Properties

Label 1110.2.u.e.191.14
Level $1110$
Weight $2$
Character 1110.191
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(191,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 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("1110.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 191.14
Character \(\chi\) \(=\) 1110.191
Dual form 1110.2.u.e.401.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.55689 + 0.759006i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.63759 - 0.564190i) q^{6} +1.92521 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.84782 - 2.36338i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.55689 + 0.759006i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.63759 - 0.564190i) q^{6} +1.92521 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.84782 - 2.36338i) q^{9} +1.00000 q^{10} -5.18734 q^{11} +(-0.759006 - 1.55689i) q^{12} +(-3.96677 - 3.96677i) q^{13} +(1.36133 + 1.36133i) q^{14} +(-0.564190 + 1.63759i) q^{15} -1.00000 q^{16} +(-3.83800 + 3.83800i) q^{17} +(2.97777 - 0.364556i) q^{18} +(0.0989804 + 0.0989804i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-2.99733 + 1.46124i) q^{21} +(-3.66800 - 3.66800i) q^{22} +(-1.07572 + 1.07572i) q^{23} +(0.564190 - 1.63759i) q^{24} -1.00000i q^{25} -5.60986i q^{26} +(-1.08303 + 5.08203i) q^{27} +1.92521i q^{28} +(-1.77763 - 1.77763i) q^{29} +(-1.55689 + 0.759006i) q^{30} +(-4.45832 + 4.45832i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.07612 - 3.93722i) q^{33} -5.42775 q^{34} +(1.36133 - 1.36133i) q^{35} +(2.36338 + 1.84782i) q^{36} +(-5.86944 - 1.59678i) q^{37} +0.139979i q^{38} +(9.18664 + 3.16503i) q^{39} +1.00000i q^{40} -12.4094 q^{41} +(-3.15269 - 1.08618i) q^{42} +(7.21797 + 7.21797i) q^{43} -5.18734i q^{44} +(-0.364556 - 2.97777i) q^{45} -1.52130 q^{46} -3.47762i q^{47} +(1.55689 - 0.759006i) q^{48} -3.29358 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.06228 - 8.88841i) q^{51} +(3.96677 - 3.96677i) q^{52} +3.95819i q^{53} +(-4.35936 + 2.82772i) q^{54} +(-3.66800 + 3.66800i) q^{55} +(-1.36133 + 1.36133i) q^{56} +(-0.229228 - 0.0789750i) q^{57} -2.51395i q^{58} +(7.83820 - 7.83820i) q^{59} +(-1.63759 - 0.564190i) q^{60} +(9.10908 - 9.10908i) q^{61} -6.30502 q^{62} +(3.55743 - 4.54999i) q^{63} -1.00000i q^{64} -5.60986 q^{65} +(8.49472 + 2.92664i) q^{66} -9.29823i q^{67} +(-3.83800 - 3.83800i) q^{68} +(0.858304 - 2.49127i) q^{69} +1.92521 q^{70} -1.23955i q^{71} +(0.364556 + 2.97777i) q^{72} +6.92368i q^{73} +(-3.02123 - 5.27941i) q^{74} +(0.759006 + 1.55689i) q^{75} +(-0.0989804 + 0.0989804i) q^{76} -9.98669 q^{77} +(4.25792 + 8.73394i) q^{78} +(-0.761048 - 0.761048i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-2.17113 - 8.73420i) q^{81} +(-8.77480 - 8.77480i) q^{82} -9.18336i q^{83} +(-1.46124 - 2.99733i) q^{84} +5.42775i q^{85} +10.2078i q^{86} +(4.11681 + 1.41835i) q^{87} +(3.66800 - 3.66800i) q^{88} +(-5.54999 - 5.54999i) q^{89} +(1.84782 - 2.36338i) q^{90} +(-7.63685 - 7.63685i) q^{91} +(-1.07572 - 1.07572i) q^{92} +(3.55723 - 10.3250i) q^{93} +(2.45905 - 2.45905i) q^{94} +0.139979 q^{95} +(1.63759 + 0.564190i) q^{96} +(3.84448 + 3.84448i) q^{97} +(-2.32892 - 2.32892i) q^{98} +(-9.58527 + 12.2597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −1.55689 + 0.759006i −0.898871 + 0.438212i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −1.63759 0.564190i −0.668542 0.230330i
\(7\) 1.92521 0.727659 0.363830 0.931466i \(-0.381469\pi\)
0.363830 + 0.931466i \(0.381469\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.84782 2.36338i 0.615940 0.787793i
\(10\) 1.00000 0.316228
\(11\) −5.18734 −1.56404 −0.782021 0.623252i \(-0.785811\pi\)
−0.782021 + 0.623252i \(0.785811\pi\)
\(12\) −0.759006 1.55689i −0.219106 0.449436i
\(13\) −3.96677 3.96677i −1.10018 1.10018i −0.994388 0.105797i \(-0.966261\pi\)
−0.105797 0.994388i \(-0.533739\pi\)
\(14\) 1.36133 + 1.36133i 0.363830 + 0.363830i
\(15\) −0.564190 + 1.63759i −0.145673 + 0.422823i
\(16\) −1.00000 −0.250000
\(17\) −3.83800 + 3.83800i −0.930851 + 0.930851i −0.997759 0.0669078i \(-0.978687\pi\)
0.0669078 + 0.997759i \(0.478687\pi\)
\(18\) 2.97777 0.364556i 0.701867 0.0859267i
\(19\) 0.0989804 + 0.0989804i 0.0227077 + 0.0227077i 0.718369 0.695662i \(-0.244889\pi\)
−0.695662 + 0.718369i \(0.744889\pi\)
\(20\) 0.707107 + 0.707107i 0.158114 + 0.158114i
\(21\) −2.99733 + 1.46124i −0.654072 + 0.318869i
\(22\) −3.66800 3.66800i −0.782021 0.782021i
\(23\) −1.07572 + 1.07572i −0.224304 + 0.224304i −0.810308 0.586004i \(-0.800700\pi\)
0.586004 + 0.810308i \(0.300700\pi\)
\(24\) 0.564190 1.63759i 0.115165 0.334271i
\(25\) 1.00000i 0.200000i
\(26\) 5.60986i 1.10018i
\(27\) −1.08303 + 5.08203i −0.208430 + 0.978037i
\(28\) 1.92521i 0.363830i
\(29\) −1.77763 1.77763i −0.330098 0.330098i 0.522526 0.852624i \(-0.324990\pi\)
−0.852624 + 0.522526i \(0.824990\pi\)
\(30\) −1.55689 + 0.759006i −0.284248 + 0.138575i
\(31\) −4.45832 + 4.45832i −0.800738 + 0.800738i −0.983211 0.182472i \(-0.941590\pi\)
0.182472 + 0.983211i \(0.441590\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 8.07612 3.93722i 1.40587 0.685382i
\(34\) −5.42775 −0.930851
\(35\) 1.36133 1.36133i 0.230106 0.230106i
\(36\) 2.36338 + 1.84782i 0.393897 + 0.307970i
\(37\) −5.86944 1.59678i −0.964930 0.262508i
\(38\) 0.139979i 0.0227077i
\(39\) 9.18664 + 3.16503i 1.47104 + 0.506810i
\(40\) 1.00000i 0.158114i
\(41\) −12.4094 −1.93803 −0.969014 0.247005i \(-0.920554\pi\)
−0.969014 + 0.247005i \(0.920554\pi\)
\(42\) −3.15269 1.08618i −0.486471 0.167601i
\(43\) 7.21797 + 7.21797i 1.10073 + 1.10073i 0.994323 + 0.106408i \(0.0339349\pi\)
0.106408 + 0.994323i \(0.466065\pi\)
\(44\) 5.18734i 0.782021i
\(45\) −0.364556 2.97777i −0.0543448 0.443899i
\(46\) −1.52130 −0.224304
\(47\) 3.47762i 0.507263i −0.967301 0.253632i \(-0.918375\pi\)
0.967301 0.253632i \(-0.0816251\pi\)
\(48\) 1.55689 0.759006i 0.224718 0.109553i
\(49\) −3.29358 −0.470512
\(50\) 0.707107 0.707107i 0.100000 0.100000i
\(51\) 3.06228 8.88841i 0.428805 1.24463i
\(52\) 3.96677 3.96677i 0.550092 0.550092i
\(53\) 3.95819i 0.543699i 0.962340 + 0.271849i \(0.0876352\pi\)
−0.962340 + 0.271849i \(0.912365\pi\)
\(54\) −4.35936 + 2.82772i −0.593234 + 0.384804i
\(55\) −3.66800 + 3.66800i −0.494593 + 0.494593i
\(56\) −1.36133 + 1.36133i −0.181915 + 0.181915i
\(57\) −0.229228 0.0789750i −0.0303620 0.0104605i
\(58\) 2.51395i 0.330098i
\(59\) 7.83820 7.83820i 1.02045 1.02045i 0.0206604 0.999787i \(-0.493423\pi\)
0.999787 0.0206604i \(-0.00657688\pi\)
\(60\) −1.63759 0.564190i −0.211412 0.0728366i
\(61\) 9.10908 9.10908i 1.16630 1.16630i 0.183228 0.983070i \(-0.441345\pi\)
0.983070 0.183228i \(-0.0586547\pi\)
\(62\) −6.30502 −0.800738
\(63\) 3.55743 4.54999i 0.448194 0.573245i
\(64\) 1.00000i 0.125000i
\(65\) −5.60986 −0.695818
\(66\) 8.49472 + 2.92664i 1.04563 + 0.360245i
\(67\) 9.29823i 1.13596i −0.823043 0.567980i \(-0.807725\pi\)
0.823043 0.567980i \(-0.192275\pi\)
\(68\) −3.83800 3.83800i −0.465426 0.465426i
\(69\) 0.858304 2.49127i 0.103328 0.299913i
\(70\) 1.92521 0.230106
\(71\) 1.23955i 0.147107i −0.997291 0.0735537i \(-0.976566\pi\)
0.997291 0.0735537i \(-0.0234340\pi\)
\(72\) 0.364556 + 2.97777i 0.0429633 + 0.350933i
\(73\) 6.92368i 0.810355i 0.914238 + 0.405178i \(0.132790\pi\)
−0.914238 + 0.405178i \(0.867210\pi\)
\(74\) −3.02123 5.27941i −0.351211 0.613719i
\(75\) 0.759006 + 1.55689i 0.0876425 + 0.179774i
\(76\) −0.0989804 + 0.0989804i −0.0113538 + 0.0113538i
\(77\) −9.98669 −1.13809
\(78\) 4.25792 + 8.73394i 0.482114 + 0.988925i
\(79\) −0.761048 0.761048i −0.0856246 0.0856246i 0.662997 0.748622i \(-0.269284\pi\)
−0.748622 + 0.662997i \(0.769284\pi\)
\(80\) −0.707107 + 0.707107i −0.0790569 + 0.0790569i
\(81\) −2.17113 8.73420i −0.241236 0.970466i
\(82\) −8.77480 8.77480i −0.969014 0.969014i
\(83\) 9.18336i 1.00800i −0.863702 0.504002i \(-0.831860\pi\)
0.863702 0.504002i \(-0.168140\pi\)
\(84\) −1.46124 2.99733i −0.159435 0.327036i
\(85\) 5.42775i 0.588722i
\(86\) 10.2078i 1.10073i
\(87\) 4.11681 + 1.41835i 0.441369 + 0.152063i
\(88\) 3.66800 3.66800i 0.391010 0.391010i
\(89\) −5.54999 5.54999i −0.588297 0.588297i 0.348873 0.937170i \(-0.386565\pi\)
−0.937170 + 0.348873i \(0.886565\pi\)
\(90\) 1.84782 2.36338i 0.194777 0.249122i
\(91\) −7.63685 7.63685i −0.800559 0.800559i
\(92\) −1.07572 1.07572i −0.112152 0.112152i
\(93\) 3.55723 10.3250i 0.368867 1.07065i
\(94\) 2.45905 2.45905i 0.253632 0.253632i
\(95\) 0.139979 0.0143616
\(96\) 1.63759 + 0.564190i 0.167135 + 0.0575824i
\(97\) 3.84448 + 3.84448i 0.390347 + 0.390347i 0.874811 0.484464i \(-0.160985\pi\)
−0.484464 + 0.874811i \(0.660985\pi\)
\(98\) −2.32892 2.32892i −0.235256 0.235256i
\(99\) −9.58527 + 12.2597i −0.963356 + 1.23214i
\(100\) 1.00000 0.100000
\(101\) 3.35861 0.334194 0.167097 0.985940i \(-0.446561\pi\)
0.167097 + 0.985940i \(0.446561\pi\)
\(102\) 8.45041 4.11969i 0.836716 0.407911i
\(103\) −10.7788 + 10.7788i −1.06207 + 1.06207i −0.0641240 + 0.997942i \(0.520425\pi\)
−0.997942 + 0.0641240i \(0.979575\pi\)
\(104\) 5.60986 0.550092
\(105\) −1.08618 + 3.15269i −0.106000 + 0.307671i
\(106\) −2.79886 + 2.79886i −0.271849 + 0.271849i
\(107\) 11.3682i 1.09901i 0.835492 + 0.549503i \(0.185183\pi\)
−0.835492 + 0.549503i \(0.814817\pi\)
\(108\) −5.08203 1.08303i −0.489019 0.104215i
\(109\) −11.3249 11.3249i −1.08473 1.08473i −0.996061 0.0886661i \(-0.971740\pi\)
−0.0886661 0.996061i \(-0.528260\pi\)
\(110\) −5.18734 −0.494593
\(111\) 10.3500 1.96893i 0.982382 0.186883i
\(112\) −1.92521 −0.181915
\(113\) 14.1216 + 14.1216i 1.32844 + 1.32844i 0.906728 + 0.421716i \(0.138572\pi\)
0.421716 + 0.906728i \(0.361428\pi\)
\(114\) −0.106245 0.217933i −0.00995078 0.0204113i
\(115\) 1.52130i 0.141862i
\(116\) 1.77763 1.77763i 0.165049 0.165049i
\(117\) −16.7049 + 2.04511i −1.54437 + 0.189070i
\(118\) 11.0849 1.02045
\(119\) −7.38893 + 7.38893i −0.677343 + 0.677343i
\(120\) −0.759006 1.55689i −0.0692875 0.142124i
\(121\) 15.9085 1.44623
\(122\) 12.8822 1.16630
\(123\) 19.3201 9.41884i 1.74204 0.849268i
\(124\) −4.45832 4.45832i −0.400369 0.400369i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 5.73281 0.701845i 0.510720 0.0625253i
\(127\) 6.10120 0.541394 0.270697 0.962665i \(-0.412746\pi\)
0.270697 + 0.962665i \(0.412746\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −16.7161 5.75911i −1.47177 0.507061i
\(130\) −3.96677 3.96677i −0.347909 0.347909i
\(131\) 5.14147 + 5.14147i 0.449212 + 0.449212i 0.895093 0.445880i \(-0.147109\pi\)
−0.445880 + 0.895093i \(0.647109\pi\)
\(132\) 3.93722 + 8.07612i 0.342691 + 0.702936i
\(133\) 0.190558 + 0.190558i 0.0165234 + 0.0165234i
\(134\) 6.57484 6.57484i 0.567980 0.567980i
\(135\) 2.82772 + 4.35936i 0.243371 + 0.375194i
\(136\) 5.42775i 0.465426i
\(137\) 2.67319i 0.228386i 0.993459 + 0.114193i \(0.0364282\pi\)
−0.993459 + 0.114193i \(0.963572\pi\)
\(138\) 2.36850 1.15468i 0.201620 0.0982928i
\(139\) 10.8710i 0.922067i 0.887383 + 0.461034i \(0.152521\pi\)
−0.887383 + 0.461034i \(0.847479\pi\)
\(140\) 1.36133 + 1.36133i 0.115053 + 0.115053i
\(141\) 2.63954 + 5.41428i 0.222289 + 0.455964i
\(142\) 0.876494 0.876494i 0.0735537 0.0735537i
\(143\) 20.5770 + 20.5770i 1.72073 + 1.72073i
\(144\) −1.84782 + 2.36338i −0.153985 + 0.196948i
\(145\) −2.51395 −0.208772
\(146\) −4.89578 + 4.89578i −0.405178 + 0.405178i
\(147\) 5.12775 2.49985i 0.422930 0.206184i
\(148\) 1.59678 5.86944i 0.131254 0.482465i
\(149\) 9.44249i 0.773559i −0.922172 0.386779i \(-0.873587\pi\)
0.922172 0.386779i \(-0.126413\pi\)
\(150\) −0.564190 + 1.63759i −0.0460659 + 0.133708i
\(151\) 12.4031i 1.00935i 0.863310 + 0.504673i \(0.168387\pi\)
−0.863310 + 0.504673i \(0.831613\pi\)
\(152\) −0.139979 −0.0113538
\(153\) 1.97872 + 16.1626i 0.159970 + 1.30667i
\(154\) −7.06166 7.06166i −0.569045 0.569045i
\(155\) 6.30502i 0.506431i
\(156\) −3.16503 + 9.18664i −0.253405 + 0.735519i
\(157\) 7.28854 0.581689 0.290844 0.956770i \(-0.406064\pi\)
0.290844 + 0.956770i \(0.406064\pi\)
\(158\) 1.07628i 0.0856246i
\(159\) −3.00429 6.16247i −0.238256 0.488715i
\(160\) −1.00000 −0.0790569
\(161\) −2.07099 + 2.07099i −0.163217 + 0.163217i
\(162\) 4.64079 7.71123i 0.364615 0.605851i
\(163\) 14.2334 14.2334i 1.11484 1.11484i 0.122356 0.992486i \(-0.460955\pi\)
0.992486 0.122356i \(-0.0390450\pi\)
\(164\) 12.4094i 0.969014i
\(165\) 2.92664 8.49472i 0.227839 0.661313i
\(166\) 6.49361 6.49361i 0.504002 0.504002i
\(167\) −12.7580 + 12.7580i −0.987247 + 0.987247i −0.999920 0.0126725i \(-0.995966\pi\)
0.0126725 + 0.999920i \(0.495966\pi\)
\(168\) 1.08618 3.15269i 0.0838007 0.243235i
\(169\) 18.4706i 1.42081i
\(170\) −3.83800 + 3.83800i −0.294361 + 0.294361i
\(171\) 0.416826 0.0510303i 0.0318755 0.00390239i
\(172\) −7.21797 + 7.21797i −0.550365 + 0.550365i
\(173\) −4.28631 −0.325882 −0.162941 0.986636i \(-0.552098\pi\)
−0.162941 + 0.986636i \(0.552098\pi\)
\(174\) 1.90810 + 3.91395i 0.144653 + 0.296716i
\(175\) 1.92521i 0.145532i
\(176\) 5.18734 0.391010
\(177\) −6.25398 + 18.1525i −0.470078 + 1.36442i
\(178\) 7.84887i 0.588297i
\(179\) 6.48181 + 6.48181i 0.484473 + 0.484473i 0.906557 0.422084i \(-0.138701\pi\)
−0.422084 + 0.906557i \(0.638701\pi\)
\(180\) 2.97777 0.364556i 0.221950 0.0271724i
\(181\) −13.5004 −1.00347 −0.501737 0.865020i \(-0.667305\pi\)
−0.501737 + 0.865020i \(0.667305\pi\)
\(182\) 10.8001i 0.800559i
\(183\) −7.26800 + 21.0957i −0.537266 + 1.55944i
\(184\) 1.52130i 0.112152i
\(185\) −5.27941 + 3.02123i −0.388150 + 0.222125i
\(186\) 9.81623 4.78555i 0.719761 0.350894i
\(187\) 19.9090 19.9090i 1.45589 1.45589i
\(188\) 3.47762 0.253632
\(189\) −2.08506 + 9.78395i −0.151666 + 0.711678i
\(190\) 0.0989804 + 0.0989804i 0.00718079 + 0.00718079i
\(191\) −9.94316 + 9.94316i −0.719462 + 0.719462i −0.968495 0.249033i \(-0.919887\pi\)
0.249033 + 0.968495i \(0.419887\pi\)
\(192\) 0.759006 + 1.55689i 0.0547765 + 0.112359i
\(193\) −14.9338 14.9338i −1.07496 1.07496i −0.996953 0.0780070i \(-0.975144\pi\)
−0.0780070 0.996953i \(-0.524856\pi\)
\(194\) 5.43691i 0.390347i
\(195\) 8.73394 4.25792i 0.625451 0.304916i
\(196\) 3.29358i 0.235256i
\(197\) 10.0071i 0.712980i 0.934299 + 0.356490i \(0.116027\pi\)
−0.934299 + 0.356490i \(0.883973\pi\)
\(198\) −15.4467 + 1.89108i −1.09775 + 0.134393i
\(199\) −12.2484 + 12.2484i −0.868264 + 0.868264i −0.992280 0.124016i \(-0.960423\pi\)
0.124016 + 0.992280i \(0.460423\pi\)
\(200\) 0.707107 + 0.707107i 0.0500000 + 0.0500000i
\(201\) 7.05741 + 14.4763i 0.497791 + 1.02108i
\(202\) 2.37490 + 2.37490i 0.167097 + 0.167097i
\(203\) −3.42231 3.42231i −0.240199 0.240199i
\(204\) 8.88841 + 3.06228i 0.622313 + 0.214403i
\(205\) −8.77480 + 8.77480i −0.612858 + 0.612858i
\(206\) −15.2435 −1.06207
\(207\) 0.554600 + 4.53009i 0.0385474 + 0.314863i
\(208\) 3.96677 + 3.96677i 0.275046 + 0.275046i
\(209\) −0.513445 0.513445i −0.0355157 0.0355157i
\(210\) −2.99733 + 1.46124i −0.206836 + 0.100835i
\(211\) −22.1119 −1.52225 −0.761124 0.648606i \(-0.775352\pi\)
−0.761124 + 0.648606i \(0.775352\pi\)
\(212\) −3.95819 −0.271849
\(213\) 0.940826 + 1.92984i 0.0644643 + 0.132231i
\(214\) −8.03854 + 8.03854i −0.549503 + 0.549503i
\(215\) 10.2078 0.696163
\(216\) −2.82772 4.35936i −0.192402 0.296617i
\(217\) −8.58319 + 8.58319i −0.582665 + 0.582665i
\(218\) 16.0158i 1.08473i
\(219\) −5.25511 10.7794i −0.355108 0.728405i
\(220\) −3.66800 3.66800i −0.247297 0.247297i
\(221\) 30.4489 2.04822
\(222\) 8.71083 + 5.92634i 0.584633 + 0.397750i
\(223\) 15.3186 1.02581 0.512904 0.858446i \(-0.328570\pi\)
0.512904 + 0.858446i \(0.328570\pi\)
\(224\) −1.36133 1.36133i −0.0909574 0.0909574i
\(225\) −2.36338 1.84782i −0.157559 0.123188i
\(226\) 19.9709i 1.32844i
\(227\) 13.6849 13.6849i 0.908298 0.908298i −0.0878367 0.996135i \(-0.527995\pi\)
0.996135 + 0.0878367i \(0.0279954\pi\)
\(228\) 0.0789750 0.229228i 0.00523024 0.0151810i
\(229\) −11.4150 −0.754322 −0.377161 0.926148i \(-0.623100\pi\)
−0.377161 + 0.926148i \(0.623100\pi\)
\(230\) −1.07572 + 1.07572i −0.0709311 + 0.0709311i
\(231\) 15.5482 7.57996i 1.02300 0.498725i
\(232\) 2.51395 0.165049
\(233\) 15.1403 0.991875 0.495937 0.868358i \(-0.334825\pi\)
0.495937 + 0.868358i \(0.334825\pi\)
\(234\) −13.2582 10.3660i −0.866718 0.677648i
\(235\) −2.45905 2.45905i −0.160411 0.160411i
\(236\) 7.83820 + 7.83820i 0.510223 + 0.510223i
\(237\) 1.76251 + 0.607229i 0.114487 + 0.0394437i
\(238\) −10.4495 −0.677343
\(239\) 5.80735 5.80735i 0.375647 0.375647i −0.493882 0.869529i \(-0.664423\pi\)
0.869529 + 0.493882i \(0.164423\pi\)
\(240\) 0.564190 1.63759i 0.0364183 0.105706i
\(241\) −18.6269 18.6269i −1.19987 1.19987i −0.974206 0.225659i \(-0.927547\pi\)
−0.225659 0.974206i \(-0.572453\pi\)
\(242\) 11.2490 + 11.2490i 0.723113 + 0.723113i
\(243\) 10.0095 + 11.9503i 0.642111 + 0.766612i
\(244\) 9.10908 + 9.10908i 0.583149 + 0.583149i
\(245\) −2.32892 + 2.32892i −0.148789 + 0.148789i
\(246\) 20.3215 + 7.00128i 1.29565 + 0.446385i
\(247\) 0.785265i 0.0499652i
\(248\) 6.30502i 0.400369i
\(249\) 6.97022 + 14.2975i 0.441720 + 0.906067i
\(250\) 1.00000i 0.0632456i
\(251\) −8.68049 8.68049i −0.547908 0.547908i 0.377927 0.925835i \(-0.376637\pi\)
−0.925835 + 0.377927i \(0.876637\pi\)
\(252\) 4.54999 + 3.55743i 0.286622 + 0.224097i
\(253\) 5.58015 5.58015i 0.350821 0.350821i
\(254\) 4.31420 + 4.31420i 0.270697 + 0.270697i
\(255\) −4.11969 8.45041i −0.257985 0.529185i
\(256\) 1.00000 0.0625000
\(257\) −6.47192 + 6.47192i −0.403707 + 0.403707i −0.879537 0.475830i \(-0.842148\pi\)
0.475830 + 0.879537i \(0.342148\pi\)
\(258\) −7.74775 15.8924i −0.482354 0.989415i
\(259\) −11.2999 3.07412i −0.702140 0.191017i
\(260\) 5.60986i 0.347909i
\(261\) −7.48596 + 0.916476i −0.463369 + 0.0567284i
\(262\) 7.27114i 0.449212i
\(263\) 21.9588 1.35404 0.677019 0.735966i \(-0.263272\pi\)
0.677019 + 0.735966i \(0.263272\pi\)
\(264\) −2.92664 + 8.49472i −0.180122 + 0.522814i
\(265\) 2.79886 + 2.79886i 0.171933 + 0.171933i
\(266\) 0.269489i 0.0165234i
\(267\) 12.8532 + 4.42825i 0.786603 + 0.271005i
\(268\) 9.29823 0.567980
\(269\) 0.470491i 0.0286863i −0.999897 0.0143432i \(-0.995434\pi\)
0.999897 0.0143432i \(-0.00456573\pi\)
\(270\) −1.08303 + 5.08203i −0.0659114 + 0.309283i
\(271\) 1.85985 0.112978 0.0564891 0.998403i \(-0.482009\pi\)
0.0564891 + 0.998403i \(0.482009\pi\)
\(272\) 3.83800 3.83800i 0.232713 0.232713i
\(273\) 17.6862 + 6.09333i 1.07042 + 0.368785i
\(274\) −1.89023 + 1.89023i −0.114193 + 0.114193i
\(275\) 5.18734i 0.312808i
\(276\) 2.49127 + 0.858304i 0.149957 + 0.0516638i
\(277\) −20.9504 + 20.9504i −1.25879 + 1.25879i −0.307118 + 0.951672i \(0.599365\pi\)
−0.951672 + 0.307118i \(0.900635\pi\)
\(278\) −7.68697 + 7.68697i −0.461034 + 0.461034i
\(279\) 2.29853 + 18.7749i 0.137610 + 1.12402i
\(280\) 1.92521i 0.115053i
\(281\) 16.4406 16.4406i 0.980762 0.980762i −0.0190566 0.999818i \(-0.506066\pi\)
0.999818 + 0.0190566i \(0.00606628\pi\)
\(282\) −1.96204 + 5.69490i −0.116838 + 0.339127i
\(283\) 3.56217 3.56217i 0.211749 0.211749i −0.593261 0.805010i \(-0.702160\pi\)
0.805010 + 0.593261i \(0.202160\pi\)
\(284\) 1.23955 0.0735537
\(285\) −0.217933 + 0.106245i −0.0129092 + 0.00629342i
\(286\) 29.1003i 1.72073i
\(287\) −23.8907 −1.41022
\(288\) −2.97777 + 0.364556i −0.175467 + 0.0214817i
\(289\) 12.4605i 0.732968i
\(290\) −1.77763 1.77763i −0.104386 0.104386i
\(291\) −8.90341 3.06745i −0.521927 0.179817i
\(292\) −6.92368 −0.405178
\(293\) 22.5243i 1.31588i 0.753069 + 0.657942i \(0.228573\pi\)
−0.753069 + 0.657942i \(0.771427\pi\)
\(294\) 5.39353 + 1.85821i 0.314557 + 0.108373i
\(295\) 11.0849i 0.645387i
\(296\) 5.27941 3.02123i 0.306860 0.175605i
\(297\) 5.61807 26.3622i 0.325993 1.52969i
\(298\) 6.67685 6.67685i 0.386779 0.386779i
\(299\) 8.53430 0.493552
\(300\) −1.55689 + 0.759006i −0.0898871 + 0.0438212i
\(301\) 13.8961 + 13.8961i 0.800957 + 0.800957i
\(302\) −8.77029 + 8.77029i −0.504673 + 0.504673i
\(303\) −5.22899 + 2.54921i −0.300398 + 0.146448i
\(304\) −0.0989804 0.0989804i −0.00567691 0.00567691i
\(305\) 12.8822i 0.737632i
\(306\) −10.0295 + 12.8278i −0.573348 + 0.733318i
\(307\) 11.0158i 0.628707i −0.949306 0.314353i \(-0.898212\pi\)
0.949306 0.314353i \(-0.101788\pi\)
\(308\) 9.98669i 0.569045i
\(309\) 8.60024 24.9626i 0.489250 1.42007i
\(310\) −4.45832 + 4.45832i −0.253216 + 0.253216i
\(311\) −18.1688 18.1688i −1.03026 1.03026i −0.999528 0.0307306i \(-0.990217\pi\)
−0.0307306 0.999528i \(-0.509783\pi\)
\(312\) −8.73394 + 4.25792i −0.494462 + 0.241057i
\(313\) 3.51658 + 3.51658i 0.198769 + 0.198769i 0.799472 0.600703i \(-0.205113\pi\)
−0.600703 + 0.799472i \(0.705113\pi\)
\(314\) 5.15378 + 5.15378i 0.290844 + 0.290844i
\(315\) −0.701845 5.73281i −0.0395445 0.323007i
\(316\) 0.761048 0.761048i 0.0428123 0.0428123i
\(317\) −11.6758 −0.655777 −0.327889 0.944716i \(-0.606337\pi\)
−0.327889 + 0.944716i \(0.606337\pi\)
\(318\) 2.23317 6.48187i 0.125230 0.363485i
\(319\) 9.22118 + 9.22118i 0.516287 + 0.516287i
\(320\) −0.707107 0.707107i −0.0395285 0.0395285i
\(321\) −8.62854 17.6991i −0.481598 0.987865i
\(322\) −2.92882 −0.163217
\(323\) −0.759773 −0.0422749
\(324\) 8.73420 2.17113i 0.485233 0.120618i
\(325\) −3.96677 + 3.96677i −0.220037 + 0.220037i
\(326\) 20.1290 1.11484
\(327\) 26.2273 + 9.03596i 1.45037 + 0.499690i
\(328\) 8.77480 8.77480i 0.484507 0.484507i
\(329\) 6.69513i 0.369115i
\(330\) 8.07612 3.93722i 0.444576 0.216737i
\(331\) −0.607386 0.607386i −0.0333850 0.0333850i 0.690217 0.723602i \(-0.257515\pi\)
−0.723602 + 0.690217i \(0.757515\pi\)
\(332\) 9.18336 0.504002
\(333\) −14.6195 + 10.9212i −0.801141 + 0.598476i
\(334\) −18.0426 −0.987247
\(335\) −6.57484 6.57484i −0.359222 0.359222i
\(336\) 2.99733 1.46124i 0.163518 0.0797173i
\(337\) 1.97402i 0.107532i 0.998554 + 0.0537659i \(0.0171225\pi\)
−0.998554 + 0.0537659i \(0.982878\pi\)
\(338\) −13.0607 + 13.0607i −0.710406 + 0.710406i
\(339\) −32.7041 11.2674i −1.77624 0.611960i
\(340\) −5.42775 −0.294361
\(341\) 23.1268 23.1268i 1.25239 1.25239i
\(342\) 0.330824 + 0.258657i 0.0178889 + 0.0139866i
\(343\) −19.8173 −1.07003
\(344\) −10.2078 −0.550365
\(345\) −1.15468 2.36850i −0.0621658 0.127516i
\(346\) −3.03088 3.03088i −0.162941 0.162941i
\(347\) −2.87749 2.87749i −0.154472 0.154472i 0.625640 0.780112i \(-0.284838\pi\)
−0.780112 + 0.625640i \(0.784838\pi\)
\(348\) −1.41835 + 4.11681i −0.0760313 + 0.220684i
\(349\) 5.35928 0.286876 0.143438 0.989659i \(-0.454184\pi\)
0.143438 + 0.989659i \(0.454184\pi\)
\(350\) 1.36133 1.36133i 0.0727659 0.0727659i
\(351\) 24.4554 15.8631i 1.30533 0.846710i
\(352\) 3.66800 + 3.66800i 0.195505 + 0.195505i
\(353\) 8.81237 + 8.81237i 0.469035 + 0.469035i 0.901602 0.432567i \(-0.142392\pi\)
−0.432567 + 0.901602i \(0.642392\pi\)
\(354\) −17.2580 + 8.41350i −0.917251 + 0.447172i
\(355\) −0.876494 0.876494i −0.0465195 0.0465195i
\(356\) 5.54999 5.54999i 0.294149 0.294149i
\(357\) 5.89552 17.1120i 0.312024 0.905664i
\(358\) 9.16666i 0.484473i
\(359\) 10.4710i 0.552637i −0.961066 0.276319i \(-0.910886\pi\)
0.961066 0.276319i \(-0.0891145\pi\)
\(360\) 2.36338 + 1.84782i 0.124561 + 0.0973886i
\(361\) 18.9804i 0.998969i
\(362\) −9.54619 9.54619i −0.501737 0.501737i
\(363\) −24.7678 + 12.0746i −1.29997 + 0.633754i
\(364\) 7.63685 7.63685i 0.400280 0.400280i
\(365\) 4.89578 + 4.89578i 0.256257 + 0.256257i
\(366\) −20.0562 + 9.77766i −1.04835 + 0.511086i
\(367\) −15.6683 −0.817877 −0.408938 0.912562i \(-0.634101\pi\)
−0.408938 + 0.912562i \(0.634101\pi\)
\(368\) 1.07572 1.07572i 0.0560760 0.0560760i
\(369\) −22.9304 + 29.3282i −1.19371 + 1.52677i
\(370\) −5.86944 1.59678i −0.305138 0.0830124i
\(371\) 7.62032i 0.395627i
\(372\) 10.3250 + 3.55723i 0.535327 + 0.184434i
\(373\) 4.20515i 0.217735i −0.994056 0.108867i \(-0.965278\pi\)
0.994056 0.108867i \(-0.0347224\pi\)
\(374\) 28.1556 1.45589
\(375\) 1.63759 + 0.564190i 0.0845646 + 0.0291346i
\(376\) 2.45905 + 2.45905i 0.126816 + 0.126816i
\(377\) 14.1029i 0.726337i
\(378\) −8.39266 + 5.44394i −0.431672 + 0.280006i
\(379\) 10.8211 0.555842 0.277921 0.960604i \(-0.410355\pi\)
0.277921 + 0.960604i \(0.410355\pi\)
\(380\) 0.139979i 0.00718079i
\(381\) −9.49890 + 4.63084i −0.486643 + 0.237245i
\(382\) −14.0617 −0.719462
\(383\) −3.27972 + 3.27972i −0.167586 + 0.167586i −0.785917 0.618332i \(-0.787809\pi\)
0.618332 + 0.785917i \(0.287809\pi\)
\(384\) −0.564190 + 1.63759i −0.0287912 + 0.0835677i
\(385\) −7.06166 + 7.06166i −0.359895 + 0.359895i
\(386\) 21.1196i 1.07496i
\(387\) 30.3963 3.72130i 1.54513 0.189164i
\(388\) −3.84448 + 3.84448i −0.195174 + 0.195174i
\(389\) 17.5886 17.5886i 0.891778 0.891778i −0.102912 0.994690i \(-0.532816\pi\)
0.994690 + 0.102912i \(0.0328162\pi\)
\(390\) 9.18664 + 3.16503i 0.465183 + 0.160267i
\(391\) 8.25726i 0.417587i
\(392\) 2.32892 2.32892i 0.117628 0.117628i
\(393\) −11.9071 4.10230i −0.600634 0.206934i
\(394\) −7.07612 + 7.07612i −0.356490 + 0.356490i
\(395\) −1.07628 −0.0541537
\(396\) −12.2597 9.58527i −0.616071 0.481678i
\(397\) 29.2824i 1.46964i −0.678262 0.734820i \(-0.737266\pi\)
0.678262 0.734820i \(-0.262734\pi\)
\(398\) −17.3218 −0.868264
\(399\) −0.441312 0.152043i −0.0220932 0.00761167i
\(400\) 1.00000i 0.0500000i
\(401\) −19.3076 19.3076i −0.964177 0.964177i 0.0352035 0.999380i \(-0.488792\pi\)
−0.999380 + 0.0352035i \(0.988792\pi\)
\(402\) −5.24597 + 15.2267i −0.261645 + 0.759436i
\(403\) 35.3703 1.76192
\(404\) 3.35861i 0.167097i
\(405\) −7.71123 4.64079i −0.383174 0.230603i
\(406\) 4.83987i 0.240199i
\(407\) 30.4468 + 8.28302i 1.50919 + 0.410574i
\(408\) 4.11969 + 8.45041i 0.203955 + 0.418358i
\(409\) 6.57668 6.57668i 0.325196 0.325196i −0.525560 0.850756i \(-0.676144\pi\)
0.850756 + 0.525560i \(0.176144\pi\)
\(410\) −12.4094 −0.612858
\(411\) −2.02897 4.16186i −0.100082 0.205290i
\(412\) −10.7788 10.7788i −0.531033 0.531033i
\(413\) 15.0901 15.0901i 0.742538 0.742538i
\(414\) −2.81109 + 3.59542i −0.138158 + 0.176705i
\(415\) −6.49361 6.49361i −0.318759 0.318759i
\(416\) 5.60986i 0.275046i
\(417\) −8.25116 16.9250i −0.404061 0.828820i
\(418\) 0.726121i 0.0355157i
\(419\) 26.3846i 1.28897i 0.764617 + 0.644485i \(0.222928\pi\)
−0.764617 + 0.644485i \(0.777072\pi\)
\(420\) −3.15269 1.08618i −0.153836 0.0530002i
\(421\) −21.6083 + 21.6083i −1.05312 + 1.05312i −0.0546159 + 0.998507i \(0.517393\pi\)
−0.998507 + 0.0546159i \(0.982607\pi\)
\(422\) −15.6355 15.6355i −0.761124 0.761124i
\(423\) −8.21894 6.42601i −0.399618 0.312444i
\(424\) −2.79886 2.79886i −0.135925 0.135925i
\(425\) 3.83800 + 3.83800i 0.186170 + 0.186170i
\(426\) −0.699341 + 2.02987i −0.0338832 + 0.0983475i
\(427\) 17.5369 17.5369i 0.848668 0.848668i
\(428\) −11.3682 −0.549503
\(429\) −47.6542 16.4181i −2.30077 0.792672i
\(430\) 7.21797 + 7.21797i 0.348082 + 0.348082i
\(431\) 16.8691 + 16.8691i 0.812557 + 0.812557i 0.985017 0.172460i \(-0.0551715\pi\)
−0.172460 + 0.985017i \(0.555172\pi\)
\(432\) 1.08303 5.08203i 0.0521075 0.244509i
\(433\) −20.9643 −1.00748 −0.503740 0.863855i \(-0.668043\pi\)
−0.503740 + 0.863855i \(0.668043\pi\)
\(434\) −12.1385 −0.582665
\(435\) 3.91395 1.90810i 0.187659 0.0914866i
\(436\) 11.3249 11.3249i 0.542364 0.542364i
\(437\) −0.212951 −0.0101868
\(438\) 3.90627 11.3381i 0.186649 0.541756i
\(439\) −1.59624 + 1.59624i −0.0761842 + 0.0761842i −0.744172 0.667988i \(-0.767156\pi\)
0.667988 + 0.744172i \(0.267156\pi\)
\(440\) 5.18734i 0.247297i
\(441\) −6.08595 + 7.78399i −0.289807 + 0.370666i
\(442\) 21.5306 + 21.5306i 1.02411 + 1.02411i
\(443\) 26.6898 1.26807 0.634035 0.773304i \(-0.281397\pi\)
0.634035 + 0.773304i \(0.281397\pi\)
\(444\) 1.96893 + 10.3500i 0.0934414 + 0.491191i
\(445\) −7.84887 −0.372072
\(446\) 10.8319 + 10.8319i 0.512904 + 0.512904i
\(447\) 7.16691 + 14.7009i 0.338983 + 0.695330i
\(448\) 1.92521i 0.0909574i
\(449\) 9.86107 9.86107i 0.465372 0.465372i −0.435039 0.900412i \(-0.643265\pi\)
0.900412 + 0.435039i \(0.143265\pi\)
\(450\) −0.364556 2.97777i −0.0171853 0.140373i
\(451\) 64.3720 3.03116
\(452\) −14.1216 + 14.1216i −0.664222 + 0.664222i
\(453\) −9.41400 19.3102i −0.442308 0.907273i
\(454\) 19.3534 0.908298
\(455\) −10.8001 −0.506318
\(456\) 0.217933 0.106245i 0.0102056 0.00497539i
\(457\) 6.55173 + 6.55173i 0.306477 + 0.306477i 0.843541 0.537064i \(-0.180467\pi\)
−0.537064 + 0.843541i \(0.680467\pi\)
\(458\) −8.07160 8.07160i −0.377161 0.377161i
\(459\) −15.3481 23.6615i −0.716390 1.10442i
\(460\) −1.52130 −0.0709311
\(461\) −14.2328 + 14.2328i −0.662887 + 0.662887i −0.956060 0.293172i \(-0.905289\pi\)
0.293172 + 0.956060i \(0.405289\pi\)
\(462\) 16.3541 + 5.63439i 0.760860 + 0.262136i
\(463\) −3.29627 3.29627i −0.153191 0.153191i 0.626351 0.779541i \(-0.284548\pi\)
−0.779541 + 0.626351i \(0.784548\pi\)
\(464\) 1.77763 + 1.77763i 0.0825245 + 0.0825245i
\(465\) −4.78555 9.81623i −0.221925 0.455217i
\(466\) 10.7058 + 10.7058i 0.495937 + 0.495937i
\(467\) −8.25546 + 8.25546i −0.382017 + 0.382017i −0.871828 0.489811i \(-0.837066\pi\)
0.489811 + 0.871828i \(0.337066\pi\)
\(468\) −2.04511 16.7049i −0.0945352 0.772183i
\(469\) 17.9010i 0.826591i
\(470\) 3.47762i 0.160411i
\(471\) −11.3475 + 5.53205i −0.522863 + 0.254903i
\(472\) 11.0849i 0.510223i
\(473\) −37.4421 37.4421i −1.72159 1.72159i
\(474\) 0.816906 + 1.67566i 0.0375218 + 0.0769655i
\(475\) 0.0989804 0.0989804i 0.00454153 0.00454153i
\(476\) −7.38893 7.38893i −0.338671 0.338671i
\(477\) 9.35470 + 7.31401i 0.428322 + 0.334886i
\(478\) 8.21284 0.375647
\(479\) −15.7716 + 15.7716i −0.720622 + 0.720622i −0.968732 0.248110i \(-0.920190\pi\)
0.248110 + 0.968732i \(0.420190\pi\)
\(480\) 1.55689 0.759006i 0.0710620 0.0346437i
\(481\) 16.9487 + 29.6168i 0.772793 + 1.35041i
\(482\) 26.3424i 1.19987i
\(483\) 1.65241 4.79620i 0.0751873 0.218235i
\(484\) 15.9085i 0.723113i
\(485\) 5.43691 0.246877
\(486\) −1.37234 + 15.5279i −0.0622506 + 0.704361i
\(487\) 12.9849 + 12.9849i 0.588400 + 0.588400i 0.937198 0.348798i \(-0.113410\pi\)
−0.348798 + 0.937198i \(0.613410\pi\)
\(488\) 12.8822i 0.583149i
\(489\) −11.3566 + 32.9630i −0.513562 + 1.49064i
\(490\) −3.29358 −0.148789
\(491\) 30.8895i 1.39402i 0.717059 + 0.697012i \(0.245488\pi\)
−0.717059 + 0.697012i \(0.754512\pi\)
\(492\) 9.41884 + 19.3201i 0.424634 + 0.871019i
\(493\) 13.6451 0.614544
\(494\) 0.555266 0.555266i 0.0249826 0.0249826i
\(495\) 1.89108 + 15.4467i 0.0849975 + 0.694277i
\(496\) 4.45832 4.45832i 0.200185 0.200185i
\(497\) 2.38639i 0.107044i
\(498\) −5.18116 + 15.0385i −0.232173 + 0.673893i
\(499\) 20.2463 20.2463i 0.906350 0.906350i −0.0896254 0.995976i \(-0.528567\pi\)
0.995976 + 0.0896254i \(0.0285670\pi\)
\(500\) 0.707107 0.707107i 0.0316228 0.0316228i
\(501\) 10.1795 29.5463i 0.454784 1.32003i
\(502\) 12.2761i 0.547908i
\(503\) −19.1000 + 19.1000i −0.851627 + 0.851627i −0.990333 0.138707i \(-0.955705\pi\)
0.138707 + 0.990333i \(0.455705\pi\)
\(504\) 0.701845 + 5.73281i 0.0312627 + 0.255360i
\(505\) 2.37490 2.37490i 0.105681 0.105681i
\(506\) 7.89152 0.350821
\(507\) −14.0193 28.7566i −0.622617 1.27713i
\(508\) 6.10120i 0.270697i
\(509\) −30.8742 −1.36848 −0.684238 0.729259i \(-0.739865\pi\)
−0.684238 + 0.729259i \(0.739865\pi\)
\(510\) 3.06228 8.88841i 0.135600 0.393585i
\(511\) 13.3295i 0.589662i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −0.610220 + 0.395822i −0.0269419 + 0.0174760i
\(514\) −9.15268 −0.403707
\(515\) 15.2435i 0.671709i
\(516\) 5.75911 16.7161i 0.253531 0.735884i
\(517\) 18.0396i 0.793381i
\(518\) −5.81649 10.1639i −0.255562 0.446578i
\(519\) 6.67332 3.25333i 0.292926 0.142806i
\(520\) 3.96677 3.96677i 0.173954 0.173954i
\(521\) 19.1245 0.837858 0.418929 0.908019i \(-0.362406\pi\)
0.418929 + 0.908019i \(0.362406\pi\)
\(522\) −5.94142 4.64533i −0.260049 0.203321i
\(523\) −5.56709 5.56709i −0.243432 0.243432i 0.574836 0.818268i \(-0.305066\pi\)
−0.818268 + 0.574836i \(0.805066\pi\)
\(524\) −5.14147 + 5.14147i −0.224606 + 0.224606i
\(525\) 1.46124 + 2.99733i 0.0637738 + 0.130814i
\(526\) 15.5272 + 15.5272i 0.677019 + 0.677019i
\(527\) 34.2221i 1.49074i
\(528\) −8.07612 + 3.93722i −0.351468 + 0.171346i
\(529\) 20.6856i 0.899375i
\(530\) 3.95819i 0.171933i
\(531\) −4.04106 33.0082i −0.175367 1.43244i
\(532\) −0.190558 + 0.190558i −0.00826172 + 0.00826172i
\(533\) 49.2254 + 49.2254i 2.13219 + 2.13219i
\(534\) 5.95734 + 12.2198i 0.257799 + 0.528804i
\(535\) 8.03854 + 8.03854i 0.347536 + 0.347536i
\(536\) 6.57484 + 6.57484i 0.283990 + 0.283990i
\(537\) −15.0112 5.17174i −0.647781 0.223177i
\(538\) 0.332687 0.332687i 0.0143432 0.0143432i
\(539\) 17.0849 0.735901
\(540\) −4.35936 + 2.82772i −0.187597 + 0.121686i
\(541\) −4.99094 4.99094i −0.214577 0.214577i 0.591631 0.806209i \(-0.298484\pi\)
−0.806209 + 0.591631i \(0.798484\pi\)
\(542\) 1.31512 + 1.31512i 0.0564891 + 0.0564891i
\(543\) 21.0186 10.2469i 0.901994 0.439735i
\(544\) 5.42775 0.232713
\(545\) −16.0158 −0.686042
\(546\) 8.19737 + 16.8146i 0.350815 + 0.719600i
\(547\) −24.8167 + 24.8167i −1.06108 + 1.06108i −0.0630758 + 0.998009i \(0.520091\pi\)
−0.998009 + 0.0630758i \(0.979909\pi\)
\(548\) −2.67319 −0.114193
\(549\) −4.69628 38.3602i −0.200432 1.63717i
\(550\) −3.66800 + 3.66800i −0.156404 + 0.156404i
\(551\) 0.351901i 0.0149915i
\(552\) 1.15468 + 2.36850i 0.0491464 + 0.100810i
\(553\) −1.46517 1.46517i −0.0623055 0.0623055i
\(554\) −29.6284 −1.25879
\(555\) 5.92634 8.71083i 0.251559 0.369754i
\(556\) −10.8710 −0.461034
\(557\) 4.85816 + 4.85816i 0.205847 + 0.205847i 0.802500 0.596653i \(-0.203503\pi\)
−0.596653 + 0.802500i \(0.703503\pi\)
\(558\) −11.6505 + 14.9012i −0.493207 + 0.630816i
\(559\) 57.2641i 2.42201i
\(560\) −1.36133 + 1.36133i −0.0575265 + 0.0575265i
\(561\) −15.8851 + 46.1072i −0.670669 + 1.94665i
\(562\) 23.2505 0.980762
\(563\) −18.9481 + 18.9481i −0.798568 + 0.798568i −0.982870 0.184302i \(-0.940998\pi\)
0.184302 + 0.982870i \(0.440998\pi\)
\(564\) −5.41428 + 2.63954i −0.227982 + 0.111144i
\(565\) 19.9709 0.840182
\(566\) 5.03767 0.211749
\(567\) −4.17986 16.8151i −0.175538 0.706169i
\(568\) 0.876494 + 0.876494i 0.0367769 + 0.0367769i
\(569\) 8.68225 + 8.68225i 0.363979 + 0.363979i 0.865276 0.501297i \(-0.167143\pi\)
−0.501297 + 0.865276i \(0.667143\pi\)
\(570\) −0.229228 0.0789750i −0.00960132 0.00330790i
\(571\) −1.59002 −0.0665404 −0.0332702 0.999446i \(-0.510592\pi\)
−0.0332702 + 0.999446i \(0.510592\pi\)
\(572\) −20.5770 + 20.5770i −0.860367 + 0.860367i
\(573\) 7.93350 23.0273i 0.331427 0.961980i
\(574\) −16.8933 16.8933i −0.705112 0.705112i
\(575\) 1.07572 + 1.07572i 0.0448608 + 0.0448608i
\(576\) −2.36338 1.84782i −0.0984741 0.0769925i
\(577\) −1.81221 1.81221i −0.0754435 0.0754435i 0.668378 0.743822i \(-0.266989\pi\)
−0.743822 + 0.668378i \(0.766989\pi\)
\(578\) 8.81088 8.81088i 0.366484 0.366484i
\(579\) 34.5852 + 11.9155i 1.43731 + 0.495190i
\(580\) 2.51395i 0.104386i
\(581\) 17.6798i 0.733484i
\(582\) −4.12665 8.46468i −0.171055 0.350872i
\(583\) 20.5325i 0.850367i
\(584\) −4.89578 4.89578i −0.202589 0.202589i
\(585\) −10.3660 + 13.2582i −0.428582 + 0.548161i
\(586\) −15.9271 + 15.9271i −0.657942 + 0.657942i
\(587\) −26.2589 26.2589i −1.08382 1.08382i −0.996150 0.0876694i \(-0.972058\pi\)
−0.0876694 0.996150i \(-0.527942\pi\)
\(588\) 2.49985 + 5.12775i 0.103092 + 0.211465i
\(589\) −0.882573 −0.0363658
\(590\) 7.83820 7.83820i 0.322694 0.322694i
\(591\) −7.59549 15.5800i −0.312437 0.640877i
\(592\) 5.86944 + 1.59678i 0.241232 + 0.0656271i
\(593\) 44.3173i 1.81989i −0.414727 0.909946i \(-0.636123\pi\)
0.414727 0.909946i \(-0.363877\pi\)
\(594\) 22.6135 14.6683i 0.927842 0.601849i
\(595\) 10.4495i 0.428389i
\(596\) 9.44249 0.386779
\(597\) 9.77279 28.3660i 0.399974 1.16094i
\(598\) 6.03466 + 6.03466i 0.246776 + 0.246776i
\(599\) 9.25641i 0.378207i 0.981957 + 0.189103i \(0.0605581\pi\)
−0.981957 + 0.189103i \(0.939442\pi\)
\(600\) −1.63759 0.564190i −0.0668542 0.0230330i
\(601\) −1.16650 −0.0475826 −0.0237913 0.999717i \(-0.507574\pi\)
−0.0237913 + 0.999717i \(0.507574\pi\)
\(602\) 19.6520i 0.800957i
\(603\) −21.9752 17.1814i −0.894901 0.699682i
\(604\) −12.4031 −0.504673
\(605\) 11.2490 11.2490i 0.457337 0.457337i
\(606\) −5.50001 1.89489i −0.223423 0.0769748i
\(607\) 15.4706 15.4706i 0.627934 0.627934i −0.319614 0.947548i \(-0.603553\pi\)
0.947548 + 0.319614i \(0.103553\pi\)
\(608\) 0.139979i 0.00567691i
\(609\) 7.92571 + 2.73061i 0.321166 + 0.110650i
\(610\) 9.10908 9.10908i 0.368816 0.368816i
\(611\) −13.7949 + 13.7949i −0.558083 + 0.558083i
\(612\) −16.1626 + 1.97872i −0.653333 + 0.0799850i
\(613\) 2.39296i 0.0966506i −0.998832 0.0483253i \(-0.984612\pi\)
0.998832 0.0483253i \(-0.0153884\pi\)
\(614\) 7.78937 7.78937i 0.314353 0.314353i
\(615\) 7.00128 20.3215i 0.282319 0.819443i
\(616\) 7.06166 7.06166i 0.284522 0.284522i
\(617\) 8.86781 0.357005 0.178502 0.983939i \(-0.442875\pi\)
0.178502 + 0.983939i \(0.442875\pi\)
\(618\) 23.7325 11.5699i 0.954661 0.465410i
\(619\) 17.1208i 0.688141i −0.938944 0.344071i \(-0.888194\pi\)
0.938944 0.344071i \(-0.111806\pi\)
\(620\) −6.30502 −0.253216
\(621\) −4.30182 6.63191i −0.172626 0.266129i
\(622\) 25.6946i 1.03026i
\(623\) −10.6849 10.6849i −0.428080 0.428080i
\(624\) −9.18664 3.16503i −0.367760 0.126703i
\(625\) −1.00000 −0.0400000
\(626\) 4.97320i 0.198769i
\(627\) 1.18909 + 0.409670i 0.0474875 + 0.0163606i
\(628\) 7.28854i 0.290844i
\(629\) 28.6553 16.3985i 1.14256 0.653850i
\(630\) 3.55743 4.54999i 0.141731 0.181276i
\(631\) −22.6451 + 22.6451i −0.901487 + 0.901487i −0.995565 0.0940780i \(-0.970010\pi\)
0.0940780 + 0.995565i \(0.470010\pi\)
\(632\) 1.07628 0.0428123
\(633\) 34.4259 16.7831i 1.36831 0.667068i
\(634\) −8.25603 8.25603i −0.327889 0.327889i
\(635\) 4.31420 4.31420i 0.171204 0.171204i
\(636\) 6.16247 3.00429i 0.244358 0.119128i
\(637\) 13.0649 + 13.0649i 0.517650 + 0.517650i
\(638\) 13.0407i 0.516287i
\(639\) −2.92953 2.29046i −0.115890 0.0906094i
\(640\) 1.00000i 0.0395285i
\(641\) 12.4293i 0.490929i −0.969406 0.245465i \(-0.921059\pi\)
0.969406 0.245465i \(-0.0789405\pi\)
\(642\) 6.41383 18.6164i 0.253134 0.734732i
\(643\) −10.0677 + 10.0677i −0.397030 + 0.397030i −0.877184 0.480154i \(-0.840581\pi\)
0.480154 + 0.877184i \(0.340581\pi\)
\(644\) −2.07099 2.07099i −0.0816084 0.0816084i
\(645\) −15.8924 + 7.74775i −0.625761 + 0.305067i
\(646\) −0.537241 0.537241i −0.0211375 0.0211375i
\(647\) −23.6939 23.6939i −0.931504 0.931504i 0.0662961 0.997800i \(-0.478882\pi\)
−0.997800 + 0.0662961i \(0.978882\pi\)
\(648\) 7.71123 + 4.64079i 0.302926 + 0.182308i
\(649\) −40.6594 + 40.6594i −1.59602 + 1.59602i
\(650\) −5.60986 −0.220037
\(651\) 6.84840 19.8778i 0.268410 0.779072i
\(652\) 14.2334 + 14.2334i 0.557421 + 0.557421i
\(653\) 16.2030 + 16.2030i 0.634071 + 0.634071i 0.949087 0.315016i \(-0.102010\pi\)
−0.315016 + 0.949087i \(0.602010\pi\)
\(654\) 12.1561 + 24.9349i 0.475341 + 0.975031i
\(655\) 7.27114 0.284107
\(656\) 12.4094 0.484507
\(657\) 16.3633 + 12.7937i 0.638392 + 0.499130i
\(658\) 4.73417 4.73417i 0.184557 0.184557i
\(659\) 22.4489 0.874484 0.437242 0.899344i \(-0.355955\pi\)
0.437242 + 0.899344i \(0.355955\pi\)
\(660\) 8.49472 + 2.92664i 0.330656 + 0.113919i
\(661\) 20.3735 20.3735i 0.792436 0.792436i −0.189453 0.981890i \(-0.560672\pi\)
0.981890 + 0.189453i \(0.0606716\pi\)
\(662\) 0.858974i 0.0333850i
\(663\) −47.4057 + 23.1109i −1.84108 + 0.897554i
\(664\) 6.49361 + 6.49361i 0.252001 + 0.252001i
\(665\) 0.269489 0.0104503
\(666\) −18.0599 2.61509i −0.699808 0.101333i
\(667\) 3.82448 0.148085
\(668\) −12.7580 12.7580i −0.493624 0.493624i
\(669\) −23.8494 + 11.6269i −0.922070 + 0.449522i
\(670\) 9.29823i 0.359222i
\(671\) −47.2519 + 47.2519i −1.82414 + 1.82414i
\(672\) 3.15269 + 1.08618i 0.121618 + 0.0419004i
\(673\) 27.9883 1.07887 0.539435 0.842027i \(-0.318638\pi\)
0.539435 + 0.842027i \(0.318638\pi\)
\(674\) −1.39584 + 1.39584i −0.0537659 + 0.0537659i
\(675\) 5.08203 + 1.08303i 0.195607 + 0.0416860i
\(676\) −18.4706 −0.710406
\(677\) −36.3628 −1.39754 −0.698769 0.715348i \(-0.746268\pi\)
−0.698769 + 0.715348i \(0.746268\pi\)
\(678\) −15.1580 31.0925i −0.582141 1.19410i
\(679\) 7.40140 + 7.40140i 0.284040 + 0.284040i
\(680\) −3.83800 3.83800i −0.147181 0.147181i
\(681\) −10.9190 + 31.6928i −0.418416 + 1.21447i
\(682\) 32.7063 1.25239
\(683\) −31.9090 + 31.9090i −1.22097 + 1.22097i −0.253677 + 0.967289i \(0.581640\pi\)
−0.967289 + 0.253677i \(0.918360\pi\)
\(684\) 0.0510303 + 0.416826i 0.00195119 + 0.0159377i
\(685\) 1.89023 + 1.89023i 0.0722220 + 0.0722220i
\(686\) −14.0129 14.0129i −0.535016 0.535016i
\(687\) 17.7719 8.66403i 0.678039 0.330553i
\(688\) −7.21797 7.21797i −0.275183 0.275183i
\(689\) 15.7012 15.7012i 0.598169 0.598169i
\(690\) 0.858304 2.49127i 0.0326751 0.0948409i
\(691\) 35.8528i 1.36391i −0.731396 0.681953i \(-0.761131\pi\)
0.731396 0.681953i \(-0.238869\pi\)
\(692\) 4.28631i 0.162941i
\(693\) −18.4536 + 23.6023i −0.700994 + 0.896579i
\(694\) 4.06939i 0.154472i
\(695\) 7.68697 + 7.68697i 0.291583 + 0.291583i
\(696\) −3.91395 + 1.90810i −0.148358 + 0.0723265i
\(697\) 47.6274 47.6274i 1.80402 1.80402i
\(698\) 3.78958 + 3.78958i 0.143438 + 0.143438i
\(699\) −23.5718 + 11.4916i −0.891568 + 0.434652i
\(700\) 1.92521 0.0727659
\(701\) 8.81865 8.81865i 0.333076 0.333076i −0.520678 0.853753i \(-0.674321\pi\)
0.853753 + 0.520678i \(0.174321\pi\)
\(702\) 28.5095 + 6.07567i 1.07602 + 0.229312i
\(703\) −0.422910 0.739009i −0.0159503 0.0278722i
\(704\) 5.18734i 0.195505i
\(705\) 5.69490 + 1.96204i 0.214483 + 0.0738946i
\(706\) 12.4626i 0.469035i
\(707\) 6.46601 0.243179
\(708\) −18.1525 6.25398i −0.682212 0.235039i
\(709\) 26.8621 + 26.8621i 1.00883 + 1.00883i 0.999961 + 0.00886777i \(0.00282274\pi\)
0.00886777 + 0.999961i \(0.497177\pi\)
\(710\) 1.23955i 0.0465195i
\(711\) −3.20492 + 0.392366i −0.120194 + 0.0147149i
\(712\) 7.84887 0.294149
\(713\) 9.59185i 0.359218i
\(714\) 16.2688 7.93126i 0.608844 0.296820i
\(715\) 29.1003 1.08829
\(716\) −6.48181 + 6.48181i −0.242237 + 0.242237i
\(717\) −4.63360 + 13.4492i −0.173045 + 0.502271i
\(718\) 7.40410 7.40410i 0.276319 0.276319i
\(719\) 32.4752i 1.21112i −0.795799 0.605561i \(-0.792949\pi\)
0.795799 0.605561i \(-0.207051\pi\)
\(720\) 0.364556 + 2.97777i 0.0135862 + 0.110975i
\(721\) −20.7514 + 20.7514i −0.772822 + 0.772822i
\(722\) 13.4212 13.4212i 0.499484 0.499484i
\(723\) 43.1380 + 14.8621i 1.60432 + 0.552729i
\(724\) 13.5004i 0.501737i
\(725\) −1.77763 + 1.77763i −0.0660196 + 0.0660196i
\(726\) −26.0515 8.97541i −0.966863 0.333109i
\(727\) 15.5520 15.5520i 0.576792 0.576792i −0.357226 0.934018i \(-0.616277\pi\)
0.934018 + 0.357226i \(0.116277\pi\)
\(728\) 10.8001 0.400280
\(729\) −24.6541 11.0080i −0.913114 0.407705i
\(730\) 6.92368i 0.256257i
\(731\) −55.4051 −2.04923
\(732\) −21.0957 7.26800i −0.779719 0.268633i
\(733\) 20.2890i 0.749390i 0.927148 + 0.374695i \(0.122253\pi\)
−0.927148 + 0.374695i \(0.877747\pi\)
\(734\) −11.0791 11.0791i −0.408938 0.408938i
\(735\) 1.85821 5.39353i 0.0685410 0.198943i
\(736\) 1.52130 0.0560760
\(737\) 48.2331i 1.77669i
\(738\) −36.9524 + 4.52393i −1.36024 + 0.166528i
\(739\) 16.8745i 0.620738i −0.950616 0.310369i \(-0.899547\pi\)
0.950616 0.310369i \(-0.100453\pi\)
\(740\) −3.02123 5.27941i −0.111063 0.194075i
\(741\) 0.596021 + 1.22257i 0.0218954 + 0.0449123i
\(742\) −5.38838 + 5.38838i −0.197814 + 0.197814i
\(743\) −19.1398 −0.702172 −0.351086 0.936343i \(-0.614187\pi\)
−0.351086 + 0.936343i \(0.614187\pi\)
\(744\) 4.78555 + 9.81623i 0.175447 + 0.359880i
\(745\) −6.67685 6.67685i −0.244621 0.244621i
\(746\) 2.97349 2.97349i 0.108867 0.108867i
\(747\) −21.7038 16.9692i −0.794099 0.620870i
\(748\) 19.9090 + 19.9090i 0.727945 + 0.727945i
\(749\) 21.8861i 0.799702i
\(750\) 0.759006 + 1.55689i 0.0277150 + 0.0568496i
\(751\) 3.29443i 0.120216i −0.998192 0.0601078i \(-0.980856\pi\)
0.998192 0.0601078i \(-0.0191444\pi\)
\(752\) 3.47762i 0.126816i
\(753\) 20.1031 + 6.92603i 0.732599 + 0.252399i
\(754\) −9.97227 + 9.97227i −0.363169 + 0.363169i
\(755\) 8.77029 + 8.77029i 0.319183 + 0.319183i
\(756\) −9.78395 2.08506i −0.355839 0.0758330i
\(757\) −26.1797 26.1797i −0.951518 0.951518i 0.0473602 0.998878i \(-0.484919\pi\)
−0.998878 + 0.0473602i \(0.984919\pi\)
\(758\) 7.65167 + 7.65167i 0.277921 + 0.277921i
\(759\) −4.45231 + 12.9230i −0.161609 + 0.469077i
\(760\) −0.0989804 + 0.0989804i −0.00359040 + 0.00359040i
\(761\) −13.0239 −0.472118 −0.236059 0.971739i \(-0.575856\pi\)
−0.236059 + 0.971739i \(0.575856\pi\)
\(762\) −9.99124 3.44223i −0.361944 0.124699i
\(763\) −21.8027 21.8027i −0.789312 0.789312i
\(764\) −9.94316 9.94316i −0.359731 0.359731i
\(765\) 12.8278 + 10.0295i 0.463791 + 0.362617i
\(766\) −4.63822 −0.167586
\(767\) −62.1847 −2.24536
\(768\) −1.55689 + 0.759006i −0.0561795 + 0.0273883i
\(769\) −22.4249 + 22.4249i −0.808662 + 0.808662i −0.984431 0.175769i \(-0.943759\pi\)
0.175769 + 0.984431i \(0.443759\pi\)
\(770\) −9.98669 −0.359895
\(771\) 5.16385 14.9883i 0.185971 0.539791i
\(772\) 14.9338 14.9338i 0.537480 0.537480i
\(773\) 20.2597i 0.728691i −0.931264 0.364345i \(-0.881293\pi\)
0.931264 0.364345i \(-0.118707\pi\)
\(774\) 24.1248 + 18.8621i 0.867148 + 0.677984i
\(775\) 4.45832 + 4.45832i 0.160148 + 0.160148i
\(776\) −5.43691 −0.195174
\(777\) 19.9259 3.79060i 0.714839 0.135987i
\(778\) 24.8741 0.891778
\(779\) −1.22829 1.22829i −0.0440081 0.0440081i
\(780\) 4.25792 + 8.73394i 0.152458 + 0.312725i
\(781\) 6.42997i 0.230082i
\(782\) 5.83876 5.83876i 0.208794 0.208794i
\(783\) 10.9592 7.10875i 0.391651 0.254046i
\(784\) 3.29358 0.117628
\(785\) 5.15378 5.15378i 0.183946 0.183946i
\(786\) −5.51884 11.3204i −0.196850 0.403784i
\(787\) −51.8393 −1.84787 −0.923936 0.382546i \(-0.875047\pi\)
−0.923936 + 0.382546i \(0.875047\pi\)
\(788\) −10.0071 −0.356490
\(789\) −34.1874 + 16.6669i −1.21711 + 0.593356i
\(790\) −0.761048 0.761048i −0.0270769 0.0270769i
\(791\) 27.1869 + 27.1869i 0.966654 + 0.966654i
\(792\) −1.89108 15.4467i −0.0671964 0.548874i
\(793\) −72.2673 −2.56629
\(794\) 20.7058 20.7058i 0.734820 0.734820i
\(795\) −6.48187 2.23317i −0.229888 0.0792023i
\(796\) −12.2484 12.2484i −0.434132 0.434132i
\(797\) −15.4144 15.4144i −0.546006 0.546006i 0.379277 0.925283i \(-0.376173\pi\)
−0.925283 + 0.379277i \(0.876173\pi\)
\(798\) −0.204544 0.419565i −0.00724077 0.0148524i
\(799\) 13.3471 + 13.3471i 0.472187 + 0.472187i
\(800\) −0.707107 + 0.707107i −0.0250000 + 0.0250000i
\(801\) −23.3721 + 2.86135i −0.825812 + 0.101101i
\(802\) 27.3051i 0.964177i
\(803\) 35.9155i 1.26743i
\(804\) −14.4763 + 7.05741i −0.510541 + 0.248896i
\(805\) 2.92882i 0.103227i
\(806\) 25.0106 + 25.0106i 0.880960 + 0.880960i
\(807\) 0.357105 + 0.732503i 0.0125707 + 0.0257853i
\(808\) −2.37490 + 2.37490i −0.0835485 + 0.0835485i
\(809\) 21.9588 + 21.9588i 0.772032 + 0.772032i 0.978461 0.206430i \(-0.0661845\pi\)
−0.206430 + 0.978461i \(0.566185\pi\)
\(810\) −2.17113 8.73420i −0.0762856 0.306888i
\(811\) 35.3528 1.24141 0.620703 0.784046i \(-0.286847\pi\)
0.620703 + 0.784046i \(0.286847\pi\)
\(812\) 3.42231 3.42231i 0.120099 0.120099i
\(813\) −2.89559 + 1.41164i −0.101553 + 0.0495084i
\(814\) 15.6721 + 27.3861i 0.549308 + 0.959882i
\(815\) 20.1290i 0.705088i
\(816\) −3.06228 + 8.88841i −0.107201 + 0.311157i
\(817\) 1.42888i 0.0499900i
\(818\) 9.30083 0.325196
\(819\) −32.1603 + 3.93725i −1.12377 + 0.137579i
\(820\) −8.77480 8.77480i −0.306429 0.306429i
\(821\) 11.3942i 0.397660i −0.980034 0.198830i \(-0.936286\pi\)
0.980034 0.198830i \(-0.0637141\pi\)
\(822\) 1.50819 4.37758i 0.0526040 0.152686i
\(823\) −24.7384 −0.862327 −0.431163 0.902274i \(-0.641897\pi\)
−0.431163 + 0.902274i \(0.641897\pi\)
\(824\) 15.2435i 0.531033i
\(825\) −3.93722 8.07612i −0.137076 0.281174i
\(826\) 21.3407 0.742538
\(827\) −0.846501 + 0.846501i −0.0294357 + 0.0294357i −0.721671 0.692236i \(-0.756626\pi\)
0.692236 + 0.721671i \(0.256626\pi\)
\(828\) −4.53009 + 0.554600i −0.157431 + 0.0192737i
\(829\) −12.4499 + 12.4499i −0.432404 + 0.432404i −0.889445 0.457041i \(-0.848909\pi\)
0.457041 + 0.889445i \(0.348909\pi\)
\(830\) 9.18336i 0.318759i
\(831\) 16.7160 48.5190i 0.579873 1.68311i
\(832\) −3.96677 + 3.96677i −0.137523 + 0.137523i
\(833\) 12.6408 12.6408i 0.437977 0.437977i
\(834\) 6.13332 17.8022i 0.212379 0.616441i
\(835\) 18.0426i 0.624390i
\(836\) 0.513445 0.513445i 0.0177579 0.0177579i
\(837\) −17.8288 27.4859i −0.616254 0.950050i
\(838\) −18.6567 + 18.6567i −0.644485 + 0.644485i
\(839\) −24.1404 −0.833419 −0.416709 0.909040i \(-0.636817\pi\)
−0.416709 + 0.909040i \(0.636817\pi\)
\(840\) −1.46124 2.99733i −0.0504177 0.103418i
\(841\) 22.6800i 0.782071i
\(842\) −30.5587 −1.05312
\(843\) −13.1177 + 38.0747i −0.451797 + 1.31136i
\(844\) 22.1119i 0.761124i
\(845\) 13.0607 + 13.0607i 0.449300 + 0.449300i
\(846\) −1.26779 10.3555i −0.0435874 0.356031i
\(847\) 30.6271 1.05236
\(848\) 3.95819i 0.135925i
\(849\) −2.84220 + 8.24962i −0.0975442 + 0.283126i
\(850\) 5.42775i 0.186170i
\(851\) 8.03159 4.59621i 0.275319 0.157556i
\(852\) −1.92984 + 0.940826i −0.0661154 + 0.0322322i
\(853\) 12.1090 12.1090i 0.414603 0.414603i −0.468735 0.883339i \(-0.655290\pi\)
0.883339 + 0.468735i \(0.155290\pi\)
\(854\) 24.8009 0.848668
\(855\) 0.258657 0.330824i 0.00884587 0.0113140i
\(856\) −8.03854 8.03854i −0.274751 0.274751i
\(857\) 9.78821 9.78821i 0.334359 0.334359i −0.519880 0.854239i \(-0.674023\pi\)
0.854239 + 0.519880i \(0.174023\pi\)
\(858\) −22.0873 45.3059i −0.754047 1.54672i
\(859\) 14.5905 + 14.5905i 0.497821 + 0.497821i 0.910759 0.412938i \(-0.135498\pi\)
−0.412938 + 0.910759i \(0.635498\pi\)
\(860\) 10.2078i 0.348082i
\(861\) 37.1952 18.1332i 1.26761 0.617978i
\(862\) 23.8565i 0.812557i
\(863\) 12.6373i 0.430178i −0.976595 0.215089i \(-0.930996\pi\)
0.976595 0.215089i \(-0.0690041\pi\)
\(864\) 4.35936 2.82772i 0.148308 0.0962009i
\(865\) −3.03088 + 3.03088i −0.103053 + 0.103053i
\(866\) −14.8240 14.8240i −0.503740 0.503740i
\(867\) 9.45757 + 19.3996i 0.321196 + 0.658844i
\(868\) −8.58319 8.58319i −0.291332 0.291332i
\(869\) 3.94781 + 3.94781i 0.133920 + 0.133920i
\(870\) 4.11681 + 1.41835i 0.139573 + 0.0480864i
\(871\) −36.8839 + 36.8839i −1.24976 + 1.24976i
\(872\) 16.0158 0.542364
\(873\) 16.1899 1.98206i 0.547943 0.0670825i
\(874\) −0.150579 0.150579i −0.00509342 0.00509342i
\(875\) −1.36133 1.36133i −0.0460212 0.0460212i
\(876\) 10.7794 5.25511i 0.364203 0.177554i
\(877\) −4.55805 −0.153914 −0.0769572 0.997034i \(-0.524520\pi\)
−0.0769572 + 0.997034i \(0.524520\pi\)
\(878\) −2.25742 −0.0761842
\(879\) −17.0961 35.0679i −0.576637 1.18281i
\(880\) 3.66800 3.66800i 0.123648 0.123648i
\(881\) −24.5294 −0.826416 −0.413208 0.910637i \(-0.635592\pi\)
−0.413208 + 0.910637i \(0.635592\pi\)
\(882\) −9.80753 + 1.20070i −0.330237 + 0.0404295i
\(883\) −30.6747 + 30.6747i −1.03229 + 1.03229i −0.0328243 + 0.999461i \(0.510450\pi\)
−0.999461 + 0.0328243i \(0.989550\pi\)
\(884\) 30.4489i 1.02411i
\(885\) 8.41350 + 17.2580i 0.282817 + 0.580120i
\(886\) 18.8725 + 18.8725i 0.634035 + 0.634035i
\(887\) 54.5342 1.83108 0.915540 0.402227i \(-0.131764\pi\)
0.915540 + 0.402227i \(0.131764\pi\)
\(888\) −5.92634 + 8.71083i −0.198875 + 0.292316i
\(889\) 11.7461 0.393950
\(890\) −5.54999 5.54999i −0.186036 0.186036i
\(891\) 11.2624 + 45.3072i 0.377303 + 1.51785i
\(892\) 15.3186i 0.512904i
\(893\) 0.344216 0.344216i 0.0115188 0.0115188i
\(894\) −5.32736 + 15.4629i −0.178173 + 0.517156i
\(895\) 9.16666 0.306408
\(896\) 1.36133 1.36133i 0.0454787 0.0454787i
\(897\) −13.2870 + 6.47759i −0.443639 + 0.216280i
\(898\) 13.9457 0.465372
\(899\) 15.8505 0.528644
\(900\) 1.84782 2.36338i 0.0615940 0.0787793i
\(901\) −15.1915 15.1915i −0.506103 0.506103i
\(902\) 45.5178 + 45.5178i 1.51558 + 1.51558i
\(903\) −32.1819 11.0875i −1.07095 0.368968i
\(904\) −19.9709 −0.664222
\(905\) −9.54619 + 9.54619i −0.317326 + 0.317326i
\(906\) 6.99768 20.3111i 0.232482 0.674791i
\(907\) 5.52271 + 5.52271i 0.183379 + 0.183379i 0.792826 0.609448i \(-0.208609\pi\)
−0.609448 + 0.792826i \(0.708609\pi\)
\(908\) 13.6849 + 13.6849i 0.454149 + 0.454149i
\(909\) 6.20610 7.93767i 0.205844 0.263276i
\(910\) −7.63685 7.63685i −0.253159 0.253159i
\(911\) 3.48960 3.48960i 0.115616 0.115616i −0.646932 0.762548i \(-0.723948\pi\)
0.762548 + 0.646932i \(0.223948\pi\)
\(912\) 0.229228 + 0.0789750i 0.00759051 + 0.00261512i
\(913\) 47.6372i 1.57656i
\(914\) 9.26555i 0.306477i
\(915\) 9.77766 + 20.0562i 0.323239 + 0.663036i
\(916\) 11.4150i 0.377161i
\(917\) 9.89838 + 9.89838i 0.326873 + 0.326873i
\(918\) 5.87844 27.5840i 0.194017 0.910407i
\(919\) 23.9392 23.9392i 0.789680 0.789680i −0.191762 0.981442i \(-0.561420\pi\)
0.981442 + 0.191762i \(0.0614201\pi\)
\(920\) −1.07572 1.07572i −0.0354656 0.0354656i
\(921\) 8.36109 + 17.1505i 0.275507 + 0.565127i
\(922\) −20.1282 −0.662887
\(923\) −4.91701 + 4.91701i −0.161845 + 0.161845i
\(924\) 7.57996 + 15.5482i 0.249362 + 0.511498i
\(925\) −1.59678 + 5.86944i −0.0525017 + 0.192986i
\(926\) 4.66163i 0.153191i
\(927\) 5.55711 + 45.3916i 0.182520 + 1.49086i
\(928\) 2.51395i 0.0825245i
\(929\) 39.0723 1.28192 0.640961 0.767574i \(-0.278536\pi\)
0.640961 + 0.767574i \(0.278536\pi\)
\(930\) 3.55723 10.3250i 0.116646 0.338571i
\(931\) −0.326000 0.326000i −0.0106842 0.0106842i
\(932\) 15.1403i 0.495937i
\(933\) 42.0771 + 14.4966i 1.37754 + 0.474598i
\(934\) −11.6750 −0.382017
\(935\) 28.1556i 0.920786i
\(936\) 10.3660 13.2582i 0.338824 0.433359i
\(937\) −5.26195 −0.171900 −0.0859502 0.996299i \(-0.527393\pi\)
−0.0859502 + 0.996299i \(0.527393\pi\)
\(938\) 12.6579 12.6579i 0.413296 0.413296i
\(939\) −8.14404 2.80583i −0.265771 0.0915647i
\(940\) 2.45905 2.45905i 0.0802053 0.0802053i
\(941\) 48.3770i 1.57704i −0.615007 0.788522i \(-0.710847\pi\)
0.615007 0.788522i \(-0.289153\pi\)
\(942\) −11.9356 4.11212i −0.388883 0.133980i
\(943\) 13.3491 13.3491i 0.434708 0.434708i
\(944\) −7.83820 + 7.83820i −0.255112 + 0.255112i
\(945\) 5.44394 + 8.39266i 0.177091 + 0.273013i
\(946\) 52.9511i 1.72159i
\(947\) 9.05959 9.05959i 0.294397 0.294397i −0.544417 0.838814i \(-0.683249\pi\)
0.838814 + 0.544417i \(0.183249\pi\)
\(948\) −0.607229 + 1.76251i −0.0197219 + 0.0572436i
\(949\) 27.4647 27.4647i 0.891540 0.891540i
\(950\) 0.139979 0.00454153
\(951\) 18.1779 8.86199i 0.589460 0.287370i
\(952\) 10.4495i 0.338671i
\(953\) 9.84569 0.318933 0.159467 0.987203i \(-0.449023\pi\)
0.159467 + 0.987203i \(0.449023\pi\)
\(954\) 1.44298 + 11.7866i 0.0467182 + 0.381604i
\(955\) 14.0617i 0.455027i
\(956\) 5.80735 + 5.80735i 0.187823 + 0.187823i
\(957\) −21.3553 7.35744i −0.690319 0.237832i
\(958\) −22.3044 −0.720622
\(959\) 5.14644i 0.166187i
\(960\) 1.63759 + 0.564190i 0.0528529 + 0.0182091i
\(961\) 8.75329i 0.282364i
\(962\) −8.95769 + 32.9267i −0.288808 + 1.06160i
\(963\) 26.8674 + 21.0064i 0.865789 + 0.676922i
\(964\) 18.6269 18.6269i 0.599933 0.599933i
\(965\) −21.1196 −0.679864
\(966\) 4.55986 2.22299i 0.146711 0.0715236i
\(967\) 23.0717 + 23.0717i 0.741937 + 0.741937i 0.972951 0.231013i \(-0.0742041\pi\)
−0.231013 + 0.972951i \(0.574204\pi\)
\(968\) −11.2490 + 11.2490i −0.361557 + 0.361557i
\(969\) 1.18288 0.576672i 0.0379997 0.0185254i
\(970\) 3.84448 + 3.84448i 0.123439 + 0.123439i
\(971\) 8.02634i 0.257577i −0.991672 0.128789i \(-0.958891\pi\)
0.991672 0.128789i \(-0.0411089\pi\)
\(972\) −11.9503 + 10.0095i −0.383306 + 0.321055i
\(973\) 20.9289i 0.670951i
\(974\) 18.3634i 0.588400i
\(975\) 3.16503 9.18664i 0.101362 0.294208i
\(976\) −9.10908 + 9.10908i −0.291575 + 0.291575i
\(977\) −17.8008 17.8008i −0.569499 0.569499i 0.362489 0.931988i \(-0.381927\pi\)
−0.931988 + 0.362489i \(0.881927\pi\)
\(978\) −31.3387 + 15.2780i −1.00210 + 0.488538i
\(979\) 28.7897 + 28.7897i 0.920122 + 0.920122i
\(980\) −2.32892 2.32892i −0.0743945 0.0743945i
\(981\) −47.6914 + 5.83866i −1.52267 + 0.186414i
\(982\) −21.8422 + 21.8422i −0.697012 + 0.697012i
\(983\) 49.9878 1.59436 0.797181 0.603740i \(-0.206323\pi\)
0.797181 + 0.603740i \(0.206323\pi\)
\(984\) −7.00128 + 20.3215i −0.223193 + 0.647827i
\(985\) 7.07612 + 7.07612i 0.225464 + 0.225464i
\(986\) 9.64854 + 9.64854i 0.307272 + 0.307272i
\(987\) 5.08165 + 10.4236i 0.161751 + 0.331787i
\(988\) 0.785265 0.0249826
\(989\) −15.5291 −0.493796
\(990\) −9.58527 + 12.2597i −0.304640 + 0.389637i
\(991\) 7.00029 7.00029i 0.222372 0.222372i −0.587125 0.809496i \(-0.699740\pi\)
0.809496 + 0.587125i \(0.199740\pi\)
\(992\) 6.30502 0.200185
\(993\) 1.40664 + 0.484624i 0.0446385 + 0.0153791i
\(994\) 1.68743 1.68743i 0.0535221 0.0535221i
\(995\) 17.3218i 0.549138i
\(996\) −14.2975 + 6.97022i −0.453033 + 0.220860i
\(997\) −4.54972 4.54972i −0.144091 0.144091i 0.631381 0.775473i \(-0.282488\pi\)
−0.775473 + 0.631381i \(0.782488\pi\)
\(998\) 28.6326 0.906350
\(999\) 14.4717 28.0993i 0.457863 0.889023i
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 1110.2.u.e.191.14 yes 40
3.2 odd 2 inner 1110.2.u.e.191.10 40
37.31 odd 4 inner 1110.2.u.e.401.10 yes 40
111.68 even 4 inner 1110.2.u.e.401.14 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.u.e.191.10 40 3.2 odd 2 inner
1110.2.u.e.191.14 yes 40 1.1 even 1 trivial
1110.2.u.e.401.10 yes 40 37.31 odd 4 inner
1110.2.u.e.401.14 yes 40 111.68 even 4 inner