Properties

Label 54.3.d.a.17.1
Level $54$
Weight $3$
Character 54.17
Analytic conductor $1.471$
Analytic rank $0$
Dimension $4$
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] = [54,3,Mod(17,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 54.d (of order \(6\), degree \(2\), not 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: \(1.47139342755\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 54.17
Dual form 54.3.d.a.35.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50000 + 2.59808i) q^{5} +(4.17423 + 7.22999i) q^{7} +2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50000 + 2.59808i) q^{5} +(4.17423 + 7.22999i) q^{7} +2.82843i q^{8} -7.34847 q^{10} +(-0.825765 + 0.476756i) q^{11} +(4.84847 - 8.39780i) q^{13} +(-10.2247 - 5.90326i) q^{14} +(-2.00000 - 3.46410i) q^{16} -18.8776i q^{17} -24.6969 q^{19} +(9.00000 - 5.19615i) q^{20} +(0.674235 - 1.16781i) q^{22} +(-0.825765 - 0.476756i) q^{23} +(1.00000 + 1.73205i) q^{25} +13.7135i q^{26} +16.6969 q^{28} +(-11.8485 + 6.84072i) q^{29} +(-1.52270 + 2.63740i) q^{31} +(4.89898 + 2.82843i) q^{32} +(13.3485 + 23.1202i) q^{34} +43.3799i q^{35} +46.6969 q^{37} +(30.2474 - 17.4634i) q^{38} +(-7.34847 + 12.7279i) q^{40} +(9.45459 + 5.45861i) q^{41} +(-22.5227 - 39.0105i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(-39.2196 + 22.6435i) q^{47} +(-10.3485 + 17.9241i) q^{49} +(-2.44949 - 1.41421i) q^{50} +(-9.69694 - 16.7956i) q^{52} -94.3879i q^{53} -4.95459 q^{55} +(-20.4495 + 11.8065i) q^{56} +(9.67423 - 16.7563i) q^{58} +(16.2650 + 9.39063i) q^{59} +(-6.54541 - 11.3370i) q^{61} -4.30686i q^{62} -8.00000 q^{64} +(43.6362 - 25.1934i) q^{65} +(-37.5227 + 64.9912i) q^{67} +(-32.6969 - 18.8776i) q^{68} +(-30.6742 - 53.1293i) q^{70} +18.0204i q^{71} -7.90918 q^{73} +(-57.1918 + 33.0197i) q^{74} +(-24.6969 + 42.7764i) q^{76} +(-6.89388 - 3.98018i) q^{77} +(21.8712 + 37.8820i) q^{79} -20.7846i q^{80} -15.4393 q^{82} +(112.871 - 65.1662i) q^{83} +(49.0454 - 84.9491i) q^{85} +(55.1691 + 31.8519i) q^{86} +(-1.34847 - 2.33562i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(-1.65153 + 0.953512i) q^{92} +(32.0227 - 55.4650i) q^{94} +(-111.136 - 64.1645i) q^{95} +(54.9393 + 95.1576i) q^{97} -29.2699i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7} - 18 q^{11} - 10 q^{13} - 36 q^{14} - 8 q^{16} - 40 q^{19} + 36 q^{20} - 12 q^{22} - 18 q^{23} + 4 q^{25} + 8 q^{28} - 18 q^{29} + 38 q^{31} + 24 q^{34} + 128 q^{37} + 72 q^{38} + 126 q^{41} - 46 q^{43} - 24 q^{46} - 54 q^{47} - 12 q^{49} + 20 q^{52} - 108 q^{55} - 72 q^{56} + 24 q^{58} - 126 q^{59} + 62 q^{61} - 32 q^{64} - 90 q^{65} - 106 q^{67} - 72 q^{68} - 108 q^{70} - 208 q^{73} - 72 q^{74} - 40 q^{76} + 90 q^{77} + 14 q^{79} + 144 q^{82} + 378 q^{83} + 108 q^{85} + 108 q^{86} + 24 q^{88} + 412 q^{91} - 36 q^{92} + 84 q^{94} - 180 q^{95} + 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 0.707107i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 4.50000 + 2.59808i 0.900000 + 0.519615i 0.877200 0.480125i \(-0.159409\pi\)
0.0227998 + 0.999740i \(0.492742\pi\)
\(6\) 0 0
\(7\) 4.17423 + 7.22999i 0.596319 + 1.03286i 0.993359 + 0.115054i \(0.0367041\pi\)
−0.397040 + 0.917801i \(0.629963\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −7.34847 −0.734847
\(11\) −0.825765 + 0.476756i −0.0750696 + 0.0433414i −0.537065 0.843541i \(-0.680467\pi\)
0.461995 + 0.886882i \(0.347134\pi\)
\(12\) 0 0
\(13\) 4.84847 8.39780i 0.372959 0.645984i −0.617060 0.786916i \(-0.711676\pi\)
0.990019 + 0.140932i \(0.0450098\pi\)
\(14\) −10.2247 5.90326i −0.730339 0.421661i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 18.8776i 1.11045i −0.831701 0.555223i \(-0.812633\pi\)
0.831701 0.555223i \(-0.187367\pi\)
\(18\) 0 0
\(19\) −24.6969 −1.29984 −0.649919 0.760003i \(-0.725197\pi\)
−0.649919 + 0.760003i \(0.725197\pi\)
\(20\) 9.00000 5.19615i 0.450000 0.259808i
\(21\) 0 0
\(22\) 0.674235 1.16781i 0.0306470 0.0530822i
\(23\) −0.825765 0.476756i −0.0359028 0.0207285i 0.481941 0.876204i \(-0.339932\pi\)
−0.517844 + 0.855475i \(0.673265\pi\)
\(24\) 0 0
\(25\) 1.00000 + 1.73205i 0.0400000 + 0.0692820i
\(26\) 13.7135i 0.527444i
\(27\) 0 0
\(28\) 16.6969 0.596319
\(29\) −11.8485 + 6.84072i −0.408568 + 0.235887i −0.690174 0.723643i \(-0.742466\pi\)
0.281606 + 0.959530i \(0.409133\pi\)
\(30\) 0 0
\(31\) −1.52270 + 2.63740i −0.0491195 + 0.0850774i −0.889540 0.456858i \(-0.848975\pi\)
0.840420 + 0.541935i \(0.182308\pi\)
\(32\) 4.89898 + 2.82843i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 13.3485 + 23.1202i 0.392602 + 0.680007i
\(35\) 43.3799i 1.23943i
\(36\) 0 0
\(37\) 46.6969 1.26208 0.631040 0.775751i \(-0.282628\pi\)
0.631040 + 0.775751i \(0.282628\pi\)
\(38\) 30.2474 17.4634i 0.795985 0.459562i
\(39\) 0 0
\(40\) −7.34847 + 12.7279i −0.183712 + 0.318198i
\(41\) 9.45459 + 5.45861i 0.230600 + 0.133137i 0.610849 0.791747i \(-0.290828\pi\)
−0.380249 + 0.924884i \(0.624162\pi\)
\(42\) 0 0
\(43\) −22.5227 39.0105i −0.523784 0.907220i −0.999617 0.0276845i \(-0.991187\pi\)
0.475833 0.879536i \(-0.342147\pi\)
\(44\) 1.90702i 0.0433414i
\(45\) 0 0
\(46\) 1.34847 0.0293145
\(47\) −39.2196 + 22.6435i −0.834460 + 0.481776i −0.855377 0.518005i \(-0.826675\pi\)
0.0209170 + 0.999781i \(0.493341\pi\)
\(48\) 0 0
\(49\) −10.3485 + 17.9241i −0.211193 + 0.365797i
\(50\) −2.44949 1.41421i −0.0489898 0.0282843i
\(51\) 0 0
\(52\) −9.69694 16.7956i −0.186480 0.322992i
\(53\) 94.3879i 1.78090i −0.455077 0.890452i \(-0.650388\pi\)
0.455077 0.890452i \(-0.349612\pi\)
\(54\) 0 0
\(55\) −4.95459 −0.0900835
\(56\) −20.4495 + 11.8065i −0.365169 + 0.210831i
\(57\) 0 0
\(58\) 9.67423 16.7563i 0.166797 0.288901i
\(59\) 16.2650 + 9.39063i 0.275679 + 0.159163i 0.631466 0.775404i \(-0.282454\pi\)
−0.355787 + 0.934567i \(0.615787\pi\)
\(60\) 0 0
\(61\) −6.54541 11.3370i −0.107302 0.185852i 0.807375 0.590039i \(-0.200888\pi\)
−0.914676 + 0.404187i \(0.867554\pi\)
\(62\) 4.30686i 0.0694654i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 43.6362 25.1934i 0.671327 0.387591i
\(66\) 0 0
\(67\) −37.5227 + 64.9912i −0.560040 + 0.970018i 0.437452 + 0.899242i \(0.355881\pi\)
−0.997492 + 0.0707765i \(0.977452\pi\)
\(68\) −32.6969 18.8776i −0.480837 0.277612i
\(69\) 0 0
\(70\) −30.6742 53.1293i −0.438203 0.758990i
\(71\) 18.0204i 0.253808i 0.991915 + 0.126904i \(0.0405041\pi\)
−0.991915 + 0.126904i \(0.959496\pi\)
\(72\) 0 0
\(73\) −7.90918 −0.108345 −0.0541725 0.998532i \(-0.517252\pi\)
−0.0541725 + 0.998532i \(0.517252\pi\)
\(74\) −57.1918 + 33.0197i −0.772863 + 0.446212i
\(75\) 0 0
\(76\) −24.6969 + 42.7764i −0.324960 + 0.562847i
\(77\) −6.89388 3.98018i −0.0895309 0.0516907i
\(78\) 0 0
\(79\) 21.8712 + 37.8820i 0.276850 + 0.479519i 0.970600 0.240697i \(-0.0773761\pi\)
−0.693750 + 0.720216i \(0.744043\pi\)
\(80\) 20.7846i 0.259808i
\(81\) 0 0
\(82\) −15.4393 −0.188284
\(83\) 112.871 65.1662i 1.35989 0.785135i 0.370284 0.928918i \(-0.379260\pi\)
0.989609 + 0.143783i \(0.0459269\pi\)
\(84\) 0 0
\(85\) 49.0454 84.9491i 0.577005 0.999402i
\(86\) 55.1691 + 31.8519i 0.641502 + 0.370371i
\(87\) 0 0
\(88\) −1.34847 2.33562i −0.0153235 0.0265411i
\(89\) 145.300i 1.63258i 0.577642 + 0.816290i \(0.303973\pi\)
−0.577642 + 0.816290i \(0.696027\pi\)
\(90\) 0 0
\(91\) 80.9546 0.889611
\(92\) −1.65153 + 0.953512i −0.0179514 + 0.0103643i
\(93\) 0 0
\(94\) 32.0227 55.4650i 0.340667 0.590053i
\(95\) −111.136 64.1645i −1.16985 0.675416i
\(96\) 0 0
\(97\) 54.9393 + 95.1576i 0.566384 + 0.981007i 0.996919 + 0.0784327i \(0.0249916\pi\)
−0.430535 + 0.902574i \(0.641675\pi\)
\(98\) 29.2699i 0.298672i
\(99\) 0 0
\(100\) 4.00000 0.0400000
\(101\) −127.772 + 73.7695i −1.26507 + 0.730391i −0.974052 0.226326i \(-0.927329\pi\)
−0.291022 + 0.956716i \(0.593995\pi\)
\(102\) 0 0
\(103\) 51.5681 89.3186i 0.500661 0.867171i −0.499338 0.866407i \(-0.666424\pi\)
1.00000 0.000763745i \(-0.000243108\pi\)
\(104\) 23.7526 + 13.7135i 0.228390 + 0.131861i
\(105\) 0 0
\(106\) 66.7423 + 115.601i 0.629645 + 1.09058i
\(107\) 36.0408i 0.336830i 0.985716 + 0.168415i \(0.0538649\pi\)
−0.985716 + 0.168415i \(0.946135\pi\)
\(108\) 0 0
\(109\) −148.272 −1.36030 −0.680149 0.733074i \(-0.738085\pi\)
−0.680149 + 0.733074i \(0.738085\pi\)
\(110\) 6.06811 3.50343i 0.0551647 0.0318493i
\(111\) 0 0
\(112\) 16.6969 28.9199i 0.149080 0.258214i
\(113\) 148.166 + 85.5439i 1.31121 + 0.757025i 0.982296 0.187336i \(-0.0599852\pi\)
0.328910 + 0.944361i \(0.393319\pi\)
\(114\) 0 0
\(115\) −2.47730 4.29080i −0.0215417 0.0373113i
\(116\) 27.3629i 0.235887i
\(117\) 0 0
\(118\) −26.5607 −0.225091
\(119\) 136.485 78.7995i 1.14693 0.662180i
\(120\) 0 0
\(121\) −60.0454 + 104.002i −0.496243 + 0.859518i
\(122\) 16.0329 + 9.25660i 0.131417 + 0.0758738i
\(123\) 0 0
\(124\) 3.04541 + 5.27480i 0.0245597 + 0.0425387i
\(125\) 119.512i 0.956092i
\(126\) 0 0
\(127\) −78.0908 −0.614888 −0.307444 0.951566i \(-0.599474\pi\)
−0.307444 + 0.951566i \(0.599474\pi\)
\(128\) 9.79796 5.65685i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −35.6288 + 61.7109i −0.274068 + 0.474700i
\(131\) −202.704 117.031i −1.54736 0.893369i −0.998342 0.0575598i \(-0.981668\pi\)
−0.549019 0.835810i \(-0.684999\pi\)
\(132\) 0 0
\(133\) −103.091 178.559i −0.775119 1.34255i
\(134\) 106.130i 0.792017i
\(135\) 0 0
\(136\) 53.3939 0.392602
\(137\) −129.758 + 74.9156i −0.947136 + 0.546829i −0.892190 0.451660i \(-0.850832\pi\)
−0.0549460 + 0.998489i \(0.517499\pi\)
\(138\) 0 0
\(139\) 42.2650 73.2052i 0.304065 0.526656i −0.672988 0.739654i \(-0.734989\pi\)
0.977053 + 0.212998i \(0.0683226\pi\)
\(140\) 75.1362 + 43.3799i 0.536687 + 0.309857i
\(141\) 0 0
\(142\) −12.7423 22.0704i −0.0897348 0.155425i
\(143\) 9.24614i 0.0646584i
\(144\) 0 0
\(145\) −71.0908 −0.490281
\(146\) 9.68673 5.59264i 0.0663475 0.0383057i
\(147\) 0 0
\(148\) 46.6969 80.8815i 0.315520 0.546496i
\(149\) −100.030 57.7524i −0.671343 0.387600i 0.125242 0.992126i \(-0.460029\pi\)
−0.796585 + 0.604526i \(0.793362\pi\)
\(150\) 0 0
\(151\) 32.3865 + 56.0950i 0.214480 + 0.371490i 0.953112 0.302619i \(-0.0978610\pi\)
−0.738632 + 0.674109i \(0.764528\pi\)
\(152\) 69.8535i 0.459562i
\(153\) 0 0
\(154\) 11.2577 0.0731016
\(155\) −13.7043 + 7.91220i −0.0884151 + 0.0510465i
\(156\) 0 0
\(157\) 10.4092 18.0292i 0.0663005 0.114836i −0.830970 0.556318i \(-0.812214\pi\)
0.897270 + 0.441482i \(0.145547\pi\)
\(158\) −53.5732 30.9305i −0.339071 0.195763i
\(159\) 0 0
\(160\) 14.6969 + 25.4558i 0.0918559 + 0.159099i
\(161\) 7.96036i 0.0494433i
\(162\) 0 0
\(163\) 133.060 0.816320 0.408160 0.912910i \(-0.366171\pi\)
0.408160 + 0.912910i \(0.366171\pi\)
\(164\) 18.9092 10.9172i 0.115300 0.0665684i
\(165\) 0 0
\(166\) −92.1589 + 159.624i −0.555174 + 0.961590i
\(167\) 255.053 + 147.255i 1.52726 + 0.881765i 0.999475 + 0.0323885i \(0.0103114\pi\)
0.527787 + 0.849377i \(0.323022\pi\)
\(168\) 0 0
\(169\) 37.4847 + 64.9254i 0.221803 + 0.384174i
\(170\) 138.721i 0.816008i
\(171\) 0 0
\(172\) −90.0908 −0.523784
\(173\) 59.9847 34.6322i 0.346732 0.200186i −0.316513 0.948588i \(-0.602512\pi\)
0.663245 + 0.748402i \(0.269179\pi\)
\(174\) 0 0
\(175\) −8.34847 + 14.4600i −0.0477055 + 0.0826284i
\(176\) 3.30306 + 1.90702i 0.0187674 + 0.0108354i
\(177\) 0 0
\(178\) −102.742 177.955i −0.577204 0.999747i
\(179\) 47.4829i 0.265268i 0.991165 + 0.132634i \(0.0423435\pi\)
−0.991165 + 0.132634i \(0.957657\pi\)
\(180\) 0 0
\(181\) 242.879 1.34187 0.670935 0.741516i \(-0.265893\pi\)
0.670935 + 0.741516i \(0.265893\pi\)
\(182\) −99.1487 + 57.2435i −0.544773 + 0.314525i
\(183\) 0 0
\(184\) 1.34847 2.33562i 0.00732864 0.0126936i
\(185\) 210.136 + 121.322i 1.13587 + 0.655796i
\(186\) 0 0
\(187\) 9.00000 + 15.5885i 0.0481283 + 0.0833607i
\(188\) 90.5739i 0.481776i
\(189\) 0 0
\(190\) 181.485 0.955183
\(191\) −6.52270 + 3.76588i −0.0341503 + 0.0197167i −0.516978 0.855999i \(-0.672943\pi\)
0.482828 + 0.875715i \(0.339610\pi\)
\(192\) 0 0
\(193\) −172.727 + 299.172i −0.894959 + 1.55011i −0.0611031 + 0.998131i \(0.519462\pi\)
−0.833856 + 0.551983i \(0.813871\pi\)
\(194\) −134.573 77.6959i −0.693676 0.400494i
\(195\) 0 0
\(196\) 20.6969 + 35.8481i 0.105597 + 0.182899i
\(197\) 77.2247i 0.392004i 0.980604 + 0.196002i \(0.0627959\pi\)
−0.980604 + 0.196002i \(0.937204\pi\)
\(198\) 0 0
\(199\) 153.485 0.771280 0.385640 0.922649i \(-0.373981\pi\)
0.385640 + 0.922649i \(0.373981\pi\)
\(200\) −4.89898 + 2.82843i −0.0244949 + 0.0141421i
\(201\) 0 0
\(202\) 104.326 180.698i 0.516464 0.894542i
\(203\) −98.9166 57.1095i −0.487274 0.281328i
\(204\) 0 0
\(205\) 28.3638 + 49.1275i 0.138360 + 0.239646i
\(206\) 145.857i 0.708042i
\(207\) 0 0
\(208\) −38.7878 −0.186480
\(209\) 20.3939 11.7744i 0.0975784 0.0563369i
\(210\) 0 0
\(211\) 25.7804 44.6529i 0.122182 0.211625i −0.798446 0.602066i \(-0.794344\pi\)
0.920628 + 0.390441i \(0.127678\pi\)
\(212\) −163.485 94.3879i −0.771154 0.445226i
\(213\) 0 0
\(214\) −25.4847 44.1408i −0.119087 0.206265i
\(215\) 234.063i 1.08866i
\(216\) 0 0
\(217\) −25.4245 −0.117164
\(218\) 181.596 104.844i 0.833009 0.480938i
\(219\) 0 0
\(220\) −4.95459 + 8.58161i −0.0225209 + 0.0390073i
\(221\) −158.530 91.5274i −0.717331 0.414151i
\(222\) 0 0
\(223\) −156.614 271.263i −0.702303 1.21642i −0.967656 0.252273i \(-0.918822\pi\)
0.265353 0.964151i \(-0.414511\pi\)
\(224\) 47.2261i 0.210831i
\(225\) 0 0
\(226\) −241.955 −1.07060
\(227\) 66.0528 38.1356i 0.290982 0.167998i −0.347403 0.937716i \(-0.612936\pi\)
0.638384 + 0.769718i \(0.279603\pi\)
\(228\) 0 0
\(229\) 60.7724 105.261i 0.265382 0.459655i −0.702282 0.711899i \(-0.747835\pi\)
0.967664 + 0.252244i \(0.0811686\pi\)
\(230\) 6.06811 + 3.50343i 0.0263831 + 0.0152323i
\(231\) 0 0
\(232\) −19.3485 33.5125i −0.0833986 0.144451i
\(233\) 151.021i 0.648157i −0.946030 0.324079i \(-0.894946\pi\)
0.946030 0.324079i \(-0.105054\pi\)
\(234\) 0 0
\(235\) −235.318 −1.00135
\(236\) 32.5301 18.7813i 0.137839 0.0795816i
\(237\) 0 0
\(238\) −111.439 + 193.019i −0.468232 + 0.811002i
\(239\) 75.9620 + 43.8567i 0.317833 + 0.183501i 0.650426 0.759570i \(-0.274590\pi\)
−0.332593 + 0.943070i \(0.607924\pi\)
\(240\) 0 0
\(241\) −100.894 174.753i −0.418647 0.725118i 0.577157 0.816633i \(-0.304162\pi\)
−0.995804 + 0.0915158i \(0.970829\pi\)
\(242\) 169.834i 0.701794i
\(243\) 0 0
\(244\) −26.1816 −0.107302
\(245\) −93.1362 + 53.7722i −0.380148 + 0.219478i
\(246\) 0 0
\(247\) −119.742 + 207.400i −0.484787 + 0.839675i
\(248\) −7.45969 4.30686i −0.0300794 0.0173664i
\(249\) 0 0
\(250\) 84.5074 + 146.371i 0.338030 + 0.585484i
\(251\) 52.6261i 0.209666i 0.994490 + 0.104833i \(0.0334307\pi\)
−0.994490 + 0.104833i \(0.966569\pi\)
\(252\) 0 0
\(253\) 0.909185 0.00359362
\(254\) 95.6413 55.2185i 0.376541 0.217396i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 69.8939 + 40.3532i 0.271961 + 0.157017i 0.629778 0.776775i \(-0.283146\pi\)
−0.357818 + 0.933791i \(0.616479\pi\)
\(258\) 0 0
\(259\) 194.924 + 337.618i 0.752602 + 1.30355i
\(260\) 100.774i 0.387591i
\(261\) 0 0
\(262\) 331.015 1.26342
\(263\) −401.614 + 231.872i −1.52705 + 0.881641i −0.527564 + 0.849515i \(0.676894\pi\)
−0.999484 + 0.0321259i \(0.989772\pi\)
\(264\) 0 0
\(265\) 245.227 424.746i 0.925385 1.60281i
\(266\) 252.520 + 145.792i 0.949323 + 0.548092i
\(267\) 0 0
\(268\) 75.0454 + 129.982i 0.280020 + 0.485009i
\(269\) 43.4762i 0.161622i −0.996729 0.0808109i \(-0.974249\pi\)
0.996729 0.0808109i \(-0.0257510\pi\)
\(270\) 0 0
\(271\) −342.636 −1.26434 −0.632169 0.774830i \(-0.717835\pi\)
−0.632169 + 0.774830i \(0.717835\pi\)
\(272\) −65.3939 + 37.7552i −0.240419 + 0.138806i
\(273\) 0 0
\(274\) 105.947 183.505i 0.386667 0.669726i
\(275\) −1.65153 0.953512i −0.00600557 0.00346732i
\(276\) 0 0
\(277\) 24.5000 + 42.4352i 0.0884477 + 0.153196i 0.906855 0.421442i \(-0.138476\pi\)
−0.818407 + 0.574638i \(0.805143\pi\)
\(278\) 119.544i 0.430013i
\(279\) 0 0
\(280\) −122.697 −0.438203
\(281\) 17.8791 10.3225i 0.0636266 0.0367349i −0.467849 0.883808i \(-0.654971\pi\)
0.531476 + 0.847073i \(0.321638\pi\)
\(282\) 0 0
\(283\) −26.7043 + 46.2533i −0.0943616 + 0.163439i −0.909342 0.416049i \(-0.863414\pi\)
0.814980 + 0.579489i \(0.196748\pi\)
\(284\) 31.2122 + 18.0204i 0.109902 + 0.0634521i
\(285\) 0 0
\(286\) −6.53801 11.3242i −0.0228602 0.0395950i
\(287\) 91.1421i 0.317568i
\(288\) 0 0
\(289\) −67.3633 −0.233091
\(290\) 87.0681 50.2688i 0.300235 0.173341i
\(291\) 0 0
\(292\) −7.90918 + 13.6991i −0.0270862 + 0.0469148i
\(293\) 12.9245 + 7.46196i 0.0441109 + 0.0254674i 0.521893 0.853011i \(-0.325226\pi\)
−0.477782 + 0.878478i \(0.658559\pi\)
\(294\) 0 0
\(295\) 48.7951 + 84.5157i 0.165407 + 0.286494i
\(296\) 132.079i 0.446212i
\(297\) 0 0
\(298\) 163.348 0.548149
\(299\) −8.00740 + 4.62307i −0.0267806 + 0.0154618i
\(300\) 0 0
\(301\) 188.030 325.678i 0.624685 1.08199i
\(302\) −79.3304 45.8014i −0.262683 0.151660i
\(303\) 0 0
\(304\) 49.3939 + 85.5527i 0.162480 + 0.281423i
\(305\) 68.0219i 0.223023i
\(306\) 0 0
\(307\) 65.9092 0.214688 0.107344 0.994222i \(-0.465765\pi\)
0.107344 + 0.994222i \(0.465765\pi\)
\(308\) −13.7878 + 7.96036i −0.0447654 + 0.0258453i
\(309\) 0 0
\(310\) 11.1895 19.3809i 0.0360953 0.0625189i
\(311\) 216.659 + 125.088i 0.696652 + 0.402213i 0.806099 0.591780i \(-0.201575\pi\)
−0.109447 + 0.993993i \(0.534908\pi\)
\(312\) 0 0
\(313\) 213.197 + 369.268i 0.681140 + 1.17977i 0.974633 + 0.223808i \(0.0718490\pi\)
−0.293493 + 0.955961i \(0.594818\pi\)
\(314\) 29.4416i 0.0937631i
\(315\) 0 0
\(316\) 87.4847 0.276850
\(317\) 401.818 231.990i 1.26756 0.731829i 0.293038 0.956101i \(-0.405334\pi\)
0.974527 + 0.224272i \(0.0720005\pi\)
\(318\) 0 0
\(319\) 6.52270 11.2977i 0.0204473 0.0354158i
\(320\) −36.0000 20.7846i −0.112500 0.0649519i
\(321\) 0 0
\(322\) 5.62883 + 9.74941i 0.0174808 + 0.0302777i
\(323\) 466.219i 1.44340i
\(324\) 0 0
\(325\) 19.3939 0.0596735
\(326\) −162.965 + 94.0878i −0.499892 + 0.288613i
\(327\) 0 0
\(328\) −15.4393 + 26.7416i −0.0470710 + 0.0815293i
\(329\) −327.424 189.038i −0.995210 0.574585i
\(330\) 0 0
\(331\) −236.401 409.459i −0.714203 1.23704i −0.963266 0.268549i \(-0.913456\pi\)
0.249063 0.968487i \(-0.419877\pi\)
\(332\) 260.665i 0.785135i
\(333\) 0 0
\(334\) −416.499 −1.24700
\(335\) −337.704 + 194.974i −1.00807 + 0.582011i
\(336\) 0 0
\(337\) −152.803 + 264.663i −0.453422 + 0.785349i −0.998596 0.0529735i \(-0.983130\pi\)
0.545174 + 0.838323i \(0.316463\pi\)
\(338\) −91.8184 53.0114i −0.271652 0.156838i
\(339\) 0 0
\(340\) −98.0908 169.898i −0.288502 0.499701i
\(341\) 2.90383i 0.00851564i
\(342\) 0 0
\(343\) 236.287 0.688884
\(344\) 110.338 63.7038i 0.320751 0.185186i
\(345\) 0 0
\(346\) −48.9773 + 84.8312i −0.141553 + 0.245177i
\(347\) −115.766 66.8373i −0.333618 0.192615i 0.323828 0.946116i \(-0.395030\pi\)
−0.657446 + 0.753501i \(0.728363\pi\)
\(348\) 0 0
\(349\) 49.3786 + 85.5262i 0.141486 + 0.245061i 0.928056 0.372440i \(-0.121479\pi\)
−0.786570 + 0.617500i \(0.788145\pi\)
\(350\) 23.6130i 0.0674658i
\(351\) 0 0
\(352\) −5.39388 −0.0153235
\(353\) 282.424 163.058i 0.800068 0.461919i −0.0434270 0.999057i \(-0.513828\pi\)
0.843495 + 0.537137i \(0.180494\pi\)
\(354\) 0 0
\(355\) −46.8184 + 81.0918i −0.131883 + 0.228428i
\(356\) 251.666 + 145.300i 0.706928 + 0.408145i
\(357\) 0 0
\(358\) −33.5755 58.1545i −0.0937863 0.162443i
\(359\) 418.736i 1.16639i −0.812331 0.583197i \(-0.801801\pi\)
0.812331 0.583197i \(-0.198199\pi\)
\(360\) 0 0
\(361\) 248.939 0.689581
\(362\) −297.464 + 171.741i −0.821725 + 0.474423i
\(363\) 0 0
\(364\) 80.9546 140.217i 0.222403 0.385213i
\(365\) −35.5913 20.5487i −0.0975105 0.0562977i
\(366\) 0 0
\(367\) −93.6135 162.143i −0.255078 0.441808i 0.709839 0.704364i \(-0.248768\pi\)
−0.964917 + 0.262557i \(0.915434\pi\)
\(368\) 3.81405i 0.0103643i
\(369\) 0 0
\(370\) −343.151 −0.927435
\(371\) 682.423 393.997i 1.83942 1.06199i
\(372\) 0 0
\(373\) −225.515 + 390.603i −0.604597 + 1.04719i 0.387518 + 0.921862i \(0.373333\pi\)
−0.992115 + 0.125331i \(0.960001\pi\)
\(374\) −22.0454 12.7279i −0.0589449 0.0340319i
\(375\) 0 0
\(376\) −64.0454 110.930i −0.170334 0.295026i
\(377\) 132.668i 0.351905i
\(378\) 0 0
\(379\) −489.666 −1.29200 −0.645998 0.763339i \(-0.723558\pi\)
−0.645998 + 0.763339i \(0.723558\pi\)
\(380\) −222.272 + 128.329i −0.584927 + 0.337708i
\(381\) 0 0
\(382\) 5.32577 9.22450i 0.0139418 0.0241479i
\(383\) −89.2492 51.5281i −0.233027 0.134538i 0.378941 0.925421i \(-0.376288\pi\)
−0.611968 + 0.790883i \(0.709622\pi\)
\(384\) 0 0
\(385\) −20.6816 35.8216i −0.0537185 0.0930432i
\(386\) 488.546i 1.26566i
\(387\) 0 0
\(388\) 219.757 0.566384
\(389\) −29.6816 + 17.1367i −0.0763024 + 0.0440532i −0.537666 0.843158i \(-0.680694\pi\)
0.461363 + 0.887211i \(0.347360\pi\)
\(390\) 0 0
\(391\) −9.00000 + 15.5885i −0.0230179 + 0.0398682i
\(392\) −50.6969 29.2699i −0.129329 0.0746681i
\(393\) 0 0
\(394\) −54.6061 94.5806i −0.138594 0.240052i
\(395\) 227.292i 0.575423i
\(396\) 0 0
\(397\) 8.27245 0.0208374 0.0104187 0.999946i \(-0.496684\pi\)
0.0104187 + 0.999946i \(0.496684\pi\)
\(398\) −187.980 + 108.530i −0.472311 + 0.272689i
\(399\) 0 0
\(400\) 4.00000 6.92820i 0.0100000 0.0173205i
\(401\) −358.636 207.059i −0.894355 0.516356i −0.0189903 0.999820i \(-0.506045\pi\)
−0.875364 + 0.483464i \(0.839378\pi\)
\(402\) 0 0
\(403\) 14.7656 + 25.5747i 0.0366391 + 0.0634608i
\(404\) 295.078i 0.730391i
\(405\) 0 0
\(406\) 161.530 0.397857
\(407\) −38.5607 + 22.2630i −0.0947438 + 0.0547003i
\(408\) 0 0
\(409\) 163.106 282.508i 0.398792 0.690729i −0.594785 0.803885i \(-0.702763\pi\)
0.993577 + 0.113156i \(0.0360960\pi\)
\(410\) −69.4768 40.1124i −0.169456 0.0978352i
\(411\) 0 0
\(412\) −103.136 178.637i −0.250331 0.433585i
\(413\) 156.795i 0.379648i
\(414\) 0 0
\(415\) 677.227 1.63187
\(416\) 47.5051 27.4271i 0.114195 0.0659305i
\(417\) 0 0
\(418\) −16.6515 + 28.8413i −0.0398362 + 0.0689983i
\(419\) 468.325 + 270.388i 1.11772 + 0.645317i 0.940818 0.338912i \(-0.110059\pi\)
0.176903 + 0.984228i \(0.443392\pi\)
\(420\) 0 0
\(421\) −141.848 245.689i −0.336932 0.583584i 0.646922 0.762556i \(-0.276056\pi\)
−0.983854 + 0.178973i \(0.942723\pi\)
\(422\) 72.9179i 0.172791i
\(423\) 0 0
\(424\) 266.969 0.629645
\(425\) 32.6969 18.8776i 0.0769340 0.0444178i
\(426\) 0 0
\(427\) 54.6441 94.6464i 0.127972 0.221654i
\(428\) 62.4245 + 36.0408i 0.145852 + 0.0842075i
\(429\) 0 0
\(430\) 165.507 + 286.667i 0.384901 + 0.666668i
\(431\) 257.429i 0.597282i −0.954365 0.298641i \(-0.903467\pi\)
0.954365 0.298641i \(-0.0965334\pi\)
\(432\) 0 0
\(433\) 476.272 1.09994 0.549968 0.835186i \(-0.314640\pi\)
0.549968 + 0.835186i \(0.314640\pi\)
\(434\) 31.1385 17.9778i 0.0717477 0.0414236i
\(435\) 0 0
\(436\) −148.272 + 256.815i −0.340074 + 0.589026i
\(437\) 20.3939 + 11.7744i 0.0466679 + 0.0269437i
\(438\) 0 0
\(439\) 278.931 + 483.123i 0.635379 + 1.10051i 0.986435 + 0.164154i \(0.0524894\pi\)
−0.351056 + 0.936355i \(0.614177\pi\)
\(440\) 14.0137i 0.0318493i
\(441\) 0 0
\(442\) 258.879 0.585698
\(443\) −720.400 + 415.923i −1.62619 + 0.938879i −0.640969 + 0.767567i \(0.721467\pi\)
−0.985217 + 0.171312i \(0.945199\pi\)
\(444\) 0 0
\(445\) −377.499 + 653.848i −0.848313 + 1.46932i
\(446\) 383.623 + 221.485i 0.860142 + 0.496603i
\(447\) 0 0
\(448\) −33.3939 57.8399i −0.0745399 0.129107i
\(449\) 729.927i 1.62567i 0.582492 + 0.812836i \(0.302078\pi\)
−0.582492 + 0.812836i \(0.697922\pi\)
\(450\) 0 0
\(451\) −10.4097 −0.0230814
\(452\) 296.333 171.088i 0.655603 0.378513i
\(453\) 0 0
\(454\) −53.9319 + 93.4128i −0.118793 + 0.205755i
\(455\) 364.296 + 210.326i 0.800650 + 0.462255i
\(456\) 0 0
\(457\) −354.818 614.563i −0.776407 1.34478i −0.934000 0.357272i \(-0.883707\pi\)
0.157594 0.987504i \(-0.449626\pi\)
\(458\) 171.890i 0.375307i
\(459\) 0 0
\(460\) −9.90918 −0.0215417
\(461\) 7.96990 4.60142i 0.0172883 0.00998140i −0.491331 0.870973i \(-0.663489\pi\)
0.508619 + 0.860992i \(0.330156\pi\)
\(462\) 0 0
\(463\) 27.5987 47.8024i 0.0596085 0.103245i −0.834681 0.550733i \(-0.814348\pi\)
0.894290 + 0.447488i \(0.147681\pi\)
\(464\) 47.3939 + 27.3629i 0.102142 + 0.0589717i
\(465\) 0 0
\(466\) 106.788 + 184.962i 0.229158 + 0.396914i
\(467\) 625.811i 1.34007i −0.742331 0.670033i \(-0.766280\pi\)
0.742331 0.670033i \(-0.233720\pi\)
\(468\) 0 0
\(469\) −626.514 −1.33585
\(470\) 288.204 166.395i 0.613201 0.354032i
\(471\) 0 0
\(472\) −26.5607 + 46.0045i −0.0562727 + 0.0974672i
\(473\) 37.1969 + 21.4757i 0.0786405 + 0.0454031i
\(474\) 0 0
\(475\) −24.6969 42.7764i −0.0519936 0.0900555i
\(476\) 315.198i 0.662180i
\(477\) 0 0
\(478\) −124.045 −0.259509
\(479\) −267.856 + 154.647i −0.559199 + 0.322854i −0.752824 0.658222i \(-0.771309\pi\)
0.193625 + 0.981076i \(0.437976\pi\)
\(480\) 0 0
\(481\) 226.409 392.151i 0.470704 0.815283i
\(482\) 247.139 + 142.685i 0.512736 + 0.296028i
\(483\) 0 0
\(484\) 120.091 + 208.003i 0.248122 + 0.429759i
\(485\) 570.946i 1.17721i
\(486\) 0 0
\(487\) −28.3337 −0.0581800 −0.0290900 0.999577i \(-0.509261\pi\)
−0.0290900 + 0.999577i \(0.509261\pi\)
\(488\) 32.0658 18.5132i 0.0657086 0.0379369i
\(489\) 0 0
\(490\) 76.0454 131.715i 0.155195 0.268805i
\(491\) −822.461 474.848i −1.67507 0.967105i −0.964727 0.263254i \(-0.915204\pi\)
−0.710348 0.703851i \(-0.751462\pi\)
\(492\) 0 0
\(493\) 129.136 + 223.670i 0.261940 + 0.453693i
\(494\) 338.682i 0.685592i
\(495\) 0 0
\(496\) 12.1816 0.0245597
\(497\) −130.287 + 75.2214i −0.262147 + 0.151351i
\(498\) 0 0
\(499\) 280.113 485.170i 0.561349 0.972284i −0.436030 0.899932i \(-0.643616\pi\)
0.997379 0.0723525i \(-0.0230507\pi\)
\(500\) −207.000 119.512i −0.414000 0.239023i
\(501\) 0 0
\(502\) −37.2122 64.4535i −0.0741280 0.128393i
\(503\) 897.832i 1.78495i −0.451094 0.892477i \(-0.648966\pi\)
0.451094 0.892477i \(-0.351034\pi\)
\(504\) 0 0
\(505\) −766.635 −1.51809
\(506\) −1.11352 + 0.642891i −0.00220063 + 0.00127053i
\(507\) 0 0
\(508\) −78.0908 + 135.257i −0.153722 + 0.266254i
\(509\) 170.454 + 98.4114i 0.334879 + 0.193343i 0.658005 0.753013i \(-0.271400\pi\)
−0.323126 + 0.946356i \(0.604734\pi\)
\(510\) 0 0
\(511\) −33.0148 57.1833i −0.0646082 0.111905i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −114.136 −0.222055
\(515\) 464.113 267.956i 0.901190 0.520302i
\(516\) 0 0
\(517\) 21.5908 37.3964i 0.0417617 0.0723334i
\(518\) −477.464 275.664i −0.921746 0.532170i
\(519\) 0 0
\(520\) 71.2577 + 123.422i 0.137034 + 0.237350i
\(521\) 375.837i 0.721377i −0.932686 0.360688i \(-0.882542\pi\)
0.932686 0.360688i \(-0.117458\pi\)
\(522\) 0 0
\(523\) 91.1827 0.174345 0.0871727 0.996193i \(-0.472217\pi\)
0.0871727 + 0.996193i \(0.472217\pi\)
\(524\) −405.409 + 234.063i −0.773681 + 0.446685i
\(525\) 0 0
\(526\) 327.916 567.967i 0.623415 1.07979i
\(527\) 49.7878 + 28.7450i 0.0944739 + 0.0545445i
\(528\) 0 0
\(529\) −264.045 457.340i −0.499141 0.864537i
\(530\) 693.607i 1.30869i
\(531\) 0 0
\(532\) −412.363 −0.775119
\(533\) 91.6806 52.9318i 0.172009 0.0993092i
\(534\) 0 0
\(535\) −93.6367 + 162.184i −0.175022 + 0.303147i
\(536\) −183.823 106.130i −0.342953 0.198004i
\(537\) 0 0
\(538\) 30.7423 + 53.2473i 0.0571419 + 0.0989727i
\(539\) 19.7348i 0.0366137i
\(540\) 0 0
\(541\) −38.8490 −0.0718096 −0.0359048 0.999355i \(-0.511431\pi\)
−0.0359048 + 0.999355i \(0.511431\pi\)
\(542\) 419.641 242.280i 0.774246 0.447011i
\(543\) 0 0
\(544\) 53.3939 92.4809i 0.0981505 0.170002i
\(545\) −667.226 385.223i −1.22427 0.706831i
\(546\) 0 0
\(547\) 233.022 + 403.606i 0.426000 + 0.737854i 0.996513 0.0834344i \(-0.0265889\pi\)
−0.570513 + 0.821289i \(0.693256\pi\)
\(548\) 299.662i 0.546829i
\(549\) 0 0
\(550\) 2.69694 0.00490352
\(551\) 292.621 168.945i 0.531072 0.306615i
\(552\) 0 0
\(553\) −182.591 + 316.257i −0.330182 + 0.571893i
\(554\) −60.0125 34.6482i −0.108326 0.0625419i
\(555\) 0 0
\(556\) −84.5301 146.410i −0.152033 0.263328i
\(557\) 695.042i 1.24783i 0.781492 + 0.623916i \(0.214459\pi\)
−0.781492 + 0.623916i \(0.785541\pi\)
\(558\) 0 0
\(559\) −436.803 −0.781400
\(560\) 150.272 86.7598i 0.268344 0.154928i
\(561\) 0 0
\(562\) −14.5982 + 25.2848i −0.0259755 + 0.0449908i
\(563\) 473.780 + 273.537i 0.841528 + 0.485857i 0.857783 0.514011i \(-0.171841\pi\)
−0.0162552 + 0.999868i \(0.505174\pi\)
\(564\) 0 0
\(565\) 444.499 + 769.895i 0.786724 + 1.36265i
\(566\) 75.5313i 0.133447i
\(567\) 0 0
\(568\) −50.9694 −0.0897348
\(569\) −215.954 + 124.681i −0.379533 + 0.219123i −0.677615 0.735417i \(-0.736986\pi\)
0.298082 + 0.954540i \(0.403653\pi\)
\(570\) 0 0
\(571\) −36.9166 + 63.9414i −0.0646525 + 0.111981i −0.896540 0.442963i \(-0.853927\pi\)
0.831887 + 0.554945i \(0.187261\pi\)
\(572\) 16.0148 + 9.24614i 0.0279979 + 0.0161646i
\(573\) 0 0
\(574\) −64.4472 111.626i −0.112277 0.194470i
\(575\) 1.90702i 0.00331656i
\(576\) 0 0
\(577\) −43.9092 −0.0760991 −0.0380496 0.999276i \(-0.512114\pi\)
−0.0380496 + 0.999276i \(0.512114\pi\)
\(578\) 82.5028 47.6330i 0.142738 0.0824101i
\(579\) 0 0
\(580\) −71.0908 + 123.133i −0.122570 + 0.212298i
\(581\) 942.302 + 544.038i 1.62186 + 0.936382i
\(582\) 0 0
\(583\) 45.0000 + 77.9423i 0.0771870 + 0.133692i
\(584\) 22.3706i 0.0383057i
\(585\) 0 0
\(586\) −21.1056 −0.0360164
\(587\) 381.386 220.194i 0.649721 0.375117i −0.138628 0.990345i \(-0.544269\pi\)
0.788349 + 0.615228i \(0.210936\pi\)
\(588\) 0 0
\(589\) 37.6061 65.1357i 0.0638474 0.110587i
\(590\) −119.523 69.0068i −0.202582 0.116961i
\(591\) 0 0
\(592\) −93.3939 161.763i −0.157760 0.273248i
\(593\) 347.232i 0.585551i −0.956181 0.292776i \(-0.905421\pi\)
0.956181 0.292776i \(-0.0945789\pi\)
\(594\) 0 0
\(595\) 818.908 1.37632
\(596\) −200.060 + 115.505i −0.335671 + 0.193800i
\(597\) 0 0
\(598\) 6.53801 11.3242i 0.0109331 0.0189367i
\(599\) 684.083 + 394.956i 1.14204 + 0.659359i 0.946936 0.321423i \(-0.104161\pi\)
0.195107 + 0.980782i \(0.437495\pi\)
\(600\) 0 0
\(601\) 353.455 + 612.201i 0.588111 + 1.01864i 0.994480 + 0.104929i \(0.0334614\pi\)
−0.406369 + 0.913709i \(0.633205\pi\)
\(602\) 531.829i 0.883438i
\(603\) 0 0
\(604\) 129.546 0.214480
\(605\) −540.409 + 312.005i −0.893237 + 0.515711i
\(606\) 0 0
\(607\) 596.628 1033.39i 0.982913 1.70246i 0.332048 0.943263i \(-0.392261\pi\)
0.650866 0.759193i \(-0.274406\pi\)
\(608\) −120.990 69.8535i −0.198996 0.114891i
\(609\) 0 0
\(610\) 48.0987 + 83.3094i 0.0788504 + 0.136573i
\(611\) 439.145i 0.718731i
\(612\) 0 0
\(613\) 629.181 1.02640 0.513198 0.858270i \(-0.328461\pi\)
0.513198 + 0.858270i \(0.328461\pi\)
\(614\) −80.7219 + 46.6048i −0.131469 + 0.0759036i
\(615\) 0 0
\(616\) 11.2577 19.4988i 0.0182754 0.0316539i
\(617\) −166.909 96.3648i −0.270516 0.156183i 0.358606 0.933489i \(-0.383252\pi\)
−0.629122 + 0.777306i \(0.716586\pi\)
\(618\) 0 0
\(619\) 76.4773 + 132.463i 0.123550 + 0.213994i 0.921165 0.389172i \(-0.127239\pi\)
−0.797615 + 0.603166i \(0.793905\pi\)
\(620\) 31.6488i 0.0510465i
\(621\) 0 0
\(622\) −353.803 −0.568814
\(623\) −1050.51 + 606.515i −1.68622 + 0.973539i
\(624\) 0 0
\(625\) 335.500 581.103i 0.536800 0.929765i
\(626\) −522.224 301.506i −0.834223 0.481639i
\(627\) 0 0
\(628\) −20.8184 36.0585i −0.0331503 0.0574180i
\(629\) 881.525i 1.40147i
\(630\) 0 0
\(631\) 44.8786 0.0711229 0.0355615 0.999367i \(-0.488678\pi\)
0.0355615 + 0.999367i \(0.488678\pi\)
\(632\) −107.146 + 61.8610i −0.169535 + 0.0978814i
\(633\) 0 0
\(634\) −328.083 + 568.256i −0.517481 + 0.896303i
\(635\) −351.409 202.886i −0.553399 0.319505i
\(636\) 0 0
\(637\) 100.348 + 173.809i 0.157533 + 0.272855i
\(638\) 18.4490i 0.0289169i
\(639\) 0 0
\(640\) 58.7878 0.0918559
\(641\) 209.106 120.727i 0.326219 0.188342i −0.327942 0.944698i \(-0.606355\pi\)
0.654161 + 0.756355i \(0.273022\pi\)
\(642\) 0 0
\(643\) −395.704 + 685.380i −0.615403 + 1.06591i 0.374910 + 0.927061i \(0.377674\pi\)
−0.990314 + 0.138849i \(0.955660\pi\)
\(644\) −13.7878 7.96036i −0.0214096 0.0123608i
\(645\) 0 0
\(646\) −329.666 570.999i −0.510319 0.883899i
\(647\) 294.028i 0.454448i 0.973842 + 0.227224i \(0.0729650\pi\)
−0.973842 + 0.227224i \(0.927035\pi\)
\(648\) 0 0
\(649\) −17.9082 −0.0275935
\(650\) −23.7526 + 13.7135i −0.0365424 + 0.0210978i
\(651\) 0 0
\(652\) 133.060 230.467i 0.204080 0.353477i
\(653\) 665.379 + 384.156i 1.01896 + 0.588295i 0.913802 0.406161i \(-0.133133\pi\)
0.105155 + 0.994456i \(0.466466\pi\)
\(654\) 0 0
\(655\) −608.113 1053.28i −0.928417 1.60807i
\(656\) 43.6689i 0.0665684i
\(657\) 0 0
\(658\) 534.681 0.812585
\(659\) 373.204 215.469i 0.566318 0.326964i −0.189359 0.981908i \(-0.560641\pi\)
0.755678 + 0.654944i \(0.227308\pi\)
\(660\) 0 0
\(661\) −506.136 + 876.653i −0.765712 + 1.32625i 0.174157 + 0.984718i \(0.444280\pi\)
−0.939869 + 0.341534i \(0.889053\pi\)
\(662\) 579.062 + 334.322i 0.874717 + 0.505018i
\(663\) 0 0
\(664\) 184.318 + 319.248i 0.277587 + 0.480795i
\(665\) 1071.35i 1.61105i
\(666\) 0 0
\(667\) 13.0454 0.0195583
\(668\) 510.106 294.510i 0.763631 0.440883i
\(669\) 0 0
\(670\) 275.734 477.586i 0.411544 0.712815i
\(671\) 10.8099 + 6.24112i 0.0161102 + 0.00930123i
\(672\) 0 0
\(673\) −281.606 487.755i −0.418433 0.724748i 0.577349 0.816498i \(-0.304087\pi\)
−0.995782 + 0.0917499i \(0.970754\pi\)
\(674\) 432.192i 0.641235i
\(675\) 0 0
\(676\) 149.939 0.221803
\(677\) 303.227 175.068i 0.447897 0.258594i −0.259044 0.965865i \(-0.583408\pi\)
0.706942 + 0.707272i \(0.250074\pi\)
\(678\) 0 0
\(679\) −458.659 + 794.421i −0.675492 + 1.16999i
\(680\) 240.272 + 138.721i 0.353342 + 0.204002i
\(681\) 0 0
\(682\) 2.05332 + 3.55645i 0.00301073 + 0.00521474i
\(683\) 502.818i 0.736190i 0.929788 + 0.368095i \(0.119990\pi\)
−0.929788 + 0.368095i \(0.880010\pi\)
\(684\) 0 0
\(685\) −778.546 −1.13656
\(686\) −289.392 + 167.080i −0.421854 + 0.243557i
\(687\) 0 0
\(688\) −90.0908 + 156.042i −0.130946 + 0.226805i
\(689\) −792.650 457.637i −1.15044 0.664205i
\(690\) 0 0
\(691\) −188.159 325.902i −0.272300 0.471638i 0.697150 0.716925i \(-0.254451\pi\)
−0.969450 + 0.245287i \(0.921118\pi\)
\(692\) 138.529i 0.200186i
\(693\) 0 0
\(694\) 189.044 0.272398
\(695\) 380.385 219.616i 0.547317 0.315994i
\(696\) 0 0
\(697\) 103.045 178.480i 0.147841 0.256069i
\(698\) −120.952 69.8318i −0.173284 0.100046i
\(699\) 0 0
\(700\) 16.6969 + 28.9199i 0.0238528 + 0.0413142i
\(701\) 489.681i 0.698546i 0.937021 + 0.349273i \(0.113571\pi\)
−0.937021 + 0.349273i \(0.886429\pi\)
\(702\) 0 0
\(703\) −1153.27 −1.64050
\(704\) 6.60612 3.81405i 0.00938370 0.00541768i
\(705\) 0 0
\(706\) −230.598 + 399.408i −0.326626 + 0.565733i
\(707\) −1066.70 615.862i −1.50878 0.871092i
\(708\) 0 0
\(709\) −237.014 410.521i −0.334294 0.579014i 0.649055 0.760741i \(-0.275164\pi\)
−0.983349 + 0.181728i \(0.941831\pi\)
\(710\) 132.422i 0.186510i
\(711\) 0 0
\(712\) −410.969 −0.577204
\(713\) 2.51479 1.45192i 0.00352706 0.00203635i
\(714\) 0 0
\(715\) −24.0222 + 41.6077i −0.0335975 + 0.0581925i
\(716\) 82.2429 + 47.4829i 0.114864 + 0.0663170i
\(717\) 0 0
\(718\) 296.091 + 512.844i 0.412383 + 0.714268i
\(719\) 108.122i 0.150379i −0.997169 0.0751894i \(-0.976044\pi\)
0.997169 0.0751894i \(-0.0239561\pi\)
\(720\) 0 0
\(721\) 861.030 1.19422
\(722\) −304.886 + 176.026i −0.422280 + 0.243804i
\(723\) 0 0
\(724\) 242.879 420.678i 0.335468 0.581047i
\(725\) −23.6969 13.6814i −0.0326854 0.0188709i
\(726\) 0 0
\(727\) 222.296 + 385.027i 0.305771 + 0.529611i 0.977433 0.211247i \(-0.0677524\pi\)
−0.671662 + 0.740858i \(0.734419\pi\)
\(728\) 228.974i 0.314525i
\(729\) 0 0
\(730\) 58.1204 0.0796170
\(731\) −736.423 + 425.174i −1.00742 + 0.581634i
\(732\) 0 0
\(733\) 358.181 620.388i 0.488651 0.846368i −0.511264 0.859424i \(-0.670823\pi\)
0.999915 + 0.0130556i \(0.00415584\pi\)
\(734\) 229.305 + 132.390i 0.312405 + 0.180367i
\(735\) 0 0
\(736\) −2.69694 4.67123i −0.00366432 0.00634679i
\(737\) 71.5567i 0.0970918i
\(738\) 0 0
\(739\) 933.362 1.26301 0.631504 0.775373i \(-0.282438\pi\)
0.631504 + 0.775373i \(0.282438\pi\)
\(740\) 420.272 242.644i 0.567936 0.327898i
\(741\) 0 0
\(742\) −557.196 + 965.093i −0.750939 + 1.30066i
\(743\) 13.7793 + 7.95550i 0.0185455 + 0.0107073i 0.509244 0.860622i \(-0.329925\pi\)
−0.490699 + 0.871329i \(0.663258\pi\)
\(744\) 0 0
\(745\) −300.090 519.772i −0.402806 0.697680i
\(746\) 637.852i 0.855030i
\(747\) 0 0
\(748\) 36.0000 0.0481283
\(749\) −260.574 + 150.443i −0.347896 + 0.200858i
\(750\) 0 0
\(751\) −404.916 + 701.334i −0.539169 + 0.933867i 0.459781 + 0.888033i \(0.347928\pi\)
−0.998949 + 0.0458347i \(0.985405\pi\)
\(752\) 156.879 + 90.5739i 0.208615 + 0.120444i
\(753\) 0 0
\(754\) −93.8105 162.484i −0.124417 0.215497i
\(755\) 336.570i 0.445788i
\(756\) 0 0
\(757\) 689.637 0.911013 0.455506 0.890232i \(-0.349458\pi\)
0.455506 + 0.890232i \(0.349458\pi\)
\(758\) 599.716 346.246i 0.791182 0.456789i
\(759\) 0 0
\(760\) 181.485 314.341i 0.238796 0.413606i
\(761\) 825.393 + 476.541i 1.08462 + 0.626204i 0.932138 0.362103i \(-0.117941\pi\)
0.152479 + 0.988307i \(0.451274\pi\)
\(762\) 0 0
\(763\) −618.924 1072.01i −0.811172 1.40499i
\(764\) 15.0635i 0.0197167i
\(765\) 0 0
\(766\) 145.743 0.190266
\(767\) 157.721 91.0604i 0.205634 0.118723i
\(768\) 0 0
\(769\) 328.348 568.715i 0.426980 0.739552i −0.569623 0.821906i \(-0.692911\pi\)
0.996603 + 0.0823545i \(0.0262440\pi\)
\(770\) 50.6594 + 29.2482i 0.0657915 + 0.0379847i
\(771\) 0 0
\(772\) 345.454 + 598.344i 0.447479 + 0.775057i
\(773\) 278.021i 0.359665i −0.983697 0.179832i \(-0.942445\pi\)
0.983697 0.179832i \(-0.0575555\pi\)
\(774\) 0 0
\(775\) −6.09082 −0.00785912
\(776\) −269.146 + 155.392i −0.346838 + 0.200247i
\(777\) 0 0
\(778\) 24.2350 41.9762i 0.0311503 0.0539539i
\(779\) −233.499 134.811i −0.299743 0.173056i
\(780\) 0 0
\(781\) −8.59133 14.8806i −0.0110004 0.0190533i
\(782\) 25.4558i 0.0325522i
\(783\) 0 0
\(784\) 82.7878 0.105597
\(785\) 93.6827 54.0877i 0.119341 0.0689015i
\(786\) 0 0
\(787\) −410.977 + 711.833i −0.522207 + 0.904489i 0.477459 + 0.878654i \(0.341558\pi\)
−0.999666 + 0.0258350i \(0.991776\pi\)
\(788\) 133.757 + 77.2247i 0.169743 + 0.0980009i
\(789\) 0 0
\(790\) −160.720 278.375i −0.203443 0.352373i
\(791\) 1428.32i 1.80572i
\(792\) 0 0
\(793\) −126.941 −0.160077
\(794\) −10.1316 + 5.84950i −0.0127602 + 0.00736713i
\(795\) 0 0
\(796\) 153.485 265.843i 0.192820 0.333974i
\(797\) −1145.33 661.257i −1.43705 0.829683i −0.439409 0.898287i \(-0.644812\pi\)
−0.997644 + 0.0686043i \(0.978145\pi\)
\(798\) 0 0
\(799\) 427.454 + 740.372i 0.534986 + 0.926624i
\(800\) 11.3137i 0.0141421i
\(801\) 0 0
\(802\) 585.650 0.730238
\(803\) 6.53113 3.77075i 0.00813341 0.00469583i
\(804\) 0 0
\(805\) 20.6816 35.8216i 0.0256915 0.0444989i
\(806\) −36.1681 20.8817i −0.0448736 0.0259078i
\(807\) 0 0
\(808\) −208.652 361.395i −0.258232 0.447271i
\(809\) 235.681i 0.291324i 0.989334 + 0.145662i \(0.0465311\pi\)
−0.989334 + 0.145662i \(0.953469\pi\)
\(810\) 0 0
\(811\) −587.362 −0.724244 −0.362122 0.932131i \(-0.617948\pi\)
−0.362122 + 0.932131i \(0.617948\pi\)
\(812\) −197.833 + 114.219i −0.243637 + 0.140664i
\(813\) 0 0
\(814\) 31.4847 54.5331i 0.0386790 0.0669940i
\(815\) 598.771 + 345.701i 0.734688 + 0.424172i
\(816\) 0 0
\(817\) 556.242 + 963.439i 0.680835 + 1.17924i
\(818\) 461.334i 0.563978i
\(819\) 0 0
\(820\) 113.455 0.138360
\(821\) 817.453 471.956i 0.995679 0.574856i 0.0887121 0.996057i \(-0.471725\pi\)
0.906967 + 0.421202i \(0.138392\pi\)
\(822\) 0 0
\(823\) 807.871 1399.27i 0.981617 1.70021i 0.325520 0.945535i \(-0.394461\pi\)
0.656097 0.754676i \(-0.272206\pi\)
\(824\) 252.631 + 145.857i 0.306591 + 0.177010i
\(825\) 0 0
\(826\) −110.871 192.034i −0.134226 0.232486i
\(827\) 582.354i 0.704177i 0.935967 + 0.352088i \(0.114528\pi\)
−0.935967 + 0.352088i \(0.885472\pi\)
\(828\) 0 0
\(829\) 877.121 1.05805 0.529024 0.848607i \(-0.322558\pi\)
0.529024 + 0.848607i \(0.322558\pi\)
\(830\) −829.430 + 478.872i −0.999314 + 0.576954i
\(831\) 0 0
\(832\) −38.7878 + 67.1824i −0.0466199 + 0.0807480i
\(833\) 338.363 + 195.354i 0.406198 + 0.234519i
\(834\) 0 0
\(835\) 765.158 + 1325.29i 0.916357 + 1.58718i
\(836\) 47.0976i 0.0563369i
\(837\) 0 0
\(838\) −764.772 −0.912616
\(839\) 984.778 568.562i 1.17375 0.677666i 0.219191 0.975682i \(-0.429658\pi\)
0.954561 + 0.298016i \(0.0963247\pi\)
\(840\) 0 0
\(841\) −326.909 + 566.223i −0.388715 + 0.673274i
\(842\) 347.456 + 200.604i 0.412656 + 0.238247i
\(843\) 0 0
\(844\) −51.5607 89.3058i −0.0610909 0.105813i
\(845\) 389.552i 0.461009i
\(846\) 0 0
\(847\) −1002.57 −1.18368
\(848\) −326.969 + 188.776i −0.385577 + 0.222613i
\(849\) 0 0
\(850\) −26.6969 + 46.2405i −0.0314082 + 0.0544005i
\(851\) −38.5607 22.2630i −0.0453122 0.0261610i
\(852\) 0 0
\(853\) 159.909 + 276.970i 0.187466 + 0.324701i 0.944405 0.328785i \(-0.106639\pi\)
−0.756939 + 0.653486i \(0.773306\pi\)
\(854\) 154.557i 0.180980i
\(855\) 0 0
\(856\) −101.939 −0.119087
\(857\) −691.061 + 398.984i −0.806372 + 0.465559i −0.845694 0.533668i \(-0.820813\pi\)
0.0393225 + 0.999227i \(0.487480\pi\)
\(858\) 0 0
\(859\) 233.901 405.128i 0.272294 0.471627i −0.697155 0.716921i \(-0.745551\pi\)
0.969449 + 0.245293i \(0.0788843\pi\)
\(860\) −405.409 234.063i −0.471405 0.272166i
\(861\) 0 0
\(862\) 182.030 + 315.284i 0.211171 + 0.365759i
\(863\) 1304.85i 1.51199i −0.654578 0.755994i \(-0.727154\pi\)
0.654578 0.755994i \(-0.272846\pi\)
\(864\) 0 0
\(865\) 359.908 0.416079
\(866\) −583.312 + 336.775i −0.673571 + 0.388886i
\(867\) 0 0
\(868\) −25.4245 + 44.0365i −0.0292909 + 0.0507333i
\(869\) −36.1209 20.8544i −0.0415661 0.0239982i
\(870\) 0 0
\(871\) 363.855 + 630.216i 0.417744 + 0.723554i
\(872\) 419.378i 0.480938i
\(873\) 0 0
\(874\) −33.3031 −0.0381042
\(875\) 864.067 498.869i 0.987505 0.570136i
\(876\) 0 0
\(877\) 186.878 323.682i 0.213088 0.369079i −0.739592 0.673056i \(-0.764981\pi\)
0.952679 + 0.303977i \(0.0983146\pi\)
\(878\) −683.240 394.469i −0.778177 0.449281i
\(879\) 0 0
\(880\) 9.90918 + 17.1632i 0.0112604 + 0.0195036i
\(881\) 229.979i 0.261043i 0.991445 + 0.130522i \(0.0416652\pi\)
−0.991445 + 0.130522i \(0.958335\pi\)
\(882\) 0 0
\(883\) −1381.79 −1.56488 −0.782439 0.622728i \(-0.786024\pi\)
−0.782439 + 0.622728i \(0.786024\pi\)
\(884\) −317.060 + 183.055i −0.358665 + 0.207076i
\(885\) 0 0
\(886\) 588.204 1018.80i 0.663888 1.14989i
\(887\) −758.794 438.090i −0.855461 0.493901i 0.00702852 0.999975i \(-0.497763\pi\)
−0.862490 + 0.506075i \(0.831096\pi\)
\(888\) 0 0
\(889\) −325.969 564.596i −0.366670 0.635091i
\(890\) 1067.73i 1.19970i
\(891\) 0 0
\(892\) −626.454 −0.702303
\(893\) 968.605 559.224i 1.08466 0.626231i
\(894\) 0 0
\(895\) −123.364 + 213.673i −0.137837 + 0.238741i
\(896\) 81.7980 + 47.2261i 0.0912924 + 0.0527077i
\(897\) 0 0
\(898\) −516.136 893.974i −0.574762 0.995517i
\(899\) 41.6655i 0.0463465i
\(900\) 0 0
\(901\) −1781.82 −1.97760
\(902\) 12.7492 7.36077i 0.0141344 0.00816050i
\(903\) 0 0
\(904\) −241.955 + 419.078i −0.267649 + 0.463581i
\(905\) 1092.95 + 631.017i 1.20768 + 0.697256i
\(906\) 0 0
\(907\) −590.037 1021.97i −0.650537 1.12676i −0.982993 0.183644i \(-0.941211\pi\)
0.332456 0.943119i \(-0.392123\pi\)
\(908\) 152.542i 0.167998i
\(909\) 0 0
\(910\) −594.892 −0.653728
\(911\) −1100.13 + 635.158i −1.20760 + 0.697210i −0.962235 0.272220i \(-0.912242\pi\)
−0.245368 + 0.969430i \(0.578909\pi\)
\(912\) 0 0
\(913\) −62.1367 + 107.624i −0.0680578 + 0.117880i
\(914\) 869.123 + 501.788i 0.950900 + 0.549002i
\(915\) 0 0
\(916\) −121.545 210.522i −0.132691 0.229827i
\(917\) 1954.07i 2.13093i
\(918\) 0 0
\(919\) 1316.63 1.43268 0.716340 0.697751i \(-0.245816\pi\)
0.716340 + 0.697751i \(0.245816\pi\)
\(920\) 12.1362 7.00685i 0.0131915 0.00761614i
\(921\) 0 0
\(922\) −6.50740 + 11.2711i −0.00705791 + 0.0122247i
\(923\) 151.332 + 87.3713i 0.163956 + 0.0946602i
\(924\) 0 0
\(925\) 46.6969 + 80.8815i 0.0504832 + 0.0874394i
\(926\) 78.0610i 0.0842991i
\(927\) 0 0
\(928\) −77.3939 −0.0833986
\(929\) −543.424 + 313.746i −0.584956 + 0.337724i −0.763100 0.646280i \(-0.776324\pi\)
0.178145 + 0.984004i \(0.442991\pi\)
\(930\) 0 0
\(931\) 255.576 442.670i 0.274517 0.475478i
\(932\) −261.576 151.021i −0.280660 0.162039i
\(933\) 0 0
\(934\) 442.515 + 766.459i 0.473785 + 0.820620i
\(935\) 93.5307i 0.100033i
\(936\) 0 0
\(937\) 469.789 0.501375 0.250688 0.968068i \(-0.419343\pi\)
0.250688 + 0.968068i \(0.419343\pi\)
\(938\) 767.320 443.012i 0.818039 0.472295i
\(939\) 0 0
\(940\) −235.318 + 407.582i −0.250338 + 0.433598i
\(941\) −805.984 465.335i −0.856518 0.494511i 0.00632656 0.999980i \(-0.497986\pi\)
−0.862845 + 0.505469i \(0.831320\pi\)
\(942\) 0 0
\(943\) −5.20485 9.01506i −0.00551946 0.00955998i
\(944\) 75.1250i 0.0795816i
\(945\) 0 0
\(946\) −60.7423 −0.0642097
\(947\) 3.14465 1.81556i 0.00332064 0.00191717i −0.498339 0.866982i \(-0.666056\pi\)
0.501659 + 0.865065i \(0.332723\pi\)
\(948\) 0 0
\(949\) −38.3474 + 66.4197i −0.0404083 + 0.0699892i
\(950\) 60.4949 + 34.9267i 0.0636788 + 0.0367650i
\(951\) 0 0
\(952\) 222.879 + 386.037i 0.234116 + 0.405501i
\(953\) 719.641i 0.755132i −0.925983 0.377566i \(-0.876761\pi\)
0.925983 0.377566i \(-0.123239\pi\)
\(954\) 0 0
\(955\) −39.1362 −0.0409803
\(956\) 151.924 87.7133i 0.158916 0.0917504i
\(957\) 0 0
\(958\) 218.704 378.806i 0.228292 0.395413i
\(959\) −1083.28 625.431i −1.12959 0.652170i
\(960\) 0 0
\(961\) 475.863 + 824.218i 0.495175 + 0.857667i
\(962\) 640.380i 0.665676i
\(963\) 0 0
\(964\) −403.576 −0.418647
\(965\) −1554.54 + 897.516i −1.61093 + 0.930068i
\(966\) 0 0
\(967\) −16.8870 + 29.2491i −0.0174633 + 0.0302473i −0.874625 0.484800i \(-0.838892\pi\)
0.857162 + 0.515047i \(0.172226\pi\)
\(968\) −294.161 169.834i −0.303886 0.175448i
\(969\) 0 0
\(970\) −403.720 699.263i −0.416206 0.720890i
\(971\) 970.472i 0.999456i 0.866182 + 0.499728i \(0.166567\pi\)
−0.866182 + 0.499728i \(0.833433\pi\)
\(972\) 0 0
\(973\) 705.697 0.725279
\(974\) 34.7015 20.0349i 0.0356278 0.0205697i
\(975\) 0 0
\(976\) −26.1816 + 45.3479i −0.0268254 + 0.0464630i
\(977\) 1359.92 + 785.151i 1.39194 + 0.803635i 0.993529 0.113574i \(-0.0362300\pi\)
0.398406 + 0.917209i \(0.369563\pi\)
\(978\) 0 0
\(979\) −69.2724 119.983i −0.0707584 0.122557i
\(980\) 215.089i 0.219478i
\(981\) 0 0
\(982\) 1343.07 1.36769
\(983\) 671.930 387.939i 0.683551 0.394648i −0.117641 0.993056i \(-0.537533\pi\)
0.801192 + 0.598408i \(0.204200\pi\)
\(984\) 0 0
\(985\) −200.636 + 347.511i −0.203691 + 0.352803i
\(986\) −316.318 182.626i −0.320809 0.185219i
\(987\) 0 0
\(988\) 239.485 + 414.800i 0.242393 + 0.419838i
\(989\) 42.9513i 0.0434290i
\(990\) 0 0
\(991\) 870.454 0.878359 0.439180 0.898399i \(-0.355269\pi\)
0.439180 + 0.898399i \(0.355269\pi\)
\(992\) −14.9194 + 8.61371i −0.0150397 + 0.00868318i
\(993\) 0 0
\(994\) 106.379 184.254i 0.107021 0.185366i
\(995\) 690.681 + 398.765i 0.694152 + 0.400769i
\(996\) 0 0
\(997\) −622.499 1078.20i −0.624372 1.08144i −0.988662 0.150159i \(-0.952022\pi\)
0.364290 0.931286i \(-0.381312\pi\)
\(998\) 792.279i 0.793867i
\(999\) 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 54.3.d.a.17.1 4
3.2 odd 2 18.3.d.a.5.2 4
4.3 odd 2 432.3.q.d.17.1 4
5.2 odd 4 1350.3.k.a.449.1 8
5.3 odd 4 1350.3.k.a.449.4 8
5.4 even 2 1350.3.i.b.1151.2 4
8.3 odd 2 1728.3.q.c.449.1 4
8.5 even 2 1728.3.q.d.449.2 4
9.2 odd 6 inner 54.3.d.a.35.1 4
9.4 even 3 162.3.b.a.161.1 4
9.5 odd 6 162.3.b.a.161.4 4
9.7 even 3 18.3.d.a.11.2 yes 4
12.11 even 2 144.3.q.c.113.2 4
15.2 even 4 450.3.k.a.149.4 8
15.8 even 4 450.3.k.a.149.1 8
15.14 odd 2 450.3.i.b.401.1 4
24.5 odd 2 576.3.q.f.257.2 4
24.11 even 2 576.3.q.e.257.1 4
36.7 odd 6 144.3.q.c.65.2 4
36.11 even 6 432.3.q.d.305.1 4
36.23 even 6 1296.3.e.g.161.4 4
36.31 odd 6 1296.3.e.g.161.2 4
45.2 even 12 1350.3.k.a.899.4 8
45.7 odd 12 450.3.k.a.299.1 8
45.29 odd 6 1350.3.i.b.251.2 4
45.34 even 6 450.3.i.b.101.1 4
45.38 even 12 1350.3.k.a.899.1 8
45.43 odd 12 450.3.k.a.299.4 8
72.11 even 6 1728.3.q.c.1601.1 4
72.29 odd 6 1728.3.q.d.1601.2 4
72.43 odd 6 576.3.q.e.65.1 4
72.61 even 6 576.3.q.f.65.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.3.d.a.5.2 4 3.2 odd 2
18.3.d.a.11.2 yes 4 9.7 even 3
54.3.d.a.17.1 4 1.1 even 1 trivial
54.3.d.a.35.1 4 9.2 odd 6 inner
144.3.q.c.65.2 4 36.7 odd 6
144.3.q.c.113.2 4 12.11 even 2
162.3.b.a.161.1 4 9.4 even 3
162.3.b.a.161.4 4 9.5 odd 6
432.3.q.d.17.1 4 4.3 odd 2
432.3.q.d.305.1 4 36.11 even 6
450.3.i.b.101.1 4 45.34 even 6
450.3.i.b.401.1 4 15.14 odd 2
450.3.k.a.149.1 8 15.8 even 4
450.3.k.a.149.4 8 15.2 even 4
450.3.k.a.299.1 8 45.7 odd 12
450.3.k.a.299.4 8 45.43 odd 12
576.3.q.e.65.1 4 72.43 odd 6
576.3.q.e.257.1 4 24.11 even 2
576.3.q.f.65.2 4 72.61 even 6
576.3.q.f.257.2 4 24.5 odd 2
1296.3.e.g.161.2 4 36.31 odd 6
1296.3.e.g.161.4 4 36.23 even 6
1350.3.i.b.251.2 4 45.29 odd 6
1350.3.i.b.1151.2 4 5.4 even 2
1350.3.k.a.449.1 8 5.2 odd 4
1350.3.k.a.449.4 8 5.3 odd 4
1350.3.k.a.899.1 8 45.38 even 12
1350.3.k.a.899.4 8 45.2 even 12
1728.3.q.c.449.1 4 8.3 odd 2
1728.3.q.c.1601.1 4 72.11 even 6
1728.3.q.d.449.2 4 8.5 even 2
1728.3.q.d.1601.2 4 72.29 odd 6