Properties

Label 1014.2.a.l.1.2
Level $1014$
Weight $2$
Character 1014.1
Self dual yes
Analytic conductor $8.097$
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] = [1014,2,Mod(1,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, 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("1014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.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: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) 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 1.2
Root \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 1014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.13706 q^{5} +1.00000 q^{6} +0.0489173 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.13706 q^{5} +1.00000 q^{6} +0.0489173 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.13706 q^{10} -6.29590 q^{11} -1.00000 q^{12} -0.0489173 q^{14} +2.13706 q^{15} +1.00000 q^{16} -2.89008 q^{17} -1.00000 q^{18} +7.20775 q^{19} -2.13706 q^{20} -0.0489173 q^{21} +6.29590 q^{22} +2.71379 q^{23} +1.00000 q^{24} -0.432960 q^{25} -1.00000 q^{27} +0.0489173 q^{28} +4.91185 q^{29} -2.13706 q^{30} -9.00969 q^{31} -1.00000 q^{32} +6.29590 q^{33} +2.89008 q^{34} -0.104539 q^{35} +1.00000 q^{36} +0.176292 q^{37} -7.20775 q^{38} +2.13706 q^{40} +8.59179 q^{41} +0.0489173 q^{42} +6.71379 q^{43} -6.29590 q^{44} -2.13706 q^{45} -2.71379 q^{46} -7.20775 q^{47} -1.00000 q^{48} -6.99761 q^{49} +0.432960 q^{50} +2.89008 q^{51} +9.34481 q^{53} +1.00000 q^{54} +13.4547 q^{55} -0.0489173 q^{56} -7.20775 q^{57} -4.91185 q^{58} +4.26875 q^{59} +2.13706 q^{60} +7.10992 q^{61} +9.00969 q^{62} +0.0489173 q^{63} +1.00000 q^{64} -6.29590 q^{66} -5.38404 q^{67} -2.89008 q^{68} -2.71379 q^{69} +0.104539 q^{70} +8.71379 q^{71} -1.00000 q^{72} +14.9487 q^{73} -0.176292 q^{74} +0.432960 q^{75} +7.20775 q^{76} -0.307979 q^{77} +13.8291 q^{79} -2.13706 q^{80} +1.00000 q^{81} -8.59179 q^{82} +11.1347 q^{83} -0.0489173 q^{84} +6.17629 q^{85} -6.71379 q^{86} -4.91185 q^{87} +6.29590 q^{88} -3.92154 q^{89} +2.13706 q^{90} +2.71379 q^{92} +9.00969 q^{93} +7.20775 q^{94} -15.4034 q^{95} +1.00000 q^{96} +2.47889 q^{97} +6.99761 q^{98} -6.29590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} - 9 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} - 9 q^{7} - 3 q^{8} + 3 q^{9} + q^{10} - 5 q^{11} - 3 q^{12} + 9 q^{14} + q^{15} + 3 q^{16} - 8 q^{17} - 3 q^{18} + 4 q^{19} - q^{20} + 9 q^{21} + 5 q^{22} + 3 q^{24} + 18 q^{25} - 3 q^{27} - 9 q^{28} + 11 q^{29} - q^{30} - 5 q^{31} - 3 q^{32} + 5 q^{33} + 8 q^{34} - 4 q^{35} + 3 q^{36} + 8 q^{37} - 4 q^{38} + q^{40} - 2 q^{41} - 9 q^{42} + 12 q^{43} - 5 q^{44} - q^{45} - 4 q^{47} - 3 q^{48} + 20 q^{49} - 18 q^{50} + 8 q^{51} + 5 q^{53} + 3 q^{54} + 18 q^{55} + 9 q^{56} - 4 q^{57} - 11 q^{58} + 5 q^{59} + q^{60} + 22 q^{61} + 5 q^{62} - 9 q^{63} + 3 q^{64} - 5 q^{66} - 6 q^{67} - 8 q^{68} + 4 q^{70} + 18 q^{71} - 3 q^{72} + 13 q^{73} - 8 q^{74} - 18 q^{75} + 4 q^{76} - 6 q^{77} + 31 q^{79} - q^{80} + 3 q^{81} + 2 q^{82} - 13 q^{83} + 9 q^{84} + 26 q^{85} - 12 q^{86} - 11 q^{87} + 5 q^{88} + 14 q^{89} + q^{90} + 5 q^{93} + 4 q^{94} + 8 q^{95} + 3 q^{96} + 23 q^{97} - 20 q^{98} - 5 q^{99}+O(q^{100}) \) 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
\(5\) −2.13706 −0.955724 −0.477862 0.878435i \(-0.658588\pi\)
−0.477862 + 0.878435i \(0.658588\pi\)
\(6\) 1.00000 0.408248
\(7\) 0.0489173 0.0184890 0.00924451 0.999957i \(-0.497057\pi\)
0.00924451 + 0.999957i \(0.497057\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.13706 0.675799
\(11\) −6.29590 −1.89828 −0.949142 0.314848i \(-0.898047\pi\)
−0.949142 + 0.314848i \(0.898047\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −0.0489173 −0.0130737
\(15\) 2.13706 0.551787
\(16\) 1.00000 0.250000
\(17\) −2.89008 −0.700948 −0.350474 0.936572i \(-0.613980\pi\)
−0.350474 + 0.936572i \(0.613980\pi\)
\(18\) −1.00000 −0.235702
\(19\) 7.20775 1.65357 0.826786 0.562517i \(-0.190167\pi\)
0.826786 + 0.562517i \(0.190167\pi\)
\(20\) −2.13706 −0.477862
\(21\) −0.0489173 −0.0106746
\(22\) 6.29590 1.34229
\(23\) 2.71379 0.565865 0.282932 0.959140i \(-0.408693\pi\)
0.282932 + 0.959140i \(0.408693\pi\)
\(24\) 1.00000 0.204124
\(25\) −0.432960 −0.0865921
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0.0489173 0.00924451
\(29\) 4.91185 0.912108 0.456054 0.889952i \(-0.349262\pi\)
0.456054 + 0.889952i \(0.349262\pi\)
\(30\) −2.13706 −0.390173
\(31\) −9.00969 −1.61819 −0.809094 0.587679i \(-0.800042\pi\)
−0.809094 + 0.587679i \(0.800042\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.29590 1.09597
\(34\) 2.89008 0.495645
\(35\) −0.104539 −0.0176704
\(36\) 1.00000 0.166667
\(37\) 0.176292 0.0289822 0.0144911 0.999895i \(-0.495387\pi\)
0.0144911 + 0.999895i \(0.495387\pi\)
\(38\) −7.20775 −1.16925
\(39\) 0 0
\(40\) 2.13706 0.337899
\(41\) 8.59179 1.34181 0.670906 0.741542i \(-0.265905\pi\)
0.670906 + 0.741542i \(0.265905\pi\)
\(42\) 0.0489173 0.00754811
\(43\) 6.71379 1.02384 0.511922 0.859032i \(-0.328934\pi\)
0.511922 + 0.859032i \(0.328934\pi\)
\(44\) −6.29590 −0.949142
\(45\) −2.13706 −0.318575
\(46\) −2.71379 −0.400127
\(47\) −7.20775 −1.05136 −0.525679 0.850683i \(-0.676189\pi\)
−0.525679 + 0.850683i \(0.676189\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.99761 −0.999658
\(50\) 0.432960 0.0612298
\(51\) 2.89008 0.404693
\(52\) 0 0
\(53\) 9.34481 1.28361 0.641804 0.766868i \(-0.278186\pi\)
0.641804 + 0.766868i \(0.278186\pi\)
\(54\) 1.00000 0.136083
\(55\) 13.4547 1.81424
\(56\) −0.0489173 −0.00653685
\(57\) −7.20775 −0.954690
\(58\) −4.91185 −0.644958
\(59\) 4.26875 0.555744 0.277872 0.960618i \(-0.410371\pi\)
0.277872 + 0.960618i \(0.410371\pi\)
\(60\) 2.13706 0.275894
\(61\) 7.10992 0.910331 0.455166 0.890407i \(-0.349580\pi\)
0.455166 + 0.890407i \(0.349580\pi\)
\(62\) 9.00969 1.14423
\(63\) 0.0489173 0.00616301
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.29590 −0.774971
\(67\) −5.38404 −0.657766 −0.328883 0.944371i \(-0.606672\pi\)
−0.328883 + 0.944371i \(0.606672\pi\)
\(68\) −2.89008 −0.350474
\(69\) −2.71379 −0.326702
\(70\) 0.104539 0.0124949
\(71\) 8.71379 1.03414 0.517068 0.855944i \(-0.327023\pi\)
0.517068 + 0.855944i \(0.327023\pi\)
\(72\) −1.00000 −0.117851
\(73\) 14.9487 1.74961 0.874806 0.484474i \(-0.160989\pi\)
0.874806 + 0.484474i \(0.160989\pi\)
\(74\) −0.176292 −0.0204935
\(75\) 0.432960 0.0499939
\(76\) 7.20775 0.826786
\(77\) −0.307979 −0.0350974
\(78\) 0 0
\(79\) 13.8291 1.55589 0.777947 0.628330i \(-0.216261\pi\)
0.777947 + 0.628330i \(0.216261\pi\)
\(80\) −2.13706 −0.238931
\(81\) 1.00000 0.111111
\(82\) −8.59179 −0.948805
\(83\) 11.1347 1.22219 0.611094 0.791558i \(-0.290730\pi\)
0.611094 + 0.791558i \(0.290730\pi\)
\(84\) −0.0489173 −0.00533732
\(85\) 6.17629 0.669913
\(86\) −6.71379 −0.723967
\(87\) −4.91185 −0.526606
\(88\) 6.29590 0.671145
\(89\) −3.92154 −0.415683 −0.207841 0.978163i \(-0.566644\pi\)
−0.207841 + 0.978163i \(0.566644\pi\)
\(90\) 2.13706 0.225266
\(91\) 0 0
\(92\) 2.71379 0.282932
\(93\) 9.00969 0.934261
\(94\) 7.20775 0.743423
\(95\) −15.4034 −1.58036
\(96\) 1.00000 0.102062
\(97\) 2.47889 0.251694 0.125847 0.992050i \(-0.459835\pi\)
0.125847 + 0.992050i \(0.459835\pi\)
\(98\) 6.99761 0.706865
\(99\) −6.29590 −0.632761
\(100\) −0.432960 −0.0432960
\(101\) 1.65279 0.164459 0.0822295 0.996613i \(-0.473796\pi\)
0.0822295 + 0.996613i \(0.473796\pi\)
\(102\) −2.89008 −0.286161
\(103\) −8.23490 −0.811409 −0.405704 0.914004i \(-0.632974\pi\)
−0.405704 + 0.914004i \(0.632974\pi\)
\(104\) 0 0
\(105\) 0.104539 0.0102020
\(106\) −9.34481 −0.907649
\(107\) −8.36658 −0.808828 −0.404414 0.914576i \(-0.632525\pi\)
−0.404414 + 0.914576i \(0.632525\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 17.4276 1.66926 0.834630 0.550811i \(-0.185682\pi\)
0.834630 + 0.550811i \(0.185682\pi\)
\(110\) −13.4547 −1.28286
\(111\) −0.176292 −0.0167329
\(112\) 0.0489173 0.00462225
\(113\) −13.9758 −1.31474 −0.657368 0.753570i \(-0.728330\pi\)
−0.657368 + 0.753570i \(0.728330\pi\)
\(114\) 7.20775 0.675068
\(115\) −5.79954 −0.540810
\(116\) 4.91185 0.456054
\(117\) 0 0
\(118\) −4.26875 −0.392970
\(119\) −0.141375 −0.0129598
\(120\) −2.13706 −0.195086
\(121\) 28.6383 2.60348
\(122\) −7.10992 −0.643702
\(123\) −8.59179 −0.774696
\(124\) −9.00969 −0.809094
\(125\) 11.6106 1.03848
\(126\) −0.0489173 −0.00435790
\(127\) −7.52111 −0.667390 −0.333695 0.942681i \(-0.608296\pi\)
−0.333695 + 0.942681i \(0.608296\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.71379 −0.591116
\(130\) 0 0
\(131\) 5.12498 0.447772 0.223886 0.974615i \(-0.428126\pi\)
0.223886 + 0.974615i \(0.428126\pi\)
\(132\) 6.29590 0.547987
\(133\) 0.352584 0.0305729
\(134\) 5.38404 0.465110
\(135\) 2.13706 0.183929
\(136\) 2.89008 0.247823
\(137\) 4.00000 0.341743 0.170872 0.985293i \(-0.445342\pi\)
0.170872 + 0.985293i \(0.445342\pi\)
\(138\) 2.71379 0.231013
\(139\) 8.68963 0.737045 0.368522 0.929619i \(-0.379864\pi\)
0.368522 + 0.929619i \(0.379864\pi\)
\(140\) −0.104539 −0.00883520
\(141\) 7.20775 0.607002
\(142\) −8.71379 −0.731245
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −10.4969 −0.871724
\(146\) −14.9487 −1.23716
\(147\) 6.99761 0.577153
\(148\) 0.176292 0.0144911
\(149\) 4.86831 0.398828 0.199414 0.979915i \(-0.436096\pi\)
0.199414 + 0.979915i \(0.436096\pi\)
\(150\) −0.432960 −0.0353511
\(151\) −14.7463 −1.20004 −0.600019 0.799986i \(-0.704840\pi\)
−0.600019 + 0.799986i \(0.704840\pi\)
\(152\) −7.20775 −0.584626
\(153\) −2.89008 −0.233649
\(154\) 0.307979 0.0248176
\(155\) 19.2543 1.54654
\(156\) 0 0
\(157\) −16.7138 −1.33391 −0.666953 0.745100i \(-0.732402\pi\)
−0.666953 + 0.745100i \(0.732402\pi\)
\(158\) −13.8291 −1.10018
\(159\) −9.34481 −0.741092
\(160\) 2.13706 0.168950
\(161\) 0.132751 0.0104623
\(162\) −1.00000 −0.0785674
\(163\) −5.54958 −0.434677 −0.217338 0.976096i \(-0.569738\pi\)
−0.217338 + 0.976096i \(0.569738\pi\)
\(164\) 8.59179 0.670906
\(165\) −13.4547 −1.04745
\(166\) −11.1347 −0.864218
\(167\) 3.92154 0.303458 0.151729 0.988422i \(-0.451516\pi\)
0.151729 + 0.988422i \(0.451516\pi\)
\(168\) 0.0489173 0.00377405
\(169\) 0 0
\(170\) −6.17629 −0.473700
\(171\) 7.20775 0.551190
\(172\) 6.71379 0.511922
\(173\) −3.48427 −0.264904 −0.132452 0.991189i \(-0.542285\pi\)
−0.132452 + 0.991189i \(0.542285\pi\)
\(174\) 4.91185 0.372367
\(175\) −0.0211793 −0.00160100
\(176\) −6.29590 −0.474571
\(177\) −4.26875 −0.320859
\(178\) 3.92154 0.293932
\(179\) 3.58881 0.268240 0.134120 0.990965i \(-0.457179\pi\)
0.134120 + 0.990965i \(0.457179\pi\)
\(180\) −2.13706 −0.159287
\(181\) 5.50604 0.409261 0.204630 0.978839i \(-0.434401\pi\)
0.204630 + 0.978839i \(0.434401\pi\)
\(182\) 0 0
\(183\) −7.10992 −0.525580
\(184\) −2.71379 −0.200063
\(185\) −0.376747 −0.0276990
\(186\) −9.00969 −0.660622
\(187\) 18.1957 1.33060
\(188\) −7.20775 −0.525679
\(189\) −0.0489173 −0.00355821
\(190\) 15.4034 1.11748
\(191\) −5.65817 −0.409411 −0.204705 0.978824i \(-0.565624\pi\)
−0.204705 + 0.978824i \(0.565624\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 13.4034 0.964799 0.482400 0.875951i \(-0.339765\pi\)
0.482400 + 0.875951i \(0.339765\pi\)
\(194\) −2.47889 −0.177974
\(195\) 0 0
\(196\) −6.99761 −0.499829
\(197\) 19.9812 1.42360 0.711801 0.702381i \(-0.247880\pi\)
0.711801 + 0.702381i \(0.247880\pi\)
\(198\) 6.29590 0.447430
\(199\) −6.24160 −0.442455 −0.221228 0.975222i \(-0.571006\pi\)
−0.221228 + 0.975222i \(0.571006\pi\)
\(200\) 0.432960 0.0306149
\(201\) 5.38404 0.379761
\(202\) −1.65279 −0.116290
\(203\) 0.240275 0.0168640
\(204\) 2.89008 0.202346
\(205\) −18.3612 −1.28240
\(206\) 8.23490 0.573753
\(207\) 2.71379 0.188622
\(208\) 0 0
\(209\) −45.3793 −3.13895
\(210\) −0.104539 −0.00721391
\(211\) −5.08575 −0.350118 −0.175059 0.984558i \(-0.556012\pi\)
−0.175059 + 0.984558i \(0.556012\pi\)
\(212\) 9.34481 0.641804
\(213\) −8.71379 −0.597059
\(214\) 8.36658 0.571928
\(215\) −14.3478 −0.978512
\(216\) 1.00000 0.0680414
\(217\) −0.440730 −0.0299187
\(218\) −17.4276 −1.18034
\(219\) −14.9487 −1.01014
\(220\) 13.4547 0.907118
\(221\) 0 0
\(222\) 0.176292 0.0118319
\(223\) −20.5483 −1.37601 −0.688006 0.725705i \(-0.741514\pi\)
−0.688006 + 0.725705i \(0.741514\pi\)
\(224\) −0.0489173 −0.00326843
\(225\) −0.432960 −0.0288640
\(226\) 13.9758 0.929659
\(227\) 4.41119 0.292781 0.146390 0.989227i \(-0.453234\pi\)
0.146390 + 0.989227i \(0.453234\pi\)
\(228\) −7.20775 −0.477345
\(229\) 0.230586 0.0152376 0.00761878 0.999971i \(-0.497575\pi\)
0.00761878 + 0.999971i \(0.497575\pi\)
\(230\) 5.79954 0.382411
\(231\) 0.307979 0.0202635
\(232\) −4.91185 −0.322479
\(233\) −7.82371 −0.512548 −0.256274 0.966604i \(-0.582495\pi\)
−0.256274 + 0.966604i \(0.582495\pi\)
\(234\) 0 0
\(235\) 15.4034 1.00481
\(236\) 4.26875 0.277872
\(237\) −13.8291 −0.898296
\(238\) 0.141375 0.00916399
\(239\) 11.1535 0.721457 0.360729 0.932671i \(-0.382528\pi\)
0.360729 + 0.932671i \(0.382528\pi\)
\(240\) 2.13706 0.137947
\(241\) −3.54527 −0.228371 −0.114185 0.993459i \(-0.536426\pi\)
−0.114185 + 0.993459i \(0.536426\pi\)
\(242\) −28.6383 −1.84094
\(243\) −1.00000 −0.0641500
\(244\) 7.10992 0.455166
\(245\) 14.9543 0.955397
\(246\) 8.59179 0.547793
\(247\) 0 0
\(248\) 9.00969 0.572116
\(249\) −11.1347 −0.705631
\(250\) −11.6106 −0.734318
\(251\) −4.17092 −0.263266 −0.131633 0.991299i \(-0.542022\pi\)
−0.131633 + 0.991299i \(0.542022\pi\)
\(252\) 0.0489173 0.00308150
\(253\) −17.0858 −1.07417
\(254\) 7.52111 0.471916
\(255\) −6.17629 −0.386774
\(256\) 1.00000 0.0625000
\(257\) −10.8901 −0.679305 −0.339652 0.940551i \(-0.610309\pi\)
−0.339652 + 0.940551i \(0.610309\pi\)
\(258\) 6.71379 0.417982
\(259\) 0.00862374 0.000535853 0
\(260\) 0 0
\(261\) 4.91185 0.304036
\(262\) −5.12498 −0.316622
\(263\) −31.2271 −1.92555 −0.962774 0.270309i \(-0.912874\pi\)
−0.962774 + 0.270309i \(0.912874\pi\)
\(264\) −6.29590 −0.387486
\(265\) −19.9705 −1.22678
\(266\) −0.352584 −0.0216183
\(267\) 3.92154 0.239995
\(268\) −5.38404 −0.328883
\(269\) 15.9172 0.970491 0.485245 0.874378i \(-0.338730\pi\)
0.485245 + 0.874378i \(0.338730\pi\)
\(270\) −2.13706 −0.130058
\(271\) 3.52111 0.213892 0.106946 0.994265i \(-0.465893\pi\)
0.106946 + 0.994265i \(0.465893\pi\)
\(272\) −2.89008 −0.175237
\(273\) 0 0
\(274\) −4.00000 −0.241649
\(275\) 2.72587 0.164376
\(276\) −2.71379 −0.163351
\(277\) −8.58104 −0.515585 −0.257792 0.966200i \(-0.582995\pi\)
−0.257792 + 0.966200i \(0.582995\pi\)
\(278\) −8.68963 −0.521169
\(279\) −9.00969 −0.539396
\(280\) 0.104539 0.00624743
\(281\) −8.07846 −0.481920 −0.240960 0.970535i \(-0.577462\pi\)
−0.240960 + 0.970535i \(0.577462\pi\)
\(282\) −7.20775 −0.429215
\(283\) −17.4034 −1.03453 −0.517263 0.855827i \(-0.673049\pi\)
−0.517263 + 0.855827i \(0.673049\pi\)
\(284\) 8.71379 0.517068
\(285\) 15.4034 0.912420
\(286\) 0 0
\(287\) 0.420288 0.0248088
\(288\) −1.00000 −0.0589256
\(289\) −8.64742 −0.508672
\(290\) 10.4969 0.616402
\(291\) −2.47889 −0.145315
\(292\) 14.9487 0.874806
\(293\) −19.3709 −1.13166 −0.565830 0.824522i \(-0.691444\pi\)
−0.565830 + 0.824522i \(0.691444\pi\)
\(294\) −6.99761 −0.408109
\(295\) −9.12259 −0.531138
\(296\) −0.176292 −0.0102468
\(297\) 6.29590 0.365325
\(298\) −4.86831 −0.282014
\(299\) 0 0
\(300\) 0.432960 0.0249970
\(301\) 0.328421 0.0189299
\(302\) 14.7463 0.848555
\(303\) −1.65279 −0.0949505
\(304\) 7.20775 0.413393
\(305\) −15.1943 −0.870025
\(306\) 2.89008 0.165215
\(307\) −12.4263 −0.709204 −0.354602 0.935017i \(-0.615384\pi\)
−0.354602 + 0.935017i \(0.615384\pi\)
\(308\) −0.307979 −0.0175487
\(309\) 8.23490 0.468467
\(310\) −19.2543 −1.09357
\(311\) 2.71379 0.153885 0.0769425 0.997036i \(-0.475484\pi\)
0.0769425 + 0.997036i \(0.475484\pi\)
\(312\) 0 0
\(313\) 15.3884 0.869801 0.434901 0.900478i \(-0.356783\pi\)
0.434901 + 0.900478i \(0.356783\pi\)
\(314\) 16.7138 0.943214
\(315\) −0.104539 −0.00589013
\(316\) 13.8291 0.777947
\(317\) 25.6528 1.44080 0.720402 0.693557i \(-0.243957\pi\)
0.720402 + 0.693557i \(0.243957\pi\)
\(318\) 9.34481 0.524031
\(319\) −30.9245 −1.73144
\(320\) −2.13706 −0.119465
\(321\) 8.36658 0.466977
\(322\) −0.132751 −0.00739795
\(323\) −20.8310 −1.15907
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 5.54958 0.307363
\(327\) −17.4276 −0.963748
\(328\) −8.59179 −0.474402
\(329\) −0.352584 −0.0194386
\(330\) 13.4547 0.740659
\(331\) −3.82371 −0.210170 −0.105085 0.994463i \(-0.533511\pi\)
−0.105085 + 0.994463i \(0.533511\pi\)
\(332\) 11.1347 0.611094
\(333\) 0.176292 0.00966074
\(334\) −3.92154 −0.214577
\(335\) 11.5060 0.628642
\(336\) −0.0489173 −0.00266866
\(337\) 20.1304 1.09657 0.548285 0.836291i \(-0.315281\pi\)
0.548285 + 0.836291i \(0.315281\pi\)
\(338\) 0 0
\(339\) 13.9758 0.759063
\(340\) 6.17629 0.334956
\(341\) 56.7241 3.07178
\(342\) −7.20775 −0.389751
\(343\) −0.684726 −0.0369717
\(344\) −6.71379 −0.361983
\(345\) 5.79954 0.312237
\(346\) 3.48427 0.187316
\(347\) 2.93900 0.157774 0.0788869 0.996884i \(-0.474863\pi\)
0.0788869 + 0.996884i \(0.474863\pi\)
\(348\) −4.91185 −0.263303
\(349\) 7.37329 0.394683 0.197342 0.980335i \(-0.436769\pi\)
0.197342 + 0.980335i \(0.436769\pi\)
\(350\) 0.0211793 0.00113208
\(351\) 0 0
\(352\) 6.29590 0.335572
\(353\) −2.01075 −0.107022 −0.0535108 0.998567i \(-0.517041\pi\)
−0.0535108 + 0.998567i \(0.517041\pi\)
\(354\) 4.26875 0.226881
\(355\) −18.6219 −0.988349
\(356\) −3.92154 −0.207841
\(357\) 0.141375 0.00748237
\(358\) −3.58881 −0.189675
\(359\) 31.4577 1.66027 0.830137 0.557559i \(-0.188262\pi\)
0.830137 + 0.557559i \(0.188262\pi\)
\(360\) 2.13706 0.112633
\(361\) 32.9517 1.73430
\(362\) −5.50604 −0.289391
\(363\) −28.6383 −1.50312
\(364\) 0 0
\(365\) −31.9463 −1.67215
\(366\) 7.10992 0.371641
\(367\) −4.49934 −0.234863 −0.117432 0.993081i \(-0.537466\pi\)
−0.117432 + 0.993081i \(0.537466\pi\)
\(368\) 2.71379 0.141466
\(369\) 8.59179 0.447271
\(370\) 0.376747 0.0195862
\(371\) 0.457123 0.0237327
\(372\) 9.00969 0.467131
\(373\) 37.8297 1.95875 0.979373 0.202060i \(-0.0647635\pi\)
0.979373 + 0.202060i \(0.0647635\pi\)
\(374\) −18.1957 −0.940876
\(375\) −11.6106 −0.599568
\(376\) 7.20775 0.371711
\(377\) 0 0
\(378\) 0.0489173 0.00251604
\(379\) −8.43967 −0.433516 −0.216758 0.976225i \(-0.569548\pi\)
−0.216758 + 0.976225i \(0.569548\pi\)
\(380\) −15.4034 −0.790179
\(381\) 7.52111 0.385318
\(382\) 5.65817 0.289497
\(383\) 1.28621 0.0657222 0.0328611 0.999460i \(-0.489538\pi\)
0.0328611 + 0.999460i \(0.489538\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0.658170 0.0335434
\(386\) −13.4034 −0.682216
\(387\) 6.71379 0.341281
\(388\) 2.47889 0.125847
\(389\) 23.3924 1.18604 0.593021 0.805187i \(-0.297935\pi\)
0.593021 + 0.805187i \(0.297935\pi\)
\(390\) 0 0
\(391\) −7.84309 −0.396642
\(392\) 6.99761 0.353433
\(393\) −5.12498 −0.258521
\(394\) −19.9812 −1.00664
\(395\) −29.5536 −1.48700
\(396\) −6.29590 −0.316381
\(397\) 37.0858 1.86128 0.930640 0.365935i \(-0.119251\pi\)
0.930640 + 0.365935i \(0.119251\pi\)
\(398\) 6.24160 0.312863
\(399\) −0.352584 −0.0176513
\(400\) −0.432960 −0.0216480
\(401\) 4.86592 0.242992 0.121496 0.992592i \(-0.461231\pi\)
0.121496 + 0.992592i \(0.461231\pi\)
\(402\) −5.38404 −0.268532
\(403\) 0 0
\(404\) 1.65279 0.0822295
\(405\) −2.13706 −0.106192
\(406\) −0.240275 −0.0119246
\(407\) −1.10992 −0.0550165
\(408\) −2.89008 −0.143080
\(409\) −0.445042 −0.0220059 −0.0110030 0.999939i \(-0.503502\pi\)
−0.0110030 + 0.999939i \(0.503502\pi\)
\(410\) 18.3612 0.906795
\(411\) −4.00000 −0.197305
\(412\) −8.23490 −0.405704
\(413\) 0.208816 0.0102752
\(414\) −2.71379 −0.133376
\(415\) −23.7955 −1.16807
\(416\) 0 0
\(417\) −8.68963 −0.425533
\(418\) 45.3793 2.21957
\(419\) 17.9869 0.878715 0.439358 0.898312i \(-0.355206\pi\)
0.439358 + 0.898312i \(0.355206\pi\)
\(420\) 0.104539 0.00510100
\(421\) −21.2814 −1.03719 −0.518597 0.855019i \(-0.673545\pi\)
−0.518597 + 0.855019i \(0.673545\pi\)
\(422\) 5.08575 0.247571
\(423\) −7.20775 −0.350453
\(424\) −9.34481 −0.453824
\(425\) 1.25129 0.0606966
\(426\) 8.71379 0.422185
\(427\) 0.347798 0.0168311
\(428\) −8.36658 −0.404414
\(429\) 0 0
\(430\) 14.3478 0.691912
\(431\) −24.7138 −1.19042 −0.595211 0.803570i \(-0.702931\pi\)
−0.595211 + 0.803570i \(0.702931\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 32.2174 1.54827 0.774136 0.633020i \(-0.218185\pi\)
0.774136 + 0.633020i \(0.218185\pi\)
\(434\) 0.440730 0.0211557
\(435\) 10.4969 0.503290
\(436\) 17.4276 0.834630
\(437\) 19.5603 0.935698
\(438\) 14.9487 0.714276
\(439\) 32.0877 1.53146 0.765731 0.643162i \(-0.222378\pi\)
0.765731 + 0.643162i \(0.222378\pi\)
\(440\) −13.4547 −0.641429
\(441\) −6.99761 −0.333219
\(442\) 0 0
\(443\) 20.5109 0.974504 0.487252 0.873261i \(-0.337999\pi\)
0.487252 + 0.873261i \(0.337999\pi\)
\(444\) −0.176292 −0.00836645
\(445\) 8.38059 0.397278
\(446\) 20.5483 0.972988
\(447\) −4.86831 −0.230263
\(448\) 0.0489173 0.00231113
\(449\) 15.3163 0.722823 0.361411 0.932406i \(-0.382295\pi\)
0.361411 + 0.932406i \(0.382295\pi\)
\(450\) 0.432960 0.0204099
\(451\) −54.0930 −2.54714
\(452\) −13.9758 −0.657368
\(453\) 14.7463 0.692842
\(454\) −4.41119 −0.207027
\(455\) 0 0
\(456\) 7.20775 0.337534
\(457\) 19.1860 0.897482 0.448741 0.893662i \(-0.351873\pi\)
0.448741 + 0.893662i \(0.351873\pi\)
\(458\) −0.230586 −0.0107746
\(459\) 2.89008 0.134898
\(460\) −5.79954 −0.270405
\(461\) −8.31229 −0.387142 −0.193571 0.981086i \(-0.562007\pi\)
−0.193571 + 0.981086i \(0.562007\pi\)
\(462\) −0.307979 −0.0143285
\(463\) 6.32842 0.294107 0.147053 0.989129i \(-0.453021\pi\)
0.147053 + 0.989129i \(0.453021\pi\)
\(464\) 4.91185 0.228027
\(465\) −19.2543 −0.892896
\(466\) 7.82371 0.362426
\(467\) −31.1879 −1.44320 −0.721602 0.692308i \(-0.756594\pi\)
−0.721602 + 0.692308i \(0.756594\pi\)
\(468\) 0 0
\(469\) −0.263373 −0.0121614
\(470\) −15.4034 −0.710507
\(471\) 16.7138 0.770131
\(472\) −4.26875 −0.196485
\(473\) −42.2693 −1.94355
\(474\) 13.8291 0.635191
\(475\) −3.12067 −0.143186
\(476\) −0.141375 −0.00647992
\(477\) 9.34481 0.427870
\(478\) −11.1535 −0.510147
\(479\) 17.9323 0.819348 0.409674 0.912232i \(-0.365643\pi\)
0.409674 + 0.912232i \(0.365643\pi\)
\(480\) −2.13706 −0.0975431
\(481\) 0 0
\(482\) 3.54527 0.161483
\(483\) −0.132751 −0.00604040
\(484\) 28.6383 1.30174
\(485\) −5.29755 −0.240549
\(486\) 1.00000 0.0453609
\(487\) −30.3279 −1.37429 −0.687145 0.726520i \(-0.741136\pi\)
−0.687145 + 0.726520i \(0.741136\pi\)
\(488\) −7.10992 −0.321851
\(489\) 5.54958 0.250961
\(490\) −14.9543 −0.675568
\(491\) 30.0954 1.35819 0.679094 0.734051i \(-0.262373\pi\)
0.679094 + 0.734051i \(0.262373\pi\)
\(492\) −8.59179 −0.387348
\(493\) −14.1957 −0.639341
\(494\) 0 0
\(495\) 13.4547 0.604745
\(496\) −9.00969 −0.404547
\(497\) 0.426256 0.0191202
\(498\) 11.1347 0.498957
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 11.6106 0.519241
\(501\) −3.92154 −0.175202
\(502\) 4.17092 0.186157
\(503\) 33.7512 1.50489 0.752446 0.658654i \(-0.228874\pi\)
0.752446 + 0.658654i \(0.228874\pi\)
\(504\) −0.0489173 −0.00217895
\(505\) −3.53212 −0.157177
\(506\) 17.0858 0.759554
\(507\) 0 0
\(508\) −7.52111 −0.333695
\(509\) 14.7439 0.653513 0.326756 0.945109i \(-0.394044\pi\)
0.326756 + 0.945109i \(0.394044\pi\)
\(510\) 6.17629 0.273491
\(511\) 0.731250 0.0323486
\(512\) −1.00000 −0.0441942
\(513\) −7.20775 −0.318230
\(514\) 10.8901 0.480341
\(515\) 17.5985 0.775483
\(516\) −6.71379 −0.295558
\(517\) 45.3793 1.99578
\(518\) −0.00862374 −0.000378905 0
\(519\) 3.48427 0.152943
\(520\) 0 0
\(521\) 22.1086 0.968595 0.484297 0.874903i \(-0.339075\pi\)
0.484297 + 0.874903i \(0.339075\pi\)
\(522\) −4.91185 −0.214986
\(523\) −17.3599 −0.759095 −0.379547 0.925172i \(-0.623920\pi\)
−0.379547 + 0.925172i \(0.623920\pi\)
\(524\) 5.12498 0.223886
\(525\) 0.0211793 0.000924339 0
\(526\) 31.2271 1.36157
\(527\) 26.0388 1.13427
\(528\) 6.29590 0.273994
\(529\) −15.6353 −0.679797
\(530\) 19.9705 0.867461
\(531\) 4.26875 0.185248
\(532\) 0.352584 0.0152865
\(533\) 0 0
\(534\) −3.92154 −0.169702
\(535\) 17.8799 0.773016
\(536\) 5.38404 0.232555
\(537\) −3.58881 −0.154869
\(538\) −15.9172 −0.686241
\(539\) 44.0562 1.89764
\(540\) 2.13706 0.0919646
\(541\) 8.83579 0.379880 0.189940 0.981796i \(-0.439171\pi\)
0.189940 + 0.981796i \(0.439171\pi\)
\(542\) −3.52111 −0.151244
\(543\) −5.50604 −0.236287
\(544\) 2.89008 0.123911
\(545\) −37.2438 −1.59535
\(546\) 0 0
\(547\) −8.10859 −0.346698 −0.173349 0.984860i \(-0.555459\pi\)
−0.173349 + 0.984860i \(0.555459\pi\)
\(548\) 4.00000 0.170872
\(549\) 7.10992 0.303444
\(550\) −2.72587 −0.116232
\(551\) 35.4034 1.50824
\(552\) 2.71379 0.115507
\(553\) 0.676482 0.0287669
\(554\) 8.58104 0.364573
\(555\) 0.376747 0.0159920
\(556\) 8.68963 0.368522
\(557\) 9.56033 0.405084 0.202542 0.979274i \(-0.435080\pi\)
0.202542 + 0.979274i \(0.435080\pi\)
\(558\) 9.00969 0.381411
\(559\) 0 0
\(560\) −0.104539 −0.00441760
\(561\) −18.1957 −0.768222
\(562\) 8.07846 0.340769
\(563\) −45.1637 −1.90342 −0.951712 0.306991i \(-0.900678\pi\)
−0.951712 + 0.306991i \(0.900678\pi\)
\(564\) 7.20775 0.303501
\(565\) 29.8672 1.25652
\(566\) 17.4034 0.731520
\(567\) 0.0489173 0.00205434
\(568\) −8.71379 −0.365623
\(569\) −3.20775 −0.134476 −0.0672380 0.997737i \(-0.521419\pi\)
−0.0672380 + 0.997737i \(0.521419\pi\)
\(570\) −15.4034 −0.645178
\(571\) 0.0241632 0.00101120 0.000505599 1.00000i \(-0.499839\pi\)
0.000505599 1.00000i \(0.499839\pi\)
\(572\) 0 0
\(573\) 5.65817 0.236373
\(574\) −0.420288 −0.0175425
\(575\) −1.17496 −0.0489994
\(576\) 1.00000 0.0416667
\(577\) −46.0200 −1.91584 −0.957918 0.287041i \(-0.907328\pi\)
−0.957918 + 0.287041i \(0.907328\pi\)
\(578\) 8.64742 0.359685
\(579\) −13.4034 −0.557027
\(580\) −10.4969 −0.435862
\(581\) 0.544678 0.0225971
\(582\) 2.47889 0.102753
\(583\) −58.8340 −2.43665
\(584\) −14.9487 −0.618581
\(585\) 0 0
\(586\) 19.3709 0.800204
\(587\) −25.9385 −1.07060 −0.535299 0.844663i \(-0.679801\pi\)
−0.535299 + 0.844663i \(0.679801\pi\)
\(588\) 6.99761 0.288576
\(589\) −64.9396 −2.67579
\(590\) 9.12259 0.375571
\(591\) −19.9812 −0.821917
\(592\) 0.176292 0.00724556
\(593\) −8.30691 −0.341124 −0.170562 0.985347i \(-0.554558\pi\)
−0.170562 + 0.985347i \(0.554558\pi\)
\(594\) −6.29590 −0.258324
\(595\) 0.302128 0.0123860
\(596\) 4.86831 0.199414
\(597\) 6.24160 0.255452
\(598\) 0 0
\(599\) 37.1702 1.51873 0.759366 0.650664i \(-0.225509\pi\)
0.759366 + 0.650664i \(0.225509\pi\)
\(600\) −0.432960 −0.0176755
\(601\) −12.5700 −0.512742 −0.256371 0.966578i \(-0.582527\pi\)
−0.256371 + 0.966578i \(0.582527\pi\)
\(602\) −0.328421 −0.0133854
\(603\) −5.38404 −0.219255
\(604\) −14.7463 −0.600019
\(605\) −61.2019 −2.48821
\(606\) 1.65279 0.0671401
\(607\) 8.04892 0.326695 0.163348 0.986569i \(-0.447771\pi\)
0.163348 + 0.986569i \(0.447771\pi\)
\(608\) −7.20775 −0.292313
\(609\) −0.240275 −0.00973643
\(610\) 15.1943 0.615201
\(611\) 0 0
\(612\) −2.89008 −0.116825
\(613\) 30.4590 1.23023 0.615115 0.788438i \(-0.289110\pi\)
0.615115 + 0.788438i \(0.289110\pi\)
\(614\) 12.4263 0.501483
\(615\) 18.3612 0.740395
\(616\) 0.307979 0.0124088
\(617\) 4.73317 0.190550 0.0952751 0.995451i \(-0.469627\pi\)
0.0952751 + 0.995451i \(0.469627\pi\)
\(618\) −8.23490 −0.331256
\(619\) −24.9095 −1.00120 −0.500598 0.865680i \(-0.666886\pi\)
−0.500598 + 0.865680i \(0.666886\pi\)
\(620\) 19.2543 0.773270
\(621\) −2.71379 −0.108901
\(622\) −2.71379 −0.108813
\(623\) −0.191831 −0.00768556
\(624\) 0 0
\(625\) −22.6477 −0.905910
\(626\) −15.3884 −0.615042
\(627\) 45.3793 1.81227
\(628\) −16.7138 −0.666953
\(629\) −0.509499 −0.0203150
\(630\) 0.104539 0.00416495
\(631\) 24.4295 0.972523 0.486262 0.873813i \(-0.338360\pi\)
0.486262 + 0.873813i \(0.338360\pi\)
\(632\) −13.8291 −0.550091
\(633\) 5.08575 0.202141
\(634\) −25.6528 −1.01880
\(635\) 16.0731 0.637841
\(636\) −9.34481 −0.370546
\(637\) 0 0
\(638\) 30.9245 1.22431
\(639\) 8.71379 0.344712
\(640\) 2.13706 0.0844748
\(641\) 48.7982 1.92741 0.963707 0.266963i \(-0.0860201\pi\)
0.963707 + 0.266963i \(0.0860201\pi\)
\(642\) −8.36658 −0.330203
\(643\) −28.2693 −1.11483 −0.557417 0.830233i \(-0.688208\pi\)
−0.557417 + 0.830233i \(0.688208\pi\)
\(644\) 0.132751 0.00523114
\(645\) 14.3478 0.564944
\(646\) 20.8310 0.819585
\(647\) 34.8961 1.37191 0.685953 0.727646i \(-0.259386\pi\)
0.685953 + 0.727646i \(0.259386\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −26.8756 −1.05496
\(650\) 0 0
\(651\) 0.440730 0.0172736
\(652\) −5.54958 −0.217338
\(653\) −11.7157 −0.458471 −0.229236 0.973371i \(-0.573623\pi\)
−0.229236 + 0.973371i \(0.573623\pi\)
\(654\) 17.4276 0.681472
\(655\) −10.9524 −0.427946
\(656\) 8.59179 0.335453
\(657\) 14.9487 0.583204
\(658\) 0.352584 0.0137452
\(659\) −7.13467 −0.277927 −0.138964 0.990297i \(-0.544377\pi\)
−0.138964 + 0.990297i \(0.544377\pi\)
\(660\) −13.4547 −0.523725
\(661\) −8.52888 −0.331735 −0.165867 0.986148i \(-0.553042\pi\)
−0.165867 + 0.986148i \(0.553042\pi\)
\(662\) 3.82371 0.148613
\(663\) 0 0
\(664\) −11.1347 −0.432109
\(665\) −0.753494 −0.0292193
\(666\) −0.176292 −0.00683118
\(667\) 13.3297 0.516130
\(668\) 3.92154 0.151729
\(669\) 20.5483 0.794441
\(670\) −11.5060 −0.444517
\(671\) −44.7633 −1.72807
\(672\) 0.0489173 0.00188703
\(673\) −31.5937 −1.21785 −0.608924 0.793229i \(-0.708399\pi\)
−0.608924 + 0.793229i \(0.708399\pi\)
\(674\) −20.1304 −0.775392
\(675\) 0.432960 0.0166646
\(676\) 0 0
\(677\) −17.3002 −0.664901 −0.332451 0.943121i \(-0.607875\pi\)
−0.332451 + 0.943121i \(0.607875\pi\)
\(678\) −13.9758 −0.536739
\(679\) 0.121261 0.00465357
\(680\) −6.17629 −0.236850
\(681\) −4.41119 −0.169037
\(682\) −56.7241 −2.17208
\(683\) 30.3957 1.16306 0.581529 0.813526i \(-0.302455\pi\)
0.581529 + 0.813526i \(0.302455\pi\)
\(684\) 7.20775 0.275595
\(685\) −8.54825 −0.326612
\(686\) 0.684726 0.0261429
\(687\) −0.230586 −0.00879741
\(688\) 6.71379 0.255961
\(689\) 0 0
\(690\) −5.79954 −0.220785
\(691\) 35.7318 1.35930 0.679652 0.733535i \(-0.262131\pi\)
0.679652 + 0.733535i \(0.262131\pi\)
\(692\) −3.48427 −0.132452
\(693\) −0.307979 −0.0116991
\(694\) −2.93900 −0.111563
\(695\) −18.5703 −0.704411
\(696\) 4.91185 0.186183
\(697\) −24.8310 −0.940541
\(698\) −7.37329 −0.279083
\(699\) 7.82371 0.295920
\(700\) −0.0211793 −0.000800501 0
\(701\) 20.1328 0.760404 0.380202 0.924904i \(-0.375855\pi\)
0.380202 + 0.924904i \(0.375855\pi\)
\(702\) 0 0
\(703\) 1.27067 0.0479242
\(704\) −6.29590 −0.237286
\(705\) −15.4034 −0.580126
\(706\) 2.01075 0.0756757
\(707\) 0.0808502 0.00304069
\(708\) −4.26875 −0.160429
\(709\) 16.6160 0.624025 0.312013 0.950078i \(-0.398997\pi\)
0.312013 + 0.950078i \(0.398997\pi\)
\(710\) 18.6219 0.698868
\(711\) 13.8291 0.518631
\(712\) 3.92154 0.146966
\(713\) −24.4504 −0.915675
\(714\) −0.141375 −0.00529083
\(715\) 0 0
\(716\) 3.58881 0.134120
\(717\) −11.1535 −0.416533
\(718\) −31.4577 −1.17399
\(719\) 2.04833 0.0763897 0.0381948 0.999270i \(-0.487839\pi\)
0.0381948 + 0.999270i \(0.487839\pi\)
\(720\) −2.13706 −0.0796436
\(721\) −0.402829 −0.0150021
\(722\) −32.9517 −1.22633
\(723\) 3.54527 0.131850
\(724\) 5.50604 0.204630
\(725\) −2.12664 −0.0789813
\(726\) 28.6383 1.06287
\(727\) 29.9377 1.11033 0.555163 0.831741i \(-0.312656\pi\)
0.555163 + 0.831741i \(0.312656\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 31.9463 1.18239
\(731\) −19.4034 −0.717661
\(732\) −7.10992 −0.262790
\(733\) −1.46250 −0.0540187 −0.0270093 0.999635i \(-0.508598\pi\)
−0.0270093 + 0.999635i \(0.508598\pi\)
\(734\) 4.49934 0.166074
\(735\) −14.9543 −0.551599
\(736\) −2.71379 −0.100032
\(737\) 33.8974 1.24863
\(738\) −8.59179 −0.316268
\(739\) 40.3866 1.48564 0.742822 0.669489i \(-0.233487\pi\)
0.742822 + 0.669489i \(0.233487\pi\)
\(740\) −0.376747 −0.0138495
\(741\) 0 0
\(742\) −0.457123 −0.0167815
\(743\) −9.77538 −0.358624 −0.179312 0.983792i \(-0.557387\pi\)
−0.179312 + 0.983792i \(0.557387\pi\)
\(744\) −9.00969 −0.330311
\(745\) −10.4039 −0.381169
\(746\) −37.8297 −1.38504
\(747\) 11.1347 0.407396
\(748\) 18.1957 0.665300
\(749\) −0.409271 −0.0149544
\(750\) 11.6106 0.423958
\(751\) 34.5459 1.26060 0.630298 0.776353i \(-0.282933\pi\)
0.630298 + 0.776353i \(0.282933\pi\)
\(752\) −7.20775 −0.262840
\(753\) 4.17092 0.151997
\(754\) 0 0
\(755\) 31.5138 1.14690
\(756\) −0.0489173 −0.00177911
\(757\) −5.14483 −0.186992 −0.0934961 0.995620i \(-0.529804\pi\)
−0.0934961 + 0.995620i \(0.529804\pi\)
\(758\) 8.43967 0.306542
\(759\) 17.0858 0.620174
\(760\) 15.4034 0.558741
\(761\) −19.5120 −0.707310 −0.353655 0.935376i \(-0.615061\pi\)
−0.353655 + 0.935376i \(0.615061\pi\)
\(762\) −7.52111 −0.272461
\(763\) 0.852511 0.0308630
\(764\) −5.65817 −0.204705
\(765\) 6.17629 0.223304
\(766\) −1.28621 −0.0464726
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 5.75600 0.207567 0.103783 0.994600i \(-0.466905\pi\)
0.103783 + 0.994600i \(0.466905\pi\)
\(770\) −0.658170 −0.0237188
\(771\) 10.8901 0.392197
\(772\) 13.4034 0.482400
\(773\) −4.12737 −0.148451 −0.0742257 0.997241i \(-0.523649\pi\)
−0.0742257 + 0.997241i \(0.523649\pi\)
\(774\) −6.71379 −0.241322
\(775\) 3.90084 0.140122
\(776\) −2.47889 −0.0889871
\(777\) −0.00862374 −0.000309375 0
\(778\) −23.3924 −0.838658
\(779\) 61.9275 2.21878
\(780\) 0 0
\(781\) −54.8611 −1.96309
\(782\) 7.84309 0.280468
\(783\) −4.91185 −0.175535
\(784\) −6.99761 −0.249915
\(785\) 35.7184 1.27485
\(786\) 5.12498 0.182802
\(787\) −16.2392 −0.578865 −0.289433 0.957198i \(-0.593467\pi\)
−0.289433 + 0.957198i \(0.593467\pi\)
\(788\) 19.9812 0.711801
\(789\) 31.2271 1.11172
\(790\) 29.5536 1.05147
\(791\) −0.683661 −0.0243082
\(792\) 6.29590 0.223715
\(793\) 0 0
\(794\) −37.0858 −1.31612
\(795\) 19.9705 0.708279
\(796\) −6.24160 −0.221228
\(797\) 16.1148 0.570816 0.285408 0.958406i \(-0.407871\pi\)
0.285408 + 0.958406i \(0.407871\pi\)
\(798\) 0.352584 0.0124813
\(799\) 20.8310 0.736948
\(800\) 0.432960 0.0153075
\(801\) −3.92154 −0.138561
\(802\) −4.86592 −0.171822
\(803\) −94.1154 −3.32126
\(804\) 5.38404 0.189881
\(805\) −0.283698 −0.00999905
\(806\) 0 0
\(807\) −15.9172 −0.560313
\(808\) −1.65279 −0.0581450
\(809\) 40.1521 1.41167 0.705837 0.708374i \(-0.250571\pi\)
0.705837 + 0.708374i \(0.250571\pi\)
\(810\) 2.13706 0.0750888
\(811\) 39.8646 1.39984 0.699918 0.714224i \(-0.253220\pi\)
0.699918 + 0.714224i \(0.253220\pi\)
\(812\) 0.240275 0.00843199
\(813\) −3.52111 −0.123491
\(814\) 1.10992 0.0389025
\(815\) 11.8598 0.415431
\(816\) 2.89008 0.101173
\(817\) 48.3913 1.69300
\(818\) 0.445042 0.0155605
\(819\) 0 0
\(820\) −18.3612 −0.641201
\(821\) −6.25428 −0.218276 −0.109138 0.994027i \(-0.534809\pi\)
−0.109138 + 0.994027i \(0.534809\pi\)
\(822\) 4.00000 0.139516
\(823\) −4.74333 −0.165342 −0.0826711 0.996577i \(-0.526345\pi\)
−0.0826711 + 0.996577i \(0.526345\pi\)
\(824\) 8.23490 0.286876
\(825\) −2.72587 −0.0949027
\(826\) −0.208816 −0.00726563
\(827\) −0.716185 −0.0249042 −0.0124521 0.999922i \(-0.503964\pi\)
−0.0124521 + 0.999922i \(0.503964\pi\)
\(828\) 2.71379 0.0943108
\(829\) −36.0060 −1.25054 −0.625269 0.780409i \(-0.715011\pi\)
−0.625269 + 0.780409i \(0.715011\pi\)
\(830\) 23.7955 0.825954
\(831\) 8.58104 0.297673
\(832\) 0 0
\(833\) 20.2237 0.700709
\(834\) 8.68963 0.300897
\(835\) −8.38059 −0.290022
\(836\) −45.3793 −1.56947
\(837\) 9.00969 0.311420
\(838\) −17.9869 −0.621346
\(839\) −21.5555 −0.744180 −0.372090 0.928197i \(-0.621359\pi\)
−0.372090 + 0.928197i \(0.621359\pi\)
\(840\) −0.104539 −0.00360695
\(841\) −4.87369 −0.168058
\(842\) 21.2814 0.733406
\(843\) 8.07846 0.278237
\(844\) −5.08575 −0.175059
\(845\) 0 0
\(846\) 7.20775 0.247808
\(847\) 1.40091 0.0481358
\(848\) 9.34481 0.320902
\(849\) 17.4034 0.597284
\(850\) −1.25129 −0.0429189
\(851\) 0.478420 0.0164000
\(852\) −8.71379 −0.298530
\(853\) 37.8237 1.29506 0.647530 0.762040i \(-0.275802\pi\)
0.647530 + 0.762040i \(0.275802\pi\)
\(854\) −0.347798 −0.0119014
\(855\) −15.4034 −0.526786
\(856\) 8.36658 0.285964
\(857\) −6.58317 −0.224877 −0.112438 0.993659i \(-0.535866\pi\)
−0.112438 + 0.993659i \(0.535866\pi\)
\(858\) 0 0
\(859\) −20.6246 −0.703702 −0.351851 0.936056i \(-0.614448\pi\)
−0.351851 + 0.936056i \(0.614448\pi\)
\(860\) −14.3478 −0.489256
\(861\) −0.420288 −0.0143234
\(862\) 24.7138 0.841755
\(863\) −15.9081 −0.541519 −0.270760 0.962647i \(-0.587275\pi\)
−0.270760 + 0.962647i \(0.587275\pi\)
\(864\) 1.00000 0.0340207
\(865\) 7.44611 0.253175
\(866\) −32.2174 −1.09479
\(867\) 8.64742 0.293682
\(868\) −0.440730 −0.0149594
\(869\) −87.0665 −2.95353
\(870\) −10.4969 −0.355880
\(871\) 0 0
\(872\) −17.4276 −0.590172
\(873\) 2.47889 0.0838978
\(874\) −19.5603 −0.661638
\(875\) 0.567959 0.0192005
\(876\) −14.9487 −0.505069
\(877\) 15.6039 0.526905 0.263453 0.964672i \(-0.415139\pi\)
0.263453 + 0.964672i \(0.415139\pi\)
\(878\) −32.0877 −1.08291
\(879\) 19.3709 0.653364
\(880\) 13.4547 0.453559
\(881\) −14.2547 −0.480255 −0.240127 0.970741i \(-0.577189\pi\)
−0.240127 + 0.970741i \(0.577189\pi\)
\(882\) 6.99761 0.235622
\(883\) 1.65817 0.0558019 0.0279009 0.999611i \(-0.491118\pi\)
0.0279009 + 0.999611i \(0.491118\pi\)
\(884\) 0 0
\(885\) 9.12259 0.306652
\(886\) −20.5109 −0.689079
\(887\) −19.2030 −0.644772 −0.322386 0.946608i \(-0.604485\pi\)
−0.322386 + 0.946608i \(0.604485\pi\)
\(888\) 0.176292 0.00591597
\(889\) −0.367913 −0.0123394
\(890\) −8.38059 −0.280918
\(891\) −6.29590 −0.210920
\(892\) −20.5483 −0.688006
\(893\) −51.9517 −1.73850
\(894\) 4.86831 0.162821
\(895\) −7.66951 −0.256364
\(896\) −0.0489173 −0.00163421
\(897\) 0 0
\(898\) −15.3163 −0.511113
\(899\) −44.2543 −1.47596
\(900\) −0.432960 −0.0144320
\(901\) −27.0073 −0.899743
\(902\) 54.0930 1.80110
\(903\) −0.328421 −0.0109292
\(904\) 13.9758 0.464829
\(905\) −11.7668 −0.391140
\(906\) −14.7463 −0.489914
\(907\) −32.3672 −1.07473 −0.537367 0.843348i \(-0.680581\pi\)
−0.537367 + 0.843348i \(0.680581\pi\)
\(908\) 4.41119 0.146390
\(909\) 1.65279 0.0548197
\(910\) 0 0
\(911\) −33.9624 −1.12523 −0.562613 0.826721i \(-0.690204\pi\)
−0.562613 + 0.826721i \(0.690204\pi\)
\(912\) −7.20775 −0.238672
\(913\) −70.1027 −2.32006
\(914\) −19.1860 −0.634616
\(915\) 15.1943 0.502309
\(916\) 0.230586 0.00761878
\(917\) 0.250700 0.00827886
\(918\) −2.89008 −0.0953870
\(919\) −20.0780 −0.662312 −0.331156 0.943576i \(-0.607439\pi\)
−0.331156 + 0.943576i \(0.607439\pi\)
\(920\) 5.79954 0.191205
\(921\) 12.4263 0.409459
\(922\) 8.31229 0.273751
\(923\) 0 0
\(924\) 0.307979 0.0101317
\(925\) −0.0763274 −0.00250963
\(926\) −6.32842 −0.207965
\(927\) −8.23490 −0.270470
\(928\) −4.91185 −0.161240
\(929\) −56.1280 −1.84150 −0.920749 0.390154i \(-0.872422\pi\)
−0.920749 + 0.390154i \(0.872422\pi\)
\(930\) 19.2543 0.631373
\(931\) −50.4370 −1.65301
\(932\) −7.82371 −0.256274
\(933\) −2.71379 −0.0888456
\(934\) 31.1879 1.02050
\(935\) −38.8853 −1.27169
\(936\) 0 0
\(937\) 27.0291 0.883001 0.441501 0.897261i \(-0.354446\pi\)
0.441501 + 0.897261i \(0.354446\pi\)
\(938\) 0.263373 0.00859944
\(939\) −15.3884 −0.502180
\(940\) 15.4034 0.502404
\(941\) 24.0277 0.783282 0.391641 0.920118i \(-0.371908\pi\)
0.391641 + 0.920118i \(0.371908\pi\)
\(942\) −16.7138 −0.544565
\(943\) 23.3163 0.759284
\(944\) 4.26875 0.138936
\(945\) 0.104539 0.00340067
\(946\) 42.2693 1.37429
\(947\) 26.7966 0.870771 0.435386 0.900244i \(-0.356612\pi\)
0.435386 + 0.900244i \(0.356612\pi\)
\(948\) −13.8291 −0.449148
\(949\) 0 0
\(950\) 3.12067 0.101248
\(951\) −25.6528 −0.831849
\(952\) 0.141375 0.00458200
\(953\) 34.4215 1.11502 0.557510 0.830170i \(-0.311757\pi\)
0.557510 + 0.830170i \(0.311757\pi\)
\(954\) −9.34481 −0.302550
\(955\) 12.0919 0.391284
\(956\) 11.1535 0.360729
\(957\) 30.9245 0.999648
\(958\) −17.9323 −0.579366
\(959\) 0.195669 0.00631849
\(960\) 2.13706 0.0689734
\(961\) 50.1745 1.61853
\(962\) 0 0
\(963\) −8.36658 −0.269609
\(964\) −3.54527 −0.114185
\(965\) −28.6440 −0.922082
\(966\) 0.132751 0.00427121
\(967\) −26.2631 −0.844565 −0.422282 0.906464i \(-0.638771\pi\)
−0.422282 + 0.906464i \(0.638771\pi\)
\(968\) −28.6383 −0.920470
\(969\) 20.8310 0.669188
\(970\) 5.29755 0.170094
\(971\) −39.9842 −1.28315 −0.641577 0.767059i \(-0.721720\pi\)
−0.641577 + 0.767059i \(0.721720\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0.425074 0.0136272
\(974\) 30.3279 0.971770
\(975\) 0 0
\(976\) 7.10992 0.227583
\(977\) −4.58317 −0.146629 −0.0733143 0.997309i \(-0.523358\pi\)
−0.0733143 + 0.997309i \(0.523358\pi\)
\(978\) −5.54958 −0.177456
\(979\) 24.6896 0.789084
\(980\) 14.9543 0.477699
\(981\) 17.4276 0.556420
\(982\) −30.0954 −0.960384
\(983\) 10.6848 0.340794 0.170397 0.985376i \(-0.445495\pi\)
0.170397 + 0.985376i \(0.445495\pi\)
\(984\) 8.59179 0.273896
\(985\) −42.7011 −1.36057
\(986\) 14.1957 0.452082
\(987\) 0.352584 0.0112229
\(988\) 0 0
\(989\) 18.2198 0.579357
\(990\) −13.4547 −0.427619
\(991\) 50.6021 1.60743 0.803714 0.595016i \(-0.202854\pi\)
0.803714 + 0.595016i \(0.202854\pi\)
\(992\) 9.00969 0.286058
\(993\) 3.82371 0.121342
\(994\) −0.426256 −0.0135200
\(995\) 13.3387 0.422865
\(996\) −11.1347 −0.352816
\(997\) −35.9603 −1.13887 −0.569437 0.822035i \(-0.692839\pi\)
−0.569437 + 0.822035i \(0.692839\pi\)
\(998\) 0 0
\(999\) −0.176292 −0.00557763
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 1014.2.a.l.1.2 3
3.2 odd 2 3042.2.a.bh.1.2 3
4.3 odd 2 8112.2.a.cj.1.2 3
13.2 odd 12 1014.2.i.h.823.2 12
13.3 even 3 1014.2.e.n.529.2 6
13.4 even 6 1014.2.e.l.991.2 6
13.5 odd 4 1014.2.b.f.337.5 6
13.6 odd 12 1014.2.i.h.361.5 12
13.7 odd 12 1014.2.i.h.361.2 12
13.8 odd 4 1014.2.b.f.337.2 6
13.9 even 3 1014.2.e.n.991.2 6
13.10 even 6 1014.2.e.l.529.2 6
13.11 odd 12 1014.2.i.h.823.5 12
13.12 even 2 1014.2.a.n.1.2 yes 3
39.5 even 4 3042.2.b.o.1351.2 6
39.8 even 4 3042.2.b.o.1351.5 6
39.38 odd 2 3042.2.a.ba.1.2 3
52.51 odd 2 8112.2.a.cm.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1014.2.a.l.1.2 3 1.1 even 1 trivial
1014.2.a.n.1.2 yes 3 13.12 even 2
1014.2.b.f.337.2 6 13.8 odd 4
1014.2.b.f.337.5 6 13.5 odd 4
1014.2.e.l.529.2 6 13.10 even 6
1014.2.e.l.991.2 6 13.4 even 6
1014.2.e.n.529.2 6 13.3 even 3
1014.2.e.n.991.2 6 13.9 even 3
1014.2.i.h.361.2 12 13.7 odd 12
1014.2.i.h.361.5 12 13.6 odd 12
1014.2.i.h.823.2 12 13.2 odd 12
1014.2.i.h.823.5 12 13.11 odd 12
3042.2.a.ba.1.2 3 39.38 odd 2
3042.2.a.bh.1.2 3 3.2 odd 2
3042.2.b.o.1351.2 6 39.5 even 4
3042.2.b.o.1351.5 6 39.8 even 4
8112.2.a.cj.1.2 3 4.3 odd 2
8112.2.a.cm.1.2 3 52.51 odd 2