Properties

Label 403.2.h.b.222.6
Level $403$
Weight $2$
Character 403.222
Analytic conductor $3.218$
Analytic rank $0$
Dimension $34$
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] = [403,2,Mod(118,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.118");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (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: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 222.6
Character \(\chi\) \(=\) 403.222
Dual form 403.2.h.b.118.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.837386 q^{2} +(0.883556 - 1.53036i) q^{3} -1.29878 q^{4} +(-2.21305 - 3.83311i) q^{5} +(-0.739877 + 1.28150i) q^{6} +(-1.99716 + 3.45918i) q^{7} +2.76236 q^{8} +(-0.0613409 - 0.106246i) q^{9} +O(q^{10})\) \(q-0.837386 q^{2} +(0.883556 - 1.53036i) q^{3} -1.29878 q^{4} +(-2.21305 - 3.83311i) q^{5} +(-0.739877 + 1.28150i) q^{6} +(-1.99716 + 3.45918i) q^{7} +2.76236 q^{8} +(-0.0613409 - 0.106246i) q^{9} +(1.85318 + 3.20980i) q^{10} +(-1.39540 - 2.41690i) q^{11} +(-1.14755 + 1.98761i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(1.67239 - 2.89667i) q^{14} -7.82141 q^{15} +0.284411 q^{16} +(-0.576858 + 0.999148i) q^{17} +(0.0513661 + 0.0889686i) q^{18} +(-1.68123 + 2.91198i) q^{19} +(2.87427 + 4.97839i) q^{20} +(3.52920 + 6.11275i) q^{21} +(1.16849 + 2.02388i) q^{22} +0.745639 q^{23} +(2.44070 - 4.22741i) q^{24} +(-7.29518 + 12.6356i) q^{25} +(0.418693 + 0.725198i) q^{26} +5.08454 q^{27} +(2.59388 - 4.49273i) q^{28} -5.02785 q^{29} +6.54954 q^{30} +(0.0190669 + 5.56773i) q^{31} -5.76287 q^{32} -4.93164 q^{33} +(0.483053 - 0.836672i) q^{34} +17.6792 q^{35} +(0.0796687 + 0.137990i) q^{36} +(-1.55308 + 2.69001i) q^{37} +(1.40784 - 2.43845i) q^{38} -1.76711 q^{39} +(-6.11323 - 10.5884i) q^{40} +(-4.81293 - 8.33625i) q^{41} +(-2.95530 - 5.11873i) q^{42} +(4.51314 - 7.81698i) q^{43} +(1.81232 + 3.13903i) q^{44} +(-0.271501 + 0.470254i) q^{45} -0.624387 q^{46} -9.11327 q^{47} +(0.251293 - 0.435252i) q^{48} +(-4.47727 - 7.75486i) q^{49} +(6.10888 - 10.5809i) q^{50} +(1.01937 + 1.76561i) q^{51} +(0.649392 + 1.12478i) q^{52} +(2.71344 + 4.69982i) q^{53} -4.25772 q^{54} +(-6.17617 + 10.6974i) q^{55} +(-5.51686 + 9.55548i) q^{56} +(2.97093 + 5.14580i) q^{57} +4.21025 q^{58} +(0.500931 - 0.867638i) q^{59} +10.1583 q^{60} -11.4247 q^{61} +(-0.0159664 - 4.66234i) q^{62} +0.490030 q^{63} +4.25693 q^{64} +(-2.21305 + 3.83311i) q^{65} +4.12969 q^{66} +(-0.828863 - 1.43563i) q^{67} +(0.749215 - 1.29768i) q^{68} +(0.658813 - 1.14110i) q^{69} -14.8043 q^{70} +(-0.716560 - 1.24112i) q^{71} +(-0.169446 - 0.293488i) q^{72} +(-6.94652 - 12.0317i) q^{73} +(1.30053 - 2.25258i) q^{74} +(12.8914 + 22.3285i) q^{75} +(2.18356 - 3.78204i) q^{76} +11.1473 q^{77} +1.47975 q^{78} +(1.40672 - 2.43651i) q^{79} +(-0.629416 - 1.09018i) q^{80} +(4.67650 - 8.09993i) q^{81} +(4.03028 + 6.98066i) q^{82} +(-5.39673 - 9.34741i) q^{83} +(-4.58367 - 7.93915i) q^{84} +5.10646 q^{85} +(-3.77924 + 6.54583i) q^{86} +(-4.44239 + 7.69444i) q^{87} +(-3.85458 - 6.67634i) q^{88} +2.37455 q^{89} +(0.227351 - 0.393784i) q^{90} +3.99431 q^{91} -0.968424 q^{92} +(8.53750 + 4.89022i) q^{93} +7.63133 q^{94} +14.8826 q^{95} +(-5.09182 + 8.81929i) q^{96} -4.35710 q^{97} +(3.74921 + 6.49381i) q^{98} +(-0.171190 + 0.296510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.837386 −0.592121 −0.296061 0.955169i \(-0.595673\pi\)
−0.296061 + 0.955169i \(0.595673\pi\)
\(3\) 0.883556 1.53036i 0.510121 0.883556i −0.489810 0.871829i \(-0.662934\pi\)
0.999931 0.0117265i \(-0.00373274\pi\)
\(4\) −1.29878 −0.649392
\(5\) −2.21305 3.83311i −0.989706 1.71422i −0.618795 0.785552i \(-0.712379\pi\)
−0.370910 0.928669i \(-0.620954\pi\)
\(6\) −0.739877 + 1.28150i −0.302054 + 0.523172i
\(7\) −1.99716 + 3.45918i −0.754854 + 1.30745i 0.190592 + 0.981669i \(0.438959\pi\)
−0.945447 + 0.325777i \(0.894374\pi\)
\(8\) 2.76236 0.976640
\(9\) −0.0613409 0.106246i −0.0204470 0.0354152i
\(10\) 1.85318 + 3.20980i 0.586026 + 1.01503i
\(11\) −1.39540 2.41690i −0.420728 0.728722i 0.575283 0.817955i \(-0.304892\pi\)
−0.996011 + 0.0892322i \(0.971559\pi\)
\(12\) −1.14755 + 1.98761i −0.331269 + 0.573774i
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 1.67239 2.89667i 0.446965 0.774167i
\(15\) −7.82141 −2.01948
\(16\) 0.284411 0.0711027
\(17\) −0.576858 + 0.999148i −0.139909 + 0.242329i −0.927462 0.373918i \(-0.878014\pi\)
0.787553 + 0.616247i \(0.211348\pi\)
\(18\) 0.0513661 + 0.0889686i 0.0121071 + 0.0209701i
\(19\) −1.68123 + 2.91198i −0.385701 + 0.668054i −0.991866 0.127285i \(-0.959374\pi\)
0.606165 + 0.795339i \(0.292707\pi\)
\(20\) 2.87427 + 4.97839i 0.642707 + 1.11320i
\(21\) 3.52920 + 6.11275i 0.770134 + 1.33391i
\(22\) 1.16849 + 2.02388i 0.249122 + 0.431492i
\(23\) 0.745639 0.155476 0.0777382 0.996974i \(-0.475230\pi\)
0.0777382 + 0.996974i \(0.475230\pi\)
\(24\) 2.44070 4.22741i 0.498205 0.862916i
\(25\) −7.29518 + 12.6356i −1.45904 + 2.52712i
\(26\) 0.418693 + 0.725198i 0.0821125 + 0.142223i
\(27\) 5.08454 0.978520
\(28\) 2.59388 4.49273i 0.490197 0.849046i
\(29\) −5.02785 −0.933649 −0.466824 0.884350i \(-0.654602\pi\)
−0.466824 + 0.884350i \(0.654602\pi\)
\(30\) 6.54954 1.19578
\(31\) 0.0190669 + 5.56773i 0.00342452 + 0.999994i
\(32\) −5.76287 −1.01874
\(33\) −4.93164 −0.858489
\(34\) 0.483053 0.836672i 0.0828429 0.143488i
\(35\) 17.6792 2.98834
\(36\) 0.0796687 + 0.137990i 0.0132781 + 0.0229984i
\(37\) −1.55308 + 2.69001i −0.255325 + 0.442235i −0.964984 0.262310i \(-0.915516\pi\)
0.709659 + 0.704545i \(0.248849\pi\)
\(38\) 1.40784 2.43845i 0.228382 0.395569i
\(39\) −1.76711 −0.282964
\(40\) −6.11323 10.5884i −0.966587 1.67418i
\(41\) −4.81293 8.33625i −0.751654 1.30190i −0.947021 0.321173i \(-0.895923\pi\)
0.195367 0.980730i \(-0.437410\pi\)
\(42\) −2.95530 5.11873i −0.456013 0.789838i
\(43\) 4.51314 7.81698i 0.688247 1.19208i −0.284158 0.958778i \(-0.591714\pi\)
0.972405 0.233301i \(-0.0749528\pi\)
\(44\) 1.81232 + 3.13903i 0.273218 + 0.473227i
\(45\) −0.271501 + 0.470254i −0.0404730 + 0.0701013i
\(46\) −0.624387 −0.0920609
\(47\) −9.11327 −1.32931 −0.664654 0.747151i \(-0.731421\pi\)
−0.664654 + 0.747151i \(0.731421\pi\)
\(48\) 0.251293 0.435252i 0.0362710 0.0628232i
\(49\) −4.47727 7.75486i −0.639610 1.10784i
\(50\) 6.10888 10.5809i 0.863926 1.49636i
\(51\) 1.01937 + 1.76561i 0.142741 + 0.247234i
\(52\) 0.649392 + 1.12478i 0.0900545 + 0.155979i
\(53\) 2.71344 + 4.69982i 0.372720 + 0.645570i 0.989983 0.141187i \(-0.0450919\pi\)
−0.617263 + 0.786757i \(0.711759\pi\)
\(54\) −4.25772 −0.579403
\(55\) −6.17617 + 10.6974i −0.832794 + 1.44244i
\(56\) −5.51686 + 9.55548i −0.737221 + 1.27690i
\(57\) 2.97093 + 5.14580i 0.393509 + 0.681577i
\(58\) 4.21025 0.552833
\(59\) 0.500931 0.867638i 0.0652157 0.112957i −0.831574 0.555414i \(-0.812560\pi\)
0.896790 + 0.442457i \(0.145893\pi\)
\(60\) 10.1583 1.31143
\(61\) −11.4247 −1.46279 −0.731394 0.681955i \(-0.761130\pi\)
−0.731394 + 0.681955i \(0.761130\pi\)
\(62\) −0.0159664 4.66234i −0.00202773 0.592118i
\(63\) 0.490030 0.0617380
\(64\) 4.25693 0.532116
\(65\) −2.21305 + 3.83311i −0.274495 + 0.475439i
\(66\) 4.12969 0.508330
\(67\) −0.828863 1.43563i −0.101262 0.175390i 0.810943 0.585125i \(-0.198955\pi\)
−0.912205 + 0.409735i \(0.865621\pi\)
\(68\) 0.749215 1.29768i 0.0908556 0.157367i
\(69\) 0.658813 1.14110i 0.0793118 0.137372i
\(70\) −14.8043 −1.76946
\(71\) −0.716560 1.24112i −0.0850401 0.147294i 0.820368 0.571836i \(-0.193768\pi\)
−0.905408 + 0.424542i \(0.860435\pi\)
\(72\) −0.169446 0.293488i −0.0199693 0.0345879i
\(73\) −6.94652 12.0317i −0.813029 1.40821i −0.910735 0.412992i \(-0.864484\pi\)
0.0977055 0.995215i \(-0.468850\pi\)
\(74\) 1.30053 2.25258i 0.151183 0.261857i
\(75\) 12.8914 + 22.3285i 1.48857 + 2.57828i
\(76\) 2.18356 3.78204i 0.250472 0.433829i
\(77\) 11.1473 1.27035
\(78\) 1.47975 0.167549
\(79\) 1.40672 2.43651i 0.158268 0.274128i −0.775976 0.630762i \(-0.782742\pi\)
0.934244 + 0.356634i \(0.116076\pi\)
\(80\) −0.629416 1.09018i −0.0703708 0.121886i
\(81\) 4.67650 8.09993i 0.519611 0.899992i
\(82\) 4.03028 + 6.98066i 0.445070 + 0.770884i
\(83\) −5.39673 9.34741i −0.592368 1.02601i −0.993913 0.110172i \(-0.964860\pi\)
0.401545 0.915839i \(-0.368473\pi\)
\(84\) −4.58367 7.93915i −0.500119 0.866232i
\(85\) 5.10646 0.553874
\(86\) −3.77924 + 6.54583i −0.407526 + 0.705855i
\(87\) −4.44239 + 7.69444i −0.476274 + 0.824931i
\(88\) −3.85458 6.67634i −0.410900 0.711700i
\(89\) 2.37455 0.251702 0.125851 0.992049i \(-0.459834\pi\)
0.125851 + 0.992049i \(0.459834\pi\)
\(90\) 0.227351 0.393784i 0.0239649 0.0415085i
\(91\) 3.99431 0.418718
\(92\) −0.968424 −0.100965
\(93\) 8.53750 + 4.89022i 0.885297 + 0.507092i
\(94\) 7.63133 0.787111
\(95\) 14.8826 1.52692
\(96\) −5.09182 + 8.81929i −0.519682 + 0.900115i
\(97\) −4.35710 −0.442397 −0.221198 0.975229i \(-0.570997\pi\)
−0.221198 + 0.975229i \(0.570997\pi\)
\(98\) 3.74921 + 6.49381i 0.378727 + 0.655974i
\(99\) −0.171190 + 0.296510i −0.0172052 + 0.0298003i
\(100\) 9.47486 16.4109i 0.947486 1.64109i
\(101\) 1.46025 0.145300 0.0726499 0.997358i \(-0.476854\pi\)
0.0726499 + 0.997358i \(0.476854\pi\)
\(102\) −0.853608 1.47849i −0.0845198 0.146393i
\(103\) −5.46261 9.46152i −0.538247 0.932271i −0.998999 0.0447418i \(-0.985753\pi\)
0.460752 0.887529i \(-0.347580\pi\)
\(104\) −1.38118 2.39227i −0.135436 0.234581i
\(105\) 15.6206 27.0556i 1.52441 2.64036i
\(106\) −2.27220 3.93556i −0.220695 0.382256i
\(107\) −7.77964 + 13.4747i −0.752086 + 1.30265i 0.194724 + 0.980858i \(0.437619\pi\)
−0.946810 + 0.321793i \(0.895714\pi\)
\(108\) −6.60372 −0.635444
\(109\) −4.37993 −0.419522 −0.209761 0.977753i \(-0.567269\pi\)
−0.209761 + 0.977753i \(0.567269\pi\)
\(110\) 5.17184 8.95788i 0.493115 0.854100i
\(111\) 2.74446 + 4.75355i 0.260493 + 0.451187i
\(112\) −0.568013 + 0.983828i −0.0536722 + 0.0929630i
\(113\) 5.62626 + 9.74497i 0.529274 + 0.916730i 0.999417 + 0.0341394i \(0.0108690\pi\)
−0.470143 + 0.882590i \(0.655798\pi\)
\(114\) −2.48781 4.30902i −0.233005 0.403576i
\(115\) −1.65014 2.85812i −0.153876 0.266521i
\(116\) 6.53010 0.606304
\(117\) −0.0613409 + 0.106246i −0.00567097 + 0.00982241i
\(118\) −0.419473 + 0.726548i −0.0386156 + 0.0668842i
\(119\) −2.30415 3.99091i −0.211221 0.365846i
\(120\) −21.6055 −1.97230
\(121\) 1.60573 2.78121i 0.145976 0.252837i
\(122\) 9.56692 0.866148
\(123\) −17.0100 −1.53374
\(124\) −0.0247638 7.23128i −0.00222386 0.649389i
\(125\) 42.4479 3.79665
\(126\) −0.410344 −0.0365564
\(127\) 1.05463 1.82667i 0.0935832 0.162091i −0.815433 0.578851i \(-0.803501\pi\)
0.909016 + 0.416760i \(0.136835\pi\)
\(128\) 7.96106 0.703665
\(129\) −7.97521 13.8135i −0.702179 1.21621i
\(130\) 1.85318 3.20980i 0.162534 0.281518i
\(131\) −6.11480 + 10.5911i −0.534252 + 0.925352i 0.464947 + 0.885339i \(0.346073\pi\)
−0.999199 + 0.0400134i \(0.987260\pi\)
\(132\) 6.40514 0.557496
\(133\) −6.71537 11.6314i −0.582297 1.00857i
\(134\) 0.694078 + 1.20218i 0.0599592 + 0.103852i
\(135\) −11.2523 19.4896i −0.968447 1.67740i
\(136\) −1.59349 + 2.76000i −0.136640 + 0.236668i
\(137\) −1.70112 2.94642i −0.145336 0.251730i 0.784162 0.620556i \(-0.213093\pi\)
−0.929498 + 0.368826i \(0.879760\pi\)
\(138\) −0.551681 + 0.955540i −0.0469622 + 0.0813409i
\(139\) 10.2497 0.869372 0.434686 0.900582i \(-0.356859\pi\)
0.434686 + 0.900582i \(0.356859\pi\)
\(140\) −22.9615 −1.94060
\(141\) −8.05208 + 13.9466i −0.678108 + 1.17452i
\(142\) 0.600038 + 1.03930i 0.0503540 + 0.0872158i
\(143\) −1.39540 + 2.41690i −0.116689 + 0.202111i
\(144\) −0.0174460 0.0302174i −0.00145384 0.00251812i
\(145\) 11.1269 + 19.2723i 0.924038 + 1.60048i
\(146\) 5.81692 + 10.0752i 0.481412 + 0.833830i
\(147\) −15.8237 −1.30511
\(148\) 2.01712 3.49375i 0.165806 0.287184i
\(149\) −9.11796 + 15.7928i −0.746972 + 1.29379i 0.202296 + 0.979324i \(0.435160\pi\)
−0.949268 + 0.314469i \(0.898174\pi\)
\(150\) −10.7951 18.6976i −0.881414 1.52665i
\(151\) 16.7337 1.36177 0.680887 0.732389i \(-0.261595\pi\)
0.680887 + 0.732389i \(0.261595\pi\)
\(152\) −4.64417 + 8.04393i −0.376692 + 0.652449i
\(153\) 0.141540 0.0114428
\(154\) −9.33460 −0.752204
\(155\) 21.2996 12.3948i 1.71082 0.995570i
\(156\) 2.29510 0.183755
\(157\) −15.2206 −1.21473 −0.607367 0.794421i \(-0.707774\pi\)
−0.607367 + 0.794421i \(0.707774\pi\)
\(158\) −1.17797 + 2.04030i −0.0937139 + 0.162317i
\(159\) 9.58991 0.760529
\(160\) 12.7535 + 22.0898i 1.00825 + 1.74635i
\(161\) −1.48916 + 2.57930i −0.117362 + 0.203277i
\(162\) −3.91603 + 6.78277i −0.307673 + 0.532905i
\(163\) −1.56277 −0.122405 −0.0612026 0.998125i \(-0.519494\pi\)
−0.0612026 + 0.998125i \(0.519494\pi\)
\(164\) 6.25096 + 10.8270i 0.488118 + 0.845446i
\(165\) 10.9140 + 18.9036i 0.849652 + 1.47164i
\(166\) 4.51915 + 7.82739i 0.350754 + 0.607523i
\(167\) 0.981987 1.70085i 0.0759884 0.131616i −0.825527 0.564362i \(-0.809122\pi\)
0.901516 + 0.432746i \(0.142455\pi\)
\(168\) 9.74890 + 16.8856i 0.752144 + 1.30275i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) −4.27608 −0.327960
\(171\) 0.412514 0.0315457
\(172\) −5.86159 + 10.1526i −0.446942 + 0.774127i
\(173\) −1.42174 2.46252i −0.108093 0.187222i 0.806905 0.590681i \(-0.201141\pi\)
−0.914998 + 0.403459i \(0.867808\pi\)
\(174\) 3.71999 6.44322i 0.282012 0.488459i
\(175\) −29.1392 50.4706i −2.20272 3.81522i
\(176\) −0.396866 0.687393i −0.0299149 0.0518142i
\(177\) −0.885201 1.53321i −0.0665358 0.115243i
\(178\) −1.98841 −0.149038
\(179\) 10.2287 17.7166i 0.764528 1.32420i −0.175968 0.984396i \(-0.556306\pi\)
0.940496 0.339805i \(-0.110361\pi\)
\(180\) 0.352621 0.610758i 0.0262829 0.0455232i
\(181\) 6.85586 + 11.8747i 0.509592 + 0.882640i 0.999938 + 0.0111118i \(0.00353708\pi\)
−0.490346 + 0.871528i \(0.663130\pi\)
\(182\) −3.34478 −0.247932
\(183\) −10.0944 + 17.4840i −0.746199 + 1.29245i
\(184\) 2.05972 0.151845
\(185\) 13.7482 1.01079
\(186\) −7.14918 4.09500i −0.524203 0.300260i
\(187\) 3.21979 0.235454
\(188\) 11.8362 0.863242
\(189\) −10.1546 + 17.5883i −0.738640 + 1.27936i
\(190\) −12.4625 −0.904124
\(191\) 3.58671 + 6.21237i 0.259525 + 0.449511i 0.966115 0.258113i \(-0.0831006\pi\)
−0.706589 + 0.707624i \(0.749767\pi\)
\(192\) 3.76123 6.51465i 0.271444 0.470154i
\(193\) −11.8483 + 20.5219i −0.852860 + 1.47720i 0.0257554 + 0.999668i \(0.491801\pi\)
−0.878616 + 0.477529i \(0.841532\pi\)
\(194\) 3.64858 0.261953
\(195\) 3.91070 + 6.77354i 0.280051 + 0.485063i
\(196\) 5.81501 + 10.0719i 0.415358 + 0.719421i
\(197\) −8.93070 15.4684i −0.636286 1.10208i −0.986241 0.165313i \(-0.947136\pi\)
0.349955 0.936767i \(-0.386197\pi\)
\(198\) 0.143352 0.248293i 0.0101876 0.0176454i
\(199\) −0.268331 0.464763i −0.0190215 0.0329462i 0.856358 0.516383i \(-0.172722\pi\)
−0.875379 + 0.483436i \(0.839388\pi\)
\(200\) −20.1519 + 34.9041i −1.42495 + 2.46809i
\(201\) −2.92939 −0.206623
\(202\) −1.22279 −0.0860352
\(203\) 10.0414 17.3922i 0.704769 1.22070i
\(204\) −1.32395 2.29314i −0.0926947 0.160552i
\(205\) −21.3025 + 36.8971i −1.48783 + 2.57700i
\(206\) 4.57431 + 7.92294i 0.318707 + 0.552017i
\(207\) −0.0457382 0.0792209i −0.00317902 0.00550623i
\(208\) −0.142205 0.246307i −0.00986018 0.0170783i
\(209\) 9.38395 0.649102
\(210\) −13.0805 + 22.6560i −0.902637 + 1.56341i
\(211\) 3.48976 6.04443i 0.240245 0.416116i −0.720539 0.693414i \(-0.756106\pi\)
0.960784 + 0.277298i \(0.0894390\pi\)
\(212\) −3.52418 6.10405i −0.242042 0.419228i
\(213\) −2.53248 −0.173523
\(214\) 6.51456 11.2835i 0.445326 0.771328i
\(215\) −39.9512 −2.72465
\(216\) 14.0453 0.955662
\(217\) −19.2979 11.0537i −1.31002 0.750373i
\(218\) 3.66770 0.248408
\(219\) −24.5506 −1.65897
\(220\) 8.02151 13.8937i 0.540810 0.936711i
\(221\) 1.15372 0.0776074
\(222\) −2.29818 3.98056i −0.154243 0.267157i
\(223\) 1.16130 2.01143i 0.0777662 0.134695i −0.824520 0.565833i \(-0.808555\pi\)
0.902286 + 0.431138i \(0.141888\pi\)
\(224\) 11.5094 19.9348i 0.769002 1.33195i
\(225\) 1.78997 0.119331
\(226\) −4.71135 8.16030i −0.313395 0.542815i
\(227\) −6.02682 10.4388i −0.400014 0.692844i 0.593713 0.804677i \(-0.297661\pi\)
−0.993727 + 0.111832i \(0.964328\pi\)
\(228\) −3.85859 6.68328i −0.255542 0.442611i
\(229\) −8.82591 + 15.2869i −0.583233 + 1.01019i 0.411861 + 0.911247i \(0.364879\pi\)
−0.995093 + 0.0989416i \(0.968454\pi\)
\(230\) 1.38180 + 2.39335i 0.0911132 + 0.157813i
\(231\) 9.84927 17.0594i 0.648034 1.12243i
\(232\) −13.8887 −0.911839
\(233\) −11.0803 −0.725895 −0.362947 0.931810i \(-0.618229\pi\)
−0.362947 + 0.931810i \(0.618229\pi\)
\(234\) 0.0513661 0.0889686i 0.00335790 0.00581606i
\(235\) 20.1681 + 34.9322i 1.31562 + 2.27873i
\(236\) −0.650602 + 1.12687i −0.0423506 + 0.0733533i
\(237\) −2.48583 4.30558i −0.161472 0.279677i
\(238\) 1.92947 + 3.34193i 0.125069 + 0.216625i
\(239\) −5.37527 9.31025i −0.347698 0.602230i 0.638142 0.769918i \(-0.279703\pi\)
−0.985840 + 0.167688i \(0.946370\pi\)
\(240\) −2.22449 −0.143591
\(241\) 5.38850 9.33316i 0.347104 0.601202i −0.638630 0.769514i \(-0.720498\pi\)
0.985734 + 0.168313i \(0.0538318\pi\)
\(242\) −1.34462 + 2.32895i −0.0864354 + 0.149710i
\(243\) −0.637079 1.10345i −0.0408687 0.0707866i
\(244\) 14.8383 0.949923
\(245\) −19.8169 + 34.3238i −1.26605 + 2.19287i
\(246\) 14.2439 0.908159
\(247\) 3.36247 0.213949
\(248\) 0.0526696 + 15.3801i 0.00334452 + 0.976635i
\(249\) −19.0732 −1.20872
\(250\) −35.5452 −2.24808
\(251\) 9.81046 16.9922i 0.619231 1.07254i −0.370395 0.928874i \(-0.620778\pi\)
0.989626 0.143665i \(-0.0458889\pi\)
\(252\) −0.636443 −0.0400922
\(253\) −1.04046 1.80213i −0.0654133 0.113299i
\(254\) −0.883132 + 1.52963i −0.0554126 + 0.0959775i
\(255\) 4.51184 7.81474i 0.282543 0.489378i
\(256\) −15.1803 −0.948771
\(257\) −6.27771 10.8733i −0.391593 0.678259i 0.601067 0.799199i \(-0.294743\pi\)
−0.992660 + 0.120940i \(0.961409\pi\)
\(258\) 6.67833 + 11.5672i 0.415775 + 0.720143i
\(259\) −6.20349 10.7448i −0.385466 0.667646i
\(260\) 2.87427 4.97839i 0.178255 0.308747i
\(261\) 0.308413 + 0.534187i 0.0190903 + 0.0330654i
\(262\) 5.12044 8.86887i 0.316342 0.547921i
\(263\) −28.1587 −1.73634 −0.868170 0.496266i \(-0.834704\pi\)
−0.868170 + 0.496266i \(0.834704\pi\)
\(264\) −13.6230 −0.838435
\(265\) 12.0100 20.8019i 0.737766 1.27785i
\(266\) 5.62336 + 9.73995i 0.344790 + 0.597194i
\(267\) 2.09805 3.63392i 0.128398 0.222392i
\(268\) 1.07651 + 1.86458i 0.0657586 + 0.113897i
\(269\) −3.10195 5.37274i −0.189129 0.327582i 0.755831 0.654767i \(-0.227233\pi\)
−0.944960 + 0.327185i \(0.893900\pi\)
\(270\) 9.42255 + 16.3203i 0.573438 + 0.993224i
\(271\) −1.44701 −0.0878995 −0.0439497 0.999034i \(-0.513994\pi\)
−0.0439497 + 0.999034i \(0.513994\pi\)
\(272\) −0.164065 + 0.284169i −0.00994789 + 0.0172302i
\(273\) 3.52920 6.11275i 0.213597 0.369961i
\(274\) 1.42449 + 2.46729i 0.0860567 + 0.149055i
\(275\) 40.7187 2.45543
\(276\) −0.855657 + 1.48204i −0.0515045 + 0.0892084i
\(277\) 20.3836 1.22473 0.612367 0.790574i \(-0.290218\pi\)
0.612367 + 0.790574i \(0.290218\pi\)
\(278\) −8.58299 −0.514774
\(279\) 0.590378 0.343556i 0.0353450 0.0205681i
\(280\) 48.8363 2.91853
\(281\) 20.0622 1.19681 0.598405 0.801194i \(-0.295801\pi\)
0.598405 + 0.801194i \(0.295801\pi\)
\(282\) 6.74270 11.6787i 0.401522 0.695457i
\(283\) 21.1954 1.25994 0.629968 0.776621i \(-0.283068\pi\)
0.629968 + 0.776621i \(0.283068\pi\)
\(284\) 0.930658 + 1.61195i 0.0552244 + 0.0956514i
\(285\) 13.1496 22.7758i 0.778916 1.34912i
\(286\) 1.16849 2.02388i 0.0690940 0.119674i
\(287\) 38.4487 2.26956
\(288\) 0.353500 + 0.612280i 0.0208302 + 0.0360790i
\(289\) 7.83447 + 13.5697i 0.460851 + 0.798218i
\(290\) −9.31750 16.1384i −0.547142 0.947679i
\(291\) −3.84974 + 6.66795i −0.225676 + 0.390882i
\(292\) 9.02204 + 15.6266i 0.527975 + 0.914479i
\(293\) −0.263737 + 0.456805i −0.0154077 + 0.0266868i −0.873626 0.486597i \(-0.838238\pi\)
0.858219 + 0.513284i \(0.171571\pi\)
\(294\) 13.2505 0.772786
\(295\) −4.43434 −0.258177
\(296\) −4.29016 + 7.43077i −0.249360 + 0.431905i
\(297\) −7.09495 12.2888i −0.411691 0.713070i
\(298\) 7.63525 13.2246i 0.442298 0.766083i
\(299\) −0.372819 0.645742i −0.0215607 0.0373442i
\(300\) −16.7431 29.0000i −0.966666 1.67431i
\(301\) 18.0269 + 31.2235i 1.03905 + 1.79969i
\(302\) −14.0126 −0.806335
\(303\) 1.29021 2.23471i 0.0741205 0.128381i
\(304\) −0.478161 + 0.828199i −0.0274244 + 0.0475005i
\(305\) 25.2835 + 43.7923i 1.44773 + 2.50754i
\(306\) −0.118524 −0.00677555
\(307\) −5.06752 + 8.77720i −0.289219 + 0.500941i −0.973623 0.228161i \(-0.926729\pi\)
0.684405 + 0.729102i \(0.260062\pi\)
\(308\) −14.4780 −0.824958
\(309\) −19.3061 −1.09828
\(310\) −17.8360 + 10.3792i −1.01301 + 0.589498i
\(311\) −23.4109 −1.32751 −0.663756 0.747949i \(-0.731039\pi\)
−0.663756 + 0.747949i \(0.731039\pi\)
\(312\) −4.88139 −0.276354
\(313\) 13.4826 23.3526i 0.762083 1.31997i −0.179692 0.983723i \(-0.557510\pi\)
0.941775 0.336244i \(-0.109157\pi\)
\(314\) 12.7455 0.719270
\(315\) −1.08446 1.87834i −0.0611024 0.105833i
\(316\) −1.82702 + 3.16450i −0.102778 + 0.178017i
\(317\) 9.08022 15.7274i 0.509996 0.883339i −0.489937 0.871758i \(-0.662980\pi\)
0.999933 0.0115811i \(-0.00368647\pi\)
\(318\) −8.03046 −0.450326
\(319\) 7.01585 + 12.1518i 0.392812 + 0.680371i
\(320\) −9.42079 16.3173i −0.526638 0.912164i
\(321\) 13.7475 + 23.8113i 0.767310 + 1.32902i
\(322\) 1.24700 2.15987i 0.0694926 0.120365i
\(323\) −1.93967 3.35960i −0.107926 0.186933i
\(324\) −6.07376 + 10.5201i −0.337431 + 0.584448i
\(325\) 14.5904 0.809327
\(326\) 1.30864 0.0724787
\(327\) −3.86991 + 6.70289i −0.214007 + 0.370671i
\(328\) −13.2950 23.0277i −0.734096 1.27149i
\(329\) 18.2006 31.5244i 1.00343 1.73800i
\(330\) −9.13921 15.8296i −0.503097 0.871389i
\(331\) 7.65564 + 13.2600i 0.420792 + 0.728833i 0.996017 0.0891618i \(-0.0284188\pi\)
−0.575225 + 0.817995i \(0.695085\pi\)
\(332\) 7.00919 + 12.1403i 0.384679 + 0.666284i
\(333\) 0.381069 0.0208825
\(334\) −0.822302 + 1.42427i −0.0449944 + 0.0779325i
\(335\) −3.66863 + 6.35425i −0.200439 + 0.347170i
\(336\) 1.00374 + 1.73853i 0.0547587 + 0.0948448i
\(337\) −11.1650 −0.608196 −0.304098 0.952641i \(-0.598355\pi\)
−0.304098 + 0.952641i \(0.598355\pi\)
\(338\) 0.418693 0.725198i 0.0227739 0.0394455i
\(339\) 19.8845 1.07998
\(340\) −6.63220 −0.359681
\(341\) 13.4300 7.81528i 0.727277 0.423221i
\(342\) −0.345433 −0.0186789
\(343\) 7.80706 0.421542
\(344\) 12.4669 21.5933i 0.672170 1.16423i
\(345\) −5.83195 −0.313981
\(346\) 1.19054 + 2.06208i 0.0640040 + 0.110858i
\(347\) 17.1043 29.6255i 0.918208 1.59038i 0.116072 0.993241i \(-0.462970\pi\)
0.802136 0.597141i \(-0.203697\pi\)
\(348\) 5.76971 9.99342i 0.309289 0.535704i
\(349\) 10.2919 0.550915 0.275458 0.961313i \(-0.411171\pi\)
0.275458 + 0.961313i \(0.411171\pi\)
\(350\) 24.4008 + 42.2634i 1.30428 + 2.25907i
\(351\) −2.54227 4.40334i −0.135696 0.235033i
\(352\) 8.04150 + 13.9283i 0.428613 + 0.742380i
\(353\) 0.0801093 0.138753i 0.00426379 0.00738510i −0.863886 0.503688i \(-0.831976\pi\)
0.868149 + 0.496303i \(0.165309\pi\)
\(354\) 0.741255 + 1.28389i 0.0393972 + 0.0682380i
\(355\) −3.17157 + 5.49332i −0.168329 + 0.291555i
\(356\) −3.08403 −0.163453
\(357\) −8.14339 −0.430994
\(358\) −8.56535 + 14.8356i −0.452693 + 0.784087i
\(359\) 1.27797 + 2.21351i 0.0674487 + 0.116825i 0.897778 0.440449i \(-0.145181\pi\)
−0.830329 + 0.557274i \(0.811847\pi\)
\(360\) −0.749983 + 1.29901i −0.0395276 + 0.0684637i
\(361\) 3.84691 + 6.66304i 0.202469 + 0.350686i
\(362\) −5.74100 9.94371i −0.301740 0.522630i
\(363\) −2.83751 4.91471i −0.148931 0.257955i
\(364\) −5.18775 −0.271912
\(365\) −30.7460 + 53.2536i −1.60932 + 2.78742i
\(366\) 8.45290 14.6409i 0.441840 0.765290i
\(367\) −14.0952 24.4135i −0.735762 1.27438i −0.954388 0.298568i \(-0.903491\pi\)
0.218627 0.975809i \(-0.429842\pi\)
\(368\) 0.212068 0.0110548
\(369\) −0.590460 + 1.02271i −0.0307381 + 0.0532400i
\(370\) −11.5125 −0.598507
\(371\) −21.6767 −1.12540
\(372\) −11.0884 6.35134i −0.574905 0.329302i
\(373\) −24.1839 −1.25219 −0.626097 0.779745i \(-0.715349\pi\)
−0.626097 + 0.779745i \(0.715349\pi\)
\(374\) −2.69620 −0.139417
\(375\) 37.5050 64.9606i 1.93675 3.35455i
\(376\) −25.1741 −1.29826
\(377\) 2.51393 + 4.35425i 0.129474 + 0.224255i
\(378\) 8.50334 14.7282i 0.437365 0.757538i
\(379\) 6.58924 11.4129i 0.338467 0.586241i −0.645678 0.763610i \(-0.723425\pi\)
0.984145 + 0.177368i \(0.0567584\pi\)
\(380\) −19.3293 −0.991573
\(381\) −1.86365 3.22793i −0.0954775 0.165372i
\(382\) −3.00346 5.20215i −0.153671 0.266165i
\(383\) −1.86301 3.22682i −0.0951952 0.164883i 0.814495 0.580171i \(-0.197014\pi\)
−0.909690 + 0.415288i \(0.863681\pi\)
\(384\) 7.03404 12.1833i 0.358954 0.621727i
\(385\) −24.6695 42.7289i −1.25728 2.17767i
\(386\) 9.92161 17.1847i 0.504997 0.874680i
\(387\) −1.10736 −0.0562903
\(388\) 5.65894 0.287289
\(389\) −6.02389 + 10.4337i −0.305424 + 0.529009i −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(390\) −3.27477 5.67207i −0.165824 0.287216i
\(391\) −0.430128 + 0.745003i −0.0217525 + 0.0376764i
\(392\) −12.3678 21.4217i −0.624669 1.08196i
\(393\) 10.8055 + 18.7157i 0.545067 + 0.944083i
\(394\) 7.47844 + 12.9530i 0.376759 + 0.652565i
\(395\) −12.4525 −0.626556
\(396\) 0.222339 0.385102i 0.0111730 0.0193521i
\(397\) 16.5205 28.6143i 0.829140 1.43611i −0.0695737 0.997577i \(-0.522164\pi\)
0.898714 0.438536i \(-0.144503\pi\)
\(398\) 0.224697 + 0.389186i 0.0112630 + 0.0195081i
\(399\) −23.7336 −1.18817
\(400\) −2.07483 + 3.59371i −0.103741 + 0.179685i
\(401\) −23.6856 −1.18280 −0.591401 0.806378i \(-0.701425\pi\)
−0.591401 + 0.806378i \(0.701425\pi\)
\(402\) 2.45303 0.122346
\(403\) 4.81226 2.80038i 0.239716 0.139497i
\(404\) −1.89654 −0.0943566
\(405\) −41.3973 −2.05705
\(406\) −8.40854 + 14.5640i −0.417309 + 0.722800i
\(407\) 8.66865 0.429689
\(408\) 2.81587 + 4.87723i 0.139406 + 0.241459i
\(409\) −17.7737 + 30.7849i −0.878851 + 1.52222i −0.0262488 + 0.999655i \(0.508356\pi\)
−0.852603 + 0.522560i \(0.824977\pi\)
\(410\) 17.8384 30.8971i 0.880977 1.52590i
\(411\) −6.01213 −0.296556
\(412\) 7.09475 + 12.2885i 0.349533 + 0.605410i
\(413\) 2.00088 + 3.46562i 0.0984567 + 0.170532i
\(414\) 0.0383005 + 0.0663384i 0.00188237 + 0.00326036i
\(415\) −23.8865 + 41.3726i −1.17254 + 2.03090i
\(416\) 2.88144 + 4.99080i 0.141274 + 0.244694i
\(417\) 9.05622 15.6858i 0.443485 0.768138i
\(418\) −7.85799 −0.384347
\(419\) 23.4933 1.14772 0.573860 0.818953i \(-0.305445\pi\)
0.573860 + 0.818953i \(0.305445\pi\)
\(420\) −20.2878 + 35.1395i −0.989942 + 1.71463i
\(421\) 10.3395 + 17.9085i 0.503914 + 0.872805i 0.999990 + 0.00452547i \(0.00144051\pi\)
−0.496076 + 0.868279i \(0.665226\pi\)
\(422\) −2.92227 + 5.06153i −0.142254 + 0.246391i
\(423\) 0.559017 + 0.968246i 0.0271803 + 0.0470777i
\(424\) 7.49549 + 12.9826i 0.364013 + 0.630490i
\(425\) −8.41657 14.5779i −0.408263 0.707133i
\(426\) 2.12067 0.102747
\(427\) 22.8170 39.5202i 1.10419 1.91252i
\(428\) 10.1041 17.5008i 0.488399 0.845932i
\(429\) 2.46582 + 4.27093i 0.119051 + 0.206202i
\(430\) 33.4546 1.61332
\(431\) −1.66248 + 2.87950i −0.0800787 + 0.138700i −0.903284 0.429044i \(-0.858851\pi\)
0.823205 + 0.567745i \(0.192184\pi\)
\(432\) 1.44610 0.0695755
\(433\) −29.7410 −1.42926 −0.714630 0.699502i \(-0.753405\pi\)
−0.714630 + 0.699502i \(0.753405\pi\)
\(434\) 16.1598 + 9.25620i 0.775693 + 0.444312i
\(435\) 39.3249 1.88548
\(436\) 5.68859 0.272434
\(437\) −1.25359 + 2.17129i −0.0599675 + 0.103867i
\(438\) 20.5583 0.982313
\(439\) −12.0902 20.9409i −0.577034 0.999453i −0.995817 0.0913666i \(-0.970876\pi\)
0.418783 0.908086i \(-0.362457\pi\)
\(440\) −17.0608 + 29.5501i −0.813340 + 1.40875i
\(441\) −0.549280 + 0.951381i −0.0261562 + 0.0453039i
\(442\) −0.966106 −0.0459530
\(443\) 8.41160 + 14.5693i 0.399647 + 0.692209i 0.993682 0.112230i \(-0.0357993\pi\)
−0.594035 + 0.804439i \(0.702466\pi\)
\(444\) −3.56447 6.17384i −0.169162 0.292997i
\(445\) −5.25499 9.10191i −0.249111 0.431472i
\(446\) −0.972454 + 1.68434i −0.0460470 + 0.0797558i
\(447\) 16.1124 + 27.9076i 0.762092 + 1.31998i
\(448\) −8.50175 + 14.7255i −0.401670 + 0.695713i
\(449\) 27.2969 1.28822 0.644109 0.764934i \(-0.277228\pi\)
0.644109 + 0.764934i \(0.277228\pi\)
\(450\) −1.49890 −0.0706587
\(451\) −13.4319 + 23.2647i −0.632484 + 1.09549i
\(452\) −7.30730 12.6566i −0.343707 0.595317i
\(453\) 14.7852 25.6087i 0.694669 1.20320i
\(454\) 5.04677 + 8.74126i 0.236857 + 0.410248i
\(455\) −8.83961 15.3107i −0.414408 0.717775i
\(456\) 8.20676 + 14.2145i 0.384317 + 0.665656i
\(457\) 0.511763 0.0239393 0.0119696 0.999928i \(-0.496190\pi\)
0.0119696 + 0.999928i \(0.496190\pi\)
\(458\) 7.39069 12.8011i 0.345344 0.598154i
\(459\) −2.93306 + 5.08021i −0.136903 + 0.237124i
\(460\) 2.14317 + 3.71208i 0.0999259 + 0.173077i
\(461\) 6.73481 0.313671 0.156836 0.987625i \(-0.449871\pi\)
0.156836 + 0.987625i \(0.449871\pi\)
\(462\) −8.24764 + 14.2853i −0.383715 + 0.664614i
\(463\) 9.38450 0.436135 0.218067 0.975934i \(-0.430025\pi\)
0.218067 + 0.975934i \(0.430025\pi\)
\(464\) −1.42998 −0.0663850
\(465\) −0.149130 43.5475i −0.00691574 2.01947i
\(466\) 9.27849 0.429818
\(467\) 16.5236 0.764622 0.382311 0.924034i \(-0.375128\pi\)
0.382311 + 0.924034i \(0.375128\pi\)
\(468\) 0.0796687 0.137990i 0.00368269 0.00637860i
\(469\) 6.62148 0.305751
\(470\) −16.8885 29.2518i −0.779009 1.34928i
\(471\) −13.4482 + 23.2930i −0.619662 + 1.07329i
\(472\) 1.38375 2.39673i 0.0636923 0.110318i
\(473\) −25.1905 −1.15826
\(474\) 2.08160 + 3.60543i 0.0956109 + 0.165603i
\(475\) −24.5298 42.4868i −1.12550 1.94943i
\(476\) 2.99260 + 5.18333i 0.137166 + 0.237578i
\(477\) 0.332890 0.576583i 0.0152420 0.0263999i
\(478\) 4.50118 + 7.79627i 0.205879 + 0.356593i
\(479\) −1.66727 + 2.88779i −0.0761794 + 0.131947i −0.901599 0.432574i \(-0.857606\pi\)
0.825419 + 0.564520i \(0.190939\pi\)
\(480\) 45.0738 2.05733
\(481\) 3.10616 0.141629
\(482\) −4.51226 + 7.81546i −0.205528 + 0.355984i
\(483\) 2.63151 + 4.55790i 0.119738 + 0.207392i
\(484\) −2.08550 + 3.61220i −0.0947955 + 0.164191i
\(485\) 9.64249 + 16.7013i 0.437843 + 0.758366i
\(486\) 0.533481 + 0.924017i 0.0241992 + 0.0419143i
\(487\) 10.1354 + 17.5549i 0.459277 + 0.795490i 0.998923 0.0464015i \(-0.0147754\pi\)
−0.539646 + 0.841892i \(0.681442\pi\)
\(488\) −31.5592 −1.42862
\(489\) −1.38079 + 2.39160i −0.0624415 + 0.108152i
\(490\) 16.5944 28.7423i 0.749656 1.29844i
\(491\) −11.7204 20.3003i −0.528934 0.916141i −0.999431 0.0337392i \(-0.989258\pi\)
0.470496 0.882402i \(-0.344075\pi\)
\(492\) 22.0923 0.995998
\(493\) 2.90036 5.02357i 0.130626 0.226250i
\(494\) −2.81568 −0.126684
\(495\) 1.51541 0.0681125
\(496\) 0.00542284 + 1.58352i 0.000243493 + 0.0711023i
\(497\) 5.72434 0.256772
\(498\) 15.9717 0.715707
\(499\) −4.49905 + 7.79258i −0.201405 + 0.348844i −0.948981 0.315332i \(-0.897884\pi\)
0.747576 + 0.664176i \(0.231217\pi\)
\(500\) −55.1306 −2.46552
\(501\) −1.73528 3.00559i −0.0775266 0.134280i
\(502\) −8.21515 + 14.2290i −0.366660 + 0.635074i
\(503\) 15.1227 26.1933i 0.674287 1.16790i −0.302390 0.953184i \(-0.597784\pi\)
0.976677 0.214715i \(-0.0688823\pi\)
\(504\) 1.35364 0.0602958
\(505\) −3.23160 5.59729i −0.143804 0.249076i
\(506\) 0.871269 + 1.50908i 0.0387326 + 0.0670868i
\(507\) 0.883556 + 1.53036i 0.0392401 + 0.0679658i
\(508\) −1.36974 + 2.37245i −0.0607722 + 0.105261i
\(509\) 6.70207 + 11.6083i 0.297064 + 0.514530i 0.975463 0.220164i \(-0.0706592\pi\)
−0.678399 + 0.734694i \(0.737326\pi\)
\(510\) −3.77816 + 6.54396i −0.167300 + 0.289771i
\(511\) 55.4932 2.45487
\(512\) −3.21031 −0.141877
\(513\) −8.54830 + 14.8061i −0.377417 + 0.653705i
\(514\) 5.25687 + 9.10516i 0.231871 + 0.401612i
\(515\) −24.1780 + 41.8776i −1.06541 + 1.84535i
\(516\) 10.3581 + 17.9407i 0.455989 + 0.789797i
\(517\) 12.7166 + 22.0259i 0.559277 + 0.968696i
\(518\) 5.19471 + 8.99751i 0.228243 + 0.395328i
\(519\) −5.02474 −0.220561
\(520\) −6.11323 + 10.5884i −0.268083 + 0.464333i
\(521\) 1.96817 3.40897i 0.0862271 0.149350i −0.819686 0.572813i \(-0.805852\pi\)
0.905913 + 0.423463i \(0.139186\pi\)
\(522\) −0.258261 0.447321i −0.0113038 0.0195787i
\(523\) −6.28091 −0.274645 −0.137323 0.990526i \(-0.543850\pi\)
−0.137323 + 0.990526i \(0.543850\pi\)
\(524\) 7.94180 13.7556i 0.346939 0.600916i
\(525\) −102.985 −4.49461
\(526\) 23.5797 1.02812
\(527\) −5.57399 3.19274i −0.242807 0.139078i
\(528\) −1.40261 −0.0610409
\(529\) −22.4440 −0.975827
\(530\) −10.0570 + 17.4192i −0.436847 + 0.756642i
\(531\) −0.122910 −0.00533385
\(532\) 8.72182 + 15.1066i 0.378139 + 0.654956i
\(533\) −4.81293 + 8.33625i −0.208471 + 0.361083i
\(534\) −1.75687 + 3.04299i −0.0760274 + 0.131683i
\(535\) 68.8669 2.97738
\(536\) −2.28961 3.96573i −0.0988963 0.171293i
\(537\) −18.0752 31.3072i −0.780003 1.35101i
\(538\) 2.59753 + 4.49905i 0.111987 + 0.193968i
\(539\) −12.4951 + 21.6422i −0.538204 + 0.932197i
\(540\) 14.6144 + 25.3128i 0.628902 + 1.08929i
\(541\) 0.630481 1.09203i 0.0271065 0.0469498i −0.852154 0.523291i \(-0.824704\pi\)
0.879260 + 0.476341i \(0.158037\pi\)
\(542\) 1.21170 0.0520472
\(543\) 24.2301 1.03981
\(544\) 3.32436 5.75796i 0.142531 0.246871i
\(545\) 9.69301 + 16.7888i 0.415203 + 0.719153i
\(546\) −2.95530 + 5.11873i −0.126475 + 0.219062i
\(547\) −7.17125 12.4210i −0.306620 0.531082i 0.671000 0.741457i \(-0.265865\pi\)
−0.977621 + 0.210375i \(0.932532\pi\)
\(548\) 2.20939 + 3.82677i 0.0943803 + 0.163471i
\(549\) 0.700804 + 1.21383i 0.0299096 + 0.0518049i
\(550\) −34.0973 −1.45391
\(551\) 8.45299 14.6410i 0.360110 0.623728i
\(552\) 1.81988 3.15212i 0.0774591 0.134163i
\(553\) 5.61887 + 9.73217i 0.238939 + 0.413854i
\(554\) −17.0690 −0.725191
\(555\) 12.1473 21.0397i 0.515623 0.893085i
\(556\) −13.3122 −0.564563
\(557\) −5.94358 −0.251838 −0.125919 0.992041i \(-0.540188\pi\)
−0.125919 + 0.992041i \(0.540188\pi\)
\(558\) −0.494374 + 0.287689i −0.0209285 + 0.0121788i
\(559\) −9.02627 −0.381771
\(560\) 5.02817 0.212479
\(561\) 2.84486 4.92744i 0.120110 0.208037i
\(562\) −16.7998 −0.708657
\(563\) 9.46829 + 16.3996i 0.399041 + 0.691159i 0.993608 0.112887i \(-0.0360098\pi\)
−0.594567 + 0.804046i \(0.702677\pi\)
\(564\) 10.4579 18.1137i 0.440358 0.762723i
\(565\) 24.9024 43.1322i 1.04765 1.81459i
\(566\) −17.7487 −0.746035
\(567\) 18.6794 + 32.3537i 0.784461 + 1.35873i
\(568\) −1.97940 3.42841i −0.0830536 0.143853i
\(569\) 4.70474 + 8.14884i 0.197233 + 0.341617i 0.947630 0.319370i \(-0.103471\pi\)
−0.750397 + 0.660987i \(0.770138\pi\)
\(570\) −11.0113 + 19.0721i −0.461213 + 0.798844i
\(571\) −18.1155 31.3770i −0.758111 1.31309i −0.943813 0.330481i \(-0.892789\pi\)
0.185701 0.982606i \(-0.440544\pi\)
\(572\) 1.81232 3.13903i 0.0757769 0.131249i
\(573\) 12.6762 0.529557
\(574\) −32.1964 −1.34385
\(575\) −5.43957 + 9.42161i −0.226846 + 0.392908i
\(576\) −0.261124 0.452280i −0.0108802 0.0188450i
\(577\) 0.0752435 0.130326i 0.00313243 0.00542552i −0.864455 0.502710i \(-0.832336\pi\)
0.867587 + 0.497285i \(0.165670\pi\)
\(578\) −6.56047 11.3631i −0.272880 0.472642i
\(579\) 20.9373 + 36.2645i 0.870124 + 1.50710i
\(580\) −14.4514 25.0306i −0.600063 1.03934i
\(581\) 43.1125 1.78861
\(582\) 3.22372 5.58365i 0.133628 0.231450i
\(583\) 7.57266 13.1162i 0.313628 0.543219i
\(584\) −19.1888 33.2359i −0.794037 1.37531i
\(585\) 0.543002 0.0224504
\(586\) 0.220849 0.382522i 0.00912320 0.0158018i
\(587\) 35.1844 1.45222 0.726108 0.687581i \(-0.241327\pi\)
0.726108 + 0.687581i \(0.241327\pi\)
\(588\) 20.5515 0.847532
\(589\) −16.2452 9.30513i −0.669371 0.383411i
\(590\) 3.71326 0.152872
\(591\) −31.5631 −1.29833
\(592\) −0.441713 + 0.765069i −0.0181543 + 0.0314441i
\(593\) −7.69506 −0.315998 −0.157999 0.987439i \(-0.550504\pi\)
−0.157999 + 0.987439i \(0.550504\pi\)
\(594\) 5.94122 + 10.2905i 0.243771 + 0.422224i
\(595\) −10.1984 + 17.6642i −0.418094 + 0.724160i
\(596\) 11.8423 20.5114i 0.485078 0.840180i
\(597\) −0.948342 −0.0388131
\(598\) 0.312194 + 0.540735i 0.0127666 + 0.0221123i
\(599\) 5.81768 + 10.0765i 0.237704 + 0.411715i 0.960055 0.279811i \(-0.0902719\pi\)
−0.722351 + 0.691526i \(0.756939\pi\)
\(600\) 35.6106 + 61.6794i 1.45380 + 2.51805i
\(601\) −20.1823 + 34.9568i −0.823255 + 1.42592i 0.0799911 + 0.996796i \(0.474511\pi\)
−0.903246 + 0.429123i \(0.858823\pi\)
\(602\) −15.0955 26.1461i −0.615245 1.06564i
\(603\) −0.101686 + 0.176126i −0.00414099 + 0.00717241i
\(604\) −21.7335 −0.884325
\(605\) −14.2143 −0.577892
\(606\) −1.08040 + 1.87131i −0.0438883 + 0.0760168i
\(607\) −9.55423 16.5484i −0.387794 0.671679i 0.604358 0.796713i \(-0.293430\pi\)
−0.992153 + 0.125033i \(0.960096\pi\)
\(608\) 9.68874 16.7814i 0.392930 0.680575i
\(609\) −17.7443 30.7340i −0.719035 1.24541i
\(610\) −21.1721 36.6711i −0.857232 1.48477i
\(611\) 4.55664 + 7.89233i 0.184342 + 0.319289i
\(612\) −0.183830 −0.00743089
\(613\) 2.84581 4.92909i 0.114941 0.199084i −0.802815 0.596228i \(-0.796665\pi\)
0.917756 + 0.397144i \(0.129999\pi\)
\(614\) 4.24347 7.34991i 0.171253 0.296618i
\(615\) 37.6439 + 65.2012i 1.51795 + 2.62917i
\(616\) 30.7928 1.24068
\(617\) 1.21982 2.11278i 0.0491079 0.0850574i −0.840427 0.541925i \(-0.817696\pi\)
0.889534 + 0.456868i \(0.151029\pi\)
\(618\) 16.1666 0.650318
\(619\) 29.6368 1.19120 0.595601 0.803281i \(-0.296914\pi\)
0.595601 + 0.803281i \(0.296914\pi\)
\(620\) −27.6635 + 16.0981i −1.11099 + 0.646516i
\(621\) 3.79123 0.152137
\(622\) 19.6040 0.786048
\(623\) −4.74235 + 8.21398i −0.189998 + 0.329086i
\(624\) −0.502586 −0.0201195
\(625\) −57.4633 99.5294i −2.29853 3.98118i
\(626\) −11.2902 + 19.5551i −0.451246 + 0.781580i
\(627\) 8.29124 14.3609i 0.331120 0.573517i
\(628\) 19.7683 0.788840
\(629\) −1.79181 3.10351i −0.0714443 0.123745i
\(630\) 0.908112 + 1.57290i 0.0361801 + 0.0626657i
\(631\) 0.837471 + 1.45054i 0.0333392 + 0.0577452i 0.882214 0.470849i \(-0.156053\pi\)
−0.848874 + 0.528595i \(0.822719\pi\)
\(632\) 3.88586 6.73050i 0.154571 0.267725i
\(633\) −6.16679 10.6812i −0.245108 0.424539i
\(634\) −7.60365 + 13.1699i −0.301980 + 0.523044i
\(635\) −9.33579 −0.370479
\(636\) −12.4552 −0.493882
\(637\) −4.47727 + 7.75486i −0.177396 + 0.307259i
\(638\) −5.87498 10.1758i −0.232593 0.402862i
\(639\) −0.0879090 + 0.152263i −0.00347763 + 0.00602343i
\(640\) −17.6182 30.5156i −0.696421 1.20624i
\(641\) −2.15900 3.73950i −0.0852754 0.147701i 0.820233 0.572029i \(-0.193844\pi\)
−0.905509 + 0.424328i \(0.860510\pi\)
\(642\) −11.5120 19.9393i −0.454341 0.786941i
\(643\) 39.2702 1.54867 0.774333 0.632778i \(-0.218085\pi\)
0.774333 + 0.632778i \(0.218085\pi\)
\(644\) 1.93410 3.34995i 0.0762140 0.132007i
\(645\) −35.2991 + 61.1398i −1.38990 + 2.40738i
\(646\) 1.62425 + 2.81328i 0.0639052 + 0.110687i
\(647\) −27.1603 −1.06778 −0.533891 0.845554i \(-0.679271\pi\)
−0.533891 + 0.845554i \(0.679271\pi\)
\(648\) 12.9182 22.3749i 0.507473 0.878969i
\(649\) −2.79599 −0.109752
\(650\) −12.2178 −0.479220
\(651\) −33.9669 + 19.7662i −1.33127 + 0.774698i
\(652\) 2.02970 0.0794890
\(653\) −40.9577 −1.60280 −0.801400 0.598129i \(-0.795911\pi\)
−0.801400 + 0.598129i \(0.795911\pi\)
\(654\) 3.24061 5.61291i 0.126718 0.219482i
\(655\) 54.1294 2.11501
\(656\) −1.36885 2.37092i −0.0534447 0.0925689i
\(657\) −0.852213 + 1.47608i −0.0332480 + 0.0575872i
\(658\) −15.2410 + 26.3981i −0.594155 + 1.02911i
\(659\) −8.47471 −0.330128 −0.165064 0.986283i \(-0.552783\pi\)
−0.165064 + 0.986283i \(0.552783\pi\)
\(660\) −14.1749 24.5516i −0.551757 0.955672i
\(661\) 4.32047 + 7.48328i 0.168047 + 0.291066i 0.937733 0.347357i \(-0.112921\pi\)
−0.769686 + 0.638422i \(0.779587\pi\)
\(662\) −6.41073 11.1037i −0.249160 0.431558i
\(663\) 1.01937 1.76561i 0.0395892 0.0685704i
\(664\) −14.9077 25.8209i −0.578530 1.00204i
\(665\) −29.7229 + 51.4816i −1.15261 + 1.99637i
\(666\) −0.319102 −0.0123650
\(667\) −3.74896 −0.145160
\(668\) −1.27539 + 2.20904i −0.0493463 + 0.0854703i
\(669\) −2.05214 3.55441i −0.0793404 0.137422i
\(670\) 3.07206 5.32096i 0.118684 0.205567i
\(671\) 15.9420 + 27.6124i 0.615436 + 1.06597i
\(672\) −20.3383 35.2270i −0.784568 1.35891i
\(673\) 15.4873 + 26.8249i 0.596993 + 1.03402i 0.993262 + 0.115888i \(0.0369713\pi\)
−0.396269 + 0.918134i \(0.629695\pi\)
\(674\) 9.34941 0.360126
\(675\) −37.0926 + 64.2463i −1.42770 + 2.47284i
\(676\) 0.649392 1.12478i 0.0249766 0.0432608i
\(677\) 5.98801 + 10.3715i 0.230138 + 0.398610i 0.957848 0.287274i \(-0.0927490\pi\)
−0.727711 + 0.685884i \(0.759416\pi\)
\(678\) −16.6510 −0.639477
\(679\) 8.70182 15.0720i 0.333945 0.578410i
\(680\) 14.1059 0.540935
\(681\) −21.3001 −0.816222
\(682\) −11.2461 + 6.54441i −0.430636 + 0.250598i
\(683\) −50.5559 −1.93447 −0.967234 0.253888i \(-0.918291\pi\)
−0.967234 + 0.253888i \(0.918291\pi\)
\(684\) −0.535767 −0.0204855
\(685\) −7.52932 + 13.0412i −0.287680 + 0.498277i
\(686\) −6.53753 −0.249604
\(687\) 15.5964 + 27.0137i 0.595038 + 1.03064i
\(688\) 1.28359 2.22324i 0.0489362 0.0847601i
\(689\) 2.71344 4.69982i 0.103374 0.179049i
\(690\) 4.88359 0.185915
\(691\) −2.55778 4.43021i −0.0973027 0.168533i 0.813265 0.581894i \(-0.197688\pi\)
−0.910567 + 0.413361i \(0.864355\pi\)
\(692\) 1.84653 + 3.19829i 0.0701946 + 0.121581i
\(693\) −0.683786 1.18435i −0.0259749 0.0449898i
\(694\) −14.3229 + 24.8080i −0.543690 + 0.941699i
\(695\) −22.6832 39.2884i −0.860422 1.49030i
\(696\) −12.2715 + 21.2548i −0.465148 + 0.805661i
\(697\) 11.1055 0.420652
\(698\) −8.61833 −0.326209
\(699\) −9.79006 + 16.9569i −0.370294 + 0.641368i
\(700\) 37.8456 + 65.5505i 1.43043 + 2.47757i
\(701\) −11.0044 + 19.0602i −0.415632 + 0.719895i −0.995495 0.0948188i \(-0.969773\pi\)
0.579863 + 0.814714i \(0.303106\pi\)
\(702\) 2.12886 + 3.68730i 0.0803487 + 0.139168i
\(703\) −5.22218 9.04508i −0.196958 0.341141i
\(704\) −5.94011 10.2886i −0.223876 0.387765i
\(705\) 71.2787 2.68451
\(706\) −0.0670824 + 0.116190i −0.00252468 + 0.00437288i
\(707\) −2.91634 + 5.05125i −0.109680 + 0.189972i
\(708\) 1.14969 + 1.99131i 0.0432078 + 0.0748381i
\(709\) 24.0908 0.904748 0.452374 0.891828i \(-0.350577\pi\)
0.452374 + 0.891828i \(0.350577\pi\)
\(710\) 2.65583 4.60003i 0.0996714 0.172636i
\(711\) −0.345158 −0.0129444
\(712\) 6.55935 0.245822
\(713\) 0.0142170 + 4.15152i 0.000532432 + 0.155476i
\(714\) 6.81916 0.255201
\(715\) 12.3523 0.461951
\(716\) −13.2849 + 23.0100i −0.496478 + 0.859926i
\(717\) −18.9974 −0.709471
\(718\) −1.07015 1.85356i −0.0399378 0.0691743i
\(719\) 2.69660 4.67065i 0.100566 0.174186i −0.811352 0.584558i \(-0.801268\pi\)
0.911918 + 0.410372i \(0.134601\pi\)
\(720\) −0.0772179 + 0.133745i −0.00287774 + 0.00498439i
\(721\) 43.6388 1.62519
\(722\) −3.22135 5.57954i −0.119886 0.207649i
\(723\) −9.52208 16.4927i −0.354130 0.613371i
\(724\) −8.90429 15.4227i −0.330925 0.573179i
\(725\) 36.6791 63.5300i 1.36223 2.35945i
\(726\) 2.37609 + 4.11551i 0.0881850 + 0.152741i
\(727\) −14.4282 + 24.9904i −0.535113 + 0.926843i 0.464045 + 0.885812i \(0.346398\pi\)
−0.999158 + 0.0410310i \(0.986936\pi\)
\(728\) 11.0337 0.408937
\(729\) 25.8074 0.955830
\(730\) 25.7463 44.5938i 0.952912 1.65049i
\(731\) 5.20688 + 9.01858i 0.192583 + 0.333564i
\(732\) 13.1104 22.7080i 0.484576 0.839310i
\(733\) −3.04248 5.26973i −0.112377 0.194642i 0.804351 0.594154i \(-0.202513\pi\)
−0.916728 + 0.399512i \(0.869180\pi\)
\(734\) 11.8031 + 20.4436i 0.435660 + 0.754585i
\(735\) 35.0186 + 60.6540i 1.29168 + 2.23725i
\(736\) −4.29702 −0.158390
\(737\) −2.31319 + 4.00656i −0.0852073 + 0.147583i
\(738\) 0.494443 0.856400i 0.0182007 0.0315245i
\(739\) 19.9983 + 34.6381i 0.735650 + 1.27418i 0.954437 + 0.298411i \(0.0964566\pi\)
−0.218787 + 0.975773i \(0.570210\pi\)
\(740\) −17.8559 −0.656396
\(741\) 2.97093 5.14580i 0.109140 0.189036i
\(742\) 18.1518 0.666372
\(743\) −31.9389 −1.17172 −0.585862 0.810411i \(-0.699244\pi\)
−0.585862 + 0.810411i \(0.699244\pi\)
\(744\) 23.5836 + 13.5085i 0.864617 + 0.495247i
\(745\) 80.7140 2.95713
\(746\) 20.2513 0.741451
\(747\) −0.662081 + 1.14676i −0.0242243 + 0.0419577i
\(748\) −4.18181 −0.152902
\(749\) −31.0743 53.8223i −1.13543 1.96662i
\(750\) −31.4062 + 54.3971i −1.14679 + 1.98630i
\(751\) 6.94224 12.0243i 0.253326 0.438773i −0.711114 0.703077i \(-0.751809\pi\)
0.964439 + 0.264304i \(0.0851422\pi\)
\(752\) −2.59192 −0.0945174
\(753\) −17.3362 30.0271i −0.631766 1.09425i
\(754\) −2.10513 3.64619i −0.0766642 0.132786i
\(755\) −37.0326 64.1424i −1.34775 2.33438i
\(756\) 13.1887 22.8435i 0.479667 0.830808i
\(757\) 20.8327 + 36.0833i 0.757178 + 1.31147i 0.944284 + 0.329132i \(0.106756\pi\)
−0.187106 + 0.982340i \(0.559911\pi\)
\(758\) −5.51774 + 9.55700i −0.200413 + 0.347126i
\(759\) −3.67722 −0.133475
\(760\) 41.1111 1.49126
\(761\) 11.4653 19.8585i 0.415616 0.719869i −0.579876 0.814704i \(-0.696899\pi\)
0.995493 + 0.0948356i \(0.0302325\pi\)
\(762\) 1.56059 + 2.70303i 0.0565343 + 0.0979203i
\(763\) 8.74741 15.1510i 0.316678 0.548502i
\(764\) −4.65837 8.06853i −0.168534 0.291909i
\(765\) −0.313235 0.542539i −0.0113250 0.0196156i
\(766\) 1.56006 + 2.70210i 0.0563671 + 0.0976307i
\(767\) −1.00186 −0.0361751
\(768\) −13.4127 + 23.2314i −0.483988 + 0.838292i
\(769\) −20.1493 + 34.8996i −0.726601 + 1.25851i 0.231710 + 0.972785i \(0.425568\pi\)
−0.958312 + 0.285725i \(0.907765\pi\)
\(770\) 20.6579 + 35.7806i 0.744460 + 1.28944i
\(771\) −22.1868 −0.799039
\(772\) 15.3884 26.6535i 0.553841 0.959281i
\(773\) −1.31154 −0.0471726 −0.0235863 0.999722i \(-0.507508\pi\)
−0.0235863 + 0.999722i \(0.507508\pi\)
\(774\) 0.927288 0.0333307
\(775\) −70.4908 40.3767i −2.53211 1.45037i
\(776\) −12.0359 −0.432063
\(777\) −21.9245 −0.786537
\(778\) 5.04432 8.73703i 0.180848 0.313238i
\(779\) 32.3667 1.15966
\(780\) −5.07916 8.79737i −0.181863 0.314996i
\(781\) −1.99977 + 3.46371i −0.0715575 + 0.123941i
\(782\) 0.360183 0.623855i 0.0128801 0.0223090i
\(783\) −25.5643 −0.913594
\(784\) −1.27339 2.20557i −0.0454780 0.0787703i
\(785\) 33.6839 + 58.3422i 1.20223 + 2.08232i
\(786\) −9.04840 15.6723i −0.322746 0.559012i
\(787\) −1.54321 + 2.67292i −0.0550096 + 0.0952794i −0.892219 0.451603i \(-0.850852\pi\)
0.837209 + 0.546883i \(0.184186\pi\)
\(788\) 11.5991 + 20.0902i 0.413199 + 0.715682i
\(789\) −24.8798 + 43.0931i −0.885744 + 1.53415i
\(790\) 10.4276 0.370997
\(791\) −44.9461 −1.59810
\(792\) −0.472888 + 0.819065i −0.0168033 + 0.0291042i
\(793\) 5.71237 + 9.89411i 0.202852 + 0.351350i
\(794\) −13.8340 + 23.9612i −0.490951 + 0.850353i
\(795\) −21.2229 36.7592i −0.752700 1.30372i
\(796\) 0.348504 + 0.603627i 0.0123524 + 0.0213950i
\(797\) −22.4317 38.8529i −0.794573 1.37624i −0.923110 0.384535i \(-0.874362\pi\)
0.128538 0.991705i \(-0.458972\pi\)
\(798\) 19.8742 0.703539
\(799\) 5.25707 9.10551i 0.185982 0.322130i
\(800\) 42.0412 72.8175i 1.48638 2.57449i
\(801\) −0.145657 0.252285i −0.00514654 0.00891407i
\(802\) 19.8340 0.700362
\(803\) −19.3863 + 33.5781i −0.684128 + 1.18494i
\(804\) 3.80464 0.134179
\(805\) 13.1823 0.464616
\(806\) −4.02972 + 2.34500i −0.141941 + 0.0825990i
\(807\) −10.9630 −0.385915
\(808\) 4.03372 0.141906
\(809\) 1.06689 1.84791i 0.0375100 0.0649692i −0.846661 0.532133i \(-0.821391\pi\)
0.884171 + 0.467164i \(0.154724\pi\)
\(810\) 34.6655 1.21802
\(811\) −9.27723 16.0686i −0.325768 0.564246i 0.655900 0.754848i \(-0.272289\pi\)
−0.981667 + 0.190602i \(0.938956\pi\)
\(812\) −13.0416 + 22.5888i −0.457672 + 0.792710i
\(813\) −1.27851 + 2.21445i −0.0448394 + 0.0776641i
\(814\) −7.25901 −0.254428
\(815\) 3.45848 + 5.99026i 0.121145 + 0.209830i
\(816\) 0.289921 + 0.502157i 0.0101493 + 0.0175790i
\(817\) 15.1753 + 26.2843i 0.530916 + 0.919573i
\(818\) 14.8834 25.7788i 0.520387 0.901336i
\(819\) −0.245015 0.424378i −0.00856152 0.0148290i
\(820\) 27.6674 47.9213i 0.966187 1.67349i
\(821\) 47.2678 1.64966 0.824828 0.565383i \(-0.191272\pi\)
0.824828 + 0.565383i \(0.191272\pi\)
\(822\) 5.03447 0.175597
\(823\) 10.1029 17.4988i 0.352166 0.609969i −0.634463 0.772953i \(-0.718779\pi\)
0.986629 + 0.162985i \(0.0521121\pi\)
\(824\) −15.0897 26.1361i −0.525674 0.910493i
\(825\) 35.9772 62.3144i 1.25257 2.16951i
\(826\) −1.67551 2.90206i −0.0582983 0.100976i
\(827\) −19.9405 34.5379i −0.693399 1.20100i −0.970717 0.240224i \(-0.922779\pi\)
0.277319 0.960778i \(-0.410554\pi\)
\(828\) 0.0594041 + 0.102891i 0.00206443 + 0.00357570i
\(829\) −30.1828 −1.04829 −0.524146 0.851628i \(-0.675615\pi\)
−0.524146 + 0.851628i \(0.675615\pi\)
\(830\) 20.0022 34.6448i 0.694286 1.20254i
\(831\) 18.0101 31.1944i 0.624762 1.08212i
\(832\) −2.12846 3.68661i −0.0737912 0.127810i
\(833\) 10.3310 0.357948
\(834\) −7.58355 + 13.1351i −0.262597 + 0.454831i
\(835\) −8.69274 −0.300825
\(836\) −12.1877 −0.421522
\(837\) 0.0969465 + 28.3094i 0.00335096 + 0.978515i
\(838\) −19.6729 −0.679590
\(839\) 25.6696 0.886213 0.443106 0.896469i \(-0.353876\pi\)
0.443106 + 0.896469i \(0.353876\pi\)
\(840\) 43.1496 74.7373i 1.48880 2.57868i
\(841\) −3.72069 −0.128300
\(842\) −8.65811 14.9963i −0.298378 0.516806i
\(843\) 17.7261 30.7024i 0.610518 1.05745i
\(844\) −4.53244 + 7.85042i −0.156013 + 0.270223i
\(845\) 4.42610 0.152262
\(846\) −0.468113 0.810795i −0.0160941 0.0278757i
\(847\) 6.41380 + 11.1090i 0.220381 + 0.381711i
\(848\) 0.771733 + 1.33668i 0.0265014 + 0.0459018i
\(849\) 18.7273 32.4367i 0.642720 1.11322i
\(850\) 7.04791 + 12.2073i 0.241741 + 0.418708i
\(851\) −1.15804 + 2.00578i −0.0396970 + 0.0687572i
\(852\) 3.28915 0.112684
\(853\) −53.5450 −1.83334 −0.916672 0.399640i \(-0.869135\pi\)
−0.916672 + 0.399640i \(0.869135\pi\)
\(854\) −19.1066 + 33.0937i −0.653816 + 1.13244i
\(855\) −0.912913 1.58121i −0.0312210 0.0540763i
\(856\) −21.4901 + 37.2220i −0.734518 + 1.27222i
\(857\) −2.57343 4.45732i −0.0879068 0.152259i 0.818719 0.574194i \(-0.194684\pi\)
−0.906626 + 0.421935i \(0.861351\pi\)
\(858\) −2.06484 3.57642i −0.0704926 0.122097i
\(859\) −12.3698 21.4252i −0.422053 0.731017i 0.574087 0.818794i \(-0.305357\pi\)
−0.996140 + 0.0877770i \(0.972024\pi\)
\(860\) 51.8880 1.76937
\(861\) 33.9716 58.8405i 1.15775 2.00528i
\(862\) 1.39214 2.41125i 0.0474163 0.0821275i
\(863\) 6.89602 + 11.9443i 0.234743 + 0.406587i 0.959198 0.282735i \(-0.0912418\pi\)
−0.724455 + 0.689322i \(0.757908\pi\)
\(864\) −29.3016 −0.996860
\(865\) −6.29275 + 10.8994i −0.213960 + 0.370590i
\(866\) 24.9047 0.846296
\(867\) 27.6888 0.940359
\(868\) 25.0638 + 14.3563i 0.850719 + 0.487286i
\(869\) −7.85172 −0.266351
\(870\) −32.9301 −1.11644
\(871\) −0.828863 + 1.43563i −0.0280849 + 0.0486446i
\(872\) −12.0989 −0.409722
\(873\) 0.267269 + 0.462923i 0.00904568 + 0.0156676i
\(874\) 1.04974 1.81820i 0.0355080 0.0615017i
\(875\) −84.7750 + 146.835i −2.86592 + 4.96392i
\(876\) 31.8859 1.07732
\(877\) −22.1956 38.4439i −0.749492 1.29816i −0.948067 0.318072i \(-0.896965\pi\)
0.198575 0.980086i \(-0.436369\pi\)
\(878\) 10.1242 + 17.5356i 0.341674 + 0.591797i
\(879\) 0.466052 + 0.807225i 0.0157195 + 0.0272270i
\(880\) −1.75657 + 3.04247i −0.0592139 + 0.102562i
\(881\) 15.7694 + 27.3135i 0.531286 + 0.920214i 0.999333 + 0.0365103i \(0.0116242\pi\)
−0.468048 + 0.883703i \(0.655042\pi\)
\(882\) 0.459960 0.796673i 0.0154876 0.0268254i
\(883\) 3.14330 0.105781 0.0528903 0.998600i \(-0.483157\pi\)
0.0528903 + 0.998600i \(0.483157\pi\)
\(884\) −1.49843 −0.0503976
\(885\) −3.91799 + 6.78615i −0.131702 + 0.228114i
\(886\) −7.04376 12.2001i −0.236640 0.409872i
\(887\) −4.22821 + 7.32347i −0.141969 + 0.245898i −0.928238 0.371986i \(-0.878677\pi\)
0.786269 + 0.617885i \(0.212010\pi\)
\(888\) 7.58119 + 13.1310i 0.254408 + 0.440647i
\(889\) 4.21252 + 7.29630i 0.141283 + 0.244710i
\(890\) 4.40046 + 7.62182i 0.147504 + 0.255484i
\(891\) −26.1023 −0.874459
\(892\) −1.50828 + 2.61241i −0.0505008 + 0.0874699i
\(893\) 15.3215 26.5377i 0.512716 0.888050i
\(894\) −13.4923 23.3694i −0.451251 0.781590i
\(895\) −90.5463 −3.02663
\(896\) −15.8995 + 27.5387i −0.531164 + 0.920004i
\(897\) −1.31763 −0.0439943
\(898\) −22.8580 −0.762781
\(899\) −0.0958656 27.9937i −0.00319730 0.933643i
\(900\) −2.32479 −0.0774929
\(901\) −6.26109 −0.208587
\(902\) 11.2477 19.4816i 0.374507 0.648665i
\(903\) 63.7110 2.12017
\(904\) 15.5417 + 26.9191i 0.516910 + 0.895315i
\(905\) 30.3447 52.5586i 1.00869 1.74711i
\(906\) −12.3809 + 21.4444i −0.411328 + 0.712442i
\(907\) −7.07756 −0.235007 −0.117503 0.993072i \(-0.537489\pi\)
−0.117503 + 0.993072i \(0.537489\pi\)
\(908\) 7.82754 + 13.5577i 0.259766 + 0.449928i
\(909\) −0.0895729 0.155145i −0.00297094 0.00514583i
\(910\) 7.40217 + 12.8209i 0.245380 + 0.425010i
\(911\) −26.4954 + 45.8913i −0.877830 + 1.52045i −0.0241133 + 0.999709i \(0.507676\pi\)
−0.853717 + 0.520737i \(0.825657\pi\)
\(912\) 0.844964 + 1.46352i 0.0279796 + 0.0484620i
\(913\) −15.0612 + 26.0867i −0.498452 + 0.863344i
\(914\) −0.428543 −0.0141750
\(915\) 89.3576 2.95407
\(916\) 11.4630 19.8544i 0.378747 0.656009i
\(917\) −24.4244 42.3043i −0.806565 1.39701i
\(918\) 2.45610 4.25409i 0.0810635 0.140406i
\(919\) 5.08334 + 8.80460i 0.167684 + 0.290437i 0.937605 0.347702i \(-0.113038\pi\)
−0.769921 + 0.638139i \(0.779705\pi\)
\(920\) −4.55826 7.89514i −0.150281 0.260295i
\(921\) 8.95487 + 15.5103i 0.295073 + 0.511081i
\(922\) −5.63963 −0.185731
\(923\) −0.716560 + 1.24112i −0.0235859 + 0.0408519i
\(924\) −12.7921 + 22.1565i −0.420828 + 0.728896i
\(925\) −22.6600 39.2482i −0.745055 1.29047i
\(926\) −7.85845 −0.258245
\(927\) −0.670163 + 1.16076i −0.0220110 + 0.0381243i
\(928\) 28.9749 0.951147
\(929\) 35.4529 1.16317 0.581586 0.813485i \(-0.302432\pi\)
0.581586 + 0.813485i \(0.302432\pi\)
\(930\) 0.124879 + 36.4661i 0.00409496 + 1.19577i
\(931\) 30.1094 0.986794
\(932\) 14.3909 0.471390
\(933\) −20.6849 + 35.8272i −0.677192 + 1.17293i
\(934\) −13.8366 −0.452749
\(935\) −7.12554 12.3418i −0.233030 0.403620i
\(936\) −0.169446 + 0.293488i −0.00553850 + 0.00959296i
\(937\) −0.226680 + 0.392621i −0.00740530 + 0.0128264i −0.869704 0.493573i \(-0.835691\pi\)
0.862299 + 0.506399i \(0.169024\pi\)
\(938\) −5.54473 −0.181042
\(939\) −23.8253 41.2666i −0.777509 1.34669i
\(940\) −26.1941 45.3694i −0.854356 1.47979i
\(941\) 3.38337 + 5.86016i 0.110295 + 0.191036i 0.915889 0.401432i \(-0.131487\pi\)
−0.805594 + 0.592467i \(0.798154\pi\)
\(942\) 11.2614 19.5053i 0.366915 0.635515i
\(943\) −3.58871 6.21583i −0.116864 0.202415i
\(944\) 0.142470 0.246766i 0.00463701 0.00803154i
\(945\) 89.8908 2.92415
\(946\) 21.0942 0.685830
\(947\) −15.8759 + 27.4979i −0.515898 + 0.893562i 0.483931 + 0.875106i \(0.339208\pi\)
−0.999830 + 0.0184561i \(0.994125\pi\)
\(948\) 3.22855 + 5.59202i 0.104859 + 0.181620i
\(949\) −6.94652 + 12.0317i −0.225494 + 0.390567i
\(950\) 20.5409 + 35.5779i 0.666435 + 1.15430i
\(951\) −16.0458 27.7921i −0.520319 0.901220i
\(952\) −6.36489 11.0243i −0.206287 0.357300i
\(953\) −46.3825 −1.50248 −0.751238 0.660031i \(-0.770543\pi\)
−0.751238 + 0.660031i \(0.770543\pi\)
\(954\) −0.278758 + 0.482822i −0.00902511 + 0.0156320i
\(955\) 15.8751 27.4966i 0.513708 0.889768i
\(956\) 6.98132 + 12.0920i 0.225792 + 0.391083i
\(957\) 24.7956 0.801527
\(958\) 1.39615 2.41820i 0.0451074 0.0781284i
\(959\) 13.5896 0.438831
\(960\) −33.2952 −1.07460
\(961\) −30.9993 + 0.212319i −0.999977 + 0.00684900i
\(962\) −2.60105 −0.0838613
\(963\) 1.90884 0.0615116
\(964\) −6.99850 + 12.1218i −0.225407 + 0.390416i
\(965\) 104.884 3.37632
\(966\) −2.20359 3.81673i −0.0708993 0.122801i
\(967\) −26.6890 + 46.2268i −0.858262 + 1.48655i 0.0153239 + 0.999883i \(0.495122\pi\)
−0.873586 + 0.486670i \(0.838211\pi\)
\(968\) 4.43561 7.68270i 0.142566 0.246931i
\(969\) −6.85521 −0.220221
\(970\) −8.07448 13.9854i −0.259256 0.449045i
\(971\) −13.4105 23.2277i −0.430364 0.745412i 0.566541 0.824034i \(-0.308281\pi\)
−0.996904 + 0.0786221i \(0.974948\pi\)
\(972\) 0.827429 + 1.43315i 0.0265398 + 0.0459683i
\(973\) −20.4703 + 35.4557i −0.656249 + 1.13666i
\(974\) −8.48720 14.7003i −0.271947 0.471027i
\(975\) 12.8914 22.3285i 0.412855 0.715086i
\(976\) −3.24932 −0.104008
\(977\) −16.0439 −0.513289 −0.256645 0.966506i \(-0.582617\pi\)
−0.256645 + 0.966506i \(0.582617\pi\)
\(978\) 1.15625 2.00269i 0.0369729 0.0640390i
\(979\) −3.31344 5.73904i −0.105898 0.183421i
\(980\) 25.7378 44.5792i 0.822165 1.42403i
\(981\) 0.268669 + 0.465349i 0.00857795 + 0.0148574i
\(982\) 9.81450 + 16.9992i 0.313193 + 0.542467i
\(983\) 27.2122 + 47.1329i 0.867934 + 1.50331i 0.864104 + 0.503313i \(0.167886\pi\)
0.00383020 + 0.999993i \(0.498781\pi\)
\(984\) −46.9876 −1.49791
\(985\) −39.5282 + 68.4648i −1.25947 + 2.18147i
\(986\) −2.42872 + 4.20667i −0.0773462 + 0.133968i
\(987\) −32.1626 55.7072i −1.02375 1.77318i
\(988\) −4.36712 −0.138937
\(989\) 3.36517 5.82865i 0.107006 0.185340i
\(990\) −1.26898 −0.0403309
\(991\) 10.8957 0.346114 0.173057 0.984912i \(-0.444635\pi\)
0.173057 + 0.984912i \(0.444635\pi\)
\(992\) −0.109880 32.0861i −0.00348870 1.01874i
\(993\) 27.0567 0.858620
\(994\) −4.79348 −0.152040
\(995\) −1.18766 + 2.05709i −0.0376514 + 0.0652141i
\(996\) 24.7720 0.784932
\(997\) −9.33568 16.1699i −0.295664 0.512105i 0.679475 0.733698i \(-0.262208\pi\)
−0.975139 + 0.221594i \(0.928874\pi\)
\(998\) 3.76744 6.52540i 0.119256 0.206558i
\(999\) −7.89669 + 13.6775i −0.249840 + 0.432736i
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 403.2.h.b.222.6 yes 34
31.25 even 3 inner 403.2.h.b.118.6 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.h.b.118.6 34 31.25 even 3 inner
403.2.h.b.222.6 yes 34 1.1 even 1 trivial