Properties

Label 177.6.a.d.1.6
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $0$
Dimension $13$
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] = [177,6,Mod(1,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.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: \(28.3879361069\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + 81977088 x^{5} - 3773728 x^{4} - 1245415104 x^{3} + \cdots - 6400833792 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-3.96558\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.96558 q^{2} -9.00000 q^{3} -16.2741 q^{4} +45.8225 q^{5} +35.6903 q^{6} +214.983 q^{7} +191.435 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-3.96558 q^{2} -9.00000 q^{3} -16.2741 q^{4} +45.8225 q^{5} +35.6903 q^{6} +214.983 q^{7} +191.435 q^{8} +81.0000 q^{9} -181.713 q^{10} -156.057 q^{11} +146.467 q^{12} +176.241 q^{13} -852.534 q^{14} -412.403 q^{15} -238.380 q^{16} -992.973 q^{17} -321.212 q^{18} -1346.21 q^{19} -745.722 q^{20} -1934.85 q^{21} +618.859 q^{22} +3041.14 q^{23} -1722.92 q^{24} -1025.30 q^{25} -698.897 q^{26} -729.000 q^{27} -3498.67 q^{28} +7850.14 q^{29} +1635.42 q^{30} +2343.28 q^{31} -5180.61 q^{32} +1404.52 q^{33} +3937.72 q^{34} +9851.07 q^{35} -1318.21 q^{36} +10906.3 q^{37} +5338.51 q^{38} -1586.17 q^{39} +8772.04 q^{40} -8949.04 q^{41} +7672.81 q^{42} -6627.71 q^{43} +2539.70 q^{44} +3711.62 q^{45} -12059.9 q^{46} -3598.67 q^{47} +2145.42 q^{48} +29410.8 q^{49} +4065.90 q^{50} +8936.76 q^{51} -2868.17 q^{52} -29978.1 q^{53} +2890.91 q^{54} -7150.95 q^{55} +41155.4 q^{56} +12115.9 q^{57} -31130.4 q^{58} +3481.00 q^{59} +6711.50 q^{60} +50916.8 q^{61} -9292.47 q^{62} +17413.6 q^{63} +28172.3 q^{64} +8075.79 q^{65} -5569.73 q^{66} +20194.9 q^{67} +16159.8 q^{68} -27370.3 q^{69} -39065.3 q^{70} +37228.5 q^{71} +15506.3 q^{72} +32443.0 q^{73} -43250.0 q^{74} +9227.67 q^{75} +21908.4 q^{76} -33549.7 q^{77} +6290.08 q^{78} +47234.2 q^{79} -10923.2 q^{80} +6561.00 q^{81} +35488.2 q^{82} -5522.34 q^{83} +31488.0 q^{84} -45500.5 q^{85} +26282.8 q^{86} -70651.3 q^{87} -29874.9 q^{88} -76315.0 q^{89} -14718.8 q^{90} +37888.8 q^{91} -49491.9 q^{92} -21089.5 q^{93} +14270.8 q^{94} -61686.7 q^{95} +46625.5 q^{96} +80922.3 q^{97} -116631. q^{98} -12640.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.96558 −0.701023 −0.350511 0.936558i \(-0.613992\pi\)
−0.350511 + 0.936558i \(0.613992\pi\)
\(3\) −9.00000 −0.577350
\(4\) −16.2741 −0.508567
\(5\) 45.8225 0.819698 0.409849 0.912153i \(-0.365581\pi\)
0.409849 + 0.912153i \(0.365581\pi\)
\(6\) 35.6903 0.404736
\(7\) 214.983 1.65829 0.829143 0.559036i \(-0.188829\pi\)
0.829143 + 0.559036i \(0.188829\pi\)
\(8\) 191.435 1.05754
\(9\) 81.0000 0.333333
\(10\) −181.713 −0.574627
\(11\) −156.057 −0.388869 −0.194434 0.980916i \(-0.562287\pi\)
−0.194434 + 0.980916i \(0.562287\pi\)
\(12\) 146.467 0.293621
\(13\) 176.241 0.289233 0.144616 0.989488i \(-0.453805\pi\)
0.144616 + 0.989488i \(0.453805\pi\)
\(14\) −852.534 −1.16250
\(15\) −412.403 −0.473253
\(16\) −238.380 −0.232793
\(17\) −992.973 −0.833327 −0.416663 0.909061i \(-0.636801\pi\)
−0.416663 + 0.909061i \(0.636801\pi\)
\(18\) −321.212 −0.233674
\(19\) −1346.21 −0.855517 −0.427758 0.903893i \(-0.640697\pi\)
−0.427758 + 0.903893i \(0.640697\pi\)
\(20\) −745.722 −0.416871
\(21\) −1934.85 −0.957412
\(22\) 618.859 0.272606
\(23\) 3041.14 1.19872 0.599359 0.800480i \(-0.295422\pi\)
0.599359 + 0.800480i \(0.295422\pi\)
\(24\) −1722.92 −0.610571
\(25\) −1025.30 −0.328095
\(26\) −698.897 −0.202759
\(27\) −729.000 −0.192450
\(28\) −3498.67 −0.843349
\(29\) 7850.14 1.73334 0.866668 0.498886i \(-0.166257\pi\)
0.866668 + 0.498886i \(0.166257\pi\)
\(30\) 1635.42 0.331761
\(31\) 2343.28 0.437945 0.218973 0.975731i \(-0.429729\pi\)
0.218973 + 0.975731i \(0.429729\pi\)
\(32\) −5180.61 −0.894347
\(33\) 1404.52 0.224513
\(34\) 3937.72 0.584181
\(35\) 9851.07 1.35929
\(36\) −1318.21 −0.169522
\(37\) 10906.3 1.30971 0.654854 0.755755i \(-0.272730\pi\)
0.654854 + 0.755755i \(0.272730\pi\)
\(38\) 5338.51 0.599737
\(39\) −1586.17 −0.166989
\(40\) 8772.04 0.866864
\(41\) −8949.04 −0.831413 −0.415707 0.909499i \(-0.636466\pi\)
−0.415707 + 0.909499i \(0.636466\pi\)
\(42\) 7672.81 0.671168
\(43\) −6627.71 −0.546629 −0.273314 0.961925i \(-0.588120\pi\)
−0.273314 + 0.961925i \(0.588120\pi\)
\(44\) 2539.70 0.197766
\(45\) 3711.62 0.273233
\(46\) −12059.9 −0.840329
\(47\) −3598.67 −0.237628 −0.118814 0.992917i \(-0.537909\pi\)
−0.118814 + 0.992917i \(0.537909\pi\)
\(48\) 2145.42 0.134403
\(49\) 29410.8 1.74991
\(50\) 4065.90 0.230002
\(51\) 8936.76 0.481121
\(52\) −2868.17 −0.147094
\(53\) −29978.1 −1.46593 −0.732966 0.680265i \(-0.761865\pi\)
−0.732966 + 0.680265i \(0.761865\pi\)
\(54\) 2890.91 0.134912
\(55\) −7150.95 −0.318755
\(56\) 41155.4 1.75370
\(57\) 12115.9 0.493933
\(58\) −31130.4 −1.21511
\(59\) 3481.00 0.130189
\(60\) 6711.50 0.240681
\(61\) 50916.8 1.75201 0.876005 0.482301i \(-0.160199\pi\)
0.876005 + 0.482301i \(0.160199\pi\)
\(62\) −9292.47 −0.307010
\(63\) 17413.6 0.552762
\(64\) 28172.3 0.859751
\(65\) 8075.79 0.237084
\(66\) −5569.73 −0.157389
\(67\) 20194.9 0.549609 0.274805 0.961500i \(-0.411387\pi\)
0.274805 + 0.961500i \(0.411387\pi\)
\(68\) 16159.8 0.423802
\(69\) −27370.3 −0.692080
\(70\) −39065.3 −0.952897
\(71\) 37228.5 0.876455 0.438227 0.898864i \(-0.355606\pi\)
0.438227 + 0.898864i \(0.355606\pi\)
\(72\) 15506.3 0.352513
\(73\) 32443.0 0.712547 0.356274 0.934382i \(-0.384047\pi\)
0.356274 + 0.934382i \(0.384047\pi\)
\(74\) −43250.0 −0.918136
\(75\) 9227.67 0.189426
\(76\) 21908.4 0.435087
\(77\) −33549.7 −0.644856
\(78\) 6290.08 0.117063
\(79\) 47234.2 0.851507 0.425754 0.904839i \(-0.360009\pi\)
0.425754 + 0.904839i \(0.360009\pi\)
\(80\) −10923.2 −0.190820
\(81\) 6561.00 0.111111
\(82\) 35488.2 0.582840
\(83\) −5522.34 −0.0879889 −0.0439944 0.999032i \(-0.514008\pi\)
−0.0439944 + 0.999032i \(0.514008\pi\)
\(84\) 31488.0 0.486908
\(85\) −45500.5 −0.683076
\(86\) 26282.8 0.383199
\(87\) −70651.3 −1.00074
\(88\) −29874.9 −0.411244
\(89\) −76315.0 −1.02126 −0.510628 0.859802i \(-0.670587\pi\)
−0.510628 + 0.859802i \(0.670587\pi\)
\(90\) −14718.8 −0.191542
\(91\) 37888.8 0.479631
\(92\) −49491.9 −0.609628
\(93\) −21089.5 −0.252848
\(94\) 14270.8 0.166583
\(95\) −61686.7 −0.701265
\(96\) 46625.5 0.516351
\(97\) 80922.3 0.873251 0.436625 0.899643i \(-0.356174\pi\)
0.436625 + 0.899643i \(0.356174\pi\)
\(98\) −116631. −1.22673
\(99\) −12640.7 −0.129623
\(100\) 16685.8 0.166858
\(101\) 82048.8 0.800329 0.400165 0.916443i \(-0.368953\pi\)
0.400165 + 0.916443i \(0.368953\pi\)
\(102\) −35439.5 −0.337277
\(103\) 133604. 1.24087 0.620434 0.784259i \(-0.286957\pi\)
0.620434 + 0.784259i \(0.286957\pi\)
\(104\) 33738.7 0.305875
\(105\) −88659.7 −0.784789
\(106\) 118881. 1.02765
\(107\) −73779.6 −0.622984 −0.311492 0.950249i \(-0.600829\pi\)
−0.311492 + 0.950249i \(0.600829\pi\)
\(108\) 11863.8 0.0978737
\(109\) 156032. 1.25790 0.628952 0.777444i \(-0.283484\pi\)
0.628952 + 0.777444i \(0.283484\pi\)
\(110\) 28357.7 0.223454
\(111\) −98157.0 −0.756160
\(112\) −51247.7 −0.386038
\(113\) −34300.6 −0.252700 −0.126350 0.991986i \(-0.540326\pi\)
−0.126350 + 0.991986i \(0.540326\pi\)
\(114\) −48046.6 −0.346258
\(115\) 139353. 0.982587
\(116\) −127754. −0.881517
\(117\) 14275.5 0.0964110
\(118\) −13804.2 −0.0912654
\(119\) −213473. −1.38189
\(120\) −78948.4 −0.500484
\(121\) −136697. −0.848781
\(122\) −201915. −1.22820
\(123\) 80541.4 0.480017
\(124\) −38134.8 −0.222724
\(125\) −190177. −1.08864
\(126\) −69055.3 −0.387499
\(127\) −156876. −0.863073 −0.431536 0.902096i \(-0.642028\pi\)
−0.431536 + 0.902096i \(0.642028\pi\)
\(128\) 54059.8 0.291642
\(129\) 59649.4 0.315596
\(130\) −32025.2 −0.166201
\(131\) 248564. 1.26549 0.632746 0.774360i \(-0.281928\pi\)
0.632746 + 0.774360i \(0.281928\pi\)
\(132\) −22857.3 −0.114180
\(133\) −289412. −1.41869
\(134\) −80084.5 −0.385289
\(135\) −33404.6 −0.157751
\(136\) −190090. −0.881276
\(137\) 130816. 0.595469 0.297735 0.954649i \(-0.403769\pi\)
0.297735 + 0.954649i \(0.403769\pi\)
\(138\) 108539. 0.485164
\(139\) 283883. 1.24624 0.623121 0.782125i \(-0.285864\pi\)
0.623121 + 0.782125i \(0.285864\pi\)
\(140\) −160318. −0.691292
\(141\) 32388.0 0.137194
\(142\) −147633. −0.614415
\(143\) −27503.7 −0.112474
\(144\) −19308.8 −0.0775977
\(145\) 359713. 1.42081
\(146\) −128655. −0.499512
\(147\) −264697. −1.01031
\(148\) −177491. −0.666074
\(149\) 102655. 0.378805 0.189403 0.981900i \(-0.439345\pi\)
0.189403 + 0.981900i \(0.439345\pi\)
\(150\) −36593.1 −0.132792
\(151\) −321646. −1.14798 −0.573992 0.818861i \(-0.694606\pi\)
−0.573992 + 0.818861i \(0.694606\pi\)
\(152\) −257712. −0.904743
\(153\) −80430.8 −0.277776
\(154\) 133044. 0.452059
\(155\) 107375. 0.358983
\(156\) 25813.5 0.0849249
\(157\) 20173.1 0.0653167 0.0326583 0.999467i \(-0.489603\pi\)
0.0326583 + 0.999467i \(0.489603\pi\)
\(158\) −187311. −0.596926
\(159\) 269803. 0.846357
\(160\) −237389. −0.733094
\(161\) 653794. 1.98782
\(162\) −26018.2 −0.0778914
\(163\) 304847. 0.898697 0.449348 0.893357i \(-0.351656\pi\)
0.449348 + 0.893357i \(0.351656\pi\)
\(164\) 145638. 0.422829
\(165\) 64358.5 0.184033
\(166\) 21899.3 0.0616822
\(167\) 399173. 1.10757 0.553784 0.832660i \(-0.313183\pi\)
0.553784 + 0.832660i \(0.313183\pi\)
\(168\) −370398. −1.01250
\(169\) −340232. −0.916344
\(170\) 180436. 0.478852
\(171\) −109043. −0.285172
\(172\) 107860. 0.277997
\(173\) −269280. −0.684052 −0.342026 0.939691i \(-0.611113\pi\)
−0.342026 + 0.939691i \(0.611113\pi\)
\(174\) 280174. 0.701543
\(175\) −220422. −0.544075
\(176\) 37201.0 0.0905259
\(177\) −31329.0 −0.0751646
\(178\) 302634. 0.715924
\(179\) −587301. −1.37002 −0.685012 0.728532i \(-0.740203\pi\)
−0.685012 + 0.728532i \(0.740203\pi\)
\(180\) −60403.5 −0.138957
\(181\) 440471. 0.999357 0.499678 0.866211i \(-0.333452\pi\)
0.499678 + 0.866211i \(0.333452\pi\)
\(182\) −150251. −0.336232
\(183\) −458251. −1.01152
\(184\) 582181. 1.26769
\(185\) 499756. 1.07357
\(186\) 83632.2 0.177252
\(187\) 154961. 0.324055
\(188\) 58565.2 0.120850
\(189\) −156723. −0.319137
\(190\) 244624. 0.491603
\(191\) 372603. 0.739031 0.369515 0.929225i \(-0.379524\pi\)
0.369515 + 0.929225i \(0.379524\pi\)
\(192\) −253551. −0.496377
\(193\) 958360. 1.85198 0.925988 0.377552i \(-0.123234\pi\)
0.925988 + 0.377552i \(0.123234\pi\)
\(194\) −320904. −0.612169
\(195\) −72682.1 −0.136880
\(196\) −478635. −0.889948
\(197\) −366511. −0.672855 −0.336428 0.941709i \(-0.609219\pi\)
−0.336428 + 0.941709i \(0.609219\pi\)
\(198\) 50127.6 0.0908686
\(199\) 456957. 0.817980 0.408990 0.912539i \(-0.365881\pi\)
0.408990 + 0.912539i \(0.365881\pi\)
\(200\) −196278. −0.346974
\(201\) −181754. −0.317317
\(202\) −325371. −0.561049
\(203\) 1.68765e6 2.87437
\(204\) −145438. −0.244682
\(205\) −410068. −0.681508
\(206\) −529817. −0.869877
\(207\) 246332. 0.399573
\(208\) −42012.3 −0.0673314
\(209\) 210086. 0.332684
\(210\) 351587. 0.550155
\(211\) −127342. −0.196909 −0.0984546 0.995142i \(-0.531390\pi\)
−0.0984546 + 0.995142i \(0.531390\pi\)
\(212\) 487867. 0.745525
\(213\) −335056. −0.506021
\(214\) 292579. 0.436726
\(215\) −303698. −0.448071
\(216\) −139556. −0.203524
\(217\) 503766. 0.726239
\(218\) −618758. −0.881819
\(219\) −291987. −0.411389
\(220\) 116375. 0.162108
\(221\) −175002. −0.241026
\(222\) 389250. 0.530086
\(223\) 998142. 1.34410 0.672048 0.740508i \(-0.265415\pi\)
0.672048 + 0.740508i \(0.265415\pi\)
\(224\) −1.11374e6 −1.48308
\(225\) −83049.0 −0.109365
\(226\) 136022. 0.177149
\(227\) −1.00518e6 −1.29474 −0.647368 0.762178i \(-0.724130\pi\)
−0.647368 + 0.762178i \(0.724130\pi\)
\(228\) −197175. −0.251198
\(229\) −363463. −0.458006 −0.229003 0.973426i \(-0.573547\pi\)
−0.229003 + 0.973426i \(0.573547\pi\)
\(230\) −552615. −0.688816
\(231\) 301948. 0.372307
\(232\) 1.50279e6 1.83307
\(233\) 74441.9 0.0898312 0.0449156 0.998991i \(-0.485698\pi\)
0.0449156 + 0.998991i \(0.485698\pi\)
\(234\) −56610.7 −0.0675863
\(235\) −164900. −0.194783
\(236\) −56650.3 −0.0662098
\(237\) −425107. −0.491618
\(238\) 846544. 0.968740
\(239\) 1.09860e6 1.24407 0.622036 0.782988i \(-0.286306\pi\)
0.622036 + 0.782988i \(0.286306\pi\)
\(240\) 98308.6 0.110170
\(241\) 120611. 0.133765 0.0668826 0.997761i \(-0.478695\pi\)
0.0668826 + 0.997761i \(0.478695\pi\)
\(242\) 542084. 0.595015
\(243\) −59049.0 −0.0641500
\(244\) −828627. −0.891014
\(245\) 1.34768e6 1.43440
\(246\) −319394. −0.336503
\(247\) −237257. −0.247444
\(248\) 448586. 0.463145
\(249\) 49701.1 0.0508004
\(250\) 754163. 0.763160
\(251\) −133146. −0.133396 −0.0666979 0.997773i \(-0.521246\pi\)
−0.0666979 + 0.997773i \(0.521246\pi\)
\(252\) −283392. −0.281116
\(253\) −474593. −0.466144
\(254\) 622105. 0.605034
\(255\) 409505. 0.394374
\(256\) −1.11589e6 −1.06420
\(257\) −932083. −0.880282 −0.440141 0.897929i \(-0.645072\pi\)
−0.440141 + 0.897929i \(0.645072\pi\)
\(258\) −236545. −0.221240
\(259\) 2.34468e6 2.17187
\(260\) −131427. −0.120573
\(261\) 635862. 0.577778
\(262\) −985700. −0.887139
\(263\) 1.66088e6 1.48064 0.740320 0.672254i \(-0.234674\pi\)
0.740320 + 0.672254i \(0.234674\pi\)
\(264\) 268874. 0.237432
\(265\) −1.37367e6 −1.20162
\(266\) 1.14769e6 0.994535
\(267\) 686835. 0.589623
\(268\) −328654. −0.279513
\(269\) −746269. −0.628803 −0.314401 0.949290i \(-0.601804\pi\)
−0.314401 + 0.949290i \(0.601804\pi\)
\(270\) 132469. 0.110587
\(271\) 1.84347e6 1.52480 0.762398 0.647108i \(-0.224022\pi\)
0.762398 + 0.647108i \(0.224022\pi\)
\(272\) 236705. 0.193993
\(273\) −340999. −0.276915
\(274\) −518762. −0.417438
\(275\) 160005. 0.127586
\(276\) 445427. 0.351969
\(277\) −1.57925e6 −1.23666 −0.618331 0.785918i \(-0.712191\pi\)
−0.618331 + 0.785918i \(0.712191\pi\)
\(278\) −1.12576e6 −0.873645
\(279\) 189806. 0.145982
\(280\) 1.88584e6 1.43751
\(281\) −1.09989e6 −0.830967 −0.415483 0.909601i \(-0.636388\pi\)
−0.415483 + 0.909601i \(0.636388\pi\)
\(282\) −128437. −0.0961765
\(283\) −2.43606e6 −1.80810 −0.904050 0.427426i \(-0.859420\pi\)
−0.904050 + 0.427426i \(0.859420\pi\)
\(284\) −605862. −0.445736
\(285\) 555180. 0.404876
\(286\) 109068. 0.0788466
\(287\) −1.92389e6 −1.37872
\(288\) −419629. −0.298116
\(289\) −433861. −0.305567
\(290\) −1.42647e6 −0.996022
\(291\) −728301. −0.504171
\(292\) −527982. −0.362378
\(293\) −696507. −0.473976 −0.236988 0.971513i \(-0.576160\pi\)
−0.236988 + 0.971513i \(0.576160\pi\)
\(294\) 1.04968e6 0.708253
\(295\) 159508. 0.106716
\(296\) 2.08786e6 1.38507
\(297\) 113766. 0.0748378
\(298\) −407088. −0.265551
\(299\) 535973. 0.346709
\(300\) −150172. −0.0963356
\(301\) −1.42485e6 −0.906467
\(302\) 1.27552e6 0.804764
\(303\) −738439. −0.462070
\(304\) 320909. 0.199158
\(305\) 2.33314e6 1.43612
\(306\) 318955. 0.194727
\(307\) 2.06876e6 1.25275 0.626375 0.779522i \(-0.284538\pi\)
0.626375 + 0.779522i \(0.284538\pi\)
\(308\) 545993. 0.327952
\(309\) −1.20243e6 −0.716415
\(310\) −425804. −0.251655
\(311\) −245921. −0.144177 −0.0720883 0.997398i \(-0.522966\pi\)
−0.0720883 + 0.997398i \(0.522966\pi\)
\(312\) −303648. −0.176597
\(313\) −909246. −0.524591 −0.262295 0.964988i \(-0.584479\pi\)
−0.262295 + 0.964988i \(0.584479\pi\)
\(314\) −79998.3 −0.0457885
\(315\) 797937. 0.453098
\(316\) −768695. −0.433048
\(317\) −1.71664e6 −0.959467 −0.479733 0.877414i \(-0.659267\pi\)
−0.479733 + 0.877414i \(0.659267\pi\)
\(318\) −1.06993e6 −0.593316
\(319\) −1.22507e6 −0.674040
\(320\) 1.29093e6 0.704736
\(321\) 664017. 0.359680
\(322\) −2.59268e6 −1.39351
\(323\) 1.33675e6 0.712925
\(324\) −106775. −0.0565074
\(325\) −180699. −0.0948959
\(326\) −1.20890e6 −0.630007
\(327\) −1.40429e6 −0.726251
\(328\) −1.71316e6 −0.879253
\(329\) −773654. −0.394055
\(330\) −255219. −0.129012
\(331\) 3.18458e6 1.59765 0.798827 0.601561i \(-0.205454\pi\)
0.798827 + 0.601561i \(0.205454\pi\)
\(332\) 89871.3 0.0447482
\(333\) 883413. 0.436569
\(334\) −1.58296e6 −0.776431
\(335\) 925380. 0.450514
\(336\) 461230. 0.222879
\(337\) −604758. −0.290073 −0.145036 0.989426i \(-0.546330\pi\)
−0.145036 + 0.989426i \(0.546330\pi\)
\(338\) 1.34922e6 0.642378
\(339\) 308705. 0.145896
\(340\) 740482. 0.347390
\(341\) −365686. −0.170303
\(342\) 432419. 0.199912
\(343\) 2.70961e6 1.24357
\(344\) −1.26878e6 −0.578082
\(345\) −1.25417e6 −0.567297
\(346\) 1.06785e6 0.479536
\(347\) −3.66370e6 −1.63341 −0.816706 0.577053i \(-0.804202\pi\)
−0.816706 + 0.577053i \(0.804202\pi\)
\(348\) 1.14979e6 0.508944
\(349\) −4.26413e6 −1.87399 −0.936995 0.349343i \(-0.886405\pi\)
−0.936995 + 0.349343i \(0.886405\pi\)
\(350\) 874101. 0.381409
\(351\) −128479. −0.0556629
\(352\) 808473. 0.347783
\(353\) 2.74711e6 1.17338 0.586692 0.809810i \(-0.300430\pi\)
0.586692 + 0.809810i \(0.300430\pi\)
\(354\) 124238. 0.0526921
\(355\) 1.70590e6 0.718428
\(356\) 1.24196e6 0.519377
\(357\) 1.92125e6 0.797837
\(358\) 2.32899e6 0.960418
\(359\) −1.97611e6 −0.809236 −0.404618 0.914486i \(-0.632595\pi\)
−0.404618 + 0.914486i \(0.632595\pi\)
\(360\) 710535. 0.288955
\(361\) −663821. −0.268091
\(362\) −1.74672e6 −0.700572
\(363\) 1.23027e6 0.490044
\(364\) −616607. −0.243924
\(365\) 1.48662e6 0.584074
\(366\) 1.81724e6 0.709101
\(367\) 2.43373e6 0.943206 0.471603 0.881811i \(-0.343676\pi\)
0.471603 + 0.881811i \(0.343676\pi\)
\(368\) −724948. −0.279053
\(369\) −724872. −0.277138
\(370\) −1.98182e6 −0.752594
\(371\) −6.44478e6 −2.43094
\(372\) 343214. 0.128590
\(373\) 2.63259e6 0.979740 0.489870 0.871796i \(-0.337044\pi\)
0.489870 + 0.871796i \(0.337044\pi\)
\(374\) −614511. −0.227170
\(375\) 1.71159e6 0.628525
\(376\) −688912. −0.251301
\(377\) 1.38351e6 0.501338
\(378\) 621498. 0.223723
\(379\) −2.43570e6 −0.871016 −0.435508 0.900185i \(-0.643431\pi\)
−0.435508 + 0.900185i \(0.643431\pi\)
\(380\) 1.00390e6 0.356640
\(381\) 1.41188e6 0.498295
\(382\) −1.47759e6 −0.518078
\(383\) −2.55420e6 −0.889728 −0.444864 0.895598i \(-0.646748\pi\)
−0.444864 + 0.895598i \(0.646748\pi\)
\(384\) −486538. −0.168379
\(385\) −1.53733e6 −0.528587
\(386\) −3.80046e6 −1.29828
\(387\) −536845. −0.182210
\(388\) −1.31694e6 −0.444106
\(389\) −4.16114e6 −1.39424 −0.697121 0.716953i \(-0.745536\pi\)
−0.697121 + 0.716953i \(0.745536\pi\)
\(390\) 288227. 0.0959563
\(391\) −3.01977e6 −0.998924
\(392\) 5.63026e6 1.85060
\(393\) −2.23707e6 −0.730632
\(394\) 1.45343e6 0.471687
\(395\) 2.16439e6 0.697979
\(396\) 205716. 0.0659219
\(397\) 3.12738e6 0.995873 0.497937 0.867213i \(-0.334091\pi\)
0.497937 + 0.867213i \(0.334091\pi\)
\(398\) −1.81210e6 −0.573423
\(399\) 2.60471e6 0.819082
\(400\) 244410. 0.0763782
\(401\) 4.53732e6 1.40909 0.704544 0.709660i \(-0.251151\pi\)
0.704544 + 0.709660i \(0.251151\pi\)
\(402\) 720760. 0.222447
\(403\) 412981. 0.126668
\(404\) −1.33527e6 −0.407021
\(405\) 300642. 0.0910776
\(406\) −6.69252e6 −2.01500
\(407\) −1.70202e6 −0.509304
\(408\) 1.71081e6 0.508805
\(409\) −3.30951e6 −0.978263 −0.489132 0.872210i \(-0.662686\pi\)
−0.489132 + 0.872210i \(0.662686\pi\)
\(410\) 1.62616e6 0.477753
\(411\) −1.17734e6 −0.343794
\(412\) −2.17428e6 −0.631064
\(413\) 748357. 0.215890
\(414\) −976852. −0.280110
\(415\) −253047. −0.0721243
\(416\) −913034. −0.258675
\(417\) −2.55495e6 −0.719518
\(418\) −833114. −0.233219
\(419\) −4.28215e6 −1.19159 −0.595795 0.803136i \(-0.703163\pi\)
−0.595795 + 0.803136i \(0.703163\pi\)
\(420\) 1.44286e6 0.399118
\(421\) −5.73100e6 −1.57589 −0.787944 0.615747i \(-0.788855\pi\)
−0.787944 + 0.615747i \(0.788855\pi\)
\(422\) 504986. 0.138038
\(423\) −291492. −0.0792093
\(424\) −5.73886e6 −1.55028
\(425\) 1.01809e6 0.273410
\(426\) 1.32869e6 0.354733
\(427\) 1.09463e7 2.90534
\(428\) 1.20070e6 0.316829
\(429\) 247533. 0.0649367
\(430\) 1.20434e6 0.314108
\(431\) 1.51057e6 0.391694 0.195847 0.980634i \(-0.437254\pi\)
0.195847 + 0.980634i \(0.437254\pi\)
\(432\) 173779. 0.0448011
\(433\) −1.90848e6 −0.489179 −0.244589 0.969627i \(-0.578653\pi\)
−0.244589 + 0.969627i \(0.578653\pi\)
\(434\) −1.99773e6 −0.509110
\(435\) −3.23742e6 −0.820306
\(436\) −2.53929e6 −0.639728
\(437\) −4.09401e6 −1.02552
\(438\) 1.15790e6 0.288393
\(439\) −2.71946e6 −0.673475 −0.336737 0.941599i \(-0.609323\pi\)
−0.336737 + 0.941599i \(0.609323\pi\)
\(440\) −1.36894e6 −0.337096
\(441\) 2.38227e6 0.583305
\(442\) 693987. 0.168964
\(443\) 5.21524e6 1.26260 0.631298 0.775540i \(-0.282522\pi\)
0.631298 + 0.775540i \(0.282522\pi\)
\(444\) 1.59742e6 0.384558
\(445\) −3.49695e6 −0.837122
\(446\) −3.95822e6 −0.942242
\(447\) −923898. −0.218703
\(448\) 6.05657e6 1.42571
\(449\) 4.09107e6 0.957680 0.478840 0.877902i \(-0.341057\pi\)
0.478840 + 0.877902i \(0.341057\pi\)
\(450\) 329338. 0.0766674
\(451\) 1.39656e6 0.323310
\(452\) 558212. 0.128515
\(453\) 2.89482e6 0.662789
\(454\) 3.98615e6 0.907640
\(455\) 1.73616e6 0.393153
\(456\) 2.31941e6 0.522354
\(457\) −1.16165e6 −0.260188 −0.130094 0.991502i \(-0.541528\pi\)
−0.130094 + 0.991502i \(0.541528\pi\)
\(458\) 1.44134e6 0.321073
\(459\) 723878. 0.160374
\(460\) −2.26785e6 −0.499711
\(461\) 2.86009e6 0.626799 0.313399 0.949621i \(-0.398532\pi\)
0.313399 + 0.949621i \(0.398532\pi\)
\(462\) −1.19740e6 −0.260996
\(463\) −6.88483e6 −1.49259 −0.746296 0.665614i \(-0.768170\pi\)
−0.746296 + 0.665614i \(0.768170\pi\)
\(464\) −1.87132e6 −0.403509
\(465\) −966374. −0.207259
\(466\) −295206. −0.0629738
\(467\) 7.95572e6 1.68806 0.844028 0.536298i \(-0.180178\pi\)
0.844028 + 0.536298i \(0.180178\pi\)
\(468\) −232321. −0.0490314
\(469\) 4.34156e6 0.911410
\(470\) 653925. 0.136547
\(471\) −181558. −0.0377106
\(472\) 666386. 0.137680
\(473\) 1.03430e6 0.212567
\(474\) 1.68580e6 0.344636
\(475\) 1.38026e6 0.280691
\(476\) 3.47408e6 0.702786
\(477\) −2.42822e6 −0.488644
\(478\) −4.35660e6 −0.872123
\(479\) −2.55762e6 −0.509328 −0.254664 0.967030i \(-0.581965\pi\)
−0.254664 + 0.967030i \(0.581965\pi\)
\(480\) 2.13650e6 0.423252
\(481\) 1.92214e6 0.378811
\(482\) −478292. −0.0937725
\(483\) −5.88415e6 −1.14767
\(484\) 2.22463e6 0.431662
\(485\) 3.70806e6 0.715802
\(486\) 234164. 0.0449706
\(487\) −1.26363e6 −0.241434 −0.120717 0.992687i \(-0.538519\pi\)
−0.120717 + 0.992687i \(0.538519\pi\)
\(488\) 9.74727e6 1.85282
\(489\) −2.74362e6 −0.518863
\(490\) −5.34433e6 −1.00555
\(491\) 2.84633e6 0.532820 0.266410 0.963860i \(-0.414162\pi\)
0.266410 + 0.963860i \(0.414162\pi\)
\(492\) −1.31074e6 −0.244121
\(493\) −7.79498e6 −1.44443
\(494\) 940862. 0.173464
\(495\) −579227. −0.106252
\(496\) −558591. −0.101951
\(497\) 8.00350e6 1.45341
\(498\) −197094. −0.0356123
\(499\) 3.80322e6 0.683754 0.341877 0.939745i \(-0.388937\pi\)
0.341877 + 0.939745i \(0.388937\pi\)
\(500\) 3.09497e6 0.553645
\(501\) −3.59256e6 −0.639455
\(502\) 528000. 0.0935136
\(503\) 4.91618e6 0.866378 0.433189 0.901303i \(-0.357388\pi\)
0.433189 + 0.901303i \(0.357388\pi\)
\(504\) 3.33358e6 0.584568
\(505\) 3.75968e6 0.656029
\(506\) 1.88204e6 0.326777
\(507\) 3.06209e6 0.529052
\(508\) 2.55302e6 0.438930
\(509\) −5.90046e6 −1.00947 −0.504733 0.863276i \(-0.668409\pi\)
−0.504733 + 0.863276i \(0.668409\pi\)
\(510\) −1.62393e6 −0.276465
\(511\) 6.97470e6 1.18161
\(512\) 2.69525e6 0.454386
\(513\) 981386. 0.164644
\(514\) 3.69626e6 0.617098
\(515\) 6.12206e6 1.01714
\(516\) −970743. −0.160502
\(517\) 561599. 0.0924060
\(518\) −9.29803e6 −1.52253
\(519\) 2.42352e6 0.394937
\(520\) 1.54599e6 0.250726
\(521\) 1.04083e7 1.67992 0.839958 0.542651i \(-0.182580\pi\)
0.839958 + 0.542651i \(0.182580\pi\)
\(522\) −2.52156e6 −0.405036
\(523\) 7.39494e6 1.18217 0.591086 0.806609i \(-0.298699\pi\)
0.591086 + 0.806609i \(0.298699\pi\)
\(524\) −4.04516e6 −0.643587
\(525\) 1.98379e6 0.314122
\(526\) −6.58637e6 −1.03796
\(527\) −2.32681e6 −0.364951
\(528\) −334809. −0.0522652
\(529\) 2.81220e6 0.436924
\(530\) 5.44741e6 0.842365
\(531\) 281961. 0.0433963
\(532\) 4.70994e6 0.721499
\(533\) −1.57719e6 −0.240472
\(534\) −2.72370e6 −0.413339
\(535\) −3.38077e6 −0.510659
\(536\) 3.86601e6 0.581234
\(537\) 5.28571e6 0.790983
\(538\) 2.95939e6 0.440805
\(539\) −4.58978e6 −0.680486
\(540\) 543631. 0.0802269
\(541\) 5.70318e6 0.837768 0.418884 0.908040i \(-0.362421\pi\)
0.418884 + 0.908040i \(0.362421\pi\)
\(542\) −7.31042e6 −1.06892
\(543\) −3.96424e6 −0.576979
\(544\) 5.14421e6 0.745283
\(545\) 7.14978e6 1.03110
\(546\) 1.35226e6 0.194124
\(547\) −602941. −0.0861602 −0.0430801 0.999072i \(-0.513717\pi\)
−0.0430801 + 0.999072i \(0.513717\pi\)
\(548\) −2.12892e6 −0.302836
\(549\) 4.12426e6 0.584004
\(550\) −634514. −0.0894406
\(551\) −1.05679e7 −1.48290
\(552\) −5.23963e6 −0.731902
\(553\) 1.01546e7 1.41204
\(554\) 6.26264e6 0.866929
\(555\) −4.49780e6 −0.619823
\(556\) −4.61995e6 −0.633797
\(557\) −5.42243e6 −0.740552 −0.370276 0.928922i \(-0.620737\pi\)
−0.370276 + 0.928922i \(0.620737\pi\)
\(558\) −752690. −0.102337
\(559\) −1.16807e6 −0.158103
\(560\) −2.34830e6 −0.316434
\(561\) −1.39465e6 −0.187093
\(562\) 4.36171e6 0.582527
\(563\) −6.66231e6 −0.885837 −0.442918 0.896562i \(-0.646057\pi\)
−0.442918 + 0.896562i \(0.646057\pi\)
\(564\) −527087. −0.0697726
\(565\) −1.57174e6 −0.207138
\(566\) 9.66042e6 1.26752
\(567\) 1.41051e6 0.184254
\(568\) 7.12684e6 0.926886
\(569\) −1.31747e7 −1.70593 −0.852964 0.521970i \(-0.825197\pi\)
−0.852964 + 0.521970i \(0.825197\pi\)
\(570\) −2.20161e6 −0.283827
\(571\) −1.36489e7 −1.75189 −0.875946 0.482410i \(-0.839762\pi\)
−0.875946 + 0.482410i \(0.839762\pi\)
\(572\) 447599. 0.0572004
\(573\) −3.35342e6 −0.426680
\(574\) 7.62937e6 0.966515
\(575\) −3.11807e6 −0.393293
\(576\) 2.28196e6 0.286584
\(577\) 4.83210e6 0.604222 0.302111 0.953273i \(-0.402309\pi\)
0.302111 + 0.953273i \(0.402309\pi\)
\(578\) 1.72051e6 0.214209
\(579\) −8.62524e6 −1.06924
\(580\) −5.85402e6 −0.722578
\(581\) −1.18721e6 −0.145911
\(582\) 2.88814e6 0.353436
\(583\) 4.67830e6 0.570055
\(584\) 6.21073e6 0.753547
\(585\) 654139. 0.0790279
\(586\) 2.76206e6 0.332268
\(587\) 4.56230e6 0.546498 0.273249 0.961943i \(-0.411902\pi\)
0.273249 + 0.961943i \(0.411902\pi\)
\(588\) 4.30772e6 0.513812
\(589\) −3.15454e6 −0.374669
\(590\) −632543. −0.0748101
\(591\) 3.29860e6 0.388473
\(592\) −2.59985e6 −0.304891
\(593\) −1.33301e7 −1.55667 −0.778333 0.627852i \(-0.783934\pi\)
−0.778333 + 0.627852i \(0.783934\pi\)
\(594\) −451148. −0.0524630
\(595\) −9.78185e6 −1.13274
\(596\) −1.67063e6 −0.192648
\(597\) −4.11261e6 −0.472261
\(598\) −2.12545e6 −0.243051
\(599\) 6.73748e6 0.767238 0.383619 0.923491i \(-0.374678\pi\)
0.383619 + 0.923491i \(0.374678\pi\)
\(600\) 1.76650e6 0.200325
\(601\) 2.33351e6 0.263526 0.131763 0.991281i \(-0.457936\pi\)
0.131763 + 0.991281i \(0.457936\pi\)
\(602\) 5.65035e6 0.635454
\(603\) 1.63578e6 0.183203
\(604\) 5.23451e6 0.583827
\(605\) −6.26380e6 −0.695744
\(606\) 2.92834e6 0.323922
\(607\) −3.92089e6 −0.431930 −0.215965 0.976401i \(-0.569290\pi\)
−0.215965 + 0.976401i \(0.569290\pi\)
\(608\) 6.97418e6 0.765128
\(609\) −1.51888e7 −1.65952
\(610\) −9.25225e6 −1.00675
\(611\) −634232. −0.0687298
\(612\) 1.30894e6 0.141267
\(613\) −4.90899e6 −0.527644 −0.263822 0.964571i \(-0.584983\pi\)
−0.263822 + 0.964571i \(0.584983\pi\)
\(614\) −8.20385e6 −0.878207
\(615\) 3.69061e6 0.393469
\(616\) −6.42260e6 −0.681960
\(617\) −760974. −0.0804742 −0.0402371 0.999190i \(-0.512811\pi\)
−0.0402371 + 0.999190i \(0.512811\pi\)
\(618\) 4.76835e6 0.502224
\(619\) −1.88832e7 −1.98083 −0.990417 0.138109i \(-0.955898\pi\)
−0.990417 + 0.138109i \(0.955898\pi\)
\(620\) −1.74743e6 −0.182567
\(621\) −2.21699e6 −0.230693
\(622\) 975221. 0.101071
\(623\) −1.64064e7 −1.69354
\(624\) 378111. 0.0388738
\(625\) −5.51034e6 −0.564259
\(626\) 3.60569e6 0.367750
\(627\) −1.89077e6 −0.192075
\(628\) −328300. −0.0332179
\(629\) −1.08297e7 −1.09141
\(630\) −3.16429e6 −0.317632
\(631\) −153973. −0.0153947 −0.00769735 0.999970i \(-0.502450\pi\)
−0.00769735 + 0.999970i \(0.502450\pi\)
\(632\) 9.04228e6 0.900503
\(633\) 1.14608e6 0.113686
\(634\) 6.80746e6 0.672608
\(635\) −7.18846e6 −0.707459
\(636\) −4.39081e6 −0.430429
\(637\) 5.18338e6 0.506133
\(638\) 4.85813e6 0.472517
\(639\) 3.01551e6 0.292152
\(640\) 2.47716e6 0.239058
\(641\) 8.57968e6 0.824757 0.412378 0.911013i \(-0.364698\pi\)
0.412378 + 0.911013i \(0.364698\pi\)
\(642\) −2.63321e6 −0.252144
\(643\) 1.98269e6 0.189116 0.0945578 0.995519i \(-0.469856\pi\)
0.0945578 + 0.995519i \(0.469856\pi\)
\(644\) −1.06399e7 −1.01094
\(645\) 2.73329e6 0.258694
\(646\) −5.30099e6 −0.499777
\(647\) 4.49937e6 0.422563 0.211281 0.977425i \(-0.432236\pi\)
0.211281 + 0.977425i \(0.432236\pi\)
\(648\) 1.25601e6 0.117504
\(649\) −543236. −0.0506264
\(650\) 716577. 0.0665242
\(651\) −4.53389e6 −0.419294
\(652\) −4.96112e6 −0.457047
\(653\) −1.51102e7 −1.38672 −0.693359 0.720593i \(-0.743870\pi\)
−0.693359 + 0.720593i \(0.743870\pi\)
\(654\) 5.56882e6 0.509119
\(655\) 1.13898e7 1.03732
\(656\) 2.13327e6 0.193547
\(657\) 2.62788e6 0.237516
\(658\) 3.06799e6 0.276242
\(659\) 43879.4 0.00393593 0.00196796 0.999998i \(-0.499374\pi\)
0.00196796 + 0.999998i \(0.499374\pi\)
\(660\) −1.04738e6 −0.0935932
\(661\) −1.40264e7 −1.24866 −0.624328 0.781162i \(-0.714627\pi\)
−0.624328 + 0.781162i \(0.714627\pi\)
\(662\) −1.26287e7 −1.11999
\(663\) 1.57502e6 0.139156
\(664\) −1.05717e6 −0.0930518
\(665\) −1.32616e7 −1.16290
\(666\) −3.50325e6 −0.306045
\(667\) 2.38734e7 2.07778
\(668\) −6.49620e6 −0.563272
\(669\) −8.98328e6 −0.776014
\(670\) −3.66967e6 −0.315820
\(671\) −7.94595e6 −0.681302
\(672\) 1.00237e7 0.856258
\(673\) −5.91918e6 −0.503760 −0.251880 0.967758i \(-0.581049\pi\)
−0.251880 + 0.967758i \(0.581049\pi\)
\(674\) 2.39822e6 0.203348
\(675\) 747441. 0.0631419
\(676\) 5.53699e6 0.466022
\(677\) 164350. 0.0137815 0.00689077 0.999976i \(-0.497807\pi\)
0.00689077 + 0.999976i \(0.497807\pi\)
\(678\) −1.22420e6 −0.102277
\(679\) 1.73969e7 1.44810
\(680\) −8.71040e6 −0.722381
\(681\) 9.04666e6 0.747516
\(682\) 1.45016e6 0.119386
\(683\) 1.51914e6 0.124608 0.0623042 0.998057i \(-0.480155\pi\)
0.0623042 + 0.998057i \(0.480155\pi\)
\(684\) 1.77458e6 0.145029
\(685\) 5.99432e6 0.488105
\(686\) −1.07452e7 −0.871772
\(687\) 3.27116e6 0.264430
\(688\) 1.57991e6 0.127251
\(689\) −5.28336e6 −0.423996
\(690\) 4.97354e6 0.397688
\(691\) −1.86505e7 −1.48592 −0.742962 0.669334i \(-0.766580\pi\)
−0.742962 + 0.669334i \(0.766580\pi\)
\(692\) 4.38230e6 0.347886
\(693\) −2.71753e6 −0.214952
\(694\) 1.45287e7 1.14506
\(695\) 1.30082e7 1.02154
\(696\) −1.35251e7 −1.05832
\(697\) 8.88616e6 0.692839
\(698\) 1.69098e7 1.31371
\(699\) −669977. −0.0518641
\(700\) 3.58717e6 0.276699
\(701\) −9.85850e6 −0.757733 −0.378866 0.925451i \(-0.623686\pi\)
−0.378866 + 0.925451i \(0.623686\pi\)
\(702\) 509496. 0.0390210
\(703\) −1.46822e7 −1.12048
\(704\) −4.39650e6 −0.334330
\(705\) 1.48410e6 0.112458
\(706\) −1.08939e7 −0.822569
\(707\) 1.76391e7 1.32718
\(708\) 509852. 0.0382262
\(709\) −1.64862e7 −1.23170 −0.615852 0.787862i \(-0.711188\pi\)
−0.615852 + 0.787862i \(0.711188\pi\)
\(710\) −6.76490e6 −0.503635
\(711\) 3.82597e6 0.283836
\(712\) −1.46094e7 −1.08002
\(713\) 7.12624e6 0.524973
\(714\) −7.61890e6 −0.559302
\(715\) −1.26029e6 −0.0921944
\(716\) 9.55781e6 0.696748
\(717\) −9.88742e6 −0.718266
\(718\) 7.83643e6 0.567293
\(719\) 8.27077e6 0.596656 0.298328 0.954463i \(-0.403571\pi\)
0.298328 + 0.954463i \(0.403571\pi\)
\(720\) −884777. −0.0636067
\(721\) 2.87226e7 2.05771
\(722\) 2.63244e6 0.187938
\(723\) −1.08550e6 −0.0772294
\(724\) −7.16828e6 −0.508240
\(725\) −8.04873e6 −0.568699
\(726\) −4.87875e6 −0.343532
\(727\) 2.13214e7 1.49617 0.748083 0.663605i \(-0.230974\pi\)
0.748083 + 0.663605i \(0.230974\pi\)
\(728\) 7.25325e6 0.507229
\(729\) 531441. 0.0370370
\(730\) −5.89532e6 −0.409449
\(731\) 6.58114e6 0.455520
\(732\) 7.45765e6 0.514427
\(733\) −193507. −0.0133026 −0.00665131 0.999978i \(-0.502117\pi\)
−0.00665131 + 0.999978i \(0.502117\pi\)
\(734\) −9.65115e6 −0.661209
\(735\) −1.21291e7 −0.828152
\(736\) −1.57550e7 −1.07207
\(737\) −3.15156e6 −0.213726
\(738\) 2.87454e6 0.194280
\(739\) 2.19214e7 1.47658 0.738289 0.674484i \(-0.235634\pi\)
0.738289 + 0.674484i \(0.235634\pi\)
\(740\) −8.13309e6 −0.545980
\(741\) 2.13531e6 0.142862
\(742\) 2.55573e7 1.70414
\(743\) −6.22559e6 −0.413722 −0.206861 0.978370i \(-0.566325\pi\)
−0.206861 + 0.978370i \(0.566325\pi\)
\(744\) −4.03727e6 −0.267397
\(745\) 4.70393e6 0.310506
\(746\) −1.04397e7 −0.686820
\(747\) −447309. −0.0293296
\(748\) −2.52186e6 −0.164803
\(749\) −1.58614e7 −1.03309
\(750\) −6.78747e6 −0.440610
\(751\) 3.89671e6 0.252114 0.126057 0.992023i \(-0.459768\pi\)
0.126057 + 0.992023i \(0.459768\pi\)
\(752\) 857851. 0.0553181
\(753\) 1.19831e6 0.0770161
\(754\) −5.48645e6 −0.351449
\(755\) −1.47386e7 −0.941001
\(756\) 2.55053e6 0.162303
\(757\) 1.24098e7 0.787094 0.393547 0.919304i \(-0.371248\pi\)
0.393547 + 0.919304i \(0.371248\pi\)
\(758\) 9.65898e6 0.610602
\(759\) 4.27134e6 0.269128
\(760\) −1.18090e7 −0.741616
\(761\) −7.36214e6 −0.460832 −0.230416 0.973092i \(-0.574009\pi\)
−0.230416 + 0.973092i \(0.574009\pi\)
\(762\) −5.59895e6 −0.349316
\(763\) 3.35443e7 2.08596
\(764\) −6.06379e6 −0.375847
\(765\) −3.68554e6 −0.227692
\(766\) 1.01289e7 0.623720
\(767\) 613494. 0.0376549
\(768\) 1.00430e7 0.614415
\(769\) −1.51054e7 −0.921121 −0.460561 0.887628i \(-0.652352\pi\)
−0.460561 + 0.887628i \(0.652352\pi\)
\(770\) 6.09643e6 0.370552
\(771\) 8.38875e6 0.508231
\(772\) −1.55965e7 −0.941854
\(773\) 3.12428e6 0.188062 0.0940309 0.995569i \(-0.470025\pi\)
0.0940309 + 0.995569i \(0.470025\pi\)
\(774\) 2.12890e6 0.127733
\(775\) −2.40256e6 −0.143688
\(776\) 1.54914e7 0.923497
\(777\) −2.11021e7 −1.25393
\(778\) 1.65014e7 0.977396
\(779\) 1.20473e7 0.711288
\(780\) 1.18284e6 0.0696128
\(781\) −5.80978e6 −0.340826
\(782\) 1.19752e7 0.700268
\(783\) −5.72275e6 −0.333581
\(784\) −7.01095e6 −0.407368
\(785\) 924384. 0.0535400
\(786\) 8.87130e6 0.512190
\(787\) 2.95424e7 1.70023 0.850117 0.526593i \(-0.176531\pi\)
0.850117 + 0.526593i \(0.176531\pi\)
\(788\) 5.96465e6 0.342192
\(789\) −1.49479e7 −0.854848
\(790\) −8.58306e6 −0.489299
\(791\) −7.37405e6 −0.419049
\(792\) −2.41987e6 −0.137081
\(793\) 8.97362e6 0.506739
\(794\) −1.24019e7 −0.698130
\(795\) 1.23630e7 0.693757
\(796\) −7.43658e6 −0.415997
\(797\) −1.70039e7 −0.948207 −0.474104 0.880469i \(-0.657228\pi\)
−0.474104 + 0.880469i \(0.657228\pi\)
\(798\) −1.03292e7 −0.574195
\(799\) 3.57338e6 0.198022
\(800\) 5.31166e6 0.293431
\(801\) −6.18152e6 −0.340419
\(802\) −1.79931e7 −0.987804
\(803\) −5.06297e6 −0.277087
\(804\) 2.95789e6 0.161377
\(805\) 2.99585e7 1.62941
\(806\) −1.63771e6 −0.0887973
\(807\) 6.71642e6 0.363039
\(808\) 1.57070e7 0.846380
\(809\) −3.02312e6 −0.162399 −0.0811997 0.996698i \(-0.525875\pi\)
−0.0811997 + 0.996698i \(0.525875\pi\)
\(810\) −1.19222e6 −0.0638475
\(811\) 9.96223e6 0.531869 0.265934 0.963991i \(-0.414320\pi\)
0.265934 + 0.963991i \(0.414320\pi\)
\(812\) −2.74650e7 −1.46181
\(813\) −1.65912e7 −0.880341
\(814\) 6.74949e6 0.357034
\(815\) 1.39689e7 0.736660
\(816\) −2.13035e6 −0.112002
\(817\) 8.92229e6 0.467650
\(818\) 1.31242e7 0.685785
\(819\) 3.06899e6 0.159877
\(820\) 6.67350e6 0.346592
\(821\) 3.74560e7 1.93938 0.969690 0.244337i \(-0.0785704\pi\)
0.969690 + 0.244337i \(0.0785704\pi\)
\(822\) 4.66886e6 0.241008
\(823\) 2.70732e7 1.39329 0.696643 0.717418i \(-0.254676\pi\)
0.696643 + 0.717418i \(0.254676\pi\)
\(824\) 2.55765e7 1.31227
\(825\) −1.44005e6 −0.0736617
\(826\) −2.96767e6 −0.151344
\(827\) −2.45396e7 −1.24768 −0.623841 0.781551i \(-0.714429\pi\)
−0.623841 + 0.781551i \(0.714429\pi\)
\(828\) −4.00885e6 −0.203209
\(829\) −3.73139e6 −0.188575 −0.0942876 0.995545i \(-0.530057\pi\)
−0.0942876 + 0.995545i \(0.530057\pi\)
\(830\) 1.00348e6 0.0505608
\(831\) 1.42132e7 0.713987
\(832\) 4.96511e6 0.248668
\(833\) −2.92041e7 −1.45825
\(834\) 1.01319e7 0.504399
\(835\) 1.82911e7 0.907872
\(836\) −3.41897e6 −0.169192
\(837\) −1.70825e6 −0.0842826
\(838\) 1.69812e7 0.835333
\(839\) −7.37449e6 −0.361682 −0.180841 0.983512i \(-0.557882\pi\)
−0.180841 + 0.983512i \(0.557882\pi\)
\(840\) −1.69726e7 −0.829946
\(841\) 4.11136e7 2.00445
\(842\) 2.27268e7 1.10473
\(843\) 9.89901e6 0.479759
\(844\) 2.07238e6 0.100142
\(845\) −1.55903e7 −0.751126
\(846\) 1.15594e6 0.0555275
\(847\) −2.93876e7 −1.40752
\(848\) 7.14618e6 0.341259
\(849\) 2.19246e7 1.04391
\(850\) −4.03733e6 −0.191667
\(851\) 3.31677e7 1.56997
\(852\) 5.45275e6 0.257346
\(853\) −3.00729e7 −1.41515 −0.707576 0.706637i \(-0.750211\pi\)
−0.707576 + 0.706637i \(0.750211\pi\)
\(854\) −4.34083e7 −2.03671
\(855\) −4.99662e6 −0.233755
\(856\) −1.41240e7 −0.658831
\(857\) −2.61992e7 −1.21853 −0.609265 0.792966i \(-0.708536\pi\)
−0.609265 + 0.792966i \(0.708536\pi\)
\(858\) −981614. −0.0455221
\(859\) 4.01687e6 0.185740 0.0928700 0.995678i \(-0.470396\pi\)
0.0928700 + 0.995678i \(0.470396\pi\)
\(860\) 4.94243e6 0.227874
\(861\) 1.73150e7 0.796005
\(862\) −5.99029e6 −0.274587
\(863\) 5.54567e6 0.253470 0.126735 0.991937i \(-0.459550\pi\)
0.126735 + 0.991937i \(0.459550\pi\)
\(864\) 3.77666e6 0.172117
\(865\) −1.23391e7 −0.560716
\(866\) 7.56824e6 0.342926
\(867\) 3.90475e6 0.176419
\(868\) −8.19835e6 −0.369341
\(869\) −7.37124e6 −0.331125
\(870\) 1.28383e7 0.575053
\(871\) 3.55916e6 0.158965
\(872\) 2.98700e7 1.33028
\(873\) 6.55471e6 0.291084
\(874\) 1.62351e7 0.718915
\(875\) −4.08849e7 −1.80527
\(876\) 4.75184e6 0.209219
\(877\) −1.76530e7 −0.775034 −0.387517 0.921863i \(-0.626667\pi\)
−0.387517 + 0.921863i \(0.626667\pi\)
\(878\) 1.07842e7 0.472121
\(879\) 6.26856e6 0.273650
\(880\) 1.70464e6 0.0742039
\(881\) 1.92089e7 0.833802 0.416901 0.908952i \(-0.363116\pi\)
0.416901 + 0.908952i \(0.363116\pi\)
\(882\) −9.44711e6 −0.408910
\(883\) 2.29461e6 0.0990391 0.0495195 0.998773i \(-0.484231\pi\)
0.0495195 + 0.998773i \(0.484231\pi\)
\(884\) 2.84801e6 0.122578
\(885\) −1.43557e6 −0.0616123
\(886\) −2.06815e7 −0.885109
\(887\) −2.42072e7 −1.03308 −0.516542 0.856262i \(-0.672781\pi\)
−0.516542 + 0.856262i \(0.672781\pi\)
\(888\) −1.87907e7 −0.799670
\(889\) −3.37257e7 −1.43122
\(890\) 1.38674e7 0.586842
\(891\) −1.02389e6 −0.0432076
\(892\) −1.62439e7 −0.683562
\(893\) 4.84456e6 0.203295
\(894\) 3.66380e6 0.153316
\(895\) −2.69116e7 −1.12301
\(896\) 1.16220e7 0.483625
\(897\) −4.82376e6 −0.200172
\(898\) −1.62235e7 −0.671356
\(899\) 1.83951e7 0.759106
\(900\) 1.35155e6 0.0556194
\(901\) 2.97674e7 1.22160
\(902\) −5.53820e6 −0.226648
\(903\) 1.28236e7 0.523349
\(904\) −6.56634e6 −0.267240
\(905\) 2.01835e7 0.819171
\(906\) −1.14796e7 −0.464631
\(907\) 4.34909e7 1.75542 0.877708 0.479195i \(-0.159071\pi\)
0.877708 + 0.479195i \(0.159071\pi\)
\(908\) 1.63585e7 0.658460
\(909\) 6.64595e6 0.266776
\(910\) −6.88489e6 −0.275609
\(911\) −1.85525e7 −0.740637 −0.370319 0.928905i \(-0.620752\pi\)
−0.370319 + 0.928905i \(0.620752\pi\)
\(912\) −2.88819e6 −0.114984
\(913\) 861802. 0.0342161
\(914\) 4.60664e6 0.182397
\(915\) −2.09982e7 −0.829144
\(916\) 5.91504e6 0.232927
\(917\) 5.34370e7 2.09855
\(918\) −2.87060e6 −0.112426
\(919\) −1.49752e7 −0.584904 −0.292452 0.956280i \(-0.594471\pi\)
−0.292452 + 0.956280i \(0.594471\pi\)
\(920\) 2.66770e7 1.03912
\(921\) −1.86189e7 −0.723276
\(922\) −1.13419e7 −0.439400
\(923\) 6.56118e6 0.253500
\(924\) −4.91394e6 −0.189343
\(925\) −1.11822e7 −0.429709
\(926\) 2.73024e7 1.04634
\(927\) 1.08219e7 0.413623
\(928\) −4.06685e7 −1.55020
\(929\) −3.39663e7 −1.29124 −0.645622 0.763657i \(-0.723402\pi\)
−0.645622 + 0.763657i \(0.723402\pi\)
\(930\) 3.83224e6 0.145293
\(931\) −3.95931e7 −1.49708
\(932\) −1.21148e6 −0.0456852
\(933\) 2.21329e6 0.0832404
\(934\) −3.15491e7 −1.18337
\(935\) 7.10070e6 0.265627
\(936\) 2.73283e6 0.101958
\(937\) 1.94117e7 0.722296 0.361148 0.932508i \(-0.382385\pi\)
0.361148 + 0.932508i \(0.382385\pi\)
\(938\) −1.72168e7 −0.638919
\(939\) 8.18322e6 0.302873
\(940\) 2.68361e6 0.0990602
\(941\) −3.93557e6 −0.144888 −0.0724442 0.997372i \(-0.523080\pi\)
−0.0724442 + 0.997372i \(0.523080\pi\)
\(942\) 719984. 0.0264360
\(943\) −2.72153e7 −0.996630
\(944\) −829801. −0.0303071
\(945\) −7.18143e6 −0.261596
\(946\) −4.10162e6 −0.149014
\(947\) 2.75055e7 0.996654 0.498327 0.866989i \(-0.333948\pi\)
0.498327 + 0.866989i \(0.333948\pi\)
\(948\) 6.91826e6 0.250021
\(949\) 5.71778e6 0.206092
\(950\) −5.47355e6 −0.196771
\(951\) 1.54497e7 0.553948
\(952\) −4.08662e7 −1.46141
\(953\) 1.01583e7 0.362317 0.181159 0.983454i \(-0.442015\pi\)
0.181159 + 0.983454i \(0.442015\pi\)
\(954\) 9.62933e6 0.342551
\(955\) 1.70736e7 0.605782
\(956\) −1.78788e7 −0.632694
\(957\) 1.10257e7 0.389157
\(958\) 1.01425e7 0.357050
\(959\) 2.81232e7 0.987459
\(960\) −1.16183e7 −0.406880
\(961\) −2.31382e7 −0.808204
\(962\) −7.62241e6 −0.265555
\(963\) −5.97615e6 −0.207661
\(964\) −1.96283e6 −0.0680285
\(965\) 4.39145e7 1.51806
\(966\) 2.33341e7 0.804541
\(967\) −6.62411e6 −0.227804 −0.113902 0.993492i \(-0.536335\pi\)
−0.113902 + 0.993492i \(0.536335\pi\)
\(968\) −2.61686e7 −0.897620
\(969\) −1.20307e7 −0.411607
\(970\) −1.47046e7 −0.501794
\(971\) 5.52548e7 1.88071 0.940355 0.340196i \(-0.110493\pi\)
0.940355 + 0.340196i \(0.110493\pi\)
\(972\) 960971. 0.0326246
\(973\) 6.10301e7 2.06663
\(974\) 5.01105e6 0.169251
\(975\) 1.62629e6 0.0547882
\(976\) −1.21376e7 −0.407856
\(977\) −3.42955e7 −1.14948 −0.574739 0.818337i \(-0.694896\pi\)
−0.574739 + 0.818337i \(0.694896\pi\)
\(978\) 1.08801e7 0.363735
\(979\) 1.19095e7 0.397135
\(980\) −2.19323e7 −0.729489
\(981\) 1.26386e7 0.419301
\(982\) −1.12873e7 −0.373519
\(983\) −1.09463e7 −0.361314 −0.180657 0.983546i \(-0.557822\pi\)
−0.180657 + 0.983546i \(0.557822\pi\)
\(984\) 1.54185e7 0.507637
\(985\) −1.67945e7 −0.551538
\(986\) 3.09117e7 1.01258
\(987\) 6.96288e6 0.227508
\(988\) 3.86115e6 0.125842
\(989\) −2.01558e7 −0.655254
\(990\) 2.29697e6 0.0744848
\(991\) 1.32919e7 0.429936 0.214968 0.976621i \(-0.431035\pi\)
0.214968 + 0.976621i \(0.431035\pi\)
\(992\) −1.21396e7 −0.391675
\(993\) −2.86612e7 −0.922406
\(994\) −3.17386e7 −1.01888
\(995\) 2.09389e7 0.670497
\(996\) −808842. −0.0258354
\(997\) 5.22001e7 1.66316 0.831579 0.555407i \(-0.187437\pi\)
0.831579 + 0.555407i \(0.187437\pi\)
\(998\) −1.50820e7 −0.479328
\(999\) −7.95072e6 −0.252053
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 177.6.a.d.1.6 13
3.2 odd 2 531.6.a.e.1.8 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.d.1.6 13 1.1 even 1 trivial
531.6.a.e.1.8 13 3.2 odd 2