Properties

Label 145.2.a.c.1.1
Level $145$
Weight $2$
Character 145.1
Self dual yes
Analytic conductor $1.158$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [145,2,Mod(1,145)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(145, 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("145.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 145 = 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 145.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: \(1.15783082931\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) 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 1.1
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 145.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.48119 q^{2} +0.806063 q^{3} +0.193937 q^{4} +1.00000 q^{5} -1.19394 q^{6} +1.19394 q^{7} +2.67513 q^{8} -2.35026 q^{9} +O(q^{10})\) \(q-1.48119 q^{2} +0.806063 q^{3} +0.193937 q^{4} +1.00000 q^{5} -1.19394 q^{6} +1.19394 q^{7} +2.67513 q^{8} -2.35026 q^{9} -1.48119 q^{10} +4.15633 q^{11} +0.156325 q^{12} +2.96239 q^{13} -1.76845 q^{14} +0.806063 q^{15} -4.35026 q^{16} +5.50659 q^{17} +3.48119 q^{18} -3.19394 q^{19} +0.193937 q^{20} +0.962389 q^{21} -6.15633 q^{22} +1.84367 q^{23} +2.15633 q^{24} +1.00000 q^{25} -4.38787 q^{26} -4.31265 q^{27} +0.231548 q^{28} -1.00000 q^{29} -1.19394 q^{30} -4.80606 q^{31} +1.09332 q^{32} +3.35026 q^{33} -8.15633 q^{34} +1.19394 q^{35} -0.455802 q^{36} -9.50659 q^{37} +4.73084 q^{38} +2.38787 q^{39} +2.67513 q^{40} -11.2750 q^{41} -1.42548 q^{42} -0.0303172 q^{43} +0.806063 q^{44} -2.35026 q^{45} -2.73084 q^{46} +4.80606 q^{47} -3.50659 q^{48} -5.57452 q^{49} -1.48119 q^{50} +4.43866 q^{51} +0.574515 q^{52} -1.35026 q^{53} +6.38787 q^{54} +4.15633 q^{55} +3.19394 q^{56} -2.57452 q^{57} +1.48119 q^{58} +13.2750 q^{59} +0.156325 q^{60} +8.88717 q^{61} +7.11871 q^{62} -2.80606 q^{63} +7.08110 q^{64} +2.96239 q^{65} -4.96239 q^{66} +5.84367 q^{67} +1.06793 q^{68} +1.48612 q^{69} -1.76845 q^{70} -1.27504 q^{71} -6.28726 q^{72} -15.2447 q^{73} +14.0811 q^{74} +0.806063 q^{75} -0.619421 q^{76} +4.96239 q^{77} -3.53690 q^{78} -4.93207 q^{79} -4.35026 q^{80} +3.57452 q^{81} +16.7005 q^{82} +4.41819 q^{83} +0.186642 q^{84} +5.50659 q^{85} +0.0449056 q^{86} -0.806063 q^{87} +11.1187 q^{88} -3.61213 q^{89} +3.48119 q^{90} +3.53690 q^{91} +0.357556 q^{92} -3.87399 q^{93} -7.11871 q^{94} -3.19394 q^{95} +0.881286 q^{96} -1.38058 q^{97} +8.25694 q^{98} -9.76845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 4 q^{6} + 4 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 4 q^{6} + 4 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} + 2 q^{11} - 10 q^{12} - 2 q^{13} + 6 q^{14} + 2 q^{15} - 3 q^{16} - 4 q^{17} + 5 q^{18} - 10 q^{19} + q^{20} - 8 q^{21} - 8 q^{22} + 16 q^{23} - 4 q^{24} + 3 q^{25} - 14 q^{26} + 8 q^{27} + 12 q^{28} - 3 q^{29} - 4 q^{30} - 14 q^{31} - 3 q^{32} - 14 q^{34} + 4 q^{35} - 11 q^{36} - 8 q^{37} - 8 q^{38} + 8 q^{39} + 3 q^{40} - 2 q^{41} - 16 q^{42} + 2 q^{43} + 2 q^{44} + 3 q^{45} + 14 q^{46} + 14 q^{47} + 10 q^{48} - 5 q^{49} + q^{50} - 16 q^{51} - 10 q^{52} + 6 q^{53} + 20 q^{54} + 2 q^{55} + 10 q^{56} + 4 q^{57} - q^{58} + 8 q^{59} - 10 q^{60} - 6 q^{61} - 8 q^{63} - 11 q^{64} - 2 q^{65} - 4 q^{66} + 28 q^{67} + 12 q^{68} + 12 q^{69} + 6 q^{70} + 28 q^{71} - 13 q^{72} - 16 q^{73} + 10 q^{74} + 2 q^{75} - 14 q^{76} + 4 q^{77} + 12 q^{78} - 6 q^{79} - 3 q^{80} - q^{81} + 30 q^{82} + 12 q^{83} - 12 q^{84} - 4 q^{85} + 24 q^{86} - 2 q^{87} + 12 q^{88} - 10 q^{89} + 5 q^{90} - 12 q^{91} + 4 q^{92} - 20 q^{93} - 10 q^{95} + 24 q^{96} + 8 q^{97} + 21 q^{98} - 18 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.48119 −1.04736 −0.523681 0.851914i \(-0.675442\pi\)
−0.523681 + 0.851914i \(0.675442\pi\)
\(3\) 0.806063 0.465381 0.232690 0.972551i \(-0.425247\pi\)
0.232690 + 0.972551i \(0.425247\pi\)
\(4\) 0.193937 0.0969683
\(5\) 1.00000 0.447214
\(6\) −1.19394 −0.487423
\(7\) 1.19394 0.451266 0.225633 0.974212i \(-0.427555\pi\)
0.225633 + 0.974212i \(0.427555\pi\)
\(8\) 2.67513 0.945802
\(9\) −2.35026 −0.783421
\(10\) −1.48119 −0.468395
\(11\) 4.15633 1.25318 0.626590 0.779349i \(-0.284450\pi\)
0.626590 + 0.779349i \(0.284450\pi\)
\(12\) 0.156325 0.0451272
\(13\) 2.96239 0.821619 0.410809 0.911721i \(-0.365246\pi\)
0.410809 + 0.911721i \(0.365246\pi\)
\(14\) −1.76845 −0.472639
\(15\) 0.806063 0.208125
\(16\) −4.35026 −1.08757
\(17\) 5.50659 1.33554 0.667772 0.744366i \(-0.267248\pi\)
0.667772 + 0.744366i \(0.267248\pi\)
\(18\) 3.48119 0.820525
\(19\) −3.19394 −0.732739 −0.366370 0.930469i \(-0.619399\pi\)
−0.366370 + 0.930469i \(0.619399\pi\)
\(20\) 0.193937 0.0433655
\(21\) 0.962389 0.210010
\(22\) −6.15633 −1.31253
\(23\) 1.84367 0.384433 0.192216 0.981353i \(-0.438432\pi\)
0.192216 + 0.981353i \(0.438432\pi\)
\(24\) 2.15633 0.440158
\(25\) 1.00000 0.200000
\(26\) −4.38787 −0.860533
\(27\) −4.31265 −0.829970
\(28\) 0.231548 0.0437585
\(29\) −1.00000 −0.185695
\(30\) −1.19394 −0.217982
\(31\) −4.80606 −0.863194 −0.431597 0.902066i \(-0.642050\pi\)
−0.431597 + 0.902066i \(0.642050\pi\)
\(32\) 1.09332 0.193274
\(33\) 3.35026 0.583206
\(34\) −8.15633 −1.39880
\(35\) 1.19394 0.201812
\(36\) −0.455802 −0.0759669
\(37\) −9.50659 −1.56287 −0.781437 0.623985i \(-0.785513\pi\)
−0.781437 + 0.623985i \(0.785513\pi\)
\(38\) 4.73084 0.767444
\(39\) 2.38787 0.382366
\(40\) 2.67513 0.422975
\(41\) −11.2750 −1.76087 −0.880433 0.474171i \(-0.842748\pi\)
−0.880433 + 0.474171i \(0.842748\pi\)
\(42\) −1.42548 −0.219957
\(43\) −0.0303172 −0.00462332 −0.00231166 0.999997i \(-0.500736\pi\)
−0.00231166 + 0.999997i \(0.500736\pi\)
\(44\) 0.806063 0.121519
\(45\) −2.35026 −0.350356
\(46\) −2.73084 −0.402640
\(47\) 4.80606 0.701036 0.350518 0.936556i \(-0.386005\pi\)
0.350518 + 0.936556i \(0.386005\pi\)
\(48\) −3.50659 −0.506132
\(49\) −5.57452 −0.796359
\(50\) −1.48119 −0.209473
\(51\) 4.43866 0.621536
\(52\) 0.574515 0.0796710
\(53\) −1.35026 −0.185473 −0.0927364 0.995691i \(-0.529561\pi\)
−0.0927364 + 0.995691i \(0.529561\pi\)
\(54\) 6.38787 0.869279
\(55\) 4.15633 0.560439
\(56\) 3.19394 0.426808
\(57\) −2.57452 −0.341003
\(58\) 1.48119 0.194490
\(59\) 13.2750 1.72826 0.864131 0.503266i \(-0.167868\pi\)
0.864131 + 0.503266i \(0.167868\pi\)
\(60\) 0.156325 0.0201815
\(61\) 8.88717 1.13788 0.568942 0.822377i \(-0.307353\pi\)
0.568942 + 0.822377i \(0.307353\pi\)
\(62\) 7.11871 0.904078
\(63\) −2.80606 −0.353531
\(64\) 7.08110 0.885138
\(65\) 2.96239 0.367439
\(66\) −4.96239 −0.610828
\(67\) 5.84367 0.713919 0.356959 0.934120i \(-0.383813\pi\)
0.356959 + 0.934120i \(0.383813\pi\)
\(68\) 1.06793 0.129505
\(69\) 1.48612 0.178908
\(70\) −1.76845 −0.211370
\(71\) −1.27504 −0.151319 −0.0756596 0.997134i \(-0.524106\pi\)
−0.0756596 + 0.997134i \(0.524106\pi\)
\(72\) −6.28726 −0.740960
\(73\) −15.2447 −1.78426 −0.892130 0.451779i \(-0.850790\pi\)
−0.892130 + 0.451779i \(0.850790\pi\)
\(74\) 14.0811 1.63689
\(75\) 0.806063 0.0930762
\(76\) −0.619421 −0.0710525
\(77\) 4.96239 0.565517
\(78\) −3.53690 −0.400476
\(79\) −4.93207 −0.554901 −0.277451 0.960740i \(-0.589490\pi\)
−0.277451 + 0.960740i \(0.589490\pi\)
\(80\) −4.35026 −0.486374
\(81\) 3.57452 0.397168
\(82\) 16.7005 1.84426
\(83\) 4.41819 0.484959 0.242480 0.970156i \(-0.422039\pi\)
0.242480 + 0.970156i \(0.422039\pi\)
\(84\) 0.186642 0.0203643
\(85\) 5.50659 0.597273
\(86\) 0.0449056 0.00484230
\(87\) −0.806063 −0.0864191
\(88\) 11.1187 1.18526
\(89\) −3.61213 −0.382885 −0.191442 0.981504i \(-0.561316\pi\)
−0.191442 + 0.981504i \(0.561316\pi\)
\(90\) 3.48119 0.366950
\(91\) 3.53690 0.370768
\(92\) 0.357556 0.0372778
\(93\) −3.87399 −0.401714
\(94\) −7.11871 −0.734239
\(95\) −3.19394 −0.327691
\(96\) 0.881286 0.0899459
\(97\) −1.38058 −0.140177 −0.0700883 0.997541i \(-0.522328\pi\)
−0.0700883 + 0.997541i \(0.522328\pi\)
\(98\) 8.25694 0.834077
\(99\) −9.76845 −0.981766
\(100\) 0.193937 0.0193937
\(101\) −13.0132 −1.29486 −0.647430 0.762125i \(-0.724156\pi\)
−0.647430 + 0.762125i \(0.724156\pi\)
\(102\) −6.57452 −0.650974
\(103\) 5.31994 0.524190 0.262095 0.965042i \(-0.415587\pi\)
0.262095 + 0.965042i \(0.415587\pi\)
\(104\) 7.92478 0.777088
\(105\) 0.962389 0.0939195
\(106\) 2.00000 0.194257
\(107\) −13.8192 −1.33596 −0.667978 0.744181i \(-0.732840\pi\)
−0.667978 + 0.744181i \(0.732840\pi\)
\(108\) −0.836381 −0.0804808
\(109\) −1.87399 −0.179496 −0.0897479 0.995965i \(-0.528606\pi\)
−0.0897479 + 0.995965i \(0.528606\pi\)
\(110\) −6.15633 −0.586983
\(111\) −7.66291 −0.727331
\(112\) −5.19394 −0.490781
\(113\) −11.7685 −1.10708 −0.553541 0.832822i \(-0.686724\pi\)
−0.553541 + 0.832822i \(0.686724\pi\)
\(114\) 3.81336 0.357154
\(115\) 1.84367 0.171924
\(116\) −0.193937 −0.0180066
\(117\) −6.96239 −0.643673
\(118\) −19.6629 −1.81012
\(119\) 6.57452 0.602685
\(120\) 2.15633 0.196845
\(121\) 6.27504 0.570458
\(122\) −13.1636 −1.19178
\(123\) −9.08840 −0.819473
\(124\) −0.932071 −0.0837025
\(125\) 1.00000 0.0894427
\(126\) 4.15633 0.370275
\(127\) 14.2677 1.26606 0.633029 0.774128i \(-0.281811\pi\)
0.633029 + 0.774128i \(0.281811\pi\)
\(128\) −12.6751 −1.12033
\(129\) −0.0244376 −0.00215161
\(130\) −4.38787 −0.384842
\(131\) 5.89446 0.515001 0.257501 0.966278i \(-0.417101\pi\)
0.257501 + 0.966278i \(0.417101\pi\)
\(132\) 0.649738 0.0565525
\(133\) −3.81336 −0.330660
\(134\) −8.65562 −0.747731
\(135\) −4.31265 −0.371174
\(136\) 14.7308 1.26316
\(137\) 18.2823 1.56197 0.780983 0.624553i \(-0.214719\pi\)
0.780983 + 0.624553i \(0.214719\pi\)
\(138\) −2.20123 −0.187381
\(139\) −11.5369 −0.978547 −0.489274 0.872130i \(-0.662738\pi\)
−0.489274 + 0.872130i \(0.662738\pi\)
\(140\) 0.231548 0.0195694
\(141\) 3.87399 0.326249
\(142\) 1.88858 0.158486
\(143\) 12.3127 1.02964
\(144\) 10.2243 0.852021
\(145\) −1.00000 −0.0830455
\(146\) 22.5804 1.86877
\(147\) −4.49341 −0.370610
\(148\) −1.84367 −0.151549
\(149\) 2.77575 0.227398 0.113699 0.993515i \(-0.463730\pi\)
0.113699 + 0.993515i \(0.463730\pi\)
\(150\) −1.19394 −0.0974845
\(151\) 1.79877 0.146382 0.0731909 0.997318i \(-0.476682\pi\)
0.0731909 + 0.997318i \(0.476682\pi\)
\(152\) −8.54420 −0.693026
\(153\) −12.9419 −1.04629
\(154\) −7.35026 −0.592301
\(155\) −4.80606 −0.386032
\(156\) 0.463096 0.0370773
\(157\) 3.76845 0.300755 0.150378 0.988629i \(-0.451951\pi\)
0.150378 + 0.988629i \(0.451951\pi\)
\(158\) 7.30536 0.581183
\(159\) −1.08840 −0.0863155
\(160\) 1.09332 0.0864346
\(161\) 2.20123 0.173481
\(162\) −5.29455 −0.415979
\(163\) 1.64244 0.128646 0.0643231 0.997929i \(-0.479511\pi\)
0.0643231 + 0.997929i \(0.479511\pi\)
\(164\) −2.18664 −0.170748
\(165\) 3.35026 0.260818
\(166\) −6.54420 −0.507928
\(167\) 8.08110 0.625334 0.312667 0.949863i \(-0.398778\pi\)
0.312667 + 0.949863i \(0.398778\pi\)
\(168\) 2.57452 0.198628
\(169\) −4.22425 −0.324943
\(170\) −8.15633 −0.625562
\(171\) 7.50659 0.574043
\(172\) −0.00587961 −0.000448316 0
\(173\) −7.73813 −0.588320 −0.294160 0.955756i \(-0.595040\pi\)
−0.294160 + 0.955756i \(0.595040\pi\)
\(174\) 1.19394 0.0905121
\(175\) 1.19394 0.0902531
\(176\) −18.0811 −1.36291
\(177\) 10.7005 0.804301
\(178\) 5.35026 0.401019
\(179\) −21.4010 −1.59959 −0.799795 0.600274i \(-0.795058\pi\)
−0.799795 + 0.600274i \(0.795058\pi\)
\(180\) −0.455802 −0.0339735
\(181\) 15.2750 1.13538 0.567692 0.823241i \(-0.307836\pi\)
0.567692 + 0.823241i \(0.307836\pi\)
\(182\) −5.23884 −0.388329
\(183\) 7.16362 0.529550
\(184\) 4.93207 0.363597
\(185\) −9.50659 −0.698938
\(186\) 5.73813 0.420740
\(187\) 22.8872 1.67368
\(188\) 0.932071 0.0679783
\(189\) −5.14903 −0.374537
\(190\) 4.73084 0.343211
\(191\) 3.31994 0.240223 0.120111 0.992760i \(-0.461675\pi\)
0.120111 + 0.992760i \(0.461675\pi\)
\(192\) 5.70782 0.411926
\(193\) −4.88129 −0.351363 −0.175681 0.984447i \(-0.556213\pi\)
−0.175681 + 0.984447i \(0.556213\pi\)
\(194\) 2.04491 0.146816
\(195\) 2.38787 0.170999
\(196\) −1.08110 −0.0772216
\(197\) −24.2374 −1.72685 −0.863423 0.504481i \(-0.831684\pi\)
−0.863423 + 0.504481i \(0.831684\pi\)
\(198\) 14.4690 1.02827
\(199\) 16.7513 1.18747 0.593734 0.804661i \(-0.297653\pi\)
0.593734 + 0.804661i \(0.297653\pi\)
\(200\) 2.67513 0.189160
\(201\) 4.71037 0.332244
\(202\) 19.2750 1.35619
\(203\) −1.19394 −0.0837979
\(204\) 0.860818 0.0602693
\(205\) −11.2750 −0.787483
\(206\) −7.87987 −0.549017
\(207\) −4.33312 −0.301173
\(208\) −12.8872 −0.893564
\(209\) −13.2750 −0.918254
\(210\) −1.42548 −0.0983678
\(211\) −25.3054 −1.74209 −0.871046 0.491201i \(-0.836558\pi\)
−0.871046 + 0.491201i \(0.836558\pi\)
\(212\) −0.261865 −0.0179850
\(213\) −1.02776 −0.0704211
\(214\) 20.4690 1.39923
\(215\) −0.0303172 −0.00206761
\(216\) −11.5369 −0.784987
\(217\) −5.73813 −0.389530
\(218\) 2.77575 0.187997
\(219\) −12.2882 −0.830360
\(220\) 0.806063 0.0543448
\(221\) 16.3127 1.09731
\(222\) 11.3503 0.761780
\(223\) 17.6932 1.18483 0.592413 0.805634i \(-0.298175\pi\)
0.592413 + 0.805634i \(0.298175\pi\)
\(224\) 1.30536 0.0872178
\(225\) −2.35026 −0.156684
\(226\) 17.4314 1.15952
\(227\) 26.8423 1.78158 0.890792 0.454412i \(-0.150151\pi\)
0.890792 + 0.454412i \(0.150151\pi\)
\(228\) −0.499293 −0.0330665
\(229\) −17.2243 −1.13821 −0.569105 0.822265i \(-0.692710\pi\)
−0.569105 + 0.822265i \(0.692710\pi\)
\(230\) −2.73084 −0.180066
\(231\) 4.00000 0.263181
\(232\) −2.67513 −0.175631
\(233\) −9.07381 −0.594445 −0.297222 0.954808i \(-0.596060\pi\)
−0.297222 + 0.954808i \(0.596060\pi\)
\(234\) 10.3127 0.674159
\(235\) 4.80606 0.313513
\(236\) 2.57452 0.167587
\(237\) −3.97556 −0.258241
\(238\) −9.73813 −0.631230
\(239\) 20.4993 1.32599 0.662995 0.748624i \(-0.269285\pi\)
0.662995 + 0.748624i \(0.269285\pi\)
\(240\) −3.50659 −0.226349
\(241\) 5.47627 0.352758 0.176379 0.984322i \(-0.443562\pi\)
0.176379 + 0.984322i \(0.443562\pi\)
\(242\) −9.29455 −0.597476
\(243\) 15.8192 1.01480
\(244\) 1.72355 0.110339
\(245\) −5.57452 −0.356143
\(246\) 13.4617 0.858285
\(247\) −9.46168 −0.602032
\(248\) −12.8568 −0.816411
\(249\) 3.56134 0.225691
\(250\) −1.48119 −0.0936790
\(251\) −29.6180 −1.86947 −0.934736 0.355343i \(-0.884364\pi\)
−0.934736 + 0.355343i \(0.884364\pi\)
\(252\) −0.544198 −0.0342813
\(253\) 7.66291 0.481763
\(254\) −21.1333 −1.32602
\(255\) 4.43866 0.277960
\(256\) 4.61213 0.288258
\(257\) 17.6629 1.10178 0.550891 0.834577i \(-0.314288\pi\)
0.550891 + 0.834577i \(0.314288\pi\)
\(258\) 0.0361968 0.00225351
\(259\) −11.3503 −0.705271
\(260\) 0.574515 0.0356299
\(261\) 2.35026 0.145478
\(262\) −8.73084 −0.539393
\(263\) 27.3561 1.68685 0.843426 0.537245i \(-0.180535\pi\)
0.843426 + 0.537245i \(0.180535\pi\)
\(264\) 8.96239 0.551597
\(265\) −1.35026 −0.0829459
\(266\) 5.64832 0.346321
\(267\) −2.91160 −0.178187
\(268\) 1.13330 0.0692275
\(269\) 10.4993 0.640153 0.320077 0.947392i \(-0.396291\pi\)
0.320077 + 0.947392i \(0.396291\pi\)
\(270\) 6.38787 0.388754
\(271\) −9.61801 −0.584252 −0.292126 0.956380i \(-0.594363\pi\)
−0.292126 + 0.956380i \(0.594363\pi\)
\(272\) −23.9551 −1.45249
\(273\) 2.85097 0.172548
\(274\) −27.0797 −1.63594
\(275\) 4.15633 0.250636
\(276\) 0.288213 0.0173484
\(277\) 13.3503 0.802139 0.401070 0.916048i \(-0.368638\pi\)
0.401070 + 0.916048i \(0.368638\pi\)
\(278\) 17.0884 1.02489
\(279\) 11.2955 0.676244
\(280\) 3.19394 0.190874
\(281\) 20.4241 1.21840 0.609199 0.793017i \(-0.291491\pi\)
0.609199 + 0.793017i \(0.291491\pi\)
\(282\) −5.73813 −0.341701
\(283\) −8.02047 −0.476767 −0.238384 0.971171i \(-0.576618\pi\)
−0.238384 + 0.971171i \(0.576618\pi\)
\(284\) −0.247277 −0.0146732
\(285\) −2.57452 −0.152501
\(286\) −18.2374 −1.07840
\(287\) −13.4617 −0.794618
\(288\) −2.56959 −0.151415
\(289\) 13.3225 0.783676
\(290\) 1.48119 0.0869787
\(291\) −1.11283 −0.0652355
\(292\) −2.95651 −0.173017
\(293\) −23.3054 −1.36151 −0.680757 0.732510i \(-0.738349\pi\)
−0.680757 + 0.732510i \(0.738349\pi\)
\(294\) 6.65562 0.388164
\(295\) 13.2750 0.772903
\(296\) −25.4314 −1.47817
\(297\) −17.9248 −1.04010
\(298\) −4.11142 −0.238168
\(299\) 5.46168 0.315857
\(300\) 0.156325 0.00902544
\(301\) −0.0361968 −0.00208635
\(302\) −2.66433 −0.153315
\(303\) −10.4894 −0.602603
\(304\) 13.8945 0.796902
\(305\) 8.88717 0.508878
\(306\) 19.1695 1.09585
\(307\) −6.73084 −0.384149 −0.192075 0.981380i \(-0.561522\pi\)
−0.192075 + 0.981380i \(0.561522\pi\)
\(308\) 0.962389 0.0548372
\(309\) 4.28821 0.243948
\(310\) 7.11871 0.404316
\(311\) −22.0567 −1.25072 −0.625359 0.780337i \(-0.715048\pi\)
−0.625359 + 0.780337i \(0.715048\pi\)
\(312\) 6.38787 0.361642
\(313\) 5.03761 0.284743 0.142371 0.989813i \(-0.454527\pi\)
0.142371 + 0.989813i \(0.454527\pi\)
\(314\) −5.58181 −0.315000
\(315\) −2.80606 −0.158104
\(316\) −0.956509 −0.0538078
\(317\) 34.2941 1.92615 0.963074 0.269237i \(-0.0867714\pi\)
0.963074 + 0.269237i \(0.0867714\pi\)
\(318\) 1.61213 0.0904036
\(319\) −4.15633 −0.232710
\(320\) 7.08110 0.395846
\(321\) −11.1392 −0.621729
\(322\) −3.26045 −0.181698
\(323\) −17.5877 −0.978605
\(324\) 0.693229 0.0385127
\(325\) 2.96239 0.164324
\(326\) −2.43278 −0.134739
\(327\) −1.51056 −0.0835340
\(328\) −30.1622 −1.66543
\(329\) 5.73813 0.316354
\(330\) −4.96239 −0.273171
\(331\) −34.8324 −1.91456 −0.957281 0.289159i \(-0.906625\pi\)
−0.957281 + 0.289159i \(0.906625\pi\)
\(332\) 0.856849 0.0470257
\(333\) 22.3430 1.22439
\(334\) −11.9697 −0.654952
\(335\) 5.84367 0.319274
\(336\) −4.18664 −0.228400
\(337\) −17.6326 −0.960509 −0.480254 0.877129i \(-0.659456\pi\)
−0.480254 + 0.877129i \(0.659456\pi\)
\(338\) 6.25694 0.340333
\(339\) −9.48612 −0.515215
\(340\) 1.06793 0.0579166
\(341\) −19.9756 −1.08174
\(342\) −11.1187 −0.601231
\(343\) −15.0132 −0.810635
\(344\) −0.0811024 −0.00437275
\(345\) 1.48612 0.0800099
\(346\) 11.4617 0.616184
\(347\) −3.11871 −0.167421 −0.0837107 0.996490i \(-0.526677\pi\)
−0.0837107 + 0.996490i \(0.526677\pi\)
\(348\) −0.156325 −0.00837991
\(349\) −13.0738 −0.699825 −0.349912 0.936782i \(-0.613789\pi\)
−0.349912 + 0.936782i \(0.613789\pi\)
\(350\) −1.76845 −0.0945277
\(351\) −12.7757 −0.681919
\(352\) 4.54420 0.242207
\(353\) 5.19982 0.276758 0.138379 0.990379i \(-0.455811\pi\)
0.138379 + 0.990379i \(0.455811\pi\)
\(354\) −15.8496 −0.842394
\(355\) −1.27504 −0.0676720
\(356\) −0.700523 −0.0371277
\(357\) 5.29948 0.280478
\(358\) 31.6991 1.67535
\(359\) 30.4182 1.60541 0.802705 0.596376i \(-0.203393\pi\)
0.802705 + 0.596376i \(0.203393\pi\)
\(360\) −6.28726 −0.331368
\(361\) −8.79877 −0.463093
\(362\) −22.6253 −1.18916
\(363\) 5.05808 0.265480
\(364\) 0.685935 0.0359528
\(365\) −15.2447 −0.797945
\(366\) −10.6107 −0.554631
\(367\) 20.6556 1.07821 0.539107 0.842237i \(-0.318762\pi\)
0.539107 + 0.842237i \(0.318762\pi\)
\(368\) −8.02047 −0.418096
\(369\) 26.4993 1.37950
\(370\) 14.0811 0.732042
\(371\) −1.61213 −0.0836975
\(372\) −0.751309 −0.0389535
\(373\) 11.0884 0.574135 0.287068 0.957910i \(-0.407320\pi\)
0.287068 + 0.957910i \(0.407320\pi\)
\(374\) −33.9003 −1.75294
\(375\) 0.806063 0.0416249
\(376\) 12.8568 0.663041
\(377\) −2.96239 −0.152571
\(378\) 7.62672 0.392276
\(379\) 10.0811 0.517831 0.258916 0.965900i \(-0.416635\pi\)
0.258916 + 0.965900i \(0.416635\pi\)
\(380\) −0.619421 −0.0317756
\(381\) 11.5007 0.589199
\(382\) −4.91748 −0.251600
\(383\) 16.3576 0.835832 0.417916 0.908486i \(-0.362761\pi\)
0.417916 + 0.908486i \(0.362761\pi\)
\(384\) −10.2170 −0.521382
\(385\) 4.96239 0.252907
\(386\) 7.23013 0.368004
\(387\) 0.0712533 0.00362201
\(388\) −0.267745 −0.0135927
\(389\) 31.9003 1.61741 0.808706 0.588213i \(-0.200169\pi\)
0.808706 + 0.588213i \(0.200169\pi\)
\(390\) −3.53690 −0.179098
\(391\) 10.1524 0.513427
\(392\) −14.9126 −0.753198
\(393\) 4.75131 0.239672
\(394\) 35.9003 1.80863
\(395\) −4.93207 −0.248159
\(396\) −1.89446 −0.0952002
\(397\) 2.98683 0.149905 0.0749523 0.997187i \(-0.476120\pi\)
0.0749523 + 0.997187i \(0.476120\pi\)
\(398\) −24.8119 −1.24371
\(399\) −3.07381 −0.153883
\(400\) −4.35026 −0.217513
\(401\) −21.9756 −1.09741 −0.548704 0.836017i \(-0.684878\pi\)
−0.548704 + 0.836017i \(0.684878\pi\)
\(402\) −6.97698 −0.347980
\(403\) −14.2374 −0.709217
\(404\) −2.52373 −0.125560
\(405\) 3.57452 0.177619
\(406\) 1.76845 0.0877668
\(407\) −39.5125 −1.95856
\(408\) 11.8740 0.587850
\(409\) −22.4387 −1.10952 −0.554760 0.832010i \(-0.687190\pi\)
−0.554760 + 0.832010i \(0.687190\pi\)
\(410\) 16.7005 0.824780
\(411\) 14.7367 0.726909
\(412\) 1.03173 0.0508298
\(413\) 15.8496 0.779906
\(414\) 6.41819 0.315437
\(415\) 4.41819 0.216880
\(416\) 3.23884 0.158797
\(417\) −9.29948 −0.455397
\(418\) 19.6629 0.961744
\(419\) 10.3634 0.506287 0.253143 0.967429i \(-0.418536\pi\)
0.253143 + 0.967429i \(0.418536\pi\)
\(420\) 0.186642 0.00910721
\(421\) 34.0362 1.65882 0.829411 0.558638i \(-0.188676\pi\)
0.829411 + 0.558638i \(0.188676\pi\)
\(422\) 37.4821 1.82460
\(423\) −11.2955 −0.549206
\(424\) −3.61213 −0.175420
\(425\) 5.50659 0.267109
\(426\) 1.52232 0.0737564
\(427\) 10.6107 0.513488
\(428\) −2.68006 −0.129545
\(429\) 9.92478 0.479173
\(430\) 0.0449056 0.00216554
\(431\) 25.7743 1.24151 0.620753 0.784006i \(-0.286827\pi\)
0.620753 + 0.784006i \(0.286827\pi\)
\(432\) 18.7612 0.902647
\(433\) 2.18076 0.104801 0.0524004 0.998626i \(-0.483313\pi\)
0.0524004 + 0.998626i \(0.483313\pi\)
\(434\) 8.49929 0.407979
\(435\) −0.806063 −0.0386478
\(436\) −0.363436 −0.0174054
\(437\) −5.88858 −0.281689
\(438\) 18.2012 0.869688
\(439\) −35.5125 −1.69492 −0.847459 0.530861i \(-0.821869\pi\)
−0.847459 + 0.530861i \(0.821869\pi\)
\(440\) 11.1187 0.530064
\(441\) 13.1016 0.623884
\(442\) −24.1622 −1.14928
\(443\) −4.34297 −0.206341 −0.103170 0.994664i \(-0.532899\pi\)
−0.103170 + 0.994664i \(0.532899\pi\)
\(444\) −1.48612 −0.0705281
\(445\) −3.61213 −0.171231
\(446\) −26.2071 −1.24094
\(447\) 2.23743 0.105827
\(448\) 8.45439 0.399432
\(449\) 31.3357 1.47882 0.739411 0.673254i \(-0.235104\pi\)
0.739411 + 0.673254i \(0.235104\pi\)
\(450\) 3.48119 0.164105
\(451\) −46.8627 −2.20668
\(452\) −2.28233 −0.107352
\(453\) 1.44992 0.0681233
\(454\) −39.7586 −1.86596
\(455\) 3.53690 0.165813
\(456\) −6.88717 −0.322521
\(457\) 34.3488 1.60677 0.803386 0.595459i \(-0.203030\pi\)
0.803386 + 0.595459i \(0.203030\pi\)
\(458\) 25.5125 1.19212
\(459\) −23.7480 −1.10846
\(460\) 0.357556 0.0166711
\(461\) 11.8641 0.552568 0.276284 0.961076i \(-0.410897\pi\)
0.276284 + 0.961076i \(0.410897\pi\)
\(462\) −5.92478 −0.275646
\(463\) 40.4953 1.88198 0.940989 0.338438i \(-0.109899\pi\)
0.940989 + 0.338438i \(0.109899\pi\)
\(464\) 4.35026 0.201956
\(465\) −3.87399 −0.179652
\(466\) 13.4401 0.622599
\(467\) −30.2071 −1.39782 −0.698909 0.715210i \(-0.746331\pi\)
−0.698909 + 0.715210i \(0.746331\pi\)
\(468\) −1.35026 −0.0624159
\(469\) 6.97698 0.322167
\(470\) −7.11871 −0.328362
\(471\) 3.03761 0.139966
\(472\) 35.5125 1.63459
\(473\) −0.126008 −0.00579385
\(474\) 5.88858 0.270471
\(475\) −3.19394 −0.146548
\(476\) 1.27504 0.0584413
\(477\) 3.17347 0.145303
\(478\) −30.3634 −1.38879
\(479\) 0.0547547 0.00250181 0.00125090 0.999999i \(-0.499602\pi\)
0.00125090 + 0.999999i \(0.499602\pi\)
\(480\) 0.881286 0.0402250
\(481\) −28.1622 −1.28409
\(482\) −8.11142 −0.369465
\(483\) 1.77433 0.0807349
\(484\) 1.21696 0.0553163
\(485\) −1.38058 −0.0626889
\(486\) −23.4314 −1.06287
\(487\) −0.881286 −0.0399349 −0.0199674 0.999801i \(-0.506356\pi\)
−0.0199674 + 0.999801i \(0.506356\pi\)
\(488\) 23.7743 1.07621
\(489\) 1.32391 0.0598695
\(490\) 8.25694 0.373011
\(491\) 41.0698 1.85346 0.926728 0.375733i \(-0.122609\pi\)
0.926728 + 0.375733i \(0.122609\pi\)
\(492\) −1.76257 −0.0794629
\(493\) −5.50659 −0.248004
\(494\) 14.0146 0.630546
\(495\) −9.76845 −0.439059
\(496\) 20.9076 0.938780
\(497\) −1.52232 −0.0682852
\(498\) −5.27504 −0.236380
\(499\) 12.3733 0.553904 0.276952 0.960884i \(-0.410676\pi\)
0.276952 + 0.960884i \(0.410676\pi\)
\(500\) 0.193937 0.00867311
\(501\) 6.51388 0.291019
\(502\) 43.8700 1.95801
\(503\) −2.26774 −0.101114 −0.0505569 0.998721i \(-0.516100\pi\)
−0.0505569 + 0.998721i \(0.516100\pi\)
\(504\) −7.50659 −0.334370
\(505\) −13.0132 −0.579079
\(506\) −11.3503 −0.504581
\(507\) −3.40502 −0.151222
\(508\) 2.76704 0.122767
\(509\) −10.9018 −0.483212 −0.241606 0.970374i \(-0.577674\pi\)
−0.241606 + 0.970374i \(0.577674\pi\)
\(510\) −6.57452 −0.291124
\(511\) −18.2012 −0.805175
\(512\) 18.5188 0.818423
\(513\) 13.7743 0.608152
\(514\) −26.1622 −1.15397
\(515\) 5.31994 0.234425
\(516\) −0.00473934 −0.000208638 0
\(517\) 19.9756 0.878524
\(518\) 16.8119 0.738674
\(519\) −6.23743 −0.273793
\(520\) 7.92478 0.347524
\(521\) −4.72496 −0.207004 −0.103502 0.994629i \(-0.533005\pi\)
−0.103502 + 0.994629i \(0.533005\pi\)
\(522\) −3.48119 −0.152368
\(523\) −1.06793 −0.0466973 −0.0233486 0.999727i \(-0.507433\pi\)
−0.0233486 + 0.999727i \(0.507433\pi\)
\(524\) 1.14315 0.0499388
\(525\) 0.962389 0.0420021
\(526\) −40.5198 −1.76675
\(527\) −26.4650 −1.15283
\(528\) −14.5745 −0.634274
\(529\) −19.6009 −0.852211
\(530\) 2.00000 0.0868744
\(531\) −31.1998 −1.35396
\(532\) −0.739549 −0.0320635
\(533\) −33.4010 −1.44676
\(534\) 4.31265 0.186627
\(535\) −13.8192 −0.597458
\(536\) 15.6326 0.675225
\(537\) −17.2506 −0.744418
\(538\) −15.5515 −0.670472
\(539\) −23.1695 −0.997981
\(540\) −0.836381 −0.0359921
\(541\) −7.46168 −0.320803 −0.160401 0.987052i \(-0.551279\pi\)
−0.160401 + 0.987052i \(0.551279\pi\)
\(542\) 14.2461 0.611924
\(543\) 12.3127 0.528386
\(544\) 6.02047 0.258125
\(545\) −1.87399 −0.0802730
\(546\) −4.22284 −0.180721
\(547\) −38.9683 −1.66616 −0.833081 0.553150i \(-0.813425\pi\)
−0.833081 + 0.553150i \(0.813425\pi\)
\(548\) 3.54561 0.151461
\(549\) −20.8872 −0.891443
\(550\) −6.15633 −0.262507
\(551\) 3.19394 0.136066
\(552\) 3.97556 0.169211
\(553\) −5.88858 −0.250408
\(554\) −19.7743 −0.840131
\(555\) −7.66291 −0.325273
\(556\) −2.23743 −0.0948881
\(557\) −22.9986 −0.974481 −0.487241 0.873268i \(-0.661997\pi\)
−0.487241 + 0.873268i \(0.661997\pi\)
\(558\) −16.7308 −0.708273
\(559\) −0.0898112 −0.00379861
\(560\) −5.19394 −0.219484
\(561\) 18.4485 0.778897
\(562\) −30.2520 −1.27610
\(563\) 11.6688 0.491781 0.245890 0.969298i \(-0.420920\pi\)
0.245890 + 0.969298i \(0.420920\pi\)
\(564\) 0.751309 0.0316358
\(565\) −11.7685 −0.495102
\(566\) 11.8799 0.499348
\(567\) 4.26774 0.179228
\(568\) −3.41090 −0.143118
\(569\) 11.3357 0.475216 0.237608 0.971361i \(-0.423637\pi\)
0.237608 + 0.971361i \(0.423637\pi\)
\(570\) 3.81336 0.159724
\(571\) 27.1754 1.13725 0.568627 0.822595i \(-0.307475\pi\)
0.568627 + 0.822595i \(0.307475\pi\)
\(572\) 2.38787 0.0998420
\(573\) 2.67609 0.111795
\(574\) 19.9394 0.832253
\(575\) 1.84367 0.0768866
\(576\) −16.6424 −0.693435
\(577\) 22.5950 0.940641 0.470321 0.882496i \(-0.344138\pi\)
0.470321 + 0.882496i \(0.344138\pi\)
\(578\) −19.7332 −0.820793
\(579\) −3.93463 −0.163517
\(580\) −0.193937 −0.00805278
\(581\) 5.27504 0.218845
\(582\) 1.64832 0.0683252
\(583\) −5.61213 −0.232431
\(584\) −40.7816 −1.68756
\(585\) −6.96239 −0.287859
\(586\) 34.5198 1.42600
\(587\) 9.31994 0.384675 0.192338 0.981329i \(-0.438393\pi\)
0.192338 + 0.981329i \(0.438393\pi\)
\(588\) −0.871437 −0.0359375
\(589\) 15.3503 0.632497
\(590\) −19.6629 −0.809509
\(591\) −19.5369 −0.803641
\(592\) 41.3561 1.69973
\(593\) −15.1246 −0.621093 −0.310546 0.950558i \(-0.600512\pi\)
−0.310546 + 0.950558i \(0.600512\pi\)
\(594\) 26.5501 1.08936
\(595\) 6.57452 0.269529
\(596\) 0.538319 0.0220504
\(597\) 13.5026 0.552625
\(598\) −8.08981 −0.330817
\(599\) 4.09569 0.167345 0.0836727 0.996493i \(-0.473335\pi\)
0.0836727 + 0.996493i \(0.473335\pi\)
\(600\) 2.15633 0.0880316
\(601\) 22.2276 0.906682 0.453341 0.891337i \(-0.350232\pi\)
0.453341 + 0.891337i \(0.350232\pi\)
\(602\) 0.0536145 0.00218516
\(603\) −13.7342 −0.559298
\(604\) 0.348847 0.0141944
\(605\) 6.27504 0.255117
\(606\) 15.5369 0.631144
\(607\) −48.2941 −1.96020 −0.980098 0.198512i \(-0.936389\pi\)
−0.980098 + 0.198512i \(0.936389\pi\)
\(608\) −3.49200 −0.141619
\(609\) −0.962389 −0.0389980
\(610\) −13.1636 −0.532979
\(611\) 14.2374 0.575985
\(612\) −2.50991 −0.101457
\(613\) −9.74798 −0.393717 −0.196859 0.980432i \(-0.563074\pi\)
−0.196859 + 0.980432i \(0.563074\pi\)
\(614\) 9.96968 0.402344
\(615\) −9.08840 −0.366480
\(616\) 13.2750 0.534867
\(617\) 18.2170 0.733387 0.366694 0.930342i \(-0.380490\pi\)
0.366694 + 0.930342i \(0.380490\pi\)
\(618\) −6.35168 −0.255502
\(619\) 25.0943 1.00862 0.504312 0.863521i \(-0.331746\pi\)
0.504312 + 0.863521i \(0.331746\pi\)
\(620\) −0.932071 −0.0374329
\(621\) −7.95112 −0.319068
\(622\) 32.6702 1.30996
\(623\) −4.31265 −0.172783
\(624\) −10.3879 −0.415848
\(625\) 1.00000 0.0400000
\(626\) −7.46168 −0.298229
\(627\) −10.7005 −0.427338
\(628\) 0.730841 0.0291637
\(629\) −52.3488 −2.08729
\(630\) 4.15633 0.165592
\(631\) 21.4617 0.854376 0.427188 0.904163i \(-0.359504\pi\)
0.427188 + 0.904163i \(0.359504\pi\)
\(632\) −13.1939 −0.524827
\(633\) −20.3977 −0.810737
\(634\) −50.7962 −2.01738
\(635\) 14.2677 0.566198
\(636\) −0.211080 −0.00836986
\(637\) −16.5139 −0.654304
\(638\) 6.15633 0.243731
\(639\) 2.99668 0.118547
\(640\) −12.6751 −0.501029
\(641\) 3.17347 0.125344 0.0626722 0.998034i \(-0.480038\pi\)
0.0626722 + 0.998034i \(0.480038\pi\)
\(642\) 16.4993 0.651175
\(643\) −2.74069 −0.108082 −0.0540411 0.998539i \(-0.517210\pi\)
−0.0540411 + 0.998539i \(0.517210\pi\)
\(644\) 0.426899 0.0168222
\(645\) −0.0244376 −0.000962228 0
\(646\) 26.0508 1.02495
\(647\) 6.34297 0.249368 0.124684 0.992197i \(-0.460208\pi\)
0.124684 + 0.992197i \(0.460208\pi\)
\(648\) 9.56230 0.375642
\(649\) 55.1754 2.16582
\(650\) −4.38787 −0.172107
\(651\) −4.62530 −0.181280
\(652\) 0.318530 0.0124746
\(653\) 4.08110 0.159706 0.0798529 0.996807i \(-0.474555\pi\)
0.0798529 + 0.996807i \(0.474555\pi\)
\(654\) 2.23743 0.0874903
\(655\) 5.89446 0.230316
\(656\) 49.0494 1.91506
\(657\) 35.8291 1.39783
\(658\) −8.49929 −0.331337
\(659\) 9.58181 0.373254 0.186627 0.982431i \(-0.440244\pi\)
0.186627 + 0.982431i \(0.440244\pi\)
\(660\) 0.649738 0.0252910
\(661\) −27.5271 −1.07068 −0.535339 0.844637i \(-0.679816\pi\)
−0.535339 + 0.844637i \(0.679816\pi\)
\(662\) 51.5936 2.00524
\(663\) 13.1490 0.510666
\(664\) 11.8192 0.458675
\(665\) −3.81336 −0.147876
\(666\) −33.0943 −1.28238
\(667\) −1.84367 −0.0713874
\(668\) 1.56722 0.0606376
\(669\) 14.2619 0.551396
\(670\) −8.65562 −0.334396
\(671\) 36.9380 1.42597
\(672\) 1.05220 0.0405895
\(673\) 3.13727 0.120933 0.0604665 0.998170i \(-0.480741\pi\)
0.0604665 + 0.998170i \(0.480741\pi\)
\(674\) 26.1173 1.00600
\(675\) −4.31265 −0.165994
\(676\) −0.819237 −0.0315091
\(677\) −46.2579 −1.77784 −0.888918 0.458067i \(-0.848542\pi\)
−0.888918 + 0.458067i \(0.848542\pi\)
\(678\) 14.0508 0.539617
\(679\) −1.64832 −0.0632569
\(680\) 14.7308 0.564902
\(681\) 21.6366 0.829115
\(682\) 29.5877 1.13297
\(683\) −9.01905 −0.345104 −0.172552 0.985000i \(-0.555201\pi\)
−0.172552 + 0.985000i \(0.555201\pi\)
\(684\) 1.45580 0.0556640
\(685\) 18.2823 0.698532
\(686\) 22.2374 0.849029
\(687\) −13.8838 −0.529702
\(688\) 0.131888 0.00502817
\(689\) −4.00000 −0.152388
\(690\) −2.20123 −0.0837994
\(691\) −50.0625 −1.90447 −0.952234 0.305368i \(-0.901221\pi\)
−0.952234 + 0.305368i \(0.901221\pi\)
\(692\) −1.50071 −0.0570483
\(693\) −11.6629 −0.443037
\(694\) 4.61942 0.175351
\(695\) −11.5369 −0.437620
\(696\) −2.15633 −0.0817353
\(697\) −62.0870 −2.35171
\(698\) 19.3649 0.732970
\(699\) −7.31406 −0.276643
\(700\) 0.231548 0.00875169
\(701\) 45.3014 1.71101 0.855505 0.517795i \(-0.173247\pi\)
0.855505 + 0.517795i \(0.173247\pi\)
\(702\) 18.9234 0.714216
\(703\) 30.3634 1.14518
\(704\) 29.4314 1.10924
\(705\) 3.87399 0.145903
\(706\) −7.70194 −0.289866
\(707\) −15.5369 −0.584325
\(708\) 2.07522 0.0779916
\(709\) −3.27504 −0.122997 −0.0614983 0.998107i \(-0.519588\pi\)
−0.0614983 + 0.998107i \(0.519588\pi\)
\(710\) 1.88858 0.0708772
\(711\) 11.5917 0.434721
\(712\) −9.66291 −0.362133
\(713\) −8.86082 −0.331840
\(714\) −7.84955 −0.293762
\(715\) 12.3127 0.460467
\(716\) −4.15045 −0.155109
\(717\) 16.5237 0.617090
\(718\) −45.0553 −1.68145
\(719\) 27.7235 1.03391 0.516957 0.856011i \(-0.327065\pi\)
0.516957 + 0.856011i \(0.327065\pi\)
\(720\) 10.2243 0.381035
\(721\) 6.35168 0.236549
\(722\) 13.0327 0.485026
\(723\) 4.41422 0.164167
\(724\) 2.96239 0.110096
\(725\) −1.00000 −0.0371391
\(726\) −7.49200 −0.278054
\(727\) −26.8930 −0.997408 −0.498704 0.866772i \(-0.666190\pi\)
−0.498704 + 0.866772i \(0.666190\pi\)
\(728\) 9.46168 0.350673
\(729\) 2.02776 0.0751023
\(730\) 22.5804 0.835738
\(731\) −0.166944 −0.00617465
\(732\) 1.38929 0.0513496
\(733\) 3.17935 0.117432 0.0587160 0.998275i \(-0.481299\pi\)
0.0587160 + 0.998275i \(0.481299\pi\)
\(734\) −30.5950 −1.12928
\(735\) −4.49341 −0.165742
\(736\) 2.01573 0.0743007
\(737\) 24.2882 0.894668
\(738\) −39.2506 −1.44483
\(739\) −29.7440 −1.09415 −0.547076 0.837083i \(-0.684259\pi\)
−0.547076 + 0.837083i \(0.684259\pi\)
\(740\) −1.84367 −0.0677748
\(741\) −7.62672 −0.280174
\(742\) 2.38787 0.0876616
\(743\) −4.34297 −0.159328 −0.0796640 0.996822i \(-0.525385\pi\)
−0.0796640 + 0.996822i \(0.525385\pi\)
\(744\) −10.3634 −0.379942
\(745\) 2.77575 0.101695
\(746\) −16.4241 −0.601328
\(747\) −10.3839 −0.379927
\(748\) 4.43866 0.162293
\(749\) −16.4993 −0.602871
\(750\) −1.19394 −0.0435964
\(751\) 22.5804 0.823970 0.411985 0.911191i \(-0.364836\pi\)
0.411985 + 0.911191i \(0.364836\pi\)
\(752\) −20.9076 −0.762423
\(753\) −23.8740 −0.870017
\(754\) 4.38787 0.159797
\(755\) 1.79877 0.0654639
\(756\) −0.998585 −0.0363182
\(757\) 9.88461 0.359262 0.179631 0.983734i \(-0.442510\pi\)
0.179631 + 0.983734i \(0.442510\pi\)
\(758\) −14.9321 −0.542357
\(759\) 6.17679 0.224203
\(760\) −8.54420 −0.309931
\(761\) 13.6991 0.496592 0.248296 0.968684i \(-0.420129\pi\)
0.248296 + 0.968684i \(0.420129\pi\)
\(762\) −17.0348 −0.617105
\(763\) −2.23743 −0.0810003
\(764\) 0.643859 0.0232940
\(765\) −12.9419 −0.467916
\(766\) −24.2287 −0.875419
\(767\) 39.3258 1.41997
\(768\) 3.71767 0.134150
\(769\) 25.0132 0.901998 0.450999 0.892524i \(-0.351068\pi\)
0.450999 + 0.892524i \(0.351068\pi\)
\(770\) −7.35026 −0.264885
\(771\) 14.2374 0.512748
\(772\) −0.946660 −0.0340710
\(773\) −35.9062 −1.29146 −0.645728 0.763567i \(-0.723446\pi\)
−0.645728 + 0.763567i \(0.723446\pi\)
\(774\) −0.105540 −0.00379356
\(775\) −4.80606 −0.172639
\(776\) −3.69323 −0.132579
\(777\) −9.14903 −0.328220
\(778\) −47.2506 −1.69402
\(779\) 36.0118 1.29026
\(780\) 0.463096 0.0165815
\(781\) −5.29948 −0.189630
\(782\) −15.0376 −0.537744
\(783\) 4.31265 0.154122
\(784\) 24.2506 0.866093
\(785\) 3.76845 0.134502
\(786\) −7.03761 −0.251023
\(787\) 50.3839 1.79599 0.897996 0.440003i \(-0.145023\pi\)
0.897996 + 0.440003i \(0.145023\pi\)
\(788\) −4.70052 −0.167449
\(789\) 22.0508 0.785029
\(790\) 7.30536 0.259913
\(791\) −14.0508 −0.499588
\(792\) −26.1319 −0.928556
\(793\) 26.3272 0.934908
\(794\) −4.42407 −0.157004
\(795\) −1.08840 −0.0386014
\(796\) 3.24869 0.115147
\(797\) −5.69323 −0.201665 −0.100832 0.994903i \(-0.532151\pi\)
−0.100832 + 0.994903i \(0.532151\pi\)
\(798\) 4.55291 0.161171
\(799\) 26.4650 0.936265
\(800\) 1.09332 0.0386547
\(801\) 8.48944 0.299960
\(802\) 32.5501 1.14938
\(803\) −63.3620 −2.23600
\(804\) 0.913513 0.0322171
\(805\) 2.20123 0.0775832
\(806\) 21.0884 0.742807
\(807\) 8.46310 0.297915
\(808\) −34.8119 −1.22468
\(809\) −7.76257 −0.272918 −0.136459 0.990646i \(-0.543572\pi\)
−0.136459 + 0.990646i \(0.543572\pi\)
\(810\) −5.29455 −0.186032
\(811\) −26.4894 −0.930170 −0.465085 0.885266i \(-0.653976\pi\)
−0.465085 + 0.885266i \(0.653976\pi\)
\(812\) −0.231548 −0.00812574
\(813\) −7.75272 −0.271900
\(814\) 58.5256 2.05132
\(815\) 1.64244 0.0575323
\(816\) −19.3093 −0.675962
\(817\) 0.0968311 0.00338769
\(818\) 33.2360 1.16207
\(819\) −8.31265 −0.290468
\(820\) −2.18664 −0.0763609
\(821\) 25.4763 0.889128 0.444564 0.895747i \(-0.353359\pi\)
0.444564 + 0.895747i \(0.353359\pi\)
\(822\) −21.8279 −0.761337
\(823\) −9.22028 −0.321399 −0.160699 0.987003i \(-0.551375\pi\)
−0.160699 + 0.987003i \(0.551375\pi\)
\(824\) 14.2315 0.495779
\(825\) 3.35026 0.116641
\(826\) −23.4763 −0.816844
\(827\) 24.5343 0.853143 0.426571 0.904454i \(-0.359721\pi\)
0.426571 + 0.904454i \(0.359721\pi\)
\(828\) −0.840350 −0.0292042
\(829\) 0.201231 0.00698903 0.00349452 0.999994i \(-0.498888\pi\)
0.00349452 + 0.999994i \(0.498888\pi\)
\(830\) −6.54420 −0.227152
\(831\) 10.7612 0.373300
\(832\) 20.9770 0.727246
\(833\) −30.6966 −1.06357
\(834\) 13.7743 0.476966
\(835\) 8.08110 0.279658
\(836\) −2.57452 −0.0890415
\(837\) 20.7269 0.716425
\(838\) −15.3503 −0.530266
\(839\) 1.45580 0.0502599 0.0251299 0.999684i \(-0.492000\pi\)
0.0251299 + 0.999684i \(0.492000\pi\)
\(840\) 2.57452 0.0888292
\(841\) 1.00000 0.0344828
\(842\) −50.4142 −1.73739
\(843\) 16.4631 0.567019
\(844\) −4.90763 −0.168928
\(845\) −4.22425 −0.145319
\(846\) 16.7308 0.575218
\(847\) 7.49200 0.257428
\(848\) 5.87399 0.201714
\(849\) −6.46501 −0.221878
\(850\) −8.15633 −0.279760
\(851\) −17.5271 −0.600820
\(852\) −0.199321 −0.00682861
\(853\) 43.1793 1.47843 0.739216 0.673468i \(-0.235196\pi\)
0.739216 + 0.673468i \(0.235196\pi\)
\(854\) −15.7165 −0.537808
\(855\) 7.50659 0.256720
\(856\) −36.9683 −1.26355
\(857\) −20.9887 −0.716962 −0.358481 0.933537i \(-0.616705\pi\)
−0.358481 + 0.933537i \(0.616705\pi\)
\(858\) −14.7005 −0.501868
\(859\) −49.4069 −1.68574 −0.842871 0.538115i \(-0.819137\pi\)
−0.842871 + 0.538115i \(0.819137\pi\)
\(860\) −0.00587961 −0.000200493 0
\(861\) −10.8510 −0.369800
\(862\) −38.1768 −1.30031
\(863\) 56.6820 1.92948 0.964738 0.263211i \(-0.0847816\pi\)
0.964738 + 0.263211i \(0.0847816\pi\)
\(864\) −4.71511 −0.160411
\(865\) −7.73813 −0.263104
\(866\) −3.23013 −0.109764
\(867\) 10.7388 0.364708
\(868\) −1.11283 −0.0377721
\(869\) −20.4993 −0.695391
\(870\) 1.19394 0.0404782
\(871\) 17.3112 0.586569
\(872\) −5.01317 −0.169767
\(873\) 3.24472 0.109817
\(874\) 8.72213 0.295031
\(875\) 1.19394 0.0403624
\(876\) −2.38313 −0.0805186
\(877\) −13.1998 −0.445726 −0.222863 0.974850i \(-0.571540\pi\)
−0.222863 + 0.974850i \(0.571540\pi\)
\(878\) 52.6009 1.77519
\(879\) −18.7856 −0.633622
\(880\) −18.0811 −0.609514
\(881\) 6.37802 0.214881 0.107441 0.994212i \(-0.465734\pi\)
0.107441 + 0.994212i \(0.465734\pi\)
\(882\) −19.4060 −0.653433
\(883\) 48.6213 1.63624 0.818119 0.575049i \(-0.195017\pi\)
0.818119 + 0.575049i \(0.195017\pi\)
\(884\) 3.16362 0.106404
\(885\) 10.7005 0.359694
\(886\) 6.43278 0.216113
\(887\) −15.0317 −0.504716 −0.252358 0.967634i \(-0.581206\pi\)
−0.252358 + 0.967634i \(0.581206\pi\)
\(888\) −20.4993 −0.687911
\(889\) 17.0348 0.571328
\(890\) 5.35026 0.179341
\(891\) 14.8568 0.497723
\(892\) 3.43136 0.114891
\(893\) −15.3503 −0.513677
\(894\) −3.31406 −0.110839
\(895\) −21.4010 −0.715358
\(896\) −15.1333 −0.505568
\(897\) 4.40246 0.146994
\(898\) −46.4142 −1.54886
\(899\) 4.80606 0.160291
\(900\) −0.455802 −0.0151934
\(901\) −7.43533 −0.247707
\(902\) 69.4128 2.31119
\(903\) −0.0291769 −0.000970946 0
\(904\) −31.4821 −1.04708
\(905\) 15.2750 0.507759
\(906\) −2.14762 −0.0713498
\(907\) −0.342968 −0.0113880 −0.00569402 0.999984i \(-0.501812\pi\)
−0.00569402 + 0.999984i \(0.501812\pi\)
\(908\) 5.20570 0.172757
\(909\) 30.5844 1.01442
\(910\) −5.23884 −0.173666
\(911\) 20.9076 0.692701 0.346350 0.938105i \(-0.387421\pi\)
0.346350 + 0.938105i \(0.387421\pi\)
\(912\) 11.1998 0.370863
\(913\) 18.3634 0.607741
\(914\) −50.8773 −1.68287
\(915\) 7.16362 0.236822
\(916\) −3.34041 −0.110370
\(917\) 7.03761 0.232402
\(918\) 35.1754 1.16096
\(919\) −1.90034 −0.0626864 −0.0313432 0.999509i \(-0.509978\pi\)
−0.0313432 + 0.999509i \(0.509978\pi\)
\(920\) 4.93207 0.162606
\(921\) −5.42548 −0.178776
\(922\) −17.5731 −0.578739
\(923\) −3.77716 −0.124327
\(924\) 0.775746 0.0255202
\(925\) −9.50659 −0.312575
\(926\) −59.9814 −1.97111
\(927\) −12.5033 −0.410661
\(928\) −1.09332 −0.0358900
\(929\) 39.3522 1.29110 0.645551 0.763717i \(-0.276628\pi\)
0.645551 + 0.763717i \(0.276628\pi\)
\(930\) 5.73813 0.188161
\(931\) 17.8046 0.583524
\(932\) −1.75974 −0.0576423
\(933\) −17.7791 −0.582061
\(934\) 44.7426 1.46402
\(935\) 22.8872 0.748490
\(936\) −18.6253 −0.608787
\(937\) −6.37802 −0.208361 −0.104180 0.994558i \(-0.533222\pi\)
−0.104180 + 0.994558i \(0.533222\pi\)
\(938\) −10.3343 −0.337426
\(939\) 4.06063 0.132514
\(940\) 0.932071 0.0304008
\(941\) −26.6253 −0.867960 −0.433980 0.900923i \(-0.642891\pi\)
−0.433980 + 0.900923i \(0.642891\pi\)
\(942\) −4.49929 −0.146595
\(943\) −20.7875 −0.676934
\(944\) −57.7499 −1.87960
\(945\) −5.14903 −0.167498
\(946\) 0.186642 0.00606827
\(947\) −12.2823 −0.399122 −0.199561 0.979885i \(-0.563952\pi\)
−0.199561 + 0.979885i \(0.563952\pi\)
\(948\) −0.771007 −0.0250411
\(949\) −45.1608 −1.46598
\(950\) 4.73084 0.153489
\(951\) 27.6432 0.896393
\(952\) 17.5877 0.570020
\(953\) 0.821792 0.0266205 0.0133102 0.999911i \(-0.495763\pi\)
0.0133102 + 0.999911i \(0.495763\pi\)
\(954\) −4.70052 −0.152185
\(955\) 3.31994 0.107431
\(956\) 3.97556 0.128579
\(957\) −3.35026 −0.108299
\(958\) −0.0811024 −0.00262030
\(959\) 21.8279 0.704861
\(960\) 5.70782 0.184219
\(961\) −7.90175 −0.254895
\(962\) 41.7137 1.34490
\(963\) 32.4788 1.04662
\(964\) 1.06205 0.0342063
\(965\) −4.88129 −0.157134
\(966\) −2.62813 −0.0845587
\(967\) −37.4314 −1.20371 −0.601856 0.798605i \(-0.705572\pi\)
−0.601856 + 0.798605i \(0.705572\pi\)
\(968\) 16.7866 0.539540
\(969\) −14.1768 −0.455424
\(970\) 2.04491 0.0656580
\(971\) −8.71625 −0.279718 −0.139859 0.990171i \(-0.544665\pi\)
−0.139859 + 0.990171i \(0.544665\pi\)
\(972\) 3.06793 0.0984039
\(973\) −13.7743 −0.441585
\(974\) 1.30536 0.0418263
\(975\) 2.38787 0.0764731
\(976\) −38.6615 −1.23752
\(977\) −33.7645 −1.08022 −0.540111 0.841594i \(-0.681618\pi\)
−0.540111 + 0.841594i \(0.681618\pi\)
\(978\) −1.96097 −0.0627050
\(979\) −15.0132 −0.479823
\(980\) −1.08110 −0.0345345
\(981\) 4.40437 0.140621
\(982\) −60.8324 −1.94124
\(983\) 43.6082 1.39088 0.695442 0.718582i \(-0.255209\pi\)
0.695442 + 0.718582i \(0.255209\pi\)
\(984\) −24.3127 −0.775059
\(985\) −24.2374 −0.772269
\(986\) 8.15633 0.259750
\(987\) 4.62530 0.147225
\(988\) −1.83497 −0.0583780
\(989\) −0.0558950 −0.00177736
\(990\) 14.4690 0.459854
\(991\) −52.9741 −1.68278 −0.841390 0.540429i \(-0.818262\pi\)
−0.841390 + 0.540429i \(0.818262\pi\)
\(992\) −5.25457 −0.166833
\(993\) −28.0771 −0.891001
\(994\) 2.25485 0.0715193
\(995\) 16.7513 0.531052
\(996\) 0.690674 0.0218849
\(997\) 13.6326 0.431749 0.215874 0.976421i \(-0.430740\pi\)
0.215874 + 0.976421i \(0.430740\pi\)
\(998\) −18.3272 −0.580139
\(999\) 40.9986 1.29714
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 145.2.a.c.1.1 3
3.2 odd 2 1305.2.a.p.1.3 3
4.3 odd 2 2320.2.a.n.1.2 3
5.2 odd 4 725.2.b.e.349.2 6
5.3 odd 4 725.2.b.e.349.5 6
5.4 even 2 725.2.a.e.1.3 3
7.6 odd 2 7105.2.a.o.1.1 3
8.3 odd 2 9280.2.a.br.1.2 3
8.5 even 2 9280.2.a.bj.1.2 3
15.14 odd 2 6525.2.a.be.1.1 3
29.28 even 2 4205.2.a.f.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
145.2.a.c.1.1 3 1.1 even 1 trivial
725.2.a.e.1.3 3 5.4 even 2
725.2.b.e.349.2 6 5.2 odd 4
725.2.b.e.349.5 6 5.3 odd 4
1305.2.a.p.1.3 3 3.2 odd 2
2320.2.a.n.1.2 3 4.3 odd 2
4205.2.a.f.1.3 3 29.28 even 2
6525.2.a.be.1.1 3 15.14 odd 2
7105.2.a.o.1.1 3 7.6 odd 2
9280.2.a.bj.1.2 3 8.5 even 2
9280.2.a.br.1.2 3 8.3 odd 2