Properties

Label 6025.2.a.k.1.5
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $0$
Dimension $25$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(25\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 6025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.96258 q^{2} -3.23511 q^{3} +1.85173 q^{4} +6.34917 q^{6} +1.21428 q^{7} +0.290989 q^{8} +7.46593 q^{9} +O(q^{10})\) \(q-1.96258 q^{2} -3.23511 q^{3} +1.85173 q^{4} +6.34917 q^{6} +1.21428 q^{7} +0.290989 q^{8} +7.46593 q^{9} +3.74603 q^{11} -5.99055 q^{12} +3.08267 q^{13} -2.38313 q^{14} -4.27455 q^{16} -7.01669 q^{17} -14.6525 q^{18} -2.30313 q^{19} -3.92834 q^{21} -7.35189 q^{22} -1.94524 q^{23} -0.941382 q^{24} -6.05000 q^{26} -14.4478 q^{27} +2.24853 q^{28} +5.85578 q^{29} -4.10334 q^{31} +7.80719 q^{32} -12.1188 q^{33} +13.7708 q^{34} +13.8249 q^{36} +11.2364 q^{37} +4.52008 q^{38} -9.97278 q^{39} -5.17567 q^{41} +7.70970 q^{42} +2.18721 q^{43} +6.93664 q^{44} +3.81770 q^{46} +9.94112 q^{47} +13.8286 q^{48} -5.52551 q^{49} +22.6998 q^{51} +5.70828 q^{52} +0.642522 q^{53} +28.3549 q^{54} +0.353344 q^{56} +7.45087 q^{57} -11.4925 q^{58} +11.8585 q^{59} -7.63058 q^{61} +8.05314 q^{62} +9.06576 q^{63} -6.77314 q^{64} +23.7842 q^{66} +14.1894 q^{67} -12.9930 q^{68} +6.29308 q^{69} +3.64949 q^{71} +2.17251 q^{72} -1.79732 q^{73} -22.0524 q^{74} -4.26478 q^{76} +4.54874 q^{77} +19.5724 q^{78} -4.41542 q^{79} +24.3423 q^{81} +10.1577 q^{82} -8.23800 q^{83} -7.27423 q^{84} -4.29258 q^{86} -18.9441 q^{87} +1.09005 q^{88} +6.52307 q^{89} +3.74324 q^{91} -3.60207 q^{92} +13.2747 q^{93} -19.5103 q^{94} -25.2571 q^{96} -1.16217 q^{97} +10.8443 q^{98} +27.9676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96258 −1.38776 −0.693878 0.720093i \(-0.744099\pi\)
−0.693878 + 0.720093i \(0.744099\pi\)
\(3\) −3.23511 −1.86779 −0.933895 0.357546i \(-0.883614\pi\)
−0.933895 + 0.357546i \(0.883614\pi\)
\(4\) 1.85173 0.925866
\(5\) 0 0
\(6\) 6.34917 2.59204
\(7\) 1.21428 0.458956 0.229478 0.973314i \(-0.426298\pi\)
0.229478 + 0.973314i \(0.426298\pi\)
\(8\) 0.290989 0.102880
\(9\) 7.46593 2.48864
\(10\) 0 0
\(11\) 3.74603 1.12947 0.564735 0.825272i \(-0.308978\pi\)
0.564735 + 0.825272i \(0.308978\pi\)
\(12\) −5.99055 −1.72932
\(13\) 3.08267 0.854979 0.427490 0.904020i \(-0.359398\pi\)
0.427490 + 0.904020i \(0.359398\pi\)
\(14\) −2.38313 −0.636919
\(15\) 0 0
\(16\) −4.27455 −1.06864
\(17\) −7.01669 −1.70180 −0.850899 0.525330i \(-0.823942\pi\)
−0.850899 + 0.525330i \(0.823942\pi\)
\(18\) −14.6525 −3.45363
\(19\) −2.30313 −0.528374 −0.264187 0.964471i \(-0.585104\pi\)
−0.264187 + 0.964471i \(0.585104\pi\)
\(20\) 0 0
\(21\) −3.92834 −0.857234
\(22\) −7.35189 −1.56743
\(23\) −1.94524 −0.405612 −0.202806 0.979219i \(-0.565006\pi\)
−0.202806 + 0.979219i \(0.565006\pi\)
\(24\) −0.941382 −0.192159
\(25\) 0 0
\(26\) −6.05000 −1.18650
\(27\) −14.4478 −2.78047
\(28\) 2.24853 0.424932
\(29\) 5.85578 1.08739 0.543696 0.839282i \(-0.317025\pi\)
0.543696 + 0.839282i \(0.317025\pi\)
\(30\) 0 0
\(31\) −4.10334 −0.736981 −0.368491 0.929632i \(-0.620125\pi\)
−0.368491 + 0.929632i \(0.620125\pi\)
\(32\) 7.80719 1.38013
\(33\) −12.1188 −2.10961
\(34\) 13.7708 2.36168
\(35\) 0 0
\(36\) 13.8249 2.30415
\(37\) 11.2364 1.84726 0.923628 0.383291i \(-0.125209\pi\)
0.923628 + 0.383291i \(0.125209\pi\)
\(38\) 4.52008 0.733254
\(39\) −9.97278 −1.59692
\(40\) 0 0
\(41\) −5.17567 −0.808304 −0.404152 0.914692i \(-0.632433\pi\)
−0.404152 + 0.914692i \(0.632433\pi\)
\(42\) 7.70970 1.18963
\(43\) 2.18721 0.333547 0.166773 0.985995i \(-0.446665\pi\)
0.166773 + 0.985995i \(0.446665\pi\)
\(44\) 6.93664 1.04574
\(45\) 0 0
\(46\) 3.81770 0.562890
\(47\) 9.94112 1.45006 0.725031 0.688717i \(-0.241826\pi\)
0.725031 + 0.688717i \(0.241826\pi\)
\(48\) 13.8286 1.99599
\(49\) −5.52551 −0.789359
\(50\) 0 0
\(51\) 22.6998 3.17860
\(52\) 5.70828 0.791596
\(53\) 0.642522 0.0882571 0.0441286 0.999026i \(-0.485949\pi\)
0.0441286 + 0.999026i \(0.485949\pi\)
\(54\) 28.3549 3.85862
\(55\) 0 0
\(56\) 0.353344 0.0472175
\(57\) 7.45087 0.986892
\(58\) −11.4925 −1.50903
\(59\) 11.8585 1.54384 0.771920 0.635720i \(-0.219297\pi\)
0.771920 + 0.635720i \(0.219297\pi\)
\(60\) 0 0
\(61\) −7.63058 −0.976995 −0.488498 0.872565i \(-0.662455\pi\)
−0.488498 + 0.872565i \(0.662455\pi\)
\(62\) 8.05314 1.02275
\(63\) 9.06576 1.14218
\(64\) −6.77314 −0.846643
\(65\) 0 0
\(66\) 23.7842 2.92763
\(67\) 14.1894 1.73351 0.866753 0.498737i \(-0.166203\pi\)
0.866753 + 0.498737i \(0.166203\pi\)
\(68\) −12.9930 −1.57564
\(69\) 6.29308 0.757598
\(70\) 0 0
\(71\) 3.64949 0.433115 0.216557 0.976270i \(-0.430517\pi\)
0.216557 + 0.976270i \(0.430517\pi\)
\(72\) 2.17251 0.256032
\(73\) −1.79732 −0.210361 −0.105180 0.994453i \(-0.533542\pi\)
−0.105180 + 0.994453i \(0.533542\pi\)
\(74\) −22.0524 −2.56354
\(75\) 0 0
\(76\) −4.26478 −0.489203
\(77\) 4.54874 0.518377
\(78\) 19.5724 2.21614
\(79\) −4.41542 −0.496774 −0.248387 0.968661i \(-0.579900\pi\)
−0.248387 + 0.968661i \(0.579900\pi\)
\(80\) 0 0
\(81\) 24.3423 2.70470
\(82\) 10.1577 1.12173
\(83\) −8.23800 −0.904238 −0.452119 0.891958i \(-0.649332\pi\)
−0.452119 + 0.891958i \(0.649332\pi\)
\(84\) −7.27423 −0.793684
\(85\) 0 0
\(86\) −4.29258 −0.462881
\(87\) −18.9441 −2.03102
\(88\) 1.09005 0.116200
\(89\) 6.52307 0.691444 0.345722 0.938337i \(-0.387634\pi\)
0.345722 + 0.938337i \(0.387634\pi\)
\(90\) 0 0
\(91\) 3.74324 0.392398
\(92\) −3.60207 −0.375542
\(93\) 13.2747 1.37653
\(94\) −19.5103 −2.01233
\(95\) 0 0
\(96\) −25.2571 −2.57779
\(97\) −1.16217 −0.118000 −0.0590000 0.998258i \(-0.518791\pi\)
−0.0590000 + 0.998258i \(0.518791\pi\)
\(98\) 10.8443 1.09544
\(99\) 27.9676 2.81085
\(100\) 0 0
\(101\) −13.3276 −1.32615 −0.663075 0.748553i \(-0.730749\pi\)
−0.663075 + 0.748553i \(0.730749\pi\)
\(102\) −44.5502 −4.41112
\(103\) −5.20580 −0.512943 −0.256471 0.966552i \(-0.582560\pi\)
−0.256471 + 0.966552i \(0.582560\pi\)
\(104\) 0.897025 0.0879605
\(105\) 0 0
\(106\) −1.26100 −0.122479
\(107\) 14.8141 1.43214 0.716069 0.698030i \(-0.245940\pi\)
0.716069 + 0.698030i \(0.245940\pi\)
\(108\) −26.7534 −2.57435
\(109\) 3.47664 0.333001 0.166501 0.986041i \(-0.446753\pi\)
0.166501 + 0.986041i \(0.446753\pi\)
\(110\) 0 0
\(111\) −36.3510 −3.45029
\(112\) −5.19052 −0.490458
\(113\) −16.7076 −1.57172 −0.785858 0.618407i \(-0.787778\pi\)
−0.785858 + 0.618407i \(0.787778\pi\)
\(114\) −14.6230 −1.36957
\(115\) 0 0
\(116\) 10.8433 1.00678
\(117\) 23.0150 2.12774
\(118\) −23.2732 −2.14247
\(119\) −8.52026 −0.781051
\(120\) 0 0
\(121\) 3.03271 0.275701
\(122\) 14.9756 1.35583
\(123\) 16.7439 1.50974
\(124\) −7.59828 −0.682345
\(125\) 0 0
\(126\) −17.7923 −1.58506
\(127\) −10.9817 −0.974468 −0.487234 0.873272i \(-0.661994\pi\)
−0.487234 + 0.873272i \(0.661994\pi\)
\(128\) −2.32152 −0.205195
\(129\) −7.07587 −0.622995
\(130\) 0 0
\(131\) 11.3267 0.989615 0.494807 0.869003i \(-0.335239\pi\)
0.494807 + 0.869003i \(0.335239\pi\)
\(132\) −22.4408 −1.95322
\(133\) −2.79665 −0.242501
\(134\) −27.8478 −2.40568
\(135\) 0 0
\(136\) −2.04178 −0.175081
\(137\) 17.8065 1.52132 0.760658 0.649153i \(-0.224876\pi\)
0.760658 + 0.649153i \(0.224876\pi\)
\(138\) −12.3507 −1.05136
\(139\) −2.75800 −0.233930 −0.116965 0.993136i \(-0.537317\pi\)
−0.116965 + 0.993136i \(0.537317\pi\)
\(140\) 0 0
\(141\) −32.1606 −2.70841
\(142\) −7.16243 −0.601058
\(143\) 11.5478 0.965673
\(144\) −31.9135 −2.65946
\(145\) 0 0
\(146\) 3.52739 0.291929
\(147\) 17.8756 1.47436
\(148\) 20.8068 1.71031
\(149\) 14.2456 1.16705 0.583523 0.812096i \(-0.301674\pi\)
0.583523 + 0.812096i \(0.301674\pi\)
\(150\) 0 0
\(151\) 10.7800 0.877268 0.438634 0.898666i \(-0.355462\pi\)
0.438634 + 0.898666i \(0.355462\pi\)
\(152\) −0.670186 −0.0543592
\(153\) −52.3861 −4.23517
\(154\) −8.92728 −0.719381
\(155\) 0 0
\(156\) −18.4669 −1.47854
\(157\) −15.2762 −1.21917 −0.609585 0.792720i \(-0.708664\pi\)
−0.609585 + 0.792720i \(0.708664\pi\)
\(158\) 8.66564 0.689401
\(159\) −2.07863 −0.164846
\(160\) 0 0
\(161\) −2.36208 −0.186158
\(162\) −47.7738 −3.75346
\(163\) −5.85982 −0.458976 −0.229488 0.973311i \(-0.573705\pi\)
−0.229488 + 0.973311i \(0.573705\pi\)
\(164\) −9.58396 −0.748381
\(165\) 0 0
\(166\) 16.1678 1.25486
\(167\) −10.3799 −0.803224 −0.401612 0.915810i \(-0.631550\pi\)
−0.401612 + 0.915810i \(0.631550\pi\)
\(168\) −1.14311 −0.0881925
\(169\) −3.49713 −0.269010
\(170\) 0 0
\(171\) −17.1950 −1.31493
\(172\) 4.05013 0.308819
\(173\) −9.47871 −0.720653 −0.360327 0.932826i \(-0.617335\pi\)
−0.360327 + 0.932826i \(0.617335\pi\)
\(174\) 37.1794 2.81856
\(175\) 0 0
\(176\) −16.0126 −1.20699
\(177\) −38.3634 −2.88357
\(178\) −12.8021 −0.959555
\(179\) 1.41908 0.106067 0.0530336 0.998593i \(-0.483111\pi\)
0.0530336 + 0.998593i \(0.483111\pi\)
\(180\) 0 0
\(181\) 23.1630 1.72169 0.860844 0.508868i \(-0.169936\pi\)
0.860844 + 0.508868i \(0.169936\pi\)
\(182\) −7.34642 −0.544553
\(183\) 24.6858 1.82482
\(184\) −0.566045 −0.0417294
\(185\) 0 0
\(186\) −26.0528 −1.91028
\(187\) −26.2847 −1.92213
\(188\) 18.4083 1.34256
\(189\) −17.5437 −1.27612
\(190\) 0 0
\(191\) 18.3255 1.32599 0.662995 0.748624i \(-0.269285\pi\)
0.662995 + 0.748624i \(0.269285\pi\)
\(192\) 21.9119 1.58135
\(193\) 13.0035 0.936011 0.468005 0.883726i \(-0.344973\pi\)
0.468005 + 0.883726i \(0.344973\pi\)
\(194\) 2.28085 0.163755
\(195\) 0 0
\(196\) −10.2318 −0.730841
\(197\) 13.3246 0.949339 0.474669 0.880164i \(-0.342568\pi\)
0.474669 + 0.880164i \(0.342568\pi\)
\(198\) −54.8887 −3.90077
\(199\) 19.9295 1.41276 0.706381 0.707832i \(-0.250327\pi\)
0.706381 + 0.707832i \(0.250327\pi\)
\(200\) 0 0
\(201\) −45.9041 −3.23783
\(202\) 26.1566 1.84037
\(203\) 7.11058 0.499065
\(204\) 42.0339 2.94296
\(205\) 0 0
\(206\) 10.2168 0.711839
\(207\) −14.5231 −1.00942
\(208\) −13.1770 −0.913664
\(209\) −8.62758 −0.596782
\(210\) 0 0
\(211\) −15.9483 −1.09793 −0.548963 0.835847i \(-0.684977\pi\)
−0.548963 + 0.835847i \(0.684977\pi\)
\(212\) 1.18978 0.0817143
\(213\) −11.8065 −0.808968
\(214\) −29.0740 −1.98746
\(215\) 0 0
\(216\) −4.20415 −0.286056
\(217\) −4.98262 −0.338242
\(218\) −6.82319 −0.462124
\(219\) 5.81453 0.392909
\(220\) 0 0
\(221\) −21.6302 −1.45500
\(222\) 71.3419 4.78816
\(223\) 13.0628 0.874749 0.437375 0.899279i \(-0.355908\pi\)
0.437375 + 0.899279i \(0.355908\pi\)
\(224\) 9.48014 0.633419
\(225\) 0 0
\(226\) 32.7900 2.18116
\(227\) −2.03254 −0.134904 −0.0674521 0.997723i \(-0.521487\pi\)
−0.0674521 + 0.997723i \(0.521487\pi\)
\(228\) 13.7970 0.913730
\(229\) 28.9057 1.91014 0.955071 0.296378i \(-0.0957787\pi\)
0.955071 + 0.296378i \(0.0957787\pi\)
\(230\) 0 0
\(231\) −14.7157 −0.968220
\(232\) 1.70397 0.111871
\(233\) −17.8688 −1.17063 −0.585313 0.810807i \(-0.699028\pi\)
−0.585313 + 0.810807i \(0.699028\pi\)
\(234\) −45.1689 −2.95278
\(235\) 0 0
\(236\) 21.9587 1.42939
\(237\) 14.2844 0.927870
\(238\) 16.7217 1.08391
\(239\) 7.36076 0.476128 0.238064 0.971249i \(-0.423487\pi\)
0.238064 + 0.971249i \(0.423487\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −5.95195 −0.382606
\(243\) −35.4067 −2.27134
\(244\) −14.1298 −0.904567
\(245\) 0 0
\(246\) −32.8612 −2.09516
\(247\) −7.09979 −0.451749
\(248\) −1.19403 −0.0758208
\(249\) 26.6508 1.68893
\(250\) 0 0
\(251\) −3.59780 −0.227091 −0.113545 0.993533i \(-0.536221\pi\)
−0.113545 + 0.993533i \(0.536221\pi\)
\(252\) 16.7874 1.05750
\(253\) −7.28694 −0.458126
\(254\) 21.5525 1.35232
\(255\) 0 0
\(256\) 18.1025 1.13140
\(257\) 15.9228 0.993236 0.496618 0.867969i \(-0.334575\pi\)
0.496618 + 0.867969i \(0.334575\pi\)
\(258\) 13.8870 0.864565
\(259\) 13.6442 0.847810
\(260\) 0 0
\(261\) 43.7189 2.70613
\(262\) −22.2295 −1.37334
\(263\) 23.4695 1.44719 0.723595 0.690224i \(-0.242488\pi\)
0.723595 + 0.690224i \(0.242488\pi\)
\(264\) −3.52644 −0.217037
\(265\) 0 0
\(266\) 5.48866 0.336532
\(267\) −21.1028 −1.29147
\(268\) 26.2749 1.60499
\(269\) 14.7420 0.898837 0.449419 0.893321i \(-0.351631\pi\)
0.449419 + 0.893321i \(0.351631\pi\)
\(270\) 0 0
\(271\) −20.3518 −1.23628 −0.618141 0.786067i \(-0.712114\pi\)
−0.618141 + 0.786067i \(0.712114\pi\)
\(272\) 29.9932 1.81861
\(273\) −12.1098 −0.732918
\(274\) −34.9468 −2.11121
\(275\) 0 0
\(276\) 11.6531 0.701434
\(277\) −23.6076 −1.41845 −0.709223 0.704984i \(-0.750954\pi\)
−0.709223 + 0.704984i \(0.750954\pi\)
\(278\) 5.41280 0.324638
\(279\) −30.6352 −1.83408
\(280\) 0 0
\(281\) −30.8608 −1.84100 −0.920502 0.390739i \(-0.872220\pi\)
−0.920502 + 0.390739i \(0.872220\pi\)
\(282\) 63.1178 3.75861
\(283\) −5.04636 −0.299975 −0.149987 0.988688i \(-0.547923\pi\)
−0.149987 + 0.988688i \(0.547923\pi\)
\(284\) 6.75788 0.401006
\(285\) 0 0
\(286\) −22.6635 −1.34012
\(287\) −6.28474 −0.370976
\(288\) 58.2879 3.43465
\(289\) 32.2339 1.89611
\(290\) 0 0
\(291\) 3.75973 0.220399
\(292\) −3.32816 −0.194766
\(293\) −20.3712 −1.19010 −0.595050 0.803689i \(-0.702868\pi\)
−0.595050 + 0.803689i \(0.702868\pi\)
\(294\) −35.0824 −2.04605
\(295\) 0 0
\(296\) 3.26968 0.190046
\(297\) −54.1217 −3.14046
\(298\) −27.9582 −1.61958
\(299\) −5.99655 −0.346790
\(300\) 0 0
\(301\) 2.65590 0.153083
\(302\) −21.1567 −1.21743
\(303\) 43.1164 2.47697
\(304\) 9.84485 0.564641
\(305\) 0 0
\(306\) 102.812 5.87738
\(307\) −16.8145 −0.959655 −0.479827 0.877363i \(-0.659301\pi\)
−0.479827 + 0.877363i \(0.659301\pi\)
\(308\) 8.42305 0.479948
\(309\) 16.8413 0.958070
\(310\) 0 0
\(311\) 0.455317 0.0258186 0.0129093 0.999917i \(-0.495891\pi\)
0.0129093 + 0.999917i \(0.495891\pi\)
\(312\) −2.90197 −0.164292
\(313\) 22.8759 1.29302 0.646511 0.762904i \(-0.276227\pi\)
0.646511 + 0.762904i \(0.276227\pi\)
\(314\) 29.9807 1.69191
\(315\) 0 0
\(316\) −8.17618 −0.459946
\(317\) −13.4104 −0.753206 −0.376603 0.926375i \(-0.622908\pi\)
−0.376603 + 0.926375i \(0.622908\pi\)
\(318\) 4.07948 0.228766
\(319\) 21.9359 1.22818
\(320\) 0 0
\(321\) −47.9254 −2.67493
\(322\) 4.63578 0.258342
\(323\) 16.1603 0.899186
\(324\) 45.0754 2.50419
\(325\) 0 0
\(326\) 11.5004 0.636947
\(327\) −11.2473 −0.621977
\(328\) −1.50607 −0.0831585
\(329\) 12.0713 0.665515
\(330\) 0 0
\(331\) 0.745486 0.0409756 0.0204878 0.999790i \(-0.493478\pi\)
0.0204878 + 0.999790i \(0.493478\pi\)
\(332\) −15.2546 −0.837203
\(333\) 83.8903 4.59716
\(334\) 20.3715 1.11468
\(335\) 0 0
\(336\) 16.7919 0.916074
\(337\) 13.0103 0.708714 0.354357 0.935110i \(-0.384700\pi\)
0.354357 + 0.935110i \(0.384700\pi\)
\(338\) 6.86341 0.373320
\(339\) 54.0508 2.93564
\(340\) 0 0
\(341\) −15.3712 −0.832398
\(342\) 33.7466 1.82481
\(343\) −15.2095 −0.821238
\(344\) 0.636455 0.0343154
\(345\) 0 0
\(346\) 18.6028 1.00009
\(347\) 4.20211 0.225581 0.112791 0.993619i \(-0.464021\pi\)
0.112791 + 0.993619i \(0.464021\pi\)
\(348\) −35.0794 −1.88045
\(349\) −30.6653 −1.64147 −0.820737 0.571306i \(-0.806437\pi\)
−0.820737 + 0.571306i \(0.806437\pi\)
\(350\) 0 0
\(351\) −44.5377 −2.37725
\(352\) 29.2459 1.55881
\(353\) −15.1231 −0.804919 −0.402460 0.915438i \(-0.631845\pi\)
−0.402460 + 0.915438i \(0.631845\pi\)
\(354\) 75.2913 4.00169
\(355\) 0 0
\(356\) 12.0790 0.640184
\(357\) 27.5640 1.45884
\(358\) −2.78507 −0.147195
\(359\) 6.66336 0.351679 0.175839 0.984419i \(-0.443736\pi\)
0.175839 + 0.984419i \(0.443736\pi\)
\(360\) 0 0
\(361\) −13.6956 −0.720821
\(362\) −45.4592 −2.38928
\(363\) −9.81116 −0.514952
\(364\) 6.93148 0.363308
\(365\) 0 0
\(366\) −48.4478 −2.53241
\(367\) 23.4363 1.22337 0.611684 0.791102i \(-0.290493\pi\)
0.611684 + 0.791102i \(0.290493\pi\)
\(368\) 8.31505 0.433452
\(369\) −38.6412 −2.01158
\(370\) 0 0
\(371\) 0.780204 0.0405062
\(372\) 24.5813 1.27448
\(373\) −3.50768 −0.181621 −0.0908104 0.995868i \(-0.528946\pi\)
−0.0908104 + 0.995868i \(0.528946\pi\)
\(374\) 51.5859 2.66744
\(375\) 0 0
\(376\) 2.89276 0.149183
\(377\) 18.0515 0.929698
\(378\) 34.4310 1.77094
\(379\) −27.5949 −1.41745 −0.708727 0.705482i \(-0.750730\pi\)
−0.708727 + 0.705482i \(0.750730\pi\)
\(380\) 0 0
\(381\) 35.5270 1.82010
\(382\) −35.9654 −1.84015
\(383\) 12.1641 0.621556 0.310778 0.950483i \(-0.399410\pi\)
0.310778 + 0.950483i \(0.399410\pi\)
\(384\) 7.51036 0.383261
\(385\) 0 0
\(386\) −25.5204 −1.29895
\(387\) 16.3296 0.830078
\(388\) −2.15202 −0.109252
\(389\) −4.54451 −0.230416 −0.115208 0.993341i \(-0.536753\pi\)
−0.115208 + 0.993341i \(0.536753\pi\)
\(390\) 0 0
\(391\) 13.6492 0.690269
\(392\) −1.60787 −0.0812095
\(393\) −36.6430 −1.84839
\(394\) −26.1506 −1.31745
\(395\) 0 0
\(396\) 51.7884 2.60247
\(397\) −21.6534 −1.08675 −0.543377 0.839489i \(-0.682855\pi\)
−0.543377 + 0.839489i \(0.682855\pi\)
\(398\) −39.1132 −1.96057
\(399\) 9.04748 0.452940
\(400\) 0 0
\(401\) 18.9808 0.947857 0.473928 0.880563i \(-0.342836\pi\)
0.473928 + 0.880563i \(0.342836\pi\)
\(402\) 90.0907 4.49331
\(403\) −12.6492 −0.630104
\(404\) −24.6792 −1.22784
\(405\) 0 0
\(406\) −13.9551 −0.692581
\(407\) 42.0919 2.08642
\(408\) 6.60538 0.327015
\(409\) −36.0879 −1.78443 −0.892216 0.451609i \(-0.850850\pi\)
−0.892216 + 0.451609i \(0.850850\pi\)
\(410\) 0 0
\(411\) −57.6061 −2.84150
\(412\) −9.63975 −0.474916
\(413\) 14.3995 0.708555
\(414\) 28.5027 1.40083
\(415\) 0 0
\(416\) 24.0670 1.17998
\(417\) 8.92242 0.436933
\(418\) 16.9323 0.828188
\(419\) 3.42426 0.167286 0.0836431 0.996496i \(-0.473344\pi\)
0.0836431 + 0.996496i \(0.473344\pi\)
\(420\) 0 0
\(421\) −29.8400 −1.45431 −0.727156 0.686473i \(-0.759158\pi\)
−0.727156 + 0.686473i \(0.759158\pi\)
\(422\) 31.2998 1.52365
\(423\) 74.2197 3.60868
\(424\) 0.186967 0.00907992
\(425\) 0 0
\(426\) 23.1712 1.12265
\(427\) −9.26569 −0.448398
\(428\) 27.4318 1.32597
\(429\) −37.3583 −1.80368
\(430\) 0 0
\(431\) −17.8468 −0.859650 −0.429825 0.902912i \(-0.641425\pi\)
−0.429825 + 0.902912i \(0.641425\pi\)
\(432\) 61.7578 2.97132
\(433\) −25.4504 −1.22307 −0.611533 0.791219i \(-0.709447\pi\)
−0.611533 + 0.791219i \(0.709447\pi\)
\(434\) 9.77880 0.469397
\(435\) 0 0
\(436\) 6.43780 0.308315
\(437\) 4.48015 0.214315
\(438\) −11.4115 −0.545262
\(439\) −35.8325 −1.71019 −0.855096 0.518469i \(-0.826502\pi\)
−0.855096 + 0.518469i \(0.826502\pi\)
\(440\) 0 0
\(441\) −41.2531 −1.96443
\(442\) 42.4510 2.01919
\(443\) 25.3602 1.20490 0.602450 0.798157i \(-0.294191\pi\)
0.602450 + 0.798157i \(0.294191\pi\)
\(444\) −67.3124 −3.19450
\(445\) 0 0
\(446\) −25.6368 −1.21394
\(447\) −46.0861 −2.17980
\(448\) −8.22452 −0.388572
\(449\) 9.57805 0.452016 0.226008 0.974125i \(-0.427432\pi\)
0.226008 + 0.974125i \(0.427432\pi\)
\(450\) 0 0
\(451\) −19.3882 −0.912955
\(452\) −30.9379 −1.45520
\(453\) −34.8746 −1.63855
\(454\) 3.98902 0.187214
\(455\) 0 0
\(456\) 2.16812 0.101532
\(457\) −19.4654 −0.910554 −0.455277 0.890350i \(-0.650460\pi\)
−0.455277 + 0.890350i \(0.650460\pi\)
\(458\) −56.7298 −2.65081
\(459\) 101.376 4.73180
\(460\) 0 0
\(461\) 11.2477 0.523859 0.261930 0.965087i \(-0.415641\pi\)
0.261930 + 0.965087i \(0.415641\pi\)
\(462\) 28.8807 1.34365
\(463\) −11.8561 −0.550999 −0.275499 0.961301i \(-0.588843\pi\)
−0.275499 + 0.961301i \(0.588843\pi\)
\(464\) −25.0309 −1.16203
\(465\) 0 0
\(466\) 35.0691 1.62454
\(467\) −22.5284 −1.04249 −0.521244 0.853408i \(-0.674532\pi\)
−0.521244 + 0.853408i \(0.674532\pi\)
\(468\) 42.6176 1.97000
\(469\) 17.2299 0.795604
\(470\) 0 0
\(471\) 49.4201 2.27716
\(472\) 3.45068 0.158831
\(473\) 8.19335 0.376731
\(474\) −28.0343 −1.28766
\(475\) 0 0
\(476\) −15.7772 −0.723148
\(477\) 4.79702 0.219641
\(478\) −14.4461 −0.660749
\(479\) 15.4805 0.707323 0.353662 0.935373i \(-0.384936\pi\)
0.353662 + 0.935373i \(0.384936\pi\)
\(480\) 0 0
\(481\) 34.6382 1.57937
\(482\) −1.96258 −0.0893932
\(483\) 7.64159 0.347704
\(484\) 5.61577 0.255262
\(485\) 0 0
\(486\) 69.4886 3.15207
\(487\) 32.2226 1.46015 0.730073 0.683370i \(-0.239486\pi\)
0.730073 + 0.683370i \(0.239486\pi\)
\(488\) −2.22042 −0.100514
\(489\) 18.9571 0.857272
\(490\) 0 0
\(491\) −9.45290 −0.426603 −0.213302 0.976986i \(-0.568422\pi\)
−0.213302 + 0.976986i \(0.568422\pi\)
\(492\) 31.0051 1.39782
\(493\) −41.0882 −1.85052
\(494\) 13.9339 0.626917
\(495\) 0 0
\(496\) 17.5399 0.787566
\(497\) 4.43152 0.198781
\(498\) −52.3045 −2.34382
\(499\) 11.4148 0.510997 0.255498 0.966810i \(-0.417760\pi\)
0.255498 + 0.966810i \(0.417760\pi\)
\(500\) 0 0
\(501\) 33.5802 1.50025
\(502\) 7.06098 0.315147
\(503\) 7.49525 0.334197 0.167098 0.985940i \(-0.446560\pi\)
0.167098 + 0.985940i \(0.446560\pi\)
\(504\) 2.63804 0.117508
\(505\) 0 0
\(506\) 14.3012 0.635767
\(507\) 11.3136 0.502455
\(508\) −20.3351 −0.902226
\(509\) −15.9234 −0.705791 −0.352896 0.935663i \(-0.614803\pi\)
−0.352896 + 0.935663i \(0.614803\pi\)
\(510\) 0 0
\(511\) −2.18246 −0.0965463
\(512\) −30.8845 −1.36492
\(513\) 33.2751 1.46913
\(514\) −31.2498 −1.37837
\(515\) 0 0
\(516\) −13.1026 −0.576810
\(517\) 37.2397 1.63780
\(518\) −26.7779 −1.17655
\(519\) 30.6647 1.34603
\(520\) 0 0
\(521\) 8.84451 0.387485 0.193743 0.981052i \(-0.437937\pi\)
0.193743 + 0.981052i \(0.437937\pi\)
\(522\) −85.8019 −3.75545
\(523\) 11.5432 0.504748 0.252374 0.967630i \(-0.418789\pi\)
0.252374 + 0.967630i \(0.418789\pi\)
\(524\) 20.9739 0.916250
\(525\) 0 0
\(526\) −46.0608 −2.00835
\(527\) 28.7918 1.25419
\(528\) 51.8025 2.25441
\(529\) −19.2160 −0.835479
\(530\) 0 0
\(531\) 88.5344 3.84206
\(532\) −5.17865 −0.224523
\(533\) −15.9549 −0.691084
\(534\) 41.4161 1.79225
\(535\) 0 0
\(536\) 4.12895 0.178344
\(537\) −4.59089 −0.198111
\(538\) −28.9325 −1.24737
\(539\) −20.6987 −0.891557
\(540\) 0 0
\(541\) 7.15787 0.307741 0.153871 0.988091i \(-0.450826\pi\)
0.153871 + 0.988091i \(0.450826\pi\)
\(542\) 39.9420 1.71566
\(543\) −74.9347 −3.21575
\(544\) −54.7806 −2.34870
\(545\) 0 0
\(546\) 23.7665 1.01711
\(547\) 14.4508 0.617871 0.308935 0.951083i \(-0.400027\pi\)
0.308935 + 0.951083i \(0.400027\pi\)
\(548\) 32.9729 1.40853
\(549\) −56.9694 −2.43139
\(550\) 0 0
\(551\) −13.4866 −0.574550
\(552\) 1.83122 0.0779418
\(553\) −5.36158 −0.227998
\(554\) 46.3319 1.96846
\(555\) 0 0
\(556\) −5.10707 −0.216588
\(557\) 24.3566 1.03202 0.516011 0.856582i \(-0.327416\pi\)
0.516011 + 0.856582i \(0.327416\pi\)
\(558\) 60.1242 2.54526
\(559\) 6.74246 0.285176
\(560\) 0 0
\(561\) 85.0339 3.59013
\(562\) 60.5670 2.55486
\(563\) 7.51196 0.316592 0.158296 0.987392i \(-0.449400\pi\)
0.158296 + 0.987392i \(0.449400\pi\)
\(564\) −59.5528 −2.50762
\(565\) 0 0
\(566\) 9.90390 0.416292
\(567\) 29.5585 1.24134
\(568\) 1.06196 0.0445590
\(569\) 9.01349 0.377865 0.188933 0.981990i \(-0.439497\pi\)
0.188933 + 0.981990i \(0.439497\pi\)
\(570\) 0 0
\(571\) 21.8260 0.913388 0.456694 0.889624i \(-0.349033\pi\)
0.456694 + 0.889624i \(0.349033\pi\)
\(572\) 21.3834 0.894084
\(573\) −59.2851 −2.47667
\(574\) 12.3343 0.514825
\(575\) 0 0
\(576\) −50.5678 −2.10699
\(577\) 26.7528 1.11373 0.556866 0.830602i \(-0.312004\pi\)
0.556866 + 0.830602i \(0.312004\pi\)
\(578\) −63.2618 −2.63134
\(579\) −42.0677 −1.74827
\(580\) 0 0
\(581\) −10.0033 −0.415006
\(582\) −7.37879 −0.305861
\(583\) 2.40690 0.0996837
\(584\) −0.523001 −0.0216419
\(585\) 0 0
\(586\) 39.9802 1.65157
\(587\) 39.1291 1.61503 0.807516 0.589846i \(-0.200811\pi\)
0.807516 + 0.589846i \(0.200811\pi\)
\(588\) 33.1009 1.36506
\(589\) 9.45051 0.389402
\(590\) 0 0
\(591\) −43.1065 −1.77317
\(592\) −48.0307 −1.97405
\(593\) 4.23212 0.173792 0.0868961 0.996217i \(-0.472305\pi\)
0.0868961 + 0.996217i \(0.472305\pi\)
\(594\) 106.218 4.35819
\(595\) 0 0
\(596\) 26.3791 1.08053
\(597\) −64.4740 −2.63874
\(598\) 11.7687 0.481259
\(599\) 28.1905 1.15183 0.575916 0.817509i \(-0.304645\pi\)
0.575916 + 0.817509i \(0.304645\pi\)
\(600\) 0 0
\(601\) −35.8977 −1.46430 −0.732149 0.681144i \(-0.761483\pi\)
−0.732149 + 0.681144i \(0.761483\pi\)
\(602\) −5.21242 −0.212442
\(603\) 105.937 4.31408
\(604\) 19.9618 0.812232
\(605\) 0 0
\(606\) −84.6195 −3.43743
\(607\) −6.86493 −0.278639 −0.139319 0.990247i \(-0.544491\pi\)
−0.139319 + 0.990247i \(0.544491\pi\)
\(608\) −17.9810 −0.729224
\(609\) −23.0035 −0.932150
\(610\) 0 0
\(611\) 30.6452 1.23977
\(612\) −97.0050 −3.92120
\(613\) −35.8712 −1.44883 −0.724413 0.689367i \(-0.757889\pi\)
−0.724413 + 0.689367i \(0.757889\pi\)
\(614\) 32.9999 1.33177
\(615\) 0 0
\(616\) 1.32363 0.0533308
\(617\) −10.4210 −0.419534 −0.209767 0.977751i \(-0.567271\pi\)
−0.209767 + 0.977751i \(0.567271\pi\)
\(618\) −33.0525 −1.32957
\(619\) 34.6351 1.39210 0.696051 0.717993i \(-0.254939\pi\)
0.696051 + 0.717993i \(0.254939\pi\)
\(620\) 0 0
\(621\) 28.1044 1.12779
\(622\) −0.893597 −0.0358300
\(623\) 7.92086 0.317343
\(624\) 42.6292 1.70653
\(625\) 0 0
\(626\) −44.8959 −1.79440
\(627\) 27.9112 1.11466
\(628\) −28.2874 −1.12879
\(629\) −78.8425 −3.14365
\(630\) 0 0
\(631\) −8.20201 −0.326517 −0.163258 0.986583i \(-0.552200\pi\)
−0.163258 + 0.986583i \(0.552200\pi\)
\(632\) −1.28484 −0.0511082
\(633\) 51.5945 2.05070
\(634\) 26.3191 1.04527
\(635\) 0 0
\(636\) −3.84906 −0.152625
\(637\) −17.0333 −0.674886
\(638\) −43.0511 −1.70441
\(639\) 27.2468 1.07787
\(640\) 0 0
\(641\) 29.5973 1.16902 0.584511 0.811386i \(-0.301286\pi\)
0.584511 + 0.811386i \(0.301286\pi\)
\(642\) 94.0575 3.71215
\(643\) 19.1406 0.754831 0.377416 0.926044i \(-0.376813\pi\)
0.377416 + 0.926044i \(0.376813\pi\)
\(644\) −4.37394 −0.172357
\(645\) 0 0
\(646\) −31.7160 −1.24785
\(647\) −11.2382 −0.441819 −0.220910 0.975294i \(-0.570903\pi\)
−0.220910 + 0.975294i \(0.570903\pi\)
\(648\) 7.08335 0.278260
\(649\) 44.4221 1.74372
\(650\) 0 0
\(651\) 16.1193 0.631765
\(652\) −10.8508 −0.424950
\(653\) 9.74451 0.381332 0.190666 0.981655i \(-0.438935\pi\)
0.190666 + 0.981655i \(0.438935\pi\)
\(654\) 22.0738 0.863152
\(655\) 0 0
\(656\) 22.1237 0.863785
\(657\) −13.4187 −0.523512
\(658\) −23.6910 −0.923572
\(659\) 25.5113 0.993779 0.496890 0.867814i \(-0.334475\pi\)
0.496890 + 0.867814i \(0.334475\pi\)
\(660\) 0 0
\(661\) 16.6125 0.646151 0.323076 0.946373i \(-0.395283\pi\)
0.323076 + 0.946373i \(0.395283\pi\)
\(662\) −1.46308 −0.0568641
\(663\) 69.9759 2.71764
\(664\) −2.39717 −0.0930282
\(665\) 0 0
\(666\) −164.642 −6.37973
\(667\) −11.3909 −0.441059
\(668\) −19.2209 −0.743678
\(669\) −42.2596 −1.63385
\(670\) 0 0
\(671\) −28.5843 −1.10349
\(672\) −30.6693 −1.18309
\(673\) 38.3964 1.48007 0.740035 0.672568i \(-0.234809\pi\)
0.740035 + 0.672568i \(0.234809\pi\)
\(674\) −25.5337 −0.983522
\(675\) 0 0
\(676\) −6.47575 −0.249067
\(677\) −16.2559 −0.624766 −0.312383 0.949956i \(-0.601127\pi\)
−0.312383 + 0.949956i \(0.601127\pi\)
\(678\) −106.079 −4.07395
\(679\) −1.41120 −0.0541569
\(680\) 0 0
\(681\) 6.57547 0.251973
\(682\) 30.1673 1.15516
\(683\) 1.61455 0.0617790 0.0308895 0.999523i \(-0.490166\pi\)
0.0308895 + 0.999523i \(0.490166\pi\)
\(684\) −31.8405 −1.21745
\(685\) 0 0
\(686\) 29.8500 1.13968
\(687\) −93.5130 −3.56775
\(688\) −9.34935 −0.356441
\(689\) 1.98068 0.0754580
\(690\) 0 0
\(691\) 45.6842 1.73791 0.868954 0.494892i \(-0.164792\pi\)
0.868954 + 0.494892i \(0.164792\pi\)
\(692\) −17.5520 −0.667228
\(693\) 33.9606 1.29006
\(694\) −8.24700 −0.313052
\(695\) 0 0
\(696\) −5.51253 −0.208952
\(697\) 36.3161 1.37557
\(698\) 60.1831 2.27797
\(699\) 57.8076 2.18648
\(700\) 0 0
\(701\) −8.16904 −0.308540 −0.154270 0.988029i \(-0.549303\pi\)
−0.154270 + 0.988029i \(0.549303\pi\)
\(702\) 87.4090 3.29904
\(703\) −25.8789 −0.976042
\(704\) −25.3724 −0.956257
\(705\) 0 0
\(706\) 29.6803 1.11703
\(707\) −16.1836 −0.608645
\(708\) −71.0387 −2.66980
\(709\) 26.7104 1.00313 0.501565 0.865120i \(-0.332758\pi\)
0.501565 + 0.865120i \(0.332758\pi\)
\(710\) 0 0
\(711\) −32.9652 −1.23629
\(712\) 1.89814 0.0711359
\(713\) 7.98199 0.298928
\(714\) −54.0965 −2.02451
\(715\) 0 0
\(716\) 2.62776 0.0982040
\(717\) −23.8129 −0.889307
\(718\) −13.0774 −0.488044
\(719\) 33.8315 1.26170 0.630850 0.775905i \(-0.282706\pi\)
0.630850 + 0.775905i \(0.282706\pi\)
\(720\) 0 0
\(721\) −6.32132 −0.235418
\(722\) 26.8787 1.00032
\(723\) −3.23511 −0.120315
\(724\) 42.8916 1.59405
\(725\) 0 0
\(726\) 19.2552 0.714628
\(727\) 17.2402 0.639402 0.319701 0.947518i \(-0.396417\pi\)
0.319701 + 0.947518i \(0.396417\pi\)
\(728\) 1.08924 0.0403700
\(729\) 41.5177 1.53769
\(730\) 0 0
\(731\) −15.3470 −0.567629
\(732\) 45.7114 1.68954
\(733\) 21.9745 0.811647 0.405824 0.913951i \(-0.366985\pi\)
0.405824 + 0.913951i \(0.366985\pi\)
\(734\) −45.9958 −1.69774
\(735\) 0 0
\(736\) −15.1869 −0.559796
\(737\) 53.1537 1.95794
\(738\) 75.8366 2.79158
\(739\) −30.0201 −1.10431 −0.552154 0.833742i \(-0.686194\pi\)
−0.552154 + 0.833742i \(0.686194\pi\)
\(740\) 0 0
\(741\) 22.9686 0.843773
\(742\) −1.53121 −0.0562127
\(743\) −22.4069 −0.822028 −0.411014 0.911629i \(-0.634825\pi\)
−0.411014 + 0.911629i \(0.634825\pi\)
\(744\) 3.86281 0.141617
\(745\) 0 0
\(746\) 6.88411 0.252045
\(747\) −61.5043 −2.25033
\(748\) −48.6722 −1.77963
\(749\) 17.9886 0.657288
\(750\) 0 0
\(751\) 42.9661 1.56786 0.783928 0.620851i \(-0.213213\pi\)
0.783928 + 0.620851i \(0.213213\pi\)
\(752\) −42.4938 −1.54959
\(753\) 11.6393 0.424158
\(754\) −35.4275 −1.29019
\(755\) 0 0
\(756\) −32.4862 −1.18151
\(757\) −8.52285 −0.309768 −0.154884 0.987933i \(-0.549500\pi\)
−0.154884 + 0.987933i \(0.549500\pi\)
\(758\) 54.1573 1.96708
\(759\) 23.5740 0.855683
\(760\) 0 0
\(761\) 53.7209 1.94738 0.973690 0.227875i \(-0.0731779\pi\)
0.973690 + 0.227875i \(0.0731779\pi\)
\(762\) −69.7246 −2.52586
\(763\) 4.22162 0.152833
\(764\) 33.9340 1.22769
\(765\) 0 0
\(766\) −23.8730 −0.862568
\(767\) 36.5557 1.31995
\(768\) −58.5634 −2.11323
\(769\) 31.4243 1.13319 0.566595 0.823996i \(-0.308260\pi\)
0.566595 + 0.823996i \(0.308260\pi\)
\(770\) 0 0
\(771\) −51.5120 −1.85516
\(772\) 24.0789 0.866620
\(773\) 48.4159 1.74140 0.870699 0.491816i \(-0.163667\pi\)
0.870699 + 0.491816i \(0.163667\pi\)
\(774\) −32.0481 −1.15195
\(775\) 0 0
\(776\) −0.338178 −0.0121399
\(777\) −44.1405 −1.58353
\(778\) 8.91899 0.319761
\(779\) 11.9202 0.427087
\(780\) 0 0
\(781\) 13.6711 0.489190
\(782\) −26.7876 −0.957924
\(783\) −84.6030 −3.02346
\(784\) 23.6191 0.843539
\(785\) 0 0
\(786\) 71.9149 2.56512
\(787\) −23.9666 −0.854316 −0.427158 0.904177i \(-0.640485\pi\)
−0.427158 + 0.904177i \(0.640485\pi\)
\(788\) 24.6736 0.878960
\(789\) −75.9263 −2.70305
\(790\) 0 0
\(791\) −20.2877 −0.721349
\(792\) 8.13826 0.289181
\(793\) −23.5226 −0.835311
\(794\) 42.4967 1.50815
\(795\) 0 0
\(796\) 36.9040 1.30803
\(797\) 5.68070 0.201221 0.100610 0.994926i \(-0.467920\pi\)
0.100610 + 0.994926i \(0.467920\pi\)
\(798\) −17.7564 −0.628571
\(799\) −69.7537 −2.46771
\(800\) 0 0
\(801\) 48.7008 1.72076
\(802\) −37.2514 −1.31539
\(803\) −6.73281 −0.237596
\(804\) −85.0021 −2.99779
\(805\) 0 0
\(806\) 24.8252 0.874430
\(807\) −47.6921 −1.67884
\(808\) −3.87820 −0.136435
\(809\) −3.08707 −0.108535 −0.0542677 0.998526i \(-0.517282\pi\)
−0.0542677 + 0.998526i \(0.517282\pi\)
\(810\) 0 0
\(811\) −7.14545 −0.250911 −0.125455 0.992099i \(-0.540039\pi\)
−0.125455 + 0.992099i \(0.540039\pi\)
\(812\) 13.1669 0.462067
\(813\) 65.8402 2.30912
\(814\) −82.6089 −2.89544
\(815\) 0 0
\(816\) −97.0313 −3.39678
\(817\) −5.03743 −0.176237
\(818\) 70.8255 2.47636
\(819\) 27.9468 0.976539
\(820\) 0 0
\(821\) −27.0857 −0.945298 −0.472649 0.881251i \(-0.656702\pi\)
−0.472649 + 0.881251i \(0.656702\pi\)
\(822\) 113.057 3.94331
\(823\) −20.4296 −0.712130 −0.356065 0.934461i \(-0.615882\pi\)
−0.356065 + 0.934461i \(0.615882\pi\)
\(824\) −1.51483 −0.0527717
\(825\) 0 0
\(826\) −28.2603 −0.983301
\(827\) −32.6171 −1.13421 −0.567103 0.823647i \(-0.691936\pi\)
−0.567103 + 0.823647i \(0.691936\pi\)
\(828\) −26.8928 −0.934590
\(829\) −41.5411 −1.44278 −0.721390 0.692529i \(-0.756497\pi\)
−0.721390 + 0.692529i \(0.756497\pi\)
\(830\) 0 0
\(831\) 76.3733 2.64936
\(832\) −20.8794 −0.723862
\(833\) 38.7708 1.34333
\(834\) −17.5110 −0.606356
\(835\) 0 0
\(836\) −15.9760 −0.552540
\(837\) 59.2841 2.04916
\(838\) −6.72040 −0.232152
\(839\) 52.1241 1.79952 0.899762 0.436381i \(-0.143740\pi\)
0.899762 + 0.436381i \(0.143740\pi\)
\(840\) 0 0
\(841\) 5.29019 0.182421
\(842\) 58.5634 2.01823
\(843\) 99.8382 3.43861
\(844\) −29.5319 −1.01653
\(845\) 0 0
\(846\) −145.662 −5.00797
\(847\) 3.68258 0.126535
\(848\) −2.74649 −0.0943150
\(849\) 16.3255 0.560290
\(850\) 0 0
\(851\) −21.8576 −0.749268
\(852\) −21.8625 −0.748996
\(853\) 33.8361 1.15853 0.579263 0.815141i \(-0.303341\pi\)
0.579263 + 0.815141i \(0.303341\pi\)
\(854\) 18.1847 0.622267
\(855\) 0 0
\(856\) 4.31076 0.147339
\(857\) 34.4148 1.17559 0.587793 0.809011i \(-0.299997\pi\)
0.587793 + 0.809011i \(0.299997\pi\)
\(858\) 73.3188 2.50306
\(859\) 17.7350 0.605111 0.302555 0.953132i \(-0.402160\pi\)
0.302555 + 0.953132i \(0.402160\pi\)
\(860\) 0 0
\(861\) 20.3318 0.692906
\(862\) 35.0258 1.19298
\(863\) −0.378077 −0.0128699 −0.00643495 0.999979i \(-0.502048\pi\)
−0.00643495 + 0.999979i \(0.502048\pi\)
\(864\) −112.796 −3.83741
\(865\) 0 0
\(866\) 49.9485 1.69732
\(867\) −104.280 −3.54154
\(868\) −9.22647 −0.313167
\(869\) −16.5403 −0.561091
\(870\) 0 0
\(871\) 43.7412 1.48211
\(872\) 1.01166 0.0342593
\(873\) −8.67665 −0.293660
\(874\) −8.79267 −0.297416
\(875\) 0 0
\(876\) 10.7669 0.363781
\(877\) 19.1653 0.647166 0.323583 0.946200i \(-0.395113\pi\)
0.323583 + 0.946200i \(0.395113\pi\)
\(878\) 70.3243 2.37333
\(879\) 65.9031 2.22286
\(880\) 0 0
\(881\) 23.0027 0.774981 0.387490 0.921874i \(-0.373342\pi\)
0.387490 + 0.921874i \(0.373342\pi\)
\(882\) 80.9626 2.72615
\(883\) −27.9811 −0.941639 −0.470819 0.882230i \(-0.656042\pi\)
−0.470819 + 0.882230i \(0.656042\pi\)
\(884\) −40.0532 −1.34714
\(885\) 0 0
\(886\) −49.7715 −1.67211
\(887\) −10.0014 −0.335814 −0.167907 0.985803i \(-0.553701\pi\)
−0.167907 + 0.985803i \(0.553701\pi\)
\(888\) −10.5778 −0.354966
\(889\) −13.3349 −0.447238
\(890\) 0 0
\(891\) 91.1870 3.05488
\(892\) 24.1888 0.809900
\(893\) −22.8957 −0.766175
\(894\) 90.4478 3.02503
\(895\) 0 0
\(896\) −2.81898 −0.0941756
\(897\) 19.3995 0.647730
\(898\) −18.7977 −0.627288
\(899\) −24.0282 −0.801387
\(900\) 0 0
\(901\) −4.50838 −0.150196
\(902\) 38.0510 1.26696
\(903\) −8.59211 −0.285928
\(904\) −4.86172 −0.161699
\(905\) 0 0
\(906\) 68.4444 2.27391
\(907\) −45.3028 −1.50425 −0.752127 0.659018i \(-0.770972\pi\)
−0.752127 + 0.659018i \(0.770972\pi\)
\(908\) −3.76371 −0.124903
\(909\) −99.5033 −3.30032
\(910\) 0 0
\(911\) 7.64639 0.253336 0.126668 0.991945i \(-0.459572\pi\)
0.126668 + 0.991945i \(0.459572\pi\)
\(912\) −31.8492 −1.05463
\(913\) −30.8598 −1.02131
\(914\) 38.2025 1.26363
\(915\) 0 0
\(916\) 53.5256 1.76853
\(917\) 13.7538 0.454190
\(918\) −198.958 −6.56659
\(919\) −2.02115 −0.0666717 −0.0333359 0.999444i \(-0.510613\pi\)
−0.0333359 + 0.999444i \(0.510613\pi\)
\(920\) 0 0
\(921\) 54.3968 1.79243
\(922\) −22.0746 −0.726989
\(923\) 11.2502 0.370304
\(924\) −27.2495 −0.896442
\(925\) 0 0
\(926\) 23.2685 0.764652
\(927\) −38.8662 −1.27653
\(928\) 45.7172 1.50074
\(929\) 19.6792 0.645654 0.322827 0.946458i \(-0.395367\pi\)
0.322827 + 0.946458i \(0.395367\pi\)
\(930\) 0 0
\(931\) 12.7260 0.417077
\(932\) −33.0883 −1.08384
\(933\) −1.47300 −0.0482238
\(934\) 44.2138 1.44672
\(935\) 0 0
\(936\) 6.69712 0.218902
\(937\) 45.8003 1.49623 0.748115 0.663569i \(-0.230959\pi\)
0.748115 + 0.663569i \(0.230959\pi\)
\(938\) −33.8151 −1.10410
\(939\) −74.0061 −2.41510
\(940\) 0 0
\(941\) 53.8116 1.75421 0.877104 0.480300i \(-0.159472\pi\)
0.877104 + 0.480300i \(0.159472\pi\)
\(942\) −96.9910 −3.16014
\(943\) 10.0680 0.327858
\(944\) −50.6896 −1.64981
\(945\) 0 0
\(946\) −16.0801 −0.522810
\(947\) −12.2954 −0.399548 −0.199774 0.979842i \(-0.564021\pi\)
−0.199774 + 0.979842i \(0.564021\pi\)
\(948\) 26.4508 0.859083
\(949\) −5.54055 −0.179854
\(950\) 0 0
\(951\) 43.3843 1.40683
\(952\) −2.47930 −0.0803547
\(953\) −36.4439 −1.18053 −0.590266 0.807209i \(-0.700977\pi\)
−0.590266 + 0.807209i \(0.700977\pi\)
\(954\) −9.41455 −0.304807
\(955\) 0 0
\(956\) 13.6301 0.440830
\(957\) −70.9651 −2.29398
\(958\) −30.3818 −0.981592
\(959\) 21.6222 0.698218
\(960\) 0 0
\(961\) −14.1626 −0.456859
\(962\) −67.9803 −2.19177
\(963\) 110.601 3.56408
\(964\) 1.85173 0.0596403
\(965\) 0 0
\(966\) −14.9972 −0.482528
\(967\) 28.2135 0.907285 0.453642 0.891184i \(-0.350124\pi\)
0.453642 + 0.891184i \(0.350124\pi\)
\(968\) 0.882487 0.0283642
\(969\) −52.2805 −1.67949
\(970\) 0 0
\(971\) −5.67228 −0.182032 −0.0910160 0.995849i \(-0.529011\pi\)
−0.0910160 + 0.995849i \(0.529011\pi\)
\(972\) −65.5638 −2.10296
\(973\) −3.34899 −0.107364
\(974\) −63.2395 −2.02632
\(975\) 0 0
\(976\) 32.6173 1.04405
\(977\) 19.6175 0.627618 0.313809 0.949486i \(-0.398395\pi\)
0.313809 + 0.949486i \(0.398395\pi\)
\(978\) −37.2050 −1.18968
\(979\) 24.4356 0.780965
\(980\) 0 0
\(981\) 25.9563 0.828722
\(982\) 18.5521 0.592021
\(983\) 15.2911 0.487710 0.243855 0.969812i \(-0.421588\pi\)
0.243855 + 0.969812i \(0.421588\pi\)
\(984\) 4.87229 0.155323
\(985\) 0 0
\(986\) 80.6390 2.56807
\(987\) −39.0521 −1.24304
\(988\) −13.1469 −0.418259
\(989\) −4.25466 −0.135290
\(990\) 0 0
\(991\) 23.6378 0.750879 0.375439 0.926847i \(-0.377492\pi\)
0.375439 + 0.926847i \(0.377492\pi\)
\(992\) −32.0355 −1.01713
\(993\) −2.41173 −0.0765339
\(994\) −8.69722 −0.275859
\(995\) 0 0
\(996\) 49.3502 1.56372
\(997\) −21.7194 −0.687860 −0.343930 0.938995i \(-0.611758\pi\)
−0.343930 + 0.938995i \(0.611758\pi\)
\(998\) −22.4025 −0.709138
\(999\) −162.341 −5.13625
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6025.2.a.k.1.5 25
5.4 even 2 1205.2.a.d.1.21 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.a.d.1.21 25 5.4 even 2
6025.2.a.k.1.5 25 1.1 even 1 trivial