Properties

Label 6025.2.a.i.1.1
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $15$
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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} - 699 x^{6} - 297 x^{5} + 394 x^{4} + 89 x^{3} - 57 x^{2} - 17 x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.34497\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q-2.34497 q^{2} +3.01587 q^{3} +3.49887 q^{4} -7.07210 q^{6} -1.32864 q^{7} -3.51479 q^{8} +6.09545 q^{9} +O(q^{10})\) \(q-2.34497 q^{2} +3.01587 q^{3} +3.49887 q^{4} -7.07210 q^{6} -1.32864 q^{7} -3.51479 q^{8} +6.09545 q^{9} -4.04712 q^{11} +10.5521 q^{12} +3.88814 q^{13} +3.11562 q^{14} +1.24433 q^{16} -2.67658 q^{17} -14.2936 q^{18} -4.01370 q^{19} -4.00701 q^{21} +9.49035 q^{22} +0.553005 q^{23} -10.6001 q^{24} -9.11755 q^{26} +9.33545 q^{27} -4.64874 q^{28} +2.20769 q^{29} -7.23013 q^{31} +4.11166 q^{32} -12.2056 q^{33} +6.27649 q^{34} +21.3272 q^{36} +1.59215 q^{37} +9.41198 q^{38} +11.7261 q^{39} -5.02098 q^{41} +9.39630 q^{42} +3.61669 q^{43} -14.1603 q^{44} -1.29678 q^{46} +5.44306 q^{47} +3.75274 q^{48} -5.23471 q^{49} -8.07221 q^{51} +13.6041 q^{52} +0.894563 q^{53} -21.8913 q^{54} +4.66990 q^{56} -12.1048 q^{57} -5.17696 q^{58} -11.5371 q^{59} +3.61517 q^{61} +16.9544 q^{62} -8.09867 q^{63} -12.1304 q^{64} +28.6216 q^{66} -5.71261 q^{67} -9.36499 q^{68} +1.66779 q^{69} +1.34797 q^{71} -21.4242 q^{72} -5.19142 q^{73} -3.73355 q^{74} -14.0434 q^{76} +5.37718 q^{77} -27.4973 q^{78} +10.0840 q^{79} +9.86813 q^{81} +11.7740 q^{82} -14.9857 q^{83} -14.0200 q^{84} -8.48101 q^{86} +6.65810 q^{87} +14.2248 q^{88} -5.29556 q^{89} -5.16595 q^{91} +1.93489 q^{92} -21.8051 q^{93} -12.7638 q^{94} +12.4002 q^{96} -5.86258 q^{97} +12.2752 q^{98} -24.6690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34497 −1.65814 −0.829071 0.559144i \(-0.811130\pi\)
−0.829071 + 0.559144i \(0.811130\pi\)
\(3\) 3.01587 1.74121 0.870605 0.491982i \(-0.163727\pi\)
0.870605 + 0.491982i \(0.163727\pi\)
\(4\) 3.49887 1.74943
\(5\) 0 0
\(6\) −7.07210 −2.88717
\(7\) −1.32864 −0.502180 −0.251090 0.967964i \(-0.580789\pi\)
−0.251090 + 0.967964i \(0.580789\pi\)
\(8\) −3.51479 −1.24267
\(9\) 6.09545 2.03182
\(10\) 0 0
\(11\) −4.04712 −1.22025 −0.610126 0.792304i \(-0.708881\pi\)
−0.610126 + 0.792304i \(0.708881\pi\)
\(12\) 10.5521 3.04613
\(13\) 3.88814 1.07838 0.539188 0.842186i \(-0.318731\pi\)
0.539188 + 0.842186i \(0.318731\pi\)
\(14\) 3.11562 0.832685
\(15\) 0 0
\(16\) 1.24433 0.311083
\(17\) −2.67658 −0.649166 −0.324583 0.945857i \(-0.605224\pi\)
−0.324583 + 0.945857i \(0.605224\pi\)
\(18\) −14.2936 −3.36904
\(19\) −4.01370 −0.920805 −0.460402 0.887710i \(-0.652295\pi\)
−0.460402 + 0.887710i \(0.652295\pi\)
\(20\) 0 0
\(21\) −4.00701 −0.874401
\(22\) 9.49035 2.02335
\(23\) 0.553005 0.115310 0.0576548 0.998337i \(-0.481638\pi\)
0.0576548 + 0.998337i \(0.481638\pi\)
\(24\) −10.6001 −2.16374
\(25\) 0 0
\(26\) −9.11755 −1.78810
\(27\) 9.33545 1.79661
\(28\) −4.64874 −0.878530
\(29\) 2.20769 0.409958 0.204979 0.978766i \(-0.434287\pi\)
0.204979 + 0.978766i \(0.434287\pi\)
\(30\) 0 0
\(31\) −7.23013 −1.29857 −0.649285 0.760545i \(-0.724932\pi\)
−0.649285 + 0.760545i \(0.724932\pi\)
\(32\) 4.11166 0.726846
\(33\) −12.2056 −2.12472
\(34\) 6.27649 1.07641
\(35\) 0 0
\(36\) 21.3272 3.55453
\(37\) 1.59215 0.261749 0.130874 0.991399i \(-0.458222\pi\)
0.130874 + 0.991399i \(0.458222\pi\)
\(38\) 9.41198 1.52682
\(39\) 11.7261 1.87768
\(40\) 0 0
\(41\) −5.02098 −0.784145 −0.392072 0.919934i \(-0.628242\pi\)
−0.392072 + 0.919934i \(0.628242\pi\)
\(42\) 9.39630 1.44988
\(43\) 3.61669 0.551540 0.275770 0.961224i \(-0.411067\pi\)
0.275770 + 0.961224i \(0.411067\pi\)
\(44\) −14.1603 −2.13475
\(45\) 0 0
\(46\) −1.29678 −0.191200
\(47\) 5.44306 0.793952 0.396976 0.917829i \(-0.370060\pi\)
0.396976 + 0.917829i \(0.370060\pi\)
\(48\) 3.75274 0.541661
\(49\) −5.23471 −0.747815
\(50\) 0 0
\(51\) −8.07221 −1.13033
\(52\) 13.6041 1.88655
\(53\) 0.894563 0.122878 0.0614388 0.998111i \(-0.480431\pi\)
0.0614388 + 0.998111i \(0.480431\pi\)
\(54\) −21.8913 −2.97903
\(55\) 0 0
\(56\) 4.66990 0.624042
\(57\) −12.1048 −1.60332
\(58\) −5.17696 −0.679768
\(59\) −11.5371 −1.50201 −0.751003 0.660298i \(-0.770430\pi\)
−0.751003 + 0.660298i \(0.770430\pi\)
\(60\) 0 0
\(61\) 3.61517 0.462876 0.231438 0.972850i \(-0.425657\pi\)
0.231438 + 0.972850i \(0.425657\pi\)
\(62\) 16.9544 2.15321
\(63\) −8.09867 −1.02034
\(64\) −12.1304 −1.51630
\(65\) 0 0
\(66\) 28.6216 3.52308
\(67\) −5.71261 −0.697907 −0.348953 0.937140i \(-0.613463\pi\)
−0.348953 + 0.937140i \(0.613463\pi\)
\(68\) −9.36499 −1.13567
\(69\) 1.66779 0.200778
\(70\) 0 0
\(71\) 1.34797 0.159974 0.0799871 0.996796i \(-0.474512\pi\)
0.0799871 + 0.996796i \(0.474512\pi\)
\(72\) −21.4242 −2.52487
\(73\) −5.19142 −0.607610 −0.303805 0.952734i \(-0.598257\pi\)
−0.303805 + 0.952734i \(0.598257\pi\)
\(74\) −3.73355 −0.434016
\(75\) 0 0
\(76\) −14.0434 −1.61089
\(77\) 5.37718 0.612786
\(78\) −27.4973 −3.11346
\(79\) 10.0840 1.13454 0.567270 0.823532i \(-0.308000\pi\)
0.567270 + 0.823532i \(0.308000\pi\)
\(80\) 0 0
\(81\) 9.86813 1.09646
\(82\) 11.7740 1.30022
\(83\) −14.9857 −1.64489 −0.822446 0.568843i \(-0.807391\pi\)
−0.822446 + 0.568843i \(0.807391\pi\)
\(84\) −14.0200 −1.52971
\(85\) 0 0
\(86\) −8.48101 −0.914531
\(87\) 6.65810 0.713823
\(88\) 14.2248 1.51637
\(89\) −5.29556 −0.561329 −0.280664 0.959806i \(-0.590555\pi\)
−0.280664 + 0.959806i \(0.590555\pi\)
\(90\) 0 0
\(91\) −5.16595 −0.541538
\(92\) 1.93489 0.201726
\(93\) −21.8051 −2.26108
\(94\) −12.7638 −1.31649
\(95\) 0 0
\(96\) 12.4002 1.26559
\(97\) −5.86258 −0.595255 −0.297627 0.954682i \(-0.596195\pi\)
−0.297627 + 0.954682i \(0.596195\pi\)
\(98\) 12.2752 1.23998
\(99\) −24.6690 −2.47933
\(100\) 0 0
\(101\) −13.4274 −1.33608 −0.668039 0.744127i \(-0.732866\pi\)
−0.668039 + 0.744127i \(0.732866\pi\)
\(102\) 18.9290 1.87426
\(103\) 14.2030 1.39946 0.699730 0.714408i \(-0.253304\pi\)
0.699730 + 0.714408i \(0.253304\pi\)
\(104\) −13.6660 −1.34006
\(105\) 0 0
\(106\) −2.09772 −0.203749
\(107\) 2.11593 0.204554 0.102277 0.994756i \(-0.467387\pi\)
0.102277 + 0.994756i \(0.467387\pi\)
\(108\) 32.6635 3.14305
\(109\) 19.1134 1.83073 0.915366 0.402622i \(-0.131901\pi\)
0.915366 + 0.402622i \(0.131901\pi\)
\(110\) 0 0
\(111\) 4.80172 0.455759
\(112\) −1.65327 −0.156220
\(113\) −13.1598 −1.23797 −0.618987 0.785401i \(-0.712457\pi\)
−0.618987 + 0.785401i \(0.712457\pi\)
\(114\) 28.3853 2.65852
\(115\) 0 0
\(116\) 7.72442 0.717194
\(117\) 23.6999 2.19106
\(118\) 27.0542 2.49054
\(119\) 3.55622 0.325998
\(120\) 0 0
\(121\) 5.37916 0.489015
\(122\) −8.47746 −0.767513
\(123\) −15.1426 −1.36536
\(124\) −25.2973 −2.27176
\(125\) 0 0
\(126\) 18.9911 1.69186
\(127\) −5.72538 −0.508045 −0.254023 0.967198i \(-0.581754\pi\)
−0.254023 + 0.967198i \(0.581754\pi\)
\(128\) 20.2220 1.78739
\(129\) 10.9074 0.960347
\(130\) 0 0
\(131\) 16.9467 1.48064 0.740319 0.672256i \(-0.234675\pi\)
0.740319 + 0.672256i \(0.234675\pi\)
\(132\) −42.7056 −3.71705
\(133\) 5.33277 0.462410
\(134\) 13.3959 1.15723
\(135\) 0 0
\(136\) 9.40762 0.806697
\(137\) −19.3019 −1.64907 −0.824537 0.565808i \(-0.808564\pi\)
−0.824537 + 0.565808i \(0.808564\pi\)
\(138\) −3.91091 −0.332919
\(139\) 5.79018 0.491116 0.245558 0.969382i \(-0.421029\pi\)
0.245558 + 0.969382i \(0.421029\pi\)
\(140\) 0 0
\(141\) 16.4155 1.38244
\(142\) −3.16094 −0.265260
\(143\) −15.7358 −1.31589
\(144\) 7.58476 0.632063
\(145\) 0 0
\(146\) 12.1737 1.00750
\(147\) −15.7872 −1.30210
\(148\) 5.57073 0.457912
\(149\) −7.06741 −0.578985 −0.289492 0.957180i \(-0.593487\pi\)
−0.289492 + 0.957180i \(0.593487\pi\)
\(150\) 0 0
\(151\) −4.88032 −0.397155 −0.198577 0.980085i \(-0.563632\pi\)
−0.198577 + 0.980085i \(0.563632\pi\)
\(152\) 14.1073 1.14425
\(153\) −16.3150 −1.31899
\(154\) −12.6093 −1.01609
\(155\) 0 0
\(156\) 41.0281 3.28487
\(157\) −6.14143 −0.490139 −0.245070 0.969506i \(-0.578811\pi\)
−0.245070 + 0.969506i \(0.578811\pi\)
\(158\) −23.6467 −1.88123
\(159\) 2.69788 0.213956
\(160\) 0 0
\(161\) −0.734747 −0.0579062
\(162\) −23.1404 −1.81808
\(163\) 17.6834 1.38507 0.692535 0.721385i \(-0.256494\pi\)
0.692535 + 0.721385i \(0.256494\pi\)
\(164\) −17.5677 −1.37181
\(165\) 0 0
\(166\) 35.1409 2.72746
\(167\) −13.6648 −1.05741 −0.528705 0.848806i \(-0.677322\pi\)
−0.528705 + 0.848806i \(0.677322\pi\)
\(168\) 14.0838 1.08659
\(169\) 2.11762 0.162893
\(170\) 0 0
\(171\) −24.4653 −1.87091
\(172\) 12.6543 0.964882
\(173\) −3.57596 −0.271875 −0.135938 0.990717i \(-0.543405\pi\)
−0.135938 + 0.990717i \(0.543405\pi\)
\(174\) −15.6130 −1.18362
\(175\) 0 0
\(176\) −5.03596 −0.379600
\(177\) −34.7944 −2.61531
\(178\) 12.4179 0.930762
\(179\) −26.2632 −1.96301 −0.981503 0.191444i \(-0.938683\pi\)
−0.981503 + 0.191444i \(0.938683\pi\)
\(180\) 0 0
\(181\) −15.9729 −1.18726 −0.593630 0.804738i \(-0.702306\pi\)
−0.593630 + 0.804738i \(0.702306\pi\)
\(182\) 12.1140 0.897947
\(183\) 10.9029 0.805964
\(184\) −1.94370 −0.143291
\(185\) 0 0
\(186\) 51.1322 3.74920
\(187\) 10.8324 0.792146
\(188\) 19.0445 1.38897
\(189\) −12.4035 −0.902221
\(190\) 0 0
\(191\) 8.91575 0.645121 0.322560 0.946549i \(-0.395456\pi\)
0.322560 + 0.946549i \(0.395456\pi\)
\(192\) −36.5836 −2.64019
\(193\) 8.53301 0.614219 0.307110 0.951674i \(-0.400638\pi\)
0.307110 + 0.951674i \(0.400638\pi\)
\(194\) 13.7475 0.987016
\(195\) 0 0
\(196\) −18.3155 −1.30825
\(197\) −19.4714 −1.38728 −0.693641 0.720321i \(-0.743994\pi\)
−0.693641 + 0.720321i \(0.743994\pi\)
\(198\) 57.8479 4.11107
\(199\) 8.98881 0.637200 0.318600 0.947889i \(-0.396787\pi\)
0.318600 + 0.947889i \(0.396787\pi\)
\(200\) 0 0
\(201\) −17.2285 −1.21520
\(202\) 31.4868 2.21541
\(203\) −2.93323 −0.205873
\(204\) −28.2436 −1.97745
\(205\) 0 0
\(206\) −33.3055 −2.32050
\(207\) 3.37081 0.234288
\(208\) 4.83813 0.335464
\(209\) 16.2439 1.12361
\(210\) 0 0
\(211\) −6.56061 −0.451651 −0.225825 0.974168i \(-0.572508\pi\)
−0.225825 + 0.974168i \(0.572508\pi\)
\(212\) 3.12996 0.214966
\(213\) 4.06529 0.278549
\(214\) −4.96178 −0.339180
\(215\) 0 0
\(216\) −32.8122 −2.23258
\(217\) 9.60627 0.652116
\(218\) −44.8203 −3.03561
\(219\) −15.6566 −1.05798
\(220\) 0 0
\(221\) −10.4069 −0.700045
\(222\) −11.2599 −0.755714
\(223\) −3.89457 −0.260800 −0.130400 0.991461i \(-0.541626\pi\)
−0.130400 + 0.991461i \(0.541626\pi\)
\(224\) −5.46294 −0.365008
\(225\) 0 0
\(226\) 30.8594 2.05274
\(227\) 11.0989 0.736659 0.368329 0.929695i \(-0.379930\pi\)
0.368329 + 0.929695i \(0.379930\pi\)
\(228\) −42.3530 −2.80489
\(229\) −23.1814 −1.53187 −0.765935 0.642918i \(-0.777724\pi\)
−0.765935 + 0.642918i \(0.777724\pi\)
\(230\) 0 0
\(231\) 16.2168 1.06699
\(232\) −7.75957 −0.509441
\(233\) 18.8689 1.23614 0.618071 0.786123i \(-0.287915\pi\)
0.618071 + 0.786123i \(0.287915\pi\)
\(234\) −55.5755 −3.63309
\(235\) 0 0
\(236\) −40.3669 −2.62766
\(237\) 30.4120 1.97547
\(238\) −8.33922 −0.540551
\(239\) −13.5375 −0.875666 −0.437833 0.899056i \(-0.644254\pi\)
−0.437833 + 0.899056i \(0.644254\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) −12.6140 −0.810855
\(243\) 1.75460 0.112558
\(244\) 12.6490 0.809770
\(245\) 0 0
\(246\) 35.5089 2.26396
\(247\) −15.6058 −0.992973
\(248\) 25.4124 1.61369
\(249\) −45.1948 −2.86410
\(250\) 0 0
\(251\) −20.5451 −1.29679 −0.648397 0.761302i \(-0.724560\pi\)
−0.648397 + 0.761302i \(0.724560\pi\)
\(252\) −28.3362 −1.78501
\(253\) −2.23808 −0.140707
\(254\) 13.4258 0.842410
\(255\) 0 0
\(256\) −23.1591 −1.44745
\(257\) −27.5851 −1.72071 −0.860356 0.509694i \(-0.829759\pi\)
−0.860356 + 0.509694i \(0.829759\pi\)
\(258\) −25.5776 −1.59239
\(259\) −2.11541 −0.131445
\(260\) 0 0
\(261\) 13.4569 0.832959
\(262\) −39.7394 −2.45511
\(263\) −9.86377 −0.608226 −0.304113 0.952636i \(-0.598360\pi\)
−0.304113 + 0.952636i \(0.598360\pi\)
\(264\) 42.9000 2.64031
\(265\) 0 0
\(266\) −12.5052 −0.766741
\(267\) −15.9707 −0.977392
\(268\) −19.9877 −1.22094
\(269\) 19.4589 1.18643 0.593214 0.805045i \(-0.297859\pi\)
0.593214 + 0.805045i \(0.297859\pi\)
\(270\) 0 0
\(271\) −25.0735 −1.52310 −0.761552 0.648104i \(-0.775562\pi\)
−0.761552 + 0.648104i \(0.775562\pi\)
\(272\) −3.33055 −0.201944
\(273\) −15.5798 −0.942933
\(274\) 45.2623 2.73440
\(275\) 0 0
\(276\) 5.83537 0.351248
\(277\) 27.5593 1.65588 0.827939 0.560819i \(-0.189514\pi\)
0.827939 + 0.560819i \(0.189514\pi\)
\(278\) −13.5778 −0.814340
\(279\) −44.0709 −2.63845
\(280\) 0 0
\(281\) 29.6910 1.77122 0.885609 0.464432i \(-0.153741\pi\)
0.885609 + 0.464432i \(0.153741\pi\)
\(282\) −38.4939 −2.29228
\(283\) 20.1705 1.19901 0.599506 0.800370i \(-0.295364\pi\)
0.599506 + 0.800370i \(0.295364\pi\)
\(284\) 4.71636 0.279864
\(285\) 0 0
\(286\) 36.8998 2.18193
\(287\) 6.67109 0.393782
\(288\) 25.0624 1.47682
\(289\) −9.83592 −0.578584
\(290\) 0 0
\(291\) −17.6807 −1.03646
\(292\) −18.1641 −1.06297
\(293\) −4.59568 −0.268483 −0.134241 0.990949i \(-0.542860\pi\)
−0.134241 + 0.990949i \(0.542860\pi\)
\(294\) 37.0204 2.15907
\(295\) 0 0
\(296\) −5.59609 −0.325266
\(297\) −37.7817 −2.19231
\(298\) 16.5728 0.960039
\(299\) 2.15016 0.124347
\(300\) 0 0
\(301\) −4.80529 −0.276972
\(302\) 11.4442 0.658539
\(303\) −40.4953 −2.32639
\(304\) −4.99437 −0.286447
\(305\) 0 0
\(306\) 38.2580 2.18706
\(307\) 2.54946 0.145505 0.0727526 0.997350i \(-0.476822\pi\)
0.0727526 + 0.997350i \(0.476822\pi\)
\(308\) 18.8140 1.07203
\(309\) 42.8342 2.43675
\(310\) 0 0
\(311\) −21.5631 −1.22273 −0.611366 0.791348i \(-0.709380\pi\)
−0.611366 + 0.791348i \(0.709380\pi\)
\(312\) −41.2148 −2.33333
\(313\) −33.2289 −1.87821 −0.939104 0.343633i \(-0.888342\pi\)
−0.939104 + 0.343633i \(0.888342\pi\)
\(314\) 14.4014 0.812720
\(315\) 0 0
\(316\) 35.2826 1.98480
\(317\) −21.5858 −1.21238 −0.606189 0.795321i \(-0.707302\pi\)
−0.606189 + 0.795321i \(0.707302\pi\)
\(318\) −6.32644 −0.354769
\(319\) −8.93479 −0.500252
\(320\) 0 0
\(321\) 6.38135 0.356172
\(322\) 1.72296 0.0960166
\(323\) 10.7430 0.597755
\(324\) 34.5273 1.91818
\(325\) 0 0
\(326\) −41.4669 −2.29664
\(327\) 57.6435 3.18769
\(328\) 17.6477 0.974430
\(329\) −7.23189 −0.398707
\(330\) 0 0
\(331\) −15.8718 −0.872391 −0.436196 0.899852i \(-0.643674\pi\)
−0.436196 + 0.899852i \(0.643674\pi\)
\(332\) −52.4329 −2.87763
\(333\) 9.70489 0.531825
\(334\) 32.0434 1.75334
\(335\) 0 0
\(336\) −4.98605 −0.272011
\(337\) 27.2339 1.48352 0.741762 0.670663i \(-0.233990\pi\)
0.741762 + 0.670663i \(0.233990\pi\)
\(338\) −4.96574 −0.270100
\(339\) −39.6883 −2.15557
\(340\) 0 0
\(341\) 29.2612 1.58458
\(342\) 57.3702 3.10223
\(343\) 16.2556 0.877718
\(344\) −12.7119 −0.685380
\(345\) 0 0
\(346\) 8.38550 0.450807
\(347\) 31.7885 1.70650 0.853249 0.521503i \(-0.174629\pi\)
0.853249 + 0.521503i \(0.174629\pi\)
\(348\) 23.2958 1.24879
\(349\) −28.3944 −1.51992 −0.759958 0.649972i \(-0.774781\pi\)
−0.759958 + 0.649972i \(0.774781\pi\)
\(350\) 0 0
\(351\) 36.2975 1.93742
\(352\) −16.6404 −0.886936
\(353\) 22.2636 1.18497 0.592485 0.805582i \(-0.298147\pi\)
0.592485 + 0.805582i \(0.298147\pi\)
\(354\) 81.5918 4.33655
\(355\) 0 0
\(356\) −18.5285 −0.982007
\(357\) 10.7251 0.567632
\(358\) 61.5864 3.25494
\(359\) 28.1144 1.48382 0.741910 0.670499i \(-0.233920\pi\)
0.741910 + 0.670499i \(0.233920\pi\)
\(360\) 0 0
\(361\) −2.89025 −0.152118
\(362\) 37.4560 1.96864
\(363\) 16.2228 0.851478
\(364\) −18.0750 −0.947385
\(365\) 0 0
\(366\) −25.5669 −1.33640
\(367\) 10.5062 0.548420 0.274210 0.961670i \(-0.411584\pi\)
0.274210 + 0.961670i \(0.411584\pi\)
\(368\) 0.688122 0.0358708
\(369\) −30.6051 −1.59324
\(370\) 0 0
\(371\) −1.18855 −0.0617067
\(372\) −76.2932 −3.95562
\(373\) −16.2726 −0.842562 −0.421281 0.906930i \(-0.638419\pi\)
−0.421281 + 0.906930i \(0.638419\pi\)
\(374\) −25.4017 −1.31349
\(375\) 0 0
\(376\) −19.1312 −0.986617
\(377\) 8.58381 0.442089
\(378\) 29.0858 1.49601
\(379\) 19.8759 1.02096 0.510478 0.859891i \(-0.329469\pi\)
0.510478 + 0.859891i \(0.329469\pi\)
\(380\) 0 0
\(381\) −17.2670 −0.884614
\(382\) −20.9071 −1.06970
\(383\) −6.83677 −0.349343 −0.174671 0.984627i \(-0.555886\pi\)
−0.174671 + 0.984627i \(0.555886\pi\)
\(384\) 60.9868 3.11222
\(385\) 0 0
\(386\) −20.0096 −1.01846
\(387\) 22.0453 1.12063
\(388\) −20.5124 −1.04136
\(389\) −16.6018 −0.841746 −0.420873 0.907120i \(-0.638276\pi\)
−0.420873 + 0.907120i \(0.638276\pi\)
\(390\) 0 0
\(391\) −1.48016 −0.0748551
\(392\) 18.3989 0.929285
\(393\) 51.1089 2.57810
\(394\) 45.6598 2.30031
\(395\) 0 0
\(396\) −86.3135 −4.33742
\(397\) 27.8469 1.39759 0.698797 0.715320i \(-0.253719\pi\)
0.698797 + 0.715320i \(0.253719\pi\)
\(398\) −21.0784 −1.05657
\(399\) 16.0829 0.805153
\(400\) 0 0
\(401\) 17.5265 0.875230 0.437615 0.899163i \(-0.355823\pi\)
0.437615 + 0.899163i \(0.355823\pi\)
\(402\) 40.4002 2.01498
\(403\) −28.1118 −1.40035
\(404\) −46.9807 −2.33738
\(405\) 0 0
\(406\) 6.87834 0.341366
\(407\) −6.44364 −0.319399
\(408\) 28.3721 1.40463
\(409\) 31.8521 1.57498 0.787492 0.616325i \(-0.211379\pi\)
0.787492 + 0.616325i \(0.211379\pi\)
\(410\) 0 0
\(411\) −58.2120 −2.87139
\(412\) 49.6943 2.44826
\(413\) 15.3287 0.754278
\(414\) −7.90445 −0.388482
\(415\) 0 0
\(416\) 15.9867 0.783813
\(417\) 17.4624 0.855137
\(418\) −38.0914 −1.86311
\(419\) −6.43813 −0.314523 −0.157262 0.987557i \(-0.550267\pi\)
−0.157262 + 0.987557i \(0.550267\pi\)
\(420\) 0 0
\(421\) 33.3455 1.62516 0.812581 0.582848i \(-0.198062\pi\)
0.812581 + 0.582848i \(0.198062\pi\)
\(422\) 15.3844 0.748901
\(423\) 33.1779 1.61316
\(424\) −3.14420 −0.152696
\(425\) 0 0
\(426\) −9.53296 −0.461874
\(427\) −4.80328 −0.232447
\(428\) 7.40335 0.357854
\(429\) −47.4569 −2.29124
\(430\) 0 0
\(431\) −29.7262 −1.43186 −0.715929 0.698173i \(-0.753997\pi\)
−0.715929 + 0.698173i \(0.753997\pi\)
\(432\) 11.6164 0.558894
\(433\) 17.4809 0.840077 0.420039 0.907506i \(-0.362017\pi\)
0.420039 + 0.907506i \(0.362017\pi\)
\(434\) −22.5264 −1.08130
\(435\) 0 0
\(436\) 66.8753 3.20274
\(437\) −2.21960 −0.106178
\(438\) 36.7142 1.75427
\(439\) −19.7835 −0.944216 −0.472108 0.881541i \(-0.656507\pi\)
−0.472108 + 0.881541i \(0.656507\pi\)
\(440\) 0 0
\(441\) −31.9079 −1.51942
\(442\) 24.4039 1.16077
\(443\) −2.71041 −0.128775 −0.0643877 0.997925i \(-0.520509\pi\)
−0.0643877 + 0.997925i \(0.520509\pi\)
\(444\) 16.8006 0.797321
\(445\) 0 0
\(446\) 9.13263 0.432443
\(447\) −21.3144 −1.00814
\(448\) 16.1169 0.761454
\(449\) 27.9994 1.32137 0.660687 0.750662i \(-0.270265\pi\)
0.660687 + 0.750662i \(0.270265\pi\)
\(450\) 0 0
\(451\) 20.3205 0.956854
\(452\) −46.0445 −2.16575
\(453\) −14.7184 −0.691531
\(454\) −26.0265 −1.22148
\(455\) 0 0
\(456\) 42.5457 1.99239
\(457\) 18.7373 0.876492 0.438246 0.898855i \(-0.355600\pi\)
0.438246 + 0.898855i \(0.355600\pi\)
\(458\) 54.3596 2.54006
\(459\) −24.9871 −1.16630
\(460\) 0 0
\(461\) 24.3566 1.13440 0.567200 0.823580i \(-0.308027\pi\)
0.567200 + 0.823580i \(0.308027\pi\)
\(462\) −38.0279 −1.76922
\(463\) −20.0566 −0.932111 −0.466055 0.884756i \(-0.654325\pi\)
−0.466055 + 0.884756i \(0.654325\pi\)
\(464\) 2.74710 0.127531
\(465\) 0 0
\(466\) −44.2469 −2.04970
\(467\) −21.0159 −0.972501 −0.486250 0.873819i \(-0.661636\pi\)
−0.486250 + 0.873819i \(0.661636\pi\)
\(468\) 82.9229 3.83311
\(469\) 7.59002 0.350475
\(470\) 0 0
\(471\) −18.5217 −0.853436
\(472\) 40.5506 1.86649
\(473\) −14.6372 −0.673017
\(474\) −71.3152 −3.27561
\(475\) 0 0
\(476\) 12.4427 0.570312
\(477\) 5.45276 0.249665
\(478\) 31.7449 1.45198
\(479\) −14.8456 −0.678314 −0.339157 0.940730i \(-0.610142\pi\)
−0.339157 + 0.940730i \(0.610142\pi\)
\(480\) 0 0
\(481\) 6.19052 0.282263
\(482\) 2.34497 0.106810
\(483\) −2.21590 −0.100827
\(484\) 18.8210 0.855498
\(485\) 0 0
\(486\) −4.11448 −0.186637
\(487\) 3.38997 0.153614 0.0768072 0.997046i \(-0.475527\pi\)
0.0768072 + 0.997046i \(0.475527\pi\)
\(488\) −12.7066 −0.575200
\(489\) 53.3307 2.41170
\(490\) 0 0
\(491\) −8.64393 −0.390095 −0.195048 0.980794i \(-0.562486\pi\)
−0.195048 + 0.980794i \(0.562486\pi\)
\(492\) −52.9819 −2.38861
\(493\) −5.90906 −0.266131
\(494\) 36.5951 1.64649
\(495\) 0 0
\(496\) −8.99668 −0.403963
\(497\) −1.79097 −0.0803359
\(498\) 105.980 4.74909
\(499\) −8.41032 −0.376498 −0.188249 0.982121i \(-0.560281\pi\)
−0.188249 + 0.982121i \(0.560281\pi\)
\(500\) 0 0
\(501\) −41.2111 −1.84117
\(502\) 48.1775 2.15027
\(503\) −5.09312 −0.227091 −0.113546 0.993533i \(-0.536221\pi\)
−0.113546 + 0.993533i \(0.536221\pi\)
\(504\) 28.4651 1.26794
\(505\) 0 0
\(506\) 5.24822 0.233312
\(507\) 6.38644 0.283632
\(508\) −20.0323 −0.888791
\(509\) 25.7848 1.14289 0.571445 0.820641i \(-0.306383\pi\)
0.571445 + 0.820641i \(0.306383\pi\)
\(510\) 0 0
\(511\) 6.89754 0.305129
\(512\) 13.8634 0.612682
\(513\) −37.4697 −1.65433
\(514\) 64.6861 2.85318
\(515\) 0 0
\(516\) 38.1637 1.68006
\(517\) −22.0287 −0.968822
\(518\) 4.96055 0.217954
\(519\) −10.7846 −0.473392
\(520\) 0 0
\(521\) 40.7411 1.78490 0.892450 0.451146i \(-0.148985\pi\)
0.892450 + 0.451146i \(0.148985\pi\)
\(522\) −31.5559 −1.38116
\(523\) −6.82084 −0.298255 −0.149127 0.988818i \(-0.547646\pi\)
−0.149127 + 0.988818i \(0.547646\pi\)
\(524\) 59.2941 2.59028
\(525\) 0 0
\(526\) 23.1302 1.00852
\(527\) 19.3520 0.842988
\(528\) −15.1878 −0.660963
\(529\) −22.6942 −0.986704
\(530\) 0 0
\(531\) −70.3240 −3.05180
\(532\) 18.6586 0.808955
\(533\) −19.5222 −0.845602
\(534\) 37.4508 1.62065
\(535\) 0 0
\(536\) 20.0786 0.867265
\(537\) −79.2064 −3.41801
\(538\) −45.6304 −1.96726
\(539\) 21.1855 0.912523
\(540\) 0 0
\(541\) −22.5367 −0.968929 −0.484464 0.874811i \(-0.660985\pi\)
−0.484464 + 0.874811i \(0.660985\pi\)
\(542\) 58.7964 2.52552
\(543\) −48.1722 −2.06727
\(544\) −11.0052 −0.471844
\(545\) 0 0
\(546\) 36.5341 1.56352
\(547\) −13.6655 −0.584295 −0.292148 0.956373i \(-0.594370\pi\)
−0.292148 + 0.956373i \(0.594370\pi\)
\(548\) −67.5348 −2.88494
\(549\) 22.0361 0.940478
\(550\) 0 0
\(551\) −8.86100 −0.377491
\(552\) −5.86193 −0.249500
\(553\) −13.3981 −0.569743
\(554\) −64.6256 −2.74568
\(555\) 0 0
\(556\) 20.2591 0.859175
\(557\) 34.1533 1.44712 0.723562 0.690260i \(-0.242504\pi\)
0.723562 + 0.690260i \(0.242504\pi\)
\(558\) 103.345 4.37493
\(559\) 14.0622 0.594767
\(560\) 0 0
\(561\) 32.6692 1.37929
\(562\) −69.6244 −2.93693
\(563\) −3.98769 −0.168061 −0.0840306 0.996463i \(-0.526779\pi\)
−0.0840306 + 0.996463i \(0.526779\pi\)
\(564\) 57.4358 2.41848
\(565\) 0 0
\(566\) −47.2992 −1.98813
\(567\) −13.1112 −0.550620
\(568\) −4.73782 −0.198795
\(569\) −41.4137 −1.73615 −0.868077 0.496429i \(-0.834644\pi\)
−0.868077 + 0.496429i \(0.834644\pi\)
\(570\) 0 0
\(571\) −20.2699 −0.848269 −0.424135 0.905599i \(-0.639422\pi\)
−0.424135 + 0.905599i \(0.639422\pi\)
\(572\) −55.0573 −2.30206
\(573\) 26.8887 1.12329
\(574\) −15.6435 −0.652946
\(575\) 0 0
\(576\) −73.9401 −3.08084
\(577\) 40.1443 1.67123 0.835615 0.549315i \(-0.185111\pi\)
0.835615 + 0.549315i \(0.185111\pi\)
\(578\) 23.0649 0.959373
\(579\) 25.7344 1.06949
\(580\) 0 0
\(581\) 19.9106 0.826032
\(582\) 41.4608 1.71860
\(583\) −3.62040 −0.149942
\(584\) 18.2467 0.755056
\(585\) 0 0
\(586\) 10.7767 0.445182
\(587\) −14.4260 −0.595425 −0.297713 0.954656i \(-0.596224\pi\)
−0.297713 + 0.954656i \(0.596224\pi\)
\(588\) −55.2372 −2.27794
\(589\) 29.0196 1.19573
\(590\) 0 0
\(591\) −58.7232 −2.41555
\(592\) 1.98117 0.0814255
\(593\) 10.7886 0.443036 0.221518 0.975156i \(-0.428899\pi\)
0.221518 + 0.975156i \(0.428899\pi\)
\(594\) 88.5967 3.63517
\(595\) 0 0
\(596\) −24.7279 −1.01290
\(597\) 27.1090 1.10950
\(598\) −5.04205 −0.206185
\(599\) 11.7886 0.481669 0.240834 0.970566i \(-0.422579\pi\)
0.240834 + 0.970566i \(0.422579\pi\)
\(600\) 0 0
\(601\) 24.9629 1.01826 0.509129 0.860690i \(-0.329967\pi\)
0.509129 + 0.860690i \(0.329967\pi\)
\(602\) 11.2682 0.459259
\(603\) −34.8209 −1.41802
\(604\) −17.0756 −0.694796
\(605\) 0 0
\(606\) 94.9600 3.85749
\(607\) 9.36804 0.380237 0.190119 0.981761i \(-0.439113\pi\)
0.190119 + 0.981761i \(0.439113\pi\)
\(608\) −16.5030 −0.669284
\(609\) −8.84624 −0.358468
\(610\) 0 0
\(611\) 21.1634 0.856179
\(612\) −57.0838 −2.30748
\(613\) 11.8795 0.479808 0.239904 0.970797i \(-0.422884\pi\)
0.239904 + 0.970797i \(0.422884\pi\)
\(614\) −5.97839 −0.241268
\(615\) 0 0
\(616\) −18.8996 −0.761488
\(617\) 30.8556 1.24220 0.621100 0.783732i \(-0.286686\pi\)
0.621100 + 0.783732i \(0.286686\pi\)
\(618\) −100.445 −4.04048
\(619\) 41.5695 1.67082 0.835409 0.549629i \(-0.185231\pi\)
0.835409 + 0.549629i \(0.185231\pi\)
\(620\) 0 0
\(621\) 5.16255 0.207166
\(622\) 50.5648 2.02746
\(623\) 7.03592 0.281888
\(624\) 14.5912 0.584114
\(625\) 0 0
\(626\) 77.9206 3.11433
\(627\) 48.9894 1.95645
\(628\) −21.4880 −0.857466
\(629\) −4.26153 −0.169918
\(630\) 0 0
\(631\) 0.426407 0.0169750 0.00848750 0.999964i \(-0.497298\pi\)
0.00848750 + 0.999964i \(0.497298\pi\)
\(632\) −35.4432 −1.40985
\(633\) −19.7859 −0.786419
\(634\) 50.6179 2.01029
\(635\) 0 0
\(636\) 9.43952 0.374301
\(637\) −20.3533 −0.806426
\(638\) 20.9518 0.829489
\(639\) 8.21646 0.325038
\(640\) 0 0
\(641\) 6.82887 0.269724 0.134862 0.990864i \(-0.456941\pi\)
0.134862 + 0.990864i \(0.456941\pi\)
\(642\) −14.9641 −0.590584
\(643\) 9.38104 0.369952 0.184976 0.982743i \(-0.440779\pi\)
0.184976 + 0.982743i \(0.440779\pi\)
\(644\) −2.57078 −0.101303
\(645\) 0 0
\(646\) −25.1919 −0.991163
\(647\) −49.7829 −1.95717 −0.978584 0.205850i \(-0.934004\pi\)
−0.978584 + 0.205850i \(0.934004\pi\)
\(648\) −34.6844 −1.36253
\(649\) 46.6921 1.83283
\(650\) 0 0
\(651\) 28.9712 1.13547
\(652\) 61.8718 2.42309
\(653\) 17.8648 0.699105 0.349553 0.936917i \(-0.386334\pi\)
0.349553 + 0.936917i \(0.386334\pi\)
\(654\) −135.172 −5.28564
\(655\) 0 0
\(656\) −6.24776 −0.243934
\(657\) −31.6440 −1.23455
\(658\) 16.9585 0.661112
\(659\) −32.3949 −1.26193 −0.630963 0.775813i \(-0.717340\pi\)
−0.630963 + 0.775813i \(0.717340\pi\)
\(660\) 0 0
\(661\) −29.6604 −1.15366 −0.576828 0.816866i \(-0.695710\pi\)
−0.576828 + 0.816866i \(0.695710\pi\)
\(662\) 37.2188 1.44655
\(663\) −31.3858 −1.21893
\(664\) 52.6715 2.04405
\(665\) 0 0
\(666\) −22.7576 −0.881841
\(667\) 1.22087 0.0472721
\(668\) −47.8111 −1.84987
\(669\) −11.7455 −0.454107
\(670\) 0 0
\(671\) −14.6310 −0.564825
\(672\) −16.4755 −0.635555
\(673\) −21.9919 −0.847724 −0.423862 0.905727i \(-0.639326\pi\)
−0.423862 + 0.905727i \(0.639326\pi\)
\(674\) −63.8626 −2.45989
\(675\) 0 0
\(676\) 7.40925 0.284971
\(677\) 4.39296 0.168835 0.0844175 0.996430i \(-0.473097\pi\)
0.0844175 + 0.996430i \(0.473097\pi\)
\(678\) 93.0678 3.57425
\(679\) 7.78927 0.298925
\(680\) 0 0
\(681\) 33.4727 1.28268
\(682\) −68.6165 −2.62746
\(683\) −44.2158 −1.69187 −0.845935 0.533286i \(-0.820957\pi\)
−0.845935 + 0.533286i \(0.820957\pi\)
\(684\) −85.6007 −3.27302
\(685\) 0 0
\(686\) −38.1187 −1.45538
\(687\) −69.9120 −2.66731
\(688\) 4.50036 0.171575
\(689\) 3.47818 0.132508
\(690\) 0 0
\(691\) −17.9956 −0.684585 −0.342292 0.939593i \(-0.611203\pi\)
−0.342292 + 0.939593i \(0.611203\pi\)
\(692\) −12.5118 −0.475627
\(693\) 32.7763 1.24507
\(694\) −74.5431 −2.82962
\(695\) 0 0
\(696\) −23.4018 −0.887044
\(697\) 13.4390 0.509040
\(698\) 66.5839 2.52024
\(699\) 56.9060 2.15238
\(700\) 0 0
\(701\) −41.1833 −1.55547 −0.777735 0.628592i \(-0.783631\pi\)
−0.777735 + 0.628592i \(0.783631\pi\)
\(702\) −85.1165 −3.21251
\(703\) −6.39042 −0.241019
\(704\) 49.0931 1.85026
\(705\) 0 0
\(706\) −52.2073 −1.96485
\(707\) 17.8402 0.670951
\(708\) −121.741 −4.57531
\(709\) 31.3551 1.17757 0.588783 0.808291i \(-0.299607\pi\)
0.588783 + 0.808291i \(0.299607\pi\)
\(710\) 0 0
\(711\) 61.4666 2.30518
\(712\) 18.6128 0.697544
\(713\) −3.99830 −0.149738
\(714\) −25.1500 −0.941213
\(715\) 0 0
\(716\) −91.8916 −3.43415
\(717\) −40.8272 −1.52472
\(718\) −65.9273 −2.46038
\(719\) −1.93864 −0.0722989 −0.0361494 0.999346i \(-0.511509\pi\)
−0.0361494 + 0.999346i \(0.511509\pi\)
\(720\) 0 0
\(721\) −18.8707 −0.702780
\(722\) 6.77753 0.252234
\(723\) −3.01587 −0.112161
\(724\) −55.8872 −2.07703
\(725\) 0 0
\(726\) −38.0420 −1.41187
\(727\) −0.936776 −0.0347431 −0.0173715 0.999849i \(-0.505530\pi\)
−0.0173715 + 0.999849i \(0.505530\pi\)
\(728\) 18.1572 0.672951
\(729\) −24.3128 −0.900472
\(730\) 0 0
\(731\) −9.68035 −0.358041
\(732\) 38.1477 1.40998
\(733\) −20.1520 −0.744332 −0.372166 0.928166i \(-0.621385\pi\)
−0.372166 + 0.928166i \(0.621385\pi\)
\(734\) −24.6367 −0.909358
\(735\) 0 0
\(736\) 2.27377 0.0838124
\(737\) 23.1196 0.851622
\(738\) 71.7679 2.64181
\(739\) −8.45213 −0.310917 −0.155458 0.987842i \(-0.549685\pi\)
−0.155458 + 0.987842i \(0.549685\pi\)
\(740\) 0 0
\(741\) −47.0650 −1.72898
\(742\) 2.78712 0.102318
\(743\) 0.812941 0.0298239 0.0149120 0.999889i \(-0.495253\pi\)
0.0149120 + 0.999889i \(0.495253\pi\)
\(744\) 76.6404 2.80977
\(745\) 0 0
\(746\) 38.1587 1.39709
\(747\) −91.3444 −3.34212
\(748\) 37.9012 1.38581
\(749\) −2.81131 −0.102723
\(750\) 0 0
\(751\) 19.5689 0.714080 0.357040 0.934089i \(-0.383786\pi\)
0.357040 + 0.934089i \(0.383786\pi\)
\(752\) 6.77297 0.246985
\(753\) −61.9612 −2.25799
\(754\) −20.1287 −0.733045
\(755\) 0 0
\(756\) −43.3981 −1.57837
\(757\) −15.0406 −0.546661 −0.273330 0.961920i \(-0.588125\pi\)
−0.273330 + 0.961920i \(0.588125\pi\)
\(758\) −46.6083 −1.69289
\(759\) −6.74974 −0.245000
\(760\) 0 0
\(761\) −32.0667 −1.16242 −0.581209 0.813754i \(-0.697420\pi\)
−0.581209 + 0.813754i \(0.697420\pi\)
\(762\) 40.4905 1.46681
\(763\) −25.3949 −0.919357
\(764\) 31.1950 1.12860
\(765\) 0 0
\(766\) 16.0320 0.579260
\(767\) −44.8580 −1.61973
\(768\) −69.8449 −2.52031
\(769\) 20.1660 0.727204 0.363602 0.931554i \(-0.381547\pi\)
0.363602 + 0.931554i \(0.381547\pi\)
\(770\) 0 0
\(771\) −83.1930 −2.99612
\(772\) 29.8558 1.07454
\(773\) −9.25347 −0.332824 −0.166412 0.986056i \(-0.553218\pi\)
−0.166412 + 0.986056i \(0.553218\pi\)
\(774\) −51.6955 −1.85816
\(775\) 0 0
\(776\) 20.6057 0.739703
\(777\) −6.37978 −0.228873
\(778\) 38.9307 1.39573
\(779\) 20.1527 0.722044
\(780\) 0 0
\(781\) −5.45538 −0.195209
\(782\) 3.47093 0.124120
\(783\) 20.6098 0.736534
\(784\) −6.51371 −0.232633
\(785\) 0 0
\(786\) −119.849 −4.27486
\(787\) −2.93319 −0.104557 −0.0522784 0.998633i \(-0.516648\pi\)
−0.0522784 + 0.998633i \(0.516648\pi\)
\(788\) −68.1279 −2.42696
\(789\) −29.7478 −1.05905
\(790\) 0 0
\(791\) 17.4847 0.621686
\(792\) 86.7063 3.08098
\(793\) 14.0563 0.499154
\(794\) −65.3000 −2.31741
\(795\) 0 0
\(796\) 31.4506 1.11474
\(797\) −27.3198 −0.967718 −0.483859 0.875146i \(-0.660765\pi\)
−0.483859 + 0.875146i \(0.660765\pi\)
\(798\) −37.7139 −1.33506
\(799\) −14.5688 −0.515407
\(800\) 0 0
\(801\) −32.2788 −1.14052
\(802\) −41.0990 −1.45125
\(803\) 21.0103 0.741437
\(804\) −60.2801 −2.12592
\(805\) 0 0
\(806\) 65.9211 2.32197
\(807\) 58.6853 2.06582
\(808\) 47.1945 1.66030
\(809\) −2.27241 −0.0798938 −0.0399469 0.999202i \(-0.512719\pi\)
−0.0399469 + 0.999202i \(0.512719\pi\)
\(810\) 0 0
\(811\) −9.79682 −0.344013 −0.172006 0.985096i \(-0.555025\pi\)
−0.172006 + 0.985096i \(0.555025\pi\)
\(812\) −10.2630 −0.360160
\(813\) −75.6182 −2.65205
\(814\) 15.1101 0.529609
\(815\) 0 0
\(816\) −10.0445 −0.351628
\(817\) −14.5163 −0.507861
\(818\) −74.6921 −2.61155
\(819\) −31.4888 −1.10031
\(820\) 0 0
\(821\) 20.5651 0.717726 0.358863 0.933390i \(-0.383165\pi\)
0.358863 + 0.933390i \(0.383165\pi\)
\(822\) 136.505 4.76116
\(823\) 10.5127 0.366449 0.183225 0.983071i \(-0.441346\pi\)
0.183225 + 0.983071i \(0.441346\pi\)
\(824\) −49.9204 −1.73906
\(825\) 0 0
\(826\) −35.9454 −1.25070
\(827\) −33.6008 −1.16842 −0.584208 0.811604i \(-0.698595\pi\)
−0.584208 + 0.811604i \(0.698595\pi\)
\(828\) 11.7940 0.409871
\(829\) 33.7332 1.17160 0.585801 0.810455i \(-0.300780\pi\)
0.585801 + 0.810455i \(0.300780\pi\)
\(830\) 0 0
\(831\) 83.1151 2.88323
\(832\) −47.1646 −1.63514
\(833\) 14.0111 0.485456
\(834\) −40.9487 −1.41794
\(835\) 0 0
\(836\) 56.8352 1.96569
\(837\) −67.4966 −2.33302
\(838\) 15.0972 0.521524
\(839\) −50.5894 −1.74654 −0.873270 0.487237i \(-0.838005\pi\)
−0.873270 + 0.487237i \(0.838005\pi\)
\(840\) 0 0
\(841\) −24.1261 −0.831934
\(842\) −78.1941 −2.69475
\(843\) 89.5441 3.08406
\(844\) −22.9547 −0.790133
\(845\) 0 0
\(846\) −77.8010 −2.67485
\(847\) −7.14699 −0.245573
\(848\) 1.11313 0.0382251
\(849\) 60.8315 2.08773
\(850\) 0 0
\(851\) 0.880470 0.0301821
\(852\) 14.2239 0.487303
\(853\) −4.82513 −0.165209 −0.0826046 0.996582i \(-0.526324\pi\)
−0.0826046 + 0.996582i \(0.526324\pi\)
\(854\) 11.2635 0.385430
\(855\) 0 0
\(856\) −7.43704 −0.254193
\(857\) 27.8017 0.949689 0.474844 0.880070i \(-0.342504\pi\)
0.474844 + 0.880070i \(0.342504\pi\)
\(858\) 111.285 3.79920
\(859\) −1.40326 −0.0478785 −0.0239392 0.999713i \(-0.507621\pi\)
−0.0239392 + 0.999713i \(0.507621\pi\)
\(860\) 0 0
\(861\) 20.1191 0.685657
\(862\) 69.7068 2.37422
\(863\) −20.1198 −0.684887 −0.342444 0.939538i \(-0.611255\pi\)
−0.342444 + 0.939538i \(0.611255\pi\)
\(864\) 38.3842 1.30586
\(865\) 0 0
\(866\) −40.9921 −1.39297
\(867\) −29.6638 −1.00744
\(868\) 33.6110 1.14083
\(869\) −40.8112 −1.38442
\(870\) 0 0
\(871\) −22.2114 −0.752605
\(872\) −67.1796 −2.27499
\(873\) −35.7350 −1.20945
\(874\) 5.20488 0.176058
\(875\) 0 0
\(876\) −54.7804 −1.85086
\(877\) 22.9122 0.773689 0.386845 0.922145i \(-0.373565\pi\)
0.386845 + 0.922145i \(0.373565\pi\)
\(878\) 46.3917 1.56564
\(879\) −13.8600 −0.467485
\(880\) 0 0
\(881\) 31.6497 1.06631 0.533153 0.846019i \(-0.321007\pi\)
0.533153 + 0.846019i \(0.321007\pi\)
\(882\) 74.8229 2.51942
\(883\) 5.43312 0.182839 0.0914195 0.995812i \(-0.470860\pi\)
0.0914195 + 0.995812i \(0.470860\pi\)
\(884\) −36.4124 −1.22468
\(885\) 0 0
\(886\) 6.35582 0.213528
\(887\) 28.1102 0.943847 0.471923 0.881640i \(-0.343560\pi\)
0.471923 + 0.881640i \(0.343560\pi\)
\(888\) −16.8771 −0.566357
\(889\) 7.60698 0.255130
\(890\) 0 0
\(891\) −39.9375 −1.33796
\(892\) −13.6266 −0.456252
\(893\) −21.8468 −0.731075
\(894\) 49.9815 1.67163
\(895\) 0 0
\(896\) −26.8678 −0.897591
\(897\) 6.48460 0.216514
\(898\) −65.6577 −2.19102
\(899\) −15.9619 −0.532359
\(900\) 0 0
\(901\) −2.39437 −0.0797680
\(902\) −47.6508 −1.58660
\(903\) −14.4921 −0.482267
\(904\) 46.2541 1.53839
\(905\) 0 0
\(906\) 34.5141 1.14666
\(907\) 34.1991 1.13556 0.567781 0.823180i \(-0.307802\pi\)
0.567781 + 0.823180i \(0.307802\pi\)
\(908\) 38.8335 1.28874
\(909\) −81.8461 −2.71466
\(910\) 0 0
\(911\) −57.4208 −1.90244 −0.951218 0.308519i \(-0.900167\pi\)
−0.951218 + 0.308519i \(0.900167\pi\)
\(912\) −15.0623 −0.498764
\(913\) 60.6488 2.00718
\(914\) −43.9382 −1.45335
\(915\) 0 0
\(916\) −81.1086 −2.67990
\(917\) −22.5161 −0.743546
\(918\) 58.5939 1.93389
\(919\) 2.33801 0.0771238 0.0385619 0.999256i \(-0.487722\pi\)
0.0385619 + 0.999256i \(0.487722\pi\)
\(920\) 0 0
\(921\) 7.68882 0.253355
\(922\) −57.1154 −1.88099
\(923\) 5.24108 0.172512
\(924\) 56.7405 1.86663
\(925\) 0 0
\(926\) 47.0321 1.54557
\(927\) 86.5734 2.84344
\(928\) 9.07729 0.297977
\(929\) 28.8794 0.947504 0.473752 0.880658i \(-0.342899\pi\)
0.473752 + 0.880658i \(0.342899\pi\)
\(930\) 0 0
\(931\) 21.0105 0.688592
\(932\) 66.0197 2.16255
\(933\) −65.0315 −2.12903
\(934\) 49.2816 1.61254
\(935\) 0 0
\(936\) −83.3003 −2.72276
\(937\) 56.3605 1.84122 0.920608 0.390487i \(-0.127693\pi\)
0.920608 + 0.390487i \(0.127693\pi\)
\(938\) −17.7983 −0.581137
\(939\) −100.214 −3.27036
\(940\) 0 0
\(941\) −27.0489 −0.881767 −0.440884 0.897564i \(-0.645335\pi\)
−0.440884 + 0.897564i \(0.645335\pi\)
\(942\) 43.4328 1.41512
\(943\) −2.77663 −0.0904194
\(944\) −14.3560 −0.467249
\(945\) 0 0
\(946\) 34.3236 1.11596
\(947\) −9.75421 −0.316969 −0.158485 0.987361i \(-0.550661\pi\)
−0.158485 + 0.987361i \(0.550661\pi\)
\(948\) 106.408 3.45596
\(949\) −20.1850 −0.655231
\(950\) 0 0
\(951\) −65.0998 −2.11100
\(952\) −12.4994 −0.405107
\(953\) −6.26546 −0.202958 −0.101479 0.994838i \(-0.532357\pi\)
−0.101479 + 0.994838i \(0.532357\pi\)
\(954\) −12.7865 −0.413979
\(955\) 0 0
\(956\) −47.3658 −1.53192
\(957\) −26.9461 −0.871044
\(958\) 34.8125 1.12474
\(959\) 25.6454 0.828132
\(960\) 0 0
\(961\) 21.2748 0.686284
\(962\) −14.5165 −0.468032
\(963\) 12.8975 0.415617
\(964\) −3.49887 −0.112691
\(965\) 0 0
\(966\) 5.19621 0.167185
\(967\) 15.8446 0.509527 0.254763 0.967003i \(-0.418002\pi\)
0.254763 + 0.967003i \(0.418002\pi\)
\(968\) −18.9066 −0.607682
\(969\) 32.3994 1.04082
\(970\) 0 0
\(971\) 33.9429 1.08928 0.544640 0.838670i \(-0.316666\pi\)
0.544640 + 0.838670i \(0.316666\pi\)
\(972\) 6.13911 0.196912
\(973\) −7.69308 −0.246629
\(974\) −7.94937 −0.254714
\(975\) 0 0
\(976\) 4.49847 0.143993
\(977\) 33.0383 1.05699 0.528495 0.848937i \(-0.322757\pi\)
0.528495 + 0.848937i \(0.322757\pi\)
\(978\) −125.059 −3.99894
\(979\) 21.4318 0.684962
\(980\) 0 0
\(981\) 116.505 3.71971
\(982\) 20.2697 0.646833
\(983\) 13.6593 0.435663 0.217831 0.975986i \(-0.430102\pi\)
0.217831 + 0.975986i \(0.430102\pi\)
\(984\) 53.2230 1.69669
\(985\) 0 0
\(986\) 13.8566 0.441283
\(987\) −21.8104 −0.694233
\(988\) −54.6026 −1.73714
\(989\) 2.00005 0.0635978
\(990\) 0 0
\(991\) −47.7712 −1.51750 −0.758751 0.651381i \(-0.774190\pi\)
−0.758751 + 0.651381i \(0.774190\pi\)
\(992\) −29.7279 −0.943861
\(993\) −47.8671 −1.51902
\(994\) 4.19976 0.133208
\(995\) 0 0
\(996\) −158.131 −5.01056
\(997\) −15.2848 −0.484073 −0.242036 0.970267i \(-0.577815\pi\)
−0.242036 + 0.970267i \(0.577815\pi\)
\(998\) 19.7219 0.624287
\(999\) 14.8635 0.470260
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.i.1.1 15
5.4 even 2 1205.2.a.c.1.15 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.a.c.1.15 15 5.4 even 2
6025.2.a.i.1.1 15 1.1 even 1 trivial