Properties

Label 6025.2.a.i.1.12
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 1.12
Root \(-1.39546\) 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)
 
\(f(q)\) \(=\) \(q+1.39546 q^{2} -2.59963 q^{3} -0.0526942 q^{4} -3.62768 q^{6} +1.49578 q^{7} -2.86445 q^{8} +3.75808 q^{9} +O(q^{10})\) \(q+1.39546 q^{2} -2.59963 q^{3} -0.0526942 q^{4} -3.62768 q^{6} +1.49578 q^{7} -2.86445 q^{8} +3.75808 q^{9} -1.55651 q^{11} +0.136985 q^{12} -0.546921 q^{13} +2.08730 q^{14} -3.89183 q^{16} +6.16738 q^{17} +5.24425 q^{18} -4.52461 q^{19} -3.88849 q^{21} -2.17205 q^{22} +0.734249 q^{23} +7.44652 q^{24} -0.763205 q^{26} -1.97074 q^{27} -0.0788191 q^{28} +3.56695 q^{29} -4.59944 q^{31} +0.298005 q^{32} +4.04635 q^{33} +8.60633 q^{34} -0.198029 q^{36} -2.22842 q^{37} -6.31391 q^{38} +1.42179 q^{39} +3.66717 q^{41} -5.42622 q^{42} +1.59094 q^{43} +0.0820190 q^{44} +1.02461 q^{46} +1.47299 q^{47} +10.1173 q^{48} -4.76263 q^{49} -16.0329 q^{51} +0.0288195 q^{52} +9.96172 q^{53} -2.75008 q^{54} -4.28460 q^{56} +11.7623 q^{57} +4.97753 q^{58} +7.91122 q^{59} -5.49744 q^{61} -6.41834 q^{62} +5.62128 q^{63} +8.19952 q^{64} +5.64652 q^{66} +9.98877 q^{67} -0.324985 q^{68} -1.90878 q^{69} -9.33755 q^{71} -10.7648 q^{72} -12.9880 q^{73} -3.10967 q^{74} +0.238421 q^{76} -2.32820 q^{77} +1.98405 q^{78} -12.9488 q^{79} -6.15106 q^{81} +5.11738 q^{82} +9.19093 q^{83} +0.204901 q^{84} +2.22009 q^{86} -9.27276 q^{87} +4.45855 q^{88} +7.28523 q^{89} -0.818075 q^{91} -0.0386907 q^{92} +11.9569 q^{93} +2.05550 q^{94} -0.774703 q^{96} +6.07774 q^{97} -6.64606 q^{98} -5.84949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39546 0.986739 0.493369 0.869820i \(-0.335765\pi\)
0.493369 + 0.869820i \(0.335765\pi\)
\(3\) −2.59963 −1.50090 −0.750449 0.660928i \(-0.770163\pi\)
−0.750449 + 0.660928i \(0.770163\pi\)
\(4\) −0.0526942 −0.0263471
\(5\) 0 0
\(6\) −3.62768 −1.48099
\(7\) 1.49578 0.565353 0.282676 0.959215i \(-0.408778\pi\)
0.282676 + 0.959215i \(0.408778\pi\)
\(8\) −2.86445 −1.01274
\(9\) 3.75808 1.25269
\(10\) 0 0
\(11\) −1.55651 −0.469305 −0.234653 0.972079i \(-0.575395\pi\)
−0.234653 + 0.972079i \(0.575395\pi\)
\(12\) 0.136985 0.0395443
\(13\) −0.546921 −0.151688 −0.0758442 0.997120i \(-0.524165\pi\)
−0.0758442 + 0.997120i \(0.524165\pi\)
\(14\) 2.08730 0.557856
\(15\) 0 0
\(16\) −3.89183 −0.972959
\(17\) 6.16738 1.49581 0.747905 0.663806i \(-0.231060\pi\)
0.747905 + 0.663806i \(0.231060\pi\)
\(18\) 5.24425 1.23608
\(19\) −4.52461 −1.03802 −0.519009 0.854769i \(-0.673699\pi\)
−0.519009 + 0.854769i \(0.673699\pi\)
\(20\) 0 0
\(21\) −3.88849 −0.848537
\(22\) −2.17205 −0.463082
\(23\) 0.734249 0.153101 0.0765507 0.997066i \(-0.475609\pi\)
0.0765507 + 0.997066i \(0.475609\pi\)
\(24\) 7.44652 1.52001
\(25\) 0 0
\(26\) −0.763205 −0.149677
\(27\) −1.97074 −0.379268
\(28\) −0.0788191 −0.0148954
\(29\) 3.56695 0.662366 0.331183 0.943567i \(-0.392552\pi\)
0.331183 + 0.943567i \(0.392552\pi\)
\(30\) 0 0
\(31\) −4.59944 −0.826085 −0.413042 0.910712i \(-0.635534\pi\)
−0.413042 + 0.910712i \(0.635534\pi\)
\(32\) 0.298005 0.0526804
\(33\) 4.04635 0.704379
\(34\) 8.60633 1.47597
\(35\) 0 0
\(36\) −0.198029 −0.0330049
\(37\) −2.22842 −0.366350 −0.183175 0.983080i \(-0.558638\pi\)
−0.183175 + 0.983080i \(0.558638\pi\)
\(38\) −6.31391 −1.02425
\(39\) 1.42179 0.227669
\(40\) 0 0
\(41\) 3.66717 0.572715 0.286358 0.958123i \(-0.407555\pi\)
0.286358 + 0.958123i \(0.407555\pi\)
\(42\) −5.42622 −0.837284
\(43\) 1.59094 0.242616 0.121308 0.992615i \(-0.461291\pi\)
0.121308 + 0.992615i \(0.461291\pi\)
\(44\) 0.0820190 0.0123648
\(45\) 0 0
\(46\) 1.02461 0.151071
\(47\) 1.47299 0.214858 0.107429 0.994213i \(-0.465738\pi\)
0.107429 + 0.994213i \(0.465738\pi\)
\(48\) 10.1173 1.46031
\(49\) −4.76263 −0.680376
\(50\) 0 0
\(51\) −16.0329 −2.24506
\(52\) 0.0288195 0.00399655
\(53\) 9.96172 1.36835 0.684174 0.729319i \(-0.260163\pi\)
0.684174 + 0.729319i \(0.260163\pi\)
\(54\) −2.75008 −0.374239
\(55\) 0 0
\(56\) −4.28460 −0.572553
\(57\) 11.7623 1.55796
\(58\) 4.97753 0.653582
\(59\) 7.91122 1.02995 0.514977 0.857204i \(-0.327801\pi\)
0.514977 + 0.857204i \(0.327801\pi\)
\(60\) 0 0
\(61\) −5.49744 −0.703875 −0.351937 0.936024i \(-0.614477\pi\)
−0.351937 + 0.936024i \(0.614477\pi\)
\(62\) −6.41834 −0.815130
\(63\) 5.62128 0.708214
\(64\) 8.19952 1.02494
\(65\) 0 0
\(66\) 5.64652 0.695038
\(67\) 9.98877 1.22032 0.610161 0.792277i \(-0.291105\pi\)
0.610161 + 0.792277i \(0.291105\pi\)
\(68\) −0.324985 −0.0394103
\(69\) −1.90878 −0.229790
\(70\) 0 0
\(71\) −9.33755 −1.10816 −0.554082 0.832462i \(-0.686931\pi\)
−0.554082 + 0.832462i \(0.686931\pi\)
\(72\) −10.7648 −1.26865
\(73\) −12.9880 −1.52013 −0.760067 0.649845i \(-0.774834\pi\)
−0.760067 + 0.649845i \(0.774834\pi\)
\(74\) −3.10967 −0.361492
\(75\) 0 0
\(76\) 0.238421 0.0273487
\(77\) −2.32820 −0.265323
\(78\) 1.98405 0.224650
\(79\) −12.9488 −1.45685 −0.728425 0.685126i \(-0.759747\pi\)
−0.728425 + 0.685126i \(0.759747\pi\)
\(80\) 0 0
\(81\) −6.15106 −0.683451
\(82\) 5.11738 0.565120
\(83\) 9.19093 1.00884 0.504418 0.863460i \(-0.331707\pi\)
0.504418 + 0.863460i \(0.331707\pi\)
\(84\) 0.204901 0.0223565
\(85\) 0 0
\(86\) 2.22009 0.239398
\(87\) −9.27276 −0.994144
\(88\) 4.45855 0.475283
\(89\) 7.28523 0.772233 0.386116 0.922450i \(-0.373816\pi\)
0.386116 + 0.922450i \(0.373816\pi\)
\(90\) 0 0
\(91\) −0.818075 −0.0857575
\(92\) −0.0386907 −0.00403378
\(93\) 11.9569 1.23987
\(94\) 2.05550 0.212009
\(95\) 0 0
\(96\) −0.774703 −0.0790678
\(97\) 6.07774 0.617101 0.308551 0.951208i \(-0.400156\pi\)
0.308551 + 0.951208i \(0.400156\pi\)
\(98\) −6.64606 −0.671353
\(99\) −5.84949 −0.587896
\(100\) 0 0
\(101\) 10.7307 1.06774 0.533870 0.845566i \(-0.320737\pi\)
0.533870 + 0.845566i \(0.320737\pi\)
\(102\) −22.3733 −2.21529
\(103\) −6.81952 −0.671947 −0.335974 0.941871i \(-0.609065\pi\)
−0.335974 + 0.941871i \(0.609065\pi\)
\(104\) 1.56663 0.153620
\(105\) 0 0
\(106\) 13.9012 1.35020
\(107\) −11.0128 −1.06465 −0.532324 0.846540i \(-0.678681\pi\)
−0.532324 + 0.846540i \(0.678681\pi\)
\(108\) 0.103846 0.00999262
\(109\) 0.696884 0.0667494 0.0333747 0.999443i \(-0.489375\pi\)
0.0333747 + 0.999443i \(0.489375\pi\)
\(110\) 0 0
\(111\) 5.79307 0.549854
\(112\) −5.82134 −0.550065
\(113\) −0.767182 −0.0721704 −0.0360852 0.999349i \(-0.511489\pi\)
−0.0360852 + 0.999349i \(0.511489\pi\)
\(114\) 16.4138 1.53730
\(115\) 0 0
\(116\) −0.187958 −0.0174514
\(117\) −2.05537 −0.190019
\(118\) 11.0398 1.01630
\(119\) 9.22507 0.845661
\(120\) 0 0
\(121\) −8.57728 −0.779752
\(122\) −7.67145 −0.694540
\(123\) −9.53328 −0.859587
\(124\) 0.242364 0.0217649
\(125\) 0 0
\(126\) 7.84426 0.698823
\(127\) −0.285703 −0.0253520 −0.0126760 0.999920i \(-0.504035\pi\)
−0.0126760 + 0.999920i \(0.504035\pi\)
\(128\) 10.8461 0.958668
\(129\) −4.13585 −0.364142
\(130\) 0 0
\(131\) −9.06655 −0.792149 −0.396074 0.918218i \(-0.629628\pi\)
−0.396074 + 0.918218i \(0.629628\pi\)
\(132\) −0.213219 −0.0185584
\(133\) −6.76784 −0.586846
\(134\) 13.9389 1.20414
\(135\) 0 0
\(136\) −17.6662 −1.51486
\(137\) 7.33267 0.626473 0.313236 0.949675i \(-0.398587\pi\)
0.313236 + 0.949675i \(0.398587\pi\)
\(138\) −2.66362 −0.226742
\(139\) −16.4589 −1.39602 −0.698011 0.716087i \(-0.745932\pi\)
−0.698011 + 0.716087i \(0.745932\pi\)
\(140\) 0 0
\(141\) −3.82924 −0.322480
\(142\) −13.0302 −1.09347
\(143\) 0.851287 0.0711882
\(144\) −14.6258 −1.21882
\(145\) 0 0
\(146\) −18.1243 −1.49997
\(147\) 12.3811 1.02117
\(148\) 0.117425 0.00965226
\(149\) 4.41947 0.362057 0.181029 0.983478i \(-0.442057\pi\)
0.181029 + 0.983478i \(0.442057\pi\)
\(150\) 0 0
\(151\) 1.74677 0.142150 0.0710751 0.997471i \(-0.477357\pi\)
0.0710751 + 0.997471i \(0.477357\pi\)
\(152\) 12.9605 1.05124
\(153\) 23.1775 1.87379
\(154\) −3.24891 −0.261805
\(155\) 0 0
\(156\) −0.0749202 −0.00599841
\(157\) −4.91853 −0.392541 −0.196271 0.980550i \(-0.562883\pi\)
−0.196271 + 0.980550i \(0.562883\pi\)
\(158\) −18.0695 −1.43753
\(159\) −25.8968 −2.05375
\(160\) 0 0
\(161\) 1.09828 0.0865564
\(162\) −8.58355 −0.674388
\(163\) 3.88912 0.304619 0.152310 0.988333i \(-0.451329\pi\)
0.152310 + 0.988333i \(0.451329\pi\)
\(164\) −0.193238 −0.0150894
\(165\) 0 0
\(166\) 12.8256 0.995457
\(167\) −12.6867 −0.981728 −0.490864 0.871236i \(-0.663319\pi\)
−0.490864 + 0.871236i \(0.663319\pi\)
\(168\) 11.1384 0.859344
\(169\) −12.7009 −0.976991
\(170\) 0 0
\(171\) −17.0039 −1.30032
\(172\) −0.0838332 −0.00639222
\(173\) −4.59895 −0.349652 −0.174826 0.984599i \(-0.555936\pi\)
−0.174826 + 0.984599i \(0.555936\pi\)
\(174\) −12.9398 −0.980960
\(175\) 0 0
\(176\) 6.05768 0.456615
\(177\) −20.5663 −1.54586
\(178\) 10.1662 0.761992
\(179\) −5.43732 −0.406405 −0.203202 0.979137i \(-0.565135\pi\)
−0.203202 + 0.979137i \(0.565135\pi\)
\(180\) 0 0
\(181\) 15.4739 1.15017 0.575084 0.818095i \(-0.304969\pi\)
0.575084 + 0.818095i \(0.304969\pi\)
\(182\) −1.14159 −0.0846203
\(183\) 14.2913 1.05644
\(184\) −2.10322 −0.155051
\(185\) 0 0
\(186\) 16.6853 1.22343
\(187\) −9.59959 −0.701992
\(188\) −0.0776183 −0.00566089
\(189\) −2.94779 −0.214421
\(190\) 0 0
\(191\) 7.05889 0.510764 0.255382 0.966840i \(-0.417799\pi\)
0.255382 + 0.966840i \(0.417799\pi\)
\(192\) −21.3157 −1.53833
\(193\) −0.916001 −0.0659352 −0.0329676 0.999456i \(-0.510496\pi\)
−0.0329676 + 0.999456i \(0.510496\pi\)
\(194\) 8.48124 0.608917
\(195\) 0 0
\(196\) 0.250963 0.0179259
\(197\) −9.83214 −0.700511 −0.350255 0.936654i \(-0.613905\pi\)
−0.350255 + 0.936654i \(0.613905\pi\)
\(198\) −8.16273 −0.580100
\(199\) −21.1464 −1.49903 −0.749514 0.661989i \(-0.769713\pi\)
−0.749514 + 0.661989i \(0.769713\pi\)
\(200\) 0 0
\(201\) −25.9671 −1.83158
\(202\) 14.9742 1.05358
\(203\) 5.33539 0.374471
\(204\) 0.844842 0.0591508
\(205\) 0 0
\(206\) −9.51636 −0.663036
\(207\) 2.75937 0.191789
\(208\) 2.12852 0.147587
\(209\) 7.04260 0.487147
\(210\) 0 0
\(211\) −8.81286 −0.606703 −0.303351 0.952879i \(-0.598106\pi\)
−0.303351 + 0.952879i \(0.598106\pi\)
\(212\) −0.524925 −0.0360520
\(213\) 24.2742 1.66324
\(214\) −15.3679 −1.05053
\(215\) 0 0
\(216\) 5.64508 0.384099
\(217\) −6.87977 −0.467029
\(218\) 0.972474 0.0658642
\(219\) 33.7641 2.28157
\(220\) 0 0
\(221\) −3.37307 −0.226897
\(222\) 8.08400 0.542562
\(223\) −27.1229 −1.81629 −0.908143 0.418660i \(-0.862500\pi\)
−0.908143 + 0.418660i \(0.862500\pi\)
\(224\) 0.445751 0.0297830
\(225\) 0 0
\(226\) −1.07057 −0.0712133
\(227\) −25.6938 −1.70536 −0.852680 0.522434i \(-0.825024\pi\)
−0.852680 + 0.522434i \(0.825024\pi\)
\(228\) −0.619806 −0.0410477
\(229\) −20.0651 −1.32594 −0.662968 0.748648i \(-0.730703\pi\)
−0.662968 + 0.748648i \(0.730703\pi\)
\(230\) 0 0
\(231\) 6.05247 0.398223
\(232\) −10.2174 −0.670802
\(233\) 2.23570 0.146466 0.0732328 0.997315i \(-0.476668\pi\)
0.0732328 + 0.997315i \(0.476668\pi\)
\(234\) −2.86819 −0.187499
\(235\) 0 0
\(236\) −0.416876 −0.0271363
\(237\) 33.6620 2.18658
\(238\) 12.8732 0.834446
\(239\) 7.02691 0.454533 0.227267 0.973833i \(-0.427021\pi\)
0.227267 + 0.973833i \(0.427021\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) −11.9692 −0.769412
\(243\) 21.9027 1.40506
\(244\) 0.289683 0.0185451
\(245\) 0 0
\(246\) −13.3033 −0.848188
\(247\) 2.47460 0.157455
\(248\) 13.1749 0.836606
\(249\) −23.8930 −1.51416
\(250\) 0 0
\(251\) 21.8840 1.38130 0.690652 0.723188i \(-0.257324\pi\)
0.690652 + 0.723188i \(0.257324\pi\)
\(252\) −0.296209 −0.0186594
\(253\) −1.14287 −0.0718513
\(254\) −0.398686 −0.0250158
\(255\) 0 0
\(256\) −1.26378 −0.0789859
\(257\) −7.72517 −0.481883 −0.240941 0.970540i \(-0.577456\pi\)
−0.240941 + 0.970540i \(0.577456\pi\)
\(258\) −5.77141 −0.359312
\(259\) −3.33324 −0.207117
\(260\) 0 0
\(261\) 13.4049 0.829742
\(262\) −12.6520 −0.781643
\(263\) −28.0301 −1.72841 −0.864206 0.503138i \(-0.832179\pi\)
−0.864206 + 0.503138i \(0.832179\pi\)
\(264\) −11.5906 −0.713351
\(265\) 0 0
\(266\) −9.44424 −0.579064
\(267\) −18.9389 −1.15904
\(268\) −0.526350 −0.0321520
\(269\) 0.617409 0.0376441 0.0188221 0.999823i \(-0.494008\pi\)
0.0188221 + 0.999823i \(0.494008\pi\)
\(270\) 0 0
\(271\) −16.8799 −1.02538 −0.512690 0.858574i \(-0.671351\pi\)
−0.512690 + 0.858574i \(0.671351\pi\)
\(272\) −24.0024 −1.45536
\(273\) 2.12669 0.128713
\(274\) 10.2324 0.618165
\(275\) 0 0
\(276\) 0.100581 0.00605429
\(277\) −4.37569 −0.262910 −0.131455 0.991322i \(-0.541965\pi\)
−0.131455 + 0.991322i \(0.541965\pi\)
\(278\) −22.9677 −1.37751
\(279\) −17.2851 −1.03483
\(280\) 0 0
\(281\) −20.0475 −1.19594 −0.597968 0.801520i \(-0.704025\pi\)
−0.597968 + 0.801520i \(0.704025\pi\)
\(282\) −5.34355 −0.318204
\(283\) −11.4403 −0.680052 −0.340026 0.940416i \(-0.610436\pi\)
−0.340026 + 0.940416i \(0.610436\pi\)
\(284\) 0.492035 0.0291969
\(285\) 0 0
\(286\) 1.18794 0.0702442
\(287\) 5.48529 0.323786
\(288\) 1.11993 0.0659924
\(289\) 21.0366 1.23745
\(290\) 0 0
\(291\) −15.7999 −0.926206
\(292\) 0.684394 0.0400511
\(293\) −27.4146 −1.60158 −0.800789 0.598947i \(-0.795586\pi\)
−0.800789 + 0.598947i \(0.795586\pi\)
\(294\) 17.2773 1.00763
\(295\) 0 0
\(296\) 6.38320 0.371016
\(297\) 3.06747 0.177993
\(298\) 6.16720 0.357256
\(299\) −0.401576 −0.0232237
\(300\) 0 0
\(301\) 2.37970 0.137164
\(302\) 2.43755 0.140265
\(303\) −27.8958 −1.60257
\(304\) 17.6090 1.00995
\(305\) 0 0
\(306\) 32.3433 1.84894
\(307\) −1.74676 −0.0996929 −0.0498465 0.998757i \(-0.515873\pi\)
−0.0498465 + 0.998757i \(0.515873\pi\)
\(308\) 0.122683 0.00699050
\(309\) 17.7282 1.00852
\(310\) 0 0
\(311\) 3.28578 0.186320 0.0931598 0.995651i \(-0.470303\pi\)
0.0931598 + 0.995651i \(0.470303\pi\)
\(312\) −4.07265 −0.230569
\(313\) 24.9618 1.41092 0.705461 0.708749i \(-0.250740\pi\)
0.705461 + 0.708749i \(0.250740\pi\)
\(314\) −6.86361 −0.387336
\(315\) 0 0
\(316\) 0.682325 0.0383838
\(317\) −13.9705 −0.784660 −0.392330 0.919825i \(-0.628331\pi\)
−0.392330 + 0.919825i \(0.628331\pi\)
\(318\) −36.1379 −2.02651
\(319\) −5.55199 −0.310852
\(320\) 0 0
\(321\) 28.6293 1.59793
\(322\) 1.53260 0.0854085
\(323\) −27.9050 −1.55268
\(324\) 0.324125 0.0180070
\(325\) 0 0
\(326\) 5.42710 0.300579
\(327\) −1.81164 −0.100184
\(328\) −10.5044 −0.580009
\(329\) 2.20328 0.121471
\(330\) 0 0
\(331\) −16.7315 −0.919644 −0.459822 0.888011i \(-0.652087\pi\)
−0.459822 + 0.888011i \(0.652087\pi\)
\(332\) −0.484309 −0.0265799
\(333\) −8.37459 −0.458925
\(334\) −17.7038 −0.968708
\(335\) 0 0
\(336\) 15.1333 0.825592
\(337\) −27.9838 −1.52437 −0.762187 0.647357i \(-0.775874\pi\)
−0.762187 + 0.647357i \(0.775874\pi\)
\(338\) −17.7236 −0.964034
\(339\) 1.99439 0.108320
\(340\) 0 0
\(341\) 7.15908 0.387686
\(342\) −23.7282 −1.28307
\(343\) −17.5943 −0.950006
\(344\) −4.55716 −0.245706
\(345\) 0 0
\(346\) −6.41765 −0.345015
\(347\) 8.11985 0.435897 0.217948 0.975960i \(-0.430064\pi\)
0.217948 + 0.975960i \(0.430064\pi\)
\(348\) 0.488621 0.0261928
\(349\) 11.8282 0.633148 0.316574 0.948568i \(-0.397467\pi\)
0.316574 + 0.948568i \(0.397467\pi\)
\(350\) 0 0
\(351\) 1.07784 0.0575306
\(352\) −0.463848 −0.0247232
\(353\) −6.31287 −0.336000 −0.168000 0.985787i \(-0.553731\pi\)
−0.168000 + 0.985787i \(0.553731\pi\)
\(354\) −28.6994 −1.52536
\(355\) 0 0
\(356\) −0.383889 −0.0203461
\(357\) −23.9818 −1.26925
\(358\) −7.58756 −0.401015
\(359\) 11.1472 0.588325 0.294163 0.955755i \(-0.404959\pi\)
0.294163 + 0.955755i \(0.404959\pi\)
\(360\) 0 0
\(361\) 1.47212 0.0774801
\(362\) 21.5932 1.13491
\(363\) 22.2978 1.17033
\(364\) 0.0431078 0.00225946
\(365\) 0 0
\(366\) 19.9429 1.04243
\(367\) 32.7868 1.71145 0.855727 0.517427i \(-0.173110\pi\)
0.855727 + 0.517427i \(0.173110\pi\)
\(368\) −2.85758 −0.148961
\(369\) 13.7815 0.717437
\(370\) 0 0
\(371\) 14.9006 0.773600
\(372\) −0.630057 −0.0326669
\(373\) 16.5445 0.856640 0.428320 0.903627i \(-0.359106\pi\)
0.428320 + 0.903627i \(0.359106\pi\)
\(374\) −13.3958 −0.692682
\(375\) 0 0
\(376\) −4.21932 −0.217595
\(377\) −1.95084 −0.100473
\(378\) −4.11353 −0.211577
\(379\) 5.75770 0.295753 0.147877 0.989006i \(-0.452756\pi\)
0.147877 + 0.989006i \(0.452756\pi\)
\(380\) 0 0
\(381\) 0.742721 0.0380508
\(382\) 9.85040 0.503990
\(383\) −6.47172 −0.330689 −0.165345 0.986236i \(-0.552874\pi\)
−0.165345 + 0.986236i \(0.552874\pi\)
\(384\) −28.1958 −1.43886
\(385\) 0 0
\(386\) −1.27824 −0.0650608
\(387\) 5.97888 0.303923
\(388\) −0.320262 −0.0162588
\(389\) −12.2278 −0.619975 −0.309987 0.950741i \(-0.600325\pi\)
−0.309987 + 0.950741i \(0.600325\pi\)
\(390\) 0 0
\(391\) 4.52839 0.229011
\(392\) 13.6423 0.689041
\(393\) 23.5697 1.18893
\(394\) −13.7203 −0.691221
\(395\) 0 0
\(396\) 0.308234 0.0154894
\(397\) 1.09657 0.0550355 0.0275177 0.999621i \(-0.491240\pi\)
0.0275177 + 0.999621i \(0.491240\pi\)
\(398\) −29.5089 −1.47915
\(399\) 17.5939 0.880796
\(400\) 0 0
\(401\) 6.55809 0.327495 0.163748 0.986502i \(-0.447642\pi\)
0.163748 + 0.986502i \(0.447642\pi\)
\(402\) −36.2360 −1.80729
\(403\) 2.51553 0.125308
\(404\) −0.565444 −0.0281319
\(405\) 0 0
\(406\) 7.44531 0.369505
\(407\) 3.46856 0.171930
\(408\) 45.9255 2.27365
\(409\) 20.0458 0.991202 0.495601 0.868550i \(-0.334948\pi\)
0.495601 + 0.868550i \(0.334948\pi\)
\(410\) 0 0
\(411\) −19.0622 −0.940271
\(412\) 0.359349 0.0177039
\(413\) 11.8335 0.582287
\(414\) 3.85058 0.189246
\(415\) 0 0
\(416\) −0.162985 −0.00799100
\(417\) 42.7870 2.09529
\(418\) 9.82767 0.480687
\(419\) 4.90086 0.239423 0.119711 0.992809i \(-0.461803\pi\)
0.119711 + 0.992809i \(0.461803\pi\)
\(420\) 0 0
\(421\) −3.63934 −0.177371 −0.0886853 0.996060i \(-0.528267\pi\)
−0.0886853 + 0.996060i \(0.528267\pi\)
\(422\) −12.2980 −0.598657
\(423\) 5.53564 0.269152
\(424\) −28.5349 −1.38578
\(425\) 0 0
\(426\) 33.8736 1.64118
\(427\) −8.22298 −0.397938
\(428\) 0.580311 0.0280504
\(429\) −2.21303 −0.106846
\(430\) 0 0
\(431\) 21.9532 1.05745 0.528725 0.848793i \(-0.322670\pi\)
0.528725 + 0.848793i \(0.322670\pi\)
\(432\) 7.66978 0.369013
\(433\) 11.2852 0.542331 0.271166 0.962533i \(-0.412591\pi\)
0.271166 + 0.962533i \(0.412591\pi\)
\(434\) −9.60044 −0.460836
\(435\) 0 0
\(436\) −0.0367218 −0.00175865
\(437\) −3.32219 −0.158922
\(438\) 47.1164 2.25131
\(439\) −17.7827 −0.848720 −0.424360 0.905493i \(-0.639501\pi\)
−0.424360 + 0.905493i \(0.639501\pi\)
\(440\) 0 0
\(441\) −17.8984 −0.852303
\(442\) −4.70698 −0.223888
\(443\) −1.37491 −0.0653239 −0.0326620 0.999466i \(-0.510398\pi\)
−0.0326620 + 0.999466i \(0.510398\pi\)
\(444\) −0.305261 −0.0144871
\(445\) 0 0
\(446\) −37.8489 −1.79220
\(447\) −11.4890 −0.543411
\(448\) 12.2647 0.579453
\(449\) −7.98926 −0.377036 −0.188518 0.982070i \(-0.560368\pi\)
−0.188518 + 0.982070i \(0.560368\pi\)
\(450\) 0 0
\(451\) −5.70798 −0.268778
\(452\) 0.0404260 0.00190148
\(453\) −4.54096 −0.213353
\(454\) −35.8547 −1.68274
\(455\) 0 0
\(456\) −33.6926 −1.57780
\(457\) 5.73846 0.268434 0.134217 0.990952i \(-0.457148\pi\)
0.134217 + 0.990952i \(0.457148\pi\)
\(458\) −28.0000 −1.30835
\(459\) −12.1543 −0.567313
\(460\) 0 0
\(461\) −10.2346 −0.476671 −0.238336 0.971183i \(-0.576602\pi\)
−0.238336 + 0.971183i \(0.576602\pi\)
\(462\) 8.44597 0.392942
\(463\) −36.0973 −1.67759 −0.838793 0.544451i \(-0.816738\pi\)
−0.838793 + 0.544451i \(0.816738\pi\)
\(464\) −13.8820 −0.644455
\(465\) 0 0
\(466\) 3.11983 0.144523
\(467\) 17.6441 0.816471 0.408235 0.912877i \(-0.366144\pi\)
0.408235 + 0.912877i \(0.366144\pi\)
\(468\) 0.108306 0.00500646
\(469\) 14.9410 0.689913
\(470\) 0 0
\(471\) 12.7864 0.589165
\(472\) −22.6613 −1.04307
\(473\) −2.47631 −0.113861
\(474\) 46.9740 2.15759
\(475\) 0 0
\(476\) −0.486108 −0.0222807
\(477\) 37.4370 1.71412
\(478\) 9.80577 0.448505
\(479\) −28.6326 −1.30826 −0.654129 0.756383i \(-0.726965\pi\)
−0.654129 + 0.756383i \(0.726965\pi\)
\(480\) 0 0
\(481\) 1.21877 0.0555711
\(482\) −1.39546 −0.0635614
\(483\) −2.85512 −0.129912
\(484\) 0.451973 0.0205442
\(485\) 0 0
\(486\) 30.5643 1.38643
\(487\) −15.0219 −0.680709 −0.340355 0.940297i \(-0.610547\pi\)
−0.340355 + 0.940297i \(0.610547\pi\)
\(488\) 15.7471 0.712839
\(489\) −10.1103 −0.457202
\(490\) 0 0
\(491\) −17.0898 −0.771252 −0.385626 0.922655i \(-0.626015\pi\)
−0.385626 + 0.922655i \(0.626015\pi\)
\(492\) 0.502349 0.0226476
\(493\) 21.9988 0.990774
\(494\) 3.45321 0.155367
\(495\) 0 0
\(496\) 17.9003 0.803746
\(497\) −13.9670 −0.626504
\(498\) −33.3417 −1.49408
\(499\) 18.3197 0.820101 0.410050 0.912063i \(-0.365511\pi\)
0.410050 + 0.912063i \(0.365511\pi\)
\(500\) 0 0
\(501\) 32.9808 1.47347
\(502\) 30.5382 1.36298
\(503\) −37.8954 −1.68967 −0.844836 0.535025i \(-0.820302\pi\)
−0.844836 + 0.535025i \(0.820302\pi\)
\(504\) −16.1019 −0.717234
\(505\) 0 0
\(506\) −1.59482 −0.0708985
\(507\) 33.0176 1.46636
\(508\) 0.0150549 0.000667952 0
\(509\) 18.1079 0.802618 0.401309 0.915943i \(-0.368555\pi\)
0.401309 + 0.915943i \(0.368555\pi\)
\(510\) 0 0
\(511\) −19.4273 −0.859412
\(512\) −23.4557 −1.03661
\(513\) 8.91682 0.393687
\(514\) −10.7802 −0.475492
\(515\) 0 0
\(516\) 0.217935 0.00959407
\(517\) −2.29273 −0.100834
\(518\) −4.65139 −0.204370
\(519\) 11.9556 0.524792
\(520\) 0 0
\(521\) −29.0795 −1.27400 −0.636998 0.770866i \(-0.719824\pi\)
−0.636998 + 0.770866i \(0.719824\pi\)
\(522\) 18.7060 0.818739
\(523\) 11.1298 0.486670 0.243335 0.969942i \(-0.421759\pi\)
0.243335 + 0.969942i \(0.421759\pi\)
\(524\) 0.477755 0.0208708
\(525\) 0 0
\(526\) −39.1149 −1.70549
\(527\) −28.3665 −1.23567
\(528\) −15.7477 −0.685332
\(529\) −22.4609 −0.976560
\(530\) 0 0
\(531\) 29.7310 1.29022
\(532\) 0.356626 0.0154617
\(533\) −2.00565 −0.0868743
\(534\) −26.4285 −1.14367
\(535\) 0 0
\(536\) −28.6123 −1.23586
\(537\) 14.1350 0.609972
\(538\) 0.861569 0.0371449
\(539\) 7.41308 0.319304
\(540\) 0 0
\(541\) 36.6182 1.57434 0.787170 0.616736i \(-0.211545\pi\)
0.787170 + 0.616736i \(0.211545\pi\)
\(542\) −23.5552 −1.01178
\(543\) −40.2265 −1.72628
\(544\) 1.83791 0.0787998
\(545\) 0 0
\(546\) 2.96771 0.127006
\(547\) 30.0556 1.28508 0.642542 0.766251i \(-0.277880\pi\)
0.642542 + 0.766251i \(0.277880\pi\)
\(548\) −0.386389 −0.0165057
\(549\) −20.6598 −0.881740
\(550\) 0 0
\(551\) −16.1391 −0.687548
\(552\) 5.46759 0.232716
\(553\) −19.3685 −0.823634
\(554\) −6.10609 −0.259423
\(555\) 0 0
\(556\) 0.867287 0.0367812
\(557\) −1.04047 −0.0440862 −0.0220431 0.999757i \(-0.507017\pi\)
−0.0220431 + 0.999757i \(0.507017\pi\)
\(558\) −24.1206 −1.02111
\(559\) −0.870117 −0.0368020
\(560\) 0 0
\(561\) 24.9554 1.05362
\(562\) −27.9755 −1.18008
\(563\) 37.5268 1.58157 0.790784 0.612096i \(-0.209673\pi\)
0.790784 + 0.612096i \(0.209673\pi\)
\(564\) 0.201779 0.00849642
\(565\) 0 0
\(566\) −15.9644 −0.671034
\(567\) −9.20065 −0.386391
\(568\) 26.7470 1.12228
\(569\) −29.4439 −1.23435 −0.617176 0.786825i \(-0.711723\pi\)
−0.617176 + 0.786825i \(0.711723\pi\)
\(570\) 0 0
\(571\) 23.6027 0.987742 0.493871 0.869535i \(-0.335581\pi\)
0.493871 + 0.869535i \(0.335581\pi\)
\(572\) −0.0448579 −0.00187560
\(573\) −18.3505 −0.766604
\(574\) 7.65449 0.319492
\(575\) 0 0
\(576\) 30.8145 1.28394
\(577\) 42.3104 1.76141 0.880703 0.473669i \(-0.157071\pi\)
0.880703 + 0.473669i \(0.157071\pi\)
\(578\) 29.3557 1.22104
\(579\) 2.38126 0.0989620
\(580\) 0 0
\(581\) 13.7476 0.570348
\(582\) −22.0481 −0.913923
\(583\) −15.5055 −0.642173
\(584\) 37.2036 1.53949
\(585\) 0 0
\(586\) −38.2559 −1.58034
\(587\) 31.7942 1.31229 0.656144 0.754636i \(-0.272186\pi\)
0.656144 + 0.754636i \(0.272186\pi\)
\(588\) −0.652411 −0.0269050
\(589\) 20.8107 0.857490
\(590\) 0 0
\(591\) 25.5599 1.05140
\(592\) 8.67265 0.356444
\(593\) 21.5382 0.884468 0.442234 0.896900i \(-0.354186\pi\)
0.442234 + 0.896900i \(0.354186\pi\)
\(594\) 4.28053 0.175632
\(595\) 0 0
\(596\) −0.232881 −0.00953916
\(597\) 54.9728 2.24989
\(598\) −0.560382 −0.0229157
\(599\) 12.1627 0.496953 0.248477 0.968638i \(-0.420070\pi\)
0.248477 + 0.968638i \(0.420070\pi\)
\(600\) 0 0
\(601\) 27.8351 1.13542 0.567708 0.823230i \(-0.307830\pi\)
0.567708 + 0.823230i \(0.307830\pi\)
\(602\) 3.32077 0.135345
\(603\) 37.5386 1.52869
\(604\) −0.0920447 −0.00374525
\(605\) 0 0
\(606\) −38.9274 −1.58132
\(607\) 16.6194 0.674562 0.337281 0.941404i \(-0.390493\pi\)
0.337281 + 0.941404i \(0.390493\pi\)
\(608\) −1.34836 −0.0546831
\(609\) −13.8700 −0.562042
\(610\) 0 0
\(611\) −0.805611 −0.0325915
\(612\) −1.22132 −0.0493690
\(613\) 37.9319 1.53205 0.766027 0.642809i \(-0.222231\pi\)
0.766027 + 0.642809i \(0.222231\pi\)
\(614\) −2.43753 −0.0983708
\(615\) 0 0
\(616\) 6.66902 0.268702
\(617\) 5.11850 0.206063 0.103032 0.994678i \(-0.467146\pi\)
0.103032 + 0.994678i \(0.467146\pi\)
\(618\) 24.7390 0.995150
\(619\) −29.4556 −1.18392 −0.591960 0.805967i \(-0.701646\pi\)
−0.591960 + 0.805967i \(0.701646\pi\)
\(620\) 0 0
\(621\) −1.44701 −0.0580665
\(622\) 4.58517 0.183849
\(623\) 10.8971 0.436584
\(624\) −5.53338 −0.221512
\(625\) 0 0
\(626\) 34.8331 1.39221
\(627\) −18.3082 −0.731158
\(628\) 0.259178 0.0103423
\(629\) −13.7435 −0.547990
\(630\) 0 0
\(631\) 36.6744 1.45998 0.729992 0.683456i \(-0.239524\pi\)
0.729992 + 0.683456i \(0.239524\pi\)
\(632\) 37.0911 1.47540
\(633\) 22.9102 0.910599
\(634\) −19.4952 −0.774254
\(635\) 0 0
\(636\) 1.36461 0.0541104
\(637\) 2.60478 0.103205
\(638\) −7.74758 −0.306730
\(639\) −35.0913 −1.38819
\(640\) 0 0
\(641\) −48.5952 −1.91940 −0.959698 0.281035i \(-0.909322\pi\)
−0.959698 + 0.281035i \(0.909322\pi\)
\(642\) 39.9510 1.57674
\(643\) −2.40148 −0.0947050 −0.0473525 0.998878i \(-0.515078\pi\)
−0.0473525 + 0.998878i \(0.515078\pi\)
\(644\) −0.0578728 −0.00228051
\(645\) 0 0
\(646\) −38.9403 −1.53209
\(647\) −10.6830 −0.419993 −0.209997 0.977702i \(-0.567345\pi\)
−0.209997 + 0.977702i \(0.567345\pi\)
\(648\) 17.6194 0.692156
\(649\) −12.3139 −0.483363
\(650\) 0 0
\(651\) 17.8849 0.700963
\(652\) −0.204934 −0.00802583
\(653\) −39.8844 −1.56080 −0.780399 0.625282i \(-0.784984\pi\)
−0.780399 + 0.625282i \(0.784984\pi\)
\(654\) −2.52807 −0.0988555
\(655\) 0 0
\(656\) −14.2720 −0.557228
\(657\) −48.8101 −1.90426
\(658\) 3.07459 0.119860
\(659\) 12.5725 0.489753 0.244877 0.969554i \(-0.421253\pi\)
0.244877 + 0.969554i \(0.421253\pi\)
\(660\) 0 0
\(661\) −14.9933 −0.583174 −0.291587 0.956544i \(-0.594183\pi\)
−0.291587 + 0.956544i \(0.594183\pi\)
\(662\) −23.3481 −0.907448
\(663\) 8.76873 0.340549
\(664\) −26.3270 −1.02168
\(665\) 0 0
\(666\) −11.6864 −0.452839
\(667\) 2.61903 0.101409
\(668\) 0.668516 0.0258657
\(669\) 70.5096 2.72606
\(670\) 0 0
\(671\) 8.55682 0.330332
\(672\) −1.15879 −0.0447012
\(673\) −26.5273 −1.02255 −0.511277 0.859416i \(-0.670827\pi\)
−0.511277 + 0.859416i \(0.670827\pi\)
\(674\) −39.0502 −1.50416
\(675\) 0 0
\(676\) 0.669263 0.0257409
\(677\) 41.7855 1.60595 0.802973 0.596015i \(-0.203250\pi\)
0.802973 + 0.596015i \(0.203250\pi\)
\(678\) 2.78309 0.106884
\(679\) 9.09098 0.348880
\(680\) 0 0
\(681\) 66.7945 2.55957
\(682\) 9.99021 0.382545
\(683\) −9.83634 −0.376377 −0.188188 0.982133i \(-0.560262\pi\)
−0.188188 + 0.982133i \(0.560262\pi\)
\(684\) 0.896005 0.0342596
\(685\) 0 0
\(686\) −24.5522 −0.937407
\(687\) 52.1617 1.99009
\(688\) −6.19167 −0.236055
\(689\) −5.44827 −0.207563
\(690\) 0 0
\(691\) −34.1488 −1.29908 −0.649541 0.760327i \(-0.725039\pi\)
−0.649541 + 0.760327i \(0.725039\pi\)
\(692\) 0.242338 0.00921231
\(693\) −8.74958 −0.332369
\(694\) 11.3309 0.430116
\(695\) 0 0
\(696\) 26.5614 1.00681
\(697\) 22.6168 0.856673
\(698\) 16.5057 0.624752
\(699\) −5.81200 −0.219830
\(700\) 0 0
\(701\) 3.15872 0.119303 0.0596517 0.998219i \(-0.481001\pi\)
0.0596517 + 0.998219i \(0.481001\pi\)
\(702\) 1.50408 0.0567677
\(703\) 10.0827 0.380278
\(704\) −12.7626 −0.481010
\(705\) 0 0
\(706\) −8.80935 −0.331544
\(707\) 16.0507 0.603650
\(708\) 1.08372 0.0407288
\(709\) 2.50229 0.0939753 0.0469876 0.998895i \(-0.485038\pi\)
0.0469876 + 0.998895i \(0.485038\pi\)
\(710\) 0 0
\(711\) −48.6625 −1.82499
\(712\) −20.8682 −0.782068
\(713\) −3.37714 −0.126475
\(714\) −33.4656 −1.25242
\(715\) 0 0
\(716\) 0.286515 0.0107076
\(717\) −18.2674 −0.682208
\(718\) 15.5554 0.580523
\(719\) −31.0417 −1.15766 −0.578830 0.815448i \(-0.696490\pi\)
−0.578830 + 0.815448i \(0.696490\pi\)
\(720\) 0 0
\(721\) −10.2005 −0.379887
\(722\) 2.05429 0.0764526
\(723\) 2.59963 0.0966813
\(724\) −0.815386 −0.0303036
\(725\) 0 0
\(726\) 31.1156 1.15481
\(727\) 11.0652 0.410386 0.205193 0.978722i \(-0.434218\pi\)
0.205193 + 0.978722i \(0.434218\pi\)
\(728\) 2.34333 0.0868498
\(729\) −38.4858 −1.42540
\(730\) 0 0
\(731\) 9.81192 0.362907
\(732\) −0.753069 −0.0278342
\(733\) −6.43274 −0.237599 −0.118799 0.992918i \(-0.537905\pi\)
−0.118799 + 0.992918i \(0.537905\pi\)
\(734\) 45.7526 1.68876
\(735\) 0 0
\(736\) 0.218810 0.00806544
\(737\) −15.5476 −0.572704
\(738\) 19.2315 0.707923
\(739\) −13.6029 −0.500392 −0.250196 0.968195i \(-0.580495\pi\)
−0.250196 + 0.968195i \(0.580495\pi\)
\(740\) 0 0
\(741\) −6.43306 −0.236324
\(742\) 20.7932 0.763341
\(743\) 21.7856 0.799237 0.399618 0.916682i \(-0.369143\pi\)
0.399618 + 0.916682i \(0.369143\pi\)
\(744\) −34.2498 −1.25566
\(745\) 0 0
\(746\) 23.0871 0.845279
\(747\) 34.5403 1.26376
\(748\) 0.505843 0.0184954
\(749\) −16.4728 −0.601902
\(750\) 0 0
\(751\) −14.2742 −0.520872 −0.260436 0.965491i \(-0.583866\pi\)
−0.260436 + 0.965491i \(0.583866\pi\)
\(752\) −5.73265 −0.209048
\(753\) −56.8902 −2.07319
\(754\) −2.72232 −0.0991409
\(755\) 0 0
\(756\) 0.155332 0.00564936
\(757\) −47.4470 −1.72449 −0.862245 0.506492i \(-0.830942\pi\)
−0.862245 + 0.506492i \(0.830942\pi\)
\(758\) 8.03464 0.291831
\(759\) 2.97103 0.107842
\(760\) 0 0
\(761\) 2.87598 0.104254 0.0521270 0.998640i \(-0.483400\pi\)
0.0521270 + 0.998640i \(0.483400\pi\)
\(762\) 1.03644 0.0375462
\(763\) 1.04239 0.0377370
\(764\) −0.371963 −0.0134571
\(765\) 0 0
\(766\) −9.03102 −0.326304
\(767\) −4.32681 −0.156232
\(768\) 3.28535 0.118550
\(769\) 35.9147 1.29512 0.647559 0.762015i \(-0.275790\pi\)
0.647559 + 0.762015i \(0.275790\pi\)
\(770\) 0 0
\(771\) 20.0826 0.723257
\(772\) 0.0482679 0.00173720
\(773\) −21.3574 −0.768172 −0.384086 0.923297i \(-0.625483\pi\)
−0.384086 + 0.923297i \(0.625483\pi\)
\(774\) 8.34328 0.299893
\(775\) 0 0
\(776\) −17.4094 −0.624961
\(777\) 8.66518 0.310862
\(778\) −17.0634 −0.611753
\(779\) −16.5925 −0.594488
\(780\) 0 0
\(781\) 14.5340 0.520067
\(782\) 6.31919 0.225974
\(783\) −7.02952 −0.251215
\(784\) 18.5354 0.661978
\(785\) 0 0
\(786\) 32.8905 1.17317
\(787\) 37.9490 1.35274 0.676368 0.736564i \(-0.263553\pi\)
0.676368 + 0.736564i \(0.263553\pi\)
\(788\) 0.518097 0.0184564
\(789\) 72.8680 2.59417
\(790\) 0 0
\(791\) −1.14754 −0.0408018
\(792\) 16.7556 0.595384
\(793\) 3.00666 0.106770
\(794\) 1.53022 0.0543056
\(795\) 0 0
\(796\) 1.11429 0.0394950
\(797\) −0.639305 −0.0226454 −0.0113227 0.999936i \(-0.503604\pi\)
−0.0113227 + 0.999936i \(0.503604\pi\)
\(798\) 24.5516 0.869116
\(799\) 9.08452 0.321387
\(800\) 0 0
\(801\) 27.3785 0.967372
\(802\) 9.15155 0.323152
\(803\) 20.2160 0.713407
\(804\) 1.36832 0.0482568
\(805\) 0 0
\(806\) 3.51032 0.123646
\(807\) −1.60504 −0.0565000
\(808\) −30.7375 −1.08134
\(809\) 33.4426 1.17578 0.587890 0.808941i \(-0.299959\pi\)
0.587890 + 0.808941i \(0.299959\pi\)
\(810\) 0 0
\(811\) 47.2141 1.65791 0.828955 0.559315i \(-0.188936\pi\)
0.828955 + 0.559315i \(0.188936\pi\)
\(812\) −0.281144 −0.00986622
\(813\) 43.8815 1.53899
\(814\) 4.84023 0.169650
\(815\) 0 0
\(816\) 62.3975 2.18435
\(817\) −7.19838 −0.251839
\(818\) 27.9731 0.978058
\(819\) −3.07439 −0.107428
\(820\) 0 0
\(821\) −43.9114 −1.53252 −0.766259 0.642532i \(-0.777884\pi\)
−0.766259 + 0.642532i \(0.777884\pi\)
\(822\) −26.6006 −0.927802
\(823\) 4.44055 0.154788 0.0773939 0.997001i \(-0.475340\pi\)
0.0773939 + 0.997001i \(0.475340\pi\)
\(824\) 19.5342 0.680505
\(825\) 0 0
\(826\) 16.5131 0.574565
\(827\) −28.1589 −0.979180 −0.489590 0.871953i \(-0.662854\pi\)
−0.489590 + 0.871953i \(0.662854\pi\)
\(828\) −0.145403 −0.00505309
\(829\) 9.65478 0.335325 0.167662 0.985844i \(-0.446378\pi\)
0.167662 + 0.985844i \(0.446378\pi\)
\(830\) 0 0
\(831\) 11.3752 0.394601
\(832\) −4.48449 −0.155472
\(833\) −29.3730 −1.01771
\(834\) 59.7075 2.06750
\(835\) 0 0
\(836\) −0.371104 −0.0128349
\(837\) 9.06429 0.313308
\(838\) 6.83895 0.236248
\(839\) −43.0759 −1.48715 −0.743573 0.668655i \(-0.766870\pi\)
−0.743573 + 0.668655i \(0.766870\pi\)
\(840\) 0 0
\(841\) −16.2769 −0.561271
\(842\) −5.07855 −0.175018
\(843\) 52.1162 1.79498
\(844\) 0.464387 0.0159849
\(845\) 0 0
\(846\) 7.72475 0.265582
\(847\) −12.8297 −0.440835
\(848\) −38.7694 −1.33135
\(849\) 29.7404 1.02069
\(850\) 0 0
\(851\) −1.63622 −0.0560887
\(852\) −1.27911 −0.0438216
\(853\) −11.0630 −0.378791 −0.189395 0.981901i \(-0.560653\pi\)
−0.189395 + 0.981901i \(0.560653\pi\)
\(854\) −11.4748 −0.392660
\(855\) 0 0
\(856\) 31.5457 1.07821
\(857\) 32.8888 1.12346 0.561730 0.827320i \(-0.310136\pi\)
0.561730 + 0.827320i \(0.310136\pi\)
\(858\) −3.08820 −0.105429
\(859\) −26.4534 −0.902579 −0.451289 0.892378i \(-0.649036\pi\)
−0.451289 + 0.892378i \(0.649036\pi\)
\(860\) 0 0
\(861\) −14.2597 −0.485970
\(862\) 30.6349 1.04343
\(863\) 17.2512 0.587238 0.293619 0.955922i \(-0.405140\pi\)
0.293619 + 0.955922i \(0.405140\pi\)
\(864\) −0.587290 −0.0199800
\(865\) 0 0
\(866\) 15.7480 0.535139
\(867\) −54.6874 −1.85728
\(868\) 0.362524 0.0123049
\(869\) 20.1549 0.683707
\(870\) 0 0
\(871\) −5.46306 −0.185109
\(872\) −1.99619 −0.0675996
\(873\) 22.8407 0.773039
\(874\) −4.63598 −0.156814
\(875\) 0 0
\(876\) −1.77917 −0.0601126
\(877\) 5.63475 0.190272 0.0951360 0.995464i \(-0.469671\pi\)
0.0951360 + 0.995464i \(0.469671\pi\)
\(878\) −24.8150 −0.837465
\(879\) 71.2678 2.40380
\(880\) 0 0
\(881\) −40.2057 −1.35456 −0.677282 0.735723i \(-0.736842\pi\)
−0.677282 + 0.735723i \(0.736842\pi\)
\(882\) −24.9764 −0.841000
\(883\) −22.0100 −0.740697 −0.370349 0.928893i \(-0.620762\pi\)
−0.370349 + 0.928893i \(0.620762\pi\)
\(884\) 0.177741 0.00597808
\(885\) 0 0
\(886\) −1.91863 −0.0644576
\(887\) 45.8151 1.53832 0.769161 0.639055i \(-0.220674\pi\)
0.769161 + 0.639055i \(0.220674\pi\)
\(888\) −16.5940 −0.556857
\(889\) −0.427349 −0.0143328
\(890\) 0 0
\(891\) 9.57419 0.320747
\(892\) 1.42922 0.0478539
\(893\) −6.66473 −0.223027
\(894\) −16.0324 −0.536205
\(895\) 0 0
\(896\) 16.2234 0.541986
\(897\) 1.04395 0.0348564
\(898\) −11.1487 −0.372036
\(899\) −16.4060 −0.547171
\(900\) 0 0
\(901\) 61.4378 2.04679
\(902\) −7.96525 −0.265214
\(903\) −6.18634 −0.205868
\(904\) 2.19755 0.0730896
\(905\) 0 0
\(906\) −6.33672 −0.210524
\(907\) 53.4694 1.77542 0.887712 0.460399i \(-0.152294\pi\)
0.887712 + 0.460399i \(0.152294\pi\)
\(908\) 1.35392 0.0449313
\(909\) 40.3267 1.33755
\(910\) 0 0
\(911\) −16.0764 −0.532634 −0.266317 0.963886i \(-0.585807\pi\)
−0.266317 + 0.963886i \(0.585807\pi\)
\(912\) −45.7770 −1.51583
\(913\) −14.3058 −0.473452
\(914\) 8.00778 0.264874
\(915\) 0 0
\(916\) 1.05731 0.0349346
\(917\) −13.5616 −0.447844
\(918\) −16.9608 −0.559790
\(919\) −31.6187 −1.04301 −0.521503 0.853250i \(-0.674628\pi\)
−0.521503 + 0.853250i \(0.674628\pi\)
\(920\) 0 0
\(921\) 4.54093 0.149629
\(922\) −14.2819 −0.470350
\(923\) 5.10690 0.168096
\(924\) −0.318930 −0.0104920
\(925\) 0 0
\(926\) −50.3724 −1.65534
\(927\) −25.6283 −0.841744
\(928\) 1.06297 0.0348937
\(929\) 7.78861 0.255536 0.127768 0.991804i \(-0.459219\pi\)
0.127768 + 0.991804i \(0.459219\pi\)
\(930\) 0 0
\(931\) 21.5491 0.706242
\(932\) −0.117808 −0.00385894
\(933\) −8.54182 −0.279647
\(934\) 24.6216 0.805643
\(935\) 0 0
\(936\) 5.88751 0.192439
\(937\) −14.6575 −0.478838 −0.239419 0.970916i \(-0.576957\pi\)
−0.239419 + 0.970916i \(0.576957\pi\)
\(938\) 20.8496 0.680764
\(939\) −64.8914 −2.11765
\(940\) 0 0
\(941\) −24.3781 −0.794703 −0.397352 0.917666i \(-0.630071\pi\)
−0.397352 + 0.917666i \(0.630071\pi\)
\(942\) 17.8429 0.581351
\(943\) 2.69261 0.0876835
\(944\) −30.7892 −1.00210
\(945\) 0 0
\(946\) −3.45559 −0.112351
\(947\) 18.4596 0.599857 0.299928 0.953962i \(-0.403037\pi\)
0.299928 + 0.953962i \(0.403037\pi\)
\(948\) −1.77379 −0.0576101
\(949\) 7.10342 0.230587
\(950\) 0 0
\(951\) 36.3181 1.17769
\(952\) −26.4248 −0.856431
\(953\) −28.1238 −0.911020 −0.455510 0.890231i \(-0.650543\pi\)
−0.455510 + 0.890231i \(0.650543\pi\)
\(954\) 52.2418 1.69139
\(955\) 0 0
\(956\) −0.370277 −0.0119756
\(957\) 14.4331 0.466557
\(958\) −39.9557 −1.29091
\(959\) 10.9681 0.354178
\(960\) 0 0
\(961\) −9.84511 −0.317584
\(962\) 1.70074 0.0548341
\(963\) −41.3871 −1.33368
\(964\) 0.0526942 0.00169717
\(965\) 0 0
\(966\) −3.98420 −0.128189
\(967\) −6.01949 −0.193574 −0.0967869 0.995305i \(-0.530857\pi\)
−0.0967869 + 0.995305i \(0.530857\pi\)
\(968\) 24.5692 0.789684
\(969\) 72.5428 2.33041
\(970\) 0 0
\(971\) −27.4218 −0.880008 −0.440004 0.897996i \(-0.645023\pi\)
−0.440004 + 0.897996i \(0.645023\pi\)
\(972\) −1.15415 −0.0370192
\(973\) −24.6189 −0.789246
\(974\) −20.9625 −0.671682
\(975\) 0 0
\(976\) 21.3951 0.684841
\(977\) −14.9584 −0.478561 −0.239280 0.970951i \(-0.576911\pi\)
−0.239280 + 0.970951i \(0.576911\pi\)
\(978\) −14.1085 −0.451139
\(979\) −11.3395 −0.362413
\(980\) 0 0
\(981\) 2.61895 0.0836166
\(982\) −23.8481 −0.761024
\(983\) −20.0229 −0.638631 −0.319316 0.947648i \(-0.603453\pi\)
−0.319316 + 0.947648i \(0.603453\pi\)
\(984\) 27.3076 0.870535
\(985\) 0 0
\(986\) 30.6984 0.977635
\(987\) −5.72772 −0.182315
\(988\) −0.130397 −0.00414849
\(989\) 1.16814 0.0371448
\(990\) 0 0
\(991\) −32.9116 −1.04547 −0.522736 0.852495i \(-0.675089\pi\)
−0.522736 + 0.852495i \(0.675089\pi\)
\(992\) −1.37066 −0.0435184
\(993\) 43.4956 1.38029
\(994\) −19.4903 −0.618195
\(995\) 0 0
\(996\) 1.25902 0.0398937
\(997\) 27.1461 0.859726 0.429863 0.902894i \(-0.358562\pi\)
0.429863 + 0.902894i \(0.358562\pi\)
\(998\) 25.5643 0.809225
\(999\) 4.39163 0.138945
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.1.12 15
5.4 even 2 1205.2.a.c.1.4 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.a.c.1.4 15 5.4 even 2
6025.2.a.i.1.12 15 1.1 even 1 trivial