Properties

Label 5225.2.a.m.1.2
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $7$
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] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 10x^{5} + 8x^{4} + 27x^{3} - 16x^{2} - 18x + 11 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.97792\) of defining polynomial
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.97792 q^{2} -2.65412 q^{3} +1.91218 q^{4} +5.24965 q^{6} -1.06653 q^{7} +0.173707 q^{8} +4.04436 q^{9} +O(q^{10})\) \(q-1.97792 q^{2} -2.65412 q^{3} +1.91218 q^{4} +5.24965 q^{6} -1.06653 q^{7} +0.173707 q^{8} +4.04436 q^{9} +1.00000 q^{11} -5.07515 q^{12} -0.939291 q^{13} +2.10952 q^{14} -4.16793 q^{16} -3.65839 q^{17} -7.99944 q^{18} -1.00000 q^{19} +2.83071 q^{21} -1.97792 q^{22} -5.35035 q^{23} -0.461041 q^{24} +1.85784 q^{26} -2.77187 q^{27} -2.03940 q^{28} -4.46966 q^{29} -2.71979 q^{31} +7.89643 q^{32} -2.65412 q^{33} +7.23600 q^{34} +7.73354 q^{36} -0.932050 q^{37} +1.97792 q^{38} +2.49299 q^{39} -1.21816 q^{41} -5.59893 q^{42} +3.58402 q^{43} +1.91218 q^{44} +10.5826 q^{46} +4.30223 q^{47} +11.0622 q^{48} -5.86250 q^{49} +9.70980 q^{51} -1.79609 q^{52} +12.1575 q^{53} +5.48254 q^{54} -0.185265 q^{56} +2.65412 q^{57} +8.84063 q^{58} -6.15610 q^{59} +2.13701 q^{61} +5.37953 q^{62} -4.31345 q^{63} -7.28267 q^{64} +5.24965 q^{66} -4.93275 q^{67} -6.99548 q^{68} +14.2005 q^{69} +7.32299 q^{71} +0.702536 q^{72} -1.14496 q^{73} +1.84352 q^{74} -1.91218 q^{76} -1.06653 q^{77} -4.93095 q^{78} -6.71067 q^{79} -4.77622 q^{81} +2.40943 q^{82} -2.82737 q^{83} +5.41282 q^{84} -7.08891 q^{86} +11.8630 q^{87} +0.173707 q^{88} -8.77091 q^{89} +1.00179 q^{91} -10.2308 q^{92} +7.21866 q^{93} -8.50948 q^{94} -20.9581 q^{96} -13.3420 q^{97} +11.5956 q^{98} +4.04436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + q^{7} - 3 q^{8} + 2 q^{9} + 7 q^{11} - 13 q^{12} - q^{13} + 12 q^{14} + 3 q^{16} - q^{17} - 7 q^{18} - 7 q^{19} + 5 q^{21} - q^{22} + 8 q^{23} + 25 q^{24} - 12 q^{27} - 4 q^{28} + 11 q^{29} + 7 q^{31} - 12 q^{32} - 3 q^{33} - 14 q^{34} + 7 q^{36} + 17 q^{37} + q^{38} + 30 q^{39} + 17 q^{41} - 33 q^{42} + 3 q^{43} + 7 q^{44} + 18 q^{46} - 14 q^{47} + 12 q^{48} + 6 q^{49} + 8 q^{51} + 17 q^{52} - 7 q^{53} - 27 q^{54} + 36 q^{56} + 3 q^{57} + 15 q^{58} + 35 q^{59} + 17 q^{61} - 46 q^{62} + 22 q^{63} + 5 q^{64} + 8 q^{66} - 4 q^{67} + 35 q^{68} - 4 q^{69} + 10 q^{71} - 12 q^{72} - 22 q^{73} - 11 q^{74} - 7 q^{76} + q^{77} + 41 q^{78} + 11 q^{79} - 21 q^{81} + 14 q^{82} - 39 q^{83} + 21 q^{84} - 24 q^{86} + 2 q^{87} - 3 q^{88} + 18 q^{89} - 22 q^{91} + 51 q^{92} - 10 q^{93} + 14 q^{94} - 11 q^{96} + 4 q^{97} + 26 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97792 −1.39860 −0.699301 0.714827i \(-0.746505\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(3\) −2.65412 −1.53236 −0.766179 0.642627i \(-0.777844\pi\)
−0.766179 + 0.642627i \(0.777844\pi\)
\(4\) 1.91218 0.956088
\(5\) 0 0
\(6\) 5.24965 2.14316
\(7\) −1.06653 −0.403112 −0.201556 0.979477i \(-0.564600\pi\)
−0.201556 + 0.979477i \(0.564600\pi\)
\(8\) 0.173707 0.0614148
\(9\) 4.04436 1.34812
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) −5.07515 −1.46507
\(13\) −0.939291 −0.260512 −0.130256 0.991480i \(-0.541580\pi\)
−0.130256 + 0.991480i \(0.541580\pi\)
\(14\) 2.10952 0.563794
\(15\) 0 0
\(16\) −4.16793 −1.04198
\(17\) −3.65839 −0.887289 −0.443645 0.896203i \(-0.646315\pi\)
−0.443645 + 0.896203i \(0.646315\pi\)
\(18\) −7.99944 −1.88549
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 2.83071 0.617712
\(22\) −1.97792 −0.421694
\(23\) −5.35035 −1.11563 −0.557813 0.829967i \(-0.688359\pi\)
−0.557813 + 0.829967i \(0.688359\pi\)
\(24\) −0.461041 −0.0941095
\(25\) 0 0
\(26\) 1.85784 0.364353
\(27\) −2.77187 −0.533446
\(28\) −2.03940 −0.385411
\(29\) −4.46966 −0.829994 −0.414997 0.909823i \(-0.636217\pi\)
−0.414997 + 0.909823i \(0.636217\pi\)
\(30\) 0 0
\(31\) −2.71979 −0.488489 −0.244244 0.969714i \(-0.578540\pi\)
−0.244244 + 0.969714i \(0.578540\pi\)
\(32\) 7.89643 1.39591
\(33\) −2.65412 −0.462023
\(34\) 7.23600 1.24096
\(35\) 0 0
\(36\) 7.73354 1.28892
\(37\) −0.932050 −0.153228 −0.0766141 0.997061i \(-0.524411\pi\)
−0.0766141 + 0.997061i \(0.524411\pi\)
\(38\) 1.97792 0.320861
\(39\) 2.49299 0.399198
\(40\) 0 0
\(41\) −1.21816 −0.190245 −0.0951227 0.995466i \(-0.530324\pi\)
−0.0951227 + 0.995466i \(0.530324\pi\)
\(42\) −5.59893 −0.863934
\(43\) 3.58402 0.546558 0.273279 0.961935i \(-0.411892\pi\)
0.273279 + 0.961935i \(0.411892\pi\)
\(44\) 1.91218 0.288272
\(45\) 0 0
\(46\) 10.5826 1.56032
\(47\) 4.30223 0.627545 0.313772 0.949498i \(-0.398407\pi\)
0.313772 + 0.949498i \(0.398407\pi\)
\(48\) 11.0622 1.59669
\(49\) −5.86250 −0.837501
\(50\) 0 0
\(51\) 9.70980 1.35964
\(52\) −1.79609 −0.249073
\(53\) 12.1575 1.66996 0.834980 0.550280i \(-0.185479\pi\)
0.834980 + 0.550280i \(0.185479\pi\)
\(54\) 5.48254 0.746079
\(55\) 0 0
\(56\) −0.185265 −0.0247571
\(57\) 2.65412 0.351547
\(58\) 8.84063 1.16083
\(59\) −6.15610 −0.801456 −0.400728 0.916197i \(-0.631243\pi\)
−0.400728 + 0.916197i \(0.631243\pi\)
\(60\) 0 0
\(61\) 2.13701 0.273616 0.136808 0.990598i \(-0.456316\pi\)
0.136808 + 0.990598i \(0.456316\pi\)
\(62\) 5.37953 0.683202
\(63\) −4.31345 −0.543444
\(64\) −7.28267 −0.910333
\(65\) 0 0
\(66\) 5.24965 0.646187
\(67\) −4.93275 −0.602631 −0.301315 0.953525i \(-0.597426\pi\)
−0.301315 + 0.953525i \(0.597426\pi\)
\(68\) −6.99548 −0.848327
\(69\) 14.2005 1.70954
\(70\) 0 0
\(71\) 7.32299 0.869079 0.434539 0.900653i \(-0.356911\pi\)
0.434539 + 0.900653i \(0.356911\pi\)
\(72\) 0.702536 0.0827946
\(73\) −1.14496 −0.134008 −0.0670038 0.997753i \(-0.521344\pi\)
−0.0670038 + 0.997753i \(0.521344\pi\)
\(74\) 1.84352 0.214305
\(75\) 0 0
\(76\) −1.91218 −0.219342
\(77\) −1.06653 −0.121543
\(78\) −4.93095 −0.558320
\(79\) −6.71067 −0.755009 −0.377505 0.926008i \(-0.623218\pi\)
−0.377505 + 0.926008i \(0.623218\pi\)
\(80\) 0 0
\(81\) −4.77622 −0.530691
\(82\) 2.40943 0.266078
\(83\) −2.82737 −0.310344 −0.155172 0.987887i \(-0.549593\pi\)
−0.155172 + 0.987887i \(0.549593\pi\)
\(84\) 5.41282 0.590588
\(85\) 0 0
\(86\) −7.08891 −0.764417
\(87\) 11.8630 1.27185
\(88\) 0.173707 0.0185173
\(89\) −8.77091 −0.929714 −0.464857 0.885386i \(-0.653894\pi\)
−0.464857 + 0.885386i \(0.653894\pi\)
\(90\) 0 0
\(91\) 1.00179 0.105016
\(92\) −10.2308 −1.06664
\(93\) 7.21866 0.748540
\(94\) −8.50948 −0.877686
\(95\) 0 0
\(96\) −20.9581 −2.13903
\(97\) −13.3420 −1.35468 −0.677339 0.735671i \(-0.736867\pi\)
−0.677339 + 0.735671i \(0.736867\pi\)
\(98\) 11.5956 1.17133
\(99\) 4.04436 0.406474
\(100\) 0 0
\(101\) −0.926286 −0.0921689 −0.0460845 0.998938i \(-0.514674\pi\)
−0.0460845 + 0.998938i \(0.514674\pi\)
\(102\) −19.2052 −1.90160
\(103\) 10.4344 1.02814 0.514068 0.857749i \(-0.328138\pi\)
0.514068 + 0.857749i \(0.328138\pi\)
\(104\) −0.163162 −0.0159993
\(105\) 0 0
\(106\) −24.0466 −2.33561
\(107\) −13.5595 −1.31085 −0.655426 0.755260i \(-0.727511\pi\)
−0.655426 + 0.755260i \(0.727511\pi\)
\(108\) −5.30030 −0.510022
\(109\) 5.85440 0.560750 0.280375 0.959891i \(-0.409541\pi\)
0.280375 + 0.959891i \(0.409541\pi\)
\(110\) 0 0
\(111\) 2.47378 0.234800
\(112\) 4.44525 0.420036
\(113\) −8.68686 −0.817191 −0.408595 0.912716i \(-0.633981\pi\)
−0.408595 + 0.912716i \(0.633981\pi\)
\(114\) −5.24965 −0.491674
\(115\) 0 0
\(116\) −8.54677 −0.793548
\(117\) −3.79883 −0.351202
\(118\) 12.1763 1.12092
\(119\) 3.90180 0.357677
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −4.22684 −0.382680
\(123\) 3.23316 0.291524
\(124\) −5.20072 −0.467039
\(125\) 0 0
\(126\) 8.53168 0.760062
\(127\) 15.9545 1.41573 0.707866 0.706347i \(-0.249658\pi\)
0.707866 + 0.706347i \(0.249658\pi\)
\(128\) −1.38832 −0.122711
\(129\) −9.51242 −0.837522
\(130\) 0 0
\(131\) 5.20014 0.454338 0.227169 0.973855i \(-0.427053\pi\)
0.227169 + 0.973855i \(0.427053\pi\)
\(132\) −5.07515 −0.441735
\(133\) 1.06653 0.0924803
\(134\) 9.75659 0.842841
\(135\) 0 0
\(136\) −0.635489 −0.0544927
\(137\) −7.54419 −0.644544 −0.322272 0.946647i \(-0.604447\pi\)
−0.322272 + 0.946647i \(0.604447\pi\)
\(138\) −28.0875 −2.39096
\(139\) 0.357301 0.0303059 0.0151529 0.999885i \(-0.495176\pi\)
0.0151529 + 0.999885i \(0.495176\pi\)
\(140\) 0 0
\(141\) −11.4186 −0.961624
\(142\) −14.4843 −1.21550
\(143\) −0.939291 −0.0785475
\(144\) −16.8566 −1.40472
\(145\) 0 0
\(146\) 2.26465 0.187423
\(147\) 15.5598 1.28335
\(148\) −1.78224 −0.146500
\(149\) −10.7634 −0.881769 −0.440884 0.897564i \(-0.645335\pi\)
−0.440884 + 0.897564i \(0.645335\pi\)
\(150\) 0 0
\(151\) 7.13976 0.581025 0.290513 0.956871i \(-0.406174\pi\)
0.290513 + 0.956871i \(0.406174\pi\)
\(152\) −0.173707 −0.0140895
\(153\) −14.7958 −1.19617
\(154\) 2.10952 0.169990
\(155\) 0 0
\(156\) 4.76704 0.381669
\(157\) −12.7164 −1.01488 −0.507440 0.861687i \(-0.669408\pi\)
−0.507440 + 0.861687i \(0.669408\pi\)
\(158\) 13.2732 1.05596
\(159\) −32.2675 −2.55898
\(160\) 0 0
\(161\) 5.70633 0.449722
\(162\) 9.44699 0.742225
\(163\) 4.45308 0.348792 0.174396 0.984676i \(-0.444203\pi\)
0.174396 + 0.984676i \(0.444203\pi\)
\(164\) −2.32935 −0.181891
\(165\) 0 0
\(166\) 5.59231 0.434047
\(167\) −10.0911 −0.780874 −0.390437 0.920630i \(-0.627676\pi\)
−0.390437 + 0.920630i \(0.627676\pi\)
\(168\) 0.491716 0.0379367
\(169\) −12.1177 −0.932133
\(170\) 0 0
\(171\) −4.04436 −0.309280
\(172\) 6.85328 0.522558
\(173\) −23.8006 −1.80952 −0.904762 0.425917i \(-0.859952\pi\)
−0.904762 + 0.425917i \(0.859952\pi\)
\(174\) −23.4641 −1.77881
\(175\) 0 0
\(176\) −4.16793 −0.314170
\(177\) 16.3390 1.22812
\(178\) 17.3482 1.30030
\(179\) 20.0682 1.49997 0.749985 0.661455i \(-0.230061\pi\)
0.749985 + 0.661455i \(0.230061\pi\)
\(180\) 0 0
\(181\) 7.49807 0.557327 0.278663 0.960389i \(-0.410109\pi\)
0.278663 + 0.960389i \(0.410109\pi\)
\(182\) −1.98146 −0.146875
\(183\) −5.67188 −0.419278
\(184\) −0.929396 −0.0685160
\(185\) 0 0
\(186\) −14.2779 −1.04691
\(187\) −3.65839 −0.267528
\(188\) 8.22663 0.599988
\(189\) 2.95629 0.215039
\(190\) 0 0
\(191\) −4.21863 −0.305250 −0.152625 0.988284i \(-0.548773\pi\)
−0.152625 + 0.988284i \(0.548773\pi\)
\(192\) 19.3291 1.39496
\(193\) −7.70714 −0.554772 −0.277386 0.960759i \(-0.589468\pi\)
−0.277386 + 0.960759i \(0.589468\pi\)
\(194\) 26.3895 1.89465
\(195\) 0 0
\(196\) −11.2101 −0.800725
\(197\) −18.4285 −1.31298 −0.656489 0.754336i \(-0.727959\pi\)
−0.656489 + 0.754336i \(0.727959\pi\)
\(198\) −7.99944 −0.568495
\(199\) −21.6489 −1.53465 −0.767324 0.641260i \(-0.778412\pi\)
−0.767324 + 0.641260i \(0.778412\pi\)
\(200\) 0 0
\(201\) 13.0921 0.923446
\(202\) 1.83212 0.128908
\(203\) 4.76704 0.334581
\(204\) 18.5669 1.29994
\(205\) 0 0
\(206\) −20.6385 −1.43795
\(207\) −21.6388 −1.50400
\(208\) 3.91490 0.271450
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) 23.9164 1.64647 0.823235 0.567700i \(-0.192167\pi\)
0.823235 + 0.567700i \(0.192167\pi\)
\(212\) 23.2473 1.59663
\(213\) −19.4361 −1.33174
\(214\) 26.8197 1.83336
\(215\) 0 0
\(216\) −0.481494 −0.0327615
\(217\) 2.90075 0.196916
\(218\) −11.5795 −0.784266
\(219\) 3.03887 0.205348
\(220\) 0 0
\(221\) 3.43629 0.231150
\(222\) −4.89294 −0.328392
\(223\) −4.18886 −0.280506 −0.140253 0.990116i \(-0.544792\pi\)
−0.140253 + 0.990116i \(0.544792\pi\)
\(224\) −8.42182 −0.562707
\(225\) 0 0
\(226\) 17.1819 1.14292
\(227\) 8.74816 0.580636 0.290318 0.956930i \(-0.406239\pi\)
0.290318 + 0.956930i \(0.406239\pi\)
\(228\) 5.07515 0.336110
\(229\) −16.8146 −1.11114 −0.555571 0.831469i \(-0.687500\pi\)
−0.555571 + 0.831469i \(0.687500\pi\)
\(230\) 0 0
\(231\) 2.83071 0.186247
\(232\) −0.776412 −0.0509740
\(233\) 7.41167 0.485554 0.242777 0.970082i \(-0.421942\pi\)
0.242777 + 0.970082i \(0.421942\pi\)
\(234\) 7.51380 0.491192
\(235\) 0 0
\(236\) −11.7716 −0.766263
\(237\) 17.8109 1.15694
\(238\) −7.71745 −0.500248
\(239\) −19.7326 −1.27640 −0.638199 0.769871i \(-0.720320\pi\)
−0.638199 + 0.769871i \(0.720320\pi\)
\(240\) 0 0
\(241\) 15.0994 0.972640 0.486320 0.873781i \(-0.338339\pi\)
0.486320 + 0.873781i \(0.338339\pi\)
\(242\) −1.97792 −0.127146
\(243\) 20.9923 1.34665
\(244\) 4.08634 0.261601
\(245\) 0 0
\(246\) −6.39493 −0.407726
\(247\) 0.939291 0.0597657
\(248\) −0.472448 −0.0300005
\(249\) 7.50417 0.475558
\(250\) 0 0
\(251\) 12.3858 0.781782 0.390891 0.920437i \(-0.372167\pi\)
0.390891 + 0.920437i \(0.372167\pi\)
\(252\) −8.24809 −0.519581
\(253\) −5.35035 −0.336374
\(254\) −31.5567 −1.98005
\(255\) 0 0
\(256\) 17.3113 1.08196
\(257\) −26.5496 −1.65612 −0.828060 0.560639i \(-0.810555\pi\)
−0.828060 + 0.560639i \(0.810555\pi\)
\(258\) 18.8148 1.17136
\(259\) 0.994064 0.0617681
\(260\) 0 0
\(261\) −18.0769 −1.11893
\(262\) −10.2855 −0.635438
\(263\) −15.0108 −0.925604 −0.462802 0.886462i \(-0.653156\pi\)
−0.462802 + 0.886462i \(0.653156\pi\)
\(264\) −0.461041 −0.0283751
\(265\) 0 0
\(266\) −2.10952 −0.129343
\(267\) 23.2791 1.42466
\(268\) −9.43228 −0.576168
\(269\) 11.8307 0.721329 0.360664 0.932696i \(-0.382550\pi\)
0.360664 + 0.932696i \(0.382550\pi\)
\(270\) 0 0
\(271\) −13.4154 −0.814927 −0.407464 0.913221i \(-0.633587\pi\)
−0.407464 + 0.913221i \(0.633587\pi\)
\(272\) 15.2479 0.924540
\(273\) −2.65886 −0.160922
\(274\) 14.9218 0.901461
\(275\) 0 0
\(276\) 27.1538 1.63447
\(277\) 0.515992 0.0310030 0.0155015 0.999880i \(-0.495066\pi\)
0.0155015 + 0.999880i \(0.495066\pi\)
\(278\) −0.706713 −0.0423859
\(279\) −10.9998 −0.658542
\(280\) 0 0
\(281\) 21.9281 1.30812 0.654061 0.756441i \(-0.273064\pi\)
0.654061 + 0.756441i \(0.273064\pi\)
\(282\) 22.5852 1.34493
\(283\) −18.6023 −1.10579 −0.552896 0.833250i \(-0.686478\pi\)
−0.552896 + 0.833250i \(0.686478\pi\)
\(284\) 14.0028 0.830916
\(285\) 0 0
\(286\) 1.85784 0.109857
\(287\) 1.29921 0.0766902
\(288\) 31.9360 1.88185
\(289\) −3.61621 −0.212718
\(290\) 0 0
\(291\) 35.4114 2.07585
\(292\) −2.18937 −0.128123
\(293\) 5.87287 0.343097 0.171548 0.985176i \(-0.445123\pi\)
0.171548 + 0.985176i \(0.445123\pi\)
\(294\) −30.7761 −1.79490
\(295\) 0 0
\(296\) −0.161904 −0.00941048
\(297\) −2.77187 −0.160840
\(298\) 21.2891 1.23324
\(299\) 5.02554 0.290634
\(300\) 0 0
\(301\) −3.82248 −0.220324
\(302\) −14.1219 −0.812623
\(303\) 2.45848 0.141236
\(304\) 4.16793 0.239047
\(305\) 0 0
\(306\) 29.2650 1.67297
\(307\) −0.566566 −0.0323356 −0.0161678 0.999869i \(-0.505147\pi\)
−0.0161678 + 0.999869i \(0.505147\pi\)
\(308\) −2.03940 −0.116206
\(309\) −27.6943 −1.57547
\(310\) 0 0
\(311\) −22.1715 −1.25723 −0.628616 0.777716i \(-0.716378\pi\)
−0.628616 + 0.777716i \(0.716378\pi\)
\(312\) 0.433051 0.0245167
\(313\) 30.3230 1.71396 0.856979 0.515351i \(-0.172338\pi\)
0.856979 + 0.515351i \(0.172338\pi\)
\(314\) 25.1521 1.41941
\(315\) 0 0
\(316\) −12.8320 −0.721856
\(317\) 13.6662 0.767569 0.383785 0.923423i \(-0.374621\pi\)
0.383785 + 0.923423i \(0.374621\pi\)
\(318\) 63.8225 3.57899
\(319\) −4.46966 −0.250253
\(320\) 0 0
\(321\) 35.9887 2.00869
\(322\) −11.2867 −0.628982
\(323\) 3.65839 0.203558
\(324\) −9.13297 −0.507387
\(325\) 0 0
\(326\) −8.80785 −0.487822
\(327\) −15.5383 −0.859269
\(328\) −0.211604 −0.0116839
\(329\) −4.58848 −0.252971
\(330\) 0 0
\(331\) 1.04337 0.0573489 0.0286745 0.999589i \(-0.490871\pi\)
0.0286745 + 0.999589i \(0.490871\pi\)
\(332\) −5.40642 −0.296716
\(333\) −3.76955 −0.206570
\(334\) 19.9595 1.09213
\(335\) 0 0
\(336\) −11.7982 −0.643646
\(337\) 32.3936 1.76459 0.882296 0.470696i \(-0.155997\pi\)
0.882296 + 0.470696i \(0.155997\pi\)
\(338\) 23.9679 1.30368
\(339\) 23.0560 1.25223
\(340\) 0 0
\(341\) −2.71979 −0.147285
\(342\) 7.99944 0.432560
\(343\) 13.7183 0.740719
\(344\) 0.622571 0.0335668
\(345\) 0 0
\(346\) 47.0757 2.53081
\(347\) −0.837115 −0.0449387 −0.0224693 0.999748i \(-0.507153\pi\)
−0.0224693 + 0.999748i \(0.507153\pi\)
\(348\) 22.6842 1.21600
\(349\) −1.98491 −0.106250 −0.0531250 0.998588i \(-0.516918\pi\)
−0.0531250 + 0.998588i \(0.516918\pi\)
\(350\) 0 0
\(351\) 2.60359 0.138969
\(352\) 7.89643 0.420881
\(353\) −0.0707574 −0.00376604 −0.00188302 0.999998i \(-0.500599\pi\)
−0.00188302 + 0.999998i \(0.500599\pi\)
\(354\) −32.3174 −1.71765
\(355\) 0 0
\(356\) −16.7715 −0.888889
\(357\) −10.3558 −0.548089
\(358\) −39.6934 −2.09786
\(359\) −23.4992 −1.24024 −0.620120 0.784507i \(-0.712916\pi\)
−0.620120 + 0.784507i \(0.712916\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −14.8306 −0.779479
\(363\) −2.65412 −0.139305
\(364\) 1.91559 0.100404
\(365\) 0 0
\(366\) 11.2185 0.586403
\(367\) 16.4763 0.860057 0.430029 0.902815i \(-0.358503\pi\)
0.430029 + 0.902815i \(0.358503\pi\)
\(368\) 22.2999 1.16246
\(369\) −4.92670 −0.256474
\(370\) 0 0
\(371\) −12.9664 −0.673181
\(372\) 13.8033 0.715670
\(373\) −1.92401 −0.0996217 −0.0498108 0.998759i \(-0.515862\pi\)
−0.0498108 + 0.998759i \(0.515862\pi\)
\(374\) 7.23600 0.374165
\(375\) 0 0
\(376\) 0.747330 0.0385406
\(377\) 4.19831 0.216224
\(378\) −5.84732 −0.300753
\(379\) −29.8162 −1.53156 −0.765779 0.643104i \(-0.777646\pi\)
−0.765779 + 0.643104i \(0.777646\pi\)
\(380\) 0 0
\(381\) −42.3452 −2.16941
\(382\) 8.34413 0.426923
\(383\) 19.4719 0.994969 0.497484 0.867473i \(-0.334257\pi\)
0.497484 + 0.867473i \(0.334257\pi\)
\(384\) 3.68477 0.188038
\(385\) 0 0
\(386\) 15.2441 0.775906
\(387\) 14.4951 0.736826
\(388\) −25.5123 −1.29519
\(389\) −11.7829 −0.597415 −0.298708 0.954345i \(-0.596556\pi\)
−0.298708 + 0.954345i \(0.596556\pi\)
\(390\) 0 0
\(391\) 19.5737 0.989882
\(392\) −1.01836 −0.0514350
\(393\) −13.8018 −0.696208
\(394\) 36.4502 1.83633
\(395\) 0 0
\(396\) 7.73354 0.388625
\(397\) −35.1177 −1.76251 −0.881254 0.472643i \(-0.843300\pi\)
−0.881254 + 0.472643i \(0.843300\pi\)
\(398\) 42.8198 2.14636
\(399\) −2.83071 −0.141713
\(400\) 0 0
\(401\) 27.0103 1.34883 0.674414 0.738353i \(-0.264396\pi\)
0.674414 + 0.738353i \(0.264396\pi\)
\(402\) −25.8952 −1.29153
\(403\) 2.55468 0.127257
\(404\) −1.77122 −0.0881216
\(405\) 0 0
\(406\) −9.42884 −0.467946
\(407\) −0.932050 −0.0462000
\(408\) 1.68667 0.0835024
\(409\) 33.0664 1.63503 0.817515 0.575907i \(-0.195351\pi\)
0.817515 + 0.575907i \(0.195351\pi\)
\(410\) 0 0
\(411\) 20.0232 0.987672
\(412\) 19.9525 0.982989
\(413\) 6.56570 0.323077
\(414\) 42.7998 2.10349
\(415\) 0 0
\(416\) −7.41705 −0.363651
\(417\) −0.948320 −0.0464394
\(418\) 1.97792 0.0967433
\(419\) 7.98503 0.390094 0.195047 0.980794i \(-0.437514\pi\)
0.195047 + 0.980794i \(0.437514\pi\)
\(420\) 0 0
\(421\) −28.8735 −1.40721 −0.703604 0.710592i \(-0.748427\pi\)
−0.703604 + 0.710592i \(0.748427\pi\)
\(422\) −47.3047 −2.30276
\(423\) 17.3998 0.846007
\(424\) 2.11185 0.102560
\(425\) 0 0
\(426\) 38.4431 1.86257
\(427\) −2.27919 −0.110298
\(428\) −25.9283 −1.25329
\(429\) 2.49299 0.120363
\(430\) 0 0
\(431\) 27.5088 1.32505 0.662527 0.749038i \(-0.269484\pi\)
0.662527 + 0.749038i \(0.269484\pi\)
\(432\) 11.5530 0.555842
\(433\) 33.5624 1.61291 0.806453 0.591299i \(-0.201385\pi\)
0.806453 + 0.591299i \(0.201385\pi\)
\(434\) −5.73746 −0.275407
\(435\) 0 0
\(436\) 11.1946 0.536126
\(437\) 5.35035 0.255942
\(438\) −6.01065 −0.287200
\(439\) 25.8608 1.23427 0.617134 0.786858i \(-0.288294\pi\)
0.617134 + 0.786858i \(0.288294\pi\)
\(440\) 0 0
\(441\) −23.7101 −1.12905
\(442\) −6.79672 −0.323287
\(443\) −2.34708 −0.111513 −0.0557566 0.998444i \(-0.517757\pi\)
−0.0557566 + 0.998444i \(0.517757\pi\)
\(444\) 4.73030 0.224490
\(445\) 0 0
\(446\) 8.28523 0.392317
\(447\) 28.5673 1.35119
\(448\) 7.76722 0.366966
\(449\) 18.4815 0.872195 0.436097 0.899899i \(-0.356360\pi\)
0.436097 + 0.899899i \(0.356360\pi\)
\(450\) 0 0
\(451\) −1.21816 −0.0573611
\(452\) −16.6108 −0.781307
\(453\) −18.9498 −0.890339
\(454\) −17.3032 −0.812079
\(455\) 0 0
\(456\) 0.461041 0.0215902
\(457\) −17.1365 −0.801612 −0.400806 0.916163i \(-0.631270\pi\)
−0.400806 + 0.916163i \(0.631270\pi\)
\(458\) 33.2581 1.55405
\(459\) 10.1406 0.473321
\(460\) 0 0
\(461\) −16.3205 −0.760122 −0.380061 0.924961i \(-0.624097\pi\)
−0.380061 + 0.924961i \(0.624097\pi\)
\(462\) −5.59893 −0.260486
\(463\) 18.2993 0.850441 0.425220 0.905090i \(-0.360197\pi\)
0.425220 + 0.905090i \(0.360197\pi\)
\(464\) 18.6292 0.864840
\(465\) 0 0
\(466\) −14.6597 −0.679098
\(467\) −3.89977 −0.180460 −0.0902299 0.995921i \(-0.528760\pi\)
−0.0902299 + 0.995921i \(0.528760\pi\)
\(468\) −7.26404 −0.335780
\(469\) 5.26094 0.242928
\(470\) 0 0
\(471\) 33.7509 1.55516
\(472\) −1.06936 −0.0492213
\(473\) 3.58402 0.164793
\(474\) −35.2286 −1.61811
\(475\) 0 0
\(476\) 7.46092 0.341971
\(477\) 49.1693 2.25131
\(478\) 39.0296 1.78517
\(479\) 16.4447 0.751377 0.375688 0.926746i \(-0.377406\pi\)
0.375688 + 0.926746i \(0.377406\pi\)
\(480\) 0 0
\(481\) 0.875467 0.0399178
\(482\) −29.8655 −1.36034
\(483\) −15.1453 −0.689135
\(484\) 1.91218 0.0869171
\(485\) 0 0
\(486\) −41.5211 −1.88343
\(487\) 28.4329 1.28842 0.644209 0.764849i \(-0.277187\pi\)
0.644209 + 0.764849i \(0.277187\pi\)
\(488\) 0.371214 0.0168041
\(489\) −11.8190 −0.534475
\(490\) 0 0
\(491\) −6.25955 −0.282490 −0.141245 0.989975i \(-0.545110\pi\)
−0.141245 + 0.989975i \(0.545110\pi\)
\(492\) 6.18237 0.278723
\(493\) 16.3517 0.736445
\(494\) −1.85784 −0.0835884
\(495\) 0 0
\(496\) 11.3359 0.508997
\(497\) −7.81022 −0.350336
\(498\) −14.8427 −0.665116
\(499\) −10.4851 −0.469378 −0.234689 0.972070i \(-0.575407\pi\)
−0.234689 + 0.972070i \(0.575407\pi\)
\(500\) 0 0
\(501\) 26.7831 1.19658
\(502\) −24.4981 −1.09340
\(503\) −18.4277 −0.821651 −0.410825 0.911714i \(-0.634759\pi\)
−0.410825 + 0.911714i \(0.634759\pi\)
\(504\) −0.749279 −0.0333755
\(505\) 0 0
\(506\) 10.5826 0.470453
\(507\) 32.1619 1.42836
\(508\) 30.5078 1.35357
\(509\) 14.0013 0.620596 0.310298 0.950639i \(-0.399571\pi\)
0.310298 + 0.950639i \(0.399571\pi\)
\(510\) 0 0
\(511\) 1.22114 0.0540201
\(512\) −31.4638 −1.39052
\(513\) 2.77187 0.122381
\(514\) 52.5131 2.31625
\(515\) 0 0
\(516\) −18.1894 −0.800745
\(517\) 4.30223 0.189212
\(518\) −1.96618 −0.0863891
\(519\) 63.1696 2.77284
\(520\) 0 0
\(521\) −36.3013 −1.59039 −0.795195 0.606353i \(-0.792632\pi\)
−0.795195 + 0.606353i \(0.792632\pi\)
\(522\) 35.7547 1.56494
\(523\) −23.2657 −1.01734 −0.508669 0.860962i \(-0.669862\pi\)
−0.508669 + 0.860962i \(0.669862\pi\)
\(524\) 9.94358 0.434387
\(525\) 0 0
\(526\) 29.6901 1.29455
\(527\) 9.95005 0.433431
\(528\) 11.0622 0.481421
\(529\) 5.62625 0.244620
\(530\) 0 0
\(531\) −24.8975 −1.08046
\(532\) 2.03940 0.0884193
\(533\) 1.14421 0.0495613
\(534\) −46.0442 −1.99253
\(535\) 0 0
\(536\) −0.856854 −0.0370105
\(537\) −53.2635 −2.29849
\(538\) −23.4001 −1.00885
\(539\) −5.86250 −0.252516
\(540\) 0 0
\(541\) 30.6302 1.31689 0.658447 0.752627i \(-0.271214\pi\)
0.658447 + 0.752627i \(0.271214\pi\)
\(542\) 26.5346 1.13976
\(543\) −19.9008 −0.854024
\(544\) −28.8882 −1.23857
\(545\) 0 0
\(546\) 5.25903 0.225066
\(547\) 14.9225 0.638040 0.319020 0.947748i \(-0.396646\pi\)
0.319020 + 0.947748i \(0.396646\pi\)
\(548\) −14.4258 −0.616241
\(549\) 8.64284 0.368867
\(550\) 0 0
\(551\) 4.46966 0.190414
\(552\) 2.46673 0.104991
\(553\) 7.15716 0.304354
\(554\) −1.02059 −0.0433608
\(555\) 0 0
\(556\) 0.683222 0.0289751
\(557\) −8.54485 −0.362057 −0.181028 0.983478i \(-0.557943\pi\)
−0.181028 + 0.983478i \(0.557943\pi\)
\(558\) 21.7568 0.921038
\(559\) −3.36644 −0.142385
\(560\) 0 0
\(561\) 9.70980 0.409948
\(562\) −43.3721 −1.82954
\(563\) −17.7855 −0.749571 −0.374786 0.927111i \(-0.622284\pi\)
−0.374786 + 0.927111i \(0.622284\pi\)
\(564\) −21.8345 −0.919397
\(565\) 0 0
\(566\) 36.7939 1.54656
\(567\) 5.09400 0.213928
\(568\) 1.27206 0.0533743
\(569\) −29.7657 −1.24785 −0.623923 0.781486i \(-0.714462\pi\)
−0.623923 + 0.781486i \(0.714462\pi\)
\(570\) 0 0
\(571\) 22.2184 0.929810 0.464905 0.885360i \(-0.346088\pi\)
0.464905 + 0.885360i \(0.346088\pi\)
\(572\) −1.79609 −0.0750983
\(573\) 11.1968 0.467752
\(574\) −2.56975 −0.107259
\(575\) 0 0
\(576\) −29.4537 −1.22724
\(577\) 12.0936 0.503464 0.251732 0.967797i \(-0.419000\pi\)
0.251732 + 0.967797i \(0.419000\pi\)
\(578\) 7.15258 0.297508
\(579\) 20.4557 0.850110
\(580\) 0 0
\(581\) 3.01548 0.125103
\(582\) −70.0409 −2.90329
\(583\) 12.1575 0.503512
\(584\) −0.198888 −0.00823006
\(585\) 0 0
\(586\) −11.6161 −0.479856
\(587\) 14.3554 0.592510 0.296255 0.955109i \(-0.404262\pi\)
0.296255 + 0.955109i \(0.404262\pi\)
\(588\) 29.7531 1.22700
\(589\) 2.71979 0.112067
\(590\) 0 0
\(591\) 48.9115 2.01195
\(592\) 3.88472 0.159661
\(593\) −7.64570 −0.313971 −0.156986 0.987601i \(-0.550178\pi\)
−0.156986 + 0.987601i \(0.550178\pi\)
\(594\) 5.48254 0.224951
\(595\) 0 0
\(596\) −20.5814 −0.843049
\(597\) 57.4587 2.35163
\(598\) −9.94012 −0.406482
\(599\) 22.5450 0.921165 0.460583 0.887617i \(-0.347641\pi\)
0.460583 + 0.887617i \(0.347641\pi\)
\(600\) 0 0
\(601\) 8.27574 0.337574 0.168787 0.985653i \(-0.446015\pi\)
0.168787 + 0.985653i \(0.446015\pi\)
\(602\) 7.56057 0.308146
\(603\) −19.9498 −0.812419
\(604\) 13.6525 0.555511
\(605\) 0 0
\(606\) −4.86267 −0.197533
\(607\) 12.8552 0.521778 0.260889 0.965369i \(-0.415984\pi\)
0.260889 + 0.965369i \(0.415984\pi\)
\(608\) −7.89643 −0.320243
\(609\) −12.6523 −0.512698
\(610\) 0 0
\(611\) −4.04105 −0.163483
\(612\) −28.2923 −1.14365
\(613\) 17.0191 0.687394 0.343697 0.939081i \(-0.388321\pi\)
0.343697 + 0.939081i \(0.388321\pi\)
\(614\) 1.12062 0.0452247
\(615\) 0 0
\(616\) −0.185265 −0.00746454
\(617\) −21.5265 −0.866625 −0.433313 0.901244i \(-0.642655\pi\)
−0.433313 + 0.901244i \(0.642655\pi\)
\(618\) 54.7771 2.20346
\(619\) 34.9987 1.40672 0.703359 0.710835i \(-0.251683\pi\)
0.703359 + 0.710835i \(0.251683\pi\)
\(620\) 0 0
\(621\) 14.8305 0.595126
\(622\) 43.8536 1.75837
\(623\) 9.35448 0.374779
\(624\) −10.3906 −0.415958
\(625\) 0 0
\(626\) −59.9766 −2.39715
\(627\) 2.65412 0.105995
\(628\) −24.3160 −0.970315
\(629\) 3.40980 0.135958
\(630\) 0 0
\(631\) 26.6365 1.06038 0.530191 0.847878i \(-0.322120\pi\)
0.530191 + 0.847878i \(0.322120\pi\)
\(632\) −1.16569 −0.0463688
\(633\) −63.4769 −2.52298
\(634\) −27.0306 −1.07352
\(635\) 0 0
\(636\) −61.7011 −2.44661
\(637\) 5.50660 0.218179
\(638\) 8.84063 0.350004
\(639\) 29.6168 1.17162
\(640\) 0 0
\(641\) −18.3904 −0.726376 −0.363188 0.931716i \(-0.618312\pi\)
−0.363188 + 0.931716i \(0.618312\pi\)
\(642\) −71.1828 −2.80936
\(643\) −10.1583 −0.400603 −0.200302 0.979734i \(-0.564192\pi\)
−0.200302 + 0.979734i \(0.564192\pi\)
\(644\) 10.9115 0.429974
\(645\) 0 0
\(646\) −7.23600 −0.284697
\(647\) −24.9283 −0.980034 −0.490017 0.871713i \(-0.663009\pi\)
−0.490017 + 0.871713i \(0.663009\pi\)
\(648\) −0.829664 −0.0325923
\(649\) −6.15610 −0.241648
\(650\) 0 0
\(651\) −7.69895 −0.301746
\(652\) 8.51508 0.333476
\(653\) −3.18346 −0.124579 −0.0622893 0.998058i \(-0.519840\pi\)
−0.0622893 + 0.998058i \(0.519840\pi\)
\(654\) 30.7335 1.20178
\(655\) 0 0
\(656\) 5.07723 0.198232
\(657\) −4.63064 −0.180659
\(658\) 9.07566 0.353806
\(659\) 44.5078 1.73378 0.866888 0.498503i \(-0.166117\pi\)
0.866888 + 0.498503i \(0.166117\pi\)
\(660\) 0 0
\(661\) 5.31054 0.206556 0.103278 0.994653i \(-0.467067\pi\)
0.103278 + 0.994653i \(0.467067\pi\)
\(662\) −2.06371 −0.0802083
\(663\) −9.12033 −0.354204
\(664\) −0.491134 −0.0190597
\(665\) 0 0
\(666\) 7.45588 0.288909
\(667\) 23.9142 0.925963
\(668\) −19.2960 −0.746585
\(669\) 11.1177 0.429836
\(670\) 0 0
\(671\) 2.13701 0.0824983
\(672\) 22.3525 0.862268
\(673\) 27.9535 1.07753 0.538765 0.842456i \(-0.318891\pi\)
0.538765 + 0.842456i \(0.318891\pi\)
\(674\) −64.0720 −2.46796
\(675\) 0 0
\(676\) −23.1712 −0.891202
\(677\) 41.9276 1.61141 0.805704 0.592319i \(-0.201787\pi\)
0.805704 + 0.592319i \(0.201787\pi\)
\(678\) −45.6029 −1.75137
\(679\) 14.2297 0.546087
\(680\) 0 0
\(681\) −23.2187 −0.889742
\(682\) 5.37953 0.205993
\(683\) −21.6527 −0.828516 −0.414258 0.910159i \(-0.635959\pi\)
−0.414258 + 0.910159i \(0.635959\pi\)
\(684\) −7.73354 −0.295699
\(685\) 0 0
\(686\) −27.1337 −1.03597
\(687\) 44.6281 1.70267
\(688\) −14.9380 −0.569504
\(689\) −11.4194 −0.435045
\(690\) 0 0
\(691\) 45.5121 1.73136 0.865681 0.500597i \(-0.166886\pi\)
0.865681 + 0.500597i \(0.166886\pi\)
\(692\) −45.5109 −1.73007
\(693\) −4.31345 −0.163855
\(694\) 1.65575 0.0628514
\(695\) 0 0
\(696\) 2.06069 0.0781104
\(697\) 4.45652 0.168803
\(698\) 3.92601 0.148602
\(699\) −19.6715 −0.744043
\(700\) 0 0
\(701\) −27.3430 −1.03273 −0.516365 0.856369i \(-0.672715\pi\)
−0.516365 + 0.856369i \(0.672715\pi\)
\(702\) −5.14970 −0.194363
\(703\) 0.932050 0.0351529
\(704\) −7.28267 −0.274476
\(705\) 0 0
\(706\) 0.139953 0.00526719
\(707\) 0.987916 0.0371544
\(708\) 31.2431 1.17419
\(709\) 3.38760 0.127224 0.0636120 0.997975i \(-0.479738\pi\)
0.0636120 + 0.997975i \(0.479738\pi\)
\(710\) 0 0
\(711\) −27.1404 −1.01784
\(712\) −1.52357 −0.0570983
\(713\) 14.5518 0.544970
\(714\) 20.4831 0.766559
\(715\) 0 0
\(716\) 38.3740 1.43410
\(717\) 52.3728 1.95590
\(718\) 46.4796 1.73460
\(719\) 33.5021 1.24942 0.624709 0.780858i \(-0.285218\pi\)
0.624709 + 0.780858i \(0.285218\pi\)
\(720\) 0 0
\(721\) −11.1287 −0.414454
\(722\) −1.97792 −0.0736106
\(723\) −40.0757 −1.49043
\(724\) 14.3376 0.532854
\(725\) 0 0
\(726\) 5.24965 0.194833
\(727\) 45.5324 1.68871 0.844353 0.535788i \(-0.179985\pi\)
0.844353 + 0.535788i \(0.179985\pi\)
\(728\) 0.174018 0.00644953
\(729\) −41.3874 −1.53287
\(730\) 0 0
\(731\) −13.1117 −0.484955
\(732\) −10.8456 −0.400866
\(733\) 4.71433 0.174128 0.0870640 0.996203i \(-0.472252\pi\)
0.0870640 + 0.996203i \(0.472252\pi\)
\(734\) −32.5889 −1.20288
\(735\) 0 0
\(736\) −42.2487 −1.55731
\(737\) −4.93275 −0.181700
\(738\) 9.74463 0.358705
\(739\) 35.7265 1.31422 0.657110 0.753795i \(-0.271779\pi\)
0.657110 + 0.753795i \(0.271779\pi\)
\(740\) 0 0
\(741\) −2.49299 −0.0915824
\(742\) 25.6465 0.941513
\(743\) 26.9341 0.988118 0.494059 0.869428i \(-0.335513\pi\)
0.494059 + 0.869428i \(0.335513\pi\)
\(744\) 1.25393 0.0459715
\(745\) 0 0
\(746\) 3.80555 0.139331
\(747\) −11.4349 −0.418381
\(748\) −6.99548 −0.255780
\(749\) 14.4617 0.528420
\(750\) 0 0
\(751\) −27.7767 −1.01358 −0.506792 0.862068i \(-0.669169\pi\)
−0.506792 + 0.862068i \(0.669169\pi\)
\(752\) −17.9314 −0.653891
\(753\) −32.8733 −1.19797
\(754\) −8.30393 −0.302411
\(755\) 0 0
\(756\) 5.65295 0.205596
\(757\) 23.4521 0.852380 0.426190 0.904634i \(-0.359855\pi\)
0.426190 + 0.904634i \(0.359855\pi\)
\(758\) 58.9742 2.14204
\(759\) 14.2005 0.515445
\(760\) 0 0
\(761\) −15.9940 −0.579783 −0.289892 0.957059i \(-0.593619\pi\)
−0.289892 + 0.957059i \(0.593619\pi\)
\(762\) 83.7554 3.03414
\(763\) −6.24392 −0.226045
\(764\) −8.06678 −0.291846
\(765\) 0 0
\(766\) −38.5139 −1.39157
\(767\) 5.78237 0.208789
\(768\) −45.9464 −1.65795
\(769\) 19.9815 0.720552 0.360276 0.932846i \(-0.382683\pi\)
0.360276 + 0.932846i \(0.382683\pi\)
\(770\) 0 0
\(771\) 70.4659 2.53777
\(772\) −14.7374 −0.530411
\(773\) −53.4366 −1.92198 −0.960991 0.276581i \(-0.910799\pi\)
−0.960991 + 0.276581i \(0.910799\pi\)
\(774\) −28.6701 −1.03053
\(775\) 0 0
\(776\) −2.31761 −0.0831973
\(777\) −2.63837 −0.0946509
\(778\) 23.3056 0.835546
\(779\) 1.21816 0.0436453
\(780\) 0 0
\(781\) 7.32299 0.262037
\(782\) −38.7152 −1.38445
\(783\) 12.3893 0.442757
\(784\) 24.4345 0.872662
\(785\) 0 0
\(786\) 27.2989 0.973719
\(787\) −6.90402 −0.246102 −0.123051 0.992400i \(-0.539268\pi\)
−0.123051 + 0.992400i \(0.539268\pi\)
\(788\) −35.2386 −1.25532
\(789\) 39.8404 1.41836
\(790\) 0 0
\(791\) 9.26484 0.329420
\(792\) 0.702536 0.0249635
\(793\) −2.00727 −0.0712804
\(794\) 69.4601 2.46505
\(795\) 0 0
\(796\) −41.3965 −1.46726
\(797\) −28.5820 −1.01243 −0.506213 0.862409i \(-0.668955\pi\)
−0.506213 + 0.862409i \(0.668955\pi\)
\(798\) 5.59893 0.198200
\(799\) −15.7392 −0.556814
\(800\) 0 0
\(801\) −35.4727 −1.25337
\(802\) −53.4242 −1.88647
\(803\) −1.14496 −0.0404048
\(804\) 25.0344 0.882896
\(805\) 0 0
\(806\) −5.05295 −0.177983
\(807\) −31.4000 −1.10533
\(808\) −0.160903 −0.00566054
\(809\) 45.3303 1.59373 0.796864 0.604158i \(-0.206491\pi\)
0.796864 + 0.604158i \(0.206491\pi\)
\(810\) 0 0
\(811\) 11.1668 0.392119 0.196060 0.980592i \(-0.437185\pi\)
0.196060 + 0.980592i \(0.437185\pi\)
\(812\) 9.11543 0.319889
\(813\) 35.6061 1.24876
\(814\) 1.84352 0.0646155
\(815\) 0 0
\(816\) −40.4698 −1.41673
\(817\) −3.58402 −0.125389
\(818\) −65.4029 −2.28676
\(819\) 4.05159 0.141574
\(820\) 0 0
\(821\) −23.2715 −0.812180 −0.406090 0.913833i \(-0.633108\pi\)
−0.406090 + 0.913833i \(0.633108\pi\)
\(822\) −39.6044 −1.38136
\(823\) 36.1529 1.26021 0.630105 0.776510i \(-0.283012\pi\)
0.630105 + 0.776510i \(0.283012\pi\)
\(824\) 1.81254 0.0631428
\(825\) 0 0
\(826\) −12.9864 −0.451856
\(827\) −10.7797 −0.374848 −0.187424 0.982279i \(-0.560014\pi\)
−0.187424 + 0.982279i \(0.560014\pi\)
\(828\) −41.3771 −1.43795
\(829\) −42.2859 −1.46865 −0.734326 0.678797i \(-0.762501\pi\)
−0.734326 + 0.678797i \(0.762501\pi\)
\(830\) 0 0
\(831\) −1.36951 −0.0475076
\(832\) 6.84054 0.237153
\(833\) 21.4473 0.743105
\(834\) 1.87570 0.0649503
\(835\) 0 0
\(836\) −1.91218 −0.0661340
\(837\) 7.53890 0.260582
\(838\) −15.7938 −0.545587
\(839\) 27.2267 0.939971 0.469986 0.882674i \(-0.344259\pi\)
0.469986 + 0.882674i \(0.344259\pi\)
\(840\) 0 0
\(841\) −9.02217 −0.311109
\(842\) 57.1095 1.96812
\(843\) −58.1999 −2.00451
\(844\) 45.7323 1.57417
\(845\) 0 0
\(846\) −34.4154 −1.18323
\(847\) −1.06653 −0.0366466
\(848\) −50.6716 −1.74007
\(849\) 49.3728 1.69447
\(850\) 0 0
\(851\) 4.98680 0.170945
\(852\) −37.1653 −1.27326
\(853\) 11.3022 0.386981 0.193490 0.981102i \(-0.438019\pi\)
0.193490 + 0.981102i \(0.438019\pi\)
\(854\) 4.50807 0.154263
\(855\) 0 0
\(856\) −2.35539 −0.0805057
\(857\) −1.20558 −0.0411817 −0.0205908 0.999788i \(-0.506555\pi\)
−0.0205908 + 0.999788i \(0.506555\pi\)
\(858\) −4.93095 −0.168340
\(859\) 28.1617 0.960865 0.480432 0.877032i \(-0.340480\pi\)
0.480432 + 0.877032i \(0.340480\pi\)
\(860\) 0 0
\(861\) −3.44827 −0.117517
\(862\) −54.4103 −1.85322
\(863\) −8.48764 −0.288923 −0.144461 0.989510i \(-0.546145\pi\)
−0.144461 + 0.989510i \(0.546145\pi\)
\(864\) −21.8879 −0.744640
\(865\) 0 0
\(866\) −66.3838 −2.25581
\(867\) 9.59785 0.325960
\(868\) 5.54675 0.188269
\(869\) −6.71067 −0.227644
\(870\) 0 0
\(871\) 4.63328 0.156993
\(872\) 1.01695 0.0344383
\(873\) −53.9600 −1.82627
\(874\) −10.5826 −0.357961
\(875\) 0 0
\(876\) 5.81086 0.196331
\(877\) −34.1439 −1.15296 −0.576478 0.817112i \(-0.695573\pi\)
−0.576478 + 0.817112i \(0.695573\pi\)
\(878\) −51.1506 −1.72625
\(879\) −15.5873 −0.525747
\(880\) 0 0
\(881\) −42.0557 −1.41689 −0.708446 0.705765i \(-0.750603\pi\)
−0.708446 + 0.705765i \(0.750603\pi\)
\(882\) 46.8967 1.57909
\(883\) 12.9984 0.437430 0.218715 0.975789i \(-0.429813\pi\)
0.218715 + 0.975789i \(0.429813\pi\)
\(884\) 6.57079 0.221000
\(885\) 0 0
\(886\) 4.64235 0.155963
\(887\) −58.3513 −1.95925 −0.979623 0.200847i \(-0.935631\pi\)
−0.979623 + 0.200847i \(0.935631\pi\)
\(888\) 0.429713 0.0144202
\(889\) −17.0160 −0.570699
\(890\) 0 0
\(891\) −4.77622 −0.160009
\(892\) −8.00983 −0.268189
\(893\) −4.30223 −0.143969
\(894\) −56.5038 −1.88977
\(895\) 0 0
\(896\) 1.48069 0.0494664
\(897\) −13.3384 −0.445356
\(898\) −36.5549 −1.21985
\(899\) 12.1565 0.405443
\(900\) 0 0
\(901\) −44.4768 −1.48174
\(902\) 2.40943 0.0802254
\(903\) 10.1453 0.337615
\(904\) −1.50897 −0.0501876
\(905\) 0 0
\(906\) 37.4812 1.24523
\(907\) 58.8388 1.95371 0.976855 0.213904i \(-0.0686181\pi\)
0.976855 + 0.213904i \(0.0686181\pi\)
\(908\) 16.7280 0.555139
\(909\) −3.74624 −0.124255
\(910\) 0 0
\(911\) −23.1241 −0.766137 −0.383068 0.923720i \(-0.625133\pi\)
−0.383068 + 0.923720i \(0.625133\pi\)
\(912\) −11.0622 −0.366306
\(913\) −2.82737 −0.0935721
\(914\) 33.8947 1.12114
\(915\) 0 0
\(916\) −32.1526 −1.06235
\(917\) −5.54613 −0.183149
\(918\) −20.0572 −0.661988
\(919\) −32.2210 −1.06287 −0.531437 0.847098i \(-0.678348\pi\)
−0.531437 + 0.847098i \(0.678348\pi\)
\(920\) 0 0
\(921\) 1.50374 0.0495498
\(922\) 32.2807 1.06311
\(923\) −6.87842 −0.226406
\(924\) 5.41282 0.178069
\(925\) 0 0
\(926\) −36.1946 −1.18943
\(927\) 42.2007 1.38605
\(928\) −35.2943 −1.15859
\(929\) −0.527392 −0.0173032 −0.00865158 0.999963i \(-0.502754\pi\)
−0.00865158 + 0.999963i \(0.502754\pi\)
\(930\) 0 0
\(931\) 5.86250 0.192136
\(932\) 14.1724 0.464233
\(933\) 58.8459 1.92653
\(934\) 7.71344 0.252392
\(935\) 0 0
\(936\) −0.659886 −0.0215690
\(937\) 41.3338 1.35032 0.675158 0.737673i \(-0.264075\pi\)
0.675158 + 0.737673i \(0.264075\pi\)
\(938\) −10.4057 −0.339759
\(939\) −80.4810 −2.62640
\(940\) 0 0
\(941\) 25.4253 0.828840 0.414420 0.910086i \(-0.363984\pi\)
0.414420 + 0.910086i \(0.363984\pi\)
\(942\) −66.7567 −2.17505
\(943\) 6.51761 0.212242
\(944\) 25.6582 0.835104
\(945\) 0 0
\(946\) −7.08891 −0.230480
\(947\) 13.9372 0.452897 0.226448 0.974023i \(-0.427289\pi\)
0.226448 + 0.974023i \(0.427289\pi\)
\(948\) 34.0577 1.10614
\(949\) 1.07545 0.0349107
\(950\) 0 0
\(951\) −36.2717 −1.17619
\(952\) 0.677771 0.0219667
\(953\) −40.7458 −1.31989 −0.659943 0.751316i \(-0.729420\pi\)
−0.659943 + 0.751316i \(0.729420\pi\)
\(954\) −97.2531 −3.14868
\(955\) 0 0
\(956\) −37.7323 −1.22035
\(957\) 11.8630 0.383477
\(958\) −32.5263 −1.05088
\(959\) 8.04614 0.259824
\(960\) 0 0
\(961\) −23.6027 −0.761379
\(962\) −1.73160 −0.0558292
\(963\) −54.8397 −1.76719
\(964\) 28.8728 0.929930
\(965\) 0 0
\(966\) 29.9562 0.963826
\(967\) 21.5806 0.693985 0.346993 0.937868i \(-0.387203\pi\)
0.346993 + 0.937868i \(0.387203\pi\)
\(968\) 0.173707 0.00558317
\(969\) −9.70980 −0.311924
\(970\) 0 0
\(971\) −40.5213 −1.30039 −0.650194 0.759768i \(-0.725313\pi\)
−0.650194 + 0.759768i \(0.725313\pi\)
\(972\) 40.1409 1.28752
\(973\) −0.381074 −0.0122167
\(974\) −56.2381 −1.80199
\(975\) 0 0
\(976\) −8.90691 −0.285103
\(977\) 51.7112 1.65439 0.827194 0.561917i \(-0.189936\pi\)
0.827194 + 0.561917i \(0.189936\pi\)
\(978\) 23.3771 0.747518
\(979\) −8.77091 −0.280319
\(980\) 0 0
\(981\) 23.6773 0.755958
\(982\) 12.3809 0.395090
\(983\) −39.5850 −1.26256 −0.631282 0.775553i \(-0.717471\pi\)
−0.631282 + 0.775553i \(0.717471\pi\)
\(984\) 0.561623 0.0179039
\(985\) 0 0
\(986\) −32.3425 −1.02999
\(987\) 12.1784 0.387642
\(988\) 1.79609 0.0571413
\(989\) −19.1758 −0.609754
\(990\) 0 0
\(991\) 42.2901 1.34339 0.671694 0.740828i \(-0.265567\pi\)
0.671694 + 0.740828i \(0.265567\pi\)
\(992\) −21.4766 −0.681884
\(993\) −2.76924 −0.0878791
\(994\) 15.4480 0.489981
\(995\) 0 0
\(996\) 14.3493 0.454675
\(997\) 40.6774 1.28827 0.644133 0.764914i \(-0.277218\pi\)
0.644133 + 0.764914i \(0.277218\pi\)
\(998\) 20.7387 0.656473
\(999\) 2.58352 0.0817389
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 5225.2.a.m.1.2 7
5.4 even 2 1045.2.a.h.1.6 7
15.14 odd 2 9405.2.a.bd.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.a.h.1.6 7 5.4 even 2
5225.2.a.m.1.2 7 1.1 even 1 trivial
9405.2.a.bd.1.2 7 15.14 odd 2