Properties

Label 6014.2.a.k.1.7
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $0$
Dimension $37$
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] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, 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("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.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: \(48.0220317756\)
Analytic rank: \(0\)
Dimension: \(37\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.26430 q^{3} +1.00000 q^{4} -0.734715 q^{5} -2.26430 q^{6} +2.48512 q^{7} +1.00000 q^{8} +2.12704 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.26430 q^{3} +1.00000 q^{4} -0.734715 q^{5} -2.26430 q^{6} +2.48512 q^{7} +1.00000 q^{8} +2.12704 q^{9} -0.734715 q^{10} -1.69143 q^{11} -2.26430 q^{12} -0.551010 q^{13} +2.48512 q^{14} +1.66361 q^{15} +1.00000 q^{16} +2.06462 q^{17} +2.12704 q^{18} -3.61939 q^{19} -0.734715 q^{20} -5.62705 q^{21} -1.69143 q^{22} -2.35182 q^{23} -2.26430 q^{24} -4.46019 q^{25} -0.551010 q^{26} +1.97663 q^{27} +2.48512 q^{28} +1.50891 q^{29} +1.66361 q^{30} +1.00000 q^{31} +1.00000 q^{32} +3.82990 q^{33} +2.06462 q^{34} -1.82585 q^{35} +2.12704 q^{36} +3.67685 q^{37} -3.61939 q^{38} +1.24765 q^{39} -0.734715 q^{40} +8.01876 q^{41} -5.62705 q^{42} +9.97495 q^{43} -1.69143 q^{44} -1.56277 q^{45} -2.35182 q^{46} -5.71342 q^{47} -2.26430 q^{48} -0.824189 q^{49} -4.46019 q^{50} -4.67492 q^{51} -0.551010 q^{52} -6.88641 q^{53} +1.97663 q^{54} +1.24272 q^{55} +2.48512 q^{56} +8.19537 q^{57} +1.50891 q^{58} +12.3451 q^{59} +1.66361 q^{60} -2.17917 q^{61} +1.00000 q^{62} +5.28596 q^{63} +1.00000 q^{64} +0.404835 q^{65} +3.82990 q^{66} +11.2992 q^{67} +2.06462 q^{68} +5.32521 q^{69} -1.82585 q^{70} -10.1686 q^{71} +2.12704 q^{72} +7.22772 q^{73} +3.67685 q^{74} +10.0992 q^{75} -3.61939 q^{76} -4.20340 q^{77} +1.24765 q^{78} -1.00514 q^{79} -0.734715 q^{80} -10.8568 q^{81} +8.01876 q^{82} -7.93622 q^{83} -5.62705 q^{84} -1.51691 q^{85} +9.97495 q^{86} -3.41662 q^{87} -1.69143 q^{88} -15.9659 q^{89} -1.56277 q^{90} -1.36933 q^{91} -2.35182 q^{92} -2.26430 q^{93} -5.71342 q^{94} +2.65922 q^{95} -2.26430 q^{96} +1.00000 q^{97} -0.824189 q^{98} -3.59775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 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
\(3\) −2.26430 −1.30729 −0.653646 0.756800i \(-0.726762\pi\)
−0.653646 + 0.756800i \(0.726762\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.734715 −0.328574 −0.164287 0.986413i \(-0.552532\pi\)
−0.164287 + 0.986413i \(0.552532\pi\)
\(6\) −2.26430 −0.924396
\(7\) 2.48512 0.939286 0.469643 0.882856i \(-0.344383\pi\)
0.469643 + 0.882856i \(0.344383\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.12704 0.709015
\(10\) −0.734715 −0.232337
\(11\) −1.69143 −0.509985 −0.254993 0.966943i \(-0.582073\pi\)
−0.254993 + 0.966943i \(0.582073\pi\)
\(12\) −2.26430 −0.653646
\(13\) −0.551010 −0.152823 −0.0764114 0.997076i \(-0.524346\pi\)
−0.0764114 + 0.997076i \(0.524346\pi\)
\(14\) 2.48512 0.664176
\(15\) 1.66361 0.429543
\(16\) 1.00000 0.250000
\(17\) 2.06462 0.500744 0.250372 0.968150i \(-0.419447\pi\)
0.250372 + 0.968150i \(0.419447\pi\)
\(18\) 2.12704 0.501349
\(19\) −3.61939 −0.830344 −0.415172 0.909743i \(-0.636279\pi\)
−0.415172 + 0.909743i \(0.636279\pi\)
\(20\) −0.734715 −0.164287
\(21\) −5.62705 −1.22792
\(22\) −1.69143 −0.360614
\(23\) −2.35182 −0.490387 −0.245194 0.969474i \(-0.578852\pi\)
−0.245194 + 0.969474i \(0.578852\pi\)
\(24\) −2.26430 −0.462198
\(25\) −4.46019 −0.892039
\(26\) −0.551010 −0.108062
\(27\) 1.97663 0.380403
\(28\) 2.48512 0.469643
\(29\) 1.50891 0.280197 0.140099 0.990138i \(-0.455258\pi\)
0.140099 + 0.990138i \(0.455258\pi\)
\(30\) 1.66361 0.303733
\(31\) 1.00000 0.179605
\(32\) 1.00000 0.176777
\(33\) 3.82990 0.666700
\(34\) 2.06462 0.354080
\(35\) −1.82585 −0.308625
\(36\) 2.12704 0.354507
\(37\) 3.67685 0.604470 0.302235 0.953233i \(-0.402267\pi\)
0.302235 + 0.953233i \(0.402267\pi\)
\(38\) −3.61939 −0.587142
\(39\) 1.24765 0.199784
\(40\) −0.734715 −0.116169
\(41\) 8.01876 1.25232 0.626160 0.779695i \(-0.284626\pi\)
0.626160 + 0.779695i \(0.284626\pi\)
\(42\) −5.62705 −0.868272
\(43\) 9.97495 1.52117 0.760583 0.649241i \(-0.224913\pi\)
0.760583 + 0.649241i \(0.224913\pi\)
\(44\) −1.69143 −0.254993
\(45\) −1.56277 −0.232964
\(46\) −2.35182 −0.346756
\(47\) −5.71342 −0.833388 −0.416694 0.909047i \(-0.636811\pi\)
−0.416694 + 0.909047i \(0.636811\pi\)
\(48\) −2.26430 −0.326823
\(49\) −0.824189 −0.117741
\(50\) −4.46019 −0.630767
\(51\) −4.67492 −0.654620
\(52\) −0.551010 −0.0764114
\(53\) −6.88641 −0.945921 −0.472961 0.881084i \(-0.656815\pi\)
−0.472961 + 0.881084i \(0.656815\pi\)
\(54\) 1.97663 0.268986
\(55\) 1.24272 0.167568
\(56\) 2.48512 0.332088
\(57\) 8.19537 1.08550
\(58\) 1.50891 0.198129
\(59\) 12.3451 1.60720 0.803598 0.595173i \(-0.202916\pi\)
0.803598 + 0.595173i \(0.202916\pi\)
\(60\) 1.66361 0.214771
\(61\) −2.17917 −0.279015 −0.139507 0.990221i \(-0.544552\pi\)
−0.139507 + 0.990221i \(0.544552\pi\)
\(62\) 1.00000 0.127000
\(63\) 5.28596 0.665968
\(64\) 1.00000 0.125000
\(65\) 0.404835 0.0502136
\(66\) 3.82990 0.471428
\(67\) 11.2992 1.38042 0.690208 0.723611i \(-0.257519\pi\)
0.690208 + 0.723611i \(0.257519\pi\)
\(68\) 2.06462 0.250372
\(69\) 5.32521 0.641080
\(70\) −1.82585 −0.218231
\(71\) −10.1686 −1.20679 −0.603397 0.797441i \(-0.706186\pi\)
−0.603397 + 0.797441i \(0.706186\pi\)
\(72\) 2.12704 0.250675
\(73\) 7.22772 0.845941 0.422970 0.906143i \(-0.360987\pi\)
0.422970 + 0.906143i \(0.360987\pi\)
\(74\) 3.67685 0.427425
\(75\) 10.0992 1.16616
\(76\) −3.61939 −0.415172
\(77\) −4.20340 −0.479022
\(78\) 1.24765 0.141269
\(79\) −1.00514 −0.113088 −0.0565438 0.998400i \(-0.518008\pi\)
−0.0565438 + 0.998400i \(0.518008\pi\)
\(80\) −0.734715 −0.0821436
\(81\) −10.8568 −1.20631
\(82\) 8.01876 0.885523
\(83\) −7.93622 −0.871113 −0.435557 0.900161i \(-0.643448\pi\)
−0.435557 + 0.900161i \(0.643448\pi\)
\(84\) −5.62705 −0.613961
\(85\) −1.51691 −0.164532
\(86\) 9.97495 1.07563
\(87\) −3.41662 −0.366300
\(88\) −1.69143 −0.180307
\(89\) −15.9659 −1.69238 −0.846191 0.532879i \(-0.821110\pi\)
−0.846191 + 0.532879i \(0.821110\pi\)
\(90\) −1.56277 −0.164730
\(91\) −1.36933 −0.143544
\(92\) −2.35182 −0.245194
\(93\) −2.26430 −0.234797
\(94\) −5.71342 −0.589294
\(95\) 2.65922 0.272830
\(96\) −2.26430 −0.231099
\(97\) 1.00000 0.101535
\(98\) −0.824189 −0.0832557
\(99\) −3.59775 −0.361587
\(100\) −4.46019 −0.446019
\(101\) −4.25993 −0.423879 −0.211940 0.977283i \(-0.567978\pi\)
−0.211940 + 0.977283i \(0.567978\pi\)
\(102\) −4.67492 −0.462886
\(103\) 16.2402 1.60019 0.800095 0.599873i \(-0.204782\pi\)
0.800095 + 0.599873i \(0.204782\pi\)
\(104\) −0.551010 −0.0540310
\(105\) 4.13427 0.403464
\(106\) −6.88641 −0.668867
\(107\) −5.63670 −0.544921 −0.272460 0.962167i \(-0.587837\pi\)
−0.272460 + 0.962167i \(0.587837\pi\)
\(108\) 1.97663 0.190202
\(109\) 16.1521 1.54710 0.773548 0.633738i \(-0.218480\pi\)
0.773548 + 0.633738i \(0.218480\pi\)
\(110\) 1.24272 0.118489
\(111\) −8.32548 −0.790219
\(112\) 2.48512 0.234822
\(113\) 13.5424 1.27396 0.636979 0.770881i \(-0.280184\pi\)
0.636979 + 0.770881i \(0.280184\pi\)
\(114\) 8.19537 0.767567
\(115\) 1.72791 0.161129
\(116\) 1.50891 0.140099
\(117\) −1.17202 −0.108354
\(118\) 12.3451 1.13646
\(119\) 5.13083 0.470342
\(120\) 1.66361 0.151866
\(121\) −8.13907 −0.739915
\(122\) −2.17917 −0.197293
\(123\) −18.1569 −1.63715
\(124\) 1.00000 0.0898027
\(125\) 6.95054 0.621675
\(126\) 5.28596 0.470910
\(127\) −8.01759 −0.711446 −0.355723 0.934591i \(-0.615765\pi\)
−0.355723 + 0.934591i \(0.615765\pi\)
\(128\) 1.00000 0.0883883
\(129\) −22.5863 −1.98861
\(130\) 0.404835 0.0355064
\(131\) 12.8938 1.12654 0.563270 0.826273i \(-0.309543\pi\)
0.563270 + 0.826273i \(0.309543\pi\)
\(132\) 3.82990 0.333350
\(133\) −8.99460 −0.779931
\(134\) 11.2992 0.976102
\(135\) −1.45226 −0.124991
\(136\) 2.06462 0.177040
\(137\) 5.41363 0.462518 0.231259 0.972892i \(-0.425716\pi\)
0.231259 + 0.972892i \(0.425716\pi\)
\(138\) 5.32521 0.453312
\(139\) −8.79368 −0.745870 −0.372935 0.927857i \(-0.621649\pi\)
−0.372935 + 0.927857i \(0.621649\pi\)
\(140\) −1.82585 −0.154313
\(141\) 12.9369 1.08948
\(142\) −10.1686 −0.853332
\(143\) 0.931995 0.0779374
\(144\) 2.12704 0.177254
\(145\) −1.10862 −0.0920657
\(146\) 7.22772 0.598171
\(147\) 1.86621 0.153922
\(148\) 3.67685 0.302235
\(149\) 12.9405 1.06013 0.530063 0.847959i \(-0.322168\pi\)
0.530063 + 0.847959i \(0.322168\pi\)
\(150\) 10.0992 0.824597
\(151\) 5.39464 0.439010 0.219505 0.975611i \(-0.429556\pi\)
0.219505 + 0.975611i \(0.429556\pi\)
\(152\) −3.61939 −0.293571
\(153\) 4.39154 0.355035
\(154\) −4.20340 −0.338720
\(155\) −0.734715 −0.0590137
\(156\) 1.24765 0.0998921
\(157\) −13.0968 −1.04524 −0.522620 0.852566i \(-0.675045\pi\)
−0.522620 + 0.852566i \(0.675045\pi\)
\(158\) −1.00514 −0.0799650
\(159\) 15.5929 1.23660
\(160\) −0.734715 −0.0580843
\(161\) −5.84454 −0.460614
\(162\) −10.8568 −0.852992
\(163\) 17.8728 1.39991 0.699954 0.714188i \(-0.253204\pi\)
0.699954 + 0.714188i \(0.253204\pi\)
\(164\) 8.01876 0.626160
\(165\) −2.81388 −0.219061
\(166\) −7.93622 −0.615970
\(167\) 4.33885 0.335750 0.167875 0.985808i \(-0.446309\pi\)
0.167875 + 0.985808i \(0.446309\pi\)
\(168\) −5.62705 −0.434136
\(169\) −12.6964 −0.976645
\(170\) −1.51691 −0.116342
\(171\) −7.69859 −0.588726
\(172\) 9.97495 0.760583
\(173\) 8.05772 0.612617 0.306309 0.951932i \(-0.400906\pi\)
0.306309 + 0.951932i \(0.400906\pi\)
\(174\) −3.41662 −0.259013
\(175\) −11.0841 −0.837880
\(176\) −1.69143 −0.127496
\(177\) −27.9530 −2.10108
\(178\) −15.9659 −1.19670
\(179\) −13.7709 −1.02929 −0.514643 0.857405i \(-0.672075\pi\)
−0.514643 + 0.857405i \(0.672075\pi\)
\(180\) −1.56277 −0.116482
\(181\) 14.8883 1.10664 0.553321 0.832968i \(-0.313360\pi\)
0.553321 + 0.832968i \(0.313360\pi\)
\(182\) −1.36933 −0.101501
\(183\) 4.93430 0.364754
\(184\) −2.35182 −0.173378
\(185\) −2.70143 −0.198613
\(186\) −2.26430 −0.166026
\(187\) −3.49216 −0.255372
\(188\) −5.71342 −0.416694
\(189\) 4.91216 0.357307
\(190\) 2.65922 0.192920
\(191\) 18.0903 1.30897 0.654483 0.756077i \(-0.272886\pi\)
0.654483 + 0.756077i \(0.272886\pi\)
\(192\) −2.26430 −0.163412
\(193\) −3.00761 −0.216493 −0.108246 0.994124i \(-0.534524\pi\)
−0.108246 + 0.994124i \(0.534524\pi\)
\(194\) 1.00000 0.0717958
\(195\) −0.916668 −0.0656439
\(196\) −0.824189 −0.0588707
\(197\) 14.9505 1.06518 0.532589 0.846374i \(-0.321219\pi\)
0.532589 + 0.846374i \(0.321219\pi\)
\(198\) −3.59775 −0.255681
\(199\) 14.2779 1.01213 0.506066 0.862495i \(-0.331099\pi\)
0.506066 + 0.862495i \(0.331099\pi\)
\(200\) −4.46019 −0.315383
\(201\) −25.5847 −1.80461
\(202\) −4.25993 −0.299728
\(203\) 3.74982 0.263186
\(204\) −4.67492 −0.327310
\(205\) −5.89150 −0.411480
\(206\) 16.2402 1.13151
\(207\) −5.00241 −0.347692
\(208\) −0.551010 −0.0382057
\(209\) 6.12194 0.423463
\(210\) 4.13427 0.285292
\(211\) 14.1715 0.975607 0.487803 0.872954i \(-0.337798\pi\)
0.487803 + 0.872954i \(0.337798\pi\)
\(212\) −6.88641 −0.472961
\(213\) 23.0248 1.57763
\(214\) −5.63670 −0.385317
\(215\) −7.32874 −0.499816
\(216\) 1.97663 0.134493
\(217\) 2.48512 0.168701
\(218\) 16.1521 1.09396
\(219\) −16.3657 −1.10589
\(220\) 1.24272 0.0837840
\(221\) −1.13763 −0.0765252
\(222\) −8.32548 −0.558769
\(223\) 13.0320 0.872688 0.436344 0.899780i \(-0.356273\pi\)
0.436344 + 0.899780i \(0.356273\pi\)
\(224\) 2.48512 0.166044
\(225\) −9.48703 −0.632469
\(226\) 13.5424 0.900824
\(227\) 11.7044 0.776847 0.388423 0.921481i \(-0.373020\pi\)
0.388423 + 0.921481i \(0.373020\pi\)
\(228\) 8.19537 0.542752
\(229\) −0.805815 −0.0532497 −0.0266249 0.999645i \(-0.508476\pi\)
−0.0266249 + 0.999645i \(0.508476\pi\)
\(230\) 1.72791 0.113935
\(231\) 9.51775 0.626222
\(232\) 1.50891 0.0990647
\(233\) 0.944506 0.0618766 0.0309383 0.999521i \(-0.490150\pi\)
0.0309383 + 0.999521i \(0.490150\pi\)
\(234\) −1.17202 −0.0766176
\(235\) 4.19773 0.273830
\(236\) 12.3451 0.803598
\(237\) 2.27595 0.147839
\(238\) 5.13083 0.332582
\(239\) 8.91165 0.576447 0.288223 0.957563i \(-0.406935\pi\)
0.288223 + 0.957563i \(0.406935\pi\)
\(240\) 1.66361 0.107386
\(241\) −14.8210 −0.954703 −0.477351 0.878712i \(-0.658403\pi\)
−0.477351 + 0.878712i \(0.658403\pi\)
\(242\) −8.13907 −0.523199
\(243\) 18.6532 1.19660
\(244\) −2.17917 −0.139507
\(245\) 0.605544 0.0386868
\(246\) −18.1569 −1.15764
\(247\) 1.99432 0.126896
\(248\) 1.00000 0.0635001
\(249\) 17.9700 1.13880
\(250\) 6.95054 0.439591
\(251\) −14.0381 −0.886078 −0.443039 0.896502i \(-0.646100\pi\)
−0.443039 + 0.896502i \(0.646100\pi\)
\(252\) 5.28596 0.332984
\(253\) 3.97793 0.250090
\(254\) −8.01759 −0.503069
\(255\) 3.43473 0.215091
\(256\) 1.00000 0.0625000
\(257\) 25.9997 1.62182 0.810909 0.585173i \(-0.198973\pi\)
0.810909 + 0.585173i \(0.198973\pi\)
\(258\) −22.5863 −1.40616
\(259\) 9.13740 0.567770
\(260\) 0.404835 0.0251068
\(261\) 3.20952 0.198664
\(262\) 12.8938 0.796584
\(263\) 4.08567 0.251933 0.125967 0.992034i \(-0.459797\pi\)
0.125967 + 0.992034i \(0.459797\pi\)
\(264\) 3.82990 0.235714
\(265\) 5.05955 0.310805
\(266\) −8.99460 −0.551494
\(267\) 36.1516 2.21244
\(268\) 11.2992 0.690208
\(269\) 23.1887 1.41384 0.706921 0.707292i \(-0.250083\pi\)
0.706921 + 0.707292i \(0.250083\pi\)
\(270\) −1.45226 −0.0883818
\(271\) 16.9915 1.03216 0.516079 0.856541i \(-0.327391\pi\)
0.516079 + 0.856541i \(0.327391\pi\)
\(272\) 2.06462 0.125186
\(273\) 3.10056 0.187655
\(274\) 5.41363 0.327049
\(275\) 7.54411 0.454927
\(276\) 5.32521 0.320540
\(277\) 31.3698 1.88483 0.942414 0.334448i \(-0.108550\pi\)
0.942414 + 0.334448i \(0.108550\pi\)
\(278\) −8.79368 −0.527410
\(279\) 2.12704 0.127343
\(280\) −1.82585 −0.109116
\(281\) −0.0450013 −0.00268455 −0.00134228 0.999999i \(-0.500427\pi\)
−0.00134228 + 0.999999i \(0.500427\pi\)
\(282\) 12.9369 0.770380
\(283\) −8.52415 −0.506708 −0.253354 0.967374i \(-0.581534\pi\)
−0.253354 + 0.967374i \(0.581534\pi\)
\(284\) −10.1686 −0.603397
\(285\) −6.02126 −0.356668
\(286\) 0.931995 0.0551100
\(287\) 19.9276 1.17629
\(288\) 2.12704 0.125337
\(289\) −12.7373 −0.749255
\(290\) −1.10862 −0.0651003
\(291\) −2.26430 −0.132735
\(292\) 7.22772 0.422970
\(293\) 25.6664 1.49945 0.749723 0.661751i \(-0.230187\pi\)
0.749723 + 0.661751i \(0.230187\pi\)
\(294\) 1.86621 0.108840
\(295\) −9.07013 −0.528083
\(296\) 3.67685 0.213712
\(297\) −3.34333 −0.194000
\(298\) 12.9405 0.749622
\(299\) 1.29587 0.0749424
\(300\) 10.0992 0.583078
\(301\) 24.7889 1.42881
\(302\) 5.39464 0.310427
\(303\) 9.64576 0.554134
\(304\) −3.61939 −0.207586
\(305\) 1.60107 0.0916770
\(306\) 4.39154 0.251048
\(307\) 30.2135 1.72438 0.862188 0.506589i \(-0.169094\pi\)
0.862188 + 0.506589i \(0.169094\pi\)
\(308\) −4.20340 −0.239511
\(309\) −36.7726 −2.09192
\(310\) −0.734715 −0.0417290
\(311\) 4.18663 0.237402 0.118701 0.992930i \(-0.462127\pi\)
0.118701 + 0.992930i \(0.462127\pi\)
\(312\) 1.24765 0.0706344
\(313\) 16.5081 0.933092 0.466546 0.884497i \(-0.345498\pi\)
0.466546 + 0.884497i \(0.345498\pi\)
\(314\) −13.0968 −0.739096
\(315\) −3.88367 −0.218820
\(316\) −1.00514 −0.0565438
\(317\) −34.2036 −1.92107 −0.960533 0.278166i \(-0.910274\pi\)
−0.960533 + 0.278166i \(0.910274\pi\)
\(318\) 15.5929 0.874406
\(319\) −2.55221 −0.142897
\(320\) −0.734715 −0.0410718
\(321\) 12.7632 0.712371
\(322\) −5.84454 −0.325703
\(323\) −7.47267 −0.415790
\(324\) −10.8568 −0.603156
\(325\) 2.45761 0.136324
\(326\) 17.8728 0.989885
\(327\) −36.5733 −2.02251
\(328\) 8.01876 0.442762
\(329\) −14.1985 −0.782790
\(330\) −2.81388 −0.154899
\(331\) 2.68074 0.147347 0.0736733 0.997282i \(-0.476528\pi\)
0.0736733 + 0.997282i \(0.476528\pi\)
\(332\) −7.93622 −0.435557
\(333\) 7.82081 0.428578
\(334\) 4.33885 0.237411
\(335\) −8.30168 −0.453569
\(336\) −5.62705 −0.306981
\(337\) −8.21743 −0.447632 −0.223816 0.974631i \(-0.571851\pi\)
−0.223816 + 0.974631i \(0.571851\pi\)
\(338\) −12.6964 −0.690592
\(339\) −30.6639 −1.66544
\(340\) −1.51691 −0.0822659
\(341\) −1.69143 −0.0915960
\(342\) −7.69859 −0.416292
\(343\) −19.4440 −1.04988
\(344\) 9.97495 0.537813
\(345\) −3.91251 −0.210642
\(346\) 8.05772 0.433186
\(347\) −15.2480 −0.818553 −0.409277 0.912410i \(-0.634219\pi\)
−0.409277 + 0.912410i \(0.634219\pi\)
\(348\) −3.41662 −0.183150
\(349\) 24.0297 1.28628 0.643141 0.765748i \(-0.277631\pi\)
0.643141 + 0.765748i \(0.277631\pi\)
\(350\) −11.0841 −0.592471
\(351\) −1.08914 −0.0581343
\(352\) −1.69143 −0.0901535
\(353\) −15.7063 −0.835961 −0.417980 0.908456i \(-0.637262\pi\)
−0.417980 + 0.908456i \(0.637262\pi\)
\(354\) −27.9530 −1.48568
\(355\) 7.47104 0.396521
\(356\) −15.9659 −0.846191
\(357\) −11.6177 −0.614875
\(358\) −13.7709 −0.727815
\(359\) 24.8295 1.31045 0.655225 0.755434i \(-0.272574\pi\)
0.655225 + 0.755434i \(0.272574\pi\)
\(360\) −1.56277 −0.0823652
\(361\) −5.90004 −0.310529
\(362\) 14.8883 0.782513
\(363\) 18.4293 0.967286
\(364\) −1.36933 −0.0717722
\(365\) −5.31031 −0.277954
\(366\) 4.93430 0.257920
\(367\) −23.1779 −1.20988 −0.604939 0.796272i \(-0.706802\pi\)
−0.604939 + 0.796272i \(0.706802\pi\)
\(368\) −2.35182 −0.122597
\(369\) 17.0562 0.887913
\(370\) −2.70143 −0.140441
\(371\) −17.1135 −0.888491
\(372\) −2.26430 −0.117398
\(373\) −10.3221 −0.534456 −0.267228 0.963633i \(-0.586108\pi\)
−0.267228 + 0.963633i \(0.586108\pi\)
\(374\) −3.49216 −0.180575
\(375\) −15.7381 −0.812712
\(376\) −5.71342 −0.294647
\(377\) −0.831425 −0.0428205
\(378\) 4.91216 0.252654
\(379\) 23.0561 1.18431 0.592155 0.805824i \(-0.298277\pi\)
0.592155 + 0.805824i \(0.298277\pi\)
\(380\) 2.65922 0.136415
\(381\) 18.1542 0.930069
\(382\) 18.0903 0.925578
\(383\) −4.03493 −0.206175 −0.103088 0.994672i \(-0.532872\pi\)
−0.103088 + 0.994672i \(0.532872\pi\)
\(384\) −2.26430 −0.115549
\(385\) 3.08830 0.157394
\(386\) −3.00761 −0.153084
\(387\) 21.2172 1.07853
\(388\) 1.00000 0.0507673
\(389\) 3.15696 0.160064 0.0800321 0.996792i \(-0.474498\pi\)
0.0800321 + 0.996792i \(0.474498\pi\)
\(390\) −0.916668 −0.0464173
\(391\) −4.85561 −0.245559
\(392\) −0.824189 −0.0416278
\(393\) −29.1955 −1.47272
\(394\) 14.9505 0.753195
\(395\) 0.738495 0.0371577
\(396\) −3.59775 −0.180794
\(397\) −12.5824 −0.631491 −0.315745 0.948844i \(-0.602255\pi\)
−0.315745 + 0.948844i \(0.602255\pi\)
\(398\) 14.2779 0.715685
\(399\) 20.3665 1.01960
\(400\) −4.46019 −0.223010
\(401\) −7.57778 −0.378416 −0.189208 0.981937i \(-0.560592\pi\)
−0.189208 + 0.981937i \(0.560592\pi\)
\(402\) −25.5847 −1.27605
\(403\) −0.551010 −0.0274478
\(404\) −4.25993 −0.211940
\(405\) 7.97666 0.396363
\(406\) 3.74982 0.186100
\(407\) −6.21913 −0.308271
\(408\) −4.67492 −0.231443
\(409\) −8.60124 −0.425304 −0.212652 0.977128i \(-0.568210\pi\)
−0.212652 + 0.977128i \(0.568210\pi\)
\(410\) −5.89150 −0.290960
\(411\) −12.2581 −0.604646
\(412\) 16.2402 0.800095
\(413\) 30.6790 1.50962
\(414\) −5.00241 −0.245855
\(415\) 5.83086 0.286226
\(416\) −0.551010 −0.0270155
\(417\) 19.9115 0.975071
\(418\) 6.12194 0.299434
\(419\) 33.9778 1.65992 0.829962 0.557820i \(-0.188362\pi\)
0.829962 + 0.557820i \(0.188362\pi\)
\(420\) 4.13427 0.201732
\(421\) −11.5606 −0.563427 −0.281714 0.959499i \(-0.590903\pi\)
−0.281714 + 0.959499i \(0.590903\pi\)
\(422\) 14.1715 0.689858
\(423\) −12.1527 −0.590884
\(424\) −6.88641 −0.334434
\(425\) −9.20862 −0.446684
\(426\) 23.0248 1.11555
\(427\) −5.41550 −0.262075
\(428\) −5.63670 −0.272460
\(429\) −2.11031 −0.101887
\(430\) −7.32874 −0.353423
\(431\) 20.5775 0.991181 0.495591 0.868556i \(-0.334952\pi\)
0.495591 + 0.868556i \(0.334952\pi\)
\(432\) 1.97663 0.0951008
\(433\) 21.6847 1.04210 0.521049 0.853527i \(-0.325541\pi\)
0.521049 + 0.853527i \(0.325541\pi\)
\(434\) 2.48512 0.119289
\(435\) 2.51024 0.120357
\(436\) 16.1521 0.773548
\(437\) 8.51213 0.407190
\(438\) −16.3657 −0.781984
\(439\) −0.185278 −0.00884285 −0.00442142 0.999990i \(-0.501407\pi\)
−0.00442142 + 0.999990i \(0.501407\pi\)
\(440\) 1.24272 0.0592443
\(441\) −1.75309 −0.0834803
\(442\) −1.13763 −0.0541115
\(443\) 0.880293 0.0418240 0.0209120 0.999781i \(-0.493343\pi\)
0.0209120 + 0.999781i \(0.493343\pi\)
\(444\) −8.32548 −0.395110
\(445\) 11.7304 0.556074
\(446\) 13.0320 0.617084
\(447\) −29.3011 −1.38589
\(448\) 2.48512 0.117411
\(449\) 29.5313 1.39367 0.696833 0.717233i \(-0.254592\pi\)
0.696833 + 0.717233i \(0.254592\pi\)
\(450\) −9.48703 −0.447223
\(451\) −13.5632 −0.638664
\(452\) 13.5424 0.636979
\(453\) −12.2151 −0.573914
\(454\) 11.7044 0.549314
\(455\) 1.00606 0.0471650
\(456\) 8.19537 0.383783
\(457\) −28.1549 −1.31703 −0.658514 0.752568i \(-0.728815\pi\)
−0.658514 + 0.752568i \(0.728815\pi\)
\(458\) −0.805815 −0.0376533
\(459\) 4.08100 0.190485
\(460\) 1.72791 0.0805644
\(461\) −15.2922 −0.712230 −0.356115 0.934442i \(-0.615899\pi\)
−0.356115 + 0.934442i \(0.615899\pi\)
\(462\) 9.51775 0.442806
\(463\) 8.84392 0.411012 0.205506 0.978656i \(-0.434116\pi\)
0.205506 + 0.978656i \(0.434116\pi\)
\(464\) 1.50891 0.0700493
\(465\) 1.66361 0.0771482
\(466\) 0.944506 0.0437534
\(467\) −5.75283 −0.266209 −0.133105 0.991102i \(-0.542495\pi\)
−0.133105 + 0.991102i \(0.542495\pi\)
\(468\) −1.17202 −0.0541768
\(469\) 28.0798 1.29661
\(470\) 4.19773 0.193627
\(471\) 29.6551 1.36643
\(472\) 12.3451 0.568230
\(473\) −16.8719 −0.775772
\(474\) 2.27595 0.104538
\(475\) 16.1432 0.740699
\(476\) 5.13083 0.235171
\(477\) −14.6477 −0.670672
\(478\) 8.91165 0.407609
\(479\) −29.9180 −1.36699 −0.683495 0.729955i \(-0.739541\pi\)
−0.683495 + 0.729955i \(0.739541\pi\)
\(480\) 1.66361 0.0759332
\(481\) −2.02598 −0.0923768
\(482\) −14.8210 −0.675077
\(483\) 13.2338 0.602158
\(484\) −8.13907 −0.369958
\(485\) −0.734715 −0.0333617
\(486\) 18.6532 0.846125
\(487\) 9.40494 0.426178 0.213089 0.977033i \(-0.431647\pi\)
0.213089 + 0.977033i \(0.431647\pi\)
\(488\) −2.17917 −0.0986465
\(489\) −40.4694 −1.83009
\(490\) 0.605544 0.0273557
\(491\) −38.5146 −1.73814 −0.869069 0.494691i \(-0.835281\pi\)
−0.869069 + 0.494691i \(0.835281\pi\)
\(492\) −18.1569 −0.818574
\(493\) 3.11533 0.140307
\(494\) 1.99432 0.0897287
\(495\) 2.64332 0.118808
\(496\) 1.00000 0.0449013
\(497\) −25.2702 −1.13352
\(498\) 17.9700 0.805253
\(499\) 29.8674 1.33705 0.668525 0.743690i \(-0.266926\pi\)
0.668525 + 0.743690i \(0.266926\pi\)
\(500\) 6.95054 0.310838
\(501\) −9.82445 −0.438924
\(502\) −14.0381 −0.626552
\(503\) −14.5502 −0.648763 −0.324382 0.945926i \(-0.605156\pi\)
−0.324382 + 0.945926i \(0.605156\pi\)
\(504\) 5.28596 0.235455
\(505\) 3.12984 0.139276
\(506\) 3.97793 0.176841
\(507\) 28.7484 1.27676
\(508\) −8.01759 −0.355723
\(509\) 0.623508 0.0276365 0.0138183 0.999905i \(-0.495601\pi\)
0.0138183 + 0.999905i \(0.495601\pi\)
\(510\) 3.43473 0.152092
\(511\) 17.9617 0.794581
\(512\) 1.00000 0.0441942
\(513\) −7.15420 −0.315865
\(514\) 25.9997 1.14680
\(515\) −11.9319 −0.525781
\(516\) −22.5863 −0.994305
\(517\) 9.66385 0.425016
\(518\) 9.13740 0.401474
\(519\) −18.2451 −0.800870
\(520\) 0.404835 0.0177532
\(521\) 27.8599 1.22056 0.610282 0.792184i \(-0.291056\pi\)
0.610282 + 0.792184i \(0.291056\pi\)
\(522\) 3.20952 0.140477
\(523\) 26.4855 1.15813 0.579065 0.815281i \(-0.303418\pi\)
0.579065 + 0.815281i \(0.303418\pi\)
\(524\) 12.8938 0.563270
\(525\) 25.0977 1.09535
\(526\) 4.08567 0.178144
\(527\) 2.06462 0.0899364
\(528\) 3.82990 0.166675
\(529\) −17.4690 −0.759520
\(530\) 5.05955 0.219773
\(531\) 26.2586 1.13953
\(532\) −8.99460 −0.389965
\(533\) −4.41842 −0.191383
\(534\) 36.1516 1.56443
\(535\) 4.14137 0.179047
\(536\) 11.2992 0.488051
\(537\) 31.1814 1.34558
\(538\) 23.1887 0.999738
\(539\) 1.39406 0.0600463
\(540\) −1.45226 −0.0624953
\(541\) −33.9847 −1.46112 −0.730558 0.682851i \(-0.760740\pi\)
−0.730558 + 0.682851i \(0.760740\pi\)
\(542\) 16.9915 0.729846
\(543\) −33.7116 −1.44670
\(544\) 2.06462 0.0885199
\(545\) −11.8672 −0.508336
\(546\) 3.10056 0.132692
\(547\) −24.0639 −1.02890 −0.514449 0.857521i \(-0.672004\pi\)
−0.514449 + 0.857521i \(0.672004\pi\)
\(548\) 5.41363 0.231259
\(549\) −4.63520 −0.197825
\(550\) 7.54411 0.321682
\(551\) −5.46132 −0.232660
\(552\) 5.32521 0.226656
\(553\) −2.49790 −0.106222
\(554\) 31.3698 1.33277
\(555\) 6.11685 0.259646
\(556\) −8.79368 −0.372935
\(557\) −33.3480 −1.41300 −0.706501 0.707712i \(-0.749727\pi\)
−0.706501 + 0.707712i \(0.749727\pi\)
\(558\) 2.12704 0.0900450
\(559\) −5.49630 −0.232469
\(560\) −1.82585 −0.0771563
\(561\) 7.90730 0.333846
\(562\) −0.0450013 −0.00189827
\(563\) 18.6596 0.786408 0.393204 0.919451i \(-0.371367\pi\)
0.393204 + 0.919451i \(0.371367\pi\)
\(564\) 12.9369 0.544741
\(565\) −9.94976 −0.418590
\(566\) −8.52415 −0.358297
\(567\) −26.9805 −1.13307
\(568\) −10.1686 −0.426666
\(569\) 5.48240 0.229834 0.114917 0.993375i \(-0.463340\pi\)
0.114917 + 0.993375i \(0.463340\pi\)
\(570\) −6.02126 −0.252203
\(571\) 20.4642 0.856399 0.428200 0.903684i \(-0.359148\pi\)
0.428200 + 0.903684i \(0.359148\pi\)
\(572\) 0.931995 0.0389687
\(573\) −40.9617 −1.71120
\(574\) 19.9276 0.831760
\(575\) 10.4896 0.437445
\(576\) 2.12704 0.0886268
\(577\) 16.0086 0.666445 0.333222 0.942848i \(-0.391864\pi\)
0.333222 + 0.942848i \(0.391864\pi\)
\(578\) −12.7373 −0.529803
\(579\) 6.81014 0.283020
\(580\) −1.10862 −0.0460328
\(581\) −19.7224 −0.818225
\(582\) −2.26430 −0.0938582
\(583\) 11.6479 0.482406
\(584\) 7.22772 0.299085
\(585\) 0.861103 0.0356022
\(586\) 25.6664 1.06027
\(587\) 9.45334 0.390181 0.195091 0.980785i \(-0.437500\pi\)
0.195091 + 0.980785i \(0.437500\pi\)
\(588\) 1.86621 0.0769612
\(589\) −3.61939 −0.149134
\(590\) −9.07013 −0.373411
\(591\) −33.8523 −1.39250
\(592\) 3.67685 0.151117
\(593\) 22.7369 0.933694 0.466847 0.884338i \(-0.345390\pi\)
0.466847 + 0.884338i \(0.345390\pi\)
\(594\) −3.34333 −0.137179
\(595\) −3.76970 −0.154542
\(596\) 12.9405 0.530063
\(597\) −32.3294 −1.32315
\(598\) 1.29587 0.0529923
\(599\) 7.73999 0.316247 0.158124 0.987419i \(-0.449456\pi\)
0.158124 + 0.987419i \(0.449456\pi\)
\(600\) 10.0992 0.412298
\(601\) −24.1112 −0.983515 −0.491758 0.870732i \(-0.663645\pi\)
−0.491758 + 0.870732i \(0.663645\pi\)
\(602\) 24.7889 1.01032
\(603\) 24.0339 0.978735
\(604\) 5.39464 0.219505
\(605\) 5.97989 0.243117
\(606\) 9.64576 0.391832
\(607\) 38.8537 1.57702 0.788512 0.615019i \(-0.210852\pi\)
0.788512 + 0.615019i \(0.210852\pi\)
\(608\) −3.61939 −0.146785
\(609\) −8.49070 −0.344061
\(610\) 1.60107 0.0648254
\(611\) 3.14815 0.127361
\(612\) 4.39154 0.177518
\(613\) 0.713440 0.0288156 0.0144078 0.999896i \(-0.495414\pi\)
0.0144078 + 0.999896i \(0.495414\pi\)
\(614\) 30.2135 1.21932
\(615\) 13.3401 0.537925
\(616\) −4.20340 −0.169360
\(617\) −48.1952 −1.94027 −0.970133 0.242572i \(-0.922009\pi\)
−0.970133 + 0.242572i \(0.922009\pi\)
\(618\) −36.7726 −1.47921
\(619\) −15.6590 −0.629388 −0.314694 0.949193i \(-0.601902\pi\)
−0.314694 + 0.949193i \(0.601902\pi\)
\(620\) −0.734715 −0.0295068
\(621\) −4.64867 −0.186545
\(622\) 4.18663 0.167868
\(623\) −39.6772 −1.58963
\(624\) 1.24765 0.0499460
\(625\) 17.1943 0.687772
\(626\) 16.5081 0.659796
\(627\) −13.8619 −0.553590
\(628\) −13.0968 −0.522620
\(629\) 7.59130 0.302685
\(630\) −3.88367 −0.154729
\(631\) −39.7457 −1.58225 −0.791125 0.611654i \(-0.790505\pi\)
−0.791125 + 0.611654i \(0.790505\pi\)
\(632\) −1.00514 −0.0399825
\(633\) −32.0885 −1.27540
\(634\) −34.2036 −1.35840
\(635\) 5.89064 0.233763
\(636\) 15.5929 0.618298
\(637\) 0.454137 0.0179936
\(638\) −2.55221 −0.101043
\(639\) −21.6291 −0.855634
\(640\) −0.734715 −0.0290421
\(641\) −10.5816 −0.417949 −0.208975 0.977921i \(-0.567013\pi\)
−0.208975 + 0.977921i \(0.567013\pi\)
\(642\) 12.7632 0.503722
\(643\) 34.9093 1.37669 0.688344 0.725384i \(-0.258338\pi\)
0.688344 + 0.725384i \(0.258338\pi\)
\(644\) −5.84454 −0.230307
\(645\) 16.5945 0.653406
\(646\) −7.47267 −0.294008
\(647\) −38.5462 −1.51541 −0.757704 0.652599i \(-0.773679\pi\)
−0.757704 + 0.652599i \(0.773679\pi\)
\(648\) −10.8568 −0.426496
\(649\) −20.8809 −0.819646
\(650\) 2.45761 0.0963955
\(651\) −5.62705 −0.220541
\(652\) 17.8728 0.699954
\(653\) −39.9980 −1.56524 −0.782621 0.622499i \(-0.786118\pi\)
−0.782621 + 0.622499i \(0.786118\pi\)
\(654\) −36.5733 −1.43013
\(655\) −9.47329 −0.370152
\(656\) 8.01876 0.313080
\(657\) 15.3737 0.599785
\(658\) −14.1985 −0.553516
\(659\) 47.8018 1.86210 0.931048 0.364897i \(-0.118896\pi\)
0.931048 + 0.364897i \(0.118896\pi\)
\(660\) −2.81388 −0.109530
\(661\) 18.0889 0.703576 0.351788 0.936080i \(-0.385574\pi\)
0.351788 + 0.936080i \(0.385574\pi\)
\(662\) 2.68074 0.104190
\(663\) 2.57593 0.100041
\(664\) −7.93622 −0.307985
\(665\) 6.60846 0.256265
\(666\) 7.82081 0.303050
\(667\) −3.54868 −0.137405
\(668\) 4.33885 0.167875
\(669\) −29.5084 −1.14086
\(670\) −8.30168 −0.320722
\(671\) 3.68592 0.142293
\(672\) −5.62705 −0.217068
\(673\) 28.9438 1.11570 0.557850 0.829942i \(-0.311626\pi\)
0.557850 + 0.829942i \(0.311626\pi\)
\(674\) −8.21743 −0.316524
\(675\) −8.81616 −0.339334
\(676\) −12.6964 −0.488323
\(677\) 13.5748 0.521723 0.260861 0.965376i \(-0.415993\pi\)
0.260861 + 0.965376i \(0.415993\pi\)
\(678\) −30.6639 −1.17764
\(679\) 2.48512 0.0953701
\(680\) −1.51691 −0.0581708
\(681\) −26.5022 −1.01557
\(682\) −1.69143 −0.0647682
\(683\) 47.3732 1.81269 0.906343 0.422543i \(-0.138862\pi\)
0.906343 + 0.422543i \(0.138862\pi\)
\(684\) −7.69859 −0.294363
\(685\) −3.97747 −0.151971
\(686\) −19.4440 −0.742377
\(687\) 1.82460 0.0696130
\(688\) 9.97495 0.380291
\(689\) 3.79448 0.144558
\(690\) −3.91251 −0.148947
\(691\) 39.3747 1.49789 0.748943 0.662635i \(-0.230562\pi\)
0.748943 + 0.662635i \(0.230562\pi\)
\(692\) 8.05772 0.306309
\(693\) −8.94082 −0.339634
\(694\) −15.2480 −0.578805
\(695\) 6.46085 0.245074
\(696\) −3.41662 −0.129507
\(697\) 16.5557 0.627092
\(698\) 24.0297 0.909538
\(699\) −2.13864 −0.0808909
\(700\) −11.0841 −0.418940
\(701\) −1.84441 −0.0696624 −0.0348312 0.999393i \(-0.511089\pi\)
−0.0348312 + 0.999393i \(0.511089\pi\)
\(702\) −1.08914 −0.0411071
\(703\) −13.3079 −0.501918
\(704\) −1.69143 −0.0637482
\(705\) −9.50492 −0.357976
\(706\) −15.7063 −0.591114
\(707\) −10.5864 −0.398144
\(708\) −27.9530 −1.05054
\(709\) −30.0606 −1.12895 −0.564474 0.825451i \(-0.690921\pi\)
−0.564474 + 0.825451i \(0.690921\pi\)
\(710\) 7.47104 0.280383
\(711\) −2.13799 −0.0801808
\(712\) −15.9659 −0.598348
\(713\) −2.35182 −0.0880762
\(714\) −11.6177 −0.434782
\(715\) −0.684751 −0.0256082
\(716\) −13.7709 −0.514643
\(717\) −20.1786 −0.753585
\(718\) 24.8295 0.926628
\(719\) −38.5415 −1.43735 −0.718677 0.695344i \(-0.755252\pi\)
−0.718677 + 0.695344i \(0.755252\pi\)
\(720\) −1.56277 −0.0582410
\(721\) 40.3587 1.50304
\(722\) −5.90004 −0.219577
\(723\) 33.5591 1.24808
\(724\) 14.8883 0.553321
\(725\) −6.73003 −0.249947
\(726\) 18.4293 0.683974
\(727\) 48.4299 1.79617 0.898083 0.439826i \(-0.144960\pi\)
0.898083 + 0.439826i \(0.144960\pi\)
\(728\) −1.36933 −0.0507506
\(729\) −9.66587 −0.357995
\(730\) −5.31031 −0.196544
\(731\) 20.5945 0.761715
\(732\) 4.93430 0.182377
\(733\) 25.9372 0.958011 0.479005 0.877812i \(-0.340997\pi\)
0.479005 + 0.877812i \(0.340997\pi\)
\(734\) −23.1779 −0.855513
\(735\) −1.37113 −0.0505750
\(736\) −2.35182 −0.0866891
\(737\) −19.1118 −0.703992
\(738\) 17.0562 0.627849
\(739\) −36.6210 −1.34712 −0.673562 0.739131i \(-0.735236\pi\)
−0.673562 + 0.739131i \(0.735236\pi\)
\(740\) −2.70143 −0.0993066
\(741\) −4.51573 −0.165890
\(742\) −17.1135 −0.628258
\(743\) −13.2562 −0.486323 −0.243161 0.969986i \(-0.578184\pi\)
−0.243161 + 0.969986i \(0.578184\pi\)
\(744\) −2.26430 −0.0830132
\(745\) −9.50756 −0.348330
\(746\) −10.3221 −0.377917
\(747\) −16.8807 −0.617632
\(748\) −3.49216 −0.127686
\(749\) −14.0079 −0.511836
\(750\) −15.7381 −0.574674
\(751\) 15.0905 0.550660 0.275330 0.961350i \(-0.411213\pi\)
0.275330 + 0.961350i \(0.411213\pi\)
\(752\) −5.71342 −0.208347
\(753\) 31.7865 1.15836
\(754\) −0.831425 −0.0302787
\(755\) −3.96352 −0.144247
\(756\) 4.91216 0.178654
\(757\) 33.7874 1.22803 0.614013 0.789296i \(-0.289554\pi\)
0.614013 + 0.789296i \(0.289554\pi\)
\(758\) 23.0561 0.837434
\(759\) −9.00722 −0.326941
\(760\) 2.65922 0.0964599
\(761\) 0.613416 0.0222363 0.0111182 0.999938i \(-0.496461\pi\)
0.0111182 + 0.999938i \(0.496461\pi\)
\(762\) 18.1542 0.657658
\(763\) 40.1400 1.45317
\(764\) 18.0903 0.654483
\(765\) −3.22653 −0.116655
\(766\) −4.03493 −0.145788
\(767\) −6.80228 −0.245616
\(768\) −2.26430 −0.0817058
\(769\) −31.8028 −1.14684 −0.573418 0.819263i \(-0.694383\pi\)
−0.573418 + 0.819263i \(0.694383\pi\)
\(770\) 3.08830 0.111295
\(771\) −58.8711 −2.12019
\(772\) −3.00761 −0.108246
\(773\) −47.5547 −1.71042 −0.855211 0.518280i \(-0.826573\pi\)
−0.855211 + 0.518280i \(0.826573\pi\)
\(774\) 21.2172 0.762635
\(775\) −4.46019 −0.160215
\(776\) 1.00000 0.0358979
\(777\) −20.6898 −0.742242
\(778\) 3.15696 0.113182
\(779\) −29.0230 −1.03986
\(780\) −0.916668 −0.0328220
\(781\) 17.1995 0.615447
\(782\) −4.85561 −0.173636
\(783\) 2.98256 0.106588
\(784\) −0.824189 −0.0294353
\(785\) 9.62242 0.343439
\(786\) −29.1955 −1.04137
\(787\) −7.57394 −0.269982 −0.134991 0.990847i \(-0.543101\pi\)
−0.134991 + 0.990847i \(0.543101\pi\)
\(788\) 14.9505 0.532589
\(789\) −9.25117 −0.329351
\(790\) 0.738495 0.0262745
\(791\) 33.6543 1.19661
\(792\) −3.59775 −0.127840
\(793\) 1.20075 0.0426398
\(794\) −12.5824 −0.446531
\(795\) −11.4563 −0.406314
\(796\) 14.2779 0.506066
\(797\) −51.4090 −1.82100 −0.910500 0.413509i \(-0.864303\pi\)
−0.910500 + 0.413509i \(0.864303\pi\)
\(798\) 20.3665 0.720965
\(799\) −11.7961 −0.417314
\(800\) −4.46019 −0.157692
\(801\) −33.9602 −1.19992
\(802\) −7.57778 −0.267581
\(803\) −12.2252 −0.431417
\(804\) −25.5847 −0.902304
\(805\) 4.29407 0.151346
\(806\) −0.551010 −0.0194085
\(807\) −52.5062 −1.84831
\(808\) −4.25993 −0.149864
\(809\) −36.7914 −1.29352 −0.646759 0.762694i \(-0.723876\pi\)
−0.646759 + 0.762694i \(0.723876\pi\)
\(810\) 7.97666 0.280271
\(811\) 4.55401 0.159913 0.0799564 0.996798i \(-0.474522\pi\)
0.0799564 + 0.996798i \(0.474522\pi\)
\(812\) 3.74982 0.131593
\(813\) −38.4738 −1.34933
\(814\) −6.21913 −0.217980
\(815\) −13.1314 −0.459974
\(816\) −4.67492 −0.163655
\(817\) −36.1032 −1.26309
\(818\) −8.60124 −0.300735
\(819\) −2.91262 −0.101775
\(820\) −5.89150 −0.205740
\(821\) 38.1829 1.33259 0.666297 0.745687i \(-0.267878\pi\)
0.666297 + 0.745687i \(0.267878\pi\)
\(822\) −12.2581 −0.427549
\(823\) 21.1201 0.736201 0.368101 0.929786i \(-0.380008\pi\)
0.368101 + 0.929786i \(0.380008\pi\)
\(824\) 16.2402 0.565753
\(825\) −17.0821 −0.594722
\(826\) 30.6790 1.06746
\(827\) −36.7906 −1.27933 −0.639667 0.768652i \(-0.720928\pi\)
−0.639667 + 0.768652i \(0.720928\pi\)
\(828\) −5.00241 −0.173846
\(829\) −6.99177 −0.242834 −0.121417 0.992602i \(-0.538744\pi\)
−0.121417 + 0.992602i \(0.538744\pi\)
\(830\) 5.83086 0.202392
\(831\) −71.0306 −2.46402
\(832\) −0.551010 −0.0191028
\(833\) −1.70164 −0.0589583
\(834\) 19.9115 0.689479
\(835\) −3.18782 −0.110319
\(836\) 6.12194 0.211732
\(837\) 1.97663 0.0683224
\(838\) 33.9778 1.17374
\(839\) 6.26794 0.216393 0.108197 0.994130i \(-0.465492\pi\)
0.108197 + 0.994130i \(0.465492\pi\)
\(840\) 4.13427 0.142646
\(841\) −26.7232 −0.921489
\(842\) −11.5606 −0.398403
\(843\) 0.101896 0.00350950
\(844\) 14.1715 0.487803
\(845\) 9.32822 0.320901
\(846\) −12.1527 −0.417818
\(847\) −20.2265 −0.694992
\(848\) −6.88641 −0.236480
\(849\) 19.3012 0.662416
\(850\) −9.20862 −0.315853
\(851\) −8.64726 −0.296424
\(852\) 23.0248 0.788816
\(853\) 27.4504 0.939885 0.469943 0.882697i \(-0.344275\pi\)
0.469943 + 0.882697i \(0.344275\pi\)
\(854\) −5.41550 −0.185315
\(855\) 5.65627 0.193440
\(856\) −5.63670 −0.192659
\(857\) −43.8912 −1.49929 −0.749647 0.661838i \(-0.769777\pi\)
−0.749647 + 0.661838i \(0.769777\pi\)
\(858\) −2.11031 −0.0720450
\(859\) 32.0026 1.09192 0.545958 0.837813i \(-0.316166\pi\)
0.545958 + 0.837813i \(0.316166\pi\)
\(860\) −7.32874 −0.249908
\(861\) −45.1219 −1.53775
\(862\) 20.5775 0.700871
\(863\) −50.0273 −1.70295 −0.851474 0.524397i \(-0.824291\pi\)
−0.851474 + 0.524397i \(0.824291\pi\)
\(864\) 1.97663 0.0672464
\(865\) −5.92013 −0.201290
\(866\) 21.6847 0.736875
\(867\) 28.8411 0.979496
\(868\) 2.48512 0.0843504
\(869\) 1.70013 0.0576730
\(870\) 2.51024 0.0851051
\(871\) −6.22597 −0.210959
\(872\) 16.1521 0.546981
\(873\) 2.12704 0.0719895
\(874\) 8.51213 0.287927
\(875\) 17.2729 0.583931
\(876\) −16.3657 −0.552946
\(877\) −8.12972 −0.274521 −0.137261 0.990535i \(-0.543830\pi\)
−0.137261 + 0.990535i \(0.543830\pi\)
\(878\) −0.185278 −0.00625284
\(879\) −58.1164 −1.96022
\(880\) 1.24272 0.0418920
\(881\) −9.12965 −0.307586 −0.153793 0.988103i \(-0.549149\pi\)
−0.153793 + 0.988103i \(0.549149\pi\)
\(882\) −1.75309 −0.0590295
\(883\) 46.4164 1.56203 0.781017 0.624509i \(-0.214701\pi\)
0.781017 + 0.624509i \(0.214701\pi\)
\(884\) −1.13763 −0.0382626
\(885\) 20.5375 0.690360
\(886\) 0.880293 0.0295740
\(887\) −35.8795 −1.20472 −0.602358 0.798226i \(-0.705772\pi\)
−0.602358 + 0.798226i \(0.705772\pi\)
\(888\) −8.32548 −0.279385
\(889\) −19.9247 −0.668252
\(890\) 11.7304 0.393203
\(891\) 18.3635 0.615202
\(892\) 13.0320 0.436344
\(893\) 20.6791 0.691999
\(894\) −29.3011 −0.979975
\(895\) 10.1177 0.338197
\(896\) 2.48512 0.0830220
\(897\) −2.93425 −0.0979716
\(898\) 29.5313 0.985471
\(899\) 1.50891 0.0503249
\(900\) −9.48703 −0.316234
\(901\) −14.2178 −0.473665
\(902\) −13.5632 −0.451604
\(903\) −56.1295 −1.86787
\(904\) 13.5424 0.450412
\(905\) −10.9387 −0.363614
\(906\) −12.2151 −0.405819
\(907\) −57.5367 −1.91047 −0.955237 0.295843i \(-0.904400\pi\)
−0.955237 + 0.295843i \(0.904400\pi\)
\(908\) 11.7044 0.388423
\(909\) −9.06107 −0.300537
\(910\) 1.00606 0.0333507
\(911\) −55.7847 −1.84823 −0.924115 0.382115i \(-0.875196\pi\)
−0.924115 + 0.382115i \(0.875196\pi\)
\(912\) 8.19537 0.271376
\(913\) 13.4236 0.444255
\(914\) −28.1549 −0.931280
\(915\) −3.62530 −0.119849
\(916\) −0.805815 −0.0266249
\(917\) 32.0427 1.05814
\(918\) 4.08100 0.134693
\(919\) 17.2992 0.570647 0.285324 0.958431i \(-0.407899\pi\)
0.285324 + 0.958431i \(0.407899\pi\)
\(920\) 1.72791 0.0569676
\(921\) −68.4124 −2.25426
\(922\) −15.2922 −0.503622
\(923\) 5.60302 0.184426
\(924\) 9.51775 0.313111
\(925\) −16.3995 −0.539211
\(926\) 8.84392 0.290629
\(927\) 34.5435 1.13456
\(928\) 1.50891 0.0495324
\(929\) −37.7190 −1.23752 −0.618761 0.785580i \(-0.712365\pi\)
−0.618761 + 0.785580i \(0.712365\pi\)
\(930\) 1.66361 0.0545520
\(931\) 2.98306 0.0977658
\(932\) 0.944506 0.0309383
\(933\) −9.47977 −0.310354
\(934\) −5.75283 −0.188238
\(935\) 2.56574 0.0839088
\(936\) −1.17202 −0.0383088
\(937\) 29.8648 0.975640 0.487820 0.872944i \(-0.337792\pi\)
0.487820 + 0.872944i \(0.337792\pi\)
\(938\) 28.0798 0.916839
\(939\) −37.3792 −1.21982
\(940\) 4.19773 0.136915
\(941\) −13.0443 −0.425231 −0.212615 0.977136i \(-0.568198\pi\)
−0.212615 + 0.977136i \(0.568198\pi\)
\(942\) 29.6551 0.966214
\(943\) −18.8586 −0.614122
\(944\) 12.3451 0.401799
\(945\) −3.60904 −0.117402
\(946\) −16.8719 −0.548554
\(947\) −43.6636 −1.41888 −0.709438 0.704768i \(-0.751051\pi\)
−0.709438 + 0.704768i \(0.751051\pi\)
\(948\) 2.27595 0.0739193
\(949\) −3.98255 −0.129279
\(950\) 16.1432 0.523753
\(951\) 77.4472 2.51140
\(952\) 5.13083 0.166291
\(953\) 58.8771 1.90722 0.953608 0.301050i \(-0.0973372\pi\)
0.953608 + 0.301050i \(0.0973372\pi\)
\(954\) −14.6477 −0.474237
\(955\) −13.2912 −0.430092
\(956\) 8.91165 0.288223
\(957\) 5.77897 0.186808
\(958\) −29.9180 −0.966608
\(959\) 13.4535 0.434436
\(960\) 1.66361 0.0536929
\(961\) 1.00000 0.0322581
\(962\) −2.02598 −0.0653202
\(963\) −11.9895 −0.386357
\(964\) −14.8210 −0.477351
\(965\) 2.20974 0.0711340
\(966\) 13.2338 0.425790
\(967\) −4.60845 −0.148198 −0.0740988 0.997251i \(-0.523608\pi\)
−0.0740988 + 0.997251i \(0.523608\pi\)
\(968\) −8.13907 −0.261599
\(969\) 16.9203 0.543560
\(970\) −0.734715 −0.0235903
\(971\) 24.9391 0.800333 0.400167 0.916442i \(-0.368952\pi\)
0.400167 + 0.916442i \(0.368952\pi\)
\(972\) 18.6532 0.598301
\(973\) −21.8533 −0.700586
\(974\) 9.40494 0.301354
\(975\) −5.56477 −0.178215
\(976\) −2.17917 −0.0697536
\(977\) 2.51429 0.0804393 0.0402197 0.999191i \(-0.487194\pi\)
0.0402197 + 0.999191i \(0.487194\pi\)
\(978\) −40.4694 −1.29407
\(979\) 27.0052 0.863090
\(980\) 0.605544 0.0193434
\(981\) 34.3563 1.09691
\(982\) −38.5146 −1.22905
\(983\) 6.30240 0.201015 0.100508 0.994936i \(-0.467953\pi\)
0.100508 + 0.994936i \(0.467953\pi\)
\(984\) −18.1569 −0.578819
\(985\) −10.9843 −0.349990
\(986\) 3.11533 0.0992122
\(987\) 32.1497 1.02334
\(988\) 1.99432 0.0634478
\(989\) −23.4592 −0.745961
\(990\) 2.64332 0.0840101
\(991\) 50.9434 1.61827 0.809135 0.587623i \(-0.199936\pi\)
0.809135 + 0.587623i \(0.199936\pi\)
\(992\) 1.00000 0.0317500
\(993\) −6.06999 −0.192625
\(994\) −25.2702 −0.801523
\(995\) −10.4902 −0.332561
\(996\) 17.9700 0.569400
\(997\) 27.2266 0.862277 0.431138 0.902286i \(-0.358112\pi\)
0.431138 + 0.902286i \(0.358112\pi\)
\(998\) 29.8674 0.945437
\(999\) 7.26777 0.229942
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 6014.2.a.k.1.7 37
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.k.1.7 37 1.1 even 1 trivial