Properties

Label 9025.2.a.bg.1.2
Level $9025$
Weight $2$
Character 9025.1
Self dual yes
Analytic conductor $72.065$
Analytic rank $1$
Dimension $4$
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: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.7537.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} + 4x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.37933\) 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)
 
\(f(q)\) \(=\) \(q-1.09744 q^{2} +0.379334 q^{3} -0.795629 q^{4} -0.416295 q^{6} -1.89307 q^{7} +3.06803 q^{8} -2.85611 q^{9} +O(q^{10})\) \(q-1.09744 q^{2} +0.379334 q^{3} -0.795629 q^{4} -0.416295 q^{6} -1.89307 q^{7} +3.06803 q^{8} -2.85611 q^{9} +0.134400 q^{11} -0.301809 q^{12} -3.51373 q^{13} +2.07752 q^{14} -1.77572 q^{16} +1.66123 q^{17} +3.13440 q^{18} -0.718104 q^{21} -0.147496 q^{22} -5.36984 q^{23} +1.16381 q^{24} +3.85611 q^{26} -2.22142 q^{27} +1.50618 q^{28} +4.97059 q^{29} +6.56472 q^{31} -4.18732 q^{32} +0.0509824 q^{33} -1.82310 q^{34} +2.27240 q^{36} +1.69819 q^{37} -1.33288 q^{39} +10.6327 q^{41} +0.788075 q^{42} -8.50784 q^{43} -0.106932 q^{44} +5.89307 q^{46} +11.1154 q^{47} -0.673589 q^{48} -3.41630 q^{49} +0.630160 q^{51} +2.79563 q^{52} +0.264847 q^{53} +2.43787 q^{54} -5.80799 q^{56} -5.45492 q^{58} -6.89667 q^{59} +9.17589 q^{61} -7.20437 q^{62} +5.40680 q^{63} +8.14676 q^{64} -0.0559501 q^{66} +2.95354 q^{67} -1.32172 q^{68} -2.03696 q^{69} +1.32835 q^{71} -8.76262 q^{72} +6.34237 q^{73} -1.86366 q^{74} -0.254428 q^{77} +1.46275 q^{78} -1.46728 q^{79} +7.72566 q^{81} -11.6688 q^{82} -7.44736 q^{83} +0.571345 q^{84} +9.33683 q^{86} +1.88551 q^{87} +0.412343 q^{88} +9.73608 q^{89} +6.65174 q^{91} +4.27240 q^{92} +2.49022 q^{93} -12.1985 q^{94} -1.58839 q^{96} -17.4689 q^{97} +3.74917 q^{98} -0.383860 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 2 q^{6} + 4 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 2 q^{6} + 4 q^{7} - 12 q^{8} + q^{9} - 2 q^{11} - 6 q^{12} - 7 q^{13} - q^{14} + 7 q^{16} + q^{17} + 10 q^{18} - 4 q^{21} - 2 q^{22} - 2 q^{23} + 23 q^{24} + 3 q^{26} - 12 q^{27} + 19 q^{28} - q^{29} - 30 q^{32} - 19 q^{33} + 15 q^{34} - 7 q^{36} + 2 q^{37} + 15 q^{39} - 8 q^{41} + 15 q^{42} - q^{43} - 12 q^{44} + 12 q^{46} + 12 q^{47} - 23 q^{48} - 10 q^{49} + 22 q^{51} + 3 q^{52} + 5 q^{53} - 34 q^{54} - 41 q^{56} + 27 q^{58} - 5 q^{59} - 37 q^{62} + 3 q^{63} + 56 q^{64} - 31 q^{66} - 4 q^{67} - 16 q^{68} - 9 q^{69} + 20 q^{71} - 17 q^{72} + 20 q^{73} + 25 q^{74} - 14 q^{77} + 18 q^{78} + 17 q^{79} + 12 q^{81} - 21 q^{82} - q^{83} - 20 q^{84} + 8 q^{86} + 16 q^{87} + 7 q^{88} + 11 q^{89} + 6 q^{91} + q^{92} + 8 q^{93} - 31 q^{94} + 21 q^{96} - q^{97} - 9 q^{98} + 38 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09744 −0.776006 −0.388003 0.921658i \(-0.626835\pi\)
−0.388003 + 0.921658i \(0.626835\pi\)
\(3\) 0.379334 0.219008 0.109504 0.993986i \(-0.465074\pi\)
0.109504 + 0.993986i \(0.465074\pi\)
\(4\) −0.795629 −0.397815
\(5\) 0 0
\(6\) −0.416295 −0.169952
\(7\) −1.89307 −0.715512 −0.357756 0.933815i \(-0.616458\pi\)
−0.357756 + 0.933815i \(0.616458\pi\)
\(8\) 3.06803 1.08471
\(9\) −2.85611 −0.952035
\(10\) 0 0
\(11\) 0.134400 0.0405231 0.0202615 0.999795i \(-0.493550\pi\)
0.0202615 + 0.999795i \(0.493550\pi\)
\(12\) −0.301809 −0.0871248
\(13\) −3.51373 −0.974534 −0.487267 0.873253i \(-0.662006\pi\)
−0.487267 + 0.873253i \(0.662006\pi\)
\(14\) 2.07752 0.555242
\(15\) 0 0
\(16\) −1.77572 −0.443929
\(17\) 1.66123 0.402907 0.201454 0.979498i \(-0.435433\pi\)
0.201454 + 0.979498i \(0.435433\pi\)
\(18\) 3.13440 0.738785
\(19\) 0 0
\(20\) 0 0
\(21\) −0.718104 −0.156703
\(22\) −0.147496 −0.0314462
\(23\) −5.36984 −1.11969 −0.559844 0.828598i \(-0.689139\pi\)
−0.559844 + 0.828598i \(0.689139\pi\)
\(24\) 1.16381 0.237561
\(25\) 0 0
\(26\) 3.85611 0.756245
\(27\) −2.22142 −0.427512
\(28\) 1.50618 0.284641
\(29\) 4.97059 0.923016 0.461508 0.887136i \(-0.347309\pi\)
0.461508 + 0.887136i \(0.347309\pi\)
\(30\) 0 0
\(31\) 6.56472 1.17906 0.589529 0.807747i \(-0.299313\pi\)
0.589529 + 0.807747i \(0.299313\pi\)
\(32\) −4.18732 −0.740221
\(33\) 0.0509824 0.00887490
\(34\) −1.82310 −0.312658
\(35\) 0 0
\(36\) 2.27240 0.378734
\(37\) 1.69819 0.279181 0.139590 0.990209i \(-0.455421\pi\)
0.139590 + 0.990209i \(0.455421\pi\)
\(38\) 0 0
\(39\) −1.33288 −0.213431
\(40\) 0 0
\(41\) 10.6327 1.66056 0.830278 0.557349i \(-0.188182\pi\)
0.830278 + 0.557349i \(0.188182\pi\)
\(42\) 0.788075 0.121603
\(43\) −8.50784 −1.29743 −0.648717 0.761030i \(-0.724694\pi\)
−0.648717 + 0.761030i \(0.724694\pi\)
\(44\) −0.106932 −0.0161207
\(45\) 0 0
\(46\) 5.89307 0.868885
\(47\) 11.1154 1.62135 0.810675 0.585497i \(-0.199101\pi\)
0.810675 + 0.585497i \(0.199101\pi\)
\(48\) −0.673589 −0.0972242
\(49\) −3.41630 −0.488042
\(50\) 0 0
\(51\) 0.630160 0.0882401
\(52\) 2.79563 0.387684
\(53\) 0.264847 0.0363796 0.0181898 0.999835i \(-0.494210\pi\)
0.0181898 + 0.999835i \(0.494210\pi\)
\(54\) 2.43787 0.331752
\(55\) 0 0
\(56\) −5.80799 −0.776125
\(57\) 0 0
\(58\) −5.45492 −0.716266
\(59\) −6.89667 −0.897870 −0.448935 0.893564i \(-0.648196\pi\)
−0.448935 + 0.893564i \(0.648196\pi\)
\(60\) 0 0
\(61\) 9.17589 1.17485 0.587426 0.809278i \(-0.300141\pi\)
0.587426 + 0.809278i \(0.300141\pi\)
\(62\) −7.20437 −0.914956
\(63\) 5.40680 0.681193
\(64\) 8.14676 1.01834
\(65\) 0 0
\(66\) −0.0559501 −0.00688698
\(67\) 2.95354 0.360833 0.180416 0.983590i \(-0.442255\pi\)
0.180416 + 0.983590i \(0.442255\pi\)
\(68\) −1.32172 −0.160282
\(69\) −2.03696 −0.245221
\(70\) 0 0
\(71\) 1.32835 0.157646 0.0788232 0.996889i \(-0.474884\pi\)
0.0788232 + 0.996889i \(0.474884\pi\)
\(72\) −8.76262 −1.03268
\(73\) 6.34237 0.742319 0.371159 0.928569i \(-0.378960\pi\)
0.371159 + 0.928569i \(0.378960\pi\)
\(74\) −1.86366 −0.216646
\(75\) 0 0
\(76\) 0 0
\(77\) −0.254428 −0.0289948
\(78\) 1.46275 0.165624
\(79\) −1.46728 −0.165082 −0.0825408 0.996588i \(-0.526303\pi\)
−0.0825408 + 0.996588i \(0.526303\pi\)
\(80\) 0 0
\(81\) 7.72566 0.858406
\(82\) −11.6688 −1.28860
\(83\) −7.44736 −0.817454 −0.408727 0.912657i \(-0.634027\pi\)
−0.408727 + 0.912657i \(0.634027\pi\)
\(84\) 0.571345 0.0623388
\(85\) 0 0
\(86\) 9.33683 1.00682
\(87\) 1.88551 0.202148
\(88\) 0.412343 0.0439559
\(89\) 9.73608 1.03202 0.516011 0.856582i \(-0.327416\pi\)
0.516011 + 0.856582i \(0.327416\pi\)
\(90\) 0 0
\(91\) 6.65174 0.697291
\(92\) 4.27240 0.445429
\(93\) 2.49022 0.258224
\(94\) −12.1985 −1.25818
\(95\) 0 0
\(96\) −1.58839 −0.162115
\(97\) −17.4689 −1.77370 −0.886851 0.462055i \(-0.847112\pi\)
−0.886851 + 0.462055i \(0.847112\pi\)
\(98\) 3.74917 0.378724
\(99\) −0.383860 −0.0385794
\(100\) 0 0
\(101\) 5.39731 0.537052 0.268526 0.963272i \(-0.413463\pi\)
0.268526 + 0.963272i \(0.413463\pi\)
\(102\) −0.691562 −0.0684749
\(103\) −2.14750 −0.211599 −0.105800 0.994387i \(-0.533740\pi\)
−0.105800 + 0.994387i \(0.533740\pi\)
\(104\) −10.7802 −1.05709
\(105\) 0 0
\(106\) −0.290654 −0.0282308
\(107\) 1.00093 0.0967631 0.0483815 0.998829i \(-0.484594\pi\)
0.0483815 + 0.998829i \(0.484594\pi\)
\(108\) 1.76743 0.170071
\(109\) 16.2629 1.55770 0.778852 0.627208i \(-0.215802\pi\)
0.778852 + 0.627208i \(0.215802\pi\)
\(110\) 0 0
\(111\) 0.644181 0.0611430
\(112\) 3.36155 0.317637
\(113\) −0.843010 −0.0793037 −0.0396519 0.999214i \(-0.512625\pi\)
−0.0396519 + 0.999214i \(0.512625\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −3.95475 −0.367189
\(117\) 10.0356 0.927791
\(118\) 7.56867 0.696752
\(119\) −3.14482 −0.288285
\(120\) 0 0
\(121\) −10.9819 −0.998358
\(122\) −10.0700 −0.911692
\(123\) 4.03336 0.363676
\(124\) −5.22308 −0.469046
\(125\) 0 0
\(126\) −5.93363 −0.528610
\(127\) −18.7397 −1.66288 −0.831439 0.555616i \(-0.812482\pi\)
−0.831439 + 0.555616i \(0.812482\pi\)
\(128\) −0.565920 −0.0500208
\(129\) −3.22731 −0.284149
\(130\) 0 0
\(131\) 2.88644 0.252189 0.126095 0.992018i \(-0.459756\pi\)
0.126095 + 0.992018i \(0.459756\pi\)
\(132\) −0.0405631 −0.00353057
\(133\) 0 0
\(134\) −3.24133 −0.280008
\(135\) 0 0
\(136\) 5.09670 0.437039
\(137\) 18.8316 1.60889 0.804445 0.594027i \(-0.202463\pi\)
0.804445 + 0.594027i \(0.202463\pi\)
\(138\) 2.23544 0.190293
\(139\) −18.1795 −1.54196 −0.770982 0.636857i \(-0.780234\pi\)
−0.770982 + 0.636857i \(0.780234\pi\)
\(140\) 0 0
\(141\) 4.21645 0.355089
\(142\) −1.45778 −0.122334
\(143\) −0.472245 −0.0394912
\(144\) 5.07163 0.422636
\(145\) 0 0
\(146\) −6.96036 −0.576044
\(147\) −1.29592 −0.106885
\(148\) −1.35113 −0.111062
\(149\) −22.2543 −1.82315 −0.911573 0.411138i \(-0.865131\pi\)
−0.911573 + 0.411138i \(0.865131\pi\)
\(150\) 0 0
\(151\) 3.33482 0.271384 0.135692 0.990751i \(-0.456674\pi\)
0.135692 + 0.990751i \(0.456674\pi\)
\(152\) 0 0
\(153\) −4.74465 −0.383582
\(154\) 0.279219 0.0225001
\(155\) 0 0
\(156\) 1.06048 0.0849061
\(157\) −7.26291 −0.579643 −0.289822 0.957081i \(-0.593596\pi\)
−0.289822 + 0.957081i \(0.593596\pi\)
\(158\) 1.61025 0.128104
\(159\) 0.100466 0.00796744
\(160\) 0 0
\(161\) 10.1655 0.801151
\(162\) −8.47843 −0.666129
\(163\) 19.7783 1.54916 0.774578 0.632478i \(-0.217962\pi\)
0.774578 + 0.632478i \(0.217962\pi\)
\(164\) −8.45972 −0.660593
\(165\) 0 0
\(166\) 8.17302 0.634350
\(167\) 3.40320 0.263348 0.131674 0.991293i \(-0.457965\pi\)
0.131674 + 0.991293i \(0.457965\pi\)
\(168\) −2.20317 −0.169978
\(169\) −0.653675 −0.0502827
\(170\) 0 0
\(171\) 0 0
\(172\) 6.76909 0.516138
\(173\) 10.5857 0.804817 0.402409 0.915460i \(-0.368173\pi\)
0.402409 + 0.915460i \(0.368173\pi\)
\(174\) −2.06923 −0.156868
\(175\) 0 0
\(176\) −0.238656 −0.0179894
\(177\) −2.61614 −0.196641
\(178\) −10.6847 −0.800855
\(179\) −14.6024 −1.09144 −0.545718 0.837969i \(-0.683743\pi\)
−0.545718 + 0.837969i \(0.683743\pi\)
\(180\) 0 0
\(181\) −5.43261 −0.403803 −0.201901 0.979406i \(-0.564712\pi\)
−0.201901 + 0.979406i \(0.564712\pi\)
\(182\) −7.29987 −0.541102
\(183\) 3.48072 0.257303
\(184\) −16.4748 −1.21454
\(185\) 0 0
\(186\) −2.73286 −0.200383
\(187\) 0.223269 0.0163271
\(188\) −8.84375 −0.644996
\(189\) 4.20530 0.305890
\(190\) 0 0
\(191\) 20.4758 1.48157 0.740787 0.671740i \(-0.234453\pi\)
0.740787 + 0.671740i \(0.234453\pi\)
\(192\) 3.09034 0.223026
\(193\) −11.0235 −0.793490 −0.396745 0.917929i \(-0.629860\pi\)
−0.396745 + 0.917929i \(0.629860\pi\)
\(194\) 19.1711 1.37640
\(195\) 0 0
\(196\) 2.71810 0.194150
\(197\) 19.8532 1.41448 0.707242 0.706971i \(-0.249939\pi\)
0.707242 + 0.706971i \(0.249939\pi\)
\(198\) 0.421263 0.0299379
\(199\) 21.0026 1.48883 0.744417 0.667715i \(-0.232728\pi\)
0.744417 + 0.667715i \(0.232728\pi\)
\(200\) 0 0
\(201\) 1.12038 0.0790254
\(202\) −5.92321 −0.416756
\(203\) −9.40967 −0.660429
\(204\) −0.501374 −0.0351032
\(205\) 0 0
\(206\) 2.35674 0.164202
\(207\) 15.3368 1.06598
\(208\) 6.23939 0.432624
\(209\) 0 0
\(210\) 0 0
\(211\) −12.8257 −0.882956 −0.441478 0.897272i \(-0.645546\pi\)
−0.441478 + 0.897272i \(0.645546\pi\)
\(212\) −0.210720 −0.0144723
\(213\) 0.503889 0.0345259
\(214\) −1.09845 −0.0750887
\(215\) 0 0
\(216\) −6.81538 −0.463728
\(217\) −12.4275 −0.843630
\(218\) −17.8475 −1.20879
\(219\) 2.40588 0.162574
\(220\) 0 0
\(221\) −5.83712 −0.392647
\(222\) −0.706949 −0.0474473
\(223\) −20.3944 −1.36571 −0.682856 0.730553i \(-0.739263\pi\)
−0.682856 + 0.730553i \(0.739263\pi\)
\(224\) 7.92688 0.529637
\(225\) 0 0
\(226\) 0.925152 0.0615402
\(227\) −25.4172 −1.68700 −0.843500 0.537129i \(-0.819509\pi\)
−0.843500 + 0.537129i \(0.819509\pi\)
\(228\) 0 0
\(229\) 2.21553 0.146406 0.0732030 0.997317i \(-0.476678\pi\)
0.0732030 + 0.997317i \(0.476678\pi\)
\(230\) 0 0
\(231\) −0.0965132 −0.00635010
\(232\) 15.2499 1.00121
\(233\) 14.1576 0.927498 0.463749 0.885967i \(-0.346504\pi\)
0.463749 + 0.885967i \(0.346504\pi\)
\(234\) −11.0134 −0.719972
\(235\) 0 0
\(236\) 5.48719 0.357186
\(237\) −0.556588 −0.0361543
\(238\) 3.45125 0.223711
\(239\) 3.01476 0.195008 0.0975042 0.995235i \(-0.468914\pi\)
0.0975042 + 0.995235i \(0.468914\pi\)
\(240\) 0 0
\(241\) −23.7792 −1.53175 −0.765877 0.642987i \(-0.777695\pi\)
−0.765877 + 0.642987i \(0.777695\pi\)
\(242\) 12.0520 0.774732
\(243\) 9.59486 0.615511
\(244\) −7.30060 −0.467373
\(245\) 0 0
\(246\) −4.42636 −0.282215
\(247\) 0 0
\(248\) 20.1407 1.27894
\(249\) −2.82504 −0.179029
\(250\) 0 0
\(251\) 17.1899 1.08502 0.542509 0.840050i \(-0.317475\pi\)
0.542509 + 0.840050i \(0.317475\pi\)
\(252\) −4.30181 −0.270988
\(253\) −0.721706 −0.0453733
\(254\) 20.5656 1.29040
\(255\) 0 0
\(256\) −15.6725 −0.979529
\(257\) 19.5429 1.21905 0.609525 0.792767i \(-0.291360\pi\)
0.609525 + 0.792767i \(0.291360\pi\)
\(258\) 3.54178 0.220501
\(259\) −3.21479 −0.199757
\(260\) 0 0
\(261\) −14.1965 −0.878744
\(262\) −3.16769 −0.195700
\(263\) −8.81360 −0.543470 −0.271735 0.962372i \(-0.587597\pi\)
−0.271735 + 0.962372i \(0.587597\pi\)
\(264\) 0.156416 0.00962672
\(265\) 0 0
\(266\) 0 0
\(267\) 3.69322 0.226022
\(268\) −2.34993 −0.143545
\(269\) 0.288362 0.0175818 0.00879088 0.999961i \(-0.497202\pi\)
0.00879088 + 0.999961i \(0.497202\pi\)
\(270\) 0 0
\(271\) −24.8712 −1.51082 −0.755409 0.655253i \(-0.772562\pi\)
−0.755409 + 0.655253i \(0.772562\pi\)
\(272\) −2.94987 −0.178862
\(273\) 2.52323 0.152713
\(274\) −20.6665 −1.24851
\(275\) 0 0
\(276\) 1.62067 0.0975526
\(277\) 4.40486 0.264662 0.132331 0.991206i \(-0.457754\pi\)
0.132331 + 0.991206i \(0.457754\pi\)
\(278\) 19.9509 1.19657
\(279\) −18.7495 −1.12250
\(280\) 0 0
\(281\) −32.7214 −1.95200 −0.975998 0.217778i \(-0.930119\pi\)
−0.975998 + 0.217778i \(0.930119\pi\)
\(282\) −4.62729 −0.275551
\(283\) 1.32893 0.0789964 0.0394982 0.999220i \(-0.487424\pi\)
0.0394982 + 0.999220i \(0.487424\pi\)
\(284\) −1.05688 −0.0627140
\(285\) 0 0
\(286\) 0.518260 0.0306454
\(287\) −20.1285 −1.18815
\(288\) 11.9594 0.704717
\(289\) −14.2403 −0.837666
\(290\) 0 0
\(291\) −6.62656 −0.388456
\(292\) −5.04618 −0.295305
\(293\) 7.72365 0.451220 0.225610 0.974218i \(-0.427562\pi\)
0.225610 + 0.974218i \(0.427562\pi\)
\(294\) 1.42219 0.0829437
\(295\) 0 0
\(296\) 5.21010 0.302831
\(297\) −0.298558 −0.0173241
\(298\) 24.4228 1.41477
\(299\) 18.8682 1.09118
\(300\) 0 0
\(301\) 16.1059 0.928330
\(302\) −3.65976 −0.210595
\(303\) 2.04738 0.117619
\(304\) 0 0
\(305\) 0 0
\(306\) 5.20696 0.297662
\(307\) 9.10002 0.519366 0.259683 0.965694i \(-0.416382\pi\)
0.259683 + 0.965694i \(0.416382\pi\)
\(308\) 0.202430 0.0115345
\(309\) −0.814618 −0.0463420
\(310\) 0 0
\(311\) −12.4569 −0.706364 −0.353182 0.935555i \(-0.614900\pi\)
−0.353182 + 0.935555i \(0.614900\pi\)
\(312\) −4.08931 −0.231512
\(313\) −2.04553 −0.115620 −0.0578101 0.998328i \(-0.518412\pi\)
−0.0578101 + 0.998328i \(0.518412\pi\)
\(314\) 7.97059 0.449807
\(315\) 0 0
\(316\) 1.16741 0.0656719
\(317\) −23.5713 −1.32389 −0.661947 0.749551i \(-0.730270\pi\)
−0.661947 + 0.749551i \(0.730270\pi\)
\(318\) −0.110255 −0.00618278
\(319\) 0.668047 0.0374035
\(320\) 0 0
\(321\) 0.379685 0.0211919
\(322\) −11.1560 −0.621698
\(323\) 0 0
\(324\) −6.14676 −0.341487
\(325\) 0 0
\(326\) −21.7055 −1.20215
\(327\) 6.16907 0.341150
\(328\) 32.6216 1.80123
\(329\) −21.0422 −1.16010
\(330\) 0 0
\(331\) −18.7175 −1.02881 −0.514403 0.857549i \(-0.671986\pi\)
−0.514403 + 0.857549i \(0.671986\pi\)
\(332\) 5.92534 0.325195
\(333\) −4.85021 −0.265790
\(334\) −3.73480 −0.204359
\(335\) 0 0
\(336\) 1.27515 0.0695651
\(337\) 32.6881 1.78063 0.890316 0.455343i \(-0.150483\pi\)
0.890316 + 0.455343i \(0.150483\pi\)
\(338\) 0.717368 0.0390197
\(339\) −0.319782 −0.0173682
\(340\) 0 0
\(341\) 0.882297 0.0477791
\(342\) 0 0
\(343\) 19.7188 1.06471
\(344\) −26.1023 −1.40734
\(345\) 0 0
\(346\) −11.6172 −0.624543
\(347\) 2.56666 0.137785 0.0688927 0.997624i \(-0.478053\pi\)
0.0688927 + 0.997624i \(0.478053\pi\)
\(348\) −1.50017 −0.0804175
\(349\) 16.6195 0.889619 0.444810 0.895625i \(-0.353271\pi\)
0.444810 + 0.895625i \(0.353271\pi\)
\(350\) 0 0
\(351\) 7.80547 0.416625
\(352\) −0.562776 −0.0299961
\(353\) −28.3629 −1.50961 −0.754803 0.655951i \(-0.772268\pi\)
−0.754803 + 0.655951i \(0.772268\pi\)
\(354\) 2.87105 0.152595
\(355\) 0 0
\(356\) −7.74631 −0.410553
\(357\) −1.19294 −0.0631369
\(358\) 16.0252 0.846961
\(359\) 17.3885 0.917733 0.458866 0.888505i \(-0.348256\pi\)
0.458866 + 0.888505i \(0.348256\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 5.96195 0.313353
\(363\) −4.16582 −0.218649
\(364\) −5.29231 −0.277393
\(365\) 0 0
\(366\) −3.81988 −0.199668
\(367\) −25.8048 −1.34700 −0.673501 0.739186i \(-0.735210\pi\)
−0.673501 + 0.739186i \(0.735210\pi\)
\(368\) 9.53531 0.497062
\(369\) −30.3683 −1.58091
\(370\) 0 0
\(371\) −0.501374 −0.0260300
\(372\) −1.98129 −0.102725
\(373\) −27.0663 −1.40144 −0.700719 0.713437i \(-0.747138\pi\)
−0.700719 + 0.713437i \(0.747138\pi\)
\(374\) −0.245024 −0.0126699
\(375\) 0 0
\(376\) 34.1024 1.75870
\(377\) −17.4653 −0.899511
\(378\) −4.61505 −0.237373
\(379\) 12.4028 0.637092 0.318546 0.947907i \(-0.396806\pi\)
0.318546 + 0.947907i \(0.396806\pi\)
\(380\) 0 0
\(381\) −7.10859 −0.364184
\(382\) −22.4709 −1.14971
\(383\) 5.35942 0.273854 0.136927 0.990581i \(-0.456277\pi\)
0.136927 + 0.990581i \(0.456277\pi\)
\(384\) −0.214673 −0.0109550
\(385\) 0 0
\(386\) 12.0976 0.615753
\(387\) 24.2993 1.23520
\(388\) 13.8988 0.705605
\(389\) 8.56933 0.434482 0.217241 0.976118i \(-0.430294\pi\)
0.217241 + 0.976118i \(0.430294\pi\)
\(390\) 0 0
\(391\) −8.92053 −0.451131
\(392\) −10.4813 −0.529386
\(393\) 1.09492 0.0552316
\(394\) −21.7877 −1.09765
\(395\) 0 0
\(396\) 0.305411 0.0153475
\(397\) 10.6445 0.534234 0.267117 0.963664i \(-0.413929\pi\)
0.267117 + 0.963664i \(0.413929\pi\)
\(398\) −23.0490 −1.15534
\(399\) 0 0
\(400\) 0 0
\(401\) 7.65209 0.382127 0.191063 0.981578i \(-0.438806\pi\)
0.191063 + 0.981578i \(0.438806\pi\)
\(402\) −1.22955 −0.0613242
\(403\) −23.0667 −1.14903
\(404\) −4.29426 −0.213647
\(405\) 0 0
\(406\) 10.3265 0.512497
\(407\) 0.228237 0.0113133
\(408\) 1.93335 0.0957152
\(409\) −17.6887 −0.874650 −0.437325 0.899304i \(-0.644074\pi\)
−0.437325 + 0.899304i \(0.644074\pi\)
\(410\) 0 0
\(411\) 7.14345 0.352361
\(412\) 1.70861 0.0841772
\(413\) 13.0559 0.642437
\(414\) −16.8312 −0.827210
\(415\) 0 0
\(416\) 14.7131 0.721371
\(417\) −6.89609 −0.337703
\(418\) 0 0
\(419\) 1.18732 0.0580045 0.0290023 0.999579i \(-0.490767\pi\)
0.0290023 + 0.999579i \(0.490767\pi\)
\(420\) 0 0
\(421\) 33.3673 1.62622 0.813111 0.582109i \(-0.197772\pi\)
0.813111 + 0.582109i \(0.197772\pi\)
\(422\) 14.0754 0.685180
\(423\) −31.7468 −1.54358
\(424\) 0.812560 0.0394614
\(425\) 0 0
\(426\) −0.552987 −0.0267923
\(427\) −17.3706 −0.840621
\(428\) −0.796365 −0.0384938
\(429\) −0.179139 −0.00864890
\(430\) 0 0
\(431\) −6.17598 −0.297486 −0.148743 0.988876i \(-0.547523\pi\)
−0.148743 + 0.988876i \(0.547523\pi\)
\(432\) 3.94461 0.189785
\(433\) 18.5552 0.891707 0.445854 0.895106i \(-0.352900\pi\)
0.445854 + 0.895106i \(0.352900\pi\)
\(434\) 13.6384 0.654662
\(435\) 0 0
\(436\) −12.9392 −0.619677
\(437\) 0 0
\(438\) −2.64030 −0.126158
\(439\) −0.227312 −0.0108490 −0.00542450 0.999985i \(-0.501727\pi\)
−0.00542450 + 0.999985i \(0.501727\pi\)
\(440\) 0 0
\(441\) 9.75730 0.464633
\(442\) 6.40588 0.304696
\(443\) 34.9827 1.66208 0.831038 0.556215i \(-0.187747\pi\)
0.831038 + 0.556215i \(0.187747\pi\)
\(444\) −0.512529 −0.0243236
\(445\) 0 0
\(446\) 22.3816 1.05980
\(447\) −8.44182 −0.399285
\(448\) −15.4224 −0.728638
\(449\) −16.9509 −0.799961 −0.399980 0.916524i \(-0.630983\pi\)
−0.399980 + 0.916524i \(0.630983\pi\)
\(450\) 0 0
\(451\) 1.42904 0.0672909
\(452\) 0.670724 0.0315482
\(453\) 1.26501 0.0594353
\(454\) 27.8938 1.30912
\(455\) 0 0
\(456\) 0 0
\(457\) −1.60241 −0.0749578 −0.0374789 0.999297i \(-0.511933\pi\)
−0.0374789 + 0.999297i \(0.511933\pi\)
\(458\) −2.43140 −0.113612
\(459\) −3.69029 −0.172248
\(460\) 0 0
\(461\) −8.74162 −0.407138 −0.203569 0.979061i \(-0.565254\pi\)
−0.203569 + 0.979061i \(0.565254\pi\)
\(462\) 0.105917 0.00492772
\(463\) −21.1886 −0.984718 −0.492359 0.870392i \(-0.663865\pi\)
−0.492359 + 0.870392i \(0.663865\pi\)
\(464\) −8.82636 −0.409753
\(465\) 0 0
\(466\) −15.5371 −0.719744
\(467\) −20.4516 −0.946388 −0.473194 0.880958i \(-0.656899\pi\)
−0.473194 + 0.880958i \(0.656899\pi\)
\(468\) −7.98461 −0.369089
\(469\) −5.59126 −0.258180
\(470\) 0 0
\(471\) −2.75507 −0.126947
\(472\) −21.1592 −0.973931
\(473\) −1.14345 −0.0525760
\(474\) 0.610821 0.0280559
\(475\) 0 0
\(476\) 2.50211 0.114684
\(477\) −0.756432 −0.0346347
\(478\) −3.30851 −0.151328
\(479\) 23.5491 1.07599 0.537994 0.842949i \(-0.319182\pi\)
0.537994 + 0.842949i \(0.319182\pi\)
\(480\) 0 0
\(481\) −5.96699 −0.272071
\(482\) 26.0962 1.18865
\(483\) 3.85611 0.175459
\(484\) 8.73755 0.397161
\(485\) 0 0
\(486\) −10.5298 −0.477640
\(487\) −36.0392 −1.63309 −0.816546 0.577280i \(-0.804114\pi\)
−0.816546 + 0.577280i \(0.804114\pi\)
\(488\) 28.1519 1.27438
\(489\) 7.50258 0.339278
\(490\) 0 0
\(491\) 20.0595 0.905271 0.452635 0.891696i \(-0.350484\pi\)
0.452635 + 0.891696i \(0.350484\pi\)
\(492\) −3.20906 −0.144676
\(493\) 8.25729 0.371890
\(494\) 0 0
\(495\) 0 0
\(496\) −11.6571 −0.523418
\(497\) −2.51466 −0.112798
\(498\) 3.10030 0.138928
\(499\) −36.8729 −1.65066 −0.825328 0.564653i \(-0.809010\pi\)
−0.825328 + 0.564653i \(0.809010\pi\)
\(500\) 0 0
\(501\) 1.29095 0.0576753
\(502\) −18.8649 −0.841980
\(503\) 21.6487 0.965268 0.482634 0.875822i \(-0.339680\pi\)
0.482634 + 0.875822i \(0.339680\pi\)
\(504\) 16.5882 0.738899
\(505\) 0 0
\(506\) 0.792028 0.0352099
\(507\) −0.247961 −0.0110123
\(508\) 14.9098 0.661517
\(509\) −36.4558 −1.61588 −0.807938 0.589267i \(-0.799417\pi\)
−0.807938 + 0.589267i \(0.799417\pi\)
\(510\) 0 0
\(511\) −12.0065 −0.531138
\(512\) 18.3314 0.810141
\(513\) 0 0
\(514\) −21.4471 −0.945990
\(515\) 0 0
\(516\) 2.56774 0.113039
\(517\) 1.49391 0.0657021
\(518\) 3.52803 0.155013
\(519\) 4.01552 0.176262
\(520\) 0 0
\(521\) −22.6092 −0.990528 −0.495264 0.868742i \(-0.664929\pi\)
−0.495264 + 0.868742i \(0.664929\pi\)
\(522\) 15.5798 0.681910
\(523\) −0.532911 −0.0233026 −0.0116513 0.999932i \(-0.503709\pi\)
−0.0116513 + 0.999932i \(0.503709\pi\)
\(524\) −2.29654 −0.100325
\(525\) 0 0
\(526\) 9.67238 0.421736
\(527\) 10.9055 0.475051
\(528\) −0.0905303 −0.00393983
\(529\) 5.83518 0.253703
\(530\) 0 0
\(531\) 19.6976 0.854804
\(532\) 0 0
\(533\) −37.3606 −1.61827
\(534\) −4.05308 −0.175394
\(535\) 0 0
\(536\) 9.06156 0.391400
\(537\) −5.53919 −0.239034
\(538\) −0.316460 −0.0136436
\(539\) −0.459150 −0.0197770
\(540\) 0 0
\(541\) 5.01640 0.215672 0.107836 0.994169i \(-0.465608\pi\)
0.107836 + 0.994169i \(0.465608\pi\)
\(542\) 27.2946 1.17240
\(543\) −2.06077 −0.0884362
\(544\) −6.95610 −0.298240
\(545\) 0 0
\(546\) −2.76909 −0.118506
\(547\) −22.6299 −0.967584 −0.483792 0.875183i \(-0.660741\pi\)
−0.483792 + 0.875183i \(0.660741\pi\)
\(548\) −14.9830 −0.640040
\(549\) −26.2073 −1.11850
\(550\) 0 0
\(551\) 0 0
\(552\) −6.24946 −0.265995
\(553\) 2.77766 0.118118
\(554\) −4.83406 −0.205380
\(555\) 0 0
\(556\) 14.4641 0.613416
\(557\) −35.2554 −1.49382 −0.746910 0.664925i \(-0.768463\pi\)
−0.746910 + 0.664925i \(0.768463\pi\)
\(558\) 20.5764 0.871070
\(559\) 29.8943 1.26439
\(560\) 0 0
\(561\) 0.0846935 0.00357576
\(562\) 35.9097 1.51476
\(563\) 24.6295 1.03801 0.519005 0.854771i \(-0.326302\pi\)
0.519005 + 0.854771i \(0.326302\pi\)
\(564\) −3.35473 −0.141260
\(565\) 0 0
\(566\) −1.45841 −0.0613017
\(567\) −14.6252 −0.614200
\(568\) 4.07542 0.171001
\(569\) −20.0193 −0.839252 −0.419626 0.907697i \(-0.637839\pi\)
−0.419626 + 0.907697i \(0.637839\pi\)
\(570\) 0 0
\(571\) −16.6121 −0.695195 −0.347597 0.937644i \(-0.613002\pi\)
−0.347597 + 0.937644i \(0.613002\pi\)
\(572\) 0.375732 0.0157102
\(573\) 7.76715 0.324477
\(574\) 22.0898 0.922010
\(575\) 0 0
\(576\) −23.2680 −0.969500
\(577\) −12.4486 −0.518244 −0.259122 0.965845i \(-0.583433\pi\)
−0.259122 + 0.965845i \(0.583433\pi\)
\(578\) 15.6279 0.650034
\(579\) −4.18159 −0.173781
\(580\) 0 0
\(581\) 14.0984 0.584899
\(582\) 7.27224 0.301444
\(583\) 0.0355955 0.00147421
\(584\) 19.4586 0.805202
\(585\) 0 0
\(586\) −8.47623 −0.350150
\(587\) −4.51144 −0.186207 −0.0931036 0.995656i \(-0.529679\pi\)
−0.0931036 + 0.995656i \(0.529679\pi\)
\(588\) 1.03107 0.0425206
\(589\) 0 0
\(590\) 0 0
\(591\) 7.53101 0.309784
\(592\) −3.01550 −0.123936
\(593\) −19.6082 −0.805213 −0.402606 0.915373i \(-0.631896\pi\)
−0.402606 + 0.915373i \(0.631896\pi\)
\(594\) 0.327650 0.0134436
\(595\) 0 0
\(596\) 17.7062 0.725274
\(597\) 7.96699 0.326067
\(598\) −20.7067 −0.846759
\(599\) 10.7759 0.440292 0.220146 0.975467i \(-0.429347\pi\)
0.220146 + 0.975467i \(0.429347\pi\)
\(600\) 0 0
\(601\) 15.0244 0.612860 0.306430 0.951893i \(-0.400866\pi\)
0.306430 + 0.951893i \(0.400866\pi\)
\(602\) −17.6753 −0.720389
\(603\) −8.43563 −0.343526
\(604\) −2.65328 −0.107960
\(605\) 0 0
\(606\) −2.24687 −0.0912730
\(607\) −25.1901 −1.02243 −0.511217 0.859452i \(-0.670805\pi\)
−0.511217 + 0.859452i \(0.670805\pi\)
\(608\) 0 0
\(609\) −3.56940 −0.144640
\(610\) 0 0
\(611\) −39.0566 −1.58006
\(612\) 3.77498 0.152595
\(613\) −16.2351 −0.655728 −0.327864 0.944725i \(-0.606329\pi\)
−0.327864 + 0.944725i \(0.606329\pi\)
\(614\) −9.98672 −0.403031
\(615\) 0 0
\(616\) −0.780593 −0.0314510
\(617\) −6.51826 −0.262415 −0.131208 0.991355i \(-0.541885\pi\)
−0.131208 + 0.991355i \(0.541885\pi\)
\(618\) 0.893993 0.0359617
\(619\) −4.39112 −0.176494 −0.0882470 0.996099i \(-0.528126\pi\)
−0.0882470 + 0.996099i \(0.528126\pi\)
\(620\) 0 0
\(621\) 11.9287 0.478681
\(622\) 13.6706 0.548142
\(623\) −18.4311 −0.738425
\(624\) 2.36681 0.0947483
\(625\) 0 0
\(626\) 2.24484 0.0897220
\(627\) 0 0
\(628\) 5.77858 0.230590
\(629\) 2.82108 0.112484
\(630\) 0 0
\(631\) −34.6209 −1.37824 −0.689118 0.724650i \(-0.742002\pi\)
−0.689118 + 0.724650i \(0.742002\pi\)
\(632\) −4.50165 −0.179066
\(633\) −4.86521 −0.193375
\(634\) 25.8680 1.02735
\(635\) 0 0
\(636\) −0.0799333 −0.00316956
\(637\) 12.0040 0.475614
\(638\) −0.733141 −0.0290253
\(639\) −3.79391 −0.150085
\(640\) 0 0
\(641\) 7.41241 0.292773 0.146386 0.989227i \(-0.453236\pi\)
0.146386 + 0.989227i \(0.453236\pi\)
\(642\) −0.416681 −0.0164451
\(643\) 16.5459 0.652506 0.326253 0.945282i \(-0.394214\pi\)
0.326253 + 0.945282i \(0.394214\pi\)
\(644\) −8.08794 −0.318710
\(645\) 0 0
\(646\) 0 0
\(647\) −29.4822 −1.15907 −0.579533 0.814949i \(-0.696765\pi\)
−0.579533 + 0.814949i \(0.696765\pi\)
\(648\) 23.7026 0.931124
\(649\) −0.926912 −0.0363845
\(650\) 0 0
\(651\) −4.71415 −0.184762
\(652\) −15.7362 −0.616277
\(653\) −6.57421 −0.257269 −0.128634 0.991692i \(-0.541059\pi\)
−0.128634 + 0.991692i \(0.541059\pi\)
\(654\) −6.77017 −0.264735
\(655\) 0 0
\(656\) −18.8807 −0.737169
\(657\) −18.1145 −0.706713
\(658\) 23.0925 0.900241
\(659\) −26.3370 −1.02594 −0.512972 0.858405i \(-0.671456\pi\)
−0.512972 + 0.858405i \(0.671456\pi\)
\(660\) 0 0
\(661\) 3.78419 0.147188 0.0735941 0.997288i \(-0.476553\pi\)
0.0735941 + 0.997288i \(0.476553\pi\)
\(662\) 20.5413 0.798359
\(663\) −2.21422 −0.0859930
\(664\) −22.8487 −0.886703
\(665\) 0 0
\(666\) 5.32281 0.206255
\(667\) −26.6913 −1.03349
\(668\) −2.70769 −0.104763
\(669\) −7.73630 −0.299103
\(670\) 0 0
\(671\) 1.23324 0.0476086
\(672\) 3.00694 0.115995
\(673\) 21.0431 0.811150 0.405575 0.914062i \(-0.367071\pi\)
0.405575 + 0.914062i \(0.367071\pi\)
\(674\) −35.8731 −1.38178
\(675\) 0 0
\(676\) 0.520083 0.0200032
\(677\) 15.2744 0.587043 0.293522 0.955952i \(-0.405173\pi\)
0.293522 + 0.955952i \(0.405173\pi\)
\(678\) 0.350941 0.0134778
\(679\) 33.0699 1.26911
\(680\) 0 0
\(681\) −9.64161 −0.369467
\(682\) −0.968267 −0.0370769
\(683\) 8.60225 0.329156 0.164578 0.986364i \(-0.447374\pi\)
0.164578 + 0.986364i \(0.447374\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −21.6401 −0.826223
\(687\) 0.840424 0.0320642
\(688\) 15.1075 0.575968
\(689\) −0.930603 −0.0354532
\(690\) 0 0
\(691\) 34.1079 1.29753 0.648763 0.760990i \(-0.275286\pi\)
0.648763 + 0.760990i \(0.275286\pi\)
\(692\) −8.42231 −0.320168
\(693\) 0.726674 0.0276040
\(694\) −2.81675 −0.106922
\(695\) 0 0
\(696\) 5.78481 0.219273
\(697\) 17.6634 0.669050
\(698\) −18.2388 −0.690350
\(699\) 5.37047 0.203130
\(700\) 0 0
\(701\) 10.7293 0.405239 0.202619 0.979258i \(-0.435055\pi\)
0.202619 + 0.979258i \(0.435055\pi\)
\(702\) −8.56603 −0.323304
\(703\) 0 0
\(704\) 1.09492 0.0412665
\(705\) 0 0
\(706\) 31.1266 1.17146
\(707\) −10.2175 −0.384267
\(708\) 2.08148 0.0782267
\(709\) −28.8476 −1.08339 −0.541697 0.840574i \(-0.682218\pi\)
−0.541697 + 0.840574i \(0.682218\pi\)
\(710\) 0 0
\(711\) 4.19070 0.157164
\(712\) 29.8706 1.11945
\(713\) −35.2515 −1.32018
\(714\) 1.30917 0.0489946
\(715\) 0 0
\(716\) 11.6181 0.434189
\(717\) 1.14360 0.0427085
\(718\) −19.0829 −0.712166
\(719\) −20.0555 −0.747944 −0.373972 0.927440i \(-0.622004\pi\)
−0.373972 + 0.927440i \(0.622004\pi\)
\(720\) 0 0
\(721\) 4.06535 0.151402
\(722\) 0 0
\(723\) −9.02026 −0.335467
\(724\) 4.32234 0.160639
\(725\) 0 0
\(726\) 4.57173 0.169673
\(727\) 0.780521 0.0289479 0.0144740 0.999895i \(-0.495393\pi\)
0.0144740 + 0.999895i \(0.495393\pi\)
\(728\) 20.4077 0.756361
\(729\) −19.5373 −0.723604
\(730\) 0 0
\(731\) −14.1335 −0.522745
\(732\) −2.76937 −0.102359
\(733\) 26.8391 0.991326 0.495663 0.868515i \(-0.334925\pi\)
0.495663 + 0.868515i \(0.334925\pi\)
\(734\) 28.3192 1.04528
\(735\) 0 0
\(736\) 22.4853 0.828817
\(737\) 0.396956 0.0146221
\(738\) 33.3273 1.22679
\(739\) 20.6530 0.759735 0.379867 0.925041i \(-0.375970\pi\)
0.379867 + 0.925041i \(0.375970\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.550227 0.0201995
\(743\) −1.47317 −0.0540454 −0.0270227 0.999635i \(-0.508603\pi\)
−0.0270227 + 0.999635i \(0.508603\pi\)
\(744\) 7.64007 0.280098
\(745\) 0 0
\(746\) 29.7036 1.08752
\(747\) 21.2705 0.778245
\(748\) −0.177639 −0.00649514
\(749\) −1.89482 −0.0692352
\(750\) 0 0
\(751\) 15.5624 0.567881 0.283940 0.958842i \(-0.408358\pi\)
0.283940 + 0.958842i \(0.408358\pi\)
\(752\) −19.7378 −0.719764
\(753\) 6.52071 0.237628
\(754\) 19.1671 0.698026
\(755\) 0 0
\(756\) −3.34586 −0.121688
\(757\) −20.1756 −0.733295 −0.366647 0.930360i \(-0.619494\pi\)
−0.366647 + 0.930360i \(0.619494\pi\)
\(758\) −13.6114 −0.494387
\(759\) −0.273767 −0.00993713
\(760\) 0 0
\(761\) −15.1076 −0.547649 −0.273825 0.961780i \(-0.588289\pi\)
−0.273825 + 0.961780i \(0.588289\pi\)
\(762\) 7.80124 0.282609
\(763\) −30.7868 −1.11456
\(764\) −16.2911 −0.589392
\(765\) 0 0
\(766\) −5.88163 −0.212512
\(767\) 24.2331 0.875005
\(768\) −5.94509 −0.214525
\(769\) 51.6580 1.86284 0.931418 0.363951i \(-0.118573\pi\)
0.931418 + 0.363951i \(0.118573\pi\)
\(770\) 0 0
\(771\) 7.41327 0.266982
\(772\) 8.77063 0.315662
\(773\) −30.1558 −1.08463 −0.542314 0.840176i \(-0.682452\pi\)
−0.542314 + 0.840176i \(0.682452\pi\)
\(774\) −26.6670 −0.958525
\(775\) 0 0
\(776\) −53.5952 −1.92396
\(777\) −1.21948 −0.0437485
\(778\) −9.40431 −0.337161
\(779\) 0 0
\(780\) 0 0
\(781\) 0.178530 0.00638832
\(782\) 9.78974 0.350080
\(783\) −11.0418 −0.394601
\(784\) 6.06637 0.216656
\(785\) 0 0
\(786\) −1.20161 −0.0428601
\(787\) −43.0969 −1.53624 −0.768119 0.640307i \(-0.778807\pi\)
−0.768119 + 0.640307i \(0.778807\pi\)
\(788\) −15.7958 −0.562703
\(789\) −3.34330 −0.119025
\(790\) 0 0
\(791\) 1.59588 0.0567428
\(792\) −1.17770 −0.0418476
\(793\) −32.2416 −1.14493
\(794\) −11.6817 −0.414569
\(795\) 0 0
\(796\) −16.7103 −0.592280
\(797\) 50.5062 1.78902 0.894510 0.447048i \(-0.147525\pi\)
0.894510 + 0.447048i \(0.147525\pi\)
\(798\) 0 0
\(799\) 18.4652 0.653253
\(800\) 0 0
\(801\) −27.8073 −0.982522
\(802\) −8.39769 −0.296533
\(803\) 0.852414 0.0300810
\(804\) −0.891406 −0.0314375
\(805\) 0 0
\(806\) 25.3142 0.891656
\(807\) 0.109386 0.00385056
\(808\) 16.5591 0.582547
\(809\) −30.0872 −1.05781 −0.528905 0.848681i \(-0.677397\pi\)
−0.528905 + 0.848681i \(0.677397\pi\)
\(810\) 0 0
\(811\) 22.9509 0.805916 0.402958 0.915218i \(-0.367982\pi\)
0.402958 + 0.915218i \(0.367982\pi\)
\(812\) 7.48661 0.262728
\(813\) −9.43449 −0.330882
\(814\) −0.250476 −0.00877917
\(815\) 0 0
\(816\) −1.11899 −0.0391723
\(817\) 0 0
\(818\) 19.4123 0.678734
\(819\) −18.9981 −0.663846
\(820\) 0 0
\(821\) −38.0807 −1.32903 −0.664513 0.747277i \(-0.731361\pi\)
−0.664513 + 0.747277i \(0.731361\pi\)
\(822\) −7.83950 −0.273434
\(823\) −53.7932 −1.87511 −0.937556 0.347835i \(-0.886917\pi\)
−0.937556 + 0.347835i \(0.886917\pi\)
\(824\) −6.58858 −0.229524
\(825\) 0 0
\(826\) −14.3280 −0.498535
\(827\) −32.4092 −1.12698 −0.563490 0.826123i \(-0.690542\pi\)
−0.563490 + 0.826123i \(0.690542\pi\)
\(828\) −12.2024 −0.424064
\(829\) −18.5305 −0.643592 −0.321796 0.946809i \(-0.604287\pi\)
−0.321796 + 0.946809i \(0.604287\pi\)
\(830\) 0 0
\(831\) 1.67091 0.0579633
\(832\) −28.6255 −0.992412
\(833\) −5.67525 −0.196636
\(834\) 7.56804 0.262060
\(835\) 0 0
\(836\) 0 0
\(837\) −14.5830 −0.504062
\(838\) −1.30301 −0.0450118
\(839\) 0.826608 0.0285377 0.0142688 0.999898i \(-0.495458\pi\)
0.0142688 + 0.999898i \(0.495458\pi\)
\(840\) 0 0
\(841\) −4.29321 −0.148042
\(842\) −36.6185 −1.26196
\(843\) −12.4123 −0.427504
\(844\) 10.2045 0.351253
\(845\) 0 0
\(846\) 34.8401 1.19783
\(847\) 20.7895 0.714337
\(848\) −0.470294 −0.0161500
\(849\) 0.504106 0.0173009
\(850\) 0 0
\(851\) −9.11901 −0.312596
\(852\) −0.400908 −0.0137349
\(853\) 7.34938 0.251638 0.125819 0.992053i \(-0.459844\pi\)
0.125819 + 0.992053i \(0.459844\pi\)
\(854\) 19.0631 0.652327
\(855\) 0 0
\(856\) 3.07087 0.104960
\(857\) 45.3496 1.54911 0.774556 0.632506i \(-0.217974\pi\)
0.774556 + 0.632506i \(0.217974\pi\)
\(858\) 0.196594 0.00671160
\(859\) 29.6285 1.01091 0.505456 0.862852i \(-0.331324\pi\)
0.505456 + 0.862852i \(0.331324\pi\)
\(860\) 0 0
\(861\) −7.63542 −0.260215
\(862\) 6.77775 0.230851
\(863\) −41.0807 −1.39840 −0.699201 0.714925i \(-0.746461\pi\)
−0.699201 + 0.714925i \(0.746461\pi\)
\(864\) 9.30180 0.316454
\(865\) 0 0
\(866\) −20.3632 −0.691970
\(867\) −5.40183 −0.183456
\(868\) 9.88764 0.335608
\(869\) −0.197202 −0.00668962
\(870\) 0 0
\(871\) −10.3780 −0.351644
\(872\) 49.8951 1.68966
\(873\) 49.8931 1.68863
\(874\) 0 0
\(875\) 0 0
\(876\) −1.91419 −0.0646743
\(877\) −54.6307 −1.84475 −0.922374 0.386298i \(-0.873754\pi\)
−0.922374 + 0.386298i \(0.873754\pi\)
\(878\) 0.249460 0.00841888
\(879\) 2.92984 0.0988211
\(880\) 0 0
\(881\) −15.4805 −0.521552 −0.260776 0.965399i \(-0.583978\pi\)
−0.260776 + 0.965399i \(0.583978\pi\)
\(882\) −10.7080 −0.360558
\(883\) 45.3495 1.52613 0.763066 0.646321i \(-0.223693\pi\)
0.763066 + 0.646321i \(0.223693\pi\)
\(884\) 4.64418 0.156201
\(885\) 0 0
\(886\) −38.3913 −1.28978
\(887\) 31.1399 1.04558 0.522788 0.852463i \(-0.324892\pi\)
0.522788 + 0.852463i \(0.324892\pi\)
\(888\) 1.97637 0.0663226
\(889\) 35.4755 1.18981
\(890\) 0 0
\(891\) 1.03833 0.0347853
\(892\) 16.2264 0.543301
\(893\) 0 0
\(894\) 9.26438 0.309847
\(895\) 0 0
\(896\) 1.07133 0.0357905
\(897\) 7.15734 0.238977
\(898\) 18.6025 0.620775
\(899\) 32.6305 1.08829
\(900\) 0 0
\(901\) 0.439972 0.0146576
\(902\) −1.56828 −0.0522181
\(903\) 6.10952 0.203312
\(904\) −2.58638 −0.0860218
\(905\) 0 0
\(906\) −1.38827 −0.0461222
\(907\) −43.5415 −1.44577 −0.722886 0.690967i \(-0.757185\pi\)
−0.722886 + 0.690967i \(0.757185\pi\)
\(908\) 20.2227 0.671113
\(909\) −15.4153 −0.511293
\(910\) 0 0
\(911\) 5.72789 0.189774 0.0948868 0.995488i \(-0.469751\pi\)
0.0948868 + 0.995488i \(0.469751\pi\)
\(912\) 0 0
\(913\) −1.00093 −0.0331258
\(914\) 1.75855 0.0581677
\(915\) 0 0
\(916\) −1.76274 −0.0582425
\(917\) −5.46422 −0.180445
\(918\) 4.04986 0.133665
\(919\) 7.93860 0.261870 0.130935 0.991391i \(-0.458202\pi\)
0.130935 + 0.991391i \(0.458202\pi\)
\(920\) 0 0
\(921\) 3.45195 0.113746
\(922\) 9.59339 0.315941
\(923\) −4.66747 −0.153632
\(924\) 0.0767887 0.00252616
\(925\) 0 0
\(926\) 23.2532 0.764147
\(927\) 6.13347 0.201450
\(928\) −20.8135 −0.683236
\(929\) −28.9567 −0.950039 −0.475019 0.879975i \(-0.657559\pi\)
−0.475019 + 0.879975i \(0.657559\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −11.2642 −0.368972
\(933\) −4.72531 −0.154700
\(934\) 22.4444 0.734403
\(935\) 0 0
\(936\) 30.7895 1.00639
\(937\) 14.6816 0.479627 0.239813 0.970819i \(-0.422914\pi\)
0.239813 + 0.970819i \(0.422914\pi\)
\(938\) 6.13606 0.200349
\(939\) −0.775939 −0.0253218
\(940\) 0 0
\(941\) −0.154755 −0.00504485 −0.00252243 0.999997i \(-0.500803\pi\)
−0.00252243 + 0.999997i \(0.500803\pi\)
\(942\) 3.02352 0.0985114
\(943\) −57.0961 −1.85931
\(944\) 12.2465 0.398590
\(945\) 0 0
\(946\) 1.25487 0.0407993
\(947\) 7.51807 0.244304 0.122152 0.992511i \(-0.461020\pi\)
0.122152 + 0.992511i \(0.461020\pi\)
\(948\) 0.442838 0.0143827
\(949\) −22.2854 −0.723415
\(950\) 0 0
\(951\) −8.94137 −0.289944
\(952\) −9.64840 −0.312706
\(953\) −22.6743 −0.734493 −0.367247 0.930124i \(-0.619700\pi\)
−0.367247 + 0.930124i \(0.619700\pi\)
\(954\) 0.830138 0.0268767
\(955\) 0 0
\(956\) −2.39863 −0.0775772
\(957\) 0.253413 0.00819167
\(958\) −25.8437 −0.834973
\(959\) −35.6494 −1.15118
\(960\) 0 0
\(961\) 12.0955 0.390177
\(962\) 6.54840 0.211129
\(963\) −2.85875 −0.0921219
\(964\) 18.9194 0.609354
\(965\) 0 0
\(966\) −4.23184 −0.136157
\(967\) −28.8344 −0.927253 −0.463627 0.886031i \(-0.653452\pi\)
−0.463627 + 0.886031i \(0.653452\pi\)
\(968\) −33.6929 −1.08293
\(969\) 0 0
\(970\) 0 0
\(971\) 26.3661 0.846130 0.423065 0.906099i \(-0.360954\pi\)
0.423065 + 0.906099i \(0.360954\pi\)
\(972\) −7.63395 −0.244859
\(973\) 34.4150 1.10329
\(974\) 39.5508 1.26729
\(975\) 0 0
\(976\) −16.2938 −0.521551
\(977\) −4.59218 −0.146917 −0.0734585 0.997298i \(-0.523404\pi\)
−0.0734585 + 0.997298i \(0.523404\pi\)
\(978\) −8.23362 −0.263282
\(979\) 1.30853 0.0418207
\(980\) 0 0
\(981\) −46.4486 −1.48299
\(982\) −22.0140 −0.702496
\(983\) −6.91473 −0.220546 −0.110273 0.993901i \(-0.535172\pi\)
−0.110273 + 0.993901i \(0.535172\pi\)
\(984\) 12.3745 0.394484
\(985\) 0 0
\(986\) −9.06187 −0.288589
\(987\) −7.98203 −0.254071
\(988\) 0 0
\(989\) 45.6857 1.45272
\(990\) 0 0
\(991\) −38.0070 −1.20733 −0.603666 0.797237i \(-0.706294\pi\)
−0.603666 + 0.797237i \(0.706294\pi\)
\(992\) −27.4886 −0.872763
\(993\) −7.10017 −0.225317
\(994\) 2.75968 0.0875318
\(995\) 0 0
\(996\) 2.24768 0.0712205
\(997\) −16.2265 −0.513899 −0.256950 0.966425i \(-0.582717\pi\)
−0.256950 + 0.966425i \(0.582717\pi\)
\(998\) 40.4657 1.28092
\(999\) −3.77239 −0.119353
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.bg.1.2 4
5.4 even 2 1805.2.a.o.1.3 4
19.7 even 3 475.2.e.e.201.3 8
19.11 even 3 475.2.e.e.26.3 8
19.18 odd 2 9025.2.a.bp.1.3 4
95.7 odd 12 475.2.j.c.49.5 16
95.49 even 6 95.2.e.c.26.2 yes 8
95.64 even 6 95.2.e.c.11.2 8
95.68 odd 12 475.2.j.c.349.5 16
95.83 odd 12 475.2.j.c.49.4 16
95.87 odd 12 475.2.j.c.349.4 16
95.94 odd 2 1805.2.a.i.1.2 4
285.239 odd 6 855.2.k.h.406.3 8
285.254 odd 6 855.2.k.h.676.3 8
380.159 odd 6 1520.2.q.o.961.2 8
380.239 odd 6 1520.2.q.o.881.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.e.c.11.2 8 95.64 even 6
95.2.e.c.26.2 yes 8 95.49 even 6
475.2.e.e.26.3 8 19.11 even 3
475.2.e.e.201.3 8 19.7 even 3
475.2.j.c.49.4 16 95.83 odd 12
475.2.j.c.49.5 16 95.7 odd 12
475.2.j.c.349.4 16 95.87 odd 12
475.2.j.c.349.5 16 95.68 odd 12
855.2.k.h.406.3 8 285.239 odd 6
855.2.k.h.676.3 8 285.254 odd 6
1520.2.q.o.881.2 8 380.239 odd 6
1520.2.q.o.961.2 8 380.159 odd 6
1805.2.a.i.1.2 4 95.94 odd 2
1805.2.a.o.1.3 4 5.4 even 2
9025.2.a.bg.1.2 4 1.1 even 1 trivial
9025.2.a.bp.1.3 4 19.18 odd 2