Properties

Label 287.3.d.d.286.7
Level $287$
Weight $3$
Character 287.286
Analytic conductor $7.820$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,3,Mod(286,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.286");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.d (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 286.7
Character \(\chi\) \(=\) 287.286
Dual form 287.3.d.d.286.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.67431 q^{2} +2.89735 q^{3} +3.15194 q^{4} -3.34396i q^{5} -7.74841 q^{6} +(-4.11915 + 5.65974i) q^{7} +2.26798 q^{8} -0.605380 q^{9} +O(q^{10})\) \(q-2.67431 q^{2} +2.89735 q^{3} +3.15194 q^{4} -3.34396i q^{5} -7.74841 q^{6} +(-4.11915 + 5.65974i) q^{7} +2.26798 q^{8} -0.605380 q^{9} +8.94280i q^{10} -15.3848i q^{11} +9.13226 q^{12} -7.80554 q^{13} +(11.0159 - 15.1359i) q^{14} -9.68862i q^{15} -18.6730 q^{16} -8.48488 q^{17} +1.61897 q^{18} -0.826108 q^{19} -10.5400i q^{20} +(-11.9346 + 16.3982i) q^{21} +41.1438i q^{22} -2.74675 q^{23} +6.57113 q^{24} +13.8179 q^{25} +20.8744 q^{26} -27.8301 q^{27} +(-12.9833 + 17.8391i) q^{28} +15.8500i q^{29} +25.9104i q^{30} -52.1405i q^{31} +40.8656 q^{32} -44.5751i q^{33} +22.6912 q^{34} +(18.9260 + 13.7743i) q^{35} -1.90812 q^{36} -39.7168 q^{37} +2.20927 q^{38} -22.6154 q^{39} -7.58404i q^{40} +(-38.1158 - 15.1057i) q^{41} +(31.9168 - 43.8539i) q^{42} -71.9168 q^{43} -48.4920i q^{44} +2.02437i q^{45} +7.34566 q^{46} +0.994000 q^{47} -54.1023 q^{48} +(-15.0652 - 46.6266i) q^{49} -36.9534 q^{50} -24.5837 q^{51} -24.6026 q^{52} +10.7924i q^{53} +74.4264 q^{54} -51.4462 q^{55} +(-9.34215 + 12.8362i) q^{56} -2.39352 q^{57} -42.3879i q^{58} -24.7187i q^{59} -30.5379i q^{60} -59.3552i q^{61} +139.440i q^{62} +(2.49365 - 3.42629i) q^{63} -34.5951 q^{64} +26.1014i q^{65} +119.208i q^{66} -3.55600i q^{67} -26.7438 q^{68} -7.95829 q^{69} +(-50.6139 - 36.8367i) q^{70} -49.0576i q^{71} -1.37299 q^{72} -106.882i q^{73} +106.215 q^{74} +40.0353 q^{75} -2.60384 q^{76} +(87.0739 + 63.3723i) q^{77} +60.4805 q^{78} +109.832i q^{79} +62.4420i q^{80} -75.1851 q^{81} +(101.934 + 40.3974i) q^{82} +117.729i q^{83} +(-37.6171 + 51.6862i) q^{84} +28.3731i q^{85} +192.328 q^{86} +45.9231i q^{87} -34.8924i q^{88} +171.753 q^{89} -5.41379i q^{90} +(32.1522 - 44.1773i) q^{91} -8.65759 q^{92} -151.069i q^{93} -2.65826 q^{94} +2.76247i q^{95} +118.402 q^{96} -41.4772 q^{97} +(40.2891 + 124.694i) q^{98} +9.31366i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9} - 92 q^{16} - 48 q^{18} - 72 q^{21} + 140 q^{23} - 500 q^{25} + 92 q^{32} - 284 q^{36} + 312 q^{37} + 140 q^{39} + 8 q^{42} - 120 q^{43} - 344 q^{46} - 552 q^{49} + 416 q^{50} - 364 q^{51} - 316 q^{57} - 320 q^{64} + 972 q^{72} + 680 q^{74} + 428 q^{77} + 1144 q^{78} - 240 q^{81} + 640 q^{84} + 260 q^{86} - 160 q^{91} + 676 q^{92} + 532 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67431 −1.33716 −0.668578 0.743642i \(-0.733097\pi\)
−0.668578 + 0.743642i \(0.733097\pi\)
\(3\) 2.89735 0.965782 0.482891 0.875680i \(-0.339587\pi\)
0.482891 + 0.875680i \(0.339587\pi\)
\(4\) 3.15194 0.787985
\(5\) 3.34396i 0.668793i −0.942433 0.334396i \(-0.891468\pi\)
0.942433 0.334396i \(-0.108532\pi\)
\(6\) −7.74841 −1.29140
\(7\) −4.11915 + 5.65974i −0.588450 + 0.808534i
\(8\) 2.26798 0.283498
\(9\) −0.605380 −0.0672645
\(10\) 8.94280i 0.894280i
\(11\) 15.3848i 1.39862i −0.714819 0.699309i \(-0.753491\pi\)
0.714819 0.699309i \(-0.246509\pi\)
\(12\) 9.13226 0.761022
\(13\) −7.80554 −0.600426 −0.300213 0.953872i \(-0.597058\pi\)
−0.300213 + 0.953872i \(0.597058\pi\)
\(14\) 11.0159 15.1359i 0.786849 1.08114i
\(15\) 9.68862i 0.645908i
\(16\) −18.6730 −1.16706
\(17\) −8.48488 −0.499111 −0.249555 0.968361i \(-0.580284\pi\)
−0.249555 + 0.968361i \(0.580284\pi\)
\(18\) 1.61897 0.0899430
\(19\) −0.826108 −0.0434793 −0.0217397 0.999764i \(-0.506920\pi\)
−0.0217397 + 0.999764i \(0.506920\pi\)
\(20\) 10.5400i 0.526998i
\(21\) −11.9346 + 16.3982i −0.568315 + 0.780868i
\(22\) 41.1438i 1.87017i
\(23\) −2.74675 −0.119424 −0.0597119 0.998216i \(-0.519018\pi\)
−0.0597119 + 0.998216i \(0.519018\pi\)
\(24\) 6.57113 0.273797
\(25\) 13.8179 0.552716
\(26\) 20.8744 0.802863
\(27\) −27.8301 −1.03075
\(28\) −12.9833 + 17.8391i −0.463689 + 0.637112i
\(29\) 15.8500i 0.546553i 0.961936 + 0.273276i \(0.0881074\pi\)
−0.961936 + 0.273276i \(0.911893\pi\)
\(30\) 25.9104i 0.863680i
\(31\) 52.1405i 1.68195i −0.541073 0.840975i \(-0.681982\pi\)
0.541073 0.840975i \(-0.318018\pi\)
\(32\) 40.8656 1.27705
\(33\) 44.5751i 1.35076i
\(34\) 22.6912 0.667389
\(35\) 18.9260 + 13.7743i 0.540741 + 0.393551i
\(36\) −1.90812 −0.0530034
\(37\) −39.7168 −1.07343 −0.536714 0.843764i \(-0.680335\pi\)
−0.536714 + 0.843764i \(0.680335\pi\)
\(38\) 2.20927 0.0581386
\(39\) −22.6154 −0.579881
\(40\) 7.58404i 0.189601i
\(41\) −38.1158 15.1057i −0.929655 0.368432i
\(42\) 31.9168 43.8539i 0.759925 1.04414i
\(43\) −71.9168 −1.67248 −0.836242 0.548361i \(-0.815252\pi\)
−0.836242 + 0.548361i \(0.815252\pi\)
\(44\) 48.4920i 1.10209i
\(45\) 2.02437i 0.0449860i
\(46\) 7.34566 0.159688
\(47\) 0.994000 0.0211489 0.0105745 0.999944i \(-0.496634\pi\)
0.0105745 + 0.999944i \(0.496634\pi\)
\(48\) −54.1023 −1.12713
\(49\) −15.0652 46.6266i −0.307453 0.951563i
\(50\) −36.9534 −0.739068
\(51\) −24.5837 −0.482032
\(52\) −24.6026 −0.473127
\(53\) 10.7924i 0.203630i 0.994803 + 0.101815i \(0.0324650\pi\)
−0.994803 + 0.101815i \(0.967535\pi\)
\(54\) 74.4264 1.37827
\(55\) −51.4462 −0.935386
\(56\) −9.34215 + 12.8362i −0.166824 + 0.229217i
\(57\) −2.39352 −0.0419916
\(58\) 42.3879i 0.730826i
\(59\) 24.7187i 0.418961i −0.977813 0.209480i \(-0.932823\pi\)
0.977813 0.209480i \(-0.0671772\pi\)
\(60\) 30.5379i 0.508966i
\(61\) 59.3552i 0.973036i −0.873671 0.486518i \(-0.838267\pi\)
0.873671 0.486518i \(-0.161733\pi\)
\(62\) 139.440i 2.24903i
\(63\) 2.49365 3.42629i 0.0395818 0.0543856i
\(64\) −34.5951 −0.540549
\(65\) 26.1014i 0.401561i
\(66\) 119.208i 1.80618i
\(67\) 3.55600i 0.0530747i −0.999648 0.0265373i \(-0.991552\pi\)
0.999648 0.0265373i \(-0.00844809\pi\)
\(68\) −26.7438 −0.393292
\(69\) −7.95829 −0.115337
\(70\) −50.6139 36.8367i −0.723055 0.526239i
\(71\) 49.0576i 0.690952i −0.938428 0.345476i \(-0.887717\pi\)
0.938428 0.345476i \(-0.112283\pi\)
\(72\) −1.37299 −0.0190693
\(73\) 106.882i 1.46414i −0.681232 0.732068i \(-0.738555\pi\)
0.681232 0.732068i \(-0.261445\pi\)
\(74\) 106.215 1.43534
\(75\) 40.0353 0.533804
\(76\) −2.60384 −0.0342611
\(77\) 87.0739 + 63.3723i 1.13083 + 0.823017i
\(78\) 60.4805 0.775391
\(79\) 109.832i 1.39028i 0.718874 + 0.695140i \(0.244658\pi\)
−0.718874 + 0.695140i \(0.755342\pi\)
\(80\) 62.4420i 0.780525i
\(81\) −75.1851 −0.928211
\(82\) 101.934 + 40.3974i 1.24309 + 0.492651i
\(83\) 117.729i 1.41842i 0.704996 + 0.709211i \(0.250949\pi\)
−0.704996 + 0.709211i \(0.749051\pi\)
\(84\) −37.6171 + 51.6862i −0.447823 + 0.615312i
\(85\) 28.3731i 0.333802i
\(86\) 192.328 2.23637
\(87\) 45.9231i 0.527851i
\(88\) 34.8924i 0.396505i
\(89\) 171.753 1.92981 0.964905 0.262598i \(-0.0845792\pi\)
0.964905 + 0.262598i \(0.0845792\pi\)
\(90\) 5.41379i 0.0601532i
\(91\) 32.1522 44.1773i 0.353321 0.485465i
\(92\) −8.65759 −0.0941042
\(93\) 151.069i 1.62440i
\(94\) −2.65826 −0.0282794
\(95\) 2.76247i 0.0290787i
\(96\) 118.402 1.23335
\(97\) −41.4772 −0.427600 −0.213800 0.976878i \(-0.568584\pi\)
−0.213800 + 0.976878i \(0.568584\pi\)
\(98\) 40.2891 + 124.694i 0.411113 + 1.27239i
\(99\) 9.31366i 0.0940773i
\(100\) 43.5532 0.435532
\(101\) 40.4210 0.400208 0.200104 0.979775i \(-0.435872\pi\)
0.200104 + 0.979775i \(0.435872\pi\)
\(102\) 65.7443 0.644552
\(103\) 105.805i 1.02723i 0.858019 + 0.513617i \(0.171695\pi\)
−0.858019 + 0.513617i \(0.828305\pi\)
\(104\) −17.7028 −0.170219
\(105\) 54.8350 + 39.9089i 0.522239 + 0.380085i
\(106\) 28.8623i 0.272286i
\(107\) 53.1045 0.496304 0.248152 0.968721i \(-0.420177\pi\)
0.248152 + 0.968721i \(0.420177\pi\)
\(108\) −87.7188 −0.812211
\(109\) 113.233i 1.03883i 0.854522 + 0.519416i \(0.173850\pi\)
−0.854522 + 0.519416i \(0.826150\pi\)
\(110\) 137.583 1.25076
\(111\) −115.073 −1.03670
\(112\) 76.9170 105.684i 0.686759 0.943611i
\(113\) 25.9757 0.229873 0.114937 0.993373i \(-0.463333\pi\)
0.114937 + 0.993373i \(0.463333\pi\)
\(114\) 6.40102 0.0561493
\(115\) 9.18503i 0.0798698i
\(116\) 49.9583i 0.430675i
\(117\) 4.72532 0.0403873
\(118\) 66.1054i 0.560215i
\(119\) 34.9505 48.0222i 0.293702 0.403548i
\(120\) 21.9736i 0.183113i
\(121\) −115.692 −0.956134
\(122\) 158.734i 1.30110i
\(123\) −110.435 43.7665i −0.897844 0.355825i
\(124\) 164.344i 1.32535i
\(125\) 129.806i 1.03845i
\(126\) −6.66880 + 9.16297i −0.0529270 + 0.0727220i
\(127\) 122.410 0.963855 0.481927 0.876211i \(-0.339937\pi\)
0.481927 + 0.876211i \(0.339937\pi\)
\(128\) −70.9442 −0.554252
\(129\) −208.368 −1.61525
\(130\) 69.8034i 0.536949i
\(131\) 48.9887i 0.373959i −0.982364 0.186980i \(-0.940130\pi\)
0.982364 0.186980i \(-0.0598699\pi\)
\(132\) 140.498i 1.06438i
\(133\) 3.40286 4.67555i 0.0255854 0.0351545i
\(134\) 9.50985i 0.0709691i
\(135\) 93.0629i 0.689355i
\(136\) −19.2436 −0.141497
\(137\) 51.3949i 0.375145i 0.982251 + 0.187573i \(0.0600620\pi\)
−0.982251 + 0.187573i \(0.939938\pi\)
\(138\) 21.2829 0.154224
\(139\) 121.729i 0.875746i −0.899037 0.437873i \(-0.855732\pi\)
0.899037 0.437873i \(-0.144268\pi\)
\(140\) 59.6534 + 43.4157i 0.426096 + 0.310112i
\(141\) 2.87996 0.0204253
\(142\) 131.195i 0.923911i
\(143\) 120.087i 0.839767i
\(144\) 11.3043 0.0785020
\(145\) 53.0019 0.365531
\(146\) 285.835i 1.95778i
\(147\) −43.6492 135.093i −0.296933 0.919003i
\(148\) −125.185 −0.845844
\(149\) 147.905i 0.992652i 0.868136 + 0.496326i \(0.165318\pi\)
−0.868136 + 0.496326i \(0.834682\pi\)
\(150\) −107.067 −0.713778
\(151\) 198.902i 1.31723i 0.752479 + 0.658616i \(0.228858\pi\)
−0.752479 + 0.658616i \(0.771142\pi\)
\(152\) −1.87360 −0.0123263
\(153\) 5.13658 0.0335724
\(154\) −232.863 169.477i −1.51210 1.10050i
\(155\) −174.356 −1.12488
\(156\) −71.2822 −0.456937
\(157\) 153.292 0.976381 0.488190 0.872737i \(-0.337657\pi\)
0.488190 + 0.872737i \(0.337657\pi\)
\(158\) 293.725i 1.85902i
\(159\) 31.2694i 0.196663i
\(160\) 136.653i 0.854081i
\(161\) 11.3143 15.5459i 0.0702750 0.0965582i
\(162\) 201.068 1.24116
\(163\) 177.866 1.09120 0.545600 0.838046i \(-0.316302\pi\)
0.545600 + 0.838046i \(0.316302\pi\)
\(164\) −120.139 47.6123i −0.732553 0.290319i
\(165\) −149.058 −0.903379
\(166\) 314.844i 1.89665i
\(167\) 123.493 0.739479 0.369739 0.929136i \(-0.379447\pi\)
0.369739 + 0.929136i \(0.379447\pi\)
\(168\) −27.0675 + 37.1908i −0.161116 + 0.221374i
\(169\) −108.074 −0.639488
\(170\) 75.8786i 0.446345i
\(171\) 0.500109 0.00292461
\(172\) −226.677 −1.31789
\(173\) 335.378i 1.93860i −0.245875 0.969301i \(-0.579075\pi\)
0.245875 0.969301i \(-0.420925\pi\)
\(174\) 122.813i 0.705819i
\(175\) −56.9180 + 78.2057i −0.325246 + 0.446890i
\(176\) 287.281i 1.63228i
\(177\) 71.6186i 0.404625i
\(178\) −459.321 −2.58046
\(179\) 262.625i 1.46718i −0.679593 0.733590i \(-0.737843\pi\)
0.679593 0.733590i \(-0.262157\pi\)
\(180\) 6.38069i 0.0354483i
\(181\) −28.4415 −0.157135 −0.0785677 0.996909i \(-0.525035\pi\)
−0.0785677 + 0.996909i \(0.525035\pi\)
\(182\) −85.9850 + 118.144i −0.472445 + 0.649142i
\(183\) 171.973i 0.939741i
\(184\) −6.22958 −0.0338564
\(185\) 132.812i 0.717901i
\(186\) 404.006i 2.17207i
\(187\) 130.538i 0.698066i
\(188\) 3.13303 0.0166650
\(189\) 114.636 157.511i 0.606542 0.833392i
\(190\) 7.38771i 0.0388827i
\(191\) 220.420i 1.15403i −0.816733 0.577016i \(-0.804217\pi\)
0.816733 0.577016i \(-0.195783\pi\)
\(192\) −100.234 −0.522052
\(193\) 19.7965i 0.102572i 0.998684 + 0.0512862i \(0.0163321\pi\)
−0.998684 + 0.0512862i \(0.983668\pi\)
\(194\) 110.923 0.571767
\(195\) 75.6250i 0.387820i
\(196\) −47.4846 146.964i −0.242269 0.749817i
\(197\) 249.634 1.26718 0.633589 0.773670i \(-0.281581\pi\)
0.633589 + 0.773670i \(0.281581\pi\)
\(198\) 24.9076i 0.125796i
\(199\) −207.110 −1.04075 −0.520376 0.853937i \(-0.674208\pi\)
−0.520376 + 0.853937i \(0.674208\pi\)
\(200\) 31.3387 0.156694
\(201\) 10.3030i 0.0512586i
\(202\) −108.098 −0.535140
\(203\) −89.7070 65.2887i −0.441906 0.321619i
\(204\) −77.4862 −0.379834
\(205\) −50.5130 + 127.458i −0.246405 + 0.621746i
\(206\) 282.956i 1.37357i
\(207\) 1.66283 0.00803298
\(208\) 145.753 0.700736
\(209\) 12.7095i 0.0608110i
\(210\) −146.646 106.729i −0.698314 0.508232i
\(211\) 342.458i 1.62302i −0.584337 0.811511i \(-0.698645\pi\)
0.584337 0.811511i \(-0.301355\pi\)
\(212\) 34.0170i 0.160458i
\(213\) 142.137i 0.667310i
\(214\) −142.018 −0.663635
\(215\) 240.487i 1.11854i
\(216\) −63.1182 −0.292214
\(217\) 295.101 + 214.774i 1.35991 + 0.989744i
\(218\) 302.819i 1.38908i
\(219\) 309.674i 1.41404i
\(220\) −162.155 −0.737070
\(221\) 66.2291 0.299679
\(222\) 307.742 1.38623
\(223\) 89.7556i 0.402491i −0.979541 0.201246i \(-0.935501\pi\)
0.979541 0.201246i \(-0.0644990\pi\)
\(224\) −168.331 + 231.288i −0.751480 + 1.03254i
\(225\) −8.36509 −0.0371782
\(226\) −69.4671 −0.307376
\(227\) 54.6292 0.240657 0.120329 0.992734i \(-0.461605\pi\)
0.120329 + 0.992734i \(0.461605\pi\)
\(228\) −7.54423 −0.0330887
\(229\) −245.368 −1.07148 −0.535739 0.844384i \(-0.679967\pi\)
−0.535739 + 0.844384i \(0.679967\pi\)
\(230\) 24.5636i 0.106798i
\(231\) 252.283 + 183.612i 1.09214 + 0.794855i
\(232\) 35.9476i 0.154946i
\(233\) 237.177i 1.01793i 0.860788 + 0.508963i \(0.169971\pi\)
−0.860788 + 0.508963i \(0.830029\pi\)
\(234\) −12.6370 −0.0540042
\(235\) 3.32390i 0.0141443i
\(236\) 77.9117i 0.330134i
\(237\) 318.222i 1.34271i
\(238\) −93.4685 + 128.426i −0.392725 + 0.539606i
\(239\) 348.003i 1.45608i 0.685535 + 0.728040i \(0.259568\pi\)
−0.685535 + 0.728040i \(0.740432\pi\)
\(240\) 180.916i 0.753817i
\(241\) 48.8897i 0.202862i −0.994843 0.101431i \(-0.967658\pi\)
0.994843 0.101431i \(-0.0323421\pi\)
\(242\) 309.397 1.27850
\(243\) 32.6338 0.134295
\(244\) 187.084i 0.766737i
\(245\) −155.918 + 50.3775i −0.636399 + 0.205623i
\(246\) 295.337 + 117.045i 1.20056 + 0.475794i
\(247\) 6.44822 0.0261061
\(248\) 118.254i 0.476829i
\(249\) 341.102i 1.36989i
\(250\) 347.141i 1.38856i
\(251\) 129.340i 0.515299i 0.966238 + 0.257650i \(0.0829480\pi\)
−0.966238 + 0.257650i \(0.917052\pi\)
\(252\) 7.85983 10.7995i 0.0311898 0.0428550i
\(253\) 42.2582i 0.167029i
\(254\) −327.361 −1.28882
\(255\) 82.2068i 0.322380i
\(256\) 328.107 1.28167
\(257\) −364.713 −1.41912 −0.709558 0.704647i \(-0.751106\pi\)
−0.709558 + 0.704647i \(0.751106\pi\)
\(258\) 557.240 2.15985
\(259\) 163.600 224.787i 0.631658 0.867902i
\(260\) 82.2701i 0.316424i
\(261\) 9.59530i 0.0367636i
\(262\) 131.011i 0.500042i
\(263\) 48.9787i 0.186231i 0.995655 + 0.0931153i \(0.0296825\pi\)
−0.995655 + 0.0931153i \(0.970317\pi\)
\(264\) 101.096i 0.382938i
\(265\) 36.0894 0.136187
\(266\) −9.10031 + 12.5039i −0.0342117 + 0.0470070i
\(267\) 497.629 1.86378
\(268\) 11.2083i 0.0418220i
\(269\) 116.578i 0.433374i 0.976241 + 0.216687i \(0.0695252\pi\)
−0.976241 + 0.216687i \(0.930475\pi\)
\(270\) 248.879i 0.921775i
\(271\) 23.3593i 0.0861967i 0.999071 + 0.0430983i \(0.0137229\pi\)
−0.999071 + 0.0430983i \(0.986277\pi\)
\(272\) 158.439 0.582495
\(273\) 93.1561 127.997i 0.341231 0.468853i
\(274\) 137.446i 0.501627i
\(275\) 212.586i 0.773039i
\(276\) −25.0840 −0.0908842
\(277\) 199.356 0.719696 0.359848 0.933011i \(-0.382829\pi\)
0.359848 + 0.933011i \(0.382829\pi\)
\(278\) 325.540i 1.17101i
\(279\) 31.5648i 0.113136i
\(280\) 42.9237 + 31.2398i 0.153299 + 0.111571i
\(281\) 192.518i 0.685119i −0.939496 0.342559i \(-0.888706\pi\)
0.939496 0.342559i \(-0.111294\pi\)
\(282\) −7.70192 −0.0273118
\(283\) 258.377i 0.912994i 0.889725 + 0.456497i \(0.150896\pi\)
−0.889725 + 0.456497i \(0.849104\pi\)
\(284\) 154.627i 0.544460i
\(285\) 8.00384i 0.0280837i
\(286\) 321.149i 1.12290i
\(287\) 242.499 153.503i 0.844945 0.534853i
\(288\) −24.7392 −0.0859000
\(289\) −217.007 −0.750888
\(290\) −141.744 −0.488771
\(291\) −120.174 −0.412968
\(292\) 336.885i 1.15372i
\(293\) −203.782 −0.695503 −0.347751 0.937587i \(-0.613055\pi\)
−0.347751 + 0.937587i \(0.613055\pi\)
\(294\) 116.731 + 361.282i 0.397046 + 1.22885i
\(295\) −82.6583 −0.280198
\(296\) −90.0770 −0.304314
\(297\) 428.161i 1.44162i
\(298\) 395.544i 1.32733i
\(299\) 21.4399 0.0717052
\(300\) 126.189 0.420629
\(301\) 296.236 407.030i 0.984173 1.35226i
\(302\) 531.926i 1.76134i
\(303\) 117.114 0.386514
\(304\) 15.4259 0.0507432
\(305\) −198.482 −0.650759
\(306\) −13.7368 −0.0448915
\(307\) 395.521i 1.28834i 0.764881 + 0.644171i \(0.222798\pi\)
−0.764881 + 0.644171i \(0.777202\pi\)
\(308\) 274.452 + 199.746i 0.891077 + 0.648525i
\(309\) 306.554i 0.992085i
\(310\) 466.282 1.50413
\(311\) 237.771 0.764537 0.382269 0.924051i \(-0.375143\pi\)
0.382269 + 0.924051i \(0.375143\pi\)
\(312\) −51.2912 −0.164395
\(313\) −435.532 −1.39148 −0.695738 0.718295i \(-0.744923\pi\)
−0.695738 + 0.718295i \(0.744923\pi\)
\(314\) −409.950 −1.30557
\(315\) −11.4574 8.33868i −0.0363727 0.0264720i
\(316\) 346.184i 1.09552i
\(317\) 169.230i 0.533849i −0.963717 0.266925i \(-0.913993\pi\)
0.963717 0.266925i \(-0.0860075\pi\)
\(318\) 83.6240i 0.262969i
\(319\) 243.850 0.764419
\(320\) 115.685i 0.361515i
\(321\) 153.862 0.479321
\(322\) −30.2579 + 41.5745i −0.0939686 + 0.129113i
\(323\) 7.00943 0.0217010
\(324\) −236.979 −0.731416
\(325\) −107.856 −0.331865
\(326\) −475.668 −1.45910
\(327\) 328.074i 1.00329i
\(328\) −86.4460 34.2595i −0.263555 0.104450i
\(329\) −4.09443 + 5.62578i −0.0124451 + 0.0170996i
\(330\) 398.626 1.20796
\(331\) 86.5093i 0.261358i −0.991425 0.130679i \(-0.958284\pi\)
0.991425 0.130679i \(-0.0417157\pi\)
\(332\) 371.075i 1.11769i
\(333\) 24.0438 0.0722035
\(334\) −330.258 −0.988798
\(335\) −11.8911 −0.0354959
\(336\) 222.855 306.205i 0.663260 0.911323i
\(337\) −380.320 −1.12855 −0.564273 0.825588i \(-0.690844\pi\)
−0.564273 + 0.825588i \(0.690844\pi\)
\(338\) 289.022 0.855095
\(339\) 75.2606 0.222008
\(340\) 89.4304i 0.263031i
\(341\) −802.171 −2.35241
\(342\) −1.33745 −0.00391066
\(343\) 325.950 + 106.797i 0.950292 + 0.311361i
\(344\) −163.106 −0.474145
\(345\) 26.6122i 0.0771369i
\(346\) 896.906i 2.59221i
\(347\) 82.6726i 0.238250i −0.992879 0.119125i \(-0.961991\pi\)
0.992879 0.119125i \(-0.0380089\pi\)
\(348\) 144.747i 0.415939i
\(349\) 315.374i 0.903651i −0.892106 0.451826i \(-0.850773\pi\)
0.892106 0.451826i \(-0.149227\pi\)
\(350\) 152.216 209.146i 0.434904 0.597561i
\(351\) 217.229 0.618886
\(352\) 628.709i 1.78611i
\(353\) 584.610i 1.65612i −0.560640 0.828060i \(-0.689445\pi\)
0.560640 0.828060i \(-0.310555\pi\)
\(354\) 191.530i 0.541046i
\(355\) −164.047 −0.462104
\(356\) 541.355 1.52066
\(357\) 101.264 139.137i 0.283652 0.389739i
\(358\) 702.341i 1.96185i
\(359\) 479.495 1.33564 0.667821 0.744322i \(-0.267227\pi\)
0.667821 + 0.744322i \(0.267227\pi\)
\(360\) 4.59123i 0.0127534i
\(361\) −360.318 −0.998110
\(362\) 76.0614 0.210114
\(363\) −335.201 −0.923418
\(364\) 101.342 139.244i 0.278411 0.382539i
\(365\) −357.409 −0.979203
\(366\) 459.908i 1.25658i
\(367\) 273.041i 0.743982i −0.928236 0.371991i \(-0.878675\pi\)
0.928236 0.371991i \(-0.121325\pi\)
\(368\) 51.2902 0.139375
\(369\) 23.0746 + 9.14471i 0.0625327 + 0.0247824i
\(370\) 355.180i 0.959945i
\(371\) −61.0822 44.4556i −0.164642 0.119826i
\(372\) 476.160i 1.28000i
\(373\) 1.89956 0.00509264 0.00254632 0.999997i \(-0.499189\pi\)
0.00254632 + 0.999997i \(0.499189\pi\)
\(374\) 349.100i 0.933422i
\(375\) 376.092i 1.00291i
\(376\) 2.25437 0.00599567
\(377\) 123.718i 0.328165i
\(378\) −306.573 + 421.234i −0.811041 + 1.11437i
\(379\) −418.879 −1.10522 −0.552611 0.833439i \(-0.686368\pi\)
−0.552611 + 0.833439i \(0.686368\pi\)
\(380\) 8.70715i 0.0229135i
\(381\) 354.663 0.930874
\(382\) 589.472i 1.54312i
\(383\) −184.199 −0.480936 −0.240468 0.970657i \(-0.577301\pi\)
−0.240468 + 0.970657i \(0.577301\pi\)
\(384\) −205.550 −0.535287
\(385\) 211.915 291.172i 0.550428 0.756291i
\(386\) 52.9419i 0.137155i
\(387\) 43.5370 0.112499
\(388\) −130.733 −0.336942
\(389\) −145.229 −0.373339 −0.186670 0.982423i \(-0.559769\pi\)
−0.186670 + 0.982423i \(0.559769\pi\)
\(390\) 202.245i 0.518576i
\(391\) 23.3059 0.0596058
\(392\) −34.1676 105.748i −0.0871623 0.269766i
\(393\) 141.937i 0.361163i
\(394\) −667.599 −1.69441
\(395\) 367.275 0.929810
\(396\) 29.3561i 0.0741315i
\(397\) 498.076 1.25460 0.627300 0.778778i \(-0.284160\pi\)
0.627300 + 0.778778i \(0.284160\pi\)
\(398\) 553.875 1.39165
\(399\) 9.85927 13.5467i 0.0247099 0.0339516i
\(400\) −258.022 −0.645056
\(401\) 165.137 0.411812 0.205906 0.978572i \(-0.433986\pi\)
0.205906 + 0.978572i \(0.433986\pi\)
\(402\) 27.5533i 0.0685407i
\(403\) 406.985i 1.00989i
\(404\) 127.404 0.315358
\(405\) 251.416i 0.620781i
\(406\) 239.904 + 174.602i 0.590898 + 0.430055i
\(407\) 611.036i 1.50132i
\(408\) −55.7552 −0.136655
\(409\) 643.763i 1.57399i −0.616958 0.786996i \(-0.711635\pi\)
0.616958 0.786996i \(-0.288365\pi\)
\(410\) 135.087 340.862i 0.329482 0.831371i
\(411\) 148.909i 0.362309i
\(412\) 333.491i 0.809445i
\(413\) 139.901 + 101.820i 0.338744 + 0.246537i
\(414\) −4.44692 −0.0107413
\(415\) 393.682 0.948630
\(416\) −318.978 −0.766774
\(417\) 352.690i 0.845780i
\(418\) 33.9892i 0.0813138i
\(419\) 755.940i 1.80415i −0.431576 0.902077i \(-0.642042\pi\)
0.431576 0.902077i \(-0.357958\pi\)
\(420\) 172.837 + 125.790i 0.411516 + 0.299501i
\(421\) 231.259i 0.549308i −0.961543 0.274654i \(-0.911437\pi\)
0.961543 0.274654i \(-0.0885633\pi\)
\(422\) 915.839i 2.17023i
\(423\) −0.601748 −0.00142257
\(424\) 24.4770i 0.0577287i
\(425\) −117.243 −0.275867
\(426\) 380.118i 0.892297i
\(427\) 335.935 + 244.493i 0.786732 + 0.572583i
\(428\) 167.382 0.391080
\(429\) 347.933i 0.811033i
\(430\) 643.137i 1.49567i
\(431\) −90.1501 −0.209165 −0.104582 0.994516i \(-0.533351\pi\)
−0.104582 + 0.994516i \(0.533351\pi\)
\(432\) 519.673 1.20295
\(433\) 391.594i 0.904373i 0.891923 + 0.452187i \(0.149356\pi\)
−0.891923 + 0.452187i \(0.850644\pi\)
\(434\) −789.193 574.374i −1.81842 1.32344i
\(435\) 153.565 0.353023
\(436\) 356.902i 0.818583i
\(437\) 2.26911 0.00519247
\(438\) 828.164i 1.89079i
\(439\) −610.875 −1.39151 −0.695757 0.718277i \(-0.744931\pi\)
−0.695757 + 0.718277i \(0.744931\pi\)
\(440\) −116.679 −0.265180
\(441\) 9.12018 + 28.2268i 0.0206807 + 0.0640064i
\(442\) −177.117 −0.400718
\(443\) 293.107 0.661640 0.330820 0.943694i \(-0.392675\pi\)
0.330820 + 0.943694i \(0.392675\pi\)
\(444\) −362.704 −0.816902
\(445\) 574.336i 1.29064i
\(446\) 240.034i 0.538194i
\(447\) 428.532i 0.958686i
\(448\) 142.502 195.799i 0.318086 0.437052i
\(449\) −317.488 −0.707101 −0.353551 0.935415i \(-0.615026\pi\)
−0.353551 + 0.935415i \(0.615026\pi\)
\(450\) 22.3708 0.0497130
\(451\) −232.399 + 586.405i −0.515296 + 1.30023i
\(452\) 81.8738 0.181137
\(453\) 576.288i 1.27216i
\(454\) −146.095 −0.321796
\(455\) −147.727 107.516i −0.324675 0.236298i
\(456\) −5.42846 −0.0119045
\(457\) 816.773i 1.78725i −0.448814 0.893625i \(-0.648154\pi\)
0.448814 0.893625i \(-0.351846\pi\)
\(458\) 656.191 1.43273
\(459\) 236.135 0.514456
\(460\) 28.9507i 0.0629362i
\(461\) 554.338i 1.20247i −0.799073 0.601235i \(-0.794676\pi\)
0.799073 0.601235i \(-0.205324\pi\)
\(462\) −674.684 491.034i −1.46036 1.06285i
\(463\) 735.278i 1.58807i 0.607870 + 0.794036i \(0.292024\pi\)
−0.607870 + 0.794036i \(0.707976\pi\)
\(464\) 295.968i 0.637863i
\(465\) −505.169 −1.08639
\(466\) 634.285i 1.36113i
\(467\) 387.715i 0.830225i 0.909770 + 0.415113i \(0.136258\pi\)
−0.909770 + 0.415113i \(0.863742\pi\)
\(468\) 14.8939 0.0318246
\(469\) 20.1260 + 14.6477i 0.0429126 + 0.0312318i
\(470\) 8.88914i 0.0189131i
\(471\) 444.139 0.942971
\(472\) 56.0615i 0.118774i
\(473\) 1106.43i 2.33917i
\(474\) 851.024i 1.79541i
\(475\) −11.4151 −0.0240317
\(476\) 110.162 151.363i 0.231432 0.317989i
\(477\) 6.53351i 0.0136971i
\(478\) 930.668i 1.94700i
\(479\) 930.051 1.94165 0.970826 0.239785i \(-0.0770770\pi\)
0.970826 + 0.239785i \(0.0770770\pi\)
\(480\) 395.931i 0.824857i
\(481\) 310.011 0.644514
\(482\) 130.746i 0.271258i
\(483\) 32.7814 45.0418i 0.0678703 0.0932542i
\(484\) −364.655 −0.753419
\(485\) 138.698i 0.285975i
\(486\) −87.2728 −0.179574
\(487\) 290.975 0.597485 0.298743 0.954334i \(-0.403433\pi\)
0.298743 + 0.954334i \(0.403433\pi\)
\(488\) 134.616i 0.275853i
\(489\) 515.338 1.05386
\(490\) 416.972 134.725i 0.850964 0.274949i
\(491\) −410.398 −0.835840 −0.417920 0.908484i \(-0.637241\pi\)
−0.417920 + 0.908484i \(0.637241\pi\)
\(492\) −348.084 137.949i −0.707487 0.280385i
\(493\) 134.486i 0.272790i
\(494\) −17.2445 −0.0349080
\(495\) 31.1445 0.0629182
\(496\) 973.621i 1.96295i
\(497\) 277.653 + 202.076i 0.558658 + 0.406591i
\(498\) 912.212i 1.83175i
\(499\) 588.240i 1.17884i 0.807828 + 0.589419i \(0.200643\pi\)
−0.807828 + 0.589419i \(0.799357\pi\)
\(500\) 409.139i 0.818279i
\(501\) 357.802 0.714175
\(502\) 345.896i 0.689035i
\(503\) −126.971 −0.252428 −0.126214 0.992003i \(-0.540283\pi\)
−0.126214 + 0.992003i \(0.540283\pi\)
\(504\) 5.65555 7.77076i 0.0112213 0.0154182i
\(505\) 135.166i 0.267656i
\(506\) 113.012i 0.223343i
\(507\) −313.126 −0.617607
\(508\) 385.827 0.759502
\(509\) −580.463 −1.14040 −0.570199 0.821506i \(-0.693134\pi\)
−0.570199 + 0.821506i \(0.693134\pi\)
\(510\) 219.847i 0.431072i
\(511\) 604.923 + 440.262i 1.18380 + 0.861570i
\(512\) −593.684 −1.15954
\(513\) 22.9907 0.0448161
\(514\) 975.356 1.89758
\(515\) 353.809 0.687007
\(516\) −656.763 −1.27280
\(517\) 15.2925i 0.0295793i
\(518\) −437.516 + 601.150i −0.844625 + 1.16052i
\(519\) 971.707i 1.87227i
\(520\) 59.1976i 0.113841i
\(521\) 104.630 0.200825 0.100412 0.994946i \(-0.467984\pi\)
0.100412 + 0.994946i \(0.467984\pi\)
\(522\) 25.6608i 0.0491586i
\(523\) 822.767i 1.57317i 0.617483 + 0.786584i \(0.288152\pi\)
−0.617483 + 0.786584i \(0.711848\pi\)
\(524\) 154.409i 0.294674i
\(525\) −164.911 + 226.589i −0.314117 + 0.431598i
\(526\) 130.984i 0.249019i
\(527\) 442.406i 0.839480i
\(528\) 832.353i 1.57643i
\(529\) −521.455 −0.985738
\(530\) −96.5144 −0.182103
\(531\) 14.9642i 0.0281812i
\(532\) 10.7256 14.7370i 0.0201609 0.0277012i
\(533\) 297.515 + 117.908i 0.558189 + 0.221216i
\(534\) −1330.81 −2.49216
\(535\) 177.579i 0.331924i
\(536\) 8.06494i 0.0150465i
\(537\) 760.916i 1.41698i
\(538\) 311.765i 0.579489i
\(539\) −717.341 + 231.775i −1.33087 + 0.430010i
\(540\) 293.329i 0.543201i
\(541\) 135.498 0.250459 0.125230 0.992128i \(-0.460033\pi\)
0.125230 + 0.992128i \(0.460033\pi\)
\(542\) 62.4700i 0.115258i
\(543\) −82.4049 −0.151759
\(544\) −346.740 −0.637389
\(545\) 378.646 0.694763
\(546\) −249.128 + 342.304i −0.456279 + 0.626930i
\(547\) 73.5580i 0.134475i −0.997737 0.0672376i \(-0.978581\pi\)
0.997737 0.0672376i \(-0.0214186\pi\)
\(548\) 161.994i 0.295609i
\(549\) 35.9324i 0.0654507i
\(550\) 568.521i 1.03367i
\(551\) 13.0938i 0.0237638i
\(552\) −18.0492 −0.0326979
\(553\) −621.621 452.415i −1.12409 0.818111i
\(554\) −533.139 −0.962346
\(555\) 384.801i 0.693336i
\(556\) 383.681i 0.690074i
\(557\) 806.927i 1.44870i −0.689431 0.724351i \(-0.742139\pi\)
0.689431 0.724351i \(-0.257861\pi\)
\(558\) 84.4141i 0.151280i
\(559\) 561.349 1.00420
\(560\) −353.405 257.208i −0.631080 0.459300i
\(561\) 378.215i 0.674180i
\(562\) 514.854i 0.916110i
\(563\) 310.513 0.551532 0.275766 0.961225i \(-0.411068\pi\)
0.275766 + 0.961225i \(0.411068\pi\)
\(564\) 9.07746 0.0160948
\(565\) 86.8618i 0.153738i
\(566\) 690.981i 1.22082i
\(567\) 309.699 425.528i 0.546206 0.750490i
\(568\) 111.262i 0.195883i
\(569\) −1064.91 −1.87155 −0.935777 0.352594i \(-0.885300\pi\)
−0.935777 + 0.352594i \(0.885300\pi\)
\(570\) 21.4048i 0.0375522i
\(571\) 571.145i 1.00025i −0.865952 0.500127i \(-0.833287\pi\)
0.865952 0.500127i \(-0.166713\pi\)
\(572\) 378.506i 0.661724i
\(573\) 638.633i 1.11454i
\(574\) −648.518 + 410.514i −1.12982 + 0.715182i
\(575\) −37.9543 −0.0660075
\(576\) 20.9432 0.0363597
\(577\) −937.964 −1.62559 −0.812793 0.582552i \(-0.802054\pi\)
−0.812793 + 0.582552i \(0.802054\pi\)
\(578\) 580.344 1.00405
\(579\) 57.3572i 0.0990625i
\(580\) 167.059 0.288032
\(581\) −666.315 484.943i −1.14684 0.834670i
\(582\) 321.382 0.552203
\(583\) 166.039 0.284801
\(584\) 242.406i 0.415079i
\(585\) 15.8013i 0.0270108i
\(586\) 544.977 0.929996
\(587\) −186.707 −0.318070 −0.159035 0.987273i \(-0.550838\pi\)
−0.159035 + 0.987273i \(0.550838\pi\)
\(588\) −137.579 425.806i −0.233979 0.724160i
\(589\) 43.0736i 0.0731301i
\(590\) 221.054 0.374668
\(591\) 723.276 1.22382
\(592\) 741.634 1.25276
\(593\) 363.034 0.612199 0.306099 0.952000i \(-0.400976\pi\)
0.306099 + 0.952000i \(0.400976\pi\)
\(594\) 1145.04i 1.92767i
\(595\) −160.584 116.873i −0.269890 0.196426i
\(596\) 466.188i 0.782194i
\(597\) −600.068 −1.00514
\(598\) −57.3369 −0.0958811
\(599\) −720.720 −1.20321 −0.601603 0.798795i \(-0.705471\pi\)
−0.601603 + 0.798795i \(0.705471\pi\)
\(600\) 90.7992 0.151332
\(601\) −769.330 −1.28008 −0.640042 0.768340i \(-0.721083\pi\)
−0.640042 + 0.768340i \(0.721083\pi\)
\(602\) −792.227 + 1088.52i −1.31599 + 1.80818i
\(603\) 2.15273i 0.00357004i
\(604\) 626.927i 1.03796i
\(605\) 386.871i 0.639456i
\(606\) −313.198 −0.516829
\(607\) 89.4029i 0.147286i −0.997285 0.0736432i \(-0.976537\pi\)
0.997285 0.0736432i \(-0.0234626\pi\)
\(608\) −33.7594 −0.0555253
\(609\) −259.912 189.164i −0.426785 0.310614i
\(610\) 530.801 0.870166
\(611\) −7.75871 −0.0126984
\(612\) 16.1902 0.0264545
\(613\) 909.661 1.48395 0.741974 0.670428i \(-0.233890\pi\)
0.741974 + 0.670428i \(0.233890\pi\)
\(614\) 1057.75i 1.72271i
\(615\) −146.354 + 369.290i −0.237973 + 0.600472i
\(616\) 197.482 + 143.727i 0.320588 + 0.233323i
\(617\) 164.383 0.266422 0.133211 0.991088i \(-0.457471\pi\)
0.133211 + 0.991088i \(0.457471\pi\)
\(618\) 819.821i 1.32657i
\(619\) 511.799i 0.826816i −0.910546 0.413408i \(-0.864338\pi\)
0.910546 0.413408i \(-0.135662\pi\)
\(620\) −549.559 −0.886385
\(621\) 76.4424 0.123096
\(622\) −635.874 −1.02230
\(623\) −707.477 + 972.078i −1.13560 + 1.56032i
\(624\) 422.298 0.676759
\(625\) −88.6178 −0.141788
\(626\) 1164.75 1.86062
\(627\) 36.8238i 0.0587302i
\(628\) 483.166 0.769373
\(629\) 336.993 0.535759
\(630\) 30.6406 + 22.3002i 0.0486359 + 0.0353972i
\(631\) 738.033 1.16962 0.584812 0.811169i \(-0.301168\pi\)
0.584812 + 0.811169i \(0.301168\pi\)
\(632\) 249.097i 0.394141i
\(633\) 992.219i 1.56749i
\(634\) 452.574i 0.713839i
\(635\) 409.333i 0.644619i
\(636\) 98.5591i 0.154967i
\(637\) 117.592 + 363.946i 0.184603 + 0.571344i
\(638\) −652.130 −1.02215
\(639\) 29.6985i 0.0464765i
\(640\) 237.235i 0.370680i
\(641\) 255.387i 0.398419i 0.979957 + 0.199209i \(0.0638374\pi\)
−0.979957 + 0.199209i \(0.936163\pi\)
\(642\) −411.475 −0.640927
\(643\) 44.4007 0.0690524 0.0345262 0.999404i \(-0.489008\pi\)
0.0345262 + 0.999404i \(0.489008\pi\)
\(644\) 35.6619 48.9996i 0.0553756 0.0760864i
\(645\) 696.775i 1.08027i
\(646\) −18.7454 −0.0290176
\(647\) 121.051i 0.187097i −0.995615 0.0935483i \(-0.970179\pi\)
0.995615 0.0935483i \(-0.0298209\pi\)
\(648\) −170.518 −0.263146
\(649\) −380.292 −0.585966
\(650\) 288.441 0.443756
\(651\) 855.011 + 622.276i 1.31338 + 0.955877i
\(652\) 560.621 0.859848
\(653\) 815.923i 1.24950i −0.780825 0.624749i \(-0.785201\pi\)
0.780825 0.624749i \(-0.214799\pi\)
\(654\) 877.373i 1.34155i
\(655\) −163.816 −0.250101
\(656\) 711.738 + 282.070i 1.08497 + 0.429984i
\(657\) 64.7042i 0.0984843i
\(658\) 10.9498 15.0451i 0.0166410 0.0228649i
\(659\) 23.2550i 0.0352883i −0.999844 0.0176442i \(-0.994383\pi\)
0.999844 0.0176442i \(-0.00561661\pi\)
\(660\) −469.820 −0.711849
\(661\) 600.186i 0.907996i 0.891003 + 0.453998i \(0.150003\pi\)
−0.891003 + 0.453998i \(0.849997\pi\)
\(662\) 231.353i 0.349476i
\(663\) 191.889 0.289425
\(664\) 267.007i 0.402119i
\(665\) −15.6349 11.3790i −0.0235111 0.0171113i
\(666\) −64.3005 −0.0965473
\(667\) 43.5361i 0.0652715i
\(668\) 389.242 0.582698
\(669\) 260.053i 0.388719i
\(670\) 31.8006 0.0474636
\(671\) −913.168 −1.36091
\(672\) −487.715 + 670.123i −0.725766 + 0.997207i
\(673\) 125.725i 0.186813i 0.995628 + 0.0934066i \(0.0297757\pi\)
−0.995628 + 0.0934066i \(0.970224\pi\)
\(674\) 1017.09 1.50904
\(675\) −384.554 −0.569710
\(676\) −340.641 −0.503907
\(677\) 218.443i 0.322663i −0.986900 0.161331i \(-0.948421\pi\)
0.986900 0.161331i \(-0.0515788\pi\)
\(678\) −201.270 −0.296859
\(679\) 170.851 234.750i 0.251621 0.345729i
\(680\) 64.3497i 0.0946320i
\(681\) 158.280 0.232422
\(682\) 2145.25 3.14553
\(683\) 1038.31i 1.52022i −0.649797 0.760108i \(-0.725146\pi\)
0.649797 0.760108i \(-0.274854\pi\)
\(684\) 1.57631 0.00230455
\(685\) 171.863 0.250894
\(686\) −871.692 285.608i −1.27069 0.416338i
\(687\) −710.917 −1.03481
\(688\) 1342.90 1.95190
\(689\) 84.2406i 0.122265i
\(690\) 71.1694i 0.103144i
\(691\) −752.770 −1.08939 −0.544696 0.838634i \(-0.683355\pi\)
−0.544696 + 0.838634i \(0.683355\pi\)
\(692\) 1057.09i 1.52759i
\(693\) −52.7128 38.3643i −0.0760647 0.0553598i
\(694\) 221.092i 0.318577i
\(695\) −407.056 −0.585692
\(696\) 104.153i 0.149645i
\(697\) 323.408 + 128.170i 0.464001 + 0.183889i
\(698\) 843.409i 1.20832i
\(699\) 687.184i 0.983096i
\(700\) −179.402 + 246.500i −0.256289 + 0.352142i
\(701\) 631.386 0.900693 0.450347 0.892854i \(-0.351300\pi\)
0.450347 + 0.892854i \(0.351300\pi\)
\(702\) −580.938 −0.827547
\(703\) 32.8104 0.0466719
\(704\) 532.239i 0.756022i
\(705\) 9.63049i 0.0136603i
\(706\) 1563.43i 2.21449i
\(707\) −166.500 + 228.772i −0.235502 + 0.323582i
\(708\) 225.737i 0.318838i
\(709\) 270.461i 0.381468i 0.981642 + 0.190734i \(0.0610868\pi\)
−0.981642 + 0.190734i \(0.938913\pi\)
\(710\) 438.712 0.617905
\(711\) 66.4902i 0.0935165i
\(712\) 389.533 0.547097
\(713\) 143.217i 0.200865i
\(714\) −270.811 + 372.096i −0.379287 + 0.521142i
\(715\) 401.566 0.561630
\(716\) 827.778i 1.15611i
\(717\) 1008.29i 1.40626i
\(718\) −1282.32 −1.78596
\(719\) 1057.01 1.47011 0.735055 0.678007i \(-0.237156\pi\)
0.735055 + 0.678007i \(0.237156\pi\)
\(720\) 37.8011i 0.0525016i
\(721\) −598.829 435.827i −0.830554 0.604476i
\(722\) 963.601 1.33463
\(723\) 141.650i 0.195920i
\(724\) −89.6458 −0.123820
\(725\) 219.014i 0.302089i
\(726\) 896.431 1.23475
\(727\) 504.265 0.693624 0.346812 0.937935i \(-0.387264\pi\)
0.346812 + 0.937935i \(0.387264\pi\)
\(728\) 72.9206 100.193i 0.100166 0.137628i
\(729\) 771.217 1.05791
\(730\) 955.823 1.30935
\(731\) 610.205 0.834754
\(732\) 542.047i 0.740501i
\(733\) 10.4157i 0.0142097i 0.999975 + 0.00710485i \(0.00226156\pi\)
−0.999975 + 0.00710485i \(0.997738\pi\)
\(734\) 730.197i 0.994819i
\(735\) −451.747 + 145.961i −0.614622 + 0.198587i
\(736\) −112.248 −0.152510
\(737\) −54.7084 −0.0742312
\(738\) −61.7086 24.4558i −0.0836159 0.0331379i
\(739\) 855.658 1.15786 0.578929 0.815378i \(-0.303471\pi\)
0.578929 + 0.815378i \(0.303471\pi\)
\(740\) 418.614i 0.565695i
\(741\) 18.6827 0.0252128
\(742\) 163.353 + 118.888i 0.220152 + 0.160226i
\(743\) −32.4259 −0.0436419 −0.0218209 0.999762i \(-0.506946\pi\)
−0.0218209 + 0.999762i \(0.506946\pi\)
\(744\) 342.622i 0.460513i
\(745\) 494.589 0.663878
\(746\) −5.08000 −0.00680966
\(747\) 71.2708i 0.0954094i
\(748\) 411.449i 0.550065i
\(749\) −218.745 + 300.557i −0.292050 + 0.401278i
\(750\) 1005.79i 1.34105i
\(751\) 1167.73i 1.55490i −0.628947 0.777448i \(-0.716514\pi\)
0.628947 0.777448i \(-0.283486\pi\)
\(752\) −18.5610 −0.0246822
\(753\) 374.743i 0.497667i
\(754\) 330.861i 0.438807i
\(755\) 665.121 0.880955
\(756\) 361.327 496.465i 0.477946 0.656700i
\(757\) 757.594i 1.00078i −0.865799 0.500392i \(-0.833189\pi\)
0.865799 0.500392i \(-0.166811\pi\)
\(758\) 1120.21 1.47785
\(759\) 122.437i 0.161313i
\(760\) 6.26524i 0.00824373i
\(761\) 1155.38i 1.51823i 0.650955 + 0.759117i \(0.274369\pi\)
−0.650955 + 0.759117i \(0.725631\pi\)
\(762\) −948.479 −1.24472
\(763\) −640.867 466.422i −0.839930 0.611300i
\(764\) 694.750i 0.909359i
\(765\) 17.1765i 0.0224530i
\(766\) 492.604 0.643086
\(767\) 192.943i 0.251555i
\(768\) 950.641 1.23781
\(769\) 425.981i 0.553942i 0.960878 + 0.276971i \(0.0893306\pi\)
−0.960878 + 0.276971i \(0.910669\pi\)
\(770\) −566.726 + 778.685i −0.736008 + 1.01128i
\(771\) −1056.70 −1.37056
\(772\) 62.3972i 0.0808254i
\(773\) 170.364 0.220393 0.110197 0.993910i \(-0.464852\pi\)
0.110197 + 0.993910i \(0.464852\pi\)
\(774\) −116.431 −0.150428
\(775\) 720.472i 0.929642i
\(776\) −94.0694 −0.121223
\(777\) 474.005 651.285i 0.610045 0.838205i
\(778\) 388.387 0.499212
\(779\) 31.4878 + 12.4790i 0.0404208 + 0.0160192i
\(780\) 238.365i 0.305596i
\(781\) −754.742 −0.966379
\(782\) −62.3271 −0.0797022
\(783\) 441.108i 0.563357i
\(784\) 281.313 + 870.660i 0.358818 + 1.11054i
\(785\) 512.602i 0.652996i
\(786\) 379.584i 0.482932i
\(787\) 644.912i 0.819456i 0.912208 + 0.409728i \(0.134376\pi\)
−0.912208 + 0.409728i \(0.865624\pi\)
\(788\) 786.831 0.998516
\(789\) 141.908i 0.179858i
\(790\) −982.207 −1.24330
\(791\) −106.998 + 147.016i −0.135269 + 0.185860i
\(792\) 21.1232i 0.0266707i
\(793\) 463.299i 0.584236i
\(794\) −1332.01 −1.67759
\(795\) 104.564 0.131527
\(796\) −652.796 −0.820096
\(797\) 22.0824i 0.0277069i 0.999904 + 0.0138535i \(0.00440984\pi\)
−0.999904 + 0.0138535i \(0.995590\pi\)
\(798\) −26.3667 + 36.2281i −0.0330410 + 0.0453986i
\(799\) −8.43397 −0.0105557
\(800\) 564.677 0.705846
\(801\) −103.976 −0.129808
\(802\) −441.626 −0.550656
\(803\) −1644.36 −2.04777
\(804\) 32.4743i 0.0403910i
\(805\) −51.9848 37.8345i −0.0645775 0.0469994i
\(806\) 1088.40i 1.35038i
\(807\) 337.766i 0.418545i
\(808\) 91.6740 0.113458
\(809\) 164.851i 0.203772i −0.994796 0.101886i \(-0.967512\pi\)
0.994796 0.101886i \(-0.0324876\pi\)
\(810\) 672.365i 0.830080i
\(811\) 851.489i 1.04992i 0.851125 + 0.524962i \(0.175921\pi\)
−0.851125 + 0.524962i \(0.824079\pi\)
\(812\) −282.751 205.786i −0.348215 0.253431i
\(813\) 67.6800i 0.0832472i
\(814\) 1634.10i 2.00749i
\(815\) 594.776i 0.729786i
\(816\) 459.051 0.562563
\(817\) 59.4110 0.0727185
\(818\) 1721.62i 2.10467i
\(819\) −19.4643 + 26.7441i −0.0237659 + 0.0326545i
\(820\) −159.214 + 401.740i −0.194163 + 0.489926i
\(821\) −439.368 −0.535162 −0.267581 0.963535i \(-0.586224\pi\)
−0.267581 + 0.963535i \(0.586224\pi\)
\(822\) 398.228i 0.484463i
\(823\) 502.881i 0.611034i −0.952187 0.305517i \(-0.901171\pi\)
0.952187 0.305517i \(-0.0988292\pi\)
\(824\) 239.964i 0.291218i
\(825\) 615.935i 0.746588i
\(826\) −374.139 272.298i −0.452953 0.329659i
\(827\) 920.174i 1.11267i −0.830960 0.556333i \(-0.812208\pi\)
0.830960 0.556333i \(-0.187792\pi\)
\(828\) 5.24113 0.00632987
\(829\) 331.557i 0.399948i 0.979801 + 0.199974i \(0.0640858\pi\)
−0.979801 + 0.199974i \(0.935914\pi\)
\(830\) −1052.83 −1.26847
\(831\) 577.603 0.695070
\(832\) 270.034 0.324560
\(833\) 127.827 + 395.621i 0.153453 + 0.474935i
\(834\) 943.203i 1.13094i
\(835\) 412.956i 0.494558i
\(836\) 40.0596i 0.0479181i
\(837\) 1451.08i 1.73366i
\(838\) 2021.62i 2.41243i
\(839\) 1249.10 1.48879 0.744397 0.667738i \(-0.232737\pi\)
0.744397 + 0.667738i \(0.232737\pi\)
\(840\) 124.365 + 90.5126i 0.148053 + 0.107753i
\(841\) 589.776 0.701280
\(842\) 618.457i 0.734510i
\(843\) 557.793i 0.661676i
\(844\) 1079.41i 1.27892i
\(845\) 361.394i 0.427685i
\(846\) 1.60926 0.00190220
\(847\) 476.554 654.788i 0.562637 0.773067i
\(848\) 201.527i 0.237650i
\(849\) 748.609i 0.881754i
\(850\) 313.545 0.368877
\(851\) 109.092 0.128193
\(852\) 448.007i 0.525830i
\(853\) 318.424i 0.373299i −0.982427 0.186650i \(-0.940237\pi\)
0.982427 0.186650i \(-0.0597629\pi\)
\(854\) −898.393 653.850i −1.05198 0.765632i
\(855\) 1.67235i 0.00195596i
\(856\) 120.440 0.140701
\(857\) 1484.46i 1.73216i −0.499902 0.866082i \(-0.666631\pi\)
0.499902 0.866082i \(-0.333369\pi\)
\(858\) 930.481i 1.08448i
\(859\) 644.561i 0.750362i −0.926952 0.375181i \(-0.877581\pi\)
0.926952 0.375181i \(-0.122419\pi\)
\(860\) 758.000i 0.881396i
\(861\) 702.604 444.751i 0.816033 0.516552i
\(862\) 241.089 0.279686
\(863\) 421.677 0.488618 0.244309 0.969697i \(-0.421439\pi\)
0.244309 + 0.969697i \(0.421439\pi\)
\(864\) −1137.29 −1.31631
\(865\) −1121.49 −1.29652
\(866\) 1047.24i 1.20929i
\(867\) −628.744 −0.725195
\(868\) 930.141 + 676.956i 1.07159 + 0.779903i
\(869\) 1689.75 1.94447
\(870\) −410.681 −0.472047
\(871\) 27.7565i 0.0318674i
\(872\) 256.809i 0.294506i
\(873\) 25.1094 0.0287623
\(874\) −6.06831 −0.00694314
\(875\) 734.666 + 534.689i 0.839618 + 0.611073i
\(876\) 976.073i 1.11424i
\(877\) −1393.92 −1.58942 −0.794711 0.606988i \(-0.792378\pi\)
−0.794711 + 0.606988i \(0.792378\pi\)
\(878\) 1633.67 1.86067
\(879\) −590.428 −0.671704
\(880\) 960.657 1.09166
\(881\) 1208.12i 1.37131i −0.727928 0.685654i \(-0.759516\pi\)
0.727928 0.685654i \(-0.240484\pi\)
\(882\) −24.3902 75.4873i −0.0276533 0.0855865i
\(883\) 474.857i 0.537777i 0.963171 + 0.268889i \(0.0866563\pi\)
−0.963171 + 0.268889i \(0.913344\pi\)
\(884\) 208.750 0.236143
\(885\) −239.490 −0.270610
\(886\) −783.858 −0.884716
\(887\) −1313.75 −1.48111 −0.740556 0.671995i \(-0.765438\pi\)
−0.740556 + 0.671995i \(0.765438\pi\)
\(888\) −260.984 −0.293901
\(889\) −504.223 + 692.806i −0.567180 + 0.779309i
\(890\) 1535.95i 1.72579i
\(891\) 1156.71i 1.29821i
\(892\) 282.904i 0.317157i
\(893\) −0.821151 −0.000919542
\(894\) 1146.03i 1.28191i
\(895\) −878.209 −0.981239
\(896\) 292.230 401.526i 0.326149 0.448131i
\(897\) 62.1187 0.0692517
\(898\) 849.063 0.945504
\(899\) 826.428 0.919275
\(900\) −26.3662 −0.0292958
\(901\) 91.5724i 0.101634i
\(902\) 621.506 1568.23i 0.689031 1.73861i
\(903\) 858.298 1179.31i 0.950496 1.30599i
\(904\) 58.9124 0.0651685
\(905\) 95.1073i 0.105091i
\(906\) 1541.17i 1.70107i
\(907\) 902.223 0.994733 0.497366 0.867541i \(-0.334300\pi\)
0.497366 + 0.867541i \(0.334300\pi\)
\(908\) 172.188 0.189634
\(909\) −24.4701 −0.0269198
\(910\) 395.069 + 287.531i 0.434141 + 0.315968i
\(911\) 188.927 0.207385 0.103692 0.994609i \(-0.466934\pi\)
0.103692 + 0.994609i \(0.466934\pi\)
\(912\) 44.6943 0.0490069
\(913\) 1811.24 1.98383
\(914\) 2184.31i 2.38983i
\(915\) −575.070 −0.628492
\(916\) −773.386 −0.844308
\(917\) 277.263 + 201.792i 0.302359 + 0.220056i
\(918\) −631.499 −0.687908
\(919\) 936.432i 1.01897i 0.860480 + 0.509484i \(0.170164\pi\)
−0.860480 + 0.509484i \(0.829836\pi\)
\(920\) 20.8315i 0.0226429i
\(921\) 1145.96i 1.24426i
\(922\) 1482.47i 1.60789i
\(923\) 382.921i 0.414866i
\(924\) 795.182 + 578.732i 0.860586 + 0.626334i
\(925\) −548.803 −0.593301
\(926\) 1966.36i 2.12350i
\(927\) 64.0523i 0.0690964i
\(928\) 647.721i 0.697975i
\(929\) −1398.53 −1.50541 −0.752705 0.658357i \(-0.771252\pi\)
−0.752705 + 0.658357i \(0.771252\pi\)
\(930\) 1350.98 1.45267
\(931\) 12.4455 + 38.5186i 0.0133679 + 0.0413733i
\(932\) 747.567i 0.802111i
\(933\) 688.905 0.738376
\(934\) 1036.87i 1.11014i
\(935\) 436.515 0.466861
\(936\) 10.7169 0.0114497
\(937\) −609.901 −0.650908 −0.325454 0.945558i \(-0.605517\pi\)
−0.325454 + 0.945558i \(0.605517\pi\)
\(938\) −53.8233 39.1725i −0.0573809 0.0417617i
\(939\) −1261.89 −1.34386
\(940\) 10.4767i 0.0111455i
\(941\) 475.722i 0.505549i 0.967525 + 0.252775i \(0.0813432\pi\)
−0.967525 + 0.252775i \(0.918657\pi\)
\(942\) −1187.77 −1.26090
\(943\) 104.695 + 41.4916i 0.111023 + 0.0439996i
\(944\) 461.573i 0.488954i
\(945\) −526.711 383.340i −0.557367 0.405651i
\(946\) 2958.93i 3.12783i
\(947\) −1018.93 −1.07596 −0.537978 0.842959i \(-0.680812\pi\)
−0.537978 + 0.842959i \(0.680812\pi\)
\(948\) 1003.02i 1.05803i
\(949\) 834.271i 0.879105i
\(950\) 30.5275 0.0321342
\(951\) 490.319i 0.515582i
\(952\) 79.2671 108.913i 0.0832637 0.114405i
\(953\) −141.741 −0.148732 −0.0743658 0.997231i \(-0.523693\pi\)
−0.0743658 + 0.997231i \(0.523693\pi\)
\(954\) 17.4726i 0.0183151i
\(955\) −737.076 −0.771808
\(956\) 1096.88i 1.14737i
\(957\) 706.517 0.738263
\(958\) −2487.25 −2.59629
\(959\) −290.881 211.703i −0.303318 0.220754i
\(960\) 335.179i 0.349145i
\(961\) −1757.63 −1.82896
\(962\) −829.067 −0.861816
\(963\) −32.1484 −0.0333836
\(964\) 154.097i 0.159852i
\(965\) 66.1986 0.0685996
\(966\) −87.6676 + 120.456i −0.0907532 + 0.124695i
\(967\) 210.263i 0.217439i −0.994072 0.108719i \(-0.965325\pi\)
0.994072 0.108719i \(-0.0346750\pi\)
\(968\) −262.388 −0.271062
\(969\) 20.3087 0.0209585
\(970\) 370.922i 0.382394i
\(971\) −386.037 −0.397566 −0.198783 0.980043i \(-0.563699\pi\)
−0.198783 + 0.980043i \(0.563699\pi\)
\(972\) 102.860 0.105823
\(973\) 688.952 + 501.419i 0.708070 + 0.515333i
\(974\) −778.159 −0.798931
\(975\) −312.497 −0.320510
\(976\) 1108.34i 1.13560i
\(977\) 991.983i 1.01534i −0.861553 0.507668i \(-0.830508\pi\)
0.861553 0.507668i \(-0.169492\pi\)
\(978\) −1378.17 −1.40918
\(979\) 2642.39i 2.69907i
\(980\) −491.443 + 158.787i −0.501472 + 0.162027i
\(981\) 68.5488i 0.0698764i
\(982\) 1097.53 1.11765
\(983\) 1043.79i 1.06185i 0.847420 + 0.530923i \(0.178155\pi\)
−0.847420 + 0.530923i \(0.821845\pi\)
\(984\) −250.464 99.2616i −0.254537 0.100876i
\(985\) 834.767i 0.847479i
\(986\) 359.657i 0.364763i
\(987\) −11.8630 + 16.2998i −0.0120192 + 0.0165145i
\(988\) 20.3244 0.0205712
\(989\) 197.537 0.199734
\(990\) −83.2901 −0.0841315
\(991\) 1131.06i 1.14134i 0.821181 + 0.570668i \(0.193316\pi\)
−0.821181 + 0.570668i \(0.806684\pi\)
\(992\) 2130.75i 2.14793i
\(993\) 250.648i 0.252415i
\(994\) −742.531 540.413i −0.747013 0.543675i
\(995\) 692.567i 0.696047i
\(996\) 1075.13i 1.07945i
\(997\) −1647.10 −1.65205 −0.826026 0.563632i \(-0.809404\pi\)
−0.826026 + 0.563632i \(0.809404\pi\)
\(998\) 1573.14i 1.57629i
\(999\) 1105.32 1.10643
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 287.3.d.d.286.7 yes 32
7.6 odd 2 inner 287.3.d.d.286.6 yes 32
41.40 even 2 inner 287.3.d.d.286.5 32
287.286 odd 2 inner 287.3.d.d.286.8 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.d.d.286.5 32 41.40 even 2 inner
287.3.d.d.286.6 yes 32 7.6 odd 2 inner
287.3.d.d.286.7 yes 32 1.1 even 1 trivial
287.3.d.d.286.8 yes 32 287.286 odd 2 inner