Properties

Label 6025.2.a.j.1.8
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $25$
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: \(1\)
Dimension: \(25\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
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)
 
\(f(q)\) \(=\) \(q-1.91059 q^{2} -2.10440 q^{3} +1.65034 q^{4} +4.02063 q^{6} -2.16427 q^{7} +0.668063 q^{8} +1.42849 q^{9} +O(q^{10})\) \(q-1.91059 q^{2} -2.10440 q^{3} +1.65034 q^{4} +4.02063 q^{6} -2.16427 q^{7} +0.668063 q^{8} +1.42849 q^{9} -4.26801 q^{11} -3.47296 q^{12} -4.06225 q^{13} +4.13502 q^{14} -4.57706 q^{16} -5.01513 q^{17} -2.72925 q^{18} -0.180581 q^{19} +4.55448 q^{21} +8.15439 q^{22} -2.32572 q^{23} -1.40587 q^{24} +7.76128 q^{26} +3.30708 q^{27} -3.57177 q^{28} -0.555774 q^{29} +3.29164 q^{31} +7.40874 q^{32} +8.98159 q^{33} +9.58183 q^{34} +2.35749 q^{36} +9.51931 q^{37} +0.345015 q^{38} +8.54860 q^{39} +3.48136 q^{41} -8.70173 q^{42} -2.90132 q^{43} -7.04365 q^{44} +4.44348 q^{46} +4.61707 q^{47} +9.63196 q^{48} -2.31594 q^{49} +10.5538 q^{51} -6.70409 q^{52} +3.83516 q^{53} -6.31846 q^{54} -1.44587 q^{56} +0.380014 q^{57} +1.06185 q^{58} -10.5916 q^{59} -2.62418 q^{61} -6.28897 q^{62} -3.09164 q^{63} -5.00091 q^{64} -17.1601 q^{66} +1.18895 q^{67} -8.27665 q^{68} +4.89423 q^{69} +11.8729 q^{71} +0.954321 q^{72} +13.5936 q^{73} -18.1875 q^{74} -0.298019 q^{76} +9.23712 q^{77} -16.3328 q^{78} -1.52109 q^{79} -11.2449 q^{81} -6.65144 q^{82} +8.04914 q^{83} +7.51643 q^{84} +5.54321 q^{86} +1.16957 q^{87} -2.85130 q^{88} -15.8320 q^{89} +8.79181 q^{91} -3.83821 q^{92} -6.92693 q^{93} -8.82130 q^{94} -15.5909 q^{96} -10.6203 q^{97} +4.42480 q^{98} -6.09681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.91059 −1.35099 −0.675494 0.737366i \(-0.736070\pi\)
−0.675494 + 0.737366i \(0.736070\pi\)
\(3\) −2.10440 −1.21497 −0.607487 0.794329i \(-0.707822\pi\)
−0.607487 + 0.794329i \(0.707822\pi\)
\(4\) 1.65034 0.825168
\(5\) 0 0
\(6\) 4.02063 1.64142
\(7\) −2.16427 −0.818017 −0.409008 0.912531i \(-0.634125\pi\)
−0.409008 + 0.912531i \(0.634125\pi\)
\(8\) 0.668063 0.236196
\(9\) 1.42849 0.476164
\(10\) 0 0
\(11\) −4.26801 −1.28685 −0.643427 0.765508i \(-0.722488\pi\)
−0.643427 + 0.765508i \(0.722488\pi\)
\(12\) −3.47296 −1.00256
\(13\) −4.06225 −1.12667 −0.563333 0.826230i \(-0.690481\pi\)
−0.563333 + 0.826230i \(0.690481\pi\)
\(14\) 4.13502 1.10513
\(15\) 0 0
\(16\) −4.57706 −1.14427
\(17\) −5.01513 −1.21635 −0.608174 0.793804i \(-0.708098\pi\)
−0.608174 + 0.793804i \(0.708098\pi\)
\(18\) −2.72925 −0.643291
\(19\) −0.180581 −0.0414281 −0.0207140 0.999785i \(-0.506594\pi\)
−0.0207140 + 0.999785i \(0.506594\pi\)
\(20\) 0 0
\(21\) 4.55448 0.993870
\(22\) 8.15439 1.73852
\(23\) −2.32572 −0.484945 −0.242473 0.970158i \(-0.577958\pi\)
−0.242473 + 0.970158i \(0.577958\pi\)
\(24\) −1.40587 −0.286972
\(25\) 0 0
\(26\) 7.76128 1.52211
\(27\) 3.30708 0.636448
\(28\) −3.57177 −0.675001
\(29\) −0.555774 −0.103205 −0.0516024 0.998668i \(-0.516433\pi\)
−0.0516024 + 0.998668i \(0.516433\pi\)
\(30\) 0 0
\(31\) 3.29164 0.591197 0.295598 0.955312i \(-0.404481\pi\)
0.295598 + 0.955312i \(0.404481\pi\)
\(32\) 7.40874 1.30969
\(33\) 8.98159 1.56349
\(34\) 9.58183 1.64327
\(35\) 0 0
\(36\) 2.35749 0.392915
\(37\) 9.51931 1.56497 0.782483 0.622672i \(-0.213953\pi\)
0.782483 + 0.622672i \(0.213953\pi\)
\(38\) 0.345015 0.0559688
\(39\) 8.54860 1.36887
\(40\) 0 0
\(41\) 3.48136 0.543697 0.271849 0.962340i \(-0.412365\pi\)
0.271849 + 0.962340i \(0.412365\pi\)
\(42\) −8.70173 −1.34271
\(43\) −2.90132 −0.442447 −0.221223 0.975223i \(-0.571005\pi\)
−0.221223 + 0.975223i \(0.571005\pi\)
\(44\) −7.04365 −1.06187
\(45\) 0 0
\(46\) 4.44348 0.655155
\(47\) 4.61707 0.673469 0.336734 0.941600i \(-0.390678\pi\)
0.336734 + 0.941600i \(0.390678\pi\)
\(48\) 9.63196 1.39025
\(49\) −2.31594 −0.330848
\(50\) 0 0
\(51\) 10.5538 1.47783
\(52\) −6.70409 −0.929689
\(53\) 3.83516 0.526800 0.263400 0.964687i \(-0.415156\pi\)
0.263400 + 0.964687i \(0.415156\pi\)
\(54\) −6.31846 −0.859833
\(55\) 0 0
\(56\) −1.44587 −0.193212
\(57\) 0.380014 0.0503340
\(58\) 1.06185 0.139428
\(59\) −10.5916 −1.37891 −0.689454 0.724330i \(-0.742149\pi\)
−0.689454 + 0.724330i \(0.742149\pi\)
\(60\) 0 0
\(61\) −2.62418 −0.335992 −0.167996 0.985788i \(-0.553730\pi\)
−0.167996 + 0.985788i \(0.553730\pi\)
\(62\) −6.28897 −0.798700
\(63\) −3.09164 −0.389510
\(64\) −5.00091 −0.625114
\(65\) 0 0
\(66\) −17.1601 −2.11226
\(67\) 1.18895 0.145254 0.0726268 0.997359i \(-0.476862\pi\)
0.0726268 + 0.997359i \(0.476862\pi\)
\(68\) −8.27665 −1.00369
\(69\) 4.89423 0.589196
\(70\) 0 0
\(71\) 11.8729 1.40905 0.704525 0.709679i \(-0.251160\pi\)
0.704525 + 0.709679i \(0.251160\pi\)
\(72\) 0.954321 0.112468
\(73\) 13.5936 1.59101 0.795505 0.605947i \(-0.207206\pi\)
0.795505 + 0.605947i \(0.207206\pi\)
\(74\) −18.1875 −2.11425
\(75\) 0 0
\(76\) −0.298019 −0.0341851
\(77\) 9.23712 1.05267
\(78\) −16.3328 −1.84933
\(79\) −1.52109 −0.171136 −0.0855680 0.996332i \(-0.527270\pi\)
−0.0855680 + 0.996332i \(0.527270\pi\)
\(80\) 0 0
\(81\) −11.2449 −1.24943
\(82\) −6.65144 −0.734528
\(83\) 8.04914 0.883507 0.441754 0.897136i \(-0.354357\pi\)
0.441754 + 0.897136i \(0.354357\pi\)
\(84\) 7.51643 0.820110
\(85\) 0 0
\(86\) 5.54321 0.597740
\(87\) 1.16957 0.125391
\(88\) −2.85130 −0.303949
\(89\) −15.8320 −1.67819 −0.839094 0.543986i \(-0.816915\pi\)
−0.839094 + 0.543986i \(0.816915\pi\)
\(90\) 0 0
\(91\) 8.79181 0.921632
\(92\) −3.83821 −0.400161
\(93\) −6.92693 −0.718289
\(94\) −8.82130 −0.909848
\(95\) 0 0
\(96\) −15.5909 −1.59124
\(97\) −10.6203 −1.07833 −0.539165 0.842200i \(-0.681260\pi\)
−0.539165 + 0.842200i \(0.681260\pi\)
\(98\) 4.42480 0.446972
\(99\) −6.09681 −0.612753
\(100\) 0 0
\(101\) −0.0821711 −0.00817633 −0.00408816 0.999992i \(-0.501301\pi\)
−0.00408816 + 0.999992i \(0.501301\pi\)
\(102\) −20.1640 −1.99653
\(103\) 1.27297 0.125429 0.0627147 0.998031i \(-0.480024\pi\)
0.0627147 + 0.998031i \(0.480024\pi\)
\(104\) −2.71384 −0.266114
\(105\) 0 0
\(106\) −7.32741 −0.711701
\(107\) −20.1502 −1.94799 −0.973995 0.226569i \(-0.927249\pi\)
−0.973995 + 0.226569i \(0.927249\pi\)
\(108\) 5.45779 0.525177
\(109\) 16.2615 1.55757 0.778787 0.627289i \(-0.215835\pi\)
0.778787 + 0.627289i \(0.215835\pi\)
\(110\) 0 0
\(111\) −20.0324 −1.90139
\(112\) 9.90600 0.936029
\(113\) 20.1200 1.89273 0.946365 0.323098i \(-0.104724\pi\)
0.946365 + 0.323098i \(0.104724\pi\)
\(114\) −0.726049 −0.0680007
\(115\) 0 0
\(116\) −0.917215 −0.0851612
\(117\) −5.80289 −0.536478
\(118\) 20.2361 1.86289
\(119\) 10.8541 0.994993
\(120\) 0 0
\(121\) 7.21590 0.655991
\(122\) 5.01372 0.453921
\(123\) −7.32617 −0.660579
\(124\) 5.43232 0.487837
\(125\) 0 0
\(126\) 5.90684 0.526223
\(127\) −16.4735 −1.46179 −0.730896 0.682489i \(-0.760897\pi\)
−0.730896 + 0.682489i \(0.760897\pi\)
\(128\) −5.26282 −0.465172
\(129\) 6.10552 0.537561
\(130\) 0 0
\(131\) 17.3756 1.51811 0.759057 0.651024i \(-0.225660\pi\)
0.759057 + 0.651024i \(0.225660\pi\)
\(132\) 14.8226 1.29015
\(133\) 0.390825 0.0338889
\(134\) −2.27159 −0.196236
\(135\) 0 0
\(136\) −3.35042 −0.287296
\(137\) 11.3396 0.968807 0.484403 0.874845i \(-0.339037\pi\)
0.484403 + 0.874845i \(0.339037\pi\)
\(138\) −9.35085 −0.795997
\(139\) 5.24580 0.444943 0.222472 0.974939i \(-0.428588\pi\)
0.222472 + 0.974939i \(0.428588\pi\)
\(140\) 0 0
\(141\) −9.71615 −0.818247
\(142\) −22.6841 −1.90361
\(143\) 17.3377 1.44985
\(144\) −6.53829 −0.544858
\(145\) 0 0
\(146\) −25.9717 −2.14944
\(147\) 4.87366 0.401973
\(148\) 15.7101 1.29136
\(149\) 5.14511 0.421504 0.210752 0.977540i \(-0.432409\pi\)
0.210752 + 0.977540i \(0.432409\pi\)
\(150\) 0 0
\(151\) 19.0727 1.55211 0.776057 0.630663i \(-0.217217\pi\)
0.776057 + 0.630663i \(0.217217\pi\)
\(152\) −0.120639 −0.00978513
\(153\) −7.16406 −0.579180
\(154\) −17.6483 −1.42214
\(155\) 0 0
\(156\) 14.1081 1.12955
\(157\) −6.58683 −0.525687 −0.262843 0.964839i \(-0.584660\pi\)
−0.262843 + 0.964839i \(0.584660\pi\)
\(158\) 2.90617 0.231203
\(159\) −8.07071 −0.640049
\(160\) 0 0
\(161\) 5.03347 0.396693
\(162\) 21.4843 1.68797
\(163\) −5.49881 −0.430700 −0.215350 0.976537i \(-0.569089\pi\)
−0.215350 + 0.976537i \(0.569089\pi\)
\(164\) 5.74542 0.448642
\(165\) 0 0
\(166\) −15.3786 −1.19361
\(167\) 18.3921 1.42322 0.711612 0.702573i \(-0.247966\pi\)
0.711612 + 0.702573i \(0.247966\pi\)
\(168\) 3.04268 0.234748
\(169\) 3.50191 0.269378
\(170\) 0 0
\(171\) −0.257958 −0.0197265
\(172\) −4.78815 −0.365093
\(173\) −1.33142 −0.101226 −0.0506129 0.998718i \(-0.516117\pi\)
−0.0506129 + 0.998718i \(0.516117\pi\)
\(174\) −2.23456 −0.169402
\(175\) 0 0
\(176\) 19.5349 1.47250
\(177\) 22.2889 1.67534
\(178\) 30.2484 2.26721
\(179\) −21.1070 −1.57761 −0.788805 0.614644i \(-0.789300\pi\)
−0.788805 + 0.614644i \(0.789300\pi\)
\(180\) 0 0
\(181\) 25.3428 1.88372 0.941859 0.336007i \(-0.109077\pi\)
0.941859 + 0.336007i \(0.109077\pi\)
\(182\) −16.7975 −1.24511
\(183\) 5.52232 0.408222
\(184\) −1.55372 −0.114542
\(185\) 0 0
\(186\) 13.2345 0.970400
\(187\) 21.4046 1.56526
\(188\) 7.61972 0.555725
\(189\) −7.15741 −0.520625
\(190\) 0 0
\(191\) −3.53179 −0.255551 −0.127776 0.991803i \(-0.540784\pi\)
−0.127776 + 0.991803i \(0.540784\pi\)
\(192\) 10.5239 0.759498
\(193\) 3.22749 0.232320 0.116160 0.993231i \(-0.462941\pi\)
0.116160 + 0.993231i \(0.462941\pi\)
\(194\) 20.2910 1.45681
\(195\) 0 0
\(196\) −3.82208 −0.273006
\(197\) 11.8399 0.843558 0.421779 0.906699i \(-0.361406\pi\)
0.421779 + 0.906699i \(0.361406\pi\)
\(198\) 11.6485 0.827821
\(199\) −7.98476 −0.566025 −0.283012 0.959116i \(-0.591334\pi\)
−0.283012 + 0.959116i \(0.591334\pi\)
\(200\) 0 0
\(201\) −2.50203 −0.176479
\(202\) 0.156995 0.0110461
\(203\) 1.20285 0.0844232
\(204\) 17.4174 1.21946
\(205\) 0 0
\(206\) −2.43212 −0.169454
\(207\) −3.32226 −0.230913
\(208\) 18.5932 1.28921
\(209\) 0.770720 0.0533118
\(210\) 0 0
\(211\) 3.80349 0.261843 0.130922 0.991393i \(-0.458206\pi\)
0.130922 + 0.991393i \(0.458206\pi\)
\(212\) 6.32931 0.434699
\(213\) −24.9852 −1.71196
\(214\) 38.4986 2.63171
\(215\) 0 0
\(216\) 2.20934 0.150326
\(217\) −7.12401 −0.483609
\(218\) −31.0691 −2.10426
\(219\) −28.6063 −1.93304
\(220\) 0 0
\(221\) 20.3727 1.37042
\(222\) 38.2736 2.56876
\(223\) 1.07200 0.0717865 0.0358932 0.999356i \(-0.488572\pi\)
0.0358932 + 0.999356i \(0.488572\pi\)
\(224\) −16.0345 −1.07135
\(225\) 0 0
\(226\) −38.4410 −2.55706
\(227\) −21.2385 −1.40965 −0.704826 0.709380i \(-0.748975\pi\)
−0.704826 + 0.709380i \(0.748975\pi\)
\(228\) 0.627150 0.0415340
\(229\) 7.29747 0.482230 0.241115 0.970497i \(-0.422487\pi\)
0.241115 + 0.970497i \(0.422487\pi\)
\(230\) 0 0
\(231\) −19.4386 −1.27896
\(232\) −0.371292 −0.0243765
\(233\) −21.8917 −1.43417 −0.717087 0.696983i \(-0.754525\pi\)
−0.717087 + 0.696983i \(0.754525\pi\)
\(234\) 11.0869 0.724775
\(235\) 0 0
\(236\) −17.4797 −1.13783
\(237\) 3.20098 0.207926
\(238\) −20.7377 −1.34422
\(239\) −4.98696 −0.322580 −0.161290 0.986907i \(-0.551565\pi\)
−0.161290 + 0.986907i \(0.551565\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) −13.7866 −0.886235
\(243\) 13.7425 0.881580
\(244\) −4.33078 −0.277250
\(245\) 0 0
\(246\) 13.9973 0.892434
\(247\) 0.733565 0.0466756
\(248\) 2.19903 0.139638
\(249\) −16.9386 −1.07344
\(250\) 0 0
\(251\) 18.4761 1.16620 0.583102 0.812399i \(-0.301839\pi\)
0.583102 + 0.812399i \(0.301839\pi\)
\(252\) −5.10224 −0.321411
\(253\) 9.92618 0.624053
\(254\) 31.4741 1.97486
\(255\) 0 0
\(256\) 20.0569 1.25356
\(257\) 12.8264 0.800091 0.400045 0.916495i \(-0.368994\pi\)
0.400045 + 0.916495i \(0.368994\pi\)
\(258\) −11.6651 −0.726239
\(259\) −20.6024 −1.28017
\(260\) 0 0
\(261\) −0.793919 −0.0491423
\(262\) −33.1976 −2.05095
\(263\) −22.0689 −1.36083 −0.680414 0.732828i \(-0.738200\pi\)
−0.680414 + 0.732828i \(0.738200\pi\)
\(264\) 6.00026 0.369291
\(265\) 0 0
\(266\) −0.746705 −0.0457834
\(267\) 33.3168 2.03896
\(268\) 1.96217 0.119859
\(269\) 6.36707 0.388207 0.194104 0.980981i \(-0.437820\pi\)
0.194104 + 0.980981i \(0.437820\pi\)
\(270\) 0 0
\(271\) −23.2942 −1.41502 −0.707510 0.706704i \(-0.750181\pi\)
−0.707510 + 0.706704i \(0.750181\pi\)
\(272\) 22.9546 1.39182
\(273\) −18.5015 −1.11976
\(274\) −21.6653 −1.30885
\(275\) 0 0
\(276\) 8.07713 0.486186
\(277\) 22.1400 1.33026 0.665131 0.746727i \(-0.268376\pi\)
0.665131 + 0.746727i \(0.268376\pi\)
\(278\) −10.0226 −0.601113
\(279\) 4.70208 0.281506
\(280\) 0 0
\(281\) 8.60586 0.513383 0.256691 0.966493i \(-0.417368\pi\)
0.256691 + 0.966493i \(0.417368\pi\)
\(282\) 18.5635 1.10544
\(283\) 15.0374 0.893882 0.446941 0.894563i \(-0.352513\pi\)
0.446941 + 0.894563i \(0.352513\pi\)
\(284\) 19.5942 1.16270
\(285\) 0 0
\(286\) −33.1252 −1.95874
\(287\) −7.53460 −0.444754
\(288\) 10.5833 0.623628
\(289\) 8.15151 0.479501
\(290\) 0 0
\(291\) 22.3494 1.31014
\(292\) 22.4340 1.31285
\(293\) −6.18210 −0.361162 −0.180581 0.983560i \(-0.557798\pi\)
−0.180581 + 0.983560i \(0.557798\pi\)
\(294\) −9.31154 −0.543060
\(295\) 0 0
\(296\) 6.35950 0.369638
\(297\) −14.1146 −0.819015
\(298\) −9.83017 −0.569446
\(299\) 9.44765 0.546372
\(300\) 0 0
\(301\) 6.27923 0.361929
\(302\) −36.4400 −2.09689
\(303\) 0.172921 0.00993403
\(304\) 0.826529 0.0474047
\(305\) 0 0
\(306\) 13.6876 0.782465
\(307\) −13.4882 −0.769812 −0.384906 0.922956i \(-0.625766\pi\)
−0.384906 + 0.922956i \(0.625766\pi\)
\(308\) 15.2444 0.868628
\(309\) −2.67884 −0.152394
\(310\) 0 0
\(311\) 3.02889 0.171752 0.0858762 0.996306i \(-0.472631\pi\)
0.0858762 + 0.996306i \(0.472631\pi\)
\(312\) 5.71100 0.323322
\(313\) −17.6844 −0.999582 −0.499791 0.866146i \(-0.666590\pi\)
−0.499791 + 0.866146i \(0.666590\pi\)
\(314\) 12.5847 0.710196
\(315\) 0 0
\(316\) −2.51031 −0.141216
\(317\) −8.57911 −0.481851 −0.240925 0.970544i \(-0.577451\pi\)
−0.240925 + 0.970544i \(0.577451\pi\)
\(318\) 15.4198 0.864698
\(319\) 2.37205 0.132809
\(320\) 0 0
\(321\) 42.4040 2.36676
\(322\) −9.61688 −0.535928
\(323\) 0.905635 0.0503909
\(324\) −18.5578 −1.03099
\(325\) 0 0
\(326\) 10.5059 0.581870
\(327\) −34.2208 −1.89241
\(328\) 2.32577 0.128419
\(329\) −9.99258 −0.550909
\(330\) 0 0
\(331\) 23.1132 1.27042 0.635208 0.772341i \(-0.280914\pi\)
0.635208 + 0.772341i \(0.280914\pi\)
\(332\) 13.2838 0.729042
\(333\) 13.5982 0.745179
\(334\) −35.1397 −1.92276
\(335\) 0 0
\(336\) −20.8462 −1.13725
\(337\) −10.9314 −0.595472 −0.297736 0.954648i \(-0.596232\pi\)
−0.297736 + 0.954648i \(0.596232\pi\)
\(338\) −6.69071 −0.363926
\(339\) −42.3405 −2.29962
\(340\) 0 0
\(341\) −14.0488 −0.760783
\(342\) 0.492851 0.0266503
\(343\) 20.1622 1.08866
\(344\) −1.93826 −0.104504
\(345\) 0 0
\(346\) 2.54379 0.136755
\(347\) −5.04505 −0.270832 −0.135416 0.990789i \(-0.543237\pi\)
−0.135416 + 0.990789i \(0.543237\pi\)
\(348\) 1.93018 0.103469
\(349\) 34.7248 1.85878 0.929389 0.369102i \(-0.120335\pi\)
0.929389 + 0.369102i \(0.120335\pi\)
\(350\) 0 0
\(351\) −13.4342 −0.717065
\(352\) −31.6206 −1.68538
\(353\) 16.3883 0.872264 0.436132 0.899883i \(-0.356348\pi\)
0.436132 + 0.899883i \(0.356348\pi\)
\(354\) −42.5849 −2.26336
\(355\) 0 0
\(356\) −26.1281 −1.38479
\(357\) −22.8413 −1.20889
\(358\) 40.3267 2.13133
\(359\) −22.0003 −1.16113 −0.580565 0.814214i \(-0.697168\pi\)
−0.580565 + 0.814214i \(0.697168\pi\)
\(360\) 0 0
\(361\) −18.9674 −0.998284
\(362\) −48.4197 −2.54488
\(363\) −15.1851 −0.797012
\(364\) 14.5094 0.760502
\(365\) 0 0
\(366\) −10.5509 −0.551502
\(367\) 13.4672 0.702985 0.351492 0.936191i \(-0.385674\pi\)
0.351492 + 0.936191i \(0.385674\pi\)
\(368\) 10.6449 0.554906
\(369\) 4.97309 0.258889
\(370\) 0 0
\(371\) −8.30032 −0.430931
\(372\) −11.4318 −0.592709
\(373\) 1.45356 0.0752624 0.0376312 0.999292i \(-0.488019\pi\)
0.0376312 + 0.999292i \(0.488019\pi\)
\(374\) −40.8953 −2.11465
\(375\) 0 0
\(376\) 3.08449 0.159070
\(377\) 2.25770 0.116277
\(378\) 13.6748 0.703358
\(379\) 5.98669 0.307516 0.153758 0.988109i \(-0.450862\pi\)
0.153758 + 0.988109i \(0.450862\pi\)
\(380\) 0 0
\(381\) 34.6669 1.77604
\(382\) 6.74778 0.345246
\(383\) 8.66966 0.442999 0.221499 0.975161i \(-0.428905\pi\)
0.221499 + 0.975161i \(0.428905\pi\)
\(384\) 11.0751 0.565172
\(385\) 0 0
\(386\) −6.16640 −0.313861
\(387\) −4.14450 −0.210677
\(388\) −17.5271 −0.889803
\(389\) −6.51323 −0.330234 −0.165117 0.986274i \(-0.552800\pi\)
−0.165117 + 0.986274i \(0.552800\pi\)
\(390\) 0 0
\(391\) 11.6638 0.589862
\(392\) −1.54719 −0.0781450
\(393\) −36.5652 −1.84447
\(394\) −22.6211 −1.13964
\(395\) 0 0
\(396\) −10.0618 −0.505624
\(397\) 14.5951 0.732506 0.366253 0.930515i \(-0.380641\pi\)
0.366253 + 0.930515i \(0.380641\pi\)
\(398\) 15.2556 0.764693
\(399\) −0.822452 −0.0411741
\(400\) 0 0
\(401\) −12.1126 −0.604874 −0.302437 0.953169i \(-0.597800\pi\)
−0.302437 + 0.953169i \(0.597800\pi\)
\(402\) 4.78034 0.238422
\(403\) −13.3715 −0.666082
\(404\) −0.135610 −0.00674684
\(405\) 0 0
\(406\) −2.29814 −0.114055
\(407\) −40.6285 −2.01388
\(408\) 7.05062 0.349058
\(409\) −9.38475 −0.464046 −0.232023 0.972710i \(-0.574535\pi\)
−0.232023 + 0.972710i \(0.574535\pi\)
\(410\) 0 0
\(411\) −23.8630 −1.17708
\(412\) 2.10083 0.103500
\(413\) 22.9231 1.12797
\(414\) 6.34747 0.311961
\(415\) 0 0
\(416\) −30.0962 −1.47559
\(417\) −11.0393 −0.540595
\(418\) −1.47253 −0.0720236
\(419\) −24.2224 −1.18334 −0.591671 0.806180i \(-0.701531\pi\)
−0.591671 + 0.806180i \(0.701531\pi\)
\(420\) 0 0
\(421\) 25.1092 1.22375 0.611873 0.790956i \(-0.290416\pi\)
0.611873 + 0.790956i \(0.290416\pi\)
\(422\) −7.26690 −0.353747
\(423\) 6.59544 0.320681
\(424\) 2.56213 0.124428
\(425\) 0 0
\(426\) 47.7365 2.31284
\(427\) 5.67943 0.274847
\(428\) −33.2545 −1.60742
\(429\) −36.4855 −1.76154
\(430\) 0 0
\(431\) −8.77815 −0.422829 −0.211414 0.977397i \(-0.567807\pi\)
−0.211414 + 0.977397i \(0.567807\pi\)
\(432\) −15.1367 −0.728266
\(433\) −0.611398 −0.0293819 −0.0146910 0.999892i \(-0.504676\pi\)
−0.0146910 + 0.999892i \(0.504676\pi\)
\(434\) 13.6110 0.653350
\(435\) 0 0
\(436\) 26.8370 1.28526
\(437\) 0.419979 0.0200903
\(438\) 54.6549 2.61151
\(439\) 16.2646 0.776268 0.388134 0.921603i \(-0.373120\pi\)
0.388134 + 0.921603i \(0.373120\pi\)
\(440\) 0 0
\(441\) −3.30830 −0.157538
\(442\) −38.9238 −1.85142
\(443\) −31.4243 −1.49301 −0.746507 0.665377i \(-0.768271\pi\)
−0.746507 + 0.665377i \(0.768271\pi\)
\(444\) −33.0602 −1.56897
\(445\) 0 0
\(446\) −2.04815 −0.0969826
\(447\) −10.8274 −0.512116
\(448\) 10.8233 0.511354
\(449\) −14.4936 −0.683995 −0.341998 0.939701i \(-0.611104\pi\)
−0.341998 + 0.939701i \(0.611104\pi\)
\(450\) 0 0
\(451\) −14.8585 −0.699659
\(452\) 33.2048 1.56182
\(453\) −40.1365 −1.88578
\(454\) 40.5780 1.90442
\(455\) 0 0
\(456\) 0.253873 0.0118887
\(457\) 11.6660 0.545711 0.272855 0.962055i \(-0.412032\pi\)
0.272855 + 0.962055i \(0.412032\pi\)
\(458\) −13.9424 −0.651487
\(459\) −16.5854 −0.774142
\(460\) 0 0
\(461\) −4.47727 −0.208527 −0.104264 0.994550i \(-0.533249\pi\)
−0.104264 + 0.994550i \(0.533249\pi\)
\(462\) 37.1391 1.72787
\(463\) 17.5232 0.814370 0.407185 0.913346i \(-0.366510\pi\)
0.407185 + 0.913346i \(0.366510\pi\)
\(464\) 2.54381 0.118094
\(465\) 0 0
\(466\) 41.8260 1.93755
\(467\) −5.20074 −0.240661 −0.120331 0.992734i \(-0.538395\pi\)
−0.120331 + 0.992734i \(0.538395\pi\)
\(468\) −9.57672 −0.442684
\(469\) −2.57321 −0.118820
\(470\) 0 0
\(471\) 13.8613 0.638696
\(472\) −7.07585 −0.325692
\(473\) 12.3828 0.569364
\(474\) −6.11574 −0.280905
\(475\) 0 0
\(476\) 17.9129 0.821036
\(477\) 5.47849 0.250843
\(478\) 9.52802 0.435801
\(479\) 24.6586 1.12668 0.563340 0.826225i \(-0.309516\pi\)
0.563340 + 0.826225i \(0.309516\pi\)
\(480\) 0 0
\(481\) −38.6699 −1.76319
\(482\) 1.91059 0.0870248
\(483\) −10.5924 −0.481972
\(484\) 11.9087 0.541303
\(485\) 0 0
\(486\) −26.2562 −1.19100
\(487\) −33.7896 −1.53115 −0.765576 0.643346i \(-0.777546\pi\)
−0.765576 + 0.643346i \(0.777546\pi\)
\(488\) −1.75312 −0.0793599
\(489\) 11.5717 0.523289
\(490\) 0 0
\(491\) 4.93113 0.222539 0.111269 0.993790i \(-0.464508\pi\)
0.111269 + 0.993790i \(0.464508\pi\)
\(492\) −12.0906 −0.545088
\(493\) 2.78728 0.125533
\(494\) −1.40154 −0.0630582
\(495\) 0 0
\(496\) −15.0661 −0.676486
\(497\) −25.6961 −1.15263
\(498\) 32.3626 1.45020
\(499\) −7.66605 −0.343179 −0.171590 0.985169i \(-0.554890\pi\)
−0.171590 + 0.985169i \(0.554890\pi\)
\(500\) 0 0
\(501\) −38.7043 −1.72918
\(502\) −35.3002 −1.57553
\(503\) −1.96005 −0.0873942 −0.0436971 0.999045i \(-0.513914\pi\)
−0.0436971 + 0.999045i \(0.513914\pi\)
\(504\) −2.06541 −0.0920006
\(505\) 0 0
\(506\) −18.9648 −0.843088
\(507\) −7.36942 −0.327288
\(508\) −27.1869 −1.20622
\(509\) 5.20406 0.230666 0.115333 0.993327i \(-0.463206\pi\)
0.115333 + 0.993327i \(0.463206\pi\)
\(510\) 0 0
\(511\) −29.4202 −1.30147
\(512\) −27.7948 −1.22837
\(513\) −0.597195 −0.0263668
\(514\) −24.5060 −1.08091
\(515\) 0 0
\(516\) 10.0762 0.443578
\(517\) −19.7057 −0.866655
\(518\) 39.3626 1.72949
\(519\) 2.80183 0.122987
\(520\) 0 0
\(521\) −27.1820 −1.19086 −0.595432 0.803405i \(-0.703019\pi\)
−0.595432 + 0.803405i \(0.703019\pi\)
\(522\) 1.51685 0.0663907
\(523\) −26.6139 −1.16374 −0.581872 0.813281i \(-0.697679\pi\)
−0.581872 + 0.813281i \(0.697679\pi\)
\(524\) 28.6756 1.25270
\(525\) 0 0
\(526\) 42.1646 1.83846
\(527\) −16.5080 −0.719101
\(528\) −41.1093 −1.78905
\(529\) −17.5910 −0.764828
\(530\) 0 0
\(531\) −15.1300 −0.656586
\(532\) 0.644993 0.0279640
\(533\) −14.1422 −0.612566
\(534\) −63.6547 −2.75461
\(535\) 0 0
\(536\) 0.794294 0.0343083
\(537\) 44.4175 1.91676
\(538\) −12.1648 −0.524463
\(539\) 9.88445 0.425753
\(540\) 0 0
\(541\) 29.7687 1.27986 0.639928 0.768435i \(-0.278964\pi\)
0.639928 + 0.768435i \(0.278964\pi\)
\(542\) 44.5055 1.91167
\(543\) −53.3314 −2.28867
\(544\) −37.1558 −1.59304
\(545\) 0 0
\(546\) 35.3486 1.51278
\(547\) −15.7917 −0.675204 −0.337602 0.941289i \(-0.609616\pi\)
−0.337602 + 0.941289i \(0.609616\pi\)
\(548\) 18.7141 0.799428
\(549\) −3.74862 −0.159987
\(550\) 0 0
\(551\) 0.100362 0.00427557
\(552\) 3.26965 0.139166
\(553\) 3.29205 0.139992
\(554\) −42.3003 −1.79717
\(555\) 0 0
\(556\) 8.65734 0.367153
\(557\) 28.0554 1.18874 0.594372 0.804190i \(-0.297401\pi\)
0.594372 + 0.804190i \(0.297401\pi\)
\(558\) −8.98373 −0.380312
\(559\) 11.7859 0.498490
\(560\) 0 0
\(561\) −45.0438 −1.90175
\(562\) −16.4422 −0.693574
\(563\) −16.3809 −0.690374 −0.345187 0.938534i \(-0.612185\pi\)
−0.345187 + 0.938534i \(0.612185\pi\)
\(564\) −16.0349 −0.675192
\(565\) 0 0
\(566\) −28.7303 −1.20762
\(567\) 24.3370 1.02206
\(568\) 7.93182 0.332812
\(569\) −0.387204 −0.0162324 −0.00811621 0.999967i \(-0.502583\pi\)
−0.00811621 + 0.999967i \(0.502583\pi\)
\(570\) 0 0
\(571\) 28.8102 1.20567 0.602835 0.797866i \(-0.294038\pi\)
0.602835 + 0.797866i \(0.294038\pi\)
\(572\) 28.6131 1.19637
\(573\) 7.43228 0.310488
\(574\) 14.3955 0.600857
\(575\) 0 0
\(576\) −7.14376 −0.297656
\(577\) −12.9248 −0.538064 −0.269032 0.963131i \(-0.586704\pi\)
−0.269032 + 0.963131i \(0.586704\pi\)
\(578\) −15.5742 −0.647799
\(579\) −6.79193 −0.282263
\(580\) 0 0
\(581\) −17.4205 −0.722724
\(582\) −42.7004 −1.76999
\(583\) −16.3685 −0.677914
\(584\) 9.08138 0.375790
\(585\) 0 0
\(586\) 11.8114 0.487925
\(587\) −36.3915 −1.50204 −0.751018 0.660282i \(-0.770437\pi\)
−0.751018 + 0.660282i \(0.770437\pi\)
\(588\) 8.04317 0.331695
\(589\) −0.594408 −0.0244921
\(590\) 0 0
\(591\) −24.9159 −1.02490
\(592\) −43.5705 −1.79074
\(593\) 35.8670 1.47288 0.736440 0.676502i \(-0.236505\pi\)
0.736440 + 0.676502i \(0.236505\pi\)
\(594\) 26.9672 1.10648
\(595\) 0 0
\(596\) 8.49116 0.347811
\(597\) 16.8031 0.687706
\(598\) −18.0505 −0.738142
\(599\) −0.855742 −0.0349647 −0.0174823 0.999847i \(-0.505565\pi\)
−0.0174823 + 0.999847i \(0.505565\pi\)
\(600\) 0 0
\(601\) 29.2622 1.19363 0.596815 0.802379i \(-0.296432\pi\)
0.596815 + 0.802379i \(0.296432\pi\)
\(602\) −11.9970 −0.488961
\(603\) 1.69841 0.0691645
\(604\) 31.4764 1.28075
\(605\) 0 0
\(606\) −0.330380 −0.0134208
\(607\) 25.5599 1.03745 0.518723 0.854942i \(-0.326408\pi\)
0.518723 + 0.854942i \(0.326408\pi\)
\(608\) −1.33788 −0.0542581
\(609\) −2.53127 −0.102572
\(610\) 0 0
\(611\) −18.7557 −0.758775
\(612\) −11.8231 −0.477921
\(613\) 9.50489 0.383899 0.191950 0.981405i \(-0.438519\pi\)
0.191950 + 0.981405i \(0.438519\pi\)
\(614\) 25.7703 1.04001
\(615\) 0 0
\(616\) 6.17097 0.248636
\(617\) 16.9425 0.682081 0.341040 0.940049i \(-0.389221\pi\)
0.341040 + 0.940049i \(0.389221\pi\)
\(618\) 5.11815 0.205882
\(619\) 12.7691 0.513233 0.256617 0.966513i \(-0.417392\pi\)
0.256617 + 0.966513i \(0.417392\pi\)
\(620\) 0 0
\(621\) −7.69133 −0.308642
\(622\) −5.78695 −0.232035
\(623\) 34.2647 1.37279
\(624\) −39.1275 −1.56635
\(625\) 0 0
\(626\) 33.7876 1.35042
\(627\) −1.62190 −0.0647725
\(628\) −10.8705 −0.433780
\(629\) −47.7406 −1.90354
\(630\) 0 0
\(631\) −2.17336 −0.0865202 −0.0432601 0.999064i \(-0.513774\pi\)
−0.0432601 + 0.999064i \(0.513774\pi\)
\(632\) −1.01618 −0.0404216
\(633\) −8.00407 −0.318133
\(634\) 16.3911 0.650975
\(635\) 0 0
\(636\) −13.3194 −0.528148
\(637\) 9.40794 0.372756
\(638\) −4.53200 −0.179424
\(639\) 16.9603 0.670939
\(640\) 0 0
\(641\) 17.2645 0.681907 0.340954 0.940080i \(-0.389250\pi\)
0.340954 + 0.940080i \(0.389250\pi\)
\(642\) −81.0164 −3.19746
\(643\) 1.98271 0.0781903 0.0390952 0.999235i \(-0.487552\pi\)
0.0390952 + 0.999235i \(0.487552\pi\)
\(644\) 8.30693 0.327339
\(645\) 0 0
\(646\) −1.73029 −0.0680775
\(647\) 5.08596 0.199950 0.0999749 0.994990i \(-0.468124\pi\)
0.0999749 + 0.994990i \(0.468124\pi\)
\(648\) −7.51229 −0.295111
\(649\) 45.2050 1.77445
\(650\) 0 0
\(651\) 14.9917 0.587573
\(652\) −9.07488 −0.355400
\(653\) −30.8609 −1.20768 −0.603841 0.797105i \(-0.706364\pi\)
−0.603841 + 0.797105i \(0.706364\pi\)
\(654\) 65.3817 2.55663
\(655\) 0 0
\(656\) −15.9344 −0.622134
\(657\) 19.4183 0.757581
\(658\) 19.0917 0.744271
\(659\) −32.9409 −1.28319 −0.641597 0.767042i \(-0.721728\pi\)
−0.641597 + 0.767042i \(0.721728\pi\)
\(660\) 0 0
\(661\) 20.4578 0.795716 0.397858 0.917447i \(-0.369754\pi\)
0.397858 + 0.917447i \(0.369754\pi\)
\(662\) −44.1597 −1.71632
\(663\) −42.8723 −1.66502
\(664\) 5.37733 0.208681
\(665\) 0 0
\(666\) −25.9806 −1.00673
\(667\) 1.29257 0.0500486
\(668\) 30.3531 1.17440
\(669\) −2.25592 −0.0872187
\(670\) 0 0
\(671\) 11.2000 0.432372
\(672\) 33.7430 1.30166
\(673\) −21.2044 −0.817368 −0.408684 0.912676i \(-0.634012\pi\)
−0.408684 + 0.912676i \(0.634012\pi\)
\(674\) 20.8854 0.804476
\(675\) 0 0
\(676\) 5.77934 0.222282
\(677\) −25.9496 −0.997326 −0.498663 0.866796i \(-0.666175\pi\)
−0.498663 + 0.866796i \(0.666175\pi\)
\(678\) 80.8951 3.10676
\(679\) 22.9852 0.882092
\(680\) 0 0
\(681\) 44.6943 1.71269
\(682\) 26.8414 1.02781
\(683\) −26.5331 −1.01526 −0.507630 0.861575i \(-0.669478\pi\)
−0.507630 + 0.861575i \(0.669478\pi\)
\(684\) −0.425717 −0.0162777
\(685\) 0 0
\(686\) −38.5216 −1.47076
\(687\) −15.3568 −0.585898
\(688\) 13.2795 0.506276
\(689\) −15.5794 −0.593528
\(690\) 0 0
\(691\) −34.3646 −1.30729 −0.653645 0.756801i \(-0.726761\pi\)
−0.653645 + 0.756801i \(0.726761\pi\)
\(692\) −2.19729 −0.0835284
\(693\) 13.1951 0.501242
\(694\) 9.63900 0.365891
\(695\) 0 0
\(696\) 0.781346 0.0296169
\(697\) −17.4595 −0.661325
\(698\) −66.3448 −2.51119
\(699\) 46.0689 1.74249
\(700\) 0 0
\(701\) −28.7634 −1.08638 −0.543190 0.839610i \(-0.682784\pi\)
−0.543190 + 0.839610i \(0.682784\pi\)
\(702\) 25.6672 0.968746
\(703\) −1.71900 −0.0648335
\(704\) 21.3439 0.804430
\(705\) 0 0
\(706\) −31.3113 −1.17842
\(707\) 0.177840 0.00668837
\(708\) 36.7842 1.38244
\(709\) −38.6338 −1.45092 −0.725462 0.688262i \(-0.758374\pi\)
−0.725462 + 0.688262i \(0.758374\pi\)
\(710\) 0 0
\(711\) −2.17286 −0.0814887
\(712\) −10.5768 −0.396381
\(713\) −7.65543 −0.286698
\(714\) 43.6403 1.63320
\(715\) 0 0
\(716\) −34.8336 −1.30179
\(717\) 10.4946 0.391926
\(718\) 42.0334 1.56867
\(719\) −42.0112 −1.56675 −0.783376 0.621548i \(-0.786504\pi\)
−0.783376 + 0.621548i \(0.786504\pi\)
\(720\) 0 0
\(721\) −2.75505 −0.102603
\(722\) 36.2388 1.34867
\(723\) 2.10440 0.0782634
\(724\) 41.8242 1.55438
\(725\) 0 0
\(726\) 29.0125 1.07675
\(727\) 18.3447 0.680367 0.340184 0.940359i \(-0.389511\pi\)
0.340184 + 0.940359i \(0.389511\pi\)
\(728\) 5.87348 0.217686
\(729\) 4.81503 0.178334
\(730\) 0 0
\(731\) 14.5505 0.538169
\(732\) 9.11368 0.336851
\(733\) −33.6042 −1.24120 −0.620599 0.784128i \(-0.713111\pi\)
−0.620599 + 0.784128i \(0.713111\pi\)
\(734\) −25.7303 −0.949724
\(735\) 0 0
\(736\) −17.2306 −0.635130
\(737\) −5.07446 −0.186920
\(738\) −9.50152 −0.349756
\(739\) 16.6117 0.611070 0.305535 0.952181i \(-0.401165\pi\)
0.305535 + 0.952181i \(0.401165\pi\)
\(740\) 0 0
\(741\) −1.54371 −0.0567097
\(742\) 15.8585 0.582183
\(743\) 50.1494 1.83980 0.919901 0.392151i \(-0.128269\pi\)
0.919901 + 0.392151i \(0.128269\pi\)
\(744\) −4.62762 −0.169657
\(745\) 0 0
\(746\) −2.77715 −0.101679
\(747\) 11.4981 0.420694
\(748\) 35.3248 1.29160
\(749\) 43.6104 1.59349
\(750\) 0 0
\(751\) 3.60036 0.131379 0.0656896 0.997840i \(-0.479075\pi\)
0.0656896 + 0.997840i \(0.479075\pi\)
\(752\) −21.1326 −0.770627
\(753\) −38.8811 −1.41691
\(754\) −4.31352 −0.157089
\(755\) 0 0
\(756\) −11.8121 −0.429603
\(757\) 21.7797 0.791598 0.395799 0.918337i \(-0.370468\pi\)
0.395799 + 0.918337i \(0.370468\pi\)
\(758\) −11.4381 −0.415450
\(759\) −20.8886 −0.758209
\(760\) 0 0
\(761\) −8.60072 −0.311776 −0.155888 0.987775i \(-0.549824\pi\)
−0.155888 + 0.987775i \(0.549824\pi\)
\(762\) −66.2341 −2.39941
\(763\) −35.1944 −1.27412
\(764\) −5.82864 −0.210873
\(765\) 0 0
\(766\) −16.5641 −0.598486
\(767\) 43.0257 1.55357
\(768\) −42.2077 −1.52304
\(769\) 34.1553 1.23167 0.615836 0.787874i \(-0.288818\pi\)
0.615836 + 0.787874i \(0.288818\pi\)
\(770\) 0 0
\(771\) −26.9919 −0.972090
\(772\) 5.32645 0.191703
\(773\) −26.5165 −0.953731 −0.476865 0.878976i \(-0.658227\pi\)
−0.476865 + 0.878976i \(0.658227\pi\)
\(774\) 7.91843 0.284622
\(775\) 0 0
\(776\) −7.09504 −0.254697
\(777\) 43.3555 1.55537
\(778\) 12.4441 0.446142
\(779\) −0.628667 −0.0225243
\(780\) 0 0
\(781\) −50.6735 −1.81324
\(782\) −22.2846 −0.796896
\(783\) −1.83799 −0.0656844
\(784\) 10.6002 0.378579
\(785\) 0 0
\(786\) 69.8609 2.49186
\(787\) 32.7986 1.16914 0.584572 0.811342i \(-0.301262\pi\)
0.584572 + 0.811342i \(0.301262\pi\)
\(788\) 19.5398 0.696077
\(789\) 46.4418 1.65337
\(790\) 0 0
\(791\) −43.5451 −1.54829
\(792\) −4.07305 −0.144730
\(793\) 10.6601 0.378551
\(794\) −27.8851 −0.989606
\(795\) 0 0
\(796\) −13.1775 −0.467066
\(797\) −18.5774 −0.658047 −0.329024 0.944322i \(-0.606720\pi\)
−0.329024 + 0.944322i \(0.606720\pi\)
\(798\) 1.57136 0.0556257
\(799\) −23.1552 −0.819172
\(800\) 0 0
\(801\) −22.6159 −0.799092
\(802\) 23.1421 0.817177
\(803\) −58.0176 −2.04740
\(804\) −4.12919 −0.145625
\(805\) 0 0
\(806\) 25.5474 0.899869
\(807\) −13.3989 −0.471662
\(808\) −0.0548954 −0.00193121
\(809\) 15.1345 0.532100 0.266050 0.963959i \(-0.414281\pi\)
0.266050 + 0.963959i \(0.414281\pi\)
\(810\) 0 0
\(811\) 23.1559 0.813113 0.406557 0.913626i \(-0.366729\pi\)
0.406557 + 0.913626i \(0.366729\pi\)
\(812\) 1.98510 0.0696633
\(813\) 49.0202 1.71921
\(814\) 77.6242 2.72073
\(815\) 0 0
\(816\) −48.3055 −1.69103
\(817\) 0.523922 0.0183297
\(818\) 17.9304 0.626921
\(819\) 12.5590 0.438848
\(820\) 0 0
\(821\) 11.4499 0.399605 0.199803 0.979836i \(-0.435970\pi\)
0.199803 + 0.979836i \(0.435970\pi\)
\(822\) 45.5923 1.59021
\(823\) −55.2246 −1.92501 −0.962504 0.271269i \(-0.912557\pi\)
−0.962504 + 0.271269i \(0.912557\pi\)
\(824\) 0.850424 0.0296259
\(825\) 0 0
\(826\) −43.7964 −1.52387
\(827\) −11.9420 −0.415264 −0.207632 0.978207i \(-0.566576\pi\)
−0.207632 + 0.978207i \(0.566576\pi\)
\(828\) −5.48285 −0.190542
\(829\) −36.3476 −1.26240 −0.631202 0.775618i \(-0.717438\pi\)
−0.631202 + 0.775618i \(0.717438\pi\)
\(830\) 0 0
\(831\) −46.5913 −1.61623
\(832\) 20.3150 0.704295
\(833\) 11.6147 0.402427
\(834\) 21.0914 0.730337
\(835\) 0 0
\(836\) 1.27195 0.0439912
\(837\) 10.8857 0.376266
\(838\) 46.2789 1.59868
\(839\) −24.9289 −0.860641 −0.430320 0.902676i \(-0.641599\pi\)
−0.430320 + 0.902676i \(0.641599\pi\)
\(840\) 0 0
\(841\) −28.6911 −0.989349
\(842\) −47.9732 −1.65327
\(843\) −18.1102 −0.623747
\(844\) 6.27704 0.216065
\(845\) 0 0
\(846\) −12.6012 −0.433236
\(847\) −15.6171 −0.536611
\(848\) −17.5538 −0.602799
\(849\) −31.6447 −1.08604
\(850\) 0 0
\(851\) −22.1392 −0.758923
\(852\) −41.2341 −1.41266
\(853\) 41.5695 1.42331 0.711657 0.702527i \(-0.247945\pi\)
0.711657 + 0.702527i \(0.247945\pi\)
\(854\) −10.8510 −0.371315
\(855\) 0 0
\(856\) −13.4616 −0.460107
\(857\) −28.3039 −0.966842 −0.483421 0.875388i \(-0.660606\pi\)
−0.483421 + 0.875388i \(0.660606\pi\)
\(858\) 69.7087 2.37981
\(859\) −12.3577 −0.421638 −0.210819 0.977525i \(-0.567613\pi\)
−0.210819 + 0.977525i \(0.567613\pi\)
\(860\) 0 0
\(861\) 15.8558 0.540364
\(862\) 16.7714 0.571237
\(863\) −20.5144 −0.698319 −0.349159 0.937063i \(-0.613533\pi\)
−0.349159 + 0.937063i \(0.613533\pi\)
\(864\) 24.5013 0.833552
\(865\) 0 0
\(866\) 1.16813 0.0396946
\(867\) −17.1540 −0.582581
\(868\) −11.7570 −0.399059
\(869\) 6.49203 0.220227
\(870\) 0 0
\(871\) −4.82983 −0.163652
\(872\) 10.8637 0.367892
\(873\) −15.1710 −0.513461
\(874\) −0.802407 −0.0271418
\(875\) 0 0
\(876\) −47.2101 −1.59508
\(877\) 33.0284 1.11529 0.557645 0.830079i \(-0.311705\pi\)
0.557645 + 0.830079i \(0.311705\pi\)
\(878\) −31.0749 −1.04873
\(879\) 13.0096 0.438803
\(880\) 0 0
\(881\) 16.5997 0.559260 0.279630 0.960108i \(-0.409788\pi\)
0.279630 + 0.960108i \(0.409788\pi\)
\(882\) 6.32078 0.212832
\(883\) −49.9499 −1.68095 −0.840473 0.541853i \(-0.817723\pi\)
−0.840473 + 0.541853i \(0.817723\pi\)
\(884\) 33.6218 1.13083
\(885\) 0 0
\(886\) 60.0388 2.01704
\(887\) −3.83231 −0.128677 −0.0643383 0.997928i \(-0.520494\pi\)
−0.0643383 + 0.997928i \(0.520494\pi\)
\(888\) −13.3829 −0.449101
\(889\) 35.6532 1.19577
\(890\) 0 0
\(891\) 47.9933 1.60784
\(892\) 1.76916 0.0592359
\(893\) −0.833754 −0.0279005
\(894\) 20.6866 0.691863
\(895\) 0 0
\(896\) 11.3902 0.380519
\(897\) −19.8816 −0.663828
\(898\) 27.6913 0.924069
\(899\) −1.82941 −0.0610143
\(900\) 0 0
\(901\) −19.2338 −0.640772
\(902\) 28.3884 0.945230
\(903\) −13.2140 −0.439734
\(904\) 13.4414 0.447055
\(905\) 0 0
\(906\) 76.6843 2.54766
\(907\) −33.5656 −1.11453 −0.557264 0.830336i \(-0.688149\pi\)
−0.557264 + 0.830336i \(0.688149\pi\)
\(908\) −35.0507 −1.16320
\(909\) −0.117381 −0.00389327
\(910\) 0 0
\(911\) −7.44125 −0.246540 −0.123270 0.992373i \(-0.539338\pi\)
−0.123270 + 0.992373i \(0.539338\pi\)
\(912\) −1.73935 −0.0575955
\(913\) −34.3538 −1.13694
\(914\) −22.2888 −0.737248
\(915\) 0 0
\(916\) 12.0433 0.397921
\(917\) −37.6055 −1.24184
\(918\) 31.6879 1.04586
\(919\) 42.2789 1.39465 0.697326 0.716754i \(-0.254373\pi\)
0.697326 + 0.716754i \(0.254373\pi\)
\(920\) 0 0
\(921\) 28.3845 0.935302
\(922\) 8.55420 0.281718
\(923\) −48.2306 −1.58753
\(924\) −32.0802 −1.05536
\(925\) 0 0
\(926\) −33.4795 −1.10020
\(927\) 1.81843 0.0597250
\(928\) −4.11759 −0.135167
\(929\) −54.0164 −1.77222 −0.886110 0.463474i \(-0.846603\pi\)
−0.886110 + 0.463474i \(0.846603\pi\)
\(930\) 0 0
\(931\) 0.418214 0.0137064
\(932\) −36.1287 −1.18344
\(933\) −6.37398 −0.208675
\(934\) 9.93645 0.325131
\(935\) 0 0
\(936\) −3.87670 −0.126714
\(937\) −5.15837 −0.168517 −0.0842584 0.996444i \(-0.526852\pi\)
−0.0842584 + 0.996444i \(0.526852\pi\)
\(938\) 4.91634 0.160524
\(939\) 37.2151 1.21447
\(940\) 0 0
\(941\) −29.7898 −0.971119 −0.485560 0.874204i \(-0.661384\pi\)
−0.485560 + 0.874204i \(0.661384\pi\)
\(942\) −26.4832 −0.862870
\(943\) −8.09666 −0.263663
\(944\) 48.4784 1.57784
\(945\) 0 0
\(946\) −23.6585 −0.769203
\(947\) 45.5068 1.47877 0.739386 0.673282i \(-0.235116\pi\)
0.739386 + 0.673282i \(0.235116\pi\)
\(948\) 5.28269 0.171574
\(949\) −55.2207 −1.79254
\(950\) 0 0
\(951\) 18.0539 0.585437
\(952\) 7.25121 0.235013
\(953\) 25.6723 0.831607 0.415803 0.909455i \(-0.363500\pi\)
0.415803 + 0.909455i \(0.363500\pi\)
\(954\) −10.4671 −0.338886
\(955\) 0 0
\(956\) −8.23016 −0.266183
\(957\) −4.99174 −0.161360
\(958\) −47.1123 −1.52213
\(959\) −24.5419 −0.792500
\(960\) 0 0
\(961\) −20.1651 −0.650486
\(962\) 73.8821 2.38205
\(963\) −28.7843 −0.927562
\(964\) −1.65034 −0.0531537
\(965\) 0 0
\(966\) 20.2377 0.651139
\(967\) −7.17383 −0.230695 −0.115347 0.993325i \(-0.536798\pi\)
−0.115347 + 0.993325i \(0.536798\pi\)
\(968\) 4.82067 0.154942
\(969\) −1.90582 −0.0612237
\(970\) 0 0
\(971\) 39.9457 1.28192 0.640959 0.767575i \(-0.278537\pi\)
0.640959 + 0.767575i \(0.278537\pi\)
\(972\) 22.6797 0.727452
\(973\) −11.3533 −0.363971
\(974\) 64.5578 2.06857
\(975\) 0 0
\(976\) 12.0110 0.384464
\(977\) 26.5270 0.848675 0.424338 0.905504i \(-0.360507\pi\)
0.424338 + 0.905504i \(0.360507\pi\)
\(978\) −22.1087 −0.706957
\(979\) 67.5711 2.15958
\(980\) 0 0
\(981\) 23.2295 0.741660
\(982\) −9.42135 −0.300647
\(983\) −39.2874 −1.25307 −0.626537 0.779392i \(-0.715528\pi\)
−0.626537 + 0.779392i \(0.715528\pi\)
\(984\) −4.89434 −0.156026
\(985\) 0 0
\(986\) −5.32534 −0.169593
\(987\) 21.0284 0.669340
\(988\) 1.21063 0.0385152
\(989\) 6.74764 0.214562
\(990\) 0 0
\(991\) 6.50257 0.206561 0.103280 0.994652i \(-0.467066\pi\)
0.103280 + 0.994652i \(0.467066\pi\)
\(992\) 24.3870 0.774287
\(993\) −48.6394 −1.54352
\(994\) 49.0946 1.55719
\(995\) 0 0
\(996\) −27.9544 −0.885768
\(997\) 45.8122 1.45089 0.725444 0.688282i \(-0.241635\pi\)
0.725444 + 0.688282i \(0.241635\pi\)
\(998\) 14.6466 0.463631
\(999\) 31.4811 0.996019
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.j.1.8 25
5.4 even 2 1205.2.a.e.1.18 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.a.e.1.18 25 5.4 even 2
6025.2.a.j.1.8 25 1.1 even 1 trivial