Properties

Label 6025.2.a.o.1.1
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
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)
 
\(f(q)\) \(=\) \(q-2.56709 q^{2} -0.178555 q^{3} +4.58996 q^{4} +0.458367 q^{6} +0.233097 q^{7} -6.64865 q^{8} -2.96812 q^{9} +O(q^{10})\) \(q-2.56709 q^{2} -0.178555 q^{3} +4.58996 q^{4} +0.458367 q^{6} +0.233097 q^{7} -6.64865 q^{8} -2.96812 q^{9} -2.70454 q^{11} -0.819560 q^{12} +4.02919 q^{13} -0.598380 q^{14} +7.88779 q^{16} +2.29567 q^{17} +7.61943 q^{18} -4.91592 q^{19} -0.0416206 q^{21} +6.94279 q^{22} +7.50314 q^{23} +1.18715 q^{24} -10.3433 q^{26} +1.06564 q^{27} +1.06990 q^{28} +4.49806 q^{29} +6.05402 q^{31} -6.95136 q^{32} +0.482909 q^{33} -5.89319 q^{34} -13.6235 q^{36} +5.80342 q^{37} +12.6196 q^{38} -0.719432 q^{39} +8.99623 q^{41} +0.106844 q^{42} -11.2724 q^{43} -12.4137 q^{44} -19.2612 q^{46} +5.27836 q^{47} -1.40840 q^{48} -6.94567 q^{49} -0.409904 q^{51} +18.4938 q^{52} +2.38830 q^{53} -2.73559 q^{54} -1.54978 q^{56} +0.877763 q^{57} -11.5469 q^{58} -9.48259 q^{59} -8.25056 q^{61} -15.5412 q^{62} -0.691859 q^{63} +2.06921 q^{64} -1.23967 q^{66} +6.20669 q^{67} +10.5370 q^{68} -1.33972 q^{69} +2.53076 q^{71} +19.7340 q^{72} -14.9325 q^{73} -14.8979 q^{74} -22.5639 q^{76} -0.630419 q^{77} +1.84685 q^{78} -11.7640 q^{79} +8.71408 q^{81} -23.0941 q^{82} +10.5955 q^{83} -0.191037 q^{84} +28.9372 q^{86} -0.803151 q^{87} +17.9815 q^{88} +8.13410 q^{89} +0.939190 q^{91} +34.4391 q^{92} -1.08098 q^{93} -13.5500 q^{94} +1.24120 q^{96} -14.0886 q^{97} +17.8302 q^{98} +8.02738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9} + q^{11} + 14 q^{12} + 9 q^{13} - q^{14} + 43 q^{16} + 12 q^{17} + 42 q^{18} + 2 q^{21} + 5 q^{22} + 77 q^{23} - 2 q^{24} + 2 q^{26} + 38 q^{27} + 42 q^{28} + 2 q^{29} + q^{31} + 72 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 28 q^{37} + 23 q^{38} - 2 q^{39} - 2 q^{41} + 37 q^{42} + 31 q^{43} + 3 q^{44} + 14 q^{46} + 96 q^{47} + 13 q^{48} + 40 q^{49} - 10 q^{51} + 42 q^{52} + 54 q^{53} + 4 q^{54} - 15 q^{56} + 37 q^{57} + 27 q^{58} + q^{59} + 5 q^{61} + 39 q^{62} + 70 q^{63} + 65 q^{64} - 52 q^{66} + 34 q^{67} + 52 q^{68} + 21 q^{69} - 9 q^{71} + 70 q^{72} + 25 q^{73} + 22 q^{74} - 47 q^{76} + 54 q^{77} + 58 q^{78} + 13 q^{79} + 12 q^{81} - 5 q^{82} + 63 q^{83} + 95 q^{84} - 18 q^{86} + 47 q^{87} + 13 q^{88} + 19 q^{89} - 31 q^{91} + 137 q^{92} + 52 q^{93} + 120 q^{94} - 49 q^{96} + 36 q^{97} + 64 q^{98} + 16 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56709 −1.81521 −0.907604 0.419828i \(-0.862090\pi\)
−0.907604 + 0.419828i \(0.862090\pi\)
\(3\) −0.178555 −0.103089 −0.0515444 0.998671i \(-0.516414\pi\)
−0.0515444 + 0.998671i \(0.516414\pi\)
\(4\) 4.58996 2.29498
\(5\) 0 0
\(6\) 0.458367 0.187128
\(7\) 0.233097 0.0881023 0.0440511 0.999029i \(-0.485974\pi\)
0.0440511 + 0.999029i \(0.485974\pi\)
\(8\) −6.64865 −2.35065
\(9\) −2.96812 −0.989373
\(10\) 0 0
\(11\) −2.70454 −0.815449 −0.407724 0.913105i \(-0.633678\pi\)
−0.407724 + 0.913105i \(0.633678\pi\)
\(12\) −0.819560 −0.236587
\(13\) 4.02919 1.11749 0.558747 0.829338i \(-0.311282\pi\)
0.558747 + 0.829338i \(0.311282\pi\)
\(14\) −0.598380 −0.159924
\(15\) 0 0
\(16\) 7.88779 1.97195
\(17\) 2.29567 0.556782 0.278391 0.960468i \(-0.410199\pi\)
0.278391 + 0.960468i \(0.410199\pi\)
\(18\) 7.61943 1.79592
\(19\) −4.91592 −1.12779 −0.563895 0.825846i \(-0.690698\pi\)
−0.563895 + 0.825846i \(0.690698\pi\)
\(20\) 0 0
\(21\) −0.0416206 −0.00908236
\(22\) 6.94279 1.48021
\(23\) 7.50314 1.56451 0.782256 0.622957i \(-0.214069\pi\)
0.782256 + 0.622957i \(0.214069\pi\)
\(24\) 1.18715 0.242326
\(25\) 0 0
\(26\) −10.3433 −2.02849
\(27\) 1.06564 0.205082
\(28\) 1.06990 0.202193
\(29\) 4.49806 0.835269 0.417634 0.908615i \(-0.362859\pi\)
0.417634 + 0.908615i \(0.362859\pi\)
\(30\) 0 0
\(31\) 6.05402 1.08733 0.543667 0.839301i \(-0.317035\pi\)
0.543667 + 0.839301i \(0.317035\pi\)
\(32\) −6.95136 −1.22884
\(33\) 0.482909 0.0840636
\(34\) −5.89319 −1.01067
\(35\) 0 0
\(36\) −13.6235 −2.27059
\(37\) 5.80342 0.954076 0.477038 0.878883i \(-0.341710\pi\)
0.477038 + 0.878883i \(0.341710\pi\)
\(38\) 12.6196 2.04717
\(39\) −0.719432 −0.115201
\(40\) 0 0
\(41\) 8.99623 1.40497 0.702487 0.711696i \(-0.252073\pi\)
0.702487 + 0.711696i \(0.252073\pi\)
\(42\) 0.106844 0.0164864
\(43\) −11.2724 −1.71902 −0.859509 0.511120i \(-0.829231\pi\)
−0.859509 + 0.511120i \(0.829231\pi\)
\(44\) −12.4137 −1.87144
\(45\) 0 0
\(46\) −19.2612 −2.83992
\(47\) 5.27836 0.769928 0.384964 0.922932i \(-0.374214\pi\)
0.384964 + 0.922932i \(0.374214\pi\)
\(48\) −1.40840 −0.203286
\(49\) −6.94567 −0.992238
\(50\) 0 0
\(51\) −0.409904 −0.0573980
\(52\) 18.4938 2.56463
\(53\) 2.38830 0.328058 0.164029 0.986455i \(-0.447551\pi\)
0.164029 + 0.986455i \(0.447551\pi\)
\(54\) −2.73559 −0.372267
\(55\) 0 0
\(56\) −1.54978 −0.207098
\(57\) 0.877763 0.116263
\(58\) −11.5469 −1.51619
\(59\) −9.48259 −1.23453 −0.617264 0.786756i \(-0.711759\pi\)
−0.617264 + 0.786756i \(0.711759\pi\)
\(60\) 0 0
\(61\) −8.25056 −1.05638 −0.528188 0.849128i \(-0.677128\pi\)
−0.528188 + 0.849128i \(0.677128\pi\)
\(62\) −15.5412 −1.97374
\(63\) −0.691859 −0.0871660
\(64\) 2.06921 0.258651
\(65\) 0 0
\(66\) −1.23967 −0.152593
\(67\) 6.20669 0.758268 0.379134 0.925342i \(-0.376222\pi\)
0.379134 + 0.925342i \(0.376222\pi\)
\(68\) 10.5370 1.27780
\(69\) −1.33972 −0.161284
\(70\) 0 0
\(71\) 2.53076 0.300345 0.150173 0.988660i \(-0.452017\pi\)
0.150173 + 0.988660i \(0.452017\pi\)
\(72\) 19.7340 2.32567
\(73\) −14.9325 −1.74771 −0.873857 0.486184i \(-0.838389\pi\)
−0.873857 + 0.486184i \(0.838389\pi\)
\(74\) −14.8979 −1.73185
\(75\) 0 0
\(76\) −22.5639 −2.58825
\(77\) −0.630419 −0.0718429
\(78\) 1.84685 0.209114
\(79\) −11.7640 −1.32355 −0.661775 0.749702i \(-0.730197\pi\)
−0.661775 + 0.749702i \(0.730197\pi\)
\(80\) 0 0
\(81\) 8.71408 0.968231
\(82\) −23.0941 −2.55032
\(83\) 10.5955 1.16300 0.581502 0.813545i \(-0.302465\pi\)
0.581502 + 0.813545i \(0.302465\pi\)
\(84\) −0.191037 −0.0208438
\(85\) 0 0
\(86\) 28.9372 3.12037
\(87\) −0.803151 −0.0861069
\(88\) 17.9815 1.91684
\(89\) 8.13410 0.862213 0.431107 0.902301i \(-0.358123\pi\)
0.431107 + 0.902301i \(0.358123\pi\)
\(90\) 0 0
\(91\) 0.939190 0.0984538
\(92\) 34.4391 3.59052
\(93\) −1.08098 −0.112092
\(94\) −13.5500 −1.39758
\(95\) 0 0
\(96\) 1.24120 0.126680
\(97\) −14.0886 −1.43048 −0.715242 0.698877i \(-0.753683\pi\)
−0.715242 + 0.698877i \(0.753683\pi\)
\(98\) 17.8302 1.80112
\(99\) 8.02738 0.806783
\(100\) 0 0
\(101\) −7.76268 −0.772416 −0.386208 0.922412i \(-0.626215\pi\)
−0.386208 + 0.922412i \(0.626215\pi\)
\(102\) 1.05226 0.104189
\(103\) 8.88600 0.875563 0.437782 0.899081i \(-0.355764\pi\)
0.437782 + 0.899081i \(0.355764\pi\)
\(104\) −26.7887 −2.62684
\(105\) 0 0
\(106\) −6.13099 −0.595494
\(107\) −12.7644 −1.23398 −0.616989 0.786972i \(-0.711648\pi\)
−0.616989 + 0.786972i \(0.711648\pi\)
\(108\) 4.89123 0.470659
\(109\) −5.34986 −0.512424 −0.256212 0.966621i \(-0.582474\pi\)
−0.256212 + 0.966621i \(0.582474\pi\)
\(110\) 0 0
\(111\) −1.03623 −0.0983546
\(112\) 1.83862 0.173733
\(113\) −3.26328 −0.306984 −0.153492 0.988150i \(-0.549052\pi\)
−0.153492 + 0.988150i \(0.549052\pi\)
\(114\) −2.25330 −0.211041
\(115\) 0 0
\(116\) 20.6459 1.91692
\(117\) −11.9591 −1.10562
\(118\) 24.3427 2.24092
\(119\) 0.535113 0.0490537
\(120\) 0 0
\(121\) −3.68548 −0.335044
\(122\) 21.1799 1.91754
\(123\) −1.60632 −0.144837
\(124\) 27.7877 2.49541
\(125\) 0 0
\(126\) 1.77606 0.158224
\(127\) 1.32893 0.117923 0.0589617 0.998260i \(-0.481221\pi\)
0.0589617 + 0.998260i \(0.481221\pi\)
\(128\) 8.59089 0.759334
\(129\) 2.01274 0.177212
\(130\) 0 0
\(131\) 5.62895 0.491803 0.245902 0.969295i \(-0.420916\pi\)
0.245902 + 0.969295i \(0.420916\pi\)
\(132\) 2.21653 0.192924
\(133\) −1.14589 −0.0993609
\(134\) −15.9331 −1.37641
\(135\) 0 0
\(136\) −15.2631 −1.30880
\(137\) −5.95727 −0.508964 −0.254482 0.967078i \(-0.581905\pi\)
−0.254482 + 0.967078i \(0.581905\pi\)
\(138\) 3.43919 0.292764
\(139\) 11.9718 1.01544 0.507718 0.861523i \(-0.330489\pi\)
0.507718 + 0.861523i \(0.330489\pi\)
\(140\) 0 0
\(141\) −0.942479 −0.0793710
\(142\) −6.49668 −0.545189
\(143\) −10.8971 −0.911260
\(144\) −23.4119 −1.95099
\(145\) 0 0
\(146\) 38.3330 3.17246
\(147\) 1.24018 0.102289
\(148\) 26.6374 2.18958
\(149\) −6.34461 −0.519770 −0.259885 0.965640i \(-0.583685\pi\)
−0.259885 + 0.965640i \(0.583685\pi\)
\(150\) 0 0
\(151\) −1.34920 −0.109797 −0.0548984 0.998492i \(-0.517483\pi\)
−0.0548984 + 0.998492i \(0.517483\pi\)
\(152\) 32.6843 2.65105
\(153\) −6.81382 −0.550865
\(154\) 1.61834 0.130410
\(155\) 0 0
\(156\) −3.30216 −0.264384
\(157\) −11.7955 −0.941380 −0.470690 0.882299i \(-0.655995\pi\)
−0.470690 + 0.882299i \(0.655995\pi\)
\(158\) 30.1992 2.40252
\(159\) −0.426443 −0.0338192
\(160\) 0 0
\(161\) 1.74896 0.137837
\(162\) −22.3698 −1.75754
\(163\) 0.738249 0.0578241 0.0289121 0.999582i \(-0.490796\pi\)
0.0289121 + 0.999582i \(0.490796\pi\)
\(164\) 41.2923 3.22439
\(165\) 0 0
\(166\) −27.1995 −2.11109
\(167\) 22.9727 1.77768 0.888841 0.458217i \(-0.151512\pi\)
0.888841 + 0.458217i \(0.151512\pi\)
\(168\) 0.276721 0.0213495
\(169\) 3.23433 0.248795
\(170\) 0 0
\(171\) 14.5910 1.11580
\(172\) −51.7396 −3.94511
\(173\) 9.38513 0.713538 0.356769 0.934193i \(-0.383878\pi\)
0.356769 + 0.934193i \(0.383878\pi\)
\(174\) 2.06176 0.156302
\(175\) 0 0
\(176\) −21.3328 −1.60802
\(177\) 1.69316 0.127266
\(178\) −20.8810 −1.56510
\(179\) 26.1678 1.95587 0.977937 0.208900i \(-0.0669883\pi\)
0.977937 + 0.208900i \(0.0669883\pi\)
\(180\) 0 0
\(181\) 21.5772 1.60382 0.801909 0.597446i \(-0.203818\pi\)
0.801909 + 0.597446i \(0.203818\pi\)
\(182\) −2.41099 −0.178714
\(183\) 1.47318 0.108901
\(184\) −49.8858 −3.67763
\(185\) 0 0
\(186\) 2.77496 0.203470
\(187\) −6.20872 −0.454027
\(188\) 24.2275 1.76697
\(189\) 0.248397 0.0180682
\(190\) 0 0
\(191\) 14.3838 1.04078 0.520388 0.853930i \(-0.325787\pi\)
0.520388 + 0.853930i \(0.325787\pi\)
\(192\) −0.369467 −0.0266640
\(193\) 17.5667 1.26448 0.632239 0.774773i \(-0.282136\pi\)
0.632239 + 0.774773i \(0.282136\pi\)
\(194\) 36.1668 2.59662
\(195\) 0 0
\(196\) −31.8803 −2.27716
\(197\) −14.9323 −1.06388 −0.531939 0.846782i \(-0.678537\pi\)
−0.531939 + 0.846782i \(0.678537\pi\)
\(198\) −20.6070 −1.46448
\(199\) 20.4277 1.44808 0.724041 0.689757i \(-0.242283\pi\)
0.724041 + 0.689757i \(0.242283\pi\)
\(200\) 0 0
\(201\) −1.10824 −0.0781690
\(202\) 19.9275 1.40210
\(203\) 1.04848 0.0735891
\(204\) −1.88144 −0.131727
\(205\) 0 0
\(206\) −22.8112 −1.58933
\(207\) −22.2702 −1.54789
\(208\) 31.7814 2.20364
\(209\) 13.2953 0.919655
\(210\) 0 0
\(211\) 20.8689 1.43667 0.718336 0.695697i \(-0.244904\pi\)
0.718336 + 0.695697i \(0.244904\pi\)
\(212\) 10.9622 0.752887
\(213\) −0.451879 −0.0309623
\(214\) 32.7673 2.23993
\(215\) 0 0
\(216\) −7.08506 −0.482077
\(217\) 1.41117 0.0957966
\(218\) 13.7336 0.930155
\(219\) 2.66627 0.180170
\(220\) 0 0
\(221\) 9.24968 0.622201
\(222\) 2.66010 0.178534
\(223\) 18.1628 1.21627 0.608136 0.793833i \(-0.291918\pi\)
0.608136 + 0.793833i \(0.291918\pi\)
\(224\) −1.62034 −0.108264
\(225\) 0 0
\(226\) 8.37714 0.557239
\(227\) −19.5161 −1.29533 −0.647664 0.761926i \(-0.724254\pi\)
−0.647664 + 0.761926i \(0.724254\pi\)
\(228\) 4.02890 0.266820
\(229\) −24.8125 −1.63966 −0.819828 0.572610i \(-0.805931\pi\)
−0.819828 + 0.572610i \(0.805931\pi\)
\(230\) 0 0
\(231\) 0.112564 0.00740620
\(232\) −29.9060 −1.96343
\(233\) 20.5870 1.34870 0.674349 0.738412i \(-0.264424\pi\)
0.674349 + 0.738412i \(0.264424\pi\)
\(234\) 30.7001 2.00693
\(235\) 0 0
\(236\) −43.5247 −2.83321
\(237\) 2.10052 0.136443
\(238\) −1.37368 −0.0890427
\(239\) −18.4486 −1.19334 −0.596670 0.802487i \(-0.703510\pi\)
−0.596670 + 0.802487i \(0.703510\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) 9.46096 0.608174
\(243\) −4.75286 −0.304896
\(244\) −37.8697 −2.42436
\(245\) 0 0
\(246\) 4.12357 0.262910
\(247\) −19.8072 −1.26030
\(248\) −40.2511 −2.55595
\(249\) −1.89187 −0.119893
\(250\) 0 0
\(251\) −20.0239 −1.26390 −0.631948 0.775011i \(-0.717744\pi\)
−0.631948 + 0.775011i \(0.717744\pi\)
\(252\) −3.17560 −0.200044
\(253\) −20.2925 −1.27578
\(254\) −3.41148 −0.214055
\(255\) 0 0
\(256\) −26.1920 −1.63700
\(257\) 13.1798 0.822135 0.411067 0.911605i \(-0.365156\pi\)
0.411067 + 0.911605i \(0.365156\pi\)
\(258\) −5.16688 −0.321676
\(259\) 1.35276 0.0840562
\(260\) 0 0
\(261\) −13.3508 −0.826392
\(262\) −14.4500 −0.892725
\(263\) 16.5297 1.01927 0.509633 0.860392i \(-0.329781\pi\)
0.509633 + 0.860392i \(0.329781\pi\)
\(264\) −3.21069 −0.197605
\(265\) 0 0
\(266\) 2.94159 0.180361
\(267\) −1.45239 −0.0888845
\(268\) 28.4885 1.74021
\(269\) −22.8468 −1.39300 −0.696498 0.717559i \(-0.745259\pi\)
−0.696498 + 0.717559i \(0.745259\pi\)
\(270\) 0 0
\(271\) 4.40601 0.267646 0.133823 0.991005i \(-0.457275\pi\)
0.133823 + 0.991005i \(0.457275\pi\)
\(272\) 18.1078 1.09794
\(273\) −0.167697 −0.0101495
\(274\) 15.2929 0.923875
\(275\) 0 0
\(276\) −6.14927 −0.370143
\(277\) −19.2045 −1.15388 −0.576942 0.816785i \(-0.695754\pi\)
−0.576942 + 0.816785i \(0.695754\pi\)
\(278\) −30.7327 −1.84323
\(279\) −17.9691 −1.07578
\(280\) 0 0
\(281\) 13.4603 0.802974 0.401487 0.915865i \(-0.368493\pi\)
0.401487 + 0.915865i \(0.368493\pi\)
\(282\) 2.41943 0.144075
\(283\) 21.3025 1.26631 0.633153 0.774027i \(-0.281761\pi\)
0.633153 + 0.774027i \(0.281761\pi\)
\(284\) 11.6161 0.689286
\(285\) 0 0
\(286\) 27.9738 1.65413
\(287\) 2.09699 0.123781
\(288\) 20.6325 1.21578
\(289\) −11.7299 −0.689994
\(290\) 0 0
\(291\) 2.51560 0.147467
\(292\) −68.5394 −4.01096
\(293\) −13.5661 −0.792538 −0.396269 0.918135i \(-0.629695\pi\)
−0.396269 + 0.918135i \(0.629695\pi\)
\(294\) −3.18367 −0.185675
\(295\) 0 0
\(296\) −38.5849 −2.24270
\(297\) −2.88206 −0.167234
\(298\) 16.2872 0.943491
\(299\) 30.2315 1.74834
\(300\) 0 0
\(301\) −2.62755 −0.151449
\(302\) 3.46353 0.199304
\(303\) 1.38607 0.0796275
\(304\) −38.7758 −2.22394
\(305\) 0 0
\(306\) 17.4917 0.999934
\(307\) 9.29421 0.530449 0.265224 0.964187i \(-0.414554\pi\)
0.265224 + 0.964187i \(0.414554\pi\)
\(308\) −2.89359 −0.164878
\(309\) −1.58664 −0.0902608
\(310\) 0 0
\(311\) −4.71432 −0.267325 −0.133662 0.991027i \(-0.542674\pi\)
−0.133662 + 0.991027i \(0.542674\pi\)
\(312\) 4.78325 0.270798
\(313\) −11.4092 −0.644883 −0.322442 0.946589i \(-0.604504\pi\)
−0.322442 + 0.946589i \(0.604504\pi\)
\(314\) 30.2800 1.70880
\(315\) 0 0
\(316\) −53.9961 −3.03752
\(317\) 29.2232 1.64134 0.820670 0.571402i \(-0.193600\pi\)
0.820670 + 0.571402i \(0.193600\pi\)
\(318\) 1.09472 0.0613888
\(319\) −12.1652 −0.681119
\(320\) 0 0
\(321\) 2.27914 0.127209
\(322\) −4.48973 −0.250203
\(323\) −11.2853 −0.627933
\(324\) 39.9972 2.22207
\(325\) 0 0
\(326\) −1.89515 −0.104963
\(327\) 0.955245 0.0528252
\(328\) −59.8128 −3.30261
\(329\) 1.23037 0.0678324
\(330\) 0 0
\(331\) −16.4423 −0.903752 −0.451876 0.892081i \(-0.649245\pi\)
−0.451876 + 0.892081i \(0.649245\pi\)
\(332\) 48.6327 2.66907
\(333\) −17.2252 −0.943937
\(334\) −58.9730 −3.22686
\(335\) 0 0
\(336\) −0.328295 −0.0179099
\(337\) 25.8566 1.40850 0.704250 0.709952i \(-0.251284\pi\)
0.704250 + 0.709952i \(0.251284\pi\)
\(338\) −8.30283 −0.451614
\(339\) 0.582676 0.0316466
\(340\) 0 0
\(341\) −16.3733 −0.886665
\(342\) −37.4565 −2.02542
\(343\) −3.25069 −0.175521
\(344\) 74.9460 4.04082
\(345\) 0 0
\(346\) −24.0925 −1.29522
\(347\) −12.0753 −0.648235 −0.324118 0.946017i \(-0.605067\pi\)
−0.324118 + 0.946017i \(0.605067\pi\)
\(348\) −3.68643 −0.197613
\(349\) 5.32729 0.285163 0.142582 0.989783i \(-0.454460\pi\)
0.142582 + 0.989783i \(0.454460\pi\)
\(350\) 0 0
\(351\) 4.29365 0.229178
\(352\) 18.8002 1.00206
\(353\) 23.9377 1.27407 0.637037 0.770833i \(-0.280160\pi\)
0.637037 + 0.770833i \(0.280160\pi\)
\(354\) −4.34651 −0.231014
\(355\) 0 0
\(356\) 37.3352 1.97876
\(357\) −0.0955472 −0.00505689
\(358\) −67.1752 −3.55032
\(359\) −36.1319 −1.90697 −0.953483 0.301446i \(-0.902531\pi\)
−0.953483 + 0.301446i \(0.902531\pi\)
\(360\) 0 0
\(361\) 5.16631 0.271911
\(362\) −55.3905 −2.91126
\(363\) 0.658061 0.0345393
\(364\) 4.31084 0.225949
\(365\) 0 0
\(366\) −3.78178 −0.197677
\(367\) 10.0823 0.526293 0.263146 0.964756i \(-0.415240\pi\)
0.263146 + 0.964756i \(0.415240\pi\)
\(368\) 59.1832 3.08514
\(369\) −26.7019 −1.39004
\(370\) 0 0
\(371\) 0.556705 0.0289027
\(372\) −4.96164 −0.257249
\(373\) 27.0997 1.40317 0.701583 0.712587i \(-0.252477\pi\)
0.701583 + 0.712587i \(0.252477\pi\)
\(374\) 15.9384 0.824153
\(375\) 0 0
\(376\) −35.0940 −1.80984
\(377\) 18.1235 0.933408
\(378\) −0.637657 −0.0327975
\(379\) 11.1061 0.570481 0.285241 0.958456i \(-0.407926\pi\)
0.285241 + 0.958456i \(0.407926\pi\)
\(380\) 0 0
\(381\) −0.237287 −0.0121566
\(382\) −36.9246 −1.88923
\(383\) −5.90068 −0.301511 −0.150755 0.988571i \(-0.548171\pi\)
−0.150755 + 0.988571i \(0.548171\pi\)
\(384\) −1.53395 −0.0782789
\(385\) 0 0
\(386\) −45.0953 −2.29529
\(387\) 33.4577 1.70075
\(388\) −64.6662 −3.28293
\(389\) 15.5666 0.789260 0.394630 0.918840i \(-0.370873\pi\)
0.394630 + 0.918840i \(0.370873\pi\)
\(390\) 0 0
\(391\) 17.2247 0.871092
\(392\) 46.1793 2.33241
\(393\) −1.00508 −0.0506994
\(394\) 38.3324 1.93116
\(395\) 0 0
\(396\) 36.8453 1.85155
\(397\) 3.12799 0.156989 0.0784947 0.996915i \(-0.474989\pi\)
0.0784947 + 0.996915i \(0.474989\pi\)
\(398\) −52.4398 −2.62857
\(399\) 0.204604 0.0102430
\(400\) 0 0
\(401\) −13.8045 −0.689366 −0.344683 0.938719i \(-0.612014\pi\)
−0.344683 + 0.938719i \(0.612014\pi\)
\(402\) 2.84494 0.141893
\(403\) 24.3928 1.21509
\(404\) −35.6304 −1.77268
\(405\) 0 0
\(406\) −2.69155 −0.133579
\(407\) −15.6956 −0.778000
\(408\) 2.72531 0.134923
\(409\) 39.2212 1.93936 0.969681 0.244372i \(-0.0785819\pi\)
0.969681 + 0.244372i \(0.0785819\pi\)
\(410\) 0 0
\(411\) 1.06370 0.0524685
\(412\) 40.7863 2.00940
\(413\) −2.21036 −0.108765
\(414\) 57.1696 2.80973
\(415\) 0 0
\(416\) −28.0083 −1.37322
\(417\) −2.13763 −0.104680
\(418\) −34.1302 −1.66936
\(419\) 31.2132 1.52487 0.762433 0.647068i \(-0.224005\pi\)
0.762433 + 0.647068i \(0.224005\pi\)
\(420\) 0 0
\(421\) 28.1438 1.37165 0.685823 0.727768i \(-0.259442\pi\)
0.685823 + 0.727768i \(0.259442\pi\)
\(422\) −53.5723 −2.60786
\(423\) −15.6668 −0.761746
\(424\) −15.8790 −0.771152
\(425\) 0 0
\(426\) 1.16002 0.0562029
\(427\) −1.92318 −0.0930691
\(428\) −58.5879 −2.83195
\(429\) 1.94573 0.0939407
\(430\) 0 0
\(431\) 5.72745 0.275881 0.137941 0.990440i \(-0.455952\pi\)
0.137941 + 0.990440i \(0.455952\pi\)
\(432\) 8.40553 0.404411
\(433\) −26.5109 −1.27403 −0.637015 0.770851i \(-0.719831\pi\)
−0.637015 + 0.770851i \(0.719831\pi\)
\(434\) −3.62261 −0.173891
\(435\) 0 0
\(436\) −24.5556 −1.17600
\(437\) −36.8849 −1.76444
\(438\) −6.84455 −0.327045
\(439\) −4.16948 −0.198998 −0.0994991 0.995038i \(-0.531724\pi\)
−0.0994991 + 0.995038i \(0.531724\pi\)
\(440\) 0 0
\(441\) 20.6156 0.981693
\(442\) −23.7448 −1.12942
\(443\) 15.9514 0.757876 0.378938 0.925422i \(-0.376289\pi\)
0.378938 + 0.925422i \(0.376289\pi\)
\(444\) −4.75625 −0.225722
\(445\) 0 0
\(446\) −46.6256 −2.20778
\(447\) 1.13286 0.0535825
\(448\) 0.482325 0.0227877
\(449\) −11.6872 −0.551555 −0.275777 0.961222i \(-0.588935\pi\)
−0.275777 + 0.961222i \(0.588935\pi\)
\(450\) 0 0
\(451\) −24.3306 −1.14568
\(452\) −14.9783 −0.704521
\(453\) 0.240907 0.0113188
\(454\) 50.0996 2.35129
\(455\) 0 0
\(456\) −5.83594 −0.273293
\(457\) 17.7543 0.830512 0.415256 0.909705i \(-0.363692\pi\)
0.415256 + 0.909705i \(0.363692\pi\)
\(458\) 63.6959 2.97631
\(459\) 2.44635 0.114186
\(460\) 0 0
\(461\) 18.4673 0.860110 0.430055 0.902803i \(-0.358494\pi\)
0.430055 + 0.902803i \(0.358494\pi\)
\(462\) −0.288963 −0.0134438
\(463\) 29.3713 1.36500 0.682501 0.730885i \(-0.260892\pi\)
0.682501 + 0.730885i \(0.260892\pi\)
\(464\) 35.4797 1.64711
\(465\) 0 0
\(466\) −52.8487 −2.44817
\(467\) −25.3892 −1.17487 −0.587436 0.809271i \(-0.699863\pi\)
−0.587436 + 0.809271i \(0.699863\pi\)
\(468\) −54.8917 −2.53737
\(469\) 1.44676 0.0668052
\(470\) 0 0
\(471\) 2.10614 0.0970458
\(472\) 63.0464 2.90195
\(473\) 30.4865 1.40177
\(474\) −5.39222 −0.247673
\(475\) 0 0
\(476\) 2.45615 0.112577
\(477\) −7.08876 −0.324572
\(478\) 47.3592 2.16616
\(479\) −0.814950 −0.0372360 −0.0186180 0.999827i \(-0.505927\pi\)
−0.0186180 + 0.999827i \(0.505927\pi\)
\(480\) 0 0
\(481\) 23.3830 1.06617
\(482\) 2.56709 0.116928
\(483\) −0.312285 −0.0142095
\(484\) −16.9162 −0.768918
\(485\) 0 0
\(486\) 12.2010 0.553449
\(487\) 35.9667 1.62980 0.814902 0.579598i \(-0.196790\pi\)
0.814902 + 0.579598i \(0.196790\pi\)
\(488\) 54.8551 2.48317
\(489\) −0.131818 −0.00596102
\(490\) 0 0
\(491\) −6.75932 −0.305044 −0.152522 0.988300i \(-0.548739\pi\)
−0.152522 + 0.988300i \(0.548739\pi\)
\(492\) −7.37295 −0.332398
\(493\) 10.3261 0.465062
\(494\) 50.8468 2.28771
\(495\) 0 0
\(496\) 47.7528 2.14417
\(497\) 0.589911 0.0264611
\(498\) 4.85661 0.217630
\(499\) 23.2029 1.03870 0.519351 0.854561i \(-0.326174\pi\)
0.519351 + 0.854561i \(0.326174\pi\)
\(500\) 0 0
\(501\) −4.10189 −0.183259
\(502\) 51.4031 2.29423
\(503\) −12.1662 −0.542466 −0.271233 0.962514i \(-0.587431\pi\)
−0.271233 + 0.962514i \(0.587431\pi\)
\(504\) 4.59993 0.204897
\(505\) 0 0
\(506\) 52.0927 2.31580
\(507\) −0.577507 −0.0256480
\(508\) 6.09973 0.270632
\(509\) −25.2595 −1.11961 −0.559803 0.828626i \(-0.689123\pi\)
−0.559803 + 0.828626i \(0.689123\pi\)
\(510\) 0 0
\(511\) −3.48071 −0.153977
\(512\) 50.0555 2.21216
\(513\) −5.23859 −0.231290
\(514\) −33.8338 −1.49234
\(515\) 0 0
\(516\) 9.23837 0.406697
\(517\) −14.2755 −0.627837
\(518\) −3.47265 −0.152580
\(519\) −1.67576 −0.0735578
\(520\) 0 0
\(521\) 14.2216 0.623061 0.311531 0.950236i \(-0.399158\pi\)
0.311531 + 0.950236i \(0.399158\pi\)
\(522\) 34.2726 1.50007
\(523\) −5.16693 −0.225934 −0.112967 0.993599i \(-0.536035\pi\)
−0.112967 + 0.993599i \(0.536035\pi\)
\(524\) 25.8366 1.12868
\(525\) 0 0
\(526\) −42.4333 −1.85018
\(527\) 13.8980 0.605408
\(528\) 3.80908 0.165769
\(529\) 33.2971 1.44770
\(530\) 0 0
\(531\) 28.1454 1.22141
\(532\) −5.25957 −0.228031
\(533\) 36.2475 1.57005
\(534\) 3.72841 0.161344
\(535\) 0 0
\(536\) −41.2662 −1.78243
\(537\) −4.67240 −0.201629
\(538\) 58.6499 2.52858
\(539\) 18.7848 0.809119
\(540\) 0 0
\(541\) 0.312394 0.0134309 0.00671544 0.999977i \(-0.497862\pi\)
0.00671544 + 0.999977i \(0.497862\pi\)
\(542\) −11.3106 −0.485833
\(543\) −3.85271 −0.165336
\(544\) −15.9580 −0.684195
\(545\) 0 0
\(546\) 0.430494 0.0184234
\(547\) −0.0177707 −0.000759822 0 −0.000379911 1.00000i \(-0.500121\pi\)
−0.000379911 1.00000i \(0.500121\pi\)
\(548\) −27.3436 −1.16806
\(549\) 24.4886 1.04515
\(550\) 0 0
\(551\) −22.1121 −0.942008
\(552\) 8.90736 0.379122
\(553\) −2.74214 −0.116608
\(554\) 49.2996 2.09454
\(555\) 0 0
\(556\) 54.9501 2.33040
\(557\) −8.43223 −0.357285 −0.178643 0.983914i \(-0.557171\pi\)
−0.178643 + 0.983914i \(0.557171\pi\)
\(558\) 46.1282 1.95276
\(559\) −45.4184 −1.92099
\(560\) 0 0
\(561\) 1.10860 0.0468051
\(562\) −34.5538 −1.45756
\(563\) 19.9555 0.841023 0.420511 0.907287i \(-0.361851\pi\)
0.420511 + 0.907287i \(0.361851\pi\)
\(564\) −4.32594 −0.182155
\(565\) 0 0
\(566\) −54.6856 −2.29861
\(567\) 2.03122 0.0853034
\(568\) −16.8261 −0.706008
\(569\) −27.4439 −1.15051 −0.575254 0.817975i \(-0.695097\pi\)
−0.575254 + 0.817975i \(0.695097\pi\)
\(570\) 0 0
\(571\) −43.2360 −1.80937 −0.904686 0.426080i \(-0.859894\pi\)
−0.904686 + 0.426080i \(0.859894\pi\)
\(572\) −50.0171 −2.09132
\(573\) −2.56830 −0.107292
\(574\) −5.38317 −0.224689
\(575\) 0 0
\(576\) −6.14165 −0.255902
\(577\) 25.9833 1.08170 0.540850 0.841119i \(-0.318103\pi\)
0.540850 + 0.841119i \(0.318103\pi\)
\(578\) 30.1117 1.25248
\(579\) −3.13662 −0.130354
\(580\) 0 0
\(581\) 2.46977 0.102463
\(582\) −6.45776 −0.267683
\(583\) −6.45925 −0.267515
\(584\) 99.2808 4.10827
\(585\) 0 0
\(586\) 34.8253 1.43862
\(587\) 24.6564 1.01768 0.508840 0.860861i \(-0.330075\pi\)
0.508840 + 0.860861i \(0.330075\pi\)
\(588\) 5.69239 0.234750
\(589\) −29.7611 −1.22629
\(590\) 0 0
\(591\) 2.66623 0.109674
\(592\) 45.7761 1.88139
\(593\) −8.55003 −0.351108 −0.175554 0.984470i \(-0.556172\pi\)
−0.175554 + 0.984470i \(0.556172\pi\)
\(594\) 7.39850 0.303564
\(595\) 0 0
\(596\) −29.1215 −1.19286
\(597\) −3.64747 −0.149281
\(598\) −77.6071 −3.17359
\(599\) 39.3935 1.60957 0.804787 0.593564i \(-0.202280\pi\)
0.804787 + 0.593564i \(0.202280\pi\)
\(600\) 0 0
\(601\) 31.7899 1.29674 0.648368 0.761327i \(-0.275452\pi\)
0.648368 + 0.761327i \(0.275452\pi\)
\(602\) 6.74516 0.274912
\(603\) −18.4222 −0.750210
\(604\) −6.19279 −0.251981
\(605\) 0 0
\(606\) −3.55816 −0.144540
\(607\) 12.1431 0.492873 0.246437 0.969159i \(-0.420740\pi\)
0.246437 + 0.969159i \(0.420740\pi\)
\(608\) 34.1724 1.38587
\(609\) −0.187212 −0.00758621
\(610\) 0 0
\(611\) 21.2675 0.860391
\(612\) −31.2751 −1.26422
\(613\) −35.4694 −1.43260 −0.716298 0.697794i \(-0.754165\pi\)
−0.716298 + 0.697794i \(0.754165\pi\)
\(614\) −23.8591 −0.962875
\(615\) 0 0
\(616\) 4.19144 0.168878
\(617\) 9.94466 0.400357 0.200178 0.979759i \(-0.435848\pi\)
0.200178 + 0.979759i \(0.435848\pi\)
\(618\) 4.07305 0.163842
\(619\) −6.24993 −0.251206 −0.125603 0.992081i \(-0.540087\pi\)
−0.125603 + 0.992081i \(0.540087\pi\)
\(620\) 0 0
\(621\) 7.99563 0.320854
\(622\) 12.1021 0.485250
\(623\) 1.89603 0.0759629
\(624\) −5.67472 −0.227171
\(625\) 0 0
\(626\) 29.2883 1.17060
\(627\) −2.37394 −0.0948062
\(628\) −54.1407 −2.16045
\(629\) 13.3227 0.531212
\(630\) 0 0
\(631\) 18.3762 0.731544 0.365772 0.930704i \(-0.380805\pi\)
0.365772 + 0.930704i \(0.380805\pi\)
\(632\) 78.2146 3.11121
\(633\) −3.72624 −0.148105
\(634\) −75.0187 −2.97937
\(635\) 0 0
\(636\) −1.95736 −0.0776142
\(637\) −27.9854 −1.10882
\(638\) 31.2291 1.23637
\(639\) −7.51158 −0.297154
\(640\) 0 0
\(641\) 3.33886 0.131877 0.0659385 0.997824i \(-0.478996\pi\)
0.0659385 + 0.997824i \(0.478996\pi\)
\(642\) −5.85077 −0.230911
\(643\) 13.7815 0.543490 0.271745 0.962369i \(-0.412399\pi\)
0.271745 + 0.962369i \(0.412399\pi\)
\(644\) 8.02764 0.316333
\(645\) 0 0
\(646\) 28.9705 1.13983
\(647\) −8.43659 −0.331677 −0.165838 0.986153i \(-0.553033\pi\)
−0.165838 + 0.986153i \(0.553033\pi\)
\(648\) −57.9369 −2.27598
\(649\) 25.6460 1.00669
\(650\) 0 0
\(651\) −0.251972 −0.00987556
\(652\) 3.38853 0.132705
\(653\) −5.61773 −0.219839 −0.109919 0.993941i \(-0.535059\pi\)
−0.109919 + 0.993941i \(0.535059\pi\)
\(654\) −2.45220 −0.0958886
\(655\) 0 0
\(656\) 70.9603 2.77054
\(657\) 44.3213 1.72914
\(658\) −3.15847 −0.123130
\(659\) 33.0347 1.28685 0.643426 0.765509i \(-0.277513\pi\)
0.643426 + 0.765509i \(0.277513\pi\)
\(660\) 0 0
\(661\) 16.3730 0.636835 0.318418 0.947951i \(-0.396849\pi\)
0.318418 + 0.947951i \(0.396849\pi\)
\(662\) 42.2089 1.64050
\(663\) −1.65158 −0.0641420
\(664\) −70.4456 −2.73382
\(665\) 0 0
\(666\) 44.2187 1.71344
\(667\) 33.7496 1.30679
\(668\) 105.444 4.07974
\(669\) −3.24306 −0.125384
\(670\) 0 0
\(671\) 22.3139 0.861420
\(672\) 0.289320 0.0111608
\(673\) −16.1568 −0.622797 −0.311399 0.950279i \(-0.600797\pi\)
−0.311399 + 0.950279i \(0.600797\pi\)
\(674\) −66.3763 −2.55672
\(675\) 0 0
\(676\) 14.8455 0.570979
\(677\) 13.6410 0.524264 0.262132 0.965032i \(-0.415574\pi\)
0.262132 + 0.965032i \(0.415574\pi\)
\(678\) −1.49578 −0.0574452
\(679\) −3.28401 −0.126029
\(680\) 0 0
\(681\) 3.48470 0.133534
\(682\) 42.0318 1.60948
\(683\) 38.5051 1.47336 0.736679 0.676243i \(-0.236393\pi\)
0.736679 + 0.676243i \(0.236393\pi\)
\(684\) 66.9723 2.56075
\(685\) 0 0
\(686\) 8.34481 0.318606
\(687\) 4.43040 0.169030
\(688\) −88.9140 −3.38981
\(689\) 9.62291 0.366604
\(690\) 0 0
\(691\) 18.7375 0.712808 0.356404 0.934332i \(-0.384003\pi\)
0.356404 + 0.934332i \(0.384003\pi\)
\(692\) 43.0773 1.63755
\(693\) 1.87116 0.0710794
\(694\) 30.9984 1.17668
\(695\) 0 0
\(696\) 5.33988 0.202407
\(697\) 20.6524 0.782264
\(698\) −13.6756 −0.517631
\(699\) −3.67591 −0.139036
\(700\) 0 0
\(701\) 19.9345 0.752915 0.376458 0.926434i \(-0.377142\pi\)
0.376458 + 0.926434i \(0.377142\pi\)
\(702\) −11.0222 −0.416006
\(703\) −28.5292 −1.07600
\(704\) −5.59624 −0.210916
\(705\) 0 0
\(706\) −61.4502 −2.31271
\(707\) −1.80946 −0.0680516
\(708\) 7.77155 0.292073
\(709\) −45.9346 −1.72511 −0.862554 0.505965i \(-0.831137\pi\)
−0.862554 + 0.505965i \(0.831137\pi\)
\(710\) 0 0
\(711\) 34.9169 1.30948
\(712\) −54.0808 −2.02676
\(713\) 45.4242 1.70115
\(714\) 0.245278 0.00917931
\(715\) 0 0
\(716\) 120.109 4.48869
\(717\) 3.29409 0.123020
\(718\) 92.7538 3.46154
\(719\) 31.3581 1.16946 0.584730 0.811228i \(-0.301200\pi\)
0.584730 + 0.811228i \(0.301200\pi\)
\(720\) 0 0
\(721\) 2.07130 0.0771391
\(722\) −13.2624 −0.493575
\(723\) 0.178555 0.00664054
\(724\) 99.0382 3.68073
\(725\) 0 0
\(726\) −1.68930 −0.0626959
\(727\) −4.85392 −0.180022 −0.0900110 0.995941i \(-0.528690\pi\)
−0.0900110 + 0.995941i \(0.528690\pi\)
\(728\) −6.24435 −0.231431
\(729\) −25.2936 −0.936800
\(730\) 0 0
\(731\) −25.8776 −0.957118
\(732\) 6.76183 0.249924
\(733\) 9.39711 0.347090 0.173545 0.984826i \(-0.444478\pi\)
0.173545 + 0.984826i \(0.444478\pi\)
\(734\) −25.8822 −0.955330
\(735\) 0 0
\(736\) −52.1571 −1.92253
\(737\) −16.7862 −0.618329
\(738\) 68.5461 2.52322
\(739\) −28.9878 −1.06633 −0.533167 0.846010i \(-0.678998\pi\)
−0.533167 + 0.846010i \(0.678998\pi\)
\(740\) 0 0
\(741\) 3.53667 0.129923
\(742\) −1.42911 −0.0524644
\(743\) 20.6365 0.757081 0.378541 0.925585i \(-0.376426\pi\)
0.378541 + 0.925585i \(0.376426\pi\)
\(744\) 7.18704 0.263490
\(745\) 0 0
\(746\) −69.5673 −2.54704
\(747\) −31.4486 −1.15064
\(748\) −28.4978 −1.04198
\(749\) −2.97533 −0.108716
\(750\) 0 0
\(751\) 31.6075 1.15337 0.576687 0.816965i \(-0.304345\pi\)
0.576687 + 0.816965i \(0.304345\pi\)
\(752\) 41.6346 1.51826
\(753\) 3.57537 0.130294
\(754\) −46.5247 −1.69433
\(755\) 0 0
\(756\) 1.14013 0.0414661
\(757\) −22.2822 −0.809860 −0.404930 0.914348i \(-0.632704\pi\)
−0.404930 + 0.914348i \(0.632704\pi\)
\(758\) −28.5103 −1.03554
\(759\) 3.62333 0.131519
\(760\) 0 0
\(761\) 37.6655 1.36537 0.682686 0.730712i \(-0.260812\pi\)
0.682686 + 0.730712i \(0.260812\pi\)
\(762\) 0.609138 0.0220667
\(763\) −1.24703 −0.0451457
\(764\) 66.0211 2.38856
\(765\) 0 0
\(766\) 15.1476 0.547304
\(767\) −38.2071 −1.37958
\(768\) 4.67672 0.168756
\(769\) 29.5848 1.06685 0.533427 0.845846i \(-0.320904\pi\)
0.533427 + 0.845846i \(0.320904\pi\)
\(770\) 0 0
\(771\) −2.35332 −0.0847529
\(772\) 80.6304 2.90195
\(773\) −13.5902 −0.488804 −0.244402 0.969674i \(-0.578592\pi\)
−0.244402 + 0.969674i \(0.578592\pi\)
\(774\) −85.8889 −3.08721
\(775\) 0 0
\(776\) 93.6704 3.36257
\(777\) −0.241542 −0.00866526
\(778\) −39.9610 −1.43267
\(779\) −44.2248 −1.58452
\(780\) 0 0
\(781\) −6.84452 −0.244916
\(782\) −44.2175 −1.58121
\(783\) 4.79330 0.171299
\(784\) −54.7859 −1.95664
\(785\) 0 0
\(786\) 2.58012 0.0920300
\(787\) −12.9687 −0.462284 −0.231142 0.972920i \(-0.574246\pi\)
−0.231142 + 0.972920i \(0.574246\pi\)
\(788\) −68.5384 −2.44158
\(789\) −2.95147 −0.105075
\(790\) 0 0
\(791\) −0.760661 −0.0270460
\(792\) −53.3713 −1.89647
\(793\) −33.2430 −1.18049
\(794\) −8.02984 −0.284969
\(795\) 0 0
\(796\) 93.7622 3.32331
\(797\) −40.4854 −1.43407 −0.717033 0.697040i \(-0.754500\pi\)
−0.717033 + 0.697040i \(0.754500\pi\)
\(798\) −0.525236 −0.0185932
\(799\) 12.1174 0.428682
\(800\) 0 0
\(801\) −24.1430 −0.853050
\(802\) 35.4375 1.25134
\(803\) 40.3854 1.42517
\(804\) −5.08676 −0.179396
\(805\) 0 0
\(806\) −62.6185 −2.20564
\(807\) 4.07942 0.143602
\(808\) 51.6114 1.81568
\(809\) −51.2205 −1.80082 −0.900409 0.435045i \(-0.856732\pi\)
−0.900409 + 0.435045i \(0.856732\pi\)
\(810\) 0 0
\(811\) −7.98579 −0.280419 −0.140210 0.990122i \(-0.544778\pi\)
−0.140210 + 0.990122i \(0.544778\pi\)
\(812\) 4.81249 0.168885
\(813\) −0.786715 −0.0275913
\(814\) 40.2919 1.41223
\(815\) 0 0
\(816\) −3.23323 −0.113186
\(817\) 55.4140 1.93869
\(818\) −100.684 −3.52035
\(819\) −2.78763 −0.0974075
\(820\) 0 0
\(821\) 5.48153 0.191307 0.0956534 0.995415i \(-0.469506\pi\)
0.0956534 + 0.995415i \(0.469506\pi\)
\(822\) −2.73062 −0.0952412
\(823\) −1.02446 −0.0357103 −0.0178552 0.999841i \(-0.505684\pi\)
−0.0178552 + 0.999841i \(0.505684\pi\)
\(824\) −59.0799 −2.05815
\(825\) 0 0
\(826\) 5.67419 0.197430
\(827\) 17.3217 0.602335 0.301167 0.953571i \(-0.402624\pi\)
0.301167 + 0.953571i \(0.402624\pi\)
\(828\) −102.219 −3.55237
\(829\) −3.16805 −0.110031 −0.0550155 0.998486i \(-0.517521\pi\)
−0.0550155 + 0.998486i \(0.517521\pi\)
\(830\) 0 0
\(831\) 3.42905 0.118953
\(832\) 8.33721 0.289041
\(833\) −15.9450 −0.552460
\(834\) 5.48749 0.190016
\(835\) 0 0
\(836\) 61.0248 2.11059
\(837\) 6.45140 0.222993
\(838\) −80.1272 −2.76795
\(839\) −11.1359 −0.384455 −0.192227 0.981350i \(-0.561571\pi\)
−0.192227 + 0.981350i \(0.561571\pi\)
\(840\) 0 0
\(841\) −8.76746 −0.302326
\(842\) −72.2478 −2.48982
\(843\) −2.40341 −0.0827777
\(844\) 95.7872 3.29713
\(845\) 0 0
\(846\) 40.2181 1.38273
\(847\) −0.859073 −0.0295181
\(848\) 18.8384 0.646914
\(849\) −3.80368 −0.130542
\(850\) 0 0
\(851\) 43.5438 1.49266
\(852\) −2.07411 −0.0710577
\(853\) −2.09383 −0.0716912 −0.0358456 0.999357i \(-0.511412\pi\)
−0.0358456 + 0.999357i \(0.511412\pi\)
\(854\) 4.93697 0.168940
\(855\) 0 0
\(856\) 84.8659 2.90066
\(857\) 25.1944 0.860623 0.430311 0.902680i \(-0.358404\pi\)
0.430311 + 0.902680i \(0.358404\pi\)
\(858\) −4.99486 −0.170522
\(859\) 8.86442 0.302450 0.151225 0.988499i \(-0.451678\pi\)
0.151225 + 0.988499i \(0.451678\pi\)
\(860\) 0 0
\(861\) −0.374428 −0.0127605
\(862\) −14.7029 −0.500782
\(863\) −22.5940 −0.769109 −0.384554 0.923102i \(-0.625645\pi\)
−0.384554 + 0.923102i \(0.625645\pi\)
\(864\) −7.40764 −0.252013
\(865\) 0 0
\(866\) 68.0558 2.31263
\(867\) 2.09443 0.0711307
\(868\) 6.47722 0.219851
\(869\) 31.8161 1.07929
\(870\) 0 0
\(871\) 25.0079 0.847361
\(872\) 35.5694 1.20453
\(873\) 41.8167 1.41528
\(874\) 94.6868 3.20283
\(875\) 0 0
\(876\) 12.2381 0.413486
\(877\) 38.0079 1.28344 0.641719 0.766940i \(-0.278222\pi\)
0.641719 + 0.766940i \(0.278222\pi\)
\(878\) 10.7034 0.361223
\(879\) 2.42229 0.0817018
\(880\) 0 0
\(881\) −6.90728 −0.232712 −0.116356 0.993208i \(-0.537121\pi\)
−0.116356 + 0.993208i \(0.537121\pi\)
\(882\) −52.9220 −1.78198
\(883\) 41.2023 1.38657 0.693283 0.720665i \(-0.256163\pi\)
0.693283 + 0.720665i \(0.256163\pi\)
\(884\) 42.4556 1.42794
\(885\) 0 0
\(886\) −40.9488 −1.37570
\(887\) −5.64594 −0.189572 −0.0947861 0.995498i \(-0.530217\pi\)
−0.0947861 + 0.995498i \(0.530217\pi\)
\(888\) 6.88953 0.231198
\(889\) 0.309769 0.0103893
\(890\) 0 0
\(891\) −23.5675 −0.789543
\(892\) 83.3665 2.79132
\(893\) −25.9480 −0.868318
\(894\) −2.90816 −0.0972634
\(895\) 0 0
\(896\) 2.00251 0.0668991
\(897\) −5.39800 −0.180234
\(898\) 30.0022 1.00119
\(899\) 27.2313 0.908216
\(900\) 0 0
\(901\) 5.48275 0.182657
\(902\) 62.4589 2.07965
\(903\) 0.469162 0.0156127
\(904\) 21.6964 0.721613
\(905\) 0 0
\(906\) −0.618431 −0.0205460
\(907\) −44.1151 −1.46482 −0.732408 0.680866i \(-0.761604\pi\)
−0.732408 + 0.680866i \(0.761604\pi\)
\(908\) −89.5780 −2.97275
\(909\) 23.0406 0.764207
\(910\) 0 0
\(911\) 15.3556 0.508755 0.254377 0.967105i \(-0.418129\pi\)
0.254377 + 0.967105i \(0.418129\pi\)
\(912\) 6.92361 0.229264
\(913\) −28.6558 −0.948369
\(914\) −45.5769 −1.50755
\(915\) 0 0
\(916\) −113.888 −3.76297
\(917\) 1.31209 0.0433290
\(918\) −6.28001 −0.207271
\(919\) −6.50537 −0.214592 −0.107296 0.994227i \(-0.534219\pi\)
−0.107296 + 0.994227i \(0.534219\pi\)
\(920\) 0 0
\(921\) −1.65953 −0.0546833
\(922\) −47.4074 −1.56128
\(923\) 10.1969 0.335635
\(924\) 0.516666 0.0169971
\(925\) 0 0
\(926\) −75.3989 −2.47776
\(927\) −26.3747 −0.866258
\(928\) −31.2676 −1.02641
\(929\) 10.5985 0.347726 0.173863 0.984770i \(-0.444375\pi\)
0.173863 + 0.984770i \(0.444375\pi\)
\(930\) 0 0
\(931\) 34.1444 1.11904
\(932\) 94.4934 3.09523
\(933\) 0.841766 0.0275582
\(934\) 65.1764 2.13264
\(935\) 0 0
\(936\) 79.5119 2.59893
\(937\) 7.20835 0.235487 0.117743 0.993044i \(-0.462434\pi\)
0.117743 + 0.993044i \(0.462434\pi\)
\(938\) −3.71396 −0.121265
\(939\) 2.03716 0.0664803
\(940\) 0 0
\(941\) 42.2737 1.37808 0.689041 0.724722i \(-0.258032\pi\)
0.689041 + 0.724722i \(0.258032\pi\)
\(942\) −5.40665 −0.176158
\(943\) 67.4999 2.19810
\(944\) −74.7966 −2.43442
\(945\) 0 0
\(946\) −78.2616 −2.54450
\(947\) 15.2553 0.495729 0.247865 0.968795i \(-0.420271\pi\)
0.247865 + 0.968795i \(0.420271\pi\)
\(948\) 9.64129 0.313134
\(949\) −60.1657 −1.95306
\(950\) 0 0
\(951\) −5.21796 −0.169204
\(952\) −3.55778 −0.115308
\(953\) −2.48489 −0.0804935 −0.0402467 0.999190i \(-0.512814\pi\)
−0.0402467 + 0.999190i \(0.512814\pi\)
\(954\) 18.1975 0.589166
\(955\) 0 0
\(956\) −84.6782 −2.73869
\(957\) 2.17215 0.0702157
\(958\) 2.09205 0.0675911
\(959\) −1.38862 −0.0448409
\(960\) 0 0
\(961\) 5.65118 0.182296
\(962\) −60.0264 −1.93533
\(963\) 37.8862 1.22086
\(964\) −4.58996 −0.147833
\(965\) 0 0
\(966\) 0.801665 0.0257931
\(967\) −10.8209 −0.347976 −0.173988 0.984748i \(-0.555665\pi\)
−0.173988 + 0.984748i \(0.555665\pi\)
\(968\) 24.5035 0.787572
\(969\) 2.01505 0.0647329
\(970\) 0 0
\(971\) −30.3893 −0.975239 −0.487619 0.873056i \(-0.662135\pi\)
−0.487619 + 0.873056i \(0.662135\pi\)
\(972\) −21.8154 −0.699730
\(973\) 2.79059 0.0894622
\(974\) −92.3297 −2.95843
\(975\) 0 0
\(976\) −65.0787 −2.08312
\(977\) 45.2298 1.44703 0.723515 0.690309i \(-0.242525\pi\)
0.723515 + 0.690309i \(0.242525\pi\)
\(978\) 0.338389 0.0108205
\(979\) −21.9990 −0.703090
\(980\) 0 0
\(981\) 15.8790 0.506978
\(982\) 17.3518 0.553718
\(983\) 48.2460 1.53881 0.769405 0.638761i \(-0.220553\pi\)
0.769405 + 0.638761i \(0.220553\pi\)
\(984\) 10.6799 0.340462
\(985\) 0 0
\(986\) −26.5079 −0.844185
\(987\) −0.219689 −0.00699277
\(988\) −90.9140 −2.89236
\(989\) −84.5781 −2.68943
\(990\) 0 0
\(991\) −24.6368 −0.782613 −0.391306 0.920260i \(-0.627977\pi\)
−0.391306 + 0.920260i \(0.627977\pi\)
\(992\) −42.0837 −1.33616
\(993\) 2.93586 0.0931667
\(994\) −1.51435 −0.0480324
\(995\) 0 0
\(996\) −8.68362 −0.275151
\(997\) 27.1574 0.860084 0.430042 0.902809i \(-0.358499\pi\)
0.430042 + 0.902809i \(0.358499\pi\)
\(998\) −59.5639 −1.88546
\(999\) 6.18434 0.195664
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.o.1.1 yes 40
5.4 even 2 6025.2.a.l.1.40 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6025.2.a.l.1.40 40 5.4 even 2
6025.2.a.o.1.1 yes 40 1.1 even 1 trivial