Properties

Label 605.2.g.q.511.6
Level $605$
Weight $2$
Character 605.511
Analytic conductor $4.831$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(81,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 511.6
Character \(\chi\) \(=\) 605.511
Dual form 605.2.g.q.251.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.810808 + 2.49541i) q^{2} +(-1.08398 - 0.787560i) q^{3} +(-3.95163 + 2.87103i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.08638 - 3.34354i) q^{6} +(2.12272 - 1.54225i) q^{7} +(-6.12296 - 4.44859i) q^{8} +(-0.372282 - 1.14577i) q^{9} +O(q^{10})\) \(q+(0.810808 + 2.49541i) q^{2} +(-1.08398 - 0.787560i) q^{3} +(-3.95163 + 2.87103i) q^{4} +(0.309017 - 0.951057i) q^{5} +(1.08638 - 3.34354i) q^{6} +(2.12272 - 1.54225i) q^{7} +(-6.12296 - 4.44859i) q^{8} +(-0.372282 - 1.14577i) q^{9} +2.62383 q^{10} +6.54461 q^{12} +(-2.07910 - 6.39883i) q^{13} +(5.56966 + 4.04660i) q^{14} +(-1.08398 + 0.787560i) q^{15} +(3.11774 - 9.59541i) q^{16} +(0.551150 - 1.69626i) q^{17} +(2.55731 - 1.85799i) q^{18} +(1.19772 + 0.870194i) q^{19} +(1.50939 + 4.64542i) q^{20} -3.51561 q^{21} +5.20473 q^{23} +(3.13365 + 9.64440i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(14.2819 - 10.3764i) q^{26} +(-1.74095 + 5.35808i) q^{27} +(-3.96038 + 12.1888i) q^{28} +(-0.952511 + 0.692040i) q^{29} +(-2.84419 - 2.06642i) q^{30} +(-1.41043 - 4.34085i) q^{31} +11.3356 q^{32} +4.67975 q^{34} +(-0.810808 - 2.49541i) q^{35} +(4.76065 + 3.45881i) q^{36} +(0.549932 - 0.399549i) q^{37} +(-1.20037 + 3.69436i) q^{38} +(-2.78574 + 8.57364i) q^{39} +(-6.12296 + 4.44859i) q^{40} +(-4.44898 - 3.23238i) q^{41} +(-2.85048 - 8.77289i) q^{42} +3.80120 q^{43} -1.20473 q^{45} +(4.22004 + 12.9879i) q^{46} +(-5.38815 - 3.91472i) q^{47} +(-10.9365 + 7.94586i) q^{48} +(-0.0356965 + 0.109863i) q^{49} +(0.810808 - 2.49541i) q^{50} +(-1.93335 + 1.40466i) q^{51} +(26.5871 + 19.3166i) q^{52} +(4.41707 + 13.5943i) q^{53} -14.7822 q^{54} -19.8582 q^{56} +(-0.612978 - 1.88655i) q^{57} +(-2.49923 - 1.81579i) q^{58} +(3.14261 - 2.28324i) q^{59} +(2.02239 - 6.22429i) q^{60} +(0.992721 - 3.05528i) q^{61} +(9.68861 - 7.03919i) q^{62} +(-2.55731 - 1.85799i) q^{63} +(2.95551 + 9.09613i) q^{64} -6.72812 q^{65} +4.66012 q^{67} +(2.69208 + 8.28538i) q^{68} +(-5.64184 - 4.09904i) q^{69} +(5.56966 - 4.04660i) q^{70} +(1.20037 - 3.69436i) q^{71} +(-2.81758 + 8.67161i) q^{72} +(2.88586 - 2.09670i) q^{73} +(1.44293 + 1.04835i) q^{74} +(0.414045 + 1.27430i) q^{75} -7.23130 q^{76} -23.6535 q^{78} +(-4.67753 - 14.3959i) q^{79} +(-8.16235 - 5.93029i) q^{80} +(3.18303 - 2.31260i) q^{81} +(4.45883 - 13.7229i) q^{82} +(2.26643 - 6.97535i) q^{83} +(13.8924 - 10.0934i) q^{84} +(-1.44293 - 1.04835i) q^{85} +(3.08204 + 9.48555i) q^{86} +1.57753 q^{87} +3.44872 q^{89} +(-0.976805 - 3.00630i) q^{90} +(-14.2819 - 10.3764i) q^{91} +(-20.5672 + 14.9429i) q^{92} +(-1.88980 + 5.81620i) q^{93} +(5.40008 - 16.6197i) q^{94} +(1.19772 - 0.870194i) q^{95} +(-12.2876 - 8.92746i) q^{96} +(0.455807 + 1.40283i) q^{97} -0.303095 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.810808 + 2.49541i 0.573328 + 1.76452i 0.641804 + 0.766869i \(0.278186\pi\)
−0.0684758 + 0.997653i \(0.521814\pi\)
\(3\) −1.08398 0.787560i −0.625838 0.454698i 0.229118 0.973399i \(-0.426416\pi\)
−0.854956 + 0.518701i \(0.826416\pi\)
\(4\) −3.95163 + 2.87103i −1.97582 + 1.43551i
\(5\) 0.309017 0.951057i 0.138197 0.425325i
\(6\) 1.08638 3.34354i 0.443514 1.36500i
\(7\) 2.12272 1.54225i 0.802314 0.582915i −0.109278 0.994011i \(-0.534854\pi\)
0.911592 + 0.411096i \(0.134854\pi\)
\(8\) −6.12296 4.44859i −2.16479 1.57281i
\(9\) −0.372282 1.14577i −0.124094 0.381922i
\(10\) 2.62383 0.829728
\(11\) 0 0
\(12\) 6.54461 1.88927
\(13\) −2.07910 6.39883i −0.576640 1.77471i −0.630526 0.776168i \(-0.717161\pi\)
0.0538866 0.998547i \(-0.482839\pi\)
\(14\) 5.56966 + 4.04660i 1.48856 + 1.08150i
\(15\) −1.08398 + 0.787560i −0.279883 + 0.203347i
\(16\) 3.11774 9.59541i 0.779435 2.39885i
\(17\) 0.551150 1.69626i 0.133673 0.411405i −0.861708 0.507405i \(-0.830605\pi\)
0.995381 + 0.0960001i \(0.0306049\pi\)
\(18\) 2.55731 1.85799i 0.602763 0.437933i
\(19\) 1.19772 + 0.870194i 0.274776 + 0.199636i 0.716636 0.697448i \(-0.245681\pi\)
−0.441860 + 0.897084i \(0.645681\pi\)
\(20\) 1.50939 + 4.64542i 0.337510 + 1.03875i
\(21\) −3.51561 −0.767169
\(22\) 0 0
\(23\) 5.20473 1.08526 0.542631 0.839971i \(-0.317428\pi\)
0.542631 + 0.839971i \(0.317428\pi\)
\(24\) 3.13365 + 9.64440i 0.639654 + 1.96865i
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) 14.2819 10.3764i 2.80092 2.03499i
\(27\) −1.74095 + 5.35808i −0.335045 + 1.03116i
\(28\) −3.96038 + 12.1888i −0.748441 + 2.30347i
\(29\) −0.952511 + 0.692040i −0.176877 + 0.128509i −0.672701 0.739914i \(-0.734866\pi\)
0.495824 + 0.868423i \(0.334866\pi\)
\(30\) −2.84419 2.06642i −0.519275 0.377276i
\(31\) −1.41043 4.34085i −0.253320 0.779639i −0.994156 0.107953i \(-0.965570\pi\)
0.740836 0.671686i \(-0.234430\pi\)
\(32\) 11.3356 2.00387
\(33\) 0 0
\(34\) 4.67975 0.802571
\(35\) −0.810808 2.49541i −0.137052 0.421801i
\(36\) 4.76065 + 3.45881i 0.793441 + 0.576469i
\(37\) 0.549932 0.399549i 0.0904083 0.0656855i −0.541663 0.840596i \(-0.682205\pi\)
0.632071 + 0.774910i \(0.282205\pi\)
\(38\) −1.20037 + 3.69436i −0.194726 + 0.599305i
\(39\) −2.78574 + 8.57364i −0.446076 + 1.37288i
\(40\) −6.12296 + 4.44859i −0.968125 + 0.703384i
\(41\) −4.44898 3.23238i −0.694815 0.504812i 0.183425 0.983034i \(-0.441282\pi\)
−0.878239 + 0.478221i \(0.841282\pi\)
\(42\) −2.85048 8.77289i −0.439839 1.35369i
\(43\) 3.80120 0.579677 0.289839 0.957076i \(-0.406398\pi\)
0.289839 + 0.957076i \(0.406398\pi\)
\(44\) 0 0
\(45\) −1.20473 −0.179591
\(46\) 4.22004 + 12.9879i 0.622210 + 1.91497i
\(47\) −5.38815 3.91472i −0.785943 0.571021i 0.120814 0.992675i \(-0.461450\pi\)
−0.906757 + 0.421654i \(0.861450\pi\)
\(48\) −10.9365 + 7.94586i −1.57855 + 1.14689i
\(49\) −0.0356965 + 0.109863i −0.00509950 + 0.0156946i
\(50\) 0.810808 2.49541i 0.114666 0.352904i
\(51\) −1.93335 + 1.40466i −0.270723 + 0.196692i
\(52\) 26.5871 + 19.3166i 3.68696 + 2.67873i
\(53\) 4.41707 + 13.5943i 0.606731 + 1.86733i 0.484420 + 0.874836i \(0.339031\pi\)
0.122311 + 0.992492i \(0.460969\pi\)
\(54\) −14.7822 −2.01160
\(55\) 0 0
\(56\) −19.8582 −2.65366
\(57\) −0.612978 1.88655i −0.0811909 0.249880i
\(58\) −2.49923 1.81579i −0.328164 0.238425i
\(59\) 3.14261 2.28324i 0.409133 0.297253i −0.364117 0.931353i \(-0.618629\pi\)
0.773251 + 0.634100i \(0.218629\pi\)
\(60\) 2.02239 6.22429i 0.261090 0.803553i
\(61\) 0.992721 3.05528i 0.127105 0.391189i −0.867174 0.498006i \(-0.834066\pi\)
0.994279 + 0.106817i \(0.0340659\pi\)
\(62\) 9.68861 7.03919i 1.23045 0.893978i
\(63\) −2.55731 1.85799i −0.322191 0.234085i
\(64\) 2.95551 + 9.09613i 0.369439 + 1.13702i
\(65\) −6.72812 −0.834521
\(66\) 0 0
\(67\) 4.66012 0.569325 0.284662 0.958628i \(-0.408119\pi\)
0.284662 + 0.958628i \(0.408119\pi\)
\(68\) 2.69208 + 8.28538i 0.326463 + 1.00475i
\(69\) −5.64184 4.09904i −0.679198 0.493466i
\(70\) 5.56966 4.04660i 0.665702 0.483661i
\(71\) 1.20037 3.69436i 0.142458 0.438440i −0.854217 0.519916i \(-0.825963\pi\)
0.996675 + 0.0814756i \(0.0259633\pi\)
\(72\) −2.81758 + 8.67161i −0.332055 + 1.02196i
\(73\) 2.88586 2.09670i 0.337764 0.245400i −0.405954 0.913894i \(-0.633061\pi\)
0.743718 + 0.668494i \(0.233061\pi\)
\(74\) 1.44293 + 1.04835i 0.167737 + 0.121868i
\(75\) 0.414045 + 1.27430i 0.0478098 + 0.147143i
\(76\) −7.23130 −0.829487
\(77\) 0 0
\(78\) −23.6535 −2.67823
\(79\) −4.67753 14.3959i −0.526263 1.61967i −0.761805 0.647806i \(-0.775687\pi\)
0.235543 0.971864i \(-0.424313\pi\)
\(80\) −8.16235 5.93029i −0.912578 0.663027i
\(81\) 3.18303 2.31260i 0.353670 0.256956i
\(82\) 4.45883 13.7229i 0.492396 1.51544i
\(83\) 2.26643 6.97535i 0.248773 0.765644i −0.746220 0.665699i \(-0.768133\pi\)
0.994993 0.0999446i \(-0.0318666\pi\)
\(84\) 13.8924 10.0934i 1.51578 1.10128i
\(85\) −1.44293 1.04835i −0.156508 0.113709i
\(86\) 3.08204 + 9.48555i 0.332345 + 1.02285i
\(87\) 1.57753 0.169129
\(88\) 0 0
\(89\) 3.44872 0.365564 0.182782 0.983153i \(-0.441490\pi\)
0.182782 + 0.983153i \(0.441490\pi\)
\(90\) −0.976805 3.00630i −0.102964 0.316891i
\(91\) −14.2819 10.3764i −1.49715 1.08775i
\(92\) −20.5672 + 14.9429i −2.14428 + 1.55791i
\(93\) −1.88980 + 5.81620i −0.195963 + 0.603112i
\(94\) 5.40008 16.6197i 0.556976 1.71420i
\(95\) 1.19772 0.870194i 0.122883 0.0892801i
\(96\) −12.2876 8.92746i −1.25410 0.911155i
\(97\) 0.455807 + 1.40283i 0.0462802 + 0.142436i 0.971526 0.236931i \(-0.0761417\pi\)
−0.925246 + 0.379367i \(0.876142\pi\)
\(98\) −0.303095 −0.0306172
\(99\) 0 0
\(100\) 4.88448 0.488448
\(101\) −1.05455 3.24557i −0.104932 0.322946i 0.884783 0.466004i \(-0.154307\pi\)
−0.989714 + 0.143057i \(0.954307\pi\)
\(102\) −5.07277 3.68559i −0.502280 0.364927i
\(103\) 4.02381 2.92347i 0.396477 0.288058i −0.371627 0.928382i \(-0.621200\pi\)
0.768105 + 0.640324i \(0.221200\pi\)
\(104\) −15.7355 + 48.4288i −1.54299 + 4.74884i
\(105\) −1.08638 + 3.34354i −0.106020 + 0.326296i
\(106\) −30.3421 + 22.0448i −2.94708 + 2.14118i
\(107\) −5.71588 4.15283i −0.552575 0.401469i 0.276159 0.961112i \(-0.410938\pi\)
−0.828734 + 0.559643i \(0.810938\pi\)
\(108\) −8.50362 26.1715i −0.818262 2.51835i
\(109\) −10.6439 −1.01950 −0.509750 0.860323i \(-0.670262\pi\)
−0.509750 + 0.860323i \(0.670262\pi\)
\(110\) 0 0
\(111\) −0.910786 −0.0864480
\(112\) −8.18042 25.1767i −0.772977 2.37898i
\(113\) 11.1393 + 8.09320i 1.04790 + 0.761344i 0.971812 0.235757i \(-0.0757570\pi\)
0.0760879 + 0.997101i \(0.475757\pi\)
\(114\) 4.21071 3.05926i 0.394370 0.286526i
\(115\) 1.60835 4.94999i 0.149979 0.461589i
\(116\) 1.77711 5.46937i 0.165000 0.507818i
\(117\) −6.55754 + 4.76434i −0.606245 + 0.440463i
\(118\) 8.24568 + 5.99084i 0.759077 + 0.551501i
\(119\) −1.44612 4.45071i −0.132566 0.407996i
\(120\) 10.1407 0.925717
\(121\) 0 0
\(122\) 8.42909 0.763134
\(123\) 2.27693 + 7.00768i 0.205304 + 0.631862i
\(124\) 18.0362 + 13.1041i 1.61970 + 1.17678i
\(125\) −0.809017 + 0.587785i −0.0723607 + 0.0525731i
\(126\) 2.56297 7.88801i 0.228327 0.702720i
\(127\) −3.80489 + 11.7102i −0.337629 + 1.03912i 0.627783 + 0.778388i \(0.283963\pi\)
−0.965412 + 0.260728i \(0.916037\pi\)
\(128\) −1.96085 + 1.42464i −0.173317 + 0.125922i
\(129\) −4.12043 2.99367i −0.362784 0.263578i
\(130\) −5.45522 16.7894i −0.478454 1.47253i
\(131\) 19.5102 1.70461 0.852306 0.523043i \(-0.175203\pi\)
0.852306 + 0.523043i \(0.175203\pi\)
\(132\) 0 0
\(133\) 3.88448 0.336827
\(134\) 3.77847 + 11.6289i 0.326410 + 1.00459i
\(135\) 4.55786 + 3.31148i 0.392278 + 0.285007i
\(136\) −10.9207 + 7.93432i −0.936439 + 0.680362i
\(137\) −2.64649 + 8.14507i −0.226105 + 0.695881i 0.772072 + 0.635535i \(0.219220\pi\)
−0.998178 + 0.0603458i \(0.980780\pi\)
\(138\) 5.65433 17.4022i 0.481329 1.48138i
\(139\) −1.60480 + 1.16595i −0.136117 + 0.0988949i −0.653760 0.756702i \(-0.726810\pi\)
0.517643 + 0.855597i \(0.326810\pi\)
\(140\) 10.3684 + 7.53309i 0.876290 + 0.636662i
\(141\) 2.75759 + 8.48699i 0.232231 + 0.714733i
\(142\) 10.1922 0.855313
\(143\) 0 0
\(144\) −12.1548 −1.01290
\(145\) 0.363827 + 1.11974i 0.0302142 + 0.0929896i
\(146\) 7.57200 + 5.50138i 0.626663 + 0.455297i
\(147\) 0.125218 0.0909760i 0.0103278 0.00750357i
\(148\) −1.02601 + 3.15774i −0.0843377 + 0.259565i
\(149\) −5.67025 + 17.4512i −0.464525 + 1.42966i 0.395055 + 0.918658i \(0.370726\pi\)
−0.859579 + 0.511002i \(0.829274\pi\)
\(150\) −2.84419 + 2.06642i −0.232227 + 0.168723i
\(151\) −13.9341 10.1237i −1.13394 0.823854i −0.147674 0.989036i \(-0.547179\pi\)
−0.986263 + 0.165182i \(0.947179\pi\)
\(152\) −3.46245 10.6563i −0.280842 0.864343i
\(153\) −2.14871 −0.173713
\(154\) 0 0
\(155\) −4.56424 −0.366608
\(156\) −13.6069 41.8778i −1.08943 3.35291i
\(157\) 16.9064 + 12.2832i 1.34928 + 0.980307i 0.999047 + 0.0436428i \(0.0138963\pi\)
0.350229 + 0.936664i \(0.386104\pi\)
\(158\) 32.1312 23.3447i 2.55622 1.85720i
\(159\) 5.91833 18.2148i 0.469354 1.44452i
\(160\) 3.50289 10.7808i 0.276928 0.852296i
\(161\) 11.0482 8.02699i 0.870720 0.632615i
\(162\) 8.35172 + 6.06788i 0.656173 + 0.476738i
\(163\) 2.92188 + 8.99261i 0.228859 + 0.704356i 0.997877 + 0.0651285i \(0.0207457\pi\)
−0.769018 + 0.639227i \(0.779254\pi\)
\(164\) 26.8610 2.09749
\(165\) 0 0
\(166\) 19.2440 1.49362
\(167\) −2.91991 8.98655i −0.225949 0.695400i −0.998194 0.0600749i \(-0.980866\pi\)
0.772245 0.635325i \(-0.219134\pi\)
\(168\) 21.5259 + 15.6395i 1.66076 + 1.20661i
\(169\) −26.1051 + 18.9664i −2.00808 + 1.45896i
\(170\) 1.44612 4.45071i 0.110913 0.341354i
\(171\) 0.551150 1.69626i 0.0421475 0.129717i
\(172\) −15.0209 + 10.9133i −1.14534 + 0.832135i
\(173\) 7.34819 + 5.33877i 0.558672 + 0.405899i 0.830973 0.556313i \(-0.187784\pi\)
−0.272300 + 0.962212i \(0.587784\pi\)
\(174\) 1.27907 + 3.93658i 0.0969662 + 0.298431i
\(175\) −2.62383 −0.198343
\(176\) 0 0
\(177\) −5.20473 −0.391211
\(178\) 2.79625 + 8.60598i 0.209588 + 0.645045i
\(179\) 11.1393 + 8.09320i 0.832593 + 0.604914i 0.920292 0.391233i \(-0.127951\pi\)
−0.0876991 + 0.996147i \(0.527951\pi\)
\(180\) 4.76065 3.45881i 0.354838 0.257805i
\(181\) −7.37258 + 22.6905i −0.548000 + 1.68657i 0.165749 + 0.986168i \(0.446996\pi\)
−0.713749 + 0.700402i \(0.753004\pi\)
\(182\) 14.3136 44.0526i 1.06099 3.26540i
\(183\) −3.48231 + 2.53005i −0.257420 + 0.187026i
\(184\) −31.8684 23.1537i −2.34937 1.70691i
\(185\) −0.210055 0.646484i −0.0154436 0.0475305i
\(186\) −16.0461 −1.17656
\(187\) 0 0
\(188\) 32.5313 2.37259
\(189\) 4.56795 + 14.0587i 0.332269 + 1.02262i
\(190\) 3.14261 + 2.28324i 0.227989 + 0.165644i
\(191\) −12.9952 + 9.44154i −0.940297 + 0.683166i −0.948492 0.316800i \(-0.897391\pi\)
0.00819487 + 0.999966i \(0.497391\pi\)
\(192\) 3.96002 12.1877i 0.285790 0.879571i
\(193\) 6.63113 20.4085i 0.477320 1.46904i −0.365484 0.930818i \(-0.619097\pi\)
0.842804 0.538221i \(-0.180903\pi\)
\(194\) −3.13107 + 2.27485i −0.224798 + 0.163325i
\(195\) 7.29317 + 5.29880i 0.522275 + 0.379455i
\(196\) −0.174359 0.536622i −0.0124542 0.0383301i
\(197\) 9.21494 0.656537 0.328269 0.944584i \(-0.393535\pi\)
0.328269 + 0.944584i \(0.393535\pi\)
\(198\) 0 0
\(199\) −16.4880 −1.16880 −0.584401 0.811465i \(-0.698670\pi\)
−0.584401 + 0.811465i \(0.698670\pi\)
\(200\) 2.33876 + 7.19797i 0.165375 + 0.508973i
\(201\) −5.05150 3.67013i −0.356305 0.258871i
\(202\) 7.24399 5.26307i 0.509686 0.370308i
\(203\) −0.954620 + 2.93802i −0.0670012 + 0.206208i
\(204\) 3.60706 11.1014i 0.252545 0.777252i
\(205\) −4.44898 + 3.23238i −0.310731 + 0.225759i
\(206\) 10.5578 + 7.67068i 0.735596 + 0.534441i
\(207\) −1.93763 5.96340i −0.134674 0.414485i
\(208\) −67.8815 −4.70673
\(209\) 0 0
\(210\) −9.22436 −0.636541
\(211\) 4.58386 + 14.1077i 0.315566 + 0.971213i 0.975521 + 0.219907i \(0.0705755\pi\)
−0.659955 + 0.751306i \(0.729424\pi\)
\(212\) −56.4844 41.0383i −3.87936 2.81852i
\(213\) −4.21071 + 3.05926i −0.288513 + 0.209617i
\(214\) 5.72854 17.6306i 0.391595 1.20520i
\(215\) 1.17463 3.61515i 0.0801094 0.246551i
\(216\) 34.4957 25.0626i 2.34713 1.70529i
\(217\) −9.68861 7.03919i −0.657706 0.477851i
\(218\) −8.63015 26.5609i −0.584508 1.79893i
\(219\) −4.77950 −0.322968
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) −0.738473 2.27279i −0.0495631 0.152539i
\(223\) −18.9333 13.7558i −1.26786 0.921157i −0.268749 0.963210i \(-0.586610\pi\)
−0.999115 + 0.0420528i \(0.986610\pi\)
\(224\) 24.0623 17.4823i 1.60773 1.16809i
\(225\) −0.372282 + 1.14577i −0.0248188 + 0.0763844i
\(226\) −11.1640 + 34.3592i −0.742618 + 2.28554i
\(227\) 2.12272 1.54225i 0.140890 0.102363i −0.515108 0.857125i \(-0.672248\pi\)
0.655998 + 0.754763i \(0.272248\pi\)
\(228\) 7.83861 + 5.69508i 0.519124 + 0.377166i
\(229\) −6.80969 20.9581i −0.449997 1.38495i −0.876910 0.480655i \(-0.840399\pi\)
0.426913 0.904293i \(-0.359601\pi\)
\(230\) 13.6563 0.900471
\(231\) 0 0
\(232\) 8.91079 0.585022
\(233\) 1.65161 + 5.08314i 0.108201 + 0.333007i 0.990468 0.137741i \(-0.0439841\pi\)
−0.882268 + 0.470748i \(0.843984\pi\)
\(234\) −17.2059 12.5008i −1.12478 0.817203i
\(235\) −5.38815 + 3.91472i −0.351484 + 0.255368i
\(236\) −5.86319 + 18.0451i −0.381661 + 1.17463i
\(237\) −6.26731 + 19.2888i −0.407105 + 1.25294i
\(238\) 9.93382 7.21734i 0.643914 0.467831i
\(239\) 10.1790 + 7.39550i 0.658427 + 0.478375i 0.866131 0.499817i \(-0.166599\pi\)
−0.207705 + 0.978192i \(0.566599\pi\)
\(240\) 4.17739 + 12.8567i 0.269649 + 0.829895i
\(241\) −4.28687 −0.276141 −0.138071 0.990422i \(-0.544090\pi\)
−0.138071 + 0.990422i \(0.544090\pi\)
\(242\) 0 0
\(243\) 11.6298 0.746052
\(244\) 4.84893 + 14.9235i 0.310421 + 0.955378i
\(245\) 0.0934546 + 0.0678988i 0.00597060 + 0.00433789i
\(246\) −15.6409 + 11.3638i −0.997227 + 0.724528i
\(247\) 3.07804 9.47323i 0.195851 0.602767i
\(248\) −10.6747 + 32.8532i −0.677842 + 2.08618i
\(249\) −7.95027 + 5.77621i −0.503828 + 0.366052i
\(250\) −2.12272 1.54225i −0.134253 0.0975404i
\(251\) 3.10961 + 9.57040i 0.196277 + 0.604078i 0.999959 + 0.00901968i \(0.00287109\pi\)
−0.803682 + 0.595058i \(0.797129\pi\)
\(252\) 15.4399 0.972621
\(253\) 0 0
\(254\) −32.3069 −2.02712
\(255\) 0.738473 + 2.27279i 0.0462450 + 0.142327i
\(256\) 10.3303 + 7.50541i 0.645644 + 0.469088i
\(257\) 2.56092 1.86062i 0.159746 0.116062i −0.505041 0.863095i \(-0.668523\pi\)
0.664786 + 0.747033i \(0.268523\pi\)
\(258\) 4.12956 12.7095i 0.257095 0.791257i
\(259\) 0.551150 1.69626i 0.0342468 0.105401i
\(260\) 26.5871 19.3166i 1.64886 1.19797i
\(261\) 1.14752 + 0.833721i 0.0710296 + 0.0516060i
\(262\) 15.8190 + 48.6859i 0.977302 + 3.00783i
\(263\) 22.3681 1.37928 0.689638 0.724155i \(-0.257770\pi\)
0.689638 + 0.724155i \(0.257770\pi\)
\(264\) 0 0
\(265\) 14.2939 0.878070
\(266\) 3.14957 + 9.69338i 0.193113 + 0.594339i
\(267\) −3.73836 2.71607i −0.228784 0.166221i
\(268\) −18.4151 + 13.3793i −1.12488 + 0.817273i
\(269\) 4.93614 15.1919i 0.300962 0.926266i −0.680191 0.733035i \(-0.738103\pi\)
0.981153 0.193231i \(-0.0618967\pi\)
\(270\) −4.56795 + 14.0587i −0.277996 + 0.855585i
\(271\) 12.6530 9.19294i 0.768615 0.558431i −0.132926 0.991126i \(-0.542437\pi\)
0.901541 + 0.432695i \(0.142437\pi\)
\(272\) −14.5580 10.5770i −0.882710 0.641326i
\(273\) 7.30932 + 22.4958i 0.442380 + 1.36151i
\(274\) −22.4711 −1.35753
\(275\) 0 0
\(276\) 34.0629 2.05035
\(277\) 7.38043 + 22.7146i 0.443447 + 1.36479i 0.884178 + 0.467150i \(0.154719\pi\)
−0.440731 + 0.897639i \(0.645281\pi\)
\(278\) −4.21071 3.05926i −0.252542 0.183482i
\(279\) −4.44852 + 3.23204i −0.266326 + 0.193497i
\(280\) −6.13652 + 18.8863i −0.366727 + 1.12867i
\(281\) 3.78356 11.6446i 0.225708 0.694659i −0.772511 0.635002i \(-0.780999\pi\)
0.998219 0.0596571i \(-0.0190007\pi\)
\(282\) −18.9426 + 13.7626i −1.12802 + 0.819553i
\(283\) 16.8709 + 12.2575i 1.00287 + 0.728630i 0.962702 0.270563i \(-0.0872098\pi\)
0.0401707 + 0.999193i \(0.487210\pi\)
\(284\) 5.86319 + 18.0451i 0.347917 + 1.07078i
\(285\) −1.98364 −0.117501
\(286\) 0 0
\(287\) −14.4291 −0.851722
\(288\) −4.22004 12.9879i −0.248668 0.765322i
\(289\) 11.1797 + 8.12256i 0.657632 + 0.477797i
\(290\) −2.49923 + 1.81579i −0.146760 + 0.106627i
\(291\) 0.610726 1.87962i 0.0358014 0.110185i
\(292\) −5.38416 + 16.5708i −0.315084 + 0.969730i
\(293\) −11.5936 + 8.42327i −0.677307 + 0.492093i −0.872463 0.488680i \(-0.837479\pi\)
0.195156 + 0.980772i \(0.437479\pi\)
\(294\) 0.328550 + 0.238706i 0.0191614 + 0.0139216i
\(295\) −1.20037 3.69436i −0.0698883 0.215094i
\(296\) −5.14464 −0.299026
\(297\) 0 0
\(298\) −48.1455 −2.78899
\(299\) −10.8212 33.3042i −0.625805 1.92603i
\(300\) −5.29470 3.84682i −0.305690 0.222096i
\(301\) 8.06889 5.86239i 0.465083 0.337903i
\(302\) 13.9649 42.9796i 0.803590 2.47320i
\(303\) −1.41297 + 4.34866i −0.0811728 + 0.249824i
\(304\) 12.0841 8.77958i 0.693068 0.503543i
\(305\) −2.59898 1.88827i −0.148817 0.108122i
\(306\) −1.74219 5.36190i −0.0995943 0.306520i
\(307\) 10.2952 0.587580 0.293790 0.955870i \(-0.405083\pi\)
0.293790 + 0.955870i \(0.405083\pi\)
\(308\) 0 0
\(309\) −6.66414 −0.379110
\(310\) −3.70072 11.3896i −0.210187 0.646888i
\(311\) 15.4944 + 11.2573i 0.878606 + 0.638345i 0.932882 0.360181i \(-0.117285\pi\)
−0.0542760 + 0.998526i \(0.517285\pi\)
\(312\) 55.1976 40.1034i 3.12495 2.27041i
\(313\) −4.62713 + 14.2408i −0.261541 + 0.804939i 0.730930 + 0.682453i \(0.239087\pi\)
−0.992470 + 0.122486i \(0.960913\pi\)
\(314\) −16.9438 + 52.1477i −0.956195 + 2.94286i
\(315\) −2.55731 + 1.85799i −0.144088 + 0.104686i
\(316\) 59.8150 + 43.4581i 3.36486 + 2.44471i
\(317\) 3.76334 + 11.5824i 0.211370 + 0.650531i 0.999391 + 0.0348827i \(0.0111057\pi\)
−0.788021 + 0.615648i \(0.788894\pi\)
\(318\) 50.2519 2.81799
\(319\) 0 0
\(320\) 9.56424 0.534657
\(321\) 2.92532 + 9.00320i 0.163275 + 0.502510i
\(322\) 28.9886 + 21.0614i 1.61547 + 1.17371i
\(323\) 2.13620 1.55204i 0.118862 0.0863580i
\(324\) −5.93859 + 18.2771i −0.329922 + 1.01539i
\(325\) −2.07910 + 6.39883i −0.115328 + 0.354943i
\(326\) −20.0712 + 14.5826i −1.11164 + 0.807654i
\(327\) 11.5378 + 8.38270i 0.638042 + 0.463565i
\(328\) 12.8614 + 39.5834i 0.710154 + 2.18563i
\(329\) −17.4750 −0.963430
\(330\) 0 0
\(331\) −15.8319 −0.870199 −0.435099 0.900382i \(-0.643287\pi\)
−0.435099 + 0.900382i \(0.643287\pi\)
\(332\) 11.0703 + 34.0710i 0.607563 + 1.86989i
\(333\) −0.662520 0.481349i −0.0363059 0.0263778i
\(334\) 20.0576 14.5727i 1.09751 0.797385i
\(335\) 1.44006 4.43204i 0.0786787 0.242148i
\(336\) −10.9607 + 33.7337i −0.597958 + 1.84033i
\(337\) −5.44317 + 3.95469i −0.296508 + 0.215426i −0.726086 0.687604i \(-0.758662\pi\)
0.429578 + 0.903030i \(0.358662\pi\)
\(338\) −68.4953 49.7647i −3.72565 2.70684i
\(339\) −5.70097 17.5458i −0.309634 0.952956i
\(340\) 8.71176 0.472462
\(341\) 0 0
\(342\) 4.67975 0.253052
\(343\) 5.76932 + 17.7561i 0.311514 + 0.958741i
\(344\) −23.2746 16.9100i −1.25488 0.911725i
\(345\) −5.64184 + 4.09904i −0.303746 + 0.220685i
\(346\) −7.36446 + 22.6655i −0.395916 + 1.21850i
\(347\) 10.3532 31.8638i 0.555788 1.71054i −0.138066 0.990423i \(-0.544088\pi\)
0.693853 0.720116i \(-0.255912\pi\)
\(348\) −6.23381 + 4.52913i −0.334167 + 0.242787i
\(349\) −18.4247 13.3863i −0.986252 0.716554i −0.0271551 0.999631i \(-0.508645\pi\)
−0.959097 + 0.283077i \(0.908645\pi\)
\(350\) −2.12742 6.54753i −0.113716 0.349980i
\(351\) 37.9050 2.02322
\(352\) 0 0
\(353\) −15.4617 −0.822942 −0.411471 0.911423i \(-0.634985\pi\)
−0.411471 + 0.911423i \(0.634985\pi\)
\(354\) −4.22004 12.9879i −0.224292 0.690301i
\(355\) −3.14261 2.28324i −0.166793 0.121182i
\(356\) −13.6281 + 9.90137i −0.722286 + 0.524772i
\(357\) −1.93763 + 5.96340i −0.102550 + 0.315617i
\(358\) −11.1640 + 34.3592i −0.590035 + 1.81594i
\(359\) −7.75526 + 5.63453i −0.409307 + 0.297379i −0.773321 0.634014i \(-0.781406\pi\)
0.364014 + 0.931393i \(0.381406\pi\)
\(360\) 7.37651 + 5.35935i 0.388776 + 0.282463i
\(361\) −5.19403 15.9856i −0.273370 0.841346i
\(362\) −62.5998 −3.29017
\(363\) 0 0
\(364\) 86.2280 4.51957
\(365\) −1.10230 3.39253i −0.0576970 0.177573i
\(366\) −9.13699 6.63841i −0.477598 0.346995i
\(367\) 8.76857 6.37074i 0.457716 0.332550i −0.334919 0.942247i \(-0.608709\pi\)
0.792635 + 0.609697i \(0.208709\pi\)
\(368\) 16.2270 49.9415i 0.845890 2.60338i
\(369\) −2.04727 + 6.30085i −0.106577 + 0.328009i
\(370\) 1.44293 1.04835i 0.0750143 0.0545011i
\(371\) 30.3421 + 22.0448i 1.57528 + 1.14451i
\(372\) −9.23069 28.4091i −0.478589 1.47295i
\(373\) −10.0212 −0.518878 −0.259439 0.965759i \(-0.583538\pi\)
−0.259439 + 0.965759i \(0.583538\pi\)
\(374\) 0 0
\(375\) 1.33988 0.0691909
\(376\) 15.5764 + 47.9394i 0.803294 + 2.47228i
\(377\) 6.40861 + 4.65613i 0.330060 + 0.239803i
\(378\) −31.3785 + 22.7978i −1.61394 + 1.17259i
\(379\) 1.29533 3.98661i 0.0665366 0.204778i −0.912261 0.409610i \(-0.865665\pi\)
0.978797 + 0.204832i \(0.0656647\pi\)
\(380\) −2.23459 + 6.87737i −0.114632 + 0.352802i
\(381\) 13.3470 9.69713i 0.683785 0.496799i
\(382\) −34.0971 24.7730i −1.74456 1.26750i
\(383\) 5.94672 + 18.3021i 0.303863 + 0.935195i 0.980099 + 0.198510i \(0.0636101\pi\)
−0.676236 + 0.736685i \(0.736390\pi\)
\(384\) 3.24753 0.165725
\(385\) 0 0
\(386\) 56.3042 2.86581
\(387\) −1.41512 4.35528i −0.0719345 0.221392i
\(388\) −5.82875 4.23483i −0.295910 0.214991i
\(389\) 22.9942 16.7063i 1.16585 0.847042i 0.175347 0.984507i \(-0.443895\pi\)
0.990507 + 0.137465i \(0.0438954\pi\)
\(390\) −7.30932 + 22.4958i −0.370122 + 1.13912i
\(391\) 2.86859 8.82860i 0.145071 0.446481i
\(392\) 0.707302 0.513885i 0.0357241 0.0259551i
\(393\) −21.1487 15.3654i −1.06681 0.775084i
\(394\) 7.47154 + 22.9951i 0.376411 + 1.15847i
\(395\) −15.1368 −0.761615
\(396\) 0 0
\(397\) −22.1784 −1.11310 −0.556552 0.830813i \(-0.687876\pi\)
−0.556552 + 0.830813i \(0.687876\pi\)
\(398\) −13.3686 41.1443i −0.670107 2.06238i
\(399\) −4.21071 3.05926i −0.210799 0.153155i
\(400\) −8.16235 + 5.93029i −0.408117 + 0.296515i
\(401\) 6.82182 20.9954i 0.340665 1.04846i −0.623198 0.782064i \(-0.714167\pi\)
0.963864 0.266396i \(-0.0858330\pi\)
\(402\) 5.06268 15.5813i 0.252503 0.777126i
\(403\) −24.8439 + 18.0502i −1.23756 + 0.899142i
\(404\) 13.4853 + 9.79765i 0.670919 + 0.487451i
\(405\) −1.21581 3.74187i −0.0604140 0.185935i
\(406\) −8.10557 −0.402273
\(407\) 0 0
\(408\) 18.0866 0.895418
\(409\) 7.62386 + 23.4638i 0.376975 + 1.16021i 0.942136 + 0.335230i \(0.108814\pi\)
−0.565161 + 0.824981i \(0.691186\pi\)
\(410\) −11.6734 8.48121i −0.576507 0.418857i
\(411\) 9.28349 6.74485i 0.457921 0.332699i
\(412\) −7.50724 + 23.1049i −0.369855 + 1.13830i
\(413\) 3.14957 9.69338i 0.154980 0.476980i
\(414\) 13.3101 9.67035i 0.654156 0.475272i
\(415\) −5.93358 4.31100i −0.291268 0.211619i
\(416\) −23.5679 72.5345i −1.15551 3.55629i
\(417\) 2.65783 0.130155
\(418\) 0 0
\(419\) 17.6535 0.862428 0.431214 0.902250i \(-0.358085\pi\)
0.431214 + 0.902250i \(0.358085\pi\)
\(420\) −5.30642 16.3315i −0.258927 0.796895i
\(421\) −1.23373 0.896358i −0.0601284 0.0436858i 0.557315 0.830301i \(-0.311832\pi\)
−0.617443 + 0.786615i \(0.711832\pi\)
\(422\) −31.4878 + 22.8772i −1.53280 + 1.11365i
\(423\) −2.47944 + 7.63094i −0.120555 + 0.371029i
\(424\) 33.4301 102.887i 1.62351 4.99665i
\(425\) −1.44293 + 1.04835i −0.0699923 + 0.0508524i
\(426\) −11.0482 8.02699i −0.535287 0.388909i
\(427\) −2.60473 8.01654i −0.126052 0.387948i
\(428\) 34.5099 1.66810
\(429\) 0 0
\(430\) 9.97370 0.480974
\(431\) −5.17583 15.9296i −0.249311 0.767300i −0.994897 0.100891i \(-0.967831\pi\)
0.745587 0.666409i \(-0.232169\pi\)
\(432\) 45.9852 + 33.4102i 2.21246 + 1.60745i
\(433\) −6.04742 + 4.39371i −0.290621 + 0.211148i −0.723537 0.690286i \(-0.757485\pi\)
0.432916 + 0.901434i \(0.357485\pi\)
\(434\) 9.71006 29.8845i 0.466098 1.43450i
\(435\) 0.487483 1.50032i 0.0233730 0.0719348i
\(436\) 42.0607 30.5589i 2.01434 1.46351i
\(437\) 6.23381 + 4.52913i 0.298204 + 0.216658i
\(438\) −3.87525 11.9268i −0.185167 0.569885i
\(439\) 17.4585 0.833250 0.416625 0.909078i \(-0.363213\pi\)
0.416625 + 0.909078i \(0.363213\pi\)
\(440\) 0 0
\(441\) 0.139166 0.00662695
\(442\) −9.72970 29.9449i −0.462794 1.42433i
\(443\) 11.8794 + 8.63091i 0.564408 + 0.410067i 0.833070 0.553168i \(-0.186581\pi\)
−0.268661 + 0.963235i \(0.586581\pi\)
\(444\) 3.59909 2.61489i 0.170805 0.124097i
\(445\) 1.06571 3.27993i 0.0505197 0.155484i
\(446\) 18.9752 58.3996i 0.898500 2.76530i
\(447\) 19.8903 14.4512i 0.940781 0.683517i
\(448\) 20.3022 + 14.7504i 0.959190 + 0.696892i
\(449\) −0.403974 1.24330i −0.0190647 0.0586752i 0.941072 0.338208i \(-0.109821\pi\)
−0.960136 + 0.279532i \(0.909821\pi\)
\(450\) −3.16101 −0.149011
\(451\) 0 0
\(452\) −67.2543 −3.16338
\(453\) 7.13128 + 21.9478i 0.335057 + 1.03120i
\(454\) 5.56966 + 4.04660i 0.261397 + 0.189916i
\(455\) −14.2819 + 10.3764i −0.669548 + 0.486455i
\(456\) −4.63926 + 14.2782i −0.217253 + 0.668637i
\(457\) 3.14957 9.69338i 0.147331 0.453437i −0.849973 0.526827i \(-0.823382\pi\)
0.997303 + 0.0733895i \(0.0233816\pi\)
\(458\) 46.7776 33.9859i 2.18577 1.58806i
\(459\) 8.12920 + 5.90621i 0.379439 + 0.275678i
\(460\) 7.85596 + 24.1782i 0.366286 + 1.12731i
\(461\) −4.12180 −0.191971 −0.0959857 0.995383i \(-0.530600\pi\)
−0.0959857 + 0.995383i \(0.530600\pi\)
\(462\) 0 0
\(463\) 32.7623 1.52259 0.761296 0.648404i \(-0.224563\pi\)
0.761296 + 0.648404i \(0.224563\pi\)
\(464\) 3.67073 + 11.2973i 0.170409 + 0.524465i
\(465\) 4.94756 + 3.59461i 0.229437 + 0.166696i
\(466\) −11.3454 + 8.24289i −0.525564 + 0.381845i
\(467\) 11.7162 36.0588i 0.542161 1.66860i −0.185485 0.982647i \(-0.559386\pi\)
0.727646 0.685953i \(-0.240614\pi\)
\(468\) 12.2345 37.6538i 0.565538 1.74055i
\(469\) 9.89215 7.18707i 0.456777 0.331868i
\(470\) −14.1376 10.2716i −0.652119 0.473792i
\(471\) −8.65248 26.6296i −0.398685 1.22703i
\(472\) −29.3993 −1.35321
\(473\) 0 0
\(474\) −53.2150 −2.44425
\(475\) −0.457488 1.40800i −0.0209910 0.0646037i
\(476\) 18.4927 + 13.4357i 0.847610 + 0.615824i
\(477\) 13.9315 10.1219i 0.637882 0.463448i
\(478\) −10.2016 + 31.3972i −0.466609 + 1.43607i
\(479\) −1.99626 + 6.14386i −0.0912116 + 0.280720i −0.986248 0.165273i \(-0.947149\pi\)
0.895036 + 0.445993i \(0.147149\pi\)
\(480\) −12.2876 + 8.92746i −0.560849 + 0.407481i
\(481\) −3.70001 2.68822i −0.168706 0.122572i
\(482\) −3.47583 10.6975i −0.158320 0.487257i
\(483\) −18.2978 −0.832579
\(484\) 0 0
\(485\) 1.47502 0.0669774
\(486\) 9.42954 + 29.0211i 0.427732 + 1.31643i
\(487\) −35.1612 25.5461i −1.59331 1.15761i −0.899019 0.437909i \(-0.855719\pi\)
−0.694288 0.719697i \(-0.744281\pi\)
\(488\) −19.6701 + 14.2912i −0.890423 + 0.646930i
\(489\) 3.91496 12.0490i 0.177040 0.544874i
\(490\) −0.0936615 + 0.288261i −0.00423120 + 0.0130223i
\(491\) 4.41213 3.20560i 0.199117 0.144667i −0.483759 0.875201i \(-0.660729\pi\)
0.682876 + 0.730534i \(0.260729\pi\)
\(492\) −29.1169 21.1546i −1.31269 0.953725i
\(493\) 0.648906 + 1.99713i 0.0292253 + 0.0899461i
\(494\) 26.1353 1.17588
\(495\) 0 0
\(496\) −46.0496 −2.06769
\(497\) −3.14957 9.69338i −0.141278 0.434808i
\(498\) −20.8602 15.1558i −0.934766 0.679147i
\(499\) −10.1030 + 7.34025i −0.452272 + 0.328595i −0.790492 0.612472i \(-0.790175\pi\)
0.338220 + 0.941067i \(0.390175\pi\)
\(500\) 1.50939 4.64542i 0.0675019 0.207750i
\(501\) −3.91232 + 12.0409i −0.174789 + 0.537946i
\(502\) −21.3608 + 15.5195i −0.953378 + 0.692670i
\(503\) 16.8709 + 12.2575i 0.752238 + 0.546533i 0.896520 0.443004i \(-0.146087\pi\)
−0.144282 + 0.989537i \(0.546087\pi\)
\(504\) 7.39284 + 22.7528i 0.329303 + 1.01349i
\(505\) −3.41259 −0.151858
\(506\) 0 0
\(507\) 43.2347 1.92012
\(508\) −18.5849 57.1985i −0.824572 2.53777i
\(509\) 21.5014 + 15.6217i 0.953033 + 0.692419i 0.951522 0.307580i \(-0.0995191\pi\)
0.00151069 + 0.999999i \(0.499519\pi\)
\(510\) −5.07277 + 3.68559i −0.224626 + 0.163201i
\(511\) 2.89225 8.90142i 0.127945 0.393776i
\(512\) −11.8511 + 36.4741i −0.523751 + 1.61194i
\(513\) −6.74774 + 4.90252i −0.297920 + 0.216452i
\(514\) 6.71941 + 4.88194i 0.296381 + 0.215333i
\(515\) −1.53696 4.73027i −0.0677264 0.208440i
\(516\) 24.8773 1.09516
\(517\) 0 0
\(518\) 4.67975 0.205617
\(519\) −3.76071 11.5743i −0.165077 0.508054i
\(520\) 41.1960 + 29.9307i 1.80657 + 1.31255i
\(521\) 18.6392 13.5421i 0.816596 0.593292i −0.0991393 0.995074i \(-0.531609\pi\)
0.915735 + 0.401782i \(0.131609\pi\)
\(522\) −1.15006 + 3.53952i −0.0503367 + 0.154920i
\(523\) −0.365665 + 1.12540i −0.0159894 + 0.0492104i −0.958733 0.284308i \(-0.908236\pi\)
0.942743 + 0.333519i \(0.108236\pi\)
\(524\) −77.0970 + 56.0143i −3.36800 + 2.44699i
\(525\) 2.84419 + 2.06642i 0.124131 + 0.0901861i
\(526\) 18.1362 + 55.8176i 0.790777 + 2.43376i
\(527\) −8.14058 −0.354609
\(528\) 0 0
\(529\) 4.08921 0.177792
\(530\) 11.5896 + 35.6693i 0.503422 + 1.54937i
\(531\) −3.78600 2.75069i −0.164298 0.119370i
\(532\) −15.3500 + 11.1525i −0.665509 + 0.483520i
\(533\) −11.4335 + 35.1887i −0.495240 + 1.52419i
\(534\) 3.74663 11.5309i 0.162133 0.498993i
\(535\) −5.71588 + 4.15283i −0.247119 + 0.179543i
\(536\) −28.5337 20.7310i −1.23247 0.895442i
\(537\) −5.70097 17.5458i −0.246015 0.757156i
\(538\) 41.9123 1.80697
\(539\) 0 0
\(540\) −27.5183 −1.18420
\(541\) −9.76663 30.0586i −0.419900 1.29232i −0.907794 0.419417i \(-0.862235\pi\)
0.487894 0.872903i \(-0.337765\pi\)
\(542\) 33.1993 + 24.1207i 1.42603 + 1.03607i
\(543\) 25.8619 18.7897i 1.10984 0.806345i
\(544\) 6.24761 19.2282i 0.267864 0.824401i
\(545\) −3.28914 + 10.1229i −0.140891 + 0.433619i
\(546\) −50.2097 + 36.4795i −2.14878 + 1.56118i
\(547\) 4.02856 + 2.92692i 0.172249 + 0.125146i 0.670570 0.741847i \(-0.266050\pi\)
−0.498321 + 0.866993i \(0.666050\pi\)
\(548\) −12.9268 39.7845i −0.552204 1.69951i
\(549\) −3.87021 −0.165177
\(550\) 0 0
\(551\) −1.74305 −0.0742564
\(552\) 16.3098 + 50.1965i 0.694192 + 2.13650i
\(553\) −32.1312 23.3447i −1.36636 0.992717i
\(554\) −50.6982 + 36.8344i −2.15396 + 1.56494i
\(555\) −0.281448 + 0.866209i −0.0119468 + 0.0367685i
\(556\) 2.99408 9.21483i 0.126977 0.390796i
\(557\) 20.3297 14.7704i 0.861399 0.625843i −0.0668666 0.997762i \(-0.521300\pi\)
0.928265 + 0.371919i \(0.121300\pi\)
\(558\) −11.6722 8.48032i −0.494122 0.359001i
\(559\) −7.90309 24.3232i −0.334265 1.02876i
\(560\) −26.4724 −1.11866
\(561\) 0 0
\(562\) 32.1258 1.35515
\(563\) −3.50289 10.7808i −0.147629 0.454356i 0.849711 0.527250i \(-0.176777\pi\)
−0.997340 + 0.0728935i \(0.976777\pi\)
\(564\) −35.2633 25.6203i −1.48485 1.07881i
\(565\) 11.1393 8.09320i 0.468635 0.340483i
\(566\) −16.9083 + 52.0384i −0.710708 + 2.18734i
\(567\) 3.19007 9.81803i 0.133970 0.412319i
\(568\) −23.7845 + 17.2805i −0.997977 + 0.725073i
\(569\) 9.67527 + 7.02949i 0.405608 + 0.294692i 0.771821 0.635839i \(-0.219346\pi\)
−0.366213 + 0.930531i \(0.619346\pi\)
\(570\) −1.60835 4.94999i −0.0673664 0.207332i
\(571\) −29.8054 −1.24732 −0.623659 0.781697i \(-0.714355\pi\)
−0.623659 + 0.781697i \(0.714355\pi\)
\(572\) 0 0
\(573\) 21.5223 0.899108
\(574\) −11.6992 36.0065i −0.488316 1.50288i
\(575\) −4.21071 3.05926i −0.175599 0.127580i
\(576\) 9.32176 6.77265i 0.388406 0.282194i
\(577\) −5.71240 + 17.5810i −0.237810 + 0.731905i 0.758926 + 0.651177i \(0.225724\pi\)
−0.996736 + 0.0807279i \(0.974276\pi\)
\(578\) −11.2045 + 34.4839i −0.466045 + 1.43434i
\(579\) −23.2610 + 16.9001i −0.966693 + 0.702344i
\(580\) −4.65252 3.38026i −0.193186 0.140357i
\(581\) −5.94672 18.3021i −0.246712 0.759300i
\(582\) 5.18561 0.214950
\(583\) 0 0
\(584\) −26.9973 −1.11716
\(585\) 2.50476 + 7.70886i 0.103559 + 0.318722i
\(586\) −30.4197 22.1012i −1.25663 0.912993i
\(587\) 2.17122 1.57748i 0.0896157 0.0651097i −0.542075 0.840330i \(-0.682361\pi\)
0.631691 + 0.775220i \(0.282361\pi\)
\(588\) −0.233620 + 0.719007i −0.00963431 + 0.0296514i
\(589\) 2.08809 6.42647i 0.0860381 0.264798i
\(590\) 8.24568 5.99084i 0.339469 0.246639i
\(591\) −9.98884 7.25731i −0.410886 0.298526i
\(592\) −2.11929 6.52252i −0.0871025 0.268074i
\(593\) −28.7251 −1.17960 −0.589800 0.807550i \(-0.700793\pi\)
−0.589800 + 0.807550i \(0.700793\pi\)
\(594\) 0 0
\(595\) −4.67975 −0.191851
\(596\) −27.6962 85.2402i −1.13448 3.49158i
\(597\) 17.8727 + 12.9853i 0.731481 + 0.531452i
\(598\) 74.3337 54.0066i 3.03973 2.20849i
\(599\) −10.5624 + 32.5078i −0.431569 + 1.32823i 0.464994 + 0.885314i \(0.346057\pi\)
−0.896562 + 0.442918i \(0.853943\pi\)
\(600\) 3.13365 9.64440i 0.127931 0.393731i
\(601\) 26.2585 19.0779i 1.07111 0.778205i 0.0949959 0.995478i \(-0.469716\pi\)
0.976111 + 0.217273i \(0.0697162\pi\)
\(602\) 21.1714 + 15.3819i 0.862882 + 0.626920i
\(603\) −1.73488 5.33941i −0.0706498 0.217438i
\(604\) 84.1276 3.42310
\(605\) 0 0
\(606\) −11.9973 −0.487359
\(607\) 1.65161 + 5.08314i 0.0670368 + 0.206318i 0.978964 0.204035i \(-0.0654055\pi\)
−0.911927 + 0.410353i \(0.865406\pi\)
\(608\) 13.5769 + 9.86417i 0.550615 + 0.400045i
\(609\) 3.34866 2.43294i 0.135694 0.0985877i
\(610\) 2.60473 8.01654i 0.105463 0.324580i
\(611\) −13.8471 + 42.6170i −0.560193 + 1.72410i
\(612\) 8.49089 6.16899i 0.343224 0.249367i
\(613\) 24.4368 + 17.7544i 0.986994 + 0.717093i 0.959261 0.282522i \(-0.0911711\pi\)
0.0277333 + 0.999615i \(0.491171\pi\)
\(614\) 8.34746 + 25.6909i 0.336876 + 1.03680i
\(615\) 7.36831 0.297119
\(616\) 0 0
\(617\) 0.973697 0.0391996 0.0195998 0.999808i \(-0.493761\pi\)
0.0195998 + 0.999808i \(0.493761\pi\)
\(618\) −5.40334 16.6298i −0.217354 0.668947i
\(619\) −1.47368 1.07069i −0.0592323 0.0430348i 0.557775 0.829992i \(-0.311655\pi\)
−0.617007 + 0.786957i \(0.711655\pi\)
\(620\) 18.0362 13.1041i 0.724350 0.526271i
\(621\) −9.06116 + 27.8874i −0.363612 + 1.11908i
\(622\) −15.5287 + 47.7924i −0.622644 + 1.91630i
\(623\) 7.32068 5.31879i 0.293297 0.213093i
\(624\) 73.5824 + 53.4607i 2.94565 + 2.14014i
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) −39.2884 −1.57028
\(627\) 0 0
\(628\) −102.073 −4.07316
\(629\) −0.374646 1.15304i −0.0149381 0.0459748i
\(630\) −6.70994 4.87506i −0.267330 0.194227i
\(631\) 26.1772 19.0189i 1.04210 0.757130i 0.0714054 0.997447i \(-0.477252\pi\)
0.970694 + 0.240318i \(0.0772516\pi\)
\(632\) −35.4014 + 108.954i −1.40819 + 4.33396i
\(633\) 6.14181 18.9026i 0.244115 0.751309i
\(634\) −25.8514 + 18.7822i −1.02669 + 0.745935i
\(635\) 9.96133 + 7.23733i 0.395303 + 0.287205i
\(636\) 28.9080 + 88.9697i 1.14628 + 3.52788i
\(637\) 0.777208 0.0307941
\(638\) 0 0
\(639\) −4.67975 −0.185128
\(640\) 0.748980 + 2.30512i 0.0296060 + 0.0911180i
\(641\) 11.1393 + 8.09320i 0.439977 + 0.319662i 0.785626 0.618702i \(-0.212341\pi\)
−0.345649 + 0.938364i \(0.612341\pi\)
\(642\) −20.0948 + 14.5997i −0.793079 + 0.576206i
\(643\) 9.93832 30.5870i 0.391929 1.20623i −0.539399 0.842051i \(-0.681348\pi\)
0.931328 0.364183i \(-0.118652\pi\)
\(644\) −20.6127 + 63.4394i −0.812254 + 2.49986i
\(645\) −4.12043 + 2.99367i −0.162242 + 0.117876i
\(646\) 5.60503 + 4.07230i 0.220527 + 0.160222i
\(647\) 6.02006 + 18.5278i 0.236673 + 0.728404i 0.996895 + 0.0787410i \(0.0250900\pi\)
−0.760222 + 0.649663i \(0.774910\pi\)
\(648\) −29.7774 −1.16977
\(649\) 0 0
\(650\) −17.6535 −0.692425
\(651\) 4.95851 + 15.2607i 0.194339 + 0.598115i
\(652\) −37.3642 27.1467i −1.46330 1.06315i
\(653\) −0.630757 + 0.458272i −0.0246834 + 0.0179336i −0.600059 0.799956i \(-0.704856\pi\)
0.575375 + 0.817890i \(0.304856\pi\)
\(654\) −11.5633 + 35.5883i −0.452163 + 1.39161i
\(655\) 6.02898 18.5553i 0.235572 0.725015i
\(656\) −44.8868 + 32.6121i −1.75253 + 1.27329i
\(657\) −3.47668 2.52596i −0.135638 0.0985469i
\(658\) −14.1689 43.6074i −0.552361 1.69999i
\(659\) −28.1929 −1.09824 −0.549119 0.835744i \(-0.685037\pi\)
−0.549119 + 0.835744i \(0.685037\pi\)
\(660\) 0 0
\(661\) 1.70340 0.0662547 0.0331274 0.999451i \(-0.489453\pi\)
0.0331274 + 0.999451i \(0.489453\pi\)
\(662\) −12.8366 39.5070i −0.498909 1.53548i
\(663\) 13.0078 + 9.45072i 0.505181 + 0.367035i
\(664\) −44.9077 + 32.6274i −1.74276 + 1.26619i
\(665\) 1.20037 3.69436i 0.0465484 0.143261i
\(666\) 0.663987 2.04354i 0.0257290 0.0791856i
\(667\) −4.95756 + 3.60188i −0.191958 + 0.139465i
\(668\) 37.3390 + 27.1284i 1.44469 + 1.04963i
\(669\) 9.68980 + 29.8221i 0.374629 + 1.15299i
\(670\) 12.2274 0.472385
\(671\) 0 0
\(672\) −39.8515 −1.53731
\(673\) 3.40056 + 10.4658i 0.131082 + 0.403429i 0.994960 0.100272i \(-0.0319713\pi\)
−0.863878 + 0.503701i \(0.831971\pi\)
\(674\) −14.2819 10.3764i −0.550120 0.399685i
\(675\) 4.55786 3.31148i 0.175432 0.127459i
\(676\) 48.7044 149.897i 1.87325 5.76526i
\(677\) −6.61012 + 20.3439i −0.254048 + 0.781878i 0.739968 + 0.672642i \(0.234840\pi\)
−0.994016 + 0.109236i \(0.965160\pi\)
\(678\) 39.1615 28.4525i 1.50399 1.09271i
\(679\) 3.13107 + 2.27485i 0.120159 + 0.0873009i
\(680\) 4.17132 + 12.8380i 0.159963 + 0.492315i
\(681\) −3.51561 −0.134718
\(682\) 0 0
\(683\) 34.0959 1.30464 0.652321 0.757942i \(-0.273795\pi\)
0.652321 + 0.757942i \(0.273795\pi\)
\(684\) 2.69208 + 8.28538i 0.102934 + 0.316799i
\(685\) 6.92861 + 5.03393i 0.264729 + 0.192337i
\(686\) −39.6310 + 28.7936i −1.51312 + 1.09935i
\(687\) −9.12414 + 28.0812i −0.348108 + 1.07137i
\(688\) 11.8511 36.4741i 0.451821 1.39056i
\(689\) 77.8043 56.5281i 2.96411 2.15355i
\(690\) −14.8032 10.7552i −0.563549 0.409443i
\(691\) 14.3136 + 44.0528i 0.544516 + 1.67585i 0.722138 + 0.691749i \(0.243160\pi\)
−0.177622 + 0.984099i \(0.556840\pi\)
\(692\) −44.3651 −1.68651
\(693\) 0 0
\(694\) 87.9077 3.33693
\(695\) 0.612978 + 1.88655i 0.0232516 + 0.0715610i
\(696\) −9.65914 7.01778i −0.366129 0.266008i
\(697\) −7.93502 + 5.76513i −0.300560 + 0.218370i
\(698\) 18.4655 56.8310i 0.698930 2.15108i
\(699\) 2.21296 6.81078i 0.0837017 0.257607i
\(700\) 10.3684 7.53309i 0.391889 0.284724i
\(701\) −35.0828 25.4891i −1.32506 0.962711i −0.999854 0.0170666i \(-0.994567\pi\)
−0.325203 0.945644i \(-0.605433\pi\)
\(702\) 30.7337 + 94.5886i 1.15997 + 3.57002i
\(703\) 1.00635 0.0379552
\(704\) 0 0
\(705\) 8.92375 0.336088
\(706\) −12.5365 38.5832i −0.471816 1.45210i
\(707\) −7.24399 5.26307i −0.272438 0.197938i
\(708\) 20.5672 14.9429i 0.772962 0.561589i
\(709\) 5.92646 18.2398i 0.222573 0.685009i −0.775956 0.630787i \(-0.782732\pi\)
0.998529 0.0542219i \(-0.0172678\pi\)
\(710\) 3.14957 9.69338i 0.118201 0.363786i
\(711\) −14.7530 + 10.7187i −0.553282 + 0.401983i
\(712\) −21.1164 15.3419i −0.791370 0.574964i
\(713\) −7.34089 22.5929i −0.274919 0.846112i
\(714\) −16.4522 −0.615708
\(715\) 0 0
\(716\) −67.2543 −2.51341
\(717\) −5.20950 16.0332i −0.194552 0.598771i
\(718\) −20.3485 14.7840i −0.759399 0.551736i
\(719\) 26.1263 18.9819i 0.974348 0.707906i 0.0179100 0.999840i \(-0.494299\pi\)
0.956438 + 0.291934i \(0.0942988\pi\)
\(720\) −3.75603 + 11.5599i −0.139979 + 0.430811i
\(721\) 4.03271 12.4114i 0.150186 0.462225i
\(722\) 35.6792 25.9225i 1.32784 0.964734i
\(723\) 4.64689 + 3.37616i 0.172820 + 0.125561i
\(724\) −36.0113 110.831i −1.33835 4.11901i
\(725\) 1.17737 0.0437264
\(726\) 0 0
\(727\) −40.8622 −1.51550 −0.757748 0.652548i \(-0.773700\pi\)
−0.757748 + 0.652548i \(0.773700\pi\)
\(728\) 41.2872 + 127.069i 1.53021 + 4.70949i
\(729\) −22.1556 16.0970i −0.820577 0.596184i
\(730\) 7.57200 5.50138i 0.280252 0.203615i
\(731\) 2.09503 6.44784i 0.0774875 0.238482i
\(732\) 6.49697 19.9956i 0.240135 0.739059i
\(733\) 8.02880 5.83326i 0.296550 0.215457i −0.429554 0.903041i \(-0.641329\pi\)
0.726104 + 0.687585i \(0.241329\pi\)
\(734\) 23.0072 + 16.7157i 0.849213 + 0.616989i
\(735\) −0.0478289 0.147202i −0.00176420 0.00542964i
\(736\) 58.9987 2.17472
\(737\) 0 0
\(738\) −17.3832 −0.639883
\(739\) 10.3127 + 31.7392i 0.379358 + 1.16754i 0.940491 + 0.339818i \(0.110366\pi\)
−0.561133 + 0.827726i \(0.689634\pi\)
\(740\) 2.68614 + 1.95159i 0.0987443 + 0.0717419i
\(741\) −10.7973 + 7.84468i −0.396648 + 0.288181i
\(742\) −30.4093 + 93.5901i −1.11636 + 3.43580i
\(743\) 1.17647 3.62081i 0.0431606 0.132835i −0.927154 0.374680i \(-0.877753\pi\)
0.970315 + 0.241845i \(0.0777526\pi\)
\(744\) 37.4451 27.2054i 1.37280 0.997399i
\(745\) 14.8449 + 10.7855i 0.543875 + 0.395148i
\(746\) −8.12528 25.0070i −0.297487 0.915572i
\(747\) −8.83587 −0.323287
\(748\) 0 0
\(749\) −18.5379 −0.677361
\(750\) 1.08638 + 3.34354i 0.0396691 + 0.122089i
\(751\) −18.2105 13.2307i −0.664509 0.482794i 0.203674 0.979039i \(-0.434712\pi\)
−0.868183 + 0.496245i \(0.834712\pi\)
\(752\) −54.3622 + 39.4965i −1.98239 + 1.44029i
\(753\) 4.16650 12.8232i 0.151836 0.467302i
\(754\) −6.42280 + 19.7673i −0.233904 + 0.719884i
\(755\) −13.9341 + 10.1237i −0.507112 + 0.368439i
\(756\) −58.4137 42.4401i −2.12449 1.54353i
\(757\) −10.4116 32.0437i −0.378417 1.16465i −0.941144 0.338005i \(-0.890248\pi\)
0.562728 0.826642i \(-0.309752\pi\)
\(758\) 10.9985 0.399483
\(759\) 0 0
\(760\) −11.2047 −0.406438
\(761\) 5.80084 + 17.8531i 0.210280 + 0.647176i 0.999455 + 0.0330075i \(0.0105085\pi\)
−0.789175 + 0.614169i \(0.789491\pi\)
\(762\) 35.0201 + 25.4436i 1.26865 + 0.921725i
\(763\) −22.5940 + 16.4155i −0.817959 + 0.594282i
\(764\) 24.2452 74.6190i 0.877160 2.69962i
\(765\) −0.663987 + 2.04354i −0.0240065 + 0.0738844i
\(766\) −40.8497 + 29.6790i −1.47596 + 1.07235i
\(767\) −21.1439 15.3619i −0.763462 0.554687i
\(768\) −5.28692 16.2715i −0.190775 0.587146i
\(769\) −21.5618 −0.777539 −0.388770 0.921335i \(-0.627100\pi\)
−0.388770 + 0.921335i \(0.627100\pi\)
\(770\) 0 0
\(771\) −4.24134 −0.152748
\(772\) 32.3897 + 99.6852i 1.16573 + 3.58775i
\(773\) 18.9174 + 13.7443i 0.680411 + 0.494347i 0.873494 0.486835i \(-0.161849\pi\)
−0.193083 + 0.981182i \(0.561849\pi\)
\(774\) 9.72083 7.06260i 0.349408 0.253860i
\(775\) −1.41043 + 4.34085i −0.0506640 + 0.155928i
\(776\) 3.44973 10.6172i 0.123838 0.381135i
\(777\) −1.93335 + 1.40466i −0.0693584 + 0.0503919i
\(778\) 60.3329 + 43.8344i 2.16304 + 1.57154i
\(779\) −2.51584 7.74296i −0.0901394 0.277420i
\(780\) −44.0329 −1.57663
\(781\) 0 0
\(782\) 24.3569 0.870999
\(783\) −2.04973 6.30843i −0.0732515 0.225445i
\(784\) 0.942884 + 0.685045i 0.0336744 + 0.0244659i
\(785\) 16.9064 12.2832i 0.603415 0.438407i
\(786\) 21.1955 65.2331i 0.756019 2.32679i
\(787\) 7.75476 23.8667i 0.276427 0.850756i −0.712411 0.701763i \(-0.752397\pi\)
0.988838 0.148993i \(-0.0476033\pi\)
\(788\) −36.4140 + 26.4563i −1.29720 + 0.942468i
\(789\) −24.2466 17.6162i −0.863203 0.627154i
\(790\) −12.2730 37.7725i −0.436655 1.34389i
\(791\) 36.1274 1.28454
\(792\) 0 0
\(793\) −21.6142 −0.767542
\(794\) −17.9824 55.3443i −0.638173 1.96410i
\(795\) −15.4944 11.2573i −0.549530 0.399257i
\(796\) 65.1544 47.3375i 2.30934 1.67783i
\(797\) −3.73177 + 11.4852i −0.132186 + 0.406827i −0.995142 0.0984529i \(-0.968611\pi\)
0.862956 + 0.505280i \(0.168611\pi\)
\(798\) 4.22004 12.9879i 0.149388 0.459768i
\(799\) −9.61008 + 6.98214i −0.339980 + 0.247010i
\(800\) −9.17069 6.66289i −0.324233 0.235569i
\(801\) −1.28390 3.95143i −0.0453643 0.139617i
\(802\) 57.9233 2.04534
\(803\) 0 0
\(804\) 30.4987 1.07561
\(805\) −4.22004 12.9879i −0.148737 0.457765i
\(806\) −65.1862 47.3605i −2.29609 1.66820i
\(807\) −17.3152 + 12.5802i −0.609525 + 0.442846i
\(808\) −7.98125 + 24.5638i −0.280779 + 0.864150i
\(809\) 2.81574 8.66595i 0.0989961 0.304679i −0.889278 0.457366i \(-0.848793\pi\)
0.988275 + 0.152688i \(0.0487928\pi\)
\(810\) 8.35172 6.06788i 0.293449 0.213204i
\(811\) −2.41895 1.75747i −0.0849409 0.0617132i 0.544504 0.838758i \(-0.316718\pi\)
−0.629445 + 0.777045i \(0.716718\pi\)
\(812\) −4.66282 14.3507i −0.163633 0.503611i
\(813\) −20.9556 −0.734946
\(814\) 0 0
\(815\) 9.45539 0.331208
\(816\) 7.45061 + 22.9306i 0.260824 + 0.802732i
\(817\) 4.55277 + 3.30778i 0.159281 + 0.115725i
\(818\) −52.3704 + 38.0493i −1.83109 + 1.33036i
\(819\) −6.57206 + 20.2267i −0.229646 + 0.706779i
\(820\) 8.30050 25.5463i 0.289866 0.892116i
\(821\) −28.5337 + 20.7310i −0.995835 + 0.723516i −0.961191 0.275884i \(-0.911030\pi\)
−0.0346436 + 0.999400i \(0.511030\pi\)
\(822\) 24.3583 + 17.6973i 0.849593 + 0.617266i
\(823\) 4.80755 + 14.7961i 0.167581 + 0.515760i 0.999217 0.0395600i \(-0.0125956\pi\)
−0.831636 + 0.555320i \(0.812596\pi\)
\(824\) −37.6429 −1.31135
\(825\) 0 0
\(826\) 26.7427 0.930496
\(827\) −3.25374 10.0140i −0.113144 0.348220i 0.878412 0.477905i \(-0.158604\pi\)
−0.991555 + 0.129684i \(0.958604\pi\)
\(828\) 24.7779 + 18.0022i 0.861091 + 0.625619i
\(829\) −20.7310 + 15.0619i −0.720016 + 0.523122i −0.886389 0.462941i \(-0.846794\pi\)
0.166373 + 0.986063i \(0.446794\pi\)
\(830\) 5.94672 18.3021i 0.206414 0.635276i
\(831\) 9.88886 30.4348i 0.343041 1.05577i
\(832\) 52.0597 37.8236i 1.80485 1.31130i
\(833\) 0.166682 + 0.121101i 0.00577518 + 0.00419592i
\(834\) 2.15499 + 6.63238i 0.0746212 + 0.229661i
\(835\) −9.44902 −0.326997
\(836\) 0 0
\(837\) 25.7141 0.888809
\(838\) 14.3136 + 44.0526i 0.494454 + 1.52177i
\(839\) −21.1362 15.3564i −0.729704 0.530161i 0.159766 0.987155i \(-0.448926\pi\)
−0.889470 + 0.456994i \(0.848926\pi\)
\(840\) 21.5259 15.6395i 0.742715 0.539614i
\(841\) −8.53313 + 26.2623i −0.294246 + 0.905596i
\(842\) 1.23646 3.80544i 0.0426113 0.131144i
\(843\) −13.2721 + 9.64278i −0.457117 + 0.332115i
\(844\) −58.6173 42.5879i −2.01769 1.46594i
\(845\) 9.97125 + 30.6884i 0.343021 + 1.05571i
\(846\) −21.0527 −0.723806
\(847\) 0 0
\(848\) 144.215 4.95235
\(849\) −8.63433 26.5737i −0.296330 0.912009i
\(850\) −3.78600 2.75069i −0.129859 0.0943479i
\(851\) 2.86225 2.07955i 0.0981166 0.0712859i
\(852\) 7.85596 24.1782i 0.269141 0.828330i
\(853\) 0.851310 2.62006i 0.0291483 0.0897092i −0.935424 0.353528i \(-0.884982\pi\)
0.964572 + 0.263819i \(0.0849820\pi\)
\(854\) 17.8926 12.9998i 0.612273 0.444842i
\(855\) −1.44293 1.04835i −0.0493471 0.0358528i
\(856\) 16.5239 + 50.8552i 0.564774 + 1.73820i
\(857\) 20.3164 0.693997 0.346998 0.937866i \(-0.387201\pi\)
0.346998 + 0.937866i \(0.387201\pi\)
\(858\) 0 0
\(859\) 22.6249 0.771951 0.385975 0.922509i \(-0.373865\pi\)
0.385975 + 0.922509i \(0.373865\pi\)
\(860\) 5.73748 + 17.6582i 0.195647 + 0.602138i
\(861\) 15.6409 + 11.3638i 0.533040 + 0.387276i
\(862\) 35.5542 25.8316i 1.21098 0.879829i
\(863\) 13.3214 40.9989i 0.453465 1.39562i −0.419464 0.907772i \(-0.637782\pi\)
0.872928 0.487848i \(-0.162218\pi\)
\(864\) −19.7347 + 60.7370i −0.671387 + 2.06632i
\(865\) 7.34819 5.33877i 0.249846 0.181524i
\(866\) −15.8674 11.5283i −0.539196 0.391749i
\(867\) −5.72165 17.6094i −0.194317 0.598048i
\(868\) 58.4955 1.98547
\(869\) 0 0
\(870\) 4.13917 0.140331
\(871\) −9.68888 29.8193i −0.328295 1.01039i
\(872\) 65.1721 + 47.3503i 2.20701 + 1.60348i
\(873\) 1.43763 1.04450i 0.0486563 0.0353509i
\(874\) −6.24761 + 19.2282i −0.211329 + 0.650402i
\(875\) −0.810808 + 2.49541i −0.0274103 + 0.0843603i
\(876\) 18.8868 13.7221i 0.638126 0.463626i
\(877\) 13.4987 + 9.80735i 0.455817 + 0.331171i 0.791888 0.610666i \(-0.209098\pi\)
−0.336071 + 0.941837i \(0.609098\pi\)
\(878\) 14.1555 + 43.5662i 0.477726 + 1.47029i
\(879\) 19.2011 0.647638
\(880\) 0 0
\(881\) −43.5116 −1.46594 −0.732972 0.680259i \(-0.761867\pi\)
−0.732972 + 0.680259i \(0.761867\pi\)
\(882\) 0.112837 + 0.347276i 0.00379941 + 0.0116934i
\(883\) 21.8431 + 15.8700i 0.735080 + 0.534067i 0.891167 0.453676i \(-0.149888\pi\)
−0.156086 + 0.987743i \(0.549888\pi\)
\(884\) 47.4196 34.4523i 1.59489 1.15876i
\(885\) −1.60835 + 4.94999i −0.0540641 + 0.166392i
\(886\) −11.9057 + 36.6420i −0.399981 + 1.23101i
\(887\) 18.5591 13.4840i 0.623153 0.452747i −0.230869 0.972985i \(-0.574157\pi\)
0.854021 + 0.520238i \(0.174157\pi\)
\(888\) 5.57671 + 4.05172i 0.187142 + 0.135967i
\(889\) 9.98338 + 30.7257i 0.334832 + 1.03051i
\(890\) 9.04886 0.303318
\(891\) 0 0
\(892\) 114.311 3.82740
\(893\) −3.04693 9.37748i −0.101962 0.313805i
\(894\) 52.1889 + 37.9174i 1.74546 + 1.26815i
\(895\) 11.1393 8.09320i 0.372347 0.270526i
\(896\) −1.96520 + 6.04825i −0.0656526 + 0.202058i
\(897\) −14.4990 + 44.6235i −0.484109 + 1.48993i
\(898\) 2.77501 2.01616i 0.0926033 0.0672802i
\(899\) 4.34749 + 3.15863i 0.144997 + 0.105346i
\(900\) −1.81841 5.59648i −0.0606135 0.186549i
\(901\) 25.4941 0.849331
\(902\) 0 0
\(903\) −13.3635 −0.444710
\(904\) −32.2023 99.1086i −1.07103 3.29630i
\(905\) 19.3017 + 14.0235i 0.641609 + 0.466156i
\(906\) −48.9867 + 35.5909i −1.62747 + 1.18243i
\(907\) 12.8964 39.6911i 0.428219 1.31792i −0.471659 0.881781i \(-0.656345\pi\)
0.899878 0.436141i \(-0.143655\pi\)
\(908\) −3.96038 + 12.1888i −0.131430 + 0.404499i
\(909\) −3.32607 + 2.41653i −0.110319 + 0.0801514i
\(910\) −37.4734 27.2260i −1.24223 0.902533i
\(911\) −11.9673 36.8316i −0.396495 1.22029i −0.927791 0.373100i \(-0.878295\pi\)
0.531296 0.847186i \(-0.321705\pi\)
\(912\) −20.0134 −0.662708
\(913\) 0 0
\(914\) 26.7427 0.884569
\(915\) 1.33012 + 4.09370i 0.0439726 + 0.135334i
\(916\) 87.0805 + 63.2677i 2.87722 + 2.09042i
\(917\) 41.4147 30.0895i 1.36763 0.993644i
\(918\) −8.14720 + 25.0745i −0.268898 + 0.827582i
\(919\) −0.881305 + 2.71238i −0.0290716 + 0.0894730i −0.964540 0.263938i \(-0.914978\pi\)
0.935468 + 0.353411i \(0.114978\pi\)
\(920\) −31.8684 + 23.1537i −1.05067 + 0.763355i
\(921\) −11.1599 8.10812i −0.367730 0.267172i
\(922\) −3.34199 10.2856i −0.110063 0.338738i
\(923\) −26.1353 −0.860253
\(924\) 0 0
\(925\) −0.679754 −0.0223502
\(926\) 26.5639 + 81.7554i 0.872945 + 2.68665i
\(927\) −4.84760 3.52199i −0.159216 0.115677i
\(928\) −10.7973 + 7.84468i −0.354438 + 0.257514i
\(929\) −4.08779 + 12.5809i −0.134116 + 0.412767i −0.995451 0.0952697i \(-0.969629\pi\)
0.861335 + 0.508037i \(0.169629\pi\)
\(930\) −4.95851 + 15.2607i −0.162596 + 0.500419i
\(931\) −0.138356 + 0.100522i −0.00453444 + 0.00329446i
\(932\) −21.1204 15.3449i −0.691821 0.502637i
\(933\) −7.92984 24.4055i −0.259611 0.799001i
\(934\) 99.4810 3.25512
\(935\) 0 0
\(936\) 61.3462 2.00516
\(937\) 0.519316 + 1.59829i 0.0169653 + 0.0522139i 0.959181 0.282794i \(-0.0912611\pi\)
−0.942215 + 0.335008i \(0.891261\pi\)
\(938\) 25.9553 + 18.8576i 0.847471 + 0.615724i
\(939\) 16.2312 11.7927i 0.529686 0.384840i
\(940\) 10.0527 30.9391i 0.327883 1.00912i
\(941\) −4.53795 + 13.9664i −0.147933 + 0.455291i −0.997377 0.0723886i \(-0.976938\pi\)
0.849443 + 0.527680i \(0.176938\pi\)
\(942\) 59.4362 43.1830i 1.93654 1.40698i
\(943\) −23.1558 16.8236i −0.754055 0.547853i
\(944\) −12.1108 37.2732i −0.394173 1.21314i
\(945\) 14.7822 0.480865
\(946\) 0 0
\(947\) 17.6535 0.573660 0.286830 0.957981i \(-0.407399\pi\)
0.286830 + 0.957981i \(0.407399\pi\)
\(948\) −30.6126 94.2158i −0.994250 3.05999i
\(949\) −19.4164 14.1068i −0.630283 0.457928i
\(950\) 3.14261 2.28324i 0.101960 0.0740782i
\(951\) 5.04241 15.5190i 0.163511 0.503237i
\(952\) −10.9448 + 33.6847i −0.354724 + 1.09173i
\(953\) −17.6106 + 12.7948i −0.570462 + 0.414465i −0.835273 0.549835i \(-0.814690\pi\)
0.264811 + 0.964300i \(0.414690\pi\)
\(954\) 36.5540 + 26.5580i 1.18348 + 0.859849i
\(955\) 4.96371 + 15.2767i 0.160622 + 0.494344i
\(956\) −61.4564 −1.98764
\(957\) 0 0
\(958\) −16.9500 −0.547631
\(959\) 6.94395 + 21.3713i 0.224232 + 0.690115i
\(960\) −10.3675 7.53241i −0.334609 0.243107i
\(961\) 8.22587 5.97645i 0.265351 0.192789i
\(962\) 3.70820 11.4127i 0.119557 0.367960i
\(963\) −2.63025 + 8.09509i −0.0847588 + 0.260861i
\(964\) 16.9401 12.3077i 0.545604 0.396405i
\(965\) −17.3605 12.6132i −0.558855 0.406032i
\(966\) −14.8360 45.6605i −0.477340 1.46910i
\(967\) −14.0684 −0.452409 −0.226204 0.974080i \(-0.572632\pi\)
−0.226204 + 0.974080i \(0.572632\pi\)
\(968\) 0 0
\(969\) −3.53793 −0.113655
\(970\) 1.19596 + 3.68079i 0.0384000 + 0.118183i
\(971\) 11.9187 + 8.65946i 0.382490 + 0.277895i 0.762371 0.647140i \(-0.224035\pi\)
−0.379881 + 0.925035i \(0.624035\pi\)
\(972\) −45.9567 + 33.3895i −1.47406 + 1.07097i
\(973\) −1.60835 + 4.94999i −0.0515613 + 0.158689i
\(974\) 35.2391 108.455i 1.12913 3.47511i
\(975\) 7.29317 5.29880i 0.233568 0.169697i
\(976\) −26.2216 19.0511i −0.839335 0.609812i
\(977\) 4.06105 + 12.4986i 0.129924 + 0.399866i 0.994766 0.102179i \(-0.0325813\pi\)
−0.864842 + 0.502045i \(0.832581\pi\)
\(978\) 33.2415 1.06294
\(979\) 0 0
\(980\) −0.564237 −0.0180239
\(981\) 3.96253 + 12.1954i 0.126514 + 0.389370i
\(982\) 11.5767 + 8.41095i 0.369426 + 0.268404i
\(983\) −14.8987 + 10.8245i −0.475193 + 0.345248i −0.799462 0.600717i \(-0.794882\pi\)
0.324269 + 0.945965i \(0.394882\pi\)
\(984\) 17.2327 53.0369i 0.549360 1.69076i
\(985\) 2.84757 8.76393i 0.0907312 0.279242i
\(986\) −4.45752 + 3.23857i −0.141956 + 0.103137i
\(987\) 18.9426 + 13.7626i 0.602951 + 0.438069i
\(988\) 15.0346 + 46.2718i 0.478315 + 1.47210i
\(989\) 19.7842 0.629101
\(990\) 0 0
\(991\) 44.3591 1.40911 0.704557 0.709647i \(-0.251146\pi\)
0.704557 + 0.709647i \(0.251146\pi\)
\(992\) −15.9880 49.2061i −0.507620 1.56229i
\(993\) 17.1615 + 12.4686i 0.544603 + 0.395678i
\(994\) 21.6353 15.7189i 0.686229 0.498575i
\(995\) −5.09507 + 15.6810i −0.161524 + 0.497121i
\(996\) 14.8329 45.6509i 0.469998 1.44650i
\(997\) −40.8497 + 29.6790i −1.29372 + 0.939944i −0.999873 0.0159081i \(-0.994936\pi\)
−0.293848 + 0.955852i \(0.594936\pi\)
\(998\) −26.5085 19.2596i −0.839113 0.609651i
\(999\) 1.18341 + 3.64218i 0.0374416 + 0.115233i
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 605.2.g.q.511.6 24
11.2 odd 10 inner 605.2.g.q.251.1 24
11.3 even 5 605.2.a.m.1.6 yes 6
11.4 even 5 inner 605.2.g.q.366.1 24
11.5 even 5 inner 605.2.g.q.81.1 24
11.6 odd 10 inner 605.2.g.q.81.6 24
11.7 odd 10 inner 605.2.g.q.366.6 24
11.8 odd 10 605.2.a.m.1.1 6
11.9 even 5 inner 605.2.g.q.251.6 24
11.10 odd 2 inner 605.2.g.q.511.1 24
33.8 even 10 5445.2.a.bx.1.6 6
33.14 odd 10 5445.2.a.bx.1.1 6
44.3 odd 10 9680.2.a.cw.1.4 6
44.19 even 10 9680.2.a.cw.1.3 6
55.14 even 10 3025.2.a.bg.1.1 6
55.19 odd 10 3025.2.a.bg.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.a.m.1.1 6 11.8 odd 10
605.2.a.m.1.6 yes 6 11.3 even 5
605.2.g.q.81.1 24 11.5 even 5 inner
605.2.g.q.81.6 24 11.6 odd 10 inner
605.2.g.q.251.1 24 11.2 odd 10 inner
605.2.g.q.251.6 24 11.9 even 5 inner
605.2.g.q.366.1 24 11.4 even 5 inner
605.2.g.q.366.6 24 11.7 odd 10 inner
605.2.g.q.511.1 24 11.10 odd 2 inner
605.2.g.q.511.6 24 1.1 even 1 trivial
3025.2.a.bg.1.1 6 55.14 even 10
3025.2.a.bg.1.6 6 55.19 odd 10
5445.2.a.bx.1.1 6 33.14 odd 10
5445.2.a.bx.1.6 6 33.8 even 10
9680.2.a.cw.1.3 6 44.19 even 10
9680.2.a.cw.1.4 6 44.3 odd 10