Properties

Label 1014.3.f.d.775.1
Level $1014$
Weight $3$
Character 1014.775
Analytic conductor $27.629$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1014,3,Mod(577,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.577");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1014.f (of order \(4\), degree \(2\), 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: \(27.6294988061\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 775.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.775
Dual form 1014.3.f.d.577.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(4.73205 + 4.73205i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-1.83013 + 1.83013i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -9.46410i q^{10} +(10.7321 - 10.7321i) q^{11} -3.46410i q^{12} +3.66025 q^{14} +(-8.19615 - 8.19615i) q^{15} -4.00000 q^{16} -5.07180i q^{17} +(-3.00000 - 3.00000i) q^{18} +(2.60770 + 2.60770i) q^{19} +(-9.46410 + 9.46410i) q^{20} +(3.16987 - 3.16987i) q^{21} -21.4641 q^{22} -31.8564i q^{23} +(-3.46410 + 3.46410i) q^{24} +19.7846i q^{25} -5.19615 q^{27} +(-3.66025 - 3.66025i) q^{28} +17.3205 q^{29} +16.3923i q^{30} +(-30.8301 - 30.8301i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-18.5885 + 18.5885i) q^{33} +(-5.07180 + 5.07180i) q^{34} -17.3205 q^{35} +6.00000i q^{36} +(36.1769 - 36.1769i) q^{37} -5.21539i q^{38} +18.9282 q^{40} +(-30.2487 - 30.2487i) q^{41} -6.33975 q^{42} +32.6603i q^{43} +(21.4641 + 21.4641i) q^{44} +(14.1962 + 14.1962i) q^{45} +(-31.8564 + 31.8564i) q^{46} +(-58.9808 + 58.9808i) q^{47} +6.92820 q^{48} +42.3013i q^{49} +(19.7846 - 19.7846i) q^{50} +8.78461i q^{51} +97.6743 q^{53} +(5.19615 + 5.19615i) q^{54} +101.569 q^{55} +7.32051i q^{56} +(-4.51666 - 4.51666i) q^{57} +(-17.3205 - 17.3205i) q^{58} +(43.2679 - 43.2679i) q^{59} +(16.3923 - 16.3923i) q^{60} +79.3013 q^{61} +61.6603i q^{62} +(-5.49038 + 5.49038i) q^{63} -8.00000i q^{64} +37.1769 q^{66} +(-46.7391 - 46.7391i) q^{67} +10.1436 q^{68} +55.1769i q^{69} +(17.3205 + 17.3205i) q^{70} +(37.9474 + 37.9474i) q^{71} +(6.00000 - 6.00000i) q^{72} +(27.5814 - 27.5814i) q^{73} -72.3538 q^{74} -34.2679i q^{75} +(-5.21539 + 5.21539i) q^{76} +39.2820i q^{77} +36.1244 q^{79} +(-18.9282 - 18.9282i) q^{80} +9.00000 q^{81} +60.4974i q^{82} +(-20.9667 - 20.9667i) q^{83} +(6.33975 + 6.33975i) q^{84} +(24.0000 - 24.0000i) q^{85} +(32.6603 - 32.6603i) q^{86} -30.0000 q^{87} -42.9282i q^{88} +(49.3590 - 49.3590i) q^{89} -28.3923i q^{90} +63.7128 q^{92} +(53.3993 + 53.3993i) q^{93} +117.962 q^{94} +24.6795i q^{95} +(-6.92820 - 6.92820i) q^{96} +(-12.9878 - 12.9878i) q^{97} +(42.3013 - 42.3013i) q^{98} +(32.1962 - 32.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 12 q^{5} + 10 q^{7} + 8 q^{8} + 12 q^{9} + 36 q^{11} - 20 q^{14} - 12 q^{15} - 16 q^{16} - 12 q^{18} + 52 q^{19} - 24 q^{20} + 30 q^{21} - 72 q^{22} + 20 q^{28} - 106 q^{31} + 16 q^{32}+ \cdots + 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.73205 −0.577350
\(4\) 2.00000i 0.500000i
\(5\) 4.73205 + 4.73205i 0.946410 + 0.946410i 0.998635 0.0522252i \(-0.0166314\pi\)
−0.0522252 + 0.998635i \(0.516631\pi\)
\(6\) 1.73205 + 1.73205i 0.288675 + 0.288675i
\(7\) −1.83013 + 1.83013i −0.261447 + 0.261447i −0.825642 0.564195i \(-0.809187\pi\)
0.564195 + 0.825642i \(0.309187\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000 0.333333
\(10\) 9.46410i 0.946410i
\(11\) 10.7321 10.7321i 0.975641 0.975641i −0.0240693 0.999710i \(-0.507662\pi\)
0.999710 + 0.0240693i \(0.00766224\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 0 0
\(14\) 3.66025 0.261447
\(15\) −8.19615 8.19615i −0.546410 0.546410i
\(16\) −4.00000 −0.250000
\(17\) 5.07180i 0.298341i −0.988811 0.149170i \(-0.952340\pi\)
0.988811 0.149170i \(-0.0476603\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) 2.60770 + 2.60770i 0.137247 + 0.137247i 0.772393 0.635145i \(-0.219060\pi\)
−0.635145 + 0.772393i \(0.719060\pi\)
\(20\) −9.46410 + 9.46410i −0.473205 + 0.473205i
\(21\) 3.16987 3.16987i 0.150946 0.150946i
\(22\) −21.4641 −0.975641
\(23\) 31.8564i 1.38506i −0.721389 0.692531i \(-0.756496\pi\)
0.721389 0.692531i \(-0.243504\pi\)
\(24\) −3.46410 + 3.46410i −0.144338 + 0.144338i
\(25\) 19.7846i 0.791384i
\(26\) 0 0
\(27\) −5.19615 −0.192450
\(28\) −3.66025 3.66025i −0.130723 0.130723i
\(29\) 17.3205 0.597259 0.298629 0.954369i \(-0.403471\pi\)
0.298629 + 0.954369i \(0.403471\pi\)
\(30\) 16.3923i 0.546410i
\(31\) −30.8301 30.8301i −0.994520 0.994520i 0.00546484 0.999985i \(-0.498260\pi\)
−0.999985 + 0.00546484i \(0.998260\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −18.5885 + 18.5885i −0.563287 + 0.563287i
\(34\) −5.07180 + 5.07180i −0.149170 + 0.149170i
\(35\) −17.3205 −0.494872
\(36\) 6.00000i 0.166667i
\(37\) 36.1769 36.1769i 0.977754 0.977754i −0.0220034 0.999758i \(-0.507004\pi\)
0.999758 + 0.0220034i \(0.00700448\pi\)
\(38\) 5.21539i 0.137247i
\(39\) 0 0
\(40\) 18.9282 0.473205
\(41\) −30.2487 30.2487i −0.737773 0.737773i 0.234373 0.972147i \(-0.424696\pi\)
−0.972147 + 0.234373i \(0.924696\pi\)
\(42\) −6.33975 −0.150946
\(43\) 32.6603i 0.759541i 0.925081 + 0.379770i \(0.123997\pi\)
−0.925081 + 0.379770i \(0.876003\pi\)
\(44\) 21.4641 + 21.4641i 0.487820 + 0.487820i
\(45\) 14.1962 + 14.1962i 0.315470 + 0.315470i
\(46\) −31.8564 + 31.8564i −0.692531 + 0.692531i
\(47\) −58.9808 + 58.9808i −1.25491 + 1.25491i −0.301418 + 0.953492i \(0.597460\pi\)
−0.953492 + 0.301418i \(0.902540\pi\)
\(48\) 6.92820 0.144338
\(49\) 42.3013i 0.863291i
\(50\) 19.7846 19.7846i 0.395692 0.395692i
\(51\) 8.78461i 0.172247i
\(52\) 0 0
\(53\) 97.6743 1.84291 0.921456 0.388483i \(-0.127001\pi\)
0.921456 + 0.388483i \(0.127001\pi\)
\(54\) 5.19615 + 5.19615i 0.0962250 + 0.0962250i
\(55\) 101.569 1.84671
\(56\) 7.32051i 0.130723i
\(57\) −4.51666 4.51666i −0.0792397 0.0792397i
\(58\) −17.3205 17.3205i −0.298629 0.298629i
\(59\) 43.2679 43.2679i 0.733355 0.733355i −0.237928 0.971283i \(-0.576468\pi\)
0.971283 + 0.237928i \(0.0764682\pi\)
\(60\) 16.3923 16.3923i 0.273205 0.273205i
\(61\) 79.3013 1.30002 0.650010 0.759925i \(-0.274765\pi\)
0.650010 + 0.759925i \(0.274765\pi\)
\(62\) 61.6603i 0.994520i
\(63\) −5.49038 + 5.49038i −0.0871489 + 0.0871489i
\(64\) 8.00000i 0.125000i
\(65\) 0 0
\(66\) 37.1769 0.563287
\(67\) −46.7391 46.7391i −0.697598 0.697598i 0.266294 0.963892i \(-0.414201\pi\)
−0.963892 + 0.266294i \(0.914201\pi\)
\(68\) 10.1436 0.149170
\(69\) 55.1769i 0.799665i
\(70\) 17.3205 + 17.3205i 0.247436 + 0.247436i
\(71\) 37.9474 + 37.9474i 0.534471 + 0.534471i 0.921900 0.387429i \(-0.126637\pi\)
−0.387429 + 0.921900i \(0.626637\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) 27.5814 27.5814i 0.377828 0.377828i −0.492490 0.870318i \(-0.663913\pi\)
0.870318 + 0.492490i \(0.163913\pi\)
\(74\) −72.3538 −0.977754
\(75\) 34.2679i 0.456906i
\(76\) −5.21539 + 5.21539i −0.0686236 + 0.0686236i
\(77\) 39.2820i 0.510156i
\(78\) 0 0
\(79\) 36.1244 0.457270 0.228635 0.973512i \(-0.426574\pi\)
0.228635 + 0.973512i \(0.426574\pi\)
\(80\) −18.9282 18.9282i −0.236603 0.236603i
\(81\) 9.00000 0.111111
\(82\) 60.4974i 0.737773i
\(83\) −20.9667 20.9667i −0.252611 0.252611i 0.569430 0.822040i \(-0.307164\pi\)
−0.822040 + 0.569430i \(0.807164\pi\)
\(84\) 6.33975 + 6.33975i 0.0754732 + 0.0754732i
\(85\) 24.0000 24.0000i 0.282353 0.282353i
\(86\) 32.6603 32.6603i 0.379770 0.379770i
\(87\) −30.0000 −0.344828
\(88\) 42.9282i 0.487820i
\(89\) 49.3590 49.3590i 0.554595 0.554595i −0.373168 0.927764i \(-0.621729\pi\)
0.927764 + 0.373168i \(0.121729\pi\)
\(90\) 28.3923i 0.315470i
\(91\) 0 0
\(92\) 63.7128 0.692531
\(93\) 53.3993 + 53.3993i 0.574187 + 0.574187i
\(94\) 117.962 1.25491
\(95\) 24.6795i 0.259784i
\(96\) −6.92820 6.92820i −0.0721688 0.0721688i
\(97\) −12.9878 12.9878i −0.133895 0.133895i 0.636983 0.770878i \(-0.280182\pi\)
−0.770878 + 0.636983i \(0.780182\pi\)
\(98\) 42.3013 42.3013i 0.431646 0.431646i
\(99\) 32.1962 32.1962i 0.325214 0.325214i
\(100\) −39.5692 −0.395692
\(101\) 138.813i 1.37438i 0.726476 + 0.687192i \(0.241157\pi\)
−0.726476 + 0.687192i \(0.758843\pi\)
\(102\) 8.78461 8.78461i 0.0861236 0.0861236i
\(103\) 107.263i 1.04139i −0.853744 0.520693i \(-0.825674\pi\)
0.853744 0.520693i \(-0.174326\pi\)
\(104\) 0 0
\(105\) 30.0000 0.285714
\(106\) −97.6743 97.6743i −0.921456 0.921456i
\(107\) 5.50258 0.0514260 0.0257130 0.999669i \(-0.491814\pi\)
0.0257130 + 0.999669i \(0.491814\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) −108.811 108.811i −0.998265 0.998265i 0.00173346 0.999998i \(-0.499448\pi\)
−0.999998 + 0.00173346i \(0.999448\pi\)
\(110\) −101.569 101.569i −0.923357 0.923357i
\(111\) −62.6603 + 62.6603i −0.564507 + 0.564507i
\(112\) 7.32051 7.32051i 0.0653617 0.0653617i
\(113\) −86.7846 −0.768005 −0.384003 0.923332i \(-0.625455\pi\)
−0.384003 + 0.923332i \(0.625455\pi\)
\(114\) 9.03332i 0.0792397i
\(115\) 150.746 150.746i 1.31084 1.31084i
\(116\) 34.6410i 0.298629i
\(117\) 0 0
\(118\) −86.5359 −0.733355
\(119\) 9.28203 + 9.28203i 0.0780003 + 0.0780003i
\(120\) −32.7846 −0.273205
\(121\) 109.354i 0.903751i
\(122\) −79.3013 79.3013i −0.650010 0.650010i
\(123\) 52.3923 + 52.3923i 0.425954 + 0.425954i
\(124\) 61.6603 61.6603i 0.497260 0.497260i
\(125\) 24.6795 24.6795i 0.197436 0.197436i
\(126\) 10.9808 0.0871489
\(127\) 178.846i 1.40824i −0.710082 0.704118i \(-0.751342\pi\)
0.710082 0.704118i \(-0.248658\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 56.5692i 0.438521i
\(130\) 0 0
\(131\) 53.6359 0.409434 0.204717 0.978821i \(-0.434373\pi\)
0.204717 + 0.978821i \(0.434373\pi\)
\(132\) −37.1769 37.1769i −0.281643 0.281643i
\(133\) −9.54483 −0.0717656
\(134\) 93.4782i 0.697598i
\(135\) −24.5885 24.5885i −0.182137 0.182137i
\(136\) −10.1436 10.1436i −0.0745852 0.0745852i
\(137\) −87.4641 + 87.4641i −0.638424 + 0.638424i −0.950167 0.311743i \(-0.899087\pi\)
0.311743 + 0.950167i \(0.399087\pi\)
\(138\) 55.1769 55.1769i 0.399833 0.399833i
\(139\) 153.708 1.10581 0.552905 0.833244i \(-0.313519\pi\)
0.552905 + 0.833244i \(0.313519\pi\)
\(140\) 34.6410i 0.247436i
\(141\) 102.158 102.158i 0.724523 0.724523i
\(142\) 75.8949i 0.534471i
\(143\) 0 0
\(144\) −12.0000 −0.0833333
\(145\) 81.9615 + 81.9615i 0.565252 + 0.565252i
\(146\) −55.1628 −0.377828
\(147\) 73.2679i 0.498421i
\(148\) 72.3538 + 72.3538i 0.488877 + 0.488877i
\(149\) 112.210 + 112.210i 0.753089 + 0.753089i 0.975054 0.221966i \(-0.0712473\pi\)
−0.221966 + 0.975054i \(0.571247\pi\)
\(150\) −34.2679 + 34.2679i −0.228453 + 0.228453i
\(151\) 158.962 158.962i 1.05273 1.05273i 0.0541950 0.998530i \(-0.482741\pi\)
0.998530 0.0541950i \(-0.0172592\pi\)
\(152\) 10.4308 0.0686236
\(153\) 15.2154i 0.0994470i
\(154\) 39.2820 39.2820i 0.255078 0.255078i
\(155\) 291.779i 1.88245i
\(156\) 0 0
\(157\) 138.569 0.882606 0.441303 0.897358i \(-0.354516\pi\)
0.441303 + 0.897358i \(0.354516\pi\)
\(158\) −36.1244 36.1244i −0.228635 0.228635i
\(159\) −169.177 −1.06401
\(160\) 37.8564i 0.236603i
\(161\) 58.3013 + 58.3013i 0.362120 + 0.362120i
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 198.347 198.347i 1.21685 1.21685i 0.248123 0.968729i \(-0.420186\pi\)
0.968729 0.248123i \(-0.0798137\pi\)
\(164\) 60.4974 60.4974i 0.368887 0.368887i
\(165\) −175.923 −1.06620
\(166\) 41.9334i 0.252611i
\(167\) −197.569 + 197.569i −1.18305 + 1.18305i −0.204099 + 0.978950i \(0.565426\pi\)
−0.978950 + 0.204099i \(0.934574\pi\)
\(168\) 12.6795i 0.0754732i
\(169\) 0 0
\(170\) −48.0000 −0.282353
\(171\) 7.82309 + 7.82309i 0.0457490 + 0.0457490i
\(172\) −65.3205 −0.379770
\(173\) 67.5411i 0.390411i −0.980762 0.195205i \(-0.937463\pi\)
0.980762 0.195205i \(-0.0625373\pi\)
\(174\) 30.0000 + 30.0000i 0.172414 + 0.172414i
\(175\) −36.2083 36.2083i −0.206905 0.206905i
\(176\) −42.9282 + 42.9282i −0.243910 + 0.243910i
\(177\) −74.9423 + 74.9423i −0.423403 + 0.423403i
\(178\) −98.7180 −0.554595
\(179\) 50.2205i 0.280562i −0.990112 0.140281i \(-0.955199\pi\)
0.990112 0.140281i \(-0.0448005\pi\)
\(180\) −28.3923 + 28.3923i −0.157735 + 0.157735i
\(181\) 302.354i 1.67046i 0.549898 + 0.835232i \(0.314666\pi\)
−0.549898 + 0.835232i \(0.685334\pi\)
\(182\) 0 0
\(183\) −137.354 −0.750567
\(184\) −63.7128 63.7128i −0.346265 0.346265i
\(185\) 342.382 1.85071
\(186\) 106.799i 0.574187i
\(187\) −54.4308 54.4308i −0.291074 0.291074i
\(188\) −117.962 117.962i −0.627455 0.627455i
\(189\) 9.50962 9.50962i 0.0503154 0.0503154i
\(190\) 24.6795 24.6795i 0.129892 0.129892i
\(191\) 162.679 0.851725 0.425863 0.904788i \(-0.359971\pi\)
0.425863 + 0.904788i \(0.359971\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −58.1506 + 58.1506i −0.301299 + 0.301299i −0.841522 0.540223i \(-0.818340\pi\)
0.540223 + 0.841522i \(0.318340\pi\)
\(194\) 25.9756i 0.133895i
\(195\) 0 0
\(196\) −84.6025 −0.431646
\(197\) 190.956 + 190.956i 0.969322 + 0.969322i 0.999543 0.0302216i \(-0.00962128\pi\)
−0.0302216 + 0.999543i \(0.509621\pi\)
\(198\) −64.3923 −0.325214
\(199\) 63.7846i 0.320526i −0.987074 0.160263i \(-0.948766\pi\)
0.987074 0.160263i \(-0.0512342\pi\)
\(200\) 39.5692 + 39.5692i 0.197846 + 0.197846i
\(201\) 80.9545 + 80.9545i 0.402759 + 0.402759i
\(202\) 138.813 138.813i 0.687192 0.687192i
\(203\) −31.6987 + 31.6987i −0.156151 + 0.156151i
\(204\) −17.5692 −0.0861236
\(205\) 286.277i 1.39647i
\(206\) −107.263 + 107.263i −0.520693 + 0.520693i
\(207\) 95.5692i 0.461687i
\(208\) 0 0
\(209\) 55.9718 0.267808
\(210\) −30.0000 30.0000i −0.142857 0.142857i
\(211\) 247.799 1.17440 0.587201 0.809441i \(-0.300230\pi\)
0.587201 + 0.809441i \(0.300230\pi\)
\(212\) 195.349i 0.921456i
\(213\) −65.7269 65.7269i −0.308577 0.308577i
\(214\) −5.50258 5.50258i −0.0257130 0.0257130i
\(215\) −154.550 + 154.550i −0.718837 + 0.718837i
\(216\) −10.3923 + 10.3923i −0.0481125 + 0.0481125i
\(217\) 112.846 0.520028
\(218\) 217.622i 0.998265i
\(219\) −47.7724 + 47.7724i −0.218139 + 0.218139i
\(220\) 203.138i 0.923357i
\(221\) 0 0
\(222\) 125.321 0.564507
\(223\) −32.5307 32.5307i −0.145878 0.145878i 0.630396 0.776274i \(-0.282893\pi\)
−0.776274 + 0.630396i \(0.782893\pi\)
\(224\) −14.6410 −0.0653617
\(225\) 59.3538i 0.263795i
\(226\) 86.7846 + 86.7846i 0.384003 + 0.384003i
\(227\) −9.71281 9.71281i −0.0427877 0.0427877i 0.685389 0.728177i \(-0.259632\pi\)
−0.728177 + 0.685389i \(0.759632\pi\)
\(228\) 9.03332 9.03332i 0.0396198 0.0396198i
\(229\) −287.315 + 287.315i −1.25465 + 1.25465i −0.301041 + 0.953611i \(0.597334\pi\)
−0.953611 + 0.301041i \(0.902666\pi\)
\(230\) −301.492 −1.31084
\(231\) 68.0385i 0.294539i
\(232\) 34.6410 34.6410i 0.149315 0.149315i
\(233\) 27.3308i 0.117300i 0.998279 + 0.0586498i \(0.0186795\pi\)
−0.998279 + 0.0586498i \(0.981320\pi\)
\(234\) 0 0
\(235\) −558.200 −2.37532
\(236\) 86.5359 + 86.5359i 0.366678 + 0.366678i
\(237\) −62.5692 −0.264005
\(238\) 18.5641i 0.0780003i
\(239\) 0.861561 + 0.861561i 0.00360486 + 0.00360486i 0.708907 0.705302i \(-0.249189\pi\)
−0.705302 + 0.708907i \(0.749189\pi\)
\(240\) 32.7846 + 32.7846i 0.136603 + 0.136603i
\(241\) 60.1769 60.1769i 0.249697 0.249697i −0.571149 0.820846i \(-0.693502\pi\)
0.820846 + 0.571149i \(0.193502\pi\)
\(242\) −109.354 + 109.354i −0.451875 + 0.451875i
\(243\) −15.5885 −0.0641500
\(244\) 158.603i 0.650010i
\(245\) −200.172 + 200.172i −0.817028 + 0.817028i
\(246\) 104.785i 0.425954i
\(247\) 0 0
\(248\) −123.321 −0.497260
\(249\) 36.3154 + 36.3154i 0.145845 + 0.145845i
\(250\) −49.3590 −0.197436
\(251\) 40.7077i 0.162182i −0.996707 0.0810910i \(-0.974160\pi\)
0.996707 0.0810910i \(-0.0258404\pi\)
\(252\) −10.9808 10.9808i −0.0435745 0.0435745i
\(253\) −341.885 341.885i −1.35132 1.35132i
\(254\) −178.846 + 178.846i −0.704118 + 0.704118i
\(255\) −41.5692 + 41.5692i −0.163017 + 0.163017i
\(256\) 16.0000 0.0625000
\(257\) 309.779i 1.20537i 0.797980 + 0.602684i \(0.205902\pi\)
−0.797980 + 0.602684i \(0.794098\pi\)
\(258\) −56.5692 + 56.5692i −0.219261 + 0.219261i
\(259\) 132.417i 0.511261i
\(260\) 0 0
\(261\) 51.9615 0.199086
\(262\) −53.6359 53.6359i −0.204717 0.204717i
\(263\) −287.636 −1.09367 −0.546836 0.837240i \(-0.684168\pi\)
−0.546836 + 0.837240i \(0.684168\pi\)
\(264\) 74.3538i 0.281643i
\(265\) 462.200 + 462.200i 1.74415 + 1.74415i
\(266\) 9.54483 + 9.54483i 0.0358828 + 0.0358828i
\(267\) −85.4923 + 85.4923i −0.320196 + 0.320196i
\(268\) 93.4782 93.4782i 0.348799 0.348799i
\(269\) 163.741 0.608703 0.304351 0.952560i \(-0.401560\pi\)
0.304351 + 0.952560i \(0.401560\pi\)
\(270\) 49.1769i 0.182137i
\(271\) 229.954 229.954i 0.848541 0.848541i −0.141411 0.989951i \(-0.545164\pi\)
0.989951 + 0.141411i \(0.0451637\pi\)
\(272\) 20.2872i 0.0745852i
\(273\) 0 0
\(274\) 174.928 0.638424
\(275\) 212.329 + 212.329i 0.772107 + 0.772107i
\(276\) −110.354 −0.399833
\(277\) 134.985i 0.487309i −0.969862 0.243654i \(-0.921654\pi\)
0.969862 0.243654i \(-0.0783463\pi\)
\(278\) −153.708 153.708i −0.552905 0.552905i
\(279\) −92.4904 92.4904i −0.331507 0.331507i
\(280\) −34.6410 + 34.6410i −0.123718 + 0.123718i
\(281\) −323.545 + 323.545i −1.15141 + 1.15141i −0.165134 + 0.986271i \(0.552806\pi\)
−0.986271 + 0.165134i \(0.947194\pi\)
\(282\) −204.315 −0.724523
\(283\) 141.354i 0.499483i 0.968312 + 0.249742i \(0.0803457\pi\)
−0.968312 + 0.249742i \(0.919654\pi\)
\(284\) −75.8949 + 75.8949i −0.267236 + 0.267236i
\(285\) 42.7461i 0.149986i
\(286\) 0 0
\(287\) 110.718 0.385777
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 263.277 0.910993
\(290\) 163.923i 0.565252i
\(291\) 22.4955 + 22.4955i 0.0773042 + 0.0773042i
\(292\) 55.1628 + 55.1628i 0.188914 + 0.188914i
\(293\) 210.473 210.473i 0.718338 0.718338i −0.249927 0.968265i \(-0.580407\pi\)
0.968265 + 0.249927i \(0.0804065\pi\)
\(294\) −73.2679 + 73.2679i −0.249211 + 0.249211i
\(295\) 409.492 1.38811
\(296\) 144.708i 0.488877i
\(297\) −55.7654 + 55.7654i −0.187762 + 0.187762i
\(298\) 224.420i 0.753089i
\(299\) 0 0
\(300\) 68.5359 0.228453
\(301\) −59.7724 59.7724i −0.198579 0.198579i
\(302\) −317.923 −1.05273
\(303\) 240.431i 0.793501i
\(304\) −10.4308 10.4308i −0.0343118 0.0343118i
\(305\) 375.258 + 375.258i 1.23035 + 1.23035i
\(306\) −15.2154 + 15.2154i −0.0497235 + 0.0497235i
\(307\) 70.0685 70.0685i 0.228236 0.228236i −0.583719 0.811956i \(-0.698403\pi\)
0.811956 + 0.583719i \(0.198403\pi\)
\(308\) −78.5641 −0.255078
\(309\) 185.785i 0.601245i
\(310\) −291.779 + 291.779i −0.941224 + 0.941224i
\(311\) 140.238i 0.450927i 0.974252 + 0.225464i \(0.0723897\pi\)
−0.974252 + 0.225464i \(0.927610\pi\)
\(312\) 0 0
\(313\) −550.286 −1.75810 −0.879051 0.476728i \(-0.841823\pi\)
−0.879051 + 0.476728i \(0.841823\pi\)
\(314\) −138.569 138.569i −0.441303 0.441303i
\(315\) −51.9615 −0.164957
\(316\) 72.2487i 0.228635i
\(317\) 31.2923 + 31.2923i 0.0987140 + 0.0987140i 0.754739 0.656025i \(-0.227763\pi\)
−0.656025 + 0.754739i \(0.727763\pi\)
\(318\) 169.177 + 169.177i 0.532003 + 0.532003i
\(319\) 185.885 185.885i 0.582710 0.582710i
\(320\) 37.8564 37.8564i 0.118301 0.118301i
\(321\) −9.53074 −0.0296908
\(322\) 116.603i 0.362120i
\(323\) 13.2257 13.2257i 0.0409464 0.0409464i
\(324\) 18.0000i 0.0555556i
\(325\) 0 0
\(326\) −396.694 −1.21685
\(327\) 188.466 + 188.466i 0.576349 + 0.576349i
\(328\) −120.995 −0.368887
\(329\) 215.885i 0.656184i
\(330\) 175.923 + 175.923i 0.533100 + 0.533100i
\(331\) 285.624 + 285.624i 0.862911 + 0.862911i 0.991675 0.128764i \(-0.0411009\pi\)
−0.128764 + 0.991675i \(0.541101\pi\)
\(332\) 41.9334 41.9334i 0.126305 0.126305i
\(333\) 108.531 108.531i 0.325918 0.325918i
\(334\) 395.138 1.18305
\(335\) 442.344i 1.32043i
\(336\) −12.6795 + 12.6795i −0.0377366 + 0.0377366i
\(337\) 638.492i 1.89464i 0.320295 + 0.947318i \(0.396218\pi\)
−0.320295 + 0.947318i \(0.603782\pi\)
\(338\) 0 0
\(339\) 150.315 0.443408
\(340\) 48.0000 + 48.0000i 0.141176 + 0.141176i
\(341\) −661.741 −1.94059
\(342\) 15.6462i 0.0457490i
\(343\) −167.093 167.093i −0.487151 0.487151i
\(344\) 65.3205 + 65.3205i 0.189885 + 0.189885i
\(345\) −261.100 + 261.100i −0.756811 + 0.756811i
\(346\) −67.5411 + 67.5411i −0.195205 + 0.195205i
\(347\) −5.70250 −0.0164337 −0.00821686 0.999966i \(-0.502616\pi\)
−0.00821686 + 0.999966i \(0.502616\pi\)
\(348\) 60.0000i 0.172414i
\(349\) −128.103 + 128.103i −0.367058 + 0.367058i −0.866403 0.499345i \(-0.833574\pi\)
0.499345 + 0.866403i \(0.333574\pi\)
\(350\) 72.4167i 0.206905i
\(351\) 0 0
\(352\) 85.8564 0.243910
\(353\) −205.037 205.037i −0.580842 0.580842i 0.354293 0.935135i \(-0.384722\pi\)
−0.935135 + 0.354293i \(0.884722\pi\)
\(354\) 149.885 0.423403
\(355\) 359.138i 1.01166i
\(356\) 98.7180 + 98.7180i 0.277298 + 0.277298i
\(357\) −16.0770 16.0770i −0.0450335 0.0450335i
\(358\) −50.2205 + 50.2205i −0.140281 + 0.140281i
\(359\) 268.277 268.277i 0.747289 0.747289i −0.226680 0.973969i \(-0.572787\pi\)
0.973969 + 0.226680i \(0.0727871\pi\)
\(360\) 56.7846 0.157735
\(361\) 347.400i 0.962326i
\(362\) 302.354 302.354i 0.835232 0.835232i
\(363\) 189.406i 0.521781i
\(364\) 0 0
\(365\) 261.033 0.715160
\(366\) 137.354 + 137.354i 0.375284 + 0.375284i
\(367\) −176.215 −0.480151 −0.240075 0.970754i \(-0.577172\pi\)
−0.240075 + 0.970754i \(0.577172\pi\)
\(368\) 127.426i 0.346265i
\(369\) −90.7461 90.7461i −0.245924 0.245924i
\(370\) −342.382 342.382i −0.925357 0.925357i
\(371\) −178.756 + 178.756i −0.481823 + 0.481823i
\(372\) −106.799 + 106.799i −0.287093 + 0.287093i
\(373\) 483.606 1.29653 0.648266 0.761414i \(-0.275495\pi\)
0.648266 + 0.761414i \(0.275495\pi\)
\(374\) 108.862i 0.291074i
\(375\) −42.7461 + 42.7461i −0.113990 + 0.113990i
\(376\) 235.923i 0.627455i
\(377\) 0 0
\(378\) −19.0192 −0.0503154
\(379\) 204.107 + 204.107i 0.538541 + 0.538541i 0.923100 0.384559i \(-0.125647\pi\)
−0.384559 + 0.923100i \(0.625647\pi\)
\(380\) −49.3590 −0.129892
\(381\) 309.771i 0.813046i
\(382\) −162.679 162.679i −0.425863 0.425863i
\(383\) 186.249 + 186.249i 0.486289 + 0.486289i 0.907133 0.420844i \(-0.138266\pi\)
−0.420844 + 0.907133i \(0.638266\pi\)
\(384\) 13.8564 13.8564i 0.0360844 0.0360844i
\(385\) −185.885 + 185.885i −0.482817 + 0.482817i
\(386\) 116.301 0.301299
\(387\) 97.9808i 0.253180i
\(388\) 25.9756 25.9756i 0.0669474 0.0669474i
\(389\) 66.2487i 0.170305i −0.996368 0.0851526i \(-0.972862\pi\)
0.996368 0.0851526i \(-0.0271378\pi\)
\(390\) 0 0
\(391\) −161.569 −0.413221
\(392\) 84.6025 + 84.6025i 0.215823 + 0.215823i
\(393\) −92.9000 −0.236387
\(394\) 381.913i 0.969322i
\(395\) 170.942 + 170.942i 0.432765 + 0.432765i
\(396\) 64.3923 + 64.3923i 0.162607 + 0.162607i
\(397\) −95.6429 + 95.6429i −0.240914 + 0.240914i −0.817228 0.576314i \(-0.804490\pi\)
0.576314 + 0.817228i \(0.304490\pi\)
\(398\) −63.7846 + 63.7846i −0.160263 + 0.160263i
\(399\) 16.5321 0.0414339
\(400\) 79.1384i 0.197846i
\(401\) 135.415 135.415i 0.337694 0.337694i −0.517805 0.855499i \(-0.673251\pi\)
0.855499 + 0.517805i \(0.173251\pi\)
\(402\) 161.909i 0.402759i
\(403\) 0 0
\(404\) −277.626 −0.687192
\(405\) 42.5885 + 42.5885i 0.105157 + 0.105157i
\(406\) 63.3975 0.156151
\(407\) 776.505i 1.90787i
\(408\) 17.5692 + 17.5692i 0.0430618 + 0.0430618i
\(409\) −392.974 392.974i −0.960816 0.960816i 0.0384448 0.999261i \(-0.487760\pi\)
−0.999261 + 0.0384448i \(0.987760\pi\)
\(410\) −286.277 + 286.277i −0.698236 + 0.698236i
\(411\) 151.492 151.492i 0.368594 0.368594i
\(412\) 214.526 0.520693
\(413\) 158.372i 0.383467i
\(414\) −95.5692 + 95.5692i −0.230844 + 0.230844i
\(415\) 198.431i 0.478146i
\(416\) 0 0
\(417\) −266.229 −0.638440
\(418\) −55.9718 55.9718i −0.133904 0.133904i
\(419\) −657.646 −1.56956 −0.784781 0.619774i \(-0.787224\pi\)
−0.784781 + 0.619774i \(0.787224\pi\)
\(420\) 60.0000i 0.142857i
\(421\) −328.035 328.035i −0.779181 0.779181i 0.200511 0.979692i \(-0.435740\pi\)
−0.979692 + 0.200511i \(0.935740\pi\)
\(422\) −247.799 247.799i −0.587201 0.587201i
\(423\) −176.942 + 176.942i −0.418303 + 0.418303i
\(424\) 195.349 195.349i 0.460728 0.460728i
\(425\) 100.344 0.236102
\(426\) 131.454i 0.308577i
\(427\) −145.131 + 145.131i −0.339886 + 0.339886i
\(428\) 11.0052i 0.0257130i
\(429\) 0 0
\(430\) 309.100 0.718837
\(431\) −22.6898 22.6898i −0.0526446 0.0526446i 0.680294 0.732939i \(-0.261852\pi\)
−0.732939 + 0.680294i \(0.761852\pi\)
\(432\) 20.7846 0.0481125
\(433\) 196.215i 0.453153i 0.973993 + 0.226577i \(0.0727534\pi\)
−0.973993 + 0.226577i \(0.927247\pi\)
\(434\) −112.846 112.846i −0.260014 0.260014i
\(435\) −141.962 141.962i −0.326348 0.326348i
\(436\) 217.622 217.622i 0.499133 0.499133i
\(437\) 83.0718 83.0718i 0.190096 0.190096i
\(438\) 95.5448 0.218139
\(439\) 41.4627i 0.0944481i −0.998884 0.0472241i \(-0.984963\pi\)
0.998884 0.0472241i \(-0.0150375\pi\)
\(440\) 203.138 203.138i 0.461678 0.461678i
\(441\) 126.904i 0.287764i
\(442\) 0 0
\(443\) −19.9718 −0.0450831 −0.0225416 0.999746i \(-0.507176\pi\)
−0.0225416 + 0.999746i \(0.507176\pi\)
\(444\) −125.321 125.321i −0.282253 0.282253i
\(445\) 467.138 1.04975
\(446\) 65.0615i 0.145878i
\(447\) −194.354 194.354i −0.434796 0.434796i
\(448\) 14.6410 + 14.6410i 0.0326808 + 0.0326808i
\(449\) 93.3064 93.3064i 0.207809 0.207809i −0.595526 0.803336i \(-0.703056\pi\)
0.803336 + 0.595526i \(0.203056\pi\)
\(450\) 59.3538 59.3538i 0.131897 0.131897i
\(451\) −649.261 −1.43960
\(452\) 173.569i 0.384003i
\(453\) −275.329 + 275.329i −0.607791 + 0.607791i
\(454\) 19.4256i 0.0427877i
\(455\) 0 0
\(456\) −18.0666 −0.0396198
\(457\) −208.519 208.519i −0.456277 0.456277i 0.441154 0.897431i \(-0.354569\pi\)
−0.897431 + 0.441154i \(0.854569\pi\)
\(458\) 574.631 1.25465
\(459\) 26.3538i 0.0574157i
\(460\) 301.492 + 301.492i 0.655418 + 0.655418i
\(461\) −332.123 332.123i −0.720440 0.720440i 0.248255 0.968695i \(-0.420143\pi\)
−0.968695 + 0.248255i \(0.920143\pi\)
\(462\) −68.0385 + 68.0385i −0.147269 + 0.147269i
\(463\) −462.599 + 462.599i −0.999134 + 0.999134i −1.00000 0.000865128i \(-0.999725\pi\)
0.000865128 1.00000i \(0.499725\pi\)
\(464\) −69.2820 −0.149315
\(465\) 505.377i 1.08683i
\(466\) 27.3308 27.3308i 0.0586498 0.0586498i
\(467\) 396.649i 0.849355i −0.905345 0.424677i \(-0.860388\pi\)
0.905345 0.424677i \(-0.139612\pi\)
\(468\) 0 0
\(469\) 171.077 0.364770
\(470\) 558.200 + 558.200i 1.18766 + 1.18766i
\(471\) −240.009 −0.509573
\(472\) 173.072i 0.366678i
\(473\) 350.512 + 350.512i 0.741039 + 0.741039i
\(474\) 62.5692 + 62.5692i 0.132003 + 0.132003i
\(475\) −51.5922 + 51.5922i −0.108615 + 0.108615i
\(476\) −18.5641 + 18.5641i −0.0390001 + 0.0390001i
\(477\) 293.023 0.614304
\(478\) 1.72312i 0.00360486i
\(479\) −254.536 + 254.536i −0.531390 + 0.531390i −0.920986 0.389596i \(-0.872615\pi\)
0.389596 + 0.920986i \(0.372615\pi\)
\(480\) 65.5692i 0.136603i
\(481\) 0 0
\(482\) −120.354 −0.249697
\(483\) −100.981 100.981i −0.209070 0.209070i
\(484\) 218.708 0.451875
\(485\) 122.918i 0.253439i
\(486\) 15.5885 + 15.5885i 0.0320750 + 0.0320750i
\(487\) 137.000 + 137.000i 0.281314 + 0.281314i 0.833633 0.552319i \(-0.186257\pi\)
−0.552319 + 0.833633i \(0.686257\pi\)
\(488\) 158.603 158.603i 0.325005 0.325005i
\(489\) −343.547 + 343.547i −0.702550 + 0.702550i
\(490\) 400.344 0.817028
\(491\) 23.0718i 0.0469894i −0.999724 0.0234947i \(-0.992521\pi\)
0.999724 0.0234947i \(-0.00747928\pi\)
\(492\) −104.785 + 104.785i −0.212977 + 0.212977i
\(493\) 87.8461i 0.178187i
\(494\) 0 0
\(495\) 304.708 0.615571
\(496\) 123.321 + 123.321i 0.248630 + 0.248630i
\(497\) −138.897 −0.279471
\(498\) 72.6307i 0.145845i
\(499\) 160.769 + 160.769i 0.322183 + 0.322183i 0.849604 0.527421i \(-0.176841\pi\)
−0.527421 + 0.849604i \(0.676841\pi\)
\(500\) 49.3590 + 49.3590i 0.0987180 + 0.0987180i
\(501\) 342.200 342.200i 0.683034 0.683034i
\(502\) −40.7077 + 40.7077i −0.0810910 + 0.0810910i
\(503\) −601.244 −1.19532 −0.597658 0.801751i \(-0.703902\pi\)
−0.597658 + 0.801751i \(0.703902\pi\)
\(504\) 21.9615i 0.0435745i
\(505\) −656.869 + 656.869i −1.30073 + 1.30073i
\(506\) 683.769i 1.35132i
\(507\) 0 0
\(508\) 357.692 0.704118
\(509\) −347.745 347.745i −0.683192 0.683192i 0.277526 0.960718i \(-0.410486\pi\)
−0.960718 + 0.277526i \(0.910486\pi\)
\(510\) 83.1384 0.163017
\(511\) 100.955i 0.197564i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −13.5500 13.5500i −0.0264132 0.0264132i
\(514\) 309.779 309.779i 0.602684 0.602684i
\(515\) 507.573 507.573i 0.985579 0.985579i
\(516\) 113.138 0.219261
\(517\) 1265.97i 2.44868i
\(518\) 132.417 132.417i 0.255631 0.255631i
\(519\) 116.985i 0.225404i
\(520\) 0 0
\(521\) 647.951 1.24367 0.621834 0.783149i \(-0.286388\pi\)
0.621834 + 0.783149i \(0.286388\pi\)
\(522\) −51.9615 51.9615i −0.0995431 0.0995431i
\(523\) −165.923 −0.317252 −0.158626 0.987339i \(-0.550706\pi\)
−0.158626 + 0.987339i \(0.550706\pi\)
\(524\) 107.272i 0.204717i
\(525\) 62.7147 + 62.7147i 0.119457 + 0.119457i
\(526\) 287.636 + 287.636i 0.546836 + 0.546836i
\(527\) −156.364 + 156.364i −0.296706 + 0.296706i
\(528\) 74.3538 74.3538i 0.140822 0.140822i
\(529\) −485.831 −0.918394
\(530\) 924.400i 1.74415i
\(531\) 129.804 129.804i 0.244452 0.244452i
\(532\) 19.0897i 0.0358828i
\(533\) 0 0
\(534\) 170.985 0.320196
\(535\) 26.0385 + 26.0385i 0.0486700 + 0.0486700i
\(536\) −186.956 −0.348799
\(537\) 86.9845i 0.161982i
\(538\) −163.741 163.741i −0.304351 0.304351i
\(539\) 453.979 + 453.979i 0.842262 + 0.842262i
\(540\) 49.1769 49.1769i 0.0910684 0.0910684i
\(541\) 210.557 210.557i 0.389200 0.389200i −0.485202 0.874402i \(-0.661254\pi\)
0.874402 + 0.485202i \(0.161254\pi\)
\(542\) −459.909 −0.848541
\(543\) 523.692i 0.964442i
\(544\) 20.2872 20.2872i 0.0372926 0.0372926i
\(545\) 1029.80i 1.88954i
\(546\) 0 0
\(547\) −392.492 −0.717536 −0.358768 0.933427i \(-0.616803\pi\)
−0.358768 + 0.933427i \(0.616803\pi\)
\(548\) −174.928 174.928i −0.319212 0.319212i
\(549\) 237.904 0.433340
\(550\) 424.659i 0.772107i
\(551\) 45.1666 + 45.1666i 0.0819721 + 0.0819721i
\(552\) 110.354 + 110.354i 0.199916 + 0.199916i
\(553\) −66.1122 + 66.1122i −0.119552 + 0.119552i
\(554\) −134.985 + 134.985i −0.243654 + 0.243654i
\(555\) −593.023 −1.06851
\(556\) 307.415i 0.552905i
\(557\) −50.1539 + 50.1539i −0.0900429 + 0.0900429i −0.750694 0.660651i \(-0.770280\pi\)
0.660651 + 0.750694i \(0.270280\pi\)
\(558\) 184.981i 0.331507i
\(559\) 0 0
\(560\) 69.2820 0.123718
\(561\) 94.2769 + 94.2769i 0.168051 + 0.168051i
\(562\) 647.090 1.15141
\(563\) 832.726i 1.47909i 0.673109 + 0.739543i \(0.264958\pi\)
−0.673109 + 0.739543i \(0.735042\pi\)
\(564\) 204.315 + 204.315i 0.362261 + 0.362261i
\(565\) −410.669 410.669i −0.726848 0.726848i
\(566\) 141.354 141.354i 0.249742 0.249742i
\(567\) −16.4711 + 16.4711i −0.0290496 + 0.0290496i
\(568\) 151.790 0.267236
\(569\) 348.431i 0.612356i −0.951974 0.306178i \(-0.900950\pi\)
0.951974 0.306178i \(-0.0990503\pi\)
\(570\) −42.7461 + 42.7461i −0.0749932 + 0.0749932i
\(571\) 411.892i 0.721352i 0.932691 + 0.360676i \(0.117454\pi\)
−0.932691 + 0.360676i \(0.882546\pi\)
\(572\) 0 0
\(573\) −281.769 −0.491744
\(574\) −110.718 110.718i −0.192888 0.192888i
\(575\) 630.267 1.09612
\(576\) 24.0000i 0.0416667i
\(577\) −39.6692 39.6692i −0.0687507 0.0687507i 0.671895 0.740646i \(-0.265480\pi\)
−0.740646 + 0.671895i \(0.765480\pi\)
\(578\) −263.277 263.277i −0.455496 0.455496i
\(579\) 100.720 100.720i 0.173955 0.173955i
\(580\) −163.923 + 163.923i −0.282626 + 0.282626i
\(581\) 76.7434 0.132088
\(582\) 44.9911i 0.0773042i
\(583\) 1048.25 1048.25i 1.79802 1.79802i
\(584\) 110.326i 0.188914i
\(585\) 0 0
\(586\) −420.946 −0.718338
\(587\) −370.004 370.004i −0.630330 0.630330i 0.317821 0.948151i \(-0.397049\pi\)
−0.948151 + 0.317821i \(0.897049\pi\)
\(588\) 146.536 0.249211
\(589\) 160.791i 0.272990i
\(590\) −409.492 409.492i −0.694055 0.694055i
\(591\) −330.746 330.746i −0.559638 0.559638i
\(592\) −144.708 + 144.708i −0.244439 + 0.244439i
\(593\) −234.771 + 234.771i −0.395903 + 0.395903i −0.876785 0.480882i \(-0.840316\pi\)
0.480882 + 0.876785i \(0.340316\pi\)
\(594\) 111.531 0.187762
\(595\) 87.8461i 0.147640i
\(596\) −224.420 + 224.420i −0.376544 + 0.376544i
\(597\) 110.478i 0.185056i
\(598\) 0 0
\(599\) −652.908 −1.09000 −0.544998 0.838437i \(-0.683470\pi\)
−0.544998 + 0.838437i \(0.683470\pi\)
\(600\) −68.5359 68.5359i −0.114226 0.114226i
\(601\) 65.5692 0.109100 0.0545501 0.998511i \(-0.482628\pi\)
0.0545501 + 0.998511i \(0.482628\pi\)
\(602\) 119.545i 0.198579i
\(603\) −140.217 140.217i −0.232533 0.232533i
\(604\) 317.923 + 317.923i 0.526363 + 0.526363i
\(605\) 517.468 517.468i 0.855319 0.855319i
\(606\) −240.431 + 240.431i −0.396750 + 0.396750i
\(607\) −776.600 −1.27941 −0.639703 0.768622i \(-0.720943\pi\)
−0.639703 + 0.768622i \(0.720943\pi\)
\(608\) 20.8616i 0.0343118i
\(609\) 54.9038 54.9038i 0.0901540 0.0901540i
\(610\) 750.515i 1.23035i
\(611\) 0 0
\(612\) 30.4308 0.0497235
\(613\) −300.757 300.757i −0.490631 0.490631i 0.417874 0.908505i \(-0.362775\pi\)
−0.908505 + 0.417874i \(0.862775\pi\)
\(614\) −140.137 −0.228236
\(615\) 495.846i 0.806254i
\(616\) 78.5641 + 78.5641i 0.127539 + 0.127539i
\(617\) 95.6603 + 95.6603i 0.155041 + 0.155041i 0.780365 0.625324i \(-0.215033\pi\)
−0.625324 + 0.780365i \(0.715033\pi\)
\(618\) 185.785 185.785i 0.300622 0.300622i
\(619\) 661.030 661.030i 1.06790 1.06790i 0.0703796 0.997520i \(-0.477579\pi\)
0.997520 0.0703796i \(-0.0224211\pi\)
\(620\) 583.559 0.941224
\(621\) 165.531i 0.266555i
\(622\) 140.238 140.238i 0.225464 0.225464i
\(623\) 180.666i 0.289994i
\(624\) 0 0
\(625\) 728.184 1.16510
\(626\) 550.286 + 550.286i 0.879051 + 0.879051i
\(627\) −96.9461 −0.154619
\(628\) 277.138i 0.441303i
\(629\) −183.482 183.482i −0.291704 0.291704i
\(630\) 51.9615 + 51.9615i 0.0824786 + 0.0824786i
\(631\) 274.445 274.445i 0.434937 0.434937i −0.455367 0.890304i \(-0.650492\pi\)
0.890304 + 0.455367i \(0.150492\pi\)
\(632\) 72.2487 72.2487i 0.114318 0.114318i
\(633\) −429.200 −0.678041
\(634\) 62.5847i 0.0987140i
\(635\) 846.309 846.309i 1.33277 1.33277i
\(636\) 338.354i 0.532003i
\(637\) 0 0
\(638\) −371.769 −0.582710
\(639\) 113.842 + 113.842i 0.178157 + 0.178157i
\(640\) −75.7128 −0.118301
\(641\) 623.387i 0.972523i 0.873813 + 0.486261i \(0.161640\pi\)
−0.873813 + 0.486261i \(0.838360\pi\)
\(642\) 9.53074 + 9.53074i 0.0148454 + 0.0148454i
\(643\) −578.270 578.270i −0.899331 0.899331i 0.0960459 0.995377i \(-0.469380\pi\)
−0.995377 + 0.0960459i \(0.969380\pi\)
\(644\) −116.603 + 116.603i −0.181060 + 0.181060i
\(645\) 267.688 267.688i 0.415021 0.415021i
\(646\) −26.4514 −0.0409464
\(647\) 286.841i 0.443340i 0.975122 + 0.221670i \(0.0711508\pi\)
−0.975122 + 0.221670i \(0.928849\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 928.708i 1.43098i
\(650\) 0 0
\(651\) −195.455 −0.300238
\(652\) 396.694 + 396.694i 0.608426 + 0.608426i
\(653\) 648.848 0.993642 0.496821 0.867853i \(-0.334500\pi\)
0.496821 + 0.867853i \(0.334500\pi\)
\(654\) 376.932i 0.576349i
\(655\) 253.808 + 253.808i 0.387493 + 0.387493i
\(656\) 120.995 + 120.995i 0.184443 + 0.184443i
\(657\) 82.7442 82.7442i 0.125943 0.125943i
\(658\) −215.885 + 215.885i −0.328092 + 0.328092i
\(659\) 456.315 0.692436 0.346218 0.938154i \(-0.387466\pi\)
0.346218 + 0.938154i \(0.387466\pi\)
\(660\) 351.846i 0.533100i
\(661\) 229.988 229.988i 0.347939 0.347939i −0.511402 0.859341i \(-0.670874\pi\)
0.859341 + 0.511402i \(0.170874\pi\)
\(662\) 571.247i 0.862911i
\(663\) 0 0
\(664\) −83.8667 −0.126305
\(665\) −45.1666 45.1666i −0.0679197 0.0679197i
\(666\) −217.061 −0.325918
\(667\) 551.769i 0.827240i
\(668\) −395.138 395.138i −0.591525 0.591525i
\(669\) 56.3449 + 56.3449i 0.0842226 + 0.0842226i
\(670\) −442.344 + 442.344i −0.660214 + 0.660214i
\(671\) 851.065 851.065i 1.26835 1.26835i
\(672\) 25.3590 0.0377366
\(673\) 1044.01i 1.55128i −0.631178 0.775638i \(-0.717428\pi\)
0.631178 0.775638i \(-0.282572\pi\)
\(674\) 638.492 638.492i 0.947318 0.947318i
\(675\) 102.804i 0.152302i
\(676\) 0 0
\(677\) −193.408 −0.285684 −0.142842 0.989746i \(-0.545624\pi\)
−0.142842 + 0.989746i \(0.545624\pi\)
\(678\) −150.315 150.315i −0.221704 0.221704i
\(679\) 47.5387 0.0700128
\(680\) 96.0000i 0.141176i
\(681\) 16.8231 + 16.8231i 0.0247035 + 0.0247035i
\(682\) 661.741 + 661.741i 0.970295 + 0.970295i
\(683\) −587.678 + 587.678i −0.860436 + 0.860436i −0.991389 0.130952i \(-0.958197\pi\)
0.130952 + 0.991389i \(0.458197\pi\)
\(684\) −15.6462 + 15.6462i −0.0228745 + 0.0228745i
\(685\) −827.769 −1.20842
\(686\) 334.186i 0.487151i
\(687\) 497.645 497.645i 0.724374 0.724374i
\(688\) 130.641i 0.189885i
\(689\) 0 0
\(690\) 522.200 0.756811
\(691\) 164.030 + 164.030i 0.237381 + 0.237381i 0.815765 0.578384i \(-0.196316\pi\)
−0.578384 + 0.815765i \(0.696316\pi\)
\(692\) 135.082 0.195205
\(693\) 117.846i 0.170052i
\(694\) 5.70250 + 5.70250i 0.00821686 + 0.00821686i
\(695\) 727.352 + 727.352i 1.04655 + 1.04655i
\(696\) −60.0000 + 60.0000i −0.0862069 + 0.0862069i
\(697\) −153.415 + 153.415i −0.220108 + 0.220108i
\(698\) 256.206 0.367058
\(699\) 47.3384i 0.0677230i
\(700\) 72.4167 72.4167i 0.103452 0.103452i
\(701\) 55.6565i 0.0793958i −0.999212 0.0396979i \(-0.987360\pi\)
0.999212 0.0396979i \(-0.0126396\pi\)
\(702\) 0 0
\(703\) 188.677 0.268388
\(704\) −85.8564 85.8564i −0.121955 0.121955i
\(705\) 966.831 1.37139
\(706\) 410.074i 0.580842i
\(707\) −254.045 254.045i −0.359328 0.359328i
\(708\) −149.885 149.885i −0.211701 0.211701i
\(709\) −219.581 + 219.581i −0.309706 + 0.309706i −0.844795 0.535090i \(-0.820278\pi\)
0.535090 + 0.844795i \(0.320278\pi\)
\(710\) 359.138 359.138i 0.505829 0.505829i
\(711\) 108.373 0.152423
\(712\) 197.436i 0.277298i
\(713\) −982.137 + 982.137i −1.37747 + 1.37747i
\(714\) 32.1539i 0.0450335i
\(715\) 0 0
\(716\) 100.441 0.140281
\(717\) −1.49227 1.49227i −0.00208127 0.00208127i
\(718\) −536.554 −0.747289
\(719\) 311.520i 0.433269i 0.976253 + 0.216635i \(0.0695080\pi\)
−0.976253 + 0.216635i \(0.930492\pi\)
\(720\) −56.7846 56.7846i −0.0788675 0.0788675i
\(721\) 196.305 + 196.305i 0.272267 + 0.272267i
\(722\) −347.400 + 347.400i −0.481163 + 0.481163i
\(723\) −104.229 + 104.229i −0.144162 + 0.144162i
\(724\) −604.708 −0.835232
\(725\) 342.679i 0.472661i
\(726\) 189.406 189.406i 0.260890 0.260890i
\(727\) 379.585i 0.522125i −0.965322 0.261062i \(-0.915927\pi\)
0.965322 0.261062i \(-0.0840728\pi\)
\(728\) 0 0
\(729\) 27.0000 0.0370370
\(730\) −261.033 261.033i −0.357580 0.357580i
\(731\) 165.646 0.226602
\(732\) 274.708i 0.375284i
\(733\) −769.627 769.627i −1.04997 1.04997i −0.998684 0.0512852i \(-0.983668\pi\)
−0.0512852 0.998684i \(-0.516332\pi\)
\(734\) 176.215 + 176.215i 0.240075 + 0.240075i
\(735\) 346.708 346.708i 0.471711 0.471711i
\(736\) 127.426 127.426i 0.173133 0.173133i
\(737\) −1003.21 −1.36121
\(738\) 181.492i 0.245924i
\(739\) −189.161 + 189.161i −0.255969 + 0.255969i −0.823413 0.567443i \(-0.807933\pi\)
0.567443 + 0.823413i \(0.307933\pi\)
\(740\) 684.764i 0.925357i
\(741\) 0 0
\(742\) 357.513 0.481823
\(743\) −783.640 783.640i −1.05470 1.05470i −0.998415 0.0562818i \(-0.982075\pi\)
−0.0562818 0.998415i \(-0.517925\pi\)
\(744\) 213.597 0.287093
\(745\) 1061.97i 1.42546i
\(746\) −483.606 483.606i −0.648266 0.648266i
\(747\) −62.9000 62.9000i −0.0842035 0.0842035i
\(748\) 108.862 108.862i 0.145537 0.145537i
\(749\) −10.0704 + 10.0704i −0.0134451 + 0.0134451i
\(750\) 85.4923 0.113990
\(751\) 367.923i 0.489911i −0.969534 0.244955i \(-0.921227\pi\)
0.969534 0.244955i \(-0.0787733\pi\)
\(752\) 235.923 235.923i 0.313727 0.313727i
\(753\) 70.5077i 0.0936358i
\(754\) 0 0
\(755\) 1504.43 1.99262
\(756\) 19.0192 + 19.0192i 0.0251577 + 0.0251577i
\(757\) 195.384 0.258104 0.129052 0.991638i \(-0.458807\pi\)
0.129052 + 0.991638i \(0.458807\pi\)
\(758\) 408.214i 0.538541i
\(759\) 592.161 + 592.161i 0.780186 + 0.780186i
\(760\) 49.3590 + 49.3590i 0.0649460 + 0.0649460i
\(761\) 861.367 861.367i 1.13189 1.13189i 0.142025 0.989863i \(-0.454639\pi\)
0.989863 0.142025i \(-0.0453612\pi\)
\(762\) 309.771 309.771i 0.406523 0.406523i
\(763\) 398.275 0.521986
\(764\) 325.359i 0.425863i
\(765\) 72.0000 72.0000i 0.0941176 0.0941176i
\(766\) 372.497i 0.486289i
\(767\) 0 0
\(768\) −27.7128 −0.0360844
\(769\) −732.685 732.685i −0.952776 0.952776i 0.0461583 0.998934i \(-0.485302\pi\)
−0.998934 + 0.0461583i \(0.985302\pi\)
\(770\) 371.769 0.482817
\(771\) 536.554i 0.695919i
\(772\) −116.301 116.301i −0.150649 0.150649i
\(773\) −662.232 662.232i −0.856704 0.856704i 0.134245 0.990948i \(-0.457139\pi\)
−0.990948 + 0.134245i \(0.957139\pi\)
\(774\) 97.9808 97.9808i 0.126590 0.126590i
\(775\) 609.962 609.962i 0.787048 0.787048i
\(776\) −51.9512 −0.0669474
\(777\) 229.352i 0.295177i
\(778\) −66.2487 + 66.2487i −0.0851526 + 0.0851526i
\(779\) 157.759i 0.202515i
\(780\) 0 0
\(781\) 814.508 1.04290
\(782\) 161.569 + 161.569i 0.206610 + 0.206610i
\(783\) −90.0000 −0.114943
\(784\) 169.205i 0.215823i
\(785\) 655.717 + 655.717i 0.835308 + 0.835308i
\(786\) 92.9000 + 92.9000i 0.118193 + 0.118193i
\(787\) −677.547 + 677.547i −0.860923 + 0.860923i −0.991445 0.130522i \(-0.958335\pi\)
0.130522 + 0.991445i \(0.458335\pi\)
\(788\) −381.913 + 381.913i −0.484661 + 0.484661i
\(789\) 498.200 0.631432
\(790\) 341.885i 0.432765i
\(791\) 158.827 158.827i 0.200792 0.200792i
\(792\) 128.785i 0.162607i
\(793\) 0 0
\(794\) 191.286 0.240914
\(795\) −800.554 800.554i −1.00699 1.00699i
\(796\) 127.569 0.160263
\(797\) 375.118i 0.470662i 0.971915 + 0.235331i \(0.0756175\pi\)
−0.971915 + 0.235331i \(0.924383\pi\)
\(798\) −16.5321 16.5321i −0.0207169 0.0207169i
\(799\) 299.138 + 299.138i 0.374391 + 0.374391i
\(800\) −79.1384 + 79.1384i −0.0989230 + 0.0989230i
\(801\) 148.077 148.077i 0.184865 0.184865i
\(802\) −270.831 −0.337694
\(803\) 592.010i 0.737248i
\(804\) −161.909 + 161.909i −0.201379 + 0.201379i
\(805\) 551.769i 0.685428i
\(806\) 0 0
\(807\) −283.608 −0.351435
\(808\) 277.626 + 277.626i 0.343596 + 0.343596i
\(809\) 752.554 0.930227 0.465114 0.885251i \(-0.346013\pi\)
0.465114 + 0.885251i \(0.346013\pi\)
\(810\) 85.1769i 0.105157i
\(811\) 49.8071 + 49.8071i 0.0614144 + 0.0614144i 0.737147 0.675732i \(-0.236173\pi\)
−0.675732 + 0.737147i \(0.736173\pi\)
\(812\) −63.3975 63.3975i −0.0780757 0.0780757i
\(813\) −398.293 + 398.293i −0.489905 + 0.489905i
\(814\) −776.505 + 776.505i −0.953937 + 0.953937i
\(815\) 1877.17 2.30328
\(816\) 35.1384i 0.0430618i
\(817\) −85.1680 + 85.1680i −0.104245 + 0.104245i
\(818\) 785.947i 0.960816i
\(819\) 0 0
\(820\) 572.554 0.698236
\(821\) 268.750 + 268.750i 0.327345 + 0.327345i 0.851576 0.524231i \(-0.175647\pi\)
−0.524231 + 0.851576i \(0.675647\pi\)
\(822\) −302.985 −0.368594
\(823\) 1326.83i 1.61219i 0.591788 + 0.806094i \(0.298422\pi\)
−0.591788 + 0.806094i \(0.701578\pi\)
\(824\) −214.526 214.526i −0.260347 0.260347i
\(825\) −367.765 367.765i −0.445776 0.445776i
\(826\) 158.372 158.372i 0.191733 0.191733i
\(827\) 178.410 178.410i 0.215732 0.215732i −0.590965 0.806697i \(-0.701253\pi\)
0.806697 + 0.590965i \(0.201253\pi\)
\(828\) 191.138 0.230844
\(829\) 969.092i 1.16899i 0.811398 + 0.584495i \(0.198707\pi\)
−0.811398 + 0.584495i \(0.801293\pi\)
\(830\) −198.431 + 198.431i −0.239073 + 0.239073i
\(831\) 233.800i 0.281348i
\(832\) 0 0
\(833\) 214.543 0.257555
\(834\) 266.229 + 266.229i 0.319220 + 0.319220i
\(835\) −1869.82 −2.23930
\(836\) 111.944i 0.133904i
\(837\) 160.198 + 160.198i 0.191396 + 0.191396i
\(838\) 657.646 + 657.646i 0.784781 + 0.784781i
\(839\) −154.070 + 154.070i −0.183636 + 0.183636i −0.792938 0.609302i \(-0.791450\pi\)
0.609302 + 0.792938i \(0.291450\pi\)
\(840\) 60.0000 60.0000i 0.0714286 0.0714286i
\(841\) −541.000 −0.643282
\(842\) 656.070i 0.779181i
\(843\) 560.396 560.396i 0.664764 0.664764i
\(844\) 495.597i 0.587201i
\(845\) 0 0
\(846\) 353.885 0.418303
\(847\) 200.131 + 200.131i 0.236283 + 0.236283i
\(848\) −390.697 −0.460728
\(849\) 244.832i 0.288377i
\(850\) −100.344 100.344i −0.118051 0.118051i
\(851\) −1152.47 1152.47i −1.35425 1.35425i
\(852\) 131.454 131.454i 0.154288 0.154288i
\(853\) 173.527 173.527i 0.203432 0.203432i −0.598037 0.801469i \(-0.704052\pi\)
0.801469 + 0.598037i \(0.204052\pi\)
\(854\) 290.263 0.339886
\(855\) 74.0385i 0.0865947i
\(856\) 11.0052 11.0052i 0.0128565 0.0128565i
\(857\) 616.543i 0.719421i 0.933064 + 0.359710i \(0.117124\pi\)
−0.933064 + 0.359710i \(0.882876\pi\)
\(858\) 0 0
\(859\) 566.398 0.659370 0.329685 0.944091i \(-0.393058\pi\)
0.329685 + 0.944091i \(0.393058\pi\)
\(860\) −309.100 309.100i −0.359419 0.359419i
\(861\) −191.769 −0.222728
\(862\) 45.3796i 0.0526446i
\(863\) −656.627 656.627i −0.760866 0.760866i 0.215613 0.976479i \(-0.430825\pi\)
−0.976479 + 0.215613i \(0.930825\pi\)
\(864\) −20.7846 20.7846i −0.0240563 0.0240563i
\(865\) 319.608 319.608i 0.369489 0.369489i
\(866\) 196.215 196.215i 0.226577 0.226577i
\(867\) −456.009 −0.525962
\(868\) 225.692i 0.260014i
\(869\) 387.688 387.688i 0.446132 0.446132i
\(870\) 283.923i 0.326348i
\(871\) 0 0
\(872\) −435.244 −0.499133
\(873\) −38.9634 38.9634i −0.0446316 0.0446316i
\(874\) −166.144 −0.190096
\(875\) 90.3332i 0.103238i
\(876\) −95.5448 95.5448i −0.109069 0.109069i
\(877\) −472.069 472.069i −0.538277 0.538277i 0.384746 0.923023i \(-0.374289\pi\)
−0.923023 + 0.384746i \(0.874289\pi\)
\(878\) −41.4627 + 41.4627i −0.0472241 + 0.0472241i
\(879\) −364.550 + 364.550i −0.414733 + 0.414733i
\(880\) −406.277 −0.461678
\(881\) 1016.34i 1.15362i 0.816880 + 0.576808i \(0.195702\pi\)
−0.816880 + 0.576808i \(0.804298\pi\)
\(882\) 126.904 126.904i 0.143882 0.143882i
\(883\) 785.277i 0.889328i −0.895697 0.444664i \(-0.853323\pi\)
0.895697 0.444664i \(-0.146677\pi\)
\(884\) 0 0
\(885\) −709.261 −0.801425
\(886\) 19.9718 + 19.9718i 0.0225416 + 0.0225416i
\(887\) 1285.06 1.44877 0.724386 0.689394i \(-0.242123\pi\)
0.724386 + 0.689394i \(0.242123\pi\)
\(888\) 250.641i 0.282253i
\(889\) 327.311 + 327.311i 0.368179 + 0.368179i
\(890\) −467.138 467.138i −0.524875 0.524875i
\(891\) 96.5885 96.5885i 0.108405 0.108405i
\(892\) 65.0615 65.0615i 0.0729389 0.0729389i
\(893\) −307.608 −0.344466
\(894\) 388.708i 0.434796i
\(895\) 237.646 237.646i 0.265526 0.265526i
\(896\) 29.2820i 0.0326808i
\(897\) 0 0
\(898\) −186.613 −0.207809
\(899\) −533.993 533.993i −0.593986 0.593986i
\(900\) −118.708 −0.131897
\(901\) 495.384i 0.549816i
\(902\) 649.261 + 649.261i 0.719802 + 0.719802i
\(903\) 103.529 + 103.529i 0.114650 + 0.114650i
\(904\) −173.569 + 173.569i −0.192001 + 0.192001i
\(905\) −1430.75 + 1430.75i −1.58094 + 1.58094i
\(906\) 550.659 0.607791
\(907\) 278.862i 0.307455i 0.988113 + 0.153727i \(0.0491278\pi\)
−0.988113 + 0.153727i \(0.950872\pi\)
\(908\) 19.4256 19.4256i 0.0213939 0.0213939i
\(909\) 416.438i 0.458128i
\(910\) 0 0
\(911\) 86.7668 0.0952434 0.0476217 0.998865i \(-0.484836\pi\)
0.0476217 + 0.998865i \(0.484836\pi\)
\(912\) 18.0666 + 18.0666i 0.0198099 + 0.0198099i
\(913\) −450.031 −0.492914
\(914\) 417.037i 0.456277i
\(915\) −649.965 649.965i −0.710345 0.710345i
\(916\) −574.631 574.631i −0.627326 0.627326i
\(917\) −98.1604 + 98.1604i −0.107045 + 0.107045i
\(918\) 26.3538 26.3538i 0.0287079 0.0287079i
\(919\) 576.862 0.627706 0.313853 0.949472i \(-0.398380\pi\)
0.313853 + 0.949472i \(0.398380\pi\)
\(920\) 602.985i 0.655418i
\(921\) −121.362 + 121.362i −0.131772 + 0.131772i
\(922\) 664.246i 0.720440i
\(923\) 0 0
\(924\) 136.077 0.147269
\(925\) 715.746 + 715.746i 0.773780 + 0.773780i
\(926\) 925.199 0.999134
\(927\) 321.788i 0.347129i
\(928\) 69.2820 + 69.2820i 0.0746574 + 0.0746574i
\(929\) −10.5434 10.5434i −0.0113492 0.0113492i 0.701409 0.712759i \(-0.252555\pi\)
−0.712759 + 0.701409i \(0.752555\pi\)
\(930\) 505.377 505.377i 0.543416 0.543416i
\(931\) −110.309 + 110.309i −0.118484 + 0.118484i
\(932\) −54.6616 −0.0586498
\(933\) 242.900i 0.260343i
\(934\) −396.649 + 396.649i −0.424677 + 0.424677i
\(935\) 515.138i 0.550950i
\(936\) 0 0
\(937\) 700.477 0.747574 0.373787 0.927515i \(-0.378059\pi\)
0.373787 + 0.927515i \(0.378059\pi\)
\(938\) −171.077 171.077i −0.182385 0.182385i
\(939\) 953.123 1.01504
\(940\) 1116.40i 1.18766i
\(941\) 1147.05 + 1147.05i 1.21897 + 1.21897i 0.967992 + 0.250983i \(0.0807538\pi\)
0.250983 + 0.967992i \(0.419246\pi\)
\(942\) 240.009 + 240.009i 0.254787 + 0.254787i
\(943\) −963.615 + 963.615i −1.02186 + 1.02186i
\(944\) −173.072 + 173.072i −0.183339 + 0.183339i
\(945\) 90.0000 0.0952381
\(946\) 701.023i 0.741039i
\(947\) −868.526 + 868.526i −0.917134 + 0.917134i −0.996820 0.0796863i \(-0.974608\pi\)
0.0796863 + 0.996820i \(0.474608\pi\)
\(948\) 125.138i 0.132003i
\(949\) 0 0
\(950\) 103.184 0.108615
\(951\) −54.1999 54.1999i −0.0569926 0.0569926i
\(952\) 37.1281 0.0390001
\(953\) 1086.62i 1.14021i −0.821573 0.570104i \(-0.806903\pi\)
0.821573 0.570104i \(-0.193097\pi\)
\(954\) −293.023 293.023i −0.307152 0.307152i
\(955\) 769.808 + 769.808i 0.806081 + 0.806081i
\(956\) −1.72312 + 1.72312i −0.00180243 + 0.00180243i
\(957\) −321.962 + 321.962i −0.336428 + 0.336428i
\(958\) 509.072 0.531390
\(959\) 320.141i 0.333828i
\(960\) −65.5692 + 65.5692i −0.0683013 + 0.0683013i
\(961\) 939.993i 0.978141i
\(962\) 0 0
\(963\) 16.5077 0.0171420
\(964\) 120.354 + 120.354i 0.124848 + 0.124848i
\(965\) −550.344 −0.570304
\(966\) 201.962i 0.209070i
\(967\) −827.831 827.831i −0.856081 0.856081i 0.134793 0.990874i \(-0.456963\pi\)
−0.990874 + 0.134793i \(0.956963\pi\)
\(968\) −218.708 218.708i −0.225938 0.225938i
\(969\) −22.9076 + 22.9076i −0.0236404 + 0.0236404i
\(970\) −122.918 + 122.918i −0.126719 + 0.126719i
\(971\) −1143.70 −1.17786 −0.588929 0.808185i \(-0.700450\pi\)
−0.588929 + 0.808185i \(0.700450\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) −281.305 + 281.305i −0.289111 + 0.289111i
\(974\) 274.000i 0.281314i
\(975\) 0 0
\(976\) −317.205 −0.325005
\(977\) 243.033 + 243.033i 0.248755 + 0.248755i 0.820459 0.571705i \(-0.193718\pi\)
−0.571705 + 0.820459i \(0.693718\pi\)
\(978\) 687.093 0.702550
\(979\) 1059.45i 1.08217i
\(980\) −400.344 400.344i −0.408514 0.408514i
\(981\) −326.433 326.433i −0.332755 0.332755i
\(982\) −23.0718 + 23.0718i −0.0234947 + 0.0234947i
\(983\) −630.073 + 630.073i −0.640970 + 0.640970i −0.950794 0.309824i \(-0.899730\pi\)
0.309824 + 0.950794i \(0.399730\pi\)
\(984\) 209.569 0.212977
\(985\) 1807.23i 1.83475i
\(986\) −87.8461 + 87.8461i −0.0890934 + 0.0890934i
\(987\) 373.923i 0.378848i
\(988\) 0 0
\(989\) 1040.44 1.05201
\(990\) −304.708 304.708i −0.307786 0.307786i
\(991\) −956.739 −0.965427 −0.482714 0.875778i \(-0.660349\pi\)
−0.482714 + 0.875778i \(0.660349\pi\)
\(992\) 246.641i 0.248630i
\(993\) −494.715 494.715i −0.498202 0.498202i
\(994\) 138.897 + 138.897i 0.139736 + 0.139736i
\(995\) 301.832 301.832i 0.303349 0.303349i
\(996\) −72.6307 + 72.6307i −0.0729224 + 0.0729224i
\(997\) −167.169 −0.167672 −0.0838360 0.996480i \(-0.526717\pi\)
−0.0838360 + 0.996480i \(0.526717\pi\)
\(998\) 321.538i 0.322183i
\(999\) −187.981 + 187.981i −0.188169 + 0.188169i
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 1014.3.f.d.775.1 4
13.5 odd 4 inner 1014.3.f.d.577.1 4
13.7 odd 12 78.3.l.a.67.1 yes 4
13.8 odd 4 1014.3.f.e.577.1 4
13.10 even 6 78.3.l.a.7.1 4
13.12 even 2 1014.3.f.e.775.1 4
39.20 even 12 234.3.bb.c.145.1 4
39.23 odd 6 234.3.bb.c.163.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.3.l.a.7.1 4 13.10 even 6
78.3.l.a.67.1 yes 4 13.7 odd 12
234.3.bb.c.145.1 4 39.20 even 12
234.3.bb.c.163.1 4 39.23 odd 6
1014.3.f.d.577.1 4 13.5 odd 4 inner
1014.3.f.d.775.1 4 1.1 even 1 trivial
1014.3.f.e.577.1 4 13.8 odd 4
1014.3.f.e.775.1 4 13.12 even 2