23 even 6
1456.2.r.p.625.2 10 84.11 even 6
5733.2.a.bl.1.1 5 1.1 even 1 trivial
5733.2.a.bm.1.1 5 7.6 odd 2
8281.2.a.bw.1.1 5 39.38 odd 2
8281.2.a.bx.1.1 5 273.272 even 2