Properties

Label 5290.2.a.o.1.2
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $1$
Dimension $2$
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] = [5290,2,Mod(1,5290)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5290, 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("5290.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.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: \(42.2408626693\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 5290.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.61803 q^{6} +0.618034 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.61803 q^{6} +0.618034 q^{7} +1.00000 q^{8} -0.381966 q^{9} -1.00000 q^{10} +2.85410 q^{11} +1.61803 q^{12} -7.09017 q^{13} +0.618034 q^{14} -1.61803 q^{15} +1.00000 q^{16} -6.09017 q^{17} -0.381966 q^{18} -1.85410 q^{19} -1.00000 q^{20} +1.00000 q^{21} +2.85410 q^{22} +1.61803 q^{24} +1.00000 q^{25} -7.09017 q^{26} -5.47214 q^{27} +0.618034 q^{28} -9.23607 q^{29} -1.61803 q^{30} +9.09017 q^{31} +1.00000 q^{32} +4.61803 q^{33} -6.09017 q^{34} -0.618034 q^{35} -0.381966 q^{36} -6.47214 q^{37} -1.85410 q^{38} -11.4721 q^{39} -1.00000 q^{40} +3.32624 q^{41} +1.00000 q^{42} +2.85410 q^{44} +0.381966 q^{45} -3.70820 q^{47} +1.61803 q^{48} -6.61803 q^{49} +1.00000 q^{50} -9.85410 q^{51} -7.09017 q^{52} -0.472136 q^{53} -5.47214 q^{54} -2.85410 q^{55} +0.618034 q^{56} -3.00000 q^{57} -9.23607 q^{58} +1.70820 q^{59} -1.61803 q^{60} +9.32624 q^{61} +9.09017 q^{62} -0.236068 q^{63} +1.00000 q^{64} +7.09017 q^{65} +4.61803 q^{66} -14.4721 q^{67} -6.09017 q^{68} -0.618034 q^{70} -4.09017 q^{71} -0.381966 q^{72} +3.23607 q^{73} -6.47214 q^{74} +1.61803 q^{75} -1.85410 q^{76} +1.76393 q^{77} -11.4721 q^{78} -1.52786 q^{79} -1.00000 q^{80} -7.70820 q^{81} +3.32624 q^{82} +6.94427 q^{83} +1.00000 q^{84} +6.09017 q^{85} -14.9443 q^{87} +2.85410 q^{88} +10.4721 q^{89} +0.381966 q^{90} -4.38197 q^{91} +14.7082 q^{93} -3.70820 q^{94} +1.85410 q^{95} +1.61803 q^{96} -12.3820 q^{97} -6.61803 q^{98} -1.09017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + q^{12} - 3 q^{13} - q^{14} - q^{15} + 2 q^{16} - q^{17} - 3 q^{18} + 3 q^{19} - 2 q^{20} + 2 q^{21} - q^{22} + q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - q^{28} - 14 q^{29} - q^{30} + 7 q^{31} + 2 q^{32} + 7 q^{33} - q^{34} + q^{35} - 3 q^{36} - 4 q^{37} + 3 q^{38} - 14 q^{39} - 2 q^{40} - 9 q^{41} + 2 q^{42} - q^{44} + 3 q^{45} + 6 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} - 13 q^{51} - 3 q^{52} + 8 q^{53} - 2 q^{54} + q^{55} - q^{56} - 6 q^{57} - 14 q^{58} - 10 q^{59} - q^{60} + 3 q^{61} + 7 q^{62} + 4 q^{63} + 2 q^{64} + 3 q^{65} + 7 q^{66} - 20 q^{67} - q^{68} + q^{70} + 3 q^{71} - 3 q^{72} + 2 q^{73} - 4 q^{74} + q^{75} + 3 q^{76} + 8 q^{77} - 14 q^{78} - 12 q^{79} - 2 q^{80} - 2 q^{81} - 9 q^{82} - 4 q^{83} + 2 q^{84} + q^{85} - 12 q^{87} - q^{88} + 12 q^{89} + 3 q^{90} - 11 q^{91} + 16 q^{93} + 6 q^{94} - 3 q^{95} + q^{96} - 27 q^{97} - 11 q^{98} + 9 q^{99}+O(q^{100}) \) 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
\(3\) 1.61803 0.934172 0.467086 0.884212i \(-0.345304\pi\)
0.467086 + 0.884212i \(0.345304\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.61803 0.660560
\(7\) 0.618034 0.233595 0.116797 0.993156i \(-0.462737\pi\)
0.116797 + 0.993156i \(0.462737\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.381966 −0.127322
\(10\) −1.00000 −0.316228
\(11\) 2.85410 0.860544 0.430272 0.902699i \(-0.358418\pi\)
0.430272 + 0.902699i \(0.358418\pi\)
\(12\) 1.61803 0.467086
\(13\) −7.09017 −1.96646 −0.983230 0.182372i \(-0.941623\pi\)
−0.983230 + 0.182372i \(0.941623\pi\)
\(14\) 0.618034 0.165177
\(15\) −1.61803 −0.417775
\(16\) 1.00000 0.250000
\(17\) −6.09017 −1.47708 −0.738542 0.674208i \(-0.764485\pi\)
−0.738542 + 0.674208i \(0.764485\pi\)
\(18\) −0.381966 −0.0900303
\(19\) −1.85410 −0.425360 −0.212680 0.977122i \(-0.568219\pi\)
−0.212680 + 0.977122i \(0.568219\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.00000 0.218218
\(22\) 2.85410 0.608497
\(23\) 0 0
\(24\) 1.61803 0.330280
\(25\) 1.00000 0.200000
\(26\) −7.09017 −1.39050
\(27\) −5.47214 −1.05311
\(28\) 0.618034 0.116797
\(29\) −9.23607 −1.71509 −0.857547 0.514405i \(-0.828013\pi\)
−0.857547 + 0.514405i \(0.828013\pi\)
\(30\) −1.61803 −0.295411
\(31\) 9.09017 1.63264 0.816321 0.577598i \(-0.196010\pi\)
0.816321 + 0.577598i \(0.196010\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.61803 0.803897
\(34\) −6.09017 −1.04446
\(35\) −0.618034 −0.104467
\(36\) −0.381966 −0.0636610
\(37\) −6.47214 −1.06401 −0.532006 0.846740i \(-0.678562\pi\)
−0.532006 + 0.846740i \(0.678562\pi\)
\(38\) −1.85410 −0.300775
\(39\) −11.4721 −1.83701
\(40\) −1.00000 −0.158114
\(41\) 3.32624 0.519471 0.259736 0.965680i \(-0.416365\pi\)
0.259736 + 0.965680i \(0.416365\pi\)
\(42\) 1.00000 0.154303
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 2.85410 0.430272
\(45\) 0.381966 0.0569401
\(46\) 0 0
\(47\) −3.70820 −0.540897 −0.270449 0.962734i \(-0.587172\pi\)
−0.270449 + 0.962734i \(0.587172\pi\)
\(48\) 1.61803 0.233543
\(49\) −6.61803 −0.945433
\(50\) 1.00000 0.141421
\(51\) −9.85410 −1.37985
\(52\) −7.09017 −0.983230
\(53\) −0.472136 −0.0648529 −0.0324264 0.999474i \(-0.510323\pi\)
−0.0324264 + 0.999474i \(0.510323\pi\)
\(54\) −5.47214 −0.744663
\(55\) −2.85410 −0.384847
\(56\) 0.618034 0.0825883
\(57\) −3.00000 −0.397360
\(58\) −9.23607 −1.21276
\(59\) 1.70820 0.222389 0.111195 0.993799i \(-0.464532\pi\)
0.111195 + 0.993799i \(0.464532\pi\)
\(60\) −1.61803 −0.208887
\(61\) 9.32624 1.19410 0.597051 0.802203i \(-0.296339\pi\)
0.597051 + 0.802203i \(0.296339\pi\)
\(62\) 9.09017 1.15445
\(63\) −0.236068 −0.0297418
\(64\) 1.00000 0.125000
\(65\) 7.09017 0.879427
\(66\) 4.61803 0.568441
\(67\) −14.4721 −1.76805 −0.884026 0.467437i \(-0.845177\pi\)
−0.884026 + 0.467437i \(0.845177\pi\)
\(68\) −6.09017 −0.738542
\(69\) 0 0
\(70\) −0.618034 −0.0738692
\(71\) −4.09017 −0.485414 −0.242707 0.970100i \(-0.578035\pi\)
−0.242707 + 0.970100i \(0.578035\pi\)
\(72\) −0.381966 −0.0450151
\(73\) 3.23607 0.378753 0.189377 0.981905i \(-0.439353\pi\)
0.189377 + 0.981905i \(0.439353\pi\)
\(74\) −6.47214 −0.752371
\(75\) 1.61803 0.186834
\(76\) −1.85410 −0.212680
\(77\) 1.76393 0.201019
\(78\) −11.4721 −1.29896
\(79\) −1.52786 −0.171898 −0.0859491 0.996300i \(-0.527392\pi\)
−0.0859491 + 0.996300i \(0.527392\pi\)
\(80\) −1.00000 −0.111803
\(81\) −7.70820 −0.856467
\(82\) 3.32624 0.367322
\(83\) 6.94427 0.762233 0.381116 0.924527i \(-0.375540\pi\)
0.381116 + 0.924527i \(0.375540\pi\)
\(84\) 1.00000 0.109109
\(85\) 6.09017 0.660572
\(86\) 0 0
\(87\) −14.9443 −1.60219
\(88\) 2.85410 0.304248
\(89\) 10.4721 1.11004 0.555022 0.831836i \(-0.312710\pi\)
0.555022 + 0.831836i \(0.312710\pi\)
\(90\) 0.381966 0.0402628
\(91\) −4.38197 −0.459355
\(92\) 0 0
\(93\) 14.7082 1.52517
\(94\) −3.70820 −0.382472
\(95\) 1.85410 0.190227
\(96\) 1.61803 0.165140
\(97\) −12.3820 −1.25720 −0.628599 0.777730i \(-0.716371\pi\)
−0.628599 + 0.777730i \(0.716371\pi\)
\(98\) −6.61803 −0.668522
\(99\) −1.09017 −0.109566
\(100\) 1.00000 0.100000
\(101\) −0.291796 −0.0290348 −0.0145174 0.999895i \(-0.504621\pi\)
−0.0145174 + 0.999895i \(0.504621\pi\)
\(102\) −9.85410 −0.975701
\(103\) −16.5623 −1.63193 −0.815966 0.578100i \(-0.803795\pi\)
−0.815966 + 0.578100i \(0.803795\pi\)
\(104\) −7.09017 −0.695248
\(105\) −1.00000 −0.0975900
\(106\) −0.472136 −0.0458579
\(107\) −18.1803 −1.75756 −0.878780 0.477227i \(-0.841642\pi\)
−0.878780 + 0.477227i \(0.841642\pi\)
\(108\) −5.47214 −0.526557
\(109\) 11.5623 1.10747 0.553734 0.832694i \(-0.313202\pi\)
0.553734 + 0.832694i \(0.313202\pi\)
\(110\) −2.85410 −0.272128
\(111\) −10.4721 −0.993971
\(112\) 0.618034 0.0583987
\(113\) −1.05573 −0.0993145 −0.0496573 0.998766i \(-0.515813\pi\)
−0.0496573 + 0.998766i \(0.515813\pi\)
\(114\) −3.00000 −0.280976
\(115\) 0 0
\(116\) −9.23607 −0.857547
\(117\) 2.70820 0.250374
\(118\) 1.70820 0.157253
\(119\) −3.76393 −0.345039
\(120\) −1.61803 −0.147706
\(121\) −2.85410 −0.259464
\(122\) 9.32624 0.844358
\(123\) 5.38197 0.485276
\(124\) 9.09017 0.816321
\(125\) −1.00000 −0.0894427
\(126\) −0.236068 −0.0210306
\(127\) 16.1803 1.43577 0.717886 0.696160i \(-0.245110\pi\)
0.717886 + 0.696160i \(0.245110\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 7.09017 0.621849
\(131\) 2.94427 0.257242 0.128621 0.991694i \(-0.458945\pi\)
0.128621 + 0.991694i \(0.458945\pi\)
\(132\) 4.61803 0.401948
\(133\) −1.14590 −0.0993620
\(134\) −14.4721 −1.25020
\(135\) 5.47214 0.470966
\(136\) −6.09017 −0.522228
\(137\) 10.3262 0.882230 0.441115 0.897451i \(-0.354583\pi\)
0.441115 + 0.897451i \(0.354583\pi\)
\(138\) 0 0
\(139\) 12.7639 1.08262 0.541311 0.840822i \(-0.317928\pi\)
0.541311 + 0.840822i \(0.317928\pi\)
\(140\) −0.618034 −0.0522334
\(141\) −6.00000 −0.505291
\(142\) −4.09017 −0.343239
\(143\) −20.2361 −1.69223
\(144\) −0.381966 −0.0318305
\(145\) 9.23607 0.767014
\(146\) 3.23607 0.267819
\(147\) −10.7082 −0.883198
\(148\) −6.47214 −0.532006
\(149\) 7.85410 0.643433 0.321717 0.946836i \(-0.395740\pi\)
0.321717 + 0.946836i \(0.395740\pi\)
\(150\) 1.61803 0.132112
\(151\) −2.56231 −0.208517 −0.104259 0.994550i \(-0.533247\pi\)
−0.104259 + 0.994550i \(0.533247\pi\)
\(152\) −1.85410 −0.150388
\(153\) 2.32624 0.188065
\(154\) 1.76393 0.142142
\(155\) −9.09017 −0.730140
\(156\) −11.4721 −0.918506
\(157\) 3.70820 0.295947 0.147973 0.988991i \(-0.452725\pi\)
0.147973 + 0.988991i \(0.452725\pi\)
\(158\) −1.52786 −0.121550
\(159\) −0.763932 −0.0605838
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −7.70820 −0.605614
\(163\) 1.38197 0.108244 0.0541220 0.998534i \(-0.482764\pi\)
0.0541220 + 0.998534i \(0.482764\pi\)
\(164\) 3.32624 0.259736
\(165\) −4.61803 −0.359513
\(166\) 6.94427 0.538980
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 1.00000 0.0771517
\(169\) 37.2705 2.86696
\(170\) 6.09017 0.467095
\(171\) 0.708204 0.0541577
\(172\) 0 0
\(173\) −1.43769 −0.109306 −0.0546529 0.998505i \(-0.517405\pi\)
−0.0546529 + 0.998505i \(0.517405\pi\)
\(174\) −14.9443 −1.13292
\(175\) 0.618034 0.0467190
\(176\) 2.85410 0.215136
\(177\) 2.76393 0.207750
\(178\) 10.4721 0.784920
\(179\) 2.18034 0.162966 0.0814831 0.996675i \(-0.474034\pi\)
0.0814831 + 0.996675i \(0.474034\pi\)
\(180\) 0.381966 0.0284701
\(181\) 12.1459 0.902797 0.451399 0.892322i \(-0.350925\pi\)
0.451399 + 0.892322i \(0.350925\pi\)
\(182\) −4.38197 −0.324813
\(183\) 15.0902 1.11550
\(184\) 0 0
\(185\) 6.47214 0.475841
\(186\) 14.7082 1.07846
\(187\) −17.3820 −1.27110
\(188\) −3.70820 −0.270449
\(189\) −3.38197 −0.246002
\(190\) 1.85410 0.134511
\(191\) 13.7082 0.991891 0.495945 0.868354i \(-0.334822\pi\)
0.495945 + 0.868354i \(0.334822\pi\)
\(192\) 1.61803 0.116772
\(193\) 0.763932 0.0549890 0.0274945 0.999622i \(-0.491247\pi\)
0.0274945 + 0.999622i \(0.491247\pi\)
\(194\) −12.3820 −0.888973
\(195\) 11.4721 0.821537
\(196\) −6.61803 −0.472717
\(197\) −22.5623 −1.60750 −0.803749 0.594969i \(-0.797164\pi\)
−0.803749 + 0.594969i \(0.797164\pi\)
\(198\) −1.09017 −0.0774750
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 1.00000 0.0707107
\(201\) −23.4164 −1.65167
\(202\) −0.291796 −0.0205307
\(203\) −5.70820 −0.400637
\(204\) −9.85410 −0.689925
\(205\) −3.32624 −0.232315
\(206\) −16.5623 −1.15395
\(207\) 0 0
\(208\) −7.09017 −0.491615
\(209\) −5.29180 −0.366041
\(210\) −1.00000 −0.0690066
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −0.472136 −0.0324264
\(213\) −6.61803 −0.453460
\(214\) −18.1803 −1.24278
\(215\) 0 0
\(216\) −5.47214 −0.372332
\(217\) 5.61803 0.381377
\(218\) 11.5623 0.783098
\(219\) 5.23607 0.353821
\(220\) −2.85410 −0.192424
\(221\) 43.1803 2.90462
\(222\) −10.4721 −0.702844
\(223\) −20.9443 −1.40253 −0.701266 0.712900i \(-0.747382\pi\)
−0.701266 + 0.712900i \(0.747382\pi\)
\(224\) 0.618034 0.0412941
\(225\) −0.381966 −0.0254644
\(226\) −1.05573 −0.0702260
\(227\) 18.7639 1.24541 0.622703 0.782458i \(-0.286035\pi\)
0.622703 + 0.782458i \(0.286035\pi\)
\(228\) −3.00000 −0.198680
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 2.85410 0.187786
\(232\) −9.23607 −0.606378
\(233\) 6.29180 0.412189 0.206095 0.978532i \(-0.433925\pi\)
0.206095 + 0.978532i \(0.433925\pi\)
\(234\) 2.70820 0.177041
\(235\) 3.70820 0.241897
\(236\) 1.70820 0.111195
\(237\) −2.47214 −0.160582
\(238\) −3.76393 −0.243979
\(239\) −20.3607 −1.31702 −0.658511 0.752571i \(-0.728814\pi\)
−0.658511 + 0.752571i \(0.728814\pi\)
\(240\) −1.61803 −0.104444
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) −2.85410 −0.183469
\(243\) 3.94427 0.253025
\(244\) 9.32624 0.597051
\(245\) 6.61803 0.422811
\(246\) 5.38197 0.343142
\(247\) 13.1459 0.836453
\(248\) 9.09017 0.577226
\(249\) 11.2361 0.712057
\(250\) −1.00000 −0.0632456
\(251\) −6.14590 −0.387926 −0.193963 0.981009i \(-0.562134\pi\)
−0.193963 + 0.981009i \(0.562134\pi\)
\(252\) −0.236068 −0.0148709
\(253\) 0 0
\(254\) 16.1803 1.01524
\(255\) 9.85410 0.617088
\(256\) 1.00000 0.0625000
\(257\) −7.81966 −0.487777 −0.243888 0.969803i \(-0.578423\pi\)
−0.243888 + 0.969803i \(0.578423\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) 7.09017 0.439714
\(261\) 3.52786 0.218369
\(262\) 2.94427 0.181898
\(263\) −20.7426 −1.27905 −0.639523 0.768772i \(-0.720868\pi\)
−0.639523 + 0.768772i \(0.720868\pi\)
\(264\) 4.61803 0.284220
\(265\) 0.472136 0.0290031
\(266\) −1.14590 −0.0702595
\(267\) 16.9443 1.03697
\(268\) −14.4721 −0.884026
\(269\) −14.1803 −0.864591 −0.432295 0.901732i \(-0.642296\pi\)
−0.432295 + 0.901732i \(0.642296\pi\)
\(270\) 5.47214 0.333024
\(271\) −30.3262 −1.84219 −0.921094 0.389341i \(-0.872703\pi\)
−0.921094 + 0.389341i \(0.872703\pi\)
\(272\) −6.09017 −0.369271
\(273\) −7.09017 −0.429117
\(274\) 10.3262 0.623831
\(275\) 2.85410 0.172109
\(276\) 0 0
\(277\) 29.4164 1.76746 0.883730 0.467996i \(-0.155024\pi\)
0.883730 + 0.467996i \(0.155024\pi\)
\(278\) 12.7639 0.765530
\(279\) −3.47214 −0.207871
\(280\) −0.618034 −0.0369346
\(281\) −22.7639 −1.35798 −0.678991 0.734146i \(-0.737583\pi\)
−0.678991 + 0.734146i \(0.737583\pi\)
\(282\) −6.00000 −0.357295
\(283\) 26.9443 1.60167 0.800835 0.598885i \(-0.204389\pi\)
0.800835 + 0.598885i \(0.204389\pi\)
\(284\) −4.09017 −0.242707
\(285\) 3.00000 0.177705
\(286\) −20.2361 −1.19658
\(287\) 2.05573 0.121346
\(288\) −0.381966 −0.0225076
\(289\) 20.0902 1.18177
\(290\) 9.23607 0.542361
\(291\) −20.0344 −1.17444
\(292\) 3.23607 0.189377
\(293\) 19.8885 1.16190 0.580951 0.813939i \(-0.302681\pi\)
0.580951 + 0.813939i \(0.302681\pi\)
\(294\) −10.7082 −0.624515
\(295\) −1.70820 −0.0994555
\(296\) −6.47214 −0.376185
\(297\) −15.6180 −0.906250
\(298\) 7.85410 0.454976
\(299\) 0 0
\(300\) 1.61803 0.0934172
\(301\) 0 0
\(302\) −2.56231 −0.147444
\(303\) −0.472136 −0.0271235
\(304\) −1.85410 −0.106340
\(305\) −9.32624 −0.534019
\(306\) 2.32624 0.132982
\(307\) −28.4508 −1.62378 −0.811888 0.583813i \(-0.801560\pi\)
−0.811888 + 0.583813i \(0.801560\pi\)
\(308\) 1.76393 0.100509
\(309\) −26.7984 −1.52451
\(310\) −9.09017 −0.516287
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) −11.4721 −0.649482
\(313\) −12.7984 −0.723407 −0.361703 0.932293i \(-0.617805\pi\)
−0.361703 + 0.932293i \(0.617805\pi\)
\(314\) 3.70820 0.209266
\(315\) 0.236068 0.0133009
\(316\) −1.52786 −0.0859491
\(317\) −11.0902 −0.622886 −0.311443 0.950265i \(-0.600812\pi\)
−0.311443 + 0.950265i \(0.600812\pi\)
\(318\) −0.763932 −0.0428392
\(319\) −26.3607 −1.47591
\(320\) −1.00000 −0.0559017
\(321\) −29.4164 −1.64186
\(322\) 0 0
\(323\) 11.2918 0.628292
\(324\) −7.70820 −0.428234
\(325\) −7.09017 −0.393292
\(326\) 1.38197 0.0765400
\(327\) 18.7082 1.03457
\(328\) 3.32624 0.183661
\(329\) −2.29180 −0.126351
\(330\) −4.61803 −0.254214
\(331\) 19.2361 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(332\) 6.94427 0.381116
\(333\) 2.47214 0.135472
\(334\) −8.00000 −0.437741
\(335\) 14.4721 0.790697
\(336\) 1.00000 0.0545545
\(337\) −13.6738 −0.744857 −0.372429 0.928061i \(-0.621475\pi\)
−0.372429 + 0.928061i \(0.621475\pi\)
\(338\) 37.2705 2.02725
\(339\) −1.70820 −0.0927769
\(340\) 6.09017 0.330286
\(341\) 25.9443 1.40496
\(342\) 0.708204 0.0382953
\(343\) −8.41641 −0.454443
\(344\) 0 0
\(345\) 0 0
\(346\) −1.43769 −0.0772909
\(347\) −6.38197 −0.342602 −0.171301 0.985219i \(-0.554797\pi\)
−0.171301 + 0.985219i \(0.554797\pi\)
\(348\) −14.9443 −0.801097
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0.618034 0.0330353
\(351\) 38.7984 2.07090
\(352\) 2.85410 0.152124
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 2.76393 0.146901
\(355\) 4.09017 0.217084
\(356\) 10.4721 0.555022
\(357\) −6.09017 −0.322326
\(358\) 2.18034 0.115235
\(359\) −26.3607 −1.39126 −0.695632 0.718399i \(-0.744875\pi\)
−0.695632 + 0.718399i \(0.744875\pi\)
\(360\) 0.381966 0.0201314
\(361\) −15.5623 −0.819069
\(362\) 12.1459 0.638374
\(363\) −4.61803 −0.242384
\(364\) −4.38197 −0.229677
\(365\) −3.23607 −0.169384
\(366\) 15.0902 0.788776
\(367\) −6.47214 −0.337843 −0.168921 0.985630i \(-0.554028\pi\)
−0.168921 + 0.985630i \(0.554028\pi\)
\(368\) 0 0
\(369\) −1.27051 −0.0661401
\(370\) 6.47214 0.336470
\(371\) −0.291796 −0.0151493
\(372\) 14.7082 0.762585
\(373\) −20.1803 −1.04490 −0.522449 0.852670i \(-0.674982\pi\)
−0.522449 + 0.852670i \(0.674982\pi\)
\(374\) −17.3820 −0.898800
\(375\) −1.61803 −0.0835549
\(376\) −3.70820 −0.191236
\(377\) 65.4853 3.37266
\(378\) −3.38197 −0.173950
\(379\) 22.4508 1.15322 0.576611 0.817019i \(-0.304375\pi\)
0.576611 + 0.817019i \(0.304375\pi\)
\(380\) 1.85410 0.0951134
\(381\) 26.1803 1.34126
\(382\) 13.7082 0.701373
\(383\) 17.8885 0.914062 0.457031 0.889451i \(-0.348913\pi\)
0.457031 + 0.889451i \(0.348913\pi\)
\(384\) 1.61803 0.0825700
\(385\) −1.76393 −0.0898983
\(386\) 0.763932 0.0388831
\(387\) 0 0
\(388\) −12.3820 −0.628599
\(389\) −21.3262 −1.08128 −0.540642 0.841253i \(-0.681818\pi\)
−0.540642 + 0.841253i \(0.681818\pi\)
\(390\) 11.4721 0.580914
\(391\) 0 0
\(392\) −6.61803 −0.334261
\(393\) 4.76393 0.240309
\(394\) −22.5623 −1.13667
\(395\) 1.52786 0.0768752
\(396\) −1.09017 −0.0547831
\(397\) 7.32624 0.367693 0.183847 0.982955i \(-0.441145\pi\)
0.183847 + 0.982955i \(0.441145\pi\)
\(398\) −2.00000 −0.100251
\(399\) −1.85410 −0.0928212
\(400\) 1.00000 0.0500000
\(401\) 1.70820 0.0853036 0.0426518 0.999090i \(-0.486419\pi\)
0.0426518 + 0.999090i \(0.486419\pi\)
\(402\) −23.4164 −1.16790
\(403\) −64.4508 −3.21053
\(404\) −0.291796 −0.0145174
\(405\) 7.70820 0.383024
\(406\) −5.70820 −0.283293
\(407\) −18.4721 −0.915630
\(408\) −9.85410 −0.487851
\(409\) −30.2148 −1.49402 −0.747012 0.664810i \(-0.768512\pi\)
−0.747012 + 0.664810i \(0.768512\pi\)
\(410\) −3.32624 −0.164271
\(411\) 16.7082 0.824155
\(412\) −16.5623 −0.815966
\(413\) 1.05573 0.0519490
\(414\) 0 0
\(415\) −6.94427 −0.340881
\(416\) −7.09017 −0.347624
\(417\) 20.6525 1.01136
\(418\) −5.29180 −0.258830
\(419\) −14.4721 −0.707010 −0.353505 0.935433i \(-0.615010\pi\)
−0.353505 + 0.935433i \(0.615010\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −13.7426 −0.669776 −0.334888 0.942258i \(-0.608698\pi\)
−0.334888 + 0.942258i \(0.608698\pi\)
\(422\) 14.0000 0.681509
\(423\) 1.41641 0.0688681
\(424\) −0.472136 −0.0229289
\(425\) −6.09017 −0.295417
\(426\) −6.61803 −0.320645
\(427\) 5.76393 0.278936
\(428\) −18.1803 −0.878780
\(429\) −32.7426 −1.58083
\(430\) 0 0
\(431\) −3.34752 −0.161245 −0.0806223 0.996745i \(-0.525691\pi\)
−0.0806223 + 0.996745i \(0.525691\pi\)
\(432\) −5.47214 −0.263278
\(433\) −8.50658 −0.408800 −0.204400 0.978887i \(-0.565524\pi\)
−0.204400 + 0.978887i \(0.565524\pi\)
\(434\) 5.61803 0.269674
\(435\) 14.9443 0.716523
\(436\) 11.5623 0.553734
\(437\) 0 0
\(438\) 5.23607 0.250189
\(439\) −13.3820 −0.638686 −0.319343 0.947639i \(-0.603462\pi\)
−0.319343 + 0.947639i \(0.603462\pi\)
\(440\) −2.85410 −0.136064
\(441\) 2.52786 0.120374
\(442\) 43.1803 2.05388
\(443\) 25.0902 1.19207 0.596035 0.802958i \(-0.296742\pi\)
0.596035 + 0.802958i \(0.296742\pi\)
\(444\) −10.4721 −0.496986
\(445\) −10.4721 −0.496427
\(446\) −20.9443 −0.991740
\(447\) 12.7082 0.601077
\(448\) 0.618034 0.0291994
\(449\) −1.56231 −0.0737298 −0.0368649 0.999320i \(-0.511737\pi\)
−0.0368649 + 0.999320i \(0.511737\pi\)
\(450\) −0.381966 −0.0180061
\(451\) 9.49342 0.447028
\(452\) −1.05573 −0.0496573
\(453\) −4.14590 −0.194791
\(454\) 18.7639 0.880635
\(455\) 4.38197 0.205430
\(456\) −3.00000 −0.140488
\(457\) 37.7771 1.76714 0.883569 0.468301i \(-0.155134\pi\)
0.883569 + 0.468301i \(0.155134\pi\)
\(458\) −10.0000 −0.467269
\(459\) 33.3262 1.55554
\(460\) 0 0
\(461\) −39.2361 −1.82741 −0.913703 0.406383i \(-0.866790\pi\)
−0.913703 + 0.406383i \(0.866790\pi\)
\(462\) 2.85410 0.132785
\(463\) 2.00000 0.0929479 0.0464739 0.998920i \(-0.485202\pi\)
0.0464739 + 0.998920i \(0.485202\pi\)
\(464\) −9.23607 −0.428774
\(465\) −14.7082 −0.682077
\(466\) 6.29180 0.291462
\(467\) 17.1246 0.792433 0.396216 0.918157i \(-0.370323\pi\)
0.396216 + 0.918157i \(0.370323\pi\)
\(468\) 2.70820 0.125187
\(469\) −8.94427 −0.413008
\(470\) 3.70820 0.171047
\(471\) 6.00000 0.276465
\(472\) 1.70820 0.0786265
\(473\) 0 0
\(474\) −2.47214 −0.113549
\(475\) −1.85410 −0.0850720
\(476\) −3.76393 −0.172520
\(477\) 0.180340 0.00825720
\(478\) −20.3607 −0.931276
\(479\) 31.8885 1.45702 0.728512 0.685033i \(-0.240212\pi\)
0.728512 + 0.685033i \(0.240212\pi\)
\(480\) −1.61803 −0.0738528
\(481\) 45.8885 2.09234
\(482\) 0 0
\(483\) 0 0
\(484\) −2.85410 −0.129732
\(485\) 12.3820 0.562236
\(486\) 3.94427 0.178916
\(487\) −19.8197 −0.898115 −0.449057 0.893503i \(-0.648240\pi\)
−0.449057 + 0.893503i \(0.648240\pi\)
\(488\) 9.32624 0.422179
\(489\) 2.23607 0.101118
\(490\) 6.61803 0.298972
\(491\) 6.18034 0.278915 0.139457 0.990228i \(-0.455464\pi\)
0.139457 + 0.990228i \(0.455464\pi\)
\(492\) 5.38197 0.242638
\(493\) 56.2492 2.53334
\(494\) 13.1459 0.591462
\(495\) 1.09017 0.0489995
\(496\) 9.09017 0.408161
\(497\) −2.52786 −0.113390
\(498\) 11.2361 0.503500
\(499\) 12.3607 0.553340 0.276670 0.960965i \(-0.410769\pi\)
0.276670 + 0.960965i \(0.410769\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −12.9443 −0.578307
\(502\) −6.14590 −0.274305
\(503\) −36.3262 −1.61971 −0.809853 0.586632i \(-0.800453\pi\)
−0.809853 + 0.586632i \(0.800453\pi\)
\(504\) −0.236068 −0.0105153
\(505\) 0.291796 0.0129848
\(506\) 0 0
\(507\) 60.3050 2.67824
\(508\) 16.1803 0.717886
\(509\) 36.6525 1.62459 0.812296 0.583245i \(-0.198217\pi\)
0.812296 + 0.583245i \(0.198217\pi\)
\(510\) 9.85410 0.436347
\(511\) 2.00000 0.0884748
\(512\) 1.00000 0.0441942
\(513\) 10.1459 0.447952
\(514\) −7.81966 −0.344910
\(515\) 16.5623 0.729822
\(516\) 0 0
\(517\) −10.5836 −0.465466
\(518\) −4.00000 −0.175750
\(519\) −2.32624 −0.102111
\(520\) 7.09017 0.310925
\(521\) 15.5279 0.680288 0.340144 0.940373i \(-0.389524\pi\)
0.340144 + 0.940373i \(0.389524\pi\)
\(522\) 3.52786 0.154410
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) 2.94427 0.128621
\(525\) 1.00000 0.0436436
\(526\) −20.7426 −0.904422
\(527\) −55.3607 −2.41155
\(528\) 4.61803 0.200974
\(529\) 0 0
\(530\) 0.472136 0.0205083
\(531\) −0.652476 −0.0283150
\(532\) −1.14590 −0.0496810
\(533\) −23.5836 −1.02152
\(534\) 16.9443 0.733250
\(535\) 18.1803 0.786005
\(536\) −14.4721 −0.625101
\(537\) 3.52786 0.152239
\(538\) −14.1803 −0.611358
\(539\) −18.8885 −0.813587
\(540\) 5.47214 0.235483
\(541\) 22.8328 0.981659 0.490830 0.871256i \(-0.336694\pi\)
0.490830 + 0.871256i \(0.336694\pi\)
\(542\) −30.3262 −1.30262
\(543\) 19.6525 0.843368
\(544\) −6.09017 −0.261114
\(545\) −11.5623 −0.495275
\(546\) −7.09017 −0.303431
\(547\) 27.9230 1.19390 0.596950 0.802278i \(-0.296379\pi\)
0.596950 + 0.802278i \(0.296379\pi\)
\(548\) 10.3262 0.441115
\(549\) −3.56231 −0.152036
\(550\) 2.85410 0.121699
\(551\) 17.1246 0.729533
\(552\) 0 0
\(553\) −0.944272 −0.0401545
\(554\) 29.4164 1.24978
\(555\) 10.4721 0.444517
\(556\) 12.7639 0.541311
\(557\) 22.8328 0.967457 0.483729 0.875218i \(-0.339282\pi\)
0.483729 + 0.875218i \(0.339282\pi\)
\(558\) −3.47214 −0.146987
\(559\) 0 0
\(560\) −0.618034 −0.0261167
\(561\) −28.1246 −1.18742
\(562\) −22.7639 −0.960239
\(563\) 13.8885 0.585332 0.292666 0.956215i \(-0.405458\pi\)
0.292666 + 0.956215i \(0.405458\pi\)
\(564\) −6.00000 −0.252646
\(565\) 1.05573 0.0444148
\(566\) 26.9443 1.13255
\(567\) −4.76393 −0.200066
\(568\) −4.09017 −0.171620
\(569\) 2.00000 0.0838444 0.0419222 0.999121i \(-0.486652\pi\)
0.0419222 + 0.999121i \(0.486652\pi\)
\(570\) 3.00000 0.125656
\(571\) −15.9787 −0.668688 −0.334344 0.942451i \(-0.608515\pi\)
−0.334344 + 0.942451i \(0.608515\pi\)
\(572\) −20.2361 −0.846113
\(573\) 22.1803 0.926597
\(574\) 2.05573 0.0858044
\(575\) 0 0
\(576\) −0.381966 −0.0159153
\(577\) −3.52786 −0.146867 −0.0734335 0.997300i \(-0.523396\pi\)
−0.0734335 + 0.997300i \(0.523396\pi\)
\(578\) 20.0902 0.835641
\(579\) 1.23607 0.0513692
\(580\) 9.23607 0.383507
\(581\) 4.29180 0.178054
\(582\) −20.0344 −0.830454
\(583\) −1.34752 −0.0558087
\(584\) 3.23607 0.133909
\(585\) −2.70820 −0.111970
\(586\) 19.8885 0.821588
\(587\) 13.6180 0.562076 0.281038 0.959697i \(-0.409321\pi\)
0.281038 + 0.959697i \(0.409321\pi\)
\(588\) −10.7082 −0.441599
\(589\) −16.8541 −0.694461
\(590\) −1.70820 −0.0703256
\(591\) −36.5066 −1.50168
\(592\) −6.47214 −0.266003
\(593\) 39.2361 1.61123 0.805616 0.592438i \(-0.201834\pi\)
0.805616 + 0.592438i \(0.201834\pi\)
\(594\) −15.6180 −0.640816
\(595\) 3.76393 0.154306
\(596\) 7.85410 0.321717
\(597\) −3.23607 −0.132443
\(598\) 0 0
\(599\) −18.3820 −0.751067 −0.375533 0.926809i \(-0.622540\pi\)
−0.375533 + 0.926809i \(0.622540\pi\)
\(600\) 1.61803 0.0660560
\(601\) −33.2705 −1.35713 −0.678566 0.734539i \(-0.737398\pi\)
−0.678566 + 0.734539i \(0.737398\pi\)
\(602\) 0 0
\(603\) 5.52786 0.225112
\(604\) −2.56231 −0.104259
\(605\) 2.85410 0.116036
\(606\) −0.472136 −0.0191792
\(607\) 26.4721 1.07447 0.537235 0.843432i \(-0.319469\pi\)
0.537235 + 0.843432i \(0.319469\pi\)
\(608\) −1.85410 −0.0751938
\(609\) −9.23607 −0.374264
\(610\) −9.32624 −0.377608
\(611\) 26.2918 1.06365
\(612\) 2.32624 0.0940326
\(613\) −19.3050 −0.779720 −0.389860 0.920874i \(-0.627477\pi\)
−0.389860 + 0.920874i \(0.627477\pi\)
\(614\) −28.4508 −1.14818
\(615\) −5.38197 −0.217022
\(616\) 1.76393 0.0710708
\(617\) −34.0902 −1.37242 −0.686209 0.727404i \(-0.740727\pi\)
−0.686209 + 0.727404i \(0.740727\pi\)
\(618\) −26.7984 −1.07799
\(619\) 2.79837 0.112476 0.0562381 0.998417i \(-0.482089\pi\)
0.0562381 + 0.998417i \(0.482089\pi\)
\(620\) −9.09017 −0.365070
\(621\) 0 0
\(622\) 4.00000 0.160385
\(623\) 6.47214 0.259301
\(624\) −11.4721 −0.459253
\(625\) 1.00000 0.0400000
\(626\) −12.7984 −0.511526
\(627\) −8.56231 −0.341946
\(628\) 3.70820 0.147973
\(629\) 39.4164 1.57164
\(630\) 0.236068 0.00940517
\(631\) −42.0689 −1.67474 −0.837368 0.546640i \(-0.815907\pi\)
−0.837368 + 0.546640i \(0.815907\pi\)
\(632\) −1.52786 −0.0607752
\(633\) 22.6525 0.900355
\(634\) −11.0902 −0.440447
\(635\) −16.1803 −0.642097
\(636\) −0.763932 −0.0302919
\(637\) 46.9230 1.85916
\(638\) −26.3607 −1.04363
\(639\) 1.56231 0.0618039
\(640\) −1.00000 −0.0395285
\(641\) −0.360680 −0.0142460 −0.00712300 0.999975i \(-0.502267\pi\)
−0.00712300 + 0.999975i \(0.502267\pi\)
\(642\) −29.4164 −1.16097
\(643\) 8.29180 0.326997 0.163498 0.986544i \(-0.447722\pi\)
0.163498 + 0.986544i \(0.447722\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 11.2918 0.444270
\(647\) −36.2492 −1.42510 −0.712552 0.701619i \(-0.752461\pi\)
−0.712552 + 0.701619i \(0.752461\pi\)
\(648\) −7.70820 −0.302807
\(649\) 4.87539 0.191376
\(650\) −7.09017 −0.278099
\(651\) 9.09017 0.356272
\(652\) 1.38197 0.0541220
\(653\) −8.03444 −0.314412 −0.157206 0.987566i \(-0.550249\pi\)
−0.157206 + 0.987566i \(0.550249\pi\)
\(654\) 18.7082 0.731549
\(655\) −2.94427 −0.115042
\(656\) 3.32624 0.129868
\(657\) −1.23607 −0.0482236
\(658\) −2.29180 −0.0893435
\(659\) 46.2492 1.80161 0.900807 0.434220i \(-0.142976\pi\)
0.900807 + 0.434220i \(0.142976\pi\)
\(660\) −4.61803 −0.179757
\(661\) −18.6738 −0.726325 −0.363163 0.931726i \(-0.618303\pi\)
−0.363163 + 0.931726i \(0.618303\pi\)
\(662\) 19.2361 0.747631
\(663\) 69.8673 2.71342
\(664\) 6.94427 0.269490
\(665\) 1.14590 0.0444360
\(666\) 2.47214 0.0957933
\(667\) 0 0
\(668\) −8.00000 −0.309529
\(669\) −33.8885 −1.31021
\(670\) 14.4721 0.559107
\(671\) 26.6180 1.02758
\(672\) 1.00000 0.0385758
\(673\) −10.9443 −0.421871 −0.210935 0.977500i \(-0.567651\pi\)
−0.210935 + 0.977500i \(0.567651\pi\)
\(674\) −13.6738 −0.526694
\(675\) −5.47214 −0.210623
\(676\) 37.2705 1.43348
\(677\) 50.9443 1.95795 0.978974 0.203986i \(-0.0653899\pi\)
0.978974 + 0.203986i \(0.0653899\pi\)
\(678\) −1.70820 −0.0656032
\(679\) −7.65248 −0.293675
\(680\) 6.09017 0.233547
\(681\) 30.3607 1.16342
\(682\) 25.9443 0.993458
\(683\) −31.5623 −1.20770 −0.603849 0.797099i \(-0.706367\pi\)
−0.603849 + 0.797099i \(0.706367\pi\)
\(684\) 0.708204 0.0270789
\(685\) −10.3262 −0.394545
\(686\) −8.41641 −0.321340
\(687\) −16.1803 −0.617318
\(688\) 0 0
\(689\) 3.34752 0.127531
\(690\) 0 0
\(691\) −29.2361 −1.11219 −0.556096 0.831118i \(-0.687701\pi\)
−0.556096 + 0.831118i \(0.687701\pi\)
\(692\) −1.43769 −0.0546529
\(693\) −0.673762 −0.0255941
\(694\) −6.38197 −0.242256
\(695\) −12.7639 −0.484164
\(696\) −14.9443 −0.566461
\(697\) −20.2574 −0.767302
\(698\) −2.00000 −0.0757011
\(699\) 10.1803 0.385056
\(700\) 0.618034 0.0233595
\(701\) −43.3394 −1.63691 −0.818453 0.574573i \(-0.805168\pi\)
−0.818453 + 0.574573i \(0.805168\pi\)
\(702\) 38.7984 1.46435
\(703\) 12.0000 0.452589
\(704\) 2.85410 0.107568
\(705\) 6.00000 0.225973
\(706\) 24.0000 0.903252
\(707\) −0.180340 −0.00678238
\(708\) 2.76393 0.103875
\(709\) 26.0902 0.979837 0.489918 0.871768i \(-0.337027\pi\)
0.489918 + 0.871768i \(0.337027\pi\)
\(710\) 4.09017 0.153501
\(711\) 0.583592 0.0218864
\(712\) 10.4721 0.392460
\(713\) 0 0
\(714\) −6.09017 −0.227919
\(715\) 20.2361 0.756786
\(716\) 2.18034 0.0814831
\(717\) −32.9443 −1.23033
\(718\) −26.3607 −0.983772
\(719\) 35.2705 1.31537 0.657684 0.753294i \(-0.271536\pi\)
0.657684 + 0.753294i \(0.271536\pi\)
\(720\) 0.381966 0.0142350
\(721\) −10.2361 −0.381211
\(722\) −15.5623 −0.579169
\(723\) 0 0
\(724\) 12.1459 0.451399
\(725\) −9.23607 −0.343019
\(726\) −4.61803 −0.171391
\(727\) −28.2016 −1.04594 −0.522970 0.852351i \(-0.675176\pi\)
−0.522970 + 0.852351i \(0.675176\pi\)
\(728\) −4.38197 −0.162406
\(729\) 29.5066 1.09284
\(730\) −3.23607 −0.119772
\(731\) 0 0
\(732\) 15.0902 0.557749
\(733\) 29.4164 1.08652 0.543260 0.839565i \(-0.317190\pi\)
0.543260 + 0.839565i \(0.317190\pi\)
\(734\) −6.47214 −0.238891
\(735\) 10.7082 0.394978
\(736\) 0 0
\(737\) −41.3050 −1.52149
\(738\) −1.27051 −0.0467681
\(739\) −13.8885 −0.510898 −0.255449 0.966822i \(-0.582223\pi\)
−0.255449 + 0.966822i \(0.582223\pi\)
\(740\) 6.47214 0.237920
\(741\) 21.2705 0.781392
\(742\) −0.291796 −0.0107122
\(743\) −33.6312 −1.23381 −0.616904 0.787038i \(-0.711613\pi\)
−0.616904 + 0.787038i \(0.711613\pi\)
\(744\) 14.7082 0.539229
\(745\) −7.85410 −0.287752
\(746\) −20.1803 −0.738855
\(747\) −2.65248 −0.0970490
\(748\) −17.3820 −0.635548
\(749\) −11.2361 −0.410557
\(750\) −1.61803 −0.0590822
\(751\) 47.0132 1.71553 0.857767 0.514038i \(-0.171851\pi\)
0.857767 + 0.514038i \(0.171851\pi\)
\(752\) −3.70820 −0.135224
\(753\) −9.94427 −0.362389
\(754\) 65.4853 2.38483
\(755\) 2.56231 0.0932519
\(756\) −3.38197 −0.123001
\(757\) 17.8885 0.650170 0.325085 0.945685i \(-0.394607\pi\)
0.325085 + 0.945685i \(0.394607\pi\)
\(758\) 22.4508 0.815452
\(759\) 0 0
\(760\) 1.85410 0.0672553
\(761\) 46.8673 1.69894 0.849468 0.527640i \(-0.176923\pi\)
0.849468 + 0.527640i \(0.176923\pi\)
\(762\) 26.1803 0.948414
\(763\) 7.14590 0.258699
\(764\) 13.7082 0.495945
\(765\) −2.32624 −0.0841053
\(766\) 17.8885 0.646339
\(767\) −12.1115 −0.437319
\(768\) 1.61803 0.0583858
\(769\) 6.58359 0.237410 0.118705 0.992930i \(-0.462126\pi\)
0.118705 + 0.992930i \(0.462126\pi\)
\(770\) −1.76393 −0.0635677
\(771\) −12.6525 −0.455668
\(772\) 0.763932 0.0274945
\(773\) −28.9443 −1.04105 −0.520527 0.853845i \(-0.674264\pi\)
−0.520527 + 0.853845i \(0.674264\pi\)
\(774\) 0 0
\(775\) 9.09017 0.326529
\(776\) −12.3820 −0.444487
\(777\) −6.47214 −0.232187
\(778\) −21.3262 −0.764583
\(779\) −6.16718 −0.220962
\(780\) 11.4721 0.410768
\(781\) −11.6738 −0.417720
\(782\) 0 0
\(783\) 50.5410 1.80619
\(784\) −6.61803 −0.236358
\(785\) −3.70820 −0.132351
\(786\) 4.76393 0.169924
\(787\) 2.87539 0.102497 0.0512483 0.998686i \(-0.483680\pi\)
0.0512483 + 0.998686i \(0.483680\pi\)
\(788\) −22.5623 −0.803749
\(789\) −33.5623 −1.19485
\(790\) 1.52786 0.0543590
\(791\) −0.652476 −0.0231994
\(792\) −1.09017 −0.0387375
\(793\) −66.1246 −2.34815
\(794\) 7.32624 0.259998
\(795\) 0.763932 0.0270939
\(796\) −2.00000 −0.0708881
\(797\) −13.7082 −0.485569 −0.242785 0.970080i \(-0.578061\pi\)
−0.242785 + 0.970080i \(0.578061\pi\)
\(798\) −1.85410 −0.0656345
\(799\) 22.5836 0.798950
\(800\) 1.00000 0.0353553
\(801\) −4.00000 −0.141333
\(802\) 1.70820 0.0603188
\(803\) 9.23607 0.325934
\(804\) −23.4164 −0.825833
\(805\) 0 0
\(806\) −64.4508 −2.27018
\(807\) −22.9443 −0.807677
\(808\) −0.291796 −0.0102653
\(809\) −46.7426 −1.64338 −0.821692 0.569932i \(-0.806970\pi\)
−0.821692 + 0.569932i \(0.806970\pi\)
\(810\) 7.70820 0.270839
\(811\) 21.8197 0.766192 0.383096 0.923709i \(-0.374858\pi\)
0.383096 + 0.923709i \(0.374858\pi\)
\(812\) −5.70820 −0.200319
\(813\) −49.0689 −1.72092
\(814\) −18.4721 −0.647448
\(815\) −1.38197 −0.0484082
\(816\) −9.85410 −0.344963
\(817\) 0 0
\(818\) −30.2148 −1.05644
\(819\) 1.67376 0.0584860
\(820\) −3.32624 −0.116157
\(821\) −33.0557 −1.15365 −0.576826 0.816867i \(-0.695709\pi\)
−0.576826 + 0.816867i \(0.695709\pi\)
\(822\) 16.7082 0.582766
\(823\) 25.4164 0.885960 0.442980 0.896531i \(-0.353921\pi\)
0.442980 + 0.896531i \(0.353921\pi\)
\(824\) −16.5623 −0.576975
\(825\) 4.61803 0.160779
\(826\) 1.05573 0.0367335
\(827\) −21.7082 −0.754868 −0.377434 0.926036i \(-0.623194\pi\)
−0.377434 + 0.926036i \(0.623194\pi\)
\(828\) 0 0
\(829\) 18.9443 0.657962 0.328981 0.944337i \(-0.393295\pi\)
0.328981 + 0.944337i \(0.393295\pi\)
\(830\) −6.94427 −0.241039
\(831\) 47.5967 1.65111
\(832\) −7.09017 −0.245807
\(833\) 40.3050 1.39648
\(834\) 20.6525 0.715137
\(835\) 8.00000 0.276851
\(836\) −5.29180 −0.183021
\(837\) −49.7426 −1.71936
\(838\) −14.4721 −0.499932
\(839\) −33.0132 −1.13974 −0.569870 0.821735i \(-0.693007\pi\)
−0.569870 + 0.821735i \(0.693007\pi\)
\(840\) −1.00000 −0.0345033
\(841\) 56.3050 1.94155
\(842\) −13.7426 −0.473603
\(843\) −36.8328 −1.26859
\(844\) 14.0000 0.481900
\(845\) −37.2705 −1.28214
\(846\) 1.41641 0.0486971
\(847\) −1.76393 −0.0606094
\(848\) −0.472136 −0.0162132
\(849\) 43.5967 1.49624
\(850\) −6.09017 −0.208891
\(851\) 0 0
\(852\) −6.61803 −0.226730
\(853\) −10.7984 −0.369729 −0.184865 0.982764i \(-0.559185\pi\)
−0.184865 + 0.982764i \(0.559185\pi\)
\(854\) 5.76393 0.197238
\(855\) −0.708204 −0.0242201
\(856\) −18.1803 −0.621391
\(857\) −6.58359 −0.224891 −0.112446 0.993658i \(-0.535868\pi\)
−0.112446 + 0.993658i \(0.535868\pi\)
\(858\) −32.7426 −1.11782
\(859\) −24.0689 −0.821220 −0.410610 0.911811i \(-0.634684\pi\)
−0.410610 + 0.911811i \(0.634684\pi\)
\(860\) 0 0
\(861\) 3.32624 0.113358
\(862\) −3.34752 −0.114017
\(863\) 32.7639 1.11530 0.557649 0.830077i \(-0.311704\pi\)
0.557649 + 0.830077i \(0.311704\pi\)
\(864\) −5.47214 −0.186166
\(865\) 1.43769 0.0488831
\(866\) −8.50658 −0.289065
\(867\) 32.5066 1.10398
\(868\) 5.61803 0.190688
\(869\) −4.36068 −0.147926
\(870\) 14.9443 0.506658
\(871\) 102.610 3.47680
\(872\) 11.5623 0.391549
\(873\) 4.72949 0.160069
\(874\) 0 0
\(875\) −0.618034 −0.0208934
\(876\) 5.23607 0.176910
\(877\) 18.7426 0.632894 0.316447 0.948610i \(-0.397510\pi\)
0.316447 + 0.948610i \(0.397510\pi\)
\(878\) −13.3820 −0.451619
\(879\) 32.1803 1.08542
\(880\) −2.85410 −0.0962118
\(881\) −8.58359 −0.289189 −0.144594 0.989491i \(-0.546188\pi\)
−0.144594 + 0.989491i \(0.546188\pi\)
\(882\) 2.52786 0.0851176
\(883\) 15.5623 0.523713 0.261857 0.965107i \(-0.415665\pi\)
0.261857 + 0.965107i \(0.415665\pi\)
\(884\) 43.1803 1.45231
\(885\) −2.76393 −0.0929086
\(886\) 25.0902 0.842921
\(887\) −5.16718 −0.173497 −0.0867485 0.996230i \(-0.527648\pi\)
−0.0867485 + 0.996230i \(0.527648\pi\)
\(888\) −10.4721 −0.351422
\(889\) 10.0000 0.335389
\(890\) −10.4721 −0.351027
\(891\) −22.0000 −0.737028
\(892\) −20.9443 −0.701266
\(893\) 6.87539 0.230076
\(894\) 12.7082 0.425026
\(895\) −2.18034 −0.0728807
\(896\) 0.618034 0.0206471
\(897\) 0 0
\(898\) −1.56231 −0.0521348
\(899\) −83.9574 −2.80014
\(900\) −0.381966 −0.0127322
\(901\) 2.87539 0.0957931
\(902\) 9.49342 0.316096
\(903\) 0 0
\(904\) −1.05573 −0.0351130
\(905\) −12.1459 −0.403743
\(906\) −4.14590 −0.137738
\(907\) −7.12461 −0.236569 −0.118284 0.992980i \(-0.537739\pi\)
−0.118284 + 0.992980i \(0.537739\pi\)
\(908\) 18.7639 0.622703
\(909\) 0.111456 0.00369677
\(910\) 4.38197 0.145261
\(911\) −36.0689 −1.19502 −0.597508 0.801863i \(-0.703842\pi\)
−0.597508 + 0.801863i \(0.703842\pi\)
\(912\) −3.00000 −0.0993399
\(913\) 19.8197 0.655935
\(914\) 37.7771 1.24955
\(915\) −15.0902 −0.498866
\(916\) −10.0000 −0.330409
\(917\) 1.81966 0.0600905
\(918\) 33.3262 1.09993
\(919\) −40.0000 −1.31948 −0.659739 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) 0 0
\(921\) −46.0344 −1.51689
\(922\) −39.2361 −1.29217
\(923\) 29.0000 0.954547
\(924\) 2.85410 0.0938931
\(925\) −6.47214 −0.212803
\(926\) 2.00000 0.0657241
\(927\) 6.32624 0.207781
\(928\) −9.23607 −0.303189
\(929\) −3.52786 −0.115745 −0.0578727 0.998324i \(-0.518432\pi\)
−0.0578727 + 0.998324i \(0.518432\pi\)
\(930\) −14.7082 −0.482301
\(931\) 12.2705 0.402150
\(932\) 6.29180 0.206095
\(933\) 6.47214 0.211888
\(934\) 17.1246 0.560334
\(935\) 17.3820 0.568451
\(936\) 2.70820 0.0885204
\(937\) 36.7984 1.20215 0.601075 0.799192i \(-0.294739\pi\)
0.601075 + 0.799192i \(0.294739\pi\)
\(938\) −8.94427 −0.292041
\(939\) −20.7082 −0.675787
\(940\) 3.70820 0.120948
\(941\) 22.4934 0.733265 0.366632 0.930366i \(-0.380511\pi\)
0.366632 + 0.930366i \(0.380511\pi\)
\(942\) 6.00000 0.195491
\(943\) 0 0
\(944\) 1.70820 0.0555973
\(945\) 3.38197 0.110015
\(946\) 0 0
\(947\) −54.6869 −1.77709 −0.888543 0.458793i \(-0.848282\pi\)
−0.888543 + 0.458793i \(0.848282\pi\)
\(948\) −2.47214 −0.0802912
\(949\) −22.9443 −0.744803
\(950\) −1.85410 −0.0601550
\(951\) −17.9443 −0.581883
\(952\) −3.76393 −0.121990
\(953\) −3.79837 −0.123041 −0.0615207 0.998106i \(-0.519595\pi\)
−0.0615207 + 0.998106i \(0.519595\pi\)
\(954\) 0.180340 0.00583872
\(955\) −13.7082 −0.443587
\(956\) −20.3607 −0.658511
\(957\) −42.6525 −1.37876
\(958\) 31.8885 1.03027
\(959\) 6.38197 0.206084
\(960\) −1.61803 −0.0522218
\(961\) 51.6312 1.66552
\(962\) 45.8885 1.47951
\(963\) 6.94427 0.223776
\(964\) 0 0
\(965\) −0.763932 −0.0245918
\(966\) 0 0
\(967\) −16.5410 −0.531923 −0.265962 0.963984i \(-0.585689\pi\)
−0.265962 + 0.963984i \(0.585689\pi\)
\(968\) −2.85410 −0.0917343
\(969\) 18.2705 0.586933
\(970\) 12.3820 0.397561
\(971\) −34.2705 −1.09979 −0.549896 0.835233i \(-0.685333\pi\)
−0.549896 + 0.835233i \(0.685333\pi\)
\(972\) 3.94427 0.126513
\(973\) 7.88854 0.252895
\(974\) −19.8197 −0.635063
\(975\) −11.4721 −0.367402
\(976\) 9.32624 0.298526
\(977\) 23.5623 0.753825 0.376912 0.926249i \(-0.376986\pi\)
0.376912 + 0.926249i \(0.376986\pi\)
\(978\) 2.23607 0.0715016
\(979\) 29.8885 0.955242
\(980\) 6.61803 0.211405
\(981\) −4.41641 −0.141005
\(982\) 6.18034 0.197223
\(983\) 14.2705 0.455159 0.227579 0.973760i \(-0.426919\pi\)
0.227579 + 0.973760i \(0.426919\pi\)
\(984\) 5.38197 0.171571
\(985\) 22.5623 0.718895
\(986\) 56.2492 1.79134
\(987\) −3.70820 −0.118033
\(988\) 13.1459 0.418227
\(989\) 0 0
\(990\) 1.09017 0.0346479
\(991\) 27.5066 0.873775 0.436888 0.899516i \(-0.356081\pi\)
0.436888 + 0.899516i \(0.356081\pi\)
\(992\) 9.09017 0.288613
\(993\) 31.1246 0.987710
\(994\) −2.52786 −0.0801790
\(995\) 2.00000 0.0634043
\(996\) 11.2361 0.356028
\(997\) 57.1935 1.81134 0.905668 0.423987i \(-0.139370\pi\)
0.905668 + 0.423987i \(0.139370\pi\)
\(998\) 12.3607 0.391270
\(999\) 35.4164 1.12053
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 5290.2.a.o.1.2 2
23.22 odd 2 230.2.a.c.1.2 2
69.68 even 2 2070.2.a.u.1.1 2
92.91 even 2 1840.2.a.l.1.1 2
115.22 even 4 1150.2.b.i.599.3 4
115.68 even 4 1150.2.b.i.599.2 4
115.114 odd 2 1150.2.a.j.1.1 2
184.45 odd 2 7360.2.a.bh.1.1 2
184.91 even 2 7360.2.a.bn.1.2 2
460.459 even 2 9200.2.a.bu.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.c.1.2 2 23.22 odd 2
1150.2.a.j.1.1 2 115.114 odd 2
1150.2.b.i.599.2 4 115.68 even 4
1150.2.b.i.599.3 4 115.22 even 4
1840.2.a.l.1.1 2 92.91 even 2
2070.2.a.u.1.1 2 69.68 even 2
5290.2.a.o.1.2 2 1.1 even 1 trivial
7360.2.a.bh.1.1 2 184.45 odd 2
7360.2.a.bn.1.2 2 184.91 even 2
9200.2.a.bu.1.2 2 460.459 even 2