Properties

Label 117.4.g.a.55.1
Level $117$
Weight $4$
Character 117.55
Analytic conductor $6.903$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,4,Mod(55,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.55");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.g (of order \(3\), 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: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 117.55
Dual form 117.4.g.a.100.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(3.50000 - 6.06218i) q^{4} -7.00000 q^{5} +(5.00000 - 8.66025i) q^{7} -15.0000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(3.50000 - 6.06218i) q^{4} -7.00000 q^{5} +(5.00000 - 8.66025i) q^{7} -15.0000 q^{8} +(3.50000 + 6.06218i) q^{10} +(-11.0000 - 19.0526i) q^{11} +(-45.5000 + 11.2583i) q^{13} -10.0000 q^{14} +(-20.5000 - 35.5070i) q^{16} +(18.5000 - 32.0429i) q^{17} +(-15.0000 + 25.9808i) q^{19} +(-24.5000 + 42.4352i) q^{20} +(-11.0000 + 19.0526i) q^{22} +(-81.0000 - 140.296i) q^{23} -76.0000 q^{25} +(32.5000 + 33.7750i) q^{26} +(-35.0000 - 60.6218i) q^{28} +(-56.5000 - 97.8609i) q^{29} +196.000 q^{31} +(-80.5000 + 139.430i) q^{32} -37.0000 q^{34} +(-35.0000 + 60.6218i) q^{35} +(-6.50000 - 11.2583i) q^{37} +30.0000 q^{38} +105.000 q^{40} +(142.500 + 246.817i) q^{41} +(123.000 - 213.042i) q^{43} -154.000 q^{44} +(-81.0000 + 140.296i) q^{46} +462.000 q^{47} +(121.500 + 210.444i) q^{49} +(38.0000 + 65.8179i) q^{50} +(-91.0000 + 315.233i) q^{52} +537.000 q^{53} +(77.0000 + 133.368i) q^{55} +(-75.0000 + 129.904i) q^{56} +(-56.5000 + 97.8609i) q^{58} +(288.000 - 498.831i) q^{59} +(317.500 - 549.926i) q^{61} +(-98.0000 - 169.741i) q^{62} -167.000 q^{64} +(318.500 - 78.8083i) q^{65} +(-101.000 - 174.937i) q^{67} +(-129.500 - 224.301i) q^{68} +70.0000 q^{70} +(-543.000 + 940.504i) q^{71} -805.000 q^{73} +(-6.50000 + 11.2583i) q^{74} +(105.000 + 181.865i) q^{76} -220.000 q^{77} +884.000 q^{79} +(143.500 + 248.549i) q^{80} +(142.500 - 246.817i) q^{82} -518.000 q^{83} +(-129.500 + 224.301i) q^{85} -246.000 q^{86} +(165.000 + 285.788i) q^{88} +(97.0000 + 168.009i) q^{89} +(-130.000 + 450.333i) q^{91} -1134.00 q^{92} +(-231.000 - 400.104i) q^{94} +(105.000 - 181.865i) q^{95} +(601.000 - 1040.96i) q^{97} +(121.500 - 210.444i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 7 q^{4} - 14 q^{5} + 10 q^{7} - 30 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + 7 q^{4} - 14 q^{5} + 10 q^{7} - 30 q^{8} + 7 q^{10} - 22 q^{11} - 91 q^{13} - 20 q^{14} - 41 q^{16} + 37 q^{17} - 30 q^{19} - 49 q^{20} - 22 q^{22} - 162 q^{23} - 152 q^{25} + 65 q^{26} - 70 q^{28} - 113 q^{29} + 392 q^{31} - 161 q^{32} - 74 q^{34} - 70 q^{35} - 13 q^{37} + 60 q^{38} + 210 q^{40} + 285 q^{41} + 246 q^{43} - 308 q^{44} - 162 q^{46} + 924 q^{47} + 243 q^{49} + 76 q^{50} - 182 q^{52} + 1074 q^{53} + 154 q^{55} - 150 q^{56} - 113 q^{58} + 576 q^{59} + 635 q^{61} - 196 q^{62} - 334 q^{64} + 637 q^{65} - 202 q^{67} - 259 q^{68} + 140 q^{70} - 1086 q^{71} - 1610 q^{73} - 13 q^{74} + 210 q^{76} - 440 q^{77} + 1768 q^{79} + 287 q^{80} + 285 q^{82} - 1036 q^{83} - 259 q^{85} - 492 q^{86} + 330 q^{88} + 194 q^{89} - 260 q^{91} - 2268 q^{92} - 462 q^{94} + 210 q^{95} + 1202 q^{97} + 243 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.176777 0.306186i 0.763998 0.645219i \(-0.223234\pi\)
−0.940775 + 0.339032i \(0.889900\pi\)
\(3\) 0 0
\(4\) 3.50000 6.06218i 0.437500 0.757772i
\(5\) −7.00000 −0.626099 −0.313050 0.949737i \(-0.601351\pi\)
−0.313050 + 0.949737i \(0.601351\pi\)
\(6\) 0 0
\(7\) 5.00000 8.66025i 0.269975 0.467610i −0.698880 0.715239i \(-0.746318\pi\)
0.968855 + 0.247629i \(0.0796514\pi\)
\(8\) −15.0000 −0.662913
\(9\) 0 0
\(10\) 3.50000 + 6.06218i 0.110680 + 0.191703i
\(11\) −11.0000 19.0526i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) −45.5000 + 11.2583i −0.970725 + 0.240192i
\(14\) −10.0000 −0.190901
\(15\) 0 0
\(16\) −20.5000 35.5070i −0.320312 0.554798i
\(17\) 18.5000 32.0429i 0.263936 0.457150i −0.703348 0.710845i \(-0.748313\pi\)
0.967284 + 0.253695i \(0.0816459\pi\)
\(18\) 0 0
\(19\) −15.0000 + 25.9808i −0.181118 + 0.313705i −0.942261 0.334878i \(-0.891305\pi\)
0.761144 + 0.648583i \(0.224638\pi\)
\(20\) −24.5000 + 42.4352i −0.273918 + 0.474440i
\(21\) 0 0
\(22\) −11.0000 + 19.0526i −0.106600 + 0.184637i
\(23\) −81.0000 140.296i −0.734333 1.27190i −0.955015 0.296557i \(-0.904162\pi\)
0.220682 0.975346i \(-0.429172\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 32.5000 + 33.7750i 0.245145 + 0.254762i
\(27\) 0 0
\(28\) −35.0000 60.6218i −0.236228 0.409159i
\(29\) −56.5000 97.8609i −0.361786 0.626631i 0.626469 0.779446i \(-0.284499\pi\)
−0.988255 + 0.152815i \(0.951166\pi\)
\(30\) 0 0
\(31\) 196.000 1.13557 0.567785 0.823177i \(-0.307801\pi\)
0.567785 + 0.823177i \(0.307801\pi\)
\(32\) −80.5000 + 139.430i −0.444704 + 0.770250i
\(33\) 0 0
\(34\) −37.0000 −0.186631
\(35\) −35.0000 + 60.6218i −0.169031 + 0.292770i
\(36\) 0 0
\(37\) −6.50000 11.2583i −0.0288809 0.0500232i 0.851224 0.524803i \(-0.175861\pi\)
−0.880105 + 0.474780i \(0.842528\pi\)
\(38\) 30.0000 0.128070
\(39\) 0 0
\(40\) 105.000 0.415049
\(41\) 142.500 + 246.817i 0.542799 + 0.940156i 0.998742 + 0.0501465i \(0.0159688\pi\)
−0.455943 + 0.890009i \(0.650698\pi\)
\(42\) 0 0
\(43\) 123.000 213.042i 0.436217 0.755550i −0.561177 0.827696i \(-0.689651\pi\)
0.997394 + 0.0721459i \(0.0229847\pi\)
\(44\) −154.000 −0.527645
\(45\) 0 0
\(46\) −81.0000 + 140.296i −0.259626 + 0.449686i
\(47\) 462.000 1.43382 0.716911 0.697165i \(-0.245555\pi\)
0.716911 + 0.697165i \(0.245555\pi\)
\(48\) 0 0
\(49\) 121.500 + 210.444i 0.354227 + 0.613540i
\(50\) 38.0000 + 65.8179i 0.107480 + 0.186161i
\(51\) 0 0
\(52\) −91.0000 + 315.233i −0.242681 + 0.840673i
\(53\) 537.000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(54\) 0 0
\(55\) 77.0000 + 133.368i 0.188776 + 0.326970i
\(56\) −75.0000 + 129.904i −0.178970 + 0.309984i
\(57\) 0 0
\(58\) −56.5000 + 97.8609i −0.127911 + 0.221548i
\(59\) 288.000 498.831i 0.635498 1.10072i −0.350911 0.936409i \(-0.614128\pi\)
0.986409 0.164307i \(-0.0525387\pi\)
\(60\) 0 0
\(61\) 317.500 549.926i 0.666421 1.15428i −0.312476 0.949926i \(-0.601159\pi\)
0.978898 0.204350i \(-0.0655082\pi\)
\(62\) −98.0000 169.741i −0.200742 0.347696i
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) 318.500 78.8083i 0.607770 0.150384i
\(66\) 0 0
\(67\) −101.000 174.937i −0.184166 0.318985i 0.759129 0.650940i \(-0.225625\pi\)
−0.943295 + 0.331955i \(0.892292\pi\)
\(68\) −129.500 224.301i −0.230944 0.400006i
\(69\) 0 0
\(70\) 70.0000 0.119523
\(71\) −543.000 + 940.504i −0.907637 + 1.57207i −0.0902997 + 0.995915i \(0.528783\pi\)
−0.817338 + 0.576159i \(0.804551\pi\)
\(72\) 0 0
\(73\) −805.000 −1.29066 −0.645330 0.763904i \(-0.723280\pi\)
−0.645330 + 0.763904i \(0.723280\pi\)
\(74\) −6.50000 + 11.2583i −0.0102109 + 0.0176859i
\(75\) 0 0
\(76\) 105.000 + 181.865i 0.158478 + 0.274492i
\(77\) −220.000 −0.325602
\(78\) 0 0
\(79\) 884.000 1.25896 0.629480 0.777017i \(-0.283268\pi\)
0.629480 + 0.777017i \(0.283268\pi\)
\(80\) 143.500 + 248.549i 0.200547 + 0.347358i
\(81\) 0 0
\(82\) 142.500 246.817i 0.191908 0.332395i
\(83\) −518.000 −0.685035 −0.342517 0.939511i \(-0.611280\pi\)
−0.342517 + 0.939511i \(0.611280\pi\)
\(84\) 0 0
\(85\) −129.500 + 224.301i −0.165250 + 0.286221i
\(86\) −246.000 −0.308452
\(87\) 0 0
\(88\) 165.000 + 285.788i 0.199876 + 0.346195i
\(89\) 97.0000 + 168.009i 0.115528 + 0.200100i 0.917991 0.396602i \(-0.129811\pi\)
−0.802463 + 0.596702i \(0.796477\pi\)
\(90\) 0 0
\(91\) −130.000 + 450.333i −0.149755 + 0.518766i
\(92\) −1134.00 −1.28508
\(93\) 0 0
\(94\) −231.000 400.104i −0.253466 0.439016i
\(95\) 105.000 181.865i 0.113398 0.196410i
\(96\) 0 0
\(97\) 601.000 1040.96i 0.629096 1.08963i −0.358638 0.933477i \(-0.616759\pi\)
0.987733 0.156149i \(-0.0499081\pi\)
\(98\) 121.500 210.444i 0.125238 0.216919i
\(99\) 0 0
\(100\) −266.000 + 460.726i −0.266000 + 0.460726i
\(101\) −214.500 371.525i −0.211322 0.366021i 0.740806 0.671719i \(-0.234444\pi\)
−0.952129 + 0.305698i \(0.901110\pi\)
\(102\) 0 0
\(103\) −1302.00 −1.24553 −0.622766 0.782408i \(-0.713991\pi\)
−0.622766 + 0.782408i \(0.713991\pi\)
\(104\) 682.500 168.875i 0.643506 0.159226i
\(105\) 0 0
\(106\) −268.500 465.056i −0.246029 0.426134i
\(107\) −669.000 1158.74i −0.604436 1.04691i −0.992140 0.125130i \(-0.960065\pi\)
0.387704 0.921784i \(-0.373268\pi\)
\(108\) 0 0
\(109\) −1034.00 −0.908617 −0.454308 0.890844i \(-0.650114\pi\)
−0.454308 + 0.890844i \(0.650114\pi\)
\(110\) 77.0000 133.368i 0.0667424 0.115601i
\(111\) 0 0
\(112\) −410.000 −0.345905
\(113\) 538.500 932.709i 0.448299 0.776477i −0.549976 0.835180i \(-0.685363\pi\)
0.998275 + 0.0587032i \(0.0186966\pi\)
\(114\) 0 0
\(115\) 567.000 + 982.073i 0.459765 + 0.796337i
\(116\) −791.000 −0.633125
\(117\) 0 0
\(118\) −576.000 −0.449365
\(119\) −185.000 320.429i −0.142512 0.246838i
\(120\) 0 0
\(121\) 423.500 733.524i 0.318182 0.551107i
\(122\) −635.000 −0.471231
\(123\) 0 0
\(124\) 686.000 1188.19i 0.496811 0.860503i
\(125\) 1407.00 1.00677
\(126\) 0 0
\(127\) 494.000 + 855.633i 0.345161 + 0.597836i 0.985383 0.170354i \(-0.0544911\pi\)
−0.640222 + 0.768190i \(0.721158\pi\)
\(128\) 727.500 + 1260.07i 0.502363 + 0.870119i
\(129\) 0 0
\(130\) −227.500 236.425i −0.153485 0.159506i
\(131\) −560.000 −0.373492 −0.186746 0.982408i \(-0.559794\pi\)
−0.186746 + 0.982408i \(0.559794\pi\)
\(132\) 0 0
\(133\) 150.000 + 259.808i 0.0977944 + 0.169385i
\(134\) −101.000 + 174.937i −0.0651125 + 0.112778i
\(135\) 0 0
\(136\) −277.500 + 480.644i −0.174966 + 0.303051i
\(137\) −259.500 + 449.467i −0.161829 + 0.280296i −0.935525 0.353261i \(-0.885073\pi\)
0.773696 + 0.633557i \(0.218406\pi\)
\(138\) 0 0
\(139\) 174.000 301.377i 0.106176 0.183903i −0.808042 0.589125i \(-0.799473\pi\)
0.914218 + 0.405222i \(0.132806\pi\)
\(140\) 245.000 + 424.352i 0.147902 + 0.256174i
\(141\) 0 0
\(142\) 1086.00 0.641796
\(143\) 715.000 + 743.050i 0.418121 + 0.434524i
\(144\) 0 0
\(145\) 395.500 + 685.026i 0.226514 + 0.392333i
\(146\) 402.500 + 697.150i 0.228158 + 0.395182i
\(147\) 0 0
\(148\) −91.0000 −0.0505416
\(149\) −322.500 + 558.586i −0.177317 + 0.307122i −0.940961 0.338516i \(-0.890075\pi\)
0.763644 + 0.645638i \(0.223408\pi\)
\(150\) 0 0
\(151\) 2914.00 1.57045 0.785225 0.619211i \(-0.212547\pi\)
0.785225 + 0.619211i \(0.212547\pi\)
\(152\) 225.000 389.711i 0.120065 0.207959i
\(153\) 0 0
\(154\) 110.000 + 190.526i 0.0575588 + 0.0996947i
\(155\) −1372.00 −0.710979
\(156\) 0 0
\(157\) −2079.00 −1.05683 −0.528415 0.848986i \(-0.677213\pi\)
−0.528415 + 0.848986i \(0.677213\pi\)
\(158\) −442.000 765.566i −0.222555 0.385476i
\(159\) 0 0
\(160\) 563.500 976.011i 0.278429 0.482253i
\(161\) −1620.00 −0.793006
\(162\) 0 0
\(163\) −850.000 + 1472.24i −0.408449 + 0.707454i −0.994716 0.102664i \(-0.967263\pi\)
0.586267 + 0.810118i \(0.300597\pi\)
\(164\) 1995.00 0.949898
\(165\) 0 0
\(166\) 259.000 + 448.601i 0.121098 + 0.209748i
\(167\) 1840.00 + 3186.97i 0.852596 + 1.47674i 0.878858 + 0.477084i \(0.158306\pi\)
−0.0262621 + 0.999655i \(0.508360\pi\)
\(168\) 0 0
\(169\) 1943.50 1024.51i 0.884615 0.466321i
\(170\) 259.000 0.116849
\(171\) 0 0
\(172\) −861.000 1491.30i −0.381690 0.661106i
\(173\) 2073.00 3590.54i 0.911025 1.57794i 0.0984052 0.995146i \(-0.468626\pi\)
0.812619 0.582795i \(-0.198041\pi\)
\(174\) 0 0
\(175\) −380.000 + 658.179i −0.164145 + 0.284307i
\(176\) −451.000 + 781.155i −0.193156 + 0.334555i
\(177\) 0 0
\(178\) 97.0000 168.009i 0.0408453 0.0707461i
\(179\) 1837.00 + 3181.78i 0.767060 + 1.32859i 0.939150 + 0.343506i \(0.111615\pi\)
−0.172090 + 0.985081i \(0.555052\pi\)
\(180\) 0 0
\(181\) −3283.00 −1.34820 −0.674098 0.738642i \(-0.735467\pi\)
−0.674098 + 0.738642i \(0.735467\pi\)
\(182\) 455.000 112.583i 0.185312 0.0458529i
\(183\) 0 0
\(184\) 1215.00 + 2104.44i 0.486799 + 0.843160i
\(185\) 45.5000 + 78.8083i 0.0180823 + 0.0313195i
\(186\) 0 0
\(187\) −814.000 −0.318319
\(188\) 1617.00 2800.73i 0.627297 1.08651i
\(189\) 0 0
\(190\) −210.000 −0.0801842
\(191\) −298.000 + 516.151i −0.112893 + 0.195536i −0.916935 0.399036i \(-0.869345\pi\)
0.804043 + 0.594572i \(0.202678\pi\)
\(192\) 0 0
\(193\) 196.500 + 340.348i 0.0732869 + 0.126937i 0.900340 0.435187i \(-0.143318\pi\)
−0.827053 + 0.562124i \(0.809984\pi\)
\(194\) −1202.00 −0.444838
\(195\) 0 0
\(196\) 1701.00 0.619898
\(197\) −1761.00 3050.14i −0.636884 1.10311i −0.986113 0.166077i \(-0.946890\pi\)
0.349229 0.937037i \(-0.386443\pi\)
\(198\) 0 0
\(199\) −1009.00 + 1747.64i −0.359428 + 0.622547i −0.987865 0.155313i \(-0.950361\pi\)
0.628438 + 0.777860i \(0.283695\pi\)
\(200\) 1140.00 0.403051
\(201\) 0 0
\(202\) −214.500 + 371.525i −0.0747137 + 0.129408i
\(203\) −1130.00 −0.390692
\(204\) 0 0
\(205\) −997.500 1727.72i −0.339846 0.588630i
\(206\) 651.000 + 1127.57i 0.220181 + 0.381365i
\(207\) 0 0
\(208\) 1332.50 + 1384.77i 0.444194 + 0.461619i
\(209\) 660.000 0.218436
\(210\) 0 0
\(211\) −80.0000 138.564i −0.0261016 0.0452092i 0.852680 0.522434i \(-0.174976\pi\)
−0.878781 + 0.477225i \(0.841643\pi\)
\(212\) 1879.50 3255.39i 0.608890 1.05463i
\(213\) 0 0
\(214\) −669.000 + 1158.74i −0.213700 + 0.370140i
\(215\) −861.000 + 1491.30i −0.273115 + 0.473049i
\(216\) 0 0
\(217\) 980.000 1697.41i 0.306575 0.531003i
\(218\) 517.000 + 895.470i 0.160622 + 0.278206i
\(219\) 0 0
\(220\) 1078.00 0.330358
\(221\) −481.000 + 1666.23i −0.146405 + 0.507163i
\(222\) 0 0
\(223\) −2036.00 3526.46i −0.611393 1.05896i −0.991006 0.133818i \(-0.957276\pi\)
0.379613 0.925145i \(-0.376057\pi\)
\(224\) 805.000 + 1394.30i 0.240118 + 0.415896i
\(225\) 0 0
\(226\) −1077.00 −0.316995
\(227\) −2897.00 + 5017.75i −0.847051 + 1.46714i 0.0367765 + 0.999324i \(0.488291\pi\)
−0.883828 + 0.467812i \(0.845042\pi\)
\(228\) 0 0
\(229\) 6482.00 1.87049 0.935246 0.353999i \(-0.115178\pi\)
0.935246 + 0.353999i \(0.115178\pi\)
\(230\) 567.000 982.073i 0.162552 0.281548i
\(231\) 0 0
\(232\) 847.500 + 1467.91i 0.239832 + 0.415402i
\(233\) −6890.00 −1.93725 −0.968624 0.248530i \(-0.920053\pi\)
−0.968624 + 0.248530i \(0.920053\pi\)
\(234\) 0 0
\(235\) −3234.00 −0.897714
\(236\) −2016.00 3491.81i −0.556061 0.963126i
\(237\) 0 0
\(238\) −185.000 + 320.429i −0.0503856 + 0.0872704i
\(239\) −2466.00 −0.667415 −0.333708 0.942677i \(-0.608300\pi\)
−0.333708 + 0.942677i \(0.608300\pi\)
\(240\) 0 0
\(241\) 1808.50 3132.41i 0.483385 0.837247i −0.516433 0.856327i \(-0.672741\pi\)
0.999818 + 0.0190805i \(0.00607389\pi\)
\(242\) −847.000 −0.224989
\(243\) 0 0
\(244\) −2222.50 3849.48i −0.583119 1.00999i
\(245\) −850.500 1473.11i −0.221781 0.384137i
\(246\) 0 0
\(247\) 390.000 1351.00i 0.100466 0.348024i
\(248\) −2940.00 −0.752783
\(249\) 0 0
\(250\) −703.500 1218.50i −0.177973 0.308258i
\(251\) 2430.00 4208.88i 0.611077 1.05842i −0.379983 0.924994i \(-0.624070\pi\)
0.991059 0.133422i \(-0.0425966\pi\)
\(252\) 0 0
\(253\) −1782.00 + 3086.51i −0.442820 + 0.766986i
\(254\) 494.000 855.633i 0.122033 0.211367i
\(255\) 0 0
\(256\) 59.5000 103.057i 0.0145264 0.0251604i
\(257\) 282.500 + 489.304i 0.0685676 + 0.118763i 0.898271 0.439442i \(-0.144824\pi\)
−0.829703 + 0.558204i \(0.811490\pi\)
\(258\) 0 0
\(259\) −130.000 −0.0311884
\(260\) 637.000 2206.63i 0.151943 0.526344i
\(261\) 0 0
\(262\) 280.000 + 484.974i 0.0660246 + 0.114358i
\(263\) −249.000 431.281i −0.0583802 0.101118i 0.835358 0.549706i \(-0.185260\pi\)
−0.893738 + 0.448588i \(0.851927\pi\)
\(264\) 0 0
\(265\) −3759.00 −0.871372
\(266\) 150.000 259.808i 0.0345755 0.0598866i
\(267\) 0 0
\(268\) −1414.00 −0.322290
\(269\) 2773.00 4802.98i 0.628523 1.08863i −0.359325 0.933213i \(-0.616993\pi\)
0.987848 0.155422i \(-0.0496737\pi\)
\(270\) 0 0
\(271\) 1128.00 + 1953.75i 0.252845 + 0.437941i 0.964308 0.264783i \(-0.0853002\pi\)
−0.711463 + 0.702724i \(0.751967\pi\)
\(272\) −1517.00 −0.338168
\(273\) 0 0
\(274\) 519.000 0.114430
\(275\) 836.000 + 1447.99i 0.183319 + 0.317518i
\(276\) 0 0
\(277\) −1154.50 + 1999.65i −0.250423 + 0.433745i −0.963642 0.267196i \(-0.913903\pi\)
0.713219 + 0.700941i \(0.247236\pi\)
\(278\) −348.000 −0.0750779
\(279\) 0 0
\(280\) 525.000 909.327i 0.112053 0.194081i
\(281\) −5833.00 −1.23832 −0.619159 0.785265i \(-0.712527\pi\)
−0.619159 + 0.785265i \(0.712527\pi\)
\(282\) 0 0
\(283\) −825.000 1428.94i −0.173290 0.300148i 0.766278 0.642509i \(-0.222107\pi\)
−0.939568 + 0.342362i \(0.888773\pi\)
\(284\) 3801.00 + 6583.53i 0.794183 + 1.37556i
\(285\) 0 0
\(286\) 286.000 990.733i 0.0591312 0.204837i
\(287\) 2850.00 0.586168
\(288\) 0 0
\(289\) 1772.00 + 3069.19i 0.360676 + 0.624709i
\(290\) 395.500 685.026i 0.0800847 0.138711i
\(291\) 0 0
\(292\) −2817.50 + 4880.05i −0.564663 + 0.978026i
\(293\) 1495.50 2590.28i 0.298184 0.516471i −0.677536 0.735489i \(-0.736952\pi\)
0.975721 + 0.219019i \(0.0702856\pi\)
\(294\) 0 0
\(295\) −2016.00 + 3491.81i −0.397885 + 0.689157i
\(296\) 97.5000 + 168.875i 0.0191455 + 0.0331610i
\(297\) 0 0
\(298\) 645.000 0.125382
\(299\) 5265.00 + 5471.55i 1.01834 + 1.05829i
\(300\) 0 0
\(301\) −1230.00 2130.42i −0.235535 0.407959i
\(302\) −1457.00 2523.60i −0.277619 0.480850i
\(303\) 0 0
\(304\) 1230.00 0.232057
\(305\) −2222.50 + 3849.48i −0.417246 + 0.722691i
\(306\) 0 0
\(307\) −2422.00 −0.450263 −0.225132 0.974328i \(-0.572281\pi\)
−0.225132 + 0.974328i \(0.572281\pi\)
\(308\) −770.000 + 1333.68i −0.142451 + 0.246732i
\(309\) 0 0
\(310\) 686.000 + 1188.19i 0.125684 + 0.217692i
\(311\) 3402.00 0.620288 0.310144 0.950690i \(-0.399623\pi\)
0.310144 + 0.950690i \(0.399623\pi\)
\(312\) 0 0
\(313\) 2310.00 0.417153 0.208577 0.978006i \(-0.433117\pi\)
0.208577 + 0.978006i \(0.433117\pi\)
\(314\) 1039.50 + 1800.47i 0.186823 + 0.323587i
\(315\) 0 0
\(316\) 3094.00 5358.97i 0.550795 0.954004i
\(317\) 257.000 0.0455349 0.0227674 0.999741i \(-0.492752\pi\)
0.0227674 + 0.999741i \(0.492752\pi\)
\(318\) 0 0
\(319\) −1243.00 + 2152.94i −0.218165 + 0.377873i
\(320\) 1169.00 0.204216
\(321\) 0 0
\(322\) 810.000 + 1402.96i 0.140185 + 0.242807i
\(323\) 555.000 + 961.288i 0.0956069 + 0.165596i
\(324\) 0 0
\(325\) 3458.00 855.633i 0.590201 0.146037i
\(326\) 1700.00 0.288817
\(327\) 0 0
\(328\) −2137.50 3702.26i −0.359828 0.623241i
\(329\) 2310.00 4001.04i 0.387096 0.670469i
\(330\) 0 0
\(331\) −514.000 + 890.274i −0.0853535 + 0.147837i −0.905542 0.424257i \(-0.860535\pi\)
0.820188 + 0.572094i \(0.193869\pi\)
\(332\) −1813.00 + 3140.21i −0.299703 + 0.519100i
\(333\) 0 0
\(334\) 1840.00 3186.97i 0.301438 0.522106i
\(335\) 707.000 + 1224.56i 0.115306 + 0.199716i
\(336\) 0 0
\(337\) 2487.00 0.402005 0.201002 0.979591i \(-0.435580\pi\)
0.201002 + 0.979591i \(0.435580\pi\)
\(338\) −1859.00 1170.87i −0.299161 0.188422i
\(339\) 0 0
\(340\) 906.500 + 1570.10i 0.144594 + 0.250444i
\(341\) −2156.00 3734.30i −0.342387 0.593032i
\(342\) 0 0
\(343\) 5860.00 0.922479
\(344\) −1845.00 + 3195.63i −0.289174 + 0.500863i
\(345\) 0 0
\(346\) −4146.00 −0.644192
\(347\) −1425.00 + 2468.17i −0.220455 + 0.381840i −0.954946 0.296779i \(-0.904088\pi\)
0.734491 + 0.678618i \(0.237421\pi\)
\(348\) 0 0
\(349\) 1009.00 + 1747.64i 0.154758 + 0.268049i 0.932971 0.359952i \(-0.117207\pi\)
−0.778213 + 0.628001i \(0.783874\pi\)
\(350\) 760.000 0.116068
\(351\) 0 0
\(352\) 3542.00 0.536333
\(353\) −2643.50 4578.68i −0.398582 0.690364i 0.594970 0.803748i \(-0.297164\pi\)
−0.993551 + 0.113385i \(0.963831\pi\)
\(354\) 0 0
\(355\) 3801.00 6583.53i 0.568271 0.984274i
\(356\) 1358.00 0.202174
\(357\) 0 0
\(358\) 1837.00 3181.78i 0.271197 0.469727i
\(359\) 7278.00 1.06997 0.534983 0.844863i \(-0.320318\pi\)
0.534983 + 0.844863i \(0.320318\pi\)
\(360\) 0 0
\(361\) 2979.50 + 5160.65i 0.434393 + 0.752390i
\(362\) 1641.50 + 2843.16i 0.238330 + 0.412799i
\(363\) 0 0
\(364\) 2275.00 + 2364.25i 0.327589 + 0.340440i
\(365\) 5635.00 0.808080
\(366\) 0 0
\(367\) 2101.00 + 3639.04i 0.298832 + 0.517592i 0.975869 0.218357i \(-0.0700697\pi\)
−0.677037 + 0.735949i \(0.736736\pi\)
\(368\) −3321.00 + 5752.14i −0.470432 + 0.814813i
\(369\) 0 0
\(370\) 45.5000 78.8083i 0.00639306 0.0110731i
\(371\) 2685.00 4650.56i 0.375737 0.650795i
\(372\) 0 0
\(373\) 791.500 1370.92i 0.109872 0.190304i −0.805846 0.592125i \(-0.798289\pi\)
0.915718 + 0.401821i \(0.131623\pi\)
\(374\) 407.000 + 704.945i 0.0562713 + 0.0974648i
\(375\) 0 0
\(376\) −6930.00 −0.950499
\(377\) 3672.50 + 3816.57i 0.501707 + 0.521389i
\(378\) 0 0
\(379\) 1026.00 + 1777.08i 0.139056 + 0.240851i 0.927139 0.374717i \(-0.122260\pi\)
−0.788084 + 0.615568i \(0.788927\pi\)
\(380\) −735.000 1273.06i −0.0992229 0.171859i
\(381\) 0 0
\(382\) 596.000 0.0798273
\(383\) −3436.00 + 5951.33i −0.458411 + 0.793991i −0.998877 0.0473746i \(-0.984915\pi\)
0.540466 + 0.841366i \(0.318248\pi\)
\(384\) 0 0
\(385\) 1540.00 0.203859
\(386\) 196.500 340.348i 0.0259108 0.0448789i
\(387\) 0 0
\(388\) −4207.00 7286.74i −0.550459 0.953423i
\(389\) 11653.0 1.51884 0.759422 0.650598i \(-0.225482\pi\)
0.759422 + 0.650598i \(0.225482\pi\)
\(390\) 0 0
\(391\) −5994.00 −0.775268
\(392\) −1822.50 3156.66i −0.234822 0.406723i
\(393\) 0 0
\(394\) −1761.00 + 3050.14i −0.225172 + 0.390010i
\(395\) −6188.00 −0.788233
\(396\) 0 0
\(397\) −3067.00 + 5312.20i −0.387729 + 0.671566i −0.992144 0.125104i \(-0.960074\pi\)
0.604415 + 0.796670i \(0.293407\pi\)
\(398\) 2018.00 0.254154
\(399\) 0 0
\(400\) 1558.00 + 2698.54i 0.194750 + 0.337317i
\(401\) −5397.50 9348.74i −0.672165 1.16422i −0.977289 0.211912i \(-0.932031\pi\)
0.305124 0.952313i \(-0.401302\pi\)
\(402\) 0 0
\(403\) −8918.00 + 2206.63i −1.10233 + 0.272755i
\(404\) −3003.00 −0.369814
\(405\) 0 0
\(406\) 565.000 + 978.609i 0.0690652 + 0.119624i
\(407\) −143.000 + 247.683i −0.0174158 + 0.0301651i
\(408\) 0 0
\(409\) 4244.50 7351.69i 0.513147 0.888796i −0.486737 0.873549i \(-0.661813\pi\)
0.999884 0.0152477i \(-0.00485367\pi\)
\(410\) −997.500 + 1727.72i −0.120154 + 0.208112i
\(411\) 0 0
\(412\) −4557.00 + 7892.96i −0.544921 + 0.943830i
\(413\) −2880.00 4988.31i −0.343137 0.594331i
\(414\) 0 0
\(415\) 3626.00 0.428900
\(416\) 2093.00 7250.36i 0.246677 0.854515i
\(417\) 0 0
\(418\) −330.000 571.577i −0.0386144 0.0668821i
\(419\) 748.000 + 1295.57i 0.0872129 + 0.151057i 0.906332 0.422566i \(-0.138871\pi\)
−0.819119 + 0.573623i \(0.805537\pi\)
\(420\) 0 0
\(421\) −11695.0 −1.35387 −0.676935 0.736043i \(-0.736692\pi\)
−0.676935 + 0.736043i \(0.736692\pi\)
\(422\) −80.0000 + 138.564i −0.00922829 + 0.0159839i
\(423\) 0 0
\(424\) −8055.00 −0.922607
\(425\) −1406.00 + 2435.26i −0.160473 + 0.277947i
\(426\) 0 0
\(427\) −3175.00 5499.26i −0.359834 0.623250i
\(428\) −9366.00 −1.05776
\(429\) 0 0
\(430\) 1722.00 0.193121
\(431\) 5295.00 + 9171.21i 0.591766 + 1.02497i 0.993995 + 0.109430i \(0.0349024\pi\)
−0.402228 + 0.915539i \(0.631764\pi\)
\(432\) 0 0
\(433\) 6974.50 12080.2i 0.774072 1.34073i −0.161243 0.986915i \(-0.551550\pi\)
0.935315 0.353817i \(-0.115116\pi\)
\(434\) −1960.00 −0.216781
\(435\) 0 0
\(436\) −3619.00 + 6268.29i −0.397520 + 0.688525i
\(437\) 4860.00 0.532003
\(438\) 0 0
\(439\) 5363.00 + 9288.99i 0.583057 + 1.00988i 0.995115 + 0.0987266i \(0.0314769\pi\)
−0.412058 + 0.911158i \(0.635190\pi\)
\(440\) −1155.00 2000.52i −0.125142 0.216752i
\(441\) 0 0
\(442\) 1683.50 416.558i 0.181167 0.0448273i
\(443\) −16228.0 −1.74044 −0.870221 0.492662i \(-0.836024\pi\)
−0.870221 + 0.492662i \(0.836024\pi\)
\(444\) 0 0
\(445\) −679.000 1176.06i −0.0723319 0.125282i
\(446\) −2036.00 + 3526.46i −0.216160 + 0.374400i
\(447\) 0 0
\(448\) −835.000 + 1446.26i −0.0880581 + 0.152521i
\(449\) 3769.00 6528.10i 0.396147 0.686147i −0.597100 0.802167i \(-0.703680\pi\)
0.993247 + 0.116020i \(0.0370136\pi\)
\(450\) 0 0
\(451\) 3135.00 5429.98i 0.327320 0.566935i
\(452\) −3769.50 6528.97i −0.392262 0.679417i
\(453\) 0 0
\(454\) 5794.00 0.598956
\(455\) 910.000 3152.33i 0.0937614 0.324799i
\(456\) 0 0
\(457\) −7769.50 13457.2i −0.795278 1.37746i −0.922663 0.385608i \(-0.873992\pi\)
0.127385 0.991853i \(-0.459342\pi\)
\(458\) −3241.00 5613.58i −0.330659 0.572719i
\(459\) 0 0
\(460\) 7938.00 0.804589
\(461\) 2405.50 4166.45i 0.243027 0.420935i −0.718548 0.695477i \(-0.755193\pi\)
0.961575 + 0.274543i \(0.0885264\pi\)
\(462\) 0 0
\(463\) 562.000 0.0564111 0.0282056 0.999602i \(-0.491021\pi\)
0.0282056 + 0.999602i \(0.491021\pi\)
\(464\) −2316.50 + 4012.30i −0.231769 + 0.401436i
\(465\) 0 0
\(466\) 3445.00 + 5966.92i 0.342460 + 0.593159i
\(467\) −4914.00 −0.486922 −0.243461 0.969911i \(-0.578283\pi\)
−0.243461 + 0.969911i \(0.578283\pi\)
\(468\) 0 0
\(469\) −2020.00 −0.198880
\(470\) 1617.00 + 2800.73i 0.158695 + 0.274868i
\(471\) 0 0
\(472\) −4320.00 + 7482.46i −0.421280 + 0.729678i
\(473\) −5412.00 −0.526097
\(474\) 0 0
\(475\) 1140.00 1974.54i 0.110120 0.190733i
\(476\) −2590.00 −0.249396
\(477\) 0 0
\(478\) 1233.00 + 2135.62i 0.117983 + 0.204353i
\(479\) −1800.00 3117.69i −0.171700 0.297392i 0.767315 0.641271i \(-0.221593\pi\)
−0.939014 + 0.343878i \(0.888259\pi\)
\(480\) 0 0
\(481\) 422.500 + 439.075i 0.0400506 + 0.0416218i
\(482\) −3617.00 −0.341805
\(483\) 0 0
\(484\) −2964.50 5134.66i −0.278409 0.482219i
\(485\) −4207.00 + 7286.74i −0.393876 + 0.682214i
\(486\) 0 0
\(487\) 8565.00 14835.0i 0.796955 1.38037i −0.124635 0.992203i \(-0.539776\pi\)
0.921590 0.388164i \(-0.126891\pi\)
\(488\) −4762.50 + 8248.89i −0.441779 + 0.765184i
\(489\) 0 0
\(490\) −850.500 + 1473.11i −0.0784116 + 0.135813i
\(491\) −5919.00 10252.0i −0.544034 0.942295i −0.998667 0.0516158i \(-0.983563\pi\)
0.454633 0.890679i \(-0.349770\pi\)
\(492\) 0 0
\(493\) −4181.00 −0.381953
\(494\) −1365.00 + 337.750i −0.124320 + 0.0307613i
\(495\) 0 0
\(496\) −4018.00 6959.38i −0.363737 0.630011i
\(497\) 5430.00 + 9405.04i 0.490078 + 0.848840i
\(498\) 0 0
\(499\) 8976.00 0.805252 0.402626 0.915364i \(-0.368097\pi\)
0.402626 + 0.915364i \(0.368097\pi\)
\(500\) 4924.50 8529.48i 0.440461 0.762900i
\(501\) 0 0
\(502\) −4860.00 −0.432096
\(503\) 841.000 1456.65i 0.0745494 0.129123i −0.826341 0.563170i \(-0.809581\pi\)
0.900890 + 0.434047i \(0.142915\pi\)
\(504\) 0 0
\(505\) 1501.50 + 2600.67i 0.132309 + 0.229165i
\(506\) 3564.00 0.313121
\(507\) 0 0
\(508\) 6916.00 0.604031
\(509\) 7583.50 + 13135.0i 0.660379 + 1.14381i 0.980516 + 0.196438i \(0.0629375\pi\)
−0.320138 + 0.947371i \(0.603729\pi\)
\(510\) 0 0
\(511\) −4025.00 + 6971.50i −0.348445 + 0.603525i
\(512\) 11521.0 0.994455
\(513\) 0 0
\(514\) 282.500 489.304i 0.0242423 0.0419889i
\(515\) 9114.00 0.779827
\(516\) 0 0
\(517\) −5082.00 8802.28i −0.432314 0.748789i
\(518\) 65.0000 + 112.583i 0.00551339 + 0.00954947i
\(519\) 0 0
\(520\) −4777.50 + 1182.12i −0.402899 + 0.0996915i
\(521\) 6783.00 0.570381 0.285191 0.958471i \(-0.407943\pi\)
0.285191 + 0.958471i \(0.407943\pi\)
\(522\) 0 0
\(523\) 6959.00 + 12053.3i 0.581828 + 1.00775i 0.995263 + 0.0972214i \(0.0309955\pi\)
−0.413435 + 0.910534i \(0.635671\pi\)
\(524\) −1960.00 + 3394.82i −0.163403 + 0.283022i
\(525\) 0 0
\(526\) −249.000 + 431.281i −0.0206405 + 0.0357504i
\(527\) 3626.00 6280.42i 0.299717 0.519126i
\(528\) 0 0
\(529\) −7038.50 + 12191.0i −0.578491 + 1.00198i
\(530\) 1879.50 + 3255.39i 0.154038 + 0.266802i
\(531\) 0 0
\(532\) 2100.00 0.171140
\(533\) −9262.50 9625.87i −0.752727 0.782257i
\(534\) 0 0
\(535\) 4683.00 + 8111.19i 0.378437 + 0.655472i
\(536\) 1515.00 + 2624.06i 0.122086 + 0.211459i
\(537\) 0 0
\(538\) −5546.00 −0.444433
\(539\) 2673.00 4629.77i 0.213607 0.369978i
\(540\) 0 0
\(541\) −1335.00 −0.106093 −0.0530463 0.998592i \(-0.516893\pi\)
−0.0530463 + 0.998592i \(0.516893\pi\)
\(542\) 1128.00 1953.75i 0.0893944 0.154836i
\(543\) 0 0
\(544\) 2978.50 + 5158.91i 0.234747 + 0.406593i
\(545\) 7238.00 0.568884
\(546\) 0 0
\(547\) −3806.00 −0.297501 −0.148750 0.988875i \(-0.547525\pi\)
−0.148750 + 0.988875i \(0.547525\pi\)
\(548\) 1816.50 + 3146.27i 0.141600 + 0.245259i
\(549\) 0 0
\(550\) 836.000 1447.99i 0.0648130 0.112259i
\(551\) 3390.00 0.262103
\(552\) 0 0
\(553\) 4420.00 7655.66i 0.339887 0.588702i
\(554\) 2309.00 0.177076
\(555\) 0 0
\(556\) −1218.00 2109.64i −0.0929041 0.160915i
\(557\) −952.500 1649.78i −0.0724573 0.125500i 0.827520 0.561436i \(-0.189751\pi\)
−0.899978 + 0.435936i \(0.856417\pi\)
\(558\) 0 0
\(559\) −3198.00 + 11078.2i −0.241970 + 0.838207i
\(560\) 2870.00 0.216571
\(561\) 0 0
\(562\) 2916.50 + 5051.53i 0.218906 + 0.379156i
\(563\) −2400.00 + 4156.92i −0.179659 + 0.311178i −0.941764 0.336275i \(-0.890833\pi\)
0.762105 + 0.647454i \(0.224166\pi\)
\(564\) 0 0
\(565\) −3769.50 + 6528.97i −0.280680 + 0.486152i
\(566\) −825.000 + 1428.94i −0.0612674 + 0.106118i
\(567\) 0 0
\(568\) 8145.00 14107.6i 0.601684 1.04215i
\(569\) 7339.00 + 12711.5i 0.540715 + 0.936546i 0.998863 + 0.0476701i \(0.0151796\pi\)
−0.458148 + 0.888876i \(0.651487\pi\)
\(570\) 0 0
\(571\) −586.000 −0.0429481 −0.0214740 0.999769i \(-0.506836\pi\)
−0.0214740 + 0.999769i \(0.506836\pi\)
\(572\) 7007.00 1733.78i 0.512198 0.126736i
\(573\) 0 0
\(574\) −1425.00 2468.17i −0.103621 0.179477i
\(575\) 6156.00 + 10662.5i 0.446475 + 0.773317i
\(576\) 0 0
\(577\) 8939.00 0.644949 0.322474 0.946578i \(-0.395485\pi\)
0.322474 + 0.946578i \(0.395485\pi\)
\(578\) 1772.00 3069.19i 0.127518 0.220868i
\(579\) 0 0
\(580\) 5537.00 0.396399
\(581\) −2590.00 + 4486.01i −0.184942 + 0.320329i
\(582\) 0 0
\(583\) −5907.00 10231.2i −0.419628 0.726816i
\(584\) 12075.0 0.855594
\(585\) 0 0
\(586\) −2991.00 −0.210848
\(587\) −6896.00 11944.2i −0.484887 0.839848i 0.514963 0.857213i \(-0.327806\pi\)
−0.999849 + 0.0173645i \(0.994472\pi\)
\(588\) 0 0
\(589\) −2940.00 + 5092.23i −0.205672 + 0.356234i
\(590\) 4032.00 0.281347
\(591\) 0 0
\(592\) −266.500 + 461.592i −0.0185018 + 0.0320461i
\(593\) −9569.00 −0.662650 −0.331325 0.943517i \(-0.607496\pi\)
−0.331325 + 0.943517i \(0.607496\pi\)
\(594\) 0 0
\(595\) 1295.00 + 2243.01i 0.0892266 + 0.154545i
\(596\) 2257.50 + 3910.10i 0.155152 + 0.268732i
\(597\) 0 0
\(598\) 2106.00 7295.40i 0.144015 0.498881i
\(599\) 5192.00 0.354156 0.177078 0.984197i \(-0.443336\pi\)
0.177078 + 0.984197i \(0.443336\pi\)
\(600\) 0 0
\(601\) 1838.50 + 3184.38i 0.124782 + 0.216129i 0.921648 0.388028i \(-0.126844\pi\)
−0.796866 + 0.604156i \(0.793510\pi\)
\(602\) −1230.00 + 2130.42i −0.0832742 + 0.144235i
\(603\) 0 0
\(604\) 10199.0 17665.2i 0.687072 1.19004i
\(605\) −2964.50 + 5134.66i −0.199213 + 0.345048i
\(606\) 0 0
\(607\) 5480.00 9491.64i 0.366435 0.634685i −0.622570 0.782564i \(-0.713911\pi\)
0.989005 + 0.147879i \(0.0472447\pi\)
\(608\) −2415.00 4182.90i −0.161087 0.279012i
\(609\) 0 0
\(610\) 4445.00 0.295037
\(611\) −21021.0 + 5201.35i −1.39185 + 0.344393i
\(612\) 0 0
\(613\) 13013.5 + 22540.0i 0.857439 + 1.48513i 0.874363 + 0.485272i \(0.161279\pi\)
−0.0169241 + 0.999857i \(0.505387\pi\)
\(614\) 1211.00 + 2097.51i 0.0795961 + 0.137864i
\(615\) 0 0
\(616\) 3300.00 0.215845
\(617\) 8840.50 15312.2i 0.576832 0.999102i −0.419008 0.907982i \(-0.637622\pi\)
0.995840 0.0911193i \(-0.0290445\pi\)
\(618\) 0 0
\(619\) 3192.00 0.207265 0.103633 0.994616i \(-0.466953\pi\)
0.103633 + 0.994616i \(0.466953\pi\)
\(620\) −4802.00 + 8317.31i −0.311053 + 0.538760i
\(621\) 0 0
\(622\) −1701.00 2946.22i −0.109653 0.189924i
\(623\) 1940.00 0.124758
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) −1155.00 2000.52i −0.0737429 0.127727i
\(627\) 0 0
\(628\) −7276.50 + 12603.3i −0.462363 + 0.800836i
\(629\) −481.000 −0.0304908
\(630\) 0 0
\(631\) −3790.00 + 6564.47i −0.239109 + 0.414148i −0.960459 0.278422i \(-0.910189\pi\)
0.721350 + 0.692571i \(0.243522\pi\)
\(632\) −13260.0 −0.834580
\(633\) 0 0
\(634\) −128.500 222.569i −0.00804951 0.0139422i
\(635\) −3458.00 5989.43i −0.216105 0.374304i
\(636\) 0 0
\(637\) −7897.50 8207.32i −0.491225 0.510496i
\(638\) 2486.00 0.154266
\(639\) 0 0
\(640\) −5092.50 8820.47i −0.314529 0.544781i
\(641\) −13853.5 + 23995.0i −0.853635 + 1.47854i 0.0242696 + 0.999705i \(0.492274\pi\)
−0.877905 + 0.478835i \(0.841059\pi\)
\(642\) 0 0
\(643\) −5608.00 + 9713.34i −0.343947 + 0.595734i −0.985162 0.171628i \(-0.945097\pi\)
0.641215 + 0.767361i \(0.278431\pi\)
\(644\) −5670.00 + 9820.73i −0.346940 + 0.600918i
\(645\) 0 0
\(646\) 555.000 961.288i 0.0338021 0.0585470i
\(647\) −1268.00 2196.24i −0.0770483 0.133452i 0.824927 0.565239i \(-0.191216\pi\)
−0.901975 + 0.431788i \(0.857883\pi\)
\(648\) 0 0
\(649\) −12672.0 −0.766440
\(650\) −2470.00 2566.90i −0.149048 0.154895i
\(651\) 0 0
\(652\) 5950.00 + 10305.7i 0.357393 + 0.619022i
\(653\) 8865.00 + 15354.6i 0.531262 + 0.920173i 0.999334 + 0.0364829i \(0.0116154\pi\)
−0.468072 + 0.883690i \(0.655051\pi\)
\(654\) 0 0
\(655\) 3920.00 0.233843
\(656\) 5842.50 10119.5i 0.347731 0.602287i
\(657\) 0 0
\(658\) −4620.00 −0.273718
\(659\) 9460.00 16385.2i 0.559195 0.968554i −0.438369 0.898795i \(-0.644444\pi\)
0.997564 0.0697586i \(-0.0222229\pi\)
\(660\) 0 0
\(661\) −2620.50 4538.84i −0.154199 0.267081i 0.778568 0.627560i \(-0.215946\pi\)
−0.932767 + 0.360480i \(0.882613\pi\)
\(662\) 1028.00 0.0603540
\(663\) 0 0
\(664\) 7770.00 0.454118
\(665\) −1050.00 1818.65i −0.0612290 0.106052i
\(666\) 0 0
\(667\) −9153.00 + 15853.5i −0.531343 + 0.920313i
\(668\) 25760.0 1.49204
\(669\) 0 0
\(670\) 707.000 1224.56i 0.0407669 0.0706103i
\(671\) −13970.0 −0.803735
\(672\) 0 0
\(673\) −10233.5 17724.9i −0.586140 1.01522i −0.994732 0.102508i \(-0.967313\pi\)
0.408592 0.912717i \(-0.366020\pi\)
\(674\) −1243.50 2153.81i −0.0710650 0.123088i
\(675\) 0 0
\(676\) 591.500 15367.6i 0.0336538 0.874353i
\(677\) 70.0000 0.00397388 0.00198694 0.999998i \(-0.499368\pi\)
0.00198694 + 0.999998i \(0.499368\pi\)
\(678\) 0 0
\(679\) −6010.00 10409.6i −0.339680 0.588343i
\(680\) 1942.50 3364.51i 0.109546 0.189740i
\(681\) 0 0
\(682\) −2156.00 + 3734.30i −0.121052 + 0.209668i
\(683\) 3216.00 5570.28i 0.180171 0.312065i −0.761768 0.647850i \(-0.775668\pi\)
0.941939 + 0.335785i \(0.109002\pi\)
\(684\) 0 0
\(685\) 1816.50 3146.27i 0.101321 0.175493i
\(686\) −2930.00 5074.91i −0.163073 0.282450i
\(687\) 0 0
\(688\) −10086.0 −0.558903
\(689\) −24433.5 + 6045.72i −1.35100 + 0.334287i
\(690\) 0 0
\(691\) 3333.00 + 5772.93i 0.183492 + 0.317818i 0.943067 0.332601i \(-0.107926\pi\)
−0.759575 + 0.650420i \(0.774593\pi\)
\(692\) −14511.0 25133.8i −0.797147 1.38070i
\(693\) 0 0
\(694\) 2850.00 0.155885
\(695\) −1218.00 + 2109.64i −0.0664768 + 0.115141i
\(696\) 0 0
\(697\) 10545.0 0.573056
\(698\) 1009.00 1747.64i 0.0547152 0.0947695i
\(699\) 0 0
\(700\) 2660.00 + 4607.26i 0.143626 + 0.248768i
\(701\) 14054.0 0.757221 0.378611 0.925556i \(-0.376402\pi\)
0.378611 + 0.925556i \(0.376402\pi\)
\(702\) 0 0
\(703\) 390.000 0.0209234
\(704\) 1837.00 + 3181.78i 0.0983445 + 0.170338i
\(705\) 0 0
\(706\) −2643.50 + 4578.68i −0.140920 + 0.244080i
\(707\) −4290.00 −0.228207
\(708\) 0 0
\(709\) 35.5000 61.4878i 0.00188044 0.00325701i −0.865084 0.501628i \(-0.832735\pi\)
0.866964 + 0.498371i \(0.166068\pi\)
\(710\) −7602.00 −0.401828
\(711\) 0 0
\(712\) −1455.00 2520.13i −0.0765849 0.132649i
\(713\) −15876.0 27498.0i −0.833886 1.44433i
\(714\) 0 0
\(715\) −5005.00 5201.35i −0.261785 0.272055i
\(716\) 25718.0 1.34236
\(717\) 0 0
\(718\) −3639.00 6302.93i −0.189145 0.327609i
\(719\) 1968.00 3408.68i 0.102078 0.176804i −0.810463 0.585790i \(-0.800784\pi\)
0.912541 + 0.408986i \(0.134118\pi\)
\(720\) 0 0
\(721\) −6510.00 + 11275.7i −0.336262 + 0.582423i
\(722\) 2979.50 5160.65i 0.153581 0.266010i
\(723\) 0 0
\(724\) −11490.5 + 19902.1i −0.589836 + 1.02163i
\(725\) 4294.00 + 7437.43i 0.219966 + 0.380992i
\(726\) 0 0
\(727\) 34202.0 1.74482 0.872409 0.488777i \(-0.162557\pi\)
0.872409 + 0.488777i \(0.162557\pi\)
\(728\) 1950.00 6755.00i 0.0992745 0.343897i
\(729\) 0 0
\(730\) −2817.50 4880.05i −0.142850 0.247423i
\(731\) −4551.00 7882.56i −0.230267 0.398833i
\(732\) 0 0
\(733\) −27363.0 −1.37882 −0.689410 0.724371i \(-0.742130\pi\)
−0.689410 + 0.724371i \(0.742130\pi\)
\(734\) 2101.00 3639.04i 0.105653 0.182996i
\(735\) 0 0
\(736\) 26082.0 1.30624
\(737\) −2222.00 + 3848.62i −0.111056 + 0.192355i
\(738\) 0 0
\(739\) −10888.0 18858.6i −0.541978 0.938733i −0.998790 0.0491701i \(-0.984342\pi\)
0.456813 0.889563i \(-0.348991\pi\)
\(740\) 637.000 0.0316440
\(741\) 0 0
\(742\) −5370.00 −0.265686
\(743\) 1242.00 + 2151.21i 0.0613251 + 0.106218i 0.895058 0.445950i \(-0.147134\pi\)
−0.833733 + 0.552168i \(0.813801\pi\)
\(744\) 0 0
\(745\) 2257.50 3910.10i 0.111018 0.192289i
\(746\) −1583.00 −0.0776914
\(747\) 0 0
\(748\) −2849.00 + 4934.61i −0.139264 + 0.241213i
\(749\) −13380.0 −0.652730
\(750\) 0 0
\(751\) −16453.0 28497.4i −0.799439 1.38467i −0.919982 0.391960i \(-0.871797\pi\)
0.120543 0.992708i \(-0.461536\pi\)
\(752\) −9471.00 16404.3i −0.459271 0.795481i
\(753\) 0 0
\(754\) 1469.00 5088.77i 0.0709520 0.245785i
\(755\) −20398.0 −0.983257
\(756\) 0 0
\(757\) 1957.00 + 3389.62i 0.0939609 + 0.162745i 0.909174 0.416415i \(-0.136714\pi\)
−0.815214 + 0.579160i \(0.803380\pi\)
\(758\) 1026.00 1777.08i 0.0491636 0.0851538i
\(759\) 0 0
\(760\) −1575.00 + 2727.98i −0.0751727 + 0.130203i
\(761\) −16519.0 + 28611.7i −0.786877 + 1.36291i 0.140995 + 0.990010i \(0.454970\pi\)
−0.927871 + 0.372900i \(0.878363\pi\)
\(762\) 0 0
\(763\) −5170.00 + 8954.70i −0.245303 + 0.424878i
\(764\) 2086.00 + 3613.06i 0.0987812 + 0.171094i
\(765\) 0 0
\(766\) 6872.00 0.324145
\(767\) −7488.00 + 25939.2i −0.352511 + 1.22113i
\(768\) 0 0
\(769\) 8793.00 + 15229.9i 0.412332 + 0.714181i 0.995144 0.0984263i \(-0.0313809\pi\)
−0.582812 + 0.812607i \(0.698048\pi\)
\(770\) −770.000 1333.68i −0.0360375 0.0624188i
\(771\) 0 0
\(772\) 2751.00 0.128252
\(773\) 9157.00 15860.4i 0.426073 0.737980i −0.570447 0.821334i \(-0.693230\pi\)
0.996520 + 0.0833544i \(0.0265633\pi\)
\(774\) 0 0
\(775\) −14896.0 −0.690426
\(776\) −9015.00 + 15614.4i −0.417036 + 0.722327i
\(777\) 0 0
\(778\) −5826.50 10091.8i −0.268496 0.465049i
\(779\) −8550.00 −0.393242
\(780\) 0 0
\(781\) 23892.0 1.09465
\(782\) 2997.00 + 5190.96i 0.137049 + 0.237376i
\(783\) 0 0
\(784\) 4981.50 8628.21i 0.226927 0.393049i
\(785\) 14553.0 0.661680
\(786\) 0 0
\(787\) 21034.0 36432.0i 0.952708 1.65014i 0.213180 0.977013i \(-0.431618\pi\)
0.739528 0.673125i \(-0.235049\pi\)
\(788\) −24654.0 −1.11455
\(789\) 0 0
\(790\) 3094.00 + 5358.97i 0.139341 + 0.241346i
\(791\) −5385.00 9327.09i −0.242059 0.419258i
\(792\) 0 0
\(793\) −8255.00 + 28596.2i −0.369664 + 1.28055i
\(794\) 6134.00 0.274166
\(795\) 0 0
\(796\) 7063.00 + 12233.5i 0.314499 + 0.544729i
\(797\) −2141.00 + 3708.32i −0.0951545 + 0.164812i −0.909673 0.415325i \(-0.863668\pi\)
0.814519 + 0.580137i \(0.197001\pi\)
\(798\) 0 0
\(799\) 8547.00 14803.8i 0.378437 0.655472i
\(800\) 6118.00 10596.7i 0.270380 0.468312i
\(801\) 0 0
\(802\) −5397.50 + 9348.74i −0.237646 + 0.411616i
\(803\) 8855.00 + 15337.3i 0.389148 + 0.674025i
\(804\) 0 0
\(805\) 11340.0 0.496500
\(806\) 6370.00 + 6619.90i 0.278379 + 0.289300i
\(807\) 0 0
\(808\) 3217.50 + 5572.87i 0.140088 + 0.242640i
\(809\) 20110.5 + 34832.4i 0.873977 + 1.51377i 0.857848 + 0.513903i \(0.171801\pi\)
0.0161288 + 0.999870i \(0.494866\pi\)
\(810\) 0 0
\(811\) −7084.00 −0.306724 −0.153362 0.988170i \(-0.549010\pi\)
−0.153362 + 0.988170i \(0.549010\pi\)
\(812\) −3955.00 + 6850.26i −0.170928 + 0.296055i
\(813\) 0 0
\(814\) 286.000 0.0123149
\(815\) 5950.00 10305.7i 0.255729 0.442936i
\(816\) 0 0
\(817\) 3690.00 + 6391.27i 0.158013 + 0.273687i
\(818\) −8489.00 −0.362850
\(819\) 0 0
\(820\) −13965.0 −0.594730
\(821\) 8669.00 + 15015.1i 0.368514 + 0.638285i 0.989333 0.145668i \(-0.0465332\pi\)
−0.620819 + 0.783954i \(0.713200\pi\)
\(822\) 0 0
\(823\) −17748.0 + 30740.4i −0.751709 + 1.30200i 0.195285 + 0.980747i \(0.437437\pi\)
−0.946994 + 0.321251i \(0.895897\pi\)
\(824\) 19530.0 0.825679
\(825\) 0 0
\(826\) −2880.00 + 4988.31i −0.121317 + 0.210128i
\(827\) 14992.0 0.630378 0.315189 0.949029i \(-0.397932\pi\)
0.315189 + 0.949029i \(0.397932\pi\)
\(828\) 0 0
\(829\) 10329.5 + 17891.2i 0.432760 + 0.749563i 0.997110 0.0759730i \(-0.0242063\pi\)
−0.564349 + 0.825536i \(0.690873\pi\)
\(830\) −1813.00 3140.21i −0.0758195 0.131323i
\(831\) 0 0
\(832\) 7598.50 1880.14i 0.316623 0.0783440i
\(833\) 8991.00 0.373973
\(834\) 0 0
\(835\) −12880.0 22308.8i −0.533809 0.924585i
\(836\) 2310.00 4001.04i 0.0955658 0.165525i
\(837\) 0 0
\(838\) 748.000 1295.57i 0.0308344 0.0534068i
\(839\) 14358.0 24868.8i 0.590814 1.02332i −0.403309 0.915064i \(-0.632140\pi\)
0.994123 0.108256i \(-0.0345268\pi\)
\(840\) 0 0
\(841\) 5810.00 10063.2i 0.238222 0.412613i
\(842\) 5847.50 + 10128.2i 0.239333 + 0.414536i
\(843\) 0 0
\(844\) −1120.00 −0.0456777
\(845\) −13604.5 + 7171.56i −0.553857 + 0.291963i
\(846\) 0 0
\(847\) −4235.00 7335.24i −0.171802 0.297570i
\(848\) −11008.5 19067.3i −0.445794 0.772138i
\(849\) 0 0
\(850\) 2812.00 0.113472
\(851\) −1053.00 + 1823.85i −0.0424164 + 0.0734674i
\(852\) 0 0
\(853\) 13377.0 0.536952 0.268476 0.963286i \(-0.413480\pi\)
0.268476 + 0.963286i \(0.413480\pi\)
\(854\) −3175.00 + 5499.26i −0.127220 + 0.220352i
\(855\) 0 0
\(856\) 10035.0 + 17381.1i 0.400688 + 0.694013i
\(857\) 27419.0 1.09290 0.546450 0.837492i \(-0.315979\pi\)
0.546450 + 0.837492i \(0.315979\pi\)
\(858\) 0 0
\(859\) 2422.00 0.0962021 0.0481010 0.998842i \(-0.484683\pi\)
0.0481010 + 0.998842i \(0.484683\pi\)
\(860\) 6027.00 + 10439.1i 0.238976 + 0.413918i
\(861\) 0 0
\(862\) 5295.00 9171.21i 0.209221 0.362381i
\(863\) 34522.0 1.36169 0.680847 0.732425i \(-0.261612\pi\)
0.680847 + 0.732425i \(0.261612\pi\)
\(864\) 0 0
\(865\) −14511.0 + 25133.8i −0.570392 + 0.987947i
\(866\) −13949.0 −0.547351
\(867\) 0 0
\(868\) −6860.00 11881.9i −0.268253 0.464628i
\(869\) −9724.00 16842.5i −0.379590 0.657470i
\(870\) 0 0
\(871\) 6565.00 + 6822.55i 0.255392 + 0.265411i
\(872\) 15510.0 0.602334
\(873\) 0 0
\(874\) −2430.00 4208.88i −0.0940457 0.162892i
\(875\) 7035.00 12185.0i 0.271802 0.470774i
\(876\) 0 0
\(877\) −6866.50 + 11893.1i −0.264385 + 0.457927i −0.967402 0.253245i \(-0.918502\pi\)
0.703018 + 0.711172i \(0.251835\pi\)
\(878\) 5363.00 9288.99i 0.206142 0.357048i
\(879\) 0 0
\(880\) 3157.00 5468.08i 0.120935 0.209465i
\(881\) −11379.5 19709.9i −0.435170 0.753737i 0.562139 0.827043i \(-0.309979\pi\)
−0.997310 + 0.0733055i \(0.976645\pi\)
\(882\) 0 0
\(883\) −2168.00 −0.0826263 −0.0413131 0.999146i \(-0.513154\pi\)
−0.0413131 + 0.999146i \(0.513154\pi\)
\(884\) 8417.50 + 8747.72i 0.320261 + 0.332826i
\(885\) 0 0
\(886\) 8114.00 + 14053.9i 0.307669 + 0.532899i
\(887\) 7944.00 + 13759.4i 0.300714 + 0.520852i 0.976298 0.216431i \(-0.0694417\pi\)
−0.675584 + 0.737283i \(0.736108\pi\)
\(888\) 0 0
\(889\) 9880.00 0.372739
\(890\) −679.000 + 1176.06i −0.0255732 + 0.0442941i
\(891\) 0 0
\(892\) −28504.0 −1.06994
\(893\) −6930.00 + 12003.1i −0.259690 + 0.449797i
\(894\) 0 0
\(895\) −12859.0 22272.4i −0.480256 0.831827i
\(896\) 14550.0 0.542502
\(897\) 0 0
\(898\) −7538.00 −0.280118
\(899\) −11074.0 19180.7i −0.410833 0.711583i
\(900\) 0 0
\(901\) 9934.50 17207.1i 0.367332 0.636238i
\(902\) −6270.00 −0.231450
\(903\) 0 0
\(904\) −8077.50 + 13990.6i −0.297183 + 0.514736i
\(905\) 22981.0 0.844104
\(906\) 0 0
\(907\) 5814.00 + 10070.1i 0.212845 + 0.368659i 0.952604 0.304214i \(-0.0983936\pi\)
−0.739759 + 0.672872i \(0.765060\pi\)
\(908\) 20279.0 + 35124.3i 0.741170 + 1.28374i
\(909\) 0 0
\(910\) −3185.00 + 788.083i −0.116024 + 0.0287085i
\(911\) 12584.0 0.457658 0.228829 0.973467i \(-0.426510\pi\)
0.228829 + 0.973467i \(0.426510\pi\)
\(912\) 0 0
\(913\) 5698.00 + 9869.23i 0.206546 + 0.357748i
\(914\) −7769.50 + 13457.2i −0.281173 + 0.487006i
\(915\) 0 0
\(916\) 22687.0 39295.0i 0.818340 1.41741i
\(917\) −2800.00 + 4849.74i −0.100833 + 0.174648i
\(918\) 0 0
\(919\) −8592.00 + 14881.8i −0.308405 + 0.534173i −0.978014 0.208541i \(-0.933128\pi\)
0.669609 + 0.742714i \(0.266462\pi\)
\(920\) −8505.00 14731.1i −0.304784 0.527902i
\(921\) 0 0
\(922\) −4811.00 −0.171846
\(923\) 14118.0 48906.2i 0.503467 1.74406i
\(924\) 0 0
\(925\) 494.000 + 855.633i 0.0175596 + 0.0304141i
\(926\) −281.000 486.706i −0.00997217 0.0172723i
\(927\) 0 0
\(928\) 18193.0 0.643550
\(929\) 6388.50 11065.2i 0.225619 0.390783i −0.730886 0.682499i \(-0.760893\pi\)
0.956505 + 0.291716i \(0.0942263\pi\)
\(930\) 0 0
\(931\) −7290.00 −0.256627
\(932\) −24115.0 + 41768.4i −0.847546 + 1.46799i
\(933\) 0 0
\(934\) 2457.00 + 4255.65i 0.0860765 + 0.149089i
\(935\) 5698.00 0.199299
\(936\) 0 0
\(937\) 9191.00 0.320445 0.160222 0.987081i \(-0.448779\pi\)
0.160222 + 0.987081i \(0.448779\pi\)
\(938\) 1010.00 + 1749.37i 0.0351574 + 0.0608945i
\(939\) 0 0
\(940\) −11319.0 + 19605.1i −0.392750 + 0.680263i
\(941\) −50498.0 −1.74940 −0.874701 0.484662i \(-0.838942\pi\)
−0.874701 + 0.484662i \(0.838942\pi\)
\(942\) 0 0
\(943\) 23085.0 39984.4i 0.797191 1.38078i
\(944\) −23616.0 −0.814232
\(945\) 0 0
\(946\) 2706.00 + 4686.93i 0.0930017 + 0.161084i
\(947\) 780.000 + 1351.00i 0.0267651 + 0.0463586i 0.879098 0.476642i \(-0.158146\pi\)
−0.852333 + 0.523000i \(0.824813\pi\)
\(948\) 0 0
\(949\) 36627.5 9062.96i 1.25288 0.310006i
\(950\) −2280.00 −0.0778663
\(951\) 0 0
\(952\) 2775.00 + 4806.44i 0.0944730 + 0.163632i
\(953\) −10749.0 + 18617.8i −0.365366 + 0.632833i −0.988835 0.149015i \(-0.952390\pi\)
0.623468 + 0.781849i \(0.285723\pi\)
\(954\) 0 0
\(955\) 2086.00 3613.06i 0.0706821 0.122425i
\(956\) −8631.00 + 14949.3i −0.291994 + 0.505749i
\(957\) 0 0
\(958\) −1800.00 + 3117.69i −0.0607050 + 0.105144i
\(959\) 2595.00 + 4494.67i 0.0873795 + 0.151346i
\(960\) 0 0
\(961\) 8625.00 0.289517
\(962\) 169.000 585.433i 0.00566401 0.0196207i
\(963\) 0 0
\(964\) −12659.5 21926.9i −0.422962 0.732591i
\(965\) −1375.50 2382.44i −0.0458849 0.0794749i
\(966\) 0 0
\(967\) −418.000 −0.0139007 −0.00695035 0.999976i \(-0.502212\pi\)
−0.00695035 + 0.999976i \(0.502212\pi\)
\(968\) −6352.50 + 11002.9i −0.210927 + 0.365336i
\(969\) 0 0
\(970\) 8414.00 0.278513
\(971\) 9066.00 15702.8i 0.299631 0.518976i −0.676420 0.736516i \(-0.736470\pi\)
0.976052 + 0.217539i \(0.0698031\pi\)
\(972\) 0 0
\(973\) −1740.00 3013.77i −0.0573297 0.0992980i
\(974\) −17130.0 −0.563532
\(975\) 0 0
\(976\) −26035.0 −0.853853
\(977\) 6250.50 + 10826.2i 0.204679 + 0.354514i 0.950030 0.312158i \(-0.101052\pi\)
−0.745352 + 0.666672i \(0.767718\pi\)
\(978\) 0 0
\(979\) 2134.00 3696.20i 0.0696659 0.120665i
\(980\) −11907.0 −0.388118
\(981\) 0 0
\(982\) −5919.00 + 10252.0i −0.192345 + 0.333151i
\(983\) 43708.0 1.41818 0.709089 0.705119i \(-0.249106\pi\)
0.709089 + 0.705119i \(0.249106\pi\)
\(984\) 0 0
\(985\) 12327.0 + 21351.0i 0.398752 + 0.690659i
\(986\) 2090.50 + 3620.85i 0.0675204 + 0.116949i
\(987\) 0 0
\(988\) −6825.00 7092.75i −0.219769 0.228391i
\(989\) −39852.0 −1.28131
\(990\) 0 0
\(991\) 19807.0 + 34306.7i 0.634904 + 1.09969i 0.986535 + 0.163548i \(0.0522938\pi\)
−0.351631 + 0.936139i \(0.614373\pi\)
\(992\) −15778.0 + 27328.3i −0.504992 + 0.874672i
\(993\) 0 0
\(994\) 5430.00 9405.04i 0.173269 0.300110i
\(995\) 7063.00 12233.5i 0.225037 0.389776i
\(996\) 0 0
\(997\) 18251.5 31612.5i 0.579770 1.00419i −0.415735 0.909486i \(-0.636476\pi\)
0.995505 0.0947056i \(-0.0301910\pi\)
\(998\) −4488.00 7773.44i −0.142350 0.246557i
\(999\) 0 0
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 117.4.g.a.55.1 2
3.2 odd 2 39.4.e.b.16.1 2
12.11 even 2 624.4.q.c.289.1 2
13.3 even 3 1521.4.a.h.1.1 1
13.9 even 3 inner 117.4.g.a.100.1 2
13.10 even 6 1521.4.a.e.1.1 1
39.2 even 12 507.4.b.d.337.2 2
39.11 even 12 507.4.b.d.337.1 2
39.23 odd 6 507.4.a.d.1.1 1
39.29 odd 6 507.4.a.b.1.1 1
39.35 odd 6 39.4.e.b.22.1 yes 2
156.35 even 6 624.4.q.c.529.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.e.b.16.1 2 3.2 odd 2
39.4.e.b.22.1 yes 2 39.35 odd 6
117.4.g.a.55.1 2 1.1 even 1 trivial
117.4.g.a.100.1 2 13.9 even 3 inner
507.4.a.b.1.1 1 39.29 odd 6
507.4.a.d.1.1 1 39.23 odd 6
507.4.b.d.337.1 2 39.11 even 12
507.4.b.d.337.2 2 39.2 even 12
624.4.q.c.289.1 2 12.11 even 2
624.4.q.c.529.1 2 156.35 even 6
1521.4.a.e.1.1 1 13.10 even 6
1521.4.a.h.1.1 1 13.3 even 3