Properties

Label 731.2.e.a.681.1
Level $731$
Weight $2$
Character 731.681
Analytic conductor $5.837$
Analytic rank $0$
Dimension $58$
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] = [731,2,Mod(307,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.e (of order \(3\), 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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 681.1
Character \(\chi\) \(=\) 731.681
Dual form 731.2.e.a.307.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.82259 q^{2} +(0.178900 + 0.309865i) q^{3} +5.96703 q^{4} +(-1.59268 - 2.75860i) q^{5} +(-0.504963 - 0.874622i) q^{6} +(1.57025 - 2.71975i) q^{7} -11.1973 q^{8} +(1.43599 - 2.48721i) q^{9} +O(q^{10})\) \(q-2.82259 q^{2} +(0.178900 + 0.309865i) q^{3} +5.96703 q^{4} +(-1.59268 - 2.75860i) q^{5} +(-0.504963 - 0.874622i) q^{6} +(1.57025 - 2.71975i) q^{7} -11.1973 q^{8} +(1.43599 - 2.48721i) q^{9} +(4.49548 + 7.78640i) q^{10} +4.39128 q^{11} +(1.06750 + 1.84897i) q^{12} +(1.82274 - 3.15707i) q^{13} +(-4.43217 + 7.67675i) q^{14} +(0.569862 - 0.987029i) q^{15} +19.6714 q^{16} +(0.500000 - 0.866025i) q^{17} +(-4.05321 + 7.02037i) q^{18} +(-1.25913 - 2.18088i) q^{19} +(-9.50356 - 16.4607i) q^{20} +1.12367 q^{21} -12.3948 q^{22} +(0.162805 + 0.281987i) q^{23} +(-2.00320 - 3.46965i) q^{24} +(-2.57325 + 4.45700i) q^{25} +(-5.14485 + 8.91114i) q^{26} +2.10100 q^{27} +(9.36972 - 16.2288i) q^{28} +(-0.148387 + 0.257014i) q^{29} +(-1.60849 + 2.78598i) q^{30} +(0.0691656 + 0.119798i) q^{31} -33.1298 q^{32} +(0.785602 + 1.36070i) q^{33} +(-1.41130 + 2.44444i) q^{34} -10.0036 q^{35} +(8.56860 - 14.8412i) q^{36} +(3.47777 + 6.02367i) q^{37} +(3.55401 + 6.15573i) q^{38} +1.30435 q^{39} +(17.8337 + 30.8889i) q^{40} +8.04403 q^{41} -3.17167 q^{42} +(-0.483355 + 6.53960i) q^{43} +26.2029 q^{44} -9.14828 q^{45} +(-0.459533 - 0.795934i) q^{46} -11.0641 q^{47} +(3.51922 + 6.09547i) q^{48} +(-1.43136 - 2.47918i) q^{49} +(7.26323 - 12.5803i) q^{50} +0.357801 q^{51} +(10.8763 - 18.8384i) q^{52} +(3.18900 + 5.52351i) q^{53} -5.93026 q^{54} +(-6.99390 - 12.1138i) q^{55} +(-17.5826 + 30.4539i) q^{56} +(0.450518 - 0.780320i) q^{57} +(0.418837 - 0.725447i) q^{58} +1.52804 q^{59} +(3.40038 - 5.88964i) q^{60} +(0.805237 - 1.39471i) q^{61} +(-0.195226 - 0.338142i) q^{62} +(-4.50972 - 7.81106i) q^{63} +54.1690 q^{64} -11.6121 q^{65} +(-2.21744 - 3.84071i) q^{66} +(-1.50104 - 2.59988i) q^{67} +(2.98352 - 5.16760i) q^{68} +(-0.0582518 + 0.100895i) q^{69} +28.2361 q^{70} +(0.468173 - 0.810899i) q^{71} +(-16.0792 + 27.8500i) q^{72} +(5.20043 - 9.00742i) q^{73} +(-9.81633 - 17.0024i) q^{74} -1.84142 q^{75} +(-7.51327 - 13.0134i) q^{76} +(6.89540 - 11.9432i) q^{77} -3.68166 q^{78} +(-6.88582 + 11.9266i) q^{79} +(-31.3302 - 54.2656i) q^{80} +(-3.93210 - 6.81059i) q^{81} -22.7050 q^{82} +(-8.28634 - 14.3524i) q^{83} +6.70499 q^{84} -3.18536 q^{85} +(1.36431 - 18.4586i) q^{86} -0.106186 q^{87} -49.1706 q^{88} +(6.25527 + 10.8344i) q^{89} +25.8219 q^{90} +(-5.72430 - 9.91478i) q^{91} +(0.971464 + 1.68262i) q^{92} +(-0.0247475 + 0.0428639i) q^{93} +31.2295 q^{94} +(-4.01078 + 6.94687i) q^{95} +(-5.92693 - 10.2657i) q^{96} -3.56126 q^{97} +(4.04014 + 6.99772i) q^{98} +(6.30584 - 10.9220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82259 −1.99587 −0.997937 0.0641944i \(-0.979552\pi\)
−0.997937 + 0.0641944i \(0.979552\pi\)
\(3\) 0.178900 + 0.309865i 0.103288 + 0.178900i 0.913038 0.407876i \(-0.133730\pi\)
−0.809749 + 0.586776i \(0.800397\pi\)
\(4\) 5.96703 2.98352
\(5\) −1.59268 2.75860i −0.712267 1.23368i −0.964004 0.265888i \(-0.914335\pi\)
0.251737 0.967796i \(-0.418998\pi\)
\(6\) −0.504963 0.874622i −0.206150 0.357063i
\(7\) 1.57025 2.71975i 0.593498 1.02797i −0.400259 0.916402i \(-0.631080\pi\)
0.993757 0.111566i \(-0.0355868\pi\)
\(8\) −11.1973 −3.95885
\(9\) 1.43599 2.48721i 0.478663 0.829069i
\(10\) 4.49548 + 7.78640i 1.42160 + 2.46228i
\(11\) 4.39128 1.32402 0.662011 0.749494i \(-0.269703\pi\)
0.662011 + 0.749494i \(0.269703\pi\)
\(12\) 1.06750 + 1.84897i 0.308162 + 0.533752i
\(13\) 1.82274 3.15707i 0.505537 0.875615i −0.494443 0.869210i \(-0.664628\pi\)
0.999979 0.00640491i \(-0.00203876\pi\)
\(14\) −4.43217 + 7.67675i −1.18455 + 2.05170i
\(15\) 0.569862 0.987029i 0.147138 0.254850i
\(16\) 19.6714 4.91785
\(17\) 0.500000 0.866025i 0.121268 0.210042i
\(18\) −4.05321 + 7.02037i −0.955352 + 1.65472i
\(19\) −1.25913 2.18088i −0.288864 0.500328i 0.684675 0.728849i \(-0.259944\pi\)
−0.973539 + 0.228521i \(0.926611\pi\)
\(20\) −9.50356 16.4607i −2.12506 3.68071i
\(21\) 1.12367 0.245205
\(22\) −12.3948 −2.64258
\(23\) 0.162805 + 0.281987i 0.0339472 + 0.0587983i 0.882500 0.470313i \(-0.155859\pi\)
−0.848553 + 0.529111i \(0.822526\pi\)
\(24\) −2.00320 3.46965i −0.408902 0.708240i
\(25\) −2.57325 + 4.45700i −0.514650 + 0.891399i
\(26\) −5.14485 + 8.91114i −1.00899 + 1.74762i
\(27\) 2.10100 0.404337
\(28\) 9.36972 16.2288i 1.77071 3.06696i
\(29\) −0.148387 + 0.257014i −0.0275548 + 0.0477264i −0.879474 0.475947i \(-0.842105\pi\)
0.851919 + 0.523673i \(0.175439\pi\)
\(30\) −1.60849 + 2.78598i −0.293668 + 0.508648i
\(31\) 0.0691656 + 0.119798i 0.0124225 + 0.0215164i 0.872170 0.489203i \(-0.162712\pi\)
−0.859747 + 0.510720i \(0.829379\pi\)
\(32\) −33.1298 −5.85657
\(33\) 0.785602 + 1.36070i 0.136756 + 0.236868i
\(34\) −1.41130 + 2.44444i −0.242035 + 0.419218i
\(35\) −10.0036 −1.69092
\(36\) 8.56860 14.8412i 1.42810 2.47354i
\(37\) 3.47777 + 6.02367i 0.571742 + 0.990286i 0.996387 + 0.0849263i \(0.0270655\pi\)
−0.424645 + 0.905360i \(0.639601\pi\)
\(38\) 3.55401 + 6.15573i 0.576537 + 0.998591i
\(39\) 1.30435 0.208864
\(40\) 17.8337 + 30.8889i 2.81976 + 4.88397i
\(41\) 8.04403 1.25627 0.628133 0.778106i \(-0.283819\pi\)
0.628133 + 0.778106i \(0.283819\pi\)
\(42\) −3.17167 −0.489399
\(43\) −0.483355 + 6.53960i −0.0737109 + 0.997280i
\(44\) 26.2029 3.95024
\(45\) −9.14828 −1.36374
\(46\) −0.459533 0.795934i −0.0677544 0.117354i
\(47\) −11.0641 −1.61387 −0.806935 0.590641i \(-0.798875\pi\)
−0.806935 + 0.590641i \(0.798875\pi\)
\(48\) 3.51922 + 6.09547i 0.507956 + 0.879806i
\(49\) −1.43136 2.47918i −0.204480 0.354169i
\(50\) 7.26323 12.5803i 1.02718 1.77912i
\(51\) 0.357801 0.0501021
\(52\) 10.8763 18.8384i 1.50828 2.61241i
\(53\) 3.18900 + 5.52351i 0.438043 + 0.758713i 0.997539 0.0701207i \(-0.0223384\pi\)
−0.559496 + 0.828833i \(0.689005\pi\)
\(54\) −5.93026 −0.807007
\(55\) −6.99390 12.1138i −0.943058 1.63342i
\(56\) −17.5826 + 30.4539i −2.34957 + 4.06957i
\(57\) 0.450518 0.780320i 0.0596726 0.103356i
\(58\) 0.418837 0.725447i 0.0549960 0.0952558i
\(59\) 1.52804 0.198934 0.0994669 0.995041i \(-0.468286\pi\)
0.0994669 + 0.995041i \(0.468286\pi\)
\(60\) 3.40038 5.88964i 0.438987 0.760349i
\(61\) 0.805237 1.39471i 0.103100 0.178574i −0.809860 0.586623i \(-0.800457\pi\)
0.912960 + 0.408048i \(0.133790\pi\)
\(62\) −0.195226 0.338142i −0.0247938 0.0429441i
\(63\) −4.50972 7.81106i −0.568171 0.984101i
\(64\) 54.1690 6.77113
\(65\) −11.6121 −1.44031
\(66\) −2.21744 3.84071i −0.272947 0.472759i
\(67\) −1.50104 2.59988i −0.183381 0.317626i 0.759649 0.650334i \(-0.225371\pi\)
−0.943030 + 0.332708i \(0.892038\pi\)
\(68\) 2.98352 5.16760i 0.361805 0.626664i
\(69\) −0.0582518 + 0.100895i −0.00701269 + 0.0121463i
\(70\) 28.2361 3.37486
\(71\) 0.468173 0.810899i 0.0555619 0.0962360i −0.836907 0.547346i \(-0.815638\pi\)
0.892469 + 0.451110i \(0.148972\pi\)
\(72\) −16.0792 + 27.8500i −1.89496 + 3.28216i
\(73\) 5.20043 9.00742i 0.608665 1.05424i −0.382796 0.923833i \(-0.625039\pi\)
0.991461 0.130405i \(-0.0416279\pi\)
\(74\) −9.81633 17.0024i −1.14113 1.97649i
\(75\) −1.84142 −0.212629
\(76\) −7.51327 13.0134i −0.861831 1.49274i
\(77\) 6.89540 11.9432i 0.785804 1.36105i
\(78\) −3.68166 −0.416866
\(79\) −6.88582 + 11.9266i −0.774715 + 1.34185i 0.160239 + 0.987078i \(0.448774\pi\)
−0.934954 + 0.354768i \(0.884560\pi\)
\(80\) −31.3302 54.2656i −3.50283 6.06707i
\(81\) −3.93210 6.81059i −0.436900 0.756733i
\(82\) −22.7050 −2.50735
\(83\) −8.28634 14.3524i −0.909544 1.57538i −0.814699 0.579885i \(-0.803098\pi\)
−0.0948454 0.995492i \(-0.530236\pi\)
\(84\) 6.70499 0.731574
\(85\) −3.18536 −0.345500
\(86\) 1.36431 18.4586i 0.147118 1.99045i
\(87\) −0.106186 −0.0113844
\(88\) −49.1706 −5.24160
\(89\) 6.25527 + 10.8344i 0.663057 + 1.14845i 0.979808 + 0.199940i \(0.0640746\pi\)
−0.316751 + 0.948509i \(0.602592\pi\)
\(90\) 25.8219 2.72186
\(91\) −5.72430 9.91478i −0.600070 1.03935i
\(92\) 0.971464 + 1.68262i 0.101282 + 0.175426i
\(93\) −0.0247475 + 0.0428639i −0.00256620 + 0.00444478i
\(94\) 31.2295 3.22108
\(95\) −4.01078 + 6.94687i −0.411497 + 0.712734i
\(96\) −5.92693 10.2657i −0.604914 1.04774i
\(97\) −3.56126 −0.361591 −0.180796 0.983521i \(-0.557867\pi\)
−0.180796 + 0.983521i \(0.557867\pi\)
\(98\) 4.04014 + 6.99772i 0.408116 + 0.706877i
\(99\) 6.30584 10.9220i 0.633760 1.09771i
\(100\) −15.3547 + 26.5950i −1.53547 + 2.65950i
\(101\) 2.58395 4.47553i 0.257113 0.445332i −0.708354 0.705857i \(-0.750562\pi\)
0.965467 + 0.260525i \(0.0838955\pi\)
\(102\) −1.00993 −0.0999976
\(103\) −6.54953 + 11.3441i −0.645344 + 1.11777i 0.338878 + 0.940830i \(0.389953\pi\)
−0.984222 + 0.176939i \(0.943381\pi\)
\(104\) −20.4098 + 35.3508i −2.00134 + 3.46643i
\(105\) −1.78965 3.09976i −0.174652 0.302506i
\(106\) −9.00125 15.5906i −0.874279 1.51430i
\(107\) 17.3827 1.68045 0.840223 0.542241i \(-0.182424\pi\)
0.840223 + 0.542241i \(0.182424\pi\)
\(108\) 12.5367 1.20635
\(109\) −6.72424 11.6467i −0.644066 1.11555i −0.984516 0.175292i \(-0.943913\pi\)
0.340451 0.940262i \(-0.389420\pi\)
\(110\) 19.7409 + 34.1923i 1.88222 + 3.26011i
\(111\) −1.24435 + 2.15528i −0.118108 + 0.204570i
\(112\) 30.8890 53.5013i 2.91874 5.05540i
\(113\) 5.54655 0.521776 0.260888 0.965369i \(-0.415985\pi\)
0.260888 + 0.965369i \(0.415985\pi\)
\(114\) −1.27163 + 2.20253i −0.119099 + 0.206285i
\(115\) 0.518593 0.898229i 0.0483590 0.0837602i
\(116\) −0.885432 + 1.53361i −0.0822103 + 0.142392i
\(117\) −5.23486 9.06705i −0.483963 0.838249i
\(118\) −4.31303 −0.397047
\(119\) −1.57025 2.71975i −0.143944 0.249319i
\(120\) −6.38092 + 11.0521i −0.582496 + 1.00891i
\(121\) 8.28337 0.753034
\(122\) −2.27286 + 3.93670i −0.205775 + 0.356412i
\(123\) 1.43908 + 2.49256i 0.129757 + 0.224746i
\(124\) 0.412713 + 0.714841i 0.0370628 + 0.0641946i
\(125\) 0.466643 0.0417378
\(126\) 12.7291 + 22.0474i 1.13400 + 1.96414i
\(127\) −2.20227 −0.195420 −0.0977101 0.995215i \(-0.531152\pi\)
−0.0977101 + 0.995215i \(0.531152\pi\)
\(128\) −86.6376 −7.65775
\(129\) −2.11286 + 1.02016i −0.186027 + 0.0898203i
\(130\) 32.7764 2.87468
\(131\) 7.33244 0.640638 0.320319 0.947310i \(-0.396210\pi\)
0.320319 + 0.947310i \(0.396210\pi\)
\(132\) 4.68771 + 8.11936i 0.408013 + 0.706700i
\(133\) −7.90859 −0.685762
\(134\) 4.23683 + 7.33840i 0.366006 + 0.633941i
\(135\) −3.34621 5.79581i −0.287996 0.498824i
\(136\) −5.59866 + 9.69716i −0.480081 + 0.831525i
\(137\) 7.65853 0.654312 0.327156 0.944970i \(-0.393910\pi\)
0.327156 + 0.944970i \(0.393910\pi\)
\(138\) 0.164421 0.284786i 0.0139965 0.0242426i
\(139\) −0.641913 1.11183i −0.0544464 0.0943039i 0.837518 0.546410i \(-0.184006\pi\)
−0.891964 + 0.452106i \(0.850673\pi\)
\(140\) −59.6918 −5.04488
\(141\) −1.97938 3.42838i −0.166694 0.288722i
\(142\) −1.32146 + 2.28884i −0.110895 + 0.192075i
\(143\) 8.00416 13.8636i 0.669341 1.15933i
\(144\) 28.2479 48.9269i 2.35399 4.07724i
\(145\) 0.945333 0.0785056
\(146\) −14.6787 + 25.4243i −1.21482 + 2.10413i
\(147\) 0.512141 0.887053i 0.0422406 0.0731629i
\(148\) 20.7520 + 35.9435i 1.70580 + 2.95453i
\(149\) 7.05465 + 12.2190i 0.577940 + 1.00102i 0.995715 + 0.0924706i \(0.0294764\pi\)
−0.417776 + 0.908550i \(0.637190\pi\)
\(150\) 5.19758 0.424381
\(151\) 4.73198 0.385083 0.192541 0.981289i \(-0.438327\pi\)
0.192541 + 0.981289i \(0.438327\pi\)
\(152\) 14.0989 + 24.4200i 1.14357 + 1.98072i
\(153\) −1.43599 2.48721i −0.116093 0.201079i
\(154\) −19.4629 + 33.7108i −1.56837 + 2.71649i
\(155\) 0.220317 0.381600i 0.0176963 0.0306509i
\(156\) 7.78312 0.623149
\(157\) 1.31521 2.27801i 0.104965 0.181805i −0.808759 0.588140i \(-0.799860\pi\)
0.913724 + 0.406336i \(0.133194\pi\)
\(158\) 19.4359 33.6639i 1.54624 2.67816i
\(159\) −1.14103 + 1.97632i −0.0904893 + 0.156732i
\(160\) 52.7650 + 91.3917i 4.17144 + 7.22515i
\(161\) 1.02258 0.0805904
\(162\) 11.0987 + 19.2235i 0.871997 + 1.51034i
\(163\) −6.48594 + 11.2340i −0.508018 + 0.879913i 0.491939 + 0.870630i \(0.336288\pi\)
−0.999957 + 0.00928345i \(0.997045\pi\)
\(164\) 47.9990 3.74809
\(165\) 2.50242 4.33432i 0.194813 0.337427i
\(166\) 23.3890 + 40.5109i 1.81534 + 3.14425i
\(167\) −2.64827 4.58694i −0.204929 0.354948i 0.745181 0.666862i \(-0.232363\pi\)
−0.950110 + 0.311914i \(0.899030\pi\)
\(168\) −12.5821 −0.970731
\(169\) −0.144748 0.250710i −0.0111344 0.0192854i
\(170\) 8.99097 0.689576
\(171\) −7.23239 −0.553075
\(172\) −2.88419 + 39.0220i −0.219918 + 2.97540i
\(173\) −18.9606 −1.44155 −0.720776 0.693168i \(-0.756214\pi\)
−0.720776 + 0.693168i \(0.756214\pi\)
\(174\) 0.299720 0.0227217
\(175\) 8.08127 + 13.9972i 0.610887 + 1.05809i
\(176\) 86.3828 6.51135
\(177\) 0.273367 + 0.473485i 0.0205475 + 0.0355893i
\(178\) −17.6561 30.5812i −1.32338 2.29216i
\(179\) −6.69797 + 11.6012i −0.500630 + 0.867117i 0.499370 + 0.866389i \(0.333565\pi\)
−1.00000 0.000727720i \(0.999768\pi\)
\(180\) −54.5881 −4.06875
\(181\) −3.89541 + 6.74705i −0.289543 + 0.501504i −0.973701 0.227830i \(-0.926837\pi\)
0.684157 + 0.729334i \(0.260170\pi\)
\(182\) 16.1574 + 27.9854i 1.19766 + 2.07442i
\(183\) 0.576229 0.0425960
\(184\) −1.82298 3.15750i −0.134392 0.232774i
\(185\) 11.0779 19.1876i 0.814466 1.41070i
\(186\) 0.0698522 0.120987i 0.00512181 0.00887123i
\(187\) 2.19564 3.80296i 0.160561 0.278100i
\(188\) −66.0200 −4.81500
\(189\) 3.29909 5.71419i 0.239973 0.415646i
\(190\) 11.3208 19.6082i 0.821297 1.42253i
\(191\) 6.62366 + 11.4725i 0.479271 + 0.830122i 0.999717 0.0237721i \(-0.00756761\pi\)
−0.520446 + 0.853895i \(0.674234\pi\)
\(192\) 9.69086 + 16.7851i 0.699377 + 1.21136i
\(193\) 3.27045 0.235412 0.117706 0.993048i \(-0.462446\pi\)
0.117706 + 0.993048i \(0.462446\pi\)
\(194\) 10.0520 0.721690
\(195\) −2.07742 3.59819i −0.148767 0.257672i
\(196\) −8.54095 14.7934i −0.610068 1.05667i
\(197\) 3.87742 6.71589i 0.276255 0.478487i −0.694196 0.719786i \(-0.744240\pi\)
0.970451 + 0.241299i \(0.0775733\pi\)
\(198\) −17.7988 + 30.8284i −1.26491 + 2.19088i
\(199\) −14.8263 −1.05101 −0.525505 0.850790i \(-0.676124\pi\)
−0.525505 + 0.850790i \(0.676124\pi\)
\(200\) 28.8135 49.9064i 2.03742 3.52892i
\(201\) 0.537074 0.930239i 0.0378823 0.0656140i
\(202\) −7.29344 + 12.6326i −0.513165 + 0.888828i
\(203\) 0.466010 + 0.807152i 0.0327075 + 0.0566510i
\(204\) 2.13501 0.149481
\(205\) −12.8115 22.1902i −0.894797 1.54983i
\(206\) 18.4867 32.0198i 1.28803 2.23093i
\(207\) 0.935146 0.0649971
\(208\) 35.8558 62.1041i 2.48615 4.30615i
\(209\) −5.52920 9.57685i −0.382463 0.662445i
\(210\) 5.05145 + 8.74936i 0.348583 + 0.603763i
\(211\) −17.8182 −1.22666 −0.613329 0.789827i \(-0.710170\pi\)
−0.613329 + 0.789827i \(0.710170\pi\)
\(212\) 19.0289 + 32.9590i 1.30691 + 2.26363i
\(213\) 0.335025 0.0229555
\(214\) −49.0642 −3.35396
\(215\) 18.8100 9.08210i 1.28283 0.619394i
\(216\) −23.5256 −1.60071
\(217\) 0.434429 0.0294909
\(218\) 18.9798 + 32.8740i 1.28547 + 2.22651i
\(219\) 3.72144 0.251472
\(220\) −41.7328 72.2834i −2.81363 4.87335i
\(221\) −1.82274 3.15707i −0.122611 0.212368i
\(222\) 3.51229 6.08347i 0.235730 0.408296i
\(223\) 3.46640 0.232127 0.116064 0.993242i \(-0.462972\pi\)
0.116064 + 0.993242i \(0.462972\pi\)
\(224\) −52.0219 + 90.1046i −3.47586 + 6.02037i
\(225\) 7.39031 + 12.8004i 0.492688 + 0.853360i
\(226\) −15.6557 −1.04140
\(227\) 1.46114 + 2.53077i 0.0969793 + 0.167973i 0.910433 0.413657i \(-0.135749\pi\)
−0.813454 + 0.581630i \(0.802415\pi\)
\(228\) 2.68825 4.65619i 0.178034 0.308364i
\(229\) −9.19255 + 15.9220i −0.607461 + 1.05215i 0.384196 + 0.923251i \(0.374479\pi\)
−0.991657 + 0.128902i \(0.958855\pi\)
\(230\) −1.46378 + 2.53533i −0.0965185 + 0.167175i
\(231\) 4.93436 0.324657
\(232\) 1.66154 2.87787i 0.109085 0.188942i
\(233\) −10.8325 + 18.7624i −0.709660 + 1.22917i 0.255323 + 0.966856i \(0.417818\pi\)
−0.964983 + 0.262312i \(0.915515\pi\)
\(234\) 14.7759 + 25.5926i 0.965930 + 1.67304i
\(235\) 17.6216 + 30.5215i 1.14951 + 1.99100i
\(236\) 9.11786 0.593522
\(237\) −4.92751 −0.320076
\(238\) 4.43217 + 7.67675i 0.287295 + 0.497609i
\(239\) −3.29020 5.69880i −0.212826 0.368625i 0.739772 0.672858i \(-0.234933\pi\)
−0.952598 + 0.304233i \(0.901600\pi\)
\(240\) 11.2100 19.4163i 0.723601 1.25331i
\(241\) −4.49404 + 7.78391i −0.289487 + 0.501406i −0.973687 0.227888i \(-0.926818\pi\)
0.684201 + 0.729294i \(0.260151\pi\)
\(242\) −23.3806 −1.50296
\(243\) 4.55841 7.89539i 0.292422 0.506490i
\(244\) 4.80487 8.32229i 0.307601 0.532780i
\(245\) −4.55938 + 7.89708i −0.291288 + 0.504526i
\(246\) −4.06194 7.03548i −0.258980 0.448566i
\(247\) −9.18026 −0.584126
\(248\) −0.774469 1.34142i −0.0491789 0.0851803i
\(249\) 2.96486 5.13529i 0.187890 0.325436i
\(250\) −1.31714 −0.0833035
\(251\) 11.4801 19.8841i 0.724618 1.25508i −0.234512 0.972113i \(-0.575349\pi\)
0.959131 0.282963i \(-0.0913173\pi\)
\(252\) −26.9096 46.6089i −1.69515 2.93608i
\(253\) 0.714924 + 1.23828i 0.0449469 + 0.0778503i
\(254\) 6.21612 0.390034
\(255\) −0.569862 0.987029i −0.0356861 0.0618102i
\(256\) 136.205 8.51279
\(257\) 14.6140 0.911596 0.455798 0.890083i \(-0.349354\pi\)
0.455798 + 0.890083i \(0.349354\pi\)
\(258\) 5.96375 2.87950i 0.371287 0.179270i
\(259\) 21.8438 1.35731
\(260\) −69.2900 −4.29718
\(261\) 0.426165 + 0.738140i 0.0263790 + 0.0456897i
\(262\) −20.6965 −1.27863
\(263\) 2.13966 + 3.70600i 0.131937 + 0.228522i 0.924423 0.381368i \(-0.124547\pi\)
−0.792486 + 0.609890i \(0.791214\pi\)
\(264\) −8.79664 15.2362i −0.541396 0.937725i
\(265\) 10.1581 17.5944i 0.624007 1.08081i
\(266\) 22.3227 1.36869
\(267\) −2.23814 + 3.87657i −0.136972 + 0.237242i
\(268\) −8.95676 15.5136i −0.547121 0.947642i
\(269\) −24.5023 −1.49393 −0.746966 0.664863i \(-0.768490\pi\)
−0.746966 + 0.664863i \(0.768490\pi\)
\(270\) 9.44500 + 16.3592i 0.574805 + 0.995591i
\(271\) −0.851697 + 1.47518i −0.0517369 + 0.0896109i −0.890734 0.454525i \(-0.849809\pi\)
0.838997 + 0.544136i \(0.183142\pi\)
\(272\) 9.83571 17.0359i 0.596377 1.03296i
\(273\) 2.04816 3.54752i 0.123960 0.214705i
\(274\) −21.6169 −1.30593
\(275\) −11.2999 + 19.5719i −0.681407 + 1.18023i
\(276\) −0.347590 + 0.602044i −0.0209225 + 0.0362388i
\(277\) −4.25903 7.37685i −0.255900 0.443232i 0.709239 0.704968i \(-0.249038\pi\)
−0.965140 + 0.261736i \(0.915705\pi\)
\(278\) 1.81186 + 3.13823i 0.108668 + 0.188219i
\(279\) 0.397284 0.0237848
\(280\) 112.013 6.69409
\(281\) 7.28338 + 12.6152i 0.434490 + 0.752559i 0.997254 0.0740587i \(-0.0235952\pi\)
−0.562764 + 0.826618i \(0.690262\pi\)
\(282\) 5.58698 + 9.67693i 0.332700 + 0.576253i
\(283\) −12.0586 + 20.8861i −0.716809 + 1.24155i 0.245448 + 0.969410i \(0.421065\pi\)
−0.962258 + 0.272140i \(0.912268\pi\)
\(284\) 2.79360 4.83866i 0.165770 0.287122i
\(285\) −2.87012 −0.170011
\(286\) −22.5925 + 39.1313i −1.33592 + 2.31388i
\(287\) 12.6311 21.8777i 0.745591 1.29140i
\(288\) −47.5740 + 82.4006i −2.80332 + 4.85550i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) −2.66829 −0.156687
\(291\) −0.637111 1.10351i −0.0373481 0.0646888i
\(292\) 31.0312 53.7475i 1.81596 3.14534i
\(293\) 8.30923 0.485430 0.242715 0.970098i \(-0.421962\pi\)
0.242715 + 0.970098i \(0.421962\pi\)
\(294\) −1.44556 + 2.50379i −0.0843070 + 0.146024i
\(295\) −2.43367 4.21525i −0.141694 0.245421i
\(296\) −38.9417 67.4490i −2.26344 3.92039i
\(297\) 9.22608 0.535351
\(298\) −19.9124 34.4893i −1.15350 1.99791i
\(299\) 1.18700 0.0686463
\(300\) −10.9878 −0.634382
\(301\) 17.0271 + 11.5834i 0.981425 + 0.667656i
\(302\) −13.3564 −0.768577
\(303\) 1.84908 0.106227
\(304\) −24.7689 42.9010i −1.42059 2.46054i
\(305\) −5.12993 −0.293739
\(306\) 4.05321 + 7.02037i 0.231707 + 0.401328i
\(307\) 10.2650 + 17.7796i 0.585857 + 1.01473i 0.994768 + 0.102160i \(0.0325753\pi\)
−0.408911 + 0.912574i \(0.634091\pi\)
\(308\) 41.1451 71.2654i 2.34446 4.06072i
\(309\) −4.68685 −0.266626
\(310\) −0.621866 + 1.07710i −0.0353196 + 0.0611753i
\(311\) 16.6907 + 28.9091i 0.946441 + 1.63928i 0.752841 + 0.658203i \(0.228683\pi\)
0.193600 + 0.981081i \(0.437984\pi\)
\(312\) −14.6053 −0.826861
\(313\) 1.17762 + 2.03970i 0.0665632 + 0.115291i 0.897386 0.441246i \(-0.145463\pi\)
−0.830823 + 0.556537i \(0.812130\pi\)
\(314\) −3.71230 + 6.42989i −0.209497 + 0.362860i
\(315\) −14.3651 + 24.8810i −0.809379 + 1.40189i
\(316\) −41.0879 + 71.1664i −2.31138 + 4.00342i
\(317\) −4.96330 −0.278766 −0.139383 0.990239i \(-0.544512\pi\)
−0.139383 + 0.990239i \(0.544512\pi\)
\(318\) 3.22066 5.57834i 0.180605 0.312818i
\(319\) −0.651611 + 1.12862i −0.0364832 + 0.0631907i
\(320\) −86.2738 149.431i −4.82285 8.35343i
\(321\) 3.10977 + 5.38627i 0.173570 + 0.300632i
\(322\) −2.88632 −0.160848
\(323\) −2.51826 −0.140120
\(324\) −23.4630 40.6390i −1.30350 2.25772i
\(325\) 9.38071 + 16.2479i 0.520348 + 0.901270i
\(326\) 18.3072 31.7090i 1.01394 1.75620i
\(327\) 2.40594 4.16721i 0.133049 0.230447i
\(328\) −90.0715 −4.97337
\(329\) −17.3734 + 30.0917i −0.957828 + 1.65901i
\(330\) −7.06332 + 12.2340i −0.388823 + 0.673462i
\(331\) 8.39827 14.5462i 0.461611 0.799533i −0.537431 0.843308i \(-0.680605\pi\)
0.999041 + 0.0437748i \(0.0139384\pi\)
\(332\) −49.4449 85.6410i −2.71364 4.70016i
\(333\) 19.9762 1.09469
\(334\) 7.47499 + 12.9471i 0.409013 + 0.708432i
\(335\) −4.78135 + 8.28154i −0.261233 + 0.452469i
\(336\) 22.1042 1.20588
\(337\) 3.93097 6.80864i 0.214134 0.370890i −0.738871 0.673847i \(-0.764641\pi\)
0.953004 + 0.302957i \(0.0979739\pi\)
\(338\) 0.408564 + 0.707653i 0.0222229 + 0.0384912i
\(339\) 0.992281 + 1.71868i 0.0538933 + 0.0933459i
\(340\) −19.0071 −1.03081
\(341\) 0.303726 + 0.526069i 0.0164477 + 0.0284882i
\(342\) 20.4141 1.10387
\(343\) 12.9931 0.701563
\(344\) 5.41228 73.2260i 0.291811 3.94808i
\(345\) 0.371106 0.0199797
\(346\) 53.5182 2.87716
\(347\) −5.75200 9.96276i −0.308784 0.534829i 0.669313 0.742981i \(-0.266589\pi\)
−0.978097 + 0.208152i \(0.933255\pi\)
\(348\) −0.633616 −0.0339654
\(349\) −16.9864 29.4213i −0.909261 1.57489i −0.815093 0.579329i \(-0.803314\pi\)
−0.0941673 0.995556i \(-0.530019\pi\)
\(350\) −22.8102 39.5083i −1.21925 2.11181i
\(351\) 3.82957 6.63301i 0.204407 0.354044i
\(352\) −145.482 −7.75423
\(353\) 5.19266 8.99394i 0.276377 0.478699i −0.694104 0.719874i \(-0.744199\pi\)
0.970482 + 0.241175i \(0.0775328\pi\)
\(354\) −0.771603 1.33646i −0.0410102 0.0710318i
\(355\) −2.98259 −0.158300
\(356\) 37.3254 + 64.6495i 1.97824 + 3.42641i
\(357\) 0.561836 0.973128i 0.0297355 0.0515034i
\(358\) 18.9057 32.7456i 0.999195 1.73066i
\(359\) −10.1640 + 17.6045i −0.536435 + 0.929132i 0.462658 + 0.886537i \(0.346896\pi\)
−0.999092 + 0.0425952i \(0.986437\pi\)
\(360\) 102.436 5.39886
\(361\) 6.32918 10.9625i 0.333115 0.576972i
\(362\) 10.9952 19.0442i 0.577892 1.00094i
\(363\) 1.48190 + 2.56672i 0.0777795 + 0.134718i
\(364\) −34.1571 59.1618i −1.79032 3.10092i
\(365\) −33.1305 −1.73413
\(366\) −1.62646 −0.0850164
\(367\) 0.226274 + 0.391918i 0.0118114 + 0.0204579i 0.871871 0.489736i \(-0.162907\pi\)
−0.860059 + 0.510194i \(0.829574\pi\)
\(368\) 3.20261 + 5.54708i 0.166947 + 0.289162i
\(369\) 11.5511 20.0072i 0.601328 1.04153i
\(370\) −31.2685 + 54.1587i −1.62557 + 2.81557i
\(371\) 20.0301 1.03991
\(372\) −0.147669 + 0.255771i −0.00765629 + 0.0132611i
\(373\) 11.2545 19.4934i 0.582738 1.00933i −0.412415 0.910996i \(-0.635315\pi\)
0.995153 0.0983359i \(-0.0313520\pi\)
\(374\) −6.19740 + 10.7342i −0.320460 + 0.555053i
\(375\) 0.0834827 + 0.144596i 0.00431103 + 0.00746692i
\(376\) 123.889 6.38907
\(377\) 0.540942 + 0.936939i 0.0278599 + 0.0482548i
\(378\) −9.31198 + 16.1288i −0.478957 + 0.829578i
\(379\) −1.95707 −0.100528 −0.0502641 0.998736i \(-0.516006\pi\)
−0.0502641 + 0.998736i \(0.516006\pi\)
\(380\) −23.9325 + 41.4522i −1.22771 + 2.12645i
\(381\) −0.393988 0.682407i −0.0201846 0.0349608i
\(382\) −18.6959 32.3823i −0.956566 1.65682i
\(383\) 1.19143 0.0608791 0.0304395 0.999537i \(-0.490309\pi\)
0.0304395 + 0.999537i \(0.490309\pi\)
\(384\) −15.4995 26.8459i −0.790955 1.36997i
\(385\) −43.9286 −2.23881
\(386\) −9.23114 −0.469853
\(387\) 15.5712 + 10.5930i 0.791531 + 0.538472i
\(388\) −21.2501 −1.07881
\(389\) 7.46160 0.378318 0.189159 0.981946i \(-0.439424\pi\)
0.189159 + 0.981946i \(0.439424\pi\)
\(390\) 5.86370 + 10.1562i 0.296920 + 0.514281i
\(391\) 0.325610 0.0164668
\(392\) 16.0274 + 27.7602i 0.809504 + 1.40210i
\(393\) 1.31178 + 2.27206i 0.0661703 + 0.114610i
\(394\) −10.9444 + 18.9562i −0.551370 + 0.955001i
\(395\) 43.8676 2.20722
\(396\) 37.6271 65.1721i 1.89083 3.27502i
\(397\) 6.19955 + 10.7379i 0.311146 + 0.538921i 0.978611 0.205720i \(-0.0659537\pi\)
−0.667464 + 0.744642i \(0.732620\pi\)
\(398\) 41.8487 2.09769
\(399\) −1.41485 2.45059i −0.0708311 0.122683i
\(400\) −50.6194 + 87.6754i −2.53097 + 4.38377i
\(401\) −10.6290 + 18.4099i −0.530786 + 0.919349i 0.468568 + 0.883427i \(0.344770\pi\)
−0.999355 + 0.0359216i \(0.988563\pi\)
\(402\) −1.51594 + 2.62569i −0.0756082 + 0.130957i
\(403\) 0.504283 0.0251201
\(404\) 15.4185 26.7057i 0.767100 1.32866i
\(405\) −12.5251 + 21.6942i −0.622379 + 1.07799i
\(406\) −1.31536 2.27826i −0.0652800 0.113068i
\(407\) 15.2719 + 26.4517i 0.756999 + 1.31116i
\(408\) −4.00641 −0.198347
\(409\) −5.32473 −0.263291 −0.131646 0.991297i \(-0.542026\pi\)
−0.131646 + 0.991297i \(0.542026\pi\)
\(410\) 36.1618 + 62.6340i 1.78590 + 3.09328i
\(411\) 1.37011 + 2.37311i 0.0675828 + 0.117057i
\(412\) −39.0813 + 67.6907i −1.92540 + 3.33488i
\(413\) 2.39940 4.15588i 0.118067 0.204498i
\(414\) −2.63954 −0.129726
\(415\) −26.3950 + 45.7174i −1.29568 + 2.24418i
\(416\) −60.3869 + 104.593i −2.96071 + 5.12810i
\(417\) 0.229677 0.397812i 0.0112473 0.0194810i
\(418\) 15.6067 + 27.0316i 0.763348 + 1.32216i
\(419\) −0.103781 −0.00507005 −0.00253503 0.999997i \(-0.500807\pi\)
−0.00253503 + 0.999997i \(0.500807\pi\)
\(420\) −10.6789 18.4964i −0.521076 0.902531i
\(421\) 13.8106 23.9206i 0.673086 1.16582i −0.303938 0.952692i \(-0.598302\pi\)
0.977024 0.213128i \(-0.0683651\pi\)
\(422\) 50.2937 2.44826
\(423\) −15.8880 + 27.5188i −0.772500 + 1.33801i
\(424\) −35.7083 61.8485i −1.73415 3.00363i
\(425\) 2.57325 + 4.45700i 0.124821 + 0.216196i
\(426\) −0.945639 −0.0458164
\(427\) −2.52884 4.38008i −0.122379 0.211967i
\(428\) 103.723 5.01364
\(429\) 5.72779 0.276540
\(430\) −53.0929 + 25.6351i −2.56037 + 1.23623i
\(431\) −19.5888 −0.943558 −0.471779 0.881717i \(-0.656388\pi\)
−0.471779 + 0.881717i \(0.656388\pi\)
\(432\) 41.3296 1.98847
\(433\) 14.9601 + 25.9117i 0.718937 + 1.24524i 0.961421 + 0.275081i \(0.0887046\pi\)
−0.242484 + 0.970155i \(0.577962\pi\)
\(434\) −1.22622 −0.0588602
\(435\) 0.169120 + 0.292925i 0.00810870 + 0.0140447i
\(436\) −40.1238 69.4964i −1.92158 3.32827i
\(437\) 0.409986 0.710116i 0.0196123 0.0339695i
\(438\) −10.5041 −0.501906
\(439\) −0.127520 + 0.220871i −0.00608618 + 0.0105416i −0.869052 0.494720i \(-0.835271\pi\)
0.862966 + 0.505262i \(0.168604\pi\)
\(440\) 78.3130 + 135.642i 3.73342 + 6.46648i
\(441\) −8.22165 −0.391507
\(442\) 5.14485 + 8.91114i 0.244715 + 0.423860i
\(443\) −16.9872 + 29.4227i −0.807087 + 1.39792i 0.107786 + 0.994174i \(0.465624\pi\)
−0.914873 + 0.403742i \(0.867709\pi\)
\(444\) −7.42507 + 12.8606i −0.352378 + 0.610337i
\(445\) 19.9253 34.5116i 0.944548 1.63600i
\(446\) −9.78424 −0.463297
\(447\) −2.52416 + 4.37197i −0.119389 + 0.206787i
\(448\) 85.0588 147.326i 4.01865 6.96050i
\(449\) −14.1419 24.4945i −0.667398 1.15597i −0.978629 0.205633i \(-0.934075\pi\)
0.311231 0.950334i \(-0.399259\pi\)
\(450\) −20.8598 36.1303i −0.983343 1.70320i
\(451\) 35.3236 1.66332
\(452\) 33.0965 1.55673
\(453\) 0.846553 + 1.46627i 0.0397745 + 0.0688915i
\(454\) −4.12421 7.14334i −0.193559 0.335253i
\(455\) −18.2339 + 31.5821i −0.854820 + 1.48059i
\(456\) −5.04459 + 8.73749i −0.236235 + 0.409170i
\(457\) 34.5658 1.61692 0.808461 0.588550i \(-0.200301\pi\)
0.808461 + 0.588550i \(0.200301\pi\)
\(458\) 25.9468 44.9412i 1.21242 2.09997i
\(459\) 1.05050 1.81952i 0.0490331 0.0849278i
\(460\) 3.09446 5.35976i 0.144280 0.249900i
\(461\) −16.0173 27.7427i −0.745998 1.29211i −0.949727 0.313079i \(-0.898639\pi\)
0.203729 0.979027i \(-0.434694\pi\)
\(462\) −13.9277 −0.647975
\(463\) 2.23485 + 3.87088i 0.103862 + 0.179895i 0.913273 0.407348i \(-0.133547\pi\)
−0.809410 + 0.587243i \(0.800213\pi\)
\(464\) −2.91899 + 5.05583i −0.135511 + 0.234711i
\(465\) 0.157659 0.00731127
\(466\) 30.5757 52.9587i 1.41639 2.45326i
\(467\) 5.21884 + 9.03930i 0.241499 + 0.418289i 0.961142 0.276056i \(-0.0890276\pi\)
−0.719642 + 0.694345i \(0.755694\pi\)
\(468\) −31.2366 54.1034i −1.44391 2.50093i
\(469\) −9.42803 −0.435346
\(470\) −49.7386 86.1498i −2.29427 3.97379i
\(471\) 0.941165 0.0433666
\(472\) −17.1099 −0.787549
\(473\) −2.12255 + 28.7172i −0.0975949 + 1.32042i
\(474\) 13.9083 0.638831
\(475\) 12.9602 0.594656
\(476\) −9.36972 16.2288i −0.429460 0.743847i
\(477\) 18.3175 0.838700
\(478\) 9.28691 + 16.0854i 0.424773 + 0.735729i
\(479\) 14.0215 + 24.2859i 0.640659 + 1.10965i 0.985286 + 0.170914i \(0.0546720\pi\)
−0.344627 + 0.938740i \(0.611995\pi\)
\(480\) −18.8794 + 32.7000i −0.861722 + 1.49255i
\(481\) 25.3563 1.15615
\(482\) 12.6849 21.9708i 0.577779 1.00074i
\(483\) 0.182940 + 0.316861i 0.00832404 + 0.0144177i
\(484\) 49.4271 2.24669
\(485\) 5.67194 + 9.82409i 0.257549 + 0.446089i
\(486\) −12.8665 + 22.2855i −0.583637 + 1.01089i
\(487\) −12.1211 + 20.9944i −0.549261 + 0.951348i 0.449064 + 0.893499i \(0.351757\pi\)
−0.998325 + 0.0578485i \(0.981576\pi\)
\(488\) −9.01649 + 15.6170i −0.408157 + 0.706949i
\(489\) −4.64135 −0.209889
\(490\) 12.8693 22.2902i 0.581375 1.00697i
\(491\) 6.17870 10.7018i 0.278841 0.482966i −0.692256 0.721652i \(-0.743383\pi\)
0.971097 + 0.238686i \(0.0767165\pi\)
\(492\) 8.58703 + 14.8732i 0.387133 + 0.670535i
\(493\) 0.148387 + 0.257014i 0.00668303 + 0.0115753i
\(494\) 25.9121 1.16584
\(495\) −40.1727 −1.80563
\(496\) 1.36059 + 2.35660i 0.0610921 + 0.105815i
\(497\) −1.47029 2.54662i −0.0659517 0.114232i
\(498\) −8.36859 + 14.4948i −0.375006 + 0.649529i
\(499\) −6.25186 + 10.8285i −0.279872 + 0.484752i −0.971353 0.237643i \(-0.923625\pi\)
0.691481 + 0.722395i \(0.256959\pi\)
\(500\) 2.78448 0.124526
\(501\) 0.947553 1.64121i 0.0423335 0.0733239i
\(502\) −32.4037 + 56.1248i −1.44625 + 2.50497i
\(503\) 12.1152 20.9842i 0.540192 0.935640i −0.458701 0.888591i \(-0.651685\pi\)
0.998893 0.0470490i \(-0.0149817\pi\)
\(504\) 50.4968 + 87.4629i 2.24930 + 3.89591i
\(505\) −16.4616 −0.732532
\(506\) −2.01794 3.49517i −0.0897083 0.155379i
\(507\) 0.0517908 0.0897043i 0.00230011 0.00398391i
\(508\) −13.1410 −0.583039
\(509\) 12.4986 21.6483i 0.553992 0.959543i −0.443989 0.896032i \(-0.646437\pi\)
0.997981 0.0635107i \(-0.0202297\pi\)
\(510\) 1.60849 + 2.78598i 0.0712250 + 0.123365i
\(511\) −16.3319 28.2877i −0.722482 1.25138i
\(512\) −211.175 −9.33270
\(513\) −2.64543 4.58202i −0.116799 0.202301i
\(514\) −41.2494 −1.81943
\(515\) 41.7252 1.83863
\(516\) −12.6075 + 6.08734i −0.555015 + 0.267980i
\(517\) −48.5857 −2.13680
\(518\) −61.6563 −2.70902
\(519\) −3.39207 5.87523i −0.148895 0.257894i
\(520\) 130.025 5.70197
\(521\) 8.89906 + 15.4136i 0.389875 + 0.675283i 0.992432 0.122792i \(-0.0391849\pi\)
−0.602558 + 0.798075i \(0.705852\pi\)
\(522\) −1.20289 2.08347i −0.0526491 0.0911909i
\(523\) 7.30486 12.6524i 0.319419 0.553251i −0.660948 0.750432i \(-0.729845\pi\)
0.980367 + 0.197181i \(0.0631788\pi\)
\(524\) 43.7529 1.91135
\(525\) −2.89149 + 5.00820i −0.126195 + 0.218576i
\(526\) −6.03938 10.4605i −0.263330 0.456100i
\(527\) 0.138331 0.00602580
\(528\) 15.4539 + 26.7670i 0.672545 + 1.16488i
\(529\) 11.4470 19.8268i 0.497695 0.862033i
\(530\) −28.6722 + 49.6617i −1.24544 + 2.15717i
\(531\) 2.19425 3.80055i 0.0952222 0.164930i
\(532\) −47.1908 −2.04598
\(533\) 14.6622 25.3956i 0.635088 1.10001i
\(534\) 6.31736 10.9420i 0.273379 0.473506i
\(535\) −27.6850 47.9518i −1.19693 2.07314i
\(536\) 16.8076 + 29.1117i 0.725979 + 1.25743i
\(537\) −4.79308 −0.206837
\(538\) 69.1600 2.98170
\(539\) −6.28549 10.8868i −0.270735 0.468927i
\(540\) −19.9670 34.5838i −0.859242 1.48825i
\(541\) 10.4354 18.0747i 0.448654 0.777091i −0.549645 0.835399i \(-0.685237\pi\)
0.998299 + 0.0583071i \(0.0185702\pi\)
\(542\) 2.40399 4.16384i 0.103260 0.178852i
\(543\) −2.78756 −0.119626
\(544\) −16.5649 + 28.6912i −0.710213 + 1.23013i
\(545\) −21.4191 + 37.0990i −0.917494 + 1.58915i
\(546\) −5.78112 + 10.0132i −0.247409 + 0.428525i
\(547\) 12.7651 + 22.1098i 0.545796 + 0.945347i 0.998556 + 0.0537143i \(0.0171060\pi\)
−0.452760 + 0.891632i \(0.649561\pi\)
\(548\) 45.6987 1.95215
\(549\) −2.31262 4.00558i −0.0987003 0.170954i
\(550\) 31.8949 55.2436i 1.36000 2.35560i
\(551\) 0.747356 0.0318384
\(552\) 0.652264 1.12975i 0.0277622 0.0480856i
\(553\) 21.6249 + 37.4554i 0.919584 + 1.59277i
\(554\) 12.0215 + 20.8219i 0.510745 + 0.884636i
\(555\) 7.92739 0.336499
\(556\) −3.83032 6.63430i −0.162442 0.281357i
\(557\) 12.5192 0.530455 0.265227 0.964186i \(-0.414553\pi\)
0.265227 + 0.964186i \(0.414553\pi\)
\(558\) −1.12137 −0.0474715
\(559\) 19.7650 + 13.4460i 0.835969 + 0.568704i
\(560\) −196.785 −8.31568
\(561\) 1.57120 0.0663363
\(562\) −20.5580 35.6075i −0.867188 1.50201i
\(563\) 16.9991 0.716425 0.358212 0.933640i \(-0.383386\pi\)
0.358212 + 0.933640i \(0.383386\pi\)
\(564\) −11.8110 20.4573i −0.497333 0.861406i
\(565\) −8.83388 15.3007i −0.371644 0.643706i
\(566\) 34.0365 58.9530i 1.43066 2.47798i
\(567\) −24.6975 −1.03720
\(568\) −5.24228 + 9.07989i −0.219961 + 0.380984i
\(569\) −12.7511 22.0856i −0.534554 0.925875i −0.999185 0.0403706i \(-0.987146\pi\)
0.464630 0.885505i \(-0.346187\pi\)
\(570\) 8.10118 0.339321
\(571\) −14.2822 24.7375i −0.597691 1.03523i −0.993161 0.116753i \(-0.962751\pi\)
0.395470 0.918479i \(-0.370582\pi\)
\(572\) 47.7611 82.7246i 1.99699 3.45889i
\(573\) −2.36995 + 4.10488i −0.0990062 + 0.171484i
\(574\) −35.6525 + 61.7519i −1.48811 + 2.57748i
\(575\) −1.67575 −0.0698837
\(576\) 77.7861 134.730i 3.24109 5.61373i
\(577\) 4.73006 8.19271i 0.196915 0.341067i −0.750612 0.660744i \(-0.770241\pi\)
0.947527 + 0.319677i \(0.103574\pi\)
\(578\) 1.41130 + 2.44444i 0.0587022 + 0.101675i
\(579\) 0.585084 + 1.01340i 0.0243153 + 0.0421153i
\(580\) 5.64083 0.234223
\(581\) −52.0464 −2.15925
\(582\) 1.79830 + 3.11475i 0.0745421 + 0.129111i
\(583\) 14.0038 + 24.2553i 0.579978 + 1.00455i
\(584\) −58.2309 + 100.859i −2.40961 + 4.17357i
\(585\) −16.6749 + 28.8818i −0.689423 + 1.19412i
\(586\) −23.4536 −0.968858
\(587\) 10.6650 18.4722i 0.440190 0.762431i −0.557513 0.830168i \(-0.688245\pi\)
0.997703 + 0.0677369i \(0.0215778\pi\)
\(588\) 3.05596 5.29308i 0.126026 0.218283i
\(589\) 0.174177 0.301684i 0.00717684 0.0124307i
\(590\) 6.86927 + 11.8979i 0.282803 + 0.489830i
\(591\) 2.77469 0.114135
\(592\) 68.4127 + 118.494i 2.81174 + 4.87008i
\(593\) 5.76285 9.98155i 0.236652 0.409893i −0.723100 0.690744i \(-0.757283\pi\)
0.959751 + 0.280851i \(0.0906166\pi\)
\(594\) −26.0415 −1.06849
\(595\) −5.00180 + 8.66337i −0.205054 + 0.355164i
\(596\) 42.0953 + 72.9113i 1.72429 + 2.98656i
\(597\) −2.65244 4.59415i −0.108557 0.188026i
\(598\) −3.35043 −0.137009
\(599\) −3.36627 5.83055i −0.137542 0.238230i 0.789024 0.614363i \(-0.210587\pi\)
−0.926566 + 0.376133i \(0.877254\pi\)
\(600\) 20.6190 0.841766
\(601\) 14.1696 0.577992 0.288996 0.957330i \(-0.406679\pi\)
0.288996 + 0.957330i \(0.406679\pi\)
\(602\) −48.0605 32.6952i −1.95880 1.33256i
\(603\) −8.62192 −0.351112
\(604\) 28.2359 1.14890
\(605\) −13.1927 22.8505i −0.536361 0.929005i
\(606\) −5.21920 −0.212015
\(607\) −6.91576 11.9785i −0.280702 0.486191i 0.690856 0.722993i \(-0.257234\pi\)
−0.971558 + 0.236802i \(0.923901\pi\)
\(608\) 41.7147 + 72.2520i 1.69175 + 2.93020i
\(609\) −0.166739 + 0.288800i −0.00675659 + 0.0117028i
\(610\) 14.4797 0.586266
\(611\) −20.1670 + 34.9303i −0.815870 + 1.41313i
\(612\) −8.56860 14.8412i −0.346365 0.599922i
\(613\) −44.7789 −1.80860 −0.904301 0.426895i \(-0.859607\pi\)
−0.904301 + 0.426895i \(0.859607\pi\)
\(614\) −28.9740 50.1845i −1.16930 2.02528i
\(615\) 4.58398 7.93969i 0.184844 0.320159i
\(616\) −77.2100 + 133.732i −3.11088 + 5.38820i
\(617\) −4.71277 + 8.16275i −0.189729 + 0.328620i −0.945160 0.326608i \(-0.894094\pi\)
0.755431 + 0.655228i \(0.227428\pi\)
\(618\) 13.2291 0.532152
\(619\) −3.28225 + 5.68502i −0.131925 + 0.228500i −0.924418 0.381380i \(-0.875449\pi\)
0.792494 + 0.609880i \(0.208782\pi\)
\(620\) 1.31464 2.27702i 0.0527972 0.0914474i
\(621\) 0.342053 + 0.592454i 0.0137261 + 0.0237744i
\(622\) −47.1109 81.5986i −1.88898 3.27180i
\(623\) 39.2893 1.57409
\(624\) 25.6585 1.02716
\(625\) 12.1230 + 20.9977i 0.484921 + 0.839908i
\(626\) −3.32395 5.75725i −0.132852 0.230106i
\(627\) 1.97835 3.42661i 0.0790078 0.136845i
\(628\) 7.84789 13.5929i 0.313165 0.542418i
\(629\) 6.95554 0.277336
\(630\) 40.5467 70.2290i 1.61542 2.79799i
\(631\) 18.0473 31.2588i 0.718450 1.24439i −0.243164 0.969985i \(-0.578185\pi\)
0.961614 0.274406i \(-0.0884813\pi\)
\(632\) 77.1027 133.546i 3.06698 5.31217i
\(633\) −3.18769 5.52124i −0.126699 0.219450i
\(634\) 14.0094 0.556383
\(635\) 3.50751 + 6.07519i 0.139191 + 0.241087i
\(636\) −6.80855 + 11.7927i −0.269976 + 0.467613i
\(637\) −10.4360 −0.413487
\(638\) 1.83923 3.18564i 0.0728159 0.126121i
\(639\) −1.34458 2.32888i −0.0531908 0.0921292i
\(640\) 137.986 + 238.998i 5.45437 + 9.44724i
\(641\) −37.4832 −1.48050 −0.740249 0.672333i \(-0.765293\pi\)
−0.740249 + 0.672333i \(0.765293\pi\)
\(642\) −8.77761 15.2033i −0.346424 0.600025i
\(643\) 7.12850 0.281121 0.140560 0.990072i \(-0.455110\pi\)
0.140560 + 0.990072i \(0.455110\pi\)
\(644\) 6.10176 0.240443
\(645\) 6.17933 + 4.20375i 0.243311 + 0.165523i
\(646\) 7.10803 0.279662
\(647\) 13.6327 0.535958 0.267979 0.963425i \(-0.413644\pi\)
0.267979 + 0.963425i \(0.413644\pi\)
\(648\) 44.0290 + 76.2604i 1.72962 + 2.99579i
\(649\) 6.71005 0.263393
\(650\) −26.4779 45.8611i −1.03855 1.79882i
\(651\) 0.0777195 + 0.134614i 0.00304607 + 0.00527594i
\(652\) −38.7018 + 67.0335i −1.51568 + 2.62524i
\(653\) −48.4798 −1.89716 −0.948581 0.316533i \(-0.897481\pi\)
−0.948581 + 0.316533i \(0.897481\pi\)
\(654\) −6.79099 + 11.7623i −0.265549 + 0.459944i
\(655\) −11.6782 20.2273i −0.456305 0.790344i
\(656\) 158.237 6.17813
\(657\) −14.9355 25.8691i −0.582691 1.00925i
\(658\) 49.0381 84.9365i 1.91170 3.31117i
\(659\) 19.9355 34.5293i 0.776577 1.34507i −0.157327 0.987547i \(-0.550288\pi\)
0.933904 0.357524i \(-0.116379\pi\)
\(660\) 14.9320 25.8631i 0.581229 1.00672i
\(661\) −12.7136 −0.494503 −0.247251 0.968951i \(-0.579527\pi\)
−0.247251 + 0.968951i \(0.579527\pi\)
\(662\) −23.7049 + 41.0581i −0.921317 + 1.59577i
\(663\) 0.652177 1.12960i 0.0253285 0.0438702i
\(664\) 92.7848 + 160.708i 3.60075 + 6.23668i
\(665\) 12.5958 + 21.8166i 0.488446 + 0.846013i
\(666\) −56.3846 −2.18486
\(667\) −0.0966329 −0.00374164
\(668\) −15.8023 27.3704i −0.611410 1.05899i
\(669\) 0.620141 + 1.07412i 0.0239760 + 0.0415277i
\(670\) 13.4958 23.3754i 0.521389 0.903072i
\(671\) 3.53602 6.12457i 0.136507 0.236436i
\(672\) −37.2270 −1.43606
\(673\) 10.5064 18.1977i 0.404993 0.701468i −0.589328 0.807894i \(-0.700607\pi\)
0.994321 + 0.106426i \(0.0339406\pi\)
\(674\) −11.0955 + 19.2180i −0.427384 + 0.740251i
\(675\) −5.40639 + 9.36414i −0.208092 + 0.360426i
\(676\) −0.863714 1.49600i −0.0332198 0.0575383i
\(677\) 32.3382 1.24286 0.621430 0.783470i \(-0.286552\pi\)
0.621430 + 0.783470i \(0.286552\pi\)
\(678\) −2.80080 4.85114i −0.107564 0.186307i
\(679\) −5.59206 + 9.68573i −0.214604 + 0.371704i
\(680\) 35.6675 1.36778
\(681\) −0.522797 + 0.905512i −0.0200336 + 0.0346993i
\(682\) −0.857294 1.48488i −0.0328275 0.0568589i
\(683\) −11.6250 20.1351i −0.444819 0.770449i 0.553221 0.833035i \(-0.313399\pi\)
−0.998040 + 0.0625857i \(0.980065\pi\)
\(684\) −43.1559 −1.65011
\(685\) −12.1976 21.1268i −0.466045 0.807214i
\(686\) −36.6743 −1.40023
\(687\) −6.57821 −0.250974
\(688\) −9.50827 + 128.643i −0.362500 + 4.90448i
\(689\) 23.2509 0.885787
\(690\) −1.04748 −0.0398769
\(691\) −4.60975 7.98431i −0.175363 0.303738i 0.764924 0.644121i \(-0.222777\pi\)
−0.940287 + 0.340383i \(0.889443\pi\)
\(692\) −113.139 −4.30089
\(693\) −19.8035 34.3006i −0.752271 1.30297i
\(694\) 16.2356 + 28.1208i 0.616294 + 1.06745i
\(695\) −2.04472 + 3.54156i −0.0775608 + 0.134339i
\(696\) 1.18900 0.0450689
\(697\) 4.02201 6.96633i 0.152345 0.263869i
\(698\) 47.9457 + 83.0444i 1.81477 + 3.14328i
\(699\) −7.75175 −0.293198
\(700\) 48.2212 + 83.5216i 1.82259 + 3.15682i
\(701\) −20.4869 + 35.4844i −0.773781 + 1.34023i 0.161696 + 0.986841i \(0.448304\pi\)
−0.935477 + 0.353387i \(0.885030\pi\)
\(702\) −10.8093 + 18.7223i −0.407971 + 0.706627i
\(703\) 8.75793 15.1692i 0.330312 0.572117i
\(704\) 237.871 8.96512
\(705\) −6.30502 + 10.9206i −0.237461 + 0.411294i
\(706\) −14.6568 + 25.3862i −0.551614 + 0.955424i
\(707\) −8.11489 14.0554i −0.305192 0.528608i
\(708\) 1.63119 + 2.82530i 0.0613038 + 0.106181i
\(709\) 22.9753 0.862857 0.431428 0.902147i \(-0.358010\pi\)
0.431428 + 0.902147i \(0.358010\pi\)
\(710\) 8.41865 0.315946
\(711\) 19.7759 + 34.2529i 0.741655 + 1.28458i
\(712\) −70.0422 121.317i −2.62494 4.54654i
\(713\) −0.0225210 + 0.0390076i −0.000843420 + 0.00146085i
\(714\) −1.58583 + 2.74675i −0.0593484 + 0.102794i
\(715\) −50.9922 −1.90700
\(716\) −39.9670 + 69.2249i −1.49364 + 2.58706i
\(717\) 1.17724 2.03904i 0.0439648 0.0761492i
\(718\) 28.6888 49.6905i 1.07066 1.85443i
\(719\) 9.63663 + 16.6911i 0.359386 + 0.622474i 0.987858 0.155357i \(-0.0496529\pi\)
−0.628473 + 0.777832i \(0.716320\pi\)
\(720\) −179.960 −6.70670
\(721\) 20.5688 + 35.6262i 0.766021 + 1.32679i
\(722\) −17.8647 + 30.9426i −0.664855 + 1.15156i
\(723\) −3.21594 −0.119602
\(724\) −23.2440 + 40.2598i −0.863858 + 1.49625i
\(725\) −0.763675 1.32272i −0.0283622 0.0491247i
\(726\) −4.18280 7.24482i −0.155238 0.268880i
\(727\) 25.8544 0.958886 0.479443 0.877573i \(-0.340839\pi\)
0.479443 + 0.877573i \(0.340839\pi\)
\(728\) 64.0968 + 111.019i 2.37559 + 4.11464i
\(729\) −20.3306 −0.752985
\(730\) 93.5138 3.46110
\(731\) 5.42178 + 3.68840i 0.200532 + 0.136420i
\(732\) 3.43838 0.127086
\(733\) −12.9458 −0.478165 −0.239082 0.970999i \(-0.576847\pi\)
−0.239082 + 0.970999i \(0.576847\pi\)
\(734\) −0.638679 1.10622i −0.0235741 0.0408315i
\(735\) −3.26270 −0.120347
\(736\) −5.39370 9.34216i −0.198814 0.344356i
\(737\) −6.59150 11.4168i −0.242801 0.420544i
\(738\) −32.6042 + 56.4721i −1.20018 + 2.07877i
\(739\) −11.5875 −0.426254 −0.213127 0.977025i \(-0.568365\pi\)
−0.213127 + 0.977025i \(0.568365\pi\)
\(740\) 66.1024 114.493i 2.42997 4.20884i
\(741\) −1.64235 2.84464i −0.0603333 0.104500i
\(742\) −56.5368 −2.07553
\(743\) 13.7149 + 23.7549i 0.503151 + 0.871483i 0.999993 + 0.00364204i \(0.00115930\pi\)
−0.496843 + 0.867841i \(0.665507\pi\)
\(744\) 0.277106 0.479961i 0.0101592 0.0175962i
\(745\) 22.4716 38.9219i 0.823295 1.42599i
\(746\) −31.7670 + 55.0220i −1.16307 + 2.01450i
\(747\) −47.5964 −1.74146
\(748\) 13.1015 22.6924i 0.479037 0.829716i
\(749\) 27.2951 47.2765i 0.997341 1.72745i
\(750\) −0.235638 0.408136i −0.00860427 0.0149030i
\(751\) 18.8035 + 32.5686i 0.686150 + 1.18845i 0.973074 + 0.230493i \(0.0740340\pi\)
−0.286924 + 0.957953i \(0.592633\pi\)
\(752\) −217.647 −7.93677
\(753\) 8.21519 0.299378
\(754\) −1.52686 2.64460i −0.0556050 0.0963106i
\(755\) −7.53652 13.0536i −0.274282 0.475070i
\(756\) 19.6858 34.0968i 0.715964 1.24009i
\(757\) 1.56322 2.70757i 0.0568162 0.0984085i −0.836218 0.548397i \(-0.815238\pi\)
0.893035 + 0.449988i \(0.148572\pi\)
\(758\) 5.52403 0.200642
\(759\) −0.255800 + 0.443059i −0.00928496 + 0.0160820i
\(760\) 44.9100 77.7864i 1.62906 2.82161i
\(761\) 2.25141 3.89955i 0.0816135 0.141359i −0.822330 0.569011i \(-0.807326\pi\)
0.903943 + 0.427653i \(0.140659\pi\)
\(762\) 1.11207 + 1.92616i 0.0402859 + 0.0697773i
\(763\) −42.2349 −1.52901
\(764\) 39.5236 + 68.4569i 1.42991 + 2.47668i
\(765\) −4.57414 + 7.92264i −0.165378 + 0.286444i
\(766\) −3.36291 −0.121507
\(767\) 2.78521 4.82413i 0.100568 0.174189i
\(768\) 24.3671 + 42.2050i 0.879270 + 1.52294i
\(769\) −1.87359 3.24515i −0.0675634 0.117023i 0.830265 0.557369i \(-0.188189\pi\)
−0.897828 + 0.440346i \(0.854856\pi\)
\(770\) 123.993 4.46839
\(771\) 2.61445 + 4.52836i 0.0941571 + 0.163085i
\(772\) 19.5149 0.702355
\(773\) −7.49980 −0.269749 −0.134875 0.990863i \(-0.543063\pi\)
−0.134875 + 0.990863i \(0.543063\pi\)
\(774\) −43.9513 29.8997i −1.57980 1.07472i
\(775\) −0.711921 −0.0255730
\(776\) 39.8765 1.43148
\(777\) 3.90787 + 6.76863i 0.140194 + 0.242823i
\(778\) −21.0611 −0.755076
\(779\) −10.1285 17.5430i −0.362890 0.628545i
\(780\) −12.3960 21.4705i −0.443848 0.768768i
\(781\) 2.05588 3.56089i 0.0735651 0.127419i
\(782\) −0.919066 −0.0328657
\(783\) −0.311761 + 0.539987i −0.0111414 + 0.0192975i
\(784\) −28.1568 48.7690i −1.00560 1.74175i
\(785\) −8.37881 −0.299053
\(786\) −3.70261 6.41311i −0.132068 0.228748i
\(787\) 0.0844320 0.146240i 0.00300967 0.00521291i −0.864517 0.502604i \(-0.832375\pi\)
0.867526 + 0.497391i \(0.165709\pi\)
\(788\) 23.1367 40.0739i 0.824211 1.42757i
\(789\) −0.765571 + 1.32601i −0.0272551 + 0.0472072i
\(790\) −123.820 −4.40533
\(791\) 8.70946 15.0852i 0.309673 0.536369i
\(792\) −70.6085 + 122.297i −2.50896 + 4.34565i
\(793\) −2.93547 5.08438i −0.104242 0.180552i
\(794\) −17.4988 30.3088i −0.621009 1.07562i
\(795\) 7.26916 0.257810
\(796\) −88.4692 −3.13571
\(797\) −3.75011 6.49538i −0.132836 0.230078i 0.791933 0.610608i \(-0.209075\pi\)
−0.924769 + 0.380530i \(0.875742\pi\)
\(798\) 3.99354 + 6.91702i 0.141370 + 0.244860i
\(799\) −5.53206 + 9.58182i −0.195710 + 0.338980i
\(800\) 85.2511 147.659i 3.01408 5.22054i
\(801\) 35.9300 1.26952
\(802\) 30.0013 51.9638i 1.05938 1.83491i
\(803\) 22.8366 39.5541i 0.805885 1.39583i
\(804\) 3.20474 5.55077i 0.113022 0.195760i
\(805\) −1.62864 2.82088i −0.0574019 0.0994231i
\(806\) −1.42339 −0.0501366
\(807\) −4.38347 7.59239i −0.154305 0.267265i
\(808\) −28.9333 + 50.1140i −1.01787 + 1.76300i
\(809\) −5.61490 −0.197409 −0.0987047 0.995117i \(-0.531470\pi\)
−0.0987047 + 0.995117i \(0.531470\pi\)
\(810\) 35.3534 61.2338i 1.24219 2.15154i
\(811\) 3.41144 + 5.90878i 0.119792 + 0.207485i 0.919685 0.392657i \(-0.128444\pi\)
−0.799893 + 0.600142i \(0.795111\pi\)
\(812\) 2.78069 + 4.81630i 0.0975832 + 0.169019i
\(813\) −0.609476 −0.0213752
\(814\) −43.1063 74.6623i −1.51087 2.61691i
\(815\) 41.3201 1.44738
\(816\) 7.03845 0.246395
\(817\) 14.8707 7.18007i 0.520259 0.251199i
\(818\) 15.0296 0.525496
\(819\) −32.8801 −1.14893
\(820\) −76.4469 132.410i −2.66964 4.62396i
\(821\) 26.3699 0.920317 0.460158 0.887837i \(-0.347793\pi\)
0.460158 + 0.887837i \(0.347793\pi\)
\(822\) −3.86728 6.69832i −0.134887 0.233631i
\(823\) −1.30821 2.26589i −0.0456015 0.0789841i 0.842324 0.538972i \(-0.181187\pi\)
−0.887925 + 0.459988i \(0.847854\pi\)
\(824\) 73.3372 127.024i 2.55482 4.42508i
\(825\) −8.08620 −0.281525
\(826\) −6.77253 + 11.7304i −0.235646 + 0.408152i
\(827\) 3.27062 + 5.66487i 0.113730 + 0.196987i 0.917272 0.398262i \(-0.130387\pi\)
−0.803541 + 0.595249i \(0.797053\pi\)
\(828\) 5.58005 0.193920
\(829\) 6.41224 + 11.1063i 0.222706 + 0.385739i 0.955629 0.294573i \(-0.0951776\pi\)
−0.732922 + 0.680312i \(0.761844\pi\)
\(830\) 74.5022 129.042i 2.58601 4.47910i
\(831\) 1.52388 2.63944i 0.0528629 0.0915613i
\(832\) 98.7359 171.016i 3.42305 5.92890i
\(833\) −2.86271 −0.0991871
\(834\) −0.648285 + 1.12286i −0.0224483 + 0.0388815i
\(835\) −8.43568 + 14.6110i −0.291929 + 0.505636i
\(836\) −32.9929 57.1454i −1.14108 1.97641i
\(837\) 0.145317 + 0.251696i 0.00502289 + 0.00869989i
\(838\) 0.292933 0.0101192
\(839\) −40.2093 −1.38818 −0.694090 0.719889i \(-0.744193\pi\)
−0.694090 + 0.719889i \(0.744193\pi\)
\(840\) 20.0393 + 34.7090i 0.691420 + 1.19757i
\(841\) 14.4560 + 25.0385i 0.498481 + 0.863395i
\(842\) −38.9816 + 67.5182i −1.34340 + 2.32683i
\(843\) −2.60600 + 4.51372i −0.0897554 + 0.155461i
\(844\) −106.322 −3.65976
\(845\) −0.461073 + 0.798601i −0.0158614 + 0.0274727i
\(846\) 44.8453 77.6743i 1.54181 2.67050i
\(847\) 13.0069 22.5287i 0.446924 0.774095i
\(848\) 62.7322 + 108.655i 2.15423 + 3.73124i
\(849\) −8.62915 −0.296152
\(850\) −7.26323 12.5803i −0.249127 0.431500i
\(851\) −1.13240 + 1.96137i −0.0388181 + 0.0672349i
\(852\) 1.99911 0.0684882
\(853\) 5.76068 9.97778i 0.197242 0.341633i −0.750391 0.660994i \(-0.770135\pi\)
0.947633 + 0.319361i \(0.103468\pi\)
\(854\) 7.13789 + 12.3632i 0.244254 + 0.423060i
\(855\) 11.5189 + 19.9513i 0.393937 + 0.682319i
\(856\) −194.639 −6.65263
\(857\) −26.0859 45.1821i −0.891077 1.54339i −0.838586 0.544769i \(-0.816617\pi\)
−0.0524903 0.998621i \(-0.516716\pi\)
\(858\) −16.1672 −0.551940
\(859\) 35.7423 1.21951 0.609757 0.792589i \(-0.291267\pi\)
0.609757 + 0.792589i \(0.291267\pi\)
\(860\) 112.240 54.1932i 3.82734 1.84797i
\(861\) 9.03885 0.308043
\(862\) 55.2911 1.88322
\(863\) 20.5485 + 35.5910i 0.699478 + 1.21153i 0.968648 + 0.248438i \(0.0799174\pi\)
−0.269170 + 0.963093i \(0.586749\pi\)
\(864\) −69.6056 −2.36803
\(865\) 30.1982 + 52.3048i 1.02677 + 1.77842i
\(866\) −42.2263 73.1382i −1.43491 2.48534i
\(867\) 0.178900 0.309865i 0.00607578 0.0105236i
\(868\) 2.59225 0.0879867
\(869\) −30.2376 + 52.3731i −1.02574 + 1.77663i
\(870\) −0.477358 0.826808i −0.0161840 0.0280314i
\(871\) −10.9440 −0.370824
\(872\) 75.2935 + 130.412i 2.54976 + 4.41631i
\(873\) −5.11393 + 8.85758i −0.173080 + 0.299784i
\(874\) −1.15722 + 2.00437i −0.0391437 + 0.0677988i
\(875\) 0.732746 1.26915i 0.0247713 0.0429052i
\(876\) 22.2059 0.750269
\(877\) 1.31335 2.27479i 0.0443487 0.0768142i −0.842999 0.537915i \(-0.819212\pi\)
0.887348 + 0.461101i \(0.152545\pi\)
\(878\) 0.359936 0.623428i 0.0121473 0.0210397i
\(879\) 1.48652 + 2.57473i 0.0501392 + 0.0868436i
\(880\) −137.580 238.295i −4.63782 8.03294i
\(881\) −0.449245 −0.0151355 −0.00756773 0.999971i \(-0.502409\pi\)
−0.00756773 + 0.999971i \(0.502409\pi\)
\(882\) 23.2064 0.781399
\(883\) 21.2816 + 36.8609i 0.716184 + 1.24047i 0.962501 + 0.271278i \(0.0874462\pi\)
−0.246317 + 0.969189i \(0.579221\pi\)
\(884\) −10.8763 18.8384i −0.365811 0.633603i
\(885\) 0.870771 1.50822i 0.0292706 0.0506982i
\(886\) 47.9480 83.0484i 1.61085 2.79007i
\(887\) 37.2616 1.25112 0.625560 0.780176i \(-0.284870\pi\)
0.625560 + 0.780176i \(0.284870\pi\)
\(888\) 13.9334 24.1333i 0.467573 0.809861i
\(889\) −3.45812 + 5.98963i −0.115982 + 0.200886i
\(890\) −56.2409 + 97.4121i −1.88520 + 3.26526i
\(891\) −17.2670 29.9072i −0.578465 1.00193i
\(892\) 20.6841 0.692556
\(893\) 13.9312 + 24.1295i 0.466189 + 0.807463i
\(894\) 7.12468 12.3403i 0.238285 0.412721i
\(895\) 42.6709 1.42633
\(896\) −136.042 + 235.632i −4.54486 + 7.87193i
\(897\) 0.212356 + 0.367811i 0.00709035 + 0.0122808i
\(898\) 39.9169 + 69.1381i 1.33204 + 2.30717i
\(899\) −0.0410532 −0.00136920
\(900\) 44.0982 + 76.3804i 1.46994 + 2.54601i
\(901\) 6.37800 0.212482
\(902\) −99.7042 −3.31979
\(903\) −0.543132 + 7.34836i −0.0180743 + 0.244538i
\(904\) −62.1065 −2.06563
\(905\) 24.8165 0.824929
\(906\) −2.38947 4.13869i −0.0793850 0.137499i
\(907\) −23.4878 −0.779900 −0.389950 0.920836i \(-0.627508\pi\)
−0.389950 + 0.920836i \(0.627508\pi\)
\(908\) 8.71868 + 15.1012i 0.289339 + 0.501151i
\(909\) −7.42105 12.8536i −0.246141 0.426328i
\(910\) 51.4670 89.1434i 1.70611 2.95508i
\(911\) 57.9009 1.91834 0.959171 0.282826i \(-0.0912717\pi\)
0.959171 + 0.282826i \(0.0912717\pi\)
\(912\) 8.86232 15.3500i 0.293461 0.508289i
\(913\) −36.3877 63.0253i −1.20426 2.08583i
\(914\) −97.5653 −3.22717
\(915\) −0.917747 1.58958i −0.0303398 0.0525500i
\(916\) −54.8523 + 95.0069i −1.81237 + 3.13912i
\(917\) 11.5137 19.9424i 0.380217 0.658556i
\(918\) −2.96513 + 5.13576i −0.0978639 + 0.169505i
\(919\) −15.5984 −0.514542 −0.257271 0.966339i \(-0.582823\pi\)
−0.257271 + 0.966339i \(0.582823\pi\)
\(920\) −5.80685 + 10.0578i −0.191446 + 0.331594i
\(921\) −3.67284 + 6.36155i −0.121024 + 0.209620i
\(922\) 45.2102 + 78.3064i 1.48892 + 2.57888i
\(923\) −1.70671 2.95611i −0.0561771 0.0973016i
\(924\) 29.4435 0.968620
\(925\) −35.7967 −1.17699
\(926\) −6.30808 10.9259i −0.207296 0.359048i
\(927\) 18.8101 + 32.5801i 0.617805 + 1.07007i
\(928\) 4.91603 8.51482i 0.161377 0.279513i
\(929\) −6.49920 + 11.2569i −0.213232 + 0.369328i −0.952724 0.303837i \(-0.901732\pi\)
0.739492 + 0.673165i \(0.235066\pi\)
\(930\) −0.445008 −0.0145924
\(931\) −3.60453 + 6.24323i −0.118134 + 0.204614i
\(932\) −64.6378 + 111.956i −2.11728 + 3.66724i
\(933\) −5.97193 + 10.3437i −0.195512 + 0.338637i
\(934\) −14.7307 25.5143i −0.482002 0.834852i
\(935\) −13.9878 −0.457450
\(936\) 58.6165 + 101.527i 1.91594 + 3.31850i
\(937\) −14.5157 + 25.1420i −0.474209 + 0.821353i −0.999564 0.0295296i \(-0.990599\pi\)
0.525355 + 0.850883i \(0.323932\pi\)
\(938\) 26.6115 0.868896
\(939\) −0.421355 + 0.729808i −0.0137504 + 0.0238164i
\(940\) 105.149 + 182.123i 3.42957 + 5.94019i
\(941\) 21.2439 + 36.7955i 0.692531 + 1.19950i 0.971006 + 0.239056i \(0.0768379\pi\)
−0.278475 + 0.960444i \(0.589829\pi\)
\(942\) −2.65653 −0.0865543
\(943\) 1.30961 + 2.26831i 0.0426467 + 0.0738663i
\(944\) 30.0587 0.978327
\(945\) −21.0175 −0.683701
\(946\) 5.99109 81.0571i 0.194787 2.63539i
\(947\) 26.2065 0.851596 0.425798 0.904818i \(-0.359993\pi\)
0.425798 + 0.904818i \(0.359993\pi\)
\(948\) −29.4026 −0.954952
\(949\) −18.9581 32.8363i −0.615405 1.06591i
\(950\) −36.5814 −1.18686
\(951\) −0.887936 1.53795i −0.0287933 0.0498714i
\(952\) 17.5826 + 30.4539i 0.569854 + 0.987017i
\(953\) −5.44630 + 9.43327i −0.176423 + 0.305574i −0.940653 0.339370i \(-0.889786\pi\)
0.764230 + 0.644944i \(0.223119\pi\)
\(954\) −51.7028 −1.67394
\(955\) 21.0987 36.5441i 0.682739 1.18254i
\(956\) −19.6328 34.0049i −0.634969 1.09980i
\(957\) −0.466294 −0.0150731
\(958\) −39.5770 68.5494i −1.27867 2.21473i
\(959\) 12.0258 20.8293i 0.388333 0.672613i
\(960\) 30.8688 53.4664i 0.996287 1.72562i
\(961\) 15.4904 26.8302i 0.499691 0.865491i
\(962\) −71.5704 −2.30752
\(963\) 24.9613 43.2343i 0.804367 1.39321i
\(964\) −26.8161 + 46.4468i −0.863688 + 1.49595i
\(965\) −5.20877 9.02185i −0.167676 0.290424i
\(966\) −0.516364 0.894369i −0.0166137 0.0287758i
\(967\) 17.0277 0.547575 0.273788 0.961790i \(-0.411723\pi\)
0.273788 + 0.961790i \(0.411723\pi\)
\(968\) −92.7515 −2.98115
\(969\) −0.450518 0.780320i −0.0144727 0.0250675i
\(970\) −16.0096 27.7294i −0.514037 0.890337i
\(971\) 8.24939 14.2884i 0.264735 0.458535i −0.702759 0.711428i \(-0.748049\pi\)
0.967494 + 0.252893i \(0.0813821\pi\)
\(972\) 27.2002 47.1121i 0.872445 1.51112i
\(973\) −4.03185 −0.129255
\(974\) 34.2130 59.2587i 1.09626 1.89877i
\(975\) −3.35643 + 5.81350i −0.107492 + 0.186181i
\(976\) 15.8401 27.4359i 0.507031 0.878203i
\(977\) 9.22895 + 15.9850i 0.295260 + 0.511406i 0.975045 0.222005i \(-0.0712603\pi\)
−0.679785 + 0.733411i \(0.737927\pi\)
\(978\) 13.1006 0.418912
\(979\) 27.4687 + 47.5771i 0.877902 + 1.52057i
\(980\) −27.2060 + 47.1221i −0.869063 + 1.50526i
\(981\) −38.6238 −1.23316
\(982\) −17.4399 + 30.2069i −0.556531 + 0.963940i
\(983\) −23.7452 41.1279i −0.757355 1.31178i −0.944195 0.329387i \(-0.893158\pi\)
0.186840 0.982390i \(-0.440175\pi\)
\(984\) −16.1138 27.9100i −0.513690 0.889738i
\(985\) −24.7019 −0.787069
\(986\) −0.418837 0.725447i −0.0133385 0.0231029i
\(987\) −12.4324 −0.395729
\(988\) −54.7789 −1.74275
\(989\) −1.92277 + 0.928381i −0.0611406 + 0.0295208i
\(990\) 113.391 3.60381
\(991\) −49.9779 −1.58760 −0.793800 0.608179i \(-0.791900\pi\)
−0.793800 + 0.608179i \(0.791900\pi\)
\(992\) −2.29144 3.96889i −0.0727533 0.126012i
\(993\) 6.00982 0.190716
\(994\) 4.15004 + 7.18808i 0.131631 + 0.227992i
\(995\) 23.6136 + 40.8999i 0.748600 + 1.29661i
\(996\) 17.6914 30.6424i 0.560574 0.970942i
\(997\) 28.9097 0.915581 0.457790 0.889060i \(-0.348641\pi\)
0.457790 + 0.889060i \(0.348641\pi\)
\(998\) 17.6465 30.5646i 0.558589 0.967504i
\(999\) 7.30679 + 12.6557i 0.231177 + 0.400410i
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 731.2.e.a.681.1 yes 58
43.6 even 3 inner 731.2.e.a.307.1 58
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.e.a.307.1 58 43.6 even 3 inner
731.2.e.a.681.1 yes 58 1.1 even 1 trivial