Properties

Label 9025.2.a.u.1.2
Level $9025$
Weight $2$
Character 9025.1
Self dual yes
Analytic conductor $72.065$
Analytic rank $0$
Dimension $2$
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] = [9025,2,Mod(1,9025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9025, 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("9025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9025 = 5^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9025.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: \(72.0649878242\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 9025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.61803 q^{2} -2.23607 q^{3} +4.85410 q^{4} -5.85410 q^{6} +4.23607 q^{7} +7.47214 q^{8} +2.00000 q^{9} +O(q^{10})\) \(q+2.61803 q^{2} -2.23607 q^{3} +4.85410 q^{4} -5.85410 q^{6} +4.23607 q^{7} +7.47214 q^{8} +2.00000 q^{9} +5.47214 q^{11} -10.8541 q^{12} -2.00000 q^{13} +11.0902 q^{14} +9.85410 q^{16} +4.85410 q^{17} +5.23607 q^{18} -9.47214 q^{21} +14.3262 q^{22} +1.23607 q^{23} -16.7082 q^{24} -5.23607 q^{26} +2.23607 q^{27} +20.5623 q^{28} -6.00000 q^{29} +1.85410 q^{31} +10.8541 q^{32} -12.2361 q^{33} +12.7082 q^{34} +9.70820 q^{36} +4.14590 q^{37} +4.47214 q^{39} +6.38197 q^{41} -24.7984 q^{42} -10.5623 q^{43} +26.5623 q^{44} +3.23607 q^{46} +7.61803 q^{47} -22.0344 q^{48} +10.9443 q^{49} -10.8541 q^{51} -9.70820 q^{52} -6.38197 q^{53} +5.85410 q^{54} +31.6525 q^{56} -15.7082 q^{58} +2.76393 q^{59} -5.56231 q^{61} +4.85410 q^{62} +8.47214 q^{63} +8.70820 q^{64} -32.0344 q^{66} -8.70820 q^{67} +23.5623 q^{68} -2.76393 q^{69} +4.52786 q^{71} +14.9443 q^{72} +10.7082 q^{73} +10.8541 q^{74} +23.1803 q^{77} +11.7082 q^{78} -1.00000 q^{79} -11.0000 q^{81} +16.7082 q^{82} -1.09017 q^{83} -45.9787 q^{84} -27.6525 q^{86} +13.4164 q^{87} +40.8885 q^{88} -3.70820 q^{89} -8.47214 q^{91} +6.00000 q^{92} -4.14590 q^{93} +19.9443 q^{94} -24.2705 q^{96} +7.38197 q^{97} +28.6525 q^{98} +10.9443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} + 3 q^{4} - 5 q^{6} + 4 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} + 3 q^{4} - 5 q^{6} + 4 q^{7} + 6 q^{8} + 4 q^{9} + 2 q^{11} - 15 q^{12} - 4 q^{13} + 11 q^{14} + 13 q^{16} + 3 q^{17} + 6 q^{18} - 10 q^{21} + 13 q^{22} - 2 q^{23} - 20 q^{24} - 6 q^{26} + 21 q^{28} - 12 q^{29} - 3 q^{31} + 15 q^{32} - 20 q^{33} + 12 q^{34} + 6 q^{36} + 15 q^{37} + 15 q^{41} - 25 q^{42} - q^{43} + 33 q^{44} + 2 q^{46} + 13 q^{47} - 15 q^{48} + 4 q^{49} - 15 q^{51} - 6 q^{52} - 15 q^{53} + 5 q^{54} + 32 q^{56} - 18 q^{58} + 10 q^{59} + 9 q^{61} + 3 q^{62} + 8 q^{63} + 4 q^{64} - 35 q^{66} - 4 q^{67} + 27 q^{68} - 10 q^{69} + 18 q^{71} + 12 q^{72} + 8 q^{73} + 15 q^{74} + 24 q^{77} + 10 q^{78} - 2 q^{79} - 22 q^{81} + 20 q^{82} + 9 q^{83} - 45 q^{84} - 24 q^{86} + 46 q^{88} + 6 q^{89} - 8 q^{91} + 12 q^{92} - 15 q^{93} + 22 q^{94} - 15 q^{96} + 17 q^{97} + 26 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.61803 1.85123 0.925615 0.378467i \(-0.123549\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) −2.23607 −1.29099 −0.645497 0.763763i \(-0.723350\pi\)
−0.645497 + 0.763763i \(0.723350\pi\)
\(4\) 4.85410 2.42705
\(5\) 0 0
\(6\) −5.85410 −2.38993
\(7\) 4.23607 1.60108 0.800542 0.599277i \(-0.204545\pi\)
0.800542 + 0.599277i \(0.204545\pi\)
\(8\) 7.47214 2.64180
\(9\) 2.00000 0.666667
\(10\) 0 0
\(11\) 5.47214 1.64991 0.824956 0.565198i \(-0.191200\pi\)
0.824956 + 0.565198i \(0.191200\pi\)
\(12\) −10.8541 −3.13331
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 11.0902 2.96397
\(15\) 0 0
\(16\) 9.85410 2.46353
\(17\) 4.85410 1.17729 0.588646 0.808391i \(-0.299661\pi\)
0.588646 + 0.808391i \(0.299661\pi\)
\(18\) 5.23607 1.23415
\(19\) 0 0
\(20\) 0 0
\(21\) −9.47214 −2.06699
\(22\) 14.3262 3.05436
\(23\) 1.23607 0.257738 0.128869 0.991662i \(-0.458865\pi\)
0.128869 + 0.991662i \(0.458865\pi\)
\(24\) −16.7082 −3.41055
\(25\) 0 0
\(26\) −5.23607 −1.02688
\(27\) 2.23607 0.430331
\(28\) 20.5623 3.88591
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 1.85410 0.333007 0.166503 0.986041i \(-0.446752\pi\)
0.166503 + 0.986041i \(0.446752\pi\)
\(32\) 10.8541 1.91875
\(33\) −12.2361 −2.13003
\(34\) 12.7082 2.17944
\(35\) 0 0
\(36\) 9.70820 1.61803
\(37\) 4.14590 0.681581 0.340791 0.940139i \(-0.389305\pi\)
0.340791 + 0.940139i \(0.389305\pi\)
\(38\) 0 0
\(39\) 4.47214 0.716115
\(40\) 0 0
\(41\) 6.38197 0.996696 0.498348 0.866977i \(-0.333940\pi\)
0.498348 + 0.866977i \(0.333940\pi\)
\(42\) −24.7984 −3.82647
\(43\) −10.5623 −1.61074 −0.805368 0.592775i \(-0.798032\pi\)
−0.805368 + 0.592775i \(0.798032\pi\)
\(44\) 26.5623 4.00442
\(45\) 0 0
\(46\) 3.23607 0.477132
\(47\) 7.61803 1.11120 0.555602 0.831448i \(-0.312488\pi\)
0.555602 + 0.831448i \(0.312488\pi\)
\(48\) −22.0344 −3.18040
\(49\) 10.9443 1.56347
\(50\) 0 0
\(51\) −10.8541 −1.51988
\(52\) −9.70820 −1.34629
\(53\) −6.38197 −0.876630 −0.438315 0.898821i \(-0.644425\pi\)
−0.438315 + 0.898821i \(0.644425\pi\)
\(54\) 5.85410 0.796642
\(55\) 0 0
\(56\) 31.6525 4.22974
\(57\) 0 0
\(58\) −15.7082 −2.06259
\(59\) 2.76393 0.359833 0.179917 0.983682i \(-0.442417\pi\)
0.179917 + 0.983682i \(0.442417\pi\)
\(60\) 0 0
\(61\) −5.56231 −0.712180 −0.356090 0.934452i \(-0.615890\pi\)
−0.356090 + 0.934452i \(0.615890\pi\)
\(62\) 4.85410 0.616472
\(63\) 8.47214 1.06739
\(64\) 8.70820 1.08853
\(65\) 0 0
\(66\) −32.0344 −3.94317
\(67\) −8.70820 −1.06388 −0.531938 0.846783i \(-0.678536\pi\)
−0.531938 + 0.846783i \(0.678536\pi\)
\(68\) 23.5623 2.85735
\(69\) −2.76393 −0.332738
\(70\) 0 0
\(71\) 4.52786 0.537359 0.268679 0.963230i \(-0.413413\pi\)
0.268679 + 0.963230i \(0.413413\pi\)
\(72\) 14.9443 1.76120
\(73\) 10.7082 1.25330 0.626650 0.779301i \(-0.284425\pi\)
0.626650 + 0.779301i \(0.284425\pi\)
\(74\) 10.8541 1.26176
\(75\) 0 0
\(76\) 0 0
\(77\) 23.1803 2.64164
\(78\) 11.7082 1.32569
\(79\) −1.00000 −0.112509 −0.0562544 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 16.7082 1.84511
\(83\) −1.09017 −0.119662 −0.0598308 0.998209i \(-0.519056\pi\)
−0.0598308 + 0.998209i \(0.519056\pi\)
\(84\) −45.9787 −5.01669
\(85\) 0 0
\(86\) −27.6525 −2.98184
\(87\) 13.4164 1.43839
\(88\) 40.8885 4.35873
\(89\) −3.70820 −0.393069 −0.196534 0.980497i \(-0.562969\pi\)
−0.196534 + 0.980497i \(0.562969\pi\)
\(90\) 0 0
\(91\) −8.47214 −0.888121
\(92\) 6.00000 0.625543
\(93\) −4.14590 −0.429910
\(94\) 19.9443 2.05709
\(95\) 0 0
\(96\) −24.2705 −2.47710
\(97\) 7.38197 0.749525 0.374763 0.927121i \(-0.377724\pi\)
0.374763 + 0.927121i \(0.377724\pi\)
\(98\) 28.6525 2.89434
\(99\) 10.9443 1.09994
\(100\) 0 0
\(101\) −13.0344 −1.29698 −0.648488 0.761225i \(-0.724598\pi\)
−0.648488 + 0.761225i \(0.724598\pi\)
\(102\) −28.4164 −2.81364
\(103\) −1.23607 −0.121793 −0.0608967 0.998144i \(-0.519396\pi\)
−0.0608967 + 0.998144i \(0.519396\pi\)
\(104\) −14.9443 −1.46541
\(105\) 0 0
\(106\) −16.7082 −1.62284
\(107\) −19.8541 −1.91937 −0.959684 0.281080i \(-0.909307\pi\)
−0.959684 + 0.281080i \(0.909307\pi\)
\(108\) 10.8541 1.04444
\(109\) −7.94427 −0.760923 −0.380462 0.924797i \(-0.624235\pi\)
−0.380462 + 0.924797i \(0.624235\pi\)
\(110\) 0 0
\(111\) −9.27051 −0.879918
\(112\) 41.7426 3.94431
\(113\) −9.32624 −0.877339 −0.438669 0.898649i \(-0.644550\pi\)
−0.438669 + 0.898649i \(0.644550\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −29.1246 −2.70415
\(117\) −4.00000 −0.369800
\(118\) 7.23607 0.666134
\(119\) 20.5623 1.88494
\(120\) 0 0
\(121\) 18.9443 1.72221
\(122\) −14.5623 −1.31841
\(123\) −14.2705 −1.28673
\(124\) 9.00000 0.808224
\(125\) 0 0
\(126\) 22.1803 1.97598
\(127\) 0.854102 0.0757893 0.0378946 0.999282i \(-0.487935\pi\)
0.0378946 + 0.999282i \(0.487935\pi\)
\(128\) 1.09017 0.0963583
\(129\) 23.6180 2.07945
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −59.3951 −5.16968
\(133\) 0 0
\(134\) −22.7984 −1.96948
\(135\) 0 0
\(136\) 36.2705 3.11017
\(137\) 9.23607 0.789091 0.394545 0.918877i \(-0.370902\pi\)
0.394545 + 0.918877i \(0.370902\pi\)
\(138\) −7.23607 −0.615975
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) −17.0344 −1.43456
\(142\) 11.8541 0.994774
\(143\) −10.9443 −0.915206
\(144\) 19.7082 1.64235
\(145\) 0 0
\(146\) 28.0344 2.32015
\(147\) −24.4721 −2.01843
\(148\) 20.1246 1.65423
\(149\) −9.47214 −0.775988 −0.387994 0.921662i \(-0.626832\pi\)
−0.387994 + 0.921662i \(0.626832\pi\)
\(150\) 0 0
\(151\) −5.79837 −0.471865 −0.235932 0.971769i \(-0.575814\pi\)
−0.235932 + 0.971769i \(0.575814\pi\)
\(152\) 0 0
\(153\) 9.70820 0.784862
\(154\) 60.6869 4.89029
\(155\) 0 0
\(156\) 21.7082 1.73805
\(157\) −1.81966 −0.145225 −0.0726123 0.997360i \(-0.523134\pi\)
−0.0726123 + 0.997360i \(0.523134\pi\)
\(158\) −2.61803 −0.208280
\(159\) 14.2705 1.13173
\(160\) 0 0
\(161\) 5.23607 0.412660
\(162\) −28.7984 −2.26261
\(163\) 2.76393 0.216488 0.108244 0.994124i \(-0.465477\pi\)
0.108244 + 0.994124i \(0.465477\pi\)
\(164\) 30.9787 2.41903
\(165\) 0 0
\(166\) −2.85410 −0.221521
\(167\) −5.23607 −0.405179 −0.202590 0.979264i \(-0.564936\pi\)
−0.202590 + 0.979264i \(0.564936\pi\)
\(168\) −70.7771 −5.46057
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) −51.2705 −3.90934
\(173\) 19.6525 1.49415 0.747075 0.664740i \(-0.231458\pi\)
0.747075 + 0.664740i \(0.231458\pi\)
\(174\) 35.1246 2.66279
\(175\) 0 0
\(176\) 53.9230 4.06460
\(177\) −6.18034 −0.464543
\(178\) −9.70820 −0.727661
\(179\) −11.1803 −0.835658 −0.417829 0.908526i \(-0.637209\pi\)
−0.417829 + 0.908526i \(0.637209\pi\)
\(180\) 0 0
\(181\) 18.7082 1.39057 0.695285 0.718734i \(-0.255278\pi\)
0.695285 + 0.718734i \(0.255278\pi\)
\(182\) −22.1803 −1.64412
\(183\) 12.4377 0.919421
\(184\) 9.23607 0.680892
\(185\) 0 0
\(186\) −10.8541 −0.795861
\(187\) 26.5623 1.94243
\(188\) 36.9787 2.69695
\(189\) 9.47214 0.688997
\(190\) 0 0
\(191\) −17.9443 −1.29840 −0.649201 0.760617i \(-0.724897\pi\)
−0.649201 + 0.760617i \(0.724897\pi\)
\(192\) −19.4721 −1.40528
\(193\) 23.2705 1.67505 0.837524 0.546401i \(-0.184002\pi\)
0.837524 + 0.546401i \(0.184002\pi\)
\(194\) 19.3262 1.38754
\(195\) 0 0
\(196\) 53.1246 3.79462
\(197\) 7.47214 0.532368 0.266184 0.963922i \(-0.414237\pi\)
0.266184 + 0.963922i \(0.414237\pi\)
\(198\) 28.6525 2.03624
\(199\) 19.4164 1.37639 0.688196 0.725525i \(-0.258403\pi\)
0.688196 + 0.725525i \(0.258403\pi\)
\(200\) 0 0
\(201\) 19.4721 1.37346
\(202\) −34.1246 −2.40100
\(203\) −25.4164 −1.78388
\(204\) −52.6869 −3.68882
\(205\) 0 0
\(206\) −3.23607 −0.225468
\(207\) 2.47214 0.171825
\(208\) −19.7082 −1.36652
\(209\) 0 0
\(210\) 0 0
\(211\) 12.2361 0.842366 0.421183 0.906976i \(-0.361615\pi\)
0.421183 + 0.906976i \(0.361615\pi\)
\(212\) −30.9787 −2.12763
\(213\) −10.1246 −0.693727
\(214\) −51.9787 −3.55319
\(215\) 0 0
\(216\) 16.7082 1.13685
\(217\) 7.85410 0.533171
\(218\) −20.7984 −1.40864
\(219\) −23.9443 −1.61800
\(220\) 0 0
\(221\) −9.70820 −0.653044
\(222\) −24.2705 −1.62893
\(223\) 18.8885 1.26487 0.632435 0.774613i \(-0.282055\pi\)
0.632435 + 0.774613i \(0.282055\pi\)
\(224\) 45.9787 3.07208
\(225\) 0 0
\(226\) −24.4164 −1.62416
\(227\) 14.4721 0.960549 0.480275 0.877118i \(-0.340537\pi\)
0.480275 + 0.877118i \(0.340537\pi\)
\(228\) 0 0
\(229\) 20.6525 1.36475 0.682377 0.731000i \(-0.260946\pi\)
0.682377 + 0.731000i \(0.260946\pi\)
\(230\) 0 0
\(231\) −51.8328 −3.41035
\(232\) −44.8328 −2.94342
\(233\) 16.5279 1.08278 0.541388 0.840773i \(-0.317899\pi\)
0.541388 + 0.840773i \(0.317899\pi\)
\(234\) −10.4721 −0.684585
\(235\) 0 0
\(236\) 13.4164 0.873334
\(237\) 2.23607 0.145248
\(238\) 53.8328 3.48946
\(239\) 0.708204 0.0458099 0.0229050 0.999738i \(-0.492708\pi\)
0.0229050 + 0.999738i \(0.492708\pi\)
\(240\) 0 0
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) 49.5967 3.18820
\(243\) 17.8885 1.14755
\(244\) −27.0000 −1.72850
\(245\) 0 0
\(246\) −37.3607 −2.38203
\(247\) 0 0
\(248\) 13.8541 0.879736
\(249\) 2.43769 0.154483
\(250\) 0 0
\(251\) 5.90983 0.373025 0.186513 0.982453i \(-0.440281\pi\)
0.186513 + 0.982453i \(0.440281\pi\)
\(252\) 41.1246 2.59061
\(253\) 6.76393 0.425245
\(254\) 2.23607 0.140303
\(255\) 0 0
\(256\) −14.5623 −0.910144
\(257\) 4.20163 0.262090 0.131045 0.991376i \(-0.458167\pi\)
0.131045 + 0.991376i \(0.458167\pi\)
\(258\) 61.8328 3.84954
\(259\) 17.5623 1.09127
\(260\) 0 0
\(261\) −12.0000 −0.742781
\(262\) −31.4164 −1.94091
\(263\) 22.6180 1.39469 0.697344 0.716737i \(-0.254365\pi\)
0.697344 + 0.716737i \(0.254365\pi\)
\(264\) −91.4296 −5.62710
\(265\) 0 0
\(266\) 0 0
\(267\) 8.29180 0.507450
\(268\) −42.2705 −2.58208
\(269\) −9.18034 −0.559735 −0.279868 0.960039i \(-0.590291\pi\)
−0.279868 + 0.960039i \(0.590291\pi\)
\(270\) 0 0
\(271\) −11.3262 −0.688020 −0.344010 0.938966i \(-0.611785\pi\)
−0.344010 + 0.938966i \(0.611785\pi\)
\(272\) 47.8328 2.90029
\(273\) 18.9443 1.14656
\(274\) 24.1803 1.46079
\(275\) 0 0
\(276\) −13.4164 −0.807573
\(277\) −12.0000 −0.721010 −0.360505 0.932757i \(-0.617396\pi\)
−0.360505 + 0.932757i \(0.617396\pi\)
\(278\) −36.6525 −2.19827
\(279\) 3.70820 0.222004
\(280\) 0 0
\(281\) −4.61803 −0.275489 −0.137744 0.990468i \(-0.543985\pi\)
−0.137744 + 0.990468i \(0.543985\pi\)
\(282\) −44.5967 −2.65570
\(283\) −23.7639 −1.41262 −0.706310 0.707903i \(-0.749641\pi\)
−0.706310 + 0.707903i \(0.749641\pi\)
\(284\) 21.9787 1.30420
\(285\) 0 0
\(286\) −28.6525 −1.69426
\(287\) 27.0344 1.59579
\(288\) 21.7082 1.27917
\(289\) 6.56231 0.386018
\(290\) 0 0
\(291\) −16.5066 −0.967633
\(292\) 51.9787 3.04182
\(293\) −13.4721 −0.787051 −0.393525 0.919314i \(-0.628745\pi\)
−0.393525 + 0.919314i \(0.628745\pi\)
\(294\) −64.0689 −3.73657
\(295\) 0 0
\(296\) 30.9787 1.80060
\(297\) 12.2361 0.710009
\(298\) −24.7984 −1.43653
\(299\) −2.47214 −0.142967
\(300\) 0 0
\(301\) −44.7426 −2.57892
\(302\) −15.1803 −0.873530
\(303\) 29.1459 1.67439
\(304\) 0 0
\(305\) 0 0
\(306\) 25.4164 1.45296
\(307\) −32.5623 −1.85843 −0.929214 0.369541i \(-0.879515\pi\)
−0.929214 + 0.369541i \(0.879515\pi\)
\(308\) 112.520 6.41141
\(309\) 2.76393 0.157235
\(310\) 0 0
\(311\) 16.2361 0.920663 0.460331 0.887747i \(-0.347731\pi\)
0.460331 + 0.887747i \(0.347731\pi\)
\(312\) 33.4164 1.89183
\(313\) 19.9443 1.12732 0.563658 0.826008i \(-0.309393\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(314\) −4.76393 −0.268844
\(315\) 0 0
\(316\) −4.85410 −0.273065
\(317\) 10.9443 0.614692 0.307346 0.951598i \(-0.400559\pi\)
0.307346 + 0.951598i \(0.400559\pi\)
\(318\) 37.3607 2.09508
\(319\) −32.8328 −1.83828
\(320\) 0 0
\(321\) 44.3951 2.47789
\(322\) 13.7082 0.763928
\(323\) 0 0
\(324\) −53.3951 −2.96640
\(325\) 0 0
\(326\) 7.23607 0.400769
\(327\) 17.7639 0.982348
\(328\) 47.6869 2.63307
\(329\) 32.2705 1.77913
\(330\) 0 0
\(331\) 13.5623 0.745452 0.372726 0.927941i \(-0.378423\pi\)
0.372726 + 0.927941i \(0.378423\pi\)
\(332\) −5.29180 −0.290425
\(333\) 8.29180 0.454388
\(334\) −13.7082 −0.750080
\(335\) 0 0
\(336\) −93.3394 −5.09208
\(337\) −4.70820 −0.256472 −0.128236 0.991744i \(-0.540932\pi\)
−0.128236 + 0.991744i \(0.540932\pi\)
\(338\) −23.5623 −1.28162
\(339\) 20.8541 1.13264
\(340\) 0 0
\(341\) 10.1459 0.549431
\(342\) 0 0
\(343\) 16.7082 0.902158
\(344\) −78.9230 −4.25524
\(345\) 0 0
\(346\) 51.4508 2.76601
\(347\) 33.4721 1.79688 0.898439 0.439098i \(-0.144702\pi\)
0.898439 + 0.439098i \(0.144702\pi\)
\(348\) 65.1246 3.49105
\(349\) −27.0689 −1.44896 −0.724482 0.689294i \(-0.757921\pi\)
−0.724482 + 0.689294i \(0.757921\pi\)
\(350\) 0 0
\(351\) −4.47214 −0.238705
\(352\) 59.3951 3.16577
\(353\) −16.5279 −0.879689 −0.439845 0.898074i \(-0.644967\pi\)
−0.439845 + 0.898074i \(0.644967\pi\)
\(354\) −16.1803 −0.859975
\(355\) 0 0
\(356\) −18.0000 −0.953998
\(357\) −45.9787 −2.43345
\(358\) −29.2705 −1.54699
\(359\) −22.5967 −1.19261 −0.596305 0.802758i \(-0.703365\pi\)
−0.596305 + 0.802758i \(0.703365\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 48.9787 2.57426
\(363\) −42.3607 −2.22336
\(364\) −41.1246 −2.15552
\(365\) 0 0
\(366\) 32.5623 1.70206
\(367\) 12.4721 0.651040 0.325520 0.945535i \(-0.394461\pi\)
0.325520 + 0.945535i \(0.394461\pi\)
\(368\) 12.1803 0.634944
\(369\) 12.7639 0.664464
\(370\) 0 0
\(371\) −27.0344 −1.40356
\(372\) −20.1246 −1.04341
\(373\) 13.1459 0.680669 0.340334 0.940304i \(-0.389460\pi\)
0.340334 + 0.940304i \(0.389460\pi\)
\(374\) 69.5410 3.59588
\(375\) 0 0
\(376\) 56.9230 2.93558
\(377\) 12.0000 0.618031
\(378\) 24.7984 1.27549
\(379\) 36.5410 1.87699 0.938493 0.345298i \(-0.112222\pi\)
0.938493 + 0.345298i \(0.112222\pi\)
\(380\) 0 0
\(381\) −1.90983 −0.0978436
\(382\) −46.9787 −2.40364
\(383\) −22.0689 −1.12767 −0.563834 0.825888i \(-0.690674\pi\)
−0.563834 + 0.825888i \(0.690674\pi\)
\(384\) −2.43769 −0.124398
\(385\) 0 0
\(386\) 60.9230 3.10090
\(387\) −21.1246 −1.07382
\(388\) 35.8328 1.81914
\(389\) −4.47214 −0.226746 −0.113373 0.993552i \(-0.536166\pi\)
−0.113373 + 0.993552i \(0.536166\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 81.7771 4.13037
\(393\) 26.8328 1.35354
\(394\) 19.5623 0.985535
\(395\) 0 0
\(396\) 53.1246 2.66961
\(397\) 9.03444 0.453426 0.226713 0.973962i \(-0.427202\pi\)
0.226713 + 0.973962i \(0.427202\pi\)
\(398\) 50.8328 2.54802
\(399\) 0 0
\(400\) 0 0
\(401\) 5.88854 0.294060 0.147030 0.989132i \(-0.453029\pi\)
0.147030 + 0.989132i \(0.453029\pi\)
\(402\) 50.9787 2.54259
\(403\) −3.70820 −0.184719
\(404\) −63.2705 −3.14783
\(405\) 0 0
\(406\) −66.5410 −3.30238
\(407\) 22.6869 1.12455
\(408\) −81.1033 −4.01521
\(409\) −16.4377 −0.812792 −0.406396 0.913697i \(-0.633215\pi\)
−0.406396 + 0.913697i \(0.633215\pi\)
\(410\) 0 0
\(411\) −20.6525 −1.01871
\(412\) −6.00000 −0.295599
\(413\) 11.7082 0.576123
\(414\) 6.47214 0.318088
\(415\) 0 0
\(416\) −21.7082 −1.06433
\(417\) 31.3050 1.53301
\(418\) 0 0
\(419\) −9.52786 −0.465467 −0.232733 0.972541i \(-0.574767\pi\)
−0.232733 + 0.972541i \(0.574767\pi\)
\(420\) 0 0
\(421\) 15.0000 0.731055 0.365528 0.930800i \(-0.380889\pi\)
0.365528 + 0.930800i \(0.380889\pi\)
\(422\) 32.0344 1.55941
\(423\) 15.2361 0.740803
\(424\) −47.6869 −2.31588
\(425\) 0 0
\(426\) −26.5066 −1.28425
\(427\) −23.5623 −1.14026
\(428\) −96.3738 −4.65841
\(429\) 24.4721 1.18153
\(430\) 0 0
\(431\) 10.6525 0.513112 0.256556 0.966529i \(-0.417412\pi\)
0.256556 + 0.966529i \(0.417412\pi\)
\(432\) 22.0344 1.06013
\(433\) 33.3607 1.60321 0.801606 0.597853i \(-0.203979\pi\)
0.801606 + 0.597853i \(0.203979\pi\)
\(434\) 20.5623 0.987022
\(435\) 0 0
\(436\) −38.5623 −1.84680
\(437\) 0 0
\(438\) −62.6869 −2.99530
\(439\) −36.5066 −1.74236 −0.871182 0.490960i \(-0.836646\pi\)
−0.871182 + 0.490960i \(0.836646\pi\)
\(440\) 0 0
\(441\) 21.8885 1.04231
\(442\) −25.4164 −1.20894
\(443\) 12.6738 0.602149 0.301074 0.953601i \(-0.402655\pi\)
0.301074 + 0.953601i \(0.402655\pi\)
\(444\) −45.0000 −2.13561
\(445\) 0 0
\(446\) 49.4508 2.34157
\(447\) 21.1803 1.00180
\(448\) 36.8885 1.74282
\(449\) −24.7984 −1.17031 −0.585154 0.810922i \(-0.698966\pi\)
−0.585154 + 0.810922i \(0.698966\pi\)
\(450\) 0 0
\(451\) 34.9230 1.64446
\(452\) −45.2705 −2.12935
\(453\) 12.9656 0.609175
\(454\) 37.8885 1.77820
\(455\) 0 0
\(456\) 0 0
\(457\) −5.56231 −0.260194 −0.130097 0.991501i \(-0.541529\pi\)
−0.130097 + 0.991501i \(0.541529\pi\)
\(458\) 54.0689 2.52647
\(459\) 10.8541 0.506626
\(460\) 0 0
\(461\) −8.03444 −0.374201 −0.187101 0.982341i \(-0.559909\pi\)
−0.187101 + 0.982341i \(0.559909\pi\)
\(462\) −135.700 −6.31334
\(463\) −41.8673 −1.94574 −0.972868 0.231360i \(-0.925683\pi\)
−0.972868 + 0.231360i \(0.925683\pi\)
\(464\) −59.1246 −2.74479
\(465\) 0 0
\(466\) 43.2705 2.00447
\(467\) 2.72949 0.126306 0.0631529 0.998004i \(-0.479884\pi\)
0.0631529 + 0.998004i \(0.479884\pi\)
\(468\) −19.4164 −0.897524
\(469\) −36.8885 −1.70335
\(470\) 0 0
\(471\) 4.06888 0.187484
\(472\) 20.6525 0.950607
\(473\) −57.7984 −2.65757
\(474\) 5.85410 0.268888
\(475\) 0 0
\(476\) 99.8115 4.57485
\(477\) −12.7639 −0.584420
\(478\) 1.85410 0.0848047
\(479\) −27.7426 −1.26759 −0.633797 0.773499i \(-0.718505\pi\)
−0.633797 + 0.773499i \(0.718505\pi\)
\(480\) 0 0
\(481\) −8.29180 −0.378073
\(482\) 34.0344 1.55023
\(483\) −11.7082 −0.532742
\(484\) 91.9574 4.17988
\(485\) 0 0
\(486\) 46.8328 2.12438
\(487\) −10.1246 −0.458790 −0.229395 0.973333i \(-0.573675\pi\)
−0.229395 + 0.973333i \(0.573675\pi\)
\(488\) −41.5623 −1.88144
\(489\) −6.18034 −0.279485
\(490\) 0 0
\(491\) −27.7639 −1.25297 −0.626484 0.779434i \(-0.715507\pi\)
−0.626484 + 0.779434i \(0.715507\pi\)
\(492\) −69.2705 −3.12296
\(493\) −29.1246 −1.31171
\(494\) 0 0
\(495\) 0 0
\(496\) 18.2705 0.820370
\(497\) 19.1803 0.860356
\(498\) 6.38197 0.285983
\(499\) −10.5967 −0.474376 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(500\) 0 0
\(501\) 11.7082 0.523084
\(502\) 15.4721 0.690555
\(503\) 18.7426 0.835693 0.417847 0.908518i \(-0.362785\pi\)
0.417847 + 0.908518i \(0.362785\pi\)
\(504\) 63.3050 2.81983
\(505\) 0 0
\(506\) 17.7082 0.787226
\(507\) 20.1246 0.893765
\(508\) 4.14590 0.183944
\(509\) −13.0344 −0.577741 −0.288871 0.957368i \(-0.593280\pi\)
−0.288871 + 0.957368i \(0.593280\pi\)
\(510\) 0 0
\(511\) 45.3607 2.00664
\(512\) −40.3050 −1.78124
\(513\) 0 0
\(514\) 11.0000 0.485189
\(515\) 0 0
\(516\) 114.644 5.04694
\(517\) 41.6869 1.83339
\(518\) 45.9787 2.02019
\(519\) −43.9443 −1.92894
\(520\) 0 0
\(521\) −20.2361 −0.886558 −0.443279 0.896384i \(-0.646185\pi\)
−0.443279 + 0.896384i \(0.646185\pi\)
\(522\) −31.4164 −1.37506
\(523\) 2.38197 0.104156 0.0520781 0.998643i \(-0.483416\pi\)
0.0520781 + 0.998643i \(0.483416\pi\)
\(524\) −58.2492 −2.54463
\(525\) 0 0
\(526\) 59.2148 2.58189
\(527\) 9.00000 0.392046
\(528\) −120.575 −5.24737
\(529\) −21.4721 −0.933571
\(530\) 0 0
\(531\) 5.52786 0.239889
\(532\) 0 0
\(533\) −12.7639 −0.552867
\(534\) 21.7082 0.939406
\(535\) 0 0
\(536\) −65.0689 −2.81055
\(537\) 25.0000 1.07883
\(538\) −24.0344 −1.03620
\(539\) 59.8885 2.57958
\(540\) 0 0
\(541\) 7.34752 0.315895 0.157947 0.987448i \(-0.449512\pi\)
0.157947 + 0.987448i \(0.449512\pi\)
\(542\) −29.6525 −1.27368
\(543\) −41.8328 −1.79522
\(544\) 52.6869 2.25893
\(545\) 0 0
\(546\) 49.5967 2.12254
\(547\) 6.41641 0.274346 0.137173 0.990547i \(-0.456198\pi\)
0.137173 + 0.990547i \(0.456198\pi\)
\(548\) 44.8328 1.91516
\(549\) −11.1246 −0.474787
\(550\) 0 0
\(551\) 0 0
\(552\) −20.6525 −0.879028
\(553\) −4.23607 −0.180136
\(554\) −31.4164 −1.33476
\(555\) 0 0
\(556\) −67.9574 −2.88204
\(557\) −42.5066 −1.80106 −0.900531 0.434792i \(-0.856822\pi\)
−0.900531 + 0.434792i \(0.856822\pi\)
\(558\) 9.70820 0.410981
\(559\) 21.1246 0.893476
\(560\) 0 0
\(561\) −59.3951 −2.50766
\(562\) −12.0902 −0.509993
\(563\) 16.5967 0.699470 0.349735 0.936849i \(-0.386272\pi\)
0.349735 + 0.936849i \(0.386272\pi\)
\(564\) −82.6869 −3.48175
\(565\) 0 0
\(566\) −62.2148 −2.61508
\(567\) −46.5967 −1.95688
\(568\) 33.8328 1.41959
\(569\) −24.7082 −1.03582 −0.517911 0.855435i \(-0.673290\pi\)
−0.517911 + 0.855435i \(0.673290\pi\)
\(570\) 0 0
\(571\) 44.2492 1.85177 0.925886 0.377803i \(-0.123320\pi\)
0.925886 + 0.377803i \(0.123320\pi\)
\(572\) −53.1246 −2.22125
\(573\) 40.1246 1.67623
\(574\) 70.7771 2.95418
\(575\) 0 0
\(576\) 17.4164 0.725684
\(577\) −47.3050 −1.96933 −0.984665 0.174453i \(-0.944184\pi\)
−0.984665 + 0.174453i \(0.944184\pi\)
\(578\) 17.1803 0.714608
\(579\) −52.0344 −2.16248
\(580\) 0 0
\(581\) −4.61803 −0.191588
\(582\) −43.2148 −1.79131
\(583\) −34.9230 −1.44636
\(584\) 80.0132 3.31097
\(585\) 0 0
\(586\) −35.2705 −1.45701
\(587\) 27.6738 1.14222 0.571109 0.820874i \(-0.306513\pi\)
0.571109 + 0.820874i \(0.306513\pi\)
\(588\) −118.790 −4.89883
\(589\) 0 0
\(590\) 0 0
\(591\) −16.7082 −0.687284
\(592\) 40.8541 1.67909
\(593\) −12.5967 −0.517286 −0.258643 0.965973i \(-0.583275\pi\)
−0.258643 + 0.965973i \(0.583275\pi\)
\(594\) 32.0344 1.31439
\(595\) 0 0
\(596\) −45.9787 −1.88336
\(597\) −43.4164 −1.77692
\(598\) −6.47214 −0.264665
\(599\) 41.0689 1.67803 0.839015 0.544109i \(-0.183132\pi\)
0.839015 + 0.544109i \(0.183132\pi\)
\(600\) 0 0
\(601\) −18.6869 −0.762255 −0.381128 0.924522i \(-0.624464\pi\)
−0.381128 + 0.924522i \(0.624464\pi\)
\(602\) −117.138 −4.77418
\(603\) −17.4164 −0.709251
\(604\) −28.1459 −1.14524
\(605\) 0 0
\(606\) 76.3050 3.09968
\(607\) 26.9787 1.09503 0.547516 0.836795i \(-0.315573\pi\)
0.547516 + 0.836795i \(0.315573\pi\)
\(608\) 0 0
\(609\) 56.8328 2.30298
\(610\) 0 0
\(611\) −15.2361 −0.616385
\(612\) 47.1246 1.90490
\(613\) 7.50658 0.303188 0.151594 0.988443i \(-0.451559\pi\)
0.151594 + 0.988443i \(0.451559\pi\)
\(614\) −85.2492 −3.44038
\(615\) 0 0
\(616\) 173.207 6.97869
\(617\) −9.50658 −0.382720 −0.191360 0.981520i \(-0.561290\pi\)
−0.191360 + 0.981520i \(0.561290\pi\)
\(618\) 7.23607 0.291077
\(619\) 36.5066 1.46732 0.733662 0.679515i \(-0.237810\pi\)
0.733662 + 0.679515i \(0.237810\pi\)
\(620\) 0 0
\(621\) 2.76393 0.110913
\(622\) 42.5066 1.70436
\(623\) −15.7082 −0.629336
\(624\) 44.0689 1.76417
\(625\) 0 0
\(626\) 52.2148 2.08692
\(627\) 0 0
\(628\) −8.83282 −0.352468
\(629\) 20.1246 0.802421
\(630\) 0 0
\(631\) −33.9787 −1.35267 −0.676336 0.736594i \(-0.736433\pi\)
−0.676336 + 0.736594i \(0.736433\pi\)
\(632\) −7.47214 −0.297226
\(633\) −27.3607 −1.08749
\(634\) 28.6525 1.13794
\(635\) 0 0
\(636\) 69.2705 2.74675
\(637\) −21.8885 −0.867256
\(638\) −85.9574 −3.40309
\(639\) 9.05573 0.358239
\(640\) 0 0
\(641\) −17.2918 −0.682985 −0.341492 0.939885i \(-0.610932\pi\)
−0.341492 + 0.939885i \(0.610932\pi\)
\(642\) 116.228 4.58715
\(643\) −38.3050 −1.51060 −0.755300 0.655379i \(-0.772509\pi\)
−0.755300 + 0.655379i \(0.772509\pi\)
\(644\) 25.4164 1.00155
\(645\) 0 0
\(646\) 0 0
\(647\) 21.5066 0.845511 0.422755 0.906244i \(-0.361063\pi\)
0.422755 + 0.906244i \(0.361063\pi\)
\(648\) −82.1935 −3.22887
\(649\) 15.1246 0.593693
\(650\) 0 0
\(651\) −17.5623 −0.688321
\(652\) 13.4164 0.525427
\(653\) −14.1246 −0.552739 −0.276369 0.961051i \(-0.589131\pi\)
−0.276369 + 0.961051i \(0.589131\pi\)
\(654\) 46.5066 1.81855
\(655\) 0 0
\(656\) 62.8885 2.45539
\(657\) 21.4164 0.835534
\(658\) 84.4853 3.29358
\(659\) −15.0689 −0.587000 −0.293500 0.955959i \(-0.594820\pi\)
−0.293500 + 0.955959i \(0.594820\pi\)
\(660\) 0 0
\(661\) 28.4164 1.10527 0.552635 0.833423i \(-0.313622\pi\)
0.552635 + 0.833423i \(0.313622\pi\)
\(662\) 35.5066 1.38000
\(663\) 21.7082 0.843077
\(664\) −8.14590 −0.316122
\(665\) 0 0
\(666\) 21.7082 0.841176
\(667\) −7.41641 −0.287164
\(668\) −25.4164 −0.983390
\(669\) −42.2361 −1.63294
\(670\) 0 0
\(671\) −30.4377 −1.17503
\(672\) −102.812 −3.96604
\(673\) 2.81966 0.108690 0.0543450 0.998522i \(-0.482693\pi\)
0.0543450 + 0.998522i \(0.482693\pi\)
\(674\) −12.3262 −0.474789
\(675\) 0 0
\(676\) −43.6869 −1.68027
\(677\) 36.0902 1.38706 0.693529 0.720429i \(-0.256055\pi\)
0.693529 + 0.720429i \(0.256055\pi\)
\(678\) 54.5967 2.09678
\(679\) 31.2705 1.20005
\(680\) 0 0
\(681\) −32.3607 −1.24006
\(682\) 26.5623 1.01712
\(683\) 36.7984 1.40805 0.704025 0.710175i \(-0.251384\pi\)
0.704025 + 0.710175i \(0.251384\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 43.7426 1.67010
\(687\) −46.1803 −1.76189
\(688\) −104.082 −3.96809
\(689\) 12.7639 0.486267
\(690\) 0 0
\(691\) −7.65248 −0.291114 −0.145557 0.989350i \(-0.546497\pi\)
−0.145557 + 0.989350i \(0.546497\pi\)
\(692\) 95.3951 3.62638
\(693\) 46.3607 1.76110
\(694\) 87.6312 3.32643
\(695\) 0 0
\(696\) 100.249 3.79994
\(697\) 30.9787 1.17340
\(698\) −70.8673 −2.68237
\(699\) −36.9574 −1.39786
\(700\) 0 0
\(701\) −48.9443 −1.84860 −0.924300 0.381667i \(-0.875350\pi\)
−0.924300 + 0.381667i \(0.875350\pi\)
\(702\) −11.7082 −0.441898
\(703\) 0 0
\(704\) 47.6525 1.79597
\(705\) 0 0
\(706\) −43.2705 −1.62851
\(707\) −55.2148 −2.07657
\(708\) −30.0000 −1.12747
\(709\) 8.83282 0.331723 0.165862 0.986149i \(-0.446959\pi\)
0.165862 + 0.986149i \(0.446959\pi\)
\(710\) 0 0
\(711\) −2.00000 −0.0750059
\(712\) −27.7082 −1.03841
\(713\) 2.29180 0.0858284
\(714\) −120.374 −4.50488
\(715\) 0 0
\(716\) −54.2705 −2.02818
\(717\) −1.58359 −0.0591403
\(718\) −59.1591 −2.20780
\(719\) −12.2361 −0.456328 −0.228164 0.973623i \(-0.573272\pi\)
−0.228164 + 0.973623i \(0.573272\pi\)
\(720\) 0 0
\(721\) −5.23607 −0.195001
\(722\) 0 0
\(723\) −29.0689 −1.08108
\(724\) 90.8115 3.37498
\(725\) 0 0
\(726\) −110.902 −4.11595
\(727\) −40.6869 −1.50899 −0.754497 0.656303i \(-0.772119\pi\)
−0.754497 + 0.656303i \(0.772119\pi\)
\(728\) −63.3050 −2.34624
\(729\) −7.00000 −0.259259
\(730\) 0 0
\(731\) −51.2705 −1.89631
\(732\) 60.3738 2.23148
\(733\) 50.1591 1.85267 0.926333 0.376705i \(-0.122943\pi\)
0.926333 + 0.376705i \(0.122943\pi\)
\(734\) 32.6525 1.20522
\(735\) 0 0
\(736\) 13.4164 0.494535
\(737\) −47.6525 −1.75530
\(738\) 33.4164 1.23007
\(739\) 1.56231 0.0574704 0.0287352 0.999587i \(-0.490852\pi\)
0.0287352 + 0.999587i \(0.490852\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −70.7771 −2.59831
\(743\) 8.76393 0.321517 0.160759 0.986994i \(-0.448606\pi\)
0.160759 + 0.986994i \(0.448606\pi\)
\(744\) −30.9787 −1.13573
\(745\) 0 0
\(746\) 34.4164 1.26007
\(747\) −2.18034 −0.0797745
\(748\) 128.936 4.71437
\(749\) −84.1033 −3.07307
\(750\) 0 0
\(751\) −27.4377 −1.00122 −0.500608 0.865674i \(-0.666890\pi\)
−0.500608 + 0.865674i \(0.666890\pi\)
\(752\) 75.0689 2.73748
\(753\) −13.2148 −0.481573
\(754\) 31.4164 1.14412
\(755\) 0 0
\(756\) 45.9787 1.67223
\(757\) −6.88854 −0.250368 −0.125184 0.992134i \(-0.539952\pi\)
−0.125184 + 0.992134i \(0.539952\pi\)
\(758\) 95.6656 3.47473
\(759\) −15.1246 −0.548989
\(760\) 0 0
\(761\) 27.3820 0.992595 0.496298 0.868152i \(-0.334692\pi\)
0.496298 + 0.868152i \(0.334692\pi\)
\(762\) −5.00000 −0.181131
\(763\) −33.6525 −1.21830
\(764\) −87.1033 −3.15129
\(765\) 0 0
\(766\) −57.7771 −2.08757
\(767\) −5.52786 −0.199600
\(768\) 32.5623 1.17499
\(769\) 15.2705 0.550669 0.275334 0.961349i \(-0.411211\pi\)
0.275334 + 0.961349i \(0.411211\pi\)
\(770\) 0 0
\(771\) −9.39512 −0.338357
\(772\) 112.957 4.06543
\(773\) 48.0344 1.72768 0.863839 0.503767i \(-0.168053\pi\)
0.863839 + 0.503767i \(0.168053\pi\)
\(774\) −55.3050 −1.98790
\(775\) 0 0
\(776\) 55.1591 1.98009
\(777\) −39.2705 −1.40882
\(778\) −11.7082 −0.419759
\(779\) 0 0
\(780\) 0 0
\(781\) 24.7771 0.886594
\(782\) 15.7082 0.561724
\(783\) −13.4164 −0.479463
\(784\) 107.846 3.85164
\(785\) 0 0
\(786\) 70.2492 2.50571
\(787\) −43.5967 −1.55406 −0.777028 0.629466i \(-0.783274\pi\)
−0.777028 + 0.629466i \(0.783274\pi\)
\(788\) 36.2705 1.29208
\(789\) −50.5755 −1.80053
\(790\) 0 0
\(791\) −39.5066 −1.40469
\(792\) 81.7771 2.90582
\(793\) 11.1246 0.395047
\(794\) 23.6525 0.839395
\(795\) 0 0
\(796\) 94.2492 3.34058
\(797\) 27.8673 0.987109 0.493554 0.869715i \(-0.335697\pi\)
0.493554 + 0.869715i \(0.335697\pi\)
\(798\) 0 0
\(799\) 36.9787 1.30821
\(800\) 0 0
\(801\) −7.41641 −0.262046
\(802\) 15.4164 0.544372
\(803\) 58.5967 2.06783
\(804\) 94.5197 3.33345
\(805\) 0 0
\(806\) −9.70820 −0.341957
\(807\) 20.5279 0.722615
\(808\) −97.3951 −3.42635
\(809\) −2.23607 −0.0786160 −0.0393080 0.999227i \(-0.512515\pi\)
−0.0393080 + 0.999227i \(0.512515\pi\)
\(810\) 0 0
\(811\) 9.61803 0.337735 0.168867 0.985639i \(-0.445989\pi\)
0.168867 + 0.985639i \(0.445989\pi\)
\(812\) −123.374 −4.32957
\(813\) 25.3262 0.888230
\(814\) 59.3951 2.08180
\(815\) 0 0
\(816\) −106.957 −3.74426
\(817\) 0 0
\(818\) −43.0344 −1.50466
\(819\) −16.9443 −0.592081
\(820\) 0 0
\(821\) 27.9230 0.974519 0.487259 0.873257i \(-0.337997\pi\)
0.487259 + 0.873257i \(0.337997\pi\)
\(822\) −54.0689 −1.88587
\(823\) 36.7426 1.28077 0.640384 0.768055i \(-0.278775\pi\)
0.640384 + 0.768055i \(0.278775\pi\)
\(824\) −9.23607 −0.321754
\(825\) 0 0
\(826\) 30.6525 1.06654
\(827\) −31.2492 −1.08664 −0.543321 0.839525i \(-0.682833\pi\)
−0.543321 + 0.839525i \(0.682833\pi\)
\(828\) 12.0000 0.417029
\(829\) −1.00000 −0.0347314 −0.0173657 0.999849i \(-0.505528\pi\)
−0.0173657 + 0.999849i \(0.505528\pi\)
\(830\) 0 0
\(831\) 26.8328 0.930820
\(832\) −17.4164 −0.603805
\(833\) 53.1246 1.84066
\(834\) 81.9574 2.83795
\(835\) 0 0
\(836\) 0 0
\(837\) 4.14590 0.143303
\(838\) −24.9443 −0.861686
\(839\) −54.2361 −1.87244 −0.936219 0.351418i \(-0.885699\pi\)
−0.936219 + 0.351418i \(0.885699\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 39.2705 1.35335
\(843\) 10.3262 0.355655
\(844\) 59.3951 2.04446
\(845\) 0 0
\(846\) 39.8885 1.37140
\(847\) 80.2492 2.75740
\(848\) −62.8885 −2.15960
\(849\) 53.1378 1.82368
\(850\) 0 0
\(851\) 5.12461 0.175669
\(852\) −49.1459 −1.68371
\(853\) 46.8541 1.60425 0.802127 0.597154i \(-0.203702\pi\)
0.802127 + 0.597154i \(0.203702\pi\)
\(854\) −61.6869 −2.11088
\(855\) 0 0
\(856\) −148.353 −5.07059
\(857\) −24.8197 −0.847823 −0.423912 0.905704i \(-0.639343\pi\)
−0.423912 + 0.905704i \(0.639343\pi\)
\(858\) 64.0689 2.18728
\(859\) 11.9098 0.406358 0.203179 0.979142i \(-0.434873\pi\)
0.203179 + 0.979142i \(0.434873\pi\)
\(860\) 0 0
\(861\) −60.4508 −2.06016
\(862\) 27.8885 0.949888
\(863\) 31.9230 1.08667 0.543336 0.839516i \(-0.317161\pi\)
0.543336 + 0.839516i \(0.317161\pi\)
\(864\) 24.2705 0.825700
\(865\) 0 0
\(866\) 87.3394 2.96791
\(867\) −14.6738 −0.498347
\(868\) 38.1246 1.29403
\(869\) −5.47214 −0.185629
\(870\) 0 0
\(871\) 17.4164 0.590132
\(872\) −59.3607 −2.01021
\(873\) 14.7639 0.499683
\(874\) 0 0
\(875\) 0 0
\(876\) −116.228 −3.92698
\(877\) −45.0344 −1.52071 −0.760353 0.649511i \(-0.774974\pi\)
−0.760353 + 0.649511i \(0.774974\pi\)
\(878\) −95.5755 −3.22552
\(879\) 30.1246 1.01608
\(880\) 0 0
\(881\) 7.47214 0.251743 0.125871 0.992047i \(-0.459827\pi\)
0.125871 + 0.992047i \(0.459827\pi\)
\(882\) 57.3050 1.92956
\(883\) −21.7771 −0.732857 −0.366429 0.930446i \(-0.619420\pi\)
−0.366429 + 0.930446i \(0.619420\pi\)
\(884\) −47.1246 −1.58497
\(885\) 0 0
\(886\) 33.1803 1.11472
\(887\) 36.9443 1.24047 0.620234 0.784417i \(-0.287038\pi\)
0.620234 + 0.784417i \(0.287038\pi\)
\(888\) −69.2705 −2.32457
\(889\) 3.61803 0.121345
\(890\) 0 0
\(891\) −60.1935 −2.01656
\(892\) 91.6869 3.06991
\(893\) 0 0
\(894\) 55.4508 1.85455
\(895\) 0 0
\(896\) 4.61803 0.154278
\(897\) 5.52786 0.184570
\(898\) −64.9230 −2.16651
\(899\) −11.1246 −0.371027
\(900\) 0 0
\(901\) −30.9787 −1.03205
\(902\) 91.4296 3.04427
\(903\) 100.048 3.32938
\(904\) −69.6869 −2.31775
\(905\) 0 0
\(906\) 33.9443 1.12772
\(907\) 38.9574 1.29356 0.646780 0.762677i \(-0.276115\pi\)
0.646780 + 0.762677i \(0.276115\pi\)
\(908\) 70.2492 2.33130
\(909\) −26.0689 −0.864650
\(910\) 0 0
\(911\) −22.8541 −0.757190 −0.378595 0.925562i \(-0.623593\pi\)
−0.378595 + 0.925562i \(0.623593\pi\)
\(912\) 0 0
\(913\) −5.96556 −0.197431
\(914\) −14.5623 −0.481678
\(915\) 0 0
\(916\) 100.249 3.31233
\(917\) −50.8328 −1.67865
\(918\) 28.4164 0.937881
\(919\) −30.5066 −1.00632 −0.503160 0.864194i \(-0.667829\pi\)
−0.503160 + 0.864194i \(0.667829\pi\)
\(920\) 0 0
\(921\) 72.8115 2.39922
\(922\) −21.0344 −0.692732
\(923\) −9.05573 −0.298073
\(924\) −251.602 −8.27709
\(925\) 0 0
\(926\) −109.610 −3.60200
\(927\) −2.47214 −0.0811956
\(928\) −65.1246 −2.13782
\(929\) 25.4721 0.835714 0.417857 0.908513i \(-0.362781\pi\)
0.417857 + 0.908513i \(0.362781\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 80.2279 2.62795
\(933\) −36.3050 −1.18857
\(934\) 7.14590 0.233821
\(935\) 0 0
\(936\) −29.8885 −0.976938
\(937\) 26.8328 0.876590 0.438295 0.898831i \(-0.355583\pi\)
0.438295 + 0.898831i \(0.355583\pi\)
\(938\) −96.5755 −3.15330
\(939\) −44.5967 −1.45536
\(940\) 0 0
\(941\) −59.7426 −1.94755 −0.973777 0.227503i \(-0.926944\pi\)
−0.973777 + 0.227503i \(0.926944\pi\)
\(942\) 10.6525 0.347076
\(943\) 7.88854 0.256886
\(944\) 27.2361 0.886459
\(945\) 0 0
\(946\) −151.318 −4.91978
\(947\) −37.6869 −1.22466 −0.612330 0.790602i \(-0.709768\pi\)
−0.612330 + 0.790602i \(0.709768\pi\)
\(948\) 10.8541 0.352525
\(949\) −21.4164 −0.695206
\(950\) 0 0
\(951\) −24.4721 −0.793563
\(952\) 153.644 4.97964
\(953\) 13.4164 0.434600 0.217300 0.976105i \(-0.430275\pi\)
0.217300 + 0.976105i \(0.430275\pi\)
\(954\) −33.4164 −1.08190
\(955\) 0 0
\(956\) 3.43769 0.111183
\(957\) 73.4164 2.37322
\(958\) −72.6312 −2.34661
\(959\) 39.1246 1.26340
\(960\) 0 0
\(961\) −27.5623 −0.889107
\(962\) −21.7082 −0.699901
\(963\) −39.7082 −1.27958
\(964\) 63.1033 2.03242
\(965\) 0 0
\(966\) −30.6525 −0.986227
\(967\) 6.09017 0.195847 0.0979233 0.995194i \(-0.468780\pi\)
0.0979233 + 0.995194i \(0.468780\pi\)
\(968\) 141.554 4.54972
\(969\) 0 0
\(970\) 0 0
\(971\) 19.2016 0.616210 0.308105 0.951352i \(-0.400305\pi\)
0.308105 + 0.951352i \(0.400305\pi\)
\(972\) 86.8328 2.78516
\(973\) −59.3050 −1.90123
\(974\) −26.5066 −0.849326
\(975\) 0 0
\(976\) −54.8115 −1.75447
\(977\) −32.2148 −1.03064 −0.515321 0.856997i \(-0.672327\pi\)
−0.515321 + 0.856997i \(0.672327\pi\)
\(978\) −16.1803 −0.517390
\(979\) −20.2918 −0.648529
\(980\) 0 0
\(981\) −15.8885 −0.507282
\(982\) −72.6869 −2.31953
\(983\) −12.9787 −0.413957 −0.206978 0.978346i \(-0.566363\pi\)
−0.206978 + 0.978346i \(0.566363\pi\)
\(984\) −106.631 −3.39928
\(985\) 0 0
\(986\) −76.2492 −2.42827
\(987\) −72.1591 −2.29685
\(988\) 0 0
\(989\) −13.0557 −0.415148
\(990\) 0 0
\(991\) 15.4164 0.489718 0.244859 0.969559i \(-0.421258\pi\)
0.244859 + 0.969559i \(0.421258\pi\)
\(992\) 20.1246 0.638957
\(993\) −30.3262 −0.962374
\(994\) 50.2148 1.59272
\(995\) 0 0
\(996\) 11.8328 0.374937
\(997\) −6.74265 −0.213542 −0.106771 0.994284i \(-0.534051\pi\)
−0.106771 + 0.994284i \(0.534051\pi\)
\(998\) −27.7426 −0.878178
\(999\) 9.27051 0.293306
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 9025.2.a.u.1.2 yes 2
5.4 even 2 9025.2.a.l.1.1 2
19.18 odd 2 9025.2.a.m.1.1 yes 2
95.94 odd 2 9025.2.a.t.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9025.2.a.l.1.1 2 5.4 even 2
9025.2.a.m.1.1 yes 2 19.18 odd 2
9025.2.a.t.1.2 yes 2 95.94 odd 2
9025.2.a.u.1.2 yes 2 1.1 even 1 trivial