Properties

Label 4018.2.a.bt.1.9
Level $4018$
Weight $2$
Character 4018.1
Self dual yes
Analytic conductor $32.084$
Analytic rank $0$
Dimension $10$
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] = [4018,2,Mod(1,4018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4018, 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("4018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.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: \(32.0838915322\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - 23x^{8} + 19x^{7} + 181x^{6} - 109x^{5} - 579x^{4} + 231x^{3} + 608x^{2} - 204x - 12 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 574)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-2.19478\) of defining polynomial
Character \(\chi\) \(=\) 4018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.19478 q^{3} +1.00000 q^{4} +2.75416 q^{5} +2.19478 q^{6} +1.00000 q^{8} +1.81704 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.19478 q^{3} +1.00000 q^{4} +2.75416 q^{5} +2.19478 q^{6} +1.00000 q^{8} +1.81704 q^{9} +2.75416 q^{10} +0.941986 q^{11} +2.19478 q^{12} +4.37963 q^{13} +6.04477 q^{15} +1.00000 q^{16} +1.93712 q^{17} +1.81704 q^{18} -2.67674 q^{19} +2.75416 q^{20} +0.941986 q^{22} -4.18718 q^{23} +2.19478 q^{24} +2.58541 q^{25} +4.37963 q^{26} -2.59633 q^{27} -0.145436 q^{29} +6.04477 q^{30} +7.42842 q^{31} +1.00000 q^{32} +2.06745 q^{33} +1.93712 q^{34} +1.81704 q^{36} -10.7123 q^{37} -2.67674 q^{38} +9.61232 q^{39} +2.75416 q^{40} -1.00000 q^{41} +8.62329 q^{43} +0.941986 q^{44} +5.00443 q^{45} -4.18718 q^{46} -4.43943 q^{47} +2.19478 q^{48} +2.58541 q^{50} +4.25155 q^{51} +4.37963 q^{52} -5.12705 q^{53} -2.59633 q^{54} +2.59438 q^{55} -5.87484 q^{57} -0.145436 q^{58} +5.20297 q^{59} +6.04477 q^{60} -1.15333 q^{61} +7.42842 q^{62} +1.00000 q^{64} +12.0622 q^{65} +2.06745 q^{66} +0.684330 q^{67} +1.93712 q^{68} -9.18993 q^{69} +4.10892 q^{71} +1.81704 q^{72} -15.0653 q^{73} -10.7123 q^{74} +5.67440 q^{75} -2.67674 q^{76} +9.61232 q^{78} -12.4752 q^{79} +2.75416 q^{80} -11.1495 q^{81} -1.00000 q^{82} -11.3239 q^{83} +5.33514 q^{85} +8.62329 q^{86} -0.319198 q^{87} +0.941986 q^{88} +11.7305 q^{89} +5.00443 q^{90} -4.18718 q^{92} +16.3037 q^{93} -4.43943 q^{94} -7.37216 q^{95} +2.19478 q^{96} +3.41721 q^{97} +1.71163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9} + 2 q^{10} + 11 q^{11} - q^{12} - 4 q^{13} + 4 q^{15} + 10 q^{16} - 5 q^{17} + 17 q^{18} + q^{19} + 2 q^{20} + 11 q^{22} + 9 q^{23} - q^{24} + 24 q^{25} - 4 q^{26} - 7 q^{27} + 23 q^{29} + 4 q^{30} + 5 q^{31} + 10 q^{32} + 5 q^{33} - 5 q^{34} + 17 q^{36} + 16 q^{37} + q^{38} - 7 q^{39} + 2 q^{40} - 10 q^{41} + 20 q^{43} + 11 q^{44} + 42 q^{45} + 9 q^{46} + 16 q^{47} - q^{48} + 24 q^{50} + 13 q^{51} - 4 q^{52} + 26 q^{53} - 7 q^{54} - 7 q^{55} + 37 q^{57} + 23 q^{58} + 10 q^{59} + 4 q^{60} + 5 q^{62} + 10 q^{64} + 18 q^{65} + 5 q^{66} + 7 q^{67} - 5 q^{68} - 39 q^{69} + 5 q^{71} + 17 q^{72} + 13 q^{73} + 16 q^{74} - 19 q^{75} + q^{76} - 7 q^{78} - q^{79} + 2 q^{80} + 18 q^{81} - 10 q^{82} - 21 q^{83} + 34 q^{85} + 20 q^{86} - 2 q^{87} + 11 q^{88} - 6 q^{89} + 42 q^{90} + 9 q^{92} - 5 q^{93} + 16 q^{94} + 24 q^{95} - q^{96} - 29 q^{97} + 48 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.19478 1.26715 0.633577 0.773679i \(-0.281586\pi\)
0.633577 + 0.773679i \(0.281586\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.75416 1.23170 0.615849 0.787864i \(-0.288813\pi\)
0.615849 + 0.787864i \(0.288813\pi\)
\(6\) 2.19478 0.896014
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.81704 0.605681
\(10\) 2.75416 0.870943
\(11\) 0.941986 0.284019 0.142010 0.989865i \(-0.454644\pi\)
0.142010 + 0.989865i \(0.454644\pi\)
\(12\) 2.19478 0.633577
\(13\) 4.37963 1.21469 0.607346 0.794437i \(-0.292234\pi\)
0.607346 + 0.794437i \(0.292234\pi\)
\(14\) 0 0
\(15\) 6.04477 1.56075
\(16\) 1.00000 0.250000
\(17\) 1.93712 0.469821 0.234910 0.972017i \(-0.424520\pi\)
0.234910 + 0.972017i \(0.424520\pi\)
\(18\) 1.81704 0.428281
\(19\) −2.67674 −0.614085 −0.307043 0.951696i \(-0.599339\pi\)
−0.307043 + 0.951696i \(0.599339\pi\)
\(20\) 2.75416 0.615849
\(21\) 0 0
\(22\) 0.941986 0.200832
\(23\) −4.18718 −0.873088 −0.436544 0.899683i \(-0.643798\pi\)
−0.436544 + 0.899683i \(0.643798\pi\)
\(24\) 2.19478 0.448007
\(25\) 2.58541 0.517082
\(26\) 4.37963 0.858917
\(27\) −2.59633 −0.499664
\(28\) 0 0
\(29\) −0.145436 −0.0270067 −0.0135034 0.999909i \(-0.504298\pi\)
−0.0135034 + 0.999909i \(0.504298\pi\)
\(30\) 6.04477 1.10362
\(31\) 7.42842 1.33418 0.667092 0.744976i \(-0.267539\pi\)
0.667092 + 0.744976i \(0.267539\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.06745 0.359897
\(34\) 1.93712 0.332213
\(35\) 0 0
\(36\) 1.81704 0.302840
\(37\) −10.7123 −1.76108 −0.880542 0.473969i \(-0.842821\pi\)
−0.880542 + 0.473969i \(0.842821\pi\)
\(38\) −2.67674 −0.434224
\(39\) 9.61232 1.53920
\(40\) 2.75416 0.435471
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 8.62329 1.31504 0.657520 0.753437i \(-0.271606\pi\)
0.657520 + 0.753437i \(0.271606\pi\)
\(44\) 0.941986 0.142010
\(45\) 5.00443 0.746016
\(46\) −4.18718 −0.617366
\(47\) −4.43943 −0.647558 −0.323779 0.946133i \(-0.604953\pi\)
−0.323779 + 0.946133i \(0.604953\pi\)
\(48\) 2.19478 0.316789
\(49\) 0 0
\(50\) 2.58541 0.365632
\(51\) 4.25155 0.595335
\(52\) 4.37963 0.607346
\(53\) −5.12705 −0.704254 −0.352127 0.935952i \(-0.614541\pi\)
−0.352127 + 0.935952i \(0.614541\pi\)
\(54\) −2.59633 −0.353315
\(55\) 2.59438 0.349826
\(56\) 0 0
\(57\) −5.87484 −0.778141
\(58\) −0.145436 −0.0190966
\(59\) 5.20297 0.677368 0.338684 0.940900i \(-0.390018\pi\)
0.338684 + 0.940900i \(0.390018\pi\)
\(60\) 6.04477 0.780376
\(61\) −1.15333 −0.147669 −0.0738344 0.997271i \(-0.523524\pi\)
−0.0738344 + 0.997271i \(0.523524\pi\)
\(62\) 7.42842 0.943410
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 12.0622 1.49613
\(66\) 2.06745 0.254485
\(67\) 0.684330 0.0836042 0.0418021 0.999126i \(-0.486690\pi\)
0.0418021 + 0.999126i \(0.486690\pi\)
\(68\) 1.93712 0.234910
\(69\) −9.18993 −1.10634
\(70\) 0 0
\(71\) 4.10892 0.487640 0.243820 0.969821i \(-0.421599\pi\)
0.243820 + 0.969821i \(0.421599\pi\)
\(72\) 1.81704 0.214140
\(73\) −15.0653 −1.76326 −0.881630 0.471941i \(-0.843553\pi\)
−0.881630 + 0.471941i \(0.843553\pi\)
\(74\) −10.7123 −1.24527
\(75\) 5.67440 0.655223
\(76\) −2.67674 −0.307043
\(77\) 0 0
\(78\) 9.61232 1.08838
\(79\) −12.4752 −1.40357 −0.701787 0.712387i \(-0.747614\pi\)
−0.701787 + 0.712387i \(0.747614\pi\)
\(80\) 2.75416 0.307925
\(81\) −11.1495 −1.23883
\(82\) −1.00000 −0.110432
\(83\) −11.3239 −1.24296 −0.621482 0.783428i \(-0.713469\pi\)
−0.621482 + 0.783428i \(0.713469\pi\)
\(84\) 0 0
\(85\) 5.33514 0.578678
\(86\) 8.62329 0.929873
\(87\) −0.319198 −0.0342217
\(88\) 0.941986 0.100416
\(89\) 11.7305 1.24343 0.621715 0.783244i \(-0.286436\pi\)
0.621715 + 0.783244i \(0.286436\pi\)
\(90\) 5.00443 0.527513
\(91\) 0 0
\(92\) −4.18718 −0.436544
\(93\) 16.3037 1.69062
\(94\) −4.43943 −0.457892
\(95\) −7.37216 −0.756368
\(96\) 2.19478 0.224003
\(97\) 3.41721 0.346965 0.173482 0.984837i \(-0.444498\pi\)
0.173482 + 0.984837i \(0.444498\pi\)
\(98\) 0 0
\(99\) 1.71163 0.172025
\(100\) 2.58541 0.258541
\(101\) −1.15934 −0.115359 −0.0576795 0.998335i \(-0.518370\pi\)
−0.0576795 + 0.998335i \(0.518370\pi\)
\(102\) 4.25155 0.420966
\(103\) −6.82644 −0.672629 −0.336315 0.941750i \(-0.609181\pi\)
−0.336315 + 0.941750i \(0.609181\pi\)
\(104\) 4.37963 0.429458
\(105\) 0 0
\(106\) −5.12705 −0.497983
\(107\) 4.00282 0.386968 0.193484 0.981103i \(-0.438021\pi\)
0.193484 + 0.981103i \(0.438021\pi\)
\(108\) −2.59633 −0.249832
\(109\) 12.6076 1.20759 0.603796 0.797139i \(-0.293654\pi\)
0.603796 + 0.797139i \(0.293654\pi\)
\(110\) 2.59438 0.247365
\(111\) −23.5110 −2.23156
\(112\) 0 0
\(113\) 16.1114 1.51563 0.757817 0.652467i \(-0.226266\pi\)
0.757817 + 0.652467i \(0.226266\pi\)
\(114\) −5.87484 −0.550229
\(115\) −11.5322 −1.07538
\(116\) −0.145436 −0.0135034
\(117\) 7.95798 0.735715
\(118\) 5.20297 0.478972
\(119\) 0 0
\(120\) 6.04477 0.551809
\(121\) −10.1127 −0.919333
\(122\) −1.15333 −0.104418
\(123\) −2.19478 −0.197896
\(124\) 7.42842 0.667092
\(125\) −6.65017 −0.594810
\(126\) 0 0
\(127\) 13.0764 1.16034 0.580172 0.814494i \(-0.302985\pi\)
0.580172 + 0.814494i \(0.302985\pi\)
\(128\) 1.00000 0.0883883
\(129\) 18.9262 1.66636
\(130\) 12.0622 1.05793
\(131\) −7.67673 −0.670719 −0.335360 0.942090i \(-0.608858\pi\)
−0.335360 + 0.942090i \(0.608858\pi\)
\(132\) 2.06745 0.179948
\(133\) 0 0
\(134\) 0.684330 0.0591171
\(135\) −7.15071 −0.615435
\(136\) 1.93712 0.166107
\(137\) 8.04741 0.687536 0.343768 0.939055i \(-0.388297\pi\)
0.343768 + 0.939055i \(0.388297\pi\)
\(138\) −9.18993 −0.782298
\(139\) −16.8676 −1.43069 −0.715346 0.698771i \(-0.753731\pi\)
−0.715346 + 0.698771i \(0.753731\pi\)
\(140\) 0 0
\(141\) −9.74356 −0.820556
\(142\) 4.10892 0.344813
\(143\) 4.12555 0.344996
\(144\) 1.81704 0.151420
\(145\) −0.400553 −0.0332641
\(146\) −15.0653 −1.24681
\(147\) 0 0
\(148\) −10.7123 −0.880542
\(149\) 13.3134 1.09067 0.545337 0.838217i \(-0.316402\pi\)
0.545337 + 0.838217i \(0.316402\pi\)
\(150\) 5.67440 0.463312
\(151\) −5.12798 −0.417309 −0.208655 0.977989i \(-0.566908\pi\)
−0.208655 + 0.977989i \(0.566908\pi\)
\(152\) −2.67674 −0.217112
\(153\) 3.51983 0.284561
\(154\) 0 0
\(155\) 20.4591 1.64331
\(156\) 9.61232 0.769601
\(157\) 18.3332 1.46315 0.731573 0.681764i \(-0.238787\pi\)
0.731573 + 0.681764i \(0.238787\pi\)
\(158\) −12.4752 −0.992476
\(159\) −11.2527 −0.892399
\(160\) 2.75416 0.217736
\(161\) 0 0
\(162\) −11.1495 −0.875986
\(163\) 10.6522 0.834345 0.417173 0.908827i \(-0.363021\pi\)
0.417173 + 0.908827i \(0.363021\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 5.69409 0.443284
\(166\) −11.3239 −0.878908
\(167\) −10.7679 −0.833247 −0.416623 0.909079i \(-0.636787\pi\)
−0.416623 + 0.909079i \(0.636787\pi\)
\(168\) 0 0
\(169\) 6.18119 0.475476
\(170\) 5.33514 0.409187
\(171\) −4.86374 −0.371940
\(172\) 8.62329 0.657520
\(173\) 4.69347 0.356838 0.178419 0.983955i \(-0.442902\pi\)
0.178419 + 0.983955i \(0.442902\pi\)
\(174\) −0.319198 −0.0241984
\(175\) 0 0
\(176\) 0.941986 0.0710049
\(177\) 11.4193 0.858330
\(178\) 11.7305 0.879237
\(179\) −1.85740 −0.138829 −0.0694145 0.997588i \(-0.522113\pi\)
−0.0694145 + 0.997588i \(0.522113\pi\)
\(180\) 5.00443 0.373008
\(181\) −22.2499 −1.65382 −0.826912 0.562331i \(-0.809905\pi\)
−0.826912 + 0.562331i \(0.809905\pi\)
\(182\) 0 0
\(183\) −2.53130 −0.187119
\(184\) −4.18718 −0.308683
\(185\) −29.5033 −2.16912
\(186\) 16.3037 1.19545
\(187\) 1.82474 0.133438
\(188\) −4.43943 −0.323779
\(189\) 0 0
\(190\) −7.37216 −0.534833
\(191\) −20.0369 −1.44982 −0.724910 0.688843i \(-0.758119\pi\)
−0.724910 + 0.688843i \(0.758119\pi\)
\(192\) 2.19478 0.158394
\(193\) 16.1054 1.15929 0.579646 0.814868i \(-0.303191\pi\)
0.579646 + 0.814868i \(0.303191\pi\)
\(194\) 3.41721 0.245341
\(195\) 26.4739 1.89583
\(196\) 0 0
\(197\) 14.7466 1.05065 0.525327 0.850901i \(-0.323943\pi\)
0.525327 + 0.850901i \(0.323943\pi\)
\(198\) 1.71163 0.121640
\(199\) 19.0221 1.34844 0.674221 0.738530i \(-0.264480\pi\)
0.674221 + 0.738530i \(0.264480\pi\)
\(200\) 2.58541 0.182816
\(201\) 1.50195 0.105939
\(202\) −1.15934 −0.0815712
\(203\) 0 0
\(204\) 4.25155 0.297668
\(205\) −2.75416 −0.192359
\(206\) −6.82644 −0.475621
\(207\) −7.60829 −0.528812
\(208\) 4.37963 0.303673
\(209\) −2.52145 −0.174412
\(210\) 0 0
\(211\) −3.92033 −0.269887 −0.134943 0.990853i \(-0.543085\pi\)
−0.134943 + 0.990853i \(0.543085\pi\)
\(212\) −5.12705 −0.352127
\(213\) 9.01817 0.617915
\(214\) 4.00282 0.273627
\(215\) 23.7499 1.61973
\(216\) −2.59633 −0.176658
\(217\) 0 0
\(218\) 12.6076 0.853896
\(219\) −33.0650 −2.23432
\(220\) 2.59438 0.174913
\(221\) 8.48388 0.570687
\(222\) −23.5110 −1.57795
\(223\) 19.3451 1.29544 0.647722 0.761877i \(-0.275722\pi\)
0.647722 + 0.761877i \(0.275722\pi\)
\(224\) 0 0
\(225\) 4.69780 0.313187
\(226\) 16.1114 1.07172
\(227\) −26.5527 −1.76236 −0.881182 0.472777i \(-0.843252\pi\)
−0.881182 + 0.472777i \(0.843252\pi\)
\(228\) −5.87484 −0.389070
\(229\) 8.09922 0.535211 0.267606 0.963529i \(-0.413768\pi\)
0.267606 + 0.963529i \(0.413768\pi\)
\(230\) −11.5322 −0.760409
\(231\) 0 0
\(232\) −0.145436 −0.00954831
\(233\) 7.49252 0.490851 0.245426 0.969415i \(-0.421072\pi\)
0.245426 + 0.969415i \(0.421072\pi\)
\(234\) 7.95798 0.520229
\(235\) −12.2269 −0.797596
\(236\) 5.20297 0.338684
\(237\) −27.3803 −1.77854
\(238\) 0 0
\(239\) −6.63573 −0.429230 −0.214615 0.976699i \(-0.568850\pi\)
−0.214615 + 0.976699i \(0.568850\pi\)
\(240\) 6.04477 0.390188
\(241\) −7.64140 −0.492226 −0.246113 0.969241i \(-0.579153\pi\)
−0.246113 + 0.969241i \(0.579153\pi\)
\(242\) −10.1127 −0.650067
\(243\) −16.6816 −1.07013
\(244\) −1.15333 −0.0738344
\(245\) 0 0
\(246\) −2.19478 −0.139934
\(247\) −11.7231 −0.745924
\(248\) 7.42842 0.471705
\(249\) −24.8535 −1.57503
\(250\) −6.65017 −0.420594
\(251\) 1.08536 0.0685073 0.0342536 0.999413i \(-0.489095\pi\)
0.0342536 + 0.999413i \(0.489095\pi\)
\(252\) 0 0
\(253\) −3.94427 −0.247974
\(254\) 13.0764 0.820488
\(255\) 11.7094 0.733274
\(256\) 1.00000 0.0625000
\(257\) −29.4160 −1.83492 −0.917460 0.397827i \(-0.869764\pi\)
−0.917460 + 0.397827i \(0.869764\pi\)
\(258\) 18.9262 1.17829
\(259\) 0 0
\(260\) 12.0622 0.748067
\(261\) −0.264263 −0.0163574
\(262\) −7.67673 −0.474270
\(263\) −8.69298 −0.536032 −0.268016 0.963414i \(-0.586368\pi\)
−0.268016 + 0.963414i \(0.586368\pi\)
\(264\) 2.06745 0.127243
\(265\) −14.1207 −0.867429
\(266\) 0 0
\(267\) 25.7458 1.57562
\(268\) 0.684330 0.0418021
\(269\) 2.35065 0.143322 0.0716608 0.997429i \(-0.477170\pi\)
0.0716608 + 0.997429i \(0.477170\pi\)
\(270\) −7.15071 −0.435178
\(271\) −7.65699 −0.465129 −0.232564 0.972581i \(-0.574712\pi\)
−0.232564 + 0.972581i \(0.574712\pi\)
\(272\) 1.93712 0.117455
\(273\) 0 0
\(274\) 8.04741 0.486162
\(275\) 2.43542 0.146861
\(276\) −9.18993 −0.553169
\(277\) 6.81703 0.409596 0.204798 0.978804i \(-0.434346\pi\)
0.204798 + 0.978804i \(0.434346\pi\)
\(278\) −16.8676 −1.01165
\(279\) 13.4977 0.808089
\(280\) 0 0
\(281\) −26.0572 −1.55444 −0.777222 0.629227i \(-0.783372\pi\)
−0.777222 + 0.629227i \(0.783372\pi\)
\(282\) −9.74356 −0.580221
\(283\) −15.6449 −0.929991 −0.464996 0.885313i \(-0.653944\pi\)
−0.464996 + 0.885313i \(0.653944\pi\)
\(284\) 4.10892 0.243820
\(285\) −16.1803 −0.958435
\(286\) 4.12555 0.243949
\(287\) 0 0
\(288\) 1.81704 0.107070
\(289\) −13.2476 −0.779269
\(290\) −0.400553 −0.0235213
\(291\) 7.50001 0.439658
\(292\) −15.0653 −0.881630
\(293\) 5.27034 0.307897 0.153948 0.988079i \(-0.450801\pi\)
0.153948 + 0.988079i \(0.450801\pi\)
\(294\) 0 0
\(295\) 14.3298 0.834314
\(296\) −10.7123 −0.622637
\(297\) −2.44570 −0.141914
\(298\) 13.3134 0.771223
\(299\) −18.3383 −1.06053
\(300\) 5.67440 0.327611
\(301\) 0 0
\(302\) −5.12798 −0.295082
\(303\) −2.54450 −0.146178
\(304\) −2.67674 −0.153521
\(305\) −3.17646 −0.181884
\(306\) 3.51983 0.201215
\(307\) 9.11497 0.520219 0.260109 0.965579i \(-0.416241\pi\)
0.260109 + 0.965579i \(0.416241\pi\)
\(308\) 0 0
\(309\) −14.9825 −0.852325
\(310\) 20.4591 1.16200
\(311\) −9.85866 −0.559033 −0.279517 0.960141i \(-0.590174\pi\)
−0.279517 + 0.960141i \(0.590174\pi\)
\(312\) 9.61232 0.544190
\(313\) −25.9767 −1.46829 −0.734146 0.678992i \(-0.762417\pi\)
−0.734146 + 0.678992i \(0.762417\pi\)
\(314\) 18.3332 1.03460
\(315\) 0 0
\(316\) −12.4752 −0.701787
\(317\) 14.1066 0.792304 0.396152 0.918185i \(-0.370345\pi\)
0.396152 + 0.918185i \(0.370345\pi\)
\(318\) −11.2527 −0.631021
\(319\) −0.136998 −0.00767043
\(320\) 2.75416 0.153962
\(321\) 8.78530 0.490348
\(322\) 0 0
\(323\) −5.18516 −0.288510
\(324\) −11.1495 −0.619416
\(325\) 11.3231 0.628095
\(326\) 10.6522 0.589971
\(327\) 27.6709 1.53021
\(328\) −1.00000 −0.0552158
\(329\) 0 0
\(330\) 5.69409 0.313449
\(331\) 19.8655 1.09191 0.545953 0.837816i \(-0.316168\pi\)
0.545953 + 0.837816i \(0.316168\pi\)
\(332\) −11.3239 −0.621482
\(333\) −19.4646 −1.06665
\(334\) −10.7679 −0.589195
\(335\) 1.88476 0.102975
\(336\) 0 0
\(337\) 3.42571 0.186610 0.0933051 0.995638i \(-0.470257\pi\)
0.0933051 + 0.995638i \(0.470257\pi\)
\(338\) 6.18119 0.336213
\(339\) 35.3610 1.92054
\(340\) 5.33514 0.289339
\(341\) 6.99747 0.378934
\(342\) −4.86374 −0.263001
\(343\) 0 0
\(344\) 8.62329 0.464937
\(345\) −25.3105 −1.36267
\(346\) 4.69347 0.252323
\(347\) 30.8446 1.65582 0.827911 0.560859i \(-0.189529\pi\)
0.827911 + 0.560859i \(0.189529\pi\)
\(348\) −0.319198 −0.0171108
\(349\) 13.8068 0.739063 0.369532 0.929218i \(-0.379518\pi\)
0.369532 + 0.929218i \(0.379518\pi\)
\(350\) 0 0
\(351\) −11.3710 −0.606937
\(352\) 0.941986 0.0502080
\(353\) 22.9751 1.22284 0.611422 0.791305i \(-0.290598\pi\)
0.611422 + 0.791305i \(0.290598\pi\)
\(354\) 11.4193 0.606931
\(355\) 11.3166 0.600625
\(356\) 11.7305 0.621715
\(357\) 0 0
\(358\) −1.85740 −0.0981669
\(359\) −13.5421 −0.714725 −0.357362 0.933966i \(-0.616324\pi\)
−0.357362 + 0.933966i \(0.616324\pi\)
\(360\) 5.00443 0.263757
\(361\) −11.8351 −0.622899
\(362\) −22.2499 −1.16943
\(363\) −22.1950 −1.16494
\(364\) 0 0
\(365\) −41.4923 −2.17181
\(366\) −2.53130 −0.132313
\(367\) 2.29213 0.119648 0.0598241 0.998209i \(-0.480946\pi\)
0.0598241 + 0.998209i \(0.480946\pi\)
\(368\) −4.18718 −0.218272
\(369\) −1.81704 −0.0945914
\(370\) −29.5033 −1.53380
\(371\) 0 0
\(372\) 16.3037 0.845308
\(373\) −4.33765 −0.224595 −0.112297 0.993675i \(-0.535821\pi\)
−0.112297 + 0.993675i \(0.535821\pi\)
\(374\) 1.82474 0.0943551
\(375\) −14.5956 −0.753716
\(376\) −4.43943 −0.228946
\(377\) −0.636954 −0.0328048
\(378\) 0 0
\(379\) −28.5685 −1.46747 −0.733733 0.679437i \(-0.762224\pi\)
−0.733733 + 0.679437i \(0.762224\pi\)
\(380\) −7.37216 −0.378184
\(381\) 28.6998 1.47034
\(382\) −20.0369 −1.02518
\(383\) −29.3175 −1.49805 −0.749026 0.662540i \(-0.769478\pi\)
−0.749026 + 0.662540i \(0.769478\pi\)
\(384\) 2.19478 0.112002
\(385\) 0 0
\(386\) 16.1054 0.819744
\(387\) 15.6689 0.796494
\(388\) 3.41721 0.173482
\(389\) 24.5307 1.24376 0.621878 0.783114i \(-0.286370\pi\)
0.621878 + 0.783114i \(0.286370\pi\)
\(390\) 26.4739 1.34056
\(391\) −8.11107 −0.410195
\(392\) 0 0
\(393\) −16.8487 −0.849905
\(394\) 14.7466 0.742924
\(395\) −34.3588 −1.72878
\(396\) 1.71163 0.0860126
\(397\) −12.4038 −0.622527 −0.311263 0.950324i \(-0.600752\pi\)
−0.311263 + 0.950324i \(0.600752\pi\)
\(398\) 19.0221 0.953492
\(399\) 0 0
\(400\) 2.58541 0.129270
\(401\) 34.7546 1.73556 0.867781 0.496948i \(-0.165546\pi\)
0.867781 + 0.496948i \(0.165546\pi\)
\(402\) 1.50195 0.0749105
\(403\) 32.5337 1.62062
\(404\) −1.15934 −0.0576795
\(405\) −30.7075 −1.52587
\(406\) 0 0
\(407\) −10.0908 −0.500182
\(408\) 4.25155 0.210483
\(409\) 8.79422 0.434846 0.217423 0.976077i \(-0.430235\pi\)
0.217423 + 0.976077i \(0.430235\pi\)
\(410\) −2.75416 −0.136018
\(411\) 17.6623 0.871215
\(412\) −6.82644 −0.336315
\(413\) 0 0
\(414\) −7.60829 −0.373927
\(415\) −31.1880 −1.53096
\(416\) 4.37963 0.214729
\(417\) −37.0206 −1.81291
\(418\) −2.52145 −0.123328
\(419\) 12.0175 0.587095 0.293548 0.955944i \(-0.405164\pi\)
0.293548 + 0.955944i \(0.405164\pi\)
\(420\) 0 0
\(421\) 30.7569 1.49900 0.749500 0.662004i \(-0.230294\pi\)
0.749500 + 0.662004i \(0.230294\pi\)
\(422\) −3.92033 −0.190839
\(423\) −8.06664 −0.392213
\(424\) −5.12705 −0.248991
\(425\) 5.00825 0.242936
\(426\) 9.01817 0.436932
\(427\) 0 0
\(428\) 4.00282 0.193484
\(429\) 9.05467 0.437163
\(430\) 23.7499 1.14532
\(431\) 6.72479 0.323922 0.161961 0.986797i \(-0.448218\pi\)
0.161961 + 0.986797i \(0.448218\pi\)
\(432\) −2.59633 −0.124916
\(433\) 22.9072 1.10085 0.550425 0.834884i \(-0.314466\pi\)
0.550425 + 0.834884i \(0.314466\pi\)
\(434\) 0 0
\(435\) −0.879124 −0.0421508
\(436\) 12.6076 0.603796
\(437\) 11.2080 0.536150
\(438\) −33.0650 −1.57990
\(439\) 35.0713 1.67386 0.836932 0.547307i \(-0.184347\pi\)
0.836932 + 0.547307i \(0.184347\pi\)
\(440\) 2.59438 0.123682
\(441\) 0 0
\(442\) 8.48388 0.403537
\(443\) −17.9822 −0.854362 −0.427181 0.904166i \(-0.640493\pi\)
−0.427181 + 0.904166i \(0.640493\pi\)
\(444\) −23.5110 −1.11578
\(445\) 32.3077 1.53153
\(446\) 19.3451 0.916017
\(447\) 29.2199 1.38205
\(448\) 0 0
\(449\) −7.69654 −0.363222 −0.181611 0.983370i \(-0.558131\pi\)
−0.181611 + 0.983370i \(0.558131\pi\)
\(450\) 4.69780 0.221456
\(451\) −0.941986 −0.0443564
\(452\) 16.1114 0.757817
\(453\) −11.2548 −0.528796
\(454\) −26.5527 −1.24618
\(455\) 0 0
\(456\) −5.87484 −0.275114
\(457\) 29.8172 1.39479 0.697394 0.716688i \(-0.254343\pi\)
0.697394 + 0.716688i \(0.254343\pi\)
\(458\) 8.09922 0.378452
\(459\) −5.02940 −0.234752
\(460\) −11.5322 −0.537691
\(461\) 23.7507 1.10618 0.553089 0.833122i \(-0.313449\pi\)
0.553089 + 0.833122i \(0.313449\pi\)
\(462\) 0 0
\(463\) −4.90522 −0.227965 −0.113982 0.993483i \(-0.536361\pi\)
−0.113982 + 0.993483i \(0.536361\pi\)
\(464\) −0.145436 −0.00675168
\(465\) 44.9031 2.08233
\(466\) 7.49252 0.347084
\(467\) 40.6774 1.88233 0.941163 0.337952i \(-0.109734\pi\)
0.941163 + 0.337952i \(0.109734\pi\)
\(468\) 7.95798 0.367858
\(469\) 0 0
\(470\) −12.2269 −0.563986
\(471\) 40.2372 1.85403
\(472\) 5.20297 0.239486
\(473\) 8.12302 0.373497
\(474\) −27.3803 −1.25762
\(475\) −6.92046 −0.317532
\(476\) 0 0
\(477\) −9.31606 −0.426553
\(478\) −6.63573 −0.303511
\(479\) 14.6318 0.668543 0.334272 0.942477i \(-0.391510\pi\)
0.334272 + 0.942477i \(0.391510\pi\)
\(480\) 6.04477 0.275905
\(481\) −46.9157 −2.13917
\(482\) −7.64140 −0.348056
\(483\) 0 0
\(484\) −10.1127 −0.459666
\(485\) 9.41155 0.427356
\(486\) −16.6816 −0.756694
\(487\) −38.1002 −1.72649 −0.863243 0.504788i \(-0.831571\pi\)
−0.863243 + 0.504788i \(0.831571\pi\)
\(488\) −1.15333 −0.0522088
\(489\) 23.3792 1.05724
\(490\) 0 0
\(491\) −28.0295 −1.26495 −0.632476 0.774580i \(-0.717961\pi\)
−0.632476 + 0.774580i \(0.717961\pi\)
\(492\) −2.19478 −0.0989481
\(493\) −0.281726 −0.0126883
\(494\) −11.7231 −0.527448
\(495\) 4.71410 0.211883
\(496\) 7.42842 0.333546
\(497\) 0 0
\(498\) −24.8535 −1.11371
\(499\) −9.47858 −0.424319 −0.212160 0.977235i \(-0.568050\pi\)
−0.212160 + 0.977235i \(0.568050\pi\)
\(500\) −6.65017 −0.297405
\(501\) −23.6332 −1.05585
\(502\) 1.08536 0.0484419
\(503\) 18.5815 0.828510 0.414255 0.910161i \(-0.364042\pi\)
0.414255 + 0.910161i \(0.364042\pi\)
\(504\) 0 0
\(505\) −3.19302 −0.142088
\(506\) −3.94427 −0.175344
\(507\) 13.5663 0.602502
\(508\) 13.0764 0.580172
\(509\) −37.4987 −1.66210 −0.831050 0.556198i \(-0.812260\pi\)
−0.831050 + 0.556198i \(0.812260\pi\)
\(510\) 11.7094 0.518503
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 6.94968 0.306836
\(514\) −29.4160 −1.29748
\(515\) −18.8011 −0.828477
\(516\) 18.9262 0.833179
\(517\) −4.18188 −0.183919
\(518\) 0 0
\(519\) 10.3011 0.452169
\(520\) 12.0622 0.528963
\(521\) −7.03604 −0.308254 −0.154127 0.988051i \(-0.549257\pi\)
−0.154127 + 0.988051i \(0.549257\pi\)
\(522\) −0.264263 −0.0115665
\(523\) 19.5035 0.852829 0.426415 0.904528i \(-0.359776\pi\)
0.426415 + 0.904528i \(0.359776\pi\)
\(524\) −7.67673 −0.335360
\(525\) 0 0
\(526\) −8.69298 −0.379032
\(527\) 14.3897 0.626827
\(528\) 2.06745 0.0899741
\(529\) −5.46751 −0.237718
\(530\) −14.1207 −0.613365
\(531\) 9.45401 0.410269
\(532\) 0 0
\(533\) −4.37963 −0.189703
\(534\) 25.7458 1.11413
\(535\) 11.0244 0.476627
\(536\) 0.684330 0.0295586
\(537\) −4.07659 −0.175918
\(538\) 2.35065 0.101344
\(539\) 0 0
\(540\) −7.15071 −0.307717
\(541\) −43.8442 −1.88501 −0.942504 0.334194i \(-0.891536\pi\)
−0.942504 + 0.334194i \(0.891536\pi\)
\(542\) −7.65699 −0.328896
\(543\) −48.8336 −2.09565
\(544\) 1.93712 0.0830533
\(545\) 34.7234 1.48739
\(546\) 0 0
\(547\) −36.9132 −1.57830 −0.789148 0.614203i \(-0.789477\pi\)
−0.789148 + 0.614203i \(0.789477\pi\)
\(548\) 8.04741 0.343768
\(549\) −2.09565 −0.0894402
\(550\) 2.43542 0.103847
\(551\) 0.389293 0.0165844
\(552\) −9.18993 −0.391149
\(553\) 0 0
\(554\) 6.81703 0.289628
\(555\) −64.7531 −2.74862
\(556\) −16.8676 −0.715346
\(557\) −34.5045 −1.46200 −0.731002 0.682375i \(-0.760947\pi\)
−0.731002 + 0.682375i \(0.760947\pi\)
\(558\) 13.4977 0.571405
\(559\) 37.7669 1.59737
\(560\) 0 0
\(561\) 4.00490 0.169087
\(562\) −26.0572 −1.09916
\(563\) −27.1529 −1.14436 −0.572179 0.820129i \(-0.693902\pi\)
−0.572179 + 0.820129i \(0.693902\pi\)
\(564\) −9.74356 −0.410278
\(565\) 44.3735 1.86681
\(566\) −15.6449 −0.657603
\(567\) 0 0
\(568\) 4.10892 0.172407
\(569\) 44.2444 1.85482 0.927411 0.374043i \(-0.122029\pi\)
0.927411 + 0.374043i \(0.122029\pi\)
\(570\) −16.1803 −0.677716
\(571\) 12.3011 0.514787 0.257393 0.966307i \(-0.417136\pi\)
0.257393 + 0.966307i \(0.417136\pi\)
\(572\) 4.12555 0.172498
\(573\) −43.9766 −1.83715
\(574\) 0 0
\(575\) −10.8256 −0.451458
\(576\) 1.81704 0.0757101
\(577\) 0.820956 0.0341768 0.0170884 0.999854i \(-0.494560\pi\)
0.0170884 + 0.999854i \(0.494560\pi\)
\(578\) −13.2476 −0.551026
\(579\) 35.3478 1.46900
\(580\) −0.400553 −0.0166321
\(581\) 0 0
\(582\) 7.50001 0.310885
\(583\) −4.82961 −0.200022
\(584\) −15.0653 −0.623407
\(585\) 21.9176 0.906180
\(586\) 5.27034 0.217716
\(587\) −16.5226 −0.681963 −0.340981 0.940070i \(-0.610759\pi\)
−0.340981 + 0.940070i \(0.610759\pi\)
\(588\) 0 0
\(589\) −19.8839 −0.819302
\(590\) 14.3298 0.589949
\(591\) 32.3655 1.33134
\(592\) −10.7123 −0.440271
\(593\) 25.4044 1.04323 0.521616 0.853180i \(-0.325329\pi\)
0.521616 + 0.853180i \(0.325329\pi\)
\(594\) −2.44570 −0.100348
\(595\) 0 0
\(596\) 13.3134 0.545337
\(597\) 41.7493 1.70868
\(598\) −18.3383 −0.749910
\(599\) 8.31627 0.339794 0.169897 0.985462i \(-0.445657\pi\)
0.169897 + 0.985462i \(0.445657\pi\)
\(600\) 5.67440 0.231656
\(601\) 15.2562 0.622314 0.311157 0.950359i \(-0.399284\pi\)
0.311157 + 0.950359i \(0.399284\pi\)
\(602\) 0 0
\(603\) 1.24346 0.0506375
\(604\) −5.12798 −0.208655
\(605\) −27.8519 −1.13234
\(606\) −2.54450 −0.103363
\(607\) −12.3665 −0.501943 −0.250971 0.967995i \(-0.580750\pi\)
−0.250971 + 0.967995i \(0.580750\pi\)
\(608\) −2.67674 −0.108556
\(609\) 0 0
\(610\) −3.17646 −0.128611
\(611\) −19.4431 −0.786583
\(612\) 3.51983 0.142281
\(613\) −22.5143 −0.909345 −0.454673 0.890659i \(-0.650244\pi\)
−0.454673 + 0.890659i \(0.650244\pi\)
\(614\) 9.11497 0.367850
\(615\) −6.04477 −0.243749
\(616\) 0 0
\(617\) −1.17499 −0.0473035 −0.0236517 0.999720i \(-0.507529\pi\)
−0.0236517 + 0.999720i \(0.507529\pi\)
\(618\) −14.9825 −0.602685
\(619\) 23.1341 0.929838 0.464919 0.885353i \(-0.346083\pi\)
0.464919 + 0.885353i \(0.346083\pi\)
\(620\) 20.4591 0.821656
\(621\) 10.8713 0.436250
\(622\) −9.85866 −0.395296
\(623\) 0 0
\(624\) 9.61232 0.384801
\(625\) −31.2427 −1.24971
\(626\) −25.9767 −1.03824
\(627\) −5.53401 −0.221007
\(628\) 18.3332 0.731573
\(629\) −20.7509 −0.827393
\(630\) 0 0
\(631\) 24.5041 0.975493 0.487747 0.872985i \(-0.337819\pi\)
0.487747 + 0.872985i \(0.337819\pi\)
\(632\) −12.4752 −0.496238
\(633\) −8.60426 −0.341988
\(634\) 14.1066 0.560243
\(635\) 36.0146 1.42920
\(636\) −11.2527 −0.446199
\(637\) 0 0
\(638\) −0.136998 −0.00542381
\(639\) 7.46609 0.295354
\(640\) 2.75416 0.108868
\(641\) −12.1070 −0.478199 −0.239100 0.970995i \(-0.576852\pi\)
−0.239100 + 0.970995i \(0.576852\pi\)
\(642\) 8.78530 0.346728
\(643\) −47.6407 −1.87876 −0.939382 0.342871i \(-0.888601\pi\)
−0.939382 + 0.342871i \(0.888601\pi\)
\(644\) 0 0
\(645\) 52.1258 2.05245
\(646\) −5.18516 −0.204007
\(647\) −35.7979 −1.40736 −0.703680 0.710517i \(-0.748461\pi\)
−0.703680 + 0.710517i \(0.748461\pi\)
\(648\) −11.1495 −0.437993
\(649\) 4.90112 0.192386
\(650\) 11.3231 0.444130
\(651\) 0 0
\(652\) 10.6522 0.417173
\(653\) 9.66097 0.378063 0.189032 0.981971i \(-0.439465\pi\)
0.189032 + 0.981971i \(0.439465\pi\)
\(654\) 27.6709 1.08202
\(655\) −21.1430 −0.826124
\(656\) −1.00000 −0.0390434
\(657\) −27.3743 −1.06797
\(658\) 0 0
\(659\) 9.42183 0.367022 0.183511 0.983018i \(-0.441254\pi\)
0.183511 + 0.983018i \(0.441254\pi\)
\(660\) 5.69409 0.221642
\(661\) −27.2806 −1.06109 −0.530546 0.847656i \(-0.678013\pi\)
−0.530546 + 0.847656i \(0.678013\pi\)
\(662\) 19.8655 0.772093
\(663\) 18.6202 0.723149
\(664\) −11.3239 −0.439454
\(665\) 0 0
\(666\) −19.4646 −0.754238
\(667\) 0.608965 0.0235792
\(668\) −10.7679 −0.416623
\(669\) 42.4582 1.64153
\(670\) 1.88476 0.0728145
\(671\) −1.08642 −0.0419408
\(672\) 0 0
\(673\) 47.9602 1.84873 0.924364 0.381511i \(-0.124596\pi\)
0.924364 + 0.381511i \(0.124596\pi\)
\(674\) 3.42571 0.131953
\(675\) −6.71257 −0.258367
\(676\) 6.18119 0.237738
\(677\) −6.18995 −0.237899 −0.118950 0.992900i \(-0.537953\pi\)
−0.118950 + 0.992900i \(0.537953\pi\)
\(678\) 35.3610 1.35803
\(679\) 0 0
\(680\) 5.33514 0.204593
\(681\) −58.2772 −2.23319
\(682\) 6.99747 0.267947
\(683\) 34.2974 1.31236 0.656178 0.754607i \(-0.272172\pi\)
0.656178 + 0.754607i \(0.272172\pi\)
\(684\) −4.86374 −0.185970
\(685\) 22.1639 0.846838
\(686\) 0 0
\(687\) 17.7760 0.678196
\(688\) 8.62329 0.328760
\(689\) −22.4546 −0.855452
\(690\) −25.3105 −0.963556
\(691\) −21.8304 −0.830467 −0.415234 0.909715i \(-0.636300\pi\)
−0.415234 + 0.909715i \(0.636300\pi\)
\(692\) 4.69347 0.178419
\(693\) 0 0
\(694\) 30.8446 1.17084
\(695\) −46.4561 −1.76218
\(696\) −0.319198 −0.0120992
\(697\) −1.93712 −0.0733737
\(698\) 13.8068 0.522597
\(699\) 16.4444 0.621985
\(700\) 0 0
\(701\) 33.0101 1.24677 0.623387 0.781914i \(-0.285756\pi\)
0.623387 + 0.781914i \(0.285756\pi\)
\(702\) −11.3710 −0.429169
\(703\) 28.6739 1.08146
\(704\) 0.941986 0.0355024
\(705\) −26.8353 −1.01068
\(706\) 22.9751 0.864681
\(707\) 0 0
\(708\) 11.4193 0.429165
\(709\) 26.9684 1.01282 0.506410 0.862293i \(-0.330972\pi\)
0.506410 + 0.862293i \(0.330972\pi\)
\(710\) 11.3166 0.424706
\(711\) −22.6680 −0.850117
\(712\) 11.7305 0.439619
\(713\) −31.1041 −1.16486
\(714\) 0 0
\(715\) 11.3624 0.424931
\(716\) −1.85740 −0.0694145
\(717\) −14.5639 −0.543901
\(718\) −13.5421 −0.505387
\(719\) 23.5529 0.878376 0.439188 0.898395i \(-0.355266\pi\)
0.439188 + 0.898395i \(0.355266\pi\)
\(720\) 5.00443 0.186504
\(721\) 0 0
\(722\) −11.8351 −0.440456
\(723\) −16.7712 −0.623726
\(724\) −22.2499 −0.826912
\(725\) −0.376010 −0.0139647
\(726\) −22.1950 −0.823735
\(727\) −20.7516 −0.769635 −0.384818 0.922993i \(-0.625736\pi\)
−0.384818 + 0.922993i \(0.625736\pi\)
\(728\) 0 0
\(729\) −3.16401 −0.117185
\(730\) −41.4923 −1.53570
\(731\) 16.7044 0.617833
\(732\) −2.53130 −0.0935596
\(733\) 23.4007 0.864323 0.432161 0.901796i \(-0.357751\pi\)
0.432161 + 0.901796i \(0.357751\pi\)
\(734\) 2.29213 0.0846041
\(735\) 0 0
\(736\) −4.18718 −0.154342
\(737\) 0.644629 0.0237452
\(738\) −1.81704 −0.0668862
\(739\) −25.0297 −0.920734 −0.460367 0.887729i \(-0.652282\pi\)
−0.460367 + 0.887729i \(0.652282\pi\)
\(740\) −29.5033 −1.08456
\(741\) −25.7296 −0.945201
\(742\) 0 0
\(743\) −15.7028 −0.576079 −0.288040 0.957619i \(-0.593003\pi\)
−0.288040 + 0.957619i \(0.593003\pi\)
\(744\) 16.3037 0.597723
\(745\) 36.6672 1.34338
\(746\) −4.33765 −0.158813
\(747\) −20.5761 −0.752839
\(748\) 1.82474 0.0667191
\(749\) 0 0
\(750\) −14.5956 −0.532957
\(751\) 17.3168 0.631900 0.315950 0.948776i \(-0.397677\pi\)
0.315950 + 0.948776i \(0.397677\pi\)
\(752\) −4.43943 −0.161889
\(753\) 2.38212 0.0868093
\(754\) −0.636954 −0.0231965
\(755\) −14.1233 −0.514000
\(756\) 0 0
\(757\) −0.571470 −0.0207704 −0.0103852 0.999946i \(-0.503306\pi\)
−0.0103852 + 0.999946i \(0.503306\pi\)
\(758\) −28.5685 −1.03766
\(759\) −8.65678 −0.314221
\(760\) −7.37216 −0.267417
\(761\) −52.3195 −1.89658 −0.948290 0.317406i \(-0.897188\pi\)
−0.948290 + 0.317406i \(0.897188\pi\)
\(762\) 28.6998 1.03968
\(763\) 0 0
\(764\) −20.0369 −0.724910
\(765\) 9.69418 0.350494
\(766\) −29.3175 −1.05928
\(767\) 22.7871 0.822794
\(768\) 2.19478 0.0791972
\(769\) 22.1042 0.797098 0.398549 0.917147i \(-0.369514\pi\)
0.398549 + 0.917147i \(0.369514\pi\)
\(770\) 0 0
\(771\) −64.5616 −2.32513
\(772\) 16.1054 0.579646
\(773\) −34.0794 −1.22575 −0.612876 0.790179i \(-0.709987\pi\)
−0.612876 + 0.790179i \(0.709987\pi\)
\(774\) 15.6689 0.563206
\(775\) 19.2055 0.689882
\(776\) 3.41721 0.122671
\(777\) 0 0
\(778\) 24.5307 0.879469
\(779\) 2.67674 0.0959040
\(780\) 26.4739 0.947917
\(781\) 3.87055 0.138499
\(782\) −8.11107 −0.290051
\(783\) 0.377598 0.0134943
\(784\) 0 0
\(785\) 50.4925 1.80215
\(786\) −16.8487 −0.600974
\(787\) −3.37218 −0.120205 −0.0601027 0.998192i \(-0.519143\pi\)
−0.0601027 + 0.998192i \(0.519143\pi\)
\(788\) 14.7466 0.525327
\(789\) −19.0791 −0.679235
\(790\) −34.3588 −1.22243
\(791\) 0 0
\(792\) 1.71163 0.0608201
\(793\) −5.05116 −0.179372
\(794\) −12.4038 −0.440193
\(795\) −30.9918 −1.09917
\(796\) 19.0221 0.674221
\(797\) −32.2341 −1.14179 −0.570895 0.821023i \(-0.693404\pi\)
−0.570895 + 0.821023i \(0.693404\pi\)
\(798\) 0 0
\(799\) −8.59971 −0.304236
\(800\) 2.58541 0.0914080
\(801\) 21.3148 0.753121
\(802\) 34.7546 1.22723
\(803\) −14.1913 −0.500800
\(804\) 1.50195 0.0529697
\(805\) 0 0
\(806\) 32.5337 1.14595
\(807\) 5.15915 0.181611
\(808\) −1.15934 −0.0407856
\(809\) 36.8897 1.29697 0.648486 0.761226i \(-0.275402\pi\)
0.648486 + 0.761226i \(0.275402\pi\)
\(810\) −30.7075 −1.07895
\(811\) 39.3323 1.38115 0.690573 0.723263i \(-0.257359\pi\)
0.690573 + 0.723263i \(0.257359\pi\)
\(812\) 0 0
\(813\) −16.8054 −0.589390
\(814\) −10.0908 −0.353682
\(815\) 29.3379 1.02766
\(816\) 4.25155 0.148834
\(817\) −23.0823 −0.807546
\(818\) 8.79422 0.307483
\(819\) 0 0
\(820\) −2.75416 −0.0961795
\(821\) 3.30152 0.115224 0.0576118 0.998339i \(-0.481651\pi\)
0.0576118 + 0.998339i \(0.481651\pi\)
\(822\) 17.6623 0.616042
\(823\) −1.01850 −0.0355026 −0.0177513 0.999842i \(-0.505651\pi\)
−0.0177513 + 0.999842i \(0.505651\pi\)
\(824\) −6.82644 −0.237810
\(825\) 5.34520 0.186096
\(826\) 0 0
\(827\) −25.2299 −0.877331 −0.438665 0.898651i \(-0.644549\pi\)
−0.438665 + 0.898651i \(0.644549\pi\)
\(828\) −7.60829 −0.264406
\(829\) −3.07175 −0.106686 −0.0533431 0.998576i \(-0.516988\pi\)
−0.0533431 + 0.998576i \(0.516988\pi\)
\(830\) −31.1880 −1.08255
\(831\) 14.9619 0.519021
\(832\) 4.37963 0.151836
\(833\) 0 0
\(834\) −37.0206 −1.28192
\(835\) −29.6566 −1.02631
\(836\) −2.52145 −0.0872061
\(837\) −19.2866 −0.666643
\(838\) 12.0175 0.415139
\(839\) −51.1235 −1.76498 −0.882490 0.470331i \(-0.844134\pi\)
−0.882490 + 0.470331i \(0.844134\pi\)
\(840\) 0 0
\(841\) −28.9788 −0.999271
\(842\) 30.7569 1.05995
\(843\) −57.1898 −1.96972
\(844\) −3.92033 −0.134943
\(845\) 17.0240 0.585644
\(846\) −8.06664 −0.277337
\(847\) 0 0
\(848\) −5.12705 −0.176063
\(849\) −34.3370 −1.17844
\(850\) 5.00825 0.171782
\(851\) 44.8541 1.53758
\(852\) 9.01817 0.308957
\(853\) −12.6692 −0.433786 −0.216893 0.976195i \(-0.569592\pi\)
−0.216893 + 0.976195i \(0.569592\pi\)
\(854\) 0 0
\(855\) −13.3955 −0.458118
\(856\) 4.00282 0.136814
\(857\) 23.7478 0.811209 0.405604 0.914049i \(-0.367061\pi\)
0.405604 + 0.914049i \(0.367061\pi\)
\(858\) 9.05467 0.309121
\(859\) 49.8074 1.69941 0.849703 0.527262i \(-0.176781\pi\)
0.849703 + 0.527262i \(0.176781\pi\)
\(860\) 23.7499 0.809866
\(861\) 0 0
\(862\) 6.72479 0.229047
\(863\) −27.8130 −0.946767 −0.473383 0.880857i \(-0.656967\pi\)
−0.473383 + 0.880857i \(0.656967\pi\)
\(864\) −2.59633 −0.0883289
\(865\) 12.9266 0.439517
\(866\) 22.9072 0.778419
\(867\) −29.0754 −0.987454
\(868\) 0 0
\(869\) −11.7515 −0.398642
\(870\) −0.879124 −0.0298051
\(871\) 2.99712 0.101553
\(872\) 12.6076 0.426948
\(873\) 6.20921 0.210150
\(874\) 11.2080 0.379116
\(875\) 0 0
\(876\) −33.0650 −1.11716
\(877\) 19.5541 0.660296 0.330148 0.943929i \(-0.392901\pi\)
0.330148 + 0.943929i \(0.392901\pi\)
\(878\) 35.0713 1.18360
\(879\) 11.5672 0.390152
\(880\) 2.59438 0.0874566
\(881\) 18.2391 0.614491 0.307245 0.951630i \(-0.400593\pi\)
0.307245 + 0.951630i \(0.400593\pi\)
\(882\) 0 0
\(883\) 22.7823 0.766685 0.383343 0.923606i \(-0.374773\pi\)
0.383343 + 0.923606i \(0.374773\pi\)
\(884\) 8.48388 0.285344
\(885\) 31.4507 1.05720
\(886\) −17.9822 −0.604125
\(887\) 13.2431 0.444661 0.222331 0.974971i \(-0.428634\pi\)
0.222331 + 0.974971i \(0.428634\pi\)
\(888\) −23.5110 −0.788977
\(889\) 0 0
\(890\) 32.3077 1.08296
\(891\) −10.5027 −0.351852
\(892\) 19.3451 0.647722
\(893\) 11.8832 0.397656
\(894\) 29.2199 0.977259
\(895\) −5.11559 −0.170995
\(896\) 0 0
\(897\) −40.2485 −1.34386
\(898\) −7.69654 −0.256837
\(899\) −1.08036 −0.0360319
\(900\) 4.69780 0.156593
\(901\) −9.93170 −0.330873
\(902\) −0.941986 −0.0313647
\(903\) 0 0
\(904\) 16.1114 0.535858
\(905\) −61.2799 −2.03701
\(906\) −11.2548 −0.373915
\(907\) −53.2128 −1.76690 −0.883451 0.468523i \(-0.844786\pi\)
−0.883451 + 0.468523i \(0.844786\pi\)
\(908\) −26.5527 −0.881182
\(909\) −2.10658 −0.0698708
\(910\) 0 0
\(911\) 20.1992 0.669230 0.334615 0.942355i \(-0.391394\pi\)
0.334615 + 0.942355i \(0.391394\pi\)
\(912\) −5.87484 −0.194535
\(913\) −10.6670 −0.353026
\(914\) 29.8172 0.986264
\(915\) −6.97162 −0.230475
\(916\) 8.09922 0.267606
\(917\) 0 0
\(918\) −5.02940 −0.165995
\(919\) −43.2365 −1.42624 −0.713120 0.701042i \(-0.752719\pi\)
−0.713120 + 0.701042i \(0.752719\pi\)
\(920\) −11.5322 −0.380205
\(921\) 20.0053 0.659198
\(922\) 23.7507 0.782187
\(923\) 17.9956 0.592332
\(924\) 0 0
\(925\) −27.6956 −0.910624
\(926\) −4.90522 −0.161196
\(927\) −12.4039 −0.407398
\(928\) −0.145436 −0.00477416
\(929\) 25.8421 0.847853 0.423927 0.905697i \(-0.360651\pi\)
0.423927 + 0.905697i \(0.360651\pi\)
\(930\) 44.9031 1.47243
\(931\) 0 0
\(932\) 7.49252 0.245426
\(933\) −21.6376 −0.708382
\(934\) 40.6774 1.33101
\(935\) 5.02563 0.164356
\(936\) 7.95798 0.260115
\(937\) 7.35449 0.240261 0.120130 0.992758i \(-0.461669\pi\)
0.120130 + 0.992758i \(0.461669\pi\)
\(938\) 0 0
\(939\) −57.0131 −1.86055
\(940\) −12.2269 −0.398798
\(941\) −22.6999 −0.739996 −0.369998 0.929033i \(-0.620642\pi\)
−0.369998 + 0.929033i \(0.620642\pi\)
\(942\) 40.2372 1.31100
\(943\) 4.18718 0.136353
\(944\) 5.20297 0.169342
\(945\) 0 0
\(946\) 8.12302 0.264102
\(947\) 27.3941 0.890190 0.445095 0.895483i \(-0.353170\pi\)
0.445095 + 0.895483i \(0.353170\pi\)
\(948\) −27.3803 −0.889272
\(949\) −65.9805 −2.14182
\(950\) −6.92046 −0.224529
\(951\) 30.9608 1.00397
\(952\) 0 0
\(953\) −9.15195 −0.296461 −0.148230 0.988953i \(-0.547358\pi\)
−0.148230 + 0.988953i \(0.547358\pi\)
\(954\) −9.31606 −0.301619
\(955\) −55.1849 −1.78574
\(956\) −6.63573 −0.214615
\(957\) −0.300681 −0.00971962
\(958\) 14.6318 0.472731
\(959\) 0 0
\(960\) 6.04477 0.195094
\(961\) 24.1814 0.780045
\(962\) −46.9157 −1.51262
\(963\) 7.27330 0.234379
\(964\) −7.64140 −0.246113
\(965\) 44.3569 1.42790
\(966\) 0 0
\(967\) −8.02296 −0.258001 −0.129000 0.991645i \(-0.541177\pi\)
−0.129000 + 0.991645i \(0.541177\pi\)
\(968\) −10.1127 −0.325033
\(969\) −11.3803 −0.365587
\(970\) 9.41155 0.302187
\(971\) −48.0783 −1.54291 −0.771454 0.636285i \(-0.780470\pi\)
−0.771454 + 0.636285i \(0.780470\pi\)
\(972\) −16.6816 −0.535064
\(973\) 0 0
\(974\) −38.1002 −1.22081
\(975\) 24.8518 0.795894
\(976\) −1.15333 −0.0369172
\(977\) 30.7114 0.982544 0.491272 0.871006i \(-0.336532\pi\)
0.491272 + 0.871006i \(0.336532\pi\)
\(978\) 23.3792 0.747585
\(979\) 11.0500 0.353158
\(980\) 0 0
\(981\) 22.9086 0.731415
\(982\) −28.0295 −0.894456
\(983\) −16.6343 −0.530552 −0.265276 0.964172i \(-0.585463\pi\)
−0.265276 + 0.964172i \(0.585463\pi\)
\(984\) −2.19478 −0.0699669
\(985\) 40.6146 1.29409
\(986\) −0.281726 −0.00897199
\(987\) 0 0
\(988\) −11.7231 −0.372962
\(989\) −36.1073 −1.14814
\(990\) 4.71410 0.149824
\(991\) −12.2790 −0.390055 −0.195028 0.980798i \(-0.562480\pi\)
−0.195028 + 0.980798i \(0.562480\pi\)
\(992\) 7.42842 0.235852
\(993\) 43.6003 1.38361
\(994\) 0 0
\(995\) 52.3900 1.66087
\(996\) −24.8535 −0.787514
\(997\) 28.3184 0.896852 0.448426 0.893820i \(-0.351985\pi\)
0.448426 + 0.893820i \(0.351985\pi\)
\(998\) −9.47858 −0.300039
\(999\) 27.8125 0.879949
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 4018.2.a.bt.1.9 10
7.2 even 3 574.2.e.h.165.2 20
7.4 even 3 574.2.e.h.247.2 yes 20
7.6 odd 2 4018.2.a.bu.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.e.h.165.2 20 7.2 even 3
574.2.e.h.247.2 yes 20 7.4 even 3
4018.2.a.bt.1.9 10 1.1 even 1 trivial
4018.2.a.bu.1.2 10 7.6 odd 2