Properties

Label 6025.2.a.i.1.7
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $15$
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] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, 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("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.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: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} - 699 x^{6} - 297 x^{5} + 394 x^{4} + 89 x^{3} - 57 x^{2} - 17 x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.596683\) of defining polynomial
Character \(\chi\) \(=\) 6025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.596683 q^{2} +3.22200 q^{3} -1.64397 q^{4} -1.92252 q^{6} -0.0914365 q^{7} +2.17430 q^{8} +7.38130 q^{9} +O(q^{10})\) \(q-0.596683 q^{2} +3.22200 q^{3} -1.64397 q^{4} -1.92252 q^{6} -0.0914365 q^{7} +2.17430 q^{8} +7.38130 q^{9} +0.938184 q^{11} -5.29687 q^{12} -6.40952 q^{13} +0.0545586 q^{14} +1.99057 q^{16} +5.47227 q^{17} -4.40430 q^{18} -4.62417 q^{19} -0.294609 q^{21} -0.559799 q^{22} -9.45757 q^{23} +7.00559 q^{24} +3.82445 q^{26} +14.1166 q^{27} +0.150319 q^{28} -0.666961 q^{29} -7.51445 q^{31} -5.53633 q^{32} +3.02283 q^{33} -3.26521 q^{34} -12.1346 q^{36} -5.97202 q^{37} +2.75917 q^{38} -20.6515 q^{39} -1.82336 q^{41} +0.175788 q^{42} -2.41367 q^{43} -1.54234 q^{44} +5.64318 q^{46} -1.50928 q^{47} +6.41363 q^{48} -6.99164 q^{49} +17.6317 q^{51} +10.5370 q^{52} +3.52075 q^{53} -8.42312 q^{54} -0.198810 q^{56} -14.8991 q^{57} +0.397965 q^{58} -14.3795 q^{59} -6.52207 q^{61} +4.48375 q^{62} -0.674920 q^{63} -0.677704 q^{64} -1.80367 q^{66} +15.3694 q^{67} -8.99624 q^{68} -30.4723 q^{69} +6.49472 q^{71} +16.0491 q^{72} +2.73165 q^{73} +3.56340 q^{74} +7.60200 q^{76} -0.0857842 q^{77} +12.3224 q^{78} -8.80094 q^{79} +23.3397 q^{81} +1.08797 q^{82} +0.402706 q^{83} +0.484327 q^{84} +1.44020 q^{86} -2.14895 q^{87} +2.03989 q^{88} +17.9570 q^{89} +0.586064 q^{91} +15.5480 q^{92} -24.2116 q^{93} +0.900560 q^{94} -17.8381 q^{96} -17.4995 q^{97} +4.17180 q^{98} +6.92502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.596683 −0.421919 −0.210959 0.977495i \(-0.567659\pi\)
−0.210959 + 0.977495i \(0.567659\pi\)
\(3\) 3.22200 1.86022 0.930112 0.367276i \(-0.119710\pi\)
0.930112 + 0.367276i \(0.119710\pi\)
\(4\) −1.64397 −0.821984
\(5\) 0 0
\(6\) −1.92252 −0.784864
\(7\) −0.0914365 −0.0345597 −0.0172799 0.999851i \(-0.505501\pi\)
−0.0172799 + 0.999851i \(0.505501\pi\)
\(8\) 2.17430 0.768730
\(9\) 7.38130 2.46043
\(10\) 0 0
\(11\) 0.938184 0.282873 0.141437 0.989947i \(-0.454828\pi\)
0.141437 + 0.989947i \(0.454828\pi\)
\(12\) −5.29687 −1.52908
\(13\) −6.40952 −1.77768 −0.888840 0.458218i \(-0.848488\pi\)
−0.888840 + 0.458218i \(0.848488\pi\)
\(14\) 0.0545586 0.0145814
\(15\) 0 0
\(16\) 1.99057 0.497643
\(17\) 5.47227 1.32722 0.663610 0.748079i \(-0.269023\pi\)
0.663610 + 0.748079i \(0.269023\pi\)
\(18\) −4.40430 −1.03810
\(19\) −4.62417 −1.06086 −0.530429 0.847729i \(-0.677969\pi\)
−0.530429 + 0.847729i \(0.677969\pi\)
\(20\) 0 0
\(21\) −0.294609 −0.0642889
\(22\) −0.559799 −0.119349
\(23\) −9.45757 −1.97204 −0.986020 0.166626i \(-0.946713\pi\)
−0.986020 + 0.166626i \(0.946713\pi\)
\(24\) 7.00559 1.43001
\(25\) 0 0
\(26\) 3.82445 0.750037
\(27\) 14.1166 2.71673
\(28\) 0.150319 0.0284076
\(29\) −0.666961 −0.123852 −0.0619258 0.998081i \(-0.519724\pi\)
−0.0619258 + 0.998081i \(0.519724\pi\)
\(30\) 0 0
\(31\) −7.51445 −1.34964 −0.674818 0.737985i \(-0.735778\pi\)
−0.674818 + 0.737985i \(0.735778\pi\)
\(32\) −5.53633 −0.978695
\(33\) 3.02283 0.526207
\(34\) −3.26521 −0.559979
\(35\) 0 0
\(36\) −12.1346 −2.02244
\(37\) −5.97202 −0.981793 −0.490897 0.871218i \(-0.663331\pi\)
−0.490897 + 0.871218i \(0.663331\pi\)
\(38\) 2.75917 0.447596
\(39\) −20.6515 −3.30688
\(40\) 0 0
\(41\) −1.82336 −0.284761 −0.142380 0.989812i \(-0.545476\pi\)
−0.142380 + 0.989812i \(0.545476\pi\)
\(42\) 0.175788 0.0271247
\(43\) −2.41367 −0.368081 −0.184041 0.982919i \(-0.558918\pi\)
−0.184041 + 0.982919i \(0.558918\pi\)
\(44\) −1.54234 −0.232517
\(45\) 0 0
\(46\) 5.64318 0.832041
\(47\) −1.50928 −0.220151 −0.110075 0.993923i \(-0.535109\pi\)
−0.110075 + 0.993923i \(0.535109\pi\)
\(48\) 6.41363 0.925727
\(49\) −6.99164 −0.998806
\(50\) 0 0
\(51\) 17.6317 2.46893
\(52\) 10.5370 1.46123
\(53\) 3.52075 0.483612 0.241806 0.970325i \(-0.422260\pi\)
0.241806 + 0.970325i \(0.422260\pi\)
\(54\) −8.42312 −1.14624
\(55\) 0 0
\(56\) −0.198810 −0.0265671
\(57\) −14.8991 −1.97343
\(58\) 0.397965 0.0522553
\(59\) −14.3795 −1.87206 −0.936028 0.351926i \(-0.885527\pi\)
−0.936028 + 0.351926i \(0.885527\pi\)
\(60\) 0 0
\(61\) −6.52207 −0.835065 −0.417533 0.908662i \(-0.637105\pi\)
−0.417533 + 0.908662i \(0.637105\pi\)
\(62\) 4.48375 0.569437
\(63\) −0.674920 −0.0850320
\(64\) −0.677704 −0.0847130
\(65\) 0 0
\(66\) −1.80367 −0.222017
\(67\) 15.3694 1.87767 0.938835 0.344369i \(-0.111907\pi\)
0.938835 + 0.344369i \(0.111907\pi\)
\(68\) −8.99624 −1.09095
\(69\) −30.4723 −3.66844
\(70\) 0 0
\(71\) 6.49472 0.770782 0.385391 0.922753i \(-0.374067\pi\)
0.385391 + 0.922753i \(0.374067\pi\)
\(72\) 16.0491 1.89141
\(73\) 2.73165 0.319716 0.159858 0.987140i \(-0.448896\pi\)
0.159858 + 0.987140i \(0.448896\pi\)
\(74\) 3.56340 0.414237
\(75\) 0 0
\(76\) 7.60200 0.872009
\(77\) −0.0857842 −0.00977602
\(78\) 12.3224 1.39524
\(79\) −8.80094 −0.990184 −0.495092 0.868841i \(-0.664866\pi\)
−0.495092 + 0.868841i \(0.664866\pi\)
\(80\) 0 0
\(81\) 23.3397 2.59330
\(82\) 1.08797 0.120146
\(83\) 0.402706 0.0442028 0.0221014 0.999756i \(-0.492964\pi\)
0.0221014 + 0.999756i \(0.492964\pi\)
\(84\) 0.484327 0.0528444
\(85\) 0 0
\(86\) 1.44020 0.155300
\(87\) −2.14895 −0.230392
\(88\) 2.03989 0.217453
\(89\) 17.9570 1.90344 0.951721 0.306964i \(-0.0993132\pi\)
0.951721 + 0.306964i \(0.0993132\pi\)
\(90\) 0 0
\(91\) 0.586064 0.0614362
\(92\) 15.5480 1.62099
\(93\) −24.2116 −2.51062
\(94\) 0.900560 0.0928857
\(95\) 0 0
\(96\) −17.8381 −1.82059
\(97\) −17.4995 −1.77680 −0.888401 0.459068i \(-0.848184\pi\)
−0.888401 + 0.459068i \(0.848184\pi\)
\(98\) 4.17180 0.421415
\(99\) 6.92502 0.695990
\(100\) 0 0
\(101\) 16.0553 1.59757 0.798783 0.601619i \(-0.205477\pi\)
0.798783 + 0.601619i \(0.205477\pi\)
\(102\) −10.5205 −1.04169
\(103\) 9.85176 0.970722 0.485361 0.874314i \(-0.338688\pi\)
0.485361 + 0.874314i \(0.338688\pi\)
\(104\) −13.9362 −1.36656
\(105\) 0 0
\(106\) −2.10077 −0.204045
\(107\) 5.96114 0.576285 0.288143 0.957588i \(-0.406962\pi\)
0.288143 + 0.957588i \(0.406962\pi\)
\(108\) −23.2072 −2.23311
\(109\) −8.70283 −0.833580 −0.416790 0.909003i \(-0.636845\pi\)
−0.416790 + 0.909003i \(0.636845\pi\)
\(110\) 0 0
\(111\) −19.2418 −1.82636
\(112\) −0.182011 −0.0171984
\(113\) −12.3991 −1.16640 −0.583202 0.812327i \(-0.698201\pi\)
−0.583202 + 0.812327i \(0.698201\pi\)
\(114\) 8.89004 0.832629
\(115\) 0 0
\(116\) 1.09646 0.101804
\(117\) −47.3106 −4.37386
\(118\) 8.58003 0.789856
\(119\) −0.500365 −0.0458684
\(120\) 0 0
\(121\) −10.1198 −0.919983
\(122\) 3.89161 0.352330
\(123\) −5.87486 −0.529718
\(124\) 12.3535 1.10938
\(125\) 0 0
\(126\) 0.402714 0.0358766
\(127\) −12.6594 −1.12334 −0.561671 0.827361i \(-0.689841\pi\)
−0.561671 + 0.827361i \(0.689841\pi\)
\(128\) 11.4770 1.01444
\(129\) −7.77685 −0.684714
\(130\) 0 0
\(131\) 7.79459 0.681017 0.340508 0.940242i \(-0.389401\pi\)
0.340508 + 0.940242i \(0.389401\pi\)
\(132\) −4.96944 −0.432534
\(133\) 0.422818 0.0366630
\(134\) −9.17066 −0.792224
\(135\) 0 0
\(136\) 11.8983 1.02027
\(137\) 11.1891 0.955948 0.477974 0.878374i \(-0.341371\pi\)
0.477974 + 0.878374i \(0.341371\pi\)
\(138\) 18.1823 1.54778
\(139\) −13.2779 −1.12622 −0.563110 0.826382i \(-0.690395\pi\)
−0.563110 + 0.826382i \(0.690395\pi\)
\(140\) 0 0
\(141\) −4.86289 −0.409529
\(142\) −3.87529 −0.325207
\(143\) −6.01330 −0.502858
\(144\) 14.6930 1.22442
\(145\) 0 0
\(146\) −1.62993 −0.134894
\(147\) −22.5271 −1.85800
\(148\) 9.81781 0.807019
\(149\) −13.4293 −1.10017 −0.550084 0.835109i \(-0.685404\pi\)
−0.550084 + 0.835109i \(0.685404\pi\)
\(150\) 0 0
\(151\) −13.2454 −1.07789 −0.538947 0.842340i \(-0.681178\pi\)
−0.538947 + 0.842340i \(0.681178\pi\)
\(152\) −10.0543 −0.815513
\(153\) 40.3925 3.26554
\(154\) 0.0511860 0.00412469
\(155\) 0 0
\(156\) 33.9504 2.71821
\(157\) 11.4227 0.911634 0.455817 0.890074i \(-0.349347\pi\)
0.455817 + 0.890074i \(0.349347\pi\)
\(158\) 5.25138 0.417777
\(159\) 11.3439 0.899628
\(160\) 0 0
\(161\) 0.864767 0.0681532
\(162\) −13.9264 −1.09416
\(163\) −4.17420 −0.326949 −0.163474 0.986548i \(-0.552270\pi\)
−0.163474 + 0.986548i \(0.552270\pi\)
\(164\) 2.99754 0.234069
\(165\) 0 0
\(166\) −0.240288 −0.0186500
\(167\) 22.4429 1.73668 0.868340 0.495969i \(-0.165187\pi\)
0.868340 + 0.495969i \(0.165187\pi\)
\(168\) −0.640566 −0.0494208
\(169\) 28.0819 2.16015
\(170\) 0 0
\(171\) −34.1324 −2.61017
\(172\) 3.96800 0.302557
\(173\) 19.0621 1.44926 0.724632 0.689136i \(-0.242010\pi\)
0.724632 + 0.689136i \(0.242010\pi\)
\(174\) 1.28224 0.0972066
\(175\) 0 0
\(176\) 1.86752 0.140770
\(177\) −46.3309 −3.48244
\(178\) −10.7147 −0.803098
\(179\) 6.78903 0.507436 0.253718 0.967278i \(-0.418346\pi\)
0.253718 + 0.967278i \(0.418346\pi\)
\(180\) 0 0
\(181\) −0.650357 −0.0483406 −0.0241703 0.999708i \(-0.507694\pi\)
−0.0241703 + 0.999708i \(0.507694\pi\)
\(182\) −0.349694 −0.0259211
\(183\) −21.0141 −1.55341
\(184\) −20.5636 −1.51597
\(185\) 0 0
\(186\) 14.4466 1.05928
\(187\) 5.13399 0.375435
\(188\) 2.48120 0.180960
\(189\) −1.29077 −0.0938896
\(190\) 0 0
\(191\) −13.4770 −0.975161 −0.487580 0.873078i \(-0.662120\pi\)
−0.487580 + 0.873078i \(0.662120\pi\)
\(192\) −2.18356 −0.157585
\(193\) −5.46458 −0.393349 −0.196675 0.980469i \(-0.563014\pi\)
−0.196675 + 0.980469i \(0.563014\pi\)
\(194\) 10.4416 0.749667
\(195\) 0 0
\(196\) 11.4940 0.821003
\(197\) 20.7161 1.47596 0.737981 0.674822i \(-0.235780\pi\)
0.737981 + 0.674822i \(0.235780\pi\)
\(198\) −4.13204 −0.293651
\(199\) −25.7071 −1.82233 −0.911165 0.412041i \(-0.864816\pi\)
−0.911165 + 0.412041i \(0.864816\pi\)
\(200\) 0 0
\(201\) 49.5202 3.49289
\(202\) −9.57996 −0.674043
\(203\) 0.0609846 0.00428028
\(204\) −28.9859 −2.02942
\(205\) 0 0
\(206\) −5.87838 −0.409566
\(207\) −69.8092 −4.85207
\(208\) −12.7586 −0.884649
\(209\) −4.33832 −0.300088
\(210\) 0 0
\(211\) 10.6358 0.732195 0.366098 0.930576i \(-0.380694\pi\)
0.366098 + 0.930576i \(0.380694\pi\)
\(212\) −5.78801 −0.397522
\(213\) 20.9260 1.43383
\(214\) −3.55691 −0.243146
\(215\) 0 0
\(216\) 30.6936 2.08843
\(217\) 0.687095 0.0466430
\(218\) 5.19283 0.351703
\(219\) 8.80139 0.594743
\(220\) 0 0
\(221\) −35.0746 −2.35937
\(222\) 11.4813 0.770574
\(223\) −11.7045 −0.783791 −0.391896 0.920010i \(-0.628181\pi\)
−0.391896 + 0.920010i \(0.628181\pi\)
\(224\) 0.506223 0.0338234
\(225\) 0 0
\(226\) 7.39831 0.492128
\(227\) 4.74976 0.315253 0.157626 0.987499i \(-0.449616\pi\)
0.157626 + 0.987499i \(0.449616\pi\)
\(228\) 24.4937 1.62213
\(229\) 3.91733 0.258864 0.129432 0.991588i \(-0.458685\pi\)
0.129432 + 0.991588i \(0.458685\pi\)
\(230\) 0 0
\(231\) −0.276397 −0.0181856
\(232\) −1.45017 −0.0952084
\(233\) −2.05639 −0.134719 −0.0673593 0.997729i \(-0.521457\pi\)
−0.0673593 + 0.997729i \(0.521457\pi\)
\(234\) 28.2294 1.84542
\(235\) 0 0
\(236\) 23.6395 1.53880
\(237\) −28.3567 −1.84196
\(238\) 0.298560 0.0193527
\(239\) −4.37294 −0.282862 −0.141431 0.989948i \(-0.545170\pi\)
−0.141431 + 0.989948i \(0.545170\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) 6.03832 0.388158
\(243\) 32.8509 2.10739
\(244\) 10.7221 0.686410
\(245\) 0 0
\(246\) 3.50543 0.223498
\(247\) 29.6387 1.88587
\(248\) −16.3386 −1.03750
\(249\) 1.29752 0.0822271
\(250\) 0 0
\(251\) −10.1344 −0.639677 −0.319839 0.947472i \(-0.603629\pi\)
−0.319839 + 0.947472i \(0.603629\pi\)
\(252\) 1.10955 0.0698949
\(253\) −8.87294 −0.557837
\(254\) 7.55367 0.473959
\(255\) 0 0
\(256\) −5.49275 −0.343297
\(257\) 7.65793 0.477689 0.238844 0.971058i \(-0.423231\pi\)
0.238844 + 0.971058i \(0.423231\pi\)
\(258\) 4.64032 0.288894
\(259\) 0.546060 0.0339305
\(260\) 0 0
\(261\) −4.92304 −0.304729
\(262\) −4.65090 −0.287334
\(263\) 7.22289 0.445382 0.222691 0.974889i \(-0.428516\pi\)
0.222691 + 0.974889i \(0.428516\pi\)
\(264\) 6.57253 0.404511
\(265\) 0 0
\(266\) −0.252289 −0.0154688
\(267\) 57.8576 3.54083
\(268\) −25.2668 −1.54341
\(269\) −3.86388 −0.235585 −0.117793 0.993038i \(-0.537582\pi\)
−0.117793 + 0.993038i \(0.537582\pi\)
\(270\) 0 0
\(271\) −30.9680 −1.88117 −0.940587 0.339554i \(-0.889724\pi\)
−0.940587 + 0.339554i \(0.889724\pi\)
\(272\) 10.8929 0.660482
\(273\) 1.88830 0.114285
\(274\) −6.67634 −0.403333
\(275\) 0 0
\(276\) 50.0956 3.01540
\(277\) 3.23714 0.194501 0.0972503 0.995260i \(-0.468995\pi\)
0.0972503 + 0.995260i \(0.468995\pi\)
\(278\) 7.92272 0.475173
\(279\) −55.4664 −3.32069
\(280\) 0 0
\(281\) 15.7837 0.941577 0.470788 0.882246i \(-0.343970\pi\)
0.470788 + 0.882246i \(0.343970\pi\)
\(282\) 2.90161 0.172788
\(283\) −17.7210 −1.05340 −0.526702 0.850050i \(-0.676571\pi\)
−0.526702 + 0.850050i \(0.676571\pi\)
\(284\) −10.6771 −0.633571
\(285\) 0 0
\(286\) 3.58804 0.212165
\(287\) 0.166721 0.00984125
\(288\) −40.8653 −2.40801
\(289\) 12.9457 0.761514
\(290\) 0 0
\(291\) −56.3834 −3.30525
\(292\) −4.49075 −0.262801
\(293\) −17.6430 −1.03072 −0.515358 0.856975i \(-0.672341\pi\)
−0.515358 + 0.856975i \(0.672341\pi\)
\(294\) 13.4415 0.783926
\(295\) 0 0
\(296\) −12.9849 −0.754734
\(297\) 13.2439 0.768491
\(298\) 8.01302 0.464182
\(299\) 60.6185 3.50566
\(300\) 0 0
\(301\) 0.220697 0.0127208
\(302\) 7.90330 0.454784
\(303\) 51.7304 2.97183
\(304\) −9.20474 −0.527928
\(305\) 0 0
\(306\) −24.1015 −1.37779
\(307\) −10.5635 −0.602891 −0.301445 0.953483i \(-0.597469\pi\)
−0.301445 + 0.953483i \(0.597469\pi\)
\(308\) 0.141027 0.00803574
\(309\) 31.7424 1.80576
\(310\) 0 0
\(311\) 15.5162 0.879843 0.439922 0.898036i \(-0.355006\pi\)
0.439922 + 0.898036i \(0.355006\pi\)
\(312\) −44.9024 −2.54210
\(313\) 16.0089 0.904874 0.452437 0.891796i \(-0.350555\pi\)
0.452437 + 0.891796i \(0.350555\pi\)
\(314\) −6.81576 −0.384636
\(315\) 0 0
\(316\) 14.4685 0.813915
\(317\) 5.93621 0.333411 0.166705 0.986007i \(-0.446687\pi\)
0.166705 + 0.986007i \(0.446687\pi\)
\(318\) −6.76870 −0.379570
\(319\) −0.625732 −0.0350343
\(320\) 0 0
\(321\) 19.2068 1.07202
\(322\) −0.515992 −0.0287551
\(323\) −25.3047 −1.40799
\(324\) −38.3697 −2.13165
\(325\) 0 0
\(326\) 2.49068 0.137946
\(327\) −28.0405 −1.55064
\(328\) −3.96452 −0.218904
\(329\) 0.138003 0.00760835
\(330\) 0 0
\(331\) −24.4916 −1.34618 −0.673091 0.739560i \(-0.735034\pi\)
−0.673091 + 0.739560i \(0.735034\pi\)
\(332\) −0.662037 −0.0363340
\(333\) −44.0812 −2.41564
\(334\) −13.3913 −0.732738
\(335\) 0 0
\(336\) −0.586439 −0.0319929
\(337\) −4.60431 −0.250813 −0.125406 0.992105i \(-0.540023\pi\)
−0.125406 + 0.992105i \(0.540023\pi\)
\(338\) −16.7560 −0.911406
\(339\) −39.9498 −2.16977
\(340\) 0 0
\(341\) −7.04993 −0.381775
\(342\) 20.3662 1.10128
\(343\) 1.27935 0.0690782
\(344\) −5.24803 −0.282955
\(345\) 0 0
\(346\) −11.3740 −0.611472
\(347\) −6.59915 −0.354261 −0.177131 0.984187i \(-0.556681\pi\)
−0.177131 + 0.984187i \(0.556681\pi\)
\(348\) 3.53281 0.189378
\(349\) −9.00022 −0.481770 −0.240885 0.970554i \(-0.577438\pi\)
−0.240885 + 0.970554i \(0.577438\pi\)
\(350\) 0 0
\(351\) −90.4803 −4.82948
\(352\) −5.19410 −0.276846
\(353\) −19.2510 −1.02463 −0.512313 0.858799i \(-0.671211\pi\)
−0.512313 + 0.858799i \(0.671211\pi\)
\(354\) 27.6449 1.46931
\(355\) 0 0
\(356\) −29.5208 −1.56460
\(357\) −1.61218 −0.0853255
\(358\) −4.05091 −0.214097
\(359\) −6.46996 −0.341472 −0.170736 0.985317i \(-0.554614\pi\)
−0.170736 + 0.985317i \(0.554614\pi\)
\(360\) 0 0
\(361\) 2.38297 0.125420
\(362\) 0.388057 0.0203958
\(363\) −32.6061 −1.71137
\(364\) −0.963470 −0.0504996
\(365\) 0 0
\(366\) 12.5388 0.655412
\(367\) −7.33529 −0.382899 −0.191450 0.981502i \(-0.561319\pi\)
−0.191450 + 0.981502i \(0.561319\pi\)
\(368\) −18.8260 −0.981372
\(369\) −13.4587 −0.700634
\(370\) 0 0
\(371\) −0.321925 −0.0167135
\(372\) 39.8031 2.06369
\(373\) 19.9506 1.03300 0.516500 0.856287i \(-0.327234\pi\)
0.516500 + 0.856287i \(0.327234\pi\)
\(374\) −3.06337 −0.158403
\(375\) 0 0
\(376\) −3.28161 −0.169236
\(377\) 4.27490 0.220169
\(378\) 0.770181 0.0396138
\(379\) −23.4451 −1.20430 −0.602148 0.798384i \(-0.705688\pi\)
−0.602148 + 0.798384i \(0.705688\pi\)
\(380\) 0 0
\(381\) −40.7887 −2.08967
\(382\) 8.04150 0.411439
\(383\) −15.0980 −0.771472 −0.385736 0.922609i \(-0.626052\pi\)
−0.385736 + 0.922609i \(0.626052\pi\)
\(384\) 36.9791 1.88708
\(385\) 0 0
\(386\) 3.26063 0.165962
\(387\) −17.8160 −0.905639
\(388\) 28.7686 1.46050
\(389\) −30.5029 −1.54656 −0.773279 0.634066i \(-0.781385\pi\)
−0.773279 + 0.634066i \(0.781385\pi\)
\(390\) 0 0
\(391\) −51.7544 −2.61733
\(392\) −15.2019 −0.767812
\(393\) 25.1142 1.26684
\(394\) −12.3610 −0.622736
\(395\) 0 0
\(396\) −11.3845 −0.572093
\(397\) 13.3211 0.668569 0.334284 0.942472i \(-0.391505\pi\)
0.334284 + 0.942472i \(0.391505\pi\)
\(398\) 15.3390 0.768876
\(399\) 1.36232 0.0682014
\(400\) 0 0
\(401\) −2.04724 −0.102234 −0.0511171 0.998693i \(-0.516278\pi\)
−0.0511171 + 0.998693i \(0.516278\pi\)
\(402\) −29.5479 −1.47371
\(403\) 48.1640 2.39922
\(404\) −26.3945 −1.31317
\(405\) 0 0
\(406\) −0.0363885 −0.00180593
\(407\) −5.60285 −0.277723
\(408\) 38.3365 1.89794
\(409\) −13.4604 −0.665575 −0.332787 0.943002i \(-0.607989\pi\)
−0.332787 + 0.943002i \(0.607989\pi\)
\(410\) 0 0
\(411\) 36.0513 1.77828
\(412\) −16.1960 −0.797919
\(413\) 1.31481 0.0646978
\(414\) 41.6540 2.04718
\(415\) 0 0
\(416\) 35.4852 1.73981
\(417\) −42.7815 −2.09502
\(418\) 2.58861 0.126613
\(419\) −11.6546 −0.569366 −0.284683 0.958622i \(-0.591888\pi\)
−0.284683 + 0.958622i \(0.591888\pi\)
\(420\) 0 0
\(421\) −6.83090 −0.332918 −0.166459 0.986048i \(-0.553233\pi\)
−0.166459 + 0.986048i \(0.553233\pi\)
\(422\) −6.34618 −0.308927
\(423\) −11.1404 −0.541666
\(424\) 7.65516 0.371767
\(425\) 0 0
\(426\) −12.4862 −0.604959
\(427\) 0.596355 0.0288596
\(428\) −9.79993 −0.473697
\(429\) −19.3749 −0.935428
\(430\) 0 0
\(431\) 19.6002 0.944109 0.472054 0.881569i \(-0.343513\pi\)
0.472054 + 0.881569i \(0.343513\pi\)
\(432\) 28.1000 1.35196
\(433\) 8.10862 0.389676 0.194838 0.980835i \(-0.437582\pi\)
0.194838 + 0.980835i \(0.437582\pi\)
\(434\) −0.409978 −0.0196796
\(435\) 0 0
\(436\) 14.3072 0.685189
\(437\) 43.7335 2.09205
\(438\) −5.25164 −0.250933
\(439\) 34.0684 1.62600 0.812998 0.582267i \(-0.197834\pi\)
0.812998 + 0.582267i \(0.197834\pi\)
\(440\) 0 0
\(441\) −51.6074 −2.45750
\(442\) 20.9284 0.995464
\(443\) −12.5494 −0.596240 −0.298120 0.954528i \(-0.596360\pi\)
−0.298120 + 0.954528i \(0.596360\pi\)
\(444\) 31.6330 1.50124
\(445\) 0 0
\(446\) 6.98388 0.330696
\(447\) −43.2691 −2.04656
\(448\) 0.0619669 0.00292766
\(449\) 23.2022 1.09498 0.547489 0.836813i \(-0.315584\pi\)
0.547489 + 0.836813i \(0.315584\pi\)
\(450\) 0 0
\(451\) −1.71064 −0.0805511
\(452\) 20.3837 0.958766
\(453\) −42.6766 −2.00512
\(454\) −2.83410 −0.133011
\(455\) 0 0
\(456\) −32.3950 −1.51704
\(457\) 12.7868 0.598140 0.299070 0.954231i \(-0.403324\pi\)
0.299070 + 0.954231i \(0.403324\pi\)
\(458\) −2.33740 −0.109220
\(459\) 77.2496 3.60570
\(460\) 0 0
\(461\) −2.71560 −0.126478 −0.0632389 0.997998i \(-0.520143\pi\)
−0.0632389 + 0.997998i \(0.520143\pi\)
\(462\) 0.164922 0.00767284
\(463\) 29.7362 1.38196 0.690979 0.722875i \(-0.257180\pi\)
0.690979 + 0.722875i \(0.257180\pi\)
\(464\) −1.32763 −0.0616339
\(465\) 0 0
\(466\) 1.22701 0.0568403
\(467\) 6.90067 0.319325 0.159662 0.987172i \(-0.448959\pi\)
0.159662 + 0.987172i \(0.448959\pi\)
\(468\) 77.7771 3.59525
\(469\) −1.40532 −0.0648918
\(470\) 0 0
\(471\) 36.8041 1.69584
\(472\) −31.2654 −1.43911
\(473\) −2.26447 −0.104120
\(474\) 16.9200 0.777159
\(475\) 0 0
\(476\) 0.822585 0.0377031
\(477\) 25.9877 1.18990
\(478\) 2.60926 0.119345
\(479\) 33.1760 1.51585 0.757924 0.652342i \(-0.226214\pi\)
0.757924 + 0.652342i \(0.226214\pi\)
\(480\) 0 0
\(481\) 38.2777 1.74531
\(482\) 0.596683 0.0271782
\(483\) 2.78628 0.126780
\(484\) 16.6367 0.756212
\(485\) 0 0
\(486\) −19.6016 −0.889146
\(487\) 3.24933 0.147241 0.0736207 0.997286i \(-0.476545\pi\)
0.0736207 + 0.997286i \(0.476545\pi\)
\(488\) −14.1809 −0.641939
\(489\) −13.4493 −0.608198
\(490\) 0 0
\(491\) −1.81775 −0.0820340 −0.0410170 0.999158i \(-0.513060\pi\)
−0.0410170 + 0.999158i \(0.513060\pi\)
\(492\) 9.65809 0.435420
\(493\) −3.64979 −0.164378
\(494\) −17.6849 −0.795682
\(495\) 0 0
\(496\) −14.9580 −0.671636
\(497\) −0.593855 −0.0266380
\(498\) −0.774209 −0.0346932
\(499\) −12.2563 −0.548667 −0.274333 0.961635i \(-0.588457\pi\)
−0.274333 + 0.961635i \(0.588457\pi\)
\(500\) 0 0
\(501\) 72.3109 3.23061
\(502\) 6.04702 0.269892
\(503\) 5.24664 0.233936 0.116968 0.993136i \(-0.462682\pi\)
0.116968 + 0.993136i \(0.462682\pi\)
\(504\) −1.46748 −0.0653666
\(505\) 0 0
\(506\) 5.29434 0.235362
\(507\) 90.4799 4.01835
\(508\) 20.8117 0.923370
\(509\) −38.3672 −1.70060 −0.850298 0.526301i \(-0.823579\pi\)
−0.850298 + 0.526301i \(0.823579\pi\)
\(510\) 0 0
\(511\) −0.249773 −0.0110493
\(512\) −19.6766 −0.869593
\(513\) −65.2774 −2.88207
\(514\) −4.56936 −0.201546
\(515\) 0 0
\(516\) 12.7849 0.562824
\(517\) −1.41598 −0.0622746
\(518\) −0.325825 −0.0143159
\(519\) 61.4181 2.69596
\(520\) 0 0
\(521\) 18.6227 0.815876 0.407938 0.913010i \(-0.366248\pi\)
0.407938 + 0.913010i \(0.366248\pi\)
\(522\) 2.93750 0.128571
\(523\) 26.1292 1.14255 0.571274 0.820759i \(-0.306449\pi\)
0.571274 + 0.820759i \(0.306449\pi\)
\(524\) −12.8141 −0.559785
\(525\) 0 0
\(526\) −4.30978 −0.187915
\(527\) −41.1211 −1.79126
\(528\) 6.01716 0.261863
\(529\) 66.4457 2.88894
\(530\) 0 0
\(531\) −106.140 −4.60607
\(532\) −0.695100 −0.0301364
\(533\) 11.6868 0.506213
\(534\) −34.5227 −1.49394
\(535\) 0 0
\(536\) 33.4176 1.44342
\(537\) 21.8743 0.943945
\(538\) 2.30552 0.0993978
\(539\) −6.55944 −0.282535
\(540\) 0 0
\(541\) 27.4175 1.17877 0.589386 0.807852i \(-0.299370\pi\)
0.589386 + 0.807852i \(0.299370\pi\)
\(542\) 18.4781 0.793703
\(543\) −2.09545 −0.0899244
\(544\) −30.2963 −1.29894
\(545\) 0 0
\(546\) −1.12672 −0.0482190
\(547\) −7.78442 −0.332838 −0.166419 0.986055i \(-0.553220\pi\)
−0.166419 + 0.986055i \(0.553220\pi\)
\(548\) −18.3945 −0.785775
\(549\) −48.1413 −2.05462
\(550\) 0 0
\(551\) 3.08414 0.131389
\(552\) −66.2559 −2.82004
\(553\) 0.804727 0.0342205
\(554\) −1.93155 −0.0820635
\(555\) 0 0
\(556\) 21.8285 0.925735
\(557\) −31.6184 −1.33971 −0.669857 0.742490i \(-0.733645\pi\)
−0.669857 + 0.742490i \(0.733645\pi\)
\(558\) 33.0959 1.40106
\(559\) 15.4705 0.654330
\(560\) 0 0
\(561\) 16.5417 0.698393
\(562\) −9.41788 −0.397269
\(563\) 13.8213 0.582498 0.291249 0.956647i \(-0.405929\pi\)
0.291249 + 0.956647i \(0.405929\pi\)
\(564\) 7.99444 0.336627
\(565\) 0 0
\(566\) 10.5738 0.444451
\(567\) −2.13410 −0.0896238
\(568\) 14.1215 0.592523
\(569\) 8.73989 0.366395 0.183198 0.983076i \(-0.441355\pi\)
0.183198 + 0.983076i \(0.441355\pi\)
\(570\) 0 0
\(571\) −11.5163 −0.481944 −0.240972 0.970532i \(-0.577466\pi\)
−0.240972 + 0.970532i \(0.577466\pi\)
\(572\) 9.88568 0.413341
\(573\) −43.4229 −1.81402
\(574\) −0.0994799 −0.00415221
\(575\) 0 0
\(576\) −5.00234 −0.208431
\(577\) 6.75615 0.281262 0.140631 0.990062i \(-0.455087\pi\)
0.140631 + 0.990062i \(0.455087\pi\)
\(578\) −7.72451 −0.321297
\(579\) −17.6069 −0.731718
\(580\) 0 0
\(581\) −0.0368221 −0.00152764
\(582\) 33.6430 1.39455
\(583\) 3.30311 0.136801
\(584\) 5.93942 0.245775
\(585\) 0 0
\(586\) 10.5273 0.434879
\(587\) 1.71413 0.0707498 0.0353749 0.999374i \(-0.488737\pi\)
0.0353749 + 0.999374i \(0.488737\pi\)
\(588\) 37.0338 1.52725
\(589\) 34.7481 1.43177
\(590\) 0 0
\(591\) 66.7473 2.74562
\(592\) −11.8877 −0.488582
\(593\) −27.1227 −1.11380 −0.556898 0.830581i \(-0.688008\pi\)
−0.556898 + 0.830581i \(0.688008\pi\)
\(594\) −7.90243 −0.324241
\(595\) 0 0
\(596\) 22.0773 0.904321
\(597\) −82.8285 −3.38994
\(598\) −36.1700 −1.47910
\(599\) 29.0181 1.18565 0.592824 0.805332i \(-0.298013\pi\)
0.592824 + 0.805332i \(0.298013\pi\)
\(600\) 0 0
\(601\) −6.46669 −0.263782 −0.131891 0.991264i \(-0.542105\pi\)
−0.131891 + 0.991264i \(0.542105\pi\)
\(602\) −0.131687 −0.00536714
\(603\) 113.446 4.61988
\(604\) 21.7750 0.886012
\(605\) 0 0
\(606\) −30.8666 −1.25387
\(607\) −16.5728 −0.672669 −0.336335 0.941743i \(-0.609187\pi\)
−0.336335 + 0.941743i \(0.609187\pi\)
\(608\) 25.6010 1.03826
\(609\) 0.196493 0.00796228
\(610\) 0 0
\(611\) 9.67373 0.391357
\(612\) −66.4040 −2.68422
\(613\) −21.8721 −0.883407 −0.441704 0.897161i \(-0.645626\pi\)
−0.441704 + 0.897161i \(0.645626\pi\)
\(614\) 6.30306 0.254371
\(615\) 0 0
\(616\) −0.186520 −0.00751512
\(617\) −10.5044 −0.422891 −0.211446 0.977390i \(-0.567817\pi\)
−0.211446 + 0.977390i \(0.567817\pi\)
\(618\) −18.9402 −0.761885
\(619\) 23.9195 0.961406 0.480703 0.876884i \(-0.340382\pi\)
0.480703 + 0.876884i \(0.340382\pi\)
\(620\) 0 0
\(621\) −133.508 −5.35751
\(622\) −9.25826 −0.371222
\(623\) −1.64193 −0.0657825
\(624\) −41.1082 −1.64565
\(625\) 0 0
\(626\) −9.55222 −0.381783
\(627\) −13.9781 −0.558231
\(628\) −18.7786 −0.749349
\(629\) −32.6805 −1.30306
\(630\) 0 0
\(631\) −14.4550 −0.575444 −0.287722 0.957714i \(-0.592898\pi\)
−0.287722 + 0.957714i \(0.592898\pi\)
\(632\) −19.1359 −0.761184
\(633\) 34.2684 1.36205
\(634\) −3.54204 −0.140672
\(635\) 0 0
\(636\) −18.6490 −0.739480
\(637\) 44.8130 1.77556
\(638\) 0.373364 0.0147816
\(639\) 47.9395 1.89646
\(640\) 0 0
\(641\) 10.0263 0.396017 0.198008 0.980200i \(-0.436553\pi\)
0.198008 + 0.980200i \(0.436553\pi\)
\(642\) −11.4604 −0.452305
\(643\) 22.8415 0.900781 0.450391 0.892832i \(-0.351285\pi\)
0.450391 + 0.892832i \(0.351285\pi\)
\(644\) −1.42165 −0.0560209
\(645\) 0 0
\(646\) 15.0989 0.594059
\(647\) −5.91891 −0.232697 −0.116348 0.993208i \(-0.537119\pi\)
−0.116348 + 0.993208i \(0.537119\pi\)
\(648\) 50.7474 1.99355
\(649\) −13.4906 −0.529554
\(650\) 0 0
\(651\) 2.21382 0.0867665
\(652\) 6.86226 0.268747
\(653\) 7.83832 0.306737 0.153369 0.988169i \(-0.450988\pi\)
0.153369 + 0.988169i \(0.450988\pi\)
\(654\) 16.7313 0.654246
\(655\) 0 0
\(656\) −3.62952 −0.141709
\(657\) 20.1631 0.786639
\(658\) −0.0823441 −0.00321011
\(659\) 8.38247 0.326535 0.163267 0.986582i \(-0.447797\pi\)
0.163267 + 0.986582i \(0.447797\pi\)
\(660\) 0 0
\(661\) 4.45841 0.173412 0.0867060 0.996234i \(-0.472366\pi\)
0.0867060 + 0.996234i \(0.472366\pi\)
\(662\) 14.6138 0.567980
\(663\) −113.010 −4.38896
\(664\) 0.875603 0.0339800
\(665\) 0 0
\(666\) 26.3026 1.01920
\(667\) 6.30784 0.244240
\(668\) −36.8954 −1.42752
\(669\) −37.7119 −1.45803
\(670\) 0 0
\(671\) −6.11890 −0.236217
\(672\) 1.63105 0.0629192
\(673\) 31.5701 1.21694 0.608470 0.793577i \(-0.291784\pi\)
0.608470 + 0.793577i \(0.291784\pi\)
\(674\) 2.74732 0.105823
\(675\) 0 0
\(676\) −46.1657 −1.77561
\(677\) 15.6023 0.599645 0.299823 0.953995i \(-0.403072\pi\)
0.299823 + 0.953995i \(0.403072\pi\)
\(678\) 23.8374 0.915469
\(679\) 1.60009 0.0614058
\(680\) 0 0
\(681\) 15.3037 0.586441
\(682\) 4.20658 0.161078
\(683\) 24.0372 0.919756 0.459878 0.887982i \(-0.347893\pi\)
0.459878 + 0.887982i \(0.347893\pi\)
\(684\) 56.1126 2.14552
\(685\) 0 0
\(686\) −0.763365 −0.0291454
\(687\) 12.6216 0.481546
\(688\) −4.80458 −0.183173
\(689\) −22.5663 −0.859708
\(690\) 0 0
\(691\) −21.8219 −0.830143 −0.415072 0.909789i \(-0.636243\pi\)
−0.415072 + 0.909789i \(0.636243\pi\)
\(692\) −31.3375 −1.19127
\(693\) −0.633199 −0.0240532
\(694\) 3.93761 0.149469
\(695\) 0 0
\(696\) −4.67246 −0.177109
\(697\) −9.97790 −0.377940
\(698\) 5.37028 0.203268
\(699\) −6.62569 −0.250607
\(700\) 0 0
\(701\) −36.9054 −1.39390 −0.696949 0.717120i \(-0.745460\pi\)
−0.696949 + 0.717120i \(0.745460\pi\)
\(702\) 53.9881 2.03765
\(703\) 27.6156 1.04154
\(704\) −0.635811 −0.0239630
\(705\) 0 0
\(706\) 11.4867 0.432309
\(707\) −1.46804 −0.0552115
\(708\) 76.1666 2.86251
\(709\) 18.5895 0.698145 0.349072 0.937096i \(-0.386497\pi\)
0.349072 + 0.937096i \(0.386497\pi\)
\(710\) 0 0
\(711\) −64.9624 −2.43628
\(712\) 39.0439 1.46323
\(713\) 71.0685 2.66154
\(714\) 0.961960 0.0360004
\(715\) 0 0
\(716\) −11.1610 −0.417105
\(717\) −14.0896 −0.526187
\(718\) 3.86052 0.144073
\(719\) 21.3723 0.797052 0.398526 0.917157i \(-0.369522\pi\)
0.398526 + 0.917157i \(0.369522\pi\)
\(720\) 0 0
\(721\) −0.900810 −0.0335479
\(722\) −1.42188 −0.0529169
\(723\) −3.22200 −0.119828
\(724\) 1.06917 0.0397353
\(725\) 0 0
\(726\) 19.4555 0.722061
\(727\) −4.55494 −0.168933 −0.0844667 0.996426i \(-0.526919\pi\)
−0.0844667 + 0.996426i \(0.526919\pi\)
\(728\) 1.27428 0.0472278
\(729\) 35.8266 1.32691
\(730\) 0 0
\(731\) −13.2083 −0.488525
\(732\) 34.5466 1.27688
\(733\) 6.73245 0.248669 0.124334 0.992240i \(-0.460320\pi\)
0.124334 + 0.992240i \(0.460320\pi\)
\(734\) 4.37685 0.161552
\(735\) 0 0
\(736\) 52.3603 1.93003
\(737\) 14.4193 0.531142
\(738\) 8.03061 0.295611
\(739\) −7.18344 −0.264247 −0.132124 0.991233i \(-0.542180\pi\)
−0.132124 + 0.991233i \(0.542180\pi\)
\(740\) 0 0
\(741\) 95.4960 3.50813
\(742\) 0.192087 0.00705175
\(743\) −30.4874 −1.11847 −0.559237 0.829008i \(-0.688906\pi\)
−0.559237 + 0.829008i \(0.688906\pi\)
\(744\) −52.6431 −1.92999
\(745\) 0 0
\(746\) −11.9042 −0.435843
\(747\) 2.97250 0.108758
\(748\) −8.44013 −0.308602
\(749\) −0.545066 −0.0199163
\(750\) 0 0
\(751\) 29.4839 1.07588 0.537942 0.842982i \(-0.319202\pi\)
0.537942 + 0.842982i \(0.319202\pi\)
\(752\) −3.00432 −0.109556
\(753\) −32.6530 −1.18994
\(754\) −2.55076 −0.0928933
\(755\) 0 0
\(756\) 2.12198 0.0771758
\(757\) 7.20199 0.261761 0.130880 0.991398i \(-0.458220\pi\)
0.130880 + 0.991398i \(0.458220\pi\)
\(758\) 13.9893 0.508115
\(759\) −28.5886 −1.03770
\(760\) 0 0
\(761\) −3.55723 −0.128950 −0.0644748 0.997919i \(-0.520537\pi\)
−0.0644748 + 0.997919i \(0.520537\pi\)
\(762\) 24.3379 0.881671
\(763\) 0.795756 0.0288083
\(764\) 22.1558 0.801567
\(765\) 0 0
\(766\) 9.00873 0.325499
\(767\) 92.1659 3.32792
\(768\) −17.6977 −0.638609
\(769\) −9.11046 −0.328532 −0.164266 0.986416i \(-0.552525\pi\)
−0.164266 + 0.986416i \(0.552525\pi\)
\(770\) 0 0
\(771\) 24.6739 0.888608
\(772\) 8.98361 0.323327
\(773\) −14.7015 −0.528777 −0.264388 0.964416i \(-0.585170\pi\)
−0.264388 + 0.964416i \(0.585170\pi\)
\(774\) 10.6305 0.382106
\(775\) 0 0
\(776\) −38.0490 −1.36588
\(777\) 1.75941 0.0631184
\(778\) 18.2006 0.652522
\(779\) 8.43152 0.302090
\(780\) 0 0
\(781\) 6.09324 0.218033
\(782\) 30.8810 1.10430
\(783\) −9.41520 −0.336472
\(784\) −13.9174 −0.497048
\(785\) 0 0
\(786\) −14.9852 −0.534505
\(787\) −41.7194 −1.48713 −0.743567 0.668661i \(-0.766868\pi\)
−0.743567 + 0.668661i \(0.766868\pi\)
\(788\) −34.0566 −1.21322
\(789\) 23.2722 0.828511
\(790\) 0 0
\(791\) 1.13373 0.0403106
\(792\) 15.0570 0.535028
\(793\) 41.8033 1.48448
\(794\) −7.94850 −0.282082
\(795\) 0 0
\(796\) 42.2617 1.49793
\(797\) −39.9649 −1.41563 −0.707815 0.706398i \(-0.750319\pi\)
−0.707815 + 0.706398i \(0.750319\pi\)
\(798\) −0.812874 −0.0287754
\(799\) −8.25917 −0.292188
\(800\) 0 0
\(801\) 132.546 4.68329
\(802\) 1.22155 0.0431346
\(803\) 2.56279 0.0904389
\(804\) −81.4097 −2.87110
\(805\) 0 0
\(806\) −28.7387 −1.01228
\(807\) −12.4494 −0.438241
\(808\) 34.9091 1.22810
\(809\) 48.1327 1.69226 0.846128 0.532980i \(-0.178928\pi\)
0.846128 + 0.532980i \(0.178928\pi\)
\(810\) 0 0
\(811\) −38.1641 −1.34012 −0.670061 0.742306i \(-0.733732\pi\)
−0.670061 + 0.742306i \(0.733732\pi\)
\(812\) −0.100257 −0.00351832
\(813\) −99.7790 −3.49940
\(814\) 3.34313 0.117177
\(815\) 0 0
\(816\) 35.0971 1.22864
\(817\) 11.1612 0.390482
\(818\) 8.03161 0.280819
\(819\) 4.32591 0.151160
\(820\) 0 0
\(821\) 25.8745 0.903025 0.451512 0.892265i \(-0.350885\pi\)
0.451512 + 0.892265i \(0.350885\pi\)
\(822\) −21.5112 −0.750289
\(823\) 0.237610 0.00828258 0.00414129 0.999991i \(-0.498682\pi\)
0.00414129 + 0.999991i \(0.498682\pi\)
\(824\) 21.4206 0.746223
\(825\) 0 0
\(826\) −0.784528 −0.0272972
\(827\) 22.1323 0.769615 0.384807 0.922997i \(-0.374268\pi\)
0.384807 + 0.922997i \(0.374268\pi\)
\(828\) 114.764 3.98833
\(829\) −17.4722 −0.606834 −0.303417 0.952858i \(-0.598128\pi\)
−0.303417 + 0.952858i \(0.598128\pi\)
\(830\) 0 0
\(831\) 10.4301 0.361815
\(832\) 4.34375 0.150593
\(833\) −38.2601 −1.32564
\(834\) 25.5270 0.883929
\(835\) 0 0
\(836\) 7.13207 0.246668
\(837\) −106.078 −3.66660
\(838\) 6.95412 0.240226
\(839\) 2.59302 0.0895208 0.0447604 0.998998i \(-0.485748\pi\)
0.0447604 + 0.998998i \(0.485748\pi\)
\(840\) 0 0
\(841\) −28.5552 −0.984661
\(842\) 4.07589 0.140464
\(843\) 50.8551 1.75154
\(844\) −17.4848 −0.601853
\(845\) 0 0
\(846\) 6.64731 0.228539
\(847\) 0.925320 0.0317944
\(848\) 7.00831 0.240666
\(849\) −57.0971 −1.95957
\(850\) 0 0
\(851\) 56.4808 1.93614
\(852\) −34.4017 −1.17858
\(853\) 14.2813 0.488984 0.244492 0.969651i \(-0.421379\pi\)
0.244492 + 0.969651i \(0.421379\pi\)
\(854\) −0.355835 −0.0121764
\(855\) 0 0
\(856\) 12.9613 0.443008
\(857\) −5.29985 −0.181039 −0.0905196 0.995895i \(-0.528853\pi\)
−0.0905196 + 0.995895i \(0.528853\pi\)
\(858\) 11.5607 0.394675
\(859\) −46.6430 −1.59144 −0.795719 0.605666i \(-0.792907\pi\)
−0.795719 + 0.605666i \(0.792907\pi\)
\(860\) 0 0
\(861\) 0.537177 0.0183069
\(862\) −11.6951 −0.398337
\(863\) −7.04585 −0.239843 −0.119922 0.992783i \(-0.538264\pi\)
−0.119922 + 0.992783i \(0.538264\pi\)
\(864\) −78.1540 −2.65885
\(865\) 0 0
\(866\) −4.83828 −0.164411
\(867\) 41.7112 1.41659
\(868\) −1.12956 −0.0383399
\(869\) −8.25690 −0.280096
\(870\) 0 0
\(871\) −98.5103 −3.33789
\(872\) −18.9225 −0.640797
\(873\) −129.169 −4.37171
\(874\) −26.0950 −0.882678
\(875\) 0 0
\(876\) −14.4692 −0.488869
\(877\) 9.94520 0.335825 0.167913 0.985802i \(-0.446297\pi\)
0.167913 + 0.985802i \(0.446297\pi\)
\(878\) −20.3280 −0.686038
\(879\) −56.8459 −1.91736
\(880\) 0 0
\(881\) 2.95289 0.0994854 0.0497427 0.998762i \(-0.484160\pi\)
0.0497427 + 0.998762i \(0.484160\pi\)
\(882\) 30.7933 1.03686
\(883\) −47.0985 −1.58499 −0.792495 0.609878i \(-0.791219\pi\)
−0.792495 + 0.609878i \(0.791219\pi\)
\(884\) 57.6615 1.93937
\(885\) 0 0
\(886\) 7.48803 0.251565
\(887\) −30.3790 −1.02003 −0.510013 0.860167i \(-0.670360\pi\)
−0.510013 + 0.860167i \(0.670360\pi\)
\(888\) −41.8375 −1.40397
\(889\) 1.15753 0.0388224
\(890\) 0 0
\(891\) 21.8969 0.733575
\(892\) 19.2418 0.644264
\(893\) 6.97915 0.233548
\(894\) 25.8180 0.863482
\(895\) 0 0
\(896\) −1.04942 −0.0350587
\(897\) 195.313 6.52131
\(898\) −13.8444 −0.461992
\(899\) 5.01185 0.167154
\(900\) 0 0
\(901\) 19.2665 0.641860
\(902\) 1.02071 0.0339860
\(903\) 0.711088 0.0236635
\(904\) −26.9592 −0.896650
\(905\) 0 0
\(906\) 25.4644 0.845999
\(907\) −3.94698 −0.131057 −0.0655287 0.997851i \(-0.520873\pi\)
−0.0655287 + 0.997851i \(0.520873\pi\)
\(908\) −7.80846 −0.259133
\(909\) 118.509 3.93071
\(910\) 0 0
\(911\) −32.1864 −1.06638 −0.533192 0.845994i \(-0.679008\pi\)
−0.533192 + 0.845994i \(0.679008\pi\)
\(912\) −29.6577 −0.982065
\(913\) 0.377813 0.0125038
\(914\) −7.62965 −0.252366
\(915\) 0 0
\(916\) −6.43996 −0.212782
\(917\) −0.712710 −0.0235358
\(918\) −46.0936 −1.52132
\(919\) −22.6485 −0.747106 −0.373553 0.927609i \(-0.621861\pi\)
−0.373553 + 0.927609i \(0.621861\pi\)
\(920\) 0 0
\(921\) −34.0356 −1.12151
\(922\) 1.62035 0.0533634
\(923\) −41.6280 −1.37020
\(924\) 0.454388 0.0149483
\(925\) 0 0
\(926\) −17.7431 −0.583074
\(927\) 72.7188 2.38840
\(928\) 3.69252 0.121213
\(929\) 9.27409 0.304273 0.152137 0.988359i \(-0.451385\pi\)
0.152137 + 0.988359i \(0.451385\pi\)
\(930\) 0 0
\(931\) 32.3305 1.05959
\(932\) 3.38064 0.110737
\(933\) 49.9932 1.63671
\(934\) −4.11751 −0.134729
\(935\) 0 0
\(936\) −102.867 −3.36232
\(937\) 37.3432 1.21995 0.609975 0.792420i \(-0.291179\pi\)
0.609975 + 0.792420i \(0.291179\pi\)
\(938\) 0.838533 0.0273791
\(939\) 51.5806 1.68327
\(940\) 0 0
\(941\) 37.4044 1.21935 0.609674 0.792652i \(-0.291300\pi\)
0.609674 + 0.792652i \(0.291300\pi\)
\(942\) −21.9604 −0.715508
\(943\) 17.2445 0.561559
\(944\) −28.6235 −0.931615
\(945\) 0 0
\(946\) 1.35117 0.0439303
\(947\) 38.2457 1.24282 0.621409 0.783486i \(-0.286560\pi\)
0.621409 + 0.783486i \(0.286560\pi\)
\(948\) 46.6175 1.51407
\(949\) −17.5086 −0.568352
\(950\) 0 0
\(951\) 19.1265 0.620218
\(952\) −1.08794 −0.0352604
\(953\) 16.0014 0.518336 0.259168 0.965832i \(-0.416552\pi\)
0.259168 + 0.965832i \(0.416552\pi\)
\(954\) −15.5064 −0.502040
\(955\) 0 0
\(956\) 7.18898 0.232508
\(957\) −2.01611 −0.0651716
\(958\) −19.7956 −0.639565
\(959\) −1.02309 −0.0330373
\(960\) 0 0
\(961\) 25.4670 0.821515
\(962\) −22.8397 −0.736381
\(963\) 44.0010 1.41791
\(964\) 1.64397 0.0529487
\(965\) 0 0
\(966\) −1.66253 −0.0534910
\(967\) −57.3667 −1.84479 −0.922394 0.386251i \(-0.873770\pi\)
−0.922394 + 0.386251i \(0.873770\pi\)
\(968\) −22.0035 −0.707218
\(969\) −81.5319 −2.61918
\(970\) 0 0
\(971\) −23.3616 −0.749711 −0.374855 0.927083i \(-0.622308\pi\)
−0.374855 + 0.927083i \(0.622308\pi\)
\(972\) −54.0059 −1.73224
\(973\) 1.21409 0.0389218
\(974\) −1.93882 −0.0621239
\(975\) 0 0
\(976\) −12.9826 −0.415564
\(977\) −21.2763 −0.680690 −0.340345 0.940301i \(-0.610544\pi\)
−0.340345 + 0.940301i \(0.610544\pi\)
\(978\) 8.02497 0.256610
\(979\) 16.8470 0.538432
\(980\) 0 0
\(981\) −64.2382 −2.05097
\(982\) 1.08462 0.0346117
\(983\) −20.2377 −0.645481 −0.322741 0.946487i \(-0.604604\pi\)
−0.322741 + 0.946487i \(0.604604\pi\)
\(984\) −12.7737 −0.407210
\(985\) 0 0
\(986\) 2.17777 0.0693544
\(987\) 0.444646 0.0141532
\(988\) −48.7251 −1.55015
\(989\) 22.8275 0.725871
\(990\) 0 0
\(991\) −0.318692 −0.0101236 −0.00506179 0.999987i \(-0.501611\pi\)
−0.00506179 + 0.999987i \(0.501611\pi\)
\(992\) 41.6025 1.32088
\(993\) −78.9121 −2.50420
\(994\) 0.354343 0.0112391
\(995\) 0 0
\(996\) −2.13308 −0.0675894
\(997\) −44.7214 −1.41634 −0.708170 0.706042i \(-0.750479\pi\)
−0.708170 + 0.706042i \(0.750479\pi\)
\(998\) 7.31312 0.231493
\(999\) −84.3043 −2.66727
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 6025.2.a.i.1.7 15
5.4 even 2 1205.2.a.c.1.9 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.a.c.1.9 15 5.4 even 2
6025.2.a.i.1.7 15 1.1 even 1 trivial