Properties

Label 4026.2.a.v.1.1
Level $4026$
Weight $2$
Character 4026.1
Self dual yes
Analytic conductor $32.148$
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] = [4026,2,Mod(1,4026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.11492689.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 9x^{3} + 13x^{2} + 18x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.42642\) of defining polynomial
Character \(\chi\) \(=\) 4026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.42642 q^{5} -1.00000 q^{6} -4.31394 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.42642 q^{5} -1.00000 q^{6} -4.31394 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.42642 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.09185 q^{13} -4.31394 q^{14} +1.42642 q^{15} +1.00000 q^{16} +2.94918 q^{17} +1.00000 q^{18} +2.11248 q^{19} -1.42642 q^{20} +4.31394 q^{21} +1.00000 q^{22} -8.99021 q^{23} -1.00000 q^{24} -2.96532 q^{25} -4.09185 q^{26} -1.00000 q^{27} -4.31394 q^{28} -0.364765 q^{29} +1.42642 q^{30} +6.51827 q^{31} +1.00000 q^{32} -1.00000 q^{33} +2.94918 q^{34} +6.15350 q^{35} +1.00000 q^{36} +8.86689 q^{37} +2.11248 q^{38} +4.09185 q^{39} -1.42642 q^{40} -7.50136 q^{41} +4.31394 q^{42} -9.40579 q^{43} +1.00000 q^{44} -1.42642 q^{45} -8.99021 q^{46} +11.3095 q^{47} -1.00000 q^{48} +11.6101 q^{49} -2.96532 q^{50} -2.94918 q^{51} -4.09185 q^{52} +0.972256 q^{53} -1.00000 q^{54} -1.42642 q^{55} -4.31394 q^{56} -2.11248 q^{57} -0.364765 q^{58} -3.18742 q^{59} +1.42642 q^{60} +1.00000 q^{61} +6.51827 q^{62} -4.31394 q^{63} +1.00000 q^{64} +5.83670 q^{65} -1.00000 q^{66} +1.61461 q^{67} +2.94918 q^{68} +8.99021 q^{69} +6.15350 q^{70} +16.3409 q^{71} +1.00000 q^{72} -2.11959 q^{73} +8.86689 q^{74} +2.96532 q^{75} +2.11248 q^{76} -4.31394 q^{77} +4.09185 q^{78} +12.7706 q^{79} -1.42642 q^{80} +1.00000 q^{81} -7.50136 q^{82} -16.6242 q^{83} +4.31394 q^{84} -4.20677 q^{85} -9.40579 q^{86} +0.364765 q^{87} +1.00000 q^{88} +6.82510 q^{89} -1.42642 q^{90} +17.6520 q^{91} -8.99021 q^{92} -6.51827 q^{93} +11.3095 q^{94} -3.01328 q^{95} -1.00000 q^{96} +18.5432 q^{97} +11.6101 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 5 q^{12} - 2 q^{13} - 7 q^{15} + 5 q^{16} + 2 q^{17} + 5 q^{18} + 18 q^{19} + 7 q^{20} + 5 q^{22} - q^{23} - 5 q^{24} + 6 q^{25} - 2 q^{26} - 5 q^{27} + 7 q^{29} - 7 q^{30} + 5 q^{32} - 5 q^{33} + 2 q^{34} + 7 q^{35} + 5 q^{36} + 11 q^{37} + 18 q^{38} + 2 q^{39} + 7 q^{40} + 8 q^{41} - 7 q^{43} + 5 q^{44} + 7 q^{45} - q^{46} + q^{47} - 5 q^{48} + 7 q^{49} + 6 q^{50} - 2 q^{51} - 2 q^{52} + 10 q^{53} - 5 q^{54} + 7 q^{55} - 18 q^{57} + 7 q^{58} + 8 q^{59} - 7 q^{60} + 5 q^{61} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} + 34 q^{71} + 5 q^{72} + 13 q^{73} + 11 q^{74} - 6 q^{75} + 18 q^{76} + 2 q^{78} + 15 q^{79} + 7 q^{80} + 5 q^{81} + 8 q^{82} - 27 q^{83} - 2 q^{85} - 7 q^{86} - 7 q^{87} + 5 q^{88} + 11 q^{89} + 7 q^{90} + q^{91} - q^{92} + q^{94} + 11 q^{95} - 5 q^{96} + 37 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) \) 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
\(5\) −1.42642 −0.637915 −0.318958 0.947769i \(-0.603333\pi\)
−0.318958 + 0.947769i \(0.603333\pi\)
\(6\) −1.00000 −0.408248
\(7\) −4.31394 −1.63052 −0.815259 0.579097i \(-0.803405\pi\)
−0.815259 + 0.579097i \(0.803405\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.42642 −0.451074
\(11\) 1.00000 0.301511
\(12\) −1.00000 −0.288675
\(13\) −4.09185 −1.13487 −0.567437 0.823417i \(-0.692065\pi\)
−0.567437 + 0.823417i \(0.692065\pi\)
\(14\) −4.31394 −1.15295
\(15\) 1.42642 0.368301
\(16\) 1.00000 0.250000
\(17\) 2.94918 0.715281 0.357641 0.933859i \(-0.383581\pi\)
0.357641 + 0.933859i \(0.383581\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.11248 0.484635 0.242318 0.970197i \(-0.422092\pi\)
0.242318 + 0.970197i \(0.422092\pi\)
\(20\) −1.42642 −0.318958
\(21\) 4.31394 0.941380
\(22\) 1.00000 0.213201
\(23\) −8.99021 −1.87459 −0.937294 0.348540i \(-0.886678\pi\)
−0.937294 + 0.348540i \(0.886678\pi\)
\(24\) −1.00000 −0.204124
\(25\) −2.96532 −0.593064
\(26\) −4.09185 −0.802478
\(27\) −1.00000 −0.192450
\(28\) −4.31394 −0.815259
\(29\) −0.364765 −0.0677353 −0.0338676 0.999426i \(-0.510782\pi\)
−0.0338676 + 0.999426i \(0.510782\pi\)
\(30\) 1.42642 0.260428
\(31\) 6.51827 1.17072 0.585358 0.810775i \(-0.300954\pi\)
0.585358 + 0.810775i \(0.300954\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.00000 −0.174078
\(34\) 2.94918 0.505780
\(35\) 6.15350 1.04013
\(36\) 1.00000 0.166667
\(37\) 8.86689 1.45771 0.728854 0.684669i \(-0.240053\pi\)
0.728854 + 0.684669i \(0.240053\pi\)
\(38\) 2.11248 0.342689
\(39\) 4.09185 0.655220
\(40\) −1.42642 −0.225537
\(41\) −7.50136 −1.17152 −0.585758 0.810486i \(-0.699203\pi\)
−0.585758 + 0.810486i \(0.699203\pi\)
\(42\) 4.31394 0.665656
\(43\) −9.40579 −1.43437 −0.717185 0.696883i \(-0.754570\pi\)
−0.717185 + 0.696883i \(0.754570\pi\)
\(44\) 1.00000 0.150756
\(45\) −1.42642 −0.212638
\(46\) −8.99021 −1.32553
\(47\) 11.3095 1.64965 0.824827 0.565385i \(-0.191272\pi\)
0.824827 + 0.565385i \(0.191272\pi\)
\(48\) −1.00000 −0.144338
\(49\) 11.6101 1.65859
\(50\) −2.96532 −0.419360
\(51\) −2.94918 −0.412968
\(52\) −4.09185 −0.567437
\(53\) 0.972256 0.133550 0.0667748 0.997768i \(-0.478729\pi\)
0.0667748 + 0.997768i \(0.478729\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.42642 −0.192339
\(56\) −4.31394 −0.576475
\(57\) −2.11248 −0.279804
\(58\) −0.364765 −0.0478961
\(59\) −3.18742 −0.414966 −0.207483 0.978239i \(-0.566527\pi\)
−0.207483 + 0.978239i \(0.566527\pi\)
\(60\) 1.42642 0.184150
\(61\) 1.00000 0.128037
\(62\) 6.51827 0.827821
\(63\) −4.31394 −0.543506
\(64\) 1.00000 0.125000
\(65\) 5.83670 0.723954
\(66\) −1.00000 −0.123091
\(67\) 1.61461 0.197256 0.0986278 0.995124i \(-0.468555\pi\)
0.0986278 + 0.995124i \(0.468555\pi\)
\(68\) 2.94918 0.357641
\(69\) 8.99021 1.08229
\(70\) 6.15350 0.735485
\(71\) 16.3409 1.93931 0.969655 0.244476i \(-0.0786160\pi\)
0.969655 + 0.244476i \(0.0786160\pi\)
\(72\) 1.00000 0.117851
\(73\) −2.11959 −0.248080 −0.124040 0.992277i \(-0.539585\pi\)
−0.124040 + 0.992277i \(0.539585\pi\)
\(74\) 8.86689 1.03076
\(75\) 2.96532 0.342406
\(76\) 2.11248 0.242318
\(77\) −4.31394 −0.491620
\(78\) 4.09185 0.463311
\(79\) 12.7706 1.43680 0.718400 0.695630i \(-0.244875\pi\)
0.718400 + 0.695630i \(0.244875\pi\)
\(80\) −1.42642 −0.159479
\(81\) 1.00000 0.111111
\(82\) −7.50136 −0.828387
\(83\) −16.6242 −1.82474 −0.912370 0.409367i \(-0.865750\pi\)
−0.912370 + 0.409367i \(0.865750\pi\)
\(84\) 4.31394 0.470690
\(85\) −4.20677 −0.456289
\(86\) −9.40579 −1.01425
\(87\) 0.364765 0.0391070
\(88\) 1.00000 0.106600
\(89\) 6.82510 0.723459 0.361730 0.932283i \(-0.382186\pi\)
0.361730 + 0.932283i \(0.382186\pi\)
\(90\) −1.42642 −0.150358
\(91\) 17.6520 1.85043
\(92\) −8.99021 −0.937294
\(93\) −6.51827 −0.675913
\(94\) 11.3095 1.16648
\(95\) −3.01328 −0.309156
\(96\) −1.00000 −0.102062
\(97\) 18.5432 1.88277 0.941386 0.337331i \(-0.109524\pi\)
0.941386 + 0.337331i \(0.109524\pi\)
\(98\) 11.6101 1.17280
\(99\) 1.00000 0.100504
\(100\) −2.96532 −0.296532
\(101\) 14.5291 1.44570 0.722850 0.691005i \(-0.242832\pi\)
0.722850 + 0.691005i \(0.242832\pi\)
\(102\) −2.94918 −0.292012
\(103\) −7.60056 −0.748905 −0.374452 0.927246i \(-0.622169\pi\)
−0.374452 + 0.927246i \(0.622169\pi\)
\(104\) −4.09185 −0.401239
\(105\) −6.15350 −0.600521
\(106\) 0.972256 0.0944338
\(107\) −5.61705 −0.543021 −0.271511 0.962435i \(-0.587523\pi\)
−0.271511 + 0.962435i \(0.587523\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 11.3889 1.09086 0.545429 0.838157i \(-0.316367\pi\)
0.545429 + 0.838157i \(0.316367\pi\)
\(110\) −1.42642 −0.136004
\(111\) −8.86689 −0.841608
\(112\) −4.31394 −0.407629
\(113\) −11.2470 −1.05803 −0.529014 0.848613i \(-0.677438\pi\)
−0.529014 + 0.848613i \(0.677438\pi\)
\(114\) −2.11248 −0.197852
\(115\) 12.8238 1.19583
\(116\) −0.364765 −0.0338676
\(117\) −4.09185 −0.378292
\(118\) −3.18742 −0.293426
\(119\) −12.7226 −1.16628
\(120\) 1.42642 0.130214
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) 7.50136 0.676375
\(124\) 6.51827 0.585358
\(125\) 11.3619 1.01624
\(126\) −4.31394 −0.384317
\(127\) −0.825867 −0.0732838 −0.0366419 0.999328i \(-0.511666\pi\)
−0.0366419 + 0.999328i \(0.511666\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.40579 0.828134
\(130\) 5.83670 0.511913
\(131\) 6.22740 0.544091 0.272045 0.962284i \(-0.412300\pi\)
0.272045 + 0.962284i \(0.412300\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −9.11311 −0.790207
\(134\) 1.61461 0.139481
\(135\) 1.42642 0.122767
\(136\) 2.94918 0.252890
\(137\) 12.8830 1.10067 0.550336 0.834943i \(-0.314500\pi\)
0.550336 + 0.834943i \(0.314500\pi\)
\(138\) 8.99021 0.765297
\(139\) 5.84201 0.495513 0.247756 0.968822i \(-0.420307\pi\)
0.247756 + 0.968822i \(0.420307\pi\)
\(140\) 6.15350 0.520066
\(141\) −11.3095 −0.952428
\(142\) 16.3409 1.37130
\(143\) −4.09185 −0.342178
\(144\) 1.00000 0.0833333
\(145\) 0.520309 0.0432093
\(146\) −2.11959 −0.175419
\(147\) −11.6101 −0.957586
\(148\) 8.86689 0.728854
\(149\) 7.92855 0.649532 0.324766 0.945794i \(-0.394714\pi\)
0.324766 + 0.945794i \(0.394714\pi\)
\(150\) 2.96532 0.242117
\(151\) 2.10164 0.171029 0.0855146 0.996337i \(-0.472747\pi\)
0.0855146 + 0.996337i \(0.472747\pi\)
\(152\) 2.11248 0.171345
\(153\) 2.94918 0.238427
\(154\) −4.31394 −0.347628
\(155\) −9.29780 −0.746818
\(156\) 4.09185 0.327610
\(157\) 8.26312 0.659469 0.329735 0.944074i \(-0.393041\pi\)
0.329735 + 0.944074i \(0.393041\pi\)
\(158\) 12.7706 1.01597
\(159\) −0.972256 −0.0771049
\(160\) −1.42642 −0.112769
\(161\) 38.7833 3.05655
\(162\) 1.00000 0.0785674
\(163\) 7.18533 0.562798 0.281399 0.959591i \(-0.409202\pi\)
0.281399 + 0.959591i \(0.409202\pi\)
\(164\) −7.50136 −0.585758
\(165\) 1.42642 0.111047
\(166\) −16.6242 −1.29029
\(167\) 3.88059 0.300289 0.150144 0.988664i \(-0.452026\pi\)
0.150144 + 0.988664i \(0.452026\pi\)
\(168\) 4.31394 0.332828
\(169\) 3.74322 0.287940
\(170\) −4.20677 −0.322645
\(171\) 2.11248 0.161545
\(172\) −9.40579 −0.717185
\(173\) 6.99265 0.531642 0.265821 0.964022i \(-0.414357\pi\)
0.265821 + 0.964022i \(0.414357\pi\)
\(174\) 0.364765 0.0276528
\(175\) 12.7922 0.967002
\(176\) 1.00000 0.0753778
\(177\) 3.18742 0.239581
\(178\) 6.82510 0.511563
\(179\) 22.3105 1.66757 0.833783 0.552093i \(-0.186171\pi\)
0.833783 + 0.552093i \(0.186171\pi\)
\(180\) −1.42642 −0.106319
\(181\) −16.3574 −1.21584 −0.607919 0.793999i \(-0.707995\pi\)
−0.607919 + 0.793999i \(0.707995\pi\)
\(182\) 17.6520 1.30845
\(183\) −1.00000 −0.0739221
\(184\) −8.99021 −0.662767
\(185\) −12.6479 −0.929894
\(186\) −6.51827 −0.477943
\(187\) 2.94918 0.215665
\(188\) 11.3095 0.824827
\(189\) 4.31394 0.313793
\(190\) −3.01328 −0.218607
\(191\) −23.6912 −1.71424 −0.857118 0.515119i \(-0.827748\pi\)
−0.857118 + 0.515119i \(0.827748\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −12.7713 −0.919300 −0.459650 0.888100i \(-0.652025\pi\)
−0.459650 + 0.888100i \(0.652025\pi\)
\(194\) 18.5432 1.33132
\(195\) −5.83670 −0.417975
\(196\) 11.6101 0.829294
\(197\) 15.2901 1.08937 0.544687 0.838639i \(-0.316648\pi\)
0.544687 + 0.838639i \(0.316648\pi\)
\(198\) 1.00000 0.0710669
\(199\) 6.97937 0.494755 0.247377 0.968919i \(-0.420431\pi\)
0.247377 + 0.968919i \(0.420431\pi\)
\(200\) −2.96532 −0.209680
\(201\) −1.61461 −0.113886
\(202\) 14.5291 1.02226
\(203\) 1.57358 0.110444
\(204\) −2.94918 −0.206484
\(205\) 10.7001 0.747328
\(206\) −7.60056 −0.529556
\(207\) −8.99021 −0.624863
\(208\) −4.09185 −0.283719
\(209\) 2.11248 0.146123
\(210\) −6.15350 −0.424632
\(211\) −16.9302 −1.16553 −0.582763 0.812642i \(-0.698028\pi\)
−0.582763 + 0.812642i \(0.698028\pi\)
\(212\) 0.972256 0.0667748
\(213\) −16.3409 −1.11966
\(214\) −5.61705 −0.383974
\(215\) 13.4166 0.915006
\(216\) −1.00000 −0.0680414
\(217\) −28.1195 −1.90887
\(218\) 11.3889 0.771353
\(219\) 2.11959 0.143229
\(220\) −1.42642 −0.0961693
\(221\) −12.0676 −0.811754
\(222\) −8.86689 −0.595107
\(223\) −0.523168 −0.0350339 −0.0175169 0.999847i \(-0.505576\pi\)
−0.0175169 + 0.999847i \(0.505576\pi\)
\(224\) −4.31394 −0.288238
\(225\) −2.96532 −0.197688
\(226\) −11.2470 −0.748138
\(227\) 11.7126 0.777394 0.388697 0.921366i \(-0.372925\pi\)
0.388697 + 0.921366i \(0.372925\pi\)
\(228\) −2.11248 −0.139902
\(229\) 16.3317 1.07923 0.539615 0.841912i \(-0.318570\pi\)
0.539615 + 0.841912i \(0.318570\pi\)
\(230\) 12.8238 0.845578
\(231\) 4.31394 0.283837
\(232\) −0.364765 −0.0239480
\(233\) 3.84287 0.251755 0.125877 0.992046i \(-0.459825\pi\)
0.125877 + 0.992046i \(0.459825\pi\)
\(234\) −4.09185 −0.267493
\(235\) −16.1321 −1.05234
\(236\) −3.18742 −0.207483
\(237\) −12.7706 −0.829537
\(238\) −12.7226 −0.824683
\(239\) −25.2682 −1.63446 −0.817232 0.576309i \(-0.804493\pi\)
−0.817232 + 0.576309i \(0.804493\pi\)
\(240\) 1.42642 0.0920751
\(241\) 2.81712 0.181467 0.0907334 0.995875i \(-0.471079\pi\)
0.0907334 + 0.995875i \(0.471079\pi\)
\(242\) 1.00000 0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 1.00000 0.0640184
\(245\) −16.5609 −1.05804
\(246\) 7.50136 0.478269
\(247\) −8.64394 −0.550001
\(248\) 6.51827 0.413911
\(249\) 16.6242 1.05351
\(250\) 11.3619 0.718590
\(251\) −13.3675 −0.843748 −0.421874 0.906654i \(-0.638628\pi\)
−0.421874 + 0.906654i \(0.638628\pi\)
\(252\) −4.31394 −0.271753
\(253\) −8.99021 −0.565209
\(254\) −0.825867 −0.0518195
\(255\) 4.20677 0.263438
\(256\) 1.00000 0.0625000
\(257\) 8.44578 0.526833 0.263417 0.964682i \(-0.415151\pi\)
0.263417 + 0.964682i \(0.415151\pi\)
\(258\) 9.40579 0.585579
\(259\) −38.2513 −2.37682
\(260\) 5.83670 0.361977
\(261\) −0.364765 −0.0225784
\(262\) 6.22740 0.384730
\(263\) 8.47107 0.522349 0.261174 0.965292i \(-0.415890\pi\)
0.261174 + 0.965292i \(0.415890\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −1.38685 −0.0851933
\(266\) −9.11311 −0.558761
\(267\) −6.82510 −0.417689
\(268\) 1.61461 0.0986278
\(269\) −20.0276 −1.22110 −0.610552 0.791976i \(-0.709053\pi\)
−0.610552 + 0.791976i \(0.709053\pi\)
\(270\) 1.42642 0.0868093
\(271\) −1.79328 −0.108934 −0.0544669 0.998516i \(-0.517346\pi\)
−0.0544669 + 0.998516i \(0.517346\pi\)
\(272\) 2.94918 0.178820
\(273\) −17.6520 −1.06835
\(274\) 12.8830 0.778293
\(275\) −2.96532 −0.178816
\(276\) 8.99021 0.541147
\(277\) −7.31639 −0.439599 −0.219800 0.975545i \(-0.570540\pi\)
−0.219800 + 0.975545i \(0.570540\pi\)
\(278\) 5.84201 0.350380
\(279\) 6.51827 0.390239
\(280\) 6.15350 0.367742
\(281\) 11.7126 0.698716 0.349358 0.936989i \(-0.386400\pi\)
0.349358 + 0.936989i \(0.386400\pi\)
\(282\) −11.3095 −0.673468
\(283\) −7.94841 −0.472484 −0.236242 0.971694i \(-0.575916\pi\)
−0.236242 + 0.971694i \(0.575916\pi\)
\(284\) 16.3409 0.969655
\(285\) 3.01328 0.178492
\(286\) −4.09185 −0.241956
\(287\) 32.3605 1.91018
\(288\) 1.00000 0.0589256
\(289\) −8.30234 −0.488373
\(290\) 0.520309 0.0305536
\(291\) −18.5432 −1.08702
\(292\) −2.11959 −0.124040
\(293\) 27.6790 1.61702 0.808512 0.588480i \(-0.200273\pi\)
0.808512 + 0.588480i \(0.200273\pi\)
\(294\) −11.6101 −0.677116
\(295\) 4.54660 0.264713
\(296\) 8.86689 0.515378
\(297\) −1.00000 −0.0580259
\(298\) 7.92855 0.459289
\(299\) 36.7866 2.12742
\(300\) 2.96532 0.171203
\(301\) 40.5761 2.33877
\(302\) 2.10164 0.120936
\(303\) −14.5291 −0.834675
\(304\) 2.11248 0.121159
\(305\) −1.42642 −0.0816767
\(306\) 2.94918 0.168593
\(307\) −5.87220 −0.335144 −0.167572 0.985860i \(-0.553593\pi\)
−0.167572 + 0.985860i \(0.553593\pi\)
\(308\) −4.31394 −0.245810
\(309\) 7.60056 0.432380
\(310\) −9.29780 −0.528080
\(311\) −2.20840 −0.125227 −0.0626135 0.998038i \(-0.519944\pi\)
−0.0626135 + 0.998038i \(0.519944\pi\)
\(312\) 4.09185 0.231655
\(313\) 5.90919 0.334007 0.167004 0.985956i \(-0.446591\pi\)
0.167004 + 0.985956i \(0.446591\pi\)
\(314\) 8.26312 0.466315
\(315\) 6.15350 0.346711
\(316\) 12.7706 0.718400
\(317\) −6.50059 −0.365110 −0.182555 0.983196i \(-0.558437\pi\)
−0.182555 + 0.983196i \(0.558437\pi\)
\(318\) −0.972256 −0.0545214
\(319\) −0.364765 −0.0204229
\(320\) −1.42642 −0.0797394
\(321\) 5.61705 0.313513
\(322\) 38.7833 2.16131
\(323\) 6.23007 0.346651
\(324\) 1.00000 0.0555556
\(325\) 12.1336 0.673053
\(326\) 7.18533 0.397958
\(327\) −11.3889 −0.629807
\(328\) −7.50136 −0.414193
\(329\) −48.7884 −2.68979
\(330\) 1.42642 0.0785219
\(331\) −12.1572 −0.668222 −0.334111 0.942534i \(-0.608436\pi\)
−0.334111 + 0.942534i \(0.608436\pi\)
\(332\) −16.6242 −0.912370
\(333\) 8.86689 0.485903
\(334\) 3.88059 0.212336
\(335\) −2.30311 −0.125832
\(336\) 4.31394 0.235345
\(337\) −5.19798 −0.283152 −0.141576 0.989927i \(-0.545217\pi\)
−0.141576 + 0.989927i \(0.545217\pi\)
\(338\) 3.74322 0.203605
\(339\) 11.2470 0.610852
\(340\) −4.20677 −0.228144
\(341\) 6.51827 0.352984
\(342\) 2.11248 0.114230
\(343\) −19.8878 −1.07384
\(344\) −9.40579 −0.507126
\(345\) −12.8238 −0.690412
\(346\) 6.99265 0.375927
\(347\) 13.3297 0.715575 0.357787 0.933803i \(-0.383531\pi\)
0.357787 + 0.933803i \(0.383531\pi\)
\(348\) 0.364765 0.0195535
\(349\) −14.1748 −0.758758 −0.379379 0.925241i \(-0.623862\pi\)
−0.379379 + 0.925241i \(0.623862\pi\)
\(350\) 12.7922 0.683773
\(351\) 4.09185 0.218407
\(352\) 1.00000 0.0533002
\(353\) 33.0438 1.75874 0.879371 0.476138i \(-0.157964\pi\)
0.879371 + 0.476138i \(0.157964\pi\)
\(354\) 3.18742 0.169409
\(355\) −23.3090 −1.23712
\(356\) 6.82510 0.361730
\(357\) 12.7226 0.673351
\(358\) 22.3105 1.17915
\(359\) 0.876687 0.0462698 0.0231349 0.999732i \(-0.492635\pi\)
0.0231349 + 0.999732i \(0.492635\pi\)
\(360\) −1.42642 −0.0751790
\(361\) −14.5374 −0.765128
\(362\) −16.3574 −0.859727
\(363\) −1.00000 −0.0524864
\(364\) 17.6520 0.925217
\(365\) 3.02343 0.158254
\(366\) −1.00000 −0.0522708
\(367\) −37.2181 −1.94277 −0.971386 0.237507i \(-0.923670\pi\)
−0.971386 + 0.237507i \(0.923670\pi\)
\(368\) −8.99021 −0.468647
\(369\) −7.50136 −0.390505
\(370\) −12.6479 −0.657535
\(371\) −4.19426 −0.217755
\(372\) −6.51827 −0.337957
\(373\) −15.6612 −0.810904 −0.405452 0.914116i \(-0.632886\pi\)
−0.405452 + 0.914116i \(0.632886\pi\)
\(374\) 2.94918 0.152498
\(375\) −11.3619 −0.586726
\(376\) 11.3095 0.583241
\(377\) 1.49257 0.0768710
\(378\) 4.31394 0.221885
\(379\) 17.7746 0.913018 0.456509 0.889719i \(-0.349100\pi\)
0.456509 + 0.889719i \(0.349100\pi\)
\(380\) −3.01328 −0.154578
\(381\) 0.825867 0.0423104
\(382\) −23.6912 −1.21215
\(383\) 5.32233 0.271958 0.135979 0.990712i \(-0.456582\pi\)
0.135979 + 0.990712i \(0.456582\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 6.15350 0.313612
\(386\) −12.7713 −0.650043
\(387\) −9.40579 −0.478123
\(388\) 18.5432 0.941386
\(389\) 6.88145 0.348903 0.174452 0.984666i \(-0.444185\pi\)
0.174452 + 0.984666i \(0.444185\pi\)
\(390\) −5.83670 −0.295553
\(391\) −26.5137 −1.34086
\(392\) 11.6101 0.586400
\(393\) −6.22740 −0.314131
\(394\) 15.2901 0.770304
\(395\) −18.2162 −0.916557
\(396\) 1.00000 0.0502519
\(397\) 9.40172 0.471859 0.235929 0.971770i \(-0.424187\pi\)
0.235929 + 0.971770i \(0.424187\pi\)
\(398\) 6.97937 0.349844
\(399\) 9.11311 0.456226
\(400\) −2.96532 −0.148266
\(401\) 14.8318 0.740665 0.370332 0.928899i \(-0.379244\pi\)
0.370332 + 0.928899i \(0.379244\pi\)
\(402\) −1.61461 −0.0805292
\(403\) −26.6718 −1.32862
\(404\) 14.5291 0.722850
\(405\) −1.42642 −0.0708795
\(406\) 1.57358 0.0780954
\(407\) 8.86689 0.439516
\(408\) −2.94918 −0.146006
\(409\) −34.9984 −1.73056 −0.865279 0.501291i \(-0.832859\pi\)
−0.865279 + 0.501291i \(0.832859\pi\)
\(410\) 10.7001 0.528441
\(411\) −12.8830 −0.635473
\(412\) −7.60056 −0.374452
\(413\) 13.7503 0.676610
\(414\) −8.99021 −0.441845
\(415\) 23.7131 1.16403
\(416\) −4.09185 −0.200619
\(417\) −5.84201 −0.286084
\(418\) 2.11248 0.103325
\(419\) −4.96323 −0.242470 −0.121235 0.992624i \(-0.538685\pi\)
−0.121235 + 0.992624i \(0.538685\pi\)
\(420\) −6.15350 −0.300260
\(421\) 25.2941 1.23276 0.616379 0.787450i \(-0.288599\pi\)
0.616379 + 0.787450i \(0.288599\pi\)
\(422\) −16.9302 −0.824151
\(423\) 11.3095 0.549885
\(424\) 0.972256 0.0472169
\(425\) −8.74526 −0.424208
\(426\) −16.3409 −0.791720
\(427\) −4.31394 −0.208766
\(428\) −5.61705 −0.271511
\(429\) 4.09185 0.197556
\(430\) 13.4166 0.647007
\(431\) 19.6236 0.945237 0.472618 0.881267i \(-0.343309\pi\)
0.472618 + 0.881267i \(0.343309\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 19.7824 0.950681 0.475341 0.879802i \(-0.342325\pi\)
0.475341 + 0.879802i \(0.342325\pi\)
\(434\) −28.1195 −1.34978
\(435\) −0.520309 −0.0249469
\(436\) 11.3889 0.545429
\(437\) −18.9916 −0.908492
\(438\) 2.11959 0.101278
\(439\) 14.8754 0.709963 0.354981 0.934873i \(-0.384487\pi\)
0.354981 + 0.934873i \(0.384487\pi\)
\(440\) −1.42642 −0.0680020
\(441\) 11.6101 0.552863
\(442\) −12.0676 −0.573997
\(443\) 7.09855 0.337262 0.168631 0.985679i \(-0.446065\pi\)
0.168631 + 0.985679i \(0.446065\pi\)
\(444\) −8.86689 −0.420804
\(445\) −9.73547 −0.461506
\(446\) −0.523168 −0.0247727
\(447\) −7.92855 −0.375008
\(448\) −4.31394 −0.203815
\(449\) −1.51664 −0.0715747 −0.0357874 0.999359i \(-0.511394\pi\)
−0.0357874 + 0.999359i \(0.511394\pi\)
\(450\) −2.96532 −0.139787
\(451\) −7.50136 −0.353225
\(452\) −11.2470 −0.529014
\(453\) −2.10164 −0.0987437
\(454\) 11.7126 0.549701
\(455\) −25.1792 −1.18042
\(456\) −2.11248 −0.0989258
\(457\) −33.1060 −1.54863 −0.774316 0.632800i \(-0.781906\pi\)
−0.774316 + 0.632800i \(0.781906\pi\)
\(458\) 16.3317 0.763131
\(459\) −2.94918 −0.137656
\(460\) 12.8238 0.597914
\(461\) 15.4501 0.719584 0.359792 0.933032i \(-0.382848\pi\)
0.359792 + 0.933032i \(0.382848\pi\)
\(462\) 4.31394 0.200703
\(463\) 14.6657 0.681573 0.340786 0.940141i \(-0.389307\pi\)
0.340786 + 0.940141i \(0.389307\pi\)
\(464\) −0.364765 −0.0169338
\(465\) 9.29780 0.431175
\(466\) 3.84287 0.178018
\(467\) −24.5598 −1.13649 −0.568246 0.822859i \(-0.692378\pi\)
−0.568246 + 0.822859i \(0.692378\pi\)
\(468\) −4.09185 −0.189146
\(469\) −6.96532 −0.321629
\(470\) −16.1321 −0.744116
\(471\) −8.26312 −0.380745
\(472\) −3.18742 −0.146713
\(473\) −9.40579 −0.432479
\(474\) −12.7706 −0.586571
\(475\) −6.26417 −0.287420
\(476\) −12.7226 −0.583139
\(477\) 0.972256 0.0445165
\(478\) −25.2682 −1.15574
\(479\) 35.0596 1.60191 0.800956 0.598723i \(-0.204325\pi\)
0.800956 + 0.598723i \(0.204325\pi\)
\(480\) 1.42642 0.0651070
\(481\) −36.2820 −1.65432
\(482\) 2.81712 0.128316
\(483\) −38.7833 −1.76470
\(484\) 1.00000 0.0454545
\(485\) −26.4504 −1.20105
\(486\) −1.00000 −0.0453609
\(487\) −34.8064 −1.57723 −0.788614 0.614889i \(-0.789201\pi\)
−0.788614 + 0.614889i \(0.789201\pi\)
\(488\) 1.00000 0.0452679
\(489\) −7.18533 −0.324932
\(490\) −16.5609 −0.748146
\(491\) −28.4117 −1.28220 −0.641102 0.767456i \(-0.721522\pi\)
−0.641102 + 0.767456i \(0.721522\pi\)
\(492\) 7.50136 0.338188
\(493\) −1.07576 −0.0484497
\(494\) −8.64394 −0.388909
\(495\) −1.42642 −0.0641129
\(496\) 6.51827 0.292679
\(497\) −70.4938 −3.16208
\(498\) 16.6242 0.744947
\(499\) −21.4703 −0.961143 −0.480571 0.876956i \(-0.659571\pi\)
−0.480571 + 0.876956i \(0.659571\pi\)
\(500\) 11.3619 0.508120
\(501\) −3.88059 −0.173372
\(502\) −13.3675 −0.596620
\(503\) −20.3715 −0.908321 −0.454161 0.890920i \(-0.650061\pi\)
−0.454161 + 0.890920i \(0.650061\pi\)
\(504\) −4.31394 −0.192158
\(505\) −20.7246 −0.922234
\(506\) −8.99021 −0.399663
\(507\) −3.74322 −0.166242
\(508\) −0.825867 −0.0366419
\(509\) 12.9596 0.574424 0.287212 0.957867i \(-0.407272\pi\)
0.287212 + 0.957867i \(0.407272\pi\)
\(510\) 4.20677 0.186279
\(511\) 9.14381 0.404498
\(512\) 1.00000 0.0441942
\(513\) −2.11248 −0.0932681
\(514\) 8.44578 0.372527
\(515\) 10.8416 0.477738
\(516\) 9.40579 0.414067
\(517\) 11.3095 0.497389
\(518\) −38.2513 −1.68067
\(519\) −6.99265 −0.306943
\(520\) 5.83670 0.255956
\(521\) 9.51995 0.417077 0.208538 0.978014i \(-0.433129\pi\)
0.208538 + 0.978014i \(0.433129\pi\)
\(522\) −0.364765 −0.0159654
\(523\) 11.1623 0.488093 0.244047 0.969763i \(-0.421525\pi\)
0.244047 + 0.969763i \(0.421525\pi\)
\(524\) 6.22740 0.272045
\(525\) −12.7922 −0.558299
\(526\) 8.47107 0.369356
\(527\) 19.2235 0.837391
\(528\) −1.00000 −0.0435194
\(529\) 57.8238 2.51408
\(530\) −1.38685 −0.0602408
\(531\) −3.18742 −0.138322
\(532\) −9.11311 −0.395103
\(533\) 30.6944 1.32952
\(534\) −6.82510 −0.295351
\(535\) 8.01229 0.346401
\(536\) 1.61461 0.0697404
\(537\) −22.3105 −0.962769
\(538\) −20.0276 −0.863452
\(539\) 11.6101 0.500083
\(540\) 1.42642 0.0613834
\(541\) 45.3700 1.95061 0.975304 0.220867i \(-0.0708886\pi\)
0.975304 + 0.220867i \(0.0708886\pi\)
\(542\) −1.79328 −0.0770279
\(543\) 16.3574 0.701964
\(544\) 2.94918 0.126445
\(545\) −16.2454 −0.695874
\(546\) −17.6520 −0.755436
\(547\) −26.5826 −1.13659 −0.568294 0.822826i \(-0.692396\pi\)
−0.568294 + 0.822826i \(0.692396\pi\)
\(548\) 12.8830 0.550336
\(549\) 1.00000 0.0426790
\(550\) −2.96532 −0.126442
\(551\) −0.770559 −0.0328269
\(552\) 8.99021 0.382649
\(553\) −55.0915 −2.34273
\(554\) −7.31639 −0.310844
\(555\) 12.6479 0.536875
\(556\) 5.84201 0.247756
\(557\) 27.0180 1.14479 0.572394 0.819979i \(-0.306015\pi\)
0.572394 + 0.819979i \(0.306015\pi\)
\(558\) 6.51827 0.275940
\(559\) 38.4871 1.62783
\(560\) 6.15350 0.260033
\(561\) −2.94918 −0.124514
\(562\) 11.7126 0.494067
\(563\) −14.6292 −0.616546 −0.308273 0.951298i \(-0.599751\pi\)
−0.308273 + 0.951298i \(0.599751\pi\)
\(564\) −11.3095 −0.476214
\(565\) 16.0429 0.674932
\(566\) −7.94841 −0.334097
\(567\) −4.31394 −0.181169
\(568\) 16.3409 0.685650
\(569\) −9.87823 −0.414117 −0.207059 0.978329i \(-0.566389\pi\)
−0.207059 + 0.978329i \(0.566389\pi\)
\(570\) 3.01328 0.126213
\(571\) 37.4785 1.56842 0.784212 0.620492i \(-0.213067\pi\)
0.784212 + 0.620492i \(0.213067\pi\)
\(572\) −4.09185 −0.171089
\(573\) 23.6912 0.989715
\(574\) 32.3605 1.35070
\(575\) 26.6588 1.11175
\(576\) 1.00000 0.0416667
\(577\) −14.9372 −0.621845 −0.310922 0.950435i \(-0.600638\pi\)
−0.310922 + 0.950435i \(0.600638\pi\)
\(578\) −8.30234 −0.345332
\(579\) 12.7713 0.530758
\(580\) 0.520309 0.0216047
\(581\) 71.7157 2.97527
\(582\) −18.5432 −0.768639
\(583\) 0.972256 0.0402667
\(584\) −2.11959 −0.0877094
\(585\) 5.83670 0.241318
\(586\) 27.6790 1.14341
\(587\) 20.6681 0.853066 0.426533 0.904472i \(-0.359735\pi\)
0.426533 + 0.904472i \(0.359735\pi\)
\(588\) −11.6101 −0.478793
\(589\) 13.7697 0.567370
\(590\) 4.54660 0.187181
\(591\) −15.2901 −0.628951
\(592\) 8.86689 0.364427
\(593\) 32.2729 1.32529 0.662644 0.748935i \(-0.269434\pi\)
0.662644 + 0.748935i \(0.269434\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 18.1478 0.743987
\(596\) 7.92855 0.324766
\(597\) −6.97937 −0.285647
\(598\) 36.7866 1.50431
\(599\) −7.86626 −0.321407 −0.160703 0.987003i \(-0.551376\pi\)
−0.160703 + 0.987003i \(0.551376\pi\)
\(600\) 2.96532 0.121059
\(601\) 47.2616 1.92784 0.963921 0.266188i \(-0.0857642\pi\)
0.963921 + 0.266188i \(0.0857642\pi\)
\(602\) 40.5761 1.65376
\(603\) 1.61461 0.0657518
\(604\) 2.10164 0.0855146
\(605\) −1.42642 −0.0579923
\(606\) −14.5291 −0.590205
\(607\) 19.5408 0.793135 0.396568 0.918006i \(-0.370201\pi\)
0.396568 + 0.918006i \(0.370201\pi\)
\(608\) 2.11248 0.0856723
\(609\) −1.57358 −0.0637646
\(610\) −1.42642 −0.0577541
\(611\) −46.2766 −1.87215
\(612\) 2.94918 0.119214
\(613\) −28.7176 −1.15989 −0.579947 0.814654i \(-0.696927\pi\)
−0.579947 + 0.814654i \(0.696927\pi\)
\(614\) −5.87220 −0.236983
\(615\) −10.7001 −0.431470
\(616\) −4.31394 −0.173814
\(617\) −28.3734 −1.14227 −0.571136 0.820856i \(-0.693497\pi\)
−0.571136 + 0.820856i \(0.693497\pi\)
\(618\) 7.60056 0.305739
\(619\) −26.0718 −1.04791 −0.523956 0.851745i \(-0.675544\pi\)
−0.523956 + 0.851745i \(0.675544\pi\)
\(620\) −9.29780 −0.373409
\(621\) 8.99021 0.360765
\(622\) −2.20840 −0.0885489
\(623\) −29.4431 −1.17961
\(624\) 4.09185 0.163805
\(625\) −1.38027 −0.0552108
\(626\) 5.90919 0.236179
\(627\) −2.11248 −0.0843642
\(628\) 8.26312 0.329735
\(629\) 26.1501 1.04267
\(630\) 6.15350 0.245162
\(631\) 5.50399 0.219110 0.109555 0.993981i \(-0.465057\pi\)
0.109555 + 0.993981i \(0.465057\pi\)
\(632\) 12.7706 0.507986
\(633\) 16.9302 0.672916
\(634\) −6.50059 −0.258172
\(635\) 1.17803 0.0467489
\(636\) −0.972256 −0.0385524
\(637\) −47.5068 −1.88229
\(638\) −0.364765 −0.0144412
\(639\) 16.3409 0.646437
\(640\) −1.42642 −0.0563843
\(641\) 23.5007 0.928223 0.464111 0.885777i \(-0.346374\pi\)
0.464111 + 0.885777i \(0.346374\pi\)
\(642\) 5.61705 0.221687
\(643\) −18.8775 −0.744454 −0.372227 0.928142i \(-0.621406\pi\)
−0.372227 + 0.928142i \(0.621406\pi\)
\(644\) 38.7833 1.52827
\(645\) −13.4166 −0.528279
\(646\) 6.23007 0.245119
\(647\) 8.49828 0.334102 0.167051 0.985948i \(-0.446576\pi\)
0.167051 + 0.985948i \(0.446576\pi\)
\(648\) 1.00000 0.0392837
\(649\) −3.18742 −0.125117
\(650\) 12.1336 0.475921
\(651\) 28.1195 1.10209
\(652\) 7.18533 0.281399
\(653\) 12.8312 0.502122 0.251061 0.967971i \(-0.419220\pi\)
0.251061 + 0.967971i \(0.419220\pi\)
\(654\) −11.3889 −0.445341
\(655\) −8.88290 −0.347084
\(656\) −7.50136 −0.292879
\(657\) −2.11959 −0.0826932
\(658\) −48.7884 −1.90197
\(659\) −35.2902 −1.37471 −0.687356 0.726321i \(-0.741229\pi\)
−0.687356 + 0.726321i \(0.741229\pi\)
\(660\) 1.42642 0.0555234
\(661\) 21.9543 0.853923 0.426962 0.904270i \(-0.359584\pi\)
0.426962 + 0.904270i \(0.359584\pi\)
\(662\) −12.1572 −0.472504
\(663\) 12.0676 0.468667
\(664\) −16.6242 −0.645143
\(665\) 12.9991 0.504085
\(666\) 8.86689 0.343585
\(667\) 3.27932 0.126976
\(668\) 3.88059 0.150144
\(669\) 0.523168 0.0202268
\(670\) −2.30311 −0.0889769
\(671\) 1.00000 0.0386046
\(672\) 4.31394 0.166414
\(673\) −29.7526 −1.14688 −0.573439 0.819248i \(-0.694391\pi\)
−0.573439 + 0.819248i \(0.694391\pi\)
\(674\) −5.19798 −0.200219
\(675\) 2.96532 0.114135
\(676\) 3.74322 0.143970
\(677\) 44.6102 1.71451 0.857255 0.514892i \(-0.172168\pi\)
0.857255 + 0.514892i \(0.172168\pi\)
\(678\) 11.2470 0.431938
\(679\) −79.9942 −3.06989
\(680\) −4.20677 −0.161322
\(681\) −11.7126 −0.448829
\(682\) 6.51827 0.249597
\(683\) 31.9359 1.22199 0.610997 0.791633i \(-0.290769\pi\)
0.610997 + 0.791633i \(0.290769\pi\)
\(684\) 2.11248 0.0807726
\(685\) −18.3766 −0.702135
\(686\) −19.8878 −0.759320
\(687\) −16.3317 −0.623094
\(688\) −9.40579 −0.358593
\(689\) −3.97832 −0.151562
\(690\) −12.8238 −0.488195
\(691\) 49.0636 1.86647 0.933235 0.359268i \(-0.116974\pi\)
0.933235 + 0.359268i \(0.116974\pi\)
\(692\) 6.99265 0.265821
\(693\) −4.31394 −0.163873
\(694\) 13.3297 0.505988
\(695\) −8.33317 −0.316095
\(696\) 0.364765 0.0138264
\(697\) −22.1229 −0.837963
\(698\) −14.1748 −0.536523
\(699\) −3.84287 −0.145351
\(700\) 12.7922 0.483501
\(701\) −45.0157 −1.70022 −0.850109 0.526606i \(-0.823464\pi\)
−0.850109 + 0.526606i \(0.823464\pi\)
\(702\) 4.09185 0.154437
\(703\) 18.7311 0.706457
\(704\) 1.00000 0.0376889
\(705\) 16.1321 0.607568
\(706\) 33.0438 1.24362
\(707\) −62.6778 −2.35724
\(708\) 3.18742 0.119790
\(709\) −35.8338 −1.34577 −0.672884 0.739748i \(-0.734945\pi\)
−0.672884 + 0.739748i \(0.734945\pi\)
\(710\) −23.3090 −0.874773
\(711\) 12.7706 0.478933
\(712\) 6.82510 0.255781
\(713\) −58.6006 −2.19461
\(714\) 12.7226 0.476131
\(715\) 5.83670 0.218280
\(716\) 22.3105 0.833783
\(717\) 25.2682 0.943658
\(718\) 0.876687 0.0327177
\(719\) 29.7875 1.11089 0.555443 0.831554i \(-0.312549\pi\)
0.555443 + 0.831554i \(0.312549\pi\)
\(720\) −1.42642 −0.0531596
\(721\) 32.7884 1.22110
\(722\) −14.5374 −0.541028
\(723\) −2.81712 −0.104770
\(724\) −16.3574 −0.607919
\(725\) 1.08165 0.0401713
\(726\) −1.00000 −0.0371135
\(727\) 18.5459 0.687829 0.343914 0.939001i \(-0.388247\pi\)
0.343914 + 0.939001i \(0.388247\pi\)
\(728\) 17.6520 0.654227
\(729\) 1.00000 0.0370370
\(730\) 3.02343 0.111902
\(731\) −27.7394 −1.02598
\(732\) −1.00000 −0.0369611
\(733\) 10.0302 0.370475 0.185238 0.982694i \(-0.440695\pi\)
0.185238 + 0.982694i \(0.440695\pi\)
\(734\) −37.2181 −1.37375
\(735\) 16.5609 0.610859
\(736\) −8.99021 −0.331383
\(737\) 1.61461 0.0594748
\(738\) −7.50136 −0.276129
\(739\) −32.5413 −1.19705 −0.598526 0.801103i \(-0.704247\pi\)
−0.598526 + 0.801103i \(0.704247\pi\)
\(740\) −12.6479 −0.464947
\(741\) 8.64394 0.317543
\(742\) −4.19426 −0.153976
\(743\) −3.08415 −0.113146 −0.0565732 0.998398i \(-0.518017\pi\)
−0.0565732 + 0.998398i \(0.518017\pi\)
\(744\) −6.51827 −0.238971
\(745\) −11.3095 −0.414346
\(746\) −15.6612 −0.573396
\(747\) −16.6242 −0.608247
\(748\) 2.94918 0.107833
\(749\) 24.2317 0.885406
\(750\) −11.3619 −0.414878
\(751\) −41.4041 −1.51086 −0.755428 0.655232i \(-0.772571\pi\)
−0.755428 + 0.655232i \(0.772571\pi\)
\(752\) 11.3095 0.412413
\(753\) 13.3675 0.487138
\(754\) 1.49257 0.0543560
\(755\) −2.99783 −0.109102
\(756\) 4.31394 0.156897
\(757\) 2.33562 0.0848894 0.0424447 0.999099i \(-0.486485\pi\)
0.0424447 + 0.999099i \(0.486485\pi\)
\(758\) 17.7746 0.645601
\(759\) 8.99021 0.326324
\(760\) −3.01328 −0.109303
\(761\) −10.1231 −0.366961 −0.183481 0.983023i \(-0.558736\pi\)
−0.183481 + 0.983023i \(0.558736\pi\)
\(762\) 0.825867 0.0299180
\(763\) −49.1310 −1.77866
\(764\) −23.6912 −0.857118
\(765\) −4.20677 −0.152096
\(766\) 5.32233 0.192304
\(767\) 13.0424 0.470935
\(768\) −1.00000 −0.0360844
\(769\) 45.6436 1.64595 0.822975 0.568078i \(-0.192313\pi\)
0.822975 + 0.568078i \(0.192313\pi\)
\(770\) 6.15350 0.221757
\(771\) −8.44578 −0.304167
\(772\) −12.7713 −0.459650
\(773\) −9.19035 −0.330554 −0.165277 0.986247i \(-0.552852\pi\)
−0.165277 + 0.986247i \(0.552852\pi\)
\(774\) −9.40579 −0.338084
\(775\) −19.3288 −0.694310
\(776\) 18.5432 0.665661
\(777\) 38.2513 1.37226
\(778\) 6.88145 0.246712
\(779\) −15.8465 −0.567758
\(780\) −5.83670 −0.208987
\(781\) 16.3409 0.584724
\(782\) −26.5137 −0.948129
\(783\) 0.364765 0.0130357
\(784\) 11.6101 0.414647
\(785\) −11.7867 −0.420685
\(786\) −6.22740 −0.222124
\(787\) 1.90275 0.0678257 0.0339129 0.999425i \(-0.489203\pi\)
0.0339129 + 0.999425i \(0.489203\pi\)
\(788\) 15.2901 0.544687
\(789\) −8.47107 −0.301578
\(790\) −18.2162 −0.648103
\(791\) 48.5189 1.72513
\(792\) 1.00000 0.0355335
\(793\) −4.09185 −0.145306
\(794\) 9.40172 0.333654
\(795\) 1.38685 0.0491864
\(796\) 6.97937 0.247377
\(797\) −30.7964 −1.09086 −0.545432 0.838155i \(-0.683635\pi\)
−0.545432 + 0.838155i \(0.683635\pi\)
\(798\) 9.11311 0.322601
\(799\) 33.3536 1.17997
\(800\) −2.96532 −0.104840
\(801\) 6.82510 0.241153
\(802\) 14.8318 0.523729
\(803\) −2.11959 −0.0747988
\(804\) −1.61461 −0.0569428
\(805\) −55.3213 −1.94982
\(806\) −26.6718 −0.939473
\(807\) 20.0276 0.705005
\(808\) 14.5291 0.511132
\(809\) −24.4553 −0.859802 −0.429901 0.902876i \(-0.641452\pi\)
−0.429901 + 0.902876i \(0.641452\pi\)
\(810\) −1.42642 −0.0501194
\(811\) −30.8476 −1.08321 −0.541603 0.840635i \(-0.682182\pi\)
−0.541603 + 0.840635i \(0.682182\pi\)
\(812\) 1.57358 0.0552218
\(813\) 1.79328 0.0628930
\(814\) 8.86689 0.310784
\(815\) −10.2493 −0.359018
\(816\) −2.94918 −0.103242
\(817\) −19.8695 −0.695147
\(818\) −34.9984 −1.22369
\(819\) 17.6520 0.616811
\(820\) 10.7001 0.373664
\(821\) −18.7136 −0.653108 −0.326554 0.945179i \(-0.605888\pi\)
−0.326554 + 0.945179i \(0.605888\pi\)
\(822\) −12.8830 −0.449347
\(823\) 14.4025 0.502041 0.251020 0.967982i \(-0.419234\pi\)
0.251020 + 0.967982i \(0.419234\pi\)
\(824\) −7.60056 −0.264778
\(825\) 2.96532 0.103239
\(826\) 13.7503 0.478436
\(827\) −21.1576 −0.735721 −0.367861 0.929881i \(-0.619910\pi\)
−0.367861 + 0.929881i \(0.619910\pi\)
\(828\) −8.99021 −0.312431
\(829\) −14.4749 −0.502734 −0.251367 0.967892i \(-0.580880\pi\)
−0.251367 + 0.967892i \(0.580880\pi\)
\(830\) 23.7131 0.823093
\(831\) 7.31639 0.253803
\(832\) −4.09185 −0.141859
\(833\) 34.2403 1.18636
\(834\) −5.84201 −0.202292
\(835\) −5.53536 −0.191559
\(836\) 2.11248 0.0730615
\(837\) −6.51827 −0.225304
\(838\) −4.96323 −0.171452
\(839\) −52.6999 −1.81940 −0.909702 0.415262i \(-0.863690\pi\)
−0.909702 + 0.415262i \(0.863690\pi\)
\(840\) −6.15350 −0.212316
\(841\) −28.8669 −0.995412
\(842\) 25.2941 0.871692
\(843\) −11.7126 −0.403404
\(844\) −16.9302 −0.582763
\(845\) −5.33942 −0.183682
\(846\) 11.3095 0.388827
\(847\) −4.31394 −0.148229
\(848\) 0.972256 0.0333874
\(849\) 7.94841 0.272789
\(850\) −8.74526 −0.299960
\(851\) −79.7152 −2.73260
\(852\) −16.3409 −0.559831
\(853\) −28.3406 −0.970362 −0.485181 0.874414i \(-0.661246\pi\)
−0.485181 + 0.874414i \(0.661246\pi\)
\(854\) −4.31394 −0.147620
\(855\) −3.01328 −0.103052
\(856\) −5.61705 −0.191987
\(857\) 51.9454 1.77442 0.887210 0.461366i \(-0.152640\pi\)
0.887210 + 0.461366i \(0.152640\pi\)
\(858\) 4.09185 0.139693
\(859\) 36.6638 1.25095 0.625476 0.780243i \(-0.284905\pi\)
0.625476 + 0.780243i \(0.284905\pi\)
\(860\) 13.4166 0.457503
\(861\) −32.3605 −1.10284
\(862\) 19.6236 0.668383
\(863\) −26.9352 −0.916885 −0.458443 0.888724i \(-0.651593\pi\)
−0.458443 + 0.888724i \(0.651593\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −9.97448 −0.339142
\(866\) 19.7824 0.672233
\(867\) 8.30234 0.281962
\(868\) −28.1195 −0.954437
\(869\) 12.7706 0.433212
\(870\) −0.520309 −0.0176401
\(871\) −6.60672 −0.223860
\(872\) 11.3889 0.385676
\(873\) 18.5432 0.627591
\(874\) −18.9916 −0.642401
\(875\) −49.0146 −1.65700
\(876\) 2.11959 0.0716144
\(877\) 15.3005 0.516662 0.258331 0.966056i \(-0.416827\pi\)
0.258331 + 0.966056i \(0.416827\pi\)
\(878\) 14.8754 0.502020
\(879\) −27.6790 −0.933589
\(880\) −1.42642 −0.0480847
\(881\) 40.5694 1.36682 0.683409 0.730036i \(-0.260497\pi\)
0.683409 + 0.730036i \(0.260497\pi\)
\(882\) 11.6101 0.390933
\(883\) −8.39786 −0.282610 −0.141305 0.989966i \(-0.545130\pi\)
−0.141305 + 0.989966i \(0.545130\pi\)
\(884\) −12.0676 −0.405877
\(885\) −4.54660 −0.152832
\(886\) 7.09855 0.238481
\(887\) 36.8832 1.23842 0.619209 0.785227i \(-0.287454\pi\)
0.619209 + 0.785227i \(0.287454\pi\)
\(888\) −8.86689 −0.297553
\(889\) 3.56274 0.119491
\(890\) −9.73547 −0.326334
\(891\) 1.00000 0.0335013
\(892\) −0.523168 −0.0175169
\(893\) 23.8910 0.799481
\(894\) −7.92855 −0.265170
\(895\) −31.8242 −1.06377
\(896\) −4.31394 −0.144119
\(897\) −36.7866 −1.22827
\(898\) −1.51664 −0.0506110
\(899\) −2.37764 −0.0792987
\(900\) −2.96532 −0.0988440
\(901\) 2.86736 0.0955255
\(902\) −7.50136 −0.249768
\(903\) −40.5761 −1.35029
\(904\) −11.2470 −0.374069
\(905\) 23.3326 0.775601
\(906\) −2.10164 −0.0698224
\(907\) 28.0051 0.929893 0.464947 0.885339i \(-0.346074\pi\)
0.464947 + 0.885339i \(0.346074\pi\)
\(908\) 11.7126 0.388697
\(909\) 14.5291 0.481900
\(910\) −25.1792 −0.834683
\(911\) 2.41431 0.0799898 0.0399949 0.999200i \(-0.487266\pi\)
0.0399949 + 0.999200i \(0.487266\pi\)
\(912\) −2.11248 −0.0699511
\(913\) −16.6242 −0.550180
\(914\) −33.1060 −1.09505
\(915\) 1.42642 0.0471561
\(916\) 16.3317 0.539615
\(917\) −26.8647 −0.887150
\(918\) −2.94918 −0.0973374
\(919\) −5.04284 −0.166348 −0.0831740 0.996535i \(-0.526506\pi\)
−0.0831740 + 0.996535i \(0.526506\pi\)
\(920\) 12.8238 0.422789
\(921\) 5.87220 0.193496
\(922\) 15.4501 0.508823
\(923\) −66.8646 −2.20087
\(924\) 4.31394 0.141918
\(925\) −26.2932 −0.864515
\(926\) 14.6657 0.481945
\(927\) −7.60056 −0.249635
\(928\) −0.364765 −0.0119740
\(929\) 27.4828 0.901682 0.450841 0.892604i \(-0.351124\pi\)
0.450841 + 0.892604i \(0.351124\pi\)
\(930\) 9.29780 0.304887
\(931\) 24.5261 0.803811
\(932\) 3.84287 0.125877
\(933\) 2.20840 0.0722999
\(934\) −24.5598 −0.803621
\(935\) −4.20677 −0.137576
\(936\) −4.09185 −0.133746
\(937\) 34.7865 1.13642 0.568212 0.822882i \(-0.307635\pi\)
0.568212 + 0.822882i \(0.307635\pi\)
\(938\) −6.96532 −0.227426
\(939\) −5.90919 −0.192839
\(940\) −16.1321 −0.526170
\(941\) 20.6215 0.672241 0.336121 0.941819i \(-0.390885\pi\)
0.336121 + 0.941819i \(0.390885\pi\)
\(942\) −8.26312 −0.269227
\(943\) 67.4388 2.19611
\(944\) −3.18742 −0.103742
\(945\) −6.15350 −0.200174
\(946\) −9.40579 −0.305809
\(947\) −46.2085 −1.50157 −0.750787 0.660544i \(-0.770326\pi\)
−0.750787 + 0.660544i \(0.770326\pi\)
\(948\) −12.7706 −0.414768
\(949\) 8.67305 0.281539
\(950\) −6.26417 −0.203237
\(951\) 6.50059 0.210796
\(952\) −12.7226 −0.412342
\(953\) 15.6775 0.507844 0.253922 0.967225i \(-0.418279\pi\)
0.253922 + 0.967225i \(0.418279\pi\)
\(954\) 0.972256 0.0314779
\(955\) 33.7937 1.09354
\(956\) −25.2682 −0.817232
\(957\) 0.364765 0.0117912
\(958\) 35.0596 1.13272
\(959\) −55.5767 −1.79467
\(960\) 1.42642 0.0460376
\(961\) 11.4878 0.370576
\(962\) −36.2820 −1.16978
\(963\) −5.61705 −0.181007
\(964\) 2.81712 0.0907334
\(965\) 18.2173 0.586436
\(966\) −38.7833 −1.24783
\(967\) 49.4316 1.58961 0.794807 0.606862i \(-0.207572\pi\)
0.794807 + 0.606862i \(0.207572\pi\)
\(968\) 1.00000 0.0321412
\(969\) −6.23007 −0.200139
\(970\) −26.4504 −0.849270
\(971\) 17.2880 0.554797 0.277399 0.960755i \(-0.410528\pi\)
0.277399 + 0.960755i \(0.410528\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −25.2021 −0.807942
\(974\) −34.8064 −1.11527
\(975\) −12.1336 −0.388588
\(976\) 1.00000 0.0320092
\(977\) 16.2088 0.518566 0.259283 0.965801i \(-0.416514\pi\)
0.259283 + 0.965801i \(0.416514\pi\)
\(978\) −7.18533 −0.229761
\(979\) 6.82510 0.218131
\(980\) −16.5609 −0.529019
\(981\) 11.3889 0.363619
\(982\) −28.4117 −0.906655
\(983\) 40.5441 1.29316 0.646578 0.762848i \(-0.276200\pi\)
0.646578 + 0.762848i \(0.276200\pi\)
\(984\) 7.50136 0.239135
\(985\) −21.8101 −0.694929
\(986\) −1.07576 −0.0342591
\(987\) 48.7884 1.55295
\(988\) −8.64394 −0.275000
\(989\) 84.5600 2.68885
\(990\) −1.42642 −0.0453347
\(991\) −49.2789 −1.56539 −0.782697 0.622403i \(-0.786157\pi\)
−0.782697 + 0.622403i \(0.786157\pi\)
\(992\) 6.51827 0.206955
\(993\) 12.1572 0.385798
\(994\) −70.4938 −2.23593
\(995\) −9.95553 −0.315611
\(996\) 16.6242 0.526757
\(997\) 5.09937 0.161499 0.0807494 0.996734i \(-0.474269\pi\)
0.0807494 + 0.996734i \(0.474269\pi\)
\(998\) −21.4703 −0.679631
\(999\) −8.86689 −0.280536
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 4026.2.a.v.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.v.1.1 5 1.1 even 1 trivial