Properties

Label 32.4.g.a.13.3
Level $32$
Weight $4$
Character 32.13
Analytic conductor $1.888$
Analytic rank $0$
Dimension $44$
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] = [32,4,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), 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: \(1.88806112018\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 13.3
Character \(\chi\) \(=\) 32.13
Dual form 32.4.g.a.5.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.10117 + 1.89344i) q^{2} +(1.94138 - 4.68690i) q^{3} +(0.829801 - 7.95685i) q^{4} +(4.93338 - 2.04347i) q^{5} +(4.79518 + 13.5238i) q^{6} +(14.0755 - 14.0755i) q^{7} +(13.3222 + 18.2898i) q^{8} +(0.893826 + 0.893826i) q^{9} +O(q^{10})\) \(q+(-2.10117 + 1.89344i) q^{2} +(1.94138 - 4.68690i) q^{3} +(0.829801 - 7.95685i) q^{4} +(4.93338 - 2.04347i) q^{5} +(4.79518 + 13.5238i) q^{6} +(14.0755 - 14.0755i) q^{7} +(13.3222 + 18.2898i) q^{8} +(0.893826 + 0.893826i) q^{9} +(-6.49667 + 13.6347i) q^{10} +(-3.78733 - 9.14343i) q^{11} +(-35.6820 - 19.3364i) q^{12} +(-64.7407 - 26.8165i) q^{13} +(-2.92391 + 56.2260i) q^{14} -27.0894i q^{15} +(-62.6229 - 13.2052i) q^{16} +79.3923i q^{17} +(-3.57048 - 0.185675i) q^{18} +(94.7756 + 39.2573i) q^{19} +(-12.1659 - 40.9498i) q^{20} +(-38.6445 - 93.2961i) q^{21} +(25.2703 + 12.0408i) q^{22} +(71.6801 + 71.6801i) q^{23} +(111.586 - 26.9325i) q^{24} +(-68.2259 + 68.2259i) q^{25} +(186.806 - 66.2365i) q^{26} +(132.471 - 54.8712i) q^{27} +(-100.317 - 123.676i) q^{28} +(-53.0409 + 128.052i) q^{29} +(51.2920 + 56.9193i) q^{30} -267.650 q^{31} +(156.584 - 90.8260i) q^{32} -50.2070 q^{33} +(-150.324 - 166.816i) q^{34} +(40.6768 - 98.2026i) q^{35} +(7.85374 - 6.37034i) q^{36} +(205.678 - 85.1946i) q^{37} +(-273.470 + 96.9653i) q^{38} +(-251.372 + 251.372i) q^{39} +(103.098 + 63.0071i) q^{40} +(210.468 + 210.468i) q^{41} +(257.849 + 122.860i) q^{42} +(-56.9749 - 137.550i) q^{43} +(-75.8956 + 22.5480i) q^{44} +(6.23610 + 2.58308i) q^{45} +(-286.334 - 14.8902i) q^{46} -173.739i q^{47} +(-183.466 + 267.871i) q^{48} -53.2384i q^{49} +(14.1726 - 272.535i) q^{50} +(372.103 + 154.130i) q^{51} +(-267.097 + 492.880i) q^{52} +(-188.605 - 455.333i) q^{53} +(-174.448 + 366.118i) q^{54} +(-37.3687 - 37.3687i) q^{55} +(444.955 + 69.9214i) q^{56} +(367.990 - 367.990i) q^{57} +(-131.011 - 369.489i) q^{58} +(-627.964 + 260.111i) q^{59} +(-215.546 - 22.4788i) q^{60} +(66.5782 - 160.734i) q^{61} +(562.378 - 506.779i) q^{62} +25.1621 q^{63} +(-157.036 + 487.323i) q^{64} -374.189 q^{65} +(105.493 - 95.0637i) q^{66} +(211.710 - 511.113i) q^{67} +(631.712 + 65.8798i) q^{68} +(475.115 - 196.799i) q^{69} +(100.471 + 283.359i) q^{70} +(-226.201 + 226.201i) q^{71} +(-4.44018 + 28.2557i) q^{72} +(802.290 + 802.290i) q^{73} +(-270.853 + 568.446i) q^{74} +(187.316 + 452.220i) q^{75} +(391.009 - 721.539i) q^{76} +(-182.007 - 75.3897i) q^{77} +(52.2177 - 1004.13i) q^{78} -552.368i q^{79} +(-335.927 + 62.8219i) q^{80} -693.272i q^{81} +(-840.736 - 43.7206i) q^{82} +(-137.983 - 57.1544i) q^{83} +(-774.410 + 230.071i) q^{84} +(162.236 + 391.672i) q^{85} +(380.155 + 181.136i) q^{86} +(497.195 + 497.195i) q^{87} +(116.776 - 191.081i) q^{88} +(-579.803 + 579.803i) q^{89} +(-17.9940 + 6.38018i) q^{90} +(-1288.71 + 533.802i) q^{91} +(629.828 - 510.868i) q^{92} +(-519.610 + 1254.45i) q^{93} +(328.964 + 365.055i) q^{94} +547.785 q^{95} +(-121.703 - 910.222i) q^{96} -912.077 q^{97} +(100.804 + 111.863i) q^{98} +(4.78742 - 11.5579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 212 q^{14} - 304 q^{16} - 184 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 192 q^{22} + 324 q^{23} - 48 q^{24} - 4 q^{25} + 16 q^{26} - 268 q^{27} + 376 q^{28} - 4 q^{29} + 1188 q^{30} - 752 q^{31} + 616 q^{32} - 8 q^{33} + 528 q^{34} - 460 q^{35} + 1456 q^{36} - 4 q^{37} + 980 q^{38} + 596 q^{39} - 536 q^{40} - 4 q^{41} - 2264 q^{42} + 804 q^{43} - 2044 q^{44} + 104 q^{45} - 1444 q^{46} - 2448 q^{48} - 3564 q^{50} - 1384 q^{51} - 2524 q^{52} + 748 q^{53} - 1088 q^{54} - 292 q^{55} + 1192 q^{56} - 4 q^{57} + 3200 q^{58} + 1372 q^{59} + 5752 q^{60} - 1828 q^{61} + 3384 q^{62} + 2512 q^{63} + 4952 q^{64} - 8 q^{65} + 5996 q^{66} + 2036 q^{67} + 2768 q^{68} - 1060 q^{69} + 1400 q^{70} + 220 q^{71} - 1708 q^{72} - 4 q^{73} - 3476 q^{74} - 1712 q^{75} - 5124 q^{76} + 1900 q^{77} - 11916 q^{78} - 10312 q^{80} - 6404 q^{82} + 2436 q^{83} - 6560 q^{84} + 496 q^{85} - 928 q^{86} - 1292 q^{87} + 1248 q^{88} - 4 q^{89} + 7400 q^{90} - 3604 q^{91} + 10152 q^{92} - 112 q^{93} + 12840 q^{94} - 6088 q^{95} + 17792 q^{96} - 8 q^{97} + 11224 q^{98} - 5424 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.10117 + 1.89344i −0.742875 + 0.669431i
\(3\) 1.94138 4.68690i 0.373618 0.901994i −0.619513 0.784986i \(-0.712670\pi\)
0.993131 0.117007i \(-0.0373301\pi\)
\(4\) 0.829801 7.95685i 0.103725 0.994606i
\(5\) 4.93338 2.04347i 0.441255 0.182774i −0.150984 0.988536i \(-0.548244\pi\)
0.592239 + 0.805762i \(0.298244\pi\)
\(6\) 4.79518 + 13.5238i 0.326271 + 0.920179i
\(7\) 14.0755 14.0755i 0.760005 0.760005i −0.216318 0.976323i \(-0.569405\pi\)
0.976323 + 0.216318i \(0.0694049\pi\)
\(8\) 13.3222 + 18.2898i 0.588765 + 0.808304i
\(9\) 0.893826 + 0.893826i 0.0331047 + 0.0331047i
\(10\) −6.49667 + 13.6347i −0.205443 + 0.431168i
\(11\) −3.78733 9.14343i −0.103811 0.250623i 0.863436 0.504458i \(-0.168308\pi\)
−0.967247 + 0.253836i \(0.918308\pi\)
\(12\) −35.6820 19.3364i −0.858375 0.465162i
\(13\) −64.7407 26.8165i −1.38122 0.572120i −0.436412 0.899747i \(-0.643751\pi\)
−0.944807 + 0.327627i \(0.893751\pi\)
\(14\) −2.92391 + 56.2260i −0.0558177 + 1.07336i
\(15\) 27.0894i 0.466297i
\(16\) −62.6229 13.2052i −0.978482 0.206331i
\(17\) 79.3923i 1.13267i 0.824174 + 0.566337i \(0.191640\pi\)
−0.824174 + 0.566337i \(0.808360\pi\)
\(18\) −3.57048 0.185675i −0.0467539 0.00243133i
\(19\) 94.7756 + 39.2573i 1.14437 + 0.474013i 0.872642 0.488361i \(-0.162405\pi\)
0.271727 + 0.962374i \(0.412405\pi\)
\(20\) −12.1659 40.9498i −0.136019 0.457833i
\(21\) −38.6445 93.2961i −0.401568 0.969471i
\(22\) 25.2703 + 12.0408i 0.244893 + 0.116687i
\(23\) 71.6801 + 71.6801i 0.649841 + 0.649841i 0.952954 0.303114i \(-0.0980261\pi\)
−0.303114 + 0.952954i \(0.598026\pi\)
\(24\) 111.586 26.9325i 0.949058 0.229065i
\(25\) −68.2259 + 68.2259i −0.545807 + 0.545807i
\(26\) 186.806 66.2365i 1.40907 0.499617i
\(27\) 132.471 54.8712i 0.944222 0.391110i
\(28\) −100.317 123.676i −0.677074 0.834737i
\(29\) −53.0409 + 128.052i −0.339636 + 0.819955i 0.658114 + 0.752918i \(0.271354\pi\)
−0.997751 + 0.0670366i \(0.978646\pi\)
\(30\) 51.2920 + 56.9193i 0.312153 + 0.346400i
\(31\) −267.650 −1.55069 −0.775346 0.631537i \(-0.782424\pi\)
−0.775346 + 0.631537i \(0.782424\pi\)
\(32\) 156.584 90.8260i 0.865014 0.501748i
\(33\) −50.2070 −0.264846
\(34\) −150.324 166.816i −0.758247 0.841435i
\(35\) 40.6768 98.2026i 0.196447 0.474265i
\(36\) 7.85374 6.37034i 0.0363599 0.0294923i
\(37\) 205.678 85.1946i 0.913872 0.378538i 0.124334 0.992240i \(-0.460321\pi\)
0.789537 + 0.613702i \(0.210321\pi\)
\(38\) −273.470 + 96.9653i −1.16744 + 0.413943i
\(39\) −251.372 + 251.372i −1.03210 + 1.03210i
\(40\) 103.098 + 63.0071i 0.407532 + 0.249057i
\(41\) 210.468 + 210.468i 0.801697 + 0.801697i 0.983361 0.181664i \(-0.0581482\pi\)
−0.181664 + 0.983361i \(0.558148\pi\)
\(42\) 257.849 + 122.860i 0.947308 + 0.451373i
\(43\) −56.9749 137.550i −0.202060 0.487817i 0.790072 0.613015i \(-0.210043\pi\)
−0.992132 + 0.125198i \(0.960043\pi\)
\(44\) −75.8956 + 22.5480i −0.260039 + 0.0772555i
\(45\) 6.23610 + 2.58308i 0.0206583 + 0.00855694i
\(46\) −286.334 14.8902i −0.917774 0.0477268i
\(47\) 173.739i 0.539201i −0.962972 0.269600i \(-0.913108\pi\)
0.962972 0.269600i \(-0.0868916\pi\)
\(48\) −183.466 + 267.871i −0.551688 + 0.805496i
\(49\) 53.2384i 0.155214i
\(50\) 14.1726 272.535i 0.0400862 0.770846i
\(51\) 372.103 + 154.130i 1.02166 + 0.423187i
\(52\) −267.097 + 492.880i −0.712301 + 1.31443i
\(53\) −188.605 455.333i −0.488810 1.18009i −0.955319 0.295575i \(-0.904489\pi\)
0.466510 0.884516i \(-0.345511\pi\)
\(54\) −174.448 + 366.118i −0.439618 + 0.922637i
\(55\) −37.3687 37.3687i −0.0916145 0.0916145i
\(56\) 444.955 + 69.9214i 1.06178 + 0.166851i
\(57\) 367.990 367.990i 0.855113 0.855113i
\(58\) −131.011 369.489i −0.296596 0.836487i
\(59\) −627.964 + 260.111i −1.38566 + 0.573959i −0.945989 0.324199i \(-0.894905\pi\)
−0.439671 + 0.898159i \(0.644905\pi\)
\(60\) −215.546 22.4788i −0.463782 0.0483667i
\(61\) 66.5782 160.734i 0.139745 0.337375i −0.838476 0.544938i \(-0.816553\pi\)
0.978222 + 0.207563i \(0.0665532\pi\)
\(62\) 562.378 506.779i 1.15197 1.03808i
\(63\) 25.1621 0.0503194
\(64\) −157.036 + 487.323i −0.306711 + 0.951803i
\(65\) −374.189 −0.714038
\(66\) 105.493 95.0637i 0.196747 0.177296i
\(67\) 211.710 511.113i 0.386037 0.931975i −0.604734 0.796428i \(-0.706721\pi\)
0.990771 0.135548i \(-0.0432794\pi\)
\(68\) 631.712 + 65.8798i 1.12656 + 0.117487i
\(69\) 475.115 196.799i 0.828945 0.343360i
\(70\) 100.471 + 283.359i 0.171552 + 0.483827i
\(71\) −226.201 + 226.201i −0.378100 + 0.378100i −0.870416 0.492316i \(-0.836150\pi\)
0.492316 + 0.870416i \(0.336150\pi\)
\(72\) −4.44018 + 28.2557i −0.00726777 + 0.0462495i
\(73\) 802.290 + 802.290i 1.28631 + 1.28631i 0.937009 + 0.349305i \(0.113582\pi\)
0.349305 + 0.937009i \(0.386418\pi\)
\(74\) −270.853 + 568.446i −0.425487 + 0.892980i
\(75\) 187.316 + 452.220i 0.288391 + 0.696238i
\(76\) 391.009 721.539i 0.590156 1.08903i
\(77\) −182.007 75.3897i −0.269371 0.111577i
\(78\) 52.2177 1004.13i 0.0758011 1.45764i
\(79\) 552.368i 0.786662i −0.919397 0.393331i \(-0.871323\pi\)
0.919397 0.393331i \(-0.128677\pi\)
\(80\) −335.927 + 62.8219i −0.469472 + 0.0877962i
\(81\) 693.272i 0.950991i
\(82\) −840.736 43.7206i −1.13224 0.0588797i
\(83\) −137.983 57.1544i −0.182477 0.0755845i 0.289574 0.957156i \(-0.406486\pi\)
−0.472051 + 0.881571i \(0.656486\pi\)
\(84\) −774.410 + 230.071i −1.00589 + 0.298843i
\(85\) 162.236 + 391.672i 0.207023 + 0.499798i
\(86\) 380.155 + 181.136i 0.476665 + 0.227121i
\(87\) 497.195 + 497.195i 0.612700 + 0.612700i
\(88\) 116.776 191.081i 0.141459 0.231469i
\(89\) −579.803 + 579.803i −0.690550 + 0.690550i −0.962353 0.271803i \(-0.912380\pi\)
0.271803 + 0.962353i \(0.412380\pi\)
\(90\) −17.9940 + 6.38018i −0.0210748 + 0.00747255i
\(91\) −1288.71 + 533.802i −1.48455 + 0.614919i
\(92\) 629.828 510.868i 0.713741 0.578931i
\(93\) −519.610 + 1254.45i −0.579366 + 1.39871i
\(94\) 328.964 + 365.055i 0.360958 + 0.400559i
\(95\) 547.785 0.591595
\(96\) −121.703 910.222i −0.129389 0.967699i
\(97\) −912.077 −0.954716 −0.477358 0.878709i \(-0.658405\pi\)
−0.477358 + 0.878709i \(0.658405\pi\)
\(98\) 100.804 + 111.863i 0.103905 + 0.115305i
\(99\) 4.78742 11.5579i 0.00486014 0.0117334i
\(100\) 486.249 + 599.477i 0.486249 + 0.599477i
\(101\) −968.800 + 401.290i −0.954447 + 0.395345i −0.804901 0.593410i \(-0.797781\pi\)
−0.149547 + 0.988755i \(0.547781\pi\)
\(102\) −1073.69 + 380.701i −1.04226 + 0.369559i
\(103\) 351.683 351.683i 0.336430 0.336430i −0.518592 0.855022i \(-0.673543\pi\)
0.855022 + 0.518592i \(0.173543\pi\)
\(104\) −372.022 1541.35i −0.350767 1.45329i
\(105\) −381.296 381.296i −0.354388 0.354388i
\(106\) 1258.44 + 599.619i 1.15311 + 0.549436i
\(107\) −95.4774 230.503i −0.0862631 0.208257i 0.874861 0.484374i \(-0.160953\pi\)
−0.961124 + 0.276116i \(0.910953\pi\)
\(108\) −326.677 1099.58i −0.291060 0.979697i
\(109\) 858.330 + 355.532i 0.754249 + 0.312420i 0.726474 0.687194i \(-0.241158\pi\)
0.0277749 + 0.999614i \(0.491158\pi\)
\(110\) 149.273 + 7.76263i 0.129388 + 0.00672852i
\(111\) 1129.39i 0.965735i
\(112\) −1067.32 + 695.577i −0.900464 + 0.586838i
\(113\) 1154.63i 0.961222i −0.876934 0.480611i \(-0.840415\pi\)
0.876934 0.480611i \(-0.159585\pi\)
\(114\) −76.4428 + 1469.97i −0.0628028 + 1.20768i
\(115\) 500.102 + 207.149i 0.405519 + 0.167972i
\(116\) 974.878 + 528.297i 0.780303 + 0.422854i
\(117\) −33.8977 81.8362i −0.0267850 0.0646646i
\(118\) 826.953 1735.55i 0.645146 1.35398i
\(119\) 1117.48 + 1117.48i 0.860838 + 0.860838i
\(120\) 495.461 360.891i 0.376910 0.274539i
\(121\) 871.901 871.901i 0.655072 0.655072i
\(122\) 164.448 + 463.790i 0.122036 + 0.344177i
\(123\) 1395.04 577.844i 1.02265 0.423597i
\(124\) −222.097 + 2129.65i −0.160846 + 1.54233i
\(125\) −452.601 + 1092.67i −0.323855 + 0.781854i
\(126\) −52.8697 + 47.6428i −0.0373810 + 0.0336854i
\(127\) 953.091 0.665930 0.332965 0.942939i \(-0.391951\pi\)
0.332965 + 0.942939i \(0.391951\pi\)
\(128\) −592.755 1321.28i −0.409318 0.912392i
\(129\) −755.290 −0.515501
\(130\) 786.234 708.504i 0.530441 0.477999i
\(131\) 26.3943 63.7216i 0.0176037 0.0424991i −0.914833 0.403832i \(-0.867678\pi\)
0.932437 + 0.361333i \(0.117678\pi\)
\(132\) −41.6618 + 399.489i −0.0274712 + 0.263417i
\(133\) 1886.58 781.446i 1.22998 0.509473i
\(134\) 522.922 + 1474.79i 0.337116 + 0.950766i
\(135\) 541.401 541.401i 0.345158 0.345158i
\(136\) −1452.07 + 1057.68i −0.915545 + 0.666879i
\(137\) −1910.45 1910.45i −1.19139 1.19139i −0.976677 0.214713i \(-0.931118\pi\)
−0.214713 0.976677i \(-0.568882\pi\)
\(138\) −625.670 + 1313.11i −0.385946 + 0.809994i
\(139\) −525.552 1268.79i −0.320696 0.774228i −0.999214 0.0396445i \(-0.987377\pi\)
0.678518 0.734584i \(-0.262623\pi\)
\(140\) −747.629 405.148i −0.451330 0.244580i
\(141\) −814.297 337.293i −0.486356 0.201455i
\(142\) 46.9888 903.583i 0.0277691 0.533993i
\(143\) 693.516i 0.405557i
\(144\) −44.1708 67.7771i −0.0255618 0.0392229i
\(145\) 740.118i 0.423886i
\(146\) −3204.83 166.660i −1.81667 0.0944718i
\(147\) −249.523 103.356i −0.140002 0.0579908i
\(148\) −507.209 1707.24i −0.281705 0.948206i
\(149\) 477.450 + 1152.67i 0.262512 + 0.633759i 0.999093 0.0425902i \(-0.0135610\pi\)
−0.736581 + 0.676349i \(0.763561\pi\)
\(150\) −1249.83 595.519i −0.680321 0.324159i
\(151\) −1185.23 1185.23i −0.638757 0.638757i 0.311492 0.950249i \(-0.399171\pi\)
−0.950249 + 0.311492i \(0.899171\pi\)
\(152\) 544.612 + 2256.42i 0.290617 + 1.20408i
\(153\) −70.9629 + 70.9629i −0.0374968 + 0.0374968i
\(154\) 525.172 186.212i 0.274802 0.0974376i
\(155\) −1320.42 + 546.937i −0.684250 + 0.283426i
\(156\) 1791.54 + 2208.72i 0.919475 + 1.13358i
\(157\) 187.368 452.347i 0.0952460 0.229944i −0.869075 0.494681i \(-0.835285\pi\)
0.964321 + 0.264737i \(0.0852850\pi\)
\(158\) 1045.87 + 1160.62i 0.526615 + 0.584391i
\(159\) −2500.25 −1.24706
\(160\) 586.889 768.055i 0.289985 0.379501i
\(161\) 2017.87 0.987764
\(162\) 1312.67 + 1456.68i 0.636623 + 0.706467i
\(163\) −926.026 + 2235.62i −0.444981 + 1.07428i 0.529197 + 0.848499i \(0.322493\pi\)
−0.974178 + 0.225781i \(0.927507\pi\)
\(164\) 1849.31 1500.02i 0.880529 0.714217i
\(165\) −247.690 + 102.597i −0.116865 + 0.0484069i
\(166\) 398.144 141.171i 0.186156 0.0660060i
\(167\) 753.289 753.289i 0.349049 0.349049i −0.510706 0.859755i \(-0.670616\pi\)
0.859755 + 0.510706i \(0.170616\pi\)
\(168\) 1191.54 1949.71i 0.547198 0.895380i
\(169\) 1918.72 + 1918.72i 0.873338 + 0.873338i
\(170\) −1082.49 515.785i −0.488372 0.232700i
\(171\) 49.6237 + 119.802i 0.0221919 + 0.0535760i
\(172\) −1141.74 + 339.202i −0.506144 + 0.150371i
\(173\) −186.646 77.3114i −0.0820257 0.0339762i 0.341293 0.939957i \(-0.389135\pi\)
−0.423319 + 0.905981i \(0.639135\pi\)
\(174\) −1986.10 103.283i −0.865319 0.0449990i
\(175\) 1920.62i 0.829632i
\(176\) 116.433 + 622.600i 0.0498662 + 0.266649i
\(177\) 3448.18i 1.46430i
\(178\) 120.443 2316.08i 0.0507167 0.975268i
\(179\) −1509.31 625.176i −0.630229 0.261049i 0.0446216 0.999004i \(-0.485792\pi\)
−0.674850 + 0.737955i \(0.735792\pi\)
\(180\) 25.7279 47.4762i 0.0106536 0.0196593i
\(181\) −772.420 1864.79i −0.317202 0.765793i −0.999400 0.0346258i \(-0.988976\pi\)
0.682199 0.731167i \(-0.261024\pi\)
\(182\) 1697.08 3561.70i 0.691186 1.45061i
\(183\) −624.090 624.090i −0.252099 0.252099i
\(184\) −356.079 + 2265.96i −0.142666 + 0.907873i
\(185\) 840.595 840.595i 0.334064 0.334064i
\(186\) −1283.43 3619.66i −0.505946 1.42691i
\(187\) 725.918 300.685i 0.283874 0.117584i
\(188\) −1382.41 144.169i −0.536292 0.0559287i
\(189\) 1092.25 2636.93i 0.420368 1.01486i
\(190\) −1150.99 + 1037.20i −0.439481 + 0.396032i
\(191\) 1509.32 0.571784 0.285892 0.958262i \(-0.407710\pi\)
0.285892 + 0.958262i \(0.407710\pi\)
\(192\) 1979.17 + 1682.09i 0.743927 + 0.632262i
\(193\) 3625.68 1.35224 0.676120 0.736791i \(-0.263660\pi\)
0.676120 + 0.736791i \(0.263660\pi\)
\(194\) 1916.43 1726.96i 0.709234 0.639116i
\(195\) −726.442 + 1753.79i −0.266778 + 0.644058i
\(196\) −423.610 44.1773i −0.154377 0.0160996i
\(197\) −1764.33 + 730.811i −0.638090 + 0.264305i −0.678186 0.734890i \(-0.737234\pi\)
0.0400962 + 0.999196i \(0.487234\pi\)
\(198\) 11.8249 + 33.3497i 0.00424424 + 0.0119700i
\(199\) −2008.70 + 2008.70i −0.715544 + 0.715544i −0.967689 0.252146i \(-0.918864\pi\)
0.252146 + 0.967689i \(0.418864\pi\)
\(200\) −2156.76 338.919i −0.762530 0.119826i
\(201\) −1984.52 1984.52i −0.696406 0.696406i
\(202\) 1275.79 2677.54i 0.444379 0.932628i
\(203\) 1055.82 + 2548.97i 0.365044 + 0.881295i
\(204\) 1535.16 2832.87i 0.526877 0.972259i
\(205\) 1468.40 + 608.233i 0.500282 + 0.207224i
\(206\) −73.0553 + 1404.83i −0.0247087 + 0.475142i
\(207\) 128.139i 0.0430255i
\(208\) 3700.13 + 2534.24i 1.23345 + 0.844798i
\(209\) 1015.25i 0.336013i
\(210\) 1523.13 + 79.2069i 0.500504 + 0.0260276i
\(211\) −1133.08 469.337i −0.369689 0.153130i 0.190101 0.981764i \(-0.439118\pi\)
−0.559790 + 0.828634i \(0.689118\pi\)
\(212\) −3779.52 + 1122.87i −1.22443 + 0.363768i
\(213\) 621.039 + 1499.32i 0.199779 + 0.482309i
\(214\) 637.056 + 303.544i 0.203497 + 0.0969620i
\(215\) −562.158 562.158i −0.178320 0.178320i
\(216\) 2768.39 + 1691.86i 0.872061 + 0.532947i
\(217\) −3767.31 + 3767.31i −1.17853 + 1.17853i
\(218\) −2476.67 + 878.161i −0.769456 + 0.272828i
\(219\) 5317.80 2202.70i 1.64084 0.679657i
\(220\) −328.346 + 266.329i −0.100623 + 0.0816176i
\(221\) 2129.02 5139.91i 0.648025 1.56447i
\(222\) 2138.42 + 2373.03i 0.646493 + 0.717420i
\(223\) −3100.74 −0.931125 −0.465562 0.885015i \(-0.654148\pi\)
−0.465562 + 0.885015i \(0.654148\pi\)
\(224\) 925.579 3482.42i 0.276084 1.03875i
\(225\) −121.964 −0.0361375
\(226\) 2186.21 + 2426.06i 0.643472 + 0.714067i
\(227\) 1661.15 4010.36i 0.485701 1.17259i −0.471162 0.882047i \(-0.656165\pi\)
0.956863 0.290539i \(-0.0938347\pi\)
\(228\) −2622.68 3233.40i −0.761804 0.939198i
\(229\) −2972.95 + 1231.44i −0.857895 + 0.355352i −0.767884 0.640589i \(-0.778690\pi\)
−0.0900110 + 0.995941i \(0.528690\pi\)
\(230\) −1443.02 + 511.656i −0.413695 + 0.146685i
\(231\) −706.687 + 706.687i −0.201284 + 0.201284i
\(232\) −3048.68 + 735.830i −0.862739 + 0.208231i
\(233\) 1590.35 + 1590.35i 0.447155 + 0.447155i 0.894408 0.447253i \(-0.147597\pi\)
−0.447253 + 0.894408i \(0.647597\pi\)
\(234\) 226.176 + 107.768i 0.0631864 + 0.0301070i
\(235\) −355.031 857.121i −0.0985518 0.237925i
\(236\) 1548.58 + 5212.45i 0.427136 + 1.43772i
\(237\) −2588.89 1072.35i −0.709564 0.293911i
\(238\) −4463.91 232.136i −1.21577 0.0632232i
\(239\) 6173.19i 1.67076i 0.549676 + 0.835378i \(0.314751\pi\)
−0.549676 + 0.835378i \(0.685249\pi\)
\(240\) −357.721 + 1696.42i −0.0962116 + 0.456263i
\(241\) 1436.00i 0.383822i −0.981412 0.191911i \(-0.938531\pi\)
0.981412 0.191911i \(-0.0614685\pi\)
\(242\) −181.120 + 3482.90i −0.0481110 + 0.925161i
\(243\) 327.413 + 135.619i 0.0864344 + 0.0358023i
\(244\) −1223.69 663.130i −0.321060 0.173986i
\(245\) −108.791 262.646i −0.0283691 0.0684890i
\(246\) −1837.10 + 3855.56i −0.476135 + 0.999276i
\(247\) −5083.09 5083.09i −1.30943 1.30943i
\(248\) −3565.70 4895.28i −0.912993 1.25343i
\(249\) −535.754 + 535.754i −0.136354 + 0.136354i
\(250\) −1117.92 3152.86i −0.282814 0.797618i
\(251\) 4781.23 1980.45i 1.20235 0.498028i 0.310589 0.950544i \(-0.399474\pi\)
0.891756 + 0.452516i \(0.149474\pi\)
\(252\) 20.8795 200.211i 0.00521939 0.0500480i
\(253\) 383.926 926.879i 0.0954040 0.230326i
\(254\) −2002.60 + 1804.62i −0.494703 + 0.445794i
\(255\) 2150.69 0.528162
\(256\) 3747.25 + 1653.89i 0.914855 + 0.403783i
\(257\) −246.466 −0.0598215 −0.0299107 0.999553i \(-0.509522\pi\)
−0.0299107 + 0.999553i \(0.509522\pi\)
\(258\) 1586.99 1430.09i 0.382952 0.345092i
\(259\) 1695.86 4094.17i 0.406856 0.982237i
\(260\) −310.503 + 2977.37i −0.0740637 + 0.710187i
\(261\) −161.866 + 67.0470i −0.0383879 + 0.0159008i
\(262\) 65.1938 + 183.866i 0.0153729 + 0.0433559i
\(263\) 3454.60 3454.60i 0.809960 0.809960i −0.174667 0.984628i \(-0.555885\pi\)
0.984628 + 0.174667i \(0.0558849\pi\)
\(264\) −668.869 918.277i −0.155932 0.214076i
\(265\) −1860.92 1860.92i −0.431380 0.431380i
\(266\) −2484.40 + 5214.06i −0.572662 + 1.20186i
\(267\) 1591.86 + 3843.09i 0.364870 + 0.880874i
\(268\) −3891.17 2108.66i −0.886907 0.480624i
\(269\) 2611.67 + 1081.79i 0.591958 + 0.245197i 0.658493 0.752587i \(-0.271194\pi\)
−0.0665350 + 0.997784i \(0.521194\pi\)
\(270\) −112.465 + 2162.68i −0.0253497 + 0.487469i
\(271\) 3464.52i 0.776585i −0.921536 0.388292i \(-0.873065\pi\)
0.921536 0.388292i \(-0.126935\pi\)
\(272\) 1048.39 4971.77i 0.233706 1.10830i
\(273\) 7076.37i 1.56880i
\(274\) 7631.47 + 396.858i 1.68261 + 0.0875003i
\(275\) 882.213 + 365.425i 0.193453 + 0.0801307i
\(276\) −1171.65 3943.73i −0.255526 0.860088i
\(277\) 1186.33 + 2864.06i 0.257328 + 0.621245i 0.998760 0.0497833i \(-0.0158531\pi\)
−0.741432 + 0.671028i \(0.765853\pi\)
\(278\) 3506.65 + 1670.85i 0.756529 + 0.360471i
\(279\) −239.233 239.233i −0.0513352 0.0513352i
\(280\) 2338.02 564.305i 0.499011 0.120442i
\(281\) 3210.39 3210.39i 0.681552 0.681552i −0.278798 0.960350i \(-0.589936\pi\)
0.960350 + 0.278798i \(0.0899360\pi\)
\(282\) 2349.61 833.110i 0.496161 0.175926i
\(283\) −2512.41 + 1040.67i −0.527729 + 0.218593i −0.630608 0.776101i \(-0.717194\pi\)
0.102879 + 0.994694i \(0.467194\pi\)
\(284\) 1612.14 + 1987.55i 0.336842 + 0.415279i
\(285\) 1063.46 2567.41i 0.221031 0.533615i
\(286\) −1313.13 1457.19i −0.271492 0.301278i
\(287\) 5924.88 1.21859
\(288\) 221.142 + 58.7764i 0.0452462 + 0.0120258i
\(289\) −1390.14 −0.282950
\(290\) −1401.37 1555.11i −0.283762 0.314894i
\(291\) −1770.68 + 4274.81i −0.356699 + 0.861147i
\(292\) 7049.44 5717.96i 1.41280 1.14595i
\(293\) −7264.11 + 3008.89i −1.44838 + 0.599937i −0.961812 0.273709i \(-0.911749\pi\)
−0.486563 + 0.873646i \(0.661749\pi\)
\(294\) 719.987 255.288i 0.142825 0.0506419i
\(295\) −2566.46 + 2566.46i −0.506525 + 0.506525i
\(296\) 4298.29 + 2626.83i 0.844030 + 0.515816i
\(297\) −1003.42 1003.42i −0.196042 0.196042i
\(298\) −3185.70 1517.92i −0.619271 0.295070i
\(299\) −2718.41 6562.83i −0.525786 1.26936i
\(300\) 3753.68 1115.19i 0.722396 0.214618i
\(301\) −2738.03 1134.13i −0.524310 0.217176i
\(302\) 4734.51 + 246.208i 0.902120 + 0.0469128i
\(303\) 5319.72i 1.00861i
\(304\) −5416.72 3709.94i −1.02194 0.699932i
\(305\) 929.012i 0.174410i
\(306\) 14.7412 283.469i 0.00275391 0.0529569i
\(307\) 1055.79 + 437.322i 0.196277 + 0.0813006i 0.478657 0.878002i \(-0.341124\pi\)
−0.282380 + 0.959303i \(0.591124\pi\)
\(308\) −750.894 + 1385.64i −0.138916 + 0.256345i
\(309\) −965.552 2331.05i −0.177762 0.429155i
\(310\) 1738.84 3649.34i 0.318578 0.668608i
\(311\) 2154.35 + 2154.35i 0.392804 + 0.392804i 0.875686 0.482882i \(-0.160410\pi\)
−0.482882 + 0.875686i \(0.660410\pi\)
\(312\) −7946.39 1248.72i −1.44191 0.226586i
\(313\) −3659.65 + 3659.65i −0.660881 + 0.660881i −0.955588 0.294706i \(-0.904778\pi\)
0.294706 + 0.955588i \(0.404778\pi\)
\(314\) 462.798 + 1305.23i 0.0831759 + 0.234580i
\(315\) 124.134 51.4180i 0.0222037 0.00919707i
\(316\) −4395.11 458.356i −0.782418 0.0815966i
\(317\) −3106.88 + 7500.68i −0.550473 + 1.32896i 0.366652 + 0.930358i \(0.380504\pi\)
−0.917125 + 0.398601i \(0.869496\pi\)
\(318\) 5253.45 4734.07i 0.926411 0.834822i
\(319\) 1371.72 0.240757
\(320\) 221.111 + 2725.05i 0.0386266 + 0.476046i
\(321\) −1265.70 −0.220076
\(322\) −4239.87 + 3820.70i −0.733785 + 0.661240i
\(323\) −3116.73 + 7524.45i −0.536902 + 1.29620i
\(324\) −5516.26 575.278i −0.945861 0.0986417i
\(325\) 6246.57 2587.41i 1.06615 0.441612i
\(326\) −2287.28 6450.79i −0.388591 1.09594i
\(327\) 3332.68 3332.68i 0.563602 0.563602i
\(328\) −1045.52 + 6653.33i −0.176004 + 1.12003i
\(329\) −2445.46 2445.46i −0.409795 0.409795i
\(330\) 326.178 684.558i 0.0544106 0.114193i
\(331\) 2372.98 + 5728.87i 0.394050 + 0.951321i 0.989048 + 0.147594i \(0.0471528\pi\)
−0.594998 + 0.803727i \(0.702847\pi\)
\(332\) −569.268 + 1050.48i −0.0941043 + 0.173653i
\(333\) 259.990 + 107.691i 0.0427848 + 0.0177220i
\(334\) −156.481 + 3009.09i −0.0256355 + 0.492964i
\(335\) 2954.14i 0.481796i
\(336\) 1188.04 + 6352.78i 0.192895 + 1.03147i
\(337\) 5514.75i 0.891418i −0.895178 0.445709i \(-0.852952\pi\)
0.895178 0.445709i \(-0.147048\pi\)
\(338\) −7664.54 398.578i −1.23342 0.0641413i
\(339\) −5411.61 2241.56i −0.867016 0.359130i
\(340\) 3251.10 965.877i 0.518576 0.154065i
\(341\) 1013.68 + 2447.24i 0.160979 + 0.388638i
\(342\) −331.105 157.765i −0.0523512 0.0249443i
\(343\) 4078.53 + 4078.53i 0.642041 + 0.642041i
\(344\) 1756.73 2874.53i 0.275338 0.450535i
\(345\) 1941.77 1941.77i 0.303019 0.303019i
\(346\) 538.559 190.959i 0.0836795 0.0296705i
\(347\) −9323.05 + 3861.74i −1.44233 + 0.597432i −0.960361 0.278758i \(-0.910077\pi\)
−0.481966 + 0.876190i \(0.660077\pi\)
\(348\) 4368.68 3543.53i 0.672947 0.545843i
\(349\) −1844.20 + 4452.29i −0.282859 + 0.682882i −0.999900 0.0141493i \(-0.995496\pi\)
0.717041 + 0.697031i \(0.245496\pi\)
\(350\) −3636.58 4035.55i −0.555381 0.616312i
\(351\) −10047.7 −1.52794
\(352\) −1423.50 1087.73i −0.215548 0.164705i
\(353\) 7343.73 1.10727 0.553636 0.832759i \(-0.313240\pi\)
0.553636 + 0.832759i \(0.313240\pi\)
\(354\) −6528.90 7245.19i −0.980246 1.08779i
\(355\) −653.700 + 1578.17i −0.0977317 + 0.235945i
\(356\) 4132.28 + 5094.52i 0.615198 + 0.758453i
\(357\) 7406.99 3068.08i 1.09809 0.454846i
\(358\) 4355.04 1544.18i 0.642935 0.227968i
\(359\) 4187.33 4187.33i 0.615596 0.615596i −0.328802 0.944399i \(-0.606645\pi\)
0.944399 + 0.328802i \(0.106645\pi\)
\(360\) 35.8347 + 148.469i 0.00524626 + 0.0217362i
\(361\) 2591.22 + 2591.22i 0.377784 + 0.377784i
\(362\) 5153.84 + 2455.70i 0.748286 + 0.356543i
\(363\) −2393.82 5779.20i −0.346124 0.835617i
\(364\) 3178.01 + 10697.0i 0.457618 + 1.54032i
\(365\) 5597.46 + 2318.54i 0.802697 + 0.332488i
\(366\) 2492.99 + 129.643i 0.356040 + 0.0185151i
\(367\) 9231.47i 1.31302i −0.754317 0.656510i \(-0.772032\pi\)
0.754317 0.656510i \(-0.227968\pi\)
\(368\) −3542.26 5435.37i −0.501775 0.769940i
\(369\) 376.244i 0.0530798i
\(370\) −174.617 + 3357.84i −0.0245349 + 0.471800i
\(371\) −9063.75 3754.33i −1.26837 0.525377i
\(372\) 9550.30 + 5175.40i 1.33107 + 0.721323i
\(373\) −117.113 282.737i −0.0162571 0.0392481i 0.915543 0.402221i \(-0.131762\pi\)
−0.931800 + 0.362973i \(0.881762\pi\)
\(374\) −955.947 + 2006.27i −0.132168 + 0.277384i
\(375\) 4242.58 + 4242.58i 0.584230 + 0.584230i
\(376\) 3177.66 2314.59i 0.435838 0.317463i
\(377\) 6867.82 6867.82i 0.938224 0.938224i
\(378\) 2697.85 + 7608.73i 0.367097 + 1.03532i
\(379\) 3068.05 1270.83i 0.415819 0.172238i −0.164958 0.986301i \(-0.552749\pi\)
0.580777 + 0.814063i \(0.302749\pi\)
\(380\) 454.553 4358.64i 0.0613633 0.588404i
\(381\) 1850.31 4467.04i 0.248804 0.600665i
\(382\) −3171.34 + 2857.81i −0.424764 + 0.382770i
\(383\) 1379.97 0.184107 0.0920537 0.995754i \(-0.470657\pi\)
0.0920537 + 0.995754i \(0.470657\pi\)
\(384\) −7343.49 + 213.072i −0.975900 + 0.0283159i
\(385\) −1051.97 −0.139255
\(386\) −7618.16 + 6865.00i −1.00454 + 0.905231i
\(387\) 72.0198 173.871i 0.00945987 0.0228381i
\(388\) −756.843 + 7257.26i −0.0990280 + 0.949566i
\(389\) 1279.89 530.148i 0.166820 0.0690992i −0.297711 0.954656i \(-0.596223\pi\)
0.464531 + 0.885557i \(0.346223\pi\)
\(390\) −1794.31 5060.47i −0.232970 0.657043i
\(391\) −5690.85 + 5690.85i −0.736058 + 0.736058i
\(392\) 973.723 709.255i 0.125460 0.0913847i
\(393\) −247.415 247.415i −0.0317568 0.0317568i
\(394\) 2323.42 4876.21i 0.297086 0.623503i
\(395\) −1128.75 2725.04i −0.143781 0.347118i
\(396\) −87.9915 47.6835i −0.0111660 0.00605098i
\(397\) −706.615 292.690i −0.0893300 0.0370017i 0.337571 0.941300i \(-0.390395\pi\)
−0.426901 + 0.904298i \(0.640395\pi\)
\(398\) 417.269 8023.97i 0.0525523 1.01057i
\(399\) 10359.3i 1.29978i
\(400\) 5173.44 3371.56i 0.646680 0.421445i
\(401\) 9680.79i 1.20557i −0.797902 0.602787i \(-0.794057\pi\)
0.797902 0.602787i \(-0.205943\pi\)
\(402\) 7927.38 + 412.246i 0.983537 + 0.0511467i
\(403\) 17327.9 + 7177.45i 2.14184 + 0.887181i
\(404\) 2389.09 + 8041.58i 0.294212 + 0.990306i
\(405\) −1416.68 3420.18i −0.173816 0.419630i
\(406\) −7044.77 3356.69i −0.861148 0.410320i
\(407\) −1557.94 1557.94i −0.189740 0.189740i
\(408\) 2138.23 + 8859.07i 0.259456 + 1.07497i
\(409\) −1231.14 + 1231.14i −0.148841 + 0.148841i −0.777600 0.628759i \(-0.783563\pi\)
0.628759 + 0.777600i \(0.283563\pi\)
\(410\) −4237.01 + 1502.33i −0.510369 + 0.180963i
\(411\) −12663.0 + 5245.17i −1.51975 + 0.629502i
\(412\) −2506.46 3090.11i −0.299719 0.369512i
\(413\) −5177.71 + 12500.1i −0.616896 + 1.48932i
\(414\) −242.623 269.242i −0.0288026 0.0319626i
\(415\) −797.516 −0.0943338
\(416\) −12573.0 + 1681.10i −1.48183 + 0.198132i
\(417\) −6967.00 −0.818167
\(418\) 1922.32 + 2133.22i 0.224937 + 0.249615i
\(419\) 3904.87 9427.19i 0.455287 1.09916i −0.514997 0.857192i \(-0.672207\pi\)
0.970284 0.241968i \(-0.0777930\pi\)
\(420\) −3350.32 + 2717.52i −0.389235 + 0.315717i
\(421\) 10566.0 4376.59i 1.22318 0.506656i 0.324758 0.945797i \(-0.394717\pi\)
0.898418 + 0.439141i \(0.144717\pi\)
\(422\) 3269.45 1159.26i 0.377143 0.133725i
\(423\) 155.292 155.292i 0.0178501 0.0178501i
\(424\) 5815.33 9515.62i 0.666079 1.08990i
\(425\) −5416.61 5416.61i −0.618222 0.618222i
\(426\) −4143.77 1974.43i −0.471283 0.224557i
\(427\) −1325.29 3199.53i −0.150199 0.362614i
\(428\) −1913.30 + 568.428i −0.216082 + 0.0641962i
\(429\) 3250.44 + 1346.37i 0.365810 + 0.151523i
\(430\) 2245.60 + 116.777i 0.251843 + 0.0130965i
\(431\) 16965.2i 1.89602i 0.318242 + 0.948010i \(0.396908\pi\)
−0.318242 + 0.948010i \(0.603092\pi\)
\(432\) −9020.28 + 1686.89i −1.00460 + 0.187871i
\(433\) 5628.82i 0.624720i −0.949964 0.312360i \(-0.898880\pi\)
0.949964 0.312360i \(-0.101120\pi\)
\(434\) 782.585 15048.9i 0.0865560 1.66445i
\(435\) 3468.86 + 1436.85i 0.382342 + 0.158371i
\(436\) 3541.16 6534.58i 0.388969 0.717775i
\(437\) 3979.55 + 9607.49i 0.435625 + 1.05169i
\(438\) −7002.90 + 14697.2i −0.763953 + 1.60333i
\(439\) 6003.38 + 6003.38i 0.652678 + 0.652678i 0.953637 0.300959i \(-0.0973068\pi\)
−0.300959 + 0.953637i \(0.597307\pi\)
\(440\) 185.633 1181.30i 0.0201130 0.127992i
\(441\) 47.5859 47.5859i 0.00513831 0.00513831i
\(442\) 5258.67 + 14831.0i 0.565903 + 1.59601i
\(443\) 1448.22 599.872i 0.155321 0.0643359i −0.303669 0.952778i \(-0.598212\pi\)
0.458989 + 0.888442i \(0.348212\pi\)
\(444\) −8986.35 937.166i −0.960526 0.100171i
\(445\) −1675.58 + 4045.20i −0.178494 + 0.430923i
\(446\) 6515.17 5871.05i 0.691709 0.623324i
\(447\) 6329.34 0.669726
\(448\) 4648.94 + 9069.67i 0.490272 + 0.956477i
\(449\) −12533.6 −1.31737 −0.658683 0.752421i \(-0.728886\pi\)
−0.658683 + 0.752421i \(0.728886\pi\)
\(450\) 256.267 230.931i 0.0268457 0.0241916i
\(451\) 1127.29 2721.51i 0.117698 0.284149i
\(452\) −9187.19 958.110i −0.956037 0.0997029i
\(453\) −7856.00 + 3254.06i −0.814806 + 0.337504i
\(454\) 4103.02 + 11571.7i 0.424150 + 1.19623i
\(455\) −5266.90 + 5266.90i −0.542672 + 0.542672i
\(456\) 11632.9 + 1828.03i 1.19465 + 0.187731i
\(457\) 11661.6 + 11661.6i 1.19367 + 1.19367i 0.976029 + 0.217641i \(0.0698361\pi\)
0.217641 + 0.976029i \(0.430164\pi\)
\(458\) 3915.01 8216.54i 0.399425 0.838283i
\(459\) 4356.35 + 10517.2i 0.443000 + 1.06950i
\(460\) 2063.24 3807.34i 0.209128 0.385909i
\(461\) −8424.31 3489.46i −0.851104 0.352539i −0.0858823 0.996305i \(-0.527371\pi\)
−0.765222 + 0.643766i \(0.777371\pi\)
\(462\) 146.801 2822.93i 0.0147831 0.284274i
\(463\) 11549.8i 1.15932i −0.814860 0.579658i \(-0.803186\pi\)
0.814860 0.579658i \(-0.196814\pi\)
\(464\) 5012.53 7318.58i 0.501510 0.732234i
\(465\) 7250.49i 0.723083i
\(466\) −6352.81 330.364i −0.631520 0.0328408i
\(467\) −6314.42 2615.52i −0.625689 0.259169i 0.0472314 0.998884i \(-0.484960\pi\)
−0.672920 + 0.739715i \(0.734960\pi\)
\(468\) −679.287 + 201.811i −0.0670941 + 0.0199331i
\(469\) −4214.24 10174.1i −0.414916 1.00170i
\(470\) 2368.88 + 1128.72i 0.232486 + 0.110775i
\(471\) −1756.35 1756.35i −0.171823 0.171823i
\(472\) −13123.3 8020.10i −1.27976 0.782108i
\(473\) −1041.89 + 1041.89i −0.101282 + 0.101282i
\(474\) 7470.13 2648.71i 0.723870 0.256665i
\(475\) −9144.51 + 3787.78i −0.883324 + 0.365885i
\(476\) 9818.95 7964.37i 0.945485 0.766904i
\(477\) 238.409 575.569i 0.0228847 0.0552484i
\(478\) −11688.5 12970.9i −1.11846 1.24116i
\(479\) −10874.6 −1.03731 −0.518655 0.854983i \(-0.673567\pi\)
−0.518655 + 0.854983i \(0.673567\pi\)
\(480\) −2460.42 4241.77i −0.233963 0.403353i
\(481\) −15600.4 −1.47883
\(482\) 2718.98 + 3017.28i 0.256942 + 0.285132i
\(483\) 3917.43 9457.52i 0.369046 0.890957i
\(484\) −6214.08 7661.08i −0.583591 0.719486i
\(485\) −4499.62 + 1863.81i −0.421273 + 0.174497i
\(486\) −944.736 + 334.978i −0.0881771 + 0.0312652i
\(487\) 538.006 538.006i 0.0500603 0.0500603i −0.681633 0.731694i \(-0.738730\pi\)
0.731694 + 0.681633i \(0.238730\pi\)
\(488\) 3826.77 923.631i 0.354979 0.0856779i
\(489\) 8680.37 + 8680.37i 0.802741 + 0.802741i
\(490\) 725.891 + 345.873i 0.0669233 + 0.0318876i
\(491\) 1701.48 + 4107.75i 0.156389 + 0.377556i 0.982582 0.185831i \(-0.0594978\pi\)
−0.826193 + 0.563387i \(0.809498\pi\)
\(492\) −3440.21 11579.6i −0.315237 1.06108i
\(493\) −10166.4 4211.04i −0.928742 0.384697i
\(494\) 20304.9 + 1055.91i 1.84932 + 0.0961697i
\(495\) 66.8023i 0.00606574i
\(496\) 16761.0 + 3534.38i 1.51732 + 0.319956i
\(497\) 6367.77i 0.574716i
\(498\) 111.292 2140.12i 0.0100143 0.192573i
\(499\) 19571.5 + 8106.78i 1.75579 + 0.727273i 0.997123 + 0.0757967i \(0.0241500\pi\)
0.758669 + 0.651476i \(0.225850\pi\)
\(500\) 8318.68 + 4507.98i 0.744045 + 0.403206i
\(501\) −2068.17 4993.00i −0.184429 0.445251i
\(502\) −6296.31 + 13214.2i −0.559797 + 1.17486i
\(503\) −373.535 373.535i −0.0331115 0.0331115i 0.690357 0.723469i \(-0.257453\pi\)
−0.723469 + 0.690357i \(0.757453\pi\)
\(504\) 335.215 + 460.210i 0.0296263 + 0.0406734i
\(505\) −3959.43 + 3959.43i −0.348896 + 0.348896i
\(506\) 948.294 + 2674.47i 0.0833139 + 0.234969i
\(507\) 12717.8 5267.90i 1.11404 0.461451i
\(508\) 790.876 7583.60i 0.0690737 0.662338i
\(509\) 874.883 2112.15i 0.0761857 0.183928i −0.881198 0.472747i \(-0.843262\pi\)
0.957384 + 0.288819i \(0.0932624\pi\)
\(510\) −4518.96 + 4072.19i −0.392358 + 0.353568i
\(511\) 22585.2 1.95521
\(512\) −11005.1 + 3620.06i −0.949927 + 0.312472i
\(513\) 14709.1 1.26593
\(514\) 517.866 466.667i 0.0444399 0.0400463i
\(515\) 1016.33 2453.64i 0.0869609 0.209942i
\(516\) −626.741 + 6009.73i −0.0534704 + 0.512720i
\(517\) −1588.57 + 658.008i −0.135136 + 0.0559751i
\(518\) 4188.77 + 11813.5i 0.355297 + 1.00204i
\(519\) −724.701 + 724.701i −0.0612926 + 0.0612926i
\(520\) −4985.04 6843.86i −0.420401 0.577160i
\(521\) 15352.0 + 15352.0i 1.29095 + 1.29095i 0.934203 + 0.356743i \(0.116113\pi\)
0.356743 + 0.934203i \(0.383887\pi\)
\(522\) 213.158 447.359i 0.0178729 0.0375103i
\(523\) −2376.45 5737.26i −0.198690 0.479680i 0.792860 0.609404i \(-0.208591\pi\)
−0.991550 + 0.129723i \(0.958591\pi\)
\(524\) −485.121 262.892i −0.0404439 0.0219170i
\(525\) 9001.77 + 3728.65i 0.748323 + 0.309965i
\(526\) −717.625 + 13799.7i −0.0594866 + 1.14391i
\(527\) 21249.4i 1.75643i
\(528\) 3144.10 + 662.993i 0.259147 + 0.0546460i
\(529\) 1890.92i 0.155414i
\(530\) 7433.65 + 386.571i 0.609240 + 0.0316822i
\(531\) −793.785 328.796i −0.0648726 0.0268711i
\(532\) −4652.36 15659.7i −0.379146 1.27619i
\(533\) −7981.84 19269.9i −0.648653 1.56599i
\(534\) −10621.4 5060.89i −0.860737 0.410124i
\(535\) −942.053 942.053i −0.0761280 0.0761280i
\(536\) 12168.6 2937.02i 0.980605 0.236679i
\(537\) −5860.27 + 5860.27i −0.470930 + 0.470930i
\(538\) −7535.86 + 2672.02i −0.603893 + 0.214124i
\(539\) −486.782 + 201.632i −0.0389002 + 0.0161130i
\(540\) −3858.59 4757.10i −0.307495 0.379098i
\(541\) 2381.59 5749.66i 0.189265 0.456926i −0.800553 0.599261i \(-0.795461\pi\)
0.989819 + 0.142335i \(0.0454610\pi\)
\(542\) 6559.84 + 7279.53i 0.519870 + 0.576905i
\(543\) −10239.6 −0.809252
\(544\) 7210.89 + 12431.6i 0.568317 + 0.979779i
\(545\) 4960.99 0.389918
\(546\) −13398.7 14868.6i −1.05020 1.16542i
\(547\) −2560.31 + 6181.14i −0.200130 + 0.483156i −0.991801 0.127791i \(-0.959211\pi\)
0.791671 + 0.610947i \(0.209211\pi\)
\(548\) −16786.4 + 13615.8i −1.30854 + 1.06139i
\(549\) 203.178 84.1589i 0.0157949 0.00654247i
\(550\) −2545.58 + 902.596i −0.197353 + 0.0699760i
\(551\) −10054.0 + 10054.0i −0.777338 + 0.777338i
\(552\) 9929.02 + 6067.98i 0.765593 + 0.467881i
\(553\) −7774.85 7774.85i −0.597866 0.597866i
\(554\) −7915.60 3771.62i −0.607043 0.289244i
\(555\) −2307.87 5571.69i −0.176511 0.426135i
\(556\) −10531.7 + 3128.89i −0.803316 + 0.238659i
\(557\) 10306.9 + 4269.27i 0.784055 + 0.324766i 0.738551 0.674198i \(-0.235511\pi\)
0.0455041 + 0.998964i \(0.485511\pi\)
\(558\) 955.641 + 49.6960i 0.0725009 + 0.00377025i
\(559\) 10432.9i 0.789384i
\(560\) −3844.09 + 5612.58i −0.290075 + 0.423526i
\(561\) 3986.05i 0.299984i
\(562\) −666.897 + 12824.2i −0.0500558 + 0.962559i
\(563\) −8478.56 3511.93i −0.634687 0.262896i 0.0420563 0.999115i \(-0.486609\pi\)
−0.676743 + 0.736219i \(0.736609\pi\)
\(564\) −3359.49 + 6199.35i −0.250816 + 0.462836i
\(565\) −2359.45 5696.21i −0.175686 0.424144i
\(566\) 3308.54 6943.72i 0.245704 0.515665i
\(567\) −9758.15 9758.15i −0.722758 0.722758i
\(568\) −7150.68 1123.68i −0.528232 0.0830078i
\(569\) 304.321 304.321i 0.0224214 0.0224214i −0.695807 0.718229i \(-0.744953\pi\)
0.718229 + 0.695807i \(0.244953\pi\)
\(570\) 2626.73 + 7408.15i 0.193020 + 0.544374i
\(571\) 7459.96 3090.02i 0.546742 0.226468i −0.0921763 0.995743i \(-0.529382\pi\)
0.638918 + 0.769275i \(0.279382\pi\)
\(572\) 5518.20 + 575.480i 0.403370 + 0.0420665i
\(573\) 2930.16 7074.04i 0.213629 0.515746i
\(574\) −12449.2 + 11218.4i −0.905257 + 0.815760i
\(575\) −9780.88 −0.709376
\(576\) −575.945 + 295.219i −0.0416627 + 0.0213555i
\(577\) −11616.3 −0.838118 −0.419059 0.907959i \(-0.637640\pi\)
−0.419059 + 0.907959i \(0.637640\pi\)
\(578\) 2920.91 2632.13i 0.210197 0.189416i
\(579\) 7038.82 16993.2i 0.505221 1.21971i
\(580\) 5889.00 + 614.150i 0.421599 + 0.0439676i
\(581\) −2746.65 + 1137.70i −0.196128 + 0.0812389i
\(582\) −4373.58 12334.8i −0.311496 0.878510i
\(583\) −3449.00 + 3449.00i −0.245014 + 0.245014i
\(584\) −3985.46 + 25362.0i −0.282396 + 1.79707i
\(585\) −334.460 334.460i −0.0236380 0.0236380i
\(586\) 9565.96 20076.3i 0.674345 1.41526i
\(587\) 6654.96 + 16066.5i 0.467938 + 1.12970i 0.965062 + 0.262023i \(0.0843897\pi\)
−0.497123 + 0.867680i \(0.665610\pi\)
\(588\) −1029.44 + 1899.65i −0.0721997 + 0.133232i
\(589\) −25366.7 10507.2i −1.77456 0.735048i
\(590\) 533.131 10252.0i 0.0372011 0.715368i
\(591\) 9688.04i 0.674302i
\(592\) −14005.2 + 2619.11i −0.972311 + 0.181832i
\(593\) 9365.10i 0.648530i 0.945966 + 0.324265i \(0.105117\pi\)
−0.945966 + 0.324265i \(0.894883\pi\)
\(594\) 4008.27 + 208.441i 0.276871 + 0.0143981i
\(595\) 7796.53 + 3229.43i 0.537187 + 0.222510i
\(596\) 9567.78 2842.51i 0.657570 0.195359i
\(597\) 5514.93 + 13314.2i 0.378076 + 0.912756i
\(598\) 18138.1 + 8642.46i 1.24034 + 0.590998i
\(599\) 12280.1 + 12280.1i 0.837647 + 0.837647i 0.988549 0.150902i \(-0.0482177\pi\)
−0.150902 + 0.988549i \(0.548218\pi\)
\(600\) −5775.56 + 9450.55i −0.392977 + 0.643028i
\(601\) 11681.6 11681.6i 0.792852 0.792852i −0.189105 0.981957i \(-0.560559\pi\)
0.981957 + 0.189105i \(0.0605587\pi\)
\(602\) 7900.45 2801.29i 0.534881 0.189654i
\(603\) 646.078 267.614i 0.0436324 0.0180731i
\(604\) −10414.2 + 8447.16i −0.701567 + 0.569056i
\(605\) 2519.71 6083.12i 0.169324 0.408784i
\(606\) −10072.5 11177.6i −0.675197 0.749273i
\(607\) −20354.6 −1.36107 −0.680535 0.732716i \(-0.738253\pi\)
−0.680535 + 0.732716i \(0.738253\pi\)
\(608\) 18405.9 2461.01i 1.22773 0.164157i
\(609\) 13996.5 0.931309
\(610\) 1759.03 + 1952.01i 0.116756 + 0.129565i
\(611\) −4659.07 + 11248.0i −0.308487 + 0.744754i
\(612\) 505.756 + 623.526i 0.0334052 + 0.0411839i
\(613\) 23946.8 9919.08i 1.57782 0.653553i 0.589751 0.807585i \(-0.299226\pi\)
0.988066 + 0.154032i \(0.0492260\pi\)
\(614\) −3046.43 + 1080.18i −0.200234 + 0.0709977i
\(615\) 5701.45 5701.45i 0.373829 0.373829i
\(616\) −1045.87 4333.23i −0.0684081 0.283427i
\(617\) −17139.4 17139.4i −1.11833 1.11833i −0.991987 0.126340i \(-0.959677\pi\)
−0.126340 0.991987i \(-0.540323\pi\)
\(618\) 6442.48 + 3069.71i 0.419344 + 0.199809i
\(619\) −9612.31 23206.2i −0.624154 1.50684i −0.846783 0.531938i \(-0.821464\pi\)
0.222629 0.974903i \(-0.428536\pi\)
\(620\) 3256.20 + 10960.2i 0.210923 + 0.709958i
\(621\) 13428.7 + 5562.35i 0.867753 + 0.359435i
\(622\) −8605.77 447.524i −0.554759 0.0288490i
\(623\) 16322.0i 1.04964i
\(624\) 19061.1 12422.2i 1.22284 0.796934i
\(625\) 5745.29i 0.367699i
\(626\) 760.222 14618.9i 0.0485377 0.933366i
\(627\) −4758.39 1970.99i −0.303081 0.125540i
\(628\) −3443.78 1866.22i −0.218824 0.118583i
\(629\) 6763.80 + 16329.2i 0.428760 + 1.03512i
\(630\) −163.470 + 343.078i −0.0103378 + 0.0216961i
\(631\) 2243.98 + 2243.98i 0.141571 + 0.141571i 0.774340 0.632769i \(-0.218082\pi\)
−0.632769 + 0.774340i \(0.718082\pi\)
\(632\) 10102.7 7358.78i 0.635862 0.463159i
\(633\) −4399.46 + 4399.46i −0.276245 + 0.276245i
\(634\) −7673.97 21642.9i −0.480714 1.35575i
\(635\) 4701.96 1947.62i 0.293845 0.121715i
\(636\) −2074.71 + 19894.1i −0.129352 + 1.24034i
\(637\) −1427.67 + 3446.70i −0.0888010 + 0.214385i
\(638\) −2882.21 + 2597.26i −0.178852 + 0.161170i
\(639\) −404.369 −0.0250338
\(640\) −5624.30 5307.12i −0.347375 0.327785i
\(641\) 19815.9 1.22103 0.610515 0.792005i \(-0.290963\pi\)
0.610515 + 0.792005i \(0.290963\pi\)
\(642\) 2659.45 2396.52i 0.163489 0.147326i
\(643\) −5189.74 + 12529.1i −0.318295 + 0.768431i 0.681050 + 0.732237i \(0.261524\pi\)
−0.999345 + 0.0361945i \(0.988476\pi\)
\(644\) 1674.43 16055.8i 0.102456 0.982436i
\(645\) −3726.13 + 1543.42i −0.227467 + 0.0942200i
\(646\) −7698.29 21711.4i −0.468863 1.32233i
\(647\) 18031.1 18031.1i 1.09563 1.09563i 0.100717 0.994915i \(-0.467886\pi\)
0.994915 0.100717i \(-0.0321136\pi\)
\(648\) 12679.8 9235.94i 0.768690 0.559910i
\(649\) 4756.62 + 4756.62i 0.287694 + 0.287694i
\(650\) −8225.98 + 17264.1i −0.496384 + 1.04177i
\(651\) 10343.2 + 24970.8i 0.622708 + 1.50335i
\(652\) 17020.1 + 9223.37i 1.02233 + 0.554011i
\(653\) 4031.36 + 1669.85i 0.241592 + 0.100071i 0.500194 0.865913i \(-0.333262\pi\)
−0.258602 + 0.965984i \(0.583262\pi\)
\(654\) −692.300 + 13312.7i −0.0413931 + 0.795978i
\(655\) 368.299i 0.0219704i
\(656\) −10400.8 15959.4i −0.619031 0.949862i
\(657\) 1434.22i 0.0851660i
\(658\) 9768.64 + 507.997i 0.578756 + 0.0300969i
\(659\) −16047.0 6646.88i −0.948561 0.392907i −0.145871 0.989304i \(-0.546599\pi\)
−0.802690 + 0.596397i \(0.796599\pi\)
\(660\) 610.812 + 2055.97i 0.0360240 + 0.121255i
\(661\) 6313.25 + 15241.5i 0.371493 + 0.896864i 0.993498 + 0.113850i \(0.0363185\pi\)
−0.622005 + 0.783014i \(0.713682\pi\)
\(662\) −15833.3 7544.23i −0.929573 0.442923i
\(663\) −19957.0 19957.0i −1.16903 1.16903i
\(664\) −792.896 3285.11i −0.0463409 0.191999i
\(665\) 7710.34 7710.34i 0.449615 0.449615i
\(666\) −750.188 + 265.996i −0.0436474 + 0.0154762i
\(667\) −12980.8 + 5376.81i −0.753550 + 0.312131i
\(668\) −5368.72 6618.88i −0.310961 0.383372i
\(669\) −6019.70 + 14532.8i −0.347885 + 0.839869i
\(670\) 5593.47 + 6207.13i 0.322529 + 0.357914i
\(671\) −1721.81 −0.0990609
\(672\) −14524.8 11098.8i −0.833792 0.637120i
\(673\) 9059.04 0.518871 0.259436 0.965760i \(-0.416463\pi\)
0.259436 + 0.965760i \(0.416463\pi\)
\(674\) 10441.8 + 11587.4i 0.596742 + 0.662212i
\(675\) −5294.30 + 12781.6i −0.301893 + 0.728834i
\(676\) 16859.2 13674.8i 0.959214 0.778040i
\(677\) 1398.12 579.121i 0.0793710 0.0328765i −0.342645 0.939465i \(-0.611323\pi\)
0.422016 + 0.906589i \(0.361323\pi\)
\(678\) 15615.0 5536.64i 0.884497 0.313619i
\(679\) −12837.9 + 12837.9i −0.725588 + 0.725588i
\(680\) −5002.28 + 8185.22i −0.282101 + 0.461601i
\(681\) −15571.2 15571.2i −0.876199 0.876199i
\(682\) −6763.61 3222.73i −0.379754 0.180945i
\(683\) −11645.5 28114.8i −0.652422 1.57509i −0.809252 0.587462i \(-0.800127\pi\)
0.156830 0.987626i \(-0.449873\pi\)
\(684\) 994.425 295.436i 0.0555889 0.0165150i
\(685\) −13328.9 5521.01i −0.743462 0.307952i
\(686\) −16292.1 847.236i −0.906758 0.0471540i
\(687\) 16324.6i 0.906582i
\(688\) 1751.56 + 9366.11i 0.0970605 + 0.519011i
\(689\) 34536.3i 1.90962i
\(690\) −403.365 + 7756.60i −0.0222549 + 0.427955i
\(691\) −4362.78 1807.12i −0.240185 0.0994879i 0.259344 0.965785i \(-0.416494\pi\)
−0.499529 + 0.866297i \(0.666494\pi\)
\(692\) −770.034 + 1420.96i −0.0423010 + 0.0780591i
\(693\) −95.2972 230.068i −0.00522372 0.0126112i
\(694\) 12277.3 25766.8i 0.671529 1.40936i
\(695\) −5185.49 5185.49i −0.283017 0.283017i
\(696\) −2469.87 + 15717.4i −0.134512 + 0.855984i
\(697\) −16709.5 + 16709.5i −0.908061 + 0.908061i
\(698\) −4555.16 12846.9i −0.247013 0.696650i
\(699\) 10541.3 4366.33i 0.570396 0.236266i
\(700\) 15282.1 + 1593.74i 0.825157 + 0.0860537i
\(701\) 6417.56 15493.3i 0.345774 0.834773i −0.651335 0.758790i \(-0.725791\pi\)
0.997109 0.0759825i \(-0.0242093\pi\)
\(702\) 21111.9 19024.7i 1.13507 1.02285i
\(703\) 22837.8 1.22524
\(704\) 5050.55 409.804i 0.270383 0.0219390i
\(705\) −4706.48 −0.251428
\(706\) −15430.4 + 13904.9i −0.822565 + 0.741242i
\(707\) −7987.97 + 19284.7i −0.424920 + 1.02585i
\(708\) 27436.6 + 2861.30i 1.45640 + 0.151885i
\(709\) −17513.4 + 7254.29i −0.927686 + 0.384260i −0.794800 0.606871i \(-0.792424\pi\)
−0.132886 + 0.991131i \(0.542424\pi\)
\(710\) −1614.63 4553.74i −0.0853466 0.240702i
\(711\) 493.721 493.721i 0.0260422 0.0260422i
\(712\) −18328.8 2880.23i −0.964746 0.151603i
\(713\) −19185.2 19185.2i −1.00770 1.00770i
\(714\) −9754.12 + 20471.2i −0.511259 + 1.07299i
\(715\) 1417.18 + 3421.38i 0.0741252 + 0.178954i
\(716\) −6226.85 + 11490.6i −0.325012 + 0.599752i
\(717\) 28933.1 + 11984.5i 1.50701 + 0.624224i
\(718\) −869.837 + 16726.7i −0.0452118 + 0.869410i
\(719\) 4682.98i 0.242901i −0.992598 0.121450i \(-0.961245\pi\)
0.992598 0.121450i \(-0.0387545\pi\)
\(720\) −356.412 244.108i −0.0184482 0.0126353i
\(721\) 9900.21i 0.511377i
\(722\) −10350.9 538.276i −0.533547 0.0277459i
\(723\) −6730.40 2787.82i −0.346205 0.143403i
\(724\) −15478.8 + 4598.63i −0.794564 + 0.236059i
\(725\) −5117.71 12355.2i −0.262161 0.632913i
\(726\) 15972.4 + 7610.50i 0.816515 + 0.389053i
\(727\) 20269.6 + 20269.6i 1.03405 + 1.03405i 0.999399 + 0.0346553i \(0.0110333\pi\)
0.0346553 + 0.999399i \(0.488967\pi\)
\(728\) −26931.7 16458.9i −1.37109 0.837922i
\(729\) 14507.1 14507.1i 0.737039 0.737039i
\(730\) −16151.2 + 5726.78i −0.818881 + 0.290353i
\(731\) 10920.4 4523.37i 0.552537 0.228868i
\(732\) −5483.66 + 4447.92i −0.276888 + 0.224590i
\(733\) 1705.29 4116.94i 0.0859297 0.207453i −0.875073 0.483990i \(-0.839187\pi\)
0.961003 + 0.276538i \(0.0891870\pi\)
\(734\) 17479.2 + 19396.8i 0.878976 + 0.975410i
\(735\) −1442.20 −0.0723758
\(736\) 17734.4 + 4713.56i 0.888178 + 0.236065i
\(737\) −5475.14 −0.273649
\(738\) −712.393 790.551i −0.0355333 0.0394317i
\(739\) −467.052 + 1127.56i −0.0232487 + 0.0561273i −0.935078 0.354443i \(-0.884670\pi\)
0.911829 + 0.410570i \(0.134670\pi\)
\(740\) −5990.96 7386.01i −0.297611 0.366912i
\(741\) −33692.1 + 13955.7i −1.67033 + 0.691872i
\(742\) 26153.0 9273.16i 1.29395 0.458798i
\(743\) 27671.7 27671.7i 1.36632 1.36632i 0.500701 0.865620i \(-0.333076\pi\)
0.865620 0.500701i \(-0.166924\pi\)
\(744\) −29866.1 + 7208.49i −1.47170 + 0.355210i
\(745\) 4710.89 + 4710.89i 0.231669 + 0.231669i
\(746\) 781.418 + 372.330i 0.0383509 + 0.0182734i
\(747\) −72.2467 174.419i −0.00353865 0.00854305i
\(748\) −1790.14 6025.53i −0.0875053 0.294539i
\(749\) −4588.33 1900.55i −0.223837 0.0927163i
\(750\) −16947.4 881.314i −0.825111 0.0429081i
\(751\) 22288.5i 1.08298i −0.840707 0.541490i \(-0.817860\pi\)
0.840707 0.541490i \(-0.182140\pi\)
\(752\) −2294.26 + 10880.0i −0.111254 + 0.527598i
\(753\) 26253.9i 1.27058i
\(754\) −1426.66 + 27434.2i −0.0689068 + 1.32506i
\(755\) −8269.15 3425.19i −0.398603 0.165107i
\(756\) −20075.3 10879.0i −0.965782 0.523367i
\(757\) 10902.9 + 26321.9i 0.523478 + 1.26379i 0.935730 + 0.352718i \(0.114742\pi\)
−0.412252 + 0.911070i \(0.635258\pi\)
\(758\) −4040.26 + 8479.39i −0.193600 + 0.406313i
\(759\) −3598.84 3598.84i −0.172108 0.172108i
\(760\) 7297.72 + 10018.9i 0.348311 + 0.478189i
\(761\) −6249.83 + 6249.83i −0.297709 + 0.297709i −0.840116 0.542407i \(-0.817513\pi\)
0.542407 + 0.840116i \(0.317513\pi\)
\(762\) 4570.25 + 12889.4i 0.217274 + 0.612776i
\(763\) 17085.7 7077.13i 0.810673 0.335792i
\(764\) 1252.44 12009.5i 0.0593084 0.568700i
\(765\) −205.076 + 495.098i −0.00969222 + 0.0233991i
\(766\) −2899.54 + 2612.88i −0.136769 + 0.123247i
\(767\) 47630.1 2.24227
\(768\) 15026.4 14352.1i 0.706016 0.674333i
\(769\) 5109.01 0.239578 0.119789 0.992799i \(-0.461778\pi\)
0.119789 + 0.992799i \(0.461778\pi\)
\(770\) 2210.35 1991.83i 0.103449 0.0932215i
\(771\) −478.483 + 1155.16i −0.0223504 + 0.0539586i
\(772\) 3008.60 28849.0i 0.140261 1.34495i
\(773\) 119.699 49.5811i 0.00556958 0.00230699i −0.379897 0.925029i \(-0.624041\pi\)
0.385466 + 0.922722i \(0.374041\pi\)
\(774\) 177.888 + 501.697i 0.00826106 + 0.0232986i
\(775\) 18260.7 18260.7i 0.846379 0.846379i
\(776\) −12150.9 16681.7i −0.562103 0.771701i
\(777\) −15896.7 15896.7i −0.733963 0.733963i
\(778\) −1685.46 + 3537.32i −0.0776693 + 0.163007i
\(779\) 11684.8 + 28209.6i 0.537422 + 1.29745i
\(780\) 13351.8 + 7235.49i 0.612912 + 0.332143i
\(781\) 2924.95 + 1211.55i 0.134011 + 0.0555094i
\(782\) 1182.16 22732.7i 0.0540589 1.03954i
\(783\) 19873.6i 0.907055i
\(784\) −703.024 + 3333.94i −0.0320255 + 0.151874i
\(785\) 2614.48i 0.118872i
\(786\) 988.325 + 51.3957i 0.0448504 + 0.00233234i
\(787\) −24341.3 10082.5i −1.10251 0.456674i −0.244157 0.969736i \(-0.578511\pi\)
−0.858352 + 0.513062i \(0.828511\pi\)
\(788\) 4350.91 + 14645.0i 0.196694 + 0.662063i
\(789\) −9484.67 22898.0i −0.427963 1.03319i
\(790\) 7531.38 + 3588.55i 0.339183 + 0.161614i
\(791\) −16251.9 16251.9i −0.730533 0.730533i
\(792\) 275.171 66.4153i 0.0123457 0.00297975i
\(793\) −8620.64 + 8620.64i −0.386038 + 0.386038i
\(794\) 2038.91 722.941i 0.0911311 0.0323126i
\(795\) −12334.7 + 5109.20i −0.550273 + 0.227930i
\(796\) 14316.1 + 17649.8i 0.637464 + 0.785904i
\(797\) 9871.79 23832.6i 0.438741 1.05921i −0.537643 0.843173i \(-0.680685\pi\)
0.976384 0.216042i \(-0.0693149\pi\)
\(798\) 19614.6 + 21766.6i 0.870113 + 0.965574i
\(799\) 13793.5 0.610739
\(800\) −4486.41 + 16879.8i −0.198273 + 0.745988i
\(801\) −1036.49 −0.0457209
\(802\) 18330.0 + 20340.9i 0.807049 + 0.895591i
\(803\) 4297.14 10374.2i 0.188845 0.455913i
\(804\) −17437.3 + 14143.8i −0.764884 + 0.620414i
\(805\) 9954.90 4123.45i 0.435856 0.180537i
\(806\) −49998.8 + 17728.2i −2.18503 + 0.774752i
\(807\) 10140.5 10140.5i 0.442332 0.442332i
\(808\) −20246.1 12373.1i −0.881504 0.538719i
\(809\) 12475.0 + 12475.0i 0.542147 + 0.542147i 0.924158 0.382011i \(-0.124768\pi\)
−0.382011 + 0.924158i \(0.624768\pi\)
\(810\) 9452.57 + 4503.96i 0.410037 + 0.195374i
\(811\) −711.024 1716.56i −0.0307860 0.0743239i 0.907739 0.419536i \(-0.137807\pi\)
−0.938525 + 0.345212i \(0.887807\pi\)
\(812\) 21157.9 6285.85i 0.914405 0.271663i
\(813\) −16237.8 6725.93i −0.700475 0.290146i
\(814\) 6223.36 + 323.632i 0.267971 + 0.0139353i
\(815\) 12921.5i 0.555362i
\(816\) −21266.9 14565.8i −0.912364 0.624883i
\(817\) 15273.0i 0.654021i
\(818\) 255.746 4917.93i 0.0109315 0.210209i
\(819\) −1629.01 674.758i −0.0695021 0.0287887i
\(820\) 6058.10 11179.2i 0.257998 0.476089i
\(821\) 7001.23 + 16902.5i 0.297618 + 0.718514i 0.999978 + 0.00669143i \(0.00212996\pi\)
−0.702359 + 0.711823i \(0.747870\pi\)
\(822\) 16675.6 34997.5i 0.707577 1.48501i
\(823\) −6527.87 6527.87i −0.276485 0.276485i 0.555219 0.831704i \(-0.312634\pi\)
−0.831704 + 0.555219i \(0.812634\pi\)
\(824\) 11117.4 + 1747.02i 0.470017 + 0.0738597i
\(825\) 3425.41 3425.41i 0.144555 0.144555i
\(826\) −12788.9 36068.4i −0.538720 1.51935i
\(827\) 22099.6 9153.94i 0.929235 0.384902i 0.133847 0.991002i \(-0.457267\pi\)
0.795388 + 0.606100i \(0.207267\pi\)
\(828\) 1019.58 + 106.330i 0.0427935 + 0.00446283i
\(829\) −13794.8 + 33303.5i −0.577939 + 1.39527i 0.316720 + 0.948519i \(0.397418\pi\)
−0.894659 + 0.446749i \(0.852582\pi\)
\(830\) 1675.71 1510.05i 0.0700782 0.0631500i
\(831\) 15726.7 0.656501
\(832\) 23234.9 27338.5i 0.968181 1.13917i
\(833\) 4226.72 0.175807
\(834\) 14638.8 13191.6i 0.607795 0.547706i
\(835\) 2176.93 5255.59i 0.0902227 0.217817i
\(836\) −8078.23 842.459i −0.334200 0.0348529i
\(837\) −35455.9 + 14686.3i −1.46420 + 0.606491i
\(838\) 9644.99 + 27201.7i 0.397590 + 1.12132i
\(839\) −22145.1 + 22145.1i −0.911243 + 0.911243i −0.996370 0.0851272i \(-0.972870\pi\)
0.0851272 + 0.996370i \(0.472870\pi\)
\(840\) 1894.13 12053.6i 0.0778020 0.495104i
\(841\) 3661.61 + 3661.61i 0.150134 + 0.150134i
\(842\) −13914.2 + 29202.1i −0.569495 + 1.19521i
\(843\) −8814.20 21279.4i −0.360115 0.869395i
\(844\) −4674.67 + 8626.28i −0.190650 + 0.351811i
\(845\) 13386.7 + 5544.93i 0.544988 + 0.225741i
\(846\) −32.2590 + 620.332i −0.00131098 + 0.0252097i
\(847\) 24544.8i 0.995715i
\(848\) 5798.23 + 31004.8i 0.234802 + 1.25556i
\(849\) 13795.7i 0.557678i
\(850\) 21637.2 + 1125.20i 0.873117 + 0.0454046i
\(851\) 20849.8 + 8636.26i 0.839861 + 0.347882i
\(852\) 12445.2 3697.38i 0.500429 0.148674i
\(853\) 9655.46 + 23310.3i 0.387569 + 0.935675i 0.990454 + 0.137847i \(0.0440181\pi\)
−0.602884 + 0.797829i \(0.705982\pi\)
\(854\) 8842.75 + 4213.39i 0.354324 + 0.168828i
\(855\) 489.625 + 489.625i 0.0195846 + 0.0195846i
\(856\) 2943.89 4817.08i 0.117547 0.192342i
\(857\) −7592.18 + 7592.18i −0.302619 + 0.302619i −0.842038 0.539419i \(-0.818644\pi\)
0.539419 + 0.842038i \(0.318644\pi\)
\(858\) −9378.98 + 3325.53i −0.373185 + 0.132322i
\(859\) −39825.7 + 16496.4i −1.58188 + 0.655237i −0.988710 0.149839i \(-0.952124\pi\)
−0.593171 + 0.805076i \(0.702124\pi\)
\(860\) −4939.48 + 4006.52i −0.195855 + 0.158862i
\(861\) 11502.4 27769.3i 0.455286 1.09916i
\(862\) −32122.5 35646.7i −1.26925 1.40850i
\(863\) −48726.7 −1.92199 −0.960995 0.276565i \(-0.910804\pi\)
−0.960995 + 0.276565i \(0.910804\pi\)
\(864\) 15759.1 20623.8i 0.620527 0.812077i
\(865\) −1078.78 −0.0424042
\(866\) 10657.8 + 11827.1i 0.418207 + 0.464089i
\(867\) −2698.78 + 6515.42i −0.105715 + 0.255219i
\(868\) 26849.8 + 33102.0i 1.04993 + 1.29442i
\(869\) −5050.54 + 2092.00i −0.197155 + 0.0816644i
\(870\) −10009.2 + 3549.00i −0.390051 + 0.138302i
\(871\) −27412.5 + 27412.5i −1.06640 + 1.06640i
\(872\) 4932.25 + 20435.2i 0.191545 + 0.793604i
\(873\) −815.239 815.239i −0.0316055 0.0316055i
\(874\) −26552.9 12651.9i −1.02765 0.489654i
\(875\) 9009.35 + 21750.5i 0.348082 + 0.840344i
\(876\) −13113.9 44140.7i −0.505795 1.70248i
\(877\) 17160.7 + 7108.21i 0.660749 + 0.273691i 0.687754 0.725944i \(-0.258597\pi\)
−0.0270046 + 0.999635i \(0.508597\pi\)
\(878\) −23981.1 1247.09i −0.921780 0.0479352i
\(879\) 39887.5i 1.53057i
\(880\) 1846.67 + 2833.60i 0.0707402 + 0.108546i
\(881\) 25601.4i 0.979039i 0.871992 + 0.489520i \(0.162828\pi\)
−0.871992 + 0.489520i \(0.837172\pi\)
\(882\) −9.88505 + 190.087i −0.000377378 + 0.00725687i
\(883\) 2470.51 + 1023.32i 0.0941555 + 0.0390005i 0.429264 0.903179i \(-0.358773\pi\)
−0.335109 + 0.942180i \(0.608773\pi\)
\(884\) −39130.9 21205.4i −1.48882 0.806805i
\(885\) 7046.25 + 17011.2i 0.267635 + 0.646129i
\(886\) −1907.13 + 4002.54i −0.0723153 + 0.151770i
\(887\) −3316.04 3316.04i −0.125526 0.125526i 0.641553 0.767079i \(-0.278291\pi\)
−0.767079 + 0.641553i \(0.778291\pi\)
\(888\) 20656.3 15045.9i 0.780608 0.568591i
\(889\) 13415.2 13415.2i 0.506110 0.506110i
\(890\) −4138.66 11672.2i −0.155874 0.439611i
\(891\) −6338.89 + 2625.65i −0.238340 + 0.0987236i
\(892\) −2573.00 + 24672.1i −0.0965811 + 0.926103i
\(893\) 6820.53 16466.2i 0.255588 0.617044i
\(894\) −13299.0 + 11984.2i −0.497522 + 0.448335i
\(895\) −8723.52 −0.325805
\(896\) −26941.0 10254.4i −1.00451 0.382339i
\(897\) −36036.8 −1.34140
\(898\) 26335.2 23731.6i 0.978637 0.881885i
\(899\) 14196.4 34273.2i 0.526671 1.27150i
\(900\) −101.206 + 970.450i −0.00374837 + 0.0359426i
\(901\) 36150.0 14973.8i 1.33666 0.553662i
\(902\) 2784.39 + 7852.80i 0.102783 + 0.289878i
\(903\) −10631.1 + 10631.1i −0.391783 + 0.391783i
\(904\) 21117.9 15382.2i 0.776960 0.565934i
\(905\) −7621.28 7621.28i −0.279934 0.279934i
\(906\) 10345.4 21712.2i 0.379363 0.796179i
\(907\) −2525.01 6095.91i −0.0924382 0.223166i 0.870897 0.491465i \(-0.163538\pi\)
−0.963336 + 0.268299i \(0.913538\pi\)
\(908\) −30531.4 16545.3i −1.11588 0.604708i
\(909\) −1224.62 507.255i −0.0446844 0.0185089i
\(910\) 1094.10 21039.2i 0.0398559 0.766419i
\(911\) 4913.39i 0.178692i −0.996001 0.0893458i \(-0.971522\pi\)
0.996001 0.0893458i \(-0.0284776\pi\)
\(912\) −27904.0 + 18185.2i −1.01315 + 0.660277i
\(913\) 1478.10i 0.0535794i
\(914\) −46583.5 2422.47i −1.68583 0.0876677i
\(915\) −4354.18 1803.56i −0.157317 0.0651628i
\(916\) 7331.39 + 24677.1i 0.264450 + 0.890126i
\(917\) −525.399 1268.42i −0.0189206 0.0456784i
\(918\) −29067.0 13849.8i −1.04505 0.497944i
\(919\) −17562.4 17562.4i −0.630392 0.630392i 0.317774 0.948166i \(-0.397065\pi\)
−0.948166 + 0.317774i \(0.897065\pi\)
\(920\) 2873.75 + 11906.5i 0.102983 + 0.426679i
\(921\) 4099.37 4099.37i 0.146665 0.146665i
\(922\) 24307.9 8618.95i 0.868264 0.307863i
\(923\) 20710.3 8578.50i 0.738557 0.305920i
\(924\) 5036.59 + 6209.41i 0.179320 + 0.221077i
\(925\) −8220.09 + 19845.0i −0.292189 + 0.705406i
\(926\) 21868.8 + 24268.0i 0.776082 + 0.861227i
\(927\) 628.687 0.0222748
\(928\) 3325.10 + 24868.5i 0.117620 + 0.879684i
\(929\) 4262.05 0.150520 0.0752602 0.997164i \(-0.476021\pi\)
0.0752602 + 0.997164i \(0.476021\pi\)
\(930\) −13728.3 15234.5i −0.484054 0.537160i
\(931\) 2090.00 5045.70i 0.0735735 0.177622i
\(932\) 13973.8 11334.5i 0.491124 0.398362i
\(933\) 14279.6 5914.81i 0.501065 0.207548i
\(934\) 18220.0 6460.31i 0.638304 0.226325i
\(935\) 2966.79 2966.79i 0.103769 0.103769i
\(936\) 1045.18 1710.22i 0.0364986 0.0597227i
\(937\) 20895.1 + 20895.1i 0.728511 + 0.728511i 0.970323 0.241812i \(-0.0777419\pi\)
−0.241812 + 0.970323i \(0.577742\pi\)
\(938\) 28118.8 + 13398.0i 0.978796 + 0.466377i
\(939\) 10047.7 + 24257.2i 0.349194 + 0.843028i
\(940\) −7114.58 + 2113.69i −0.246864 + 0.0733414i
\(941\) −16995.0 7039.57i −0.588759 0.243872i 0.0683579 0.997661i \(-0.478224\pi\)
−0.657116 + 0.753789i \(0.728224\pi\)
\(942\) 7015.93 + 364.848i 0.242666 + 0.0126193i
\(943\) 30172.8i 1.04195i
\(944\) 42759.7 7996.52i 1.47427 0.275704i
\(945\) 15241.0i 0.524644i
\(946\) 216.433 4161.95i 0.00743852 0.143041i
\(947\) 36843.7 + 15261.2i 1.26427 + 0.523676i 0.911216 0.411928i \(-0.135144\pi\)
0.353050 + 0.935604i \(0.385144\pi\)
\(948\) −10680.8 + 19709.6i −0.365925 + 0.675250i
\(949\) −30426.2 73455.4i −1.04076 2.51261i
\(950\) 12042.2 25273.3i 0.411264 0.863131i
\(951\) 29123.3 + 29123.3i 0.993046 + 0.993046i
\(952\) −5551.22 + 35326.0i −0.188988 + 1.20265i
\(953\) −9331.21 + 9331.21i −0.317175 + 0.317175i −0.847681 0.530506i \(-0.822002\pi\)
0.530506 + 0.847681i \(0.322002\pi\)
\(954\) 588.867 + 1660.78i 0.0199846 + 0.0563623i
\(955\) 7446.06 3084.26i 0.252303 0.104507i
\(956\) 49119.2 + 5122.52i 1.66174 + 0.173299i
\(957\) 2663.02 6429.11i 0.0899513 0.217162i
\(958\) 22849.3 20590.3i 0.770592 0.694408i
\(959\) −53780.9 −1.81092
\(960\) 13201.3 + 4254.02i 0.443822 + 0.143019i
\(961\) 41845.8 1.40465
\(962\) 32779.0 29538.3i 1.09858 0.989971i
\(963\) 120.689 291.370i 0.00403859 0.00975001i
\(964\) −11426.1 1191.60i −0.381752 0.0398120i
\(965\) 17886.9 7408.99i 0.596683 0.247154i
\(966\) 9676.03 + 27289.2i 0.322279 + 0.908920i
\(967\) −16402.9 + 16402.9i −0.545483 + 0.545483i −0.925131 0.379648i \(-0.876045\pi\)
0.379648 + 0.925131i \(0.376045\pi\)
\(968\) 27562.6 + 4331.26i 0.915181 + 0.143814i
\(969\) 29215.6 + 29215.6i 0.968565 + 0.968565i
\(970\) 5925.46 12435.9i 0.196139 0.411642i
\(971\) −2483.25 5995.10i −0.0820714 0.198138i 0.877517 0.479546i \(-0.159199\pi\)
−0.959588 + 0.281408i \(0.909199\pi\)
\(972\) 1350.79 2492.64i 0.0445746 0.0822546i
\(973\) −25256.3 10461.5i −0.832147 0.344687i
\(974\) −111.760 + 2149.12i −0.00367662 + 0.0707004i
\(975\) 34300.2i 1.12665i
\(976\) −6291.84 + 9186.44i −0.206349 + 0.301282i
\(977\) 26525.8i 0.868613i −0.900765 0.434307i \(-0.856993\pi\)
0.900765 0.434307i \(-0.143007\pi\)
\(978\) −34674.6 1803.18i −1.13371 0.0589563i
\(979\) 7497.30 + 3105.48i 0.244754 + 0.101381i
\(980\) −2180.11 + 647.693i −0.0710622 + 0.0211120i
\(981\) 449.414 + 1084.98i 0.0146266 + 0.0353117i
\(982\) −11352.9 5409.41i −0.368925 0.175785i
\(983\) 3562.07 + 3562.07i 0.115577 + 0.115577i 0.762530 0.646953i \(-0.223957\pi\)
−0.646953 + 0.762530i \(0.723957\pi\)
\(984\) 29153.7 + 17816.9i 0.944498 + 0.577216i
\(985\) −7210.74 + 7210.74i −0.233252 + 0.233252i
\(986\) 29334.5 10401.2i 0.947467 0.335946i
\(987\) −16209.2 + 6714.06i −0.522739 + 0.216526i
\(988\) −44663.4 + 36227.5i −1.43819 + 1.16655i
\(989\) 5775.60 13943.5i 0.185696 0.448310i
\(990\) 126.486 + 140.363i 0.00406059 + 0.00450608i
\(991\) −10011.3 −0.320907 −0.160453 0.987043i \(-0.551296\pi\)
−0.160453 + 0.987043i \(0.551296\pi\)
\(992\) −41909.9 + 24309.6i −1.34137 + 0.778056i
\(993\) 31457.5 1.00531
\(994\) −12057.0 13379.8i −0.384732 0.426942i
\(995\) −5804.97 + 14014.4i −0.184955 + 0.446520i
\(996\) 3818.34 + 4707.48i 0.121475 + 0.149761i
\(997\) 19700.4 8160.16i 0.625795 0.259213i −0.0471705 0.998887i \(-0.515020\pi\)
0.672965 + 0.739674i \(0.265020\pi\)
\(998\) −56472.6 + 20023.7i −1.79119 + 0.635109i
\(999\) 22571.6 22571.6i 0.714848 0.714848i
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 32.4.g.a.13.3 yes 44
4.3 odd 2 128.4.g.a.17.3 44
8.3 odd 2 256.4.g.a.33.9 44
8.5 even 2 256.4.g.b.33.3 44
32.5 even 8 inner 32.4.g.a.5.3 44
32.11 odd 8 256.4.g.a.225.9 44
32.21 even 8 256.4.g.b.225.3 44
32.27 odd 8 128.4.g.a.113.3 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.4.g.a.5.3 44 32.5 even 8 inner
32.4.g.a.13.3 yes 44 1.1 even 1 trivial
128.4.g.a.17.3 44 4.3 odd 2
128.4.g.a.113.3 44 32.27 odd 8
256.4.g.a.33.9 44 8.3 odd 2
256.4.g.a.225.9 44 32.11 odd 8
256.4.g.b.33.3 44 8.5 even 2
256.4.g.b.225.3 44 32.21 even 8