Properties

Label 187.2.e.b.89.7
Level $187$
Weight $2$
Character 187.89
Analytic conductor $1.493$
Analytic rank $0$
Dimension $28$
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] = [187,2,Mod(89,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 89.7
Character \(\chi\) \(=\) 187.89
Dual form 187.2.e.b.166.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.0421125i q^{2} +(-0.440583 + 0.440583i) q^{3} +1.99823 q^{4} +(2.27271 - 2.27271i) q^{5} +(-0.0185541 - 0.0185541i) q^{6} +(-3.03167 - 3.03167i) q^{7} +0.168375i q^{8} +2.61177i q^{9} +O(q^{10})\) \(q+0.0421125i q^{2} +(-0.440583 + 0.440583i) q^{3} +1.99823 q^{4} +(2.27271 - 2.27271i) q^{5} +(-0.0185541 - 0.0185541i) q^{6} +(-3.03167 - 3.03167i) q^{7} +0.168375i q^{8} +2.61177i q^{9} +(0.0957096 + 0.0957096i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-0.880384 + 0.880384i) q^{12} +3.32292 q^{13} +(0.127671 - 0.127671i) q^{14} +2.00264i q^{15} +3.98936 q^{16} +(-4.00134 - 0.994644i) q^{17} -0.109988 q^{18} +5.85419i q^{19} +(4.54139 - 4.54139i) q^{20} +2.67140 q^{21} +(0.0297780 - 0.0297780i) q^{22} +(3.81234 + 3.81234i) q^{23} +(-0.0741833 - 0.0741833i) q^{24} -5.33044i q^{25} +0.139937i q^{26} +(-2.47245 - 2.47245i) q^{27} +(-6.05796 - 6.05796i) q^{28} +(0.616737 - 0.616737i) q^{29} -0.0843361 q^{30} +(-6.28124 + 6.28124i) q^{31} +0.504753i q^{32} +0.623078 q^{33} +(0.0418870 - 0.168506i) q^{34} -13.7802 q^{35} +5.21891i q^{36} +(-0.532669 + 0.532669i) q^{37} -0.246535 q^{38} +(-1.46402 + 1.46402i) q^{39} +(0.382669 + 0.382669i) q^{40} +(-4.20082 - 4.20082i) q^{41} +0.112499i q^{42} +0.849123i q^{43} +(-1.41296 - 1.41296i) q^{44} +(5.93581 + 5.93581i) q^{45} +(-0.160547 + 0.160547i) q^{46} -8.83981 q^{47} +(-1.75764 + 1.75764i) q^{48} +11.3820i q^{49} +0.224478 q^{50} +(2.20114 - 1.32470i) q^{51} +6.63995 q^{52} -3.41117i q^{53} +(0.104121 - 0.104121i) q^{54} -3.21410 q^{55} +(0.510458 - 0.510458i) q^{56} +(-2.57926 - 2.57926i) q^{57} +(0.0259723 + 0.0259723i) q^{58} -12.4757i q^{59} +4.00172i q^{60} +(8.41215 + 8.41215i) q^{61} +(-0.264519 - 0.264519i) q^{62} +(7.91803 - 7.91803i) q^{63} +7.95747 q^{64} +(7.55205 - 7.55205i) q^{65} +0.0262394i q^{66} +4.87083 q^{67} +(-7.99557 - 1.98752i) q^{68} -3.35930 q^{69} -0.580320i q^{70} +(-2.47830 + 2.47830i) q^{71} -0.439758 q^{72} +(-3.10492 + 3.10492i) q^{73} +(-0.0224320 - 0.0224320i) q^{74} +(2.34850 + 2.34850i) q^{75} +11.6980i q^{76} +4.28743i q^{77} +(-0.0616537 - 0.0616537i) q^{78} +(-4.40437 - 4.40437i) q^{79} +(9.06667 - 9.06667i) q^{80} -5.65668 q^{81} +(0.176907 - 0.176907i) q^{82} -6.33683i q^{83} +5.33807 q^{84} +(-11.3544 + 6.83334i) q^{85} -0.0357587 q^{86} +0.543447i q^{87} +(0.119059 - 0.119059i) q^{88} +0.373263 q^{89} +(-0.249972 + 0.249972i) q^{90} +(-10.0740 - 10.0740i) q^{91} +(7.61791 + 7.61791i) q^{92} -5.53482i q^{93} -0.372267i q^{94} +(13.3049 + 13.3049i) q^{95} +(-0.222386 - 0.222386i) q^{96} +(8.46506 - 8.46506i) q^{97} -0.479326 q^{98} +(1.84680 - 1.84680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0421125i 0.0297780i 0.999889 + 0.0148890i \(0.00473950\pi\)
−0.999889 + 0.0148890i \(0.995261\pi\)
\(3\) −0.440583 + 0.440583i −0.254371 + 0.254371i −0.822760 0.568389i \(-0.807567\pi\)
0.568389 + 0.822760i \(0.307567\pi\)
\(4\) 1.99823 0.999113
\(5\) 2.27271 2.27271i 1.01639 1.01639i 0.0165243 0.999863i \(-0.494740\pi\)
0.999863 0.0165243i \(-0.00526008\pi\)
\(6\) −0.0185541 0.0185541i −0.00757466 0.00757466i
\(7\) −3.03167 3.03167i −1.14586 1.14586i −0.987358 0.158505i \(-0.949333\pi\)
−0.158505 0.987358i \(-0.550667\pi\)
\(8\) 0.168375i 0.0595297i
\(9\) 2.61177i 0.870591i
\(10\) 0.0957096 + 0.0957096i 0.0302660 + 0.0302660i
\(11\) −0.707107 0.707107i −0.213201 0.213201i
\(12\) −0.880384 + 0.880384i −0.254145 + 0.254145i
\(13\) 3.32292 0.921613 0.460806 0.887501i \(-0.347560\pi\)
0.460806 + 0.887501i \(0.347560\pi\)
\(14\) 0.127671 0.127671i 0.0341216 0.0341216i
\(15\) 2.00264i 0.517078i
\(16\) 3.98936 0.997341
\(17\) −4.00134 0.994644i −0.970466 0.241237i
\(18\) −0.109988 −0.0259245
\(19\) 5.85419i 1.34304i 0.740985 + 0.671521i \(0.234359\pi\)
−0.740985 + 0.671521i \(0.765641\pi\)
\(20\) 4.54139 4.54139i 1.01549 1.01549i
\(21\) 2.67140 0.582948
\(22\) 0.0297780 0.0297780i 0.00634870 0.00634870i
\(23\) 3.81234 + 3.81234i 0.794927 + 0.794927i 0.982291 0.187363i \(-0.0599942\pi\)
−0.187363 + 0.982291i \(0.559994\pi\)
\(24\) −0.0741833 0.0741833i −0.0151426 0.0151426i
\(25\) 5.33044i 1.06609i
\(26\) 0.139937i 0.0274438i
\(27\) −2.47245 2.47245i −0.475824 0.475824i
\(28\) −6.05796 6.05796i −1.14485 1.14485i
\(29\) 0.616737 0.616737i 0.114525 0.114525i −0.647522 0.762047i \(-0.724195\pi\)
0.762047 + 0.647522i \(0.224195\pi\)
\(30\) −0.0843361 −0.0153976
\(31\) −6.28124 + 6.28124i −1.12814 + 1.12814i −0.137666 + 0.990479i \(0.543960\pi\)
−0.990479 + 0.137666i \(0.956040\pi\)
\(32\) 0.504753i 0.0892286i
\(33\) 0.623078 0.108464
\(34\) 0.0418870 0.168506i 0.00718356 0.0288986i
\(35\) −13.7802 −2.32928
\(36\) 5.21891i 0.869819i
\(37\) −0.532669 + 0.532669i −0.0875702 + 0.0875702i −0.749535 0.661965i \(-0.769723\pi\)
0.661965 + 0.749535i \(0.269723\pi\)
\(38\) −0.246535 −0.0399932
\(39\) −1.46402 + 1.46402i −0.234431 + 0.234431i
\(40\) 0.382669 + 0.382669i 0.0605053 + 0.0605053i
\(41\) −4.20082 4.20082i −0.656057 0.656057i 0.298388 0.954445i \(-0.403551\pi\)
−0.954445 + 0.298388i \(0.903551\pi\)
\(42\) 0.112499i 0.0173590i
\(43\) 0.849123i 0.129490i 0.997902 + 0.0647450i \(0.0206234\pi\)
−0.997902 + 0.0647450i \(0.979377\pi\)
\(44\) −1.41296 1.41296i −0.213012 0.213012i
\(45\) 5.93581 + 5.93581i 0.884858 + 0.884858i
\(46\) −0.160547 + 0.160547i −0.0236714 + 0.0236714i
\(47\) −8.83981 −1.28942 −0.644709 0.764428i \(-0.723022\pi\)
−0.644709 + 0.764428i \(0.723022\pi\)
\(48\) −1.75764 + 1.75764i −0.253694 + 0.253694i
\(49\) 11.3820i 1.62600i
\(50\) 0.224478 0.0317460
\(51\) 2.20114 1.32470i 0.308222 0.185495i
\(52\) 6.63995 0.920796
\(53\) 3.41117i 0.468560i −0.972169 0.234280i \(-0.924727\pi\)
0.972169 0.234280i \(-0.0752733\pi\)
\(54\) 0.104121 0.104121i 0.0141691 0.0141691i
\(55\) −3.21410 −0.433389
\(56\) 0.510458 0.510458i 0.0682129 0.0682129i
\(57\) −2.57926 2.57926i −0.341631 0.341631i
\(58\) 0.0259723 + 0.0259723i 0.00341033 + 0.00341033i
\(59\) 12.4757i 1.62419i −0.583524 0.812096i \(-0.698326\pi\)
0.583524 0.812096i \(-0.301674\pi\)
\(60\) 4.00172i 0.516620i
\(61\) 8.41215 + 8.41215i 1.07707 + 1.07707i 0.996771 + 0.0802943i \(0.0255860\pi\)
0.0802943 + 0.996771i \(0.474414\pi\)
\(62\) −0.264519 0.264519i −0.0335940 0.0335940i
\(63\) 7.91803 7.91803i 0.997578 0.997578i
\(64\) 7.95747 0.994684
\(65\) 7.55205 7.55205i 0.936716 0.936716i
\(66\) 0.0262394i 0.00322985i
\(67\) 4.87083 0.595066 0.297533 0.954711i \(-0.403836\pi\)
0.297533 + 0.954711i \(0.403836\pi\)
\(68\) −7.99557 1.98752i −0.969606 0.241023i
\(69\) −3.35930 −0.404412
\(70\) 0.580320i 0.0693615i
\(71\) −2.47830 + 2.47830i −0.294120 + 0.294120i −0.838705 0.544585i \(-0.816687\pi\)
0.544585 + 0.838705i \(0.316687\pi\)
\(72\) −0.439758 −0.0518260
\(73\) −3.10492 + 3.10492i −0.363404 + 0.363404i −0.865064 0.501661i \(-0.832723\pi\)
0.501661 + 0.865064i \(0.332723\pi\)
\(74\) −0.0224320 0.0224320i −0.00260767 0.00260767i
\(75\) 2.34850 + 2.34850i 0.271182 + 0.271182i
\(76\) 11.6980i 1.34185i
\(77\) 4.28743i 0.488598i
\(78\) −0.0616537 0.0616537i −0.00698091 0.00698091i
\(79\) −4.40437 4.40437i −0.495530 0.495530i 0.414513 0.910043i \(-0.363952\pi\)
−0.910043 + 0.414513i \(0.863952\pi\)
\(80\) 9.06667 9.06667i 1.01368 1.01368i
\(81\) −5.65668 −0.628520
\(82\) 0.176907 0.176907i 0.0195361 0.0195361i
\(83\) 6.33683i 0.695557i −0.937577 0.347779i \(-0.886936\pi\)
0.937577 0.347779i \(-0.113064\pi\)
\(84\) 5.33807 0.582431
\(85\) −11.3544 + 6.83334i −1.23156 + 0.741180i
\(86\) −0.0357587 −0.00385596
\(87\) 0.543447i 0.0582637i
\(88\) 0.119059 0.119059i 0.0126918 0.0126918i
\(89\) 0.373263 0.0395658 0.0197829 0.999804i \(-0.493702\pi\)
0.0197829 + 0.999804i \(0.493702\pi\)
\(90\) −0.249972 + 0.249972i −0.0263493 + 0.0263493i
\(91\) −10.0740 10.0740i −1.05604 1.05604i
\(92\) 7.61791 + 7.61791i 0.794222 + 0.794222i
\(93\) 5.53482i 0.573934i
\(94\) 0.372267i 0.0383964i
\(95\) 13.3049 + 13.3049i 1.36505 + 1.36505i
\(96\) −0.222386 0.222386i −0.0226971 0.0226971i
\(97\) 8.46506 8.46506i 0.859496 0.859496i −0.131782 0.991279i \(-0.542070\pi\)
0.991279 + 0.131782i \(0.0420700\pi\)
\(98\) −0.479326 −0.0484192
\(99\) 1.84680 1.84680i 0.185611 0.185611i
\(100\) 10.6514i 1.06514i
\(101\) 3.81697 0.379803 0.189902 0.981803i \(-0.439183\pi\)
0.189902 + 0.981803i \(0.439183\pi\)
\(102\) 0.0557863 + 0.0926957i 0.00552367 + 0.00917824i
\(103\) −9.47135 −0.933240 −0.466620 0.884458i \(-0.654528\pi\)
−0.466620 + 0.884458i \(0.654528\pi\)
\(104\) 0.559498i 0.0548633i
\(105\) 6.07133 6.07133i 0.592501 0.592501i
\(106\) 0.143653 0.0139528
\(107\) 3.83640 3.83640i 0.370879 0.370879i −0.496918 0.867797i \(-0.665535\pi\)
0.867797 + 0.496918i \(0.165535\pi\)
\(108\) −4.94052 4.94052i −0.475402 0.475402i
\(109\) 12.3314 + 12.3314i 1.18113 + 1.18113i 0.979451 + 0.201681i \(0.0646405\pi\)
0.201681 + 0.979451i \(0.435359\pi\)
\(110\) 0.135354i 0.0129055i
\(111\) 0.469370i 0.0445506i
\(112\) −12.0944 12.0944i −1.14282 1.14282i
\(113\) −4.00505 4.00505i −0.376763 0.376763i 0.493170 0.869933i \(-0.335838\pi\)
−0.869933 + 0.493170i \(0.835838\pi\)
\(114\) 0.108619 0.108619i 0.0101731 0.0101731i
\(115\) 17.3287 1.61591
\(116\) 1.23238 1.23238i 0.114424 0.114424i
\(117\) 8.67872i 0.802348i
\(118\) 0.525381 0.0483653
\(119\) 9.11529 + 15.1462i 0.835597 + 1.38845i
\(120\) −0.337195 −0.0307815
\(121\) 1.00000i 0.0909091i
\(122\) −0.354257 + 0.354257i −0.0320729 + 0.0320729i
\(123\) 3.70161 0.333763
\(124\) −12.5514 + 12.5514i −1.12714 + 1.12714i
\(125\) −0.750996 0.750996i −0.0671711 0.0671711i
\(126\) 0.333448 + 0.333448i 0.0297059 + 0.0297059i
\(127\) 11.5162i 1.02190i 0.859610 + 0.510950i \(0.170706\pi\)
−0.859610 + 0.510950i \(0.829294\pi\)
\(128\) 1.34461i 0.118848i
\(129\) −0.374109 0.374109i −0.0329385 0.0329385i
\(130\) 0.318036 + 0.318036i 0.0278936 + 0.0278936i
\(131\) 1.71986 1.71986i 0.150264 0.150264i −0.627972 0.778236i \(-0.716115\pi\)
0.778236 + 0.627972i \(0.216115\pi\)
\(132\) 1.24505 0.108368
\(133\) 17.7480 17.7480i 1.53894 1.53894i
\(134\) 0.205123i 0.0177199i
\(135\) −11.2383 −0.967242
\(136\) 0.167474 0.673726i 0.0143607 0.0577716i
\(137\) 9.77215 0.834891 0.417445 0.908702i \(-0.362925\pi\)
0.417445 + 0.908702i \(0.362925\pi\)
\(138\) 0.141469i 0.0120426i
\(139\) −2.28918 + 2.28918i −0.194165 + 0.194165i −0.797493 0.603328i \(-0.793841\pi\)
0.603328 + 0.797493i \(0.293841\pi\)
\(140\) −27.5360 −2.32722
\(141\) 3.89467 3.89467i 0.327990 0.327990i
\(142\) −0.104368 0.104368i −0.00875833 0.00875833i
\(143\) −2.34966 2.34966i −0.196489 0.196489i
\(144\) 10.4193i 0.868276i
\(145\) 2.80333i 0.232804i
\(146\) −0.130756 0.130756i −0.0108215 0.0108215i
\(147\) −5.01473 5.01473i −0.413608 0.413608i
\(148\) −1.06439 + 1.06439i −0.0874926 + 0.0874926i
\(149\) −12.9589 −1.06164 −0.530818 0.847486i \(-0.678115\pi\)
−0.530818 + 0.847486i \(0.678115\pi\)
\(150\) −0.0989013 + 0.0989013i −0.00807526 + 0.00807526i
\(151\) 12.3703i 1.00668i −0.864087 0.503342i \(-0.832103\pi\)
0.864087 0.503342i \(-0.167897\pi\)
\(152\) −0.985701 −0.0799509
\(153\) 2.59779 10.4506i 0.210018 0.844879i
\(154\) −0.180554 −0.0145495
\(155\) 28.5509i 2.29327i
\(156\) −2.92545 + 2.92545i −0.234223 + 0.234223i
\(157\) 1.85459 0.148012 0.0740062 0.997258i \(-0.476422\pi\)
0.0740062 + 0.997258i \(0.476422\pi\)
\(158\) 0.185479 0.185479i 0.0147559 0.0147559i
\(159\) 1.50290 + 1.50290i 0.119188 + 0.119188i
\(160\) 1.14716 + 1.14716i 0.0906908 + 0.0906908i
\(161\) 23.1155i 1.82176i
\(162\) 0.238217i 0.0187161i
\(163\) 4.73123 + 4.73123i 0.370578 + 0.370578i 0.867688 0.497109i \(-0.165605\pi\)
−0.497109 + 0.867688i \(0.665605\pi\)
\(164\) −8.39418 8.39418i −0.655475 0.655475i
\(165\) 1.41608 1.41608i 0.110241 0.110241i
\(166\) 0.266860 0.0207123
\(167\) 10.3728 10.3728i 0.802668 0.802668i −0.180844 0.983512i \(-0.557883\pi\)
0.983512 + 0.180844i \(0.0578828\pi\)
\(168\) 0.449798i 0.0347027i
\(169\) −1.95819 −0.150630
\(170\) −0.287769 0.478163i −0.0220709 0.0366735i
\(171\) −15.2898 −1.16924
\(172\) 1.69674i 0.129375i
\(173\) −9.74046 + 9.74046i −0.740554 + 0.740554i −0.972685 0.232131i \(-0.925430\pi\)
0.232131 + 0.972685i \(0.425430\pi\)
\(174\) −0.0228859 −0.00173498
\(175\) −16.1601 + 16.1601i −1.22159 + 1.22159i
\(176\) −2.82091 2.82091i −0.212634 0.212634i
\(177\) 5.49656 + 5.49656i 0.413147 + 0.413147i
\(178\) 0.0157191i 0.00117819i
\(179\) 8.44838i 0.631462i 0.948849 + 0.315731i \(0.102250\pi\)
−0.948849 + 0.315731i \(0.897750\pi\)
\(180\) 11.8611 + 11.8611i 0.884074 + 0.884074i
\(181\) −16.3200 16.3200i −1.21305 1.21305i −0.970017 0.243036i \(-0.921857\pi\)
−0.243036 0.970017i \(-0.578143\pi\)
\(182\) 0.424242 0.424242i 0.0314469 0.0314469i
\(183\) −7.41250 −0.547948
\(184\) −0.641904 + 0.641904i −0.0473218 + 0.0473218i
\(185\) 2.42121i 0.178011i
\(186\) 0.233085 0.0170906
\(187\) 2.12605 + 3.53269i 0.155472 + 0.258336i
\(188\) −17.6639 −1.28828
\(189\) 14.9913i 1.09046i
\(190\) −0.560302 + 0.560302i −0.0406486 + 0.0406486i
\(191\) 23.4963 1.70013 0.850067 0.526675i \(-0.176561\pi\)
0.850067 + 0.526675i \(0.176561\pi\)
\(192\) −3.50592 + 3.50592i −0.253018 + 0.253018i
\(193\) −1.92992 1.92992i −0.138919 0.138919i 0.634227 0.773147i \(-0.281318\pi\)
−0.773147 + 0.634227i \(0.781318\pi\)
\(194\) 0.356485 + 0.356485i 0.0255941 + 0.0255941i
\(195\) 6.65461i 0.476546i
\(196\) 22.7439i 1.62456i
\(197\) −5.43997 5.43997i −0.387582 0.387582i 0.486242 0.873824i \(-0.338367\pi\)
−0.873824 + 0.486242i \(0.838367\pi\)
\(198\) 0.0777735 + 0.0777735i 0.00552712 + 0.00552712i
\(199\) 7.38138 7.38138i 0.523252 0.523252i −0.395300 0.918552i \(-0.629359\pi\)
0.918552 + 0.395300i \(0.129359\pi\)
\(200\) 0.897515 0.0634639
\(201\) −2.14600 + 2.14600i −0.151367 + 0.151367i
\(202\) 0.160742i 0.0113098i
\(203\) −3.73948 −0.262460
\(204\) 4.39838 2.64704i 0.307948 0.185330i
\(205\) −19.0945 −1.33362
\(206\) 0.398862i 0.0277901i
\(207\) −9.95696 + 9.95696i −0.692057 + 0.692057i
\(208\) 13.2563 0.919162
\(209\) 4.13954 4.13954i 0.286338 0.286338i
\(210\) 0.255679 + 0.255679i 0.0176435 + 0.0176435i
\(211\) −7.36939 7.36939i −0.507330 0.507330i 0.406376 0.913706i \(-0.366792\pi\)
−0.913706 + 0.406376i \(0.866792\pi\)
\(212\) 6.81629i 0.468145i
\(213\) 2.18379i 0.149631i
\(214\) 0.161560 + 0.161560i 0.0110440 + 0.0110440i
\(215\) 1.92981 + 1.92981i 0.131612 + 0.131612i
\(216\) 0.416300 0.416300i 0.0283256 0.0283256i
\(217\) 38.0853 2.58540
\(218\) −0.519306 + 0.519306i −0.0351718 + 0.0351718i
\(219\) 2.73595i 0.184878i
\(220\) −6.42250 −0.433005
\(221\) −13.2961 3.30513i −0.894394 0.222327i
\(222\) 0.0197663 0.00132663
\(223\) 23.8482i 1.59699i −0.602000 0.798496i \(-0.705629\pi\)
0.602000 0.798496i \(-0.294371\pi\)
\(224\) 1.53024 1.53024i 0.102244 0.102244i
\(225\) 13.9219 0.928127
\(226\) 0.168663 0.168663i 0.0112193 0.0112193i
\(227\) −14.3074 14.3074i −0.949614 0.949614i 0.0491757 0.998790i \(-0.484341\pi\)
−0.998790 + 0.0491757i \(0.984341\pi\)
\(228\) −5.15394 5.15394i −0.341328 0.341328i
\(229\) 27.5015i 1.81735i −0.417501 0.908676i \(-0.637094\pi\)
0.417501 0.908676i \(-0.362906\pi\)
\(230\) 0.729755i 0.0481186i
\(231\) −1.88897 1.88897i −0.124285 0.124285i
\(232\) 0.103843 + 0.103843i 0.00681764 + 0.00681764i
\(233\) −20.3914 + 20.3914i −1.33589 + 1.33589i −0.435882 + 0.900004i \(0.643563\pi\)
−0.900004 + 0.435882i \(0.856437\pi\)
\(234\) −0.365483 −0.0238924
\(235\) −20.0903 + 20.0903i −1.31055 + 1.31055i
\(236\) 24.9292i 1.62275i
\(237\) 3.88098 0.252097
\(238\) −0.637843 + 0.383868i −0.0413452 + 0.0248825i
\(239\) 15.8428 1.02479 0.512394 0.858751i \(-0.328759\pi\)
0.512394 + 0.858751i \(0.328759\pi\)
\(240\) 7.98924i 0.515703i
\(241\) 10.0506 10.0506i 0.647413 0.647413i −0.304954 0.952367i \(-0.598641\pi\)
0.952367 + 0.304954i \(0.0986411\pi\)
\(242\) −0.0421125 −0.00270710
\(243\) 9.90959 9.90959i 0.635701 0.635701i
\(244\) 16.8094 + 16.8094i 1.07611 + 1.07611i
\(245\) 25.8681 + 25.8681i 1.65265 + 1.65265i
\(246\) 0.155884i 0.00993882i
\(247\) 19.4530i 1.23777i
\(248\) −1.05761 1.05761i −0.0671581 0.0671581i
\(249\) 2.79190 + 2.79190i 0.176929 + 0.176929i
\(250\) 0.0316263 0.0316263i 0.00200022 0.00200022i
\(251\) 0.885722 0.0559063 0.0279532 0.999609i \(-0.491101\pi\)
0.0279532 + 0.999609i \(0.491101\pi\)
\(252\) 15.8220 15.8220i 0.996694 0.996694i
\(253\) 5.39146i 0.338958i
\(254\) −0.484978 −0.0304302
\(255\) 1.99191 8.01322i 0.124738 0.501807i
\(256\) 15.8583 0.991144
\(257\) 6.69991i 0.417929i 0.977923 + 0.208964i \(0.0670093\pi\)
−0.977923 + 0.208964i \(0.932991\pi\)
\(258\) 0.0157547 0.0157547i 0.000980843 0.000980843i
\(259\) 3.22975 0.200687
\(260\) 15.0907 15.0907i 0.935885 0.935885i
\(261\) 1.61078 + 1.61078i 0.0997045 + 0.0997045i
\(262\) 0.0724274 + 0.0724274i 0.00447458 + 0.00447458i
\(263\) 4.25215i 0.262199i 0.991369 + 0.131099i \(0.0418507\pi\)
−0.991369 + 0.131099i \(0.958149\pi\)
\(264\) 0.104911i 0.00645683i
\(265\) −7.75261 7.75261i −0.476239 0.476239i
\(266\) 0.747411 + 0.747411i 0.0458267 + 0.0458267i
\(267\) −0.164453 + 0.164453i −0.0100644 + 0.0100644i
\(268\) 9.73302 0.594539
\(269\) −18.3428 + 18.3428i −1.11838 + 1.11838i −0.126404 + 0.991979i \(0.540344\pi\)
−0.991979 + 0.126404i \(0.959656\pi\)
\(270\) 0.473275i 0.0288026i
\(271\) 14.9592 0.908704 0.454352 0.890822i \(-0.349871\pi\)
0.454352 + 0.890822i \(0.349871\pi\)
\(272\) −15.9628 3.96800i −0.967885 0.240595i
\(273\) 8.87686 0.537252
\(274\) 0.411530i 0.0248614i
\(275\) −3.76919 + 3.76919i −0.227291 + 0.227291i
\(276\) −6.71264 −0.404054
\(277\) 6.93979 6.93979i 0.416972 0.416972i −0.467187 0.884159i \(-0.654732\pi\)
0.884159 + 0.467187i \(0.154732\pi\)
\(278\) −0.0964029 0.0964029i −0.00578186 0.00578186i
\(279\) −16.4052 16.4052i −0.982153 0.982153i
\(280\) 2.32025i 0.138661i
\(281\) 12.7856i 0.762726i −0.924425 0.381363i \(-0.875455\pi\)
0.924425 0.381363i \(-0.124545\pi\)
\(282\) 0.164014 + 0.164014i 0.00976691 + 0.00976691i
\(283\) 8.74159 + 8.74159i 0.519633 + 0.519633i 0.917460 0.397827i \(-0.130236\pi\)
−0.397827 + 0.917460i \(0.630236\pi\)
\(284\) −4.95221 + 4.95221i −0.293859 + 0.293859i
\(285\) −11.7238 −0.694458
\(286\) 0.0989502 0.0989502i 0.00585105 0.00585105i
\(287\) 25.4710i 1.50350i
\(288\) −1.31830 −0.0776816
\(289\) 15.0214 + 7.95981i 0.883610 + 0.468224i
\(290\) 0.118055 0.00693244
\(291\) 7.45912i 0.437261i
\(292\) −6.20434 + 6.20434i −0.363081 + 0.363081i
\(293\) 15.5310 0.907333 0.453667 0.891171i \(-0.350116\pi\)
0.453667 + 0.891171i \(0.350116\pi\)
\(294\) 0.211183 0.211183i 0.0123164 0.0123164i
\(295\) −28.3536 28.3536i −1.65081 1.65081i
\(296\) −0.0896883 0.0896883i −0.00521303 0.00521303i
\(297\) 3.49657i 0.202892i
\(298\) 0.545733i 0.0316134i
\(299\) 12.6681 + 12.6681i 0.732615 + 0.732615i
\(300\) 4.69284 + 4.69284i 0.270941 + 0.270941i
\(301\) 2.57426 2.57426i 0.148378 0.148378i
\(302\) 0.520947 0.0299771
\(303\) −1.68169 + 1.68169i −0.0966108 + 0.0966108i
\(304\) 23.3545i 1.33947i
\(305\) 38.2368 2.18943
\(306\) 0.440100 + 0.109399i 0.0251589 + 0.00625394i
\(307\) −29.4466 −1.68060 −0.840302 0.542119i \(-0.817622\pi\)
−0.840302 + 0.542119i \(0.817622\pi\)
\(308\) 8.56725i 0.488164i
\(309\) 4.17291 4.17291i 0.237389 0.237389i
\(310\) −1.20235 −0.0682890
\(311\) 8.53182 8.53182i 0.483795 0.483795i −0.422546 0.906341i \(-0.638864\pi\)
0.906341 + 0.422546i \(0.138864\pi\)
\(312\) −0.246505 0.246505i −0.0139556 0.0139556i
\(313\) −5.96937 5.96937i −0.337409 0.337409i 0.517982 0.855391i \(-0.326683\pi\)
−0.855391 + 0.517982i \(0.826683\pi\)
\(314\) 0.0781014i 0.00440752i
\(315\) 35.9908i 2.02785i
\(316\) −8.80092 8.80092i −0.495091 0.495091i
\(317\) −14.2038 14.2038i −0.797764 0.797764i 0.184978 0.982743i \(-0.440779\pi\)
−0.982743 + 0.184978i \(0.940779\pi\)
\(318\) −0.0632911 + 0.0632911i −0.00354919 + 0.00354919i
\(319\) −0.872197 −0.0488337
\(320\) 18.0850 18.0850i 1.01098 1.01098i
\(321\) 3.38050i 0.188681i
\(322\) 0.973451 0.0542483
\(323\) 5.82283 23.4246i 0.323991 1.30338i
\(324\) −11.3033 −0.627963
\(325\) 17.7126i 0.982521i
\(326\) −0.199244 + 0.199244i −0.0110351 + 0.0110351i
\(327\) −10.8660 −0.600891
\(328\) 0.707314 0.707314i 0.0390549 0.0390549i
\(329\) 26.7994 + 26.7994i 1.47750 + 1.47750i
\(330\) 0.0596346 + 0.0596346i 0.00328278 + 0.00328278i
\(331\) 6.00340i 0.329976i 0.986296 + 0.164988i \(0.0527586\pi\)
−0.986296 + 0.164988i \(0.947241\pi\)
\(332\) 12.6624i 0.694941i
\(333\) −1.39121 1.39121i −0.0762379 0.0762379i
\(334\) 0.436823 + 0.436823i 0.0239019 + 0.0239019i
\(335\) 11.0700 11.0700i 0.604818 0.604818i
\(336\) 10.6572 0.581398
\(337\) −18.2603 + 18.2603i −0.994703 + 0.994703i −0.999986 0.00528322i \(-0.998318\pi\)
0.00528322 + 0.999986i \(0.498318\pi\)
\(338\) 0.0824641i 0.00448546i
\(339\) 3.52911 0.191675
\(340\) −22.6887 + 13.6546i −1.23047 + 0.740523i
\(341\) 8.88302 0.481043
\(342\) 0.643893i 0.0348177i
\(343\) 13.2848 13.2848i 0.717314 0.717314i
\(344\) −0.142971 −0.00770850
\(345\) −7.63472 + 7.63472i −0.411040 + 0.411040i
\(346\) −0.410195 0.410195i −0.0220522 0.0220522i
\(347\) 7.48979 + 7.48979i 0.402073 + 0.402073i 0.878963 0.476890i \(-0.158236\pi\)
−0.476890 + 0.878963i \(0.658236\pi\)
\(348\) 1.08593i 0.0582120i
\(349\) 14.7061i 0.787198i 0.919282 + 0.393599i \(0.128770\pi\)
−0.919282 + 0.393599i \(0.871230\pi\)
\(350\) −0.680544 0.680544i −0.0363766 0.0363766i
\(351\) −8.21576 8.21576i −0.438525 0.438525i
\(352\) 0.356914 0.356914i 0.0190236 0.0190236i
\(353\) −31.0800 −1.65422 −0.827110 0.562040i \(-0.810017\pi\)
−0.827110 + 0.562040i \(0.810017\pi\)
\(354\) −0.231474 + 0.231474i −0.0123027 + 0.0123027i
\(355\) 11.2649i 0.597880i
\(356\) 0.745865 0.0395308
\(357\) −10.6892 2.65709i −0.565731 0.140628i
\(358\) −0.355783 −0.0188037
\(359\) 14.3294i 0.756276i 0.925749 + 0.378138i \(0.123435\pi\)
−0.925749 + 0.378138i \(0.876565\pi\)
\(360\) −0.999444 + 0.999444i −0.0526753 + 0.0526753i
\(361\) −15.2715 −0.803764
\(362\) 0.687275 0.687275i 0.0361223 0.0361223i
\(363\) −0.440583 0.440583i −0.0231246 0.0231246i
\(364\) −20.1301 20.1301i −1.05511 1.05511i
\(365\) 14.1132i 0.738718i
\(366\) 0.312159i 0.0163168i
\(367\) 15.1132 + 15.1132i 0.788902 + 0.788902i 0.981314 0.192412i \(-0.0616310\pi\)
−0.192412 + 0.981314i \(0.561631\pi\)
\(368\) 15.2088 + 15.2088i 0.792813 + 0.792813i
\(369\) 10.9716 10.9716i 0.571157 0.571157i
\(370\) −0.101963 −0.00530081
\(371\) −10.3415 + 10.3415i −0.536906 + 0.536906i
\(372\) 11.0598i 0.573425i
\(373\) −4.14225 −0.214477 −0.107239 0.994233i \(-0.534201\pi\)
−0.107239 + 0.994233i \(0.534201\pi\)
\(374\) −0.148771 + 0.0895334i −0.00769274 + 0.00462966i
\(375\) 0.661752 0.0341727
\(376\) 1.48841i 0.0767587i
\(377\) 2.04937 2.04937i 0.105548 0.105548i
\(378\) −0.631322 −0.0324717
\(379\) 2.74157 2.74157i 0.140825 0.140825i −0.633180 0.774005i \(-0.718251\pi\)
0.774005 + 0.633180i \(0.218251\pi\)
\(380\) 26.5862 + 26.5862i 1.36384 + 1.36384i
\(381\) −5.07386 5.07386i −0.259942 0.259942i
\(382\) 0.989489i 0.0506267i
\(383\) 17.8600i 0.912604i 0.889825 + 0.456302i \(0.150826\pi\)
−0.889825 + 0.456302i \(0.849174\pi\)
\(384\) −0.592414 0.592414i −0.0302315 0.0302315i
\(385\) 9.74409 + 9.74409i 0.496605 + 0.496605i
\(386\) 0.0812740 0.0812740i 0.00413674 0.00413674i
\(387\) −2.21772 −0.112733
\(388\) 16.9151 16.9151i 0.858734 0.858734i
\(389\) 10.6554i 0.540249i 0.962825 + 0.270124i \(0.0870648\pi\)
−0.962825 + 0.270124i \(0.912935\pi\)
\(390\) −0.280242 −0.0141906
\(391\) −11.4625 19.0464i −0.579684 0.963216i
\(392\) −1.91645 −0.0967955
\(393\) 1.51548i 0.0764457i
\(394\) 0.229091 0.229091i 0.0115414 0.0115414i
\(395\) −20.0197 −1.00730
\(396\) 3.69033 3.69033i 0.185446 0.185446i
\(397\) −2.22024 2.22024i −0.111431 0.111431i 0.649193 0.760624i \(-0.275107\pi\)
−0.760624 + 0.649193i \(0.775107\pi\)
\(398\) 0.310848 + 0.310848i 0.0155814 + 0.0155814i
\(399\) 15.6389i 0.782924i
\(400\) 21.2651i 1.06325i
\(401\) 5.43167 + 5.43167i 0.271245 + 0.271245i 0.829601 0.558357i \(-0.188568\pi\)
−0.558357 + 0.829601i \(0.688568\pi\)
\(402\) −0.0903736 0.0903736i −0.00450743 0.00450743i
\(403\) −20.8721 + 20.8721i −1.03971 + 1.03971i
\(404\) 7.62718 0.379466
\(405\) −12.8560 + 12.8560i −0.638820 + 0.638820i
\(406\) 0.157479i 0.00781555i
\(407\) 0.753308 0.0373401
\(408\) 0.223046 + 0.370618i 0.0110424 + 0.0183483i
\(409\) 18.2193 0.900889 0.450444 0.892805i \(-0.351266\pi\)
0.450444 + 0.892805i \(0.351266\pi\)
\(410\) 0.804117i 0.0397125i
\(411\) −4.30544 + 4.30544i −0.212372 + 0.212372i
\(412\) −18.9259 −0.932412
\(413\) −37.8221 + 37.8221i −1.86110 + 1.86110i
\(414\) −0.419313 0.419313i −0.0206081 0.0206081i
\(415\) −14.4018 14.4018i −0.706956 0.706956i
\(416\) 1.67725i 0.0822342i
\(417\) 2.01714i 0.0987799i
\(418\) 0.174326 + 0.174326i 0.00852658 + 0.00852658i
\(419\) 3.89911 + 3.89911i 0.190484 + 0.190484i 0.795905 0.605421i \(-0.206995\pi\)
−0.605421 + 0.795905i \(0.706995\pi\)
\(420\) 12.1319 12.1319i 0.591976 0.591976i
\(421\) −15.5720 −0.758933 −0.379467 0.925205i \(-0.623893\pi\)
−0.379467 + 0.925205i \(0.623893\pi\)
\(422\) 0.310343 0.310343i 0.0151073 0.0151073i
\(423\) 23.0876i 1.12256i
\(424\) 0.574357 0.0278933
\(425\) −5.30189 + 21.3289i −0.257179 + 1.03460i
\(426\) 0.0919651 0.00445572
\(427\) 51.0057i 2.46834i
\(428\) 7.66600 7.66600i 0.370550 0.370550i
\(429\) 2.07044 0.0999618
\(430\) −0.0812692 + 0.0812692i −0.00391915 + 0.00391915i
\(431\) 17.4564 + 17.4564i 0.840844 + 0.840844i 0.988969 0.148125i \(-0.0473238\pi\)
−0.148125 + 0.988969i \(0.547324\pi\)
\(432\) −9.86350 9.86350i −0.474558 0.474558i
\(433\) 27.4120i 1.31734i −0.752433 0.658669i \(-0.771120\pi\)
0.752433 0.658669i \(-0.228880\pi\)
\(434\) 1.60387i 0.0769881i
\(435\) 1.23510 + 1.23510i 0.0592185 + 0.0592185i
\(436\) 24.6409 + 24.6409i 1.18009 + 1.18009i
\(437\) −22.3181 + 22.3181i −1.06762 + 1.06762i
\(438\) 0.115218 0.00550532
\(439\) −5.64043 + 5.64043i −0.269203 + 0.269203i −0.828779 0.559576i \(-0.810964\pi\)
0.559576 + 0.828779i \(0.310964\pi\)
\(440\) 0.541175i 0.0257995i
\(441\) −29.7273 −1.41558
\(442\) 0.139187 0.559933i 0.00662046 0.0266333i
\(443\) −19.4155 −0.922458 −0.461229 0.887281i \(-0.652591\pi\)
−0.461229 + 0.887281i \(0.652591\pi\)
\(444\) 0.937907i 0.0445111i
\(445\) 0.848320 0.848320i 0.0402142 0.0402142i
\(446\) 1.00431 0.0475553
\(447\) 5.70948 5.70948i 0.270049 0.270049i
\(448\) −24.1244 24.1244i −1.13977 1.13977i
\(449\) −3.24976 3.24976i −0.153366 0.153366i 0.626254 0.779619i \(-0.284587\pi\)
−0.779619 + 0.626254i \(0.784587\pi\)
\(450\) 0.586286i 0.0276378i
\(451\) 5.94085i 0.279744i
\(452\) −8.00300 8.00300i −0.376429 0.376429i
\(453\) 5.45016 + 5.45016i 0.256071 + 0.256071i
\(454\) 0.602520 0.602520i 0.0282777 0.0282777i
\(455\) −45.7906 −2.14670
\(456\) 0.434283 0.434283i 0.0203372 0.0203372i
\(457\) 15.5847i 0.729023i 0.931199 + 0.364511i \(0.118764\pi\)
−0.931199 + 0.364511i \(0.881236\pi\)
\(458\) 1.15816 0.0541172
\(459\) 7.43390 + 12.3523i 0.346985 + 0.576557i
\(460\) 34.6266 1.61448
\(461\) 27.3289i 1.27284i −0.771344 0.636418i \(-0.780415\pi\)
0.771344 0.636418i \(-0.219585\pi\)
\(462\) 0.0795492 0.0795492i 0.00370096 0.00370096i
\(463\) −2.64550 −0.122947 −0.0614734 0.998109i \(-0.519580\pi\)
−0.0614734 + 0.998109i \(0.519580\pi\)
\(464\) 2.46039 2.46039i 0.114221 0.114221i
\(465\) −12.5790 12.5790i −0.583339 0.583339i
\(466\) −0.858734 0.858734i −0.0397801 0.0397801i
\(467\) 13.4709i 0.623358i 0.950187 + 0.311679i \(0.100891\pi\)
−0.950187 + 0.311679i \(0.899109\pi\)
\(468\) 17.3421i 0.801637i
\(469\) −14.7667 14.7667i −0.681865 0.681865i
\(470\) −0.846055 0.846055i −0.0390256 0.0390256i
\(471\) −0.817100 + 0.817100i −0.0376500 + 0.0376500i
\(472\) 2.10059 0.0966877
\(473\) 0.600420 0.600420i 0.0276074 0.0276074i
\(474\) 0.163438i 0.00750694i
\(475\) 31.2054 1.43180
\(476\) 18.2144 + 30.2654i 0.834856 + 1.38721i
\(477\) 8.90921 0.407925
\(478\) 0.667182i 0.0305162i
\(479\) 26.0378 26.0378i 1.18970 1.18970i 0.212548 0.977151i \(-0.431824\pi\)
0.977151 0.212548i \(-0.0681761\pi\)
\(480\) −1.01084 −0.0461382
\(481\) −1.77002 + 1.77002i −0.0807059 + 0.0807059i
\(482\) 0.423254 + 0.423254i 0.0192787 + 0.0192787i
\(483\) 10.1843 + 10.1843i 0.463401 + 0.463401i
\(484\) 1.99823i 0.0908285i
\(485\) 38.4773i 1.74716i
\(486\) 0.417318 + 0.417318i 0.0189299 + 0.0189299i
\(487\) 15.2870 + 15.2870i 0.692721 + 0.692721i 0.962830 0.270109i \(-0.0870596\pi\)
−0.270109 + 0.962830i \(0.587060\pi\)
\(488\) −1.41640 + 1.41640i −0.0641174 + 0.0641174i
\(489\) −4.16900 −0.188529
\(490\) −1.08937 + 1.08937i −0.0492127 + 0.0492127i
\(491\) 14.5982i 0.658806i −0.944189 0.329403i \(-0.893153\pi\)
0.944189 0.329403i \(-0.106847\pi\)
\(492\) 7.39666 0.333467
\(493\) −3.08120 + 1.85434i −0.138770 + 0.0835151i
\(494\) −0.819215 −0.0368582
\(495\) 8.39450i 0.377305i
\(496\) −25.0582 + 25.0582i −1.12514 + 1.12514i
\(497\) 15.0268 0.674043
\(498\) −0.117574 + 0.117574i −0.00526861 + 0.00526861i
\(499\) 3.59392 + 3.59392i 0.160886 + 0.160886i 0.782959 0.622073i \(-0.213709\pi\)
−0.622073 + 0.782959i \(0.713709\pi\)
\(500\) −1.50066 1.50066i −0.0671115 0.0671115i
\(501\) 9.14012i 0.408351i
\(502\) 0.0373000i 0.00166478i
\(503\) 7.77722 + 7.77722i 0.346769 + 0.346769i 0.858905 0.512135i \(-0.171145\pi\)
−0.512135 + 0.858905i \(0.671145\pi\)
\(504\) 1.33320 + 1.33320i 0.0593855 + 0.0593855i
\(505\) 8.67488 8.67488i 0.386027 0.386027i
\(506\) 0.227048 0.0100935
\(507\) 0.862743 0.862743i 0.0383158 0.0383158i
\(508\) 23.0120i 1.02099i
\(509\) −25.8733 −1.14681 −0.573406 0.819271i \(-0.694378\pi\)
−0.573406 + 0.819271i \(0.694378\pi\)
\(510\) 0.337457 + 0.0838844i 0.0149428 + 0.00371446i
\(511\) 18.8262 0.832822
\(512\) 3.35706i 0.148363i
\(513\) 14.4742 14.4742i 0.639051 0.639051i
\(514\) −0.282150 −0.0124451
\(515\) −21.5256 + 21.5256i −0.948533 + 0.948533i
\(516\) −0.747554 0.747554i −0.0329093 0.0329093i
\(517\) 6.25069 + 6.25069i 0.274905 + 0.274905i
\(518\) 0.136013i 0.00597607i
\(519\) 8.58296i 0.376750i
\(520\) 1.27158 + 1.27158i 0.0557624 + 0.0557624i
\(521\) 2.23810 + 2.23810i 0.0980528 + 0.0980528i 0.754432 0.656379i \(-0.227913\pi\)
−0.656379 + 0.754432i \(0.727913\pi\)
\(522\) −0.0678338 + 0.0678338i −0.00296901 + 0.00296901i
\(523\) 35.3598 1.54618 0.773088 0.634299i \(-0.218711\pi\)
0.773088 + 0.634299i \(0.218711\pi\)
\(524\) 3.43666 3.43666i 0.150131 0.150131i
\(525\) 14.2398i 0.621474i
\(526\) −0.179069 −0.00780776
\(527\) 31.3810 18.8858i 1.36698 0.822677i
\(528\) 2.48569 0.108176
\(529\) 6.06782i 0.263818i
\(530\) 0.326482 0.326482i 0.0141815 0.0141815i
\(531\) 32.5836 1.41401
\(532\) 35.4644 35.4644i 1.53758 1.53758i
\(533\) −13.9590 13.9590i −0.604631 0.604631i
\(534\) −0.00692555 0.00692555i −0.000299698 0.000299698i
\(535\) 17.4381i 0.753913i
\(536\) 0.820128i 0.0354241i
\(537\) −3.72221 3.72221i −0.160625 0.160625i
\(538\) −0.772464 0.772464i −0.0333033 0.0333033i
\(539\) 8.04831 8.04831i 0.346665 0.346665i
\(540\) −22.4568 −0.966385
\(541\) −1.69022 + 1.69022i −0.0726683 + 0.0726683i −0.742507 0.669839i \(-0.766363\pi\)
0.669839 + 0.742507i \(0.266363\pi\)
\(542\) 0.629968i 0.0270594i
\(543\) 14.3806 0.617130
\(544\) 0.502050 2.01969i 0.0215252 0.0865933i
\(545\) 56.0514 2.40098
\(546\) 0.373827i 0.0159983i
\(547\) 13.5713 13.5713i 0.580268 0.580268i −0.354709 0.934977i \(-0.615420\pi\)
0.934977 + 0.354709i \(0.115420\pi\)
\(548\) 19.5270 0.834150
\(549\) −21.9706 + 21.9706i −0.937684 + 0.937684i
\(550\) −0.158730 0.158730i −0.00676827 0.00676827i
\(551\) 3.61049 + 3.61049i 0.153812 + 0.153812i
\(552\) 0.565624i 0.0240745i
\(553\) 26.7052i 1.13562i
\(554\) 0.292252 + 0.292252i 0.0124166 + 0.0124166i
\(555\) −1.06674 1.06674i −0.0452807 0.0452807i
\(556\) −4.57429 + 4.57429i −0.193993 + 0.193993i
\(557\) −3.48978 −0.147867 −0.0739334 0.997263i \(-0.523555\pi\)
−0.0739334 + 0.997263i \(0.523555\pi\)
\(558\) 0.690864 0.690864i 0.0292466 0.0292466i
\(559\) 2.82157i 0.119340i
\(560\) −54.9743 −2.32309
\(561\) −2.49315 0.619741i −0.105261 0.0261655i
\(562\) 0.538434 0.0227125
\(563\) 5.42665i 0.228706i 0.993440 + 0.114353i \(0.0364795\pi\)
−0.993440 + 0.114353i \(0.963520\pi\)
\(564\) 7.78243 7.78243i 0.327700 0.327700i
\(565\) −18.2046 −0.765875
\(566\) −0.368130 + 0.368130i −0.0154737 + 0.0154737i
\(567\) 17.1492 + 17.1492i 0.720198 + 0.720198i
\(568\) −0.417285 0.417285i −0.0175089 0.0175089i
\(569\) 16.3440i 0.685175i −0.939486 0.342588i \(-0.888697\pi\)
0.939486 0.342588i \(-0.111303\pi\)
\(570\) 0.493719i 0.0206796i
\(571\) −19.6882 19.6882i −0.823924 0.823924i 0.162744 0.986668i \(-0.447965\pi\)
−0.986668 + 0.162744i \(0.947965\pi\)
\(572\) −4.69516 4.69516i −0.196314 0.196314i
\(573\) −10.3521 + 10.3521i −0.432464 + 0.432464i
\(574\) −1.07265 −0.0447714
\(575\) 20.3214 20.3214i 0.847462 0.847462i
\(576\) 20.7831i 0.865963i
\(577\) −30.8328 −1.28359 −0.641794 0.766877i \(-0.721810\pi\)
−0.641794 + 0.766877i \(0.721810\pi\)
\(578\) −0.335208 + 0.632588i −0.0139428 + 0.0263122i
\(579\) 1.70058 0.0706739
\(580\) 5.60169i 0.232597i
\(581\) −19.2112 + 19.2112i −0.797014 + 0.797014i
\(582\) −0.314122 −0.0130208
\(583\) −2.41206 + 2.41206i −0.0998974 + 0.0998974i
\(584\) −0.522793 0.522793i −0.0216333 0.0216333i
\(585\) 19.7242 + 19.7242i 0.815497 + 0.815497i
\(586\) 0.654052i 0.0270186i
\(587\) 13.1242i 0.541695i 0.962622 + 0.270848i \(0.0873040\pi\)
−0.962622 + 0.270848i \(0.912696\pi\)
\(588\) −10.0206 10.0206i −0.413241 0.413241i
\(589\) −36.7716 36.7716i −1.51515 1.51515i
\(590\) 1.19404 1.19404i 0.0491579 0.0491579i
\(591\) 4.79352 0.197179
\(592\) −2.12501 + 2.12501i −0.0873373 + 0.0873373i
\(593\) 9.08497i 0.373075i −0.982448 0.186538i \(-0.940273\pi\)
0.982448 0.186538i \(-0.0597266\pi\)
\(594\) −0.147250 −0.00604172
\(595\) 55.1393 + 13.7064i 2.26049 + 0.561908i
\(596\) −25.8948 −1.06069
\(597\) 6.50422i 0.266200i
\(598\) −0.533486 + 0.533486i −0.0218159 + 0.0218159i
\(599\) −29.2400 −1.19471 −0.597357 0.801975i \(-0.703783\pi\)
−0.597357 + 0.801975i \(0.703783\pi\)
\(600\) −0.395430 + 0.395430i −0.0161434 + 0.0161434i
\(601\) 7.83026 + 7.83026i 0.319403 + 0.319403i 0.848538 0.529135i \(-0.177483\pi\)
−0.529135 + 0.848538i \(0.677483\pi\)
\(602\) 0.108409 + 0.108409i 0.00441840 + 0.00441840i
\(603\) 12.7215i 0.518060i
\(604\) 24.7188i 1.00579i
\(605\) 2.27271 + 2.27271i 0.0923989 + 0.0923989i
\(606\) −0.0708204 0.0708204i −0.00287688 0.00287688i
\(607\) 3.98442 3.98442i 0.161723 0.161723i −0.621607 0.783329i \(-0.713520\pi\)
0.783329 + 0.621607i \(0.213520\pi\)
\(608\) −2.95492 −0.119838
\(609\) 1.64755 1.64755i 0.0667622 0.0667622i
\(610\) 1.61025i 0.0651970i
\(611\) −29.3740 −1.18835
\(612\) 5.19096 20.8826i 0.209832 0.844130i
\(613\) 15.3457 0.619806 0.309903 0.950768i \(-0.399703\pi\)
0.309903 + 0.950768i \(0.399703\pi\)
\(614\) 1.24007i 0.0500451i
\(615\) 8.41270 8.41270i 0.339233 0.339233i
\(616\) −0.721897 −0.0290861
\(617\) 24.3795 24.3795i 0.981482 0.981482i −0.0183496 0.999832i \(-0.505841\pi\)
0.999832 + 0.0183496i \(0.00584119\pi\)
\(618\) 0.175732 + 0.175732i 0.00706898 + 0.00706898i
\(619\) −3.81518 3.81518i −0.153345 0.153345i 0.626265 0.779610i \(-0.284583\pi\)
−0.779610 + 0.626265i \(0.784583\pi\)
\(620\) 57.0512i 2.29123i
\(621\) 18.8516i 0.756490i
\(622\) 0.359296 + 0.359296i 0.0144065 + 0.0144065i
\(623\) −1.13161 1.13161i −0.0453370 0.0453370i
\(624\) −5.84052 + 5.84052i −0.233808 + 0.233808i
\(625\) 23.2386 0.929544
\(626\) 0.251385 0.251385i 0.0100474 0.0100474i
\(627\) 3.64762i 0.145672i
\(628\) 3.70589 0.147881
\(629\) 2.66120 1.60157i 0.106109 0.0638588i
\(630\) 1.51566 0.0603855
\(631\) 10.7782i 0.429071i 0.976716 + 0.214536i \(0.0688238\pi\)
−0.976716 + 0.214536i \(0.931176\pi\)
\(632\) 0.741587 0.741587i 0.0294987 0.0294987i
\(633\) 6.49365 0.258100
\(634\) 0.598157 0.598157i 0.0237559 0.0237559i
\(635\) 26.1731 + 26.1731i 1.03865 + 1.03865i
\(636\) 3.00314 + 3.00314i 0.119082 + 0.119082i
\(637\) 37.8216i 1.49855i
\(638\) 0.0367304i 0.00145417i
\(639\) −6.47276 6.47276i −0.256058 0.256058i
\(640\) 3.05592 + 3.05592i 0.120796 + 0.120796i
\(641\) 15.7482 15.7482i 0.622015 0.622015i −0.324031 0.946046i \(-0.605038\pi\)
0.946046 + 0.324031i \(0.105038\pi\)
\(642\) −0.142362 −0.00561856
\(643\) −14.6821 + 14.6821i −0.579004 + 0.579004i −0.934629 0.355625i \(-0.884268\pi\)
0.355625 + 0.934629i \(0.384268\pi\)
\(644\) 46.1900i 1.82014i
\(645\) −1.70048 −0.0669565
\(646\) 0.986468 + 0.245214i 0.0388120 + 0.00964782i
\(647\) 5.79889 0.227978 0.113989 0.993482i \(-0.463637\pi\)
0.113989 + 0.993482i \(0.463637\pi\)
\(648\) 0.952446i 0.0374156i
\(649\) −8.82162 + 8.82162i −0.346279 + 0.346279i
\(650\) 0.745924 0.0292575
\(651\) −16.7797 + 16.7797i −0.657650 + 0.657650i
\(652\) 9.45407 + 9.45407i 0.370250 + 0.370250i
\(653\) 0.360205 + 0.360205i 0.0140959 + 0.0140959i 0.714120 0.700024i \(-0.246827\pi\)
−0.700024 + 0.714120i \(0.746827\pi\)
\(654\) 0.457594i 0.0178934i
\(655\) 7.81747i 0.305454i
\(656\) −16.7586 16.7586i −0.654312 0.654312i
\(657\) −8.10935 8.10935i −0.316376 0.316376i
\(658\) −1.12859 + 1.12859i −0.0439970 + 0.0439970i
\(659\) 27.7963 1.08279 0.541395 0.840768i \(-0.317896\pi\)
0.541395 + 0.840768i \(0.317896\pi\)
\(660\) 2.82964 2.82964i 0.110144 0.110144i
\(661\) 3.34455i 0.130088i 0.997882 + 0.0650439i \(0.0207187\pi\)
−0.997882 + 0.0650439i \(0.979281\pi\)
\(662\) −0.252818 −0.00982606
\(663\) 7.31423 4.40186i 0.284061 0.170954i
\(664\) 1.06697 0.0414063
\(665\) 80.6720i 3.12833i
\(666\) 0.0585874 0.0585874i 0.00227021 0.00227021i
\(667\) 4.70242 0.182078
\(668\) 20.7271 20.7271i 0.801957 0.801957i
\(669\) 10.5071 + 10.5071i 0.406228 + 0.406228i
\(670\) 0.466185 + 0.466185i 0.0180103 + 0.0180103i
\(671\) 11.8966i 0.459262i
\(672\) 1.34840i 0.0520156i
\(673\) −5.72194 5.72194i −0.220564 0.220564i 0.588172 0.808736i \(-0.299848\pi\)
−0.808736 + 0.588172i \(0.799848\pi\)
\(674\) −0.768988 0.768988i −0.0296203 0.0296203i
\(675\) −13.1793 + 13.1793i −0.507270 + 0.507270i
\(676\) −3.91290 −0.150496
\(677\) −24.2745 + 24.2745i −0.932944 + 0.932944i −0.997889 0.0649453i \(-0.979313\pi\)
0.0649453 + 0.997889i \(0.479313\pi\)
\(678\) 0.148620i 0.00570771i
\(679\) −51.3265 −1.96973
\(680\) −1.15057 1.91181i −0.0441222 0.0733144i
\(681\) 12.6072 0.483108
\(682\) 0.374086i 0.0143245i
\(683\) 4.42455 4.42455i 0.169301 0.169301i −0.617371 0.786672i \(-0.711802\pi\)
0.786672 + 0.617371i \(0.211802\pi\)
\(684\) −30.5525 −1.16820
\(685\) 22.2093 22.2093i 0.848573 0.848573i
\(686\) 0.559458 + 0.559458i 0.0213602 + 0.0213602i
\(687\) 12.1167 + 12.1167i 0.462281 + 0.462281i
\(688\) 3.38746i 0.129146i
\(689\) 11.3351i 0.431831i
\(690\) −0.321517 0.321517i −0.0122400 0.0122400i
\(691\) 31.5883 + 31.5883i 1.20167 + 1.20167i 0.973657 + 0.228017i \(0.0732243\pi\)
0.228017 + 0.973657i \(0.426776\pi\)
\(692\) −19.4636 + 19.4636i −0.739897 + 0.739897i
\(693\) −11.1978 −0.425369
\(694\) −0.315414 + 0.315414i −0.0119729 + 0.0119729i
\(695\) 10.4053i 0.394695i
\(696\) −0.0915031 −0.00346842
\(697\) 12.6306 + 20.9872i 0.478416 + 0.794946i
\(698\) −0.619309 −0.0234412
\(699\) 17.9682i 0.679620i
\(700\) −32.2916 + 32.2916i −1.22051 + 1.22051i
\(701\) 46.1860 1.74442 0.872210 0.489132i \(-0.162686\pi\)
0.872210 + 0.489132i \(0.162686\pi\)
\(702\) 0.345987 0.345987i 0.0130584 0.0130584i
\(703\) −3.11834 3.11834i −0.117611 0.117611i
\(704\) −5.62678 5.62678i −0.212067 0.212067i
\(705\) 17.7029i 0.666731i
\(706\) 1.30886i 0.0492594i
\(707\) −11.5718 11.5718i −0.435202 0.435202i
\(708\) 10.9834 + 10.9834i 0.412780 + 0.412780i
\(709\) −34.1833 + 34.1833i −1.28378 + 1.28378i −0.345281 + 0.938499i \(0.612216\pi\)
−0.938499 + 0.345281i \(0.887784\pi\)
\(710\) −0.474395 −0.0178037
\(711\) 11.5032 11.5032i 0.431404 0.431404i
\(712\) 0.0628484i 0.00235534i
\(713\) −47.8924 −1.79359
\(714\) 0.111897 0.450148i 0.00418764 0.0168464i
\(715\) −10.6802 −0.399417
\(716\) 16.8818i 0.630902i
\(717\) −6.98008 + 6.98008i −0.260676 + 0.260676i
\(718\) −0.603446 −0.0225204
\(719\) −7.44830 + 7.44830i −0.277775 + 0.277775i −0.832220 0.554445i \(-0.812930\pi\)
0.554445 + 0.832220i \(0.312930\pi\)
\(720\) 23.6801 + 23.6801i 0.882505 + 0.882505i
\(721\) 28.7140 + 28.7140i 1.06936 + 1.06936i
\(722\) 0.643122i 0.0239345i
\(723\) 8.85620i 0.329366i
\(724\) −32.6110 32.6110i −1.21198 1.21198i
\(725\) −3.28748 3.28748i −0.122094 0.122094i
\(726\) 0.0185541 0.0185541i 0.000688606 0.000688606i
\(727\) −47.6233 −1.76625 −0.883125 0.469137i \(-0.844565\pi\)
−0.883125 + 0.469137i \(0.844565\pi\)
\(728\) 1.69621 1.69621i 0.0628659 0.0628659i
\(729\) 8.23805i 0.305113i
\(730\) −0.594342 −0.0219976
\(731\) 0.844575 3.39762i 0.0312377 0.125666i
\(732\) −14.8119 −0.547462
\(733\) 42.3340i 1.56364i 0.623503 + 0.781821i \(0.285709\pi\)
−0.623503 + 0.781821i \(0.714291\pi\)
\(734\) −0.636455 + 0.636455i −0.0234920 + 0.0234920i
\(735\) −22.7941 −0.840771
\(736\) −1.92429 + 1.92429i −0.0709302 + 0.0709302i
\(737\) −3.44420 3.44420i −0.126869 0.126869i
\(738\) 0.462041 + 0.462041i 0.0170080 + 0.0170080i
\(739\) 18.3674i 0.675657i −0.941208 0.337828i \(-0.890308\pi\)
0.941208 0.337828i \(-0.109692\pi\)
\(740\) 4.83812i 0.177853i
\(741\) −8.57066 8.57066i −0.314851 0.314851i
\(742\) −0.435508 0.435508i −0.0159880 0.0159880i
\(743\) −22.4691 + 22.4691i −0.824310 + 0.824310i −0.986723 0.162413i \(-0.948072\pi\)
0.162413 + 0.986723i \(0.448072\pi\)
\(744\) 0.931927 0.0341661
\(745\) −29.4519 + 29.4519i −1.07903 + 1.07903i
\(746\) 0.174441i 0.00638672i
\(747\) 16.5504 0.605546
\(748\) 4.24833 + 7.05912i 0.155334 + 0.258107i
\(749\) −23.2614 −0.849953
\(750\) 0.0278680i 0.00101760i
\(751\) −26.0044 + 26.0044i −0.948915 + 0.948915i −0.998757 0.0498422i \(-0.984128\pi\)
0.0498422 + 0.998757i \(0.484128\pi\)
\(752\) −35.2652 −1.28599
\(753\) −0.390234 + 0.390234i −0.0142209 + 0.0142209i
\(754\) 0.0863040 + 0.0863040i 0.00314301 + 0.00314301i
\(755\) −28.1142 28.1142i −1.02318 1.02318i
\(756\) 29.9560i 1.08949i
\(757\) 6.40521i 0.232801i −0.993202 0.116401i \(-0.962864\pi\)
0.993202 0.116401i \(-0.0371357\pi\)
\(758\) 0.115454 + 0.115454i 0.00419349 + 0.00419349i
\(759\) 2.37538 + 2.37538i 0.0862210 + 0.0862210i
\(760\) −2.24021 + 2.24021i −0.0812611 + 0.0812611i
\(761\) 25.8600 0.937424 0.468712 0.883351i \(-0.344718\pi\)
0.468712 + 0.883351i \(0.344718\pi\)
\(762\) 0.213673 0.213673i 0.00774055 0.00774055i
\(763\) 74.7693i 2.70683i
\(764\) 46.9510 1.69863
\(765\) −17.8471 29.6552i −0.645265 1.07219i
\(766\) −0.752130 −0.0271756
\(767\) 41.4556i 1.49688i
\(768\) −6.98690 + 6.98690i −0.252118 + 0.252118i
\(769\) −7.38242 −0.266217 −0.133108 0.991101i \(-0.542496\pi\)
−0.133108 + 0.991101i \(0.542496\pi\)
\(770\) −0.410348 + 0.410348i −0.0147879 + 0.0147879i
\(771\) −2.95187 2.95187i −0.106309 0.106309i
\(772\) −3.85643 3.85643i −0.138796 0.138796i
\(773\) 0.0674286i 0.00242524i 0.999999 + 0.00121262i \(0.000385989\pi\)
−0.999999 + 0.00121262i \(0.999614\pi\)
\(774\) 0.0933936i 0.00335696i
\(775\) 33.4818 + 33.4818i 1.20270 + 1.20270i
\(776\) 1.42531 + 1.42531i 0.0511655 + 0.0511655i
\(777\) −1.42297 + 1.42297i −0.0510489 + 0.0510489i
\(778\) −0.448724 −0.0160875
\(779\) 24.5924 24.5924i 0.881113 0.881113i
\(780\) 13.2974i 0.476124i
\(781\) 3.50485 0.125413
\(782\) 0.802090 0.482716i 0.0286827 0.0172619i
\(783\) −3.04970 −0.108987
\(784\) 45.4070i 1.62168i
\(785\) 4.21495 4.21495i 0.150438 0.150438i
\(786\) −0.0638206 −0.00227641
\(787\) 19.0961 19.0961i 0.680701 0.680701i −0.279457 0.960158i \(-0.590154\pi\)
0.960158 + 0.279457i \(0.0901545\pi\)
\(788\) −10.8703 10.8703i −0.387238 0.387238i
\(789\) −1.87342 1.87342i −0.0666956 0.0666956i
\(790\) 0.843081i 0.0299955i
\(791\) 24.2840i 0.863438i
\(792\) 0.310956 + 0.310956i 0.0110493 + 0.0110493i
\(793\) 27.9529 + 27.9529i 0.992637 + 0.992637i
\(794\) 0.0934998 0.0934998i 0.00331818 0.00331818i
\(795\) 6.83134 0.242282
\(796\) 14.7497 14.7497i 0.522788 0.522788i
\(797\) 34.1361i 1.20916i 0.796543 + 0.604581i \(0.206660\pi\)
−0.796543 + 0.604581i \(0.793340\pi\)
\(798\) −0.658593 −0.0233139
\(799\) 35.3710 + 8.79247i 1.25134 + 0.311055i
\(800\) 2.69056 0.0951255
\(801\) 0.974879i 0.0344457i
\(802\) −0.228741 + 0.228741i −0.00807713 + 0.00807713i
\(803\) 4.39102 0.154956
\(804\) −4.28820 + 4.28820i −0.151233 + 0.151233i
\(805\) −52.5348 52.5348i −1.85161 1.85161i
\(806\) −0.878976 0.878976i −0.0309606 0.0309606i
\(807\) 16.1631i 0.568968i
\(808\) 0.642685i 0.0226096i
\(809\) −1.17665 1.17665i −0.0413689 0.0413689i 0.686120 0.727489i \(-0.259313\pi\)
−0.727489 + 0.686120i \(0.759313\pi\)
\(810\) −0.541399 0.541399i −0.0190228 0.0190228i
\(811\) 3.97883 3.97883i 0.139716 0.139716i −0.633790 0.773505i \(-0.718502\pi\)
0.773505 + 0.633790i \(0.218502\pi\)
\(812\) −7.47233 −0.262227
\(813\) −6.59075 + 6.59075i −0.231148 + 0.231148i
\(814\) 0.0317237i 0.00111191i
\(815\) 21.5054 0.753303
\(816\) 8.78116 5.28470i 0.307402 0.185001i
\(817\) −4.97092 −0.173911
\(818\) 0.767262i 0.0268267i
\(819\) 26.3110 26.3110i 0.919381 0.919381i
\(820\) −38.1551 −1.33243
\(821\) 16.6320 16.6320i 0.580459 0.580459i −0.354570 0.935029i \(-0.615373\pi\)
0.935029 + 0.354570i \(0.115373\pi\)
\(822\) −0.181313 0.181313i −0.00632402 0.00632402i
\(823\) −10.2199 10.2199i −0.356242 0.356242i 0.506184 0.862426i \(-0.331056\pi\)
−0.862426 + 0.506184i \(0.831056\pi\)
\(824\) 1.59474i 0.0555555i
\(825\) 3.32128i 0.115632i
\(826\) −1.59278 1.59278i −0.0554200 0.0554200i
\(827\) 9.07308 + 9.07308i 0.315502 + 0.315502i 0.847037 0.531535i \(-0.178384\pi\)
−0.531535 + 0.847037i \(0.678384\pi\)
\(828\) −19.8963 + 19.8963i −0.691443 + 0.691443i
\(829\) 39.8821 1.38516 0.692580 0.721341i \(-0.256474\pi\)
0.692580 + 0.721341i \(0.256474\pi\)
\(830\) 0.606496 0.606496i 0.0210518 0.0210518i
\(831\) 6.11511i 0.212131i
\(832\) 26.4421 0.916713
\(833\) 11.3211 45.5433i 0.392252 1.57798i
\(834\) 0.0849470 0.00294147
\(835\) 47.1486i 1.63164i
\(836\) 8.27173 8.27173i 0.286084 0.286084i
\(837\) 31.0601 1.07360
\(838\) −0.164201 + 0.164201i −0.00567224 + 0.00567224i
\(839\) 8.61493 + 8.61493i 0.297420 + 0.297420i 0.840003 0.542582i \(-0.182553\pi\)
−0.542582 + 0.840003i \(0.682553\pi\)
\(840\) 1.02226 + 1.02226i 0.0352714 + 0.0352714i
\(841\) 28.2393i 0.973768i
\(842\) 0.655777i 0.0225996i
\(843\) 5.63312 + 5.63312i 0.194015 + 0.194015i
\(844\) −14.7257 14.7257i −0.506880 0.506880i
\(845\) −4.45039 + 4.45039i −0.153098 + 0.153098i
\(846\) 0.972276 0.0334275
\(847\) 3.03167 3.03167i 0.104169 0.104169i
\(848\) 13.6084i 0.467314i
\(849\) −7.70279 −0.264359
\(850\) −0.898213 0.223276i −0.0308084 0.00765830i
\(851\) −4.06143 −0.139224
\(852\) 4.36372i 0.149498i
\(853\) −30.4312 + 30.4312i −1.04195 + 1.04195i −0.0428649 + 0.999081i \(0.513649\pi\)
−0.999081 + 0.0428649i \(0.986351\pi\)
\(854\) 2.14798 0.0735023
\(855\) −34.7493 + 34.7493i −1.18840 + 1.18840i
\(856\) 0.645955 + 0.645955i 0.0220783 + 0.0220783i
\(857\) 10.6678 + 10.6678i 0.364406 + 0.364406i 0.865432 0.501026i \(-0.167044\pi\)
−0.501026 + 0.865432i \(0.667044\pi\)
\(858\) 0.0871915i 0.00297667i
\(859\) 1.91593i 0.0653706i −0.999466 0.0326853i \(-0.989594\pi\)
0.999466 0.0326853i \(-0.0104059\pi\)
\(860\) 3.85620 + 3.85620i 0.131495 + 0.131495i
\(861\) −11.2221 11.2221i −0.382447 0.382447i
\(862\) −0.735132 + 0.735132i −0.0250387 + 0.0250387i
\(863\) 55.0897 1.87527 0.937637 0.347616i \(-0.113009\pi\)
0.937637 + 0.347616i \(0.113009\pi\)
\(864\) 1.24798 1.24798i 0.0424570 0.0424570i
\(865\) 44.2745i 1.50538i
\(866\) 1.15439 0.0392278
\(867\) −10.1251 + 3.11120i −0.343867 + 0.105662i
\(868\) 76.1031 2.58311
\(869\) 6.22872i 0.211295i
\(870\) −0.0520131 + 0.0520131i −0.00176341 + 0.00176341i
\(871\) 16.1854 0.548421
\(872\) −2.07630 + 2.07630i −0.0703125 + 0.0703125i
\(873\) 22.1088 + 22.1088i 0.748270 + 0.748270i
\(874\) −0.939873 0.939873i −0.0317917 0.0317917i
\(875\) 4.55354i 0.153938i
\(876\) 5.46705i 0.184715i
\(877\) 30.1385 + 30.1385i 1.01770 + 1.01770i 0.999840 + 0.0178634i \(0.00568641\pi\)
0.0178634 + 0.999840i \(0.494314\pi\)
\(878\) −0.237533 0.237533i −0.00801634 0.00801634i
\(879\) −6.84271 + 6.84271i −0.230799 + 0.230799i
\(880\) −12.8222 −0.432237
\(881\) −15.1513 + 15.1513i −0.510461 + 0.510461i −0.914668 0.404207i \(-0.867548\pi\)
0.404207 + 0.914668i \(0.367548\pi\)
\(882\) 1.25189i 0.0421533i
\(883\) 11.2898 0.379931 0.189965 0.981791i \(-0.439162\pi\)
0.189965 + 0.981791i \(0.439162\pi\)
\(884\) −26.5687 6.60439i −0.893601 0.222130i
\(885\) 24.9842 0.839835
\(886\) 0.817636i 0.0274690i
\(887\) −36.1491 + 36.1491i −1.21377 + 1.21377i −0.243989 + 0.969778i \(0.578456\pi\)
−0.969778 + 0.243989i \(0.921544\pi\)
\(888\) 0.0790303 0.00265208
\(889\) 34.9134 34.9134i 1.17096 1.17096i
\(890\) 0.0357249 + 0.0357249i 0.00119750 + 0.00119750i
\(891\) 3.99988 + 3.99988i 0.134001 + 0.134001i
\(892\) 47.6541i 1.59558i
\(893\) 51.7499i 1.73174i
\(894\) 0.240440 + 0.240440i 0.00804153 + 0.00804153i
\(895\) 19.2007 + 19.2007i 0.641810 + 0.641810i
\(896\) 4.07643 4.07643i 0.136184 0.136184i
\(897\) −11.1627 −0.372712
\(898\) 0.136855 0.136855i 0.00456693 0.00456693i
\(899\) 7.74775i 0.258402i
\(900\) 27.8191 0.927304
\(901\) −3.39290 + 13.6492i −0.113034 + 0.454722i
\(902\) −0.250184 −0.00833022
\(903\) 2.26835i 0.0754859i
\(904\) 0.674352 0.674352i 0.0224286 0.0224286i
\(905\) −74.1811 −2.46586
\(906\) −0.229520 + 0.229520i −0.00762530 + 0.00762530i
\(907\) −2.74071 2.74071i −0.0910037 0.0910037i 0.660139 0.751143i \(-0.270497\pi\)
−0.751143 + 0.660139i \(0.770497\pi\)
\(908\) −28.5894 28.5894i −0.948772 0.948772i
\(909\) 9.96907i 0.330653i
\(910\) 1.92836i 0.0639244i
\(911\) 5.34710 + 5.34710i 0.177157 + 0.177157i 0.790115 0.612958i \(-0.210021\pi\)
−0.612958 + 0.790115i \(0.710021\pi\)
\(912\) −10.2896 10.2896i −0.340722 0.340722i
\(913\) −4.48082 + 4.48082i −0.148293 + 0.148293i
\(914\) −0.656312 −0.0217089
\(915\) −16.8465 + 16.8465i −0.556927 + 0.556927i
\(916\) 54.9543i 1.81574i
\(917\) −10.4281 −0.344365
\(918\) −0.520187 + 0.313060i −0.0171687 + 0.0103325i
\(919\) 33.0326 1.08965 0.544823 0.838551i \(-0.316597\pi\)
0.544823 + 0.838551i \(0.316597\pi\)
\(920\) 2.91772i 0.0961945i
\(921\) 12.9737 12.9737i 0.427496 0.427496i
\(922\) 1.15089 0.0379026
\(923\) −8.23520 + 8.23520i −0.271065 + 0.271065i
\(924\) −3.77458 3.77458i −0.124175 0.124175i
\(925\) 2.83936 + 2.83936i 0.0933576 + 0.0933576i
\(926\) 0.111409i 0.00366112i
\(927\) 24.7370i 0.812470i
\(928\) 0.311300 + 0.311300i 0.0102189 + 0.0102189i
\(929\) −9.16467 9.16467i −0.300683 0.300683i 0.540598 0.841281i \(-0.318198\pi\)
−0.841281 + 0.540598i \(0.818198\pi\)
\(930\) 0.529735 0.529735i 0.0173707 0.0173707i
\(931\) −66.6325 −2.18379
\(932\) −40.7467 + 40.7467i −1.33470 + 1.33470i
\(933\) 7.51795i 0.246126i
\(934\) −0.567293 −0.0185624
\(935\) 12.8607 + 3.19689i 0.420590 + 0.104549i
\(936\) −1.46128 −0.0477635
\(937\) 45.8455i 1.49771i −0.662735 0.748854i \(-0.730604\pi\)
0.662735 0.748854i \(-0.269396\pi\)
\(938\) 0.621865 0.621865i 0.0203046 0.0203046i
\(939\) 5.26001 0.171654
\(940\) −40.1451 + 40.1451i −1.30939 + 1.30939i
\(941\) −9.19706 9.19706i −0.299816 0.299816i 0.541126 0.840942i \(-0.317998\pi\)
−0.840942 + 0.541126i \(0.817998\pi\)
\(942\) −0.0344102 0.0344102i −0.00112114 0.00112114i
\(943\) 32.0298i 1.04304i
\(944\) 49.7699i 1.61987i
\(945\) 34.0709 + 34.0709i 1.10833 + 1.10833i
\(946\) 0.0252852 + 0.0252852i 0.000822093 + 0.000822093i
\(947\) 15.3572 15.3572i 0.499042 0.499042i −0.412098 0.911140i \(-0.635204\pi\)
0.911140 + 0.412098i \(0.135204\pi\)
\(948\) 7.75507 0.251873
\(949\) −10.3174 + 10.3174i −0.334918 + 0.334918i
\(950\) 1.31414i 0.0426363i
\(951\) 12.5159 0.405856
\(952\) −2.55024 + 1.53479i −0.0826537 + 0.0497428i
\(953\) 15.5511 0.503748 0.251874 0.967760i \(-0.418953\pi\)
0.251874 + 0.967760i \(0.418953\pi\)
\(954\) 0.375189i 0.0121472i
\(955\) 53.4004 53.4004i 1.72800 1.72800i
\(956\) 31.6576 1.02388
\(957\) 0.384275 0.384275i 0.0124219 0.0124219i
\(958\) 1.09652 + 1.09652i 0.0354269 + 0.0354269i
\(959\) −29.6259 29.6259i −0.956670 0.956670i
\(960\) 15.9359i 0.514329i
\(961\) 47.9081i 1.54542i
\(962\) −0.0745399 0.0745399i −0.00240326 0.00240326i
\(963\) 10.0198 + 10.0198i 0.322884 + 0.322884i
\(964\) 20.0833 20.0833i 0.646839 0.646839i
\(965\) −8.77233 −0.282391
\(966\) −0.428886 + 0.428886i −0.0137992 + 0.0137992i
\(967\) 14.2821i 0.459282i −0.973275 0.229641i \(-0.926245\pi\)
0.973275 0.229641i \(-0.0737553\pi\)
\(968\) −0.168375 −0.00541179
\(969\) 7.75502 + 12.8859i 0.249127 + 0.413955i
\(970\) 1.62037 0.0520271
\(971\) 34.3172i 1.10129i −0.834739 0.550646i \(-0.814381\pi\)
0.834739 0.550646i \(-0.185619\pi\)
\(972\) 19.8016 19.8016i 0.635137 0.635137i
\(973\) 13.8800 0.444974
\(974\) −0.643775 + 0.643775i −0.0206279 + 0.0206279i
\(975\) 7.80389 + 7.80389i 0.249924 + 0.249924i
\(976\) 33.5591 + 33.5591i 1.07420 + 1.07420i
\(977\) 40.5801i 1.29827i 0.760673 + 0.649136i \(0.224869\pi\)
−0.760673 + 0.649136i \(0.775131\pi\)
\(978\) 0.175567i 0.00561401i
\(979\) −0.263937 0.263937i −0.00843547 0.00843547i
\(980\) 51.6903 + 51.6903i 1.65118 + 1.65118i
\(981\) −32.2068 + 32.2068i −1.02828 + 1.02828i
\(982\) 0.614765 0.0196180
\(983\) 6.75509 6.75509i 0.215454 0.215454i −0.591126 0.806579i \(-0.701316\pi\)
0.806579 + 0.591126i \(0.201316\pi\)
\(984\) 0.623261i 0.0198688i
\(985\) −24.7270 −0.787867
\(986\) −0.0780908 0.129757i −0.00248692 0.00413231i
\(987\) −23.6147 −0.751664
\(988\) 38.8715i 1.23667i
\(989\) −3.23714 + 3.23714i −0.102935 + 0.102935i
\(990\) 0.353514 0.0112354
\(991\) 35.4347 35.4347i 1.12562 1.12562i 0.134740 0.990881i \(-0.456980\pi\)
0.990881 0.134740i \(-0.0430198\pi\)
\(992\) −3.17048 3.17048i −0.100663 0.100663i
\(993\) −2.64499 2.64499i −0.0839363 0.0839363i
\(994\) 0.632815i 0.0200717i
\(995\) 33.5515i 1.06365i
\(996\) 5.57885 + 5.57885i 0.176773 + 0.176773i
\(997\) 38.7189 + 38.7189i 1.22624 + 1.22624i 0.965375 + 0.260865i \(0.0840078\pi\)
0.260865 + 0.965375i \(0.415992\pi\)
\(998\) −0.151349 + 0.151349i −0.00479087 + 0.00479087i
\(999\) 2.63400 0.0833359
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 187.2.e.b.89.7 28
17.8 even 8 3179.2.a.be.1.7 14
17.9 even 8 3179.2.a.bd.1.7 14
17.13 even 4 inner 187.2.e.b.166.8 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.e.b.89.7 28 1.1 even 1 trivial
187.2.e.b.166.8 yes 28 17.13 even 4 inner
3179.2.a.bd.1.7 14 17.9 even 8
3179.2.a.be.1.7 14 17.8 even 8