Properties

Label 931.2.a.q.1.1
Level $931$
Weight $2$
Character 931.1
Self dual yes
Analytic conductor $7.434$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [931,2,Mod(1,931)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(931, 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("931.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.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: \(7.43407242818\)
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: \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.76052\) of defining polynomial
Character \(\chi\) \(=\) 931.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.76052 q^{2} -0.148409 q^{3} +5.62048 q^{4} +2.53457 q^{5} +0.409686 q^{6} -9.99440 q^{8} -2.97797 q^{9} +O(q^{10})\) \(q-2.76052 q^{2} -0.148409 q^{3} +5.62048 q^{4} +2.53457 q^{5} +0.409686 q^{6} -9.99440 q^{8} -2.97797 q^{9} -6.99673 q^{10} +1.58351 q^{11} -0.834129 q^{12} -6.17112 q^{13} -0.376152 q^{15} +16.3488 q^{16} +3.03303 q^{17} +8.22076 q^{18} +1.00000 q^{19} +14.2455 q^{20} -4.37132 q^{22} +6.07217 q^{23} +1.48326 q^{24} +1.42404 q^{25} +17.0355 q^{26} +0.887185 q^{27} +1.46356 q^{29} +1.03838 q^{30} +7.46482 q^{31} -25.1424 q^{32} -0.235007 q^{33} -8.37274 q^{34} -16.7376 q^{36} -0.493725 q^{37} -2.76052 q^{38} +0.915849 q^{39} -25.3315 q^{40} +6.46929 q^{41} +0.636828 q^{43} +8.90010 q^{44} -7.54788 q^{45} -16.7624 q^{46} -3.56543 q^{47} -2.42631 q^{48} -3.93108 q^{50} -0.450128 q^{51} -34.6846 q^{52} +11.0835 q^{53} -2.44909 q^{54} +4.01352 q^{55} -0.148409 q^{57} -4.04019 q^{58} +13.7225 q^{59} -2.11416 q^{60} +3.53613 q^{61} -20.6068 q^{62} +36.7086 q^{64} -15.6411 q^{65} +0.648743 q^{66} -4.76008 q^{67} +17.0471 q^{68} -0.901165 q^{69} -0.975752 q^{71} +29.7631 q^{72} -1.26338 q^{73} +1.36294 q^{74} -0.211340 q^{75} +5.62048 q^{76} -2.52822 q^{78} -16.2898 q^{79} +41.4372 q^{80} +8.80226 q^{81} -17.8586 q^{82} +0.284058 q^{83} +7.68741 q^{85} -1.75798 q^{86} -0.217205 q^{87} -15.8263 q^{88} +6.16563 q^{89} +20.8361 q^{90} +34.1285 q^{92} -1.10785 q^{93} +9.84245 q^{94} +2.53457 q^{95} +3.73136 q^{96} +13.9410 q^{97} -4.71566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76052 −1.95198 −0.975992 0.217808i \(-0.930109\pi\)
−0.975992 + 0.217808i \(0.930109\pi\)
\(3\) −0.148409 −0.0856839 −0.0428420 0.999082i \(-0.513641\pi\)
−0.0428420 + 0.999082i \(0.513641\pi\)
\(4\) 5.62048 2.81024
\(5\) 2.53457 1.13349 0.566747 0.823892i \(-0.308202\pi\)
0.566747 + 0.823892i \(0.308202\pi\)
\(6\) 0.409686 0.167254
\(7\) 0 0
\(8\) −9.99440 −3.53355
\(9\) −2.97797 −0.992658
\(10\) −6.99673 −2.21256
\(11\) 1.58351 0.477447 0.238724 0.971088i \(-0.423271\pi\)
0.238724 + 0.971088i \(0.423271\pi\)
\(12\) −0.834129 −0.240792
\(13\) −6.17112 −1.71156 −0.855780 0.517340i \(-0.826922\pi\)
−0.855780 + 0.517340i \(0.826922\pi\)
\(14\) 0 0
\(15\) −0.376152 −0.0971221
\(16\) 16.3488 4.08720
\(17\) 3.03303 0.735617 0.367809 0.929902i \(-0.380108\pi\)
0.367809 + 0.929902i \(0.380108\pi\)
\(18\) 8.22076 1.93765
\(19\) 1.00000 0.229416
\(20\) 14.2455 3.18539
\(21\) 0 0
\(22\) −4.37132 −0.931969
\(23\) 6.07217 1.26614 0.633068 0.774096i \(-0.281795\pi\)
0.633068 + 0.774096i \(0.281795\pi\)
\(24\) 1.48326 0.302769
\(25\) 1.42404 0.284807
\(26\) 17.0355 3.34094
\(27\) 0.887185 0.170739
\(28\) 0 0
\(29\) 1.46356 0.271776 0.135888 0.990724i \(-0.456611\pi\)
0.135888 + 0.990724i \(0.456611\pi\)
\(30\) 1.03838 0.189581
\(31\) 7.46482 1.34072 0.670361 0.742035i \(-0.266139\pi\)
0.670361 + 0.742035i \(0.266139\pi\)
\(32\) −25.1424 −4.44459
\(33\) −0.235007 −0.0409095
\(34\) −8.37274 −1.43591
\(35\) 0 0
\(36\) −16.7376 −2.78961
\(37\) −0.493725 −0.0811678 −0.0405839 0.999176i \(-0.512922\pi\)
−0.0405839 + 0.999176i \(0.512922\pi\)
\(38\) −2.76052 −0.447816
\(39\) 0.915849 0.146653
\(40\) −25.3315 −4.00526
\(41\) 6.46929 1.01033 0.505166 0.863022i \(-0.331431\pi\)
0.505166 + 0.863022i \(0.331431\pi\)
\(42\) 0 0
\(43\) 0.636828 0.0971153 0.0485576 0.998820i \(-0.484538\pi\)
0.0485576 + 0.998820i \(0.484538\pi\)
\(44\) 8.90010 1.34174
\(45\) −7.54788 −1.12517
\(46\) −16.7624 −2.47148
\(47\) −3.56543 −0.520072 −0.260036 0.965599i \(-0.583734\pi\)
−0.260036 + 0.965599i \(0.583734\pi\)
\(48\) −2.42631 −0.350207
\(49\) 0 0
\(50\) −3.93108 −0.555939
\(51\) −0.450128 −0.0630306
\(52\) −34.6846 −4.80989
\(53\) 11.0835 1.52244 0.761219 0.648495i \(-0.224601\pi\)
0.761219 + 0.648495i \(0.224601\pi\)
\(54\) −2.44909 −0.333279
\(55\) 4.01352 0.541183
\(56\) 0 0
\(57\) −0.148409 −0.0196572
\(58\) −4.04019 −0.530502
\(59\) 13.7225 1.78652 0.893260 0.449539i \(-0.148412\pi\)
0.893260 + 0.449539i \(0.148412\pi\)
\(60\) −2.11416 −0.272936
\(61\) 3.53613 0.452754 0.226377 0.974040i \(-0.427312\pi\)
0.226377 + 0.974040i \(0.427312\pi\)
\(62\) −20.6068 −2.61707
\(63\) 0 0
\(64\) 36.7086 4.58857
\(65\) −15.6411 −1.94004
\(66\) 0.648743 0.0798547
\(67\) −4.76008 −0.581537 −0.290768 0.956793i \(-0.593911\pi\)
−0.290768 + 0.956793i \(0.593911\pi\)
\(68\) 17.0471 2.06726
\(69\) −0.901165 −0.108487
\(70\) 0 0
\(71\) −0.975752 −0.115800 −0.0579002 0.998322i \(-0.518441\pi\)
−0.0579002 + 0.998322i \(0.518441\pi\)
\(72\) 29.7631 3.50761
\(73\) −1.26338 −0.147868 −0.0739339 0.997263i \(-0.523555\pi\)
−0.0739339 + 0.997263i \(0.523555\pi\)
\(74\) 1.36294 0.158438
\(75\) −0.211340 −0.0244034
\(76\) 5.62048 0.644713
\(77\) 0 0
\(78\) −2.52822 −0.286264
\(79\) −16.2898 −1.83275 −0.916373 0.400327i \(-0.868897\pi\)
−0.916373 + 0.400327i \(0.868897\pi\)
\(80\) 41.4372 4.63282
\(81\) 8.80226 0.978029
\(82\) −17.8586 −1.97215
\(83\) 0.284058 0.0311794 0.0155897 0.999878i \(-0.495037\pi\)
0.0155897 + 0.999878i \(0.495037\pi\)
\(84\) 0 0
\(85\) 7.68741 0.833817
\(86\) −1.75798 −0.189567
\(87\) −0.217205 −0.0232868
\(88\) −15.8263 −1.68709
\(89\) 6.16563 0.653556 0.326778 0.945101i \(-0.394037\pi\)
0.326778 + 0.945101i \(0.394037\pi\)
\(90\) 20.8361 2.19632
\(91\) 0 0
\(92\) 34.1285 3.55814
\(93\) −1.10785 −0.114878
\(94\) 9.84245 1.01517
\(95\) 2.53457 0.260041
\(96\) 3.73136 0.380830
\(97\) 13.9410 1.41549 0.707747 0.706466i \(-0.249712\pi\)
0.707747 + 0.706466i \(0.249712\pi\)
\(98\) 0 0
\(99\) −4.71566 −0.473942
\(100\) 8.00376 0.800376
\(101\) 16.2153 1.61348 0.806740 0.590907i \(-0.201230\pi\)
0.806740 + 0.590907i \(0.201230\pi\)
\(102\) 1.24259 0.123035
\(103\) 7.62785 0.751595 0.375797 0.926702i \(-0.377369\pi\)
0.375797 + 0.926702i \(0.377369\pi\)
\(104\) 61.6766 6.04789
\(105\) 0 0
\(106\) −30.5963 −2.97177
\(107\) 2.72492 0.263428 0.131714 0.991288i \(-0.457952\pi\)
0.131714 + 0.991288i \(0.457952\pi\)
\(108\) 4.98640 0.479817
\(109\) 2.84550 0.272549 0.136275 0.990671i \(-0.456487\pi\)
0.136275 + 0.990671i \(0.456487\pi\)
\(110\) −11.0794 −1.05638
\(111\) 0.0732731 0.00695478
\(112\) 0 0
\(113\) −6.07066 −0.571080 −0.285540 0.958367i \(-0.592173\pi\)
−0.285540 + 0.958367i \(0.592173\pi\)
\(114\) 0.409686 0.0383706
\(115\) 15.3903 1.43516
\(116\) 8.22590 0.763756
\(117\) 18.3774 1.69899
\(118\) −37.8813 −3.48726
\(119\) 0 0
\(120\) 3.75942 0.343186
\(121\) −8.49249 −0.772044
\(122\) −9.76155 −0.883769
\(123\) −0.960100 −0.0865693
\(124\) 41.9559 3.76775
\(125\) −9.06353 −0.810666
\(126\) 0 0
\(127\) −11.4368 −1.01485 −0.507426 0.861695i \(-0.669403\pi\)
−0.507426 + 0.861695i \(0.669403\pi\)
\(128\) −51.0499 −4.51222
\(129\) −0.0945109 −0.00832122
\(130\) 43.1776 3.78693
\(131\) −11.9389 −1.04311 −0.521554 0.853218i \(-0.674647\pi\)
−0.521554 + 0.853218i \(0.674647\pi\)
\(132\) −1.32085 −0.114966
\(133\) 0 0
\(134\) 13.1403 1.13515
\(135\) 2.24863 0.193531
\(136\) −30.3133 −2.59934
\(137\) −9.26003 −0.791138 −0.395569 0.918436i \(-0.629453\pi\)
−0.395569 + 0.918436i \(0.629453\pi\)
\(138\) 2.48768 0.211766
\(139\) 6.14306 0.521048 0.260524 0.965467i \(-0.416105\pi\)
0.260524 + 0.965467i \(0.416105\pi\)
\(140\) 0 0
\(141\) 0.529142 0.0445618
\(142\) 2.69358 0.226040
\(143\) −9.77204 −0.817179
\(144\) −48.6863 −4.05719
\(145\) 3.70949 0.308056
\(146\) 3.48759 0.288635
\(147\) 0 0
\(148\) −2.77497 −0.228101
\(149\) 12.0740 0.989141 0.494571 0.869138i \(-0.335325\pi\)
0.494571 + 0.869138i \(0.335325\pi\)
\(150\) 0.583407 0.0476350
\(151\) 6.45109 0.524983 0.262491 0.964934i \(-0.415456\pi\)
0.262491 + 0.964934i \(0.415456\pi\)
\(152\) −9.99440 −0.810653
\(153\) −9.03228 −0.730217
\(154\) 0 0
\(155\) 18.9201 1.51970
\(156\) 5.14751 0.412130
\(157\) 4.02184 0.320977 0.160489 0.987038i \(-0.448693\pi\)
0.160489 + 0.987038i \(0.448693\pi\)
\(158\) 44.9683 3.57749
\(159\) −1.64489 −0.130448
\(160\) −63.7252 −5.03792
\(161\) 0 0
\(162\) −24.2988 −1.90910
\(163\) −11.9800 −0.938346 −0.469173 0.883106i \(-0.655448\pi\)
−0.469173 + 0.883106i \(0.655448\pi\)
\(164\) 36.3605 2.83928
\(165\) −0.595642 −0.0463707
\(166\) −0.784147 −0.0608616
\(167\) 15.1250 1.17041 0.585204 0.810886i \(-0.301015\pi\)
0.585204 + 0.810886i \(0.301015\pi\)
\(168\) 0 0
\(169\) 25.0827 1.92944
\(170\) −21.2213 −1.62760
\(171\) −2.97797 −0.227731
\(172\) 3.57927 0.272917
\(173\) 14.8273 1.12730 0.563649 0.826014i \(-0.309397\pi\)
0.563649 + 0.826014i \(0.309397\pi\)
\(174\) 0.599600 0.0454555
\(175\) 0 0
\(176\) 25.8885 1.95142
\(177\) −2.03655 −0.153076
\(178\) −17.0204 −1.27573
\(179\) −16.2947 −1.21792 −0.608961 0.793200i \(-0.708414\pi\)
−0.608961 + 0.793200i \(0.708414\pi\)
\(180\) −42.4227 −3.16200
\(181\) 1.03994 0.0772982 0.0386491 0.999253i \(-0.487695\pi\)
0.0386491 + 0.999253i \(0.487695\pi\)
\(182\) 0 0
\(183\) −0.524792 −0.0387938
\(184\) −60.6878 −4.47396
\(185\) −1.25138 −0.0920032
\(186\) 3.05823 0.224240
\(187\) 4.80284 0.351218
\(188\) −20.0394 −1.46153
\(189\) 0 0
\(190\) −6.99673 −0.507596
\(191\) 3.77831 0.273389 0.136694 0.990613i \(-0.456352\pi\)
0.136694 + 0.990613i \(0.456352\pi\)
\(192\) −5.44788 −0.393167
\(193\) 10.4678 0.753491 0.376746 0.926317i \(-0.377043\pi\)
0.376746 + 0.926317i \(0.377043\pi\)
\(194\) −38.4844 −2.76302
\(195\) 2.32128 0.166230
\(196\) 0 0
\(197\) −13.4885 −0.961014 −0.480507 0.876991i \(-0.659547\pi\)
−0.480507 + 0.876991i \(0.659547\pi\)
\(198\) 13.0177 0.925126
\(199\) −17.9294 −1.27098 −0.635491 0.772109i \(-0.719202\pi\)
−0.635491 + 0.772109i \(0.719202\pi\)
\(200\) −14.2324 −1.00638
\(201\) 0.706439 0.0498284
\(202\) −44.7626 −3.14949
\(203\) 0 0
\(204\) −2.52994 −0.177131
\(205\) 16.3968 1.14521
\(206\) −21.0568 −1.46710
\(207\) −18.0828 −1.25684
\(208\) −100.890 −6.99549
\(209\) 1.58351 0.109534
\(210\) 0 0
\(211\) 7.90422 0.544149 0.272074 0.962276i \(-0.412290\pi\)
0.272074 + 0.962276i \(0.412290\pi\)
\(212\) 62.2946 4.27841
\(213\) 0.144810 0.00992223
\(214\) −7.52221 −0.514208
\(215\) 1.61408 0.110080
\(216\) −8.86688 −0.603315
\(217\) 0 0
\(218\) −7.85506 −0.532012
\(219\) 0.187497 0.0126699
\(220\) 22.5579 1.52085
\(221\) −18.7172 −1.25905
\(222\) −0.202272 −0.0135756
\(223\) 4.22024 0.282608 0.141304 0.989966i \(-0.454870\pi\)
0.141304 + 0.989966i \(0.454870\pi\)
\(224\) 0 0
\(225\) −4.24074 −0.282716
\(226\) 16.7582 1.11474
\(227\) −16.1145 −1.06956 −0.534778 0.844993i \(-0.679605\pi\)
−0.534778 + 0.844993i \(0.679605\pi\)
\(228\) −0.834129 −0.0552415
\(229\) 13.2448 0.875240 0.437620 0.899160i \(-0.355821\pi\)
0.437620 + 0.899160i \(0.355821\pi\)
\(230\) −42.4854 −2.80140
\(231\) 0 0
\(232\) −14.6274 −0.960336
\(233\) 16.9074 1.10764 0.553821 0.832636i \(-0.313169\pi\)
0.553821 + 0.832636i \(0.313169\pi\)
\(234\) −50.7313 −3.31641
\(235\) −9.03683 −0.589498
\(236\) 77.1272 5.02055
\(237\) 2.41755 0.157037
\(238\) 0 0
\(239\) −6.77655 −0.438338 −0.219169 0.975687i \(-0.570335\pi\)
−0.219169 + 0.975687i \(0.570335\pi\)
\(240\) −6.14964 −0.396958
\(241\) 22.6252 1.45742 0.728708 0.684824i \(-0.240121\pi\)
0.728708 + 0.684824i \(0.240121\pi\)
\(242\) 23.4437 1.50702
\(243\) −3.96789 −0.254540
\(244\) 19.8747 1.27235
\(245\) 0 0
\(246\) 2.65038 0.168982
\(247\) −6.17112 −0.392659
\(248\) −74.6064 −4.73751
\(249\) −0.0421567 −0.00267157
\(250\) 25.0201 1.58241
\(251\) 11.3603 0.717053 0.358527 0.933520i \(-0.383279\pi\)
0.358527 + 0.933520i \(0.383279\pi\)
\(252\) 0 0
\(253\) 9.61537 0.604513
\(254\) 31.5715 1.98097
\(255\) −1.14088 −0.0714447
\(256\) 67.5073 4.21921
\(257\) −17.5409 −1.09417 −0.547085 0.837077i \(-0.684263\pi\)
−0.547085 + 0.837077i \(0.684263\pi\)
\(258\) 0.260899 0.0162429
\(259\) 0 0
\(260\) −87.9105 −5.45198
\(261\) −4.35844 −0.269781
\(262\) 32.9576 2.03613
\(263\) −15.3999 −0.949596 −0.474798 0.880095i \(-0.657479\pi\)
−0.474798 + 0.880095i \(0.657479\pi\)
\(264\) 2.34876 0.144556
\(265\) 28.0919 1.72567
\(266\) 0 0
\(267\) −0.915035 −0.0559992
\(268\) −26.7539 −1.63426
\(269\) 7.92775 0.483363 0.241682 0.970356i \(-0.422301\pi\)
0.241682 + 0.970356i \(0.422301\pi\)
\(270\) −6.20739 −0.377770
\(271\) −8.75327 −0.531723 −0.265862 0.964011i \(-0.585656\pi\)
−0.265862 + 0.964011i \(0.585656\pi\)
\(272\) 49.5864 3.00662
\(273\) 0 0
\(274\) 25.5625 1.54429
\(275\) 2.25498 0.135980
\(276\) −5.06498 −0.304876
\(277\) 18.4795 1.11032 0.555162 0.831742i \(-0.312656\pi\)
0.555162 + 0.831742i \(0.312656\pi\)
\(278\) −16.9581 −1.01708
\(279\) −22.2300 −1.33088
\(280\) 0 0
\(281\) −3.48167 −0.207699 −0.103850 0.994593i \(-0.533116\pi\)
−0.103850 + 0.994593i \(0.533116\pi\)
\(282\) −1.46071 −0.0869839
\(283\) −11.3181 −0.672791 −0.336395 0.941721i \(-0.609208\pi\)
−0.336395 + 0.941721i \(0.609208\pi\)
\(284\) −5.48419 −0.325427
\(285\) −0.376152 −0.0222813
\(286\) 26.9759 1.59512
\(287\) 0 0
\(288\) 74.8735 4.41196
\(289\) −7.80074 −0.458867
\(290\) −10.2401 −0.601321
\(291\) −2.06897 −0.121285
\(292\) −7.10081 −0.415544
\(293\) −15.0868 −0.881381 −0.440691 0.897659i \(-0.645266\pi\)
−0.440691 + 0.897659i \(0.645266\pi\)
\(294\) 0 0
\(295\) 34.7807 2.02501
\(296\) 4.93448 0.286811
\(297\) 1.40487 0.0815187
\(298\) −33.3305 −1.93079
\(299\) −37.4721 −2.16707
\(300\) −1.18783 −0.0685793
\(301\) 0 0
\(302\) −17.8084 −1.02476
\(303\) −2.40649 −0.138249
\(304\) 16.3488 0.937668
\(305\) 8.96255 0.513194
\(306\) 24.9338 1.42537
\(307\) −6.07516 −0.346728 −0.173364 0.984858i \(-0.555464\pi\)
−0.173364 + 0.984858i \(0.555464\pi\)
\(308\) 0 0
\(309\) −1.13204 −0.0643996
\(310\) −52.2293 −2.96643
\(311\) 18.5023 1.04917 0.524586 0.851358i \(-0.324220\pi\)
0.524586 + 0.851358i \(0.324220\pi\)
\(312\) −9.15336 −0.518207
\(313\) −11.8582 −0.670263 −0.335131 0.942171i \(-0.608781\pi\)
−0.335131 + 0.942171i \(0.608781\pi\)
\(314\) −11.1024 −0.626543
\(315\) 0 0
\(316\) −91.5564 −5.15045
\(317\) −2.28430 −0.128299 −0.0641495 0.997940i \(-0.520433\pi\)
−0.0641495 + 0.997940i \(0.520433\pi\)
\(318\) 4.54076 0.254633
\(319\) 2.31756 0.129759
\(320\) 93.0404 5.20111
\(321\) −0.404403 −0.0225716
\(322\) 0 0
\(323\) 3.03303 0.168762
\(324\) 49.4729 2.74849
\(325\) −8.78789 −0.487464
\(326\) 33.0710 1.83163
\(327\) −0.422297 −0.0233531
\(328\) −64.6567 −3.57007
\(329\) 0 0
\(330\) 1.64428 0.0905148
\(331\) 21.2867 1.17002 0.585011 0.811026i \(-0.301090\pi\)
0.585011 + 0.811026i \(0.301090\pi\)
\(332\) 1.59654 0.0876215
\(333\) 1.47030 0.0805719
\(334\) −41.7529 −2.28462
\(335\) −12.0648 −0.659168
\(336\) 0 0
\(337\) 17.1088 0.931978 0.465989 0.884791i \(-0.345699\pi\)
0.465989 + 0.884791i \(0.345699\pi\)
\(338\) −69.2413 −3.76623
\(339\) 0.900941 0.0489324
\(340\) 43.2069 2.34323
\(341\) 11.8206 0.640124
\(342\) 8.22076 0.444528
\(343\) 0 0
\(344\) −6.36471 −0.343162
\(345\) −2.28406 −0.122970
\(346\) −40.9311 −2.20047
\(347\) 10.7992 0.579729 0.289865 0.957068i \(-0.406390\pi\)
0.289865 + 0.957068i \(0.406390\pi\)
\(348\) −1.22080 −0.0654416
\(349\) −20.7117 −1.10867 −0.554336 0.832293i \(-0.687028\pi\)
−0.554336 + 0.832293i \(0.687028\pi\)
\(350\) 0 0
\(351\) −5.47492 −0.292230
\(352\) −39.8133 −2.12206
\(353\) 16.9047 0.899749 0.449874 0.893092i \(-0.351469\pi\)
0.449874 + 0.893092i \(0.351469\pi\)
\(354\) 5.62193 0.298802
\(355\) −2.47311 −0.131259
\(356\) 34.6538 1.83665
\(357\) 0 0
\(358\) 44.9819 2.37736
\(359\) 15.5071 0.818433 0.409217 0.912437i \(-0.365802\pi\)
0.409217 + 0.912437i \(0.365802\pi\)
\(360\) 75.4366 3.97586
\(361\) 1.00000 0.0526316
\(362\) −2.87078 −0.150885
\(363\) 1.26036 0.0661518
\(364\) 0 0
\(365\) −3.20213 −0.167607
\(366\) 1.44870 0.0757248
\(367\) 2.71781 0.141869 0.0709343 0.997481i \(-0.477402\pi\)
0.0709343 + 0.997481i \(0.477402\pi\)
\(368\) 99.2728 5.17495
\(369\) −19.2654 −1.00292
\(370\) 3.45446 0.179589
\(371\) 0 0
\(372\) −6.22662 −0.322835
\(373\) −16.3916 −0.848727 −0.424364 0.905492i \(-0.639502\pi\)
−0.424364 + 0.905492i \(0.639502\pi\)
\(374\) −13.2583 −0.685572
\(375\) 1.34511 0.0694611
\(376\) 35.6344 1.83770
\(377\) −9.03179 −0.465161
\(378\) 0 0
\(379\) −26.4759 −1.35998 −0.679988 0.733223i \(-0.738015\pi\)
−0.679988 + 0.733223i \(0.738015\pi\)
\(380\) 14.2455 0.730778
\(381\) 1.69732 0.0869565
\(382\) −10.4301 −0.533650
\(383\) −8.97673 −0.458689 −0.229345 0.973345i \(-0.573658\pi\)
−0.229345 + 0.973345i \(0.573658\pi\)
\(384\) 7.57627 0.386625
\(385\) 0 0
\(386\) −28.8967 −1.47080
\(387\) −1.89646 −0.0964023
\(388\) 78.3551 3.97788
\(389\) −22.0155 −1.11623 −0.558115 0.829763i \(-0.688475\pi\)
−0.558115 + 0.829763i \(0.688475\pi\)
\(390\) −6.40794 −0.324479
\(391\) 18.4171 0.931391
\(392\) 0 0
\(393\) 1.77184 0.0893775
\(394\) 37.2352 1.87588
\(395\) −41.2876 −2.07740
\(396\) −26.5043 −1.33189
\(397\) −3.35484 −0.168374 −0.0841872 0.996450i \(-0.526829\pi\)
−0.0841872 + 0.996450i \(0.526829\pi\)
\(398\) 49.4945 2.48093
\(399\) 0 0
\(400\) 23.2813 1.16406
\(401\) −20.1098 −1.00423 −0.502117 0.864800i \(-0.667445\pi\)
−0.502117 + 0.864800i \(0.667445\pi\)
\(402\) −1.95014 −0.0972641
\(403\) −46.0663 −2.29472
\(404\) 91.1376 4.53426
\(405\) 22.3099 1.10859
\(406\) 0 0
\(407\) −0.781819 −0.0387533
\(408\) 4.49876 0.222722
\(409\) −2.44826 −0.121059 −0.0605294 0.998166i \(-0.519279\pi\)
−0.0605294 + 0.998166i \(0.519279\pi\)
\(410\) −45.2638 −2.23542
\(411\) 1.37427 0.0677878
\(412\) 42.8722 2.11216
\(413\) 0 0
\(414\) 49.9179 2.45333
\(415\) 0.719963 0.0353416
\(416\) 155.157 7.60719
\(417\) −0.911685 −0.0446454
\(418\) −4.37132 −0.213808
\(419\) −36.0307 −1.76022 −0.880108 0.474774i \(-0.842530\pi\)
−0.880108 + 0.474774i \(0.842530\pi\)
\(420\) 0 0
\(421\) −21.2289 −1.03463 −0.517316 0.855795i \(-0.673069\pi\)
−0.517316 + 0.855795i \(0.673069\pi\)
\(422\) −21.8198 −1.06217
\(423\) 10.6178 0.516254
\(424\) −110.773 −5.37962
\(425\) 4.31914 0.209509
\(426\) −0.399752 −0.0193680
\(427\) 0 0
\(428\) 15.3154 0.740297
\(429\) 1.45026 0.0700191
\(430\) −4.45571 −0.214873
\(431\) −11.3811 −0.548208 −0.274104 0.961700i \(-0.588381\pi\)
−0.274104 + 0.961700i \(0.588381\pi\)
\(432\) 14.5044 0.697844
\(433\) 23.1101 1.11060 0.555300 0.831650i \(-0.312604\pi\)
0.555300 + 0.831650i \(0.312604\pi\)
\(434\) 0 0
\(435\) −0.550521 −0.0263955
\(436\) 15.9931 0.765929
\(437\) 6.07217 0.290471
\(438\) −0.517590 −0.0247314
\(439\) −27.9702 −1.33494 −0.667472 0.744635i \(-0.732624\pi\)
−0.667472 + 0.744635i \(0.732624\pi\)
\(440\) −40.1127 −1.91230
\(441\) 0 0
\(442\) 51.6691 2.45765
\(443\) 28.6352 1.36050 0.680249 0.732981i \(-0.261872\pi\)
0.680249 + 0.732981i \(0.261872\pi\)
\(444\) 0.411830 0.0195446
\(445\) 15.6272 0.740801
\(446\) −11.6501 −0.551646
\(447\) −1.79189 −0.0847535
\(448\) 0 0
\(449\) 1.51721 0.0716016 0.0358008 0.999359i \(-0.488602\pi\)
0.0358008 + 0.999359i \(0.488602\pi\)
\(450\) 11.7067 0.551857
\(451\) 10.2442 0.482380
\(452\) −34.1200 −1.60487
\(453\) −0.957400 −0.0449826
\(454\) 44.4844 2.08776
\(455\) 0 0
\(456\) 1.48326 0.0694599
\(457\) 8.02405 0.375349 0.187675 0.982231i \(-0.439905\pi\)
0.187675 + 0.982231i \(0.439905\pi\)
\(458\) −36.5625 −1.70845
\(459\) 2.69086 0.125598
\(460\) 86.5010 4.03313
\(461\) 19.3393 0.900719 0.450360 0.892847i \(-0.351296\pi\)
0.450360 + 0.892847i \(0.351296\pi\)
\(462\) 0 0
\(463\) 32.2738 1.49989 0.749946 0.661499i \(-0.230080\pi\)
0.749946 + 0.661499i \(0.230080\pi\)
\(464\) 23.9274 1.11080
\(465\) −2.80791 −0.130214
\(466\) −46.6733 −2.16210
\(467\) 32.1680 1.48856 0.744278 0.667870i \(-0.232794\pi\)
0.744278 + 0.667870i \(0.232794\pi\)
\(468\) 103.290 4.77458
\(469\) 0 0
\(470\) 24.9464 1.15069
\(471\) −0.596876 −0.0275026
\(472\) −137.148 −6.31277
\(473\) 1.00842 0.0463674
\(474\) −6.67370 −0.306533
\(475\) 1.42404 0.0653392
\(476\) 0 0
\(477\) −33.0064 −1.51126
\(478\) 18.7068 0.855629
\(479\) −7.81799 −0.357213 −0.178606 0.983921i \(-0.557159\pi\)
−0.178606 + 0.983921i \(0.557159\pi\)
\(480\) 9.45738 0.431669
\(481\) 3.04683 0.138924
\(482\) −62.4573 −2.84485
\(483\) 0 0
\(484\) −47.7318 −2.16963
\(485\) 35.3344 1.60445
\(486\) 10.9534 0.496858
\(487\) −29.7980 −1.35027 −0.675137 0.737692i \(-0.735916\pi\)
−0.675137 + 0.737692i \(0.735916\pi\)
\(488\) −35.3415 −1.59983
\(489\) 1.77794 0.0804011
\(490\) 0 0
\(491\) 19.8290 0.894872 0.447436 0.894316i \(-0.352337\pi\)
0.447436 + 0.894316i \(0.352337\pi\)
\(492\) −5.39622 −0.243280
\(493\) 4.43901 0.199923
\(494\) 17.0355 0.766463
\(495\) −11.9522 −0.537210
\(496\) 122.041 5.47980
\(497\) 0 0
\(498\) 0.116374 0.00521486
\(499\) −30.6722 −1.37308 −0.686539 0.727093i \(-0.740871\pi\)
−0.686539 + 0.727093i \(0.740871\pi\)
\(500\) −50.9413 −2.27817
\(501\) −2.24468 −0.100285
\(502\) −31.3602 −1.39968
\(503\) −36.5009 −1.62750 −0.813748 0.581218i \(-0.802576\pi\)
−0.813748 + 0.581218i \(0.802576\pi\)
\(504\) 0 0
\(505\) 41.0987 1.82887
\(506\) −26.5434 −1.18000
\(507\) −3.72249 −0.165322
\(508\) −64.2802 −2.85197
\(509\) 4.95937 0.219820 0.109910 0.993942i \(-0.464944\pi\)
0.109910 + 0.993942i \(0.464944\pi\)
\(510\) 3.14943 0.139459
\(511\) 0 0
\(512\) −84.2554 −3.72360
\(513\) 0.887185 0.0391702
\(514\) 48.4220 2.13580
\(515\) 19.3333 0.851928
\(516\) −0.531196 −0.0233846
\(517\) −5.64591 −0.248307
\(518\) 0 0
\(519\) −2.20050 −0.0965914
\(520\) 156.324 6.85524
\(521\) −33.8799 −1.48431 −0.742153 0.670231i \(-0.766195\pi\)
−0.742153 + 0.670231i \(0.766195\pi\)
\(522\) 12.0316 0.526608
\(523\) −25.7088 −1.12417 −0.562083 0.827081i \(-0.690000\pi\)
−0.562083 + 0.827081i \(0.690000\pi\)
\(524\) −67.1024 −2.93138
\(525\) 0 0
\(526\) 42.5116 1.85360
\(527\) 22.6410 0.986258
\(528\) −3.84209 −0.167206
\(529\) 13.8713 0.603100
\(530\) −77.5483 −3.36848
\(531\) −40.8653 −1.77340
\(532\) 0 0
\(533\) −39.9227 −1.72924
\(534\) 2.52597 0.109310
\(535\) 6.90651 0.298594
\(536\) 47.5742 2.05489
\(537\) 2.41828 0.104356
\(538\) −21.8847 −0.943517
\(539\) 0 0
\(540\) 12.6384 0.543869
\(541\) 21.7172 0.933697 0.466849 0.884337i \(-0.345389\pi\)
0.466849 + 0.884337i \(0.345389\pi\)
\(542\) 24.1636 1.03791
\(543\) −0.154336 −0.00662321
\(544\) −76.2576 −3.26952
\(545\) 7.21211 0.308933
\(546\) 0 0
\(547\) 26.1501 1.11810 0.559049 0.829135i \(-0.311166\pi\)
0.559049 + 0.829135i \(0.311166\pi\)
\(548\) −52.0458 −2.22329
\(549\) −10.5305 −0.449430
\(550\) −6.22492 −0.265431
\(551\) 1.46356 0.0623497
\(552\) 9.00660 0.383346
\(553\) 0 0
\(554\) −51.0130 −2.16733
\(555\) 0.185716 0.00788319
\(556\) 34.5269 1.46427
\(557\) −17.5350 −0.742983 −0.371492 0.928436i \(-0.621154\pi\)
−0.371492 + 0.928436i \(0.621154\pi\)
\(558\) 61.3665 2.59785
\(559\) −3.92994 −0.166219
\(560\) 0 0
\(561\) −0.712784 −0.0300938
\(562\) 9.61123 0.405425
\(563\) −23.0311 −0.970644 −0.485322 0.874335i \(-0.661298\pi\)
−0.485322 + 0.874335i \(0.661298\pi\)
\(564\) 2.97403 0.125229
\(565\) −15.3865 −0.647315
\(566\) 31.2438 1.31328
\(567\) 0 0
\(568\) 9.75205 0.409187
\(569\) −41.3636 −1.73405 −0.867027 0.498261i \(-0.833972\pi\)
−0.867027 + 0.498261i \(0.833972\pi\)
\(570\) 1.03838 0.0434928
\(571\) −28.2907 −1.18393 −0.591964 0.805965i \(-0.701647\pi\)
−0.591964 + 0.805965i \(0.701647\pi\)
\(572\) −54.9235 −2.29647
\(573\) −0.560734 −0.0234250
\(574\) 0 0
\(575\) 8.64699 0.360604
\(576\) −109.317 −4.55488
\(577\) 29.7398 1.23808 0.619041 0.785359i \(-0.287521\pi\)
0.619041 + 0.785359i \(0.287521\pi\)
\(578\) 21.5341 0.895701
\(579\) −1.55352 −0.0645621
\(580\) 20.8491 0.865712
\(581\) 0 0
\(582\) 5.71143 0.236746
\(583\) 17.5509 0.726883
\(584\) 12.6268 0.522499
\(585\) 46.5788 1.92580
\(586\) 41.6475 1.72044
\(587\) 7.21249 0.297691 0.148846 0.988860i \(-0.452444\pi\)
0.148846 + 0.988860i \(0.452444\pi\)
\(588\) 0 0
\(589\) 7.46482 0.307583
\(590\) −96.0128 −3.95278
\(591\) 2.00181 0.0823435
\(592\) −8.07181 −0.331749
\(593\) 5.16126 0.211948 0.105974 0.994369i \(-0.466204\pi\)
0.105974 + 0.994369i \(0.466204\pi\)
\(594\) −3.87817 −0.159123
\(595\) 0 0
\(596\) 67.8617 2.77972
\(597\) 2.66088 0.108903
\(598\) 103.442 4.23008
\(599\) 32.8017 1.34024 0.670121 0.742252i \(-0.266242\pi\)
0.670121 + 0.742252i \(0.266242\pi\)
\(600\) 2.11221 0.0862307
\(601\) −24.6906 −1.00715 −0.503576 0.863951i \(-0.667983\pi\)
−0.503576 + 0.863951i \(0.667983\pi\)
\(602\) 0 0
\(603\) 14.1754 0.577267
\(604\) 36.2582 1.47533
\(605\) −21.5248 −0.875107
\(606\) 6.64317 0.269860
\(607\) −17.4222 −0.707146 −0.353573 0.935407i \(-0.615033\pi\)
−0.353573 + 0.935407i \(0.615033\pi\)
\(608\) −25.1424 −1.01966
\(609\) 0 0
\(610\) −24.7413 −1.00175
\(611\) 22.0027 0.890134
\(612\) −50.7657 −2.05208
\(613\) −28.0331 −1.13225 −0.566123 0.824321i \(-0.691557\pi\)
−0.566123 + 0.824321i \(0.691557\pi\)
\(614\) 16.7706 0.676806
\(615\) −2.43344 −0.0981257
\(616\) 0 0
\(617\) −7.79442 −0.313791 −0.156896 0.987615i \(-0.550149\pi\)
−0.156896 + 0.987615i \(0.550149\pi\)
\(618\) 3.12502 0.125707
\(619\) −21.1086 −0.848424 −0.424212 0.905563i \(-0.639449\pi\)
−0.424212 + 0.905563i \(0.639449\pi\)
\(620\) 106.340 4.27072
\(621\) 5.38714 0.216178
\(622\) −51.0761 −2.04797
\(623\) 0 0
\(624\) 14.9730 0.599401
\(625\) −30.0923 −1.20369
\(626\) 32.7347 1.30834
\(627\) −0.235007 −0.00938529
\(628\) 22.6046 0.902023
\(629\) −1.49748 −0.0597084
\(630\) 0 0
\(631\) 27.8768 1.10976 0.554880 0.831931i \(-0.312764\pi\)
0.554880 + 0.831931i \(0.312764\pi\)
\(632\) 162.807 6.47611
\(633\) −1.17306 −0.0466248
\(634\) 6.30585 0.250437
\(635\) −28.9873 −1.15033
\(636\) −9.24507 −0.366591
\(637\) 0 0
\(638\) −6.39769 −0.253287
\(639\) 2.90576 0.114950
\(640\) −129.390 −5.11457
\(641\) 22.5527 0.890780 0.445390 0.895337i \(-0.353065\pi\)
0.445390 + 0.895337i \(0.353065\pi\)
\(642\) 1.11636 0.0440593
\(643\) 16.1900 0.638472 0.319236 0.947675i \(-0.396574\pi\)
0.319236 + 0.947675i \(0.396574\pi\)
\(644\) 0 0
\(645\) −0.239544 −0.00943205
\(646\) −8.37274 −0.329421
\(647\) −29.3233 −1.15282 −0.576408 0.817162i \(-0.695546\pi\)
−0.576408 + 0.817162i \(0.695546\pi\)
\(648\) −87.9733 −3.45592
\(649\) 21.7298 0.852969
\(650\) 24.2592 0.951522
\(651\) 0 0
\(652\) −67.3333 −2.63697
\(653\) −6.28876 −0.246098 −0.123049 0.992401i \(-0.539267\pi\)
−0.123049 + 0.992401i \(0.539267\pi\)
\(654\) 1.16576 0.0455849
\(655\) −30.2600 −1.18236
\(656\) 105.765 4.12943
\(657\) 3.76232 0.146782
\(658\) 0 0
\(659\) −8.10004 −0.315533 −0.157766 0.987476i \(-0.550429\pi\)
−0.157766 + 0.987476i \(0.550429\pi\)
\(660\) −3.34779 −0.130313
\(661\) −9.95412 −0.387170 −0.193585 0.981083i \(-0.562012\pi\)
−0.193585 + 0.981083i \(0.562012\pi\)
\(662\) −58.7623 −2.28386
\(663\) 2.77779 0.107881
\(664\) −2.83899 −0.110174
\(665\) 0 0
\(666\) −4.05879 −0.157275
\(667\) 8.88699 0.344105
\(668\) 85.0097 3.28912
\(669\) −0.626321 −0.0242150
\(670\) 33.3050 1.28668
\(671\) 5.59950 0.216166
\(672\) 0 0
\(673\) −35.7331 −1.37741 −0.688704 0.725042i \(-0.741820\pi\)
−0.688704 + 0.725042i \(0.741820\pi\)
\(674\) −47.2293 −1.81920
\(675\) 1.26338 0.0486276
\(676\) 140.977 5.42218
\(677\) 5.43480 0.208876 0.104438 0.994531i \(-0.466696\pi\)
0.104438 + 0.994531i \(0.466696\pi\)
\(678\) −2.48707 −0.0955152
\(679\) 0 0
\(680\) −76.8311 −2.94634
\(681\) 2.39153 0.0916437
\(682\) −32.6311 −1.24951
\(683\) 20.9587 0.801963 0.400982 0.916086i \(-0.368669\pi\)
0.400982 + 0.916086i \(0.368669\pi\)
\(684\) −16.7376 −0.639980
\(685\) −23.4702 −0.896749
\(686\) 0 0
\(687\) −1.96564 −0.0749940
\(688\) 10.4114 0.396930
\(689\) −68.3976 −2.60574
\(690\) 6.30520 0.240035
\(691\) 41.0627 1.56210 0.781049 0.624470i \(-0.214685\pi\)
0.781049 + 0.624470i \(0.214685\pi\)
\(692\) 83.3365 3.16798
\(693\) 0 0
\(694\) −29.8113 −1.13162
\(695\) 15.5700 0.590604
\(696\) 2.17084 0.0822853
\(697\) 19.6215 0.743218
\(698\) 57.1751 2.16411
\(699\) −2.50921 −0.0949071
\(700\) 0 0
\(701\) −39.6574 −1.49784 −0.748920 0.662661i \(-0.769427\pi\)
−0.748920 + 0.662661i \(0.769427\pi\)
\(702\) 15.1136 0.570427
\(703\) −0.493725 −0.0186212
\(704\) 58.1285 2.19080
\(705\) 1.34115 0.0505105
\(706\) −46.6659 −1.75629
\(707\) 0 0
\(708\) −11.4464 −0.430180
\(709\) −38.7028 −1.45351 −0.726757 0.686894i \(-0.758973\pi\)
−0.726757 + 0.686894i \(0.758973\pi\)
\(710\) 6.82707 0.256215
\(711\) 48.5106 1.81929
\(712\) −61.6218 −2.30937
\(713\) 45.3277 1.69754
\(714\) 0 0
\(715\) −24.7679 −0.926267
\(716\) −91.5840 −3.42265
\(717\) 1.00570 0.0375585
\(718\) −42.8077 −1.59757
\(719\) 25.4944 0.950781 0.475390 0.879775i \(-0.342307\pi\)
0.475390 + 0.879775i \(0.342307\pi\)
\(720\) −123.399 −4.59880
\(721\) 0 0
\(722\) −2.76052 −0.102736
\(723\) −3.35778 −0.124877
\(724\) 5.84496 0.217226
\(725\) 2.08416 0.0774038
\(726\) −3.47925 −0.129127
\(727\) 22.6721 0.840860 0.420430 0.907325i \(-0.361879\pi\)
0.420430 + 0.907325i \(0.361879\pi\)
\(728\) 0 0
\(729\) −25.8179 −0.956219
\(730\) 8.83955 0.327166
\(731\) 1.93152 0.0714397
\(732\) −2.94958 −0.109020
\(733\) −9.50433 −0.351050 −0.175525 0.984475i \(-0.556162\pi\)
−0.175525 + 0.984475i \(0.556162\pi\)
\(734\) −7.50258 −0.276925
\(735\) 0 0
\(736\) −152.669 −5.62746
\(737\) −7.53765 −0.277653
\(738\) 53.1825 1.95767
\(739\) 14.2287 0.523410 0.261705 0.965148i \(-0.415715\pi\)
0.261705 + 0.965148i \(0.415715\pi\)
\(740\) −7.03334 −0.258551
\(741\) 0.915849 0.0336445
\(742\) 0 0
\(743\) −32.0267 −1.17494 −0.587472 0.809244i \(-0.699877\pi\)
−0.587472 + 0.809244i \(0.699877\pi\)
\(744\) 11.0723 0.405929
\(745\) 30.6024 1.12118
\(746\) 45.2495 1.65670
\(747\) −0.845916 −0.0309505
\(748\) 26.9942 0.987007
\(749\) 0 0
\(750\) −3.71320 −0.135587
\(751\) −7.55357 −0.275634 −0.137817 0.990458i \(-0.544009\pi\)
−0.137817 + 0.990458i \(0.544009\pi\)
\(752\) −58.2906 −2.12564
\(753\) −1.68596 −0.0614399
\(754\) 24.9325 0.907986
\(755\) 16.3507 0.595064
\(756\) 0 0
\(757\) −25.3179 −0.920193 −0.460097 0.887869i \(-0.652185\pi\)
−0.460097 + 0.887869i \(0.652185\pi\)
\(758\) 73.0873 2.65465
\(759\) −1.42701 −0.0517970
\(760\) −25.3315 −0.918870
\(761\) 5.14945 0.186667 0.0933337 0.995635i \(-0.470248\pi\)
0.0933337 + 0.995635i \(0.470248\pi\)
\(762\) −4.68549 −0.169738
\(763\) 0 0
\(764\) 21.2359 0.768287
\(765\) −22.8929 −0.827696
\(766\) 24.7804 0.895354
\(767\) −84.6833 −3.05774
\(768\) −10.0187 −0.361518
\(769\) −30.5976 −1.10338 −0.551689 0.834050i \(-0.686017\pi\)
−0.551689 + 0.834050i \(0.686017\pi\)
\(770\) 0 0
\(771\) 2.60322 0.0937528
\(772\) 58.8342 2.11749
\(773\) 49.6897 1.78721 0.893606 0.448851i \(-0.148167\pi\)
0.893606 + 0.448851i \(0.148167\pi\)
\(774\) 5.23521 0.188176
\(775\) 10.6302 0.381847
\(776\) −139.332 −5.00173
\(777\) 0 0
\(778\) 60.7743 2.17886
\(779\) 6.46929 0.231786
\(780\) 13.0467 0.467147
\(781\) −1.54512 −0.0552886
\(782\) −50.8407 −1.81806
\(783\) 1.29845 0.0464027
\(784\) 0 0
\(785\) 10.1936 0.363826
\(786\) −4.89120 −0.174463
\(787\) 13.4645 0.479957 0.239978 0.970778i \(-0.422860\pi\)
0.239978 + 0.970778i \(0.422860\pi\)
\(788\) −75.8117 −2.70068
\(789\) 2.28548 0.0813651
\(790\) 113.975 4.05506
\(791\) 0 0
\(792\) 47.1302 1.67470
\(793\) −21.8218 −0.774916
\(794\) 9.26110 0.328664
\(795\) −4.16909 −0.147862
\(796\) −100.772 −3.57176
\(797\) 10.9902 0.389293 0.194647 0.980873i \(-0.437644\pi\)
0.194647 + 0.980873i \(0.437644\pi\)
\(798\) 0 0
\(799\) −10.8141 −0.382574
\(800\) −35.8037 −1.26585
\(801\) −18.3611 −0.648757
\(802\) 55.5134 1.96025
\(803\) −2.00058 −0.0705990
\(804\) 3.97052 0.140030
\(805\) 0 0
\(806\) 127.167 4.47926
\(807\) −1.17655 −0.0414165
\(808\) −162.062 −5.70132
\(809\) 20.0635 0.705396 0.352698 0.935737i \(-0.385264\pi\)
0.352698 + 0.935737i \(0.385264\pi\)
\(810\) −61.5870 −2.16395
\(811\) 1.57184 0.0551948 0.0275974 0.999619i \(-0.491214\pi\)
0.0275974 + 0.999619i \(0.491214\pi\)
\(812\) 0 0
\(813\) 1.29906 0.0455601
\(814\) 2.15823 0.0756459
\(815\) −30.3641 −1.06361
\(816\) −7.35906 −0.257619
\(817\) 0.636828 0.0222798
\(818\) 6.75848 0.236305
\(819\) 0 0
\(820\) 92.1581 3.21830
\(821\) 3.08159 0.107548 0.0537742 0.998553i \(-0.482875\pi\)
0.0537742 + 0.998553i \(0.482875\pi\)
\(822\) −3.79370 −0.132321
\(823\) 49.4005 1.72199 0.860996 0.508612i \(-0.169841\pi\)
0.860996 + 0.508612i \(0.169841\pi\)
\(824\) −76.2358 −2.65580
\(825\) −0.334659 −0.0116513
\(826\) 0 0
\(827\) 19.8375 0.689817 0.344909 0.938636i \(-0.387910\pi\)
0.344909 + 0.938636i \(0.387910\pi\)
\(828\) −101.634 −3.53202
\(829\) 40.6536 1.41196 0.705979 0.708233i \(-0.250507\pi\)
0.705979 + 0.708233i \(0.250507\pi\)
\(830\) −1.98747 −0.0689862
\(831\) −2.74252 −0.0951369
\(832\) −226.533 −7.85361
\(833\) 0 0
\(834\) 2.51673 0.0871471
\(835\) 38.3353 1.32665
\(836\) 8.90010 0.307816
\(837\) 6.62268 0.228913
\(838\) 99.4635 3.43591
\(839\) 21.7950 0.752448 0.376224 0.926529i \(-0.377222\pi\)
0.376224 + 0.926529i \(0.377222\pi\)
\(840\) 0 0
\(841\) −26.8580 −0.926138
\(842\) 58.6027 2.01958
\(843\) 0.516711 0.0177965
\(844\) 44.4255 1.52919
\(845\) 63.5737 2.18700
\(846\) −29.3106 −1.00772
\(847\) 0 0
\(848\) 181.202 6.22251
\(849\) 1.67971 0.0576474
\(850\) −11.9231 −0.408958
\(851\) −2.99798 −0.102769
\(852\) 0.813902 0.0278838
\(853\) 52.6727 1.80348 0.901740 0.432280i \(-0.142291\pi\)
0.901740 + 0.432280i \(0.142291\pi\)
\(854\) 0 0
\(855\) −7.54788 −0.258132
\(856\) −27.2340 −0.930839
\(857\) 25.9375 0.886007 0.443003 0.896520i \(-0.353913\pi\)
0.443003 + 0.896520i \(0.353913\pi\)
\(858\) −4.00347 −0.136676
\(859\) −41.6061 −1.41958 −0.709791 0.704413i \(-0.751210\pi\)
−0.709791 + 0.704413i \(0.751210\pi\)
\(860\) 9.07191 0.309350
\(861\) 0 0
\(862\) 31.4178 1.07009
\(863\) 26.6445 0.906990 0.453495 0.891259i \(-0.350177\pi\)
0.453495 + 0.891259i \(0.350177\pi\)
\(864\) −22.3060 −0.758864
\(865\) 37.5808 1.27779
\(866\) −63.7959 −2.16787
\(867\) 1.15770 0.0393175
\(868\) 0 0
\(869\) −25.7951 −0.875039
\(870\) 1.51973 0.0515235
\(871\) 29.3750 0.995335
\(872\) −28.4391 −0.963068
\(873\) −41.5159 −1.40510
\(874\) −16.7624 −0.566995
\(875\) 0 0
\(876\) 1.05382 0.0356054
\(877\) −21.6320 −0.730461 −0.365230 0.930917i \(-0.619010\pi\)
−0.365230 + 0.930917i \(0.619010\pi\)
\(878\) 77.2123 2.60579
\(879\) 2.23902 0.0755202
\(880\) 65.6163 2.21192
\(881\) −36.3647 −1.22516 −0.612579 0.790409i \(-0.709868\pi\)
−0.612579 + 0.790409i \(0.709868\pi\)
\(882\) 0 0
\(883\) −45.8156 −1.54182 −0.770908 0.636946i \(-0.780197\pi\)
−0.770908 + 0.636946i \(0.780197\pi\)
\(884\) −105.199 −3.53824
\(885\) −5.16176 −0.173511
\(886\) −79.0479 −2.65567
\(887\) −20.6252 −0.692526 −0.346263 0.938138i \(-0.612549\pi\)
−0.346263 + 0.938138i \(0.612549\pi\)
\(888\) −0.732321 −0.0245751
\(889\) 0 0
\(890\) −43.1393 −1.44603
\(891\) 13.9385 0.466957
\(892\) 23.7198 0.794196
\(893\) −3.56543 −0.119313
\(894\) 4.94655 0.165437
\(895\) −41.3000 −1.38051
\(896\) 0 0
\(897\) 5.56119 0.185683
\(898\) −4.18829 −0.139765
\(899\) 10.9252 0.364376
\(900\) −23.8350 −0.794500
\(901\) 33.6166 1.11993
\(902\) −28.2793 −0.941599
\(903\) 0 0
\(904\) 60.6727 2.01794
\(905\) 2.63580 0.0876169
\(906\) 2.64292 0.0878052
\(907\) 8.54091 0.283596 0.141798 0.989896i \(-0.454712\pi\)
0.141798 + 0.989896i \(0.454712\pi\)
\(908\) −90.5711 −3.00571
\(909\) −48.2887 −1.60163
\(910\) 0 0
\(911\) −43.6287 −1.44548 −0.722742 0.691118i \(-0.757119\pi\)
−0.722742 + 0.691118i \(0.757119\pi\)
\(912\) −2.42631 −0.0803431
\(913\) 0.449809 0.0148865
\(914\) −22.1505 −0.732675
\(915\) −1.33012 −0.0439725
\(916\) 74.4420 2.45963
\(917\) 0 0
\(918\) −7.42816 −0.245166
\(919\) −49.8066 −1.64297 −0.821484 0.570231i \(-0.806854\pi\)
−0.821484 + 0.570231i \(0.806854\pi\)
\(920\) −153.817 −5.07120
\(921\) 0.901607 0.0297090
\(922\) −53.3864 −1.75819
\(923\) 6.02148 0.198199
\(924\) 0 0
\(925\) −0.703081 −0.0231172
\(926\) −89.0926 −2.92776
\(927\) −22.7156 −0.746077
\(928\) −36.7974 −1.20793
\(929\) 44.5895 1.46293 0.731467 0.681876i \(-0.238836\pi\)
0.731467 + 0.681876i \(0.238836\pi\)
\(930\) 7.75130 0.254175
\(931\) 0 0
\(932\) 95.0277 3.11274
\(933\) −2.74591 −0.0898971
\(934\) −88.8004 −2.90564
\(935\) 12.1731 0.398104
\(936\) −183.671 −6.00349
\(937\) −52.7172 −1.72219 −0.861097 0.508440i \(-0.830222\pi\)
−0.861097 + 0.508440i \(0.830222\pi\)
\(938\) 0 0
\(939\) 1.75986 0.0574307
\(940\) −50.7913 −1.65663
\(941\) 15.0751 0.491436 0.245718 0.969341i \(-0.420976\pi\)
0.245718 + 0.969341i \(0.420976\pi\)
\(942\) 1.64769 0.0536846
\(943\) 39.2826 1.27922
\(944\) 224.347 7.30187
\(945\) 0 0
\(946\) −2.78378 −0.0905084
\(947\) −12.9216 −0.419895 −0.209948 0.977713i \(-0.567329\pi\)
−0.209948 + 0.977713i \(0.567329\pi\)
\(948\) 13.5878 0.441311
\(949\) 7.79648 0.253085
\(950\) −3.93108 −0.127541
\(951\) 0.339010 0.0109932
\(952\) 0 0
\(953\) −16.3314 −0.529026 −0.264513 0.964382i \(-0.585211\pi\)
−0.264513 + 0.964382i \(0.585211\pi\)
\(954\) 91.1149 2.94995
\(955\) 9.57638 0.309884
\(956\) −38.0874 −1.23184
\(957\) −0.343947 −0.0111182
\(958\) 21.5817 0.697274
\(959\) 0 0
\(960\) −13.8080 −0.445652
\(961\) 24.7236 0.797534
\(962\) −8.41084 −0.271176
\(963\) −8.11476 −0.261494
\(964\) 127.164 4.09569
\(965\) 26.5314 0.854077
\(966\) 0 0
\(967\) 56.7625 1.82536 0.912679 0.408678i \(-0.134010\pi\)
0.912679 + 0.408678i \(0.134010\pi\)
\(968\) 84.8773 2.72806
\(969\) −0.450128 −0.0144602
\(970\) −97.5414 −3.13187
\(971\) −6.73556 −0.216154 −0.108077 0.994143i \(-0.534469\pi\)
−0.108077 + 0.994143i \(0.534469\pi\)
\(972\) −22.3014 −0.715318
\(973\) 0 0
\(974\) 82.2579 2.63571
\(975\) 1.30420 0.0417679
\(976\) 57.8114 1.85050
\(977\) 21.3172 0.681997 0.340999 0.940064i \(-0.389235\pi\)
0.340999 + 0.940064i \(0.389235\pi\)
\(978\) −4.90804 −0.156942
\(979\) 9.76336 0.312038
\(980\) 0 0
\(981\) −8.47382 −0.270548
\(982\) −54.7385 −1.74678
\(983\) −21.2637 −0.678206 −0.339103 0.940749i \(-0.610124\pi\)
−0.339103 + 0.940749i \(0.610124\pi\)
\(984\) 9.59562 0.305897
\(985\) −34.1875 −1.08930
\(986\) −12.2540 −0.390247
\(987\) 0 0
\(988\) −34.6846 −1.10346
\(989\) 3.86693 0.122961
\(990\) 32.9942 1.04862
\(991\) −43.6356 −1.38613 −0.693065 0.720875i \(-0.743740\pi\)
−0.693065 + 0.720875i \(0.743740\pi\)
\(992\) −187.684 −5.95896
\(993\) −3.15913 −0.100252
\(994\) 0 0
\(995\) −45.4433 −1.44065
\(996\) −0.236941 −0.00750775
\(997\) 51.7772 1.63980 0.819901 0.572506i \(-0.194029\pi\)
0.819901 + 0.572506i \(0.194029\pi\)
\(998\) 84.6714 2.68023
\(999\) −0.438025 −0.0138585
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 931.2.a.q.1.1 yes 10
3.2 odd 2 8379.2.a.cs.1.10 10
7.2 even 3 931.2.f.q.704.10 20
7.3 odd 6 931.2.f.r.324.10 20
7.4 even 3 931.2.f.q.324.10 20
7.5 odd 6 931.2.f.r.704.10 20
7.6 odd 2 931.2.a.p.1.1 10
21.20 even 2 8379.2.a.ct.1.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
931.2.a.p.1.1 10 7.6 odd 2
931.2.a.q.1.1 yes 10 1.1 even 1 trivial
931.2.f.q.324.10 20 7.4 even 3
931.2.f.q.704.10 20 7.2 even 3
931.2.f.r.324.10 20 7.3 odd 6
931.2.f.r.704.10 20 7.5 odd 6
8379.2.a.cs.1.10 10 3.2 odd 2
8379.2.a.ct.1.10 10 21.20 even 2