Properties

Label 4025.2.a.bc.1.12
Level $4025$
Weight $2$
Character 4025.1
Self dual yes
Analytic conductor $32.140$
Analytic rank $0$
Dimension $14$
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} - 1853 x^{5} + 539 x^{4} + 891 x^{3} - 218 x^{2} - 133 x - 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(2.30520\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q+2.30520 q^{2} +0.930494 q^{3} +3.31395 q^{4} +2.14497 q^{6} +1.00000 q^{7} +3.02891 q^{8} -2.13418 q^{9} +O(q^{10})\) \(q+2.30520 q^{2} +0.930494 q^{3} +3.31395 q^{4} +2.14497 q^{6} +1.00000 q^{7} +3.02891 q^{8} -2.13418 q^{9} +0.709352 q^{11} +3.08361 q^{12} +3.91757 q^{13} +2.30520 q^{14} +0.354347 q^{16} +4.79009 q^{17} -4.91971 q^{18} +2.72673 q^{19} +0.930494 q^{21} +1.63520 q^{22} +1.00000 q^{23} +2.81838 q^{24} +9.03077 q^{26} -4.77732 q^{27} +3.31395 q^{28} +9.19789 q^{29} +4.59512 q^{31} -5.24098 q^{32} +0.660048 q^{33} +11.0421 q^{34} -7.07256 q^{36} +0.806689 q^{37} +6.28566 q^{38} +3.64527 q^{39} -5.49453 q^{41} +2.14497 q^{42} -11.2721 q^{43} +2.35076 q^{44} +2.30520 q^{46} +3.17718 q^{47} +0.329718 q^{48} +1.00000 q^{49} +4.45715 q^{51} +12.9826 q^{52} -14.0152 q^{53} -11.0127 q^{54} +3.02891 q^{56} +2.53721 q^{57} +21.2030 q^{58} -12.6497 q^{59} -4.77144 q^{61} +10.5927 q^{62} -2.13418 q^{63} -12.7902 q^{64} +1.52154 q^{66} +13.6404 q^{67} +15.8741 q^{68} +0.930494 q^{69} +16.5093 q^{71} -6.46424 q^{72} +8.26175 q^{73} +1.85958 q^{74} +9.03624 q^{76} +0.709352 q^{77} +8.40308 q^{78} +14.9425 q^{79} +1.95727 q^{81} -12.6660 q^{82} -3.90233 q^{83} +3.08361 q^{84} -25.9845 q^{86} +8.55858 q^{87} +2.14856 q^{88} +14.7492 q^{89} +3.91757 q^{91} +3.31395 q^{92} +4.27573 q^{93} +7.32404 q^{94} -4.87670 q^{96} +14.9733 q^{97} +2.30520 q^{98} -1.51389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{11} + 17 q^{12} + 11 q^{13} + 3 q^{14} + 23 q^{16} + 3 q^{17} + 15 q^{18} - 2 q^{19} + 4 q^{21} + 23 q^{22} + 14 q^{23} - 12 q^{24} - 9 q^{26} + 25 q^{27} + 17 q^{28} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 6 q^{33} - 14 q^{34} + 13 q^{36} + 22 q^{37} + 20 q^{38} - 10 q^{39} - 17 q^{41} - 4 q^{42} + 18 q^{43} + 28 q^{44} + 3 q^{46} + 30 q^{47} + 8 q^{48} + 14 q^{49} + 4 q^{51} + 8 q^{52} + 11 q^{53} + 20 q^{54} + 3 q^{56} + 18 q^{57} + 38 q^{58} - 22 q^{59} - 8 q^{61} - 22 q^{62} + 18 q^{63} + 29 q^{64} - 9 q^{66} + 39 q^{67} + q^{68} + 4 q^{69} - 5 q^{71} - 24 q^{72} + 18 q^{73} + 35 q^{74} - 41 q^{76} + 5 q^{77} - 22 q^{78} + 10 q^{79} + 2 q^{81} - 8 q^{82} + 24 q^{83} + 17 q^{84} - 26 q^{86} + 5 q^{87} + 58 q^{88} + 25 q^{89} + 11 q^{91} + 17 q^{92} + 47 q^{93} - 2 q^{94} - 117 q^{96} + 43 q^{97} + 3 q^{98} + 55 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30520 1.63002 0.815011 0.579445i \(-0.196731\pi\)
0.815011 + 0.579445i \(0.196731\pi\)
\(3\) 0.930494 0.537221 0.268610 0.963249i \(-0.413436\pi\)
0.268610 + 0.963249i \(0.413436\pi\)
\(4\) 3.31395 1.65697
\(5\) 0 0
\(6\) 2.14497 0.875682
\(7\) 1.00000 0.377964
\(8\) 3.02891 1.07088
\(9\) −2.13418 −0.711394
\(10\) 0 0
\(11\) 0.709352 0.213878 0.106939 0.994266i \(-0.465895\pi\)
0.106939 + 0.994266i \(0.465895\pi\)
\(12\) 3.08361 0.890160
\(13\) 3.91757 1.08654 0.543269 0.839559i \(-0.317186\pi\)
0.543269 + 0.839559i \(0.317186\pi\)
\(14\) 2.30520 0.616091
\(15\) 0 0
\(16\) 0.354347 0.0885869
\(17\) 4.79009 1.16177 0.580884 0.813986i \(-0.302707\pi\)
0.580884 + 0.813986i \(0.302707\pi\)
\(18\) −4.91971 −1.15959
\(19\) 2.72673 0.625555 0.312777 0.949826i \(-0.398741\pi\)
0.312777 + 0.949826i \(0.398741\pi\)
\(20\) 0 0
\(21\) 0.930494 0.203050
\(22\) 1.63520 0.348626
\(23\) 1.00000 0.208514
\(24\) 2.81838 0.575300
\(25\) 0 0
\(26\) 9.03077 1.77108
\(27\) −4.77732 −0.919396
\(28\) 3.31395 0.626277
\(29\) 9.19789 1.70801 0.854003 0.520268i \(-0.174168\pi\)
0.854003 + 0.520268i \(0.174168\pi\)
\(30\) 0 0
\(31\) 4.59512 0.825309 0.412654 0.910888i \(-0.364602\pi\)
0.412654 + 0.910888i \(0.364602\pi\)
\(32\) −5.24098 −0.926482
\(33\) 0.660048 0.114900
\(34\) 11.0421 1.89371
\(35\) 0 0
\(36\) −7.07256 −1.17876
\(37\) 0.806689 0.132619 0.0663095 0.997799i \(-0.478878\pi\)
0.0663095 + 0.997799i \(0.478878\pi\)
\(38\) 6.28566 1.01967
\(39\) 3.64527 0.583711
\(40\) 0 0
\(41\) −5.49453 −0.858102 −0.429051 0.903280i \(-0.641152\pi\)
−0.429051 + 0.903280i \(0.641152\pi\)
\(42\) 2.14497 0.330977
\(43\) −11.2721 −1.71898 −0.859492 0.511149i \(-0.829220\pi\)
−0.859492 + 0.511149i \(0.829220\pi\)
\(44\) 2.35076 0.354390
\(45\) 0 0
\(46\) 2.30520 0.339883
\(47\) 3.17718 0.463440 0.231720 0.972783i \(-0.425565\pi\)
0.231720 + 0.972783i \(0.425565\pi\)
\(48\) 0.329718 0.0475907
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 4.45715 0.624126
\(52\) 12.9826 1.80036
\(53\) −14.0152 −1.92514 −0.962568 0.271042i \(-0.912632\pi\)
−0.962568 + 0.271042i \(0.912632\pi\)
\(54\) −11.0127 −1.49864
\(55\) 0 0
\(56\) 3.02891 0.404755
\(57\) 2.53721 0.336061
\(58\) 21.2030 2.78409
\(59\) −12.6497 −1.64685 −0.823425 0.567425i \(-0.807940\pi\)
−0.823425 + 0.567425i \(0.807940\pi\)
\(60\) 0 0
\(61\) −4.77144 −0.610921 −0.305460 0.952205i \(-0.598810\pi\)
−0.305460 + 0.952205i \(0.598810\pi\)
\(62\) 10.5927 1.34527
\(63\) −2.13418 −0.268882
\(64\) −12.7902 −1.59877
\(65\) 0 0
\(66\) 1.52154 0.187289
\(67\) 13.6404 1.66644 0.833218 0.552944i \(-0.186496\pi\)
0.833218 + 0.552944i \(0.186496\pi\)
\(68\) 15.8741 1.92502
\(69\) 0.930494 0.112018
\(70\) 0 0
\(71\) 16.5093 1.95929 0.979646 0.200732i \(-0.0643320\pi\)
0.979646 + 0.200732i \(0.0643320\pi\)
\(72\) −6.46424 −0.761818
\(73\) 8.26175 0.966964 0.483482 0.875354i \(-0.339372\pi\)
0.483482 + 0.875354i \(0.339372\pi\)
\(74\) 1.85958 0.216172
\(75\) 0 0
\(76\) 9.03624 1.03653
\(77\) 0.709352 0.0808382
\(78\) 8.40308 0.951461
\(79\) 14.9425 1.68117 0.840584 0.541682i \(-0.182212\pi\)
0.840584 + 0.541682i \(0.182212\pi\)
\(80\) 0 0
\(81\) 1.95727 0.217475
\(82\) −12.6660 −1.39873
\(83\) −3.90233 −0.428337 −0.214168 0.976797i \(-0.568704\pi\)
−0.214168 + 0.976797i \(0.568704\pi\)
\(84\) 3.08361 0.336449
\(85\) 0 0
\(86\) −25.9845 −2.80198
\(87\) 8.55858 0.917576
\(88\) 2.14856 0.229038
\(89\) 14.7492 1.56341 0.781704 0.623649i \(-0.214351\pi\)
0.781704 + 0.623649i \(0.214351\pi\)
\(90\) 0 0
\(91\) 3.91757 0.410673
\(92\) 3.31395 0.345503
\(93\) 4.27573 0.443373
\(94\) 7.32404 0.755417
\(95\) 0 0
\(96\) −4.87670 −0.497726
\(97\) 14.9733 1.52031 0.760155 0.649741i \(-0.225123\pi\)
0.760155 + 0.649741i \(0.225123\pi\)
\(98\) 2.30520 0.232860
\(99\) −1.51389 −0.152151
\(100\) 0 0
\(101\) 1.93634 0.192673 0.0963365 0.995349i \(-0.469288\pi\)
0.0963365 + 0.995349i \(0.469288\pi\)
\(102\) 10.2746 1.01734
\(103\) −2.08106 −0.205053 −0.102526 0.994730i \(-0.532693\pi\)
−0.102526 + 0.994730i \(0.532693\pi\)
\(104\) 11.8660 1.16355
\(105\) 0 0
\(106\) −32.3078 −3.13801
\(107\) 4.86119 0.469949 0.234974 0.972002i \(-0.424499\pi\)
0.234974 + 0.972002i \(0.424499\pi\)
\(108\) −15.8318 −1.52342
\(109\) −6.18163 −0.592093 −0.296046 0.955174i \(-0.595668\pi\)
−0.296046 + 0.955174i \(0.595668\pi\)
\(110\) 0 0
\(111\) 0.750619 0.0712456
\(112\) 0.354347 0.0334827
\(113\) −2.56109 −0.240927 −0.120463 0.992718i \(-0.538438\pi\)
−0.120463 + 0.992718i \(0.538438\pi\)
\(114\) 5.84877 0.547787
\(115\) 0 0
\(116\) 30.4813 2.83012
\(117\) −8.36080 −0.772956
\(118\) −29.1601 −2.68440
\(119\) 4.79009 0.439107
\(120\) 0 0
\(121\) −10.4968 −0.954256
\(122\) −10.9991 −0.995814
\(123\) −5.11263 −0.460990
\(124\) 15.2280 1.36751
\(125\) 0 0
\(126\) −4.91971 −0.438283
\(127\) −7.51001 −0.666406 −0.333203 0.942855i \(-0.608129\pi\)
−0.333203 + 0.942855i \(0.608129\pi\)
\(128\) −19.0020 −1.67956
\(129\) −10.4886 −0.923474
\(130\) 0 0
\(131\) −19.6300 −1.71509 −0.857543 0.514413i \(-0.828010\pi\)
−0.857543 + 0.514413i \(0.828010\pi\)
\(132\) 2.18736 0.190386
\(133\) 2.72673 0.236438
\(134\) 31.4438 2.71633
\(135\) 0 0
\(136\) 14.5088 1.24412
\(137\) 15.6513 1.33718 0.668592 0.743630i \(-0.266897\pi\)
0.668592 + 0.743630i \(0.266897\pi\)
\(138\) 2.14497 0.182592
\(139\) −1.70351 −0.144489 −0.0722447 0.997387i \(-0.523016\pi\)
−0.0722447 + 0.997387i \(0.523016\pi\)
\(140\) 0 0
\(141\) 2.95635 0.248970
\(142\) 38.0572 3.19369
\(143\) 2.77893 0.232386
\(144\) −0.756242 −0.0630201
\(145\) 0 0
\(146\) 19.0450 1.57617
\(147\) 0.930494 0.0767458
\(148\) 2.67333 0.219746
\(149\) −23.7205 −1.94326 −0.971631 0.236501i \(-0.923999\pi\)
−0.971631 + 0.236501i \(0.923999\pi\)
\(150\) 0 0
\(151\) −8.33717 −0.678469 −0.339235 0.940702i \(-0.610168\pi\)
−0.339235 + 0.940702i \(0.610168\pi\)
\(152\) 8.25902 0.669895
\(153\) −10.2229 −0.826475
\(154\) 1.63520 0.131768
\(155\) 0 0
\(156\) 12.0802 0.967193
\(157\) −16.1332 −1.28757 −0.643786 0.765205i \(-0.722637\pi\)
−0.643786 + 0.765205i \(0.722637\pi\)
\(158\) 34.4455 2.74034
\(159\) −13.0411 −1.03422
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 4.51191 0.354489
\(163\) −2.98990 −0.234187 −0.117093 0.993121i \(-0.537358\pi\)
−0.117093 + 0.993121i \(0.537358\pi\)
\(164\) −18.2086 −1.42185
\(165\) 0 0
\(166\) −8.99566 −0.698199
\(167\) −16.9421 −1.31102 −0.655510 0.755186i \(-0.727546\pi\)
−0.655510 + 0.755186i \(0.727546\pi\)
\(168\) 2.81838 0.217443
\(169\) 2.34733 0.180564
\(170\) 0 0
\(171\) −5.81934 −0.445016
\(172\) −37.3552 −2.84831
\(173\) −25.8095 −1.96226 −0.981132 0.193340i \(-0.938068\pi\)
−0.981132 + 0.193340i \(0.938068\pi\)
\(174\) 19.7292 1.49567
\(175\) 0 0
\(176\) 0.251357 0.0189468
\(177\) −11.7705 −0.884722
\(178\) 33.9998 2.54839
\(179\) 19.7074 1.47300 0.736499 0.676439i \(-0.236478\pi\)
0.736499 + 0.676439i \(0.236478\pi\)
\(180\) 0 0
\(181\) −16.7299 −1.24352 −0.621761 0.783207i \(-0.713583\pi\)
−0.621761 + 0.783207i \(0.713583\pi\)
\(182\) 9.03077 0.669405
\(183\) −4.43980 −0.328199
\(184\) 3.02891 0.223294
\(185\) 0 0
\(186\) 9.85642 0.722708
\(187\) 3.39786 0.248476
\(188\) 10.5290 0.767907
\(189\) −4.77732 −0.347499
\(190\) 0 0
\(191\) −0.000216850 0 −1.56907e−5 0 −7.84536e−6 1.00000i \(-0.500002\pi\)
−7.84536e−6 1.00000i \(0.500002\pi\)
\(192\) −11.9012 −0.858895
\(193\) −4.11572 −0.296256 −0.148128 0.988968i \(-0.547325\pi\)
−0.148128 + 0.988968i \(0.547325\pi\)
\(194\) 34.5165 2.47814
\(195\) 0 0
\(196\) 3.31395 0.236710
\(197\) −3.37351 −0.240353 −0.120176 0.992753i \(-0.538346\pi\)
−0.120176 + 0.992753i \(0.538346\pi\)
\(198\) −3.48981 −0.248010
\(199\) 11.3857 0.807110 0.403555 0.914955i \(-0.367774\pi\)
0.403555 + 0.914955i \(0.367774\pi\)
\(200\) 0 0
\(201\) 12.6923 0.895244
\(202\) 4.46365 0.314061
\(203\) 9.19789 0.645566
\(204\) 14.7708 1.03416
\(205\) 0 0
\(206\) −4.79725 −0.334240
\(207\) −2.13418 −0.148336
\(208\) 1.38818 0.0962529
\(209\) 1.93421 0.133792
\(210\) 0 0
\(211\) −7.81930 −0.538303 −0.269152 0.963098i \(-0.586743\pi\)
−0.269152 + 0.963098i \(0.586743\pi\)
\(212\) −46.4456 −3.18990
\(213\) 15.3618 1.05257
\(214\) 11.2060 0.766027
\(215\) 0 0
\(216\) −14.4701 −0.984564
\(217\) 4.59512 0.311937
\(218\) −14.2499 −0.965124
\(219\) 7.68750 0.519473
\(220\) 0 0
\(221\) 18.7655 1.26230
\(222\) 1.73033 0.116132
\(223\) −13.9469 −0.933956 −0.466978 0.884269i \(-0.654657\pi\)
−0.466978 + 0.884269i \(0.654657\pi\)
\(224\) −5.24098 −0.350177
\(225\) 0 0
\(226\) −5.90382 −0.392716
\(227\) 2.91510 0.193482 0.0967411 0.995310i \(-0.469158\pi\)
0.0967411 + 0.995310i \(0.469158\pi\)
\(228\) 8.40816 0.556844
\(229\) −8.49122 −0.561115 −0.280558 0.959837i \(-0.590519\pi\)
−0.280558 + 0.959837i \(0.590519\pi\)
\(230\) 0 0
\(231\) 0.660048 0.0434280
\(232\) 27.8596 1.82907
\(233\) 16.3911 1.07382 0.536910 0.843640i \(-0.319592\pi\)
0.536910 + 0.843640i \(0.319592\pi\)
\(234\) −19.2733 −1.25994
\(235\) 0 0
\(236\) −41.9204 −2.72879
\(237\) 13.9039 0.903158
\(238\) 11.0421 0.715754
\(239\) 13.2165 0.854904 0.427452 0.904038i \(-0.359411\pi\)
0.427452 + 0.904038i \(0.359411\pi\)
\(240\) 0 0
\(241\) 3.98974 0.257002 0.128501 0.991709i \(-0.458984\pi\)
0.128501 + 0.991709i \(0.458984\pi\)
\(242\) −24.1973 −1.55546
\(243\) 16.1532 1.03623
\(244\) −15.8123 −1.01228
\(245\) 0 0
\(246\) −11.7856 −0.751424
\(247\) 10.6821 0.679689
\(248\) 13.9182 0.883807
\(249\) −3.63110 −0.230111
\(250\) 0 0
\(251\) −28.3197 −1.78753 −0.893763 0.448540i \(-0.851944\pi\)
−0.893763 + 0.448540i \(0.851944\pi\)
\(252\) −7.07256 −0.445530
\(253\) 0.709352 0.0445966
\(254\) −17.3121 −1.08626
\(255\) 0 0
\(256\) −18.2230 −1.13894
\(257\) −10.6757 −0.665930 −0.332965 0.942939i \(-0.608049\pi\)
−0.332965 + 0.942939i \(0.608049\pi\)
\(258\) −24.1784 −1.50528
\(259\) 0.806689 0.0501252
\(260\) 0 0
\(261\) −19.6300 −1.21506
\(262\) −45.2512 −2.79563
\(263\) −6.86062 −0.423044 −0.211522 0.977373i \(-0.567842\pi\)
−0.211522 + 0.977373i \(0.567842\pi\)
\(264\) 1.99922 0.123044
\(265\) 0 0
\(266\) 6.28566 0.385398
\(267\) 13.7240 0.839896
\(268\) 45.2035 2.76124
\(269\) −24.4928 −1.49335 −0.746676 0.665188i \(-0.768352\pi\)
−0.746676 + 0.665188i \(0.768352\pi\)
\(270\) 0 0
\(271\) −24.9077 −1.51303 −0.756517 0.653974i \(-0.773100\pi\)
−0.756517 + 0.653974i \(0.773100\pi\)
\(272\) 1.69736 0.102917
\(273\) 3.64527 0.220622
\(274\) 36.0795 2.17964
\(275\) 0 0
\(276\) 3.08361 0.185611
\(277\) 8.34715 0.501532 0.250766 0.968048i \(-0.419318\pi\)
0.250766 + 0.968048i \(0.419318\pi\)
\(278\) −3.92692 −0.235521
\(279\) −9.80683 −0.587119
\(280\) 0 0
\(281\) −2.02096 −0.120561 −0.0602803 0.998181i \(-0.519199\pi\)
−0.0602803 + 0.998181i \(0.519199\pi\)
\(282\) 6.81498 0.405826
\(283\) 6.65672 0.395701 0.197850 0.980232i \(-0.436604\pi\)
0.197850 + 0.980232i \(0.436604\pi\)
\(284\) 54.7109 3.24649
\(285\) 0 0
\(286\) 6.40600 0.378795
\(287\) −5.49453 −0.324332
\(288\) 11.1852 0.659094
\(289\) 5.94499 0.349706
\(290\) 0 0
\(291\) 13.9326 0.816743
\(292\) 27.3790 1.60223
\(293\) −23.0991 −1.34947 −0.674733 0.738062i \(-0.735741\pi\)
−0.674733 + 0.738062i \(0.735741\pi\)
\(294\) 2.14497 0.125097
\(295\) 0 0
\(296\) 2.44339 0.142019
\(297\) −3.38881 −0.196638
\(298\) −54.6806 −3.16756
\(299\) 3.91757 0.226559
\(300\) 0 0
\(301\) −11.2721 −0.649715
\(302\) −19.2188 −1.10592
\(303\) 1.80175 0.103508
\(304\) 0.966210 0.0554159
\(305\) 0 0
\(306\) −23.5659 −1.34717
\(307\) −12.4205 −0.708873 −0.354436 0.935080i \(-0.615327\pi\)
−0.354436 + 0.935080i \(0.615327\pi\)
\(308\) 2.35076 0.133947
\(309\) −1.93641 −0.110159
\(310\) 0 0
\(311\) 31.3617 1.77836 0.889179 0.457559i \(-0.151276\pi\)
0.889179 + 0.457559i \(0.151276\pi\)
\(312\) 11.0412 0.625084
\(313\) 20.9153 1.18220 0.591101 0.806597i \(-0.298693\pi\)
0.591101 + 0.806597i \(0.298693\pi\)
\(314\) −37.1903 −2.09877
\(315\) 0 0
\(316\) 49.5188 2.78565
\(317\) −0.597601 −0.0335646 −0.0167823 0.999859i \(-0.505342\pi\)
−0.0167823 + 0.999859i \(0.505342\pi\)
\(318\) −30.0622 −1.68581
\(319\) 6.52455 0.365304
\(320\) 0 0
\(321\) 4.52330 0.252466
\(322\) 2.30520 0.128464
\(323\) 13.0613 0.726750
\(324\) 6.48630 0.360350
\(325\) 0 0
\(326\) −6.89231 −0.381730
\(327\) −5.75197 −0.318085
\(328\) −16.6424 −0.918925
\(329\) 3.17718 0.175164
\(330\) 0 0
\(331\) −25.4744 −1.40020 −0.700099 0.714046i \(-0.746861\pi\)
−0.700099 + 0.714046i \(0.746861\pi\)
\(332\) −12.9321 −0.709742
\(333\) −1.72162 −0.0943443
\(334\) −39.0550 −2.13699
\(335\) 0 0
\(336\) 0.329718 0.0179876
\(337\) 14.5255 0.791254 0.395627 0.918411i \(-0.370527\pi\)
0.395627 + 0.918411i \(0.370527\pi\)
\(338\) 5.41106 0.294323
\(339\) −2.38308 −0.129431
\(340\) 0 0
\(341\) 3.25956 0.176515
\(342\) −13.4147 −0.725386
\(343\) 1.00000 0.0539949
\(344\) −34.1423 −1.84083
\(345\) 0 0
\(346\) −59.4962 −3.19853
\(347\) −0.842635 −0.0452350 −0.0226175 0.999744i \(-0.507200\pi\)
−0.0226175 + 0.999744i \(0.507200\pi\)
\(348\) 28.3627 1.52040
\(349\) −15.8934 −0.850756 −0.425378 0.905016i \(-0.639859\pi\)
−0.425378 + 0.905016i \(0.639859\pi\)
\(350\) 0 0
\(351\) −18.7155 −0.998959
\(352\) −3.71770 −0.198154
\(353\) −22.4359 −1.19414 −0.597071 0.802188i \(-0.703669\pi\)
−0.597071 + 0.802188i \(0.703669\pi\)
\(354\) −27.1333 −1.44212
\(355\) 0 0
\(356\) 48.8779 2.59053
\(357\) 4.45715 0.235897
\(358\) 45.4294 2.40102
\(359\) −22.2373 −1.17364 −0.586820 0.809717i \(-0.699621\pi\)
−0.586820 + 0.809717i \(0.699621\pi\)
\(360\) 0 0
\(361\) −11.5649 −0.608681
\(362\) −38.5657 −2.02697
\(363\) −9.76722 −0.512646
\(364\) 12.9826 0.680473
\(365\) 0 0
\(366\) −10.2346 −0.534972
\(367\) 10.1232 0.528428 0.264214 0.964464i \(-0.414888\pi\)
0.264214 + 0.964464i \(0.414888\pi\)
\(368\) 0.354347 0.0184716
\(369\) 11.7263 0.610448
\(370\) 0 0
\(371\) −14.0152 −0.727633
\(372\) 14.1696 0.734657
\(373\) 5.50875 0.285232 0.142616 0.989778i \(-0.454449\pi\)
0.142616 + 0.989778i \(0.454449\pi\)
\(374\) 7.83275 0.405022
\(375\) 0 0
\(376\) 9.62340 0.496289
\(377\) 36.0334 1.85581
\(378\) −11.0127 −0.566431
\(379\) 20.6238 1.05937 0.529687 0.848193i \(-0.322309\pi\)
0.529687 + 0.848193i \(0.322309\pi\)
\(380\) 0 0
\(381\) −6.98802 −0.358007
\(382\) −0.000499883 0 −2.55762e−5 0
\(383\) 8.06269 0.411984 0.205992 0.978554i \(-0.433958\pi\)
0.205992 + 0.978554i \(0.433958\pi\)
\(384\) −17.6812 −0.902292
\(385\) 0 0
\(386\) −9.48755 −0.482904
\(387\) 24.0568 1.22287
\(388\) 49.6208 2.51911
\(389\) 17.9274 0.908953 0.454477 0.890759i \(-0.349826\pi\)
0.454477 + 0.890759i \(0.349826\pi\)
\(390\) 0 0
\(391\) 4.79009 0.242245
\(392\) 3.02891 0.152983
\(393\) −18.2656 −0.921380
\(394\) −7.77662 −0.391781
\(395\) 0 0
\(396\) −5.01694 −0.252111
\(397\) 29.2823 1.46963 0.734817 0.678265i \(-0.237268\pi\)
0.734817 + 0.678265i \(0.237268\pi\)
\(398\) 26.2463 1.31561
\(399\) 2.53721 0.127019
\(400\) 0 0
\(401\) 4.35453 0.217455 0.108727 0.994072i \(-0.465322\pi\)
0.108727 + 0.994072i \(0.465322\pi\)
\(402\) 29.2582 1.45927
\(403\) 18.0017 0.896729
\(404\) 6.41693 0.319254
\(405\) 0 0
\(406\) 21.2030 1.05229
\(407\) 0.572227 0.0283642
\(408\) 13.5003 0.668365
\(409\) −30.1195 −1.48932 −0.744658 0.667447i \(-0.767387\pi\)
−0.744658 + 0.667447i \(0.767387\pi\)
\(410\) 0 0
\(411\) 14.5635 0.718363
\(412\) −6.89651 −0.339767
\(413\) −12.6497 −0.622451
\(414\) −4.91971 −0.241791
\(415\) 0 0
\(416\) −20.5319 −1.00666
\(417\) −1.58510 −0.0776227
\(418\) 4.45875 0.218084
\(419\) −19.6444 −0.959690 −0.479845 0.877353i \(-0.659307\pi\)
−0.479845 + 0.877353i \(0.659307\pi\)
\(420\) 0 0
\(421\) −10.4256 −0.508114 −0.254057 0.967189i \(-0.581765\pi\)
−0.254057 + 0.967189i \(0.581765\pi\)
\(422\) −18.0251 −0.877446
\(423\) −6.78069 −0.329688
\(424\) −42.4507 −2.06159
\(425\) 0 0
\(426\) 35.4120 1.71572
\(427\) −4.77144 −0.230906
\(428\) 16.1097 0.778692
\(429\) 2.58578 0.124843
\(430\) 0 0
\(431\) −12.3810 −0.596370 −0.298185 0.954508i \(-0.596381\pi\)
−0.298185 + 0.954508i \(0.596381\pi\)
\(432\) −1.69283 −0.0814464
\(433\) 31.6045 1.51882 0.759409 0.650614i \(-0.225488\pi\)
0.759409 + 0.650614i \(0.225488\pi\)
\(434\) 10.5927 0.508465
\(435\) 0 0
\(436\) −20.4856 −0.981082
\(437\) 2.72673 0.130437
\(438\) 17.7212 0.846753
\(439\) −21.9482 −1.04753 −0.523766 0.851862i \(-0.675473\pi\)
−0.523766 + 0.851862i \(0.675473\pi\)
\(440\) 0 0
\(441\) −2.13418 −0.101628
\(442\) 43.2582 2.05758
\(443\) 36.6972 1.74354 0.871768 0.489919i \(-0.162974\pi\)
0.871768 + 0.489919i \(0.162974\pi\)
\(444\) 2.48751 0.118052
\(445\) 0 0
\(446\) −32.1505 −1.52237
\(447\) −22.0718 −1.04396
\(448\) −12.7902 −0.604280
\(449\) −13.5442 −0.639192 −0.319596 0.947554i \(-0.603547\pi\)
−0.319596 + 0.947554i \(0.603547\pi\)
\(450\) 0 0
\(451\) −3.89756 −0.183529
\(452\) −8.48730 −0.399209
\(453\) −7.75768 −0.364488
\(454\) 6.71990 0.315380
\(455\) 0 0
\(456\) 7.68496 0.359881
\(457\) −20.7225 −0.969358 −0.484679 0.874692i \(-0.661064\pi\)
−0.484679 + 0.874692i \(0.661064\pi\)
\(458\) −19.5739 −0.914631
\(459\) −22.8838 −1.06813
\(460\) 0 0
\(461\) 30.4075 1.41622 0.708110 0.706102i \(-0.249548\pi\)
0.708110 + 0.706102i \(0.249548\pi\)
\(462\) 1.52154 0.0707885
\(463\) 2.56874 0.119379 0.0596896 0.998217i \(-0.480989\pi\)
0.0596896 + 0.998217i \(0.480989\pi\)
\(464\) 3.25925 0.151307
\(465\) 0 0
\(466\) 37.7849 1.75035
\(467\) 10.3342 0.478211 0.239105 0.970994i \(-0.423146\pi\)
0.239105 + 0.970994i \(0.423146\pi\)
\(468\) −27.7072 −1.28077
\(469\) 13.6404 0.629854
\(470\) 0 0
\(471\) −15.0119 −0.691711
\(472\) −38.3148 −1.76358
\(473\) −7.99591 −0.367652
\(474\) 32.0514 1.47217
\(475\) 0 0
\(476\) 15.8741 0.727589
\(477\) 29.9110 1.36953
\(478\) 30.4667 1.39351
\(479\) −3.13603 −0.143289 −0.0716444 0.997430i \(-0.522825\pi\)
−0.0716444 + 0.997430i \(0.522825\pi\)
\(480\) 0 0
\(481\) 3.16026 0.144095
\(482\) 9.19714 0.418918
\(483\) 0.930494 0.0423389
\(484\) −34.7859 −1.58118
\(485\) 0 0
\(486\) 37.2364 1.68908
\(487\) 21.1409 0.957987 0.478993 0.877818i \(-0.341002\pi\)
0.478993 + 0.877818i \(0.341002\pi\)
\(488\) −14.4523 −0.654223
\(489\) −2.78208 −0.125810
\(490\) 0 0
\(491\) −30.5820 −1.38015 −0.690073 0.723740i \(-0.742422\pi\)
−0.690073 + 0.723740i \(0.742422\pi\)
\(492\) −16.9430 −0.763848
\(493\) 44.0588 1.98431
\(494\) 24.6245 1.10791
\(495\) 0 0
\(496\) 1.62827 0.0731115
\(497\) 16.5093 0.740543
\(498\) −8.37040 −0.375087
\(499\) −2.28112 −0.102117 −0.0510586 0.998696i \(-0.516260\pi\)
−0.0510586 + 0.998696i \(0.516260\pi\)
\(500\) 0 0
\(501\) −15.7645 −0.704308
\(502\) −65.2826 −2.91371
\(503\) −15.2047 −0.677943 −0.338971 0.940797i \(-0.610079\pi\)
−0.338971 + 0.940797i \(0.610079\pi\)
\(504\) −6.46424 −0.287940
\(505\) 0 0
\(506\) 1.63520 0.0726934
\(507\) 2.18417 0.0970025
\(508\) −24.8878 −1.10422
\(509\) −31.9407 −1.41575 −0.707874 0.706338i \(-0.750346\pi\)
−0.707874 + 0.706338i \(0.750346\pi\)
\(510\) 0 0
\(511\) 8.26175 0.365478
\(512\) −4.00370 −0.176940
\(513\) −13.0265 −0.575133
\(514\) −24.6095 −1.08548
\(515\) 0 0
\(516\) −34.7588 −1.53017
\(517\) 2.25374 0.0991195
\(518\) 1.85958 0.0817053
\(519\) −24.0156 −1.05417
\(520\) 0 0
\(521\) 41.6912 1.82652 0.913261 0.407374i \(-0.133556\pi\)
0.913261 + 0.407374i \(0.133556\pi\)
\(522\) −45.2510 −1.98058
\(523\) 22.0295 0.963281 0.481641 0.876369i \(-0.340041\pi\)
0.481641 + 0.876369i \(0.340041\pi\)
\(524\) −65.0529 −2.84185
\(525\) 0 0
\(526\) −15.8151 −0.689571
\(527\) 22.0111 0.958817
\(528\) 0.233886 0.0101786
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 26.9967 1.17156
\(532\) 9.03624 0.391771
\(533\) −21.5252 −0.932360
\(534\) 31.6366 1.36905
\(535\) 0 0
\(536\) 41.3154 1.78456
\(537\) 18.3376 0.791325
\(538\) −56.4608 −2.43420
\(539\) 0.709352 0.0305540
\(540\) 0 0
\(541\) 13.7712 0.592068 0.296034 0.955177i \(-0.404336\pi\)
0.296034 + 0.955177i \(0.404336\pi\)
\(542\) −57.4172 −2.46628
\(543\) −15.5671 −0.668046
\(544\) −25.1048 −1.07636
\(545\) 0 0
\(546\) 8.40308 0.359619
\(547\) 26.4745 1.13197 0.565984 0.824416i \(-0.308496\pi\)
0.565984 + 0.824416i \(0.308496\pi\)
\(548\) 51.8677 2.21568
\(549\) 10.1831 0.434605
\(550\) 0 0
\(551\) 25.0802 1.06845
\(552\) 2.81838 0.119958
\(553\) 14.9425 0.635422
\(554\) 19.2419 0.817508
\(555\) 0 0
\(556\) −5.64533 −0.239415
\(557\) 5.83619 0.247287 0.123644 0.992327i \(-0.460542\pi\)
0.123644 + 0.992327i \(0.460542\pi\)
\(558\) −22.6067 −0.957018
\(559\) −44.1593 −1.86774
\(560\) 0 0
\(561\) 3.16169 0.133487
\(562\) −4.65873 −0.196516
\(563\) −7.24108 −0.305175 −0.152588 0.988290i \(-0.548761\pi\)
−0.152588 + 0.988290i \(0.548761\pi\)
\(564\) 9.79718 0.412536
\(565\) 0 0
\(566\) 15.3451 0.645001
\(567\) 1.95727 0.0821978
\(568\) 50.0051 2.09817
\(569\) 23.9768 1.00516 0.502580 0.864531i \(-0.332384\pi\)
0.502580 + 0.864531i \(0.332384\pi\)
\(570\) 0 0
\(571\) −16.1798 −0.677104 −0.338552 0.940948i \(-0.609937\pi\)
−0.338552 + 0.940948i \(0.609937\pi\)
\(572\) 9.20924 0.385058
\(573\) −0.000201778 0 −8.42938e−6 0
\(574\) −12.6660 −0.528668
\(575\) 0 0
\(576\) 27.2966 1.13736
\(577\) 1.21253 0.0504782 0.0252391 0.999681i \(-0.491965\pi\)
0.0252391 + 0.999681i \(0.491965\pi\)
\(578\) 13.7044 0.570028
\(579\) −3.82965 −0.159155
\(580\) 0 0
\(581\) −3.90233 −0.161896
\(582\) 32.1174 1.33131
\(583\) −9.94171 −0.411744
\(584\) 25.0241 1.03550
\(585\) 0 0
\(586\) −53.2481 −2.19966
\(587\) −31.6048 −1.30447 −0.652235 0.758017i \(-0.726169\pi\)
−0.652235 + 0.758017i \(0.726169\pi\)
\(588\) 3.08361 0.127166
\(589\) 12.5297 0.516276
\(590\) 0 0
\(591\) −3.13903 −0.129123
\(592\) 0.285848 0.0117483
\(593\) −12.7135 −0.522080 −0.261040 0.965328i \(-0.584065\pi\)
−0.261040 + 0.965328i \(0.584065\pi\)
\(594\) −7.81187 −0.320525
\(595\) 0 0
\(596\) −78.6086 −3.21993
\(597\) 10.5943 0.433597
\(598\) 9.03077 0.369296
\(599\) −4.67856 −0.191161 −0.0955804 0.995422i \(-0.530471\pi\)
−0.0955804 + 0.995422i \(0.530471\pi\)
\(600\) 0 0
\(601\) 40.3668 1.64659 0.823297 0.567611i \(-0.192132\pi\)
0.823297 + 0.567611i \(0.192132\pi\)
\(602\) −25.9845 −1.05905
\(603\) −29.1110 −1.18549
\(604\) −27.6289 −1.12421
\(605\) 0 0
\(606\) 4.15340 0.168720
\(607\) 19.3976 0.787325 0.393662 0.919255i \(-0.371208\pi\)
0.393662 + 0.919255i \(0.371208\pi\)
\(608\) −14.2907 −0.579566
\(609\) 8.55858 0.346811
\(610\) 0 0
\(611\) 12.4468 0.503545
\(612\) −33.8782 −1.36945
\(613\) 14.0340 0.566830 0.283415 0.958997i \(-0.408533\pi\)
0.283415 + 0.958997i \(0.408533\pi\)
\(614\) −28.6316 −1.15548
\(615\) 0 0
\(616\) 2.14856 0.0865681
\(617\) −29.0055 −1.16772 −0.583860 0.811855i \(-0.698458\pi\)
−0.583860 + 0.811855i \(0.698458\pi\)
\(618\) −4.46381 −0.179561
\(619\) −9.40330 −0.377950 −0.188975 0.981982i \(-0.560517\pi\)
−0.188975 + 0.981982i \(0.560517\pi\)
\(620\) 0 0
\(621\) −4.77732 −0.191707
\(622\) 72.2950 2.89876
\(623\) 14.7492 0.590913
\(624\) 1.29169 0.0517091
\(625\) 0 0
\(626\) 48.2139 1.92702
\(627\) 1.79977 0.0718760
\(628\) −53.4647 −2.13347
\(629\) 3.86412 0.154072
\(630\) 0 0
\(631\) −14.3553 −0.571474 −0.285737 0.958308i \(-0.592238\pi\)
−0.285737 + 0.958308i \(0.592238\pi\)
\(632\) 45.2596 1.80033
\(633\) −7.27581 −0.289188
\(634\) −1.37759 −0.0547110
\(635\) 0 0
\(636\) −43.2173 −1.71368
\(637\) 3.91757 0.155220
\(638\) 15.0404 0.595455
\(639\) −35.2338 −1.39383
\(640\) 0 0
\(641\) 34.2916 1.35444 0.677218 0.735782i \(-0.263185\pi\)
0.677218 + 0.735782i \(0.263185\pi\)
\(642\) 10.4271 0.411526
\(643\) −13.1024 −0.516707 −0.258353 0.966050i \(-0.583180\pi\)
−0.258353 + 0.966050i \(0.583180\pi\)
\(644\) 3.31395 0.130588
\(645\) 0 0
\(646\) 30.1089 1.18462
\(647\) 13.4922 0.530435 0.265217 0.964189i \(-0.414556\pi\)
0.265217 + 0.964189i \(0.414556\pi\)
\(648\) 5.92841 0.232890
\(649\) −8.97309 −0.352224
\(650\) 0 0
\(651\) 4.27573 0.167579
\(652\) −9.90836 −0.388041
\(653\) −26.3357 −1.03060 −0.515298 0.857011i \(-0.672319\pi\)
−0.515298 + 0.857011i \(0.672319\pi\)
\(654\) −13.2594 −0.518485
\(655\) 0 0
\(656\) −1.94697 −0.0760165
\(657\) −17.6321 −0.687892
\(658\) 7.32404 0.285521
\(659\) 30.7155 1.19651 0.598253 0.801307i \(-0.295862\pi\)
0.598253 + 0.801307i \(0.295862\pi\)
\(660\) 0 0
\(661\) −14.5710 −0.566745 −0.283372 0.959010i \(-0.591453\pi\)
−0.283372 + 0.959010i \(0.591453\pi\)
\(662\) −58.7235 −2.28235
\(663\) 17.4612 0.678136
\(664\) −11.8198 −0.458698
\(665\) 0 0
\(666\) −3.96868 −0.153783
\(667\) 9.19789 0.356144
\(668\) −56.1453 −2.17233
\(669\) −12.9775 −0.501740
\(670\) 0 0
\(671\) −3.38463 −0.130662
\(672\) −4.87670 −0.188123
\(673\) −14.3211 −0.552038 −0.276019 0.961152i \(-0.589015\pi\)
−0.276019 + 0.961152i \(0.589015\pi\)
\(674\) 33.4842 1.28976
\(675\) 0 0
\(676\) 7.77891 0.299189
\(677\) 28.3658 1.09019 0.545094 0.838375i \(-0.316494\pi\)
0.545094 + 0.838375i \(0.316494\pi\)
\(678\) −5.49346 −0.210975
\(679\) 14.9733 0.574623
\(680\) 0 0
\(681\) 2.71249 0.103943
\(682\) 7.51394 0.287724
\(683\) 3.53372 0.135214 0.0676071 0.997712i \(-0.478464\pi\)
0.0676071 + 0.997712i \(0.478464\pi\)
\(684\) −19.2850 −0.737379
\(685\) 0 0
\(686\) 2.30520 0.0880129
\(687\) −7.90102 −0.301443
\(688\) −3.99425 −0.152279
\(689\) −54.9055 −2.09173
\(690\) 0 0
\(691\) 21.9959 0.836764 0.418382 0.908271i \(-0.362597\pi\)
0.418382 + 0.908271i \(0.362597\pi\)
\(692\) −85.5315 −3.25142
\(693\) −1.51389 −0.0575078
\(694\) −1.94244 −0.0737341
\(695\) 0 0
\(696\) 25.9232 0.982615
\(697\) −26.3193 −0.996915
\(698\) −36.6376 −1.38675
\(699\) 15.2519 0.576878
\(700\) 0 0
\(701\) 33.0978 1.25009 0.625043 0.780591i \(-0.285082\pi\)
0.625043 + 0.780591i \(0.285082\pi\)
\(702\) −43.1429 −1.62832
\(703\) 2.19962 0.0829604
\(704\) −9.07275 −0.341942
\(705\) 0 0
\(706\) −51.7192 −1.94648
\(707\) 1.93634 0.0728236
\(708\) −39.0067 −1.46596
\(709\) 32.1089 1.20588 0.602938 0.797788i \(-0.293997\pi\)
0.602938 + 0.797788i \(0.293997\pi\)
\(710\) 0 0
\(711\) −31.8901 −1.19597
\(712\) 44.6739 1.67422
\(713\) 4.59512 0.172089
\(714\) 10.2746 0.384518
\(715\) 0 0
\(716\) 65.3092 2.44072
\(717\) 12.2979 0.459272
\(718\) −51.2615 −1.91306
\(719\) −35.4855 −1.32339 −0.661694 0.749774i \(-0.730162\pi\)
−0.661694 + 0.749774i \(0.730162\pi\)
\(720\) 0 0
\(721\) −2.08106 −0.0775026
\(722\) −26.6595 −0.992164
\(723\) 3.71243 0.138067
\(724\) −55.4420 −2.06048
\(725\) 0 0
\(726\) −22.5154 −0.835625
\(727\) 17.0021 0.630574 0.315287 0.948996i \(-0.397899\pi\)
0.315287 + 0.948996i \(0.397899\pi\)
\(728\) 11.8660 0.439781
\(729\) 9.15863 0.339209
\(730\) 0 0
\(731\) −53.9946 −1.99706
\(732\) −14.7132 −0.543817
\(733\) 53.1566 1.96339 0.981693 0.190472i \(-0.0610019\pi\)
0.981693 + 0.190472i \(0.0610019\pi\)
\(734\) 23.3360 0.861349
\(735\) 0 0
\(736\) −5.24098 −0.193185
\(737\) 9.67583 0.356414
\(738\) 27.0315 0.995044
\(739\) 0.0204752 0.000753191 0 0.000376596 1.00000i \(-0.499880\pi\)
0.000376596 1.00000i \(0.499880\pi\)
\(740\) 0 0
\(741\) 9.93967 0.365143
\(742\) −32.3078 −1.18606
\(743\) 41.1435 1.50941 0.754704 0.656065i \(-0.227780\pi\)
0.754704 + 0.656065i \(0.227780\pi\)
\(744\) 12.9508 0.474800
\(745\) 0 0
\(746\) 12.6988 0.464935
\(747\) 8.32829 0.304716
\(748\) 11.2603 0.411719
\(749\) 4.86119 0.177624
\(750\) 0 0
\(751\) 46.5976 1.70037 0.850186 0.526483i \(-0.176490\pi\)
0.850186 + 0.526483i \(0.176490\pi\)
\(752\) 1.12583 0.0410547
\(753\) −26.3513 −0.960296
\(754\) 83.0641 3.02502
\(755\) 0 0
\(756\) −15.8318 −0.575797
\(757\) 33.1567 1.20510 0.602550 0.798081i \(-0.294151\pi\)
0.602550 + 0.798081i \(0.294151\pi\)
\(758\) 47.5420 1.72680
\(759\) 0.660048 0.0239582
\(760\) 0 0
\(761\) 10.0225 0.363316 0.181658 0.983362i \(-0.441854\pi\)
0.181658 + 0.983362i \(0.441854\pi\)
\(762\) −16.1088 −0.583560
\(763\) −6.18163 −0.223790
\(764\) −0.000718629 0 −2.59991e−5 0
\(765\) 0 0
\(766\) 18.5861 0.671543
\(767\) −49.5560 −1.78936
\(768\) −16.9564 −0.611861
\(769\) −9.36109 −0.337570 −0.168785 0.985653i \(-0.553984\pi\)
−0.168785 + 0.985653i \(0.553984\pi\)
\(770\) 0 0
\(771\) −9.93364 −0.357751
\(772\) −13.6393 −0.490888
\(773\) 3.48472 0.125337 0.0626684 0.998034i \(-0.480039\pi\)
0.0626684 + 0.998034i \(0.480039\pi\)
\(774\) 55.4557 1.99331
\(775\) 0 0
\(776\) 45.3528 1.62807
\(777\) 0.750619 0.0269283
\(778\) 41.3261 1.48161
\(779\) −14.9821 −0.536790
\(780\) 0 0
\(781\) 11.7109 0.419049
\(782\) 11.0421 0.394865
\(783\) −43.9413 −1.57033
\(784\) 0.354347 0.0126553
\(785\) 0 0
\(786\) −42.1059 −1.50187
\(787\) 32.7487 1.16736 0.583682 0.811982i \(-0.301611\pi\)
0.583682 + 0.811982i \(0.301611\pi\)
\(788\) −11.1796 −0.398258
\(789\) −6.38376 −0.227268
\(790\) 0 0
\(791\) −2.56109 −0.0910618
\(792\) −4.58542 −0.162936
\(793\) −18.6924 −0.663788
\(794\) 67.5014 2.39554
\(795\) 0 0
\(796\) 37.7316 1.33736
\(797\) −21.2625 −0.753158 −0.376579 0.926385i \(-0.622900\pi\)
−0.376579 + 0.926385i \(0.622900\pi\)
\(798\) 5.84877 0.207044
\(799\) 15.2190 0.538410
\(800\) 0 0
\(801\) −31.4774 −1.11220
\(802\) 10.0381 0.354456
\(803\) 5.86049 0.206812
\(804\) 42.0615 1.48340
\(805\) 0 0
\(806\) 41.4975 1.46169
\(807\) −22.7904 −0.802260
\(808\) 5.86500 0.206330
\(809\) −21.5257 −0.756803 −0.378402 0.925641i \(-0.623526\pi\)
−0.378402 + 0.925641i \(0.623526\pi\)
\(810\) 0 0
\(811\) −0.613016 −0.0215259 −0.0107630 0.999942i \(-0.503426\pi\)
−0.0107630 + 0.999942i \(0.503426\pi\)
\(812\) 30.4813 1.06968
\(813\) −23.1764 −0.812833
\(814\) 1.31910 0.0462343
\(815\) 0 0
\(816\) 1.57938 0.0552894
\(817\) −30.7361 −1.07532
\(818\) −69.4315 −2.42762
\(819\) −8.36080 −0.292150
\(820\) 0 0
\(821\) 8.87035 0.309577 0.154789 0.987948i \(-0.450530\pi\)
0.154789 + 0.987948i \(0.450530\pi\)
\(822\) 33.5717 1.17095
\(823\) −7.92495 −0.276246 −0.138123 0.990415i \(-0.544107\pi\)
−0.138123 + 0.990415i \(0.544107\pi\)
\(824\) −6.30333 −0.219587
\(825\) 0 0
\(826\) −29.1601 −1.01461
\(827\) 36.0984 1.25526 0.627632 0.778510i \(-0.284024\pi\)
0.627632 + 0.778510i \(0.284024\pi\)
\(828\) −7.07256 −0.245789
\(829\) −0.675531 −0.0234622 −0.0117311 0.999931i \(-0.503734\pi\)
−0.0117311 + 0.999931i \(0.503734\pi\)
\(830\) 0 0
\(831\) 7.76697 0.269433
\(832\) −50.1064 −1.73713
\(833\) 4.79009 0.165967
\(834\) −3.65398 −0.126527
\(835\) 0 0
\(836\) 6.40988 0.221690
\(837\) −21.9524 −0.758786
\(838\) −45.2842 −1.56432
\(839\) −29.8282 −1.02979 −0.514893 0.857255i \(-0.672168\pi\)
−0.514893 + 0.857255i \(0.672168\pi\)
\(840\) 0 0
\(841\) 55.6013 1.91728
\(842\) −24.0331 −0.828237
\(843\) −1.88049 −0.0647677
\(844\) −25.9128 −0.891954
\(845\) 0 0
\(846\) −15.6308 −0.537399
\(847\) −10.4968 −0.360675
\(848\) −4.96625 −0.170542
\(849\) 6.19404 0.212579
\(850\) 0 0
\(851\) 0.806689 0.0276530
\(852\) 50.9082 1.74408
\(853\) −43.2041 −1.47928 −0.739639 0.673004i \(-0.765004\pi\)
−0.739639 + 0.673004i \(0.765004\pi\)
\(854\) −10.9991 −0.376382
\(855\) 0 0
\(856\) 14.7241 0.503259
\(857\) −11.0759 −0.378346 −0.189173 0.981944i \(-0.560581\pi\)
−0.189173 + 0.981944i \(0.560581\pi\)
\(858\) 5.96074 0.203496
\(859\) 34.7012 1.18399 0.591995 0.805942i \(-0.298340\pi\)
0.591995 + 0.805942i \(0.298340\pi\)
\(860\) 0 0
\(861\) −5.11263 −0.174238
\(862\) −28.5406 −0.972097
\(863\) 53.4387 1.81907 0.909537 0.415623i \(-0.136436\pi\)
0.909537 + 0.415623i \(0.136436\pi\)
\(864\) 25.0378 0.851805
\(865\) 0 0
\(866\) 72.8548 2.47571
\(867\) 5.53178 0.187869
\(868\) 15.2280 0.516872
\(869\) 10.5995 0.359564
\(870\) 0 0
\(871\) 53.4371 1.81065
\(872\) −18.7236 −0.634061
\(873\) −31.9558 −1.08154
\(874\) 6.28566 0.212616
\(875\) 0 0
\(876\) 25.4760 0.860753
\(877\) −10.2527 −0.346208 −0.173104 0.984904i \(-0.555380\pi\)
−0.173104 + 0.984904i \(0.555380\pi\)
\(878\) −50.5950 −1.70750
\(879\) −21.4936 −0.724961
\(880\) 0 0
\(881\) −21.7396 −0.732424 −0.366212 0.930531i \(-0.619346\pi\)
−0.366212 + 0.930531i \(0.619346\pi\)
\(882\) −4.91971 −0.165655
\(883\) −16.1632 −0.543935 −0.271968 0.962306i \(-0.587674\pi\)
−0.271968 + 0.962306i \(0.587674\pi\)
\(884\) 62.1879 2.09160
\(885\) 0 0
\(886\) 84.5944 2.84200
\(887\) 3.60774 0.121136 0.0605681 0.998164i \(-0.480709\pi\)
0.0605681 + 0.998164i \(0.480709\pi\)
\(888\) 2.27356 0.0762956
\(889\) −7.51001 −0.251878
\(890\) 0 0
\(891\) 1.38840 0.0465130
\(892\) −46.2194 −1.54754
\(893\) 8.66332 0.289907
\(894\) −50.8799 −1.70168
\(895\) 0 0
\(896\) −19.0020 −0.634812
\(897\) 3.64527 0.121712
\(898\) −31.2222 −1.04190
\(899\) 42.2655 1.40963
\(900\) 0 0
\(901\) −67.1341 −2.23656
\(902\) −8.98465 −0.299156
\(903\) −10.4886 −0.349040
\(904\) −7.75730 −0.258004
\(905\) 0 0
\(906\) −17.8830 −0.594123
\(907\) 11.8255 0.392659 0.196330 0.980538i \(-0.437098\pi\)
0.196330 + 0.980538i \(0.437098\pi\)
\(908\) 9.66050 0.320595
\(909\) −4.13250 −0.137066
\(910\) 0 0
\(911\) −48.1231 −1.59439 −0.797195 0.603722i \(-0.793684\pi\)
−0.797195 + 0.603722i \(0.793684\pi\)
\(912\) 0.899052 0.0297706
\(913\) −2.76813 −0.0916117
\(914\) −47.7695 −1.58007
\(915\) 0 0
\(916\) −28.1394 −0.929753
\(917\) −19.6300 −0.648241
\(918\) −52.7518 −1.74107
\(919\) 36.8685 1.21618 0.608089 0.793869i \(-0.291936\pi\)
0.608089 + 0.793869i \(0.291936\pi\)
\(920\) 0 0
\(921\) −11.5572 −0.380821
\(922\) 70.0954 2.30847
\(923\) 64.6762 2.12884
\(924\) 2.18736 0.0719590
\(925\) 0 0
\(926\) 5.92145 0.194591
\(927\) 4.44135 0.145873
\(928\) −48.2059 −1.58244
\(929\) −27.5807 −0.904893 −0.452446 0.891792i \(-0.649449\pi\)
−0.452446 + 0.891792i \(0.649449\pi\)
\(930\) 0 0
\(931\) 2.72673 0.0893650
\(932\) 54.3194 1.77929
\(933\) 29.1819 0.955371
\(934\) 23.8224 0.779494
\(935\) 0 0
\(936\) −25.3241 −0.827744
\(937\) 26.5360 0.866892 0.433446 0.901180i \(-0.357297\pi\)
0.433446 + 0.901180i \(0.357297\pi\)
\(938\) 31.4438 1.02668
\(939\) 19.4615 0.635104
\(940\) 0 0
\(941\) 39.9295 1.30166 0.650832 0.759222i \(-0.274420\pi\)
0.650832 + 0.759222i \(0.274420\pi\)
\(942\) −34.6054 −1.12750
\(943\) −5.49453 −0.178927
\(944\) −4.48239 −0.145889
\(945\) 0 0
\(946\) −18.4322 −0.599282
\(947\) 5.28432 0.171717 0.0858586 0.996307i \(-0.472637\pi\)
0.0858586 + 0.996307i \(0.472637\pi\)
\(948\) 46.0769 1.49651
\(949\) 32.3659 1.05064
\(950\) 0 0
\(951\) −0.556064 −0.0180316
\(952\) 14.5088 0.470231
\(953\) 43.2605 1.40134 0.700672 0.713483i \(-0.252884\pi\)
0.700672 + 0.713483i \(0.252884\pi\)
\(954\) 68.9508 2.23236
\(955\) 0 0
\(956\) 43.7988 1.41655
\(957\) 6.07105 0.196249
\(958\) −7.22917 −0.233564
\(959\) 15.6513 0.505408
\(960\) 0 0
\(961\) −9.88484 −0.318866
\(962\) 7.28503 0.234879
\(963\) −10.3747 −0.334319
\(964\) 13.2218 0.425845
\(965\) 0 0
\(966\) 2.14497 0.0690134
\(967\) −15.3544 −0.493766 −0.246883 0.969045i \(-0.579406\pi\)
−0.246883 + 0.969045i \(0.579406\pi\)
\(968\) −31.7939 −1.02189
\(969\) 12.1535 0.390425
\(970\) 0 0
\(971\) −41.9060 −1.34483 −0.672414 0.740175i \(-0.734743\pi\)
−0.672414 + 0.740175i \(0.734743\pi\)
\(972\) 53.5308 1.71700
\(973\) −1.70351 −0.0546119
\(974\) 48.7341 1.56154
\(975\) 0 0
\(976\) −1.69075 −0.0541195
\(977\) −35.8935 −1.14833 −0.574167 0.818738i \(-0.694674\pi\)
−0.574167 + 0.818738i \(0.694674\pi\)
\(978\) −6.41325 −0.205073
\(979\) 10.4624 0.334378
\(980\) 0 0
\(981\) 13.1927 0.421211
\(982\) −70.4976 −2.24967
\(983\) 36.1916 1.15433 0.577167 0.816626i \(-0.304158\pi\)
0.577167 + 0.816626i \(0.304158\pi\)
\(984\) −15.4857 −0.493666
\(985\) 0 0
\(986\) 101.564 3.23447
\(987\) 2.95635 0.0941016
\(988\) 35.4001 1.12623
\(989\) −11.2721 −0.358433
\(990\) 0 0
\(991\) −23.6677 −0.751829 −0.375914 0.926654i \(-0.622671\pi\)
−0.375914 + 0.926654i \(0.622671\pi\)
\(992\) −24.0829 −0.764634
\(993\) −23.7037 −0.752215
\(994\) 38.0572 1.20710
\(995\) 0 0
\(996\) −12.0333 −0.381288
\(997\) 47.9363 1.51816 0.759078 0.650999i \(-0.225650\pi\)
0.759078 + 0.650999i \(0.225650\pi\)
\(998\) −5.25845 −0.166453
\(999\) −3.85382 −0.121929
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.bc.1.12 yes 14
5.4 even 2 4025.2.a.z.1.3 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4025.2.a.z.1.3 14 5.4 even 2
4025.2.a.bc.1.12 yes 14 1.1 even 1 trivial