Properties

Label 4025.2.a.be.1.15
Level $4025$
Weight $2$
Character 4025.1
Self dual yes
Analytic conductor $32.140$
Analytic rank $0$
Dimension $21$
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] = [4025,2,Mod(1,4025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4025, 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("4025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4025.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: \(32.1397868136\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 805)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 4025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.50084 q^{2} -0.816695 q^{3} +0.252529 q^{4} -1.22573 q^{6} +1.00000 q^{7} -2.62268 q^{8} -2.33301 q^{9} +O(q^{10})\) \(q+1.50084 q^{2} -0.816695 q^{3} +0.252529 q^{4} -1.22573 q^{6} +1.00000 q^{7} -2.62268 q^{8} -2.33301 q^{9} -5.57614 q^{11} -0.206239 q^{12} +4.04443 q^{13} +1.50084 q^{14} -4.44129 q^{16} +6.57649 q^{17} -3.50148 q^{18} +0.0315796 q^{19} -0.816695 q^{21} -8.36892 q^{22} +1.00000 q^{23} +2.14193 q^{24} +6.07006 q^{26} +4.35544 q^{27} +0.252529 q^{28} -6.35790 q^{29} +1.36927 q^{31} -1.42032 q^{32} +4.55401 q^{33} +9.87028 q^{34} -0.589153 q^{36} -2.86325 q^{37} +0.0473961 q^{38} -3.30307 q^{39} -4.54127 q^{41} -1.22573 q^{42} +1.93731 q^{43} -1.40814 q^{44} +1.50084 q^{46} +1.87483 q^{47} +3.62718 q^{48} +1.00000 q^{49} -5.37099 q^{51} +1.02134 q^{52} +1.12976 q^{53} +6.53684 q^{54} -2.62268 q^{56} -0.0257909 q^{57} -9.54221 q^{58} +5.50239 q^{59} +12.8429 q^{61} +2.05506 q^{62} -2.33301 q^{63} +6.75090 q^{64} +6.83485 q^{66} -1.66458 q^{67} +1.66075 q^{68} -0.816695 q^{69} +10.4018 q^{71} +6.11873 q^{72} +7.21105 q^{73} -4.29728 q^{74} +0.00797478 q^{76} -5.57614 q^{77} -4.95739 q^{78} +5.58626 q^{79} +3.44196 q^{81} -6.81573 q^{82} +11.1128 q^{83} -0.206239 q^{84} +2.90759 q^{86} +5.19247 q^{87} +14.6244 q^{88} +16.6306 q^{89} +4.04443 q^{91} +0.252529 q^{92} -1.11828 q^{93} +2.81383 q^{94} +1.15997 q^{96} -13.8986 q^{97} +1.50084 q^{98} +13.0092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9} + 7 q^{11} - 22 q^{12} - 3 q^{13} + 2 q^{14} + 56 q^{16} + 7 q^{17} + 24 q^{19} - q^{21} + 4 q^{22} + 21 q^{23} + 24 q^{24} - 2 q^{26} - 19 q^{27} + 30 q^{28} + 11 q^{29} + 46 q^{31} - 6 q^{32} - 3 q^{33} + 28 q^{34} + 58 q^{36} + 24 q^{37} - 4 q^{38} + 31 q^{39} + 14 q^{41} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 2 q^{46} - 25 q^{47} - 36 q^{48} + 21 q^{49} + 17 q^{51} - 8 q^{52} + 22 q^{53} - 6 q^{54} + 6 q^{56} + 40 q^{57} + 6 q^{58} + 10 q^{59} + 38 q^{61} - 54 q^{62} + 30 q^{63} + 100 q^{64} + 38 q^{66} + 12 q^{67} + 18 q^{68} - q^{69} + 56 q^{71} + 42 q^{72} - 40 q^{73} - 20 q^{74} + 60 q^{76} + 7 q^{77} + 38 q^{78} + 49 q^{79} + 57 q^{81} + 16 q^{82} - 2 q^{83} - 22 q^{84} + 16 q^{86} - 23 q^{87} + 12 q^{88} + 28 q^{89} - 3 q^{91} + 30 q^{92} - 30 q^{93} + 66 q^{94} + 46 q^{96} - q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50084 1.06126 0.530628 0.847605i \(-0.321956\pi\)
0.530628 + 0.847605i \(0.321956\pi\)
\(3\) −0.816695 −0.471519 −0.235760 0.971811i \(-0.575758\pi\)
−0.235760 + 0.971811i \(0.575758\pi\)
\(4\) 0.252529 0.126265
\(5\) 0 0
\(6\) −1.22573 −0.500403
\(7\) 1.00000 0.377964
\(8\) −2.62268 −0.927257
\(9\) −2.33301 −0.777670
\(10\) 0 0
\(11\) −5.57614 −1.68127 −0.840635 0.541601i \(-0.817818\pi\)
−0.840635 + 0.541601i \(0.817818\pi\)
\(12\) −0.206239 −0.0595362
\(13\) 4.04443 1.12172 0.560862 0.827909i \(-0.310470\pi\)
0.560862 + 0.827909i \(0.310470\pi\)
\(14\) 1.50084 0.401117
\(15\) 0 0
\(16\) −4.44129 −1.11032
\(17\) 6.57649 1.59503 0.797516 0.603297i \(-0.206147\pi\)
0.797516 + 0.603297i \(0.206147\pi\)
\(18\) −3.50148 −0.825307
\(19\) 0.0315796 0.00724487 0.00362243 0.999993i \(-0.498847\pi\)
0.00362243 + 0.999993i \(0.498847\pi\)
\(20\) 0 0
\(21\) −0.816695 −0.178218
\(22\) −8.36892 −1.78426
\(23\) 1.00000 0.208514
\(24\) 2.14193 0.437220
\(25\) 0 0
\(26\) 6.07006 1.19044
\(27\) 4.35544 0.838205
\(28\) 0.252529 0.0477235
\(29\) −6.35790 −1.18063 −0.590317 0.807172i \(-0.700997\pi\)
−0.590317 + 0.807172i \(0.700997\pi\)
\(30\) 0 0
\(31\) 1.36927 0.245929 0.122964 0.992411i \(-0.460760\pi\)
0.122964 + 0.992411i \(0.460760\pi\)
\(32\) −1.42032 −0.251079
\(33\) 4.55401 0.792752
\(34\) 9.87028 1.69274
\(35\) 0 0
\(36\) −0.589153 −0.0981921
\(37\) −2.86325 −0.470715 −0.235357 0.971909i \(-0.575626\pi\)
−0.235357 + 0.971909i \(0.575626\pi\)
\(38\) 0.0473961 0.00768866
\(39\) −3.30307 −0.528914
\(40\) 0 0
\(41\) −4.54127 −0.709227 −0.354613 0.935013i \(-0.615388\pi\)
−0.354613 + 0.935013i \(0.615388\pi\)
\(42\) −1.22573 −0.189134
\(43\) 1.93731 0.295437 0.147718 0.989029i \(-0.452807\pi\)
0.147718 + 0.989029i \(0.452807\pi\)
\(44\) −1.40814 −0.212285
\(45\) 0 0
\(46\) 1.50084 0.221287
\(47\) 1.87483 0.273472 0.136736 0.990608i \(-0.456339\pi\)
0.136736 + 0.990608i \(0.456339\pi\)
\(48\) 3.62718 0.523538
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −5.37099 −0.752089
\(52\) 1.02134 0.141634
\(53\) 1.12976 0.155184 0.0775919 0.996985i \(-0.475277\pi\)
0.0775919 + 0.996985i \(0.475277\pi\)
\(54\) 6.53684 0.889551
\(55\) 0 0
\(56\) −2.62268 −0.350470
\(57\) −0.0257909 −0.00341609
\(58\) −9.54221 −1.25295
\(59\) 5.50239 0.716350 0.358175 0.933654i \(-0.383399\pi\)
0.358175 + 0.933654i \(0.383399\pi\)
\(60\) 0 0
\(61\) 12.8429 1.64437 0.822185 0.569221i \(-0.192755\pi\)
0.822185 + 0.569221i \(0.192755\pi\)
\(62\) 2.05506 0.260993
\(63\) −2.33301 −0.293931
\(64\) 6.75090 0.843863
\(65\) 0 0
\(66\) 6.83485 0.841312
\(67\) −1.66458 −0.203361 −0.101680 0.994817i \(-0.532422\pi\)
−0.101680 + 0.994817i \(0.532422\pi\)
\(68\) 1.66075 0.201396
\(69\) −0.816695 −0.0983186
\(70\) 0 0
\(71\) 10.4018 1.23446 0.617231 0.786782i \(-0.288254\pi\)
0.617231 + 0.786782i \(0.288254\pi\)
\(72\) 6.11873 0.721100
\(73\) 7.21105 0.843990 0.421995 0.906598i \(-0.361330\pi\)
0.421995 + 0.906598i \(0.361330\pi\)
\(74\) −4.29728 −0.499549
\(75\) 0 0
\(76\) 0.00797478 0.000914770 0
\(77\) −5.57614 −0.635461
\(78\) −4.95739 −0.561313
\(79\) 5.58626 0.628504 0.314252 0.949340i \(-0.398246\pi\)
0.314252 + 0.949340i \(0.398246\pi\)
\(80\) 0 0
\(81\) 3.44196 0.382440
\(82\) −6.81573 −0.752671
\(83\) 11.1128 1.21979 0.609894 0.792483i \(-0.291212\pi\)
0.609894 + 0.792483i \(0.291212\pi\)
\(84\) −0.206239 −0.0225026
\(85\) 0 0
\(86\) 2.90759 0.313534
\(87\) 5.19247 0.556691
\(88\) 14.6244 1.55897
\(89\) 16.6306 1.76284 0.881418 0.472337i \(-0.156590\pi\)
0.881418 + 0.472337i \(0.156590\pi\)
\(90\) 0 0
\(91\) 4.04443 0.423972
\(92\) 0.252529 0.0263280
\(93\) −1.11828 −0.115960
\(94\) 2.81383 0.290224
\(95\) 0 0
\(96\) 1.15997 0.118388
\(97\) −13.8986 −1.41119 −0.705597 0.708614i \(-0.749321\pi\)
−0.705597 + 0.708614i \(0.749321\pi\)
\(98\) 1.50084 0.151608
\(99\) 13.0092 1.30747
\(100\) 0 0
\(101\) 8.56886 0.852634 0.426317 0.904574i \(-0.359811\pi\)
0.426317 + 0.904574i \(0.359811\pi\)
\(102\) −8.06101 −0.798159
\(103\) 7.41286 0.730411 0.365205 0.930927i \(-0.380999\pi\)
0.365205 + 0.930927i \(0.380999\pi\)
\(104\) −10.6072 −1.04013
\(105\) 0 0
\(106\) 1.69559 0.164690
\(107\) −3.54317 −0.342532 −0.171266 0.985225i \(-0.554786\pi\)
−0.171266 + 0.985225i \(0.554786\pi\)
\(108\) 1.09988 0.105836
\(109\) −12.4712 −1.19452 −0.597261 0.802047i \(-0.703744\pi\)
−0.597261 + 0.802047i \(0.703744\pi\)
\(110\) 0 0
\(111\) 2.33840 0.221951
\(112\) −4.44129 −0.419662
\(113\) −9.56214 −0.899530 −0.449765 0.893147i \(-0.648492\pi\)
−0.449765 + 0.893147i \(0.648492\pi\)
\(114\) −0.0387082 −0.00362535
\(115\) 0 0
\(116\) −1.60556 −0.149072
\(117\) −9.43569 −0.872330
\(118\) 8.25822 0.760231
\(119\) 6.57649 0.602866
\(120\) 0 0
\(121\) 20.0934 1.82667
\(122\) 19.2752 1.74510
\(123\) 3.70883 0.334414
\(124\) 0.345781 0.0310521
\(125\) 0 0
\(126\) −3.50148 −0.311937
\(127\) 16.6954 1.48148 0.740739 0.671793i \(-0.234476\pi\)
0.740739 + 0.671793i \(0.234476\pi\)
\(128\) 12.9727 1.14663
\(129\) −1.58219 −0.139304
\(130\) 0 0
\(131\) −1.51048 −0.131972 −0.0659858 0.997821i \(-0.521019\pi\)
−0.0659858 + 0.997821i \(0.521019\pi\)
\(132\) 1.15002 0.100096
\(133\) 0.0315796 0.00273830
\(134\) −2.49827 −0.215818
\(135\) 0 0
\(136\) −17.2480 −1.47901
\(137\) 5.80267 0.495756 0.247878 0.968791i \(-0.420267\pi\)
0.247878 + 0.968791i \(0.420267\pi\)
\(138\) −1.22573 −0.104341
\(139\) −7.01912 −0.595354 −0.297677 0.954667i \(-0.596212\pi\)
−0.297677 + 0.954667i \(0.596212\pi\)
\(140\) 0 0
\(141\) −1.53117 −0.128947
\(142\) 15.6114 1.31008
\(143\) −22.5523 −1.88592
\(144\) 10.3616 0.863464
\(145\) 0 0
\(146\) 10.8227 0.895689
\(147\) −0.816695 −0.0673599
\(148\) −0.723053 −0.0594346
\(149\) −21.2940 −1.74447 −0.872235 0.489087i \(-0.837330\pi\)
−0.872235 + 0.489087i \(0.837330\pi\)
\(150\) 0 0
\(151\) 2.55312 0.207770 0.103885 0.994589i \(-0.466873\pi\)
0.103885 + 0.994589i \(0.466873\pi\)
\(152\) −0.0828233 −0.00671785
\(153\) −15.3430 −1.24041
\(154\) −8.36892 −0.674386
\(155\) 0 0
\(156\) −0.834121 −0.0667831
\(157\) 7.81119 0.623401 0.311700 0.950180i \(-0.399101\pi\)
0.311700 + 0.950180i \(0.399101\pi\)
\(158\) 8.38410 0.667003
\(159\) −0.922666 −0.0731722
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 5.16584 0.405866
\(163\) 23.2397 1.82027 0.910137 0.414307i \(-0.135976\pi\)
0.910137 + 0.414307i \(0.135976\pi\)
\(164\) −1.14680 −0.0895502
\(165\) 0 0
\(166\) 16.6786 1.29451
\(167\) 10.4503 0.808672 0.404336 0.914611i \(-0.367503\pi\)
0.404336 + 0.914611i \(0.367503\pi\)
\(168\) 2.14193 0.165253
\(169\) 3.35743 0.258264
\(170\) 0 0
\(171\) −0.0736756 −0.00563411
\(172\) 0.489226 0.0373032
\(173\) 11.1955 0.851177 0.425588 0.904917i \(-0.360067\pi\)
0.425588 + 0.904917i \(0.360067\pi\)
\(174\) 7.79308 0.590792
\(175\) 0 0
\(176\) 24.7653 1.86675
\(177\) −4.49377 −0.337773
\(178\) 24.9599 1.87082
\(179\) −6.43423 −0.480917 −0.240458 0.970659i \(-0.577298\pi\)
−0.240458 + 0.970659i \(0.577298\pi\)
\(180\) 0 0
\(181\) −16.3430 −1.21476 −0.607382 0.794410i \(-0.707780\pi\)
−0.607382 + 0.794410i \(0.707780\pi\)
\(182\) 6.07006 0.449942
\(183\) −10.4888 −0.775352
\(184\) −2.62268 −0.193346
\(185\) 0 0
\(186\) −1.67836 −0.123063
\(187\) −36.6714 −2.68168
\(188\) 0.473449 0.0345298
\(189\) 4.35544 0.316812
\(190\) 0 0
\(191\) 15.4727 1.11957 0.559783 0.828639i \(-0.310884\pi\)
0.559783 + 0.828639i \(0.310884\pi\)
\(192\) −5.51343 −0.397898
\(193\) −17.7528 −1.27787 −0.638936 0.769260i \(-0.720625\pi\)
−0.638936 + 0.769260i \(0.720625\pi\)
\(194\) −20.8597 −1.49764
\(195\) 0 0
\(196\) 0.252529 0.0180378
\(197\) −12.4152 −0.884546 −0.442273 0.896880i \(-0.645828\pi\)
−0.442273 + 0.896880i \(0.645828\pi\)
\(198\) 19.5248 1.38756
\(199\) 13.7043 0.971473 0.485736 0.874105i \(-0.338552\pi\)
0.485736 + 0.874105i \(0.338552\pi\)
\(200\) 0 0
\(201\) 1.35945 0.0958885
\(202\) 12.8605 0.904863
\(203\) −6.35790 −0.446237
\(204\) −1.35633 −0.0949621
\(205\) 0 0
\(206\) 11.1255 0.775153
\(207\) −2.33301 −0.162155
\(208\) −17.9625 −1.24547
\(209\) −0.176093 −0.0121806
\(210\) 0 0
\(211\) 16.4605 1.13319 0.566595 0.823996i \(-0.308260\pi\)
0.566595 + 0.823996i \(0.308260\pi\)
\(212\) 0.285296 0.0195942
\(213\) −8.49508 −0.582073
\(214\) −5.31775 −0.363514
\(215\) 0 0
\(216\) −11.4229 −0.777232
\(217\) 1.36927 0.0929523
\(218\) −18.7173 −1.26769
\(219\) −5.88923 −0.397957
\(220\) 0 0
\(221\) 26.5982 1.78919
\(222\) 3.50957 0.235547
\(223\) 14.8249 0.992749 0.496374 0.868108i \(-0.334664\pi\)
0.496374 + 0.868108i \(0.334664\pi\)
\(224\) −1.42032 −0.0948988
\(225\) 0 0
\(226\) −14.3513 −0.954632
\(227\) 18.2901 1.21396 0.606979 0.794718i \(-0.292381\pi\)
0.606979 + 0.794718i \(0.292381\pi\)
\(228\) −0.00651296 −0.000431332 0
\(229\) 26.0017 1.71824 0.859120 0.511774i \(-0.171011\pi\)
0.859120 + 0.511774i \(0.171011\pi\)
\(230\) 0 0
\(231\) 4.55401 0.299632
\(232\) 16.6747 1.09475
\(233\) −9.49697 −0.622167 −0.311084 0.950383i \(-0.600692\pi\)
−0.311084 + 0.950383i \(0.600692\pi\)
\(234\) −14.1615 −0.925766
\(235\) 0 0
\(236\) 1.38951 0.0904496
\(237\) −4.56228 −0.296352
\(238\) 9.87028 0.639795
\(239\) −26.3213 −1.70258 −0.851291 0.524694i \(-0.824180\pi\)
−0.851291 + 0.524694i \(0.824180\pi\)
\(240\) 0 0
\(241\) −11.2193 −0.722701 −0.361351 0.932430i \(-0.617684\pi\)
−0.361351 + 0.932430i \(0.617684\pi\)
\(242\) 30.1570 1.93857
\(243\) −15.8774 −1.01853
\(244\) 3.24322 0.207626
\(245\) 0 0
\(246\) 5.56637 0.354899
\(247\) 0.127722 0.00812674
\(248\) −3.59116 −0.228039
\(249\) −9.07578 −0.575154
\(250\) 0 0
\(251\) −6.14342 −0.387769 −0.193885 0.981024i \(-0.562109\pi\)
−0.193885 + 0.981024i \(0.562109\pi\)
\(252\) −0.589153 −0.0371131
\(253\) −5.57614 −0.350569
\(254\) 25.0572 1.57223
\(255\) 0 0
\(256\) 5.96814 0.373009
\(257\) −22.3978 −1.39714 −0.698568 0.715544i \(-0.746179\pi\)
−0.698568 + 0.715544i \(0.746179\pi\)
\(258\) −2.37462 −0.147837
\(259\) −2.86325 −0.177913
\(260\) 0 0
\(261\) 14.8330 0.918142
\(262\) −2.26700 −0.140056
\(263\) 20.5242 1.26558 0.632789 0.774324i \(-0.281910\pi\)
0.632789 + 0.774324i \(0.281910\pi\)
\(264\) −11.9437 −0.735085
\(265\) 0 0
\(266\) 0.0473961 0.00290604
\(267\) −13.5821 −0.831211
\(268\) −0.420355 −0.0256772
\(269\) −18.4098 −1.12246 −0.561232 0.827658i \(-0.689673\pi\)
−0.561232 + 0.827658i \(0.689673\pi\)
\(270\) 0 0
\(271\) 4.23951 0.257532 0.128766 0.991675i \(-0.458898\pi\)
0.128766 + 0.991675i \(0.458898\pi\)
\(272\) −29.2081 −1.77100
\(273\) −3.30307 −0.199911
\(274\) 8.70890 0.526124
\(275\) 0 0
\(276\) −0.206239 −0.0124141
\(277\) −3.50266 −0.210454 −0.105227 0.994448i \(-0.533557\pi\)
−0.105227 + 0.994448i \(0.533557\pi\)
\(278\) −10.5346 −0.631823
\(279\) −3.19452 −0.191251
\(280\) 0 0
\(281\) −17.7739 −1.06030 −0.530151 0.847903i \(-0.677865\pi\)
−0.530151 + 0.847903i \(0.677865\pi\)
\(282\) −2.29804 −0.136846
\(283\) −24.4579 −1.45387 −0.726934 0.686707i \(-0.759056\pi\)
−0.726934 + 0.686707i \(0.759056\pi\)
\(284\) 2.62675 0.155869
\(285\) 0 0
\(286\) −33.8475 −2.00145
\(287\) −4.54127 −0.268063
\(288\) 3.31361 0.195256
\(289\) 26.2502 1.54413
\(290\) 0 0
\(291\) 11.3510 0.665405
\(292\) 1.82100 0.106566
\(293\) −1.58615 −0.0926639 −0.0463320 0.998926i \(-0.514753\pi\)
−0.0463320 + 0.998926i \(0.514753\pi\)
\(294\) −1.22573 −0.0714861
\(295\) 0 0
\(296\) 7.50938 0.436474
\(297\) −24.2866 −1.40925
\(298\) −31.9589 −1.85133
\(299\) 4.04443 0.233896
\(300\) 0 0
\(301\) 1.93731 0.111665
\(302\) 3.83183 0.220497
\(303\) −6.99815 −0.402033
\(304\) −0.140254 −0.00804413
\(305\) 0 0
\(306\) −23.0274 −1.31639
\(307\) −9.24426 −0.527598 −0.263799 0.964578i \(-0.584976\pi\)
−0.263799 + 0.964578i \(0.584976\pi\)
\(308\) −1.40814 −0.0802361
\(309\) −6.05405 −0.344403
\(310\) 0 0
\(311\) −19.4611 −1.10354 −0.551768 0.833998i \(-0.686047\pi\)
−0.551768 + 0.833998i \(0.686047\pi\)
\(312\) 8.66289 0.490439
\(313\) 25.4236 1.43702 0.718512 0.695514i \(-0.244823\pi\)
0.718512 + 0.695514i \(0.244823\pi\)
\(314\) 11.7234 0.661588
\(315\) 0 0
\(316\) 1.41069 0.0793577
\(317\) −6.44839 −0.362178 −0.181089 0.983467i \(-0.557962\pi\)
−0.181089 + 0.983467i \(0.557962\pi\)
\(318\) −1.38478 −0.0776544
\(319\) 35.4526 1.98496
\(320\) 0 0
\(321\) 2.89369 0.161510
\(322\) 1.50084 0.0836387
\(323\) 0.207683 0.0115558
\(324\) 0.869194 0.0482886
\(325\) 0 0
\(326\) 34.8791 1.93178
\(327\) 10.1851 0.563240
\(328\) 11.9103 0.657636
\(329\) 1.87483 0.103363
\(330\) 0 0
\(331\) 23.7887 1.30755 0.653774 0.756690i \(-0.273185\pi\)
0.653774 + 0.756690i \(0.273185\pi\)
\(332\) 2.80631 0.154016
\(333\) 6.67998 0.366061
\(334\) 15.6843 0.858208
\(335\) 0 0
\(336\) 3.62718 0.197879
\(337\) 18.0792 0.984838 0.492419 0.870358i \(-0.336113\pi\)
0.492419 + 0.870358i \(0.336113\pi\)
\(338\) 5.03897 0.274084
\(339\) 7.80935 0.424146
\(340\) 0 0
\(341\) −7.63526 −0.413473
\(342\) −0.110575 −0.00597924
\(343\) 1.00000 0.0539949
\(344\) −5.08094 −0.273946
\(345\) 0 0
\(346\) 16.8027 0.903316
\(347\) −3.93025 −0.210987 −0.105494 0.994420i \(-0.533642\pi\)
−0.105494 + 0.994420i \(0.533642\pi\)
\(348\) 1.31125 0.0702904
\(349\) −9.77290 −0.523131 −0.261566 0.965186i \(-0.584239\pi\)
−0.261566 + 0.965186i \(0.584239\pi\)
\(350\) 0 0
\(351\) 17.6153 0.940235
\(352\) 7.91989 0.422131
\(353\) 23.1310 1.23114 0.615570 0.788082i \(-0.288926\pi\)
0.615570 + 0.788082i \(0.288926\pi\)
\(354\) −6.74445 −0.358463
\(355\) 0 0
\(356\) 4.19970 0.222584
\(357\) −5.37099 −0.284263
\(358\) −9.65677 −0.510376
\(359\) 6.64008 0.350450 0.175225 0.984528i \(-0.443935\pi\)
0.175225 + 0.984528i \(0.443935\pi\)
\(360\) 0 0
\(361\) −18.9990 −0.999948
\(362\) −24.5282 −1.28918
\(363\) −16.4102 −0.861311
\(364\) 1.02134 0.0535326
\(365\) 0 0
\(366\) −15.7420 −0.822847
\(367\) −12.6692 −0.661325 −0.330662 0.943749i \(-0.607272\pi\)
−0.330662 + 0.943749i \(0.607272\pi\)
\(368\) −4.44129 −0.231518
\(369\) 10.5948 0.551544
\(370\) 0 0
\(371\) 1.12976 0.0586540
\(372\) −0.282398 −0.0146416
\(373\) −6.00241 −0.310793 −0.155396 0.987852i \(-0.549665\pi\)
−0.155396 + 0.987852i \(0.549665\pi\)
\(374\) −55.0381 −2.84595
\(375\) 0 0
\(376\) −4.91708 −0.253579
\(377\) −25.7141 −1.32434
\(378\) 6.53684 0.336219
\(379\) 31.3566 1.61068 0.805340 0.592814i \(-0.201983\pi\)
0.805340 + 0.592814i \(0.201983\pi\)
\(380\) 0 0
\(381\) −13.6351 −0.698545
\(382\) 23.2221 1.18815
\(383\) 5.53739 0.282948 0.141474 0.989942i \(-0.454816\pi\)
0.141474 + 0.989942i \(0.454816\pi\)
\(384\) −10.5947 −0.540660
\(385\) 0 0
\(386\) −26.6441 −1.35615
\(387\) −4.51976 −0.229752
\(388\) −3.50981 −0.178184
\(389\) 8.20381 0.415950 0.207975 0.978134i \(-0.433313\pi\)
0.207975 + 0.978134i \(0.433313\pi\)
\(390\) 0 0
\(391\) 6.57649 0.332587
\(392\) −2.62268 −0.132465
\(393\) 1.23361 0.0622272
\(394\) −18.6333 −0.938730
\(395\) 0 0
\(396\) 3.28520 0.165087
\(397\) 9.62114 0.482871 0.241436 0.970417i \(-0.422382\pi\)
0.241436 + 0.970417i \(0.422382\pi\)
\(398\) 20.5680 1.03098
\(399\) −0.0257909 −0.00129116
\(400\) 0 0
\(401\) 26.8333 1.33999 0.669996 0.742365i \(-0.266296\pi\)
0.669996 + 0.742365i \(0.266296\pi\)
\(402\) 2.04033 0.101762
\(403\) 5.53793 0.275864
\(404\) 2.16389 0.107657
\(405\) 0 0
\(406\) −9.54221 −0.473572
\(407\) 15.9659 0.791399
\(408\) 14.0864 0.697380
\(409\) 36.4908 1.80436 0.902178 0.431365i \(-0.141968\pi\)
0.902178 + 0.431365i \(0.141968\pi\)
\(410\) 0 0
\(411\) −4.73902 −0.233758
\(412\) 1.87196 0.0922250
\(413\) 5.50239 0.270755
\(414\) −3.50148 −0.172088
\(415\) 0 0
\(416\) −5.74437 −0.281641
\(417\) 5.73248 0.280721
\(418\) −0.264287 −0.0129267
\(419\) −11.8204 −0.577465 −0.288733 0.957410i \(-0.593234\pi\)
−0.288733 + 0.957410i \(0.593234\pi\)
\(420\) 0 0
\(421\) −10.0249 −0.488583 −0.244291 0.969702i \(-0.578555\pi\)
−0.244291 + 0.969702i \(0.578555\pi\)
\(422\) 24.7047 1.20261
\(423\) −4.37400 −0.212671
\(424\) −2.96299 −0.143895
\(425\) 0 0
\(426\) −12.7498 −0.617728
\(427\) 12.8429 0.621513
\(428\) −0.894754 −0.0432496
\(429\) 18.4184 0.889248
\(430\) 0 0
\(431\) −27.9864 −1.34806 −0.674029 0.738705i \(-0.735438\pi\)
−0.674029 + 0.738705i \(0.735438\pi\)
\(432\) −19.3438 −0.930678
\(433\) −17.0989 −0.821719 −0.410859 0.911699i \(-0.634771\pi\)
−0.410859 + 0.911699i \(0.634771\pi\)
\(434\) 2.05506 0.0986462
\(435\) 0 0
\(436\) −3.14933 −0.150826
\(437\) 0.0315796 0.00151066
\(438\) −8.83881 −0.422335
\(439\) 24.6894 1.17836 0.589180 0.808002i \(-0.299451\pi\)
0.589180 + 0.808002i \(0.299451\pi\)
\(440\) 0 0
\(441\) −2.33301 −0.111096
\(442\) 39.9197 1.89878
\(443\) −22.3512 −1.06194 −0.530968 0.847392i \(-0.678172\pi\)
−0.530968 + 0.847392i \(0.678172\pi\)
\(444\) 0.590514 0.0280246
\(445\) 0 0
\(446\) 22.2499 1.05356
\(447\) 17.3907 0.822551
\(448\) 6.75090 0.318950
\(449\) −14.0885 −0.664878 −0.332439 0.943125i \(-0.607871\pi\)
−0.332439 + 0.943125i \(0.607871\pi\)
\(450\) 0 0
\(451\) 25.3228 1.19240
\(452\) −2.41472 −0.113579
\(453\) −2.08512 −0.0979675
\(454\) 27.4506 1.28832
\(455\) 0 0
\(456\) 0.0676414 0.00316760
\(457\) 29.8888 1.39814 0.699070 0.715054i \(-0.253598\pi\)
0.699070 + 0.715054i \(0.253598\pi\)
\(458\) 39.0245 1.82349
\(459\) 28.6435 1.33697
\(460\) 0 0
\(461\) −29.6760 −1.38215 −0.691074 0.722784i \(-0.742862\pi\)
−0.691074 + 0.722784i \(0.742862\pi\)
\(462\) 6.83485 0.317986
\(463\) 13.0213 0.605153 0.302576 0.953125i \(-0.402153\pi\)
0.302576 + 0.953125i \(0.402153\pi\)
\(464\) 28.2373 1.31088
\(465\) 0 0
\(466\) −14.2535 −0.660279
\(467\) 9.14341 0.423107 0.211553 0.977366i \(-0.432148\pi\)
0.211553 + 0.977366i \(0.432148\pi\)
\(468\) −2.38279 −0.110144
\(469\) −1.66458 −0.0768631
\(470\) 0 0
\(471\) −6.37936 −0.293945
\(472\) −14.4310 −0.664241
\(473\) −10.8027 −0.496709
\(474\) −6.84726 −0.314505
\(475\) 0 0
\(476\) 1.66075 0.0761206
\(477\) −2.63573 −0.120682
\(478\) −39.5041 −1.80688
\(479\) −9.02717 −0.412462 −0.206231 0.978503i \(-0.566120\pi\)
−0.206231 + 0.978503i \(0.566120\pi\)
\(480\) 0 0
\(481\) −11.5802 −0.528012
\(482\) −16.8385 −0.766971
\(483\) −0.816695 −0.0371609
\(484\) 5.07416 0.230644
\(485\) 0 0
\(486\) −23.8294 −1.08092
\(487\) −32.3124 −1.46421 −0.732107 0.681189i \(-0.761463\pi\)
−0.732107 + 0.681189i \(0.761463\pi\)
\(488\) −33.6829 −1.52475
\(489\) −18.9798 −0.858294
\(490\) 0 0
\(491\) 20.5131 0.925742 0.462871 0.886426i \(-0.346819\pi\)
0.462871 + 0.886426i \(0.346819\pi\)
\(492\) 0.936588 0.0422246
\(493\) −41.8127 −1.88315
\(494\) 0.191690 0.00862455
\(495\) 0 0
\(496\) −6.08133 −0.273060
\(497\) 10.4018 0.466583
\(498\) −13.6213 −0.610386
\(499\) 24.9439 1.11664 0.558322 0.829624i \(-0.311445\pi\)
0.558322 + 0.829624i \(0.311445\pi\)
\(500\) 0 0
\(501\) −8.53474 −0.381304
\(502\) −9.22031 −0.411523
\(503\) −18.3089 −0.816353 −0.408177 0.912903i \(-0.633835\pi\)
−0.408177 + 0.912903i \(0.633835\pi\)
\(504\) 6.11873 0.272550
\(505\) 0 0
\(506\) −8.36892 −0.372044
\(507\) −2.74200 −0.121776
\(508\) 4.21607 0.187058
\(509\) 15.6600 0.694118 0.347059 0.937843i \(-0.387180\pi\)
0.347059 + 0.937843i \(0.387180\pi\)
\(510\) 0 0
\(511\) 7.21105 0.318998
\(512\) −16.9881 −0.750776
\(513\) 0.137543 0.00607269
\(514\) −33.6156 −1.48272
\(515\) 0 0
\(516\) −0.399549 −0.0175892
\(517\) −10.4543 −0.459781
\(518\) −4.29728 −0.188812
\(519\) −9.14330 −0.401346
\(520\) 0 0
\(521\) −21.8013 −0.955131 −0.477566 0.878596i \(-0.658481\pi\)
−0.477566 + 0.878596i \(0.658481\pi\)
\(522\) 22.2621 0.974384
\(523\) 24.7544 1.08244 0.541218 0.840883i \(-0.317964\pi\)
0.541218 + 0.840883i \(0.317964\pi\)
\(524\) −0.381441 −0.0166633
\(525\) 0 0
\(526\) 30.8036 1.34310
\(527\) 9.00501 0.392264
\(528\) −20.2257 −0.880209
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −12.8371 −0.557084
\(532\) 0.00797478 0.000345751 0
\(533\) −18.3668 −0.795557
\(534\) −20.3846 −0.882128
\(535\) 0 0
\(536\) 4.36566 0.188568
\(537\) 5.25481 0.226762
\(538\) −27.6302 −1.19122
\(539\) −5.57614 −0.240182
\(540\) 0 0
\(541\) 25.9715 1.11660 0.558302 0.829638i \(-0.311453\pi\)
0.558302 + 0.829638i \(0.311453\pi\)
\(542\) 6.36283 0.273307
\(543\) 13.3472 0.572785
\(544\) −9.34069 −0.400479
\(545\) 0 0
\(546\) −4.95739 −0.212157
\(547\) −18.5380 −0.792626 −0.396313 0.918115i \(-0.629711\pi\)
−0.396313 + 0.918115i \(0.629711\pi\)
\(548\) 1.46534 0.0625964
\(549\) −29.9627 −1.27878
\(550\) 0 0
\(551\) −0.200780 −0.00855353
\(552\) 2.14193 0.0911666
\(553\) 5.58626 0.237552
\(554\) −5.25694 −0.223346
\(555\) 0 0
\(556\) −1.77253 −0.0751721
\(557\) −0.901162 −0.0381834 −0.0190917 0.999818i \(-0.506077\pi\)
−0.0190917 + 0.999818i \(0.506077\pi\)
\(558\) −4.79448 −0.202967
\(559\) 7.83531 0.331398
\(560\) 0 0
\(561\) 29.9494 1.26446
\(562\) −26.6758 −1.12525
\(563\) −38.6739 −1.62991 −0.814955 0.579525i \(-0.803238\pi\)
−0.814955 + 0.579525i \(0.803238\pi\)
\(564\) −0.386664 −0.0162815
\(565\) 0 0
\(566\) −36.7074 −1.54293
\(567\) 3.44196 0.144549
\(568\) −27.2805 −1.14466
\(569\) 12.1566 0.509631 0.254816 0.966990i \(-0.417985\pi\)
0.254816 + 0.966990i \(0.417985\pi\)
\(570\) 0 0
\(571\) −43.6516 −1.82676 −0.913382 0.407104i \(-0.866539\pi\)
−0.913382 + 0.407104i \(0.866539\pi\)
\(572\) −5.69512 −0.238125
\(573\) −12.6365 −0.527897
\(574\) −6.81573 −0.284483
\(575\) 0 0
\(576\) −15.7499 −0.656247
\(577\) −9.86386 −0.410638 −0.205319 0.978695i \(-0.565823\pi\)
−0.205319 + 0.978695i \(0.565823\pi\)
\(578\) 39.3974 1.63872
\(579\) 14.4986 0.602541
\(580\) 0 0
\(581\) 11.1128 0.461037
\(582\) 17.0360 0.706165
\(583\) −6.29968 −0.260906
\(584\) −18.9123 −0.782595
\(585\) 0 0
\(586\) −2.38056 −0.0983401
\(587\) 42.5969 1.75816 0.879080 0.476674i \(-0.158158\pi\)
0.879080 + 0.476674i \(0.158158\pi\)
\(588\) −0.206239 −0.00850517
\(589\) 0.0432411 0.00178172
\(590\) 0 0
\(591\) 10.1394 0.417080
\(592\) 12.7165 0.522645
\(593\) −9.47386 −0.389045 −0.194522 0.980898i \(-0.562316\pi\)
−0.194522 + 0.980898i \(0.562316\pi\)
\(594\) −36.4503 −1.49558
\(595\) 0 0
\(596\) −5.37735 −0.220265
\(597\) −11.1922 −0.458068
\(598\) 6.07006 0.248223
\(599\) 38.5320 1.57438 0.787188 0.616713i \(-0.211536\pi\)
0.787188 + 0.616713i \(0.211536\pi\)
\(600\) 0 0
\(601\) 36.3755 1.48379 0.741895 0.670517i \(-0.233927\pi\)
0.741895 + 0.670517i \(0.233927\pi\)
\(602\) 2.90759 0.118505
\(603\) 3.88348 0.158147
\(604\) 0.644737 0.0262340
\(605\) 0 0
\(606\) −10.5031 −0.426660
\(607\) −15.4526 −0.627202 −0.313601 0.949555i \(-0.601535\pi\)
−0.313601 + 0.949555i \(0.601535\pi\)
\(608\) −0.0448531 −0.00181903
\(609\) 5.19247 0.210410
\(610\) 0 0
\(611\) 7.58263 0.306760
\(612\) −3.87456 −0.156620
\(613\) −33.8611 −1.36764 −0.683818 0.729653i \(-0.739682\pi\)
−0.683818 + 0.729653i \(0.739682\pi\)
\(614\) −13.8742 −0.559916
\(615\) 0 0
\(616\) 14.6244 0.589235
\(617\) −45.4881 −1.83128 −0.915640 0.401998i \(-0.868316\pi\)
−0.915640 + 0.401998i \(0.868316\pi\)
\(618\) −9.08617 −0.365500
\(619\) 1.72666 0.0694001 0.0347001 0.999398i \(-0.488952\pi\)
0.0347001 + 0.999398i \(0.488952\pi\)
\(620\) 0 0
\(621\) 4.35544 0.174778
\(622\) −29.2080 −1.17113
\(623\) 16.6306 0.666289
\(624\) 14.6699 0.587265
\(625\) 0 0
\(626\) 38.1568 1.52505
\(627\) 0.143814 0.00574338
\(628\) 1.97255 0.0787134
\(629\) −18.8301 −0.750806
\(630\) 0 0
\(631\) −37.8555 −1.50700 −0.753502 0.657446i \(-0.771637\pi\)
−0.753502 + 0.657446i \(0.771637\pi\)
\(632\) −14.6510 −0.582785
\(633\) −13.4432 −0.534321
\(634\) −9.67803 −0.384363
\(635\) 0 0
\(636\) −0.233000 −0.00923905
\(637\) 4.04443 0.160246
\(638\) 53.2088 2.10656
\(639\) −24.2674 −0.960004
\(640\) 0 0
\(641\) −37.6517 −1.48715 −0.743577 0.668650i \(-0.766872\pi\)
−0.743577 + 0.668650i \(0.766872\pi\)
\(642\) 4.34298 0.171404
\(643\) 34.8532 1.37448 0.687238 0.726433i \(-0.258823\pi\)
0.687238 + 0.726433i \(0.258823\pi\)
\(644\) 0.252529 0.00995104
\(645\) 0 0
\(646\) 0.311700 0.0122637
\(647\) −5.50383 −0.216378 −0.108189 0.994130i \(-0.534505\pi\)
−0.108189 + 0.994130i \(0.534505\pi\)
\(648\) −9.02715 −0.354620
\(649\) −30.6821 −1.20438
\(650\) 0 0
\(651\) −1.11828 −0.0438288
\(652\) 5.86870 0.229836
\(653\) 31.9836 1.25162 0.625808 0.779977i \(-0.284770\pi\)
0.625808 + 0.779977i \(0.284770\pi\)
\(654\) 15.2863 0.597742
\(655\) 0 0
\(656\) 20.1691 0.787470
\(657\) −16.8234 −0.656345
\(658\) 2.81383 0.109694
\(659\) −12.6793 −0.493915 −0.246958 0.969026i \(-0.579431\pi\)
−0.246958 + 0.969026i \(0.579431\pi\)
\(660\) 0 0
\(661\) 14.9284 0.580647 0.290323 0.956929i \(-0.406237\pi\)
0.290323 + 0.956929i \(0.406237\pi\)
\(662\) 35.7032 1.38764
\(663\) −21.7226 −0.843636
\(664\) −29.1453 −1.13106
\(665\) 0 0
\(666\) 10.0256 0.388484
\(667\) −6.35790 −0.246179
\(668\) 2.63901 0.102107
\(669\) −12.1074 −0.468100
\(670\) 0 0
\(671\) −71.6141 −2.76463
\(672\) 1.15997 0.0447466
\(673\) 35.8357 1.38136 0.690682 0.723158i \(-0.257310\pi\)
0.690682 + 0.723158i \(0.257310\pi\)
\(674\) 27.1341 1.04517
\(675\) 0 0
\(676\) 0.847848 0.0326095
\(677\) −3.09993 −0.119140 −0.0595700 0.998224i \(-0.518973\pi\)
−0.0595700 + 0.998224i \(0.518973\pi\)
\(678\) 11.7206 0.450127
\(679\) −13.8986 −0.533381
\(680\) 0 0
\(681\) −14.9374 −0.572404
\(682\) −11.4593 −0.438800
\(683\) −21.9949 −0.841610 −0.420805 0.907151i \(-0.638252\pi\)
−0.420805 + 0.907151i \(0.638252\pi\)
\(684\) −0.0186052 −0.000711389 0
\(685\) 0 0
\(686\) 1.50084 0.0573024
\(687\) −21.2355 −0.810183
\(688\) −8.60414 −0.328030
\(689\) 4.56922 0.174073
\(690\) 0 0
\(691\) 26.7812 1.01881 0.509403 0.860528i \(-0.329866\pi\)
0.509403 + 0.860528i \(0.329866\pi\)
\(692\) 2.82718 0.107473
\(693\) 13.0092 0.494178
\(694\) −5.89869 −0.223911
\(695\) 0 0
\(696\) −13.6182 −0.516196
\(697\) −29.8656 −1.13124
\(698\) −14.6676 −0.555176
\(699\) 7.75613 0.293364
\(700\) 0 0
\(701\) −16.1107 −0.608493 −0.304246 0.952593i \(-0.598405\pi\)
−0.304246 + 0.952593i \(0.598405\pi\)
\(702\) 26.4378 0.997830
\(703\) −0.0904203 −0.00341027
\(704\) −37.6440 −1.41876
\(705\) 0 0
\(706\) 34.7161 1.30656
\(707\) 8.56886 0.322265
\(708\) −1.13481 −0.0426487
\(709\) −51.1562 −1.92121 −0.960606 0.277913i \(-0.910357\pi\)
−0.960606 + 0.277913i \(0.910357\pi\)
\(710\) 0 0
\(711\) −13.0328 −0.488768
\(712\) −43.6166 −1.63460
\(713\) 1.36927 0.0512797
\(714\) −8.06101 −0.301676
\(715\) 0 0
\(716\) −1.62483 −0.0607227
\(717\) 21.4965 0.802800
\(718\) 9.96572 0.371917
\(719\) 23.1532 0.863467 0.431734 0.902001i \(-0.357902\pi\)
0.431734 + 0.902001i \(0.357902\pi\)
\(720\) 0 0
\(721\) 7.41286 0.276069
\(722\) −28.5145 −1.06120
\(723\) 9.16278 0.340767
\(724\) −4.12708 −0.153382
\(725\) 0 0
\(726\) −24.6291 −0.914071
\(727\) −15.4927 −0.574593 −0.287297 0.957842i \(-0.592757\pi\)
−0.287297 + 0.957842i \(0.592757\pi\)
\(728\) −10.6072 −0.393131
\(729\) 2.64110 0.0978184
\(730\) 0 0
\(731\) 12.7407 0.471231
\(732\) −2.64872 −0.0978995
\(733\) −3.41564 −0.126159 −0.0630797 0.998008i \(-0.520092\pi\)
−0.0630797 + 0.998008i \(0.520092\pi\)
\(734\) −19.0144 −0.701835
\(735\) 0 0
\(736\) −1.42032 −0.0523535
\(737\) 9.28193 0.341904
\(738\) 15.9012 0.585330
\(739\) 17.9699 0.661033 0.330516 0.943800i \(-0.392777\pi\)
0.330516 + 0.943800i \(0.392777\pi\)
\(740\) 0 0
\(741\) −0.104310 −0.00383191
\(742\) 1.69559 0.0622469
\(743\) 1.24775 0.0457755 0.0228877 0.999738i \(-0.492714\pi\)
0.0228877 + 0.999738i \(0.492714\pi\)
\(744\) 2.93289 0.107525
\(745\) 0 0
\(746\) −9.00867 −0.329831
\(747\) −25.9263 −0.948593
\(748\) −9.26061 −0.338601
\(749\) −3.54317 −0.129465
\(750\) 0 0
\(751\) 47.7360 1.74191 0.870956 0.491361i \(-0.163501\pi\)
0.870956 + 0.491361i \(0.163501\pi\)
\(752\) −8.32666 −0.303642
\(753\) 5.01731 0.182841
\(754\) −38.5928 −1.40547
\(755\) 0 0
\(756\) 1.09988 0.0400021
\(757\) 2.61944 0.0952052 0.0476026 0.998866i \(-0.484842\pi\)
0.0476026 + 0.998866i \(0.484842\pi\)
\(758\) 47.0613 1.70934
\(759\) 4.55401 0.165300
\(760\) 0 0
\(761\) 27.4578 0.995346 0.497673 0.867365i \(-0.334188\pi\)
0.497673 + 0.867365i \(0.334188\pi\)
\(762\) −20.4641 −0.741335
\(763\) −12.4712 −0.451487
\(764\) 3.90731 0.141362
\(765\) 0 0
\(766\) 8.31076 0.300280
\(767\) 22.2540 0.803547
\(768\) −4.87415 −0.175881
\(769\) −15.8642 −0.572077 −0.286038 0.958218i \(-0.592338\pi\)
−0.286038 + 0.958218i \(0.592338\pi\)
\(770\) 0 0
\(771\) 18.2922 0.658777
\(772\) −4.48309 −0.161350
\(773\) 44.2624 1.59201 0.796004 0.605292i \(-0.206944\pi\)
0.796004 + 0.605292i \(0.206944\pi\)
\(774\) −6.78344 −0.243826
\(775\) 0 0
\(776\) 36.4517 1.30854
\(777\) 2.33840 0.0838896
\(778\) 12.3126 0.441429
\(779\) −0.143412 −0.00513826
\(780\) 0 0
\(781\) −58.0018 −2.07547
\(782\) 9.87028 0.352960
\(783\) −27.6915 −0.989613
\(784\) −4.44129 −0.158617
\(785\) 0 0
\(786\) 1.85145 0.0660390
\(787\) 13.2515 0.472367 0.236183 0.971709i \(-0.424103\pi\)
0.236183 + 0.971709i \(0.424103\pi\)
\(788\) −3.13520 −0.111687
\(789\) −16.7620 −0.596744
\(790\) 0 0
\(791\) −9.56214 −0.339990
\(792\) −34.1189 −1.21236
\(793\) 51.9424 1.84453
\(794\) 14.4398 0.512450
\(795\) 0 0
\(796\) 3.46074 0.122663
\(797\) 22.6458 0.802156 0.401078 0.916044i \(-0.368636\pi\)
0.401078 + 0.916044i \(0.368636\pi\)
\(798\) −0.0387082 −0.00137025
\(799\) 12.3298 0.436197
\(800\) 0 0
\(801\) −38.7992 −1.37090
\(802\) 40.2726 1.42207
\(803\) −40.2099 −1.41898
\(804\) 0.343302 0.0121073
\(805\) 0 0
\(806\) 8.31156 0.292762
\(807\) 15.0352 0.529264
\(808\) −22.4734 −0.790610
\(809\) −1.76330 −0.0619942 −0.0309971 0.999519i \(-0.509868\pi\)
−0.0309971 + 0.999519i \(0.509868\pi\)
\(810\) 0 0
\(811\) −18.9434 −0.665194 −0.332597 0.943069i \(-0.607925\pi\)
−0.332597 + 0.943069i \(0.607925\pi\)
\(812\) −1.60556 −0.0563440
\(813\) −3.46239 −0.121431
\(814\) 23.9623 0.839877
\(815\) 0 0
\(816\) 23.8541 0.835060
\(817\) 0.0611795 0.00214040
\(818\) 54.7670 1.91488
\(819\) −9.43569 −0.329710
\(820\) 0 0
\(821\) −52.4982 −1.83220 −0.916099 0.400952i \(-0.868679\pi\)
−0.916099 + 0.400952i \(0.868679\pi\)
\(822\) −7.11252 −0.248078
\(823\) −31.5761 −1.10067 −0.550336 0.834943i \(-0.685500\pi\)
−0.550336 + 0.834943i \(0.685500\pi\)
\(824\) −19.4416 −0.677279
\(825\) 0 0
\(826\) 8.25822 0.287340
\(827\) 0.407237 0.0141610 0.00708050 0.999975i \(-0.497746\pi\)
0.00708050 + 0.999975i \(0.497746\pi\)
\(828\) −0.589153 −0.0204745
\(829\) 46.9030 1.62901 0.814504 0.580158i \(-0.197009\pi\)
0.814504 + 0.580158i \(0.197009\pi\)
\(830\) 0 0
\(831\) 2.86060 0.0992333
\(832\) 27.3036 0.946581
\(833\) 6.57649 0.227862
\(834\) 8.60355 0.297917
\(835\) 0 0
\(836\) −0.0444685 −0.00153798
\(837\) 5.96379 0.206139
\(838\) −17.7406 −0.612838
\(839\) 42.3064 1.46058 0.730289 0.683138i \(-0.239385\pi\)
0.730289 + 0.683138i \(0.239385\pi\)
\(840\) 0 0
\(841\) 11.4229 0.393895
\(842\) −15.0458 −0.518511
\(843\) 14.5159 0.499953
\(844\) 4.15676 0.143082
\(845\) 0 0
\(846\) −6.56468 −0.225698
\(847\) 20.0934 0.690417
\(848\) −5.01757 −0.172304
\(849\) 19.9746 0.685527
\(850\) 0 0
\(851\) −2.86325 −0.0981508
\(852\) −2.14525 −0.0734952
\(853\) −0.228036 −0.00780779 −0.00390390 0.999992i \(-0.501243\pi\)
−0.00390390 + 0.999992i \(0.501243\pi\)
\(854\) 19.2752 0.659585
\(855\) 0 0
\(856\) 9.29261 0.317615
\(857\) 25.4818 0.870440 0.435220 0.900324i \(-0.356671\pi\)
0.435220 + 0.900324i \(0.356671\pi\)
\(858\) 27.6431 0.943720
\(859\) −47.1913 −1.61015 −0.805073 0.593175i \(-0.797874\pi\)
−0.805073 + 0.593175i \(0.797874\pi\)
\(860\) 0 0
\(861\) 3.70883 0.126397
\(862\) −42.0032 −1.43063
\(863\) 1.79277 0.0610267 0.0305133 0.999534i \(-0.490286\pi\)
0.0305133 + 0.999534i \(0.490286\pi\)
\(864\) −6.18610 −0.210456
\(865\) 0 0
\(866\) −25.6627 −0.872054
\(867\) −21.4384 −0.728087
\(868\) 0.345781 0.0117366
\(869\) −31.1498 −1.05668
\(870\) 0 0
\(871\) −6.73227 −0.228114
\(872\) 32.7079 1.10763
\(873\) 32.4257 1.09744
\(874\) 0.0473961 0.00160320
\(875\) 0 0
\(876\) −1.48720 −0.0502479
\(877\) −32.3361 −1.09191 −0.545957 0.837813i \(-0.683834\pi\)
−0.545957 + 0.837813i \(0.683834\pi\)
\(878\) 37.0549 1.25054
\(879\) 1.29540 0.0436928
\(880\) 0 0
\(881\) 47.1294 1.58783 0.793914 0.608030i \(-0.208040\pi\)
0.793914 + 0.608030i \(0.208040\pi\)
\(882\) −3.50148 −0.117901
\(883\) −53.7694 −1.80948 −0.904742 0.425960i \(-0.859936\pi\)
−0.904742 + 0.425960i \(0.859936\pi\)
\(884\) 6.71681 0.225911
\(885\) 0 0
\(886\) −33.5456 −1.12699
\(887\) 13.4916 0.453005 0.226502 0.974011i \(-0.427271\pi\)
0.226502 + 0.974011i \(0.427271\pi\)
\(888\) −6.13287 −0.205806
\(889\) 16.6954 0.559946
\(890\) 0 0
\(891\) −19.1928 −0.642984
\(892\) 3.74372 0.125349
\(893\) 0.0592065 0.00198127
\(894\) 26.1007 0.872938
\(895\) 0 0
\(896\) 12.9727 0.433387
\(897\) −3.30307 −0.110286
\(898\) −21.1446 −0.705605
\(899\) −8.70570 −0.290351
\(900\) 0 0
\(901\) 7.42983 0.247523
\(902\) 38.0055 1.26544
\(903\) −1.58219 −0.0526520
\(904\) 25.0784 0.834096
\(905\) 0 0
\(906\) −3.12944 −0.103969
\(907\) 32.7055 1.08597 0.542985 0.839742i \(-0.317294\pi\)
0.542985 + 0.839742i \(0.317294\pi\)
\(908\) 4.61878 0.153280
\(909\) −19.9912 −0.663067
\(910\) 0 0
\(911\) 0.0799151 0.00264771 0.00132385 0.999999i \(-0.499579\pi\)
0.00132385 + 0.999999i \(0.499579\pi\)
\(912\) 0.114545 0.00379296
\(913\) −61.9666 −2.05080
\(914\) 44.8584 1.48378
\(915\) 0 0
\(916\) 6.56618 0.216953
\(917\) −1.51048 −0.0498806
\(918\) 42.9894 1.41886
\(919\) 42.9841 1.41792 0.708958 0.705251i \(-0.249166\pi\)
0.708958 + 0.705251i \(0.249166\pi\)
\(920\) 0 0
\(921\) 7.54974 0.248773
\(922\) −44.5389 −1.46681
\(923\) 42.0692 1.38473
\(924\) 1.15002 0.0378329
\(925\) 0 0
\(926\) 19.5430 0.642222
\(927\) −17.2943 −0.568018
\(928\) 9.03023 0.296432
\(929\) 23.3398 0.765754 0.382877 0.923799i \(-0.374933\pi\)
0.382877 + 0.923799i \(0.374933\pi\)
\(930\) 0 0
\(931\) 0.0315796 0.00103498
\(932\) −2.39826 −0.0785577
\(933\) 15.8938 0.520339
\(934\) 13.7228 0.449024
\(935\) 0 0
\(936\) 24.7468 0.808874
\(937\) 11.7697 0.384500 0.192250 0.981346i \(-0.438422\pi\)
0.192250 + 0.981346i \(0.438422\pi\)
\(938\) −2.49827 −0.0815714
\(939\) −20.7633 −0.677585
\(940\) 0 0
\(941\) −4.51567 −0.147207 −0.0736034 0.997288i \(-0.523450\pi\)
−0.0736034 + 0.997288i \(0.523450\pi\)
\(942\) −9.57442 −0.311951
\(943\) −4.54127 −0.147884
\(944\) −24.4377 −0.795379
\(945\) 0 0
\(946\) −16.2132 −0.527135
\(947\) −19.0220 −0.618133 −0.309066 0.951040i \(-0.600017\pi\)
−0.309066 + 0.951040i \(0.600017\pi\)
\(948\) −1.15211 −0.0374187
\(949\) 29.1646 0.946723
\(950\) 0 0
\(951\) 5.26637 0.170774
\(952\) −17.2480 −0.559012
\(953\) 43.3856 1.40540 0.702699 0.711488i \(-0.251978\pi\)
0.702699 + 0.711488i \(0.251978\pi\)
\(954\) −3.95582 −0.128074
\(955\) 0 0
\(956\) −6.64689 −0.214976
\(957\) −28.9540 −0.935949
\(958\) −13.5484 −0.437728
\(959\) 5.80267 0.187378
\(960\) 0 0
\(961\) −29.1251 −0.939519
\(962\) −17.3801 −0.560356
\(963\) 8.26625 0.266376
\(964\) −2.83321 −0.0912515
\(965\) 0 0
\(966\) −1.22573 −0.0394373
\(967\) −41.0523 −1.32015 −0.660076 0.751199i \(-0.729476\pi\)
−0.660076 + 0.751199i \(0.729476\pi\)
\(968\) −52.6985 −1.69379
\(969\) −0.169614 −0.00544878
\(970\) 0 0
\(971\) −38.5361 −1.23668 −0.618341 0.785910i \(-0.712195\pi\)
−0.618341 + 0.785910i \(0.712195\pi\)
\(972\) −4.00949 −0.128605
\(973\) −7.01912 −0.225023
\(974\) −48.4958 −1.55391
\(975\) 0 0
\(976\) −57.0392 −1.82578
\(977\) 37.5284 1.20064 0.600320 0.799760i \(-0.295040\pi\)
0.600320 + 0.799760i \(0.295040\pi\)
\(978\) −28.4856 −0.910870
\(979\) −92.7344 −2.96380
\(980\) 0 0
\(981\) 29.0953 0.928943
\(982\) 30.7869 0.982449
\(983\) 48.9074 1.55990 0.779952 0.625839i \(-0.215243\pi\)
0.779952 + 0.625839i \(0.215243\pi\)
\(984\) −9.72708 −0.310088
\(985\) 0 0
\(986\) −62.7543 −1.99850
\(987\) −1.53117 −0.0487375
\(988\) 0.0322534 0.00102612
\(989\) 1.93731 0.0616028
\(990\) 0 0
\(991\) −8.69537 −0.276217 −0.138109 0.990417i \(-0.544102\pi\)
−0.138109 + 0.990417i \(0.544102\pi\)
\(992\) −1.94480 −0.0617474
\(993\) −19.4282 −0.616534
\(994\) 15.6114 0.495164
\(995\) 0 0
\(996\) −2.29190 −0.0726215
\(997\) 13.9339 0.441290 0.220645 0.975354i \(-0.429184\pi\)
0.220645 + 0.975354i \(0.429184\pi\)
\(998\) 37.4369 1.18505
\(999\) −12.4707 −0.394556
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 4025.2.a.be.1.15 21
5.2 odd 4 805.2.c.c.484.30 yes 42
5.3 odd 4 805.2.c.c.484.13 42
5.4 even 2 4025.2.a.bd.1.7 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
805.2.c.c.484.13 42 5.3 odd 4
805.2.c.c.484.30 yes 42 5.2 odd 4
4025.2.a.bd.1.7 21 5.4 even 2
4025.2.a.be.1.15 21 1.1 even 1 trivial