Properties

Label 241.2.a.a.1.4
Level $241$
Weight $2$
Character 241.1
Self dual yes
Analytic conductor $1.924$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [241,2,Mod(1,241)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(241, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("241.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 241.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: \(1.92439468871\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.31056073.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.369356\) of defining polynomial
Character \(\chi\) \(=\) 241.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.630644 q^{2} +2.33806 q^{3} -1.60229 q^{4} -3.89634 q^{5} -1.47449 q^{6} -3.68231 q^{7} +2.27176 q^{8} +2.46654 q^{9} +O(q^{10})\) \(q-0.630644 q^{2} +2.33806 q^{3} -1.60229 q^{4} -3.89634 q^{5} -1.47449 q^{6} -3.68231 q^{7} +2.27176 q^{8} +2.46654 q^{9} +2.45721 q^{10} -4.96431 q^{11} -3.74625 q^{12} -1.69048 q^{13} +2.32223 q^{14} -9.10989 q^{15} +1.77190 q^{16} +5.52260 q^{17} -1.55551 q^{18} +4.21489 q^{19} +6.24306 q^{20} -8.60948 q^{21} +3.13071 q^{22} -2.77495 q^{23} +5.31152 q^{24} +10.1815 q^{25} +1.06609 q^{26} -1.24727 q^{27} +5.90013 q^{28} -2.31253 q^{29} +5.74510 q^{30} -0.199515 q^{31} -5.66096 q^{32} -11.6069 q^{33} -3.48280 q^{34} +14.3476 q^{35} -3.95210 q^{36} +1.79089 q^{37} -2.65809 q^{38} -3.95245 q^{39} -8.85157 q^{40} -12.1960 q^{41} +5.42952 q^{42} -5.34523 q^{43} +7.95425 q^{44} -9.61047 q^{45} +1.75001 q^{46} -10.7345 q^{47} +4.14282 q^{48} +6.55944 q^{49} -6.42090 q^{50} +12.9122 q^{51} +2.70864 q^{52} +1.32229 q^{53} +0.786587 q^{54} +19.3426 q^{55} -8.36534 q^{56} +9.85467 q^{57} +1.45838 q^{58} +5.78578 q^{59} +14.5967 q^{60} -0.0766435 q^{61} +0.125823 q^{62} -9.08256 q^{63} +0.0262532 q^{64} +6.58670 q^{65} +7.31980 q^{66} +12.6166 q^{67} -8.84880 q^{68} -6.48800 q^{69} -9.04821 q^{70} -5.20391 q^{71} +5.60338 q^{72} -14.0733 q^{73} -1.12941 q^{74} +23.8050 q^{75} -6.75346 q^{76} +18.2801 q^{77} +2.49259 q^{78} +7.82844 q^{79} -6.90393 q^{80} -10.3158 q^{81} +7.69137 q^{82} +2.55372 q^{83} +13.7949 q^{84} -21.5180 q^{85} +3.37094 q^{86} -5.40683 q^{87} -11.2777 q^{88} -4.35327 q^{89} +6.06079 q^{90} +6.22489 q^{91} +4.44627 q^{92} -0.466479 q^{93} +6.76964 q^{94} -16.4226 q^{95} -13.2357 q^{96} +9.02693 q^{97} -4.13668 q^{98} -12.2446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9} + 3 q^{10} - 18 q^{11} + q^{12} - q^{13} - 6 q^{14} - 11 q^{15} + 4 q^{16} - 2 q^{17} + 8 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 10 q^{22} - 22 q^{23} - 3 q^{24} + 5 q^{25} + 8 q^{26} + 3 q^{27} + 9 q^{28} - 16 q^{29} + 29 q^{30} - 18 q^{31} - 6 q^{32} + 4 q^{33} + 11 q^{34} + 7 q^{35} - 7 q^{36} + 8 q^{37} + 16 q^{38} - 9 q^{39} + 14 q^{40} - 15 q^{41} + 19 q^{42} + 14 q^{43} - 4 q^{44} + 3 q^{45} + 11 q^{46} - 10 q^{47} + 31 q^{48} + 6 q^{49} - 4 q^{50} + 13 q^{51} + 27 q^{52} + 15 q^{53} + 16 q^{54} + 29 q^{55} + 13 q^{56} + 14 q^{57} + 17 q^{58} - 18 q^{59} + 15 q^{60} + 4 q^{61} + 13 q^{62} - 16 q^{63} + 2 q^{64} - 7 q^{65} + 16 q^{66} + 18 q^{67} - 15 q^{68} + 26 q^{69} + 8 q^{70} - 50 q^{71} + 30 q^{72} + 10 q^{74} + 16 q^{75} - 20 q^{76} + 17 q^{77} - 32 q^{78} - 15 q^{79} - 11 q^{80} - 9 q^{81} + 45 q^{82} - 24 q^{83} + 6 q^{84} - 2 q^{85} - 23 q^{86} + 12 q^{87} + 8 q^{88} - 13 q^{89} - 39 q^{90} - 12 q^{91} - 10 q^{92} + 14 q^{93} - 32 q^{94} - 41 q^{95} - 15 q^{96} + q^{97} + 9 q^{98} - 20 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.630644 −0.445933 −0.222966 0.974826i \(-0.571574\pi\)
−0.222966 + 0.974826i \(0.571574\pi\)
\(3\) 2.33806 1.34988 0.674940 0.737872i \(-0.264169\pi\)
0.674940 + 0.737872i \(0.264169\pi\)
\(4\) −1.60229 −0.801144
\(5\) −3.89634 −1.74250 −0.871249 0.490842i \(-0.836689\pi\)
−0.871249 + 0.490842i \(0.836689\pi\)
\(6\) −1.47449 −0.601956
\(7\) −3.68231 −1.39178 −0.695892 0.718146i \(-0.744991\pi\)
−0.695892 + 0.718146i \(0.744991\pi\)
\(8\) 2.27176 0.803189
\(9\) 2.46654 0.822178
\(10\) 2.45721 0.777037
\(11\) −4.96431 −1.49679 −0.748397 0.663250i \(-0.769176\pi\)
−0.748397 + 0.663250i \(0.769176\pi\)
\(12\) −3.74625 −1.08145
\(13\) −1.69048 −0.468855 −0.234428 0.972134i \(-0.575322\pi\)
−0.234428 + 0.972134i \(0.575322\pi\)
\(14\) 2.32223 0.620642
\(15\) −9.10989 −2.35216
\(16\) 1.77190 0.442975
\(17\) 5.52260 1.33943 0.669714 0.742619i \(-0.266417\pi\)
0.669714 + 0.742619i \(0.266417\pi\)
\(18\) −1.55551 −0.366636
\(19\) 4.21489 0.966961 0.483481 0.875355i \(-0.339372\pi\)
0.483481 + 0.875355i \(0.339372\pi\)
\(20\) 6.24306 1.39599
\(21\) −8.60948 −1.87874
\(22\) 3.13071 0.667470
\(23\) −2.77495 −0.578617 −0.289308 0.957236i \(-0.593425\pi\)
−0.289308 + 0.957236i \(0.593425\pi\)
\(24\) 5.31152 1.08421
\(25\) 10.1815 2.03630
\(26\) 1.06609 0.209078
\(27\) −1.24727 −0.240038
\(28\) 5.90013 1.11502
\(29\) −2.31253 −0.429425 −0.214713 0.976677i \(-0.568881\pi\)
−0.214713 + 0.976677i \(0.568881\pi\)
\(30\) 5.74510 1.04891
\(31\) −0.199515 −0.0358340 −0.0179170 0.999839i \(-0.505703\pi\)
−0.0179170 + 0.999839i \(0.505703\pi\)
\(32\) −5.66096 −1.00073
\(33\) −11.6069 −2.02049
\(34\) −3.48280 −0.597295
\(35\) 14.3476 2.42518
\(36\) −3.95210 −0.658683
\(37\) 1.79089 0.294420 0.147210 0.989105i \(-0.452971\pi\)
0.147210 + 0.989105i \(0.452971\pi\)
\(38\) −2.65809 −0.431200
\(39\) −3.95245 −0.632899
\(40\) −8.85157 −1.39956
\(41\) −12.1960 −1.90470 −0.952351 0.305003i \(-0.901343\pi\)
−0.952351 + 0.305003i \(0.901343\pi\)
\(42\) 5.42952 0.837793
\(43\) −5.34523 −0.815139 −0.407570 0.913174i \(-0.633624\pi\)
−0.407570 + 0.913174i \(0.633624\pi\)
\(44\) 7.95425 1.19915
\(45\) −9.61047 −1.43264
\(46\) 1.75001 0.258024
\(47\) −10.7345 −1.56579 −0.782893 0.622157i \(-0.786257\pi\)
−0.782893 + 0.622157i \(0.786257\pi\)
\(48\) 4.14282 0.597964
\(49\) 6.55944 0.937063
\(50\) −6.42090 −0.908052
\(51\) 12.9122 1.80807
\(52\) 2.70864 0.375621
\(53\) 1.32229 0.181631 0.0908154 0.995868i \(-0.471053\pi\)
0.0908154 + 0.995868i \(0.471053\pi\)
\(54\) 0.786587 0.107041
\(55\) 19.3426 2.60816
\(56\) −8.36534 −1.11787
\(57\) 9.85467 1.30528
\(58\) 1.45838 0.191495
\(59\) 5.78578 0.753244 0.376622 0.926367i \(-0.377086\pi\)
0.376622 + 0.926367i \(0.377086\pi\)
\(60\) 14.5967 1.88442
\(61\) −0.0766435 −0.00981320 −0.00490660 0.999988i \(-0.501562\pi\)
−0.00490660 + 0.999988i \(0.501562\pi\)
\(62\) 0.125823 0.0159795
\(63\) −9.08256 −1.14429
\(64\) 0.0262532 0.00328165
\(65\) 6.58670 0.816979
\(66\) 7.31980 0.901005
\(67\) 12.6166 1.54136 0.770681 0.637221i \(-0.219916\pi\)
0.770681 + 0.637221i \(0.219916\pi\)
\(68\) −8.84880 −1.07307
\(69\) −6.48800 −0.781064
\(70\) −9.04821 −1.08147
\(71\) −5.20391 −0.617591 −0.308796 0.951128i \(-0.599926\pi\)
−0.308796 + 0.951128i \(0.599926\pi\)
\(72\) 5.60338 0.660365
\(73\) −14.0733 −1.64715 −0.823577 0.567204i \(-0.808025\pi\)
−0.823577 + 0.567204i \(0.808025\pi\)
\(74\) −1.12941 −0.131291
\(75\) 23.8050 2.74876
\(76\) −6.75346 −0.774675
\(77\) 18.2801 2.08322
\(78\) 2.49259 0.282230
\(79\) 7.82844 0.880769 0.440384 0.897809i \(-0.354842\pi\)
0.440384 + 0.897809i \(0.354842\pi\)
\(80\) −6.90393 −0.771883
\(81\) −10.3158 −1.14620
\(82\) 7.69137 0.849370
\(83\) 2.55372 0.280307 0.140153 0.990130i \(-0.455240\pi\)
0.140153 + 0.990130i \(0.455240\pi\)
\(84\) 13.7949 1.50514
\(85\) −21.5180 −2.33395
\(86\) 3.37094 0.363497
\(87\) −5.40683 −0.579673
\(88\) −11.2777 −1.20221
\(89\) −4.35327 −0.461446 −0.230723 0.973019i \(-0.574109\pi\)
−0.230723 + 0.973019i \(0.574109\pi\)
\(90\) 6.06079 0.638863
\(91\) 6.22489 0.652546
\(92\) 4.44627 0.463555
\(93\) −0.466479 −0.0483716
\(94\) 6.76964 0.698235
\(95\) −16.4226 −1.68493
\(96\) −13.2357 −1.35086
\(97\) 9.02693 0.916546 0.458273 0.888811i \(-0.348468\pi\)
0.458273 + 0.888811i \(0.348468\pi\)
\(98\) −4.13668 −0.417867
\(99\) −12.2446 −1.23063
\(100\) −16.3137 −1.63137
\(101\) 6.94323 0.690877 0.345439 0.938441i \(-0.387730\pi\)
0.345439 + 0.938441i \(0.387730\pi\)
\(102\) −8.14300 −0.806277
\(103\) −0.105009 −0.0103469 −0.00517343 0.999987i \(-0.501647\pi\)
−0.00517343 + 0.999987i \(0.501647\pi\)
\(104\) −3.84037 −0.376580
\(105\) 33.5455 3.27371
\(106\) −0.833897 −0.0809952
\(107\) −18.1842 −1.75793 −0.878966 0.476885i \(-0.841766\pi\)
−0.878966 + 0.476885i \(0.841766\pi\)
\(108\) 1.99849 0.192305
\(109\) 14.6576 1.40394 0.701972 0.712205i \(-0.252303\pi\)
0.701972 + 0.712205i \(0.252303\pi\)
\(110\) −12.1983 −1.16307
\(111\) 4.18720 0.397432
\(112\) −6.52470 −0.616526
\(113\) 1.08836 0.102384 0.0511922 0.998689i \(-0.483698\pi\)
0.0511922 + 0.998689i \(0.483698\pi\)
\(114\) −6.21479 −0.582068
\(115\) 10.8122 1.00824
\(116\) 3.70533 0.344031
\(117\) −4.16963 −0.385483
\(118\) −3.64877 −0.335896
\(119\) −20.3360 −1.86420
\(120\) −20.6955 −1.88923
\(121\) 13.6443 1.24040
\(122\) 0.0483348 0.00437603
\(123\) −28.5151 −2.57112
\(124\) 0.319681 0.0287082
\(125\) −20.1889 −1.80575
\(126\) 5.72786 0.510279
\(127\) 0.364538 0.0323475 0.0161737 0.999869i \(-0.494852\pi\)
0.0161737 + 0.999869i \(0.494852\pi\)
\(128\) 11.3054 0.999263
\(129\) −12.4975 −1.10034
\(130\) −4.15386 −0.364318
\(131\) 5.48865 0.479546 0.239773 0.970829i \(-0.422927\pi\)
0.239773 + 0.970829i \(0.422927\pi\)
\(132\) 18.5975 1.61871
\(133\) −15.5205 −1.34580
\(134\) −7.95658 −0.687344
\(135\) 4.85981 0.418266
\(136\) 12.5460 1.07581
\(137\) −17.1533 −1.46551 −0.732754 0.680493i \(-0.761766\pi\)
−0.732754 + 0.680493i \(0.761766\pi\)
\(138\) 4.09162 0.348302
\(139\) −19.6074 −1.66308 −0.831539 0.555467i \(-0.812540\pi\)
−0.831539 + 0.555467i \(0.812540\pi\)
\(140\) −22.9889 −1.94292
\(141\) −25.0979 −2.11362
\(142\) 3.28182 0.275404
\(143\) 8.39207 0.701780
\(144\) 4.37046 0.364205
\(145\) 9.01039 0.748272
\(146\) 8.87525 0.734521
\(147\) 15.3364 1.26492
\(148\) −2.86951 −0.235873
\(149\) 19.0508 1.56070 0.780350 0.625343i \(-0.215041\pi\)
0.780350 + 0.625343i \(0.215041\pi\)
\(150\) −15.0125 −1.22576
\(151\) −4.76802 −0.388016 −0.194008 0.981000i \(-0.562149\pi\)
−0.194008 + 0.981000i \(0.562149\pi\)
\(152\) 9.57522 0.776653
\(153\) 13.6217 1.10125
\(154\) −11.5283 −0.928974
\(155\) 0.777379 0.0624406
\(156\) 6.33297 0.507043
\(157\) 6.12724 0.489007 0.244503 0.969648i \(-0.421375\pi\)
0.244503 + 0.969648i \(0.421375\pi\)
\(158\) −4.93696 −0.392764
\(159\) 3.09160 0.245180
\(160\) 22.0571 1.74376
\(161\) 10.2182 0.805310
\(162\) 6.50561 0.511129
\(163\) −1.20414 −0.0943159 −0.0471579 0.998887i \(-0.515016\pi\)
−0.0471579 + 0.998887i \(0.515016\pi\)
\(164\) 19.5416 1.52594
\(165\) 45.2243 3.52071
\(166\) −1.61049 −0.124998
\(167\) −0.900391 −0.0696744 −0.0348372 0.999393i \(-0.511091\pi\)
−0.0348372 + 0.999393i \(0.511091\pi\)
\(168\) −19.5587 −1.50899
\(169\) −10.1423 −0.780175
\(170\) 13.5702 1.04079
\(171\) 10.3962 0.795015
\(172\) 8.56459 0.653044
\(173\) 12.3564 0.939436 0.469718 0.882817i \(-0.344356\pi\)
0.469718 + 0.882817i \(0.344356\pi\)
\(174\) 3.40979 0.258495
\(175\) −37.4915 −2.83409
\(176\) −8.79626 −0.663043
\(177\) 13.5275 1.01679
\(178\) 2.74537 0.205774
\(179\) −10.0258 −0.749367 −0.374683 0.927153i \(-0.622249\pi\)
−0.374683 + 0.927153i \(0.622249\pi\)
\(180\) 15.3987 1.14775
\(181\) −17.0491 −1.26725 −0.633623 0.773642i \(-0.718433\pi\)
−0.633623 + 0.773642i \(0.718433\pi\)
\(182\) −3.92569 −0.290992
\(183\) −0.179197 −0.0132467
\(184\) −6.30402 −0.464739
\(185\) −6.97790 −0.513026
\(186\) 0.294182 0.0215705
\(187\) −27.4159 −2.00485
\(188\) 17.1997 1.25442
\(189\) 4.59286 0.334081
\(190\) 10.3568 0.751365
\(191\) −23.7744 −1.72026 −0.860129 0.510077i \(-0.829617\pi\)
−0.860129 + 0.510077i \(0.829617\pi\)
\(192\) 0.0613816 0.00442984
\(193\) 7.49373 0.539411 0.269705 0.962943i \(-0.413074\pi\)
0.269705 + 0.962943i \(0.413074\pi\)
\(194\) −5.69278 −0.408718
\(195\) 15.4001 1.10282
\(196\) −10.5101 −0.750723
\(197\) 1.85647 0.132268 0.0661339 0.997811i \(-0.478934\pi\)
0.0661339 + 0.997811i \(0.478934\pi\)
\(198\) 7.72201 0.548779
\(199\) 3.46667 0.245746 0.122873 0.992422i \(-0.460789\pi\)
0.122873 + 0.992422i \(0.460789\pi\)
\(200\) 23.1299 1.63553
\(201\) 29.4984 2.08066
\(202\) −4.37871 −0.308085
\(203\) 8.51545 0.597667
\(204\) −20.6890 −1.44852
\(205\) 47.5200 3.31894
\(206\) 0.0662234 0.00461400
\(207\) −6.84451 −0.475726
\(208\) −2.99537 −0.207691
\(209\) −20.9240 −1.44734
\(210\) −21.1553 −1.45985
\(211\) −2.33201 −0.160542 −0.0802711 0.996773i \(-0.525579\pi\)
−0.0802711 + 0.996773i \(0.525579\pi\)
\(212\) −2.11869 −0.145512
\(213\) −12.1671 −0.833674
\(214\) 11.4678 0.783919
\(215\) 20.8268 1.42038
\(216\) −2.83351 −0.192796
\(217\) 0.734678 0.0498732
\(218\) −9.24373 −0.626065
\(219\) −32.9042 −2.22346
\(220\) −30.9925 −2.08951
\(221\) −9.33587 −0.627998
\(222\) −2.64063 −0.177228
\(223\) −1.75535 −0.117547 −0.0587734 0.998271i \(-0.518719\pi\)
−0.0587734 + 0.998271i \(0.518719\pi\)
\(224\) 20.8455 1.39280
\(225\) 25.1130 1.67420
\(226\) −0.686369 −0.0456566
\(227\) 4.35631 0.289139 0.144569 0.989495i \(-0.453820\pi\)
0.144569 + 0.989495i \(0.453820\pi\)
\(228\) −15.7900 −1.04572
\(229\) 6.24160 0.412457 0.206228 0.978504i \(-0.433881\pi\)
0.206228 + 0.978504i \(0.433881\pi\)
\(230\) −6.81862 −0.449607
\(231\) 42.7401 2.81209
\(232\) −5.25351 −0.344910
\(233\) 13.8315 0.906135 0.453067 0.891476i \(-0.350330\pi\)
0.453067 + 0.891476i \(0.350330\pi\)
\(234\) 2.62956 0.171899
\(235\) 41.8252 2.72838
\(236\) −9.27048 −0.603457
\(237\) 18.3034 1.18893
\(238\) 12.8248 0.831306
\(239\) −19.3924 −1.25439 −0.627194 0.778863i \(-0.715797\pi\)
−0.627194 + 0.778863i \(0.715797\pi\)
\(240\) −16.1418 −1.04195
\(241\) −1.00000 −0.0644157
\(242\) −8.60473 −0.553133
\(243\) −20.3772 −1.30720
\(244\) 0.122805 0.00786178
\(245\) −25.5578 −1.63283
\(246\) 17.9829 1.14655
\(247\) −7.12519 −0.453365
\(248\) −0.453251 −0.0287815
\(249\) 5.97075 0.378381
\(250\) 12.7320 0.805242
\(251\) −14.4441 −0.911705 −0.455852 0.890055i \(-0.650666\pi\)
−0.455852 + 0.890055i \(0.650666\pi\)
\(252\) 14.5529 0.916745
\(253\) 13.7757 0.866071
\(254\) −0.229894 −0.0144248
\(255\) −50.3103 −3.15056
\(256\) −7.18218 −0.448886
\(257\) 28.9004 1.80276 0.901379 0.433031i \(-0.142556\pi\)
0.901379 + 0.433031i \(0.142556\pi\)
\(258\) 7.88146 0.490678
\(259\) −6.59460 −0.409769
\(260\) −10.5538 −0.654518
\(261\) −5.70393 −0.353064
\(262\) −3.46139 −0.213845
\(263\) 26.3078 1.62221 0.811103 0.584903i \(-0.198867\pi\)
0.811103 + 0.584903i \(0.198867\pi\)
\(264\) −26.3680 −1.62284
\(265\) −5.15211 −0.316491
\(266\) 9.78794 0.600137
\(267\) −10.1782 −0.622897
\(268\) −20.2154 −1.23485
\(269\) −9.42450 −0.574622 −0.287311 0.957837i \(-0.592761\pi\)
−0.287311 + 0.957837i \(0.592761\pi\)
\(270\) −3.06481 −0.186518
\(271\) −5.86519 −0.356285 −0.178142 0.984005i \(-0.557009\pi\)
−0.178142 + 0.984005i \(0.557009\pi\)
\(272\) 9.78551 0.593334
\(273\) 14.5542 0.880859
\(274\) 10.8177 0.653519
\(275\) −50.5440 −3.04792
\(276\) 10.3956 0.625744
\(277\) 5.60395 0.336708 0.168354 0.985727i \(-0.446155\pi\)
0.168354 + 0.985727i \(0.446155\pi\)
\(278\) 12.3653 0.741621
\(279\) −0.492111 −0.0294619
\(280\) 32.5943 1.94788
\(281\) −4.71669 −0.281374 −0.140687 0.990054i \(-0.544931\pi\)
−0.140687 + 0.990054i \(0.544931\pi\)
\(282\) 15.8278 0.942534
\(283\) 19.2068 1.14173 0.570864 0.821044i \(-0.306608\pi\)
0.570864 + 0.821044i \(0.306608\pi\)
\(284\) 8.33817 0.494779
\(285\) −38.3972 −2.27445
\(286\) −5.29241 −0.312947
\(287\) 44.9097 2.65094
\(288\) −13.9630 −0.822776
\(289\) 13.4992 0.794069
\(290\) −5.68235 −0.333679
\(291\) 21.1055 1.23723
\(292\) 22.5495 1.31961
\(293\) 13.0140 0.760289 0.380144 0.924927i \(-0.375874\pi\)
0.380144 + 0.924927i \(0.375874\pi\)
\(294\) −9.67181 −0.564071
\(295\) −22.5434 −1.31253
\(296\) 4.06847 0.236475
\(297\) 6.19185 0.359288
\(298\) −12.0143 −0.695968
\(299\) 4.69100 0.271288
\(300\) −38.1424 −2.20215
\(301\) 19.6828 1.13450
\(302\) 3.00692 0.173029
\(303\) 16.2337 0.932602
\(304\) 7.46836 0.428340
\(305\) 0.298630 0.0170995
\(306\) −8.59045 −0.491083
\(307\) −11.5372 −0.658463 −0.329232 0.944249i \(-0.606790\pi\)
−0.329232 + 0.944249i \(0.606790\pi\)
\(308\) −29.2900 −1.66896
\(309\) −0.245518 −0.0139670
\(310\) −0.490250 −0.0278443
\(311\) −23.1542 −1.31296 −0.656478 0.754345i \(-0.727955\pi\)
−0.656478 + 0.754345i \(0.727955\pi\)
\(312\) −8.97903 −0.508338
\(313\) −7.88902 −0.445914 −0.222957 0.974828i \(-0.571571\pi\)
−0.222957 + 0.974828i \(0.571571\pi\)
\(314\) −3.86411 −0.218064
\(315\) 35.3888 1.99393
\(316\) −12.5434 −0.705623
\(317\) −2.38325 −0.133857 −0.0669283 0.997758i \(-0.521320\pi\)
−0.0669283 + 0.997758i \(0.521320\pi\)
\(318\) −1.94970 −0.109334
\(319\) 11.4801 0.642761
\(320\) −0.102292 −0.00571827
\(321\) −42.5157 −2.37300
\(322\) −6.44407 −0.359114
\(323\) 23.2772 1.29518
\(324\) 16.5289 0.918272
\(325\) −17.2116 −0.954729
\(326\) 0.759387 0.0420585
\(327\) 34.2704 1.89516
\(328\) −27.7065 −1.52984
\(329\) 39.5278 2.17924
\(330\) −28.5205 −1.57000
\(331\) −3.05598 −0.167972 −0.0839860 0.996467i \(-0.526765\pi\)
−0.0839860 + 0.996467i \(0.526765\pi\)
\(332\) −4.09179 −0.224566
\(333\) 4.41728 0.242066
\(334\) 0.567827 0.0310701
\(335\) −49.1586 −2.68582
\(336\) −15.2551 −0.832237
\(337\) −16.1755 −0.881134 −0.440567 0.897720i \(-0.645223\pi\)
−0.440567 + 0.897720i \(0.645223\pi\)
\(338\) 6.39617 0.347906
\(339\) 2.54466 0.138207
\(340\) 34.4780 1.86983
\(341\) 0.990454 0.0536361
\(342\) −6.55628 −0.354523
\(343\) 1.62227 0.0875943
\(344\) −12.1431 −0.654711
\(345\) 25.2795 1.36100
\(346\) −7.79246 −0.418925
\(347\) 24.4716 1.31370 0.656851 0.754020i \(-0.271888\pi\)
0.656851 + 0.754020i \(0.271888\pi\)
\(348\) 8.66329 0.464401
\(349\) −13.0468 −0.698380 −0.349190 0.937052i \(-0.613543\pi\)
−0.349190 + 0.937052i \(0.613543\pi\)
\(350\) 23.6438 1.26381
\(351\) 2.10849 0.112543
\(352\) 28.1028 1.49788
\(353\) 23.6788 1.26029 0.630147 0.776476i \(-0.282995\pi\)
0.630147 + 0.776476i \(0.282995\pi\)
\(354\) −8.53104 −0.453420
\(355\) 20.2762 1.07615
\(356\) 6.97519 0.369685
\(357\) −47.5468 −2.51644
\(358\) 6.32274 0.334167
\(359\) −25.5499 −1.34847 −0.674236 0.738516i \(-0.735527\pi\)
−0.674236 + 0.738516i \(0.735527\pi\)
\(360\) −21.8327 −1.15068
\(361\) −1.23473 −0.0649857
\(362\) 10.7519 0.565107
\(363\) 31.9013 1.67439
\(364\) −9.97406 −0.522783
\(365\) 54.8344 2.87016
\(366\) 0.113010 0.00590712
\(367\) 8.35766 0.436266 0.218133 0.975919i \(-0.430003\pi\)
0.218133 + 0.975919i \(0.430003\pi\)
\(368\) −4.91693 −0.256313
\(369\) −30.0820 −1.56601
\(370\) 4.40058 0.228775
\(371\) −4.86910 −0.252791
\(372\) 0.747433 0.0387526
\(373\) −24.6934 −1.27858 −0.639288 0.768968i \(-0.720771\pi\)
−0.639288 + 0.768968i \(0.720771\pi\)
\(374\) 17.2897 0.894028
\(375\) −47.2028 −2.43754
\(376\) −24.3862 −1.25762
\(377\) 3.90928 0.201338
\(378\) −2.89646 −0.148978
\(379\) 18.6593 0.958465 0.479232 0.877688i \(-0.340915\pi\)
0.479232 + 0.877688i \(0.340915\pi\)
\(380\) 26.3138 1.34987
\(381\) 0.852312 0.0436652
\(382\) 14.9932 0.767119
\(383\) 11.9780 0.612049 0.306025 0.952024i \(-0.401001\pi\)
0.306025 + 0.952024i \(0.401001\pi\)
\(384\) 26.4327 1.34889
\(385\) −71.2257 −3.63000
\(386\) −4.72588 −0.240541
\(387\) −13.1842 −0.670190
\(388\) −14.4637 −0.734285
\(389\) −7.62670 −0.386689 −0.193344 0.981131i \(-0.561933\pi\)
−0.193344 + 0.981131i \(0.561933\pi\)
\(390\) −9.71199 −0.491786
\(391\) −15.3249 −0.775016
\(392\) 14.9015 0.752639
\(393\) 12.8328 0.647330
\(394\) −1.17077 −0.0589826
\(395\) −30.5023 −1.53474
\(396\) 19.6194 0.985914
\(397\) −33.4013 −1.67636 −0.838181 0.545392i \(-0.816381\pi\)
−0.838181 + 0.545392i \(0.816381\pi\)
\(398\) −2.18624 −0.109586
\(399\) −36.2880 −1.81667
\(400\) 18.0406 0.902030
\(401\) −1.73530 −0.0866566 −0.0433283 0.999061i \(-0.513796\pi\)
−0.0433283 + 0.999061i \(0.513796\pi\)
\(402\) −18.6030 −0.927833
\(403\) 0.337277 0.0168010
\(404\) −11.1251 −0.553492
\(405\) 40.1939 1.99725
\(406\) −5.37022 −0.266519
\(407\) −8.89050 −0.440686
\(408\) 29.3334 1.45222
\(409\) −3.81908 −0.188841 −0.0944207 0.995532i \(-0.530100\pi\)
−0.0944207 + 0.995532i \(0.530100\pi\)
\(410\) −29.9682 −1.48002
\(411\) −40.1056 −1.97826
\(412\) 0.168255 0.00828932
\(413\) −21.3050 −1.04835
\(414\) 4.31645 0.212142
\(415\) −9.95015 −0.488434
\(416\) 9.56976 0.469196
\(417\) −45.8433 −2.24496
\(418\) 13.1956 0.645418
\(419\) 0.640088 0.0312703 0.0156352 0.999878i \(-0.495023\pi\)
0.0156352 + 0.999878i \(0.495023\pi\)
\(420\) −53.7495 −2.62271
\(421\) 13.2765 0.647057 0.323528 0.946218i \(-0.395131\pi\)
0.323528 + 0.946218i \(0.395131\pi\)
\(422\) 1.47067 0.0715910
\(423\) −26.4770 −1.28735
\(424\) 3.00394 0.145884
\(425\) 56.2283 2.72748
\(426\) 7.67310 0.371763
\(427\) 0.282226 0.0136579
\(428\) 29.1363 1.40836
\(429\) 19.6212 0.947320
\(430\) −13.1343 −0.633393
\(431\) −26.8180 −1.29178 −0.645888 0.763432i \(-0.723513\pi\)
−0.645888 + 0.763432i \(0.723513\pi\)
\(432\) −2.21005 −0.106331
\(433\) −20.7392 −0.996664 −0.498332 0.866986i \(-0.666054\pi\)
−0.498332 + 0.866986i \(0.666054\pi\)
\(434\) −0.463320 −0.0222401
\(435\) 21.0669 1.01008
\(436\) −23.4857 −1.12476
\(437\) −11.6961 −0.559500
\(438\) 20.7509 0.991515
\(439\) −12.7382 −0.607960 −0.303980 0.952678i \(-0.598316\pi\)
−0.303980 + 0.952678i \(0.598316\pi\)
\(440\) 43.9419 2.09485
\(441\) 16.1791 0.770433
\(442\) 5.88761 0.280045
\(443\) 23.4058 1.11204 0.556022 0.831167i \(-0.312327\pi\)
0.556022 + 0.831167i \(0.312327\pi\)
\(444\) −6.70910 −0.318400
\(445\) 16.9618 0.804068
\(446\) 1.10700 0.0524180
\(447\) 44.5419 2.10676
\(448\) −0.0966726 −0.00456735
\(449\) 35.8887 1.69369 0.846846 0.531838i \(-0.178498\pi\)
0.846846 + 0.531838i \(0.178498\pi\)
\(450\) −15.8374 −0.746581
\(451\) 60.5449 2.85095
\(452\) −1.74387 −0.0820247
\(453\) −11.1479 −0.523775
\(454\) −2.74728 −0.128936
\(455\) −24.2543 −1.13706
\(456\) 22.3875 1.04839
\(457\) −23.4014 −1.09467 −0.547336 0.836913i \(-0.684358\pi\)
−0.547336 + 0.836913i \(0.684358\pi\)
\(458\) −3.93623 −0.183928
\(459\) −6.88820 −0.321514
\(460\) −17.3242 −0.807744
\(461\) 17.9146 0.834366 0.417183 0.908822i \(-0.363017\pi\)
0.417183 + 0.908822i \(0.363017\pi\)
\(462\) −26.9538 −1.25400
\(463\) −32.0159 −1.48790 −0.743952 0.668233i \(-0.767051\pi\)
−0.743952 + 0.668233i \(0.767051\pi\)
\(464\) −4.09757 −0.190225
\(465\) 1.81756 0.0842874
\(466\) −8.72279 −0.404075
\(467\) −12.2949 −0.568940 −0.284470 0.958685i \(-0.591818\pi\)
−0.284470 + 0.958685i \(0.591818\pi\)
\(468\) 6.68095 0.308827
\(469\) −46.4583 −2.14524
\(470\) −26.3768 −1.21667
\(471\) 14.3259 0.660101
\(472\) 13.1439 0.604997
\(473\) 26.5353 1.22010
\(474\) −11.5429 −0.530184
\(475\) 42.9138 1.96902
\(476\) 32.5841 1.49349
\(477\) 3.26148 0.149333
\(478\) 12.2297 0.559373
\(479\) 15.1555 0.692472 0.346236 0.938148i \(-0.387460\pi\)
0.346236 + 0.938148i \(0.387460\pi\)
\(480\) 51.5708 2.35387
\(481\) −3.02746 −0.138040
\(482\) 0.630644 0.0287251
\(483\) 23.8909 1.08707
\(484\) −21.8622 −0.993735
\(485\) −35.1720 −1.59708
\(486\) 12.8508 0.582922
\(487\) −15.5008 −0.702407 −0.351204 0.936299i \(-0.614227\pi\)
−0.351204 + 0.936299i \(0.614227\pi\)
\(488\) −0.174116 −0.00788186
\(489\) −2.81536 −0.127315
\(490\) 16.1179 0.728133
\(491\) 12.5838 0.567901 0.283950 0.958839i \(-0.408355\pi\)
0.283950 + 0.958839i \(0.408355\pi\)
\(492\) 45.6894 2.05984
\(493\) −12.7712 −0.575184
\(494\) 4.49346 0.202170
\(495\) 47.7093 2.14437
\(496\) −0.353521 −0.0158736
\(497\) 19.1625 0.859553
\(498\) −3.76542 −0.168732
\(499\) −41.9638 −1.87856 −0.939280 0.343152i \(-0.888505\pi\)
−0.939280 + 0.343152i \(0.888505\pi\)
\(500\) 32.3484 1.44666
\(501\) −2.10517 −0.0940521
\(502\) 9.10910 0.406559
\(503\) 7.23458 0.322574 0.161287 0.986908i \(-0.448436\pi\)
0.161287 + 0.986908i \(0.448436\pi\)
\(504\) −20.6334 −0.919085
\(505\) −27.0532 −1.20385
\(506\) −8.68756 −0.386209
\(507\) −23.7133 −1.05314
\(508\) −0.584094 −0.0259150
\(509\) 43.2945 1.91899 0.959497 0.281718i \(-0.0909041\pi\)
0.959497 + 0.281718i \(0.0909041\pi\)
\(510\) 31.7279 1.40494
\(511\) 51.8223 2.29248
\(512\) −18.0813 −0.799090
\(513\) −5.25712 −0.232108
\(514\) −18.2259 −0.803909
\(515\) 0.409152 0.0180294
\(516\) 20.0245 0.881531
\(517\) 53.2893 2.34366
\(518\) 4.15885 0.182729
\(519\) 28.8899 1.26813
\(520\) 14.9634 0.656189
\(521\) −22.7560 −0.996961 −0.498480 0.866901i \(-0.666108\pi\)
−0.498480 + 0.866901i \(0.666108\pi\)
\(522\) 3.59715 0.157443
\(523\) 36.7529 1.60709 0.803547 0.595241i \(-0.202944\pi\)
0.803547 + 0.595241i \(0.202944\pi\)
\(524\) −8.79440 −0.384185
\(525\) −87.6573 −3.82568
\(526\) −16.5908 −0.723395
\(527\) −1.10184 −0.0479970
\(528\) −20.5662 −0.895029
\(529\) −15.2997 −0.665203
\(530\) 3.24915 0.141134
\(531\) 14.2708 0.619301
\(532\) 24.8684 1.07818
\(533\) 20.6172 0.893030
\(534\) 6.41884 0.277770
\(535\) 70.8518 3.06319
\(536\) 28.6619 1.23801
\(537\) −23.4410 −1.01156
\(538\) 5.94351 0.256243
\(539\) −32.5631 −1.40259
\(540\) −7.78681 −0.335091
\(541\) −19.7726 −0.850089 −0.425045 0.905172i \(-0.639742\pi\)
−0.425045 + 0.905172i \(0.639742\pi\)
\(542\) 3.69885 0.158879
\(543\) −39.8617 −1.71063
\(544\) −31.2633 −1.34040
\(545\) −57.1110 −2.44637
\(546\) −9.17851 −0.392804
\(547\) −9.94319 −0.425140 −0.212570 0.977146i \(-0.568183\pi\)
−0.212570 + 0.977146i \(0.568183\pi\)
\(548\) 27.4846 1.17408
\(549\) −0.189044 −0.00806820
\(550\) 31.8753 1.35917
\(551\) −9.74703 −0.415238
\(552\) −14.7392 −0.627342
\(553\) −28.8268 −1.22584
\(554\) −3.53410 −0.150149
\(555\) −16.3148 −0.692524
\(556\) 31.4167 1.33236
\(557\) −7.84163 −0.332260 −0.166130 0.986104i \(-0.553127\pi\)
−0.166130 + 0.986104i \(0.553127\pi\)
\(558\) 0.310347 0.0131380
\(559\) 9.03601 0.382182
\(560\) 25.4225 1.07430
\(561\) −64.1001 −2.70631
\(562\) 2.97455 0.125474
\(563\) −19.2105 −0.809625 −0.404813 0.914400i \(-0.632663\pi\)
−0.404813 + 0.914400i \(0.632663\pi\)
\(564\) 40.2140 1.69332
\(565\) −4.24063 −0.178405
\(566\) −12.1127 −0.509134
\(567\) 37.9861 1.59526
\(568\) −11.8221 −0.496043
\(569\) 25.1338 1.05366 0.526831 0.849970i \(-0.323380\pi\)
0.526831 + 0.849970i \(0.323380\pi\)
\(570\) 24.2150 1.01425
\(571\) −18.1912 −0.761277 −0.380638 0.924724i \(-0.624296\pi\)
−0.380638 + 0.924724i \(0.624296\pi\)
\(572\) −13.4465 −0.562227
\(573\) −55.5861 −2.32214
\(574\) −28.3220 −1.18214
\(575\) −28.2531 −1.17824
\(576\) 0.0647545 0.00269810
\(577\) 28.9417 1.20486 0.602429 0.798172i \(-0.294200\pi\)
0.602429 + 0.798172i \(0.294200\pi\)
\(578\) −8.51317 −0.354101
\(579\) 17.5208 0.728140
\(580\) −14.4372 −0.599474
\(581\) −9.40358 −0.390126
\(582\) −13.3101 −0.551721
\(583\) −6.56427 −0.271864
\(584\) −31.9712 −1.32298
\(585\) 16.2463 0.671703
\(586\) −8.20724 −0.339038
\(587\) −21.9772 −0.907098 −0.453549 0.891231i \(-0.649842\pi\)
−0.453549 + 0.891231i \(0.649842\pi\)
\(588\) −24.5733 −1.01339
\(589\) −0.840934 −0.0346501
\(590\) 14.2168 0.585298
\(591\) 4.34054 0.178546
\(592\) 3.17327 0.130421
\(593\) 15.0138 0.616544 0.308272 0.951298i \(-0.400249\pi\)
0.308272 + 0.951298i \(0.400249\pi\)
\(594\) −3.90486 −0.160218
\(595\) 79.2359 3.24836
\(596\) −30.5248 −1.25035
\(597\) 8.10529 0.331728
\(598\) −2.95835 −0.120976
\(599\) −31.7086 −1.29558 −0.647789 0.761820i \(-0.724306\pi\)
−0.647789 + 0.761820i \(0.724306\pi\)
\(600\) 54.0792 2.20777
\(601\) 5.63682 0.229931 0.114965 0.993369i \(-0.463324\pi\)
0.114965 + 0.993369i \(0.463324\pi\)
\(602\) −12.4129 −0.505910
\(603\) 31.1193 1.26727
\(604\) 7.63973 0.310856
\(605\) −53.1631 −2.16139
\(606\) −10.2377 −0.415878
\(607\) 39.7534 1.61354 0.806770 0.590866i \(-0.201214\pi\)
0.806770 + 0.590866i \(0.201214\pi\)
\(608\) −23.8603 −0.967664
\(609\) 19.9096 0.806780
\(610\) −0.188329 −0.00762522
\(611\) 18.1465 0.734127
\(612\) −21.8259 −0.882259
\(613\) 30.3066 1.22407 0.612035 0.790831i \(-0.290351\pi\)
0.612035 + 0.790831i \(0.290351\pi\)
\(614\) 7.27588 0.293631
\(615\) 111.105 4.48017
\(616\) 41.5281 1.67322
\(617\) 18.2240 0.733670 0.366835 0.930286i \(-0.380441\pi\)
0.366835 + 0.930286i \(0.380441\pi\)
\(618\) 0.154834 0.00622836
\(619\) −26.3431 −1.05882 −0.529409 0.848366i \(-0.677586\pi\)
−0.529409 + 0.848366i \(0.677586\pi\)
\(620\) −1.24559 −0.0500239
\(621\) 3.46112 0.138890
\(622\) 14.6021 0.585491
\(623\) 16.0301 0.642233
\(624\) −7.00335 −0.280359
\(625\) 27.7553 1.11021
\(626\) 4.97516 0.198848
\(627\) −48.9216 −1.95374
\(628\) −9.81759 −0.391765
\(629\) 9.89035 0.394354
\(630\) −22.3177 −0.889160
\(631\) 18.4187 0.733236 0.366618 0.930372i \(-0.380516\pi\)
0.366618 + 0.930372i \(0.380516\pi\)
\(632\) 17.7844 0.707424
\(633\) −5.45238 −0.216713
\(634\) 1.50298 0.0596910
\(635\) −1.42036 −0.0563654
\(636\) −4.95364 −0.196425
\(637\) −11.0886 −0.439347
\(638\) −7.23985 −0.286629
\(639\) −12.8356 −0.507770
\(640\) −44.0496 −1.74121
\(641\) −12.6956 −0.501446 −0.250723 0.968059i \(-0.580668\pi\)
−0.250723 + 0.968059i \(0.580668\pi\)
\(642\) 26.8123 1.05820
\(643\) −35.1591 −1.38654 −0.693270 0.720678i \(-0.743831\pi\)
−0.693270 + 0.720678i \(0.743831\pi\)
\(644\) −16.3725 −0.645169
\(645\) 48.6944 1.91734
\(646\) −14.6796 −0.577561
\(647\) 19.7535 0.776588 0.388294 0.921535i \(-0.373064\pi\)
0.388294 + 0.921535i \(0.373064\pi\)
\(648\) −23.4351 −0.920616
\(649\) −28.7224 −1.12745
\(650\) 10.8544 0.425745
\(651\) 1.71772 0.0673228
\(652\) 1.92939 0.0755606
\(653\) −44.0129 −1.72236 −0.861178 0.508303i \(-0.830273\pi\)
−0.861178 + 0.508303i \(0.830273\pi\)
\(654\) −21.6124 −0.845113
\(655\) −21.3857 −0.835608
\(656\) −21.6102 −0.843736
\(657\) −34.7123 −1.35426
\(658\) −24.9280 −0.971793
\(659\) −32.2032 −1.25446 −0.627229 0.778835i \(-0.715811\pi\)
−0.627229 + 0.778835i \(0.715811\pi\)
\(660\) −72.4623 −2.82059
\(661\) 29.5485 1.14930 0.574651 0.818398i \(-0.305138\pi\)
0.574651 + 0.818398i \(0.305138\pi\)
\(662\) 1.92724 0.0749043
\(663\) −21.8278 −0.847723
\(664\) 5.80143 0.225139
\(665\) 60.4734 2.34506
\(666\) −2.78573 −0.107945
\(667\) 6.41714 0.248473
\(668\) 1.44269 0.0558192
\(669\) −4.10412 −0.158674
\(670\) 31.0016 1.19770
\(671\) 0.380482 0.0146883
\(672\) 48.7380 1.88011
\(673\) 28.4424 1.09637 0.548186 0.836356i \(-0.315319\pi\)
0.548186 + 0.836356i \(0.315319\pi\)
\(674\) 10.2010 0.392927
\(675\) −12.6991 −0.488789
\(676\) 16.2508 0.625032
\(677\) 16.9259 0.650514 0.325257 0.945626i \(-0.394549\pi\)
0.325257 + 0.945626i \(0.394549\pi\)
\(678\) −1.60477 −0.0616310
\(679\) −33.2400 −1.27563
\(680\) −48.8837 −1.87460
\(681\) 10.1853 0.390303
\(682\) −0.624625 −0.0239181
\(683\) −29.0324 −1.11090 −0.555448 0.831551i \(-0.687453\pi\)
−0.555448 + 0.831551i \(0.687453\pi\)
\(684\) −16.6576 −0.636921
\(685\) 66.8353 2.55365
\(686\) −1.02307 −0.0390612
\(687\) 14.5933 0.556767
\(688\) −9.47121 −0.361087
\(689\) −2.23531 −0.0851586
\(690\) −15.9424 −0.606915
\(691\) −21.5798 −0.820935 −0.410467 0.911875i \(-0.634634\pi\)
−0.410467 + 0.911875i \(0.634634\pi\)
\(692\) −19.7984 −0.752623
\(693\) 45.0886 1.71277
\(694\) −15.4329 −0.585823
\(695\) 76.3972 2.89791
\(696\) −12.2830 −0.465587
\(697\) −67.3540 −2.55121
\(698\) 8.22790 0.311431
\(699\) 32.3390 1.22317
\(700\) 60.0721 2.27051
\(701\) −13.2247 −0.499489 −0.249744 0.968312i \(-0.580347\pi\)
−0.249744 + 0.968312i \(0.580347\pi\)
\(702\) −1.32971 −0.0501867
\(703\) 7.54838 0.284692
\(704\) −0.130329 −0.00491196
\(705\) 97.7900 3.68298
\(706\) −14.9329 −0.562006
\(707\) −25.5672 −0.961552
\(708\) −21.6750 −0.814595
\(709\) 18.8314 0.707228 0.353614 0.935391i \(-0.384953\pi\)
0.353614 + 0.935391i \(0.384953\pi\)
\(710\) −12.7871 −0.479891
\(711\) 19.3091 0.724149
\(712\) −9.88960 −0.370628
\(713\) 0.553644 0.0207341
\(714\) 29.9851 1.12216
\(715\) −32.6984 −1.22285
\(716\) 16.0643 0.600351
\(717\) −45.3406 −1.69328
\(718\) 16.1129 0.601328
\(719\) −37.7936 −1.40946 −0.704731 0.709475i \(-0.748932\pi\)
−0.704731 + 0.709475i \(0.748932\pi\)
\(720\) −17.0288 −0.634626
\(721\) 0.386677 0.0144006
\(722\) 0.778675 0.0289793
\(723\) −2.33806 −0.0869535
\(724\) 27.3175 1.01525
\(725\) −23.5450 −0.874438
\(726\) −20.1184 −0.746664
\(727\) −9.96692 −0.369653 −0.184826 0.982771i \(-0.559172\pi\)
−0.184826 + 0.982771i \(0.559172\pi\)
\(728\) 14.1415 0.524118
\(729\) −16.6957 −0.618359
\(730\) −34.5810 −1.27990
\(731\) −29.5196 −1.09182
\(732\) 0.287126 0.0106125
\(733\) 46.8282 1.72964 0.864819 0.502083i \(-0.167433\pi\)
0.864819 + 0.502083i \(0.167433\pi\)
\(734\) −5.27071 −0.194546
\(735\) −59.7558 −2.20413
\(736\) 15.7089 0.579037
\(737\) −62.6326 −2.30710
\(738\) 18.9710 0.698333
\(739\) 31.1213 1.14482 0.572408 0.819969i \(-0.306009\pi\)
0.572408 + 0.819969i \(0.306009\pi\)
\(740\) 11.1806 0.411007
\(741\) −16.6591 −0.611989
\(742\) 3.07067 0.112728
\(743\) −22.3465 −0.819815 −0.409907 0.912127i \(-0.634439\pi\)
−0.409907 + 0.912127i \(0.634439\pi\)
\(744\) −1.05973 −0.0388516
\(745\) −74.2283 −2.71952
\(746\) 15.5728 0.570159
\(747\) 6.29883 0.230462
\(748\) 43.9282 1.60617
\(749\) 66.9599 2.44666
\(750\) 29.7682 1.08698
\(751\) −41.3430 −1.50863 −0.754313 0.656515i \(-0.772030\pi\)
−0.754313 + 0.656515i \(0.772030\pi\)
\(752\) −19.0204 −0.693604
\(753\) −33.7713 −1.23069
\(754\) −2.46537 −0.0897834
\(755\) 18.5778 0.676116
\(756\) −7.35908 −0.267647
\(757\) −5.70532 −0.207364 −0.103682 0.994611i \(-0.533062\pi\)
−0.103682 + 0.994611i \(0.533062\pi\)
\(758\) −11.7674 −0.427411
\(759\) 32.2084 1.16909
\(760\) −37.3083 −1.35332
\(761\) 15.1656 0.549754 0.274877 0.961479i \(-0.411363\pi\)
0.274877 + 0.961479i \(0.411363\pi\)
\(762\) −0.537505 −0.0194718
\(763\) −53.9739 −1.95399
\(764\) 38.0935 1.37817
\(765\) −53.0748 −1.91892
\(766\) −7.55388 −0.272933
\(767\) −9.78075 −0.353162
\(768\) −16.7924 −0.605943
\(769\) 5.23538 0.188793 0.0943964 0.995535i \(-0.469908\pi\)
0.0943964 + 0.995535i \(0.469908\pi\)
\(770\) 44.9181 1.61874
\(771\) 67.5710 2.43351
\(772\) −12.0071 −0.432145
\(773\) −27.0422 −0.972641 −0.486321 0.873780i \(-0.661661\pi\)
−0.486321 + 0.873780i \(0.661661\pi\)
\(774\) 8.31453 0.298860
\(775\) −2.03136 −0.0729687
\(776\) 20.5070 0.736160
\(777\) −15.4186 −0.553139
\(778\) 4.80973 0.172437
\(779\) −51.4050 −1.84177
\(780\) −24.6754 −0.883521
\(781\) 25.8338 0.924407
\(782\) 9.66459 0.345605
\(783\) 2.88435 0.103078
\(784\) 11.6227 0.415096
\(785\) −23.8738 −0.852093
\(786\) −8.09294 −0.288666
\(787\) −25.6221 −0.913329 −0.456665 0.889639i \(-0.650956\pi\)
−0.456665 + 0.889639i \(0.650956\pi\)
\(788\) −2.97459 −0.105966
\(789\) 61.5092 2.18979
\(790\) 19.2361 0.684390
\(791\) −4.00769 −0.142497
\(792\) −27.8169 −0.988431
\(793\) 0.129565 0.00460097
\(794\) 21.0643 0.747545
\(795\) −12.0459 −0.427226
\(796\) −5.55460 −0.196878
\(797\) 28.8151 1.02068 0.510341 0.859972i \(-0.329519\pi\)
0.510341 + 0.859972i \(0.329519\pi\)
\(798\) 22.8848 0.810114
\(799\) −59.2823 −2.09726
\(800\) −57.6371 −2.03778
\(801\) −10.7375 −0.379391
\(802\) 1.09436 0.0386430
\(803\) 69.8642 2.46545
\(804\) −47.2649 −1.66690
\(805\) −39.8137 −1.40325
\(806\) −0.212702 −0.00749210
\(807\) −22.0351 −0.775671
\(808\) 15.7734 0.554905
\(809\) 20.6265 0.725188 0.362594 0.931947i \(-0.381891\pi\)
0.362594 + 0.931947i \(0.381891\pi\)
\(810\) −25.3481 −0.890641
\(811\) 45.2088 1.58749 0.793747 0.608248i \(-0.208127\pi\)
0.793747 + 0.608248i \(0.208127\pi\)
\(812\) −13.6442 −0.478817
\(813\) −13.7132 −0.480942
\(814\) 5.60675 0.196516
\(815\) 4.69176 0.164345
\(816\) 22.8791 0.800930
\(817\) −22.5295 −0.788208
\(818\) 2.40848 0.0842106
\(819\) 15.3539 0.536509
\(820\) −76.1407 −2.65895
\(821\) 23.2674 0.812039 0.406019 0.913864i \(-0.366917\pi\)
0.406019 + 0.913864i \(0.366917\pi\)
\(822\) 25.2924 0.882172
\(823\) 2.12031 0.0739095 0.0369547 0.999317i \(-0.488234\pi\)
0.0369547 + 0.999317i \(0.488234\pi\)
\(824\) −0.238556 −0.00831049
\(825\) −118.175 −4.11433
\(826\) 13.4359 0.467495
\(827\) −16.5417 −0.575213 −0.287606 0.957749i \(-0.592859\pi\)
−0.287606 + 0.957749i \(0.592859\pi\)
\(828\) 10.9669 0.381125
\(829\) 2.61675 0.0908835 0.0454418 0.998967i \(-0.485530\pi\)
0.0454418 + 0.998967i \(0.485530\pi\)
\(830\) 6.27501 0.217809
\(831\) 13.1024 0.454516
\(832\) −0.0443806 −0.00153862
\(833\) 36.2252 1.25513
\(834\) 28.9108 1.00110
\(835\) 3.50823 0.121407
\(836\) 33.5263 1.15953
\(837\) 0.248850 0.00860152
\(838\) −0.403668 −0.0139445
\(839\) 40.9480 1.41368 0.706841 0.707373i \(-0.250120\pi\)
0.706841 + 0.707373i \(0.250120\pi\)
\(840\) 76.2074 2.62940
\(841\) −23.6522 −0.815594
\(842\) −8.37275 −0.288544
\(843\) −11.0279 −0.379821
\(844\) 3.73655 0.128617
\(845\) 39.5178 1.35945
\(846\) 16.6976 0.574074
\(847\) −50.2428 −1.72636
\(848\) 2.34297 0.0804580
\(849\) 44.9068 1.54120
\(850\) −35.4601 −1.21627
\(851\) −4.96961 −0.170356
\(852\) 19.4952 0.667893
\(853\) 17.3933 0.595537 0.297768 0.954638i \(-0.403758\pi\)
0.297768 + 0.954638i \(0.403758\pi\)
\(854\) −0.177984 −0.00609049
\(855\) −40.5070 −1.38531
\(856\) −41.3101 −1.41195
\(857\) 16.7101 0.570805 0.285402 0.958408i \(-0.407873\pi\)
0.285402 + 0.958408i \(0.407873\pi\)
\(858\) −12.3740 −0.422441
\(859\) 13.9877 0.477255 0.238628 0.971111i \(-0.423302\pi\)
0.238628 + 0.971111i \(0.423302\pi\)
\(860\) −33.3706 −1.13793
\(861\) 105.002 3.57845
\(862\) 16.9126 0.576045
\(863\) −23.1575 −0.788290 −0.394145 0.919048i \(-0.628959\pi\)
−0.394145 + 0.919048i \(0.628959\pi\)
\(864\) 7.06078 0.240212
\(865\) −48.1446 −1.63696
\(866\) 13.0791 0.444445
\(867\) 31.5619 1.07190
\(868\) −1.17716 −0.0399556
\(869\) −38.8628 −1.31833
\(870\) −13.2857 −0.450427
\(871\) −21.3281 −0.722676
\(872\) 33.2986 1.12763
\(873\) 22.2652 0.753564
\(874\) 7.37608 0.249499
\(875\) 74.3418 2.51321
\(876\) 52.7221 1.78131
\(877\) 40.3104 1.36119 0.680594 0.732661i \(-0.261722\pi\)
0.680594 + 0.732661i \(0.261722\pi\)
\(878\) 8.03326 0.271110
\(879\) 30.4276 1.02630
\(880\) 34.2733 1.15535
\(881\) −23.2156 −0.782152 −0.391076 0.920358i \(-0.627897\pi\)
−0.391076 + 0.920358i \(0.627897\pi\)
\(882\) −10.2033 −0.343562
\(883\) −0.920055 −0.0309623 −0.0154812 0.999880i \(-0.504928\pi\)
−0.0154812 + 0.999880i \(0.504928\pi\)
\(884\) 14.9587 0.503117
\(885\) −52.7078 −1.77175
\(886\) −14.7608 −0.495897
\(887\) −28.9082 −0.970643 −0.485321 0.874336i \(-0.661297\pi\)
−0.485321 + 0.874336i \(0.661297\pi\)
\(888\) 9.51233 0.319213
\(889\) −1.34234 −0.0450207
\(890\) −10.6969 −0.358561
\(891\) 51.2109 1.71563
\(892\) 2.81257 0.0941720
\(893\) −45.2446 −1.51405
\(894\) −28.0901 −0.939473
\(895\) 39.0641 1.30577
\(896\) −41.6299 −1.39076
\(897\) 10.9679 0.366206
\(898\) −22.6330 −0.755273
\(899\) 0.461384 0.0153880
\(900\) −40.2383 −1.34128
\(901\) 7.30250 0.243282
\(902\) −38.1823 −1.27133
\(903\) 46.0196 1.53144
\(904\) 2.47250 0.0822341
\(905\) 66.4290 2.20817
\(906\) 7.03037 0.233568
\(907\) 36.3884 1.20826 0.604128 0.796887i \(-0.293522\pi\)
0.604128 + 0.796887i \(0.293522\pi\)
\(908\) −6.98007 −0.231642
\(909\) 17.1257 0.568024
\(910\) 15.2958 0.507052
\(911\) −10.8289 −0.358776 −0.179388 0.983778i \(-0.557412\pi\)
−0.179388 + 0.983778i \(0.557412\pi\)
\(912\) 17.4615 0.578208
\(913\) −12.6774 −0.419562
\(914\) 14.7580 0.488150
\(915\) 0.698214 0.0230823
\(916\) −10.0008 −0.330437
\(917\) −20.2110 −0.667424
\(918\) 4.34401 0.143374
\(919\) 28.3998 0.936823 0.468412 0.883510i \(-0.344826\pi\)
0.468412 + 0.883510i \(0.344826\pi\)
\(920\) 24.5626 0.809806
\(921\) −26.9747 −0.888847
\(922\) −11.2977 −0.372071
\(923\) 8.79712 0.289561
\(924\) −68.4820 −2.25289
\(925\) 18.2339 0.599526
\(926\) 20.1906 0.663505
\(927\) −0.259009 −0.00850696
\(928\) 13.0911 0.429737
\(929\) −32.8431 −1.07755 −0.538774 0.842451i \(-0.681112\pi\)
−0.538774 + 0.842451i \(0.681112\pi\)
\(930\) −1.14623 −0.0375865
\(931\) 27.6473 0.906104
\(932\) −22.1621 −0.725944
\(933\) −54.1361 −1.77233
\(934\) 7.75371 0.253709
\(935\) 106.822 3.49345
\(936\) −9.47242 −0.309616
\(937\) 4.11911 0.134566 0.0672828 0.997734i \(-0.478567\pi\)
0.0672828 + 0.997734i \(0.478567\pi\)
\(938\) 29.2986 0.956635
\(939\) −18.4450 −0.601930
\(940\) −67.0161 −2.18582
\(941\) −8.26409 −0.269402 −0.134701 0.990886i \(-0.543007\pi\)
−0.134701 + 0.990886i \(0.543007\pi\)
\(942\) −9.03452 −0.294361
\(943\) 33.8434 1.10209
\(944\) 10.2518 0.333668
\(945\) −17.8953 −0.582136
\(946\) −16.7344 −0.544081
\(947\) 43.3860 1.40986 0.704928 0.709279i \(-0.250979\pi\)
0.704928 + 0.709279i \(0.250979\pi\)
\(948\) −29.3273 −0.952506
\(949\) 23.7907 0.772277
\(950\) −27.0634 −0.878051
\(951\) −5.57218 −0.180690
\(952\) −46.1985 −1.49730
\(953\) −26.7790 −0.867457 −0.433728 0.901044i \(-0.642802\pi\)
−0.433728 + 0.901044i \(0.642802\pi\)
\(954\) −2.05684 −0.0665925
\(955\) 92.6333 2.99754
\(956\) 31.0722 1.00495
\(957\) 26.8412 0.867651
\(958\) −9.55772 −0.308796
\(959\) 63.1640 2.03967
\(960\) −0.239164 −0.00771898
\(961\) −30.9602 −0.998716
\(962\) 1.90925 0.0615567
\(963\) −44.8519 −1.44533
\(964\) 1.60229 0.0516062
\(965\) −29.1981 −0.939922
\(966\) −15.0666 −0.484761
\(967\) 7.46107 0.239932 0.119966 0.992778i \(-0.461721\pi\)
0.119966 + 0.992778i \(0.461721\pi\)
\(968\) 30.9967 0.996272
\(969\) 54.4234 1.74833
\(970\) 22.1810 0.712190
\(971\) −21.4365 −0.687931 −0.343966 0.938982i \(-0.611770\pi\)
−0.343966 + 0.938982i \(0.611770\pi\)
\(972\) 32.6501 1.04725
\(973\) 72.2006 2.31465
\(974\) 9.77548 0.313226
\(975\) −40.2419 −1.28877
\(976\) −0.135805 −0.00434700
\(977\) −30.9584 −0.990446 −0.495223 0.868766i \(-0.664914\pi\)
−0.495223 + 0.868766i \(0.664914\pi\)
\(978\) 1.77549 0.0567740
\(979\) 21.6110 0.690690
\(980\) 40.9510 1.30813
\(981\) 36.1535 1.15429
\(982\) −7.93592 −0.253246
\(983\) 13.6397 0.435040 0.217520 0.976056i \(-0.430203\pi\)
0.217520 + 0.976056i \(0.430203\pi\)
\(984\) −64.7796 −2.06510
\(985\) −7.23343 −0.230476
\(986\) 8.05406 0.256494
\(987\) 92.4183 2.94171
\(988\) 11.4166 0.363211
\(989\) 14.8327 0.471653
\(990\) −30.0876 −0.956247
\(991\) −46.0458 −1.46269 −0.731347 0.682006i \(-0.761108\pi\)
−0.731347 + 0.682006i \(0.761108\pi\)
\(992\) 1.12945 0.0358600
\(993\) −7.14508 −0.226742
\(994\) −12.0847 −0.383303
\(995\) −13.5073 −0.428211
\(996\) −9.56685 −0.303137
\(997\) 57.1775 1.81083 0.905415 0.424527i \(-0.139560\pi\)
0.905415 + 0.424527i \(0.139560\pi\)
\(998\) 26.4643 0.837711
\(999\) −2.23373 −0.0706719
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 241.2.a.a.1.4 7
3.2 odd 2 2169.2.a.e.1.4 7
4.3 odd 2 3856.2.a.j.1.1 7
5.4 even 2 6025.2.a.f.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.4 7 1.1 even 1 trivial
2169.2.a.e.1.4 7 3.2 odd 2
3856.2.a.j.1.1 7 4.3 odd 2
6025.2.a.f.1.4 7 5.4 even 2