Properties

Label 725.2.a.e.1.3
Level $725$
Weight $2$
Character 725.1
Self dual yes
Analytic conductor $5.789$
Analytic rank $1$
Dimension $3$
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] = [725,2,Mod(1,725)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(725, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("725.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 725.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: \(5.78915414654\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 145)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 725.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.48119 q^{2} -0.806063 q^{3} +0.193937 q^{4} -1.19394 q^{6} -1.19394 q^{7} -2.67513 q^{8} -2.35026 q^{9} +O(q^{10})\) \(q+1.48119 q^{2} -0.806063 q^{3} +0.193937 q^{4} -1.19394 q^{6} -1.19394 q^{7} -2.67513 q^{8} -2.35026 q^{9} +4.15633 q^{11} -0.156325 q^{12} -2.96239 q^{13} -1.76845 q^{14} -4.35026 q^{16} -5.50659 q^{17} -3.48119 q^{18} -3.19394 q^{19} +0.962389 q^{21} +6.15633 q^{22} -1.84367 q^{23} +2.15633 q^{24} -4.38787 q^{26} +4.31265 q^{27} -0.231548 q^{28} -1.00000 q^{29} -4.80606 q^{31} -1.09332 q^{32} -3.35026 q^{33} -8.15633 q^{34} -0.455802 q^{36} +9.50659 q^{37} -4.73084 q^{38} +2.38787 q^{39} -11.2750 q^{41} +1.42548 q^{42} +0.0303172 q^{43} +0.806063 q^{44} -2.73084 q^{46} -4.80606 q^{47} +3.50659 q^{48} -5.57452 q^{49} +4.43866 q^{51} -0.574515 q^{52} +1.35026 q^{53} +6.38787 q^{54} +3.19394 q^{56} +2.57452 q^{57} -1.48119 q^{58} +13.2750 q^{59} +8.88717 q^{61} -7.11871 q^{62} +2.80606 q^{63} +7.08110 q^{64} -4.96239 q^{66} -5.84367 q^{67} -1.06793 q^{68} +1.48612 q^{69} -1.27504 q^{71} +6.28726 q^{72} +15.2447 q^{73} +14.0811 q^{74} -0.619421 q^{76} -4.96239 q^{77} +3.53690 q^{78} -4.93207 q^{79} +3.57452 q^{81} -16.7005 q^{82} -4.41819 q^{83} +0.186642 q^{84} +0.0449056 q^{86} +0.806063 q^{87} -11.1187 q^{88} -3.61213 q^{89} +3.53690 q^{91} -0.357556 q^{92} +3.87399 q^{93} -7.11871 q^{94} +0.881286 q^{96} +1.38058 q^{97} -8.25694 q^{98} -9.76845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{2} - 2 q^{3} + q^{4} - 4 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{2} - 2 q^{3} + q^{4} - 4 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} - 3 q^{16} + 4 q^{17} - 5 q^{18} - 10 q^{19} - 8 q^{21} + 8 q^{22} - 16 q^{23} - 4 q^{24} - 14 q^{26} - 8 q^{27} - 12 q^{28} - 3 q^{29} - 14 q^{31} + 3 q^{32} - 14 q^{34} - 11 q^{36} + 8 q^{37} + 8 q^{38} + 8 q^{39} - 2 q^{41} + 16 q^{42} - 2 q^{43} + 2 q^{44} + 14 q^{46} - 14 q^{47} - 10 q^{48} - 5 q^{49} - 16 q^{51} + 10 q^{52} - 6 q^{53} + 20 q^{54} + 10 q^{56} - 4 q^{57} + q^{58} + 8 q^{59} - 6 q^{61} + 8 q^{63} - 11 q^{64} - 4 q^{66} - 28 q^{67} - 12 q^{68} + 12 q^{69} + 28 q^{71} + 13 q^{72} + 16 q^{73} + 10 q^{74} - 14 q^{76} - 4 q^{77} - 12 q^{78} - 6 q^{79} - q^{81} - 30 q^{82} - 12 q^{83} - 12 q^{84} + 24 q^{86} + 2 q^{87} - 12 q^{88} - 10 q^{89} - 12 q^{91} - 4 q^{92} + 20 q^{93} + 24 q^{96} - 8 q^{97} - 21 q^{98} - 18 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48119 1.04736 0.523681 0.851914i \(-0.324558\pi\)
0.523681 + 0.851914i \(0.324558\pi\)
\(3\) −0.806063 −0.465381 −0.232690 0.972551i \(-0.574753\pi\)
−0.232690 + 0.972551i \(0.574753\pi\)
\(4\) 0.193937 0.0969683
\(5\) 0 0
\(6\) −1.19394 −0.487423
\(7\) −1.19394 −0.451266 −0.225633 0.974212i \(-0.572445\pi\)
−0.225633 + 0.974212i \(0.572445\pi\)
\(8\) −2.67513 −0.945802
\(9\) −2.35026 −0.783421
\(10\) 0 0
\(11\) 4.15633 1.25318 0.626590 0.779349i \(-0.284450\pi\)
0.626590 + 0.779349i \(0.284450\pi\)
\(12\) −0.156325 −0.0451272
\(13\) −2.96239 −0.821619 −0.410809 0.911721i \(-0.634754\pi\)
−0.410809 + 0.911721i \(0.634754\pi\)
\(14\) −1.76845 −0.472639
\(15\) 0 0
\(16\) −4.35026 −1.08757
\(17\) −5.50659 −1.33554 −0.667772 0.744366i \(-0.732752\pi\)
−0.667772 + 0.744366i \(0.732752\pi\)
\(18\) −3.48119 −0.820525
\(19\) −3.19394 −0.732739 −0.366370 0.930469i \(-0.619399\pi\)
−0.366370 + 0.930469i \(0.619399\pi\)
\(20\) 0 0
\(21\) 0.962389 0.210010
\(22\) 6.15633 1.31253
\(23\) −1.84367 −0.384433 −0.192216 0.981353i \(-0.561568\pi\)
−0.192216 + 0.981353i \(0.561568\pi\)
\(24\) 2.15633 0.440158
\(25\) 0 0
\(26\) −4.38787 −0.860533
\(27\) 4.31265 0.829970
\(28\) −0.231548 −0.0437585
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −4.80606 −0.863194 −0.431597 0.902066i \(-0.642050\pi\)
−0.431597 + 0.902066i \(0.642050\pi\)
\(32\) −1.09332 −0.193274
\(33\) −3.35026 −0.583206
\(34\) −8.15633 −1.39880
\(35\) 0 0
\(36\) −0.455802 −0.0759669
\(37\) 9.50659 1.56287 0.781437 0.623985i \(-0.214487\pi\)
0.781437 + 0.623985i \(0.214487\pi\)
\(38\) −4.73084 −0.767444
\(39\) 2.38787 0.382366
\(40\) 0 0
\(41\) −11.2750 −1.76087 −0.880433 0.474171i \(-0.842748\pi\)
−0.880433 + 0.474171i \(0.842748\pi\)
\(42\) 1.42548 0.219957
\(43\) 0.0303172 0.00462332 0.00231166 0.999997i \(-0.499264\pi\)
0.00231166 + 0.999997i \(0.499264\pi\)
\(44\) 0.806063 0.121519
\(45\) 0 0
\(46\) −2.73084 −0.402640
\(47\) −4.80606 −0.701036 −0.350518 0.936556i \(-0.613995\pi\)
−0.350518 + 0.936556i \(0.613995\pi\)
\(48\) 3.50659 0.506132
\(49\) −5.57452 −0.796359
\(50\) 0 0
\(51\) 4.43866 0.621536
\(52\) −0.574515 −0.0796710
\(53\) 1.35026 0.185473 0.0927364 0.995691i \(-0.470439\pi\)
0.0927364 + 0.995691i \(0.470439\pi\)
\(54\) 6.38787 0.869279
\(55\) 0 0
\(56\) 3.19394 0.426808
\(57\) 2.57452 0.341003
\(58\) −1.48119 −0.194490
\(59\) 13.2750 1.72826 0.864131 0.503266i \(-0.167868\pi\)
0.864131 + 0.503266i \(0.167868\pi\)
\(60\) 0 0
\(61\) 8.88717 1.13788 0.568942 0.822377i \(-0.307353\pi\)
0.568942 + 0.822377i \(0.307353\pi\)
\(62\) −7.11871 −0.904078
\(63\) 2.80606 0.353531
\(64\) 7.08110 0.885138
\(65\) 0 0
\(66\) −4.96239 −0.610828
\(67\) −5.84367 −0.713919 −0.356959 0.934120i \(-0.616187\pi\)
−0.356959 + 0.934120i \(0.616187\pi\)
\(68\) −1.06793 −0.129505
\(69\) 1.48612 0.178908
\(70\) 0 0
\(71\) −1.27504 −0.151319 −0.0756596 0.997134i \(-0.524106\pi\)
−0.0756596 + 0.997134i \(0.524106\pi\)
\(72\) 6.28726 0.740960
\(73\) 15.2447 1.78426 0.892130 0.451779i \(-0.149210\pi\)
0.892130 + 0.451779i \(0.149210\pi\)
\(74\) 14.0811 1.63689
\(75\) 0 0
\(76\) −0.619421 −0.0710525
\(77\) −4.96239 −0.565517
\(78\) 3.53690 0.400476
\(79\) −4.93207 −0.554901 −0.277451 0.960740i \(-0.589490\pi\)
−0.277451 + 0.960740i \(0.589490\pi\)
\(80\) 0 0
\(81\) 3.57452 0.397168
\(82\) −16.7005 −1.84426
\(83\) −4.41819 −0.484959 −0.242480 0.970156i \(-0.577961\pi\)
−0.242480 + 0.970156i \(0.577961\pi\)
\(84\) 0.186642 0.0203643
\(85\) 0 0
\(86\) 0.0449056 0.00484230
\(87\) 0.806063 0.0864191
\(88\) −11.1187 −1.18526
\(89\) −3.61213 −0.382885 −0.191442 0.981504i \(-0.561316\pi\)
−0.191442 + 0.981504i \(0.561316\pi\)
\(90\) 0 0
\(91\) 3.53690 0.370768
\(92\) −0.357556 −0.0372778
\(93\) 3.87399 0.401714
\(94\) −7.11871 −0.734239
\(95\) 0 0
\(96\) 0.881286 0.0899459
\(97\) 1.38058 0.140177 0.0700883 0.997541i \(-0.477672\pi\)
0.0700883 + 0.997541i \(0.477672\pi\)
\(98\) −8.25694 −0.834077
\(99\) −9.76845 −0.981766
\(100\) 0 0
\(101\) −13.0132 −1.29486 −0.647430 0.762125i \(-0.724156\pi\)
−0.647430 + 0.762125i \(0.724156\pi\)
\(102\) 6.57452 0.650974
\(103\) −5.31994 −0.524190 −0.262095 0.965042i \(-0.584413\pi\)
−0.262095 + 0.965042i \(0.584413\pi\)
\(104\) 7.92478 0.777088
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 13.8192 1.33596 0.667978 0.744181i \(-0.267160\pi\)
0.667978 + 0.744181i \(0.267160\pi\)
\(108\) 0.836381 0.0804808
\(109\) −1.87399 −0.179496 −0.0897479 0.995965i \(-0.528606\pi\)
−0.0897479 + 0.995965i \(0.528606\pi\)
\(110\) 0 0
\(111\) −7.66291 −0.727331
\(112\) 5.19394 0.490781
\(113\) 11.7685 1.10708 0.553541 0.832822i \(-0.313276\pi\)
0.553541 + 0.832822i \(0.313276\pi\)
\(114\) 3.81336 0.357154
\(115\) 0 0
\(116\) −0.193937 −0.0180066
\(117\) 6.96239 0.643673
\(118\) 19.6629 1.81012
\(119\) 6.57452 0.602685
\(120\) 0 0
\(121\) 6.27504 0.570458
\(122\) 13.1636 1.19178
\(123\) 9.08840 0.819473
\(124\) −0.932071 −0.0837025
\(125\) 0 0
\(126\) 4.15633 0.370275
\(127\) −14.2677 −1.26606 −0.633029 0.774128i \(-0.718189\pi\)
−0.633029 + 0.774128i \(0.718189\pi\)
\(128\) 12.6751 1.12033
\(129\) −0.0244376 −0.00215161
\(130\) 0 0
\(131\) 5.89446 0.515001 0.257501 0.966278i \(-0.417101\pi\)
0.257501 + 0.966278i \(0.417101\pi\)
\(132\) −0.649738 −0.0565525
\(133\) 3.81336 0.330660
\(134\) −8.65562 −0.747731
\(135\) 0 0
\(136\) 14.7308 1.26316
\(137\) −18.2823 −1.56197 −0.780983 0.624553i \(-0.785281\pi\)
−0.780983 + 0.624553i \(0.785281\pi\)
\(138\) 2.20123 0.187381
\(139\) −11.5369 −0.978547 −0.489274 0.872130i \(-0.662738\pi\)
−0.489274 + 0.872130i \(0.662738\pi\)
\(140\) 0 0
\(141\) 3.87399 0.326249
\(142\) −1.88858 −0.158486
\(143\) −12.3127 −1.02964
\(144\) 10.2243 0.852021
\(145\) 0 0
\(146\) 22.5804 1.86877
\(147\) 4.49341 0.370610
\(148\) 1.84367 0.151549
\(149\) 2.77575 0.227398 0.113699 0.993515i \(-0.463730\pi\)
0.113699 + 0.993515i \(0.463730\pi\)
\(150\) 0 0
\(151\) 1.79877 0.146382 0.0731909 0.997318i \(-0.476682\pi\)
0.0731909 + 0.997318i \(0.476682\pi\)
\(152\) 8.54420 0.693026
\(153\) 12.9419 1.04629
\(154\) −7.35026 −0.592301
\(155\) 0 0
\(156\) 0.463096 0.0370773
\(157\) −3.76845 −0.300755 −0.150378 0.988629i \(-0.548049\pi\)
−0.150378 + 0.988629i \(0.548049\pi\)
\(158\) −7.30536 −0.581183
\(159\) −1.08840 −0.0863155
\(160\) 0 0
\(161\) 2.20123 0.173481
\(162\) 5.29455 0.415979
\(163\) −1.64244 −0.128646 −0.0643231 0.997929i \(-0.520489\pi\)
−0.0643231 + 0.997929i \(0.520489\pi\)
\(164\) −2.18664 −0.170748
\(165\) 0 0
\(166\) −6.54420 −0.507928
\(167\) −8.08110 −0.625334 −0.312667 0.949863i \(-0.601222\pi\)
−0.312667 + 0.949863i \(0.601222\pi\)
\(168\) −2.57452 −0.198628
\(169\) −4.22425 −0.324943
\(170\) 0 0
\(171\) 7.50659 0.574043
\(172\) 0.00587961 0.000448316 0
\(173\) 7.73813 0.588320 0.294160 0.955756i \(-0.404960\pi\)
0.294160 + 0.955756i \(0.404960\pi\)
\(174\) 1.19394 0.0905121
\(175\) 0 0
\(176\) −18.0811 −1.36291
\(177\) −10.7005 −0.804301
\(178\) −5.35026 −0.401019
\(179\) −21.4010 −1.59959 −0.799795 0.600274i \(-0.795058\pi\)
−0.799795 + 0.600274i \(0.795058\pi\)
\(180\) 0 0
\(181\) 15.2750 1.13538 0.567692 0.823241i \(-0.307836\pi\)
0.567692 + 0.823241i \(0.307836\pi\)
\(182\) 5.23884 0.388329
\(183\) −7.16362 −0.529550
\(184\) 4.93207 0.363597
\(185\) 0 0
\(186\) 5.73813 0.420740
\(187\) −22.8872 −1.67368
\(188\) −0.932071 −0.0679783
\(189\) −5.14903 −0.374537
\(190\) 0 0
\(191\) 3.31994 0.240223 0.120111 0.992760i \(-0.461675\pi\)
0.120111 + 0.992760i \(0.461675\pi\)
\(192\) −5.70782 −0.411926
\(193\) 4.88129 0.351363 0.175681 0.984447i \(-0.443787\pi\)
0.175681 + 0.984447i \(0.443787\pi\)
\(194\) 2.04491 0.146816
\(195\) 0 0
\(196\) −1.08110 −0.0772216
\(197\) 24.2374 1.72685 0.863423 0.504481i \(-0.168316\pi\)
0.863423 + 0.504481i \(0.168316\pi\)
\(198\) −14.4690 −1.02827
\(199\) 16.7513 1.18747 0.593734 0.804661i \(-0.297653\pi\)
0.593734 + 0.804661i \(0.297653\pi\)
\(200\) 0 0
\(201\) 4.71037 0.332244
\(202\) −19.2750 −1.35619
\(203\) 1.19394 0.0837979
\(204\) 0.860818 0.0602693
\(205\) 0 0
\(206\) −7.87987 −0.549017
\(207\) 4.33312 0.301173
\(208\) 12.8872 0.893564
\(209\) −13.2750 −0.918254
\(210\) 0 0
\(211\) −25.3054 −1.74209 −0.871046 0.491201i \(-0.836558\pi\)
−0.871046 + 0.491201i \(0.836558\pi\)
\(212\) 0.261865 0.0179850
\(213\) 1.02776 0.0704211
\(214\) 20.4690 1.39923
\(215\) 0 0
\(216\) −11.5369 −0.784987
\(217\) 5.73813 0.389530
\(218\) −2.77575 −0.187997
\(219\) −12.2882 −0.830360
\(220\) 0 0
\(221\) 16.3127 1.09731
\(222\) −11.3503 −0.761780
\(223\) −17.6932 −1.18483 −0.592413 0.805634i \(-0.701825\pi\)
−0.592413 + 0.805634i \(0.701825\pi\)
\(224\) 1.30536 0.0872178
\(225\) 0 0
\(226\) 17.4314 1.15952
\(227\) −26.8423 −1.78158 −0.890792 0.454412i \(-0.849849\pi\)
−0.890792 + 0.454412i \(0.849849\pi\)
\(228\) 0.499293 0.0330665
\(229\) −17.2243 −1.13821 −0.569105 0.822265i \(-0.692710\pi\)
−0.569105 + 0.822265i \(0.692710\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) 2.67513 0.175631
\(233\) 9.07381 0.594445 0.297222 0.954808i \(-0.403940\pi\)
0.297222 + 0.954808i \(0.403940\pi\)
\(234\) 10.3127 0.674159
\(235\) 0 0
\(236\) 2.57452 0.167587
\(237\) 3.97556 0.258241
\(238\) 9.73813 0.631230
\(239\) 20.4993 1.32599 0.662995 0.748624i \(-0.269285\pi\)
0.662995 + 0.748624i \(0.269285\pi\)
\(240\) 0 0
\(241\) 5.47627 0.352758 0.176379 0.984322i \(-0.443562\pi\)
0.176379 + 0.984322i \(0.443562\pi\)
\(242\) 9.29455 0.597476
\(243\) −15.8192 −1.01480
\(244\) 1.72355 0.110339
\(245\) 0 0
\(246\) 13.4617 0.858285
\(247\) 9.46168 0.602032
\(248\) 12.8568 0.816411
\(249\) 3.56134 0.225691
\(250\) 0 0
\(251\) −29.6180 −1.86947 −0.934736 0.355343i \(-0.884364\pi\)
−0.934736 + 0.355343i \(0.884364\pi\)
\(252\) 0.544198 0.0342813
\(253\) −7.66291 −0.481763
\(254\) −21.1333 −1.32602
\(255\) 0 0
\(256\) 4.61213 0.288258
\(257\) −17.6629 −1.10178 −0.550891 0.834577i \(-0.685712\pi\)
−0.550891 + 0.834577i \(0.685712\pi\)
\(258\) −0.0361968 −0.00225351
\(259\) −11.3503 −0.705271
\(260\) 0 0
\(261\) 2.35026 0.145478
\(262\) 8.73084 0.539393
\(263\) −27.3561 −1.68685 −0.843426 0.537245i \(-0.819465\pi\)
−0.843426 + 0.537245i \(0.819465\pi\)
\(264\) 8.96239 0.551597
\(265\) 0 0
\(266\) 5.64832 0.346321
\(267\) 2.91160 0.178187
\(268\) −1.13330 −0.0692275
\(269\) 10.4993 0.640153 0.320077 0.947392i \(-0.396291\pi\)
0.320077 + 0.947392i \(0.396291\pi\)
\(270\) 0 0
\(271\) −9.61801 −0.584252 −0.292126 0.956380i \(-0.594363\pi\)
−0.292126 + 0.956380i \(0.594363\pi\)
\(272\) 23.9551 1.45249
\(273\) −2.85097 −0.172548
\(274\) −27.0797 −1.63594
\(275\) 0 0
\(276\) 0.288213 0.0173484
\(277\) −13.3503 −0.802139 −0.401070 0.916048i \(-0.631362\pi\)
−0.401070 + 0.916048i \(0.631362\pi\)
\(278\) −17.0884 −1.02489
\(279\) 11.2955 0.676244
\(280\) 0 0
\(281\) 20.4241 1.21840 0.609199 0.793017i \(-0.291491\pi\)
0.609199 + 0.793017i \(0.291491\pi\)
\(282\) 5.73813 0.341701
\(283\) 8.02047 0.476767 0.238384 0.971171i \(-0.423382\pi\)
0.238384 + 0.971171i \(0.423382\pi\)
\(284\) −0.247277 −0.0146732
\(285\) 0 0
\(286\) −18.2374 −1.07840
\(287\) 13.4617 0.794618
\(288\) 2.56959 0.151415
\(289\) 13.3225 0.783676
\(290\) 0 0
\(291\) −1.11283 −0.0652355
\(292\) 2.95651 0.173017
\(293\) 23.3054 1.36151 0.680757 0.732510i \(-0.261651\pi\)
0.680757 + 0.732510i \(0.261651\pi\)
\(294\) 6.65562 0.388164
\(295\) 0 0
\(296\) −25.4314 −1.47817
\(297\) 17.9248 1.04010
\(298\) 4.11142 0.238168
\(299\) 5.46168 0.315857
\(300\) 0 0
\(301\) −0.0361968 −0.00208635
\(302\) 2.66433 0.153315
\(303\) 10.4894 0.602603
\(304\) 13.8945 0.796902
\(305\) 0 0
\(306\) 19.1695 1.09585
\(307\) 6.73084 0.384149 0.192075 0.981380i \(-0.438478\pi\)
0.192075 + 0.981380i \(0.438478\pi\)
\(308\) −0.962389 −0.0548372
\(309\) 4.28821 0.243948
\(310\) 0 0
\(311\) −22.0567 −1.25072 −0.625359 0.780337i \(-0.715048\pi\)
−0.625359 + 0.780337i \(0.715048\pi\)
\(312\) −6.38787 −0.361642
\(313\) −5.03761 −0.284743 −0.142371 0.989813i \(-0.545473\pi\)
−0.142371 + 0.989813i \(0.545473\pi\)
\(314\) −5.58181 −0.315000
\(315\) 0 0
\(316\) −0.956509 −0.0538078
\(317\) −34.2941 −1.92615 −0.963074 0.269237i \(-0.913229\pi\)
−0.963074 + 0.269237i \(0.913229\pi\)
\(318\) −1.61213 −0.0904036
\(319\) −4.15633 −0.232710
\(320\) 0 0
\(321\) −11.1392 −0.621729
\(322\) 3.26045 0.181698
\(323\) 17.5877 0.978605
\(324\) 0.693229 0.0385127
\(325\) 0 0
\(326\) −2.43278 −0.134739
\(327\) 1.51056 0.0835340
\(328\) 30.1622 1.66543
\(329\) 5.73813 0.316354
\(330\) 0 0
\(331\) −34.8324 −1.91456 −0.957281 0.289159i \(-0.906625\pi\)
−0.957281 + 0.289159i \(0.906625\pi\)
\(332\) −0.856849 −0.0470257
\(333\) −22.3430 −1.22439
\(334\) −11.9697 −0.654952
\(335\) 0 0
\(336\) −4.18664 −0.228400
\(337\) 17.6326 0.960509 0.480254 0.877129i \(-0.340544\pi\)
0.480254 + 0.877129i \(0.340544\pi\)
\(338\) −6.25694 −0.340333
\(339\) −9.48612 −0.515215
\(340\) 0 0
\(341\) −19.9756 −1.08174
\(342\) 11.1187 0.601231
\(343\) 15.0132 0.810635
\(344\) −0.0811024 −0.00437275
\(345\) 0 0
\(346\) 11.4617 0.616184
\(347\) 3.11871 0.167421 0.0837107 0.996490i \(-0.473323\pi\)
0.0837107 + 0.996490i \(0.473323\pi\)
\(348\) 0.156325 0.00837991
\(349\) −13.0738 −0.699825 −0.349912 0.936782i \(-0.613789\pi\)
−0.349912 + 0.936782i \(0.613789\pi\)
\(350\) 0 0
\(351\) −12.7757 −0.681919
\(352\) −4.54420 −0.242207
\(353\) −5.19982 −0.276758 −0.138379 0.990379i \(-0.544189\pi\)
−0.138379 + 0.990379i \(0.544189\pi\)
\(354\) −15.8496 −0.842394
\(355\) 0 0
\(356\) −0.700523 −0.0371277
\(357\) −5.29948 −0.280478
\(358\) −31.6991 −1.67535
\(359\) 30.4182 1.60541 0.802705 0.596376i \(-0.203393\pi\)
0.802705 + 0.596376i \(0.203393\pi\)
\(360\) 0 0
\(361\) −8.79877 −0.463093
\(362\) 22.6253 1.18916
\(363\) −5.05808 −0.265480
\(364\) 0.685935 0.0359528
\(365\) 0 0
\(366\) −10.6107 −0.554631
\(367\) −20.6556 −1.07821 −0.539107 0.842237i \(-0.681238\pi\)
−0.539107 + 0.842237i \(0.681238\pi\)
\(368\) 8.02047 0.418096
\(369\) 26.4993 1.37950
\(370\) 0 0
\(371\) −1.61213 −0.0836975
\(372\) 0.751309 0.0389535
\(373\) −11.0884 −0.574135 −0.287068 0.957910i \(-0.592680\pi\)
−0.287068 + 0.957910i \(0.592680\pi\)
\(374\) −33.9003 −1.75294
\(375\) 0 0
\(376\) 12.8568 0.663041
\(377\) 2.96239 0.152571
\(378\) −7.62672 −0.392276
\(379\) 10.0811 0.517831 0.258916 0.965900i \(-0.416635\pi\)
0.258916 + 0.965900i \(0.416635\pi\)
\(380\) 0 0
\(381\) 11.5007 0.589199
\(382\) 4.91748 0.251600
\(383\) −16.3576 −0.835832 −0.417916 0.908486i \(-0.637239\pi\)
−0.417916 + 0.908486i \(0.637239\pi\)
\(384\) −10.2170 −0.521382
\(385\) 0 0
\(386\) 7.23013 0.368004
\(387\) −0.0712533 −0.00362201
\(388\) 0.267745 0.0135927
\(389\) 31.9003 1.61741 0.808706 0.588213i \(-0.200169\pi\)
0.808706 + 0.588213i \(0.200169\pi\)
\(390\) 0 0
\(391\) 10.1524 0.513427
\(392\) 14.9126 0.753198
\(393\) −4.75131 −0.239672
\(394\) 35.9003 1.80863
\(395\) 0 0
\(396\) −1.89446 −0.0952002
\(397\) −2.98683 −0.149905 −0.0749523 0.997187i \(-0.523880\pi\)
−0.0749523 + 0.997187i \(0.523880\pi\)
\(398\) 24.8119 1.24371
\(399\) −3.07381 −0.153883
\(400\) 0 0
\(401\) −21.9756 −1.09741 −0.548704 0.836017i \(-0.684878\pi\)
−0.548704 + 0.836017i \(0.684878\pi\)
\(402\) 6.97698 0.347980
\(403\) 14.2374 0.709217
\(404\) −2.52373 −0.125560
\(405\) 0 0
\(406\) 1.76845 0.0877668
\(407\) 39.5125 1.95856
\(408\) −11.8740 −0.587850
\(409\) −22.4387 −1.10952 −0.554760 0.832010i \(-0.687190\pi\)
−0.554760 + 0.832010i \(0.687190\pi\)
\(410\) 0 0
\(411\) 14.7367 0.726909
\(412\) −1.03173 −0.0508298
\(413\) −15.8496 −0.779906
\(414\) 6.41819 0.315437
\(415\) 0 0
\(416\) 3.23884 0.158797
\(417\) 9.29948 0.455397
\(418\) −19.6629 −0.961744
\(419\) 10.3634 0.506287 0.253143 0.967429i \(-0.418536\pi\)
0.253143 + 0.967429i \(0.418536\pi\)
\(420\) 0 0
\(421\) 34.0362 1.65882 0.829411 0.558638i \(-0.188676\pi\)
0.829411 + 0.558638i \(0.188676\pi\)
\(422\) −37.4821 −1.82460
\(423\) 11.2955 0.549206
\(424\) −3.61213 −0.175420
\(425\) 0 0
\(426\) 1.52232 0.0737564
\(427\) −10.6107 −0.513488
\(428\) 2.68006 0.129545
\(429\) 9.92478 0.479173
\(430\) 0 0
\(431\) 25.7743 1.24151 0.620753 0.784006i \(-0.286827\pi\)
0.620753 + 0.784006i \(0.286827\pi\)
\(432\) −18.7612 −0.902647
\(433\) −2.18076 −0.104801 −0.0524004 0.998626i \(-0.516687\pi\)
−0.0524004 + 0.998626i \(0.516687\pi\)
\(434\) 8.49929 0.407979
\(435\) 0 0
\(436\) −0.363436 −0.0174054
\(437\) 5.88858 0.281689
\(438\) −18.2012 −0.869688
\(439\) −35.5125 −1.69492 −0.847459 0.530861i \(-0.821869\pi\)
−0.847459 + 0.530861i \(0.821869\pi\)
\(440\) 0 0
\(441\) 13.1016 0.623884
\(442\) 24.1622 1.14928
\(443\) 4.34297 0.206341 0.103170 0.994664i \(-0.467101\pi\)
0.103170 + 0.994664i \(0.467101\pi\)
\(444\) −1.48612 −0.0705281
\(445\) 0 0
\(446\) −26.2071 −1.24094
\(447\) −2.23743 −0.105827
\(448\) −8.45439 −0.399432
\(449\) 31.3357 1.47882 0.739411 0.673254i \(-0.235104\pi\)
0.739411 + 0.673254i \(0.235104\pi\)
\(450\) 0 0
\(451\) −46.8627 −2.20668
\(452\) 2.28233 0.107352
\(453\) −1.44992 −0.0681233
\(454\) −39.7586 −1.86596
\(455\) 0 0
\(456\) −6.88717 −0.322521
\(457\) −34.3488 −1.60677 −0.803386 0.595459i \(-0.796970\pi\)
−0.803386 + 0.595459i \(0.796970\pi\)
\(458\) −25.5125 −1.19212
\(459\) −23.7480 −1.10846
\(460\) 0 0
\(461\) 11.8641 0.552568 0.276284 0.961076i \(-0.410897\pi\)
0.276284 + 0.961076i \(0.410897\pi\)
\(462\) 5.92478 0.275646
\(463\) −40.4953 −1.88198 −0.940989 0.338438i \(-0.890101\pi\)
−0.940989 + 0.338438i \(0.890101\pi\)
\(464\) 4.35026 0.201956
\(465\) 0 0
\(466\) 13.4401 0.622599
\(467\) 30.2071 1.39782 0.698909 0.715210i \(-0.253669\pi\)
0.698909 + 0.715210i \(0.253669\pi\)
\(468\) 1.35026 0.0624159
\(469\) 6.97698 0.322167
\(470\) 0 0
\(471\) 3.03761 0.139966
\(472\) −35.5125 −1.63459
\(473\) 0.126008 0.00579385
\(474\) 5.88858 0.270471
\(475\) 0 0
\(476\) 1.27504 0.0584413
\(477\) −3.17347 −0.145303
\(478\) 30.3634 1.38879
\(479\) 0.0547547 0.00250181 0.00125090 0.999999i \(-0.499602\pi\)
0.00125090 + 0.999999i \(0.499602\pi\)
\(480\) 0 0
\(481\) −28.1622 −1.28409
\(482\) 8.11142 0.369465
\(483\) −1.77433 −0.0807349
\(484\) 1.21696 0.0553163
\(485\) 0 0
\(486\) −23.4314 −1.06287
\(487\) 0.881286 0.0399349 0.0199674 0.999801i \(-0.493644\pi\)
0.0199674 + 0.999801i \(0.493644\pi\)
\(488\) −23.7743 −1.07621
\(489\) 1.32391 0.0598695
\(490\) 0 0
\(491\) 41.0698 1.85346 0.926728 0.375733i \(-0.122609\pi\)
0.926728 + 0.375733i \(0.122609\pi\)
\(492\) 1.76257 0.0794629
\(493\) 5.50659 0.248004
\(494\) 14.0146 0.630546
\(495\) 0 0
\(496\) 20.9076 0.938780
\(497\) 1.52232 0.0682852
\(498\) 5.27504 0.236380
\(499\) 12.3733 0.553904 0.276952 0.960884i \(-0.410676\pi\)
0.276952 + 0.960884i \(0.410676\pi\)
\(500\) 0 0
\(501\) 6.51388 0.291019
\(502\) −43.8700 −1.95801
\(503\) 2.26774 0.101114 0.0505569 0.998721i \(-0.483900\pi\)
0.0505569 + 0.998721i \(0.483900\pi\)
\(504\) −7.50659 −0.334370
\(505\) 0 0
\(506\) −11.3503 −0.504581
\(507\) 3.40502 0.151222
\(508\) −2.76704 −0.122767
\(509\) −10.9018 −0.483212 −0.241606 0.970374i \(-0.577674\pi\)
−0.241606 + 0.970374i \(0.577674\pi\)
\(510\) 0 0
\(511\) −18.2012 −0.805175
\(512\) −18.5188 −0.818423
\(513\) −13.7743 −0.608152
\(514\) −26.1622 −1.15397
\(515\) 0 0
\(516\) −0.00473934 −0.000208638 0
\(517\) −19.9756 −0.878524
\(518\) −16.8119 −0.738674
\(519\) −6.23743 −0.273793
\(520\) 0 0
\(521\) −4.72496 −0.207004 −0.103502 0.994629i \(-0.533005\pi\)
−0.103502 + 0.994629i \(0.533005\pi\)
\(522\) 3.48119 0.152368
\(523\) 1.06793 0.0466973 0.0233486 0.999727i \(-0.492567\pi\)
0.0233486 + 0.999727i \(0.492567\pi\)
\(524\) 1.14315 0.0499388
\(525\) 0 0
\(526\) −40.5198 −1.76675
\(527\) 26.4650 1.15283
\(528\) 14.5745 0.634274
\(529\) −19.6009 −0.852211
\(530\) 0 0
\(531\) −31.1998 −1.35396
\(532\) 0.739549 0.0320635
\(533\) 33.4010 1.44676
\(534\) 4.31265 0.186627
\(535\) 0 0
\(536\) 15.6326 0.675225
\(537\) 17.2506 0.744418
\(538\) 15.5515 0.670472
\(539\) −23.1695 −0.997981
\(540\) 0 0
\(541\) −7.46168 −0.320803 −0.160401 0.987052i \(-0.551279\pi\)
−0.160401 + 0.987052i \(0.551279\pi\)
\(542\) −14.2461 −0.611924
\(543\) −12.3127 −0.528386
\(544\) 6.02047 0.258125
\(545\) 0 0
\(546\) −4.22284 −0.180721
\(547\) 38.9683 1.66616 0.833081 0.553150i \(-0.186575\pi\)
0.833081 + 0.553150i \(0.186575\pi\)
\(548\) −3.54561 −0.151461
\(549\) −20.8872 −0.891443
\(550\) 0 0
\(551\) 3.19394 0.136066
\(552\) −3.97556 −0.169211
\(553\) 5.88858 0.250408
\(554\) −19.7743 −0.840131
\(555\) 0 0
\(556\) −2.23743 −0.0948881
\(557\) 22.9986 0.974481 0.487241 0.873268i \(-0.338003\pi\)
0.487241 + 0.873268i \(0.338003\pi\)
\(558\) 16.7308 0.708273
\(559\) −0.0898112 −0.00379861
\(560\) 0 0
\(561\) 18.4485 0.778897
\(562\) 30.2520 1.27610
\(563\) −11.6688 −0.491781 −0.245890 0.969298i \(-0.579080\pi\)
−0.245890 + 0.969298i \(0.579080\pi\)
\(564\) 0.751309 0.0316358
\(565\) 0 0
\(566\) 11.8799 0.499348
\(567\) −4.26774 −0.179228
\(568\) 3.41090 0.143118
\(569\) 11.3357 0.475216 0.237608 0.971361i \(-0.423637\pi\)
0.237608 + 0.971361i \(0.423637\pi\)
\(570\) 0 0
\(571\) 27.1754 1.13725 0.568627 0.822595i \(-0.307475\pi\)
0.568627 + 0.822595i \(0.307475\pi\)
\(572\) −2.38787 −0.0998420
\(573\) −2.67609 −0.111795
\(574\) 19.9394 0.832253
\(575\) 0 0
\(576\) −16.6424 −0.693435
\(577\) −22.5950 −0.940641 −0.470321 0.882496i \(-0.655862\pi\)
−0.470321 + 0.882496i \(0.655862\pi\)
\(578\) 19.7332 0.820793
\(579\) −3.93463 −0.163517
\(580\) 0 0
\(581\) 5.27504 0.218845
\(582\) −1.64832 −0.0683252
\(583\) 5.61213 0.232431
\(584\) −40.7816 −1.68756
\(585\) 0 0
\(586\) 34.5198 1.42600
\(587\) −9.31994 −0.384675 −0.192338 0.981329i \(-0.561607\pi\)
−0.192338 + 0.981329i \(0.561607\pi\)
\(588\) 0.871437 0.0359375
\(589\) 15.3503 0.632497
\(590\) 0 0
\(591\) −19.5369 −0.803641
\(592\) −41.3561 −1.69973
\(593\) 15.1246 0.621093 0.310546 0.950558i \(-0.399488\pi\)
0.310546 + 0.950558i \(0.399488\pi\)
\(594\) 26.5501 1.08936
\(595\) 0 0
\(596\) 0.538319 0.0220504
\(597\) −13.5026 −0.552625
\(598\) 8.08981 0.330817
\(599\) 4.09569 0.167345 0.0836727 0.996493i \(-0.473335\pi\)
0.0836727 + 0.996493i \(0.473335\pi\)
\(600\) 0 0
\(601\) 22.2276 0.906682 0.453341 0.891337i \(-0.350232\pi\)
0.453341 + 0.891337i \(0.350232\pi\)
\(602\) −0.0536145 −0.00218516
\(603\) 13.7342 0.559298
\(604\) 0.348847 0.0141944
\(605\) 0 0
\(606\) 15.5369 0.631144
\(607\) 48.2941 1.96020 0.980098 0.198512i \(-0.0636110\pi\)
0.980098 + 0.198512i \(0.0636110\pi\)
\(608\) 3.49200 0.141619
\(609\) −0.962389 −0.0389980
\(610\) 0 0
\(611\) 14.2374 0.575985
\(612\) 2.50991 0.101457
\(613\) 9.74798 0.393717 0.196859 0.980432i \(-0.436926\pi\)
0.196859 + 0.980432i \(0.436926\pi\)
\(614\) 9.96968 0.402344
\(615\) 0 0
\(616\) 13.2750 0.534867
\(617\) −18.2170 −0.733387 −0.366694 0.930342i \(-0.619510\pi\)
−0.366694 + 0.930342i \(0.619510\pi\)
\(618\) 6.35168 0.255502
\(619\) 25.0943 1.00862 0.504312 0.863521i \(-0.331746\pi\)
0.504312 + 0.863521i \(0.331746\pi\)
\(620\) 0 0
\(621\) −7.95112 −0.319068
\(622\) −32.6702 −1.30996
\(623\) 4.31265 0.172783
\(624\) −10.3879 −0.415848
\(625\) 0 0
\(626\) −7.46168 −0.298229
\(627\) 10.7005 0.427338
\(628\) −0.730841 −0.0291637
\(629\) −52.3488 −2.08729
\(630\) 0 0
\(631\) 21.4617 0.854376 0.427188 0.904163i \(-0.359504\pi\)
0.427188 + 0.904163i \(0.359504\pi\)
\(632\) 13.1939 0.524827
\(633\) 20.3977 0.810737
\(634\) −50.7962 −2.01738
\(635\) 0 0
\(636\) −0.211080 −0.00836986
\(637\) 16.5139 0.654304
\(638\) −6.15633 −0.243731
\(639\) 2.99668 0.118547
\(640\) 0 0
\(641\) 3.17347 0.125344 0.0626722 0.998034i \(-0.480038\pi\)
0.0626722 + 0.998034i \(0.480038\pi\)
\(642\) −16.4993 −0.651175
\(643\) 2.74069 0.108082 0.0540411 0.998539i \(-0.482790\pi\)
0.0540411 + 0.998539i \(0.482790\pi\)
\(644\) 0.426899 0.0168222
\(645\) 0 0
\(646\) 26.0508 1.02495
\(647\) −6.34297 −0.249368 −0.124684 0.992197i \(-0.539792\pi\)
−0.124684 + 0.992197i \(0.539792\pi\)
\(648\) −9.56230 −0.375642
\(649\) 55.1754 2.16582
\(650\) 0 0
\(651\) −4.62530 −0.181280
\(652\) −0.318530 −0.0124746
\(653\) −4.08110 −0.159706 −0.0798529 0.996807i \(-0.525445\pi\)
−0.0798529 + 0.996807i \(0.525445\pi\)
\(654\) 2.23743 0.0874903
\(655\) 0 0
\(656\) 49.0494 1.91506
\(657\) −35.8291 −1.39783
\(658\) 8.49929 0.331337
\(659\) 9.58181 0.373254 0.186627 0.982431i \(-0.440244\pi\)
0.186627 + 0.982431i \(0.440244\pi\)
\(660\) 0 0
\(661\) −27.5271 −1.07068 −0.535339 0.844637i \(-0.679816\pi\)
−0.535339 + 0.844637i \(0.679816\pi\)
\(662\) −51.5936 −2.00524
\(663\) −13.1490 −0.510666
\(664\) 11.8192 0.458675
\(665\) 0 0
\(666\) −33.0943 −1.28238
\(667\) 1.84367 0.0713874
\(668\) −1.56722 −0.0606376
\(669\) 14.2619 0.551396
\(670\) 0 0
\(671\) 36.9380 1.42597
\(672\) −1.05220 −0.0405895
\(673\) −3.13727 −0.120933 −0.0604665 0.998170i \(-0.519259\pi\)
−0.0604665 + 0.998170i \(0.519259\pi\)
\(674\) 26.1173 1.00600
\(675\) 0 0
\(676\) −0.819237 −0.0315091
\(677\) 46.2579 1.77784 0.888918 0.458067i \(-0.151458\pi\)
0.888918 + 0.458067i \(0.151458\pi\)
\(678\) −14.0508 −0.539617
\(679\) −1.64832 −0.0632569
\(680\) 0 0
\(681\) 21.6366 0.829115
\(682\) −29.5877 −1.13297
\(683\) 9.01905 0.345104 0.172552 0.985000i \(-0.444799\pi\)
0.172552 + 0.985000i \(0.444799\pi\)
\(684\) 1.45580 0.0556640
\(685\) 0 0
\(686\) 22.2374 0.849029
\(687\) 13.8838 0.529702
\(688\) −0.131888 −0.00502817
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) −50.0625 −1.90447 −0.952234 0.305368i \(-0.901221\pi\)
−0.952234 + 0.305368i \(0.901221\pi\)
\(692\) 1.50071 0.0570483
\(693\) 11.6629 0.443037
\(694\) 4.61942 0.175351
\(695\) 0 0
\(696\) −2.15633 −0.0817353
\(697\) 62.0870 2.35171
\(698\) −19.3649 −0.732970
\(699\) −7.31406 −0.276643
\(700\) 0 0
\(701\) 45.3014 1.71101 0.855505 0.517795i \(-0.173247\pi\)
0.855505 + 0.517795i \(0.173247\pi\)
\(702\) −18.9234 −0.714216
\(703\) −30.3634 −1.14518
\(704\) 29.4314 1.10924
\(705\) 0 0
\(706\) −7.70194 −0.289866
\(707\) 15.5369 0.584325
\(708\) −2.07522 −0.0779916
\(709\) −3.27504 −0.122997 −0.0614983 0.998107i \(-0.519588\pi\)
−0.0614983 + 0.998107i \(0.519588\pi\)
\(710\) 0 0
\(711\) 11.5917 0.434721
\(712\) 9.66291 0.362133
\(713\) 8.86082 0.331840
\(714\) −7.84955 −0.293762
\(715\) 0 0
\(716\) −4.15045 −0.155109
\(717\) −16.5237 −0.617090
\(718\) 45.0553 1.68145
\(719\) 27.7235 1.03391 0.516957 0.856011i \(-0.327065\pi\)
0.516957 + 0.856011i \(0.327065\pi\)
\(720\) 0 0
\(721\) 6.35168 0.236549
\(722\) −13.0327 −0.485026
\(723\) −4.41422 −0.164167
\(724\) 2.96239 0.110096
\(725\) 0 0
\(726\) −7.49200 −0.278054
\(727\) 26.8930 0.997408 0.498704 0.866772i \(-0.333810\pi\)
0.498704 + 0.866772i \(0.333810\pi\)
\(728\) −9.46168 −0.350673
\(729\) 2.02776 0.0751023
\(730\) 0 0
\(731\) −0.166944 −0.00617465
\(732\) −1.38929 −0.0513496
\(733\) −3.17935 −0.117432 −0.0587160 0.998275i \(-0.518701\pi\)
−0.0587160 + 0.998275i \(0.518701\pi\)
\(734\) −30.5950 −1.12928
\(735\) 0 0
\(736\) 2.01573 0.0743007
\(737\) −24.2882 −0.894668
\(738\) 39.2506 1.44483
\(739\) −29.7440 −1.09415 −0.547076 0.837083i \(-0.684259\pi\)
−0.547076 + 0.837083i \(0.684259\pi\)
\(740\) 0 0
\(741\) −7.62672 −0.280174
\(742\) −2.38787 −0.0876616
\(743\) 4.34297 0.159328 0.0796640 0.996822i \(-0.474615\pi\)
0.0796640 + 0.996822i \(0.474615\pi\)
\(744\) −10.3634 −0.379942
\(745\) 0 0
\(746\) −16.4241 −0.601328
\(747\) 10.3839 0.379927
\(748\) −4.43866 −0.162293
\(749\) −16.4993 −0.602871
\(750\) 0 0
\(751\) 22.5804 0.823970 0.411985 0.911191i \(-0.364836\pi\)
0.411985 + 0.911191i \(0.364836\pi\)
\(752\) 20.9076 0.762423
\(753\) 23.8740 0.870017
\(754\) 4.38787 0.159797
\(755\) 0 0
\(756\) −0.998585 −0.0363182
\(757\) −9.88461 −0.359262 −0.179631 0.983734i \(-0.557490\pi\)
−0.179631 + 0.983734i \(0.557490\pi\)
\(758\) 14.9321 0.542357
\(759\) 6.17679 0.224203
\(760\) 0 0
\(761\) 13.6991 0.496592 0.248296 0.968684i \(-0.420129\pi\)
0.248296 + 0.968684i \(0.420129\pi\)
\(762\) 17.0348 0.617105
\(763\) 2.23743 0.0810003
\(764\) 0.643859 0.0232940
\(765\) 0 0
\(766\) −24.2287 −0.875419
\(767\) −39.3258 −1.41997
\(768\) −3.71767 −0.134150
\(769\) 25.0132 0.901998 0.450999 0.892524i \(-0.351068\pi\)
0.450999 + 0.892524i \(0.351068\pi\)
\(770\) 0 0
\(771\) 14.2374 0.512748
\(772\) 0.946660 0.0340710
\(773\) 35.9062 1.29146 0.645728 0.763567i \(-0.276554\pi\)
0.645728 + 0.763567i \(0.276554\pi\)
\(774\) −0.105540 −0.00379356
\(775\) 0 0
\(776\) −3.69323 −0.132579
\(777\) 9.14903 0.328220
\(778\) 47.2506 1.69402
\(779\) 36.0118 1.29026
\(780\) 0 0
\(781\) −5.29948 −0.189630
\(782\) 15.0376 0.537744
\(783\) −4.31265 −0.154122
\(784\) 24.2506 0.866093
\(785\) 0 0
\(786\) −7.03761 −0.251023
\(787\) −50.3839 −1.79599 −0.897996 0.440003i \(-0.854977\pi\)
−0.897996 + 0.440003i \(0.854977\pi\)
\(788\) 4.70052 0.167449
\(789\) 22.0508 0.785029
\(790\) 0 0
\(791\) −14.0508 −0.499588
\(792\) 26.1319 0.928556
\(793\) −26.3272 −0.934908
\(794\) −4.42407 −0.157004
\(795\) 0 0
\(796\) 3.24869 0.115147
\(797\) 5.69323 0.201665 0.100832 0.994903i \(-0.467849\pi\)
0.100832 + 0.994903i \(0.467849\pi\)
\(798\) −4.55291 −0.161171
\(799\) 26.4650 0.936265
\(800\) 0 0
\(801\) 8.48944 0.299960
\(802\) −32.5501 −1.14938
\(803\) 63.3620 2.23600
\(804\) 0.913513 0.0322171
\(805\) 0 0
\(806\) 21.0884 0.742807
\(807\) −8.46310 −0.297915
\(808\) 34.8119 1.22468
\(809\) −7.76257 −0.272918 −0.136459 0.990646i \(-0.543572\pi\)
−0.136459 + 0.990646i \(0.543572\pi\)
\(810\) 0 0
\(811\) −26.4894 −0.930170 −0.465085 0.885266i \(-0.653976\pi\)
−0.465085 + 0.885266i \(0.653976\pi\)
\(812\) 0.231548 0.00812574
\(813\) 7.75272 0.271900
\(814\) 58.5256 2.05132
\(815\) 0 0
\(816\) −19.3093 −0.675962
\(817\) −0.0968311 −0.00338769
\(818\) −33.2360 −1.16207
\(819\) −8.31265 −0.290468
\(820\) 0 0
\(821\) 25.4763 0.889128 0.444564 0.895747i \(-0.353359\pi\)
0.444564 + 0.895747i \(0.353359\pi\)
\(822\) 21.8279 0.761337
\(823\) 9.22028 0.321399 0.160699 0.987003i \(-0.448625\pi\)
0.160699 + 0.987003i \(0.448625\pi\)
\(824\) 14.2315 0.495779
\(825\) 0 0
\(826\) −23.4763 −0.816844
\(827\) −24.5343 −0.853143 −0.426571 0.904454i \(-0.640279\pi\)
−0.426571 + 0.904454i \(0.640279\pi\)
\(828\) 0.840350 0.0292042
\(829\) 0.201231 0.00698903 0.00349452 0.999994i \(-0.498888\pi\)
0.00349452 + 0.999994i \(0.498888\pi\)
\(830\) 0 0
\(831\) 10.7612 0.373300
\(832\) −20.9770 −0.727246
\(833\) 30.6966 1.06357
\(834\) 13.7743 0.476966
\(835\) 0 0
\(836\) −2.57452 −0.0890415
\(837\) −20.7269 −0.716425
\(838\) 15.3503 0.530266
\(839\) 1.45580 0.0502599 0.0251299 0.999684i \(-0.492000\pi\)
0.0251299 + 0.999684i \(0.492000\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 50.4142 1.73739
\(843\) −16.4631 −0.567019
\(844\) −4.90763 −0.168928
\(845\) 0 0
\(846\) 16.7308 0.575218
\(847\) −7.49200 −0.257428
\(848\) −5.87399 −0.201714
\(849\) −6.46501 −0.221878
\(850\) 0 0
\(851\) −17.5271 −0.600820
\(852\) 0.199321 0.00682861
\(853\) −43.1793 −1.47843 −0.739216 0.673468i \(-0.764804\pi\)
−0.739216 + 0.673468i \(0.764804\pi\)
\(854\) −15.7165 −0.537808
\(855\) 0 0
\(856\) −36.9683 −1.26355
\(857\) 20.9887 0.716962 0.358481 0.933537i \(-0.383295\pi\)
0.358481 + 0.933537i \(0.383295\pi\)
\(858\) 14.7005 0.501868
\(859\) −49.4069 −1.68574 −0.842871 0.538115i \(-0.819137\pi\)
−0.842871 + 0.538115i \(0.819137\pi\)
\(860\) 0 0
\(861\) −10.8510 −0.369800
\(862\) 38.1768 1.30031
\(863\) −56.6820 −1.92948 −0.964738 0.263211i \(-0.915218\pi\)
−0.964738 + 0.263211i \(0.915218\pi\)
\(864\) −4.71511 −0.160411
\(865\) 0 0
\(866\) −3.23013 −0.109764
\(867\) −10.7388 −0.364708
\(868\) 1.11283 0.0377721
\(869\) −20.4993 −0.695391
\(870\) 0 0
\(871\) 17.3112 0.586569
\(872\) 5.01317 0.169767
\(873\) −3.24472 −0.109817
\(874\) 8.72213 0.295031
\(875\) 0 0
\(876\) −2.38313 −0.0805186
\(877\) 13.1998 0.445726 0.222863 0.974850i \(-0.428460\pi\)
0.222863 + 0.974850i \(0.428460\pi\)
\(878\) −52.6009 −1.77519
\(879\) −18.7856 −0.633622
\(880\) 0 0
\(881\) 6.37802 0.214881 0.107441 0.994212i \(-0.465734\pi\)
0.107441 + 0.994212i \(0.465734\pi\)
\(882\) 19.4060 0.653433
\(883\) −48.6213 −1.63624 −0.818119 0.575049i \(-0.804983\pi\)
−0.818119 + 0.575049i \(0.804983\pi\)
\(884\) 3.16362 0.106404
\(885\) 0 0
\(886\) 6.43278 0.216113
\(887\) 15.0317 0.504716 0.252358 0.967634i \(-0.418794\pi\)
0.252358 + 0.967634i \(0.418794\pi\)
\(888\) 20.4993 0.687911
\(889\) 17.0348 0.571328
\(890\) 0 0
\(891\) 14.8568 0.497723
\(892\) −3.43136 −0.114891
\(893\) 15.3503 0.513677
\(894\) −3.31406 −0.110839
\(895\) 0 0
\(896\) −15.1333 −0.505568
\(897\) −4.40246 −0.146994
\(898\) 46.4142 1.54886
\(899\) 4.80606 0.160291
\(900\) 0 0
\(901\) −7.43533 −0.247707
\(902\) −69.4128 −2.31119
\(903\) 0.0291769 0.000970946 0
\(904\) −31.4821 −1.04708
\(905\) 0 0
\(906\) −2.14762 −0.0713498
\(907\) 0.342968 0.0113880 0.00569402 0.999984i \(-0.498188\pi\)
0.00569402 + 0.999984i \(0.498188\pi\)
\(908\) −5.20570 −0.172757
\(909\) 30.5844 1.01442
\(910\) 0 0
\(911\) 20.9076 0.692701 0.346350 0.938105i \(-0.387421\pi\)
0.346350 + 0.938105i \(0.387421\pi\)
\(912\) −11.1998 −0.370863
\(913\) −18.3634 −0.607741
\(914\) −50.8773 −1.68287
\(915\) 0 0
\(916\) −3.34041 −0.110370
\(917\) −7.03761 −0.232402
\(918\) −35.1754 −1.16096
\(919\) −1.90034 −0.0626864 −0.0313432 0.999509i \(-0.509978\pi\)
−0.0313432 + 0.999509i \(0.509978\pi\)
\(920\) 0 0
\(921\) −5.42548 −0.178776
\(922\) 17.5731 0.578739
\(923\) 3.77716 0.124327
\(924\) 0.775746 0.0255202
\(925\) 0 0
\(926\) −59.9814 −1.97111
\(927\) 12.5033 0.410661
\(928\) 1.09332 0.0358900
\(929\) 39.3522 1.29110 0.645551 0.763717i \(-0.276628\pi\)
0.645551 + 0.763717i \(0.276628\pi\)
\(930\) 0 0
\(931\) 17.8046 0.583524
\(932\) 1.75974 0.0576423
\(933\) 17.7791 0.582061
\(934\) 44.7426 1.46402
\(935\) 0 0
\(936\) −18.6253 −0.608787
\(937\) 6.37802 0.208361 0.104180 0.994558i \(-0.466778\pi\)
0.104180 + 0.994558i \(0.466778\pi\)
\(938\) 10.3343 0.337426
\(939\) 4.06063 0.132514
\(940\) 0 0
\(941\) −26.6253 −0.867960 −0.433980 0.900923i \(-0.642891\pi\)
−0.433980 + 0.900923i \(0.642891\pi\)
\(942\) 4.49929 0.146595
\(943\) 20.7875 0.676934
\(944\) −57.7499 −1.87960
\(945\) 0 0
\(946\) 0.186642 0.00606827
\(947\) 12.2823 0.399122 0.199561 0.979885i \(-0.436048\pi\)
0.199561 + 0.979885i \(0.436048\pi\)
\(948\) 0.771007 0.0250411
\(949\) −45.1608 −1.46598
\(950\) 0 0
\(951\) 27.6432 0.896393
\(952\) −17.5877 −0.570020
\(953\) −0.821792 −0.0266205 −0.0133102 0.999911i \(-0.504237\pi\)
−0.0133102 + 0.999911i \(0.504237\pi\)
\(954\) −4.70052 −0.152185
\(955\) 0 0
\(956\) 3.97556 0.128579
\(957\) 3.35026 0.108299
\(958\) 0.0811024 0.00262030
\(959\) 21.8279 0.704861
\(960\) 0 0
\(961\) −7.90175 −0.254895
\(962\) −41.7137 −1.34490
\(963\) −32.4788 −1.04662
\(964\) 1.06205 0.0342063
\(965\) 0 0
\(966\) −2.62813 −0.0845587
\(967\) 37.4314 1.20371 0.601856 0.798605i \(-0.294428\pi\)
0.601856 + 0.798605i \(0.294428\pi\)
\(968\) −16.7866 −0.539540
\(969\) −14.1768 −0.455424
\(970\) 0 0
\(971\) −8.71625 −0.279718 −0.139859 0.990171i \(-0.544665\pi\)
−0.139859 + 0.990171i \(0.544665\pi\)
\(972\) −3.06793 −0.0984039
\(973\) 13.7743 0.441585
\(974\) 1.30536 0.0418263
\(975\) 0 0
\(976\) −38.6615 −1.23752
\(977\) 33.7645 1.08022 0.540111 0.841594i \(-0.318382\pi\)
0.540111 + 0.841594i \(0.318382\pi\)
\(978\) 1.96097 0.0627050
\(979\) −15.0132 −0.479823
\(980\) 0 0
\(981\) 4.40437 0.140621
\(982\) 60.8324 1.94124
\(983\) −43.6082 −1.39088 −0.695442 0.718582i \(-0.744791\pi\)
−0.695442 + 0.718582i \(0.744791\pi\)
\(984\) −24.3127 −0.775059
\(985\) 0 0
\(986\) 8.15633 0.259750
\(987\) −4.62530 −0.147225
\(988\) 1.83497 0.0583780
\(989\) −0.0558950 −0.00177736
\(990\) 0 0
\(991\) −52.9741 −1.68278 −0.841390 0.540429i \(-0.818262\pi\)
−0.841390 + 0.540429i \(0.818262\pi\)
\(992\) 5.25457 0.166833
\(993\) 28.0771 0.891001
\(994\) 2.25485 0.0715193
\(995\) 0 0
\(996\) 0.690674 0.0218849
\(997\) −13.6326 −0.431749 −0.215874 0.976421i \(-0.569260\pi\)
−0.215874 + 0.976421i \(0.569260\pi\)
\(998\) 18.3272 0.580139
\(999\) 40.9986 1.29714
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 725.2.a.e.1.3 3
3.2 odd 2 6525.2.a.be.1.1 3
5.2 odd 4 725.2.b.e.349.5 6
5.3 odd 4 725.2.b.e.349.2 6
5.4 even 2 145.2.a.c.1.1 3
15.14 odd 2 1305.2.a.p.1.3 3
20.19 odd 2 2320.2.a.n.1.2 3
35.34 odd 2 7105.2.a.o.1.1 3
40.19 odd 2 9280.2.a.br.1.2 3
40.29 even 2 9280.2.a.bj.1.2 3
145.144 even 2 4205.2.a.f.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
145.2.a.c.1.1 3 5.4 even 2
725.2.a.e.1.3 3 1.1 even 1 trivial
725.2.b.e.349.2 6 5.3 odd 4
725.2.b.e.349.5 6 5.2 odd 4
1305.2.a.p.1.3 3 15.14 odd 2
2320.2.a.n.1.2 3 20.19 odd 2
4205.2.a.f.1.3 3 145.144 even 2
6525.2.a.be.1.1 3 3.2 odd 2
7105.2.a.o.1.1 3 35.34 odd 2
9280.2.a.bj.1.2 3 40.29 even 2
9280.2.a.br.1.2 3 40.19 odd 2