Properties

Label 6025.2.a.n.1.9
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 1.9
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)
 
\(f(q)\) \(=\) \(q-1.70335 q^{2} -3.34921 q^{3} +0.901404 q^{4} +5.70487 q^{6} +4.14952 q^{7} +1.87129 q^{8} +8.21718 q^{9} +O(q^{10})\) \(q-1.70335 q^{2} -3.34921 q^{3} +0.901404 q^{4} +5.70487 q^{6} +4.14952 q^{7} +1.87129 q^{8} +8.21718 q^{9} -3.44777 q^{11} -3.01899 q^{12} +2.03856 q^{13} -7.06810 q^{14} -4.99028 q^{16} -2.85104 q^{17} -13.9967 q^{18} -5.67321 q^{19} -13.8976 q^{21} +5.87276 q^{22} +7.45830 q^{23} -6.26735 q^{24} -3.47238 q^{26} -17.4734 q^{27} +3.74040 q^{28} -9.40832 q^{29} -4.10525 q^{31} +4.75761 q^{32} +11.5473 q^{33} +4.85632 q^{34} +7.40700 q^{36} -5.25822 q^{37} +9.66347 q^{38} -6.82756 q^{39} +6.62215 q^{41} +23.6725 q^{42} -2.58576 q^{43} -3.10783 q^{44} -12.7041 q^{46} +9.69060 q^{47} +16.7135 q^{48} +10.2186 q^{49} +9.54873 q^{51} +1.83757 q^{52} +1.63816 q^{53} +29.7634 q^{54} +7.76498 q^{56} +19.0008 q^{57} +16.0257 q^{58} +0.368987 q^{59} +6.74043 q^{61} +6.99269 q^{62} +34.0974 q^{63} +1.87669 q^{64} -19.6691 q^{66} -7.33641 q^{67} -2.56994 q^{68} -24.9794 q^{69} -7.51810 q^{71} +15.3768 q^{72} -13.1573 q^{73} +8.95659 q^{74} -5.11386 q^{76} -14.3066 q^{77} +11.6297 q^{78} +12.0667 q^{79} +33.8706 q^{81} -11.2798 q^{82} +11.5430 q^{83} -12.5274 q^{84} +4.40445 q^{86} +31.5104 q^{87} -6.45179 q^{88} -18.4526 q^{89} +8.45906 q^{91} +6.72294 q^{92} +13.7493 q^{93} -16.5065 q^{94} -15.9342 q^{96} -16.8218 q^{97} -17.4058 q^{98} -28.3309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70335 −1.20445 −0.602225 0.798326i \(-0.705719\pi\)
−0.602225 + 0.798326i \(0.705719\pi\)
\(3\) −3.34921 −1.93367 −0.966833 0.255411i \(-0.917789\pi\)
−0.966833 + 0.255411i \(0.917789\pi\)
\(4\) 0.901404 0.450702
\(5\) 0 0
\(6\) 5.70487 2.32900
\(7\) 4.14952 1.56837 0.784186 0.620525i \(-0.213081\pi\)
0.784186 + 0.620525i \(0.213081\pi\)
\(8\) 1.87129 0.661603
\(9\) 8.21718 2.73906
\(10\) 0 0
\(11\) −3.44777 −1.03954 −0.519771 0.854306i \(-0.673983\pi\)
−0.519771 + 0.854306i \(0.673983\pi\)
\(12\) −3.01899 −0.871507
\(13\) 2.03856 0.565395 0.282697 0.959209i \(-0.408771\pi\)
0.282697 + 0.959209i \(0.408771\pi\)
\(14\) −7.06810 −1.88903
\(15\) 0 0
\(16\) −4.99028 −1.24757
\(17\) −2.85104 −0.691479 −0.345740 0.938330i \(-0.612372\pi\)
−0.345740 + 0.938330i \(0.612372\pi\)
\(18\) −13.9967 −3.29906
\(19\) −5.67321 −1.30152 −0.650762 0.759282i \(-0.725550\pi\)
−0.650762 + 0.759282i \(0.725550\pi\)
\(20\) 0 0
\(21\) −13.8976 −3.03271
\(22\) 5.87276 1.25208
\(23\) 7.45830 1.55516 0.777581 0.628783i \(-0.216446\pi\)
0.777581 + 0.628783i \(0.216446\pi\)
\(24\) −6.26735 −1.27932
\(25\) 0 0
\(26\) −3.47238 −0.680991
\(27\) −17.4734 −3.36276
\(28\) 3.74040 0.706869
\(29\) −9.40832 −1.74708 −0.873540 0.486752i \(-0.838182\pi\)
−0.873540 + 0.486752i \(0.838182\pi\)
\(30\) 0 0
\(31\) −4.10525 −0.737325 −0.368663 0.929563i \(-0.620184\pi\)
−0.368663 + 0.929563i \(0.620184\pi\)
\(32\) 4.75761 0.841034
\(33\) 11.5473 2.01012
\(34\) 4.85632 0.832853
\(35\) 0 0
\(36\) 7.40700 1.23450
\(37\) −5.25822 −0.864446 −0.432223 0.901767i \(-0.642271\pi\)
−0.432223 + 0.901767i \(0.642271\pi\)
\(38\) 9.66347 1.56762
\(39\) −6.82756 −1.09328
\(40\) 0 0
\(41\) 6.62215 1.03421 0.517103 0.855923i \(-0.327010\pi\)
0.517103 + 0.855923i \(0.327010\pi\)
\(42\) 23.6725 3.65275
\(43\) −2.58576 −0.394324 −0.197162 0.980371i \(-0.563173\pi\)
−0.197162 + 0.980371i \(0.563173\pi\)
\(44\) −3.10783 −0.468523
\(45\) 0 0
\(46\) −12.7041 −1.87312
\(47\) 9.69060 1.41352 0.706760 0.707454i \(-0.250156\pi\)
0.706760 + 0.707454i \(0.250156\pi\)
\(48\) 16.7135 2.41238
\(49\) 10.2186 1.45979
\(50\) 0 0
\(51\) 9.54873 1.33709
\(52\) 1.83757 0.254825
\(53\) 1.63816 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(54\) 29.7634 4.05028
\(55\) 0 0
\(56\) 7.76498 1.03764
\(57\) 19.0008 2.51671
\(58\) 16.0257 2.10427
\(59\) 0.368987 0.0480380 0.0240190 0.999712i \(-0.492354\pi\)
0.0240190 + 0.999712i \(0.492354\pi\)
\(60\) 0 0
\(61\) 6.74043 0.863024 0.431512 0.902107i \(-0.357980\pi\)
0.431512 + 0.902107i \(0.357980\pi\)
\(62\) 6.99269 0.888072
\(63\) 34.0974 4.29587
\(64\) 1.87669 0.234586
\(65\) 0 0
\(66\) −19.6691 −2.42110
\(67\) −7.33641 −0.896285 −0.448142 0.893962i \(-0.647914\pi\)
−0.448142 + 0.893962i \(0.647914\pi\)
\(68\) −2.56994 −0.311651
\(69\) −24.9794 −3.00716
\(70\) 0 0
\(71\) −7.51810 −0.892235 −0.446117 0.894974i \(-0.647194\pi\)
−0.446117 + 0.894974i \(0.647194\pi\)
\(72\) 15.3768 1.81217
\(73\) −13.1573 −1.53995 −0.769973 0.638076i \(-0.779730\pi\)
−0.769973 + 0.638076i \(0.779730\pi\)
\(74\) 8.95659 1.04118
\(75\) 0 0
\(76\) −5.11386 −0.586599
\(77\) −14.3066 −1.63039
\(78\) 11.6297 1.31681
\(79\) 12.0667 1.35761 0.678803 0.734321i \(-0.262499\pi\)
0.678803 + 0.734321i \(0.262499\pi\)
\(80\) 0 0
\(81\) 33.8706 3.76339
\(82\) −11.2798 −1.24565
\(83\) 11.5430 1.26701 0.633505 0.773739i \(-0.281616\pi\)
0.633505 + 0.773739i \(0.281616\pi\)
\(84\) −12.5274 −1.36685
\(85\) 0 0
\(86\) 4.40445 0.474944
\(87\) 31.5104 3.37827
\(88\) −6.45179 −0.687763
\(89\) −18.4526 −1.95597 −0.977984 0.208681i \(-0.933083\pi\)
−0.977984 + 0.208681i \(0.933083\pi\)
\(90\) 0 0
\(91\) 8.45906 0.886750
\(92\) 6.72294 0.700915
\(93\) 13.7493 1.42574
\(94\) −16.5065 −1.70251
\(95\) 0 0
\(96\) −15.9342 −1.62628
\(97\) −16.8218 −1.70799 −0.853996 0.520280i \(-0.825828\pi\)
−0.853996 + 0.520280i \(0.825828\pi\)
\(98\) −17.4058 −1.75825
\(99\) −28.3309 −2.84737
\(100\) 0 0
\(101\) 6.59929 0.656654 0.328327 0.944564i \(-0.393515\pi\)
0.328327 + 0.944564i \(0.393515\pi\)
\(102\) −16.2648 −1.61046
\(103\) 9.15606 0.902174 0.451087 0.892480i \(-0.351036\pi\)
0.451087 + 0.892480i \(0.351036\pi\)
\(104\) 3.81475 0.374067
\(105\) 0 0
\(106\) −2.79036 −0.271024
\(107\) −9.01519 −0.871532 −0.435766 0.900060i \(-0.643522\pi\)
−0.435766 + 0.900060i \(0.643522\pi\)
\(108\) −15.7506 −1.51560
\(109\) −9.46531 −0.906612 −0.453306 0.891355i \(-0.649756\pi\)
−0.453306 + 0.891355i \(0.649756\pi\)
\(110\) 0 0
\(111\) 17.6109 1.67155
\(112\) −20.7073 −1.95665
\(113\) 4.31866 0.406265 0.203133 0.979151i \(-0.434888\pi\)
0.203133 + 0.979151i \(0.434888\pi\)
\(114\) −32.3650 −3.03126
\(115\) 0 0
\(116\) −8.48070 −0.787413
\(117\) 16.7512 1.54865
\(118\) −0.628513 −0.0578594
\(119\) −11.8305 −1.08450
\(120\) 0 0
\(121\) 0.887101 0.0806456
\(122\) −11.4813 −1.03947
\(123\) −22.1790 −1.99981
\(124\) −3.70049 −0.332314
\(125\) 0 0
\(126\) −58.0798 −5.17416
\(127\) 6.79536 0.602990 0.301495 0.953468i \(-0.402514\pi\)
0.301495 + 0.953468i \(0.402514\pi\)
\(128\) −12.7119 −1.12358
\(129\) 8.66023 0.762491
\(130\) 0 0
\(131\) 11.8118 1.03200 0.516000 0.856588i \(-0.327420\pi\)
0.516000 + 0.856588i \(0.327420\pi\)
\(132\) 10.4088 0.905967
\(133\) −23.5411 −2.04128
\(134\) 12.4965 1.07953
\(135\) 0 0
\(136\) −5.33514 −0.457484
\(137\) 18.5142 1.58178 0.790890 0.611959i \(-0.209618\pi\)
0.790890 + 0.611959i \(0.209618\pi\)
\(138\) 42.5486 3.62198
\(139\) 14.1839 1.20306 0.601532 0.798849i \(-0.294557\pi\)
0.601532 + 0.798849i \(0.294557\pi\)
\(140\) 0 0
\(141\) −32.4558 −2.73327
\(142\) 12.8060 1.07465
\(143\) −7.02848 −0.587751
\(144\) −41.0060 −3.41717
\(145\) 0 0
\(146\) 22.4115 1.85479
\(147\) −34.2241 −2.82275
\(148\) −4.73978 −0.389607
\(149\) 19.2334 1.57566 0.787832 0.615890i \(-0.211204\pi\)
0.787832 + 0.615890i \(0.211204\pi\)
\(150\) 0 0
\(151\) −0.221080 −0.0179912 −0.00899561 0.999960i \(-0.502863\pi\)
−0.00899561 + 0.999960i \(0.502863\pi\)
\(152\) −10.6163 −0.861092
\(153\) −23.4275 −1.89400
\(154\) 24.3692 1.96372
\(155\) 0 0
\(156\) −6.15439 −0.492746
\(157\) −16.5832 −1.32348 −0.661742 0.749732i \(-0.730182\pi\)
−0.661742 + 0.749732i \(0.730182\pi\)
\(158\) −20.5538 −1.63517
\(159\) −5.48653 −0.435110
\(160\) 0 0
\(161\) 30.9484 2.43907
\(162\) −57.6934 −4.53282
\(163\) 9.77856 0.765916 0.382958 0.923766i \(-0.374905\pi\)
0.382958 + 0.923766i \(0.374905\pi\)
\(164\) 5.96923 0.466119
\(165\) 0 0
\(166\) −19.6618 −1.52605
\(167\) 20.2250 1.56506 0.782530 0.622613i \(-0.213929\pi\)
0.782530 + 0.622613i \(0.213929\pi\)
\(168\) −26.0065 −2.00645
\(169\) −8.84427 −0.680328
\(170\) 0 0
\(171\) −46.6178 −3.56495
\(172\) −2.33081 −0.177723
\(173\) 9.77541 0.743211 0.371605 0.928391i \(-0.378807\pi\)
0.371605 + 0.928391i \(0.378807\pi\)
\(174\) −53.6733 −4.06896
\(175\) 0 0
\(176\) 17.2053 1.29690
\(177\) −1.23581 −0.0928893
\(178\) 31.4312 2.35587
\(179\) −10.5767 −0.790542 −0.395271 0.918565i \(-0.629349\pi\)
−0.395271 + 0.918565i \(0.629349\pi\)
\(180\) 0 0
\(181\) −5.53036 −0.411068 −0.205534 0.978650i \(-0.565893\pi\)
−0.205534 + 0.978650i \(0.565893\pi\)
\(182\) −14.4087 −1.06805
\(183\) −22.5751 −1.66880
\(184\) 13.9567 1.02890
\(185\) 0 0
\(186\) −23.4200 −1.71723
\(187\) 9.82973 0.718821
\(188\) 8.73515 0.637076
\(189\) −72.5064 −5.27406
\(190\) 0 0
\(191\) 6.09836 0.441262 0.220631 0.975357i \(-0.429188\pi\)
0.220631 + 0.975357i \(0.429188\pi\)
\(192\) −6.28541 −0.453610
\(193\) 2.25558 0.162360 0.0811801 0.996699i \(-0.474131\pi\)
0.0811801 + 0.996699i \(0.474131\pi\)
\(194\) 28.6534 2.05719
\(195\) 0 0
\(196\) 9.21105 0.657932
\(197\) 12.2908 0.875681 0.437840 0.899053i \(-0.355743\pi\)
0.437840 + 0.899053i \(0.355743\pi\)
\(198\) 48.2575 3.42951
\(199\) −7.85504 −0.556829 −0.278414 0.960461i \(-0.589809\pi\)
−0.278414 + 0.960461i \(0.589809\pi\)
\(200\) 0 0
\(201\) 24.5711 1.73311
\(202\) −11.2409 −0.790908
\(203\) −39.0400 −2.74007
\(204\) 8.60726 0.602629
\(205\) 0 0
\(206\) −15.5960 −1.08662
\(207\) 61.2862 4.25968
\(208\) −10.1730 −0.705370
\(209\) 19.5599 1.35299
\(210\) 0 0
\(211\) −1.76828 −0.121733 −0.0608666 0.998146i \(-0.519386\pi\)
−0.0608666 + 0.998146i \(0.519386\pi\)
\(212\) 1.47664 0.101416
\(213\) 25.1797 1.72528
\(214\) 15.3560 1.04972
\(215\) 0 0
\(216\) −32.6979 −2.22481
\(217\) −17.0349 −1.15640
\(218\) 16.1227 1.09197
\(219\) 44.0665 2.97774
\(220\) 0 0
\(221\) −5.81202 −0.390959
\(222\) −29.9975 −2.01330
\(223\) −10.9721 −0.734745 −0.367373 0.930074i \(-0.619743\pi\)
−0.367373 + 0.930074i \(0.619743\pi\)
\(224\) 19.7418 1.31905
\(225\) 0 0
\(226\) −7.35619 −0.489326
\(227\) 4.57187 0.303446 0.151723 0.988423i \(-0.451518\pi\)
0.151723 + 0.988423i \(0.451518\pi\)
\(228\) 17.1274 1.13429
\(229\) −20.3548 −1.34509 −0.672543 0.740058i \(-0.734798\pi\)
−0.672543 + 0.740058i \(0.734798\pi\)
\(230\) 0 0
\(231\) 47.9157 3.15262
\(232\) −17.6057 −1.15587
\(233\) 7.99344 0.523667 0.261834 0.965113i \(-0.415673\pi\)
0.261834 + 0.965113i \(0.415673\pi\)
\(234\) −28.5332 −1.86527
\(235\) 0 0
\(236\) 0.332606 0.0216508
\(237\) −40.4137 −2.62516
\(238\) 20.1514 1.30622
\(239\) −2.75869 −0.178445 −0.0892224 0.996012i \(-0.528438\pi\)
−0.0892224 + 0.996012i \(0.528438\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −1.51104 −0.0971336
\(243\) −61.0192 −3.91438
\(244\) 6.07585 0.388966
\(245\) 0 0
\(246\) 37.7785 2.40867
\(247\) −11.5652 −0.735875
\(248\) −7.68214 −0.487816
\(249\) −38.6599 −2.44997
\(250\) 0 0
\(251\) −10.2806 −0.648908 −0.324454 0.945902i \(-0.605180\pi\)
−0.324454 + 0.945902i \(0.605180\pi\)
\(252\) 30.7355 1.93616
\(253\) −25.7145 −1.61665
\(254\) −11.5749 −0.726272
\(255\) 0 0
\(256\) 17.8994 1.11871
\(257\) −7.25132 −0.452325 −0.226162 0.974090i \(-0.572618\pi\)
−0.226162 + 0.974090i \(0.572618\pi\)
\(258\) −14.7514 −0.918383
\(259\) −21.8191 −1.35577
\(260\) 0 0
\(261\) −77.3099 −4.78536
\(262\) −20.1196 −1.24299
\(263\) −7.18915 −0.443302 −0.221651 0.975126i \(-0.571145\pi\)
−0.221651 + 0.975126i \(0.571145\pi\)
\(264\) 21.6084 1.32990
\(265\) 0 0
\(266\) 40.0988 2.45862
\(267\) 61.8014 3.78219
\(268\) −6.61307 −0.403957
\(269\) −15.4444 −0.941662 −0.470831 0.882223i \(-0.656046\pi\)
−0.470831 + 0.882223i \(0.656046\pi\)
\(270\) 0 0
\(271\) 1.50201 0.0912408 0.0456204 0.998959i \(-0.485474\pi\)
0.0456204 + 0.998959i \(0.485474\pi\)
\(272\) 14.2275 0.862669
\(273\) −28.3311 −1.71468
\(274\) −31.5363 −1.90518
\(275\) 0 0
\(276\) −22.5165 −1.35533
\(277\) 21.7350 1.30593 0.652964 0.757389i \(-0.273525\pi\)
0.652964 + 0.757389i \(0.273525\pi\)
\(278\) −24.1602 −1.44903
\(279\) −33.7336 −2.01958
\(280\) 0 0
\(281\) 12.2708 0.732014 0.366007 0.930612i \(-0.380725\pi\)
0.366007 + 0.930612i \(0.380725\pi\)
\(282\) 55.2837 3.29209
\(283\) 8.41799 0.500397 0.250199 0.968195i \(-0.419504\pi\)
0.250199 + 0.968195i \(0.419504\pi\)
\(284\) −6.77685 −0.402132
\(285\) 0 0
\(286\) 11.9720 0.707918
\(287\) 27.4788 1.62202
\(288\) 39.0941 2.30364
\(289\) −8.87156 −0.521856
\(290\) 0 0
\(291\) 56.3396 3.30268
\(292\) −11.8600 −0.694057
\(293\) 21.5920 1.26142 0.630710 0.776018i \(-0.282764\pi\)
0.630710 + 0.776018i \(0.282764\pi\)
\(294\) 58.2956 3.39987
\(295\) 0 0
\(296\) −9.83967 −0.571919
\(297\) 60.2443 3.49573
\(298\) −32.7613 −1.89781
\(299\) 15.2042 0.879281
\(300\) 0 0
\(301\) −10.7297 −0.618447
\(302\) 0.376576 0.0216695
\(303\) −22.1024 −1.26975
\(304\) 28.3109 1.62374
\(305\) 0 0
\(306\) 39.9053 2.28123
\(307\) 21.2041 1.21018 0.605091 0.796156i \(-0.293137\pi\)
0.605091 + 0.796156i \(0.293137\pi\)
\(308\) −12.8960 −0.734819
\(309\) −30.6655 −1.74450
\(310\) 0 0
\(311\) −2.46816 −0.139956 −0.0699782 0.997549i \(-0.522293\pi\)
−0.0699782 + 0.997549i \(0.522293\pi\)
\(312\) −12.7764 −0.723320
\(313\) 29.6149 1.67393 0.836966 0.547256i \(-0.184327\pi\)
0.836966 + 0.547256i \(0.184327\pi\)
\(314\) 28.2470 1.59407
\(315\) 0 0
\(316\) 10.8769 0.611876
\(317\) 0.493768 0.0277328 0.0138664 0.999904i \(-0.495586\pi\)
0.0138664 + 0.999904i \(0.495586\pi\)
\(318\) 9.34549 0.524069
\(319\) 32.4377 1.81616
\(320\) 0 0
\(321\) 30.1937 1.68525
\(322\) −52.7160 −2.93775
\(323\) 16.1746 0.899977
\(324\) 30.5310 1.69617
\(325\) 0 0
\(326\) −16.6563 −0.922508
\(327\) 31.7013 1.75308
\(328\) 12.3920 0.684234
\(329\) 40.2114 2.21693
\(330\) 0 0
\(331\) −4.38776 −0.241173 −0.120587 0.992703i \(-0.538478\pi\)
−0.120587 + 0.992703i \(0.538478\pi\)
\(332\) 10.4049 0.571044
\(333\) −43.2077 −2.36777
\(334\) −34.4503 −1.88504
\(335\) 0 0
\(336\) 69.3530 3.78351
\(337\) −18.0535 −0.983438 −0.491719 0.870754i \(-0.663631\pi\)
−0.491719 + 0.870754i \(0.663631\pi\)
\(338\) 15.0649 0.819422
\(339\) −14.4641 −0.785581
\(340\) 0 0
\(341\) 14.1540 0.766480
\(342\) 79.4065 4.29381
\(343\) 13.3555 0.721128
\(344\) −4.83871 −0.260886
\(345\) 0 0
\(346\) −16.6510 −0.895161
\(347\) 15.8576 0.851278 0.425639 0.904893i \(-0.360049\pi\)
0.425639 + 0.904893i \(0.360049\pi\)
\(348\) 28.4036 1.52259
\(349\) 9.18886 0.491868 0.245934 0.969287i \(-0.420905\pi\)
0.245934 + 0.969287i \(0.420905\pi\)
\(350\) 0 0
\(351\) −35.6206 −1.90129
\(352\) −16.4031 −0.874289
\(353\) −33.2136 −1.76778 −0.883890 0.467695i \(-0.845084\pi\)
−0.883890 + 0.467695i \(0.845084\pi\)
\(354\) 2.10502 0.111881
\(355\) 0 0
\(356\) −16.6332 −0.881558
\(357\) 39.6227 2.09705
\(358\) 18.0159 0.952169
\(359\) 8.91354 0.470438 0.235219 0.971942i \(-0.424419\pi\)
0.235219 + 0.971942i \(0.424419\pi\)
\(360\) 0 0
\(361\) 13.1853 0.693965
\(362\) 9.42014 0.495112
\(363\) −2.97109 −0.155942
\(364\) 7.62503 0.399660
\(365\) 0 0
\(366\) 38.4533 2.00999
\(367\) 6.75941 0.352838 0.176419 0.984315i \(-0.443549\pi\)
0.176419 + 0.984315i \(0.443549\pi\)
\(368\) −37.2190 −1.94017
\(369\) 54.4154 2.83276
\(370\) 0 0
\(371\) 6.79758 0.352913
\(372\) 12.3937 0.642584
\(373\) −1.71386 −0.0887403 −0.0443701 0.999015i \(-0.514128\pi\)
−0.0443701 + 0.999015i \(0.514128\pi\)
\(374\) −16.7435 −0.865785
\(375\) 0 0
\(376\) 18.1340 0.935188
\(377\) −19.1794 −0.987791
\(378\) 123.504 6.35235
\(379\) −0.756164 −0.0388415 −0.0194208 0.999811i \(-0.506182\pi\)
−0.0194208 + 0.999811i \(0.506182\pi\)
\(380\) 0 0
\(381\) −22.7590 −1.16598
\(382\) −10.3877 −0.531479
\(383\) 14.5628 0.744124 0.372062 0.928208i \(-0.378651\pi\)
0.372062 + 0.928208i \(0.378651\pi\)
\(384\) 42.5747 2.17263
\(385\) 0 0
\(386\) −3.84204 −0.195555
\(387\) −21.2476 −1.08008
\(388\) −15.1632 −0.769795
\(389\) 14.0887 0.714323 0.357162 0.934043i \(-0.383745\pi\)
0.357162 + 0.934043i \(0.383745\pi\)
\(390\) 0 0
\(391\) −21.2639 −1.07536
\(392\) 19.1219 0.965803
\(393\) −39.5601 −1.99554
\(394\) −20.9355 −1.05471
\(395\) 0 0
\(396\) −25.5376 −1.28331
\(397\) −17.1658 −0.861525 −0.430762 0.902465i \(-0.641755\pi\)
−0.430762 + 0.902465i \(0.641755\pi\)
\(398\) 13.3799 0.670673
\(399\) 78.8441 3.94714
\(400\) 0 0
\(401\) 1.12010 0.0559354 0.0279677 0.999609i \(-0.491096\pi\)
0.0279677 + 0.999609i \(0.491096\pi\)
\(402\) −41.8533 −2.08745
\(403\) −8.36881 −0.416880
\(404\) 5.94863 0.295955
\(405\) 0 0
\(406\) 66.4989 3.30028
\(407\) 18.1291 0.898627
\(408\) 17.8685 0.884622
\(409\) −31.8966 −1.57718 −0.788592 0.614916i \(-0.789190\pi\)
−0.788592 + 0.614916i \(0.789190\pi\)
\(410\) 0 0
\(411\) −62.0080 −3.05863
\(412\) 8.25331 0.406611
\(413\) 1.53112 0.0753414
\(414\) −104.392 −5.13058
\(415\) 0 0
\(416\) 9.69867 0.475516
\(417\) −47.5049 −2.32632
\(418\) −33.3174 −1.62961
\(419\) −22.4444 −1.09648 −0.548241 0.836320i \(-0.684702\pi\)
−0.548241 + 0.836320i \(0.684702\pi\)
\(420\) 0 0
\(421\) 4.39850 0.214370 0.107185 0.994239i \(-0.465816\pi\)
0.107185 + 0.994239i \(0.465816\pi\)
\(422\) 3.01200 0.146622
\(423\) 79.6295 3.87172
\(424\) 3.06548 0.148873
\(425\) 0 0
\(426\) −42.8898 −2.07802
\(427\) 27.9696 1.35354
\(428\) −8.12633 −0.392801
\(429\) 23.5398 1.13651
\(430\) 0 0
\(431\) 33.0770 1.59327 0.796633 0.604464i \(-0.206613\pi\)
0.796633 + 0.604464i \(0.206613\pi\)
\(432\) 87.1973 4.19528
\(433\) 23.2564 1.11763 0.558815 0.829292i \(-0.311256\pi\)
0.558815 + 0.829292i \(0.311256\pi\)
\(434\) 29.0163 1.39283
\(435\) 0 0
\(436\) −8.53207 −0.408612
\(437\) −42.3125 −2.02408
\(438\) −75.0608 −3.58654
\(439\) 29.1885 1.39309 0.696547 0.717511i \(-0.254719\pi\)
0.696547 + 0.717511i \(0.254719\pi\)
\(440\) 0 0
\(441\) 83.9677 3.99846
\(442\) 9.89991 0.470891
\(443\) 33.9523 1.61312 0.806561 0.591151i \(-0.201326\pi\)
0.806561 + 0.591151i \(0.201326\pi\)
\(444\) 15.8745 0.753370
\(445\) 0 0
\(446\) 18.6893 0.884964
\(447\) −64.4167 −3.04681
\(448\) 7.78735 0.367918
\(449\) −27.5194 −1.29872 −0.649359 0.760482i \(-0.724963\pi\)
−0.649359 + 0.760482i \(0.724963\pi\)
\(450\) 0 0
\(451\) −22.8316 −1.07510
\(452\) 3.89286 0.183105
\(453\) 0.740442 0.0347890
\(454\) −7.78751 −0.365486
\(455\) 0 0
\(456\) 35.5560 1.66506
\(457\) −39.0884 −1.82848 −0.914239 0.405175i \(-0.867211\pi\)
−0.914239 + 0.405175i \(0.867211\pi\)
\(458\) 34.6714 1.62009
\(459\) 49.8175 2.32528
\(460\) 0 0
\(461\) 32.4048 1.50924 0.754621 0.656161i \(-0.227821\pi\)
0.754621 + 0.656161i \(0.227821\pi\)
\(462\) −81.6173 −3.79718
\(463\) −4.89462 −0.227472 −0.113736 0.993511i \(-0.536282\pi\)
−0.113736 + 0.993511i \(0.536282\pi\)
\(464\) 46.9501 2.17961
\(465\) 0 0
\(466\) −13.6156 −0.630732
\(467\) −28.0745 −1.29913 −0.649567 0.760305i \(-0.725050\pi\)
−0.649567 + 0.760305i \(0.725050\pi\)
\(468\) 15.0996 0.697980
\(469\) −30.4426 −1.40571
\(470\) 0 0
\(471\) 55.5405 2.55917
\(472\) 0.690482 0.0317820
\(473\) 8.91509 0.409916
\(474\) 68.8388 3.16187
\(475\) 0 0
\(476\) −10.6640 −0.488785
\(477\) 13.4610 0.616339
\(478\) 4.69902 0.214928
\(479\) −20.3401 −0.929363 −0.464682 0.885478i \(-0.653831\pi\)
−0.464682 + 0.885478i \(0.653831\pi\)
\(480\) 0 0
\(481\) −10.7192 −0.488753
\(482\) −1.70335 −0.0775855
\(483\) −103.653 −4.71635
\(484\) 0.799637 0.0363471
\(485\) 0 0
\(486\) 103.937 4.71468
\(487\) 9.01739 0.408617 0.204309 0.978907i \(-0.434505\pi\)
0.204309 + 0.978907i \(0.434505\pi\)
\(488\) 12.6133 0.570979
\(489\) −32.7504 −1.48102
\(490\) 0 0
\(491\) −24.5791 −1.10924 −0.554620 0.832104i \(-0.687136\pi\)
−0.554620 + 0.832104i \(0.687136\pi\)
\(492\) −19.9922 −0.901318
\(493\) 26.8235 1.20807
\(494\) 19.6996 0.886326
\(495\) 0 0
\(496\) 20.4864 0.919865
\(497\) −31.1966 −1.39936
\(498\) 65.8514 2.95087
\(499\) 2.71603 0.121586 0.0607931 0.998150i \(-0.480637\pi\)
0.0607931 + 0.998150i \(0.480637\pi\)
\(500\) 0 0
\(501\) −67.7378 −3.02630
\(502\) 17.5115 0.781577
\(503\) −7.15729 −0.319128 −0.159564 0.987188i \(-0.551009\pi\)
−0.159564 + 0.987188i \(0.551009\pi\)
\(504\) 63.8063 2.84216
\(505\) 0 0
\(506\) 43.8008 1.94718
\(507\) 29.6213 1.31553
\(508\) 6.12536 0.271769
\(509\) 3.93159 0.174265 0.0871324 0.996197i \(-0.472230\pi\)
0.0871324 + 0.996197i \(0.472230\pi\)
\(510\) 0 0
\(511\) −54.5966 −2.41521
\(512\) −5.06522 −0.223853
\(513\) 99.1304 4.37672
\(514\) 12.3515 0.544803
\(515\) 0 0
\(516\) 7.80637 0.343656
\(517\) −33.4109 −1.46941
\(518\) 37.1656 1.63296
\(519\) −32.7399 −1.43712
\(520\) 0 0
\(521\) −13.1579 −0.576456 −0.288228 0.957562i \(-0.593066\pi\)
−0.288228 + 0.957562i \(0.593066\pi\)
\(522\) 131.686 5.76373
\(523\) 27.2969 1.19361 0.596805 0.802386i \(-0.296436\pi\)
0.596805 + 0.802386i \(0.296436\pi\)
\(524\) 10.6472 0.465125
\(525\) 0 0
\(526\) 12.2456 0.533935
\(527\) 11.7043 0.509845
\(528\) −57.6242 −2.50777
\(529\) 32.6262 1.41853
\(530\) 0 0
\(531\) 3.03203 0.131579
\(532\) −21.2201 −0.920007
\(533\) 13.4997 0.584735
\(534\) −105.270 −4.55546
\(535\) 0 0
\(536\) −13.7286 −0.592984
\(537\) 35.4237 1.52864
\(538\) 26.3072 1.13419
\(539\) −35.2312 −1.51752
\(540\) 0 0
\(541\) 19.1975 0.825366 0.412683 0.910875i \(-0.364592\pi\)
0.412683 + 0.910875i \(0.364592\pi\)
\(542\) −2.55845 −0.109895
\(543\) 18.5223 0.794869
\(544\) −13.5641 −0.581558
\(545\) 0 0
\(546\) 48.2579 2.06525
\(547\) 5.94146 0.254038 0.127019 0.991900i \(-0.459459\pi\)
0.127019 + 0.991900i \(0.459459\pi\)
\(548\) 16.6888 0.712911
\(549\) 55.3874 2.36387
\(550\) 0 0
\(551\) 53.3754 2.27387
\(552\) −46.7438 −1.98955
\(553\) 50.0709 2.12923
\(554\) −37.0223 −1.57293
\(555\) 0 0
\(556\) 12.7854 0.542223
\(557\) −4.79293 −0.203083 −0.101542 0.994831i \(-0.532377\pi\)
−0.101542 + 0.994831i \(0.532377\pi\)
\(558\) 57.4602 2.43248
\(559\) −5.27122 −0.222949
\(560\) 0 0
\(561\) −32.9218 −1.38996
\(562\) −20.9015 −0.881675
\(563\) 28.7817 1.21300 0.606502 0.795082i \(-0.292572\pi\)
0.606502 + 0.795082i \(0.292572\pi\)
\(564\) −29.2558 −1.23189
\(565\) 0 0
\(566\) −14.3388 −0.602704
\(567\) 140.547 5.90241
\(568\) −14.0686 −0.590305
\(569\) −17.0870 −0.716325 −0.358162 0.933659i \(-0.616597\pi\)
−0.358162 + 0.933659i \(0.616597\pi\)
\(570\) 0 0
\(571\) 22.4735 0.940487 0.470244 0.882537i \(-0.344166\pi\)
0.470244 + 0.882537i \(0.344166\pi\)
\(572\) −6.33550 −0.264901
\(573\) −20.4247 −0.853253
\(574\) −46.8060 −1.95365
\(575\) 0 0
\(576\) 15.4211 0.642544
\(577\) 13.6344 0.567606 0.283803 0.958883i \(-0.408404\pi\)
0.283803 + 0.958883i \(0.408404\pi\)
\(578\) 15.1114 0.628550
\(579\) −7.55440 −0.313950
\(580\) 0 0
\(581\) 47.8980 1.98714
\(582\) −95.9661 −3.97792
\(583\) −5.64799 −0.233916
\(584\) −24.6212 −1.01883
\(585\) 0 0
\(586\) −36.7788 −1.51932
\(587\) −11.4588 −0.472953 −0.236477 0.971637i \(-0.575993\pi\)
−0.236477 + 0.971637i \(0.575993\pi\)
\(588\) −30.8497 −1.27222
\(589\) 23.2900 0.959647
\(590\) 0 0
\(591\) −41.1643 −1.69327
\(592\) 26.2400 1.07846
\(593\) −18.5153 −0.760332 −0.380166 0.924918i \(-0.624133\pi\)
−0.380166 + 0.924918i \(0.624133\pi\)
\(594\) −102.617 −4.21043
\(595\) 0 0
\(596\) 17.3371 0.710155
\(597\) 26.3081 1.07672
\(598\) −25.8981 −1.05905
\(599\) −8.73124 −0.356749 −0.178374 0.983963i \(-0.557084\pi\)
−0.178374 + 0.983963i \(0.557084\pi\)
\(600\) 0 0
\(601\) 38.8705 1.58556 0.792781 0.609507i \(-0.208633\pi\)
0.792781 + 0.609507i \(0.208633\pi\)
\(602\) 18.2764 0.744890
\(603\) −60.2846 −2.45498
\(604\) −0.199282 −0.00810867
\(605\) 0 0
\(606\) 37.6481 1.52935
\(607\) 0.383862 0.0155805 0.00779024 0.999970i \(-0.497520\pi\)
0.00779024 + 0.999970i \(0.497520\pi\)
\(608\) −26.9909 −1.09463
\(609\) 130.753 5.29839
\(610\) 0 0
\(611\) 19.7549 0.799197
\(612\) −21.1177 −0.853631
\(613\) 14.9460 0.603663 0.301831 0.953361i \(-0.402402\pi\)
0.301831 + 0.953361i \(0.402402\pi\)
\(614\) −36.1180 −1.45761
\(615\) 0 0
\(616\) −26.7719 −1.07867
\(617\) 1.94032 0.0781145 0.0390572 0.999237i \(-0.487565\pi\)
0.0390572 + 0.999237i \(0.487565\pi\)
\(618\) 52.2342 2.10117
\(619\) 33.5002 1.34649 0.673244 0.739421i \(-0.264901\pi\)
0.673244 + 0.739421i \(0.264901\pi\)
\(620\) 0 0
\(621\) −130.322 −5.22964
\(622\) 4.20414 0.168571
\(623\) −76.5694 −3.06769
\(624\) 34.0714 1.36395
\(625\) 0 0
\(626\) −50.4445 −2.01617
\(627\) −65.5102 −2.61623
\(628\) −14.9482 −0.596496
\(629\) 14.9914 0.597746
\(630\) 0 0
\(631\) 11.2379 0.447372 0.223686 0.974661i \(-0.428191\pi\)
0.223686 + 0.974661i \(0.428191\pi\)
\(632\) 22.5803 0.898195
\(633\) 5.92233 0.235391
\(634\) −0.841060 −0.0334027
\(635\) 0 0
\(636\) −4.94558 −0.196105
\(637\) 20.8311 0.825360
\(638\) −55.2528 −2.18748
\(639\) −61.7776 −2.44389
\(640\) 0 0
\(641\) 20.9440 0.827240 0.413620 0.910450i \(-0.364264\pi\)
0.413620 + 0.910450i \(0.364264\pi\)
\(642\) −51.4305 −2.02980
\(643\) −35.2924 −1.39180 −0.695898 0.718141i \(-0.744993\pi\)
−0.695898 + 0.718141i \(0.744993\pi\)
\(644\) 27.8970 1.09930
\(645\) 0 0
\(646\) −27.5510 −1.08398
\(647\) −27.2642 −1.07186 −0.535932 0.844261i \(-0.680040\pi\)
−0.535932 + 0.844261i \(0.680040\pi\)
\(648\) 63.3818 2.48987
\(649\) −1.27218 −0.0499374
\(650\) 0 0
\(651\) 57.0532 2.23609
\(652\) 8.81443 0.345200
\(653\) −13.5779 −0.531345 −0.265673 0.964063i \(-0.585594\pi\)
−0.265673 + 0.964063i \(0.585594\pi\)
\(654\) −53.9984 −2.11150
\(655\) 0 0
\(656\) −33.0464 −1.29024
\(657\) −108.116 −4.21801
\(658\) −68.4941 −2.67018
\(659\) 9.26564 0.360938 0.180469 0.983581i \(-0.442238\pi\)
0.180469 + 0.983581i \(0.442238\pi\)
\(660\) 0 0
\(661\) −7.59898 −0.295566 −0.147783 0.989020i \(-0.547214\pi\)
−0.147783 + 0.989020i \(0.547214\pi\)
\(662\) 7.47390 0.290481
\(663\) 19.4657 0.755984
\(664\) 21.6004 0.838257
\(665\) 0 0
\(666\) 73.5979 2.85186
\(667\) −70.1700 −2.71699
\(668\) 18.2309 0.705376
\(669\) 36.7478 1.42075
\(670\) 0 0
\(671\) −23.2394 −0.897149
\(672\) −66.1194 −2.55061
\(673\) −26.4922 −1.02120 −0.510599 0.859819i \(-0.670576\pi\)
−0.510599 + 0.859819i \(0.670576\pi\)
\(674\) 30.7515 1.18450
\(675\) 0 0
\(676\) −7.97226 −0.306625
\(677\) −30.7992 −1.18371 −0.591855 0.806044i \(-0.701604\pi\)
−0.591855 + 0.806044i \(0.701604\pi\)
\(678\) 24.6374 0.946194
\(679\) −69.8023 −2.67877
\(680\) 0 0
\(681\) −15.3122 −0.586763
\(682\) −24.1092 −0.923187
\(683\) 36.6918 1.40397 0.701987 0.712190i \(-0.252296\pi\)
0.701987 + 0.712190i \(0.252296\pi\)
\(684\) −42.0215 −1.60673
\(685\) 0 0
\(686\) −22.7491 −0.868563
\(687\) 68.1726 2.60095
\(688\) 12.9036 0.491947
\(689\) 3.33949 0.127224
\(690\) 0 0
\(691\) −34.0646 −1.29588 −0.647939 0.761692i \(-0.724369\pi\)
−0.647939 + 0.761692i \(0.724369\pi\)
\(692\) 8.81159 0.334966
\(693\) −117.560 −4.46573
\(694\) −27.0110 −1.02532
\(695\) 0 0
\(696\) 58.9652 2.23507
\(697\) −18.8800 −0.715132
\(698\) −15.6518 −0.592431
\(699\) −26.7717 −1.01260
\(700\) 0 0
\(701\) 42.5893 1.60858 0.804289 0.594239i \(-0.202547\pi\)
0.804289 + 0.594239i \(0.202547\pi\)
\(702\) 60.6744 2.29001
\(703\) 29.8310 1.12510
\(704\) −6.47037 −0.243861
\(705\) 0 0
\(706\) 56.5744 2.12920
\(707\) 27.3839 1.02988
\(708\) −1.11397 −0.0418654
\(709\) 47.5412 1.78545 0.892724 0.450605i \(-0.148792\pi\)
0.892724 + 0.450605i \(0.148792\pi\)
\(710\) 0 0
\(711\) 99.1540 3.71857
\(712\) −34.5302 −1.29407
\(713\) −30.6182 −1.14666
\(714\) −67.4913 −2.52580
\(715\) 0 0
\(716\) −9.53391 −0.356299
\(717\) 9.23942 0.345053
\(718\) −15.1829 −0.566620
\(719\) −27.3690 −1.02069 −0.510345 0.859970i \(-0.670482\pi\)
−0.510345 + 0.859970i \(0.670482\pi\)
\(720\) 0 0
\(721\) 37.9933 1.41494
\(722\) −22.4593 −0.835847
\(723\) −3.34921 −0.124558
\(724\) −4.98509 −0.185269
\(725\) 0 0
\(726\) 5.06080 0.187824
\(727\) −38.0410 −1.41086 −0.705431 0.708778i \(-0.749247\pi\)
−0.705431 + 0.708778i \(0.749247\pi\)
\(728\) 15.8294 0.586676
\(729\) 102.754 3.80571
\(730\) 0 0
\(731\) 7.37210 0.272667
\(732\) −20.3493 −0.752131
\(733\) 35.5280 1.31226 0.656128 0.754649i \(-0.272193\pi\)
0.656128 + 0.754649i \(0.272193\pi\)
\(734\) −11.5136 −0.424976
\(735\) 0 0
\(736\) 35.4836 1.30794
\(737\) 25.2942 0.931725
\(738\) −92.6886 −3.41191
\(739\) −35.3767 −1.30135 −0.650676 0.759356i \(-0.725514\pi\)
−0.650676 + 0.759356i \(0.725514\pi\)
\(740\) 0 0
\(741\) 38.7342 1.42294
\(742\) −11.5787 −0.425066
\(743\) 31.3223 1.14910 0.574551 0.818469i \(-0.305177\pi\)
0.574551 + 0.818469i \(0.305177\pi\)
\(744\) 25.7291 0.943273
\(745\) 0 0
\(746\) 2.91930 0.106883
\(747\) 94.8510 3.47042
\(748\) 8.86056 0.323974
\(749\) −37.4088 −1.36689
\(750\) 0 0
\(751\) 6.82636 0.249098 0.124549 0.992213i \(-0.460252\pi\)
0.124549 + 0.992213i \(0.460252\pi\)
\(752\) −48.3588 −1.76346
\(753\) 34.4320 1.25477
\(754\) 32.6693 1.18975
\(755\) 0 0
\(756\) −65.3576 −2.37703
\(757\) −28.2519 −1.02683 −0.513415 0.858140i \(-0.671620\pi\)
−0.513415 + 0.858140i \(0.671620\pi\)
\(758\) 1.28801 0.0467827
\(759\) 86.1231 3.12607
\(760\) 0 0
\(761\) −33.4825 −1.21374 −0.606870 0.794801i \(-0.707575\pi\)
−0.606870 + 0.794801i \(0.707575\pi\)
\(762\) 38.7666 1.40437
\(763\) −39.2765 −1.42191
\(764\) 5.49709 0.198878
\(765\) 0 0
\(766\) −24.8055 −0.896260
\(767\) 0.752201 0.0271604
\(768\) −59.9488 −2.16321
\(769\) 34.2877 1.23645 0.618223 0.786003i \(-0.287853\pi\)
0.618223 + 0.786003i \(0.287853\pi\)
\(770\) 0 0
\(771\) 24.2862 0.874645
\(772\) 2.03319 0.0731760
\(773\) 21.5846 0.776343 0.388171 0.921587i \(-0.373107\pi\)
0.388171 + 0.921587i \(0.373107\pi\)
\(774\) 36.1922 1.30090
\(775\) 0 0
\(776\) −31.4785 −1.13001
\(777\) 73.0767 2.62161
\(778\) −23.9979 −0.860367
\(779\) −37.5689 −1.34604
\(780\) 0 0
\(781\) 25.9207 0.927515
\(782\) 36.2199 1.29522
\(783\) 164.396 5.87502
\(784\) −50.9934 −1.82119
\(785\) 0 0
\(786\) 67.3847 2.40353
\(787\) 45.4179 1.61897 0.809486 0.587139i \(-0.199746\pi\)
0.809486 + 0.587139i \(0.199746\pi\)
\(788\) 11.0789 0.394671
\(789\) 24.0779 0.857198
\(790\) 0 0
\(791\) 17.9204 0.637175
\(792\) −53.0155 −1.88382
\(793\) 13.7408 0.487949
\(794\) 29.2393 1.03766
\(795\) 0 0
\(796\) −7.08056 −0.250964
\(797\) −27.1274 −0.960901 −0.480451 0.877022i \(-0.659527\pi\)
−0.480451 + 0.877022i \(0.659527\pi\)
\(798\) −134.299 −4.75414
\(799\) −27.6283 −0.977419
\(800\) 0 0
\(801\) −151.628 −5.35752
\(802\) −1.90793 −0.0673714
\(803\) 45.3633 1.60084
\(804\) 22.1485 0.781118
\(805\) 0 0
\(806\) 14.2550 0.502112
\(807\) 51.7265 1.82086
\(808\) 12.3492 0.434444
\(809\) 43.6473 1.53456 0.767278 0.641314i \(-0.221611\pi\)
0.767278 + 0.641314i \(0.221611\pi\)
\(810\) 0 0
\(811\) −12.8136 −0.449946 −0.224973 0.974365i \(-0.572229\pi\)
−0.224973 + 0.974365i \(0.572229\pi\)
\(812\) −35.1909 −1.23496
\(813\) −5.03055 −0.176429
\(814\) −30.8802 −1.08235
\(815\) 0 0
\(816\) −47.6508 −1.66811
\(817\) 14.6695 0.513223
\(818\) 54.3311 1.89964
\(819\) 69.5096 2.42886
\(820\) 0 0
\(821\) 0.684233 0.0238799 0.0119399 0.999929i \(-0.496199\pi\)
0.0119399 + 0.999929i \(0.496199\pi\)
\(822\) 105.621 3.68397
\(823\) 1.37574 0.0479553 0.0239777 0.999712i \(-0.492367\pi\)
0.0239777 + 0.999712i \(0.492367\pi\)
\(824\) 17.1337 0.596880
\(825\) 0 0
\(826\) −2.60803 −0.0907450
\(827\) −8.09126 −0.281361 −0.140680 0.990055i \(-0.544929\pi\)
−0.140680 + 0.990055i \(0.544929\pi\)
\(828\) 55.2436 1.91985
\(829\) −25.7872 −0.895628 −0.447814 0.894127i \(-0.647797\pi\)
−0.447814 + 0.894127i \(0.647797\pi\)
\(830\) 0 0
\(831\) −72.7949 −2.52523
\(832\) 3.82574 0.132634
\(833\) −29.1335 −1.00942
\(834\) 80.9174 2.80194
\(835\) 0 0
\(836\) 17.6314 0.609794
\(837\) 71.7328 2.47945
\(838\) 38.2307 1.32066
\(839\) 36.3743 1.25578 0.627890 0.778302i \(-0.283919\pi\)
0.627890 + 0.778302i \(0.283919\pi\)
\(840\) 0 0
\(841\) 59.5165 2.05229
\(842\) −7.49219 −0.258198
\(843\) −41.0974 −1.41547
\(844\) −1.59393 −0.0548654
\(845\) 0 0
\(846\) −135.637 −4.66329
\(847\) 3.68105 0.126482
\(848\) −8.17487 −0.280726
\(849\) −28.1936 −0.967601
\(850\) 0 0
\(851\) −39.2173 −1.34435
\(852\) 22.6971 0.777589
\(853\) 51.6439 1.76825 0.884127 0.467248i \(-0.154754\pi\)
0.884127 + 0.467248i \(0.154754\pi\)
\(854\) −47.6420 −1.63028
\(855\) 0 0
\(856\) −16.8701 −0.576607
\(857\) −18.4802 −0.631271 −0.315636 0.948880i \(-0.602218\pi\)
−0.315636 + 0.948880i \(0.602218\pi\)
\(858\) −40.0966 −1.36888
\(859\) −4.69833 −0.160305 −0.0801525 0.996783i \(-0.525541\pi\)
−0.0801525 + 0.996783i \(0.525541\pi\)
\(860\) 0 0
\(861\) −92.0321 −3.13645
\(862\) −56.3418 −1.91901
\(863\) 32.2110 1.09647 0.548237 0.836323i \(-0.315299\pi\)
0.548237 + 0.836323i \(0.315299\pi\)
\(864\) −83.1317 −2.82820
\(865\) 0 0
\(866\) −39.6138 −1.34613
\(867\) 29.7127 1.00910
\(868\) −15.3553 −0.521192
\(869\) −41.6031 −1.41129
\(870\) 0 0
\(871\) −14.9557 −0.506755
\(872\) −17.7124 −0.599817
\(873\) −138.228 −4.67829
\(874\) 72.0730 2.43791
\(875\) 0 0
\(876\) 39.7217 1.34207
\(877\) 10.4199 0.351855 0.175928 0.984403i \(-0.443708\pi\)
0.175928 + 0.984403i \(0.443708\pi\)
\(878\) −49.7183 −1.67791
\(879\) −72.3162 −2.43916
\(880\) 0 0
\(881\) −22.1951 −0.747770 −0.373885 0.927475i \(-0.621975\pi\)
−0.373885 + 0.927475i \(0.621975\pi\)
\(882\) −143.027 −4.81595
\(883\) −4.48659 −0.150986 −0.0754930 0.997146i \(-0.524053\pi\)
−0.0754930 + 0.997146i \(0.524053\pi\)
\(884\) −5.23898 −0.176206
\(885\) 0 0
\(886\) −57.8327 −1.94293
\(887\) 28.1286 0.944465 0.472232 0.881474i \(-0.343448\pi\)
0.472232 + 0.881474i \(0.343448\pi\)
\(888\) 32.9551 1.10590
\(889\) 28.1975 0.945714
\(890\) 0 0
\(891\) −116.778 −3.91220
\(892\) −9.89028 −0.331151
\(893\) −54.9768 −1.83973
\(894\) 109.724 3.66973
\(895\) 0 0
\(896\) −52.7482 −1.76219
\(897\) −50.9220 −1.70023
\(898\) 46.8751 1.56424
\(899\) 38.6235 1.28817
\(900\) 0 0
\(901\) −4.67046 −0.155596
\(902\) 38.8903 1.29491
\(903\) 35.9359 1.19587
\(904\) 8.08148 0.268786
\(905\) 0 0
\(906\) −1.26123 −0.0419016
\(907\) 24.5132 0.813948 0.406974 0.913440i \(-0.366584\pi\)
0.406974 + 0.913440i \(0.366584\pi\)
\(908\) 4.12111 0.136764
\(909\) 54.2276 1.79862
\(910\) 0 0
\(911\) 47.3648 1.56926 0.784632 0.619961i \(-0.212852\pi\)
0.784632 + 0.619961i \(0.212852\pi\)
\(912\) −94.8191 −3.13977
\(913\) −39.7976 −1.31711
\(914\) 66.5813 2.20231
\(915\) 0 0
\(916\) −18.3479 −0.606233
\(917\) 49.0133 1.61856
\(918\) −84.8566 −2.80069
\(919\) 44.5247 1.46873 0.734367 0.678753i \(-0.237479\pi\)
0.734367 + 0.678753i \(0.237479\pi\)
\(920\) 0 0
\(921\) −71.0169 −2.34009
\(922\) −55.1968 −1.81781
\(923\) −15.3261 −0.504465
\(924\) 43.1914 1.42089
\(925\) 0 0
\(926\) 8.33725 0.273979
\(927\) 75.2371 2.47111
\(928\) −44.7611 −1.46935
\(929\) 19.3204 0.633882 0.316941 0.948445i \(-0.397344\pi\)
0.316941 + 0.948445i \(0.397344\pi\)
\(930\) 0 0
\(931\) −57.9720 −1.89996
\(932\) 7.20532 0.236018
\(933\) 8.26637 0.270629
\(934\) 47.8207 1.56474
\(935\) 0 0
\(936\) 31.3465 1.02459
\(937\) −14.0035 −0.457474 −0.228737 0.973488i \(-0.573460\pi\)
−0.228737 + 0.973488i \(0.573460\pi\)
\(938\) 51.8544 1.69311
\(939\) −99.1863 −3.23682
\(940\) 0 0
\(941\) 21.4573 0.699487 0.349744 0.936845i \(-0.386269\pi\)
0.349744 + 0.936845i \(0.386269\pi\)
\(942\) −94.6050 −3.08240
\(943\) 49.3900 1.60836
\(944\) −1.84135 −0.0599307
\(945\) 0 0
\(946\) −15.1855 −0.493724
\(947\) −19.1248 −0.621473 −0.310737 0.950496i \(-0.600576\pi\)
−0.310737 + 0.950496i \(0.600576\pi\)
\(948\) −36.4291 −1.18316
\(949\) −26.8220 −0.870678
\(950\) 0 0
\(951\) −1.65373 −0.0536259
\(952\) −22.1383 −0.717506
\(953\) −0.297849 −0.00964829 −0.00482414 0.999988i \(-0.501536\pi\)
−0.00482414 + 0.999988i \(0.501536\pi\)
\(954\) −22.9289 −0.742350
\(955\) 0 0
\(956\) −2.48669 −0.0804254
\(957\) −108.641 −3.51185
\(958\) 34.6463 1.11937
\(959\) 76.8253 2.48082
\(960\) 0 0
\(961\) −14.1469 −0.456351
\(962\) 18.2586 0.588679
\(963\) −74.0795 −2.38718
\(964\) 0.901404 0.0290323
\(965\) 0 0
\(966\) 176.557 5.68062
\(967\) 28.6330 0.920775 0.460387 0.887718i \(-0.347711\pi\)
0.460387 + 0.887718i \(0.347711\pi\)
\(968\) 1.66003 0.0533553
\(969\) −54.1720 −1.74025
\(970\) 0 0
\(971\) 48.1006 1.54362 0.771811 0.635852i \(-0.219351\pi\)
0.771811 + 0.635852i \(0.219351\pi\)
\(972\) −55.0029 −1.76422
\(973\) 58.8565 1.88685
\(974\) −15.3598 −0.492159
\(975\) 0 0
\(976\) −33.6366 −1.07668
\(977\) 50.2504 1.60765 0.803827 0.594864i \(-0.202794\pi\)
0.803827 + 0.594864i \(0.202794\pi\)
\(978\) 55.7854 1.78382
\(979\) 63.6201 2.03331
\(980\) 0 0
\(981\) −77.7782 −2.48327
\(982\) 41.8668 1.33602
\(983\) 20.1224 0.641804 0.320902 0.947112i \(-0.396014\pi\)
0.320902 + 0.947112i \(0.396014\pi\)
\(984\) −41.5034 −1.32308
\(985\) 0 0
\(986\) −45.6899 −1.45506
\(987\) −134.676 −4.28679
\(988\) −10.4249 −0.331660
\(989\) −19.2853 −0.613238
\(990\) 0 0
\(991\) 11.6831 0.371126 0.185563 0.982632i \(-0.440589\pi\)
0.185563 + 0.982632i \(0.440589\pi\)
\(992\) −19.5312 −0.620116
\(993\) 14.6955 0.466348
\(994\) 53.1387 1.68546
\(995\) 0 0
\(996\) −34.8482 −1.10421
\(997\) 11.1289 0.352457 0.176229 0.984349i \(-0.443610\pi\)
0.176229 + 0.984349i \(0.443610\pi\)
\(998\) −4.62635 −0.146445
\(999\) 91.8791 2.90693
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.n.1.9 yes 40
5.4 even 2 6025.2.a.m.1.32 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6025.2.a.m.1.32 40 5.4 even 2
6025.2.a.n.1.9 yes 40 1.1 even 1 trivial