Properties

Label 5610.2.a.cj.1.4
Level $5610$
Weight $2$
Character 5610.1
Self dual yes
Analytic conductor $44.796$
Analytic rank $0$
Dimension $5$
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] = [5610,2,Mod(1,5610)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5610, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("5610.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.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: \(44.7960755339\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.1284160.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 7x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(3.11852\) of defining polynomial
Character \(\chi\) \(=\) 5610.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.25889 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.25889 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -0.258895 q^{13} +2.25889 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -4.14701 q^{19} +1.00000 q^{20} +2.25889 q^{21} +1.00000 q^{22} -5.76174 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.258895 q^{26} +1.00000 q^{27} +2.25889 q^{28} +10.4741 q^{29} +1.00000 q^{30} -1.28266 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +2.25889 q^{35} +1.00000 q^{36} +4.71734 q^{37} -4.14701 q^{38} -0.258895 q^{39} +1.00000 q^{40} +12.5860 q^{41} +2.25889 q^{42} -3.54156 q^{43} +1.00000 q^{44} +1.00000 q^{45} -5.76174 q^{46} +1.43468 q^{47} +1.00000 q^{48} -1.89740 q^{49} +1.00000 q^{50} +1.00000 q^{51} -0.258895 q^{52} -9.04440 q^{53} +1.00000 q^{54} +1.00000 q^{55} +2.25889 q^{56} -4.14701 q^{57} +10.4741 q^{58} +12.9325 q^{59} +1.00000 q^{60} +14.8061 q^{61} -1.28266 q^{62} +2.25889 q^{63} +1.00000 q^{64} -0.258895 q^{65} +1.00000 q^{66} -9.30330 q^{67} +1.00000 q^{68} -5.76174 q^{69} +2.25889 q^{70} +7.83557 q^{71} +1.00000 q^{72} +15.4503 q^{73} +4.71734 q^{74} +1.00000 q^{75} -4.14701 q^{76} +2.25889 q^{77} -0.258895 q^{78} -11.3384 q^{79} +1.00000 q^{80} +1.00000 q^{81} +12.5860 q^{82} -11.7092 q^{83} +2.25889 q^{84} +1.00000 q^{85} -3.54156 q^{86} +10.4741 q^{87} +1.00000 q^{88} -5.08311 q^{89} +1.00000 q^{90} -0.584816 q^{91} -5.76174 q^{92} -1.28266 q^{93} +1.43468 q^{94} -4.14701 q^{95} +1.00000 q^{96} +9.68856 q^{97} -1.89740 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} + 5 q^{11} + 5 q^{12} + 9 q^{13} + q^{14} + 5 q^{15} + 5 q^{16} + 5 q^{17} + 5 q^{18} - 5 q^{19} + 5 q^{20} + q^{21} + 5 q^{22} + 11 q^{23} + 5 q^{24} + 5 q^{25} + 9 q^{26} + 5 q^{27} + q^{28} - 2 q^{29} + 5 q^{30} - 7 q^{31} + 5 q^{32} + 5 q^{33} + 5 q^{34} + q^{35} + 5 q^{36} + 23 q^{37} - 5 q^{38} + 9 q^{39} + 5 q^{40} + 14 q^{41} + q^{42} - 8 q^{43} + 5 q^{44} + 5 q^{45} + 11 q^{46} + 6 q^{47} + 5 q^{48} + 14 q^{49} + 5 q^{50} + 5 q^{51} + 9 q^{52} - 6 q^{53} + 5 q^{54} + 5 q^{55} + q^{56} - 5 q^{57} - 2 q^{58} + 20 q^{59} + 5 q^{60} - 5 q^{61} - 7 q^{62} + q^{63} + 5 q^{64} + 9 q^{65} + 5 q^{66} + 3 q^{67} + 5 q^{68} + 11 q^{69} + q^{70} - 2 q^{71} + 5 q^{72} + 12 q^{73} + 23 q^{74} + 5 q^{75} - 5 q^{76} + q^{77} + 9 q^{78} + 14 q^{79} + 5 q^{80} + 5 q^{81} + 14 q^{82} + 17 q^{83} + q^{84} + 5 q^{85} - 8 q^{86} - 2 q^{87} + 5 q^{88} - 6 q^{89} + 5 q^{90} - 47 q^{91} + 11 q^{92} - 7 q^{93} + 6 q^{94} - 5 q^{95} + 5 q^{96} + 23 q^{97} + 14 q^{98} + 5 q^{99}+O(q^{100}) \) 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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.00000 0.408248
\(7\) 2.25889 0.853782 0.426891 0.904303i \(-0.359609\pi\)
0.426891 + 0.904303i \(0.359609\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) −0.258895 −0.0718044 −0.0359022 0.999355i \(-0.511430\pi\)
−0.0359022 + 0.999355i \(0.511430\pi\)
\(14\) 2.25889 0.603715
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) −4.14701 −0.951389 −0.475694 0.879611i \(-0.657803\pi\)
−0.475694 + 0.879611i \(0.657803\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.25889 0.492931
\(22\) 1.00000 0.213201
\(23\) −5.76174 −1.20141 −0.600703 0.799472i \(-0.705113\pi\)
−0.600703 + 0.799472i \(0.705113\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) −0.258895 −0.0507734
\(27\) 1.00000 0.192450
\(28\) 2.25889 0.426891
\(29\) 10.4741 1.94499 0.972493 0.232932i \(-0.0748319\pi\)
0.972493 + 0.232932i \(0.0748319\pi\)
\(30\) 1.00000 0.182574
\(31\) −1.28266 −0.230373 −0.115186 0.993344i \(-0.536747\pi\)
−0.115186 + 0.993344i \(0.536747\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) 2.25889 0.381823
\(36\) 1.00000 0.166667
\(37\) 4.71734 0.775526 0.387763 0.921759i \(-0.373248\pi\)
0.387763 + 0.921759i \(0.373248\pi\)
\(38\) −4.14701 −0.672733
\(39\) −0.258895 −0.0414563
\(40\) 1.00000 0.158114
\(41\) 12.5860 1.96560 0.982798 0.184683i \(-0.0591258\pi\)
0.982798 + 0.184683i \(0.0591258\pi\)
\(42\) 2.25889 0.348555
\(43\) −3.54156 −0.540082 −0.270041 0.962849i \(-0.587037\pi\)
−0.270041 + 0.962849i \(0.587037\pi\)
\(44\) 1.00000 0.150756
\(45\) 1.00000 0.149071
\(46\) −5.76174 −0.849522
\(47\) 1.43468 0.209269 0.104635 0.994511i \(-0.466633\pi\)
0.104635 + 0.994511i \(0.466633\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.89740 −0.271056
\(50\) 1.00000 0.141421
\(51\) 1.00000 0.140028
\(52\) −0.258895 −0.0359022
\(53\) −9.04440 −1.24234 −0.621172 0.783674i \(-0.713343\pi\)
−0.621172 + 0.783674i \(0.713343\pi\)
\(54\) 1.00000 0.136083
\(55\) 1.00000 0.134840
\(56\) 2.25889 0.301857
\(57\) −4.14701 −0.549285
\(58\) 10.4741 1.37531
\(59\) 12.9325 1.68367 0.841835 0.539735i \(-0.181476\pi\)
0.841835 + 0.539735i \(0.181476\pi\)
\(60\) 1.00000 0.129099
\(61\) 14.8061 1.89573 0.947866 0.318668i \(-0.103236\pi\)
0.947866 + 0.318668i \(0.103236\pi\)
\(62\) −1.28266 −0.162898
\(63\) 2.25889 0.284594
\(64\) 1.00000 0.125000
\(65\) −0.258895 −0.0321119
\(66\) 1.00000 0.123091
\(67\) −9.30330 −1.13658 −0.568289 0.822829i \(-0.692395\pi\)
−0.568289 + 0.822829i \(0.692395\pi\)
\(68\) 1.00000 0.121268
\(69\) −5.76174 −0.693632
\(70\) 2.25889 0.269990
\(71\) 7.83557 0.929911 0.464956 0.885334i \(-0.346070\pi\)
0.464956 + 0.885334i \(0.346070\pi\)
\(72\) 1.00000 0.117851
\(73\) 15.4503 1.80832 0.904161 0.427193i \(-0.140497\pi\)
0.904161 + 0.427193i \(0.140497\pi\)
\(74\) 4.71734 0.548380
\(75\) 1.00000 0.115470
\(76\) −4.14701 −0.475694
\(77\) 2.25889 0.257425
\(78\) −0.258895 −0.0293140
\(79\) −11.3384 −1.27567 −0.637836 0.770172i \(-0.720170\pi\)
−0.637836 + 0.770172i \(0.720170\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 12.5860 1.38989
\(83\) −11.7092 −1.28525 −0.642626 0.766180i \(-0.722155\pi\)
−0.642626 + 0.766180i \(0.722155\pi\)
\(84\) 2.25889 0.246466
\(85\) 1.00000 0.108465
\(86\) −3.54156 −0.381896
\(87\) 10.4741 1.12294
\(88\) 1.00000 0.106600
\(89\) −5.08311 −0.538809 −0.269404 0.963027i \(-0.586827\pi\)
−0.269404 + 0.963027i \(0.586827\pi\)
\(90\) 1.00000 0.105409
\(91\) −0.584816 −0.0613053
\(92\) −5.76174 −0.600703
\(93\) −1.28266 −0.133006
\(94\) 1.43468 0.147976
\(95\) −4.14701 −0.425474
\(96\) 1.00000 0.102062
\(97\) 9.68856 0.983724 0.491862 0.870673i \(-0.336316\pi\)
0.491862 + 0.870673i \(0.336316\pi\)
\(98\) −1.89740 −0.191666
\(99\) 1.00000 0.100504
\(100\) 1.00000 0.100000
\(101\) −9.84058 −0.979174 −0.489587 0.871954i \(-0.662853\pi\)
−0.489587 + 0.871954i \(0.662853\pi\)
\(102\) 1.00000 0.0990148
\(103\) 2.89740 0.285489 0.142744 0.989760i \(-0.454407\pi\)
0.142744 + 0.989760i \(0.454407\pi\)
\(104\) −0.258895 −0.0253867
\(105\) 2.25889 0.220446
\(106\) −9.04440 −0.878470
\(107\) −4.18006 −0.404101 −0.202051 0.979375i \(-0.564761\pi\)
−0.202051 + 0.979375i \(0.564761\pi\)
\(108\) 1.00000 0.0962250
\(109\) 3.28266 0.314422 0.157211 0.987565i \(-0.449750\pi\)
0.157211 + 0.987565i \(0.449750\pi\)
\(110\) 1.00000 0.0953463
\(111\) 4.71734 0.447750
\(112\) 2.25889 0.213445
\(113\) −5.38214 −0.506309 −0.253154 0.967426i \(-0.581468\pi\)
−0.253154 + 0.967426i \(0.581468\pi\)
\(114\) −4.14701 −0.388403
\(115\) −5.76174 −0.537285
\(116\) 10.4741 0.972493
\(117\) −0.258895 −0.0239348
\(118\) 12.9325 1.19053
\(119\) 2.25889 0.207073
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) 14.8061 1.34049
\(123\) 12.5860 1.13484
\(124\) −1.28266 −0.115186
\(125\) 1.00000 0.0894427
\(126\) 2.25889 0.201238
\(127\) 3.08311 0.273582 0.136791 0.990600i \(-0.456321\pi\)
0.136791 + 0.990600i \(0.456321\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.54156 −0.311817
\(130\) −0.258895 −0.0227066
\(131\) −13.2389 −1.15669 −0.578346 0.815792i \(-0.696302\pi\)
−0.578346 + 0.815792i \(0.696302\pi\)
\(132\) 1.00000 0.0870388
\(133\) −9.36765 −0.812278
\(134\) −9.30330 −0.803682
\(135\) 1.00000 0.0860663
\(136\) 1.00000 0.0857493
\(137\) 14.6598 1.25247 0.626235 0.779634i \(-0.284595\pi\)
0.626235 + 0.779634i \(0.284595\pi\)
\(138\) −5.76174 −0.490472
\(139\) 7.03939 0.597073 0.298537 0.954398i \(-0.403501\pi\)
0.298537 + 0.954398i \(0.403501\pi\)
\(140\) 2.25889 0.190911
\(141\) 1.43468 0.120822
\(142\) 7.83557 0.657546
\(143\) −0.258895 −0.0216499
\(144\) 1.00000 0.0833333
\(145\) 10.4741 0.869824
\(146\) 15.4503 1.27868
\(147\) −1.89740 −0.156495
\(148\) 4.71734 0.387763
\(149\) −4.81539 −0.394492 −0.197246 0.980354i \(-0.563200\pi\)
−0.197246 + 0.980354i \(0.563200\pi\)
\(150\) 1.00000 0.0816497
\(151\) −3.23513 −0.263271 −0.131636 0.991298i \(-0.542023\pi\)
−0.131636 + 0.991298i \(0.542023\pi\)
\(152\) −4.14701 −0.336367
\(153\) 1.00000 0.0808452
\(154\) 2.25889 0.182027
\(155\) −1.28266 −0.103026
\(156\) −0.258895 −0.0207282
\(157\) −15.2652 −1.21830 −0.609149 0.793056i \(-0.708489\pi\)
−0.609149 + 0.793056i \(0.708489\pi\)
\(158\) −11.3384 −0.902036
\(159\) −9.04440 −0.717268
\(160\) 1.00000 0.0790569
\(161\) −13.0152 −1.02574
\(162\) 1.00000 0.0785674
\(163\) −21.8650 −1.71260 −0.856301 0.516478i \(-0.827243\pi\)
−0.856301 + 0.516478i \(0.827243\pi\)
\(164\) 12.5860 0.982798
\(165\) 1.00000 0.0778499
\(166\) −11.7092 −0.908810
\(167\) −14.4265 −1.11636 −0.558180 0.829720i \(-0.688500\pi\)
−0.558180 + 0.829720i \(0.688500\pi\)
\(168\) 2.25889 0.174278
\(169\) −12.9330 −0.994844
\(170\) 1.00000 0.0766965
\(171\) −4.14701 −0.317130
\(172\) −3.54156 −0.270041
\(173\) 6.10830 0.464405 0.232203 0.972667i \(-0.425407\pi\)
0.232203 + 0.972667i \(0.425407\pi\)
\(174\) 10.4741 0.794037
\(175\) 2.25889 0.170756
\(176\) 1.00000 0.0753778
\(177\) 12.9325 0.972067
\(178\) −5.08311 −0.380995
\(179\) −11.0707 −0.827463 −0.413731 0.910399i \(-0.635775\pi\)
−0.413731 + 0.910399i \(0.635775\pi\)
\(180\) 1.00000 0.0745356
\(181\) −12.3828 −0.920408 −0.460204 0.887813i \(-0.652224\pi\)
−0.460204 + 0.887813i \(0.652224\pi\)
\(182\) −0.584816 −0.0433494
\(183\) 14.8061 1.09450
\(184\) −5.76174 −0.424761
\(185\) 4.71734 0.346826
\(186\) −1.28266 −0.0940492
\(187\) 1.00000 0.0731272
\(188\) 1.43468 0.104635
\(189\) 2.25889 0.164310
\(190\) −4.14701 −0.300856
\(191\) −19.4798 −1.40951 −0.704753 0.709453i \(-0.748942\pi\)
−0.704753 + 0.709453i \(0.748942\pi\)
\(192\) 1.00000 0.0721688
\(193\) 6.17330 0.444364 0.222182 0.975005i \(-0.428682\pi\)
0.222182 + 0.975005i \(0.428682\pi\)
\(194\) 9.68856 0.695598
\(195\) −0.258895 −0.0185398
\(196\) −1.89740 −0.135528
\(197\) 3.23894 0.230765 0.115383 0.993321i \(-0.463191\pi\)
0.115383 + 0.993321i \(0.463191\pi\)
\(198\) 1.00000 0.0710669
\(199\) 6.71734 0.476180 0.238090 0.971243i \(-0.423479\pi\)
0.238090 + 0.971243i \(0.423479\pi\)
\(200\) 1.00000 0.0707107
\(201\) −9.30330 −0.656204
\(202\) −9.84058 −0.692381
\(203\) 23.6598 1.66059
\(204\) 1.00000 0.0700140
\(205\) 12.5860 0.879041
\(206\) 2.89740 0.201871
\(207\) −5.76174 −0.400469
\(208\) −0.258895 −0.0179511
\(209\) −4.14701 −0.286854
\(210\) 2.25889 0.155879
\(211\) 22.7206 1.56415 0.782074 0.623186i \(-0.214162\pi\)
0.782074 + 0.623186i \(0.214162\pi\)
\(212\) −9.04440 −0.621172
\(213\) 7.83557 0.536884
\(214\) −4.18006 −0.285743
\(215\) −3.54156 −0.241532
\(216\) 1.00000 0.0680414
\(217\) −2.89740 −0.196688
\(218\) 3.28266 0.222330
\(219\) 15.4503 1.04403
\(220\) 1.00000 0.0674200
\(221\) −0.258895 −0.0174151
\(222\) 4.71734 0.316607
\(223\) 11.1914 0.749432 0.374716 0.927140i \(-0.377740\pi\)
0.374716 + 0.927140i \(0.377740\pi\)
\(224\) 2.25889 0.150929
\(225\) 1.00000 0.0666667
\(226\) −5.38214 −0.358014
\(227\) −8.87317 −0.588933 −0.294467 0.955662i \(-0.595142\pi\)
−0.294467 + 0.955662i \(0.595142\pi\)
\(228\) −4.14701 −0.274642
\(229\) 28.4209 1.87810 0.939052 0.343774i \(-0.111706\pi\)
0.939052 + 0.343774i \(0.111706\pi\)
\(230\) −5.76174 −0.379918
\(231\) 2.25889 0.148624
\(232\) 10.4741 0.687656
\(233\) −17.8949 −1.17233 −0.586167 0.810190i \(-0.699364\pi\)
−0.586167 + 0.810190i \(0.699364\pi\)
\(234\) −0.258895 −0.0169245
\(235\) 1.43468 0.0935881
\(236\) 12.9325 0.841835
\(237\) −11.3384 −0.736509
\(238\) 2.25889 0.146422
\(239\) −8.29401 −0.536495 −0.268248 0.963350i \(-0.586445\pi\)
−0.268248 + 0.963350i \(0.586445\pi\)
\(240\) 1.00000 0.0645497
\(241\) −14.2657 −0.918934 −0.459467 0.888195i \(-0.651960\pi\)
−0.459467 + 0.888195i \(0.651960\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) 14.8061 0.947866
\(245\) −1.89740 −0.121220
\(246\) 12.5860 0.802451
\(247\) 1.07364 0.0683139
\(248\) −1.28266 −0.0814490
\(249\) −11.7092 −0.742040
\(250\) 1.00000 0.0632456
\(251\) 18.6892 1.17965 0.589827 0.807529i \(-0.299196\pi\)
0.589827 + 0.807529i \(0.299196\pi\)
\(252\) 2.25889 0.142297
\(253\) −5.76174 −0.362238
\(254\) 3.08311 0.193452
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) 14.6204 0.911997 0.455999 0.889980i \(-0.349282\pi\)
0.455999 + 0.889980i \(0.349282\pi\)
\(258\) −3.54156 −0.220488
\(259\) 10.6560 0.662130
\(260\) −0.258895 −0.0160560
\(261\) 10.4741 0.648329
\(262\) −13.2389 −0.817905
\(263\) 11.1914 0.690092 0.345046 0.938586i \(-0.387863\pi\)
0.345046 + 0.938586i \(0.387863\pi\)
\(264\) 1.00000 0.0615457
\(265\) −9.04440 −0.555593
\(266\) −9.36765 −0.574368
\(267\) −5.08311 −0.311081
\(268\) −9.30330 −0.568289
\(269\) −8.13818 −0.496194 −0.248097 0.968735i \(-0.579805\pi\)
−0.248097 + 0.968735i \(0.579805\pi\)
\(270\) 1.00000 0.0608581
\(271\) 3.19707 0.194208 0.0971041 0.995274i \(-0.469042\pi\)
0.0971041 + 0.995274i \(0.469042\pi\)
\(272\) 1.00000 0.0606339
\(273\) −0.584816 −0.0353946
\(274\) 14.6598 0.885630
\(275\) 1.00000 0.0603023
\(276\) −5.76174 −0.346816
\(277\) 11.9087 0.715527 0.357764 0.933812i \(-0.383539\pi\)
0.357764 + 0.933812i \(0.383539\pi\)
\(278\) 7.03939 0.422195
\(279\) −1.28266 −0.0767909
\(280\) 2.25889 0.134995
\(281\) −24.3126 −1.45037 −0.725183 0.688556i \(-0.758245\pi\)
−0.725183 + 0.688556i \(0.758245\pi\)
\(282\) 1.43468 0.0854339
\(283\) 6.42654 0.382018 0.191009 0.981588i \(-0.438824\pi\)
0.191009 + 0.981588i \(0.438824\pi\)
\(284\) 7.83557 0.464956
\(285\) −4.14701 −0.245648
\(286\) −0.258895 −0.0153088
\(287\) 28.4304 1.67819
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 10.4741 0.615059
\(291\) 9.68856 0.567954
\(292\) 15.4503 0.904161
\(293\) −6.75921 −0.394877 −0.197439 0.980315i \(-0.563262\pi\)
−0.197439 + 0.980315i \(0.563262\pi\)
\(294\) −1.89740 −0.110658
\(295\) 12.9325 0.752960
\(296\) 4.71734 0.274190
\(297\) 1.00000 0.0580259
\(298\) −4.81539 −0.278948
\(299\) 1.49168 0.0862663
\(300\) 1.00000 0.0577350
\(301\) −8.00000 −0.461112
\(302\) −3.23513 −0.186161
\(303\) −9.84058 −0.565327
\(304\) −4.14701 −0.237847
\(305\) 14.8061 0.847797
\(306\) 1.00000 0.0571662
\(307\) −14.4009 −0.821902 −0.410951 0.911657i \(-0.634803\pi\)
−0.410951 + 0.911657i \(0.634803\pi\)
\(308\) 2.25889 0.128712
\(309\) 2.89740 0.164827
\(310\) −1.28266 −0.0728502
\(311\) 15.8768 0.900293 0.450147 0.892955i \(-0.351372\pi\)
0.450147 + 0.892955i \(0.351372\pi\)
\(312\) −0.258895 −0.0146570
\(313\) −11.6587 −0.658987 −0.329494 0.944158i \(-0.606878\pi\)
−0.329494 + 0.944158i \(0.606878\pi\)
\(314\) −15.2652 −0.861467
\(315\) 2.25889 0.127274
\(316\) −11.3384 −0.637836
\(317\) −8.08881 −0.454313 −0.227156 0.973858i \(-0.572943\pi\)
−0.227156 + 0.973858i \(0.572943\pi\)
\(318\) −9.04440 −0.507185
\(319\) 10.4741 0.586435
\(320\) 1.00000 0.0559017
\(321\) −4.18006 −0.233308
\(322\) −13.0152 −0.725307
\(323\) −4.14701 −0.230746
\(324\) 1.00000 0.0555556
\(325\) −0.258895 −0.0143609
\(326\) −21.8650 −1.21099
\(327\) 3.28266 0.181532
\(328\) 12.5860 0.694943
\(329\) 3.24079 0.178670
\(330\) 1.00000 0.0550482
\(331\) 16.1363 0.886933 0.443467 0.896291i \(-0.353748\pi\)
0.443467 + 0.896291i \(0.353748\pi\)
\(332\) −11.7092 −0.642626
\(333\) 4.71734 0.258509
\(334\) −14.4265 −0.789385
\(335\) −9.30330 −0.508293
\(336\) 2.25889 0.123233
\(337\) 16.4859 0.898043 0.449022 0.893521i \(-0.351773\pi\)
0.449022 + 0.893521i \(0.351773\pi\)
\(338\) −12.9330 −0.703461
\(339\) −5.38214 −0.292317
\(340\) 1.00000 0.0542326
\(341\) −1.28266 −0.0694600
\(342\) −4.14701 −0.224244
\(343\) −20.0983 −1.08521
\(344\) −3.54156 −0.190948
\(345\) −5.76174 −0.310202
\(346\) 6.10830 0.328384
\(347\) 7.71486 0.414155 0.207078 0.978325i \(-0.433605\pi\)
0.207078 + 0.978325i \(0.433605\pi\)
\(348\) 10.4741 0.561469
\(349\) 5.47720 0.293188 0.146594 0.989197i \(-0.453169\pi\)
0.146594 + 0.989197i \(0.453169\pi\)
\(350\) 2.25889 0.120743
\(351\) −0.258895 −0.0138188
\(352\) 1.00000 0.0533002
\(353\) 11.4190 0.607772 0.303886 0.952708i \(-0.401716\pi\)
0.303886 + 0.952708i \(0.401716\pi\)
\(354\) 12.9325 0.687355
\(355\) 7.83557 0.415869
\(356\) −5.08311 −0.269404
\(357\) 2.25889 0.119553
\(358\) −11.0707 −0.585105
\(359\) −29.4659 −1.55515 −0.777576 0.628789i \(-0.783551\pi\)
−0.777576 + 0.628789i \(0.783551\pi\)
\(360\) 1.00000 0.0527046
\(361\) −1.80233 −0.0948595
\(362\) −12.3828 −0.650827
\(363\) 1.00000 0.0524864
\(364\) −0.584816 −0.0306527
\(365\) 15.4503 0.808706
\(366\) 14.8061 0.773930
\(367\) 10.0068 0.522351 0.261175 0.965291i \(-0.415890\pi\)
0.261175 + 0.965291i \(0.415890\pi\)
\(368\) −5.76174 −0.300352
\(369\) 12.5860 0.655199
\(370\) 4.71734 0.245243
\(371\) −20.4304 −1.06069
\(372\) −1.28266 −0.0665029
\(373\) −15.9681 −0.826797 −0.413398 0.910550i \(-0.635658\pi\)
−0.413398 + 0.910550i \(0.635658\pi\)
\(374\) 1.00000 0.0517088
\(375\) 1.00000 0.0516398
\(376\) 1.43468 0.0739879
\(377\) −2.71168 −0.139659
\(378\) 2.25889 0.116185
\(379\) 13.9191 0.714978 0.357489 0.933917i \(-0.383633\pi\)
0.357489 + 0.933917i \(0.383633\pi\)
\(380\) −4.14701 −0.212737
\(381\) 3.08311 0.157953
\(382\) −19.4798 −0.996671
\(383\) −35.2997 −1.80373 −0.901865 0.432017i \(-0.857802\pi\)
−0.901865 + 0.432017i \(0.857802\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.25889 0.115124
\(386\) 6.17330 0.314213
\(387\) −3.54156 −0.180027
\(388\) 9.68856 0.491862
\(389\) −3.88310 −0.196881 −0.0984405 0.995143i \(-0.531385\pi\)
−0.0984405 + 0.995143i \(0.531385\pi\)
\(390\) −0.258895 −0.0131096
\(391\) −5.76174 −0.291384
\(392\) −1.89740 −0.0958329
\(393\) −13.2389 −0.667816
\(394\) 3.23894 0.163176
\(395\) −11.3384 −0.570498
\(396\) 1.00000 0.0502519
\(397\) −17.3334 −0.869939 −0.434969 0.900445i \(-0.643241\pi\)
−0.434969 + 0.900445i \(0.643241\pi\)
\(398\) 6.71734 0.336710
\(399\) −9.36765 −0.468969
\(400\) 1.00000 0.0500000
\(401\) 9.63221 0.481009 0.240505 0.970648i \(-0.422687\pi\)
0.240505 + 0.970648i \(0.422687\pi\)
\(402\) −9.30330 −0.464006
\(403\) 0.332074 0.0165418
\(404\) −9.84058 −0.489587
\(405\) 1.00000 0.0496904
\(406\) 23.6598 1.17422
\(407\) 4.71734 0.233830
\(408\) 1.00000 0.0495074
\(409\) −25.8075 −1.27610 −0.638049 0.769996i \(-0.720258\pi\)
−0.638049 + 0.769996i \(0.720258\pi\)
\(410\) 12.5860 0.621576
\(411\) 14.6598 0.723114
\(412\) 2.89740 0.142744
\(413\) 29.2132 1.43749
\(414\) −5.76174 −0.283174
\(415\) −11.7092 −0.574782
\(416\) −0.258895 −0.0126934
\(417\) 7.03939 0.344721
\(418\) −4.14701 −0.202837
\(419\) 11.0057 0.537663 0.268832 0.963187i \(-0.413362\pi\)
0.268832 + 0.963187i \(0.413362\pi\)
\(420\) 2.25889 0.110223
\(421\) −30.5210 −1.48750 −0.743751 0.668456i \(-0.766955\pi\)
−0.743751 + 0.668456i \(0.766955\pi\)
\(422\) 22.7206 1.10602
\(423\) 1.43468 0.0697565
\(424\) −9.04440 −0.439235
\(425\) 1.00000 0.0485071
\(426\) 7.83557 0.379635
\(427\) 33.4455 1.61854
\(428\) −4.18006 −0.202051
\(429\) −0.258895 −0.0124995
\(430\) −3.54156 −0.170789
\(431\) −19.8406 −0.955687 −0.477844 0.878445i \(-0.658581\pi\)
−0.477844 + 0.878445i \(0.658581\pi\)
\(432\) 1.00000 0.0481125
\(433\) 7.84738 0.377121 0.188561 0.982062i \(-0.439618\pi\)
0.188561 + 0.982062i \(0.439618\pi\)
\(434\) −2.89740 −0.139079
\(435\) 10.4741 0.502193
\(436\) 3.28266 0.157211
\(437\) 23.8940 1.14300
\(438\) 15.4503 0.738244
\(439\) 20.3840 0.972876 0.486438 0.873715i \(-0.338296\pi\)
0.486438 + 0.873715i \(0.338296\pi\)
\(440\) 1.00000 0.0476731
\(441\) −1.89740 −0.0903522
\(442\) −0.258895 −0.0123144
\(443\) −14.1889 −0.674134 −0.337067 0.941481i \(-0.609435\pi\)
−0.337067 + 0.941481i \(0.609435\pi\)
\(444\) 4.71734 0.223875
\(445\) −5.08311 −0.240963
\(446\) 11.1914 0.529929
\(447\) −4.81539 −0.227760
\(448\) 2.25889 0.106723
\(449\) −24.7330 −1.16722 −0.583610 0.812034i \(-0.698360\pi\)
−0.583610 + 0.812034i \(0.698360\pi\)
\(450\) 1.00000 0.0471405
\(451\) 12.5860 0.592650
\(452\) −5.38214 −0.253154
\(453\) −3.23513 −0.152000
\(454\) −8.87317 −0.416439
\(455\) −0.584816 −0.0274166
\(456\) −4.14701 −0.194201
\(457\) −23.1002 −1.08058 −0.540290 0.841479i \(-0.681685\pi\)
−0.540290 + 0.841479i \(0.681685\pi\)
\(458\) 28.4209 1.32802
\(459\) 1.00000 0.0466760
\(460\) −5.76174 −0.268643
\(461\) −24.9237 −1.16081 −0.580406 0.814327i \(-0.697106\pi\)
−0.580406 + 0.814327i \(0.697106\pi\)
\(462\) 2.25889 0.105093
\(463\) 29.1751 1.35588 0.677942 0.735116i \(-0.262872\pi\)
0.677942 + 0.735116i \(0.262872\pi\)
\(464\) 10.4741 0.486247
\(465\) −1.28266 −0.0594820
\(466\) −17.8949 −0.828966
\(467\) −2.33654 −0.108122 −0.0540610 0.998538i \(-0.517217\pi\)
−0.0540610 + 0.998538i \(0.517217\pi\)
\(468\) −0.258895 −0.0119674
\(469\) −21.0152 −0.970390
\(470\) 1.43468 0.0661768
\(471\) −15.2652 −0.703385
\(472\) 12.9325 0.595267
\(473\) −3.54156 −0.162841
\(474\) −11.3384 −0.520791
\(475\) −4.14701 −0.190278
\(476\) 2.25889 0.103536
\(477\) −9.04440 −0.414115
\(478\) −8.29401 −0.379359
\(479\) −15.6549 −0.715289 −0.357645 0.933858i \(-0.616420\pi\)
−0.357645 + 0.933858i \(0.616420\pi\)
\(480\) 1.00000 0.0456435
\(481\) −1.22129 −0.0556862
\(482\) −14.2657 −0.649785
\(483\) −13.0152 −0.592211
\(484\) 1.00000 0.0454545
\(485\) 9.68856 0.439935
\(486\) 1.00000 0.0453609
\(487\) 31.1787 1.41284 0.706421 0.707792i \(-0.250308\pi\)
0.706421 + 0.707792i \(0.250308\pi\)
\(488\) 14.8061 0.670243
\(489\) −21.8650 −0.988771
\(490\) −1.89740 −0.0857156
\(491\) 39.3953 1.77789 0.888943 0.458018i \(-0.151441\pi\)
0.888943 + 0.458018i \(0.151441\pi\)
\(492\) 12.5860 0.567419
\(493\) 10.4741 0.471728
\(494\) 1.07364 0.0483052
\(495\) 1.00000 0.0449467
\(496\) −1.28266 −0.0575932
\(497\) 17.6997 0.793941
\(498\) −11.7092 −0.524702
\(499\) 17.2859 0.773822 0.386911 0.922117i \(-0.373542\pi\)
0.386911 + 0.922117i \(0.373542\pi\)
\(500\) 1.00000 0.0447214
\(501\) −14.4265 −0.644530
\(502\) 18.6892 0.834142
\(503\) −20.8342 −0.928950 −0.464475 0.885586i \(-0.653757\pi\)
−0.464475 + 0.885586i \(0.653757\pi\)
\(504\) 2.25889 0.100619
\(505\) −9.84058 −0.437900
\(506\) −5.76174 −0.256141
\(507\) −12.9330 −0.574374
\(508\) 3.08311 0.136791
\(509\) −4.63469 −0.205429 −0.102714 0.994711i \(-0.532753\pi\)
−0.102714 + 0.994711i \(0.532753\pi\)
\(510\) 1.00000 0.0442807
\(511\) 34.9006 1.54391
\(512\) 1.00000 0.0441942
\(513\) −4.14701 −0.183095
\(514\) 14.6204 0.644879
\(515\) 2.89740 0.127674
\(516\) −3.54156 −0.155908
\(517\) 1.43468 0.0630971
\(518\) 10.6560 0.468197
\(519\) 6.10830 0.268125
\(520\) −0.258895 −0.0113533
\(521\) 23.8337 1.04417 0.522087 0.852892i \(-0.325154\pi\)
0.522087 + 0.852892i \(0.325154\pi\)
\(522\) 10.4741 0.458438
\(523\) −29.4066 −1.28586 −0.642930 0.765925i \(-0.722281\pi\)
−0.642930 + 0.765925i \(0.722281\pi\)
\(524\) −13.2389 −0.578346
\(525\) 2.25889 0.0985862
\(526\) 11.1914 0.487969
\(527\) −1.28266 −0.0558736
\(528\) 1.00000 0.0435194
\(529\) 10.1977 0.443377
\(530\) −9.04440 −0.392864
\(531\) 12.9325 0.561223
\(532\) −9.36765 −0.406139
\(533\) −3.25844 −0.141139
\(534\) −5.08311 −0.219968
\(535\) −4.18006 −0.180720
\(536\) −9.30330 −0.401841
\(537\) −11.0707 −0.477736
\(538\) −8.13818 −0.350862
\(539\) −1.89740 −0.0817266
\(540\) 1.00000 0.0430331
\(541\) 33.2560 1.42979 0.714893 0.699234i \(-0.246475\pi\)
0.714893 + 0.699234i \(0.246475\pi\)
\(542\) 3.19707 0.137326
\(543\) −12.3828 −0.531398
\(544\) 1.00000 0.0428746
\(545\) 3.28266 0.140614
\(546\) −0.584816 −0.0250278
\(547\) −3.96667 −0.169603 −0.0848013 0.996398i \(-0.527026\pi\)
−0.0848013 + 0.996398i \(0.527026\pi\)
\(548\) 14.6598 0.626235
\(549\) 14.8061 0.631911
\(550\) 1.00000 0.0426401
\(551\) −43.4360 −1.85044
\(552\) −5.76174 −0.245236
\(553\) −25.6123 −1.08915
\(554\) 11.9087 0.505954
\(555\) 4.71734 0.200240
\(556\) 7.03939 0.298537
\(557\) −2.53544 −0.107430 −0.0537150 0.998556i \(-0.517106\pi\)
−0.0537150 + 0.998556i \(0.517106\pi\)
\(558\) −1.28266 −0.0542994
\(559\) 0.916889 0.0387803
\(560\) 2.25889 0.0954557
\(561\) 1.00000 0.0422200
\(562\) −24.3126 −1.02556
\(563\) −8.55585 −0.360586 −0.180293 0.983613i \(-0.557705\pi\)
−0.180293 + 0.983613i \(0.557705\pi\)
\(564\) 1.43468 0.0604109
\(565\) −5.38214 −0.226428
\(566\) 6.42654 0.270128
\(567\) 2.25889 0.0948647
\(568\) 7.83557 0.328773
\(569\) 5.20273 0.218110 0.109055 0.994036i \(-0.465218\pi\)
0.109055 + 0.994036i \(0.465218\pi\)
\(570\) −4.14701 −0.173699
\(571\) −24.8732 −1.04091 −0.520455 0.853889i \(-0.674238\pi\)
−0.520455 + 0.853889i \(0.674238\pi\)
\(572\) −0.258895 −0.0108249
\(573\) −19.4798 −0.813779
\(574\) 28.4304 1.18666
\(575\) −5.76174 −0.240281
\(576\) 1.00000 0.0416667
\(577\) −13.0057 −0.541434 −0.270717 0.962659i \(-0.587261\pi\)
−0.270717 + 0.962659i \(0.587261\pi\)
\(578\) 1.00000 0.0415945
\(579\) 6.17330 0.256554
\(580\) 10.4741 0.434912
\(581\) −26.4498 −1.09732
\(582\) 9.68856 0.401604
\(583\) −9.04440 −0.374581
\(584\) 15.4503 0.639338
\(585\) −0.258895 −0.0107040
\(586\) −6.75921 −0.279220
\(587\) 4.95315 0.204438 0.102219 0.994762i \(-0.467406\pi\)
0.102219 + 0.994762i \(0.467406\pi\)
\(588\) −1.89740 −0.0782473
\(589\) 5.31920 0.219174
\(590\) 12.9325 0.532423
\(591\) 3.23894 0.133232
\(592\) 4.71734 0.193881
\(593\) −33.8175 −1.38872 −0.694359 0.719629i \(-0.744312\pi\)
−0.694359 + 0.719629i \(0.744312\pi\)
\(594\) 1.00000 0.0410305
\(595\) 2.25889 0.0926056
\(596\) −4.81539 −0.197246
\(597\) 6.71734 0.274922
\(598\) 1.49168 0.0609995
\(599\) 36.4873 1.49083 0.745415 0.666600i \(-0.232251\pi\)
0.745415 + 0.666600i \(0.232251\pi\)
\(600\) 1.00000 0.0408248
\(601\) −40.1307 −1.63697 −0.818483 0.574530i \(-0.805185\pi\)
−0.818483 + 0.574530i \(0.805185\pi\)
\(602\) −8.00000 −0.326056
\(603\) −9.30330 −0.378860
\(604\) −3.23513 −0.131636
\(605\) 1.00000 0.0406558
\(606\) −9.84058 −0.399746
\(607\) −19.7525 −0.801729 −0.400865 0.916137i \(-0.631290\pi\)
−0.400865 + 0.916137i \(0.631290\pi\)
\(608\) −4.14701 −0.168183
\(609\) 23.6598 0.958744
\(610\) 14.8061 0.599483
\(611\) −0.371431 −0.0150265
\(612\) 1.00000 0.0404226
\(613\) 39.0588 1.57757 0.788786 0.614668i \(-0.210710\pi\)
0.788786 + 0.614668i \(0.210710\pi\)
\(614\) −14.4009 −0.581173
\(615\) 12.5860 0.507515
\(616\) 2.25889 0.0910135
\(617\) −24.2827 −0.977586 −0.488793 0.872400i \(-0.662563\pi\)
−0.488793 + 0.872400i \(0.662563\pi\)
\(618\) 2.89740 0.116550
\(619\) −28.5547 −1.14771 −0.573855 0.818957i \(-0.694553\pi\)
−0.573855 + 0.818957i \(0.694553\pi\)
\(620\) −1.28266 −0.0515129
\(621\) −5.76174 −0.231211
\(622\) 15.8768 0.636603
\(623\) −11.4822 −0.460025
\(624\) −0.258895 −0.0103641
\(625\) 1.00000 0.0400000
\(626\) −11.6587 −0.465975
\(627\) −4.14701 −0.165616
\(628\) −15.2652 −0.609149
\(629\) 4.71734 0.188093
\(630\) 2.25889 0.0899965
\(631\) −6.46024 −0.257178 −0.128589 0.991698i \(-0.541045\pi\)
−0.128589 + 0.991698i \(0.541045\pi\)
\(632\) −11.3384 −0.451018
\(633\) 22.7206 0.903061
\(634\) −8.08881 −0.321247
\(635\) 3.08311 0.122350
\(636\) −9.04440 −0.358634
\(637\) 0.491225 0.0194631
\(638\) 10.4741 0.414672
\(639\) 7.83557 0.309970
\(640\) 1.00000 0.0395285
\(641\) 34.4536 1.36083 0.680417 0.732825i \(-0.261799\pi\)
0.680417 + 0.732825i \(0.261799\pi\)
\(642\) −4.18006 −0.164974
\(643\) 8.13634 0.320866 0.160433 0.987047i \(-0.448711\pi\)
0.160433 + 0.987047i \(0.448711\pi\)
\(644\) −13.0152 −0.512869
\(645\) −3.54156 −0.139449
\(646\) −4.14701 −0.163162
\(647\) 16.3529 0.642900 0.321450 0.946927i \(-0.395830\pi\)
0.321450 + 0.946927i \(0.395830\pi\)
\(648\) 1.00000 0.0392837
\(649\) 12.9325 0.507646
\(650\) −0.258895 −0.0101547
\(651\) −2.89740 −0.113558
\(652\) −21.8650 −0.856301
\(653\) 28.3828 1.11071 0.555353 0.831615i \(-0.312583\pi\)
0.555353 + 0.831615i \(0.312583\pi\)
\(654\) 3.28266 0.128362
\(655\) −13.2389 −0.517288
\(656\) 12.5860 0.491399
\(657\) 15.4503 0.602774
\(658\) 3.24079 0.126339
\(659\) −21.3703 −0.832470 −0.416235 0.909257i \(-0.636651\pi\)
−0.416235 + 0.909257i \(0.636651\pi\)
\(660\) 1.00000 0.0389249
\(661\) −9.32775 −0.362807 −0.181404 0.983409i \(-0.558064\pi\)
−0.181404 + 0.983409i \(0.558064\pi\)
\(662\) 16.1363 0.627157
\(663\) −0.258895 −0.0100546
\(664\) −11.7092 −0.454405
\(665\) −9.36765 −0.363262
\(666\) 4.71734 0.182793
\(667\) −60.3489 −2.33672
\(668\) −14.4265 −0.558180
\(669\) 11.1914 0.432685
\(670\) −9.30330 −0.359418
\(671\) 14.8061 0.571585
\(672\) 2.25889 0.0871388
\(673\) 48.5171 1.87020 0.935099 0.354386i \(-0.115310\pi\)
0.935099 + 0.354386i \(0.115310\pi\)
\(674\) 16.4859 0.635012
\(675\) 1.00000 0.0384900
\(676\) −12.9330 −0.497422
\(677\) −1.77623 −0.0682659 −0.0341329 0.999417i \(-0.510867\pi\)
−0.0341329 + 0.999417i \(0.510867\pi\)
\(678\) −5.38214 −0.206700
\(679\) 21.8854 0.839886
\(680\) 1.00000 0.0383482
\(681\) −8.87317 −0.340021
\(682\) −1.28266 −0.0491156
\(683\) 23.8455 0.912424 0.456212 0.889871i \(-0.349206\pi\)
0.456212 + 0.889871i \(0.349206\pi\)
\(684\) −4.14701 −0.158565
\(685\) 14.6598 0.560122
\(686\) −20.0983 −0.767356
\(687\) 28.4209 1.08432
\(688\) −3.54156 −0.135021
\(689\) 2.34155 0.0892058
\(690\) −5.76174 −0.219346
\(691\) −18.7309 −0.712559 −0.356279 0.934379i \(-0.615955\pi\)
−0.356279 + 0.934379i \(0.615955\pi\)
\(692\) 6.10830 0.232203
\(693\) 2.25889 0.0858083
\(694\) 7.71486 0.292852
\(695\) 7.03939 0.267019
\(696\) 10.4741 0.397019
\(697\) 12.5860 0.476727
\(698\) 5.47720 0.207315
\(699\) −17.8949 −0.676848
\(700\) 2.25889 0.0853782
\(701\) 5.24253 0.198008 0.0990038 0.995087i \(-0.468434\pi\)
0.0990038 + 0.995087i \(0.468434\pi\)
\(702\) −0.258895 −0.00977135
\(703\) −19.5628 −0.737826
\(704\) 1.00000 0.0376889
\(705\) 1.43468 0.0540331
\(706\) 11.4190 0.429760
\(707\) −22.2288 −0.836001
\(708\) 12.9325 0.486034
\(709\) 21.2295 0.797289 0.398645 0.917105i \(-0.369481\pi\)
0.398645 + 0.917105i \(0.369481\pi\)
\(710\) 7.83557 0.294064
\(711\) −11.3384 −0.425224
\(712\) −5.08311 −0.190498
\(713\) 7.39036 0.276771
\(714\) 2.25889 0.0845370
\(715\) −0.258895 −0.00968211
\(716\) −11.0707 −0.413731
\(717\) −8.29401 −0.309746
\(718\) −29.4659 −1.09966
\(719\) 40.8611 1.52386 0.761931 0.647658i \(-0.224251\pi\)
0.761931 + 0.647658i \(0.224251\pi\)
\(720\) 1.00000 0.0372678
\(721\) 6.54491 0.243745
\(722\) −1.80233 −0.0670758
\(723\) −14.2657 −0.530547
\(724\) −12.3828 −0.460204
\(725\) 10.4741 0.388997
\(726\) 1.00000 0.0371135
\(727\) −26.0712 −0.966926 −0.483463 0.875365i \(-0.660621\pi\)
−0.483463 + 0.875365i \(0.660621\pi\)
\(728\) −0.584816 −0.0216747
\(729\) 1.00000 0.0370370
\(730\) 15.4503 0.571841
\(731\) −3.54156 −0.130989
\(732\) 14.8061 0.547251
\(733\) −52.8492 −1.95203 −0.976015 0.217703i \(-0.930144\pi\)
−0.976015 + 0.217703i \(0.930144\pi\)
\(734\) 10.0068 0.369358
\(735\) −1.89740 −0.0699865
\(736\) −5.76174 −0.212381
\(737\) −9.30330 −0.342691
\(738\) 12.5860 0.463296
\(739\) 15.3252 0.563746 0.281873 0.959452i \(-0.409044\pi\)
0.281873 + 0.959452i \(0.409044\pi\)
\(740\) 4.71734 0.173413
\(741\) 1.07364 0.0394411
\(742\) −20.4304 −0.750022
\(743\) −26.5316 −0.973351 −0.486675 0.873583i \(-0.661791\pi\)
−0.486675 + 0.873583i \(0.661791\pi\)
\(744\) −1.28266 −0.0470246
\(745\) −4.81539 −0.176422
\(746\) −15.9681 −0.584633
\(747\) −11.7092 −0.428417
\(748\) 1.00000 0.0365636
\(749\) −9.44231 −0.345014
\(750\) 1.00000 0.0365148
\(751\) 11.6346 0.424552 0.212276 0.977210i \(-0.431912\pi\)
0.212276 + 0.977210i \(0.431912\pi\)
\(752\) 1.43468 0.0523173
\(753\) 18.6892 0.681074
\(754\) −2.71168 −0.0987536
\(755\) −3.23513 −0.117738
\(756\) 2.25889 0.0821552
\(757\) 15.0402 0.546644 0.273322 0.961923i \(-0.411878\pi\)
0.273322 + 0.961923i \(0.411878\pi\)
\(758\) 13.9191 0.505566
\(759\) −5.76174 −0.209138
\(760\) −4.14701 −0.150428
\(761\) −43.2979 −1.56955 −0.784773 0.619783i \(-0.787221\pi\)
−0.784773 + 0.619783i \(0.787221\pi\)
\(762\) 3.08311 0.111689
\(763\) 7.41518 0.268448
\(764\) −19.4798 −0.704753
\(765\) 1.00000 0.0361551
\(766\) −35.2997 −1.27543
\(767\) −3.34816 −0.120895
\(768\) 1.00000 0.0360844
\(769\) 9.69596 0.349645 0.174823 0.984600i \(-0.444065\pi\)
0.174823 + 0.984600i \(0.444065\pi\)
\(770\) 2.25889 0.0814049
\(771\) 14.6204 0.526542
\(772\) 6.17330 0.222182
\(773\) −36.2358 −1.30331 −0.651656 0.758515i \(-0.725925\pi\)
−0.651656 + 0.758515i \(0.725925\pi\)
\(774\) −3.54156 −0.127299
\(775\) −1.28266 −0.0460745
\(776\) 9.68856 0.347799
\(777\) 10.6560 0.382281
\(778\) −3.88310 −0.139216
\(779\) −52.1941 −1.87005
\(780\) −0.258895 −0.00926991
\(781\) 7.83557 0.280379
\(782\) −5.76174 −0.206039
\(783\) 10.4741 0.374313
\(784\) −1.89740 −0.0677641
\(785\) −15.2652 −0.544840
\(786\) −13.2389 −0.472217
\(787\) −48.9076 −1.74337 −0.871684 0.490068i \(-0.836972\pi\)
−0.871684 + 0.490068i \(0.836972\pi\)
\(788\) 3.23894 0.115383
\(789\) 11.1914 0.398425
\(790\) −11.3384 −0.403403
\(791\) −12.1577 −0.432277
\(792\) 1.00000 0.0355335
\(793\) −3.83323 −0.136122
\(794\) −17.3334 −0.615140
\(795\) −9.04440 −0.320772
\(796\) 6.71734 0.238090
\(797\) −17.7892 −0.630125 −0.315063 0.949071i \(-0.602025\pi\)
−0.315063 + 0.949071i \(0.602025\pi\)
\(798\) −9.36765 −0.331611
\(799\) 1.43468 0.0507553
\(800\) 1.00000 0.0353553
\(801\) −5.08311 −0.179603
\(802\) 9.63221 0.340125
\(803\) 15.4503 0.545229
\(804\) −9.30330 −0.328102
\(805\) −13.0152 −0.458724
\(806\) 0.332074 0.0116968
\(807\) −8.13818 −0.286478
\(808\) −9.84058 −0.346190
\(809\) 9.63918 0.338896 0.169448 0.985539i \(-0.445802\pi\)
0.169448 + 0.985539i \(0.445802\pi\)
\(810\) 1.00000 0.0351364
\(811\) −32.3577 −1.13623 −0.568116 0.822949i \(-0.692327\pi\)
−0.568116 + 0.822949i \(0.692327\pi\)
\(812\) 23.6598 0.830297
\(813\) 3.19707 0.112126
\(814\) 4.71734 0.165343
\(815\) −21.8650 −0.765899
\(816\) 1.00000 0.0350070
\(817\) 14.6869 0.513828
\(818\) −25.8075 −0.902337
\(819\) −0.584816 −0.0204351
\(820\) 12.5860 0.439521
\(821\) −46.5153 −1.62340 −0.811698 0.584077i \(-0.801457\pi\)
−0.811698 + 0.584077i \(0.801457\pi\)
\(822\) 14.6598 0.511319
\(823\) −7.09487 −0.247312 −0.123656 0.992325i \(-0.539462\pi\)
−0.123656 + 0.992325i \(0.539462\pi\)
\(824\) 2.89740 0.100936
\(825\) 1.00000 0.0348155
\(826\) 29.2132 1.01646
\(827\) 19.5011 0.678120 0.339060 0.940765i \(-0.389891\pi\)
0.339060 + 0.940765i \(0.389891\pi\)
\(828\) −5.76174 −0.200234
\(829\) 9.43283 0.327616 0.163808 0.986492i \(-0.447622\pi\)
0.163808 + 0.986492i \(0.447622\pi\)
\(830\) −11.7092 −0.406432
\(831\) 11.9087 0.413110
\(832\) −0.258895 −0.00897555
\(833\) −1.89740 −0.0657409
\(834\) 7.03939 0.243754
\(835\) −14.4265 −0.499251
\(836\) −4.14701 −0.143427
\(837\) −1.28266 −0.0443352
\(838\) 11.0057 0.380185
\(839\) −24.5771 −0.848497 −0.424248 0.905546i \(-0.639462\pi\)
−0.424248 + 0.905546i \(0.639462\pi\)
\(840\) 2.25889 0.0779393
\(841\) 80.7062 2.78297
\(842\) −30.5210 −1.05182
\(843\) −24.3126 −0.837370
\(844\) 22.7206 0.782074
\(845\) −12.9330 −0.444908
\(846\) 1.43468 0.0493253
\(847\) 2.25889 0.0776165
\(848\) −9.04440 −0.310586
\(849\) 6.42654 0.220558
\(850\) 1.00000 0.0342997
\(851\) −27.1801 −0.931722
\(852\) 7.83557 0.268442
\(853\) −2.25747 −0.0772944 −0.0386472 0.999253i \(-0.512305\pi\)
−0.0386472 + 0.999253i \(0.512305\pi\)
\(854\) 33.4455 1.14448
\(855\) −4.14701 −0.141825
\(856\) −4.18006 −0.142871
\(857\) 28.3158 0.967249 0.483625 0.875276i \(-0.339320\pi\)
0.483625 + 0.875276i \(0.339320\pi\)
\(858\) −0.258895 −0.00883852
\(859\) 6.02988 0.205737 0.102868 0.994695i \(-0.467198\pi\)
0.102868 + 0.994695i \(0.467198\pi\)
\(860\) −3.54156 −0.120766
\(861\) 28.4304 0.968904
\(862\) −19.8406 −0.675773
\(863\) −32.2550 −1.09797 −0.548987 0.835831i \(-0.684986\pi\)
−0.548987 + 0.835831i \(0.684986\pi\)
\(864\) 1.00000 0.0340207
\(865\) 6.10830 0.207688
\(866\) 7.84738 0.266665
\(867\) 1.00000 0.0339618
\(868\) −2.89740 −0.0983440
\(869\) −11.3384 −0.384629
\(870\) 10.4741 0.355104
\(871\) 2.40857 0.0816114
\(872\) 3.28266 0.111165
\(873\) 9.68856 0.327908
\(874\) 23.8940 0.808226
\(875\) 2.25889 0.0763646
\(876\) 15.4503 0.522017
\(877\) 19.1105 0.645317 0.322659 0.946515i \(-0.395423\pi\)
0.322659 + 0.946515i \(0.395423\pi\)
\(878\) 20.3840 0.687927
\(879\) −6.75921 −0.227983
\(880\) 1.00000 0.0337100
\(881\) 11.7767 0.396768 0.198384 0.980124i \(-0.436431\pi\)
0.198384 + 0.980124i \(0.436431\pi\)
\(882\) −1.89740 −0.0638886
\(883\) −31.1887 −1.04958 −0.524792 0.851230i \(-0.675857\pi\)
−0.524792 + 0.851230i \(0.675857\pi\)
\(884\) −0.258895 −0.00870757
\(885\) 12.9325 0.434722
\(886\) −14.1889 −0.476685
\(887\) −26.8782 −0.902483 −0.451241 0.892402i \(-0.649019\pi\)
−0.451241 + 0.892402i \(0.649019\pi\)
\(888\) 4.71734 0.158304
\(889\) 6.96442 0.233579
\(890\) −5.08311 −0.170386
\(891\) 1.00000 0.0335013
\(892\) 11.1914 0.374716
\(893\) −5.94962 −0.199097
\(894\) −4.81539 −0.161051
\(895\) −11.0707 −0.370053
\(896\) 2.25889 0.0754644
\(897\) 1.49168 0.0498059
\(898\) −24.7330 −0.825350
\(899\) −13.4347 −0.448072
\(900\) 1.00000 0.0333333
\(901\) −9.04440 −0.301313
\(902\) 12.5860 0.419067
\(903\) −8.00000 −0.266223
\(904\) −5.38214 −0.179007
\(905\) −12.3828 −0.411619
\(906\) −3.23513 −0.107480
\(907\) 38.8906 1.29134 0.645670 0.763616i \(-0.276578\pi\)
0.645670 + 0.763616i \(0.276578\pi\)
\(908\) −8.87317 −0.294467
\(909\) −9.84058 −0.326391
\(910\) −0.584816 −0.0193864
\(911\) −29.3889 −0.973699 −0.486849 0.873486i \(-0.661854\pi\)
−0.486849 + 0.873486i \(0.661854\pi\)
\(912\) −4.14701 −0.137321
\(913\) −11.7092 −0.387518
\(914\) −23.1002 −0.764085
\(915\) 14.8061 0.489476
\(916\) 28.4209 0.939052
\(917\) −29.9054 −0.987562
\(918\) 1.00000 0.0330049
\(919\) 4.64214 0.153130 0.0765650 0.997065i \(-0.475605\pi\)
0.0765650 + 0.997065i \(0.475605\pi\)
\(920\) −5.76174 −0.189959
\(921\) −14.4009 −0.474525
\(922\) −24.9237 −0.820818
\(923\) −2.02859 −0.0667717
\(924\) 2.25889 0.0743122
\(925\) 4.71734 0.155105
\(926\) 29.1751 0.958754
\(927\) 2.89740 0.0951629
\(928\) 10.4741 0.343828
\(929\) 31.5810 1.03614 0.518069 0.855339i \(-0.326651\pi\)
0.518069 + 0.855339i \(0.326651\pi\)
\(930\) −1.28266 −0.0420601
\(931\) 7.86851 0.257880
\(932\) −17.8949 −0.586167
\(933\) 15.8768 0.519784
\(934\) −2.33654 −0.0764538
\(935\) 1.00000 0.0327035
\(936\) −0.258895 −0.00846223
\(937\) 52.8673 1.72710 0.863549 0.504264i \(-0.168236\pi\)
0.863549 + 0.504264i \(0.168236\pi\)
\(938\) −21.0152 −0.686170
\(939\) −11.6587 −0.380467
\(940\) 1.43468 0.0467941
\(941\) −39.3343 −1.28226 −0.641131 0.767431i \(-0.721535\pi\)
−0.641131 + 0.767431i \(0.721535\pi\)
\(942\) −15.2652 −0.497368
\(943\) −72.5170 −2.36148
\(944\) 12.9325 0.420918
\(945\) 2.25889 0.0734818
\(946\) −3.54156 −0.115146
\(947\) 9.96009 0.323660 0.161830 0.986819i \(-0.448260\pi\)
0.161830 + 0.986819i \(0.448260\pi\)
\(948\) −11.3384 −0.368255
\(949\) −4.00000 −0.129845
\(950\) −4.14701 −0.134547
\(951\) −8.08881 −0.262297
\(952\) 2.25889 0.0732112
\(953\) 2.07612 0.0672521 0.0336260 0.999434i \(-0.489294\pi\)
0.0336260 + 0.999434i \(0.489294\pi\)
\(954\) −9.04440 −0.292823
\(955\) −19.4798 −0.630350
\(956\) −8.29401 −0.268248
\(957\) 10.4741 0.338579
\(958\) −15.6549 −0.505786
\(959\) 33.1149 1.06934
\(960\) 1.00000 0.0322749
\(961\) −29.3548 −0.946928
\(962\) −1.22129 −0.0393761
\(963\) −4.18006 −0.134700
\(964\) −14.2657 −0.459467
\(965\) 6.17330 0.198726
\(966\) −13.0152 −0.418756
\(967\) 41.1471 1.32320 0.661601 0.749856i \(-0.269877\pi\)
0.661601 + 0.749856i \(0.269877\pi\)
\(968\) 1.00000 0.0321412
\(969\) −4.14701 −0.133221
\(970\) 9.68856 0.311081
\(971\) −45.9187 −1.47360 −0.736801 0.676110i \(-0.763664\pi\)
−0.736801 + 0.676110i \(0.763664\pi\)
\(972\) 1.00000 0.0320750
\(973\) 15.9012 0.509770
\(974\) 31.1787 0.999031
\(975\) −0.258895 −0.00829126
\(976\) 14.8061 0.473933
\(977\) 4.18190 0.133791 0.0668954 0.997760i \(-0.478691\pi\)
0.0668954 + 0.997760i \(0.478691\pi\)
\(978\) −21.8650 −0.699167
\(979\) −5.08311 −0.162457
\(980\) −1.89740 −0.0606101
\(981\) 3.28266 0.104807
\(982\) 39.3953 1.25716
\(983\) −16.4951 −0.526113 −0.263056 0.964780i \(-0.584731\pi\)
−0.263056 + 0.964780i \(0.584731\pi\)
\(984\) 12.5860 0.401226
\(985\) 3.23894 0.103201
\(986\) 10.4741 0.333562
\(987\) 3.24079 0.103155
\(988\) 1.07364 0.0341570
\(989\) 20.4055 0.648858
\(990\) 1.00000 0.0317821
\(991\) 6.06321 0.192604 0.0963022 0.995352i \(-0.469298\pi\)
0.0963022 + 0.995352i \(0.469298\pi\)
\(992\) −1.28266 −0.0407245
\(993\) 16.1363 0.512071
\(994\) 17.6997 0.561401
\(995\) 6.71734 0.212954
\(996\) −11.7092 −0.371020
\(997\) 43.2759 1.37056 0.685280 0.728280i \(-0.259680\pi\)
0.685280 + 0.728280i \(0.259680\pi\)
\(998\) 17.2859 0.547175
\(999\) 4.71734 0.149250
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 5610.2.a.cj.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.cj.1.4 5 1.1 even 1 trivial