Properties

Label 4025.2.a.ba.1.11
Level $4025$
Weight $2$
Character 4025.1
Self dual yes
Analytic conductor $32.140$
Analytic rank $1$
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: \(1\)
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: \( x^{14} - x^{13} - 22 x^{12} + 18 x^{11} + 187 x^{10} - 118 x^{9} - 772 x^{8} + 346 x^{7} + 1581 x^{6} - 443 x^{5} - 1429 x^{4} + 193 x^{3} + 386 x^{2} - 3 x - 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-1.76659\) 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)
 
\(f(q)\) \(=\) \(q+1.76659 q^{2} +0.991358 q^{3} +1.12083 q^{4} +1.75132 q^{6} -1.00000 q^{7} -1.55314 q^{8} -2.01721 q^{9} +O(q^{10})\) \(q+1.76659 q^{2} +0.991358 q^{3} +1.12083 q^{4} +1.75132 q^{6} -1.00000 q^{7} -1.55314 q^{8} -2.01721 q^{9} +3.44676 q^{11} +1.11114 q^{12} +1.76768 q^{13} -1.76659 q^{14} -4.98540 q^{16} -3.70284 q^{17} -3.56357 q^{18} -8.16438 q^{19} -0.991358 q^{21} +6.08900 q^{22} +1.00000 q^{23} -1.53971 q^{24} +3.12276 q^{26} -4.97385 q^{27} -1.12083 q^{28} +1.63532 q^{29} -6.49337 q^{31} -5.70087 q^{32} +3.41697 q^{33} -6.54138 q^{34} -2.26094 q^{36} -1.57716 q^{37} -14.4231 q^{38} +1.75240 q^{39} +5.67517 q^{41} -1.75132 q^{42} -12.0844 q^{43} +3.86322 q^{44} +1.76659 q^{46} -8.58989 q^{47} -4.94232 q^{48} +1.00000 q^{49} -3.67084 q^{51} +1.98126 q^{52} +11.1369 q^{53} -8.78674 q^{54} +1.55314 q^{56} -8.09382 q^{57} +2.88894 q^{58} -0.498851 q^{59} +4.17193 q^{61} -11.4711 q^{62} +2.01721 q^{63} -0.100276 q^{64} +6.03638 q^{66} -0.0800684 q^{67} -4.15024 q^{68} +0.991358 q^{69} -9.21407 q^{71} +3.13300 q^{72} +16.3786 q^{73} -2.78619 q^{74} -9.15085 q^{76} -3.44676 q^{77} +3.09577 q^{78} -4.09934 q^{79} +1.12076 q^{81} +10.0257 q^{82} -14.8510 q^{83} -1.11114 q^{84} -21.3481 q^{86} +1.62119 q^{87} -5.35328 q^{88} -7.81583 q^{89} -1.76768 q^{91} +1.12083 q^{92} -6.43726 q^{93} -15.1748 q^{94} -5.65160 q^{96} +4.40745 q^{97} +1.76659 q^{98} -6.95283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9} - 3 q^{11} - 11 q^{12} - 15 q^{13} + q^{14} + 23 q^{16} - 9 q^{17} - 17 q^{18} - 4 q^{19} + 6 q^{21} - 9 q^{22} + 14 q^{23} + 10 q^{24} - 5 q^{26} - 33 q^{27} - 17 q^{28} + 11 q^{29} - q^{31} - 24 q^{32} - 26 q^{33} - 6 q^{34} + 13 q^{36} - 18 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{41} + 4 q^{42} - 18 q^{43} - 16 q^{44} - q^{46} - 10 q^{47} - 40 q^{48} + 14 q^{49} + 28 q^{51} - 46 q^{52} - 5 q^{53} - 24 q^{54} + 9 q^{56} + 26 q^{57} - 2 q^{58} - 24 q^{59} - 6 q^{61} + 16 q^{62} - 18 q^{63} + 29 q^{64} + 27 q^{66} - 61 q^{67} - 35 q^{68} - 6 q^{69} + 11 q^{71} - 12 q^{72} - 28 q^{73} - 49 q^{74} - 27 q^{76} + 3 q^{77} - 38 q^{78} + 6 q^{79} + 26 q^{81} + 14 q^{82} - 16 q^{83} + 11 q^{84} + 46 q^{86} - 61 q^{87} - 58 q^{88} - 39 q^{89} + 15 q^{91} + 17 q^{92} - 21 q^{93} - 74 q^{94} + 41 q^{96} - 19 q^{97} - q^{98} - 9 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.76659 1.24917 0.624583 0.780959i \(-0.285269\pi\)
0.624583 + 0.780959i \(0.285269\pi\)
\(3\) 0.991358 0.572361 0.286180 0.958176i \(-0.407614\pi\)
0.286180 + 0.958176i \(0.407614\pi\)
\(4\) 1.12083 0.560413
\(5\) 0 0
\(6\) 1.75132 0.714973
\(7\) −1.00000 −0.377964
\(8\) −1.55314 −0.549116
\(9\) −2.01721 −0.672403
\(10\) 0 0
\(11\) 3.44676 1.03924 0.519619 0.854398i \(-0.326074\pi\)
0.519619 + 0.854398i \(0.326074\pi\)
\(12\) 1.11114 0.320759
\(13\) 1.76768 0.490266 0.245133 0.969489i \(-0.421168\pi\)
0.245133 + 0.969489i \(0.421168\pi\)
\(14\) −1.76659 −0.472140
\(15\) 0 0
\(16\) −4.98540 −1.24635
\(17\) −3.70284 −0.898070 −0.449035 0.893514i \(-0.648232\pi\)
−0.449035 + 0.893514i \(0.648232\pi\)
\(18\) −3.56357 −0.839942
\(19\) −8.16438 −1.87304 −0.936519 0.350618i \(-0.885972\pi\)
−0.936519 + 0.350618i \(0.885972\pi\)
\(20\) 0 0
\(21\) −0.991358 −0.216332
\(22\) 6.08900 1.29818
\(23\) 1.00000 0.208514
\(24\) −1.53971 −0.314293
\(25\) 0 0
\(26\) 3.12276 0.612423
\(27\) −4.97385 −0.957218
\(28\) −1.12083 −0.211816
\(29\) 1.63532 0.303672 0.151836 0.988406i \(-0.451481\pi\)
0.151836 + 0.988406i \(0.451481\pi\)
\(30\) 0 0
\(31\) −6.49337 −1.16624 −0.583122 0.812384i \(-0.698169\pi\)
−0.583122 + 0.812384i \(0.698169\pi\)
\(32\) −5.70087 −1.00778
\(33\) 3.41697 0.594819
\(34\) −6.54138 −1.12184
\(35\) 0 0
\(36\) −2.26094 −0.376824
\(37\) −1.57716 −0.259284 −0.129642 0.991561i \(-0.541383\pi\)
−0.129642 + 0.991561i \(0.541383\pi\)
\(38\) −14.4231 −2.33973
\(39\) 1.75240 0.280609
\(40\) 0 0
\(41\) 5.67517 0.886312 0.443156 0.896444i \(-0.353859\pi\)
0.443156 + 0.896444i \(0.353859\pi\)
\(42\) −1.75132 −0.270234
\(43\) −12.0844 −1.84285 −0.921427 0.388552i \(-0.872975\pi\)
−0.921427 + 0.388552i \(0.872975\pi\)
\(44\) 3.86322 0.582402
\(45\) 0 0
\(46\) 1.76659 0.260469
\(47\) −8.58989 −1.25296 −0.626482 0.779436i \(-0.715506\pi\)
−0.626482 + 0.779436i \(0.715506\pi\)
\(48\) −4.94232 −0.713362
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −3.67084 −0.514020
\(52\) 1.98126 0.274752
\(53\) 11.1369 1.52977 0.764884 0.644168i \(-0.222796\pi\)
0.764884 + 0.644168i \(0.222796\pi\)
\(54\) −8.78674 −1.19572
\(55\) 0 0
\(56\) 1.55314 0.207546
\(57\) −8.09382 −1.07205
\(58\) 2.88894 0.379337
\(59\) −0.498851 −0.0649448 −0.0324724 0.999473i \(-0.510338\pi\)
−0.0324724 + 0.999473i \(0.510338\pi\)
\(60\) 0 0
\(61\) 4.17193 0.534161 0.267080 0.963674i \(-0.413941\pi\)
0.267080 + 0.963674i \(0.413941\pi\)
\(62\) −11.4711 −1.45683
\(63\) 2.01721 0.254144
\(64\) −0.100276 −0.0125345
\(65\) 0 0
\(66\) 6.03638 0.743027
\(67\) −0.0800684 −0.00978191 −0.00489096 0.999988i \(-0.501557\pi\)
−0.00489096 + 0.999988i \(0.501557\pi\)
\(68\) −4.15024 −0.503291
\(69\) 0.991358 0.119345
\(70\) 0 0
\(71\) −9.21407 −1.09351 −0.546754 0.837293i \(-0.684137\pi\)
−0.546754 + 0.837293i \(0.684137\pi\)
\(72\) 3.13300 0.369227
\(73\) 16.3786 1.91697 0.958486 0.285139i \(-0.0920398\pi\)
0.958486 + 0.285139i \(0.0920398\pi\)
\(74\) −2.78619 −0.323888
\(75\) 0 0
\(76\) −9.15085 −1.04968
\(77\) −3.44676 −0.392795
\(78\) 3.09577 0.350527
\(79\) −4.09934 −0.461212 −0.230606 0.973047i \(-0.574071\pi\)
−0.230606 + 0.973047i \(0.574071\pi\)
\(80\) 0 0
\(81\) 1.12076 0.124529
\(82\) 10.0257 1.10715
\(83\) −14.8510 −1.63011 −0.815055 0.579383i \(-0.803293\pi\)
−0.815055 + 0.579383i \(0.803293\pi\)
\(84\) −1.11114 −0.121235
\(85\) 0 0
\(86\) −21.3481 −2.30203
\(87\) 1.62119 0.173810
\(88\) −5.35328 −0.570662
\(89\) −7.81583 −0.828476 −0.414238 0.910169i \(-0.635952\pi\)
−0.414238 + 0.910169i \(0.635952\pi\)
\(90\) 0 0
\(91\) −1.76768 −0.185303
\(92\) 1.12083 0.116854
\(93\) −6.43726 −0.667513
\(94\) −15.1748 −1.56516
\(95\) 0 0
\(96\) −5.65160 −0.576814
\(97\) 4.40745 0.447509 0.223754 0.974646i \(-0.428169\pi\)
0.223754 + 0.974646i \(0.428169\pi\)
\(98\) 1.76659 0.178452
\(99\) −6.95283 −0.698786
\(100\) 0 0
\(101\) −0.153094 −0.0152334 −0.00761671 0.999971i \(-0.502424\pi\)
−0.00761671 + 0.999971i \(0.502424\pi\)
\(102\) −6.48485 −0.642096
\(103\) 9.09068 0.895732 0.447866 0.894101i \(-0.352184\pi\)
0.447866 + 0.894101i \(0.352184\pi\)
\(104\) −2.74545 −0.269213
\(105\) 0 0
\(106\) 19.6743 1.91093
\(107\) −3.62325 −0.350272 −0.175136 0.984544i \(-0.556037\pi\)
−0.175136 + 0.984544i \(0.556037\pi\)
\(108\) −5.57483 −0.536438
\(109\) 16.3042 1.56166 0.780828 0.624746i \(-0.214798\pi\)
0.780828 + 0.624746i \(0.214798\pi\)
\(110\) 0 0
\(111\) −1.56353 −0.148404
\(112\) 4.98540 0.471076
\(113\) −8.05224 −0.757491 −0.378746 0.925501i \(-0.623644\pi\)
−0.378746 + 0.925501i \(0.623644\pi\)
\(114\) −14.2984 −1.33917
\(115\) 0 0
\(116\) 1.83292 0.170182
\(117\) −3.56578 −0.329656
\(118\) −0.881263 −0.0811268
\(119\) 3.70284 0.339439
\(120\) 0 0
\(121\) 0.880150 0.0800137
\(122\) 7.37007 0.667255
\(123\) 5.62612 0.507291
\(124\) −7.27795 −0.653579
\(125\) 0 0
\(126\) 3.56357 0.317468
\(127\) −9.41174 −0.835157 −0.417578 0.908641i \(-0.637121\pi\)
−0.417578 + 0.908641i \(0.637121\pi\)
\(128\) 11.2246 0.992123
\(129\) −11.9800 −1.05478
\(130\) 0 0
\(131\) −14.8642 −1.29869 −0.649345 0.760494i \(-0.724957\pi\)
−0.649345 + 0.760494i \(0.724957\pi\)
\(132\) 3.82983 0.333344
\(133\) 8.16438 0.707941
\(134\) −0.141448 −0.0122192
\(135\) 0 0
\(136\) 5.75101 0.493145
\(137\) −9.55643 −0.816461 −0.408231 0.912879i \(-0.633854\pi\)
−0.408231 + 0.912879i \(0.633854\pi\)
\(138\) 1.75132 0.149082
\(139\) −4.27083 −0.362247 −0.181124 0.983460i \(-0.557973\pi\)
−0.181124 + 0.983460i \(0.557973\pi\)
\(140\) 0 0
\(141\) −8.51566 −0.717148
\(142\) −16.2774 −1.36597
\(143\) 6.09277 0.509503
\(144\) 10.0566 0.838050
\(145\) 0 0
\(146\) 28.9342 2.39461
\(147\) 0.991358 0.0817658
\(148\) −1.76772 −0.145306
\(149\) −8.75790 −0.717475 −0.358738 0.933438i \(-0.616793\pi\)
−0.358738 + 0.933438i \(0.616793\pi\)
\(150\) 0 0
\(151\) 13.8015 1.12315 0.561575 0.827426i \(-0.310196\pi\)
0.561575 + 0.827426i \(0.310196\pi\)
\(152\) 12.6804 1.02852
\(153\) 7.46940 0.603865
\(154\) −6.08900 −0.490665
\(155\) 0 0
\(156\) 1.96414 0.157257
\(157\) −0.268103 −0.0213969 −0.0106985 0.999943i \(-0.503405\pi\)
−0.0106985 + 0.999943i \(0.503405\pi\)
\(158\) −7.24183 −0.576129
\(159\) 11.0406 0.875579
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 1.97992 0.155557
\(163\) 11.9784 0.938218 0.469109 0.883140i \(-0.344575\pi\)
0.469109 + 0.883140i \(0.344575\pi\)
\(164\) 6.36088 0.496701
\(165\) 0 0
\(166\) −26.2356 −2.03628
\(167\) 4.20255 0.325203 0.162602 0.986692i \(-0.448011\pi\)
0.162602 + 0.986692i \(0.448011\pi\)
\(168\) 1.53971 0.118791
\(169\) −9.87531 −0.759639
\(170\) 0 0
\(171\) 16.4693 1.25944
\(172\) −13.5445 −1.03276
\(173\) −19.1127 −1.45311 −0.726556 0.687107i \(-0.758880\pi\)
−0.726556 + 0.687107i \(0.758880\pi\)
\(174\) 2.86398 0.217117
\(175\) 0 0
\(176\) −17.1835 −1.29525
\(177\) −0.494540 −0.0371719
\(178\) −13.8073 −1.03490
\(179\) −4.53066 −0.338638 −0.169319 0.985561i \(-0.554157\pi\)
−0.169319 + 0.985561i \(0.554157\pi\)
\(180\) 0 0
\(181\) 16.3314 1.21390 0.606952 0.794739i \(-0.292392\pi\)
0.606952 + 0.794739i \(0.292392\pi\)
\(182\) −3.12276 −0.231474
\(183\) 4.13587 0.305733
\(184\) −1.55314 −0.114499
\(185\) 0 0
\(186\) −11.3720 −0.833833
\(187\) −12.7628 −0.933308
\(188\) −9.62778 −0.702178
\(189\) 4.97385 0.361794
\(190\) 0 0
\(191\) 4.74923 0.343642 0.171821 0.985128i \(-0.445035\pi\)
0.171821 + 0.985128i \(0.445035\pi\)
\(192\) −0.0994097 −0.00717428
\(193\) −26.8798 −1.93485 −0.967423 0.253164i \(-0.918529\pi\)
−0.967423 + 0.253164i \(0.918529\pi\)
\(194\) 7.78614 0.559012
\(195\) 0 0
\(196\) 1.12083 0.0800591
\(197\) 25.7687 1.83594 0.917972 0.396646i \(-0.129826\pi\)
0.917972 + 0.396646i \(0.129826\pi\)
\(198\) −12.2828 −0.872899
\(199\) −24.5630 −1.74123 −0.870614 0.491968i \(-0.836278\pi\)
−0.870614 + 0.491968i \(0.836278\pi\)
\(200\) 0 0
\(201\) −0.0793764 −0.00559878
\(202\) −0.270454 −0.0190290
\(203\) −1.63532 −0.114777
\(204\) −4.11437 −0.288064
\(205\) 0 0
\(206\) 16.0595 1.11892
\(207\) −2.01721 −0.140206
\(208\) −8.81259 −0.611043
\(209\) −28.1407 −1.94653
\(210\) 0 0
\(211\) 18.6762 1.28573 0.642863 0.765981i \(-0.277747\pi\)
0.642863 + 0.765981i \(0.277747\pi\)
\(212\) 12.4825 0.857303
\(213\) −9.13444 −0.625882
\(214\) −6.40078 −0.437548
\(215\) 0 0
\(216\) 7.72506 0.525624
\(217\) 6.49337 0.440799
\(218\) 28.8027 1.95077
\(219\) 16.2371 1.09720
\(220\) 0 0
\(221\) −6.54543 −0.440293
\(222\) −2.76211 −0.185381
\(223\) −5.74937 −0.385006 −0.192503 0.981296i \(-0.561661\pi\)
−0.192503 + 0.981296i \(0.561661\pi\)
\(224\) 5.70087 0.380905
\(225\) 0 0
\(226\) −14.2250 −0.946232
\(227\) 4.73284 0.314130 0.157065 0.987588i \(-0.449797\pi\)
0.157065 + 0.987588i \(0.449797\pi\)
\(228\) −9.07177 −0.600793
\(229\) 11.2504 0.743445 0.371723 0.928344i \(-0.378767\pi\)
0.371723 + 0.928344i \(0.378767\pi\)
\(230\) 0 0
\(231\) −3.41697 −0.224820
\(232\) −2.53988 −0.166751
\(233\) −12.6822 −0.830839 −0.415419 0.909630i \(-0.636365\pi\)
−0.415419 + 0.909630i \(0.636365\pi\)
\(234\) −6.29926 −0.411795
\(235\) 0 0
\(236\) −0.559125 −0.0363960
\(237\) −4.06391 −0.263979
\(238\) 6.54138 0.424015
\(239\) 8.19034 0.529789 0.264895 0.964277i \(-0.414663\pi\)
0.264895 + 0.964277i \(0.414663\pi\)
\(240\) 0 0
\(241\) 3.26668 0.210425 0.105213 0.994450i \(-0.466448\pi\)
0.105213 + 0.994450i \(0.466448\pi\)
\(242\) 1.55486 0.0999503
\(243\) 16.0326 1.02849
\(244\) 4.67601 0.299351
\(245\) 0 0
\(246\) 9.93903 0.633690
\(247\) −14.4320 −0.918287
\(248\) 10.0851 0.640404
\(249\) −14.7227 −0.933011
\(250\) 0 0
\(251\) −8.14200 −0.513918 −0.256959 0.966422i \(-0.582721\pi\)
−0.256959 + 0.966422i \(0.582721\pi\)
\(252\) 2.26094 0.142426
\(253\) 3.44676 0.216696
\(254\) −16.6266 −1.04325
\(255\) 0 0
\(256\) 20.0298 1.25186
\(257\) −6.24425 −0.389506 −0.194753 0.980852i \(-0.562390\pi\)
−0.194753 + 0.980852i \(0.562390\pi\)
\(258\) −21.1636 −1.31759
\(259\) 1.57716 0.0980000
\(260\) 0 0
\(261\) −3.29879 −0.204190
\(262\) −26.2589 −1.62228
\(263\) 2.46177 0.151799 0.0758997 0.997115i \(-0.475817\pi\)
0.0758997 + 0.997115i \(0.475817\pi\)
\(264\) −5.30702 −0.326625
\(265\) 0 0
\(266\) 14.4231 0.884336
\(267\) −7.74828 −0.474187
\(268\) −0.0897428 −0.00548191
\(269\) 6.46545 0.394205 0.197103 0.980383i \(-0.436847\pi\)
0.197103 + 0.980383i \(0.436847\pi\)
\(270\) 0 0
\(271\) 24.9101 1.51318 0.756589 0.653891i \(-0.226864\pi\)
0.756589 + 0.653891i \(0.226864\pi\)
\(272\) 18.4601 1.11931
\(273\) −1.75240 −0.106060
\(274\) −16.8823 −1.01989
\(275\) 0 0
\(276\) 1.11114 0.0668828
\(277\) −27.1737 −1.63271 −0.816355 0.577551i \(-0.804009\pi\)
−0.816355 + 0.577551i \(0.804009\pi\)
\(278\) −7.54479 −0.452506
\(279\) 13.0985 0.784186
\(280\) 0 0
\(281\) 16.2788 0.971112 0.485556 0.874206i \(-0.338617\pi\)
0.485556 + 0.874206i \(0.338617\pi\)
\(282\) −15.0436 −0.895836
\(283\) −18.1155 −1.07685 −0.538427 0.842672i \(-0.680981\pi\)
−0.538427 + 0.842672i \(0.680981\pi\)
\(284\) −10.3274 −0.612817
\(285\) 0 0
\(286\) 10.7634 0.636453
\(287\) −5.67517 −0.334995
\(288\) 11.4998 0.677635
\(289\) −3.28899 −0.193470
\(290\) 0 0
\(291\) 4.36936 0.256136
\(292\) 18.3576 1.07430
\(293\) −20.7733 −1.21359 −0.606796 0.794858i \(-0.707545\pi\)
−0.606796 + 0.794858i \(0.707545\pi\)
\(294\) 1.75132 0.102139
\(295\) 0 0
\(296\) 2.44954 0.142377
\(297\) −17.1437 −0.994776
\(298\) −15.4716 −0.896245
\(299\) 1.76768 0.102228
\(300\) 0 0
\(301\) 12.0844 0.696533
\(302\) 24.3815 1.40300
\(303\) −0.151771 −0.00871901
\(304\) 40.7027 2.33446
\(305\) 0 0
\(306\) 13.1953 0.754327
\(307\) 5.15026 0.293941 0.146970 0.989141i \(-0.453048\pi\)
0.146970 + 0.989141i \(0.453048\pi\)
\(308\) −3.86322 −0.220127
\(309\) 9.01212 0.512682
\(310\) 0 0
\(311\) 13.1433 0.745287 0.372643 0.927975i \(-0.378451\pi\)
0.372643 + 0.927975i \(0.378451\pi\)
\(312\) −2.72172 −0.154087
\(313\) 31.3762 1.77349 0.886744 0.462261i \(-0.152962\pi\)
0.886744 + 0.462261i \(0.152962\pi\)
\(314\) −0.473626 −0.0267283
\(315\) 0 0
\(316\) −4.59465 −0.258469
\(317\) 9.97763 0.560399 0.280200 0.959942i \(-0.409599\pi\)
0.280200 + 0.959942i \(0.409599\pi\)
\(318\) 19.5042 1.09374
\(319\) 5.63657 0.315587
\(320\) 0 0
\(321\) −3.59193 −0.200482
\(322\) −1.76659 −0.0984480
\(323\) 30.2314 1.68212
\(324\) 1.25618 0.0697877
\(325\) 0 0
\(326\) 21.1608 1.17199
\(327\) 16.1633 0.893830
\(328\) −8.81431 −0.486689
\(329\) 8.58989 0.473576
\(330\) 0 0
\(331\) 30.3591 1.66869 0.834344 0.551245i \(-0.185847\pi\)
0.834344 + 0.551245i \(0.185847\pi\)
\(332\) −16.6454 −0.913536
\(333\) 3.18146 0.174343
\(334\) 7.42417 0.406232
\(335\) 0 0
\(336\) 4.94232 0.269626
\(337\) 32.0709 1.74701 0.873506 0.486814i \(-0.161841\pi\)
0.873506 + 0.486814i \(0.161841\pi\)
\(338\) −17.4456 −0.948915
\(339\) −7.98265 −0.433558
\(340\) 0 0
\(341\) −22.3811 −1.21200
\(342\) 29.0944 1.57324
\(343\) −1.00000 −0.0539949
\(344\) 18.7687 1.01194
\(345\) 0 0
\(346\) −33.7642 −1.81518
\(347\) 17.5315 0.941141 0.470571 0.882362i \(-0.344048\pi\)
0.470571 + 0.882362i \(0.344048\pi\)
\(348\) 1.81708 0.0974055
\(349\) −14.7333 −0.788657 −0.394329 0.918970i \(-0.629023\pi\)
−0.394329 + 0.918970i \(0.629023\pi\)
\(350\) 0 0
\(351\) −8.79218 −0.469292
\(352\) −19.6495 −1.04732
\(353\) 11.2457 0.598546 0.299273 0.954167i \(-0.403256\pi\)
0.299273 + 0.954167i \(0.403256\pi\)
\(354\) −0.873647 −0.0464338
\(355\) 0 0
\(356\) −8.76019 −0.464289
\(357\) 3.67084 0.194281
\(358\) −8.00380 −0.423014
\(359\) 29.1214 1.53697 0.768485 0.639868i \(-0.221011\pi\)
0.768485 + 0.639868i \(0.221011\pi\)
\(360\) 0 0
\(361\) 47.6571 2.50827
\(362\) 28.8508 1.51637
\(363\) 0.872544 0.0457967
\(364\) −1.98126 −0.103846
\(365\) 0 0
\(366\) 7.30638 0.381910
\(367\) −26.7214 −1.39484 −0.697422 0.716660i \(-0.745670\pi\)
−0.697422 + 0.716660i \(0.745670\pi\)
\(368\) −4.98540 −0.259882
\(369\) −11.4480 −0.595959
\(370\) 0 0
\(371\) −11.1369 −0.578198
\(372\) −7.21505 −0.374083
\(373\) 10.2153 0.528930 0.264465 0.964395i \(-0.414805\pi\)
0.264465 + 0.964395i \(0.414805\pi\)
\(374\) −22.5466 −1.16586
\(375\) 0 0
\(376\) 13.3413 0.688023
\(377\) 2.89073 0.148880
\(378\) 8.78674 0.451941
\(379\) 27.7864 1.42729 0.713646 0.700506i \(-0.247042\pi\)
0.713646 + 0.700506i \(0.247042\pi\)
\(380\) 0 0
\(381\) −9.33040 −0.478011
\(382\) 8.38992 0.429266
\(383\) −10.8751 −0.555692 −0.277846 0.960626i \(-0.589620\pi\)
−0.277846 + 0.960626i \(0.589620\pi\)
\(384\) 11.1276 0.567852
\(385\) 0 0
\(386\) −47.4854 −2.41694
\(387\) 24.3768 1.23914
\(388\) 4.93999 0.250790
\(389\) 31.8089 1.61277 0.806387 0.591388i \(-0.201420\pi\)
0.806387 + 0.591388i \(0.201420\pi\)
\(390\) 0 0
\(391\) −3.70284 −0.187261
\(392\) −1.55314 −0.0784452
\(393\) −14.7357 −0.743320
\(394\) 45.5226 2.29340
\(395\) 0 0
\(396\) −7.79292 −0.391609
\(397\) −4.64600 −0.233176 −0.116588 0.993180i \(-0.537196\pi\)
−0.116588 + 0.993180i \(0.537196\pi\)
\(398\) −43.3927 −2.17508
\(399\) 8.09382 0.405198
\(400\) 0 0
\(401\) −0.00993722 −0.000496241 0 −0.000248120 1.00000i \(-0.500079\pi\)
−0.000248120 1.00000i \(0.500079\pi\)
\(402\) −0.140225 −0.00699380
\(403\) −11.4782 −0.571770
\(404\) −0.171592 −0.00853701
\(405\) 0 0
\(406\) −2.88894 −0.143376
\(407\) −5.43609 −0.269457
\(408\) 5.70131 0.282257
\(409\) 28.9009 1.42906 0.714529 0.699606i \(-0.246641\pi\)
0.714529 + 0.699606i \(0.246641\pi\)
\(410\) 0 0
\(411\) −9.47385 −0.467310
\(412\) 10.1891 0.501980
\(413\) 0.498851 0.0245468
\(414\) −3.56357 −0.175140
\(415\) 0 0
\(416\) −10.0773 −0.494081
\(417\) −4.23392 −0.207336
\(418\) −49.7129 −2.43154
\(419\) −34.8023 −1.70020 −0.850101 0.526620i \(-0.823459\pi\)
−0.850101 + 0.526620i \(0.823459\pi\)
\(420\) 0 0
\(421\) −26.9555 −1.31373 −0.656865 0.754008i \(-0.728118\pi\)
−0.656865 + 0.754008i \(0.728118\pi\)
\(422\) 32.9932 1.60608
\(423\) 17.3276 0.842497
\(424\) −17.2971 −0.840020
\(425\) 0 0
\(426\) −16.1368 −0.781830
\(427\) −4.17193 −0.201894
\(428\) −4.06103 −0.196297
\(429\) 6.04011 0.291619
\(430\) 0 0
\(431\) 10.9939 0.529557 0.264779 0.964309i \(-0.414701\pi\)
0.264779 + 0.964309i \(0.414701\pi\)
\(432\) 24.7966 1.19303
\(433\) −36.7288 −1.76508 −0.882538 0.470241i \(-0.844167\pi\)
−0.882538 + 0.470241i \(0.844167\pi\)
\(434\) 11.4711 0.550631
\(435\) 0 0
\(436\) 18.2741 0.875173
\(437\) −8.16438 −0.390555
\(438\) 28.6842 1.37058
\(439\) 17.8485 0.851865 0.425932 0.904755i \(-0.359946\pi\)
0.425932 + 0.904755i \(0.359946\pi\)
\(440\) 0 0
\(441\) −2.01721 −0.0960576
\(442\) −11.5631 −0.549999
\(443\) 14.5466 0.691128 0.345564 0.938395i \(-0.387688\pi\)
0.345564 + 0.938395i \(0.387688\pi\)
\(444\) −1.75245 −0.0831674
\(445\) 0 0
\(446\) −10.1568 −0.480936
\(447\) −8.68221 −0.410655
\(448\) 0.100276 0.00473761
\(449\) 2.58177 0.121841 0.0609207 0.998143i \(-0.480596\pi\)
0.0609207 + 0.998143i \(0.480596\pi\)
\(450\) 0 0
\(451\) 19.5609 0.921089
\(452\) −9.02517 −0.424508
\(453\) 13.6822 0.642847
\(454\) 8.36098 0.392400
\(455\) 0 0
\(456\) 12.5708 0.588682
\(457\) −36.1923 −1.69300 −0.846502 0.532385i \(-0.821296\pi\)
−0.846502 + 0.532385i \(0.821296\pi\)
\(458\) 19.8747 0.928686
\(459\) 18.4174 0.859649
\(460\) 0 0
\(461\) 3.30197 0.153788 0.0768939 0.997039i \(-0.475500\pi\)
0.0768939 + 0.997039i \(0.475500\pi\)
\(462\) −6.03638 −0.280838
\(463\) −28.8596 −1.34122 −0.670610 0.741810i \(-0.733968\pi\)
−0.670610 + 0.741810i \(0.733968\pi\)
\(464\) −8.15275 −0.378482
\(465\) 0 0
\(466\) −22.4042 −1.03785
\(467\) −38.2124 −1.76826 −0.884130 0.467240i \(-0.845248\pi\)
−0.884130 + 0.467240i \(0.845248\pi\)
\(468\) −3.99662 −0.184744
\(469\) 0.0800684 0.00369721
\(470\) 0 0
\(471\) −0.265786 −0.0122468
\(472\) 0.774783 0.0356623
\(473\) −41.6520 −1.91516
\(474\) −7.17925 −0.329754
\(475\) 0 0
\(476\) 4.15024 0.190226
\(477\) −22.4654 −1.02862
\(478\) 14.4689 0.661794
\(479\) −4.22746 −0.193158 −0.0965788 0.995325i \(-0.530790\pi\)
−0.0965788 + 0.995325i \(0.530790\pi\)
\(480\) 0 0
\(481\) −2.78791 −0.127118
\(482\) 5.77086 0.262856
\(483\) −0.991358 −0.0451084
\(484\) 0.986496 0.0448407
\(485\) 0 0
\(486\) 28.3230 1.28476
\(487\) −29.1490 −1.32087 −0.660433 0.750885i \(-0.729627\pi\)
−0.660433 + 0.750885i \(0.729627\pi\)
\(488\) −6.47957 −0.293316
\(489\) 11.8748 0.536999
\(490\) 0 0
\(491\) −5.13897 −0.231918 −0.115959 0.993254i \(-0.536994\pi\)
−0.115959 + 0.993254i \(0.536994\pi\)
\(492\) 6.30591 0.284292
\(493\) −6.05534 −0.272719
\(494\) −25.4954 −1.14709
\(495\) 0 0
\(496\) 32.3721 1.45355
\(497\) 9.21407 0.413308
\(498\) −26.0089 −1.16549
\(499\) 15.8487 0.709483 0.354742 0.934964i \(-0.384569\pi\)
0.354742 + 0.934964i \(0.384569\pi\)
\(500\) 0 0
\(501\) 4.16623 0.186133
\(502\) −14.3835 −0.641969
\(503\) −20.9422 −0.933766 −0.466883 0.884319i \(-0.654623\pi\)
−0.466883 + 0.884319i \(0.654623\pi\)
\(504\) −3.13300 −0.139555
\(505\) 0 0
\(506\) 6.08900 0.270689
\(507\) −9.78997 −0.434788
\(508\) −10.5489 −0.468033
\(509\) 22.2352 0.985558 0.492779 0.870154i \(-0.335981\pi\)
0.492779 + 0.870154i \(0.335981\pi\)
\(510\) 0 0
\(511\) −16.3786 −0.724547
\(512\) 12.9351 0.571657
\(513\) 40.6084 1.79290
\(514\) −11.0310 −0.486557
\(515\) 0 0
\(516\) −13.4275 −0.591111
\(517\) −29.6073 −1.30213
\(518\) 2.78619 0.122418
\(519\) −18.9475 −0.831704
\(520\) 0 0
\(521\) −22.9572 −1.00577 −0.502886 0.864353i \(-0.667728\pi\)
−0.502886 + 0.864353i \(0.667728\pi\)
\(522\) −5.82760 −0.255067
\(523\) −11.5417 −0.504682 −0.252341 0.967638i \(-0.581200\pi\)
−0.252341 + 0.967638i \(0.581200\pi\)
\(524\) −16.6602 −0.727804
\(525\) 0 0
\(526\) 4.34894 0.189623
\(527\) 24.0439 1.04737
\(528\) −17.0350 −0.741352
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 1.00629 0.0436691
\(532\) 9.15085 0.396740
\(533\) 10.0319 0.434529
\(534\) −13.6880 −0.592338
\(535\) 0 0
\(536\) 0.124357 0.00537141
\(537\) −4.49151 −0.193823
\(538\) 11.4218 0.492428
\(539\) 3.44676 0.148462
\(540\) 0 0
\(541\) −28.7878 −1.23768 −0.618841 0.785516i \(-0.712398\pi\)
−0.618841 + 0.785516i \(0.712398\pi\)
\(542\) 44.0058 1.89021
\(543\) 16.1903 0.694791
\(544\) 21.1094 0.905058
\(545\) 0 0
\(546\) −3.09577 −0.132487
\(547\) 24.8991 1.06461 0.532304 0.846553i \(-0.321326\pi\)
0.532304 + 0.846553i \(0.321326\pi\)
\(548\) −10.7111 −0.457556
\(549\) −8.41565 −0.359171
\(550\) 0 0
\(551\) −13.3514 −0.568789
\(552\) −1.53971 −0.0655345
\(553\) 4.09934 0.174322
\(554\) −48.0047 −2.03952
\(555\) 0 0
\(556\) −4.78686 −0.203008
\(557\) −12.5854 −0.533262 −0.266631 0.963799i \(-0.585910\pi\)
−0.266631 + 0.963799i \(0.585910\pi\)
\(558\) 23.1396 0.979578
\(559\) −21.3614 −0.903489
\(560\) 0 0
\(561\) −12.6525 −0.534189
\(562\) 28.7579 1.21308
\(563\) −16.9502 −0.714366 −0.357183 0.934034i \(-0.616263\pi\)
−0.357183 + 0.934034i \(0.616263\pi\)
\(564\) −9.54458 −0.401899
\(565\) 0 0
\(566\) −32.0025 −1.34517
\(567\) −1.12076 −0.0470675
\(568\) 14.3107 0.600464
\(569\) 17.9630 0.753049 0.376525 0.926407i \(-0.377119\pi\)
0.376525 + 0.926407i \(0.377119\pi\)
\(570\) 0 0
\(571\) −23.3483 −0.977097 −0.488549 0.872537i \(-0.662474\pi\)
−0.488549 + 0.872537i \(0.662474\pi\)
\(572\) 6.82894 0.285532
\(573\) 4.70819 0.196687
\(574\) −10.0257 −0.418464
\(575\) 0 0
\(576\) 0.202278 0.00842826
\(577\) 26.0419 1.08414 0.542068 0.840334i \(-0.317641\pi\)
0.542068 + 0.840334i \(0.317641\pi\)
\(578\) −5.81028 −0.241676
\(579\) −26.6475 −1.10743
\(580\) 0 0
\(581\) 14.8510 0.616124
\(582\) 7.71885 0.319957
\(583\) 38.3861 1.58979
\(584\) −25.4382 −1.05264
\(585\) 0 0
\(586\) −36.6979 −1.51598
\(587\) 23.4126 0.966339 0.483170 0.875527i \(-0.339485\pi\)
0.483170 + 0.875527i \(0.339485\pi\)
\(588\) 1.11114 0.0458227
\(589\) 53.0144 2.18442
\(590\) 0 0
\(591\) 25.5460 1.05082
\(592\) 7.86277 0.323158
\(593\) −13.8008 −0.566732 −0.283366 0.959012i \(-0.591451\pi\)
−0.283366 + 0.959012i \(0.591451\pi\)
\(594\) −30.2858 −1.24264
\(595\) 0 0
\(596\) −9.81609 −0.402083
\(597\) −24.3508 −0.996610
\(598\) 3.12276 0.127699
\(599\) 45.7819 1.87060 0.935298 0.353860i \(-0.115131\pi\)
0.935298 + 0.353860i \(0.115131\pi\)
\(600\) 0 0
\(601\) −0.844411 −0.0344442 −0.0172221 0.999852i \(-0.505482\pi\)
−0.0172221 + 0.999852i \(0.505482\pi\)
\(602\) 21.3481 0.870085
\(603\) 0.161515 0.00657739
\(604\) 15.4691 0.629428
\(605\) 0 0
\(606\) −0.268116 −0.0108915
\(607\) −20.8458 −0.846105 −0.423052 0.906105i \(-0.639041\pi\)
−0.423052 + 0.906105i \(0.639041\pi\)
\(608\) 46.5441 1.88761
\(609\) −1.62119 −0.0656940
\(610\) 0 0
\(611\) −15.1842 −0.614286
\(612\) 8.37190 0.338414
\(613\) −14.1486 −0.571458 −0.285729 0.958310i \(-0.592236\pi\)
−0.285729 + 0.958310i \(0.592236\pi\)
\(614\) 9.09838 0.367181
\(615\) 0 0
\(616\) 5.35328 0.215690
\(617\) 5.61486 0.226046 0.113023 0.993592i \(-0.463947\pi\)
0.113023 + 0.993592i \(0.463947\pi\)
\(618\) 15.9207 0.640424
\(619\) −21.2289 −0.853261 −0.426631 0.904426i \(-0.640300\pi\)
−0.426631 + 0.904426i \(0.640300\pi\)
\(620\) 0 0
\(621\) −4.97385 −0.199594
\(622\) 23.2187 0.930986
\(623\) 7.81583 0.313134
\(624\) −8.73643 −0.349737
\(625\) 0 0
\(626\) 55.4288 2.21538
\(627\) −27.8975 −1.11412
\(628\) −0.300496 −0.0119911
\(629\) 5.83997 0.232855
\(630\) 0 0
\(631\) −13.1170 −0.522181 −0.261090 0.965314i \(-0.584082\pi\)
−0.261090 + 0.965314i \(0.584082\pi\)
\(632\) 6.36683 0.253259
\(633\) 18.5148 0.735899
\(634\) 17.6263 0.700031
\(635\) 0 0
\(636\) 12.3746 0.490686
\(637\) 1.76768 0.0700380
\(638\) 9.95749 0.394221
\(639\) 18.5867 0.735279
\(640\) 0 0
\(641\) −10.1415 −0.400566 −0.200283 0.979738i \(-0.564186\pi\)
−0.200283 + 0.979738i \(0.564186\pi\)
\(642\) −6.34546 −0.250435
\(643\) −21.4125 −0.844428 −0.422214 0.906496i \(-0.638747\pi\)
−0.422214 + 0.906496i \(0.638747\pi\)
\(644\) −1.12083 −0.0441668
\(645\) 0 0
\(646\) 53.4063 2.10124
\(647\) 25.0768 0.985872 0.492936 0.870066i \(-0.335924\pi\)
0.492936 + 0.870066i \(0.335924\pi\)
\(648\) −1.74069 −0.0683809
\(649\) −1.71942 −0.0674931
\(650\) 0 0
\(651\) 6.43726 0.252296
\(652\) 13.4257 0.525790
\(653\) 21.5701 0.844102 0.422051 0.906572i \(-0.361310\pi\)
0.422051 + 0.906572i \(0.361310\pi\)
\(654\) 28.5538 1.11654
\(655\) 0 0
\(656\) −28.2930 −1.10466
\(657\) −33.0391 −1.28898
\(658\) 15.1748 0.591575
\(659\) 35.9704 1.40121 0.700604 0.713550i \(-0.252914\pi\)
0.700604 + 0.713550i \(0.252914\pi\)
\(660\) 0 0
\(661\) −5.66323 −0.220274 −0.110137 0.993916i \(-0.535129\pi\)
−0.110137 + 0.993916i \(0.535129\pi\)
\(662\) 53.6320 2.08447
\(663\) −6.48887 −0.252007
\(664\) 23.0656 0.895120
\(665\) 0 0
\(666\) 5.62033 0.217783
\(667\) 1.63532 0.0633200
\(668\) 4.71033 0.182248
\(669\) −5.69968 −0.220363
\(670\) 0 0
\(671\) 14.3796 0.555119
\(672\) 5.65160 0.218015
\(673\) 6.36930 0.245519 0.122759 0.992436i \(-0.460826\pi\)
0.122759 + 0.992436i \(0.460826\pi\)
\(674\) 56.6559 2.18231
\(675\) 0 0
\(676\) −11.0685 −0.425712
\(677\) −23.2321 −0.892881 −0.446440 0.894813i \(-0.647309\pi\)
−0.446440 + 0.894813i \(0.647309\pi\)
\(678\) −14.1020 −0.541586
\(679\) −4.40745 −0.169142
\(680\) 0 0
\(681\) 4.69194 0.179796
\(682\) −39.5381 −1.51399
\(683\) −35.9894 −1.37710 −0.688548 0.725191i \(-0.741751\pi\)
−0.688548 + 0.725191i \(0.741751\pi\)
\(684\) 18.4592 0.705805
\(685\) 0 0
\(686\) −1.76659 −0.0674486
\(687\) 11.1531 0.425519
\(688\) 60.2456 2.29684
\(689\) 19.6864 0.749994
\(690\) 0 0
\(691\) −30.3624 −1.15504 −0.577519 0.816377i \(-0.695979\pi\)
−0.577519 + 0.816377i \(0.695979\pi\)
\(692\) −21.4220 −0.814343
\(693\) 6.95283 0.264116
\(694\) 30.9709 1.17564
\(695\) 0 0
\(696\) −2.51793 −0.0954419
\(697\) −21.0142 −0.795971
\(698\) −26.0277 −0.985163
\(699\) −12.5726 −0.475539
\(700\) 0 0
\(701\) −28.5382 −1.07787 −0.538936 0.842347i \(-0.681174\pi\)
−0.538936 + 0.842347i \(0.681174\pi\)
\(702\) −15.5321 −0.586223
\(703\) 12.8765 0.485648
\(704\) −0.345628 −0.0130264
\(705\) 0 0
\(706\) 19.8664 0.747683
\(707\) 0.153094 0.00575769
\(708\) −0.554293 −0.0208316
\(709\) −7.71848 −0.289874 −0.144937 0.989441i \(-0.546298\pi\)
−0.144937 + 0.989441i \(0.546298\pi\)
\(710\) 0 0
\(711\) 8.26922 0.310120
\(712\) 12.1390 0.454930
\(713\) −6.49337 −0.243179
\(714\) 6.48485 0.242689
\(715\) 0 0
\(716\) −5.07809 −0.189777
\(717\) 8.11956 0.303231
\(718\) 51.4455 1.91993
\(719\) −17.4122 −0.649366 −0.324683 0.945823i \(-0.605258\pi\)
−0.324683 + 0.945823i \(0.605258\pi\)
\(720\) 0 0
\(721\) −9.09068 −0.338555
\(722\) 84.1904 3.13324
\(723\) 3.23845 0.120439
\(724\) 18.3047 0.680288
\(725\) 0 0
\(726\) 1.54142 0.0572076
\(727\) 1.06900 0.0396470 0.0198235 0.999803i \(-0.493690\pi\)
0.0198235 + 0.999803i \(0.493690\pi\)
\(728\) 2.74545 0.101753
\(729\) 12.5318 0.464140
\(730\) 0 0
\(731\) 44.7466 1.65501
\(732\) 4.63560 0.171337
\(733\) −26.2852 −0.970866 −0.485433 0.874274i \(-0.661338\pi\)
−0.485433 + 0.874274i \(0.661338\pi\)
\(734\) −47.2056 −1.74239
\(735\) 0 0
\(736\) −5.70087 −0.210137
\(737\) −0.275976 −0.0101657
\(738\) −20.2239 −0.744451
\(739\) −26.6622 −0.980783 −0.490392 0.871502i \(-0.663146\pi\)
−0.490392 + 0.871502i \(0.663146\pi\)
\(740\) 0 0
\(741\) −14.3073 −0.525591
\(742\) −19.6743 −0.722265
\(743\) −28.5431 −1.04714 −0.523572 0.851981i \(-0.675401\pi\)
−0.523572 + 0.851981i \(0.675401\pi\)
\(744\) 9.99793 0.366542
\(745\) 0 0
\(746\) 18.0463 0.660721
\(747\) 29.9576 1.09609
\(748\) −14.3049 −0.523038
\(749\) 3.62325 0.132391
\(750\) 0 0
\(751\) 10.0773 0.367728 0.183864 0.982952i \(-0.441139\pi\)
0.183864 + 0.982952i \(0.441139\pi\)
\(752\) 42.8240 1.56163
\(753\) −8.07163 −0.294147
\(754\) 5.10672 0.185976
\(755\) 0 0
\(756\) 5.57483 0.202754
\(757\) 26.3007 0.955916 0.477958 0.878383i \(-0.341377\pi\)
0.477958 + 0.878383i \(0.341377\pi\)
\(758\) 49.0871 1.78292
\(759\) 3.41697 0.124028
\(760\) 0 0
\(761\) −14.2702 −0.517294 −0.258647 0.965972i \(-0.583277\pi\)
−0.258647 + 0.965972i \(0.583277\pi\)
\(762\) −16.4830 −0.597115
\(763\) −16.3042 −0.590250
\(764\) 5.32306 0.192582
\(765\) 0 0
\(766\) −19.2118 −0.694151
\(767\) −0.881809 −0.0318403
\(768\) 19.8567 0.716516
\(769\) 6.90481 0.248994 0.124497 0.992220i \(-0.460268\pi\)
0.124497 + 0.992220i \(0.460268\pi\)
\(770\) 0 0
\(771\) −6.19029 −0.222938
\(772\) −30.1275 −1.08431
\(773\) 14.5844 0.524565 0.262283 0.964991i \(-0.415525\pi\)
0.262283 + 0.964991i \(0.415525\pi\)
\(774\) 43.0637 1.54789
\(775\) 0 0
\(776\) −6.84537 −0.245734
\(777\) 1.56353 0.0560913
\(778\) 56.1931 2.01462
\(779\) −46.3342 −1.66010
\(780\) 0 0
\(781\) −31.7587 −1.13641
\(782\) −6.54138 −0.233919
\(783\) −8.13386 −0.290680
\(784\) −4.98540 −0.178050
\(785\) 0 0
\(786\) −26.0320 −0.928529
\(787\) −35.9750 −1.28237 −0.641186 0.767386i \(-0.721557\pi\)
−0.641186 + 0.767386i \(0.721557\pi\)
\(788\) 28.8822 1.02889
\(789\) 2.44050 0.0868841
\(790\) 0 0
\(791\) 8.05224 0.286305
\(792\) 10.7987 0.383715
\(793\) 7.37463 0.261881
\(794\) −8.20755 −0.291275
\(795\) 0 0
\(796\) −27.5309 −0.975807
\(797\) −48.5020 −1.71803 −0.859014 0.511951i \(-0.828923\pi\)
−0.859014 + 0.511951i \(0.828923\pi\)
\(798\) 14.2984 0.506159
\(799\) 31.8070 1.12525
\(800\) 0 0
\(801\) 15.7662 0.557070
\(802\) −0.0175550 −0.000619887 0
\(803\) 56.4532 1.99219
\(804\) −0.0889672 −0.00313763
\(805\) 0 0
\(806\) −20.2772 −0.714235
\(807\) 6.40957 0.225628
\(808\) 0.237776 0.00836491
\(809\) 32.9628 1.15891 0.579455 0.815004i \(-0.303265\pi\)
0.579455 + 0.815004i \(0.303265\pi\)
\(810\) 0 0
\(811\) −9.93536 −0.348878 −0.174439 0.984668i \(-0.555811\pi\)
−0.174439 + 0.984668i \(0.555811\pi\)
\(812\) −1.83292 −0.0643227
\(813\) 24.6948 0.866084
\(814\) −9.60332 −0.336596
\(815\) 0 0
\(816\) 18.3006 0.640649
\(817\) 98.6616 3.45173
\(818\) 51.0559 1.78513
\(819\) 3.56578 0.124598
\(820\) 0 0
\(821\) −4.56735 −0.159402 −0.0797008 0.996819i \(-0.525396\pi\)
−0.0797008 + 0.996819i \(0.525396\pi\)
\(822\) −16.7364 −0.583748
\(823\) 17.7786 0.619721 0.309861 0.950782i \(-0.399718\pi\)
0.309861 + 0.950782i \(0.399718\pi\)
\(824\) −14.1191 −0.491861
\(825\) 0 0
\(826\) 0.881263 0.0306631
\(827\) −43.2668 −1.50453 −0.752266 0.658859i \(-0.771039\pi\)
−0.752266 + 0.658859i \(0.771039\pi\)
\(828\) −2.26094 −0.0785732
\(829\) 13.1864 0.457983 0.228992 0.973428i \(-0.426457\pi\)
0.228992 + 0.973428i \(0.426457\pi\)
\(830\) 0 0
\(831\) −26.9389 −0.934499
\(832\) −0.177256 −0.00614526
\(833\) −3.70284 −0.128296
\(834\) −7.47959 −0.258997
\(835\) 0 0
\(836\) −31.5408 −1.09086
\(837\) 32.2971 1.11635
\(838\) −61.4812 −2.12383
\(839\) −50.7869 −1.75336 −0.876679 0.481077i \(-0.840246\pi\)
−0.876679 + 0.481077i \(0.840246\pi\)
\(840\) 0 0
\(841\) −26.3257 −0.907783
\(842\) −47.6192 −1.64106
\(843\) 16.1381 0.555826
\(844\) 20.9328 0.720538
\(845\) 0 0
\(846\) 30.6107 1.05242
\(847\) −0.880150 −0.0302423
\(848\) −55.5218 −1.90663
\(849\) −17.9589 −0.616349
\(850\) 0 0
\(851\) −1.57716 −0.0540643
\(852\) −10.2381 −0.350752
\(853\) 3.62258 0.124035 0.0620174 0.998075i \(-0.480247\pi\)
0.0620174 + 0.998075i \(0.480247\pi\)
\(854\) −7.37007 −0.252199
\(855\) 0 0
\(856\) 5.62739 0.192340
\(857\) 23.6336 0.807310 0.403655 0.914911i \(-0.367740\pi\)
0.403655 + 0.914911i \(0.367740\pi\)
\(858\) 10.6704 0.364281
\(859\) −50.9839 −1.73955 −0.869774 0.493450i \(-0.835736\pi\)
−0.869774 + 0.493450i \(0.835736\pi\)
\(860\) 0 0
\(861\) −5.62612 −0.191738
\(862\) 19.4217 0.661505
\(863\) −44.8025 −1.52509 −0.762547 0.646933i \(-0.776051\pi\)
−0.762547 + 0.646933i \(0.776051\pi\)
\(864\) 28.3553 0.964666
\(865\) 0 0
\(866\) −64.8847 −2.20487
\(867\) −3.26057 −0.110735
\(868\) 7.27795 0.247030
\(869\) −14.1294 −0.479308
\(870\) 0 0
\(871\) −0.141535 −0.00479574
\(872\) −25.3226 −0.857530
\(873\) −8.89075 −0.300906
\(874\) −14.4231 −0.487868
\(875\) 0 0
\(876\) 18.1989 0.614886
\(877\) −10.3876 −0.350763 −0.175381 0.984501i \(-0.556116\pi\)
−0.175381 + 0.984501i \(0.556116\pi\)
\(878\) 31.5310 1.06412
\(879\) −20.5938 −0.694612
\(880\) 0 0
\(881\) −8.08491 −0.272388 −0.136194 0.990682i \(-0.543487\pi\)
−0.136194 + 0.990682i \(0.543487\pi\)
\(882\) −3.56357 −0.119992
\(883\) −4.95000 −0.166581 −0.0832903 0.996525i \(-0.526543\pi\)
−0.0832903 + 0.996525i \(0.526543\pi\)
\(884\) −7.33630 −0.246746
\(885\) 0 0
\(886\) 25.6978 0.863333
\(887\) 12.0450 0.404431 0.202215 0.979341i \(-0.435186\pi\)
0.202215 + 0.979341i \(0.435186\pi\)
\(888\) 2.42837 0.0814909
\(889\) 9.41174 0.315660
\(890\) 0 0
\(891\) 3.86299 0.129415
\(892\) −6.44405 −0.215763
\(893\) 70.1311 2.34685
\(894\) −15.3379 −0.512975
\(895\) 0 0
\(896\) −11.2246 −0.374987
\(897\) 1.75240 0.0585111
\(898\) 4.56092 0.152200
\(899\) −10.6188 −0.354156
\(900\) 0 0
\(901\) −41.2381 −1.37384
\(902\) 34.5561 1.15059
\(903\) 11.9800 0.398668
\(904\) 12.5062 0.415951
\(905\) 0 0
\(906\) 24.1708 0.803022
\(907\) −50.9499 −1.69176 −0.845881 0.533372i \(-0.820925\pi\)
−0.845881 + 0.533372i \(0.820925\pi\)
\(908\) 5.30470 0.176043
\(909\) 0.308822 0.0102430
\(910\) 0 0
\(911\) 37.3203 1.23648 0.618239 0.785990i \(-0.287846\pi\)
0.618239 + 0.785990i \(0.287846\pi\)
\(912\) 40.3510 1.33615
\(913\) −51.1879 −1.69407
\(914\) −63.9368 −2.11484
\(915\) 0 0
\(916\) 12.6097 0.416637
\(917\) 14.8642 0.490859
\(918\) 32.5359 1.07384
\(919\) 42.6489 1.40686 0.703429 0.710766i \(-0.251651\pi\)
0.703429 + 0.710766i \(0.251651\pi\)
\(920\) 0 0
\(921\) 5.10575 0.168240
\(922\) 5.83321 0.192106
\(923\) −16.2875 −0.536110
\(924\) −3.82983 −0.125992
\(925\) 0 0
\(926\) −50.9830 −1.67541
\(927\) −18.3378 −0.602293
\(928\) −9.32277 −0.306035
\(929\) 23.8363 0.782044 0.391022 0.920381i \(-0.372122\pi\)
0.391022 + 0.920381i \(0.372122\pi\)
\(930\) 0 0
\(931\) −8.16438 −0.267577
\(932\) −14.2145 −0.465613
\(933\) 13.0297 0.426573
\(934\) −67.5056 −2.20885
\(935\) 0 0
\(936\) 5.53814 0.181020
\(937\) −33.5831 −1.09711 −0.548555 0.836114i \(-0.684822\pi\)
−0.548555 + 0.836114i \(0.684822\pi\)
\(938\) 0.141448 0.00461843
\(939\) 31.1050 1.01507
\(940\) 0 0
\(941\) 16.1410 0.526183 0.263092 0.964771i \(-0.415258\pi\)
0.263092 + 0.964771i \(0.415258\pi\)
\(942\) −0.469533 −0.0152982
\(943\) 5.67517 0.184809
\(944\) 2.48697 0.0809440
\(945\) 0 0
\(946\) −73.5819 −2.39235
\(947\) 54.8866 1.78358 0.891788 0.452454i \(-0.149451\pi\)
0.891788 + 0.452454i \(0.149451\pi\)
\(948\) −4.55494 −0.147938
\(949\) 28.9522 0.939827
\(950\) 0 0
\(951\) 9.89140 0.320751
\(952\) −5.75101 −0.186391
\(953\) −18.3821 −0.595455 −0.297728 0.954651i \(-0.596229\pi\)
−0.297728 + 0.954651i \(0.596229\pi\)
\(954\) −39.6871 −1.28492
\(955\) 0 0
\(956\) 9.17995 0.296901
\(957\) 5.58786 0.180630
\(958\) −7.46817 −0.241286
\(959\) 9.55643 0.308593
\(960\) 0 0
\(961\) 11.1639 0.360126
\(962\) −4.92509 −0.158791
\(963\) 7.30885 0.235524
\(964\) 3.66138 0.117925
\(965\) 0 0
\(966\) −1.75132 −0.0563478
\(967\) −5.46628 −0.175784 −0.0878918 0.996130i \(-0.528013\pi\)
−0.0878918 + 0.996130i \(0.528013\pi\)
\(968\) −1.36699 −0.0439368
\(969\) 29.9701 0.962779
\(970\) 0 0
\(971\) −12.4172 −0.398486 −0.199243 0.979950i \(-0.563848\pi\)
−0.199243 + 0.979950i \(0.563848\pi\)
\(972\) 17.9698 0.576382
\(973\) 4.27083 0.136917
\(974\) −51.4942 −1.64998
\(975\) 0 0
\(976\) −20.7987 −0.665751
\(977\) 8.42191 0.269441 0.134720 0.990884i \(-0.456986\pi\)
0.134720 + 0.990884i \(0.456986\pi\)
\(978\) 20.9779 0.670801
\(979\) −26.9393 −0.860983
\(980\) 0 0
\(981\) −32.8889 −1.05006
\(982\) −9.07843 −0.289704
\(983\) 28.0046 0.893207 0.446603 0.894732i \(-0.352633\pi\)
0.446603 + 0.894732i \(0.352633\pi\)
\(984\) −8.73813 −0.278561
\(985\) 0 0
\(986\) −10.6973 −0.340671
\(987\) 8.51566 0.271056
\(988\) −16.1758 −0.514620
\(989\) −12.0844 −0.384262
\(990\) 0 0
\(991\) −32.4173 −1.02977 −0.514885 0.857259i \(-0.672165\pi\)
−0.514885 + 0.857259i \(0.672165\pi\)
\(992\) 37.0179 1.17532
\(993\) 30.0967 0.955091
\(994\) 16.2774 0.516289
\(995\) 0 0
\(996\) −16.5016 −0.522872
\(997\) −11.6906 −0.370244 −0.185122 0.982716i \(-0.559268\pi\)
−0.185122 + 0.982716i \(0.559268\pi\)
\(998\) 27.9980 0.886262
\(999\) 7.84456 0.248191
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.ba.1.11 14
5.4 even 2 4025.2.a.bb.1.4 yes 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4025.2.a.ba.1.11 14 1.1 even 1 trivial
4025.2.a.bb.1.4 yes 14 5.4 even 2