Properties

Label 430.2.a.h.1.3
Level $430$
Weight $2$
Character 430.1
Self dual yes
Analytic conductor $3.434$
Analytic rank $0$
Dimension $3$
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] = [430,2,Mod(1,430)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(430, 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("430.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 430.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: \(3.43356728692\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.470683\) of defining polynomial
Character \(\chi\) \(=\) 430.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.24914 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.24914 q^{6} +0.778457 q^{7} -1.00000 q^{8} +2.05863 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.24914 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.24914 q^{6} +0.778457 q^{7} -1.00000 q^{8} +2.05863 q^{9} +1.00000 q^{10} +5.19051 q^{11} +2.24914 q^{12} -3.83709 q^{13} -0.778457 q^{14} -2.24914 q^{15} +1.00000 q^{16} +5.30777 q^{17} -2.05863 q^{18} +3.71982 q^{19} -1.00000 q^{20} +1.75086 q^{21} -5.19051 q^{22} +7.30777 q^{23} -2.24914 q^{24} +1.00000 q^{25} +3.83709 q^{26} -2.11727 q^{27} +0.778457 q^{28} -9.52588 q^{29} +2.24914 q^{30} -0.412050 q^{31} -1.00000 q^{32} +11.6742 q^{33} -5.30777 q^{34} -0.778457 q^{35} +2.05863 q^{36} -10.8647 q^{37} -3.71982 q^{38} -8.63016 q^{39} +1.00000 q^{40} +8.66119 q^{41} -1.75086 q^{42} +1.00000 q^{43} +5.19051 q^{44} -2.05863 q^{45} -7.30777 q^{46} +2.24914 q^{47} +2.24914 q^{48} -6.39400 q^{49} -1.00000 q^{50} +11.9379 q^{51} -3.83709 q^{52} -4.05520 q^{53} +2.11727 q^{54} -5.19051 q^{55} -0.778457 q^{56} +8.36641 q^{57} +9.52588 q^{58} +10.6155 q^{59} -2.24914 q^{60} +10.5845 q^{61} +0.412050 q^{62} +1.60256 q^{63} +1.00000 q^{64} +3.83709 q^{65} -11.6742 q^{66} -13.9690 q^{67} +5.30777 q^{68} +16.4362 q^{69} +0.778457 q^{70} +1.19051 q^{71} -2.05863 q^{72} -9.85170 q^{73} +10.8647 q^{74} +2.24914 q^{75} +3.71982 q^{76} +4.04059 q^{77} +8.63016 q^{78} +4.08623 q^{79} -1.00000 q^{80} -10.9379 q^{81} -8.66119 q^{82} -10.0552 q^{83} +1.75086 q^{84} -5.30777 q^{85} -1.00000 q^{86} -21.4250 q^{87} -5.19051 q^{88} -12.9820 q^{89} +2.05863 q^{90} -2.98701 q^{91} +7.30777 q^{92} -0.926759 q^{93} -2.24914 q^{94} -3.71982 q^{95} -2.24914 q^{96} -10.8647 q^{97} +6.39400 q^{98} +10.6854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9} + 3 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{14} + 2 q^{15} + 3 q^{16} + 8 q^{17} - 7 q^{18} + 2 q^{19} - 3 q^{20} + 14 q^{21} - 6 q^{22} + 14 q^{23} + 2 q^{24} + 3 q^{25} + 4 q^{26} - 8 q^{27} - 6 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{32} + 20 q^{33} - 8 q^{34} + 6 q^{35} + 7 q^{36} - 8 q^{37} - 2 q^{38} + 2 q^{39} + 3 q^{40} + 16 q^{41} - 14 q^{42} + 3 q^{43} + 6 q^{44} - 7 q^{45} - 14 q^{46} - 2 q^{47} - 2 q^{48} + 5 q^{49} - 3 q^{50} - 4 q^{52} + 22 q^{53} + 8 q^{54} - 6 q^{55} + 6 q^{56} + 18 q^{57} - 6 q^{58} + 16 q^{59} + 2 q^{60} - 2 q^{61} - 6 q^{63} + 3 q^{64} + 4 q^{65} - 20 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 6 q^{70} - 6 q^{71} - 7 q^{72} - 10 q^{73} + 8 q^{74} - 2 q^{75} + 2 q^{76} - 10 q^{77} - 2 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 16 q^{82} + 4 q^{83} + 14 q^{84} - 8 q^{85} - 3 q^{86} - 58 q^{87} - 6 q^{88} - 16 q^{89} + 7 q^{90} - 14 q^{91} + 14 q^{92} - 14 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} - 8 q^{97} - 5 q^{98} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 2.24914 1.29854 0.649271 0.760557i \(-0.275074\pi\)
0.649271 + 0.760557i \(0.275074\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −2.24914 −0.918208
\(7\) 0.778457 0.294229 0.147115 0.989119i \(-0.453001\pi\)
0.147115 + 0.989119i \(0.453001\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.05863 0.686211
\(10\) 1.00000 0.316228
\(11\) 5.19051 1.56500 0.782498 0.622653i \(-0.213945\pi\)
0.782498 + 0.622653i \(0.213945\pi\)
\(12\) 2.24914 0.649271
\(13\) −3.83709 −1.06422 −0.532109 0.846676i \(-0.678600\pi\)
−0.532109 + 0.846676i \(0.678600\pi\)
\(14\) −0.778457 −0.208051
\(15\) −2.24914 −0.580726
\(16\) 1.00000 0.250000
\(17\) 5.30777 1.28732 0.643662 0.765310i \(-0.277414\pi\)
0.643662 + 0.765310i \(0.277414\pi\)
\(18\) −2.05863 −0.485224
\(19\) 3.71982 0.853386 0.426693 0.904396i \(-0.359678\pi\)
0.426693 + 0.904396i \(0.359678\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.75086 0.382069
\(22\) −5.19051 −1.10662
\(23\) 7.30777 1.52378 0.761888 0.647709i \(-0.224273\pi\)
0.761888 + 0.647709i \(0.224273\pi\)
\(24\) −2.24914 −0.459104
\(25\) 1.00000 0.200000
\(26\) 3.83709 0.752515
\(27\) −2.11727 −0.407468
\(28\) 0.778457 0.147115
\(29\) −9.52588 −1.76891 −0.884456 0.466624i \(-0.845470\pi\)
−0.884456 + 0.466624i \(0.845470\pi\)
\(30\) 2.24914 0.410635
\(31\) −0.412050 −0.0740064 −0.0370032 0.999315i \(-0.511781\pi\)
−0.0370032 + 0.999315i \(0.511781\pi\)
\(32\) −1.00000 −0.176777
\(33\) 11.6742 2.03221
\(34\) −5.30777 −0.910276
\(35\) −0.778457 −0.131583
\(36\) 2.05863 0.343106
\(37\) −10.8647 −1.78614 −0.893072 0.449914i \(-0.851455\pi\)
−0.893072 + 0.449914i \(0.851455\pi\)
\(38\) −3.71982 −0.603435
\(39\) −8.63016 −1.38193
\(40\) 1.00000 0.158114
\(41\) 8.66119 1.35265 0.676325 0.736603i \(-0.263571\pi\)
0.676325 + 0.736603i \(0.263571\pi\)
\(42\) −1.75086 −0.270163
\(43\) 1.00000 0.152499
\(44\) 5.19051 0.782498
\(45\) −2.05863 −0.306883
\(46\) −7.30777 −1.07747
\(47\) 2.24914 0.328071 0.164035 0.986454i \(-0.447549\pi\)
0.164035 + 0.986454i \(0.447549\pi\)
\(48\) 2.24914 0.324635
\(49\) −6.39400 −0.913429
\(50\) −1.00000 −0.141421
\(51\) 11.9379 1.67164
\(52\) −3.83709 −0.532109
\(53\) −4.05520 −0.557024 −0.278512 0.960433i \(-0.589841\pi\)
−0.278512 + 0.960433i \(0.589841\pi\)
\(54\) 2.11727 0.288123
\(55\) −5.19051 −0.699888
\(56\) −0.778457 −0.104026
\(57\) 8.36641 1.10816
\(58\) 9.52588 1.25081
\(59\) 10.6155 1.38203 0.691013 0.722842i \(-0.257165\pi\)
0.691013 + 0.722842i \(0.257165\pi\)
\(60\) −2.24914 −0.290363
\(61\) 10.5845 1.35521 0.677604 0.735427i \(-0.263018\pi\)
0.677604 + 0.735427i \(0.263018\pi\)
\(62\) 0.412050 0.0523304
\(63\) 1.60256 0.201903
\(64\) 1.00000 0.125000
\(65\) 3.83709 0.475932
\(66\) −11.6742 −1.43699
\(67\) −13.9690 −1.70658 −0.853290 0.521436i \(-0.825396\pi\)
−0.853290 + 0.521436i \(0.825396\pi\)
\(68\) 5.30777 0.643662
\(69\) 16.4362 1.97869
\(70\) 0.778457 0.0930434
\(71\) 1.19051 0.141287 0.0706436 0.997502i \(-0.477495\pi\)
0.0706436 + 0.997502i \(0.477495\pi\)
\(72\) −2.05863 −0.242612
\(73\) −9.85170 −1.15305 −0.576527 0.817078i \(-0.695592\pi\)
−0.576527 + 0.817078i \(0.695592\pi\)
\(74\) 10.8647 1.26299
\(75\) 2.24914 0.259708
\(76\) 3.71982 0.426693
\(77\) 4.04059 0.460468
\(78\) 8.63016 0.977173
\(79\) 4.08623 0.459737 0.229868 0.973222i \(-0.426170\pi\)
0.229868 + 0.973222i \(0.426170\pi\)
\(80\) −1.00000 −0.111803
\(81\) −10.9379 −1.21533
\(82\) −8.66119 −0.956469
\(83\) −10.0552 −1.10370 −0.551851 0.833943i \(-0.686078\pi\)
−0.551851 + 0.833943i \(0.686078\pi\)
\(84\) 1.75086 0.191034
\(85\) −5.30777 −0.575709
\(86\) −1.00000 −0.107833
\(87\) −21.4250 −2.29701
\(88\) −5.19051 −0.553310
\(89\) −12.9820 −1.37608 −0.688042 0.725671i \(-0.741530\pi\)
−0.688042 + 0.725671i \(0.741530\pi\)
\(90\) 2.05863 0.216999
\(91\) −2.98701 −0.313124
\(92\) 7.30777 0.761888
\(93\) −0.926759 −0.0961004
\(94\) −2.24914 −0.231981
\(95\) −3.71982 −0.381646
\(96\) −2.24914 −0.229552
\(97\) −10.8647 −1.10314 −0.551571 0.834128i \(-0.685971\pi\)
−0.551571 + 0.834128i \(0.685971\pi\)
\(98\) 6.39400 0.645892
\(99\) 10.6854 1.07392
\(100\) 1.00000 0.100000
\(101\) −0.809493 −0.0805475 −0.0402738 0.999189i \(-0.512823\pi\)
−0.0402738 + 0.999189i \(0.512823\pi\)
\(102\) −11.9379 −1.18203
\(103\) −1.05863 −0.104310 −0.0521551 0.998639i \(-0.516609\pi\)
−0.0521551 + 0.998639i \(0.516609\pi\)
\(104\) 3.83709 0.376258
\(105\) −1.75086 −0.170866
\(106\) 4.05520 0.393875
\(107\) −9.64315 −0.932238 −0.466119 0.884722i \(-0.654348\pi\)
−0.466119 + 0.884722i \(0.654348\pi\)
\(108\) −2.11727 −0.203734
\(109\) 3.05863 0.292964 0.146482 0.989213i \(-0.453205\pi\)
0.146482 + 0.989213i \(0.453205\pi\)
\(110\) 5.19051 0.494895
\(111\) −24.4362 −2.31938
\(112\) 0.778457 0.0735573
\(113\) 1.91377 0.180032 0.0900161 0.995940i \(-0.471308\pi\)
0.0900161 + 0.995940i \(0.471308\pi\)
\(114\) −8.36641 −0.783586
\(115\) −7.30777 −0.681453
\(116\) −9.52588 −0.884456
\(117\) −7.89916 −0.730278
\(118\) −10.6155 −0.977240
\(119\) 4.13187 0.378768
\(120\) 2.24914 0.205318
\(121\) 15.9414 1.44922
\(122\) −10.5845 −0.958277
\(123\) 19.4802 1.75647
\(124\) −0.412050 −0.0370032
\(125\) −1.00000 −0.0894427
\(126\) −1.60256 −0.142767
\(127\) 2.61555 0.232092 0.116046 0.993244i \(-0.462978\pi\)
0.116046 + 0.993244i \(0.462978\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.24914 0.198026
\(130\) −3.83709 −0.336535
\(131\) −3.93793 −0.344058 −0.172029 0.985092i \(-0.555032\pi\)
−0.172029 + 0.985092i \(0.555032\pi\)
\(132\) 11.6742 1.01611
\(133\) 2.89572 0.251091
\(134\) 13.9690 1.20673
\(135\) 2.11727 0.182225
\(136\) −5.30777 −0.455138
\(137\) −0.855136 −0.0730592 −0.0365296 0.999333i \(-0.511630\pi\)
−0.0365296 + 0.999333i \(0.511630\pi\)
\(138\) −16.4362 −1.39914
\(139\) 2.80949 0.238298 0.119149 0.992876i \(-0.461983\pi\)
0.119149 + 0.992876i \(0.461983\pi\)
\(140\) −0.778457 −0.0657916
\(141\) 5.05863 0.426014
\(142\) −1.19051 −0.0999052
\(143\) −19.9164 −1.66550
\(144\) 2.05863 0.171553
\(145\) 9.52588 0.791081
\(146\) 9.85170 0.815332
\(147\) −14.3810 −1.18613
\(148\) −10.8647 −0.893072
\(149\) −13.2913 −1.08887 −0.544435 0.838803i \(-0.683256\pi\)
−0.544435 + 0.838803i \(0.683256\pi\)
\(150\) −2.24914 −0.183642
\(151\) −5.05863 −0.411666 −0.205833 0.978587i \(-0.565990\pi\)
−0.205833 + 0.978587i \(0.565990\pi\)
\(152\) −3.71982 −0.301718
\(153\) 10.9268 0.883376
\(154\) −4.04059 −0.325600
\(155\) 0.412050 0.0330967
\(156\) −8.63016 −0.690965
\(157\) 19.3630 1.54533 0.772667 0.634812i \(-0.218922\pi\)
0.772667 + 0.634812i \(0.218922\pi\)
\(158\) −4.08623 −0.325083
\(159\) −9.12070 −0.723319
\(160\) 1.00000 0.0790569
\(161\) 5.68879 0.448339
\(162\) 10.9379 0.859365
\(163\) −17.2311 −1.34964 −0.674822 0.737981i \(-0.735779\pi\)
−0.674822 + 0.737981i \(0.735779\pi\)
\(164\) 8.66119 0.676325
\(165\) −11.6742 −0.908834
\(166\) 10.0552 0.780435
\(167\) −11.8061 −0.913580 −0.456790 0.889575i \(-0.651001\pi\)
−0.456790 + 0.889575i \(0.651001\pi\)
\(168\) −1.75086 −0.135082
\(169\) 1.72326 0.132559
\(170\) 5.30777 0.407088
\(171\) 7.65775 0.585603
\(172\) 1.00000 0.0762493
\(173\) 1.39400 0.105984 0.0529921 0.998595i \(-0.483124\pi\)
0.0529921 + 0.998595i \(0.483124\pi\)
\(174\) 21.4250 1.62423
\(175\) 0.778457 0.0588458
\(176\) 5.19051 0.391249
\(177\) 23.8759 1.79462
\(178\) 12.9820 0.973039
\(179\) 17.7750 1.32857 0.664284 0.747481i \(-0.268737\pi\)
0.664284 + 0.747481i \(0.268737\pi\)
\(180\) −2.05863 −0.153441
\(181\) −18.5389 −1.37798 −0.688992 0.724769i \(-0.741946\pi\)
−0.688992 + 0.724769i \(0.741946\pi\)
\(182\) 2.98701 0.221412
\(183\) 23.8061 1.75979
\(184\) −7.30777 −0.538736
\(185\) 10.8647 0.798788
\(186\) 0.926759 0.0679533
\(187\) 27.5500 2.01466
\(188\) 2.24914 0.164035
\(189\) −1.64820 −0.119889
\(190\) 3.71982 0.269864
\(191\) 14.4216 1.04351 0.521755 0.853095i \(-0.325277\pi\)
0.521755 + 0.853095i \(0.325277\pi\)
\(192\) 2.24914 0.162318
\(193\) 20.9414 1.50739 0.753696 0.657223i \(-0.228269\pi\)
0.753696 + 0.657223i \(0.228269\pi\)
\(194\) 10.8647 0.780039
\(195\) 8.63016 0.618018
\(196\) −6.39400 −0.456715
\(197\) 9.22154 0.657008 0.328504 0.944503i \(-0.393456\pi\)
0.328504 + 0.944503i \(0.393456\pi\)
\(198\) −10.6854 −0.759375
\(199\) −13.6888 −0.970372 −0.485186 0.874411i \(-0.661248\pi\)
−0.485186 + 0.874411i \(0.661248\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −31.4182 −2.21607
\(202\) 0.809493 0.0569557
\(203\) −7.41549 −0.520465
\(204\) 11.9379 0.835822
\(205\) −8.66119 −0.604924
\(206\) 1.05863 0.0737585
\(207\) 15.0440 1.04563
\(208\) −3.83709 −0.266054
\(209\) 19.3078 1.33555
\(210\) 1.75086 0.120821
\(211\) 4.88617 0.336378 0.168189 0.985755i \(-0.446208\pi\)
0.168189 + 0.985755i \(0.446208\pi\)
\(212\) −4.05520 −0.278512
\(213\) 2.67762 0.183467
\(214\) 9.64315 0.659192
\(215\) −1.00000 −0.0681994
\(216\) 2.11727 0.144062
\(217\) −0.320763 −0.0217748
\(218\) −3.05863 −0.207157
\(219\) −22.1579 −1.49729
\(220\) −5.19051 −0.349944
\(221\) −20.3664 −1.36999
\(222\) 24.4362 1.64005
\(223\) −17.5569 −1.17570 −0.587849 0.808971i \(-0.700025\pi\)
−0.587849 + 0.808971i \(0.700025\pi\)
\(224\) −0.778457 −0.0520129
\(225\) 2.05863 0.137242
\(226\) −1.91377 −0.127302
\(227\) −3.61211 −0.239744 −0.119872 0.992789i \(-0.538248\pi\)
−0.119872 + 0.992789i \(0.538248\pi\)
\(228\) 8.36641 0.554079
\(229\) 5.26719 0.348065 0.174033 0.984740i \(-0.444320\pi\)
0.174033 + 0.984740i \(0.444320\pi\)
\(230\) 7.30777 0.481860
\(231\) 9.08785 0.597937
\(232\) 9.52588 0.625405
\(233\) 26.6707 1.74726 0.873629 0.486592i \(-0.161760\pi\)
0.873629 + 0.486592i \(0.161760\pi\)
\(234\) 7.89916 0.516384
\(235\) −2.24914 −0.146718
\(236\) 10.6155 0.691013
\(237\) 9.19051 0.596988
\(238\) −4.13187 −0.267830
\(239\) 6.20350 0.401271 0.200635 0.979666i \(-0.435699\pi\)
0.200635 + 0.979666i \(0.435699\pi\)
\(240\) −2.24914 −0.145181
\(241\) 11.9233 0.768049 0.384024 0.923323i \(-0.374538\pi\)
0.384024 + 0.923323i \(0.374538\pi\)
\(242\) −15.9414 −1.02475
\(243\) −18.2491 −1.17068
\(244\) 10.5845 0.677604
\(245\) 6.39400 0.408498
\(246\) −19.4802 −1.24201
\(247\) −14.2733 −0.908188
\(248\) 0.412050 0.0261652
\(249\) −22.6155 −1.43320
\(250\) 1.00000 0.0632456
\(251\) −7.20512 −0.454783 −0.227391 0.973803i \(-0.573020\pi\)
−0.227391 + 0.973803i \(0.573020\pi\)
\(252\) 1.60256 0.100952
\(253\) 37.9311 2.38470
\(254\) −2.61555 −0.164114
\(255\) −11.9379 −0.747582
\(256\) 1.00000 0.0625000
\(257\) −8.20350 −0.511720 −0.255860 0.966714i \(-0.582359\pi\)
−0.255860 + 0.966714i \(0.582359\pi\)
\(258\) −2.24914 −0.140025
\(259\) −8.45769 −0.525536
\(260\) 3.83709 0.237966
\(261\) −19.6103 −1.21385
\(262\) 3.93793 0.243286
\(263\) 1.43010 0.0881835 0.0440917 0.999027i \(-0.485961\pi\)
0.0440917 + 0.999027i \(0.485961\pi\)
\(264\) −11.6742 −0.718496
\(265\) 4.05520 0.249109
\(266\) −2.89572 −0.177548
\(267\) −29.1982 −1.78690
\(268\) −13.9690 −0.853290
\(269\) 21.0518 1.28355 0.641774 0.766894i \(-0.278199\pi\)
0.641774 + 0.766894i \(0.278199\pi\)
\(270\) −2.11727 −0.128853
\(271\) 21.9069 1.33075 0.665375 0.746510i \(-0.268272\pi\)
0.665375 + 0.746510i \(0.268272\pi\)
\(272\) 5.30777 0.321831
\(273\) −6.71821 −0.406604
\(274\) 0.855136 0.0516607
\(275\) 5.19051 0.312999
\(276\) 16.4362 0.989344
\(277\) 20.9414 1.25824 0.629122 0.777306i \(-0.283414\pi\)
0.629122 + 0.777306i \(0.283414\pi\)
\(278\) −2.80949 −0.168502
\(279\) −0.848260 −0.0507840
\(280\) 0.778457 0.0465217
\(281\) 27.3871 1.63378 0.816890 0.576794i \(-0.195697\pi\)
0.816890 + 0.576794i \(0.195697\pi\)
\(282\) −5.05863 −0.301237
\(283\) 9.64315 0.573225 0.286613 0.958047i \(-0.407471\pi\)
0.286613 + 0.958047i \(0.407471\pi\)
\(284\) 1.19051 0.0706436
\(285\) −8.36641 −0.495583
\(286\) 19.9164 1.17768
\(287\) 6.74237 0.397989
\(288\) −2.05863 −0.121306
\(289\) 11.1725 0.657204
\(290\) −9.52588 −0.559379
\(291\) −24.4362 −1.43248
\(292\) −9.85170 −0.576527
\(293\) −6.99656 −0.408744 −0.204372 0.978893i \(-0.565515\pi\)
−0.204372 + 0.978893i \(0.565515\pi\)
\(294\) 14.3810 0.838718
\(295\) −10.6155 −0.618061
\(296\) 10.8647 0.631497
\(297\) −10.9897 −0.637686
\(298\) 13.2913 0.769947
\(299\) −28.0406 −1.62163
\(300\) 2.24914 0.129854
\(301\) 0.778457 0.0448695
\(302\) 5.05863 0.291092
\(303\) −1.82066 −0.104594
\(304\) 3.71982 0.213347
\(305\) −10.5845 −0.606067
\(306\) −10.9268 −0.624641
\(307\) −27.4638 −1.56744 −0.783721 0.621113i \(-0.786681\pi\)
−0.783721 + 0.621113i \(0.786681\pi\)
\(308\) 4.04059 0.230234
\(309\) −2.38101 −0.135451
\(310\) −0.412050 −0.0234029
\(311\) 6.29478 0.356944 0.178472 0.983945i \(-0.442885\pi\)
0.178472 + 0.983945i \(0.442885\pi\)
\(312\) 8.63016 0.488586
\(313\) −10.9966 −0.621562 −0.310781 0.950481i \(-0.600591\pi\)
−0.310781 + 0.950481i \(0.600591\pi\)
\(314\) −19.3630 −1.09272
\(315\) −1.60256 −0.0902939
\(316\) 4.08623 0.229868
\(317\) 8.10084 0.454988 0.227494 0.973779i \(-0.426947\pi\)
0.227494 + 0.973779i \(0.426947\pi\)
\(318\) 9.12070 0.511464
\(319\) −49.4441 −2.76834
\(320\) −1.00000 −0.0559017
\(321\) −21.6888 −1.21055
\(322\) −5.68879 −0.317024
\(323\) 19.7440 1.09858
\(324\) −10.9379 −0.607663
\(325\) −3.83709 −0.212843
\(326\) 17.2311 0.954342
\(327\) 6.87930 0.380426
\(328\) −8.66119 −0.478234
\(329\) 1.75086 0.0965280
\(330\) 11.6742 0.642642
\(331\) −2.28973 −0.125855 −0.0629274 0.998018i \(-0.520044\pi\)
−0.0629274 + 0.998018i \(0.520044\pi\)
\(332\) −10.0552 −0.551851
\(333\) −22.3664 −1.22567
\(334\) 11.8061 0.645999
\(335\) 13.9690 0.763206
\(336\) 1.75086 0.0955172
\(337\) 15.8827 0.865188 0.432594 0.901589i \(-0.357598\pi\)
0.432594 + 0.901589i \(0.357598\pi\)
\(338\) −1.72326 −0.0937331
\(339\) 4.30434 0.233779
\(340\) −5.30777 −0.287854
\(341\) −2.13875 −0.115820
\(342\) −7.65775 −0.414084
\(343\) −10.4267 −0.562987
\(344\) −1.00000 −0.0539164
\(345\) −16.4362 −0.884896
\(346\) −1.39400 −0.0749421
\(347\) 16.6922 0.896086 0.448043 0.894012i \(-0.352121\pi\)
0.448043 + 0.894012i \(0.352121\pi\)
\(348\) −21.4250 −1.14850
\(349\) −23.2603 −1.24510 −0.622548 0.782582i \(-0.713902\pi\)
−0.622548 + 0.782582i \(0.713902\pi\)
\(350\) −0.778457 −0.0416103
\(351\) 8.12414 0.433635
\(352\) −5.19051 −0.276655
\(353\) −17.8681 −0.951024 −0.475512 0.879709i \(-0.657737\pi\)
−0.475512 + 0.879709i \(0.657737\pi\)
\(354\) −23.8759 −1.26899
\(355\) −1.19051 −0.0631856
\(356\) −12.9820 −0.688042
\(357\) 9.29317 0.491846
\(358\) −17.7750 −0.939439
\(359\) 1.53275 0.0808957 0.0404478 0.999182i \(-0.487122\pi\)
0.0404478 + 0.999182i \(0.487122\pi\)
\(360\) 2.05863 0.108499
\(361\) −5.16291 −0.271732
\(362\) 18.5389 0.974381
\(363\) 35.8544 1.88187
\(364\) −2.98701 −0.156562
\(365\) 9.85170 0.515661
\(366\) −23.8061 −1.24436
\(367\) 0.234533 0.0122425 0.00612125 0.999981i \(-0.498052\pi\)
0.00612125 + 0.999981i \(0.498052\pi\)
\(368\) 7.30777 0.380944
\(369\) 17.8302 0.928204
\(370\) −10.8647 −0.564828
\(371\) −3.15680 −0.163893
\(372\) −0.926759 −0.0480502
\(373\) 4.74742 0.245812 0.122906 0.992418i \(-0.460779\pi\)
0.122906 + 0.992418i \(0.460779\pi\)
\(374\) −27.5500 −1.42458
\(375\) −2.24914 −0.116145
\(376\) −2.24914 −0.115991
\(377\) 36.5517 1.88251
\(378\) 1.64820 0.0847743
\(379\) 14.2897 0.734014 0.367007 0.930218i \(-0.380383\pi\)
0.367007 + 0.930218i \(0.380383\pi\)
\(380\) −3.71982 −0.190823
\(381\) 5.88273 0.301382
\(382\) −14.4216 −0.737873
\(383\) 3.71982 0.190074 0.0950371 0.995474i \(-0.469703\pi\)
0.0950371 + 0.995474i \(0.469703\pi\)
\(384\) −2.24914 −0.114776
\(385\) −4.04059 −0.205927
\(386\) −20.9414 −1.06589
\(387\) 2.05863 0.104646
\(388\) −10.8647 −0.551571
\(389\) −22.6087 −1.14631 −0.573153 0.819449i \(-0.694280\pi\)
−0.573153 + 0.819449i \(0.694280\pi\)
\(390\) −8.63016 −0.437005
\(391\) 38.7880 1.96159
\(392\) 6.39400 0.322946
\(393\) −8.85696 −0.446774
\(394\) −9.22154 −0.464575
\(395\) −4.08623 −0.205601
\(396\) 10.6854 0.536959
\(397\) −8.20855 −0.411975 −0.205988 0.978555i \(-0.566041\pi\)
−0.205988 + 0.978555i \(0.566041\pi\)
\(398\) 13.6888 0.686157
\(399\) 6.51289 0.326052
\(400\) 1.00000 0.0500000
\(401\) −36.5370 −1.82457 −0.912287 0.409552i \(-0.865685\pi\)
−0.912287 + 0.409552i \(0.865685\pi\)
\(402\) 31.4182 1.56700
\(403\) 1.58107 0.0787589
\(404\) −0.809493 −0.0402738
\(405\) 10.9379 0.543510
\(406\) 7.41549 0.368024
\(407\) −56.3932 −2.79531
\(408\) −11.9379 −0.591016
\(409\) 34.6302 1.71235 0.856175 0.516685i \(-0.172834\pi\)
0.856175 + 0.516685i \(0.172834\pi\)
\(410\) 8.66119 0.427746
\(411\) −1.92332 −0.0948704
\(412\) −1.05863 −0.0521551
\(413\) 8.26375 0.406632
\(414\) −15.0440 −0.739374
\(415\) 10.0552 0.493590
\(416\) 3.83709 0.188129
\(417\) 6.31894 0.309440
\(418\) −19.3078 −0.944374
\(419\) 34.6803 1.69424 0.847122 0.531399i \(-0.178334\pi\)
0.847122 + 0.531399i \(0.178334\pi\)
\(420\) −1.75086 −0.0854332
\(421\) 9.46381 0.461238 0.230619 0.973044i \(-0.425925\pi\)
0.230619 + 0.973044i \(0.425925\pi\)
\(422\) −4.88617 −0.237855
\(423\) 4.63016 0.225126
\(424\) 4.05520 0.196938
\(425\) 5.30777 0.257465
\(426\) −2.67762 −0.129731
\(427\) 8.23959 0.398742
\(428\) −9.64315 −0.466119
\(429\) −44.7949 −2.16272
\(430\) 1.00000 0.0482243
\(431\) −18.8172 −0.906394 −0.453197 0.891410i \(-0.649717\pi\)
−0.453197 + 0.891410i \(0.649717\pi\)
\(432\) −2.11727 −0.101867
\(433\) −9.11888 −0.438226 −0.219113 0.975700i \(-0.570316\pi\)
−0.219113 + 0.975700i \(0.570316\pi\)
\(434\) 0.320763 0.0153971
\(435\) 21.4250 1.02725
\(436\) 3.05863 0.146482
\(437\) 27.1836 1.30037
\(438\) 22.1579 1.05874
\(439\) −21.8827 −1.04441 −0.522203 0.852821i \(-0.674890\pi\)
−0.522203 + 0.852821i \(0.674890\pi\)
\(440\) 5.19051 0.247448
\(441\) −13.1629 −0.626805
\(442\) 20.3664 0.968731
\(443\) 34.6397 1.64578 0.822891 0.568199i \(-0.192360\pi\)
0.822891 + 0.568199i \(0.192360\pi\)
\(444\) −24.4362 −1.15969
\(445\) 12.9820 0.615404
\(446\) 17.5569 0.831344
\(447\) −29.8941 −1.41394
\(448\) 0.778457 0.0367786
\(449\) −34.7405 −1.63951 −0.819754 0.572716i \(-0.805890\pi\)
−0.819754 + 0.572716i \(0.805890\pi\)
\(450\) −2.05863 −0.0970449
\(451\) 44.9560 2.11689
\(452\) 1.91377 0.0900161
\(453\) −11.3776 −0.534565
\(454\) 3.61211 0.169525
\(455\) 2.98701 0.140033
\(456\) −8.36641 −0.391793
\(457\) 28.4914 1.33277 0.666386 0.745607i \(-0.267840\pi\)
0.666386 + 0.745607i \(0.267840\pi\)
\(458\) −5.26719 −0.246119
\(459\) −11.2380 −0.524544
\(460\) −7.30777 −0.340727
\(461\) −20.3112 −0.945987 −0.472994 0.881066i \(-0.656827\pi\)
−0.472994 + 0.881066i \(0.656827\pi\)
\(462\) −9.08785 −0.422805
\(463\) 39.5665 1.83881 0.919405 0.393313i \(-0.128671\pi\)
0.919405 + 0.393313i \(0.128671\pi\)
\(464\) −9.52588 −0.442228
\(465\) 0.926759 0.0429774
\(466\) −26.6707 −1.23550
\(467\) 7.48024 0.346144 0.173072 0.984909i \(-0.444631\pi\)
0.173072 + 0.984909i \(0.444631\pi\)
\(468\) −7.89916 −0.365139
\(469\) −10.8742 −0.502126
\(470\) 2.24914 0.103745
\(471\) 43.5500 2.00668
\(472\) −10.6155 −0.488620
\(473\) 5.19051 0.238660
\(474\) −9.19051 −0.422134
\(475\) 3.71982 0.170677
\(476\) 4.13187 0.189384
\(477\) −8.34816 −0.382236
\(478\) −6.20350 −0.283741
\(479\) −6.14648 −0.280840 −0.140420 0.990092i \(-0.544845\pi\)
−0.140420 + 0.990092i \(0.544845\pi\)
\(480\) 2.24914 0.102659
\(481\) 41.6888 1.90085
\(482\) −11.9233 −0.543092
\(483\) 12.7949 0.582187
\(484\) 15.9414 0.724608
\(485\) 10.8647 0.493340
\(486\) 18.2491 0.827798
\(487\) 39.3561 1.78339 0.891697 0.452632i \(-0.149515\pi\)
0.891697 + 0.452632i \(0.149515\pi\)
\(488\) −10.5845 −0.479138
\(489\) −38.7552 −1.75257
\(490\) −6.39400 −0.288852
\(491\) −1.29317 −0.0583598 −0.0291799 0.999574i \(-0.509290\pi\)
−0.0291799 + 0.999574i \(0.509290\pi\)
\(492\) 19.4802 0.878237
\(493\) −50.5612 −2.27716
\(494\) 14.2733 0.642186
\(495\) −10.6854 −0.480271
\(496\) −0.412050 −0.0185016
\(497\) 0.926759 0.0415708
\(498\) 22.6155 1.01343
\(499\) −25.7750 −1.15385 −0.576924 0.816798i \(-0.695747\pi\)
−0.576924 + 0.816798i \(0.695747\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −26.5535 −1.18632
\(502\) 7.20512 0.321580
\(503\) 23.0518 1.02783 0.513914 0.857842i \(-0.328195\pi\)
0.513914 + 0.857842i \(0.328195\pi\)
\(504\) −1.60256 −0.0713836
\(505\) 0.809493 0.0360219
\(506\) −37.9311 −1.68624
\(507\) 3.87586 0.172133
\(508\) 2.61555 0.116046
\(509\) 15.1690 0.672355 0.336178 0.941799i \(-0.390866\pi\)
0.336178 + 0.941799i \(0.390866\pi\)
\(510\) 11.9379 0.528620
\(511\) −7.66912 −0.339262
\(512\) −1.00000 −0.0441942
\(513\) −7.87586 −0.347728
\(514\) 8.20350 0.361841
\(515\) 1.05863 0.0466490
\(516\) 2.24914 0.0990129
\(517\) 11.6742 0.513430
\(518\) 8.45769 0.371610
\(519\) 3.13531 0.137625
\(520\) −3.83709 −0.168268
\(521\) −36.7665 −1.61077 −0.805385 0.592752i \(-0.798042\pi\)
−0.805385 + 0.592752i \(0.798042\pi\)
\(522\) 19.6103 0.858319
\(523\) 12.8026 0.559819 0.279910 0.960026i \(-0.409695\pi\)
0.279910 + 0.960026i \(0.409695\pi\)
\(524\) −3.93793 −0.172029
\(525\) 1.75086 0.0764138
\(526\) −1.43010 −0.0623551
\(527\) −2.18707 −0.0952702
\(528\) 11.6742 0.508053
\(529\) 30.4036 1.32189
\(530\) −4.05520 −0.176146
\(531\) 21.8535 0.948362
\(532\) 2.89572 0.125546
\(533\) −33.2338 −1.43951
\(534\) 29.1982 1.26353
\(535\) 9.64315 0.416910
\(536\) 13.9690 0.603367
\(537\) 39.9785 1.72520
\(538\) −21.0518 −0.907606
\(539\) −33.1881 −1.42951
\(540\) 2.11727 0.0911126
\(541\) −10.7328 −0.461440 −0.230720 0.973020i \(-0.574108\pi\)
−0.230720 + 0.973020i \(0.574108\pi\)
\(542\) −21.9069 −0.940982
\(543\) −41.6965 −1.78937
\(544\) −5.30777 −0.227569
\(545\) −3.05863 −0.131017
\(546\) 6.71821 0.287513
\(547\) 7.76547 0.332027 0.166014 0.986123i \(-0.446910\pi\)
0.166014 + 0.986123i \(0.446910\pi\)
\(548\) −0.855136 −0.0365296
\(549\) 21.7896 0.929959
\(550\) −5.19051 −0.221324
\(551\) −35.4346 −1.50956
\(552\) −16.4362 −0.699572
\(553\) 3.18096 0.135268
\(554\) −20.9414 −0.889713
\(555\) 24.4362 1.03726
\(556\) 2.80949 0.119149
\(557\) −32.0388 −1.35753 −0.678763 0.734357i \(-0.737484\pi\)
−0.678763 + 0.734357i \(0.737484\pi\)
\(558\) 0.848260 0.0359097
\(559\) −3.83709 −0.162292
\(560\) −0.778457 −0.0328958
\(561\) 61.9639 2.61612
\(562\) −27.3871 −1.15526
\(563\) −5.31733 −0.224099 −0.112049 0.993703i \(-0.535741\pi\)
−0.112049 + 0.993703i \(0.535741\pi\)
\(564\) 5.05863 0.213007
\(565\) −1.91377 −0.0805129
\(566\) −9.64315 −0.405332
\(567\) −8.51471 −0.357584
\(568\) −1.19051 −0.0499526
\(569\) 8.95779 0.375530 0.187765 0.982214i \(-0.439876\pi\)
0.187765 + 0.982214i \(0.439876\pi\)
\(570\) 8.36641 0.350430
\(571\) −29.3251 −1.22722 −0.613608 0.789611i \(-0.710282\pi\)
−0.613608 + 0.789611i \(0.710282\pi\)
\(572\) −19.9164 −0.832748
\(573\) 32.4362 1.35504
\(574\) −6.74237 −0.281421
\(575\) 7.30777 0.304755
\(576\) 2.05863 0.0857764
\(577\) −32.1706 −1.33928 −0.669641 0.742685i \(-0.733552\pi\)
−0.669641 + 0.742685i \(0.733552\pi\)
\(578\) −11.1725 −0.464713
\(579\) 47.1001 1.95741
\(580\) 9.52588 0.395541
\(581\) −7.82754 −0.324741
\(582\) 24.4362 1.01291
\(583\) −21.0485 −0.871741
\(584\) 9.85170 0.407666
\(585\) 7.89916 0.326590
\(586\) 6.99656 0.289025
\(587\) −27.9785 −1.15480 −0.577398 0.816462i \(-0.695932\pi\)
−0.577398 + 0.816462i \(0.695932\pi\)
\(588\) −14.3810 −0.593063
\(589\) −1.53275 −0.0631560
\(590\) 10.6155 0.437035
\(591\) 20.7405 0.853152
\(592\) −10.8647 −0.446536
\(593\) −4.06025 −0.166735 −0.0833673 0.996519i \(-0.526567\pi\)
−0.0833673 + 0.996519i \(0.526567\pi\)
\(594\) 10.9897 0.450912
\(595\) −4.13187 −0.169390
\(596\) −13.2913 −0.544435
\(597\) −30.7880 −1.26007
\(598\) 28.0406 1.14666
\(599\) 29.9639 1.22429 0.612146 0.790745i \(-0.290306\pi\)
0.612146 + 0.790745i \(0.290306\pi\)
\(600\) −2.24914 −0.0918208
\(601\) −12.9706 −0.529081 −0.264541 0.964375i \(-0.585220\pi\)
−0.264541 + 0.964375i \(0.585220\pi\)
\(602\) −0.778457 −0.0317275
\(603\) −28.7570 −1.17107
\(604\) −5.05863 −0.205833
\(605\) −15.9414 −0.648109
\(606\) 1.82066 0.0739594
\(607\) 15.0518 0.610932 0.305466 0.952203i \(-0.401188\pi\)
0.305466 + 0.952203i \(0.401188\pi\)
\(608\) −3.71982 −0.150859
\(609\) −16.6785 −0.675846
\(610\) 10.5845 0.428554
\(611\) −8.63016 −0.349139
\(612\) 10.9268 0.441688
\(613\) −17.0682 −0.689378 −0.344689 0.938717i \(-0.612016\pi\)
−0.344689 + 0.938717i \(0.612016\pi\)
\(614\) 27.4638 1.10835
\(615\) −19.4802 −0.785519
\(616\) −4.04059 −0.162800
\(617\) 48.6639 1.95913 0.979567 0.201119i \(-0.0644579\pi\)
0.979567 + 0.201119i \(0.0644579\pi\)
\(618\) 2.38101 0.0957785
\(619\) −14.5750 −0.585817 −0.292909 0.956140i \(-0.594623\pi\)
−0.292909 + 0.956140i \(0.594623\pi\)
\(620\) 0.412050 0.0165483
\(621\) −15.4725 −0.620890
\(622\) −6.29478 −0.252398
\(623\) −10.1059 −0.404884
\(624\) −8.63016 −0.345483
\(625\) 1.00000 0.0400000
\(626\) 10.9966 0.439511
\(627\) 43.4259 1.73426
\(628\) 19.3630 0.772667
\(629\) −57.6673 −2.29935
\(630\) 1.60256 0.0638474
\(631\) 9.09922 0.362234 0.181117 0.983462i \(-0.442029\pi\)
0.181117 + 0.983462i \(0.442029\pi\)
\(632\) −4.08623 −0.162542
\(633\) 10.9897 0.436801
\(634\) −8.10084 −0.321725
\(635\) −2.61555 −0.103795
\(636\) −9.12070 −0.361659
\(637\) 24.5344 0.972087
\(638\) 49.4441 1.95751
\(639\) 2.45082 0.0969529
\(640\) 1.00000 0.0395285
\(641\) −7.38445 −0.291668 −0.145834 0.989309i \(-0.546587\pi\)
−0.145834 + 0.989309i \(0.546587\pi\)
\(642\) 21.6888 0.855988
\(643\) −1.47068 −0.0579981 −0.0289990 0.999579i \(-0.509232\pi\)
−0.0289990 + 0.999579i \(0.509232\pi\)
\(644\) 5.68879 0.224170
\(645\) −2.24914 −0.0885598
\(646\) −19.7440 −0.776817
\(647\) 49.1234 1.93124 0.965620 0.259959i \(-0.0837090\pi\)
0.965620 + 0.259959i \(0.0837090\pi\)
\(648\) 10.9379 0.429682
\(649\) 55.1001 2.16287
\(650\) 3.83709 0.150503
\(651\) −0.721442 −0.0282755
\(652\) −17.2311 −0.674822
\(653\) 7.30090 0.285706 0.142853 0.989744i \(-0.454372\pi\)
0.142853 + 0.989744i \(0.454372\pi\)
\(654\) −6.87930 −0.269002
\(655\) 3.93793 0.153868
\(656\) 8.66119 0.338163
\(657\) −20.2810 −0.791238
\(658\) −1.75086 −0.0682556
\(659\) 19.3370 0.753262 0.376631 0.926363i \(-0.377082\pi\)
0.376631 + 0.926363i \(0.377082\pi\)
\(660\) −11.6742 −0.454417
\(661\) 28.5941 1.11218 0.556090 0.831122i \(-0.312301\pi\)
0.556090 + 0.831122i \(0.312301\pi\)
\(662\) 2.28973 0.0889928
\(663\) −45.8069 −1.77899
\(664\) 10.0552 0.390217
\(665\) −2.89572 −0.112291
\(666\) 22.3664 0.866681
\(667\) −69.6130 −2.69542
\(668\) −11.8061 −0.456790
\(669\) −39.4880 −1.52669
\(670\) −13.9690 −0.539668
\(671\) 54.9390 2.12090
\(672\) −1.75086 −0.0675409
\(673\) −7.08279 −0.273022 −0.136511 0.990639i \(-0.543589\pi\)
−0.136511 + 0.990639i \(0.543589\pi\)
\(674\) −15.8827 −0.611780
\(675\) −2.11727 −0.0814936
\(676\) 1.72326 0.0662793
\(677\) −12.6155 −0.484855 −0.242427 0.970170i \(-0.577944\pi\)
−0.242427 + 0.970170i \(0.577944\pi\)
\(678\) −4.30434 −0.165307
\(679\) −8.45769 −0.324576
\(680\) 5.30777 0.203544
\(681\) −8.12414 −0.311318
\(682\) 2.13875 0.0818970
\(683\) 0.967346 0.0370145 0.0185072 0.999829i \(-0.494109\pi\)
0.0185072 + 0.999829i \(0.494109\pi\)
\(684\) 7.65775 0.292802
\(685\) 0.855136 0.0326731
\(686\) 10.4267 0.398092
\(687\) 11.8466 0.451978
\(688\) 1.00000 0.0381246
\(689\) 15.5602 0.592795
\(690\) 16.4362 0.625716
\(691\) 1.21199 0.0461063 0.0230532 0.999734i \(-0.492661\pi\)
0.0230532 + 0.999734i \(0.492661\pi\)
\(692\) 1.39400 0.0529921
\(693\) 8.31809 0.315978
\(694\) −16.6922 −0.633628
\(695\) −2.80949 −0.106570
\(696\) 21.4250 0.812114
\(697\) 45.9716 1.74130
\(698\) 23.2603 0.880416
\(699\) 59.9862 2.26889
\(700\) 0.778457 0.0294229
\(701\) 38.3336 1.44784 0.723919 0.689885i \(-0.242339\pi\)
0.723919 + 0.689885i \(0.242339\pi\)
\(702\) −8.12414 −0.306626
\(703\) −40.4147 −1.52427
\(704\) 5.19051 0.195625
\(705\) −5.05863 −0.190519
\(706\) 17.8681 0.672476
\(707\) −0.630155 −0.0236994
\(708\) 23.8759 0.897310
\(709\) 18.8647 0.708478 0.354239 0.935155i \(-0.384740\pi\)
0.354239 + 0.935155i \(0.384740\pi\)
\(710\) 1.19051 0.0446789
\(711\) 8.41205 0.315477
\(712\) 12.9820 0.486519
\(713\) −3.01117 −0.112769
\(714\) −9.29317 −0.347788
\(715\) 19.9164 0.744833
\(716\) 17.7750 0.664284
\(717\) 13.9525 0.521067
\(718\) −1.53275 −0.0572019
\(719\) −43.2863 −1.61431 −0.807153 0.590342i \(-0.798993\pi\)
−0.807153 + 0.590342i \(0.798993\pi\)
\(720\) −2.05863 −0.0767207
\(721\) −0.824101 −0.0306911
\(722\) 5.16291 0.192144
\(723\) 26.8172 0.997343
\(724\) −18.5389 −0.688992
\(725\) −9.52588 −0.353782
\(726\) −35.8544 −1.33068
\(727\) 35.9379 1.33286 0.666432 0.745566i \(-0.267821\pi\)
0.666432 + 0.745566i \(0.267821\pi\)
\(728\) 2.98701 0.110706
\(729\) −8.23109 −0.304855
\(730\) −9.85170 −0.364628
\(731\) 5.30777 0.196315
\(732\) 23.8061 0.879897
\(733\) −10.6922 −0.394926 −0.197463 0.980310i \(-0.563270\pi\)
−0.197463 + 0.980310i \(0.563270\pi\)
\(734\) −0.234533 −0.00865676
\(735\) 14.3810 0.530452
\(736\) −7.30777 −0.269368
\(737\) −72.5060 −2.67079
\(738\) −17.8302 −0.656339
\(739\) −6.10084 −0.224423 −0.112211 0.993684i \(-0.535793\pi\)
−0.112211 + 0.993684i \(0.535793\pi\)
\(740\) 10.8647 0.399394
\(741\) −32.1027 −1.17932
\(742\) 3.15680 0.115890
\(743\) −24.7785 −0.909033 −0.454517 0.890738i \(-0.650188\pi\)
−0.454517 + 0.890738i \(0.650188\pi\)
\(744\) 0.926759 0.0339766
\(745\) 13.2913 0.486957
\(746\) −4.74742 −0.173815
\(747\) −20.7000 −0.757372
\(748\) 27.5500 1.00733
\(749\) −7.50677 −0.274292
\(750\) 2.24914 0.0821270
\(751\) 19.3991 0.707882 0.353941 0.935268i \(-0.384841\pi\)
0.353941 + 0.935268i \(0.384841\pi\)
\(752\) 2.24914 0.0820177
\(753\) −16.2053 −0.590555
\(754\) −36.5517 −1.33113
\(755\) 5.05863 0.184103
\(756\) −1.64820 −0.0599445
\(757\) −42.7191 −1.55265 −0.776325 0.630332i \(-0.782919\pi\)
−0.776325 + 0.630332i \(0.782919\pi\)
\(758\) −14.2897 −0.519026
\(759\) 85.3123 3.09664
\(760\) 3.71982 0.134932
\(761\) −34.7191 −1.25857 −0.629283 0.777177i \(-0.716651\pi\)
−0.629283 + 0.777177i \(0.716651\pi\)
\(762\) −5.88273 −0.213109
\(763\) 2.38101 0.0861985
\(764\) 14.4216 0.521755
\(765\) −10.9268 −0.395058
\(766\) −3.71982 −0.134403
\(767\) −40.7328 −1.47078
\(768\) 2.24914 0.0811589
\(769\) 43.1234 1.55507 0.777534 0.628840i \(-0.216470\pi\)
0.777534 + 0.628840i \(0.216470\pi\)
\(770\) 4.04059 0.145613
\(771\) −18.4508 −0.664490
\(772\) 20.9414 0.753696
\(773\) −0.747422 −0.0268829 −0.0134414 0.999910i \(-0.504279\pi\)
−0.0134414 + 0.999910i \(0.504279\pi\)
\(774\) −2.05863 −0.0739960
\(775\) −0.412050 −0.0148013
\(776\) 10.8647 0.390020
\(777\) −19.0225 −0.682430
\(778\) 22.6087 0.810560
\(779\) 32.2181 1.15433
\(780\) 8.63016 0.309009
\(781\) 6.17934 0.221114
\(782\) −38.7880 −1.38706
\(783\) 20.1688 0.720775
\(784\) −6.39400 −0.228357
\(785\) −19.3630 −0.691094
\(786\) 8.85696 0.315917
\(787\) −37.9260 −1.35192 −0.675958 0.736940i \(-0.736270\pi\)
−0.675958 + 0.736940i \(0.736270\pi\)
\(788\) 9.22154 0.328504
\(789\) 3.21649 0.114510
\(790\) 4.08623 0.145382
\(791\) 1.48979 0.0529707
\(792\) −10.6854 −0.379687
\(793\) −40.6137 −1.44224
\(794\) 8.20855 0.291311
\(795\) 9.12070 0.323478
\(796\) −13.6888 −0.485186
\(797\) −8.63198 −0.305760 −0.152880 0.988245i \(-0.548855\pi\)
−0.152880 + 0.988245i \(0.548855\pi\)
\(798\) −6.51289 −0.230554
\(799\) 11.9379 0.422334
\(800\) −1.00000 −0.0353553
\(801\) −26.7251 −0.944284
\(802\) 36.5370 1.29017
\(803\) −51.1353 −1.80453
\(804\) −31.4182 −1.10803
\(805\) −5.68879 −0.200503
\(806\) −1.58107 −0.0556910
\(807\) 47.3484 1.66674
\(808\) 0.809493 0.0284779
\(809\) 49.3611 1.73545 0.867723 0.497048i \(-0.165583\pi\)
0.867723 + 0.497048i \(0.165583\pi\)
\(810\) −10.9379 −0.384320
\(811\) 26.5991 0.934021 0.467011 0.884252i \(-0.345331\pi\)
0.467011 + 0.884252i \(0.345331\pi\)
\(812\) −7.41549 −0.260233
\(813\) 49.2717 1.72803
\(814\) 56.3932 1.97658
\(815\) 17.2311 0.603579
\(816\) 11.9379 0.417911
\(817\) 3.71982 0.130140
\(818\) −34.6302 −1.21081
\(819\) −6.14916 −0.214869
\(820\) −8.66119 −0.302462
\(821\) −50.6087 −1.76625 −0.883127 0.469133i \(-0.844566\pi\)
−0.883127 + 0.469133i \(0.844566\pi\)
\(822\) 1.92332 0.0670835
\(823\) −48.8103 −1.70142 −0.850711 0.525634i \(-0.823828\pi\)
−0.850711 + 0.525634i \(0.823828\pi\)
\(824\) 1.05863 0.0368792
\(825\) 11.6742 0.406443
\(826\) −8.26375 −0.287533
\(827\) 47.2293 1.64232 0.821161 0.570696i \(-0.193327\pi\)
0.821161 + 0.570696i \(0.193327\pi\)
\(828\) 15.0440 0.522816
\(829\) −7.44147 −0.258453 −0.129226 0.991615i \(-0.541249\pi\)
−0.129226 + 0.991615i \(0.541249\pi\)
\(830\) −10.0552 −0.349021
\(831\) 47.1001 1.63388
\(832\) −3.83709 −0.133027
\(833\) −33.9379 −1.17588
\(834\) −6.31894 −0.218807
\(835\) 11.8061 0.408565
\(836\) 19.3078 0.667773
\(837\) 0.872420 0.0301553
\(838\) −34.6803 −1.19801
\(839\) 16.5389 0.570985 0.285493 0.958381i \(-0.407843\pi\)
0.285493 + 0.958381i \(0.407843\pi\)
\(840\) 1.75086 0.0604104
\(841\) 61.7424 2.12905
\(842\) −9.46381 −0.326144
\(843\) 61.5975 2.12153
\(844\) 4.88617 0.168189
\(845\) −1.72326 −0.0592820
\(846\) −4.63016 −0.159188
\(847\) 12.4097 0.426401
\(848\) −4.05520 −0.139256
\(849\) 21.6888 0.744357
\(850\) −5.30777 −0.182055
\(851\) −79.3967 −2.72168
\(852\) 2.67762 0.0917337
\(853\) −34.8862 −1.19448 −0.597240 0.802063i \(-0.703736\pi\)
−0.597240 + 0.802063i \(0.703736\pi\)
\(854\) −8.23959 −0.281953
\(855\) −7.65775 −0.261890
\(856\) 9.64315 0.329596
\(857\) 10.0698 0.343978 0.171989 0.985099i \(-0.444981\pi\)
0.171989 + 0.985099i \(0.444981\pi\)
\(858\) 44.7949 1.52927
\(859\) −36.1560 −1.23363 −0.616814 0.787109i \(-0.711577\pi\)
−0.616814 + 0.787109i \(0.711577\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 15.1645 0.516806
\(862\) 18.8172 0.640917
\(863\) −38.3189 −1.30439 −0.652196 0.758050i \(-0.726152\pi\)
−0.652196 + 0.758050i \(0.726152\pi\)
\(864\) 2.11727 0.0720309
\(865\) −1.39400 −0.0473976
\(866\) 9.11888 0.309872
\(867\) 25.1284 0.853406
\(868\) −0.320763 −0.0108874
\(869\) 21.2096 0.719487
\(870\) −21.4250 −0.726377
\(871\) 53.6002 1.81617
\(872\) −3.05863 −0.103578
\(873\) −22.3664 −0.756988
\(874\) −27.1836 −0.919500
\(875\) −0.778457 −0.0263167
\(876\) −22.1579 −0.748644
\(877\) 34.5174 1.16557 0.582785 0.812627i \(-0.301963\pi\)
0.582785 + 0.812627i \(0.301963\pi\)
\(878\) 21.8827 0.738506
\(879\) −15.7363 −0.530771
\(880\) −5.19051 −0.174972
\(881\) −21.1303 −0.711896 −0.355948 0.934506i \(-0.615842\pi\)
−0.355948 + 0.934506i \(0.615842\pi\)
\(882\) 13.1629 0.443218
\(883\) −6.99838 −0.235514 −0.117757 0.993042i \(-0.537570\pi\)
−0.117757 + 0.993042i \(0.537570\pi\)
\(884\) −20.3664 −0.684996
\(885\) −23.8759 −0.802578
\(886\) −34.6397 −1.16374
\(887\) 38.3216 1.28671 0.643357 0.765566i \(-0.277541\pi\)
0.643357 + 0.765566i \(0.277541\pi\)
\(888\) 24.4362 0.820026
\(889\) 2.03609 0.0682883
\(890\) −12.9820 −0.435156
\(891\) −56.7734 −1.90198
\(892\) −17.5569 −0.587849
\(893\) 8.36641 0.279971
\(894\) 29.8941 0.999808
\(895\) −17.7750 −0.594153
\(896\) −0.778457 −0.0260064
\(897\) −63.0672 −2.10575
\(898\) 34.7405 1.15931
\(899\) 3.92514 0.130911
\(900\) 2.05863 0.0686211
\(901\) −21.5241 −0.717070
\(902\) −44.9560 −1.49687
\(903\) 1.75086 0.0582650
\(904\) −1.91377 −0.0636510
\(905\) 18.5389 0.616253
\(906\) 11.3776 0.377995
\(907\) −55.4829 −1.84228 −0.921140 0.389232i \(-0.872741\pi\)
−0.921140 + 0.389232i \(0.872741\pi\)
\(908\) −3.61211 −0.119872
\(909\) −1.66645 −0.0552726
\(910\) −2.98701 −0.0990184
\(911\) −25.2717 −0.837288 −0.418644 0.908150i \(-0.637495\pi\)
−0.418644 + 0.908150i \(0.637495\pi\)
\(912\) 8.36641 0.277039
\(913\) −52.1916 −1.72729
\(914\) −28.4914 −0.942412
\(915\) −23.8061 −0.787004
\(916\) 5.26719 0.174033
\(917\) −3.06551 −0.101232
\(918\) 11.2380 0.370908
\(919\) 21.1741 0.698468 0.349234 0.937035i \(-0.386442\pi\)
0.349234 + 0.937035i \(0.386442\pi\)
\(920\) 7.30777 0.240930
\(921\) −61.7700 −2.03539
\(922\) 20.3112 0.668914
\(923\) −4.56808 −0.150360
\(924\) 9.08785 0.298968
\(925\) −10.8647 −0.357229
\(926\) −39.5665 −1.30023
\(927\) −2.17934 −0.0715788
\(928\) 9.52588 0.312702
\(929\) −27.4948 −0.902077 −0.451038 0.892505i \(-0.648946\pi\)
−0.451038 + 0.892505i \(0.648946\pi\)
\(930\) −0.926759 −0.0303896
\(931\) −23.7846 −0.779508
\(932\) 26.6707 0.873629
\(933\) 14.1579 0.463507
\(934\) −7.48024 −0.244761
\(935\) −27.5500 −0.900983
\(936\) 7.89916 0.258192
\(937\) −39.7914 −1.29993 −0.649965 0.759964i \(-0.725216\pi\)
−0.649965 + 0.759964i \(0.725216\pi\)
\(938\) 10.8742 0.355057
\(939\) −24.7328 −0.807125
\(940\) −2.24914 −0.0733589
\(941\) 23.7079 0.772855 0.386428 0.922320i \(-0.373709\pi\)
0.386428 + 0.922320i \(0.373709\pi\)
\(942\) −43.5500 −1.41894
\(943\) 63.2940 2.06114
\(944\) 10.6155 0.345507
\(945\) 1.64820 0.0536160
\(946\) −5.19051 −0.168758
\(947\) 13.1932 0.428721 0.214360 0.976755i \(-0.431233\pi\)
0.214360 + 0.976755i \(0.431233\pi\)
\(948\) 9.19051 0.298494
\(949\) 37.8019 1.22710
\(950\) −3.71982 −0.120687
\(951\) 18.2199 0.590822
\(952\) −4.13187 −0.133915
\(953\) 26.6949 0.864733 0.432366 0.901698i \(-0.357679\pi\)
0.432366 + 0.901698i \(0.357679\pi\)
\(954\) 8.34816 0.270282
\(955\) −14.4216 −0.466672
\(956\) 6.20350 0.200635
\(957\) −111.207 −3.59481
\(958\) 6.14648 0.198584
\(959\) −0.665687 −0.0214961
\(960\) −2.24914 −0.0725907
\(961\) −30.8302 −0.994523
\(962\) −41.6888 −1.34410
\(963\) −19.8517 −0.639712
\(964\) 11.9233 0.384024
\(965\) −20.9414 −0.674126
\(966\) −12.7949 −0.411669
\(967\) 14.6233 0.470253 0.235126 0.971965i \(-0.424450\pi\)
0.235126 + 0.971965i \(0.424450\pi\)
\(968\) −15.9414 −0.512375
\(969\) 44.4070 1.42656
\(970\) −10.8647 −0.348844
\(971\) −15.1836 −0.487266 −0.243633 0.969868i \(-0.578339\pi\)
−0.243633 + 0.969868i \(0.578339\pi\)
\(972\) −18.2491 −0.585341
\(973\) 2.18707 0.0701142
\(974\) −39.3561 −1.26105
\(975\) −8.63016 −0.276386
\(976\) 10.5845 0.338802
\(977\) −8.27836 −0.264848 −0.132424 0.991193i \(-0.542276\pi\)
−0.132424 + 0.991193i \(0.542276\pi\)
\(978\) 38.7552 1.23925
\(979\) −67.3829 −2.15357
\(980\) 6.39400 0.204249
\(981\) 6.29660 0.201035
\(982\) 1.29317 0.0412666
\(983\) 34.6803 1.10613 0.553065 0.833138i \(-0.313458\pi\)
0.553065 + 0.833138i \(0.313458\pi\)
\(984\) −19.4802 −0.621007
\(985\) −9.22154 −0.293823
\(986\) 50.5612 1.61020
\(987\) 3.93793 0.125346
\(988\) −14.2733 −0.454094
\(989\) 7.30777 0.232374
\(990\) 10.6854 0.339603
\(991\) −30.6967 −0.975114 −0.487557 0.873091i \(-0.662112\pi\)
−0.487557 + 0.873091i \(0.662112\pi\)
\(992\) 0.412050 0.0130826
\(993\) −5.14992 −0.163428
\(994\) −0.926759 −0.0293950
\(995\) 13.6888 0.433964
\(996\) −22.6155 −0.716601
\(997\) 52.1656 1.65210 0.826050 0.563596i \(-0.190583\pi\)
0.826050 + 0.563596i \(0.190583\pi\)
\(998\) 25.7750 0.815894
\(999\) 23.0034 0.727797
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 430.2.a.h.1.3 3
3.2 odd 2 3870.2.a.bn.1.3 3
4.3 odd 2 3440.2.a.n.1.1 3
5.2 odd 4 2150.2.b.t.1549.1 6
5.3 odd 4 2150.2.b.t.1549.6 6
5.4 even 2 2150.2.a.bf.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
430.2.a.h.1.3 3 1.1 even 1 trivial
2150.2.a.bf.1.1 3 5.4 even 2
2150.2.b.t.1549.1 6 5.2 odd 4
2150.2.b.t.1549.6 6 5.3 odd 4
3440.2.a.n.1.1 3 4.3 odd 2
3870.2.a.bn.1.3 3 3.2 odd 2