Properties

Label 471.2.l.b.50.1
Level $471$
Weight $2$
Character 471.50
Analytic conductor $3.761$
Analytic rank $0$
Dimension $200$
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] = [471,2,Mod(50,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.50");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.l (of order \(12\), degree \(4\), 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: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(50\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 50.1
Character \(\chi\) \(=\) 471.50
Dual form 471.2.l.b.179.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96449 + 1.96449i) q^{2} +(1.24725 - 1.20182i) q^{3} -5.71848i q^{4} +(0.309034 + 1.15333i) q^{5} +(-0.0892417 + 4.81118i) q^{6} +(0.541767 - 0.541767i) q^{7} +(7.30492 + 7.30492i) q^{8} +(0.111255 - 2.99794i) q^{9} +O(q^{10})\) \(q+(-1.96449 + 1.96449i) q^{2} +(1.24725 - 1.20182i) q^{3} -5.71848i q^{4} +(0.309034 + 1.15333i) q^{5} +(-0.0892417 + 4.81118i) q^{6} +(0.541767 - 0.541767i) q^{7} +(7.30492 + 7.30492i) q^{8} +(0.111255 - 2.99794i) q^{9} +(-2.87281 - 1.65862i) q^{10} +(1.31307 + 0.758101i) q^{11} +(-6.87258 - 7.13236i) q^{12} +(2.56534 - 1.48110i) q^{13} +2.12860i q^{14} +(1.77154 + 1.06709i) q^{15} -17.2640 q^{16} +(-5.32373 - 3.07366i) q^{17} +(5.67087 + 6.10799i) q^{18} +(-0.00374694 + 0.00648989i) q^{19} +(6.59530 - 1.76721i) q^{20} +(0.0246110 - 1.32682i) q^{21} +(-4.06880 + 1.09023i) q^{22} +(0.588702 + 0.588702i) q^{23} +(17.8903 + 0.331843i) q^{24} +(3.09545 - 1.78716i) q^{25} +(-2.12998 + 7.94921i) q^{26} +(-3.46422 - 3.87288i) q^{27} +(-3.09808 - 3.09808i) q^{28} +(4.12702 - 4.12702i) q^{29} +(-5.57647 + 1.38390i) q^{30} +(4.08023 - 2.35572i) q^{31} +(19.3052 - 19.3052i) q^{32} +(2.54883 - 0.632534i) q^{33} +(16.4966 - 4.42026i) q^{34} +(0.792262 + 0.457413i) q^{35} +(-17.1436 - 0.636207i) q^{36} +(4.71018 + 8.15826i) q^{37} +(-0.00538851 - 0.0201102i) q^{38} +(1.41960 - 4.93038i) q^{39} +(-6.16753 + 10.6825i) q^{40} +(6.88990 - 6.88990i) q^{41} +(2.55819 + 2.65489i) q^{42} +(1.01943 - 3.80457i) q^{43} +(4.33518 - 7.50876i) q^{44} +(3.49200 - 0.798152i) q^{45} -2.31300 q^{46} +(-9.16831 + 5.29333i) q^{47} +(-21.5325 + 20.7482i) q^{48} +6.41298i q^{49} +(-2.57013 + 9.59187i) q^{50} +(-10.3340 + 2.56456i) q^{51} +(-8.46963 - 14.6698i) q^{52} +(-0.178270 + 0.665312i) q^{53} +(14.4137 + 0.802807i) q^{54} +(-0.468559 + 1.74869i) q^{55} +7.91513 q^{56} +(0.00312632 + 0.0125977i) q^{57} +16.2150i q^{58} +(2.91251 - 2.91251i) q^{59} +(6.10211 - 10.1305i) q^{60} +(-7.70188 + 2.06371i) q^{61} +(-3.38779 + 12.6434i) q^{62} +(-1.56391 - 1.68446i) q^{63} +41.3219i q^{64} +(2.50098 + 2.50098i) q^{65} +(-3.76454 + 6.24976i) q^{66} +12.8409 q^{67} +(-17.5766 + 30.4436i) q^{68} +(1.44177 + 0.0267432i) q^{69} +(-2.45498 + 0.657809i) q^{70} +(2.72295 - 1.57210i) q^{71} +(22.7124 - 21.0870i) q^{72} +(-7.31642 + 1.96043i) q^{73} +(-25.2800 - 6.77375i) q^{74} +(1.71295 - 5.94921i) q^{75} +(0.0371123 + 0.0214268i) q^{76} +(1.12209 - 0.300664i) q^{77} +(6.89690 + 12.4745i) q^{78} +(10.9814 - 10.9814i) q^{79} +(-5.33517 - 19.9111i) q^{80} +(-8.97524 - 0.667069i) q^{81} +27.0703i q^{82} +(0.00582342 - 0.0217333i) q^{83} +(-7.58741 - 0.140738i) q^{84} +(1.89973 - 7.08990i) q^{85} +(5.47138 + 9.47672i) q^{86} +(0.187480 - 10.1074i) q^{87} +(4.05400 + 15.1298i) q^{88} +(-12.2712 - 7.08476i) q^{89} +(-5.29205 + 8.42798i) q^{90} +(0.587405 - 2.19223i) q^{91} +(3.36648 - 3.36648i) q^{92} +(2.25790 - 7.84188i) q^{93} +(7.61238 - 28.4098i) q^{94} +(-0.00864293 - 0.00231587i) q^{95} +(0.876984 - 47.2798i) q^{96} +(-5.87011 - 1.57289i) q^{97} +(-12.5983 - 12.5983i) q^{98} +(2.41883 - 3.85216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200 q - 6 q^{3} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 200 q - 6 q^{3} - 10 q^{9} - 36 q^{10} - 16 q^{12} - 24 q^{13} + 8 q^{15} - 208 q^{16} + 8 q^{18} - 12 q^{19} - 24 q^{22} - 20 q^{24} - 24 q^{25} + 64 q^{28} - 14 q^{30} - 48 q^{31} + 18 q^{33} + 32 q^{34} + 78 q^{36} + 44 q^{37} - 72 q^{39} + 60 q^{40} + 42 q^{42} - 24 q^{43} - 32 q^{45} - 32 q^{46} - 102 q^{48} - 54 q^{51} + 36 q^{52} + 48 q^{54} - 20 q^{55} - 6 q^{57} - 8 q^{61} - 8 q^{63} - 32 q^{66} - 16 q^{67} - 52 q^{69} + 60 q^{70} - 42 q^{72} - 64 q^{73} - 32 q^{75} + 132 q^{76} + 106 q^{78} + 40 q^{79} + 14 q^{81} + 172 q^{84} - 160 q^{85} - 88 q^{87} + 8 q^{88} + 84 q^{91} + 220 q^{93} + 128 q^{94} - 108 q^{96} - 36 q^{97} - 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96449 + 1.96449i −1.38911 + 1.38911i −0.561906 + 0.827201i \(0.689932\pi\)
−0.827201 + 0.561906i \(0.810068\pi\)
\(3\) 1.24725 1.20182i 0.720099 0.693871i
\(4\) 5.71848i 2.85924i
\(5\) 0.309034 + 1.15333i 0.138204 + 0.515786i 0.999964 + 0.00846922i \(0.00269587\pi\)
−0.861760 + 0.507317i \(0.830637\pi\)
\(6\) −0.0892417 + 4.81118i −0.0364328 + 1.96416i
\(7\) 0.541767 0.541767i 0.204769 0.204769i −0.597271 0.802040i \(-0.703748\pi\)
0.802040 + 0.597271i \(0.203748\pi\)
\(8\) 7.30492 + 7.30492i 2.58268 + 2.58268i
\(9\) 0.111255 2.99794i 0.0370849 0.999312i
\(10\) −2.87281 1.65862i −0.908463 0.524501i
\(11\) 1.31307 + 0.758101i 0.395906 + 0.228576i 0.684716 0.728810i \(-0.259926\pi\)
−0.288810 + 0.957386i \(0.593260\pi\)
\(12\) −6.87258 7.13236i −1.98394 2.05893i
\(13\) 2.56534 1.48110i 0.711497 0.410783i −0.100118 0.994976i \(-0.531922\pi\)
0.811615 + 0.584192i \(0.198589\pi\)
\(14\) 2.12860i 0.568891i
\(15\) 1.77154 + 1.06709i 0.457410 + 0.275521i
\(16\) −17.2640 −4.31600
\(17\) −5.32373 3.07366i −1.29119 0.745471i −0.312328 0.949974i \(-0.601109\pi\)
−0.978866 + 0.204503i \(0.934442\pi\)
\(18\) 5.67087 + 6.10799i 1.33664 + 1.43967i
\(19\) −0.00374694 + 0.00648989i −0.000859607 + 0.00148888i −0.866455 0.499255i \(-0.833607\pi\)
0.865595 + 0.500744i \(0.166940\pi\)
\(20\) 6.59530 1.76721i 1.47475 0.395159i
\(21\) 0.0246110 1.32682i 0.00537057 0.289537i
\(22\) −4.06880 + 1.09023i −0.867472 + 0.232438i
\(23\) 0.588702 + 0.588702i 0.122753 + 0.122753i 0.765814 0.643062i \(-0.222336\pi\)
−0.643062 + 0.765814i \(0.722336\pi\)
\(24\) 17.8903 + 0.331843i 3.65183 + 0.0677372i
\(25\) 3.09545 1.78716i 0.619091 0.357432i
\(26\) −2.12998 + 7.94921i −0.417724 + 1.55897i
\(27\) −3.46422 3.87288i −0.666689 0.745336i
\(28\) −3.09808 3.09808i −0.585482 0.585482i
\(29\) 4.12702 4.12702i 0.766369 0.766369i −0.211096 0.977465i \(-0.567703\pi\)
0.977465 + 0.211096i \(0.0677033\pi\)
\(30\) −5.57647 + 1.38390i −1.01812 + 0.252664i
\(31\) 4.08023 2.35572i 0.732831 0.423100i −0.0866257 0.996241i \(-0.527608\pi\)
0.819457 + 0.573141i \(0.194275\pi\)
\(32\) 19.3052 19.3052i 3.41271 3.41271i
\(33\) 2.54883 0.632534i 0.443694 0.110110i
\(34\) 16.4966 4.42026i 2.82915 0.758068i
\(35\) 0.792262 + 0.457413i 0.133917 + 0.0773168i
\(36\) −17.1436 0.636207i −2.85727 0.106035i
\(37\) 4.71018 + 8.15826i 0.774348 + 1.34121i 0.935160 + 0.354225i \(0.115255\pi\)
−0.160812 + 0.986985i \(0.551411\pi\)
\(38\) −0.00538851 0.0201102i −0.000874132 0.00326230i
\(39\) 1.41960 4.93038i 0.227318 0.789492i
\(40\) −6.16753 + 10.6825i −0.975172 + 1.68905i
\(41\) 6.88990 6.88990i 1.07602 1.07602i 0.0791595 0.996862i \(-0.474776\pi\)
0.996862 0.0791595i \(-0.0252237\pi\)
\(42\) 2.55819 + 2.65489i 0.394737 + 0.409658i
\(43\) 1.01943 3.80457i 0.155462 0.580191i −0.843604 0.536966i \(-0.819570\pi\)
0.999065 0.0432247i \(-0.0137631\pi\)
\(44\) 4.33518 7.50876i 0.653554 1.13199i
\(45\) 3.49200 0.798152i 0.520556 0.118981i
\(46\) −2.31300 −0.341034
\(47\) −9.16831 + 5.29333i −1.33734 + 0.772111i −0.986412 0.164293i \(-0.947466\pi\)
−0.350924 + 0.936404i \(0.614132\pi\)
\(48\) −21.5325 + 20.7482i −3.10795 + 2.99475i
\(49\) 6.41298i 0.916140i
\(50\) −2.57013 + 9.59187i −0.363472 + 1.35650i
\(51\) −10.3340 + 2.56456i −1.44705 + 0.359110i
\(52\) −8.46963 14.6698i −1.17453 2.03434i
\(53\) −0.178270 + 0.665312i −0.0244872 + 0.0913876i −0.977088 0.212836i \(-0.931730\pi\)
0.952601 + 0.304223i \(0.0983968\pi\)
\(54\) 14.4137 + 0.802807i 1.96145 + 0.109248i
\(55\) −0.468559 + 1.74869i −0.0631805 + 0.235793i
\(56\) 7.91513 1.05770
\(57\) 0.00312632 + 0.0125977i 0.000414091 + 0.00166860i
\(58\) 16.2150i 2.12914i
\(59\) 2.91251 2.91251i 0.379176 0.379176i −0.491629 0.870805i \(-0.663598\pi\)
0.870805 + 0.491629i \(0.163598\pi\)
\(60\) 6.10211 10.1305i 0.787779 1.30784i
\(61\) −7.70188 + 2.06371i −0.986125 + 0.264231i −0.715622 0.698488i \(-0.753857\pi\)
−0.270503 + 0.962719i \(0.587190\pi\)
\(62\) −3.38779 + 12.6434i −0.430250 + 1.60571i
\(63\) −1.56391 1.68446i −0.197034 0.212222i
\(64\) 41.3219i 5.16524i
\(65\) 2.50098 + 2.50098i 0.310208 + 0.310208i
\(66\) −3.76454 + 6.24976i −0.463383 + 0.769293i
\(67\) 12.8409 1.56876 0.784381 0.620279i \(-0.212981\pi\)
0.784381 + 0.620279i \(0.212981\pi\)
\(68\) −17.5766 + 30.4436i −2.13148 + 3.69183i
\(69\) 1.44177 + 0.0267432i 0.173569 + 0.00321950i
\(70\) −2.45498 + 0.657809i −0.293426 + 0.0786233i
\(71\) 2.72295 1.57210i 0.323155 0.186573i −0.329643 0.944106i \(-0.606928\pi\)
0.652798 + 0.757532i \(0.273595\pi\)
\(72\) 22.7124 21.0870i 2.67668 2.48513i
\(73\) −7.31642 + 1.96043i −0.856323 + 0.229451i −0.660164 0.751121i \(-0.729513\pi\)
−0.196158 + 0.980572i \(0.562847\pi\)
\(74\) −25.2800 6.77375i −2.93874 0.787432i
\(75\) 1.71295 5.94921i 0.197795 0.686956i
\(76\) 0.0371123 + 0.0214268i 0.00425707 + 0.00245782i
\(77\) 1.12209 0.300664i 0.127874 0.0342638i
\(78\) 6.89690 + 12.4745i 0.780921 + 1.41246i
\(79\) 10.9814 10.9814i 1.23550 1.23550i 0.273681 0.961821i \(-0.411759\pi\)
0.961821 0.273681i \(-0.0882412\pi\)
\(80\) −5.33517 19.9111i −0.596491 2.22613i
\(81\) −8.97524 0.667069i −0.997249 0.0741188i
\(82\) 27.0703i 2.98942i
\(83\) 0.00582342 0.0217333i 0.000639204 0.00238554i −0.965605 0.260012i \(-0.916274\pi\)
0.966245 + 0.257626i \(0.0829403\pi\)
\(84\) −7.58741 0.140738i −0.827854 0.0153557i
\(85\) 1.89973 7.08990i 0.206055 0.769007i
\(86\) 5.47138 + 9.47672i 0.589995 + 1.02190i
\(87\) 0.187480 10.1074i 0.0200999 1.08362i
\(88\) 4.05400 + 15.1298i 0.432158 + 1.61284i
\(89\) −12.2712 7.08476i −1.30074 0.750983i −0.320209 0.947347i \(-0.603753\pi\)
−0.980531 + 0.196364i \(0.937087\pi\)
\(90\) −5.29205 + 8.42798i −0.557831 + 0.888387i
\(91\) 0.587405 2.19223i 0.0615768 0.229808i
\(92\) 3.36648 3.36648i 0.350979 0.350979i
\(93\) 2.25790 7.84188i 0.234134 0.813165i
\(94\) 7.61238 28.4098i 0.785157 2.93025i
\(95\) −0.00864293 0.00231587i −0.000886746 0.000237603i
\(96\) 0.876984 47.2798i 0.0895068 4.82547i
\(97\) −5.87011 1.57289i −0.596019 0.159703i −0.0518164 0.998657i \(-0.516501\pi\)
−0.544203 + 0.838954i \(0.683168\pi\)
\(98\) −12.5983 12.5983i −1.27262 1.27262i
\(99\) 2.41883 3.85216i 0.243101 0.387157i
\(100\) −10.2198 17.7013i −1.02198 1.77013i
\(101\) 13.8430i 1.37743i 0.725031 + 0.688717i \(0.241826\pi\)
−0.725031 + 0.688717i \(0.758174\pi\)
\(102\) 15.2630 25.3391i 1.51126 2.50895i
\(103\) 4.37535 + 4.37535i 0.431116 + 0.431116i 0.889008 0.457892i \(-0.151395\pi\)
−0.457892 + 0.889008i \(0.651395\pi\)
\(104\) 29.5589 + 7.92029i 2.89849 + 0.776649i
\(105\) 1.53787 0.381650i 0.150081 0.0372452i
\(106\) −0.956791 1.65721i −0.0929317 0.160963i
\(107\) 10.1518 + 2.72016i 0.981409 + 0.262968i 0.713638 0.700515i \(-0.247046\pi\)
0.267771 + 0.963482i \(0.413713\pi\)
\(108\) −22.1470 + 19.8101i −2.13109 + 1.90622i
\(109\) −5.50360 + 9.53251i −0.527149 + 0.913049i 0.472351 + 0.881411i \(0.343406\pi\)
−0.999499 + 0.0316378i \(0.989928\pi\)
\(110\) −2.51480 4.35576i −0.239777 0.415306i
\(111\) 15.6795 + 4.51459i 1.48823 + 0.428506i
\(112\) −9.35307 + 9.35307i −0.883782 + 0.883782i
\(113\) 8.16907 + 4.71642i 0.768482 + 0.443683i 0.832333 0.554276i \(-0.187005\pi\)
−0.0638509 + 0.997959i \(0.520338\pi\)
\(114\) −0.0308897 0.0186064i −0.00289308 0.00174265i
\(115\) −0.497040 + 0.860898i −0.0463492 + 0.0802791i
\(116\) −23.6003 23.6003i −2.19123 2.19123i
\(117\) −4.15484 7.85551i −0.384115 0.726242i
\(118\) 11.4432i 1.05343i
\(119\) −4.54943 + 1.21901i −0.417045 + 0.111747i
\(120\) 5.14598 + 20.7360i 0.469762 + 1.89293i
\(121\) −4.35056 7.53540i −0.395506 0.685036i
\(122\) 11.0762 19.1845i 1.00279 1.73688i
\(123\) 0.312990 16.8738i 0.0282213 1.52146i
\(124\) −13.4711 23.3327i −1.20974 2.09534i
\(125\) 7.23928 + 7.23928i 0.647501 + 0.647501i
\(126\) 6.38139 + 0.236816i 0.568500 + 0.0210973i
\(127\) −7.18114 + 4.14603i −0.637223 + 0.367901i −0.783544 0.621336i \(-0.786590\pi\)
0.146321 + 0.989237i \(0.453257\pi\)
\(128\) −42.5662 42.5662i −3.76236 3.76236i
\(129\) −3.30092 5.97041i −0.290630 0.525665i
\(130\) −9.82632 −0.861825
\(131\) −13.7967 3.69682i −1.20542 0.322992i −0.400459 0.916315i \(-0.631149\pi\)
−0.804965 + 0.593323i \(0.797816\pi\)
\(132\) −3.61713 14.5754i −0.314831 1.26863i
\(133\) 0.00148604 + 0.00554598i 0.000128856 + 0.000480897i
\(134\) −25.2258 + 25.2258i −2.17918 + 2.17918i
\(135\) 3.39615 5.19225i 0.292294 0.446878i
\(136\) −16.4366 61.3423i −1.40943 5.26006i
\(137\) 1.40183 + 5.23168i 0.119766 + 0.446973i 0.999599 0.0283097i \(-0.00901247\pi\)
−0.879833 + 0.475283i \(0.842346\pi\)
\(138\) −2.88489 + 2.77981i −0.245578 + 0.236633i
\(139\) −19.0911 5.11545i −1.61929 0.433887i −0.668496 0.743716i \(-0.733062\pi\)
−0.950792 + 0.309828i \(0.899728\pi\)
\(140\) 2.61570 4.53053i 0.221067 0.382900i
\(141\) −5.07353 + 17.6208i −0.427268 + 1.48394i
\(142\) −2.26085 + 8.43759i −0.189726 + 0.708067i
\(143\) 4.49130 0.375581
\(144\) −1.92070 + 51.7564i −0.160058 + 4.31303i
\(145\) 6.03522 + 3.48444i 0.501198 + 0.289367i
\(146\) 10.5218 18.2243i 0.870792 1.50826i
\(147\) 7.70725 + 7.99857i 0.635683 + 0.659711i
\(148\) 46.6528 26.9350i 3.83484 2.21405i
\(149\) 1.08749 1.08749i 0.0890910 0.0890910i −0.661157 0.750248i \(-0.729934\pi\)
0.750248 + 0.661157i \(0.229934\pi\)
\(150\) 8.32211 + 15.0523i 0.679498 + 1.22901i
\(151\) 3.39495 0.909674i 0.276277 0.0740283i −0.118020 0.993011i \(-0.537655\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(152\) −0.0747793 + 0.0200370i −0.00606540 + 0.00162522i
\(153\) −9.80692 + 15.6182i −0.792842 + 1.26266i
\(154\) −1.61369 + 2.79500i −0.130035 + 0.225227i
\(155\) 3.97786 + 3.97786i 0.319510 + 0.319510i
\(156\) −28.1942 8.11794i −2.25735 0.649955i
\(157\) 0.851339 + 12.5010i 0.0679443 + 0.997689i
\(158\) 43.1457i 3.43249i
\(159\) 0.577239 + 1.04406i 0.0457780 + 0.0827991i
\(160\) 28.2313 + 16.2993i 2.23188 + 1.28858i
\(161\) 0.637878 0.0502718
\(162\) 18.9423 16.3214i 1.48825 1.28233i
\(163\) 1.80318 + 6.72957i 0.141236 + 0.527100i 0.999894 + 0.0145515i \(0.00463204\pi\)
−0.858658 + 0.512549i \(0.828701\pi\)
\(164\) −39.3997 39.3997i −3.07660 3.07660i
\(165\) 1.51720 + 2.74417i 0.118114 + 0.213633i
\(166\) 0.0312549 + 0.0541351i 0.00242585 + 0.00420169i
\(167\) −3.84807 + 6.66505i −0.297772 + 0.515757i −0.975626 0.219440i \(-0.929577\pi\)
0.677854 + 0.735197i \(0.262910\pi\)
\(168\) 9.87213 9.51257i 0.761651 0.733910i
\(169\) −2.11269 + 3.65928i −0.162514 + 0.281483i
\(170\) 10.1960 + 17.6601i 0.782001 + 1.35447i
\(171\) 0.0190394 + 0.0119551i 0.00145598 + 0.000914231i
\(172\) −21.7563 5.82959i −1.65890 0.444502i
\(173\) 8.93317i 0.679176i −0.940574 0.339588i \(-0.889712\pi\)
0.940574 0.339588i \(-0.110288\pi\)
\(174\) 19.4876 + 20.2242i 1.47735 + 1.53319i
\(175\) 0.708790 2.64524i 0.0535795 0.199961i
\(176\) −22.6689 13.0879i −1.70873 0.986535i
\(177\) 0.132307 7.13292i 0.00994483 0.536143i
\(178\) 38.0246 10.1887i 2.85006 0.763672i
\(179\) 6.90624 + 25.7745i 0.516197 + 1.92647i 0.330126 + 0.943937i \(0.392909\pi\)
0.186071 + 0.982536i \(0.440425\pi\)
\(180\) −4.56421 19.9689i −0.340196 1.48839i
\(181\) −0.143431 + 0.0384323i −0.0106612 + 0.00285665i −0.264146 0.964483i \(-0.585090\pi\)
0.253485 + 0.967339i \(0.418423\pi\)
\(182\) 3.15266 + 5.46057i 0.233691 + 0.404764i
\(183\) −7.12595 + 11.8302i −0.526765 + 0.874517i
\(184\) 8.60084i 0.634063i
\(185\) −7.95358 + 7.95358i −0.584759 + 0.584759i
\(186\) 10.9697 + 19.8410i 0.804336 + 1.45481i
\(187\) −4.66029 8.07186i −0.340794 0.590273i
\(188\) 30.2698 + 52.4288i 2.20765 + 3.82376i
\(189\) −3.97500 0.221398i −0.289138 0.0161043i
\(190\) 0.0215285 0.0124295i 0.00156184 0.000901730i
\(191\) −5.63406 21.0266i −0.407666 1.52143i −0.799085 0.601218i \(-0.794682\pi\)
0.391419 0.920212i \(-0.371984\pi\)
\(192\) 49.6615 + 51.5386i 3.58401 + 3.71948i
\(193\) −17.5879 + 10.1544i −1.26601 + 0.730928i −0.974230 0.225558i \(-0.927579\pi\)
−0.291776 + 0.956487i \(0.594246\pi\)
\(194\) 14.6217 8.44186i 1.04978 0.606090i
\(195\) 6.12507 + 0.113613i 0.438625 + 0.00813598i
\(196\) 36.6725 2.61946
\(197\) −8.27273 4.77626i −0.589407 0.340295i 0.175456 0.984487i \(-0.443860\pi\)
−0.764863 + 0.644193i \(0.777193\pi\)
\(198\) 2.81578 + 12.3193i 0.200108 + 0.875495i
\(199\) −9.05741 5.22930i −0.642063 0.370695i 0.143346 0.989673i \(-0.454214\pi\)
−0.785409 + 0.618977i \(0.787547\pi\)
\(200\) 35.6671 + 9.55698i 2.52205 + 0.675780i
\(201\) 16.0158 15.4324i 1.12966 1.08852i
\(202\) −27.1946 27.1946i −1.91340 1.91340i
\(203\) 4.47177i 0.313857i
\(204\) 14.6654 + 59.0947i 1.02678 + 4.13746i
\(205\) 10.0756 + 5.81713i 0.703708 + 0.406286i
\(206\) −17.1907 −1.19773
\(207\) 1.83039 1.69939i 0.127221 0.118116i
\(208\) −44.2881 + 25.5697i −3.07082 + 1.77294i
\(209\) −0.00983999 + 0.00568112i −0.000680646 + 0.000392971i
\(210\) −2.27140 + 3.77089i −0.156741 + 0.260216i
\(211\) −6.03975 + 6.03975i −0.415793 + 0.415793i −0.883751 0.467958i \(-0.844990\pi\)
0.467958 + 0.883751i \(0.344990\pi\)
\(212\) 3.80457 + 1.01943i 0.261299 + 0.0700148i
\(213\) 1.50682 5.23329i 0.103245 0.358579i
\(214\) −25.2868 + 14.5994i −1.72857 + 0.997992i
\(215\) 4.70297 0.320740
\(216\) 2.98522 53.5969i 0.203118 3.64681i
\(217\) 0.934282 3.48679i 0.0634232 0.236699i
\(218\) −7.91477 29.5383i −0.536056 2.00059i
\(219\) −6.76931 + 11.2382i −0.457428 + 0.759405i
\(220\) 9.99982 + 2.67944i 0.674187 + 0.180648i
\(221\) −18.2096 −1.22491
\(222\) −39.6712 + 21.9335i −2.66256 + 1.47208i
\(223\) −2.91756 0.781757i −0.195374 0.0523503i 0.159805 0.987149i \(-0.448913\pi\)
−0.355179 + 0.934798i \(0.615580\pi\)
\(224\) 20.9178i 1.39763i
\(225\) −5.01341 9.47880i −0.334227 0.631920i
\(226\) −25.3135 + 6.78272i −1.68383 + 0.451180i
\(227\) 4.30898 + 16.0813i 0.285997 + 1.06735i 0.948108 + 0.317949i \(0.102994\pi\)
−0.662111 + 0.749406i \(0.730339\pi\)
\(228\) 0.0720394 0.0178778i 0.00477092 0.00118399i
\(229\) 0.938898 + 0.251577i 0.0620442 + 0.0166247i 0.289708 0.957115i \(-0.406442\pi\)
−0.227663 + 0.973740i \(0.573109\pi\)
\(230\) −0.714797 2.66766i −0.0471324 0.175900i
\(231\) 1.03818 1.72356i 0.0683074 0.113402i
\(232\) 60.2952 3.95857
\(233\) 6.53444 11.3180i 0.428085 0.741466i −0.568618 0.822602i \(-0.692522\pi\)
0.996703 + 0.0811364i \(0.0258549\pi\)
\(234\) 23.5942 + 7.26994i 1.54240 + 0.475251i
\(235\) −8.93829 8.93829i −0.583070 0.583070i
\(236\) −16.6551 16.6551i −1.08415 1.08415i
\(237\) 0.498855 26.8941i 0.0324041 1.74696i
\(238\) 6.54257 11.3321i 0.424092 0.734549i
\(239\) 5.84761 0.378250 0.189125 0.981953i \(-0.439435\pi\)
0.189125 + 0.981953i \(0.439435\pi\)
\(240\) −30.5839 18.4222i −1.97418 1.18915i
\(241\) −0.0128862 0.0480921i −0.000830076 0.00309789i 0.965510 0.260368i \(-0.0838438\pi\)
−0.966340 + 0.257270i \(0.917177\pi\)
\(242\) 23.3499 + 6.25659i 1.50099 + 0.402189i
\(243\) −11.9961 + 9.95463i −0.769547 + 0.638590i
\(244\) 11.8013 + 44.0430i 0.755501 + 2.81957i
\(245\) −7.39629 + 1.98183i −0.472532 + 0.126615i
\(246\) 32.5337 + 33.7634i 2.07427 + 2.15268i
\(247\) 0.0221984i 0.00141245i
\(248\) 47.0142 + 12.5974i 2.98540 + 0.799936i
\(249\) −0.0188563 0.0341055i −0.00119497 0.00216135i
\(250\) −28.4431 −1.79890
\(251\) 17.5175 + 4.69379i 1.10569 + 0.296269i 0.765081 0.643934i \(-0.222699\pi\)
0.340612 + 0.940204i \(0.389366\pi\)
\(252\) −9.63252 + 8.94317i −0.606792 + 0.563367i
\(253\) 0.326711 + 1.21930i 0.0205402 + 0.0766569i
\(254\) 5.96245 22.2522i 0.374117 1.39623i
\(255\) −6.15135 11.1260i −0.385212 0.696737i
\(256\) 84.5984 5.28740
\(257\) −24.5754 + 14.1886i −1.53297 + 0.885063i −0.533752 + 0.845641i \(0.679218\pi\)
−0.999223 + 0.0394220i \(0.987448\pi\)
\(258\) 18.2135 + 5.24419i 1.13392 + 0.326489i
\(259\) 6.97169 + 1.86806i 0.433200 + 0.116076i
\(260\) 14.3018 14.3018i 0.886959 0.886959i
\(261\) −11.9134 12.8317i −0.737421 0.794263i
\(262\) 34.3659 19.8412i 2.12313 1.22579i
\(263\) −0.989643 + 0.571371i −0.0610240 + 0.0352322i −0.530202 0.847872i \(-0.677884\pi\)
0.469178 + 0.883104i \(0.344550\pi\)
\(264\) 23.2396 + 13.9984i 1.43030 + 0.861540i
\(265\) −0.822417 −0.0505207
\(266\) −0.0138144 0.00797572i −0.000847012 0.000489023i
\(267\) −23.8198 + 5.91128i −1.45775 + 0.361765i
\(268\) 73.4302i 4.48546i
\(269\) −1.17971 1.17971i −0.0719280 0.0719280i 0.670228 0.742156i \(-0.266196\pi\)
−0.742156 + 0.670228i \(0.766196\pi\)
\(270\) 3.52842 + 16.8719i 0.214733 + 1.02679i
\(271\) 7.73832 + 2.07348i 0.470069 + 0.125955i 0.486075 0.873917i \(-0.338428\pi\)
−0.0160055 + 0.999872i \(0.505095\pi\)
\(272\) 91.9089 + 53.0636i 5.57280 + 3.21746i
\(273\) −1.90202 3.44021i −0.115116 0.208211i
\(274\) −13.0315 7.52374i −0.787261 0.454525i
\(275\) 5.41940 0.326802
\(276\) 0.152930 8.24473i 0.00920531 0.496275i
\(277\) −8.86309 + 5.11711i −0.532532 + 0.307457i −0.742047 0.670348i \(-0.766145\pi\)
0.209515 + 0.977805i \(0.432811\pi\)
\(278\) 47.5537 27.4551i 2.85208 1.64665i
\(279\) −6.60836 12.4944i −0.395632 0.748018i
\(280\) 2.44605 + 9.12877i 0.146179 + 0.545549i
\(281\) −24.3523 + 14.0598i −1.45274 + 0.838739i −0.998636 0.0522102i \(-0.983373\pi\)
−0.454103 + 0.890949i \(0.650040\pi\)
\(282\) −24.6490 44.5828i −1.46782 2.65487i
\(283\) −4.60995 7.98466i −0.274033 0.474639i 0.695858 0.718180i \(-0.255024\pi\)
−0.969891 + 0.243541i \(0.921691\pi\)
\(284\) −8.98999 15.5711i −0.533458 0.923976i
\(285\) −0.0135631 + 0.00749880i −0.000803411 + 0.000444190i
\(286\) −8.82312 + 8.82312i −0.521722 + 0.521722i
\(287\) 7.46544i 0.440671i
\(288\) −55.7280 60.0236i −3.28380 3.53692i
\(289\) 10.3947 + 18.0042i 0.611455 + 1.05907i
\(290\) −18.7013 + 5.01100i −1.09818 + 0.294256i
\(291\) −9.21181 + 5.09303i −0.540006 + 0.298559i
\(292\) 11.2107 + 41.8388i 0.656055 + 2.44843i
\(293\) 2.02383 0.542283i 0.118233 0.0316805i −0.199217 0.979955i \(-0.563840\pi\)
0.317451 + 0.948275i \(0.397173\pi\)
\(294\) −30.8540 0.572305i −1.79944 0.0333775i
\(295\) 4.25915 + 2.45902i 0.247977 + 0.143170i
\(296\) −25.1880 + 94.0030i −1.46402 + 5.46381i
\(297\) −1.61273 7.71159i −0.0935800 0.447472i
\(298\) 4.27275i 0.247514i
\(299\) 2.38215 + 0.638294i 0.137763 + 0.0369135i
\(300\) −34.0204 9.79547i −1.96417 0.565542i
\(301\) −1.50889 2.61348i −0.0869712 0.150639i
\(302\) −4.88231 + 8.45641i −0.280945 + 0.486612i
\(303\) 16.6368 + 17.2657i 0.955762 + 0.991888i
\(304\) 0.0646872 0.112042i 0.00371007 0.00642602i
\(305\) −4.76030 8.24507i −0.272574 0.472112i
\(306\) −11.4163 49.9476i −0.652628 2.85531i
\(307\) 11.0169 + 11.0169i 0.628767 + 0.628767i 0.947758 0.318991i \(-0.103344\pi\)
−0.318991 + 0.947758i \(0.603344\pi\)
\(308\) −1.71934 6.41666i −0.0979684 0.365623i
\(309\) 10.7155 + 0.198761i 0.609586 + 0.0113071i
\(310\) −15.6290 −0.887667
\(311\) −8.63376 4.98470i −0.489575 0.282656i 0.234823 0.972038i \(-0.424549\pi\)
−0.724398 + 0.689382i \(0.757882\pi\)
\(312\) 46.3861 25.6460i 2.62610 1.45192i
\(313\) 22.8426i 1.29114i 0.763702 + 0.645569i \(0.223380\pi\)
−0.763702 + 0.645569i \(0.776620\pi\)
\(314\) −26.2306 22.8857i −1.48028 1.29152i
\(315\) 1.45944 2.32426i 0.0822299 0.130957i
\(316\) −62.7967 62.7967i −3.53259 3.53259i
\(317\) 6.09882 10.5635i 0.342544 0.593304i −0.642360 0.766403i \(-0.722045\pi\)
0.984904 + 0.173099i \(0.0553781\pi\)
\(318\) −3.18502 0.917061i −0.178607 0.0514262i
\(319\) 8.54778 2.29037i 0.478584 0.128236i
\(320\) −47.6579 + 12.7699i −2.66416 + 0.713858i
\(321\) 15.9309 8.80790i 0.889178 0.491609i
\(322\) −1.25311 + 1.25311i −0.0698330 + 0.0698330i
\(323\) 0.0398954 0.0230336i 0.00221984 0.00128162i
\(324\) −3.81462 + 51.3247i −0.211923 + 2.85137i
\(325\) 5.29393 9.16935i 0.293654 0.508624i
\(326\) −16.7625 9.67786i −0.928391 0.536007i
\(327\) 4.59201 + 18.5037i 0.253939 + 1.02326i
\(328\) 100.660 5.55804
\(329\) −2.09934 + 7.83483i −0.115740 + 0.431948i
\(330\) −8.37143 2.41038i −0.460832 0.132687i
\(331\) −15.9703 + 27.6613i −0.877806 + 1.52040i −0.0240630 + 0.999710i \(0.507660\pi\)
−0.853743 + 0.520694i \(0.825673\pi\)
\(332\) −0.124281 0.0333011i −0.00682083 0.00182764i
\(333\) 24.9820 13.2132i 1.36900 0.724077i
\(334\) −5.53394 20.6529i −0.302804 1.13008i
\(335\) 3.96827 + 14.8098i 0.216810 + 0.809145i
\(336\) −0.424885 + 22.9063i −0.0231794 + 1.24964i
\(337\) −9.82705 + 9.82705i −0.535314 + 0.535314i −0.922149 0.386835i \(-0.873568\pi\)
0.386835 + 0.922149i \(0.373568\pi\)
\(338\) −3.03827 11.3390i −0.165260 0.616760i
\(339\) 15.8571 3.93522i 0.861242 0.213732i
\(340\) −40.5434 10.8636i −2.19877 0.589160i
\(341\) 7.14351 0.386843
\(342\) −0.0608886 + 0.0139171i −0.00329248 + 0.000752548i
\(343\) 7.26671 + 7.26671i 0.392365 + 0.392365i
\(344\) 35.2389 20.3452i 1.89996 1.09694i
\(345\) 0.414713 + 1.67111i 0.0223274 + 0.0899693i
\(346\) 17.5492 + 17.5492i 0.943448 + 0.943448i
\(347\) −4.09598 7.09444i −0.219884 0.380850i 0.734889 0.678188i \(-0.237234\pi\)
−0.954772 + 0.297338i \(0.903901\pi\)
\(348\) −57.7987 1.07210i −3.09834 0.0574705i
\(349\) 3.42483 5.93198i 0.183327 0.317532i −0.759684 0.650292i \(-0.774647\pi\)
0.943012 + 0.332760i \(0.107980\pi\)
\(350\) 3.80414 + 6.58897i 0.203340 + 0.352195i
\(351\) −14.6230 4.80439i −0.780519 0.256440i
\(352\) 39.9844 10.7138i 2.13117 0.571047i
\(353\) 19.6375i 1.04520i 0.852579 + 0.522599i \(0.175037\pi\)
−0.852579 + 0.522599i \(0.824963\pi\)
\(354\) 13.7527 + 14.2725i 0.730946 + 0.758575i
\(355\) 2.65463 + 2.65463i 0.140893 + 0.140893i
\(356\) −40.5140 + 70.1723i −2.14724 + 3.71913i
\(357\) −4.20922 + 6.98801i −0.222776 + 0.369845i
\(358\) −64.2010 37.0665i −3.39313 1.95902i
\(359\) 10.7875 10.7875i 0.569343 0.569343i −0.362601 0.931944i \(-0.618111\pi\)
0.931944 + 0.362601i \(0.118111\pi\)
\(360\) 31.3392 + 19.6783i 1.65172 + 1.03714i
\(361\) 9.49997 + 16.4544i 0.499999 + 0.866023i
\(362\) 0.206270 0.357270i 0.0108413 0.0187777i
\(363\) −14.4824 4.16991i −0.760130 0.218864i
\(364\) −12.5362 3.35906i −0.657075 0.176063i
\(365\) −4.52205 7.83243i −0.236695 0.409968i
\(366\) −9.24157 37.2393i −0.483065 1.94653i
\(367\) 25.3253 + 6.78591i 1.32197 + 0.354221i 0.849716 0.527240i \(-0.176773\pi\)
0.472256 + 0.881462i \(0.343440\pi\)
\(368\) −10.1634 10.1634i −0.529801 0.529801i
\(369\) −19.8889 21.4220i −1.03538 1.11519i
\(370\) 31.2495i 1.62459i
\(371\) 0.263863 + 0.457024i 0.0136991 + 0.0237275i
\(372\) −44.8436 12.9118i −2.32503 0.669444i
\(373\) 5.54367 + 5.54367i 0.287040 + 0.287040i 0.835909 0.548869i \(-0.184941\pi\)
−0.548869 + 0.835909i \(0.684941\pi\)
\(374\) 25.0122 + 6.70200i 1.29335 + 0.346552i
\(375\) 17.7295 + 0.328861i 0.915547 + 0.0169823i
\(376\) −105.641 28.3065i −5.44803 1.45979i
\(377\) 4.47469 16.6998i 0.230458 0.860081i
\(378\) 8.24379 7.37392i 0.424015 0.379274i
\(379\) 6.14647 6.14647i 0.315723 0.315723i −0.531399 0.847122i \(-0.678333\pi\)
0.847122 + 0.531399i \(0.178333\pi\)
\(380\) −0.0132432 + 0.0494244i −0.000679363 + 0.00253542i
\(381\) −3.97387 + 13.8016i −0.203588 + 0.707076i
\(382\) 52.3747 + 30.2385i 2.67972 + 1.54714i
\(383\) 2.56877 + 9.58679i 0.131258 + 0.489862i 0.999985 0.00542900i \(-0.00172811\pi\)
−0.868727 + 0.495291i \(0.835061\pi\)
\(384\) −104.248 1.93367i −5.31986 0.0986772i
\(385\) 0.693530 + 1.20123i 0.0353456 + 0.0612203i
\(386\) 14.6031 54.4996i 0.743279 2.77396i
\(387\) −11.2924 3.47946i −0.574027 0.176871i
\(388\) −8.99454 + 33.5681i −0.456628 + 1.70416i
\(389\) 27.3719i 1.38781i −0.720067 0.693905i \(-0.755889\pi\)
0.720067 0.693905i \(-0.244111\pi\)
\(390\) −12.2559 + 11.8095i −0.620599 + 0.597996i
\(391\) −1.32462 4.94356i −0.0669890 0.250006i
\(392\) −46.8463 + 46.8463i −2.36610 + 2.36610i
\(393\) −21.6508 + 11.9703i −1.09214 + 0.603823i
\(394\) 25.6347 6.86879i 1.29146 0.346045i
\(395\) 16.0588 + 9.27155i 0.808006 + 0.466502i
\(396\) −22.0285 13.8320i −1.10697 0.695084i
\(397\) 8.81509 + 2.36200i 0.442416 + 0.118545i 0.473149 0.880983i \(-0.343117\pi\)
−0.0307324 + 0.999528i \(0.509784\pi\)
\(398\) 28.0662 7.52030i 1.40683 0.376959i
\(399\) 0.00851873 + 0.00513125i 0.000426470 + 0.000256884i
\(400\) −53.4399 + 30.8536i −2.67200 + 1.54268i
\(401\) 2.96170 0.793584i 0.147900 0.0396297i −0.184109 0.982906i \(-0.558940\pi\)
0.332009 + 0.943276i \(0.392273\pi\)
\(402\) −1.14594 + 61.7798i −0.0571544 + 3.08129i
\(403\) 6.97812 12.0865i 0.347605 0.602070i
\(404\) 79.1610 3.93841
\(405\) −2.00431 10.5576i −0.0995949 0.524611i
\(406\) 8.78477 + 8.78477i 0.435981 + 0.435981i
\(407\) 14.2832i 0.707990i
\(408\) −94.2229 56.7552i −4.66473 2.80980i
\(409\) −3.72440 + 13.8997i −0.184160 + 0.687294i 0.810649 + 0.585532i \(0.199114\pi\)
−0.994809 + 0.101761i \(0.967552\pi\)
\(410\) −31.2211 + 8.36567i −1.54190 + 0.413151i
\(411\) 8.03597 + 4.84046i 0.396385 + 0.238763i
\(412\) 25.0203 25.0203i 1.23266 1.23266i
\(413\) 3.15580i 0.155287i
\(414\) −0.257332 + 6.93423i −0.0126472 + 0.340799i
\(415\) 0.0268654 0.00131877
\(416\) 20.9315 78.1173i 1.02625 3.83002i
\(417\) −29.9592 + 16.5639i −1.46711 + 0.811137i
\(418\) 0.00817008 0.0304911i 0.000399611 0.00149137i
\(419\) 7.12773 + 12.3456i 0.348212 + 0.603122i 0.985932 0.167147i \(-0.0534555\pi\)
−0.637720 + 0.770269i \(0.720122\pi\)
\(420\) −2.18245 8.79430i −0.106493 0.429118i
\(421\) 7.82682 29.2101i 0.381456 1.42361i −0.462222 0.886764i \(-0.652948\pi\)
0.843678 0.536849i \(-0.180385\pi\)
\(422\) 23.7301i 1.15516i
\(423\) 14.8490 + 28.0749i 0.721985 + 1.36505i
\(424\) −6.16230 + 3.55780i −0.299268 + 0.172782i
\(425\) −21.9725 −1.06582
\(426\) 7.32064 + 13.2409i 0.354686 + 0.641524i
\(427\) −3.05457 + 5.29068i −0.147821 + 0.256034i
\(428\) 15.5552 58.0527i 0.751888 2.80608i
\(429\) 5.60176 5.39773i 0.270455 0.260605i
\(430\) −9.23896 + 9.23896i −0.445542 + 0.445542i
\(431\) 8.61646 14.9242i 0.415040 0.718871i −0.580392 0.814337i \(-0.697101\pi\)
0.995433 + 0.0954660i \(0.0304341\pi\)
\(432\) 59.8063 + 66.8614i 2.87743 + 3.21687i
\(433\) −9.86480 36.8159i −0.474072 1.76926i −0.624905 0.780701i \(-0.714862\pi\)
0.150833 0.988559i \(-0.451804\pi\)
\(434\) 5.01438 + 8.68516i 0.240698 + 0.416901i
\(435\) 11.7151 2.90730i 0.561695 0.139394i
\(436\) 54.5114 + 31.4722i 2.61062 + 1.50724i
\(437\) −0.00602644 + 0.00161478i −0.000288284 + 7.72454e-5i
\(438\) −8.77905 35.3756i −0.419479 1.69031i
\(439\) 14.5839 14.5839i 0.696051 0.696051i −0.267505 0.963556i \(-0.586199\pi\)
0.963556 + 0.267505i \(0.0861992\pi\)
\(440\) −16.1968 + 9.35123i −0.772152 + 0.445802i
\(441\) 19.2257 + 0.713474i 0.915509 + 0.0339749i
\(442\) 35.7726 35.7726i 1.70153 1.70153i
\(443\) 9.51225 + 9.51225i 0.451940 + 0.451940i 0.895998 0.444058i \(-0.146461\pi\)
−0.444058 + 0.895998i \(0.646461\pi\)
\(444\) 25.8166 89.6630i 1.22520 4.25522i
\(445\) 4.37887 16.3422i 0.207578 0.774693i
\(446\) 7.26728 4.19576i 0.344116 0.198675i
\(447\) 0.0494020 2.66335i 0.00233663 0.125972i
\(448\) 22.3868 + 22.3868i 1.05768 + 1.05768i
\(449\) −2.24339 + 0.601115i −0.105872 + 0.0283684i −0.311366 0.950290i \(-0.600787\pi\)
0.205494 + 0.978658i \(0.434120\pi\)
\(450\) 28.4699 + 8.77224i 1.34208 + 0.413527i
\(451\) 14.2702 3.82368i 0.671956 0.180050i
\(452\) 26.9707 46.7146i 1.26860 2.19727i
\(453\) 3.14108 5.21471i 0.147581 0.245009i
\(454\) −40.0566 23.1267i −1.87995 1.08539i
\(455\) 2.70989 0.127042
\(456\) −0.0691874 + 0.114862i −0.00323999 + 0.00537893i
\(457\) 30.2802i 1.41645i −0.705987 0.708225i \(-0.749496\pi\)
0.705987 0.708225i \(-0.250504\pi\)
\(458\) −2.33868 + 1.35024i −0.109279 + 0.0630925i
\(459\) 6.53867 + 31.2660i 0.305199 + 1.45937i
\(460\) 4.92302 + 2.84231i 0.229537 + 0.132523i
\(461\) −4.71135 2.72010i −0.219429 0.126688i 0.386257 0.922391i \(-0.373768\pi\)
−0.605686 + 0.795704i \(0.707101\pi\)
\(462\) 1.34641 + 5.42542i 0.0626407 + 0.252413i
\(463\) 21.4285 + 21.4285i 0.995867 + 0.995867i 0.999991 0.00412419i \(-0.00131277\pi\)
−0.00412419 + 0.999991i \(0.501313\pi\)
\(464\) −71.2490 + 71.2490i −3.30765 + 3.30765i
\(465\) 9.74206 + 0.180704i 0.451777 + 0.00837994i
\(466\) 9.39724 + 35.0710i 0.435319 + 1.62463i
\(467\) 8.73919i 0.404401i −0.979344 0.202201i \(-0.935191\pi\)
0.979344 0.202201i \(-0.0648093\pi\)
\(468\) −44.9215 + 23.7593i −2.07650 + 1.09828i
\(469\) 6.95676 6.95676i 0.321233 0.321233i
\(470\) 35.1184 1.61989
\(471\) 16.0858 + 14.5687i 0.741195 + 0.671290i
\(472\) 42.5513 1.95858
\(473\) 4.22283 4.22283i 0.194166 0.194166i
\(474\) 51.8534 + 53.8134i 2.38171 + 2.47173i
\(475\) 0.0267855i 0.00122901i
\(476\) 6.97091 + 26.0158i 0.319511 + 1.19243i
\(477\) 1.97473 + 0.608460i 0.0904166 + 0.0278595i
\(478\) −11.4876 + 11.4876i −0.525430 + 0.525430i
\(479\) −17.4740 17.4740i −0.798407 0.798407i 0.184437 0.982844i \(-0.440954\pi\)
−0.982844 + 0.184437i \(0.940954\pi\)
\(480\) 54.8003 13.5996i 2.50128 0.620735i
\(481\) 24.1664 + 13.9525i 1.10189 + 0.636178i
\(482\) 0.119792 + 0.0691617i 0.00545636 + 0.00315023i
\(483\) 0.795592 0.766615i 0.0362007 0.0348822i
\(484\) −43.0910 + 24.8786i −1.95868 + 1.13085i
\(485\) 7.25626i 0.329490i
\(486\) 4.01036 43.1220i 0.181913 1.95605i
\(487\) 5.44061 0.246538 0.123269 0.992373i \(-0.460662\pi\)
0.123269 + 0.992373i \(0.460662\pi\)
\(488\) −71.3369 41.1864i −3.22927 1.86442i
\(489\) 10.3367 + 6.22634i 0.467444 + 0.281565i
\(490\) 10.6367 18.4233i 0.480516 0.832279i
\(491\) 18.4565 4.94541i 0.832931 0.223183i 0.182939 0.983124i \(-0.441439\pi\)
0.649992 + 0.759941i \(0.274772\pi\)
\(492\) −96.4926 1.78982i −4.35022 0.0806915i
\(493\) −34.6562 + 9.28611i −1.56084 + 0.418225i
\(494\) −0.0436086 0.0436086i −0.00196204 0.00196204i
\(495\) 5.19032 + 1.59926i 0.233287 + 0.0718814i
\(496\) −70.4412 + 40.6692i −3.16290 + 1.82610i
\(497\) 0.623495 2.32691i 0.0279676 0.104376i
\(498\) 0.104043 + 0.0299571i 0.00466229 + 0.00134241i
\(499\) −6.72413 6.72413i −0.301013 0.301013i 0.540397 0.841410i \(-0.318274\pi\)
−0.841410 + 0.540397i \(0.818274\pi\)
\(500\) 41.3977 41.3977i 1.85136 1.85136i
\(501\) 3.21070 + 12.9376i 0.143443 + 0.578012i
\(502\) −43.6339 + 25.1920i −1.94748 + 1.12438i
\(503\) 11.2298 11.2298i 0.500712 0.500712i −0.410947 0.911659i \(-0.634802\pi\)
0.911659 + 0.410947i \(0.134802\pi\)
\(504\) 0.880595 23.7291i 0.0392248 1.05698i
\(505\) −15.9656 + 4.27797i −0.710461 + 0.190367i
\(506\) −3.03714 1.75349i −0.135017 0.0779522i
\(507\) 1.76275 + 7.10310i 0.0782867 + 0.315460i
\(508\) 23.7090 + 41.0652i 1.05192 + 1.82197i
\(509\) 5.07239 + 18.9304i 0.224830 + 0.839076i 0.982473 + 0.186407i \(0.0596842\pi\)
−0.757643 + 0.652669i \(0.773649\pi\)
\(510\) 33.9412 + 9.77267i 1.50294 + 0.432741i
\(511\) −2.90170 + 5.02589i −0.128364 + 0.222332i
\(512\) −81.0606 + 81.0606i −3.58241 + 3.58241i
\(513\) 0.0381148 0.00797096i 0.00168281 0.000351927i
\(514\) 20.4048 76.1518i 0.900018 3.35891i
\(515\) −3.69410 + 6.39837i −0.162782 + 0.281946i
\(516\) −34.1416 + 18.8763i −1.50300 + 0.830981i
\(517\) −16.0515 −0.705945
\(518\) −17.3656 + 10.0261i −0.763003 + 0.440520i
\(519\) −10.7361 11.1419i −0.471261 0.489074i
\(520\) 36.5389i 1.60234i
\(521\) −7.79561 + 29.0936i −0.341532 + 1.27461i 0.555080 + 0.831797i \(0.312688\pi\)
−0.896612 + 0.442817i \(0.853979\pi\)
\(522\) 48.6116 + 1.80400i 2.12767 + 0.0789588i
\(523\) 6.16550 + 10.6790i 0.269599 + 0.466959i 0.968758 0.248007i \(-0.0797756\pi\)
−0.699160 + 0.714966i \(0.746442\pi\)
\(524\) −21.1401 + 78.8961i −0.923512 + 3.44659i
\(525\) −2.29507 4.15111i −0.100165 0.181169i
\(526\) 0.821694 3.06660i 0.0358276 0.133710i
\(527\) −28.9627 −1.26164
\(528\) −44.0030 + 10.9201i −1.91498 + 0.475235i
\(529\) 22.3069i 0.969863i
\(530\) 1.61563 1.61563i 0.0701786 0.0701786i
\(531\) −8.40747 9.05553i −0.364853 0.392977i
\(532\) 0.0317145 0.00849788i 0.00137500 0.000368430i
\(533\) 7.47031 27.8796i 0.323575 1.20760i
\(534\) 35.1811 58.4065i 1.52244 2.52750i
\(535\) 12.5490i 0.542540i
\(536\) 93.8016 + 93.8016i 4.05161 + 4.05161i
\(537\) 39.5901 + 23.8471i 1.70844 + 1.02908i
\(538\) 4.63506 0.199832
\(539\) −4.86169 + 8.42069i −0.209408 + 0.362705i
\(540\) −29.6917 19.4208i −1.27773 0.835739i
\(541\) −15.9721 + 4.27971i −0.686695 + 0.183999i −0.585263 0.810843i \(-0.699009\pi\)
−0.101431 + 0.994843i \(0.532342\pi\)
\(542\) −19.2752 + 11.1285i −0.827941 + 0.478012i
\(543\) −0.132706 + 0.220313i −0.00569494 + 0.00945455i
\(544\) −162.113 + 43.4381i −6.95055 + 1.86239i
\(545\) −12.6949 3.40160i −0.543792 0.145709i
\(546\) 10.4948 + 3.02175i 0.449135 + 0.129319i
\(547\) 4.12871 + 2.38371i 0.176531 + 0.101920i 0.585662 0.810556i \(-0.300835\pi\)
−0.409131 + 0.912476i \(0.634168\pi\)
\(548\) 29.9173 8.01630i 1.27800 0.342440i
\(549\) 5.33001 + 23.3194i 0.227479 + 0.995246i
\(550\) −10.6464 + 10.6464i −0.453963 + 0.453963i
\(551\) 0.0113202 + 0.0422477i 0.000482258 + 0.00179981i
\(552\) 10.3367 + 10.7274i 0.439958 + 0.456588i
\(553\) 11.8987i 0.505984i
\(554\) 7.35896 27.4640i 0.312652 1.16683i
\(555\) −0.361310 + 19.4789i −0.0153368 + 0.826832i
\(556\) −29.2526 + 109.172i −1.24059 + 4.62993i
\(557\) 19.6801 + 34.0869i 0.833871 + 1.44431i 0.894947 + 0.446173i \(0.147213\pi\)
−0.0610759 + 0.998133i \(0.519453\pi\)
\(558\) 37.5272 + 11.5630i 1.58865 + 0.489501i
\(559\) −3.01976 11.2699i −0.127722 0.476665i
\(560\) −13.6776 7.89677i −0.577985 0.333700i
\(561\) −15.5135 4.46678i −0.654979 0.188587i
\(562\) 20.2196 75.4605i 0.852911 3.18311i
\(563\) 24.7568 24.7568i 1.04337 1.04337i 0.0443571 0.999016i \(-0.485876\pi\)
0.999016 0.0443571i \(-0.0141239\pi\)
\(564\) 100.764 + 29.0128i 4.24292 + 1.22166i
\(565\) −2.91507 + 10.8792i −0.122638 + 0.457691i
\(566\) 24.7420 + 6.62961i 1.03999 + 0.278663i
\(567\) −5.22389 + 4.50109i −0.219383 + 0.189028i
\(568\) 31.3750 + 8.40690i 1.31647 + 0.352746i
\(569\) −5.12708 5.12708i −0.214938 0.214938i 0.591423 0.806361i \(-0.298566\pi\)
−0.806361 + 0.591423i \(0.798566\pi\)
\(570\) 0.0119134 0.0413760i 0.000498996 0.00173305i
\(571\) −12.4244 21.5197i −0.519945 0.900571i −0.999731 0.0231859i \(-0.992619\pi\)
0.479786 0.877386i \(-0.340714\pi\)
\(572\) 25.6834i 1.07388i
\(573\) −32.2972 19.4542i −1.34924 0.812712i
\(574\) 14.6658 + 14.6658i 0.612139 + 0.612139i
\(575\) 2.87440 + 0.770194i 0.119871 + 0.0321193i
\(576\) 123.880 + 4.59725i 5.16168 + 0.191552i
\(577\) 10.7827 + 18.6762i 0.448889 + 0.777499i 0.998314 0.0580443i \(-0.0184865\pi\)
−0.549425 + 0.835543i \(0.685153\pi\)
\(578\) −55.7896 14.9488i −2.32054 0.621787i
\(579\) −9.73273 + 33.8025i −0.404479 + 1.40479i
\(580\) 19.9257 34.5123i 0.827368 1.43304i
\(581\) −0.00861945 0.0149293i −0.000357595 0.000619373i
\(582\) 8.09132 28.1018i 0.335396 1.16486i
\(583\) −0.738454 + 0.738454i −0.0305836 + 0.0305836i
\(584\) −67.7667 39.1251i −2.80421 1.61901i
\(585\) 7.77602 7.21953i 0.321499 0.298491i
\(586\) −2.91049 + 5.04111i −0.120231 + 0.208246i
\(587\) −0.171672 0.171672i −0.00708565 0.00708565i 0.703555 0.710641i \(-0.251595\pi\)
−0.710641 + 0.703555i \(0.751595\pi\)
\(588\) 45.7396 44.0737i 1.88627 1.81757i
\(589\) 0.0353070i 0.00145480i
\(590\) −13.1978 + 3.53634i −0.543345 + 0.145589i
\(591\) −16.0584 + 3.98515i −0.660552 + 0.163927i
\(592\) −81.3165 140.844i −3.34209 5.78867i
\(593\) −10.3945 + 18.0039i −0.426852 + 0.739330i −0.996591 0.0824960i \(-0.973711\pi\)
0.569739 + 0.821825i \(0.307044\pi\)
\(594\) 18.3176 + 11.9812i 0.751579 + 0.491594i
\(595\) −2.81186 4.87028i −0.115275 0.199662i
\(596\) −6.21881 6.21881i −0.254732 0.254732i
\(597\) −17.5815 + 4.36315i −0.719564 + 0.178572i
\(598\) −5.93364 + 3.42579i −0.242645 + 0.140091i
\(599\) 0.547707 + 0.547707i 0.0223787 + 0.0223787i 0.718208 0.695829i \(-0.244963\pi\)
−0.695829 + 0.718208i \(0.744963\pi\)
\(600\) 55.9715 30.9456i 2.28503 1.26335i
\(601\) 23.7414 0.968433 0.484217 0.874948i \(-0.339105\pi\)
0.484217 + 0.874948i \(0.339105\pi\)
\(602\) 8.09838 + 2.16996i 0.330065 + 0.0884408i
\(603\) 1.42861 38.4961i 0.0581774 1.56768i
\(604\) −5.20195 19.4139i −0.211664 0.789942i
\(605\) 7.34634 7.34634i 0.298671 0.298671i
\(606\) −66.6013 1.23538i −2.70549 0.0501837i
\(607\) 4.04250 + 15.0868i 0.164080 + 0.612355i 0.998156 + 0.0607051i \(0.0193349\pi\)
−0.834076 + 0.551650i \(0.813998\pi\)
\(608\) 0.0529532 + 0.197624i 0.00214754 + 0.00801471i
\(609\) −5.37426 5.57741i −0.217776 0.226008i
\(610\) 25.5490 + 6.84583i 1.03445 + 0.277179i
\(611\) −15.6799 + 27.1584i −0.634340 + 1.09871i
\(612\) 89.3126 + 56.0806i 3.61025 + 2.26692i
\(613\) 7.24233 27.0287i 0.292515 1.09168i −0.650656 0.759373i \(-0.725506\pi\)
0.943171 0.332308i \(-0.107827\pi\)
\(614\) −43.2852 −1.74685
\(615\) 19.5579 4.85362i 0.788649 0.195717i
\(616\) 10.3931 + 6.00047i 0.418751 + 0.241766i
\(617\) −4.73031 + 8.19313i −0.190435 + 0.329843i −0.945394 0.325928i \(-0.894323\pi\)
0.754959 + 0.655771i \(0.227657\pi\)
\(618\) −21.4411 + 20.6601i −0.862487 + 0.831073i
\(619\) 10.0999 5.83117i 0.405949 0.234375i −0.283099 0.959091i \(-0.591362\pi\)
0.689048 + 0.724716i \(0.258029\pi\)
\(620\) 22.7473 22.7473i 0.913554 0.913554i
\(621\) 0.240578 4.31936i 0.00965406 0.173330i
\(622\) 26.7534 7.16855i 1.07271 0.287433i
\(623\) −10.4864 + 2.80982i −0.420128 + 0.112573i
\(624\) −24.5080 + 85.1181i −0.981104 + 3.40745i
\(625\) 2.82370 4.89079i 0.112948 0.195631i
\(626\) −44.8741 44.8741i −1.79353 1.79353i
\(627\) −0.00544522 + 0.0189117i −0.000217461 + 0.000755259i
\(628\) 71.4867 4.86836i 2.85263 0.194269i
\(629\) 57.9099i 2.30902i
\(630\) 1.69894 + 7.43305i 0.0676875 + 0.296140i
\(631\) 9.59404 + 5.53912i 0.381933 + 0.220509i 0.678659 0.734454i \(-0.262561\pi\)
−0.296726 + 0.954963i \(0.595895\pi\)
\(632\) 160.436 6.38181
\(633\) −0.274370 + 14.7918i −0.0109052 + 0.587919i
\(634\) 8.77077 + 32.7330i 0.348332 + 1.29999i
\(635\) −7.00097 7.00097i −0.277825 0.277825i
\(636\) 5.97041 3.30092i 0.236742 0.130890i
\(637\) 9.49826 + 16.4515i 0.376335 + 0.651831i
\(638\) −12.2926 + 21.2915i −0.486670 + 0.842938i
\(639\) −4.41010 8.33813i −0.174461 0.329852i
\(640\) 35.9386 62.2474i 1.42060 2.46055i
\(641\) −10.6798 18.4980i −0.421827 0.730627i 0.574291 0.818651i \(-0.305278\pi\)
−0.996118 + 0.0880247i \(0.971945\pi\)
\(642\) −13.9931 + 48.5993i −0.552265 + 1.91806i
\(643\) 10.0539 + 2.69394i 0.396488 + 0.106239i 0.451553 0.892244i \(-0.350870\pi\)
−0.0550656 + 0.998483i \(0.517537\pi\)
\(644\) 3.64769i 0.143739i
\(645\) 5.86577 5.65212i 0.230964 0.222552i
\(646\) −0.0331249 + 0.123624i −0.00130328 + 0.00486391i
\(647\) 17.1951 + 9.92759i 0.676009 + 0.390294i 0.798350 0.602194i \(-0.205707\pi\)
−0.122341 + 0.992488i \(0.539040\pi\)
\(648\) −60.6906 70.4364i −2.38415 2.76700i
\(649\) 6.03230 1.61635i 0.236788 0.0634473i
\(650\) 7.61325 + 28.4130i 0.298616 + 1.11445i
\(651\) −3.02521 5.47173i −0.118567 0.214454i
\(652\) 38.4829 10.3115i 1.50711 0.403828i
\(653\) −13.6315 23.6105i −0.533443 0.923950i −0.999237 0.0390568i \(-0.987565\pi\)
0.465794 0.884893i \(-0.345769\pi\)
\(654\) −45.3715 27.3295i −1.77416 1.06867i
\(655\) 17.0546i 0.666379i
\(656\) −118.947 + 118.947i −4.64411 + 4.64411i
\(657\) 5.06326 + 22.1523i 0.197537 + 0.864243i
\(658\) −11.2674 19.5156i −0.439247 0.760798i
\(659\) −20.8636 36.1368i −0.812730 1.40769i −0.910947 0.412524i \(-0.864647\pi\)
0.0982173 0.995165i \(-0.468686\pi\)
\(660\) 15.6925 8.67606i 0.610828 0.337715i
\(661\) −22.5016 + 12.9913i −0.875212 + 0.505304i −0.869077 0.494677i \(-0.835286\pi\)
−0.00613528 + 0.999981i \(0.501953\pi\)
\(662\) −22.9670 85.7141i −0.892638 3.33137i
\(663\) −22.7119 + 21.8846i −0.882055 + 0.849929i
\(664\) 0.201300 0.116221i 0.00781195 0.00451023i
\(665\) −0.00593711 + 0.00342779i −0.000230231 + 0.000132924i
\(666\) −23.1198 + 75.0341i −0.895873 + 2.90751i
\(667\) 4.85917 0.188148
\(668\) 38.1139 + 22.0051i 1.47467 + 0.851402i
\(669\) −4.57845 + 2.53133i −0.177013 + 0.0978670i
\(670\) −36.8894 21.2981i −1.42516 0.822818i
\(671\) −11.6776 3.12901i −0.450810 0.120794i
\(672\) −25.1395 26.0897i −0.969777 1.00643i
\(673\) 12.8930 + 12.8930i 0.496988 + 0.496988i 0.910499 0.413511i \(-0.135698\pi\)
−0.413511 + 0.910499i \(0.635698\pi\)
\(674\) 38.6104i 1.48722i
\(675\) −17.6448 5.79720i −0.679148 0.223134i
\(676\) 20.9255 + 12.0813i 0.804827 + 0.464667i
\(677\) 11.7461 0.451438 0.225719 0.974192i \(-0.427527\pi\)
0.225719 + 0.974192i \(0.427527\pi\)
\(678\) −23.4206 + 38.8820i −0.899461 + 1.49325i
\(679\) −4.03237 + 2.32809i −0.154748 + 0.0893439i
\(680\) 65.6685 37.9137i 2.51827 1.45393i
\(681\) 24.7012 + 14.8788i 0.946553 + 0.570156i
\(682\) −14.0334 + 14.0334i −0.537366 + 0.537366i
\(683\) −10.2126 2.73646i −0.390774 0.104708i 0.0580817 0.998312i \(-0.481502\pi\)
−0.448856 + 0.893604i \(0.648168\pi\)
\(684\) 0.0683651 0.108876i 0.00261400 0.00416299i
\(685\) −5.60066 + 3.23354i −0.213990 + 0.123547i
\(686\) −28.5508 −1.09007
\(687\) 1.47339 0.814608i 0.0562133 0.0310793i
\(688\) −17.5995 + 65.6821i −0.670973 + 2.50411i
\(689\) 0.528070 + 1.97079i 0.0201179 + 0.0750809i
\(690\) −4.09758 2.46818i −0.155992 0.0939618i
\(691\) −38.0979 10.2083i −1.44931 0.388342i −0.553528 0.832831i \(-0.686719\pi\)
−0.895784 + 0.444489i \(0.853385\pi\)
\(692\) −51.0841 −1.94193
\(693\) −0.776533 3.39741i −0.0294980 0.129057i
\(694\) 21.9835 + 5.89047i 0.834483 + 0.223599i
\(695\) 23.5993i 0.895171i
\(696\) 75.2031 72.4640i 2.85056 2.74674i
\(697\) −57.8572 + 15.5028i −2.19150 + 0.587210i
\(698\) 4.92529 + 18.3814i 0.186425 + 0.695747i
\(699\) −5.45212 21.9696i −0.206218 0.830965i
\(700\) −15.1267 4.05320i −0.571737 0.153196i
\(701\) 0.793669 + 2.96201i 0.0299765 + 0.111874i 0.979293 0.202448i \(-0.0648897\pi\)
−0.949317 + 0.314322i \(0.898223\pi\)
\(702\) 38.1650 19.2886i 1.44045 0.728003i
\(703\) −0.0705950 −0.00266254
\(704\) −31.3262 + 54.2585i −1.18065 + 2.04495i
\(705\) −21.8905 0.406043i −0.824443 0.0152924i
\(706\) −38.5777 38.5777i −1.45189 1.45189i
\(707\) 7.49970 + 7.49970i 0.282055 + 0.282055i
\(708\) −40.7895 0.756596i −1.53296 0.0284346i
\(709\) 5.22843 9.05591i 0.196358 0.340102i −0.750987 0.660317i \(-0.770422\pi\)
0.947345 + 0.320215i \(0.103755\pi\)
\(710\) −10.4300 −0.391432
\(711\) −31.6997 34.1432i −1.18883 1.28047i
\(712\) −37.8863 141.393i −1.41985 5.29895i
\(713\) 3.78886 + 1.01522i 0.141894 + 0.0380204i
\(714\) −5.45890 21.9969i −0.204294 0.823213i
\(715\) 1.38797 + 5.17996i 0.0519070 + 0.193719i
\(716\) 147.391 39.4932i 5.50824 1.47593i
\(717\) 7.29342 7.02778i 0.272378 0.262457i
\(718\) 42.3840i 1.58176i
\(719\) 42.7650 + 11.4589i 1.59487 + 0.427343i 0.943487 0.331409i \(-0.107524\pi\)
0.651379 + 0.758752i \(0.274191\pi\)
\(720\) −60.2859 + 13.7793i −2.24672 + 0.513524i
\(721\) 4.74084 0.176558
\(722\) −50.9873 13.6620i −1.89755 0.508447i
\(723\) −0.0738704 0.0444958i −0.00274727 0.00165482i
\(724\) 0.219774 + 0.820208i 0.00816784 + 0.0304828i
\(725\) 5.39936 20.1507i 0.200527 0.748377i
\(726\) 36.6424 20.2589i 1.35993 0.751878i
\(727\) 8.52619 0.316219 0.158109 0.987422i \(-0.449460\pi\)
0.158109 + 0.987422i \(0.449460\pi\)
\(728\) 20.3050 11.7231i 0.752553 0.434487i
\(729\) −2.99837 + 26.8330i −0.111051 + 0.993815i
\(730\) 24.2703 + 6.50321i 0.898284 + 0.240695i
\(731\) −17.1211 + 17.1211i −0.633247 + 0.633247i
\(732\) 67.6510 + 40.7495i 2.50045 + 1.50615i
\(733\) −27.4290 + 15.8361i −1.01311 + 0.584921i −0.912101 0.409965i \(-0.865541\pi\)
−0.101011 + 0.994885i \(0.532208\pi\)
\(734\) −63.0824 + 36.4206i −2.32841 + 1.34431i
\(735\) −6.84321 + 11.3609i −0.252415 + 0.419051i
\(736\) 22.7300 0.837839
\(737\) 16.8610 + 9.73468i 0.621082 + 0.358582i
\(738\) 81.1551 + 3.01170i 2.98736 + 0.110862i
\(739\) 6.97712i 0.256657i 0.991732 + 0.128329i \(0.0409613\pi\)
−0.991732 + 0.128329i \(0.959039\pi\)
\(740\) 45.4824 + 45.4824i 1.67196 + 1.67196i
\(741\) 0.0266785 + 0.0276869i 0.000980058 + 0.00101710i
\(742\) −1.41618 0.379464i −0.0519896 0.0139306i
\(743\) 37.7148 + 21.7746i 1.38362 + 0.798834i 0.992586 0.121542i \(-0.0387840\pi\)
0.391034 + 0.920376i \(0.372117\pi\)
\(744\) 73.7781 40.7905i 2.70484 1.49545i
\(745\) 1.59032 + 0.918169i 0.0582647 + 0.0336391i
\(746\) −21.7810 −0.797459
\(747\) −0.0645072 0.0198762i −0.00236020 0.000727232i
\(748\) −46.1587 + 26.6497i −1.68773 + 0.974411i
\(749\) 6.97359 4.02620i 0.254809 0.147114i
\(750\) −35.4755 + 34.1834i −1.29538 + 1.24820i
\(751\) 0.995518 + 3.71532i 0.0363270 + 0.135574i 0.981708 0.190394i \(-0.0609765\pi\)
−0.945381 + 0.325968i \(0.894310\pi\)
\(752\) 158.282 91.3840i 5.77194 3.33243i
\(753\) 27.4897 15.1985i 1.00178 0.553865i
\(754\) 24.0161 + 41.5971i 0.874614 + 1.51488i
\(755\) 2.09831 + 3.63439i 0.0763655 + 0.132269i
\(756\) −1.26606 + 22.7309i −0.0460460 + 0.826715i
\(757\) −31.9355 + 31.9355i −1.16072 + 1.16072i −0.176398 + 0.984319i \(0.556445\pi\)
−0.984319 + 0.176398i \(0.943555\pi\)
\(758\) 24.1494i 0.877145i
\(759\) 1.87287 + 1.12812i 0.0679810 + 0.0409483i
\(760\) −0.0462187 0.0800532i −0.00167653 0.00290383i
\(761\) −23.4245 + 6.27657i −0.849137 + 0.227525i −0.657045 0.753852i \(-0.728194\pi\)
−0.192092 + 0.981377i \(0.561527\pi\)
\(762\) −19.3065 34.9198i −0.699399 1.26501i
\(763\) 2.18273 + 8.14606i 0.0790201 + 0.294907i
\(764\) −120.240 + 32.2182i −4.35013 + 1.16561i
\(765\) −21.0437 6.48406i −0.760837 0.234432i
\(766\) −23.8795 13.7869i −0.862802 0.498139i
\(767\) 3.15786 11.7853i 0.114024 0.425542i
\(768\) 105.515 101.672i 3.80745 3.66878i
\(769\) 24.3795i 0.879146i −0.898207 0.439573i \(-0.855130\pi\)
0.898207 0.439573i \(-0.144870\pi\)
\(770\) −3.72224 0.997372i −0.134140 0.0359428i
\(771\) −13.5995 + 47.2320i −0.489773 + 1.70102i
\(772\) 58.0676 + 100.576i 2.08990 + 3.61981i
\(773\) 21.5608 37.3444i 0.775488 1.34319i −0.159031 0.987274i \(-0.550837\pi\)
0.934520 0.355911i \(-0.115830\pi\)
\(774\) 29.0193 15.3485i 1.04308 0.551692i
\(775\) 8.42011 14.5841i 0.302459 0.523875i
\(776\) −31.3908 54.3705i −1.12687 1.95179i
\(777\) 10.9405 6.04879i 0.392488 0.216999i
\(778\) 53.7719 + 53.7719i 1.92782 + 1.92782i
\(779\) 0.0188987 + 0.0705307i 0.000677115 + 0.00252703i
\(780\) 0.649692 35.0260i 0.0232627 1.25413i
\(781\) 4.76723 0.170585
\(782\) 12.3138 + 7.10938i 0.440341 + 0.254231i
\(783\) −30.2804 1.68654i −1.08213 0.0602722i
\(784\) 110.714i 3.95406i
\(785\) −14.1547 + 4.84512i −0.505204 + 0.172930i
\(786\) 19.0173 66.0485i 0.678324 2.35587i
\(787\) −21.0854 21.0854i −0.751614 0.751614i 0.223167 0.974780i \(-0.428361\pi\)
−0.974780 + 0.223167i \(0.928361\pi\)
\(788\) −27.3129 + 47.3074i −0.972983 + 1.68526i
\(789\) −0.547645 + 1.90201i −0.0194967 + 0.0677135i
\(790\) −49.7613 + 13.3335i −1.77043 + 0.474385i
\(791\) 6.98093 1.87053i 0.248213 0.0665086i
\(792\) 45.8091 10.4704i 1.62775 0.372049i
\(793\) −16.7014 + 16.7014i −0.593084 + 0.593084i
\(794\) −21.9573 + 12.6771i −0.779236 + 0.449892i
\(795\) −1.02576 + 0.988397i −0.0363799 + 0.0350548i
\(796\) −29.9036 + 51.7946i −1.05991 + 1.83581i
\(797\) −22.9822 13.2688i −0.814073 0.470005i 0.0342955 0.999412i \(-0.489081\pi\)
−0.848368 + 0.529407i \(0.822415\pi\)
\(798\) −0.0268153 + 0.00665467i −0.000949252 + 0.000235573i
\(799\) 65.0795 2.30235
\(800\) 25.2569 94.2599i 0.892965 3.33259i
\(801\) −22.6049 + 35.9999i −0.798704 + 1.27200i
\(802\) −4.25924 + 7.37723i −0.150399 + 0.260499i
\(803\) −11.0932 2.97241i −0.391470 0.104894i
\(804\) −88.2499 91.5857i −3.11234 3.22998i
\(805\) 0.197126 + 0.735686i 0.00694779 + 0.0259295i
\(806\) 10.0353 + 37.4523i 0.353479 + 1.31920i
\(807\) −2.88918 0.0535910i −0.101704 0.00188649i
\(808\) −101.122 + 101.122i −3.55747 + 3.55747i
\(809\) 6.53225 + 24.3787i 0.229662 + 0.857109i 0.980483 + 0.196604i \(0.0629912\pi\)
−0.750821 + 0.660505i \(0.770342\pi\)
\(810\) 24.6778 + 16.8029i 0.867088 + 0.590393i
\(811\) 30.8859 + 8.27585i 1.08455 + 0.290604i 0.756458 0.654042i \(-0.226928\pi\)
0.328091 + 0.944646i \(0.393595\pi\)
\(812\) −25.5717 −0.897391
\(813\) 12.1435 6.71393i 0.425893 0.235468i
\(814\) −28.0592 28.0592i −0.983474 0.983474i
\(815\) −7.20418 + 4.15934i −0.252352 + 0.145695i
\(816\) 178.406 44.2745i 6.24547 1.54992i
\(817\) 0.0208715 + 0.0208715i 0.000730201 + 0.000730201i
\(818\) −19.9892 34.6224i −0.698907 1.21054i
\(819\) −6.50681 2.00490i −0.227366 0.0700569i
\(820\) 33.2651 57.6168i 1.16167 2.01207i
\(821\) 4.12342 + 7.14197i 0.143908 + 0.249257i 0.928965 0.370167i \(-0.120700\pi\)
−0.785057 + 0.619424i \(0.787366\pi\)
\(822\) −25.2957 + 6.27755i −0.882288 + 0.218955i
\(823\) 19.0337 5.10006i 0.663472 0.177777i 0.0886596 0.996062i \(-0.471742\pi\)
0.574812 + 0.818285i \(0.305075\pi\)
\(824\) 63.9232i 2.22687i
\(825\) 6.75933 6.51314i 0.235330 0.226759i
\(826\) 6.19955 + 6.19955i 0.215710 + 0.215710i
\(827\) 11.3588 19.6740i 0.394983 0.684131i −0.598116 0.801410i \(-0.704084\pi\)
0.993099 + 0.117279i \(0.0374171\pi\)
\(828\) −9.71795 10.4670i −0.337722 0.363754i
\(829\) 4.14724 + 2.39441i 0.144039 + 0.0831612i 0.570288 0.821445i \(-0.306832\pi\)
−0.426248 + 0.904606i \(0.640165\pi\)
\(830\) −0.0527769 + 0.0527769i −0.00183191 + 0.00183191i
\(831\) −4.90463 + 17.0342i −0.170140 + 0.590908i
\(832\) 61.2018 + 106.005i 2.12179 + 3.67505i
\(833\) 19.7113 34.1410i 0.682956 1.18291i
\(834\) 26.3151 91.3944i 0.911217 3.16473i
\(835\) −8.87620 2.37837i −0.307173 0.0823069i
\(836\) 0.0324874 + 0.0562697i 0.00112360 + 0.00194613i
\(837\) −23.2582 7.64150i −0.803923 0.264129i
\(838\) −38.2552 10.2505i −1.32150 0.354096i
\(839\) −4.09116 4.09116i −0.141243 0.141243i 0.632950 0.774193i \(-0.281844\pi\)
−0.774193 + 0.632950i \(0.781844\pi\)
\(840\) 14.0220 + 8.44613i 0.483804 + 0.291419i
\(841\) 5.06466i 0.174644i
\(842\) 42.0073 + 72.7588i 1.44767 + 2.50743i
\(843\) −13.4760 + 46.8032i −0.464139 + 1.61199i
\(844\) 34.5381 + 34.5381i 1.18885 + 1.18885i
\(845\) −4.87326 1.30579i −0.167645 0.0449204i
\(846\) −84.3239 25.9822i −2.89911 0.893285i
\(847\) −6.43942 1.72544i −0.221261 0.0592867i
\(848\) 3.07765 11.4859i 0.105687 0.394429i
\(849\) −15.3459 4.41852i −0.526669 0.151643i
\(850\) 43.1648 43.1648i 1.48054 1.48054i
\(851\) −2.02990 + 7.57567i −0.0695839 + 0.259691i
\(852\) −29.9264 8.61669i −1.02526 0.295203i
\(853\) −37.8800 21.8700i −1.29698 0.748815i −0.317103 0.948391i \(-0.602710\pi\)
−0.979882 + 0.199577i \(0.936043\pi\)
\(854\) −4.39281 16.3942i −0.150319 0.560998i
\(855\) −0.00790439 + 0.0256533i −0.000270324 + 0.000877325i
\(856\) 54.2874 + 94.0285i 1.85550 + 3.21383i
\(857\) −7.03591 + 26.2584i −0.240342 + 0.896969i 0.735326 + 0.677714i \(0.237029\pi\)
−0.975668 + 0.219255i \(0.929637\pi\)
\(858\) −0.400811 + 21.6084i −0.0136835 + 0.737700i
\(859\) 12.4370 46.4154i 0.424344 1.58367i −0.341006 0.940061i \(-0.610768\pi\)
0.765351 0.643614i \(-0.222566\pi\)
\(860\) 26.8938i 0.917071i
\(861\) −8.97212 9.31125i −0.305769 0.317327i
\(862\) 12.3914 + 46.2454i 0.422053 + 1.57512i
\(863\) 35.9822 35.9822i 1.22485 1.22485i 0.258960 0.965888i \(-0.416620\pi\)
0.965888 0.258960i \(-0.0833798\pi\)
\(864\) −141.644 7.88924i −4.81883 0.268397i
\(865\) 10.3029 2.76066i 0.350309 0.0938651i
\(866\) 91.7040 + 52.9453i 3.11623 + 1.79916i
\(867\) 34.6026 + 9.96311i 1.17517 + 0.338365i
\(868\) −19.9391 5.34267i −0.676777 0.181342i
\(869\) 22.7443 6.09432i 0.771548 0.206736i
\(870\) −17.3029 + 28.7256i −0.586622 + 0.973889i
\(871\) 32.9412 19.0186i 1.11617 0.644421i
\(872\) −109.838 + 29.4309i −3.71957 + 0.996656i
\(873\) −5.36850 + 17.4232i −0.181696 + 0.589687i
\(874\) 0.00866668 0.0150111i 0.000293155 0.000507759i
\(875\) 7.84400 0.265176
\(876\) 64.2652 + 38.7101i 2.17132 + 1.30789i
\(877\) −12.4200 12.4200i −0.419394 0.419394i 0.465601 0.884995i \(-0.345838\pi\)
−0.884995 + 0.465601i \(0.845838\pi\)
\(878\) 57.3000i 1.93378i
\(879\) 1.87249 3.10864i 0.0631575 0.104852i
\(880\) 8.08921 30.1893i 0.272687 1.01768i
\(881\) 8.77936 2.35242i 0.295784 0.0792551i −0.107875 0.994164i \(-0.534405\pi\)
0.403659 + 0.914909i \(0.367738\pi\)
\(882\) −39.1704 + 36.3672i −1.31894 + 1.22455i
\(883\) −34.1160 + 34.1160i −1.14810 + 1.14810i −0.161169 + 0.986927i \(0.551527\pi\)
−0.986927 + 0.161169i \(0.948473\pi\)
\(884\) 104.131i 3.50230i
\(885\) 8.26752 2.05172i 0.277910 0.0689680i
\(886\) −37.3735 −1.25559
\(887\) −0.304496 + 1.13639i −0.0102240 + 0.0381563i −0.970849 0.239690i \(-0.922954\pi\)
0.960625 + 0.277847i \(0.0896207\pi\)
\(888\) 81.5590 + 147.516i 2.73694 + 4.95033i
\(889\) −1.64432 + 6.13669i −0.0551487 + 0.205818i
\(890\) 23.5018 + 40.7063i 0.787783 + 1.36448i
\(891\) −11.2794 7.68005i −0.377875 0.257292i
\(892\) −4.47046 + 16.6840i −0.149682 + 0.558621i
\(893\) 0.0793351i 0.00265485i
\(894\) 5.13508 + 5.32918i 0.171743 + 0.178235i
\(895\) −27.5922 + 15.9304i −0.922307 + 0.532494i
\(896\) −46.1219 −1.54083
\(897\) 3.73824 2.06680i 0.124816 0.0690085i
\(898\) 3.22625 5.58802i 0.107661 0.186475i
\(899\) 7.11709 26.5613i 0.237368 0.885871i
\(900\) −54.2043 + 28.6691i −1.80681 + 0.955636i
\(901\) 2.99400 2.99400i 0.0997446 0.0997446i
\(902\) −20.5221 + 35.5453i −0.683310 + 1.18353i
\(903\) −5.02290 1.44624i −0.167152 0.0481278i
\(904\) 25.2214 + 94.1275i 0.838851 + 3.13063i
\(905\) −0.0886504 0.153547i −0.00294684 0.00510408i
\(906\) 4.07364 + 16.4149i 0.135338 + 0.545349i
\(907\) −33.9671 19.6109i −1.12786 0.651170i −0.184464 0.982839i \(-0.559055\pi\)
−0.943396 + 0.331669i \(0.892388\pi\)
\(908\) 91.9606 24.6408i 3.05182 0.817733i
\(909\) 41.5005 + 1.54010i 1.37649 + 0.0510820i
\(910\) −5.32357 + 5.32357i −0.176475 + 0.176475i
\(911\) −39.3454 + 22.7161i −1.30357 + 0.752618i −0.981015 0.193932i \(-0.937876\pi\)
−0.322557 + 0.946550i \(0.604543\pi\)
\(912\) −0.0539728 0.217486i −0.00178722 0.00720168i
\(913\) 0.0241226 0.0241226i 0.000798342 0.000798342i
\(914\) 59.4853 + 59.4853i 1.96760 + 1.96760i
\(915\) −15.8464 4.56263i −0.523865 0.150836i
\(916\) 1.43864 5.36907i 0.0475339 0.177399i
\(917\) −9.47741 + 5.47178i −0.312972 + 0.180694i
\(918\) −74.2670 48.5767i −2.45118 1.60327i
\(919\) −10.8372 10.8372i −0.357485 0.357485i 0.505400 0.862885i \(-0.331345\pi\)
−0.862885 + 0.505400i \(0.831345\pi\)
\(920\) −9.91963 + 2.65796i −0.327041 + 0.0876302i
\(921\) 26.9811 + 0.500468i 0.889058 + 0.0164910i
\(922\) 14.5990 3.91180i 0.480793 0.128828i
\(923\) 4.65686 8.06592i 0.153283 0.265493i
\(924\) −9.85611 5.93683i −0.324242 0.195307i
\(925\) 29.1603 + 16.8357i 0.958784 + 0.553554i
\(926\) −84.1924 −2.76673
\(927\) 13.6038 12.6302i 0.446808 0.414832i
\(928\) 159.346i 5.23079i
\(929\) 6.76773 3.90735i 0.222042 0.128196i −0.384853 0.922978i \(-0.625748\pi\)
0.606895 + 0.794782i \(0.292415\pi\)
\(930\) −19.4932 + 18.7832i −0.639208 + 0.615926i
\(931\) −0.0416195 0.0240290i −0.00136402 0.000787520i
\(932\) −64.7216 37.3670i −2.12003 1.22400i
\(933\) −16.7591 + 4.15907i −0.548670 + 0.136162i
\(934\) 17.1681 + 17.1681i 0.561757 + 0.561757i
\(935\) 7.86934 7.86934i 0.257355 0.257355i
\(936\) 27.0331 87.7346i 0.883605 2.86770i
\(937\) −6.44207 24.0421i −0.210453 0.785422i −0.987718 0.156248i \(-0.950060\pi\)
0.777265 0.629174i \(-0.216607\pi\)
\(938\) 27.3330i 0.892455i
\(939\) 27.4527 + 28.4904i 0.895884 + 0.929748i
\(940\) −51.1134 + 51.1134i −1.66713 + 1.66713i
\(941\) −10.4928 −0.342055 −0.171027 0.985266i \(-0.554709\pi\)
−0.171027 + 0.985266i \(0.554709\pi\)
\(942\) −60.2206 + 2.98034i −1.96209 + 0.0971046i
\(943\) 8.11219 0.264169
\(944\) −50.2815 + 50.2815i −1.63652 + 1.63652i
\(945\) −0.973066 4.65291i −0.0316538 0.151359i
\(946\) 16.5915i 0.539435i
\(947\) 8.61161 + 32.1390i 0.279840 + 1.04438i 0.952528 + 0.304451i \(0.0984728\pi\)
−0.672688 + 0.739926i \(0.734861\pi\)
\(948\) −153.793 2.85269i −4.99498 0.0926510i
\(949\) −15.8655 + 15.8655i −0.515017 + 0.515017i
\(950\) −0.0526200 0.0526200i −0.00170722 0.00170722i
\(951\) −5.08865 20.5050i −0.165011 0.664919i
\(952\) −42.1380 24.3284i −1.36570 0.788488i
\(953\) 2.46738 + 1.42454i 0.0799263 + 0.0461455i 0.539431 0.842030i \(-0.318640\pi\)
−0.459504 + 0.888176i \(0.651973\pi\)
\(954\) −5.07466 + 2.68403i −0.164298 + 0.0868985i
\(955\) 22.5095 12.9959i 0.728391 0.420537i
\(956\) 33.4394i 1.08151i
\(957\) 7.90858 13.1296i 0.255648 0.424418i
\(958\) 68.6551 2.21815
\(959\) 3.59382 + 2.07489i 0.116050 + 0.0670017i
\(960\) −44.0941 + 73.2034i −1.42313 + 2.36263i
\(961\) −4.40113 + 7.62299i −0.141972 + 0.245903i
\(962\) −74.8843 + 20.0652i −2.41437 + 0.646928i
\(963\) 9.28430 30.1318i 0.299182 0.970982i
\(964\) −0.275014 + 0.0736897i −0.00885759 + 0.00237338i
\(965\) −17.1466 17.1466i −0.551970 0.551970i
\(966\) −0.0569254 + 3.06895i −0.00183154 + 0.0987418i
\(967\) −19.3438 + 11.1682i −0.622056 + 0.359144i −0.777669 0.628674i \(-0.783598\pi\)
0.155613 + 0.987818i \(0.450265\pi\)
\(968\) 23.2650 86.8260i 0.747764 2.79069i
\(969\) 0.0220772 0.0766757i 0.000709221 0.00246318i
\(970\) 14.2549 + 14.2549i 0.457697 + 0.457697i
\(971\) −1.91995 + 1.91995i −0.0616140 + 0.0616140i −0.737242 0.675628i \(-0.763872\pi\)
0.675628 + 0.737242i \(0.263872\pi\)
\(972\) 56.9253 + 68.5991i 1.82588 + 2.20032i
\(973\) −13.1143 + 7.57156i −0.420426 + 0.242733i
\(974\) −10.6880 + 10.6880i −0.342467 + 0.342467i
\(975\) −4.41708 17.7988i −0.141460 0.570018i
\(976\) 132.965 35.6280i 4.25612 1.14042i
\(977\) −3.77882 2.18170i −0.120895 0.0697989i 0.438333 0.898813i \(-0.355569\pi\)
−0.559228 + 0.829014i \(0.688902\pi\)
\(978\) −32.5381 + 8.07488i −1.04045 + 0.258206i
\(979\) −10.7419 18.6056i −0.343314 0.594637i
\(980\) 11.3331 + 42.2955i 0.362021 + 1.35108i
\(981\) 27.9655 + 17.5600i 0.892871 + 0.560646i
\(982\) −26.5425 + 45.9729i −0.847005 + 1.46706i
\(983\) −43.8265 + 43.8265i −1.39785 + 1.39785i −0.591664 + 0.806185i \(0.701529\pi\)
−0.806185 + 0.591664i \(0.798471\pi\)
\(984\) 125.548 120.976i 4.00234 3.85656i
\(985\) 2.95206 11.0172i 0.0940604 0.351038i
\(986\) 49.8394 86.3245i 1.58721 2.74913i
\(987\) 6.79767 + 12.2950i 0.216372 + 0.391354i
\(988\) 0.126941 0.00403853
\(989\) 2.83990 1.63961i 0.0903034 0.0521367i
\(990\) −13.3381 + 7.05462i −0.423912 + 0.224210i
\(991\) 6.36327i 0.202136i −0.994880 0.101068i \(-0.967774\pi\)
0.994880 0.101068i \(-0.0322260\pi\)
\(992\) 33.2920 124.247i 1.05702 3.94486i
\(993\) 13.3251 + 53.6940i 0.422858 + 1.70393i
\(994\) 3.34636 + 5.79606i 0.106140 + 0.183840i
\(995\) 3.23207 12.0622i 0.102463 0.382399i
\(996\) −0.195032 + 0.107829i −0.00617982 + 0.00341670i
\(997\) −11.3532 + 42.3707i −0.359559 + 1.34189i 0.515090 + 0.857136i \(0.327759\pi\)
−0.874649 + 0.484757i \(0.838908\pi\)
\(998\) 26.4190 0.836280
\(999\) 15.2789 46.5040i 0.483402 1.47132i
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 471.2.l.b.50.1 200
3.2 odd 2 inner 471.2.l.b.50.50 yes 200
157.22 odd 12 inner 471.2.l.b.179.50 yes 200
471.179 even 12 inner 471.2.l.b.179.1 yes 200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.l.b.50.1 200 1.1 even 1 trivial
471.2.l.b.50.50 yes 200 3.2 odd 2 inner
471.2.l.b.179.1 yes 200 471.179 even 12 inner
471.2.l.b.179.50 yes 200 157.22 odd 12 inner