Properties

Label 77.2.e.b.67.3
Level $77$
Weight $2$
Character 77.67
Analytic conductor $0.615$
Analytic rank $0$
Dimension $6$
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] = [77,2,Mod(23,77)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(77, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("77.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.614848095564\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.3
Root \(0.356769 - 0.617942i\) of defining polynomial
Character \(\chi\) \(=\) 77.67
Dual form 77.2.e.b.23.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.24543 + 2.15715i) q^{2} +(0.356769 - 0.617942i) q^{3} +(-2.10220 + 3.64112i) q^{4} +(-1.10220 - 1.90907i) q^{5} +1.77733 q^{6} +(-1.10220 - 2.40523i) q^{7} -5.49086 q^{8} +(1.24543 + 2.15715i) q^{9} +O(q^{10})\) \(q+(1.24543 + 2.15715i) q^{2} +(0.356769 - 0.617942i) q^{3} +(-2.10220 + 3.64112i) q^{4} +(-1.10220 - 1.90907i) q^{5} +1.77733 q^{6} +(-1.10220 - 2.40523i) q^{7} -5.49086 q^{8} +(1.24543 + 2.15715i) q^{9} +(2.74543 - 4.75523i) q^{10} +(0.500000 - 0.866025i) q^{11} +(1.50000 + 2.59808i) q^{12} -3.28646 q^{13} +(3.81574 - 5.37317i) q^{14} -1.57292 q^{15} +(-2.63409 - 4.56239i) q^{16} +(-0.745432 + 1.29113i) q^{17} +(-3.10220 + 5.37317i) q^{18} +(3.45897 + 5.99111i) q^{19} +9.26819 q^{20} +(-1.87953 - 0.177017i) q^{21} +2.49086 q^{22} +(-3.24543 - 5.62125i) q^{23} +(-1.95897 + 3.39304i) q^{24} +(0.0703069 - 0.121775i) q^{25} +(-4.09306 - 7.08940i) q^{26} +3.91794 q^{27} +(11.0748 + 1.04304i) q^{28} -1.64975 q^{29} +(-1.95897 - 3.39304i) q^{30} +(1.17512 - 2.03538i) q^{31} +(1.07031 - 1.85383i) q^{32} +(-0.356769 - 0.617942i) q^{33} -3.71354 q^{34} +(-3.37691 + 4.75523i) q^{35} -10.4726 q^{36} +(2.77733 + 4.81047i) q^{37} +(-8.61582 + 14.9230i) q^{38} +(-1.17251 + 2.03084i) q^{39} +(6.05203 + 10.4824i) q^{40} -11.2499 q^{41} +(-1.95897 - 4.27489i) q^{42} +5.26819 q^{43} +(2.10220 + 3.64112i) q^{44} +(2.74543 - 4.75523i) q^{45} +(8.08393 - 14.0018i) q^{46} +(-0.745432 - 1.29113i) q^{47} -3.75905 q^{48} +(-4.57031 + 5.30210i) q^{49} +0.350250 q^{50} +(0.531894 + 0.921267i) q^{51} +(6.90880 - 11.9664i) q^{52} +(-0.152367 + 0.263908i) q^{53} +(4.87953 + 8.45159i) q^{54} -2.20440 q^{55} +(6.05203 + 13.2068i) q^{56} +4.93621 q^{57} +(-2.05465 - 3.55876i) q^{58} +(6.32936 - 10.9628i) q^{59} +(3.30660 - 5.72720i) q^{60} +(6.49086 + 11.2425i) q^{61} +5.85415 q^{62} +(3.81574 - 5.37317i) q^{63} -5.20440 q^{64} +(3.62234 + 6.27408i) q^{65} +(0.888663 - 1.53921i) q^{66} +(2.28646 - 3.96027i) q^{67} +(-3.13409 - 5.42841i) q^{68} -4.63148 q^{69} +(-14.4635 - 1.36219i) q^{70} +11.3267 q^{71} +(-6.83850 - 11.8446i) q^{72} +(4.28384 - 7.41984i) q^{73} +(-6.91794 + 11.9822i) q^{74} +(-0.0501666 - 0.0868912i) q^{75} -29.0858 q^{76} +(-2.63409 - 0.248083i) q^{77} -5.84111 q^{78} +(-2.31574 - 4.01098i) q^{79} +(-5.80660 + 10.0573i) q^{80} +(-2.33850 + 4.05039i) q^{81} +(-14.0110 - 24.2678i) q^{82} -1.93621 q^{83} +(4.59568 - 6.47145i) q^{84} +3.28646 q^{85} +(6.56117 + 11.3643i) q^{86} +(-0.588580 + 1.01945i) q^{87} +(-2.74543 + 4.75523i) q^{88} +(-1.60220 - 2.77509i) q^{89} +13.6770 q^{90} +(3.62234 + 7.90471i) q^{91} +27.2902 q^{92} +(-0.838496 - 1.45232i) q^{93} +(1.85677 - 3.21602i) q^{94} +(7.62496 - 13.2068i) q^{95} +(-0.763705 - 1.32278i) q^{96} +1.85939 q^{97} +(-17.1294 - 3.25544i) q^{98} +2.49086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8} + 9 q^{10} + 3 q^{11} + 9 q^{12} - 22 q^{13} + 12 q^{14} - 14 q^{15} - 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} + 28 q^{20} + 10 q^{21} - 12 q^{23} - 2 q^{24} - 3 q^{25} - q^{26} + 4 q^{27} + 13 q^{28} - 18 q^{29} - 2 q^{30} + 3 q^{31} + 3 q^{32} - q^{33} - 20 q^{34} + 9 q^{35} - 18 q^{36} + 4 q^{37} - 8 q^{38} + 5 q^{39} + 3 q^{40} - 10 q^{41} - 2 q^{42} + 4 q^{43} + 4 q^{44} + 9 q^{45} + 10 q^{46} + 3 q^{47} + 20 q^{48} - 24 q^{49} - 6 q^{50} - 2 q^{51} + 7 q^{52} - 17 q^{53} + 8 q^{54} + 4 q^{55} + 3 q^{56} + 40 q^{57} + 13 q^{58} - 8 q^{59} - 6 q^{60} + 24 q^{61} + 26 q^{62} + 12 q^{63} - 14 q^{64} - 15 q^{65} - q^{66} + 16 q^{67} - 5 q^{68} - 6 q^{69} - 27 q^{70} + 14 q^{71} - 10 q^{72} + 20 q^{73} - 22 q^{74} - 25 q^{75} - 78 q^{76} - 2 q^{77} - 12 q^{78} - 3 q^{79} - 9 q^{80} + 17 q^{81} - 41 q^{82} - 22 q^{83} + 12 q^{84} + 22 q^{85} + 21 q^{86} - 30 q^{87} - 9 q^{88} - q^{89} + 20 q^{90} - 15 q^{91} + 50 q^{92} + 26 q^{93} + 10 q^{94} + 17 q^{95} - 27 q^{96} + 18 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24543 + 2.15715i 0.880653 + 1.52534i 0.850616 + 0.525787i \(0.176229\pi\)
0.0300373 + 0.999549i \(0.490437\pi\)
\(3\) 0.356769 0.617942i 0.205981 0.356769i −0.744464 0.667663i \(-0.767295\pi\)
0.950445 + 0.310894i \(0.100628\pi\)
\(4\) −2.10220 + 3.64112i −1.05110 + 1.82056i
\(5\) −1.10220 1.90907i −0.492919 0.853761i 0.507048 0.861918i \(-0.330737\pi\)
−0.999967 + 0.00815703i \(0.997404\pi\)
\(6\) 1.77733 0.725590
\(7\) −1.10220 2.40523i −0.416593 0.909093i
\(8\) −5.49086 −1.94131
\(9\) 1.24543 + 2.15715i 0.415144 + 0.719050i
\(10\) 2.74543 4.75523i 0.868182 1.50373i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 1.50000 + 2.59808i 0.433013 + 0.750000i
\(13\) −3.28646 −0.911501 −0.455750 0.890108i \(-0.650629\pi\)
−0.455750 + 0.890108i \(0.650629\pi\)
\(14\) 3.81574 5.37317i 1.01980 1.43604i
\(15\) −1.57292 −0.406127
\(16\) −2.63409 4.56239i −0.658524 1.14060i
\(17\) −0.745432 + 1.29113i −0.180794 + 0.313144i −0.942151 0.335189i \(-0.891200\pi\)
0.761357 + 0.648333i \(0.224533\pi\)
\(18\) −3.10220 + 5.37317i −0.731196 + 1.26647i
\(19\) 3.45897 + 5.99111i 0.793542 + 1.37446i 0.923761 + 0.382970i \(0.125099\pi\)
−0.130219 + 0.991485i \(0.541568\pi\)
\(20\) 9.26819 2.07243
\(21\) −1.87953 0.177017i −0.410146 0.0386283i
\(22\) 2.49086 0.531054
\(23\) −3.24543 5.62125i −0.676719 1.17211i −0.975963 0.217936i \(-0.930068\pi\)
0.299244 0.954177i \(-0.403266\pi\)
\(24\) −1.95897 + 3.39304i −0.399873 + 0.692600i
\(25\) 0.0703069 0.121775i 0.0140614 0.0243550i
\(26\) −4.09306 7.08940i −0.802716 1.39034i
\(27\) 3.91794 0.754008
\(28\) 11.0748 + 1.04304i 2.09294 + 0.197116i
\(29\) −1.64975 −0.306351 −0.153175 0.988199i \(-0.548950\pi\)
−0.153175 + 0.988199i \(0.548950\pi\)
\(30\) −1.95897 3.39304i −0.357657 0.619481i
\(31\) 1.17512 2.03538i 0.211059 0.365564i −0.740987 0.671519i \(-0.765642\pi\)
0.952046 + 0.305955i \(0.0989756\pi\)
\(32\) 1.07031 1.85383i 0.189205 0.327713i
\(33\) −0.356769 0.617942i −0.0621055 0.107570i
\(34\) −3.71354 −0.636867
\(35\) −3.37691 + 4.75523i −0.570802 + 0.803780i
\(36\) −10.4726 −1.74543
\(37\) 2.77733 + 4.81047i 0.456590 + 0.790836i 0.998778 0.0494206i \(-0.0157375\pi\)
−0.542189 + 0.840257i \(0.682404\pi\)
\(38\) −8.61582 + 14.9230i −1.39767 + 2.42084i
\(39\) −1.17251 + 2.03084i −0.187751 + 0.325195i
\(40\) 6.05203 + 10.4824i 0.956911 + 1.65742i
\(41\) −11.2499 −1.75694 −0.878471 0.477796i \(-0.841436\pi\)
−0.878471 + 0.477796i \(0.841436\pi\)
\(42\) −1.95897 4.27489i −0.302276 0.659629i
\(43\) 5.26819 0.803391 0.401696 0.915773i \(-0.368421\pi\)
0.401696 + 0.915773i \(0.368421\pi\)
\(44\) 2.10220 + 3.64112i 0.316919 + 0.548919i
\(45\) 2.74543 4.75523i 0.409265 0.708867i
\(46\) 8.08393 14.0018i 1.19191 2.06445i
\(47\) −0.745432 1.29113i −0.108732 0.188330i 0.806525 0.591201i \(-0.201346\pi\)
−0.915257 + 0.402871i \(0.868012\pi\)
\(48\) −3.75905 −0.542573
\(49\) −4.57031 + 5.30210i −0.652901 + 0.757443i
\(50\) 0.350250 0.0495328
\(51\) 0.531894 + 0.921267i 0.0744800 + 0.129003i
\(52\) 6.90880 11.9664i 0.958079 1.65944i
\(53\) −0.152367 + 0.263908i −0.0209293 + 0.0362506i −0.876300 0.481765i \(-0.839996\pi\)
0.855371 + 0.518016i \(0.173329\pi\)
\(54\) 4.87953 + 8.45159i 0.664019 + 1.15012i
\(55\) −2.20440 −0.297241
\(56\) 6.05203 + 13.2068i 0.808737 + 1.76483i
\(57\) 4.93621 0.653817
\(58\) −2.05465 3.55876i −0.269789 0.467288i
\(59\) 6.32936 10.9628i 0.824012 1.42723i −0.0786592 0.996902i \(-0.525064\pi\)
0.902672 0.430330i \(-0.141603\pi\)
\(60\) 3.30660 5.72720i 0.426881 0.739379i
\(61\) 6.49086 + 11.2425i 0.831070 + 1.43946i 0.897191 + 0.441644i \(0.145604\pi\)
−0.0661206 + 0.997812i \(0.521062\pi\)
\(62\) 5.85415 0.743478
\(63\) 3.81574 5.37317i 0.480738 0.676956i
\(64\) −5.20440 −0.650550
\(65\) 3.62234 + 6.27408i 0.449296 + 0.778204i
\(66\) 0.888663 1.53921i 0.109387 0.189464i
\(67\) 2.28646 3.96027i 0.279336 0.483824i −0.691884 0.722009i \(-0.743219\pi\)
0.971220 + 0.238185i \(0.0765524\pi\)
\(68\) −3.13409 5.42841i −0.380065 0.658292i
\(69\) −4.63148 −0.557564
\(70\) −14.4635 1.36219i −1.72871 0.162813i
\(71\) 11.3267 1.34424 0.672119 0.740444i \(-0.265385\pi\)
0.672119 + 0.740444i \(0.265385\pi\)
\(72\) −6.83850 11.8446i −0.805925 1.39590i
\(73\) 4.28384 7.41984i 0.501386 0.868426i −0.498613 0.866825i \(-0.666157\pi\)
0.999999 0.00160129i \(-0.000509706\pi\)
\(74\) −6.91794 + 11.9822i −0.804194 + 1.39291i
\(75\) −0.0501666 0.0868912i −0.00579274 0.0100333i
\(76\) −29.0858 −3.33637
\(77\) −2.63409 0.248083i −0.300183 0.0282717i
\(78\) −5.84111 −0.661376
\(79\) −2.31574 4.01098i −0.260541 0.451270i 0.705845 0.708366i \(-0.250568\pi\)
−0.966386 + 0.257096i \(0.917234\pi\)
\(80\) −5.80660 + 10.0573i −0.649198 + 1.12444i
\(81\) −2.33850 + 4.05039i −0.259833 + 0.450044i
\(82\) −14.0110 24.2678i −1.54726 2.67993i
\(83\) −1.93621 −0.212527 −0.106263 0.994338i \(-0.533889\pi\)
−0.106263 + 0.994338i \(0.533889\pi\)
\(84\) 4.59568 6.47145i 0.501430 0.706093i
\(85\) 3.28646 0.356467
\(86\) 6.56117 + 11.3643i 0.707509 + 1.22544i
\(87\) −0.588580 + 1.01945i −0.0631024 + 0.109297i
\(88\) −2.74543 + 4.75523i −0.292664 + 0.506909i
\(89\) −1.60220 2.77509i −0.169833 0.294159i 0.768528 0.639816i \(-0.220989\pi\)
−0.938361 + 0.345657i \(0.887656\pi\)
\(90\) 13.6770 1.44168
\(91\) 3.62234 + 7.90471i 0.379725 + 0.828639i
\(92\) 27.2902 2.84520
\(93\) −0.838496 1.45232i −0.0869480 0.150598i
\(94\) 1.85677 3.21602i 0.191511 0.331707i
\(95\) 7.62496 13.2068i 0.782304 1.35499i
\(96\) −0.763705 1.32278i −0.0779453 0.135005i
\(97\) 1.85939 0.188792 0.0943960 0.995535i \(-0.469908\pi\)
0.0943960 + 0.995535i \(0.469908\pi\)
\(98\) −17.1294 3.25544i −1.73034 0.328849i
\(99\) 2.49086 0.250341
\(100\) 0.295598 + 0.511992i 0.0295598 + 0.0511992i
\(101\) −3.02276 + 5.23557i −0.300776 + 0.520959i −0.976312 0.216368i \(-0.930579\pi\)
0.675536 + 0.737327i \(0.263912\pi\)
\(102\) −1.32488 + 2.29475i −0.131182 + 0.227214i
\(103\) 0.531894 + 0.921267i 0.0524091 + 0.0907752i 0.891040 0.453925i \(-0.149977\pi\)
−0.838631 + 0.544700i \(0.816643\pi\)
\(104\) 18.0455 1.76951
\(105\) 1.73368 + 3.78325i 0.169190 + 0.369208i
\(106\) −0.759053 −0.0737257
\(107\) 3.16599 + 5.48365i 0.306068 + 0.530125i 0.977498 0.210943i \(-0.0676533\pi\)
−0.671431 + 0.741067i \(0.734320\pi\)
\(108\) −8.23630 + 14.2657i −0.792538 + 1.37272i
\(109\) 1.40694 2.43688i 0.134760 0.233411i −0.790746 0.612145i \(-0.790307\pi\)
0.925506 + 0.378734i \(0.123640\pi\)
\(110\) −2.74543 4.75523i −0.261767 0.453393i
\(111\) 3.96345 0.376194
\(112\) −8.07031 + 11.3643i −0.762572 + 1.07382i
\(113\) −12.7538 −1.19978 −0.599889 0.800083i \(-0.704789\pi\)
−0.599889 + 0.800083i \(0.704789\pi\)
\(114\) 6.14772 + 10.6482i 0.575786 + 0.997291i
\(115\) −7.15423 + 12.3915i −0.667136 + 1.15551i
\(116\) 3.46811 6.00694i 0.322006 0.557730i
\(117\) −4.09306 7.08940i −0.378404 0.655415i
\(118\) 31.5311 2.90268
\(119\) 3.92708 + 0.369859i 0.359994 + 0.0339049i
\(120\) 8.63671 0.788420
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −16.1679 + 28.0035i −1.46377 + 2.53532i
\(123\) −4.01362 + 6.95180i −0.361896 + 0.626822i
\(124\) 4.94070 + 8.55754i 0.443688 + 0.768490i
\(125\) −11.3320 −1.01356
\(126\) 16.3430 + 1.53921i 1.45595 + 0.137124i
\(127\) −12.3775 −1.09832 −0.549162 0.835716i \(-0.685053\pi\)
−0.549162 + 0.835716i \(0.685053\pi\)
\(128\) −8.62234 14.9343i −0.762114 1.32002i
\(129\) 1.87953 3.25544i 0.165483 0.286625i
\(130\) −9.02276 + 15.6279i −0.791348 + 1.37066i
\(131\) −0.379526 0.657359i −0.0331594 0.0574337i 0.848969 0.528442i \(-0.177224\pi\)
−0.882129 + 0.471008i \(0.843890\pi\)
\(132\) 3.00000 0.261116
\(133\) 10.5975 14.9230i 0.918924 1.29399i
\(134\) 11.3905 0.983992
\(135\) −4.31836 7.47961i −0.371665 0.643742i
\(136\) 4.09306 7.08940i 0.350977 0.607911i
\(137\) 2.92056 5.05855i 0.249520 0.432181i −0.713873 0.700275i \(-0.753060\pi\)
0.963393 + 0.268094i \(0.0863938\pi\)
\(138\) −5.76819 9.99080i −0.491021 0.850473i
\(139\) −5.57292 −0.472689 −0.236345 0.971669i \(-0.575949\pi\)
−0.236345 + 0.971669i \(0.575949\pi\)
\(140\) −10.2154 22.2922i −0.863359 1.88403i
\(141\) −1.06379 −0.0895871
\(142\) 14.1067 + 24.4335i 1.18381 + 2.05041i
\(143\) −1.64323 + 2.84616i −0.137414 + 0.238008i
\(144\) 6.56117 11.3643i 0.546764 0.947023i
\(145\) 1.81836 + 3.14948i 0.151006 + 0.261550i
\(146\) 21.3409 1.76619
\(147\) 1.64585 + 4.71581i 0.135747 + 0.388953i
\(148\) −23.3540 −1.91969
\(149\) 0.500000 + 0.866025i 0.0409616 + 0.0709476i 0.885779 0.464107i \(-0.153625\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(150\) 0.124958 0.216434i 0.0102028 0.0176718i
\(151\) −7.42056 + 12.8528i −0.603876 + 1.04594i 0.388352 + 0.921511i \(0.373045\pi\)
−0.992228 + 0.124433i \(0.960289\pi\)
\(152\) −18.9927 32.8964i −1.54051 2.66825i
\(153\) −3.71354 −0.300222
\(154\) −2.74543 5.99111i −0.221233 0.482778i
\(155\) −5.18089 −0.416139
\(156\) −4.92969 8.53848i −0.394691 0.683625i
\(157\) −3.19527 + 5.53436i −0.255010 + 0.441690i −0.964898 0.262624i \(-0.915412\pi\)
0.709888 + 0.704314i \(0.248745\pi\)
\(158\) 5.76819 9.99080i 0.458893 0.794825i
\(159\) 0.108720 + 0.188308i 0.00862205 + 0.0149338i
\(160\) −4.71877 −0.373052
\(161\) −9.94331 + 14.0018i −0.783643 + 1.10349i
\(162\) −11.6498 −0.915291
\(163\) −4.97259 8.61278i −0.389483 0.674605i 0.602897 0.797819i \(-0.294013\pi\)
−0.992380 + 0.123214i \(0.960680\pi\)
\(164\) 23.6496 40.9623i 1.84672 3.19862i
\(165\) −0.786462 + 1.36219i −0.0612260 + 0.106047i
\(166\) −2.41142 4.17670i −0.187163 0.324175i
\(167\) −1.94145 −0.150234 −0.0751168 0.997175i \(-0.523933\pi\)
−0.0751168 + 0.997175i \(0.523933\pi\)
\(168\) 10.3202 + 0.971976i 0.796223 + 0.0749896i
\(169\) −2.19917 −0.169167
\(170\) 4.09306 + 7.08940i 0.313924 + 0.543732i
\(171\) −8.61582 + 14.9230i −0.658868 + 1.14119i
\(172\) −11.0748 + 19.1821i −0.844445 + 1.46262i
\(173\) −3.21616 5.57054i −0.244520 0.423521i 0.717477 0.696582i \(-0.245297\pi\)
−0.961996 + 0.273062i \(0.911964\pi\)
\(174\) −2.93214 −0.222285
\(175\) −0.370390 0.0348840i −0.0279989 0.00263698i
\(176\) −5.26819 −0.397105
\(177\) −4.51624 7.82235i −0.339461 0.587964i
\(178\) 3.99086 6.91238i 0.299128 0.518105i
\(179\) 1.79298 3.10553i 0.134014 0.232119i −0.791207 0.611549i \(-0.790547\pi\)
0.925220 + 0.379430i \(0.123880\pi\)
\(180\) 11.5429 + 19.9929i 0.860357 + 1.49018i
\(181\) 12.2134 0.907813 0.453906 0.891049i \(-0.350030\pi\)
0.453906 + 0.891049i \(0.350030\pi\)
\(182\) −12.5403 + 17.6587i −0.929547 + 1.30895i
\(183\) 9.26295 0.684737
\(184\) 17.8202 + 30.8655i 1.31372 + 2.27544i
\(185\) 6.12234 10.6042i 0.450123 0.779637i
\(186\) 2.08858 3.61753i 0.153142 0.265250i
\(187\) 0.745432 + 1.29113i 0.0545114 + 0.0944165i
\(188\) 6.26819 0.457155
\(189\) −4.31836 9.42356i −0.314114 0.685463i
\(190\) 37.9855 2.75576
\(191\) −6.05465 10.4870i −0.438099 0.758810i 0.559444 0.828868i \(-0.311015\pi\)
−0.997543 + 0.0700583i \(0.977681\pi\)
\(192\) −1.85677 + 3.21602i −0.134001 + 0.232096i
\(193\) 5.96997 10.3403i 0.429728 0.744311i −0.567121 0.823635i \(-0.691943\pi\)
0.996849 + 0.0793237i \(0.0252761\pi\)
\(194\) 2.31574 + 4.01098i 0.166260 + 0.287971i
\(195\) 5.16936 0.370185
\(196\) −9.69788 27.7871i −0.692706 1.98479i
\(197\) 12.1626 0.866551 0.433275 0.901262i \(-0.357358\pi\)
0.433275 + 0.901262i \(0.357358\pi\)
\(198\) 3.10220 + 5.37317i 0.220464 + 0.381855i
\(199\) −0.952451 + 1.64969i −0.0675174 + 0.116944i −0.897808 0.440387i \(-0.854841\pi\)
0.830290 + 0.557331i \(0.188174\pi\)
\(200\) −0.386046 + 0.668651i −0.0272975 + 0.0472807i
\(201\) −1.63148 2.82580i −0.115076 0.199317i
\(202\) −15.0586 −1.05952
\(203\) 1.81836 + 3.96804i 0.127624 + 0.278502i
\(204\) −4.47259 −0.313144
\(205\) 12.3997 + 21.4769i 0.866030 + 1.50001i
\(206\) −1.32488 + 2.29475i −0.0923084 + 0.159883i
\(207\) 8.08393 14.0018i 0.561872 0.973191i
\(208\) 8.65685 + 14.9941i 0.600245 + 1.03965i
\(209\) 6.91794 0.478524
\(210\) −6.00187 + 8.45159i −0.414168 + 0.583215i
\(211\) −16.2447 −1.11833 −0.559165 0.829056i \(-0.688878\pi\)
−0.559165 + 0.829056i \(0.688878\pi\)
\(212\) −0.640614 1.10958i −0.0439975 0.0762060i
\(213\) 4.04103 6.99927i 0.276887 0.479582i
\(214\) −7.88605 + 13.6590i −0.539079 + 0.933712i
\(215\) −5.80660 10.0573i −0.396007 0.685904i
\(216\) −21.5129 −1.46377
\(217\) −6.19078 0.583058i −0.420258 0.0395806i
\(218\) 7.00897 0.474707
\(219\) −3.05669 5.29434i −0.206552 0.357758i
\(220\) 4.63409 8.02649i 0.312431 0.541146i
\(221\) 2.44983 4.24324i 0.164794 0.285431i
\(222\) 4.93621 + 8.54977i 0.331297 + 0.573823i
\(223\) 3.03655 0.203342 0.101671 0.994818i \(-0.467581\pi\)
0.101671 + 0.994818i \(0.467581\pi\)
\(224\) −5.63858 0.531051i −0.376743 0.0354823i
\(225\) 0.350250 0.0233500
\(226\) −15.8840 27.5119i −1.05659 1.83007i
\(227\) −9.22454 + 15.9774i −0.612254 + 1.06046i 0.378605 + 0.925558i \(0.376404\pi\)
−0.990860 + 0.134897i \(0.956930\pi\)
\(228\) −10.3769 + 17.9733i −0.687228 + 1.19031i
\(229\) 12.7499 + 22.0835i 0.842538 + 1.45932i 0.887742 + 0.460341i \(0.152273\pi\)
−0.0452039 + 0.998978i \(0.514394\pi\)
\(230\) −35.6404 −2.35006
\(231\) −1.09306 + 1.53921i −0.0719184 + 0.101273i
\(232\) 9.05855 0.594723
\(233\) −1.90880 3.30614i −0.125050 0.216593i 0.796703 0.604372i \(-0.206576\pi\)
−0.921752 + 0.387779i \(0.873242\pi\)
\(234\) 10.1953 17.6587i 0.666485 1.15439i
\(235\) −1.64323 + 2.84616i −0.107193 + 0.185663i
\(236\) 26.6112 + 46.0919i 1.73224 + 3.00033i
\(237\) −3.30473 −0.214666
\(238\) 4.09306 + 8.93193i 0.265314 + 0.578971i
\(239\) 13.0037 0.841142 0.420571 0.907260i \(-0.361830\pi\)
0.420571 + 0.907260i \(0.361830\pi\)
\(240\) 4.14323 + 7.17629i 0.267444 + 0.463227i
\(241\) 0.225292 0.390216i 0.0145123 0.0251360i −0.858678 0.512515i \(-0.828714\pi\)
0.873190 + 0.487379i \(0.162047\pi\)
\(242\) 1.24543 2.15715i 0.0800594 0.138667i
\(243\) 7.54551 + 13.0692i 0.484045 + 0.838391i
\(244\) −54.5804 −3.49415
\(245\) 15.1595 + 2.88104i 0.968503 + 0.184063i
\(246\) −19.9948 −1.27482
\(247\) −11.3678 19.6896i −0.723314 1.25282i
\(248\) −6.45245 + 11.1760i −0.409731 + 0.709675i
\(249\) −0.690780 + 1.19647i −0.0437764 + 0.0758230i
\(250\) −14.1132 24.4448i −0.892597 1.54602i
\(251\) 1.11861 0.0706058 0.0353029 0.999377i \(-0.488760\pi\)
0.0353029 + 0.999377i \(0.488760\pi\)
\(252\) 11.5429 + 25.1890i 0.727134 + 1.58676i
\(253\) −6.49086 −0.408077
\(254\) −15.4153 26.7001i −0.967243 1.67531i
\(255\) 1.17251 2.03084i 0.0734253 0.127176i
\(256\) 16.2727 28.1851i 1.01704 1.76157i
\(257\) 11.4198 + 19.7797i 0.712348 + 1.23382i 0.963974 + 0.265998i \(0.0857015\pi\)
−0.251626 + 0.967825i \(0.580965\pi\)
\(258\) 9.36329 0.582933
\(259\) 8.50914 11.9822i 0.528732 0.744539i
\(260\) −30.4596 −1.88902
\(261\) −2.05465 3.55876i −0.127180 0.220282i
\(262\) 0.945349 1.63739i 0.0584038 0.101158i
\(263\) 4.59568 7.95995i 0.283382 0.490832i −0.688834 0.724919i \(-0.741877\pi\)
0.972215 + 0.234088i \(0.0752103\pi\)
\(264\) 1.95897 + 3.39304i 0.120566 + 0.208827i
\(265\) 0.671758 0.0412658
\(266\) 45.3898 + 4.27489i 2.78303 + 0.262110i
\(267\) −2.28646 −0.139929
\(268\) 9.61320 + 16.6506i 0.587220 + 1.01709i
\(269\) 7.80660 13.5214i 0.475977 0.824416i −0.523644 0.851937i \(-0.675428\pi\)
0.999621 + 0.0275208i \(0.00876123\pi\)
\(270\) 10.7564 18.6307i 0.654616 1.13383i
\(271\) −13.8723 24.0275i −0.842680 1.45956i −0.887621 0.460574i \(-0.847643\pi\)
0.0449415 0.998990i \(-0.485690\pi\)
\(272\) 7.85415 0.476228
\(273\) 6.17699 + 0.581759i 0.373849 + 0.0352097i
\(274\) 14.5494 0.878962
\(275\) −0.0703069 0.121775i −0.00423967 0.00734332i
\(276\) 9.73630 16.8638i 0.586056 1.01508i
\(277\) −7.40619 + 12.8279i −0.444995 + 0.770753i −0.998052 0.0623900i \(-0.980128\pi\)
0.553057 + 0.833143i \(0.313461\pi\)
\(278\) −6.94070 12.0216i −0.416275 0.721010i
\(279\) 5.85415 0.350479
\(280\) 18.5421 26.1103i 1.10811 1.56039i
\(281\) 15.2227 0.908109 0.454054 0.890974i \(-0.349977\pi\)
0.454054 + 0.890974i \(0.349977\pi\)
\(282\) −1.32488 2.29475i −0.0788952 0.136650i
\(283\) −10.8586 + 18.8077i −0.645479 + 1.11800i 0.338712 + 0.940890i \(0.390009\pi\)
−0.984191 + 0.177112i \(0.943324\pi\)
\(284\) −23.8111 + 41.2420i −1.41293 + 2.44726i
\(285\) −5.44070 9.42356i −0.322279 0.558204i
\(286\) −8.18613 −0.484056
\(287\) 12.3997 + 27.0587i 0.731929 + 1.59722i
\(288\) 5.33198 0.314190
\(289\) 7.38866 + 12.7975i 0.434627 + 0.752796i
\(290\) −4.52928 + 7.84494i −0.265968 + 0.460671i
\(291\) 0.663371 1.14899i 0.0388875 0.0673551i
\(292\) 18.0110 + 31.1960i 1.05401 + 1.82561i
\(293\) 11.1276 0.650080 0.325040 0.945700i \(-0.394622\pi\)
0.325040 + 0.945700i \(0.394622\pi\)
\(294\) −8.12292 + 9.42356i −0.473739 + 0.549593i
\(295\) −27.9049 −1.62469
\(296\) −15.2499 26.4136i −0.886383 1.53526i
\(297\) 1.95897 3.39304i 0.113671 0.196884i
\(298\) −1.24543 + 2.15715i −0.0721459 + 0.124960i
\(299\) 10.6660 + 18.4740i 0.616830 + 1.06838i
\(300\) 0.421841 0.0243550
\(301\) −5.80660 12.6712i −0.334687 0.730358i
\(302\) −36.9672 −2.12722
\(303\) 2.15685 + 3.73578i 0.123908 + 0.214615i
\(304\) 18.2225 31.5623i 1.04513 1.81022i
\(305\) 14.3085 24.7830i 0.819301 1.41907i
\(306\) −4.62496 8.01066i −0.264391 0.457939i
\(307\) 24.9855 1.42600 0.712998 0.701166i \(-0.247337\pi\)
0.712998 + 0.701166i \(0.247337\pi\)
\(308\) 6.44070 9.06953i 0.366993 0.516784i
\(309\) 0.759053 0.0431810
\(310\) −6.45245 11.1760i −0.366475 0.634753i
\(311\) −17.3704 + 30.0864i −0.984984 + 1.70604i −0.342979 + 0.939343i \(0.611436\pi\)
−0.642005 + 0.766700i \(0.721897\pi\)
\(312\) 6.43808 11.1511i 0.364484 0.631306i
\(313\) −11.8547 20.5330i −0.670069 1.16059i −0.977884 0.209148i \(-0.932931\pi\)
0.307815 0.951446i \(-0.400402\pi\)
\(314\) −15.9179 −0.898301
\(315\) −14.4635 1.36219i −0.814923 0.0767508i
\(316\) 19.4726 1.09542
\(317\) −9.83850 17.0408i −0.552585 0.957105i −0.998087 0.0618244i \(-0.980308\pi\)
0.445502 0.895281i \(-0.353025\pi\)
\(318\) −0.270807 + 0.469051i −0.0151861 + 0.0263031i
\(319\) −0.824875 + 1.42873i −0.0461841 + 0.0799933i
\(320\) 5.73630 + 9.93556i 0.320669 + 0.555414i
\(321\) 4.51811 0.252176
\(322\) −42.5877 4.01098i −2.37332 0.223523i
\(323\) −10.3137 −0.573870
\(324\) −9.83198 17.0295i −0.546221 0.946082i
\(325\) −0.231061 + 0.400209i −0.0128170 + 0.0221996i
\(326\) 12.3860 21.4533i 0.686000 1.18819i
\(327\) −1.00390 1.73881i −0.0555159 0.0961564i
\(328\) 61.7718 3.41077
\(329\) −2.28384 + 3.21602i −0.125912 + 0.177305i
\(330\) −3.91794 −0.215675
\(331\) 14.0949 + 24.4131i 0.774728 + 1.34187i 0.934947 + 0.354786i \(0.115446\pi\)
−0.160220 + 0.987081i \(0.551220\pi\)
\(332\) 4.07031 7.04998i 0.223387 0.386918i
\(333\) −6.91794 + 11.9822i −0.379101 + 0.656622i
\(334\) −2.41794 4.18799i −0.132304 0.229157i
\(335\) −10.0806 −0.550760
\(336\) 4.14323 + 9.04140i 0.226032 + 0.493249i
\(337\) 21.7460 1.18458 0.592290 0.805725i \(-0.298224\pi\)
0.592290 + 0.805725i \(0.298224\pi\)
\(338\) −2.73891 4.74394i −0.148977 0.258036i
\(339\) −4.55017 + 7.88112i −0.247131 + 0.428044i
\(340\) −6.90880 + 11.9664i −0.374682 + 0.648969i
\(341\) −1.17512 2.03538i −0.0636366 0.110222i
\(342\) −42.9217 −2.32094
\(343\) 17.7902 + 5.14868i 0.960580 + 0.278003i
\(344\) −28.9269 −1.55963
\(345\) 5.10482 + 8.84180i 0.274834 + 0.476027i
\(346\) 8.01100 13.8755i 0.430674 0.745950i
\(347\) 1.97072 3.41339i 0.105794 0.183241i −0.808268 0.588814i \(-0.799595\pi\)
0.914062 + 0.405574i \(0.132928\pi\)
\(348\) −2.47463 4.28618i −0.132654 0.229763i
\(349\) −14.1093 −0.755254 −0.377627 0.925958i \(-0.623260\pi\)
−0.377627 + 0.925958i \(0.623260\pi\)
\(350\) −0.386046 0.842433i −0.0206350 0.0450299i
\(351\) −12.8762 −0.687279
\(352\) −1.07031 1.85383i −0.0570475 0.0988093i
\(353\) 2.48434 4.30301i 0.132228 0.229026i −0.792307 0.610123i \(-0.791120\pi\)
0.924535 + 0.381097i \(0.124453\pi\)
\(354\) 11.2493 19.4844i 0.597895 1.03559i
\(355\) −12.4843 21.6235i −0.662600 1.14766i
\(356\) 13.4726 0.714046
\(357\) 1.62961 2.29475i 0.0862481 0.121451i
\(358\) 8.93214 0.472078
\(359\) 2.03580 + 3.52610i 0.107445 + 0.186101i 0.914735 0.404055i \(-0.132400\pi\)
−0.807289 + 0.590156i \(0.799066\pi\)
\(360\) −15.0748 + 26.1103i −0.794511 + 1.37613i
\(361\) −14.4289 + 24.9917i −0.759418 + 1.31535i
\(362\) 15.2109 + 26.3461i 0.799468 + 1.38472i
\(363\) −0.713538 −0.0374510
\(364\) −36.3969 3.42792i −1.90772 0.179672i
\(365\) −18.8866 −0.988571
\(366\) 11.5364 + 19.9816i 0.603016 + 1.04445i
\(367\) 9.01100 15.6075i 0.470371 0.814706i −0.529055 0.848587i \(-0.677454\pi\)
0.999426 + 0.0338816i \(0.0107869\pi\)
\(368\) −17.0975 + 29.6138i −0.891271 + 1.54373i
\(369\) −14.0110 24.2678i −0.729384 1.26333i
\(370\) 30.4998 1.58561
\(371\) 0.802700 + 0.0755997i 0.0416741 + 0.00392494i
\(372\) 7.05075 0.365564
\(373\) −14.4582 25.0424i −0.748618 1.29664i −0.948485 0.316822i \(-0.897384\pi\)
0.199867 0.979823i \(-0.435949\pi\)
\(374\) −1.85677 + 3.21602i −0.0960112 + 0.166296i
\(375\) −4.04290 + 7.00250i −0.208774 + 0.361608i
\(376\) 4.09306 + 7.08940i 0.211084 + 0.365608i
\(377\) 5.42184 0.279239
\(378\) 14.9498 21.0518i 0.768936 1.08279i
\(379\) 4.30847 0.221311 0.110656 0.993859i \(-0.464705\pi\)
0.110656 + 0.993859i \(0.464705\pi\)
\(380\) 32.0584 + 55.5268i 1.64456 + 2.84846i
\(381\) −4.41591 + 7.64857i −0.226234 + 0.391848i
\(382\) 15.0813 26.1216i 0.771627 1.33650i
\(383\) 6.17438 + 10.6943i 0.315496 + 0.546455i 0.979543 0.201236i \(-0.0644958\pi\)
−0.664047 + 0.747691i \(0.731163\pi\)
\(384\) −12.3047 −0.627923
\(385\) 2.42969 + 5.30210i 0.123829 + 0.270220i
\(386\) 29.7408 1.51377
\(387\) 6.56117 + 11.3643i 0.333523 + 0.577679i
\(388\) −3.90880 + 6.77025i −0.198439 + 0.343707i
\(389\) −14.7115 + 25.4811i −0.745903 + 1.29194i 0.203869 + 0.978998i \(0.434648\pi\)
−0.949772 + 0.312943i \(0.898685\pi\)
\(390\) 6.43808 + 11.1511i 0.326005 + 0.564657i
\(391\) 9.67699 0.489387
\(392\) 25.0949 29.1131i 1.26749 1.47043i
\(393\) −0.541613 −0.0273208
\(394\) 15.1477 + 26.2366i 0.763131 + 1.32178i
\(395\) −5.10482 + 8.84180i −0.256851 + 0.444879i
\(396\) −5.23630 + 9.06953i −0.263134 + 0.455761i
\(397\) 8.64975 + 14.9818i 0.434119 + 0.751915i 0.997223 0.0744702i \(-0.0237266\pi\)
−0.563105 + 0.826386i \(0.690393\pi\)
\(398\) −4.74485 −0.237838
\(399\) −5.44070 11.8727i −0.272376 0.594381i
\(400\) −0.740780 −0.0370390
\(401\) 12.4752 + 21.6077i 0.622982 + 1.07904i 0.988927 + 0.148400i \(0.0474124\pi\)
−0.365945 + 0.930636i \(0.619254\pi\)
\(402\) 4.06379 7.03869i 0.202683 0.351058i
\(403\) −3.86200 + 6.68919i −0.192380 + 0.333212i
\(404\) −12.7089 22.0124i −0.632291 1.09516i
\(405\) 10.3100 0.512306
\(406\) −6.29502 + 8.86439i −0.312416 + 0.439932i
\(407\) 5.55465 0.275334
\(408\) −2.92056 5.05855i −0.144589 0.250436i
\(409\) 19.2792 33.3925i 0.953295 1.65115i 0.215072 0.976598i \(-0.431001\pi\)
0.738223 0.674557i \(-0.235665\pi\)
\(410\) −30.8859 + 53.4959i −1.52534 + 2.64197i
\(411\) −2.08393 3.60947i −0.102793 0.178042i
\(412\) −4.47259 −0.220349
\(413\) −33.3443 3.14042i −1.64076 0.154530i
\(414\) 40.2719 1.97926
\(415\) 2.13409 + 3.69636i 0.104759 + 0.181447i
\(416\) −3.51752 + 6.09253i −0.172461 + 0.298711i
\(417\) −1.98825 + 3.44374i −0.0973648 + 0.168641i
\(418\) 8.61582 + 14.9230i 0.421414 + 0.729910i
\(419\) 0.908970 0.0444061 0.0222030 0.999753i \(-0.492932\pi\)
0.0222030 + 0.999753i \(0.492932\pi\)
\(420\) −17.4198 1.64063i −0.850000 0.0800544i
\(421\) 15.5532 0.758014 0.379007 0.925394i \(-0.376266\pi\)
0.379007 + 0.925394i \(0.376266\pi\)
\(422\) −20.2316 35.0422i −0.984861 1.70583i
\(423\) 1.85677 3.21602i 0.0902792 0.156368i
\(424\) 0.836629 1.44908i 0.0406303 0.0703737i
\(425\) 0.104818 + 0.181550i 0.00508442 + 0.00880647i
\(426\) 20.1313 0.975365
\(427\) 19.8866 28.0035i 0.962381 1.35519i
\(428\) −26.6222 −1.28683
\(429\) 1.17251 + 2.03084i 0.0566092 + 0.0980500i
\(430\) 14.4635 25.0514i 0.697490 1.20809i
\(431\) −1.76819 + 3.06259i −0.0851707 + 0.147520i −0.905464 0.424423i \(-0.860477\pi\)
0.820293 + 0.571943i \(0.193810\pi\)
\(432\) −10.3202 17.8752i −0.496532 0.860019i
\(433\) 17.6457 0.847997 0.423999 0.905663i \(-0.360626\pi\)
0.423999 + 0.905663i \(0.360626\pi\)
\(434\) −6.45245 14.0806i −0.309728 0.675891i
\(435\) 2.59493 0.124417
\(436\) 5.91532 + 10.2456i 0.283293 + 0.490677i
\(437\) 22.4517 38.8875i 1.07401 1.86024i
\(438\) 7.61379 13.1875i 0.363801 0.630122i
\(439\) −7.51362 13.0140i −0.358606 0.621123i 0.629123 0.777306i \(-0.283414\pi\)
−0.987728 + 0.156183i \(0.950081\pi\)
\(440\) 12.1041 0.577039
\(441\) −17.1294 3.25544i −0.815688 0.155021i
\(442\) 12.2044 0.580504
\(443\) −6.61134 11.4512i −0.314114 0.544062i 0.665135 0.746723i \(-0.268374\pi\)
−0.979249 + 0.202662i \(0.935041\pi\)
\(444\) −8.33198 + 14.4314i −0.395418 + 0.684884i
\(445\) −3.53189 + 6.11742i −0.167428 + 0.289994i
\(446\) 3.78181 + 6.55029i 0.179074 + 0.310165i
\(447\) 0.713538 0.0337492
\(448\) 5.73630 + 12.5178i 0.271014 + 0.591411i
\(449\) −9.90864 −0.467617 −0.233809 0.972283i \(-0.575119\pi\)
−0.233809 + 0.972283i \(0.575119\pi\)
\(450\) 0.436212 + 0.755542i 0.0205632 + 0.0356166i
\(451\) −5.62496 + 9.74271i −0.264869 + 0.458766i
\(452\) 26.8111 46.4382i 1.26109 2.18427i
\(453\) 5.29485 + 9.17095i 0.248774 + 0.430889i
\(454\) −45.9542 −2.15674
\(455\) 11.0981 15.6279i 0.520286 0.732646i
\(456\) −27.1041 −1.26926
\(457\) −5.17251 8.95905i −0.241960 0.419087i 0.719313 0.694686i \(-0.244457\pi\)
−0.961272 + 0.275600i \(0.911124\pi\)
\(458\) −31.7583 + 55.0070i −1.48397 + 2.57031i
\(459\) −2.92056 + 5.05855i −0.136320 + 0.236113i
\(460\) −30.0793 52.0988i −1.40245 2.42912i
\(461\) −15.3372 −0.714325 −0.357163 0.934042i \(-0.616256\pi\)
−0.357163 + 0.934042i \(0.616256\pi\)
\(462\) −4.68164 0.440925i −0.217810 0.0205137i
\(463\) −25.1313 −1.16795 −0.583976 0.811771i \(-0.698504\pi\)
−0.583976 + 0.811771i \(0.698504\pi\)
\(464\) 4.34560 + 7.52680i 0.201739 + 0.349423i
\(465\) −1.84838 + 3.20149i −0.0857167 + 0.148466i
\(466\) 4.75457 8.23515i 0.220251 0.381486i
\(467\) 0.373007 + 0.646068i 0.0172607 + 0.0298964i 0.874527 0.484977i \(-0.161172\pi\)
−0.857266 + 0.514874i \(0.827839\pi\)
\(468\) 34.4178 1.59096
\(469\) −12.0455 1.13447i −0.556210 0.0523848i
\(470\) −8.18613 −0.377598
\(471\) 2.27994 + 3.94898i 0.105054 + 0.181959i
\(472\) −34.7537 + 60.1951i −1.59967 + 2.77070i
\(473\) 2.63409 4.56239i 0.121116 0.209779i
\(474\) −4.11582 7.12881i −0.189046 0.327437i
\(475\) 0.972758 0.0446332
\(476\) −9.60220 + 13.5214i −0.440116 + 0.619754i
\(477\) −0.759053 −0.0347546
\(478\) 16.1953 + 28.0510i 0.740754 + 1.28302i
\(479\) 10.0565 17.4184i 0.459494 0.795867i −0.539440 0.842024i \(-0.681364\pi\)
0.998934 + 0.0461569i \(0.0146974\pi\)
\(480\) −1.68351 + 2.91593i −0.0768414 + 0.133093i
\(481\) −9.12758 15.8094i −0.416182 0.720848i
\(482\) 1.12234 0.0511212
\(483\) 5.10482 + 11.1398i 0.232277 + 0.506878i
\(484\) 4.20440 0.191109
\(485\) −2.04942 3.54969i −0.0930592 0.161183i
\(486\) −18.7948 + 32.5536i −0.852552 + 1.47666i
\(487\) 2.12496 3.68054i 0.0962911 0.166781i −0.813856 0.581067i \(-0.802635\pi\)
0.910147 + 0.414286i \(0.135969\pi\)
\(488\) −35.6404 61.7311i −1.61337 2.79443i
\(489\) −7.09626 −0.320904
\(490\) 12.6652 + 36.2894i 0.572157 + 1.63939i
\(491\) 30.3279 1.36868 0.684340 0.729163i \(-0.260091\pi\)
0.684340 + 0.729163i \(0.260091\pi\)
\(492\) −16.8749 29.2281i −0.760778 1.31771i
\(493\) 1.22978 2.13003i 0.0553863 0.0959320i
\(494\) 28.3156 49.0440i 1.27398 2.20659i
\(495\) −2.74543 4.75523i −0.123398 0.213732i
\(496\) −12.3816 −0.555948
\(497\) −12.4843 27.2435i −0.559999 1.22204i
\(498\) −3.44128 −0.154207
\(499\) −7.22064 12.5065i −0.323240 0.559869i 0.657914 0.753093i \(-0.271439\pi\)
−0.981155 + 0.193224i \(0.938106\pi\)
\(500\) 23.8221 41.2611i 1.06536 1.84525i
\(501\) −0.692648 + 1.19970i −0.0309452 + 0.0535987i
\(502\) 1.39315 + 2.41300i 0.0621792 + 0.107698i
\(503\) −2.95822 −0.131901 −0.0659503 0.997823i \(-0.521008\pi\)
−0.0659503 + 0.997823i \(0.521008\pi\)
\(504\) −20.9517 + 29.5033i −0.933263 + 1.31418i
\(505\) 13.3267 0.593032
\(506\) −8.08393 14.0018i −0.359374 0.622455i
\(507\) −0.784595 + 1.35896i −0.0348451 + 0.0603534i
\(508\) 26.0200 45.0679i 1.15445 1.99957i
\(509\) 12.4953 + 21.6426i 0.553847 + 0.959290i 0.997992 + 0.0633358i \(0.0201739\pi\)
−0.444146 + 0.895955i \(0.646493\pi\)
\(510\) 5.84111 0.258649
\(511\) −22.5681 2.12550i −0.998354 0.0940267i
\(512\) 46.5767 2.05842
\(513\) 13.5520 + 23.4728i 0.598337 + 1.03635i
\(514\) −28.4452 + 49.2685i −1.25466 + 2.17314i
\(515\) 1.17251 2.03084i 0.0516669 0.0894896i
\(516\) 7.90228 + 13.6872i 0.347879 + 0.602544i
\(517\) −1.49086 −0.0655681
\(518\) 36.4450 + 3.43245i 1.60130 + 0.150813i
\(519\) −4.58970 −0.201465
\(520\) −19.8898 34.4501i −0.872225 1.51074i
\(521\) −14.4316 + 24.9962i −0.632258 + 1.09510i 0.354831 + 0.934931i \(0.384538\pi\)
−0.987089 + 0.160173i \(0.948795\pi\)
\(522\) 5.11786 8.86439i 0.224002 0.387984i
\(523\) −0.236295 0.409276i −0.0103325 0.0178964i 0.860813 0.508921i \(-0.169956\pi\)
−0.871145 + 0.491025i \(0.836622\pi\)
\(524\) 3.19136 0.139415
\(525\) −0.153700 + 0.216434i −0.00670802 + 0.00944596i
\(526\) 22.8944 0.998245
\(527\) 1.75195 + 3.03447i 0.0763162 + 0.132184i
\(528\) −1.87953 + 3.25544i −0.0817959 + 0.141675i
\(529\) −9.56566 + 16.5682i −0.415898 + 0.720357i
\(530\) 0.836629 + 1.44908i 0.0363408 + 0.0629442i
\(531\) 31.5311 1.36834
\(532\) 32.0584 + 69.9582i 1.38991 + 3.03307i
\(533\) 36.9724 1.60145
\(534\) −2.84763 4.93224i −0.123229 0.213439i
\(535\) 6.97911 12.0882i 0.301733 0.522617i
\(536\) −12.5547 + 21.7453i −0.542278 + 0.939254i
\(537\) −1.27936 2.21592i −0.0552085 0.0956239i
\(538\) 38.8904 1.67668
\(539\) 2.30660 + 6.60905i 0.0993524 + 0.284672i
\(540\) 36.3122 1.56263
\(541\) −7.72978 13.3884i −0.332329 0.575611i 0.650639 0.759387i \(-0.274501\pi\)
−0.982968 + 0.183776i \(0.941168\pi\)
\(542\) 34.5539 59.8491i 1.48422 2.57074i
\(543\) 4.35735 7.54715i 0.186992 0.323879i
\(544\) 1.59568 + 2.76380i 0.0684143 + 0.118497i
\(545\) −6.20290 −0.265703
\(546\) 6.43808 + 14.0492i 0.275524 + 0.601252i
\(547\) −35.0440 −1.49837 −0.749187 0.662359i \(-0.769556\pi\)
−0.749187 + 0.662359i \(0.769556\pi\)
\(548\) 12.2792 + 21.2682i 0.524541 + 0.908532i
\(549\) −16.1679 + 28.0035i −0.690027 + 1.19516i
\(550\) 0.175125 0.303325i 0.00746735 0.0129338i
\(551\) −5.70644 9.88384i −0.243102 0.421066i
\(552\) 25.4308 1.08241
\(553\) −7.09493 + 9.99080i −0.301707 + 0.424852i
\(554\) −36.8956 −1.56754
\(555\) −4.36852 7.56650i −0.185433 0.321180i
\(556\) 11.7154 20.2917i 0.496844 0.860559i
\(557\) −5.26632 + 9.12154i −0.223141 + 0.386492i −0.955760 0.294147i \(-0.904964\pi\)
0.732619 + 0.680639i \(0.238298\pi\)
\(558\) 7.29095 + 12.6283i 0.308650 + 0.534598i
\(559\) −17.3137 −0.732292
\(560\) 30.5903 + 2.88104i 1.29268 + 0.121746i
\(561\) 1.06379 0.0449132
\(562\) 18.9588 + 32.8376i 0.799729 + 1.38517i
\(563\) 15.3574 26.5997i 0.647235 1.12104i −0.336545 0.941667i \(-0.609258\pi\)
0.983780 0.179377i \(-0.0574082\pi\)
\(564\) 2.23630 3.87338i 0.0941650 0.163099i
\(565\) 14.0573 + 24.3479i 0.591394 + 1.02432i
\(566\) −54.0948 −2.27377
\(567\) 12.3196 + 1.16028i 0.517376 + 0.0487274i
\(568\) −62.1936 −2.60959
\(569\) 15.3860 + 26.6494i 0.645017 + 1.11720i 0.984298 + 0.176516i \(0.0564829\pi\)
−0.339281 + 0.940685i \(0.610184\pi\)
\(570\) 13.5520 23.4728i 0.567632 0.983168i
\(571\) 3.75847 6.50986i 0.157287 0.272429i −0.776602 0.629991i \(-0.783059\pi\)
0.933889 + 0.357562i \(0.116392\pi\)
\(572\) −6.90880 11.9664i −0.288872 0.500340i
\(573\) −8.64045 −0.360960
\(574\) −42.9267 + 60.4477i −1.79173 + 2.52304i
\(575\) −0.912705 −0.0380624
\(576\) −6.48173 11.2267i −0.270072 0.467778i
\(577\) −13.8092 + 23.9183i −0.574885 + 0.995731i 0.421169 + 0.906982i \(0.361620\pi\)
−0.996054 + 0.0887483i \(0.971713\pi\)
\(578\) −18.4042 + 31.8769i −0.765512 + 1.32591i
\(579\) −4.25980 7.37819i −0.177031 0.306627i
\(580\) −15.2902 −0.634891
\(581\) 2.13409 + 4.65704i 0.0885372 + 0.193207i
\(582\) 3.30473 0.136986
\(583\) 0.152367 + 0.263908i 0.00631041 + 0.0109300i
\(584\) −23.5220 + 40.7413i −0.973348 + 1.68589i
\(585\) −9.02276 + 15.6279i −0.373045 + 0.646133i
\(586\) 13.8586 + 24.0039i 0.572495 + 0.991590i
\(587\) −29.9582 −1.23651 −0.618254 0.785978i \(-0.712160\pi\)
−0.618254 + 0.785978i \(0.712160\pi\)
\(588\) −20.6307 3.92085i −0.850797 0.161693i
\(589\) 16.2589 0.669936
\(590\) −34.7537 60.1951i −1.43079 2.47819i
\(591\) 4.33925 7.51579i 0.178493 0.309158i
\(592\) 14.6315 25.3425i 0.601350 1.04157i
\(593\) −6.33401 10.9708i −0.260107 0.450518i 0.706163 0.708049i \(-0.250424\pi\)
−0.966270 + 0.257531i \(0.917091\pi\)
\(594\) 9.75905 0.400419
\(595\) −3.62234 7.90471i −0.148502 0.324062i
\(596\) −4.20440 −0.172219
\(597\) 0.679610 + 1.17712i 0.0278146 + 0.0481762i
\(598\) −26.5675 + 46.0163i −1.08643 + 1.88175i
\(599\) −0.647133 + 1.12087i −0.0264411 + 0.0457974i −0.878943 0.476926i \(-0.841751\pi\)
0.852502 + 0.522724i \(0.175084\pi\)
\(600\) 0.275458 + 0.477108i 0.0112455 + 0.0194778i
\(601\) −41.0220 −1.67332 −0.836661 0.547721i \(-0.815496\pi\)
−0.836661 + 0.547721i \(0.815496\pi\)
\(602\) 20.1020 28.3069i 0.819298 1.15370i
\(603\) 11.3905 0.463858
\(604\) −31.1990 54.0383i −1.26947 2.19879i
\(605\) −1.10220 + 1.90907i −0.0448108 + 0.0776146i
\(606\) −5.37242 + 9.30531i −0.218240 + 0.378002i
\(607\) 10.5884 + 18.3397i 0.429770 + 0.744384i 0.996853 0.0792770i \(-0.0252612\pi\)
−0.567082 + 0.823661i \(0.691928\pi\)
\(608\) 14.8086 0.600570
\(609\) 3.10075 + 0.292034i 0.125649 + 0.0118338i
\(610\) 71.2809 2.88608
\(611\) 2.44983 + 4.24324i 0.0991096 + 0.171663i
\(612\) 7.80660 13.5214i 0.315563 0.546571i
\(613\) −3.38156 + 5.85704i −0.136580 + 0.236563i −0.926200 0.377033i \(-0.876944\pi\)
0.789620 + 0.613596i \(0.210278\pi\)
\(614\) 31.1177 + 53.8974i 1.25581 + 2.17512i
\(615\) 17.6953 0.713542
\(616\) 14.4635 + 1.36219i 0.582749 + 0.0548843i
\(617\) −41.0728 −1.65353 −0.826763 0.562550i \(-0.809820\pi\)
−0.826763 + 0.562550i \(0.809820\pi\)
\(618\) 0.945349 + 1.63739i 0.0380275 + 0.0658656i
\(619\) 15.2134 26.3503i 0.611477 1.05911i −0.379515 0.925186i \(-0.623909\pi\)
0.990992 0.133924i \(-0.0427577\pi\)
\(620\) 10.8913 18.8643i 0.437404 0.757607i
\(621\) −12.7154 22.0237i −0.510252 0.883782i
\(622\) −86.5345 −3.46972
\(623\) −4.90880 + 6.91238i −0.196667 + 0.276939i
\(624\) 12.3540 0.494555
\(625\) 12.1386 + 21.0246i 0.485543 + 0.840985i
\(626\) 29.5285 51.1449i 1.18020 2.04416i
\(627\) 2.46811 4.27489i 0.0985667 0.170722i
\(628\) −13.4342 23.2687i −0.536082 0.928521i
\(629\) −8.28123 −0.330194
\(630\) −15.0748 32.8964i −0.600594 1.31062i
\(631\) 12.3670 0.492323 0.246162 0.969229i \(-0.420831\pi\)
0.246162 + 0.969229i \(0.420831\pi\)
\(632\) 12.7154 + 22.0237i 0.505792 + 0.876057i
\(633\) −5.79560 + 10.0383i −0.230354 + 0.398985i
\(634\) 24.5064 42.4462i 0.973272 1.68576i
\(635\) 13.6425 + 23.6295i 0.541385 + 0.937707i
\(636\) −0.914205 −0.0362506
\(637\) 15.0201 17.4252i 0.595120 0.690410i
\(638\) −4.10930 −0.162689
\(639\) 14.1067 + 24.4335i 0.558052 + 0.966574i
\(640\) −19.0071 + 32.9213i −0.751322 + 1.30133i
\(641\) 23.5657 40.8169i 0.930787 1.61217i 0.148809 0.988866i \(-0.452456\pi\)
0.781979 0.623305i \(-0.214211\pi\)
\(642\) 5.62699 + 9.74624i 0.222080 + 0.384653i
\(643\) 1.87242 0.0738412 0.0369206 0.999318i \(-0.488245\pi\)
0.0369206 + 0.999318i \(0.488245\pi\)
\(644\) −30.0793 65.6393i −1.18529 2.58655i
\(645\) −8.28646 −0.326279
\(646\) −12.8450 22.2482i −0.505380 0.875344i
\(647\) 0.917939 1.58992i 0.0360879 0.0625061i −0.847417 0.530927i \(-0.821844\pi\)
0.883505 + 0.468421i \(0.155177\pi\)
\(648\) 12.8404 22.2402i 0.504417 0.873676i
\(649\) −6.32936 10.9628i −0.248449 0.430326i
\(650\) −1.15108 −0.0451492
\(651\) −2.56897 + 3.61753i −0.100686 + 0.141782i
\(652\) 41.8135 1.63754
\(653\) 9.08858 + 15.7419i 0.355664 + 0.616027i 0.987231 0.159293i \(-0.0509216\pi\)
−0.631568 + 0.775321i \(0.717588\pi\)
\(654\) 2.50058 4.33114i 0.0977805 0.169361i
\(655\) −0.836629 + 1.44908i −0.0326898 + 0.0566204i
\(656\) 29.6333 + 51.3265i 1.15699 + 2.00396i
\(657\) 21.3409 0.832590
\(658\) −9.78181 0.921267i −0.381335 0.0359147i
\(659\) −16.8997 −0.658318 −0.329159 0.944275i \(-0.606765\pi\)
−0.329159 + 0.944275i \(0.606765\pi\)
\(660\) −3.30660 5.72720i −0.128709 0.222931i
\(661\) 22.6516 39.2338i 0.881046 1.52602i 0.0308661 0.999524i \(-0.490173\pi\)
0.850180 0.526493i \(-0.176493\pi\)
\(662\) −35.1086 + 60.8098i −1.36453 + 2.36344i
\(663\) −1.74805 3.02771i −0.0678886 0.117587i
\(664\) 10.6315 0.412581
\(665\) −40.1697 3.78325i −1.55772 0.146708i
\(666\) −34.4633 −1.33543
\(667\) 5.35415 + 9.27366i 0.207314 + 0.359078i
\(668\) 4.08131 7.06904i 0.157911 0.273509i
\(669\) 1.08335 1.87641i 0.0418845 0.0725462i
\(670\) −12.5547 21.7453i −0.485028 0.840094i
\(671\) 12.9817 0.501154
\(672\) −2.33983 + 3.29485i −0.0902609 + 0.127102i
\(673\) 39.5076 1.52291 0.761454 0.648219i \(-0.224486\pi\)
0.761454 + 0.648219i \(0.224486\pi\)
\(674\) 27.0832 + 46.9094i 1.04321 + 1.80688i
\(675\) 0.275458 0.477108i 0.0106024 0.0183639i
\(676\) 4.62309 8.00743i 0.177811 0.307978i
\(677\) 17.0669 + 29.5608i 0.655936 + 1.13611i 0.981658 + 0.190649i \(0.0610591\pi\)
−0.325723 + 0.945465i \(0.605608\pi\)
\(678\) −22.6677 −0.870547
\(679\) −2.04942 4.47226i −0.0786494 0.171630i
\(680\) −18.0455 −0.692014
\(681\) 6.58206 + 11.4005i 0.252225 + 0.436867i
\(682\) 2.92708 5.06984i 0.112084 0.194134i
\(683\) −11.8931 + 20.5995i −0.455079 + 0.788219i −0.998693 0.0511160i \(-0.983722\pi\)
0.543614 + 0.839335i \(0.317056\pi\)
\(684\) −36.2244 62.7425i −1.38507 2.39902i
\(685\) −12.8762 −0.491973
\(686\) 11.0500 + 44.7885i 0.421891 + 1.71003i
\(687\) 18.1951 0.694186
\(688\) −13.8769 24.0355i −0.529052 0.916345i
\(689\) 0.500750 0.867324i 0.0190770 0.0330424i
\(690\) −12.7154 + 22.0237i −0.484067 + 0.838429i
\(691\) 10.2812 + 17.8076i 0.391116 + 0.677433i 0.992597 0.121454i \(-0.0387557\pi\)
−0.601481 + 0.798887i \(0.705422\pi\)
\(692\) 27.0440 1.02806
\(693\) −2.74543 5.99111i −0.104290 0.227584i
\(694\) 9.81761 0.372671
\(695\) 6.14248 + 10.6391i 0.232998 + 0.403564i
\(696\) 3.23181 5.59766i 0.122501 0.212179i
\(697\) 8.38605 14.5251i 0.317644 0.550176i
\(698\) −17.5722 30.4359i −0.665117 1.15202i
\(699\) −2.72401 −0.103031
\(700\) 0.905651 1.27530i 0.0342304 0.0482019i
\(701\) −23.9907 −0.906116 −0.453058 0.891481i \(-0.649667\pi\)
−0.453058 + 0.891481i \(0.649667\pi\)
\(702\) −16.0364 27.7758i −0.605254 1.04833i
\(703\) −19.2134 + 33.2785i −0.724646 + 1.25512i
\(704\) −2.60220 + 4.50714i −0.0980741 + 0.169869i
\(705\) 1.17251 + 2.03084i 0.0441592 + 0.0764860i
\(706\) 12.3763 0.465789
\(707\) 15.9245 + 1.49979i 0.598901 + 0.0564055i
\(708\) 37.9762 1.42723
\(709\) 25.8559 + 44.7836i 0.971037 + 1.68189i 0.692437 + 0.721478i \(0.256537\pi\)
0.278599 + 0.960407i \(0.410130\pi\)
\(710\) 31.0968 53.8612i 1.16704 2.02138i
\(711\) 5.76819 9.99080i 0.216324 0.374684i
\(712\) 8.79747 + 15.2377i 0.329699 + 0.571055i
\(713\) −15.2552 −0.571310
\(714\) 6.97969 + 0.657359i 0.261208 + 0.0246010i
\(715\) 7.24468 0.270936
\(716\) 7.53841 + 13.0569i 0.281724 + 0.487960i
\(717\) 4.63933 8.03555i 0.173259 0.300093i
\(718\) −5.07089 + 8.78304i −0.189244 + 0.327780i
\(719\) −12.8926 22.3306i −0.480812 0.832790i 0.518946 0.854807i \(-0.326325\pi\)
−0.999758 + 0.0220170i \(0.992991\pi\)
\(720\) −28.9269 −1.07804
\(721\) 1.62961 2.29475i 0.0606898 0.0854610i
\(722\) −71.8811 −2.67514
\(723\) −0.160754 0.278434i −0.00597851 0.0103551i
\(724\) −25.6750 + 44.4703i −0.954202 + 1.65273i
\(725\) −0.115989 + 0.200899i −0.00430772 + 0.00746118i
\(726\) −0.888663 1.53921i −0.0329814 0.0571254i
\(727\) 32.7330 1.21400 0.606999 0.794702i \(-0.292373\pi\)
0.606999 + 0.794702i \(0.292373\pi\)
\(728\) −19.8898 43.4037i −0.737164 1.60865i
\(729\) −3.26295 −0.120850
\(730\) −23.5220 40.7413i −0.870589 1.50790i
\(731\) −3.92708 + 6.80189i −0.145248 + 0.251577i
\(732\) −19.4726 + 33.7275i −0.719728 + 1.24660i
\(733\) 4.64136 + 8.03908i 0.171433 + 0.296930i 0.938921 0.344133i \(-0.111827\pi\)
−0.767488 + 0.641063i \(0.778494\pi\)
\(734\) 44.8904 1.65693
\(735\) 7.18875 8.33981i 0.265161 0.307618i
\(736\) −13.8944 −0.512156
\(737\) −2.28646 3.96027i −0.0842229 0.145878i
\(738\) 34.8995 60.4477i 1.28467 2.22511i
\(739\) 25.0466 43.3820i 0.921355 1.59583i 0.124035 0.992278i \(-0.460417\pi\)
0.797320 0.603556i \(-0.206250\pi\)
\(740\) 25.7408 + 44.5843i 0.946250 + 1.63895i
\(741\) −16.2227 −0.595955
\(742\) 0.836629 + 1.82570i 0.0307136 + 0.0670236i
\(743\) 13.1679 0.483082 0.241541 0.970391i \(-0.422347\pi\)
0.241541 + 0.970391i \(0.422347\pi\)
\(744\) 4.60407 + 7.97448i 0.168793 + 0.292359i
\(745\) 1.10220 1.90907i 0.0403815 0.0699428i
\(746\) 36.0135 62.3771i 1.31855 2.28379i
\(747\) −2.41142 4.17670i −0.0882293 0.152818i
\(748\) −6.26819 −0.229188
\(749\) 9.69992 13.6590i 0.354427 0.499090i
\(750\) −20.1406 −0.735431
\(751\) −20.6569 35.7787i −0.753779 1.30558i −0.945979 0.324228i \(-0.894895\pi\)
0.192200 0.981356i \(-0.438438\pi\)
\(752\) −3.92708 + 6.80189i −0.143206 + 0.248040i
\(753\) 0.399084 0.691234i 0.0145434 0.0251900i
\(754\) 6.75253 + 11.6957i 0.245913 + 0.425933i
\(755\) 32.7158 1.19065
\(756\) 43.3904 + 4.08658i 1.57809 + 0.148627i
\(757\) −45.5114 −1.65414 −0.827069 0.562100i \(-0.809994\pi\)
−0.827069 + 0.562100i \(0.809994\pi\)
\(758\) 5.36591 + 9.29402i 0.194898 + 0.337574i
\(759\) −2.31574 + 4.01098i −0.0840560 + 0.145589i
\(760\) −41.8676 + 72.5168i −1.51870 + 2.63046i
\(761\) −15.6360 27.0823i −0.566803 0.981732i −0.996879 0.0789393i \(-0.974847\pi\)
0.430076 0.902793i \(-0.358487\pi\)
\(762\) −21.9988 −0.796934
\(763\) −7.41200 0.698075i −0.268333 0.0252720i
\(764\) 50.9124 1.84194
\(765\) 4.09306 + 7.08940i 0.147985 + 0.256318i
\(766\) −15.3795 + 26.6381i −0.555685 + 0.962474i
\(767\) −20.8012 + 36.0287i −0.751088 + 1.30092i
\(768\) −11.6112 20.1111i −0.418982 0.725698i
\(769\) 42.0467 1.51624 0.758121 0.652114i \(-0.226118\pi\)
0.758121 + 0.652114i \(0.226118\pi\)
\(770\) −8.41142 + 11.8446i −0.303127 + 0.426851i
\(771\) 16.2969 0.586920
\(772\) 25.1002 + 43.4748i 0.903375 + 1.56469i
\(773\) −3.82226 + 6.62034i −0.137477 + 0.238117i −0.926541 0.376194i \(-0.877233\pi\)
0.789064 + 0.614311i \(0.210566\pi\)
\(774\) −16.3430 + 28.3069i −0.587436 + 1.01747i
\(775\) −0.165239 0.286202i −0.00593555 0.0102807i
\(776\) −10.2096 −0.366505
\(777\) −4.36852 9.53304i −0.156720 0.341996i
\(778\) −73.2887 −2.62753
\(779\) −38.9131 67.3995i −1.39421 2.41484i
\(780\) −10.8670 + 18.8222i −0.389102 + 0.673944i
\(781\) 5.66337 9.80925i 0.202651 0.351002i
\(782\) 12.0520 + 20.8747i 0.430980 + 0.746479i
\(783\) −6.46362 −0.230991
\(784\) 36.2289 + 6.88526i 1.29389 + 0.245902i
\(785\) 14.0873 0.502797
\(786\) −0.674542 1.16834i −0.0240601 0.0416734i
\(787\) 13.9517 24.1651i 0.497324 0.861391i −0.502671 0.864478i \(-0.667649\pi\)
0.999995 + 0.00308674i \(0.000982540\pi\)
\(788\) −25.5683 + 44.2855i −0.910832 + 1.57761i
\(789\) −3.27919 5.67973i −0.116742 0.202204i
\(790\) −25.4308 −0.904788
\(791\) 14.0573 + 30.6759i 0.499819 + 1.09071i
\(792\) −13.6770 −0.485991
\(793\) −21.3320 36.9481i −0.757521 1.31206i
\(794\) −21.5453 + 37.3176i −0.764616 + 1.32435i
\(795\) 0.239662 0.415107i 0.00849995 0.0147223i
\(796\) −4.00448 6.93597i −0.141935 0.245839i
\(797\) 10.0560 0.356201 0.178101 0.984012i \(-0.443005\pi\)
0.178101 + 0.984012i \(0.443005\pi\)
\(798\) 18.8353 26.5231i 0.666762 0.938908i
\(799\) 2.22267 0.0786326
\(800\) −0.150500 0.260674i −0.00532098 0.00921620i
\(801\) 3.99086 6.91238i 0.141010 0.244237i
\(802\) −31.0740 + 53.8218i −1.09726 + 1.90051i
\(803\) −4.28384 7.41984i −0.151174 0.261840i
\(804\) 13.7188 0.483824
\(805\) 37.6899 + 3.54969i 1.32839 + 0.125110i
\(806\) −19.2394 −0.677681
\(807\) −5.57031 9.64805i −0.196084 0.339628i
\(808\) 16.5975 28.7478i 0.583900 1.01134i
\(809\) −19.2863 + 33.4048i −0.678070 + 1.17445i 0.297491 + 0.954725i \(0.403850\pi\)
−0.975561 + 0.219727i \(0.929483\pi\)
\(810\) 12.8404 + 22.2402i 0.451164 + 0.781440i
\(811\) 12.3760 0.434580 0.217290 0.976107i \(-0.430278\pi\)
0.217290 + 0.976107i \(0.430278\pi\)
\(812\) −18.2706 1.72076i −0.641174 0.0603868i
\(813\) −19.7968 −0.694303
\(814\) 6.91794 + 11.9822i 0.242474 + 0.419977i
\(815\) −10.9616 + 18.9860i −0.383968 + 0.665051i
\(816\) 2.80212 4.85341i 0.0980937 0.169903i
\(817\) 18.2225 + 31.5623i 0.637525 + 1.10423i
\(818\) 96.0437 3.35809
\(819\) −12.5403 + 17.6587i −0.438193 + 0.617046i
\(820\) −104.266 −3.64114
\(821\) −14.8691 25.7540i −0.518934 0.898820i −0.999758 0.0220025i \(-0.992996\pi\)
0.480824 0.876817i \(-0.340338\pi\)
\(822\) 5.19078 8.99070i 0.181049 0.313587i
\(823\) −20.3885 + 35.3139i −0.710698 + 1.23097i 0.253897 + 0.967231i \(0.418288\pi\)
−0.964595 + 0.263734i \(0.915046\pi\)
\(824\) −2.92056 5.05855i −0.101742 0.176223i
\(825\) −0.100333 −0.00349316
\(826\) −34.7537 75.8398i −1.20923 2.63880i
\(827\) −18.8411 −0.655170 −0.327585 0.944822i \(-0.606235\pi\)
−0.327585 + 0.944822i \(0.606235\pi\)
\(828\) 33.9881 + 58.8691i 1.18117 + 2.04584i
\(829\) 15.5703 26.9686i 0.540779 0.936657i −0.458080 0.888911i \(-0.651463\pi\)
0.998860 0.0477461i \(-0.0152038\pi\)
\(830\) −5.31574 + 9.20713i −0.184512 + 0.319584i
\(831\) 5.28459 + 9.15319i 0.183321 + 0.317521i
\(832\) 17.1041 0.592977
\(833\) −3.43883 9.85320i −0.119148 0.341393i
\(834\) −9.90490 −0.342979
\(835\) 2.13986 + 3.70635i 0.0740530 + 0.128264i
\(836\) −14.5429 + 25.1890i −0.502977 + 0.871181i
\(837\) 4.60407 7.97448i 0.159140 0.275638i
\(838\) 1.13206 + 1.96079i 0.0391064 + 0.0677342i
\(839\) 10.2589 0.354176 0.177088 0.984195i \(-0.443332\pi\)
0.177088 + 0.984195i \(0.443332\pi\)
\(840\) −9.51939 20.7733i −0.328450 0.716748i
\(841\) −26.2783 −0.906149
\(842\) 19.3704 + 33.5505i 0.667548 + 1.15623i
\(843\) 5.43098 9.40673i 0.187053 0.323985i
\(844\) 34.1496 59.1488i 1.17548 2.03599i
\(845\) 2.42392 + 4.19836i 0.0833855 + 0.144428i
\(846\) 9.24992 0.318019
\(847\) −1.53189 + 2.15715i −0.0526365 + 0.0741206i
\(848\) 1.60540 0.0551297
\(849\) 7.74805 + 13.4200i 0.265912 + 0.460574i
\(850\) −0.261087 + 0.452217i −0.00895522 + 0.0155109i
\(851\) 18.0272 31.2241i 0.617966 1.07035i
\(852\) 16.9901 + 29.4277i 0.582072 + 1.00818i
\(853\) 3.04435 0.104237 0.0521183 0.998641i \(-0.483403\pi\)
0.0521183 + 0.998641i \(0.483403\pi\)
\(854\) 85.1753 + 8.02195i 2.91464 + 0.274506i
\(855\) 37.9855 1.29908
\(856\) −17.3840 30.1100i −0.594173 1.02914i
\(857\) −24.7766 + 42.9143i −0.846352 + 1.46592i 0.0380904 + 0.999274i \(0.487873\pi\)
−0.884442 + 0.466650i \(0.845461\pi\)
\(858\) −2.92056 + 5.05855i −0.0997062 + 0.172696i
\(859\) −18.4373 31.9344i −0.629074 1.08959i −0.987738 0.156121i \(-0.950101\pi\)
0.358664 0.933467i \(-0.383232\pi\)
\(860\) 48.8266 1.66497
\(861\) 21.1445 + 1.99143i 0.720603 + 0.0678676i
\(862\) −8.80864 −0.300023
\(863\) 23.2115 + 40.2035i 0.790129 + 1.36854i 0.925887 + 0.377801i \(0.123320\pi\)
−0.135758 + 0.990742i \(0.543347\pi\)
\(864\) 4.19340 7.26318i 0.142662 0.247098i
\(865\) −7.08970 + 12.2797i −0.241057 + 0.417523i
\(866\) 21.9765 + 38.0644i 0.746792 + 1.29348i
\(867\) 10.5442 0.358099
\(868\) 15.1372 21.3157i 0.513792 0.723501i
\(869\) −4.63148 −0.157112
\(870\) 3.23181 + 5.59766i 0.109569 + 0.189778i
\(871\) −7.51437 + 13.0153i −0.254615 + 0.441006i
\(872\) −7.72529 + 13.3806i −0.261611 + 0.453124i
\(873\) 2.31574 + 4.01098i 0.0783759 + 0.135751i
\(874\) 111.848 3.78332
\(875\) 12.4901 + 27.2561i 0.422243 + 0.921423i
\(876\) 25.7031 0.868426
\(877\) −19.5155 33.8018i −0.658991 1.14141i −0.980877 0.194628i \(-0.937650\pi\)
0.321886 0.946778i \(-0.395683\pi\)
\(878\) 18.7154 32.4160i 0.631614 1.09399i
\(879\) 3.96997 6.87620i 0.133904 0.231928i
\(880\) 5.80660 + 10.0573i 0.195741 + 0.339033i
\(881\) −44.0049 −1.48256 −0.741281 0.671194i \(-0.765782\pi\)
−0.741281 + 0.671194i \(0.765782\pi\)
\(882\) −14.3111 41.0052i −0.481879 1.38072i
\(883\) −23.3596 −0.786112 −0.393056 0.919515i \(-0.628582\pi\)
−0.393056 + 0.919515i \(0.628582\pi\)
\(884\) 10.3001 + 17.8403i 0.346429 + 0.600033i
\(885\) −9.95560 + 17.2436i −0.334654 + 0.579638i
\(886\) 16.4679 28.5233i 0.553251 0.958259i
\(887\) −20.9588 36.3017i −0.703728 1.21889i −0.967149 0.254211i \(-0.918184\pi\)
0.263421 0.964681i \(-0.415149\pi\)
\(888\) −21.7628 −0.730311
\(889\) 13.6425 + 29.7708i 0.457554 + 0.998480i
\(890\) −17.5949 −0.589783
\(891\) 2.33850 + 4.05039i 0.0783426 + 0.135693i
\(892\) −6.38343 + 11.0564i −0.213733 + 0.370196i
\(893\) 5.15685 8.93193i 0.172567 0.298896i
\(894\) 0.888663 + 1.53921i 0.0297213 + 0.0514789i
\(895\) −7.90490 −0.264232
\(896\) −26.4170 + 37.1994i −0.882531 + 1.24274i
\(897\) 15.2212 0.508220
\(898\) −12.3405 21.3744i −0.411809 0.713274i
\(899\) −1.93866 + 3.35786i −0.0646580 + 0.111991i
\(900\) −0.736295 + 1.27530i −0.0245432 + 0.0425100i
\(901\) −0.227159 0.393451i −0.00756776 0.0131078i
\(902\) −28.0220 −0.933031
\(903\) −9.90170 0.932559i −0.329508 0.0310336i
\(904\) 70.0295 2.32915
\(905\) −13.4616 23.3162i −0.447478 0.775055i
\(906\) −13.1887 + 22.8436i −0.438167 + 0.758927i
\(907\) 10.2591 17.7692i 0.340646 0.590017i −0.643907 0.765104i \(-0.722687\pi\)
0.984553 + 0.175087i \(0.0560208\pi\)
\(908\) −38.7837 67.1753i −1.28708 2.22929i
\(909\) −15.0586 −0.499461
\(910\) 47.5336 + 4.47679i 1.57572 + 0.148404i
\(911\) 27.6755 0.916930 0.458465 0.888712i \(-0.348399\pi\)
0.458465 + 0.888712i \(0.348399\pi\)
\(912\) −13.0025 22.5209i −0.430554 0.745742i
\(913\) −0.968106 + 1.67681i −0.0320396 + 0.0554943i
\(914\) 12.8840 22.3158i 0.426165 0.738140i
\(915\) −10.2096 17.6836i −0.337520 0.584602i
\(916\) −107.212 −3.54237
\(917\) −1.16279 + 1.63739i −0.0383987 + 0.0540714i
\(918\) −14.5494 −0.480202
\(919\) −0.481727 0.834376i −0.0158907 0.0275235i 0.857971 0.513699i \(-0.171725\pi\)
−0.873861 + 0.486175i \(0.838392\pi\)
\(920\) 39.2829 68.0400i 1.29512 2.24321i
\(921\) 8.91404 15.4396i 0.293728 0.508751i
\(922\) −19.1015 33.0847i −0.629073 1.08959i
\(923\) −37.2249 −1.22527
\(924\) −3.30660 7.21570i −0.108779 0.237379i
\(925\) 0.781061 0.0256811
\(926\) −31.2993 54.2120i −1.02856 1.78152i
\(927\) −1.32488 + 2.29475i −0.0435146 + 0.0753695i
\(928\) −1.76574 + 3.05835i −0.0579632 + 0.100395i
\(929\) −13.1660 22.8042i −0.431962 0.748180i 0.565080 0.825036i \(-0.308845\pi\)
−0.997042 + 0.0768558i \(0.975512\pi\)
\(930\) −9.20814 −0.301947
\(931\) −47.5740 9.04140i −1.55918 0.296320i
\(932\) 16.0507 0.525760
\(933\) 12.3944 + 21.4678i 0.405775 + 0.702824i
\(934\) −0.929110 + 1.60927i −0.0304014 + 0.0526568i
\(935\) 1.64323 2.84616i 0.0537394 0.0930794i
\(936\) 22.4745 + 38.9269i 0.734601 + 1.27237i
\(937\) −21.3865 −0.698665 −0.349333 0.936999i \(-0.613592\pi\)
−0.349333 + 0.936999i \(0.613592\pi\)
\(938\) −12.5547 27.3969i −0.409924 0.894540i
\(939\) −16.9176 −0.552085
\(940\) −6.90880 11.9664i −0.225340 0.390301i
\(941\) −7.41142 + 12.8370i −0.241605 + 0.418473i −0.961172 0.275951i \(-0.911007\pi\)
0.719566 + 0.694424i \(0.244341\pi\)
\(942\) −5.67903 + 9.83636i −0.185033 + 0.320486i
\(943\) 36.5108 + 63.2386i 1.18896 + 2.05933i
\(944\) −66.6885 −2.17053
\(945\) −13.2305 + 18.6307i −0.430389 + 0.606056i
\(946\) 13.1223 0.426644
\(947\) −15.8560 27.4634i −0.515251 0.892442i −0.999843 0.0177013i \(-0.994365\pi\)
0.484592 0.874740i \(-0.338968\pi\)
\(948\) 6.94722 12.0329i 0.225635 0.390811i
\(949\) −14.0787 + 24.3850i −0.457014 + 0.791571i
\(950\) 1.21150 + 2.09839i 0.0393064 + 0.0680806i
\(951\) −14.0403 −0.455287
\(952\) −21.5630 2.03084i −0.698862 0.0658200i
\(953\) 49.9620 1.61843 0.809213 0.587515i \(-0.199894\pi\)
0.809213 + 0.587515i \(0.199894\pi\)
\(954\) −0.945349 1.63739i −0.0306068 0.0530125i
\(955\) −13.3469 + 23.1175i −0.431895 + 0.748064i
\(956\) −27.3365 + 47.3481i −0.884124 + 1.53135i
\(957\) 0.588580 + 1.01945i 0.0190261 + 0.0329541i
\(958\) 50.0988 1.61862
\(959\) −15.3860 1.44908i −0.496841 0.0467933i
\(960\) 8.18613 0.264206
\(961\) 12.7382 + 22.0631i 0.410908 + 0.711714i
\(962\) 22.7355 39.3791i 0.733023 1.26963i
\(963\) −7.88605 + 13.6590i −0.254124 + 0.440156i
\(964\) 0.947216 + 1.64063i 0.0305078 + 0.0528410i
\(965\) −26.3204 −0.847285
\(966\) −17.6725 + 24.8857i −0.568604 + 0.800685i
\(967\) −52.4581 −1.68694 −0.843469 0.537178i \(-0.819490\pi\)
−0.843469 + 0.537178i \(0.819490\pi\)
\(968\) 2.74543 + 4.75523i 0.0882415 + 0.152839i
\(969\) −3.67961 + 6.37327i −0.118206 + 0.204739i
\(970\) 5.10482 8.84180i 0.163906 0.283893i
\(971\) −15.4133 26.6966i −0.494636 0.856735i 0.505345 0.862917i \(-0.331365\pi\)
−0.999981 + 0.00618284i \(0.998032\pi\)
\(972\) −63.4487 −2.03512
\(973\) 6.14248 + 13.4042i 0.196919 + 0.429719i
\(974\) 10.5860 0.339196
\(975\) 0.164871 + 0.285565i 0.00528009 + 0.00914538i
\(976\) 34.1951 59.2276i 1.09456 1.89583i
\(977\) −12.3678 + 21.4216i −0.395680 + 0.685338i −0.993188 0.116525i \(-0.962824\pi\)
0.597508 + 0.801863i \(0.296158\pi\)
\(978\) −8.83791 15.3077i −0.282605 0.489487i
\(979\) −3.20440 −0.102413
\(980\) −42.3585 + 49.1409i −1.35309 + 1.56975i
\(981\) 7.00897 0.223779
\(982\) 37.7713 + 65.4219i 1.20533 + 2.08770i
\(983\) −6.11192 + 10.5862i −0.194940 + 0.337646i −0.946881 0.321585i \(-0.895785\pi\)
0.751941 + 0.659231i \(0.229118\pi\)
\(984\) 22.0382 38.1714i 0.702554 1.21686i
\(985\) −13.4057 23.2193i −0.427140 0.739827i
\(986\) 6.12641 0.195105
\(987\) 1.17251 + 2.55866i 0.0373213 + 0.0814430i
\(988\) 95.5894 3.04110
\(989\) −17.0975 29.6138i −0.543670 0.941665i
\(990\) 6.83850 11.8446i 0.217342 0.376447i
\(991\) −2.30008 + 3.98386i −0.0730645 + 0.126552i −0.900243 0.435388i \(-0.856611\pi\)
0.827178 + 0.561939i \(0.189945\pi\)
\(992\) −2.51549 4.35695i −0.0798668 0.138333i
\(993\) 20.1145 0.638316
\(994\) 43.2199 60.8605i 1.37085 1.93038i
\(995\) 4.19917 0.133123
\(996\) −2.90432 5.03043i −0.0920268 0.159395i
\(997\) 17.2382 29.8574i 0.545938 0.945593i −0.452609 0.891709i \(-0.649507\pi\)
0.998547 0.0538835i \(-0.0171600\pi\)
\(998\) 17.9856 31.1520i 0.569325 0.986100i
\(999\) 10.8814 + 18.8471i 0.344272 + 0.596297i
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 77.2.e.b.67.3 yes 6
3.2 odd 2 693.2.i.g.298.1 6
4.3 odd 2 1232.2.q.k.529.2 6
7.2 even 3 inner 77.2.e.b.23.3 6
7.3 odd 6 539.2.a.i.1.1 3
7.4 even 3 539.2.a.h.1.1 3
7.5 odd 6 539.2.e.l.177.3 6
7.6 odd 2 539.2.e.l.67.3 6
11.2 odd 10 847.2.n.d.81.1 24
11.3 even 5 847.2.n.e.130.3 24
11.4 even 5 847.2.n.e.753.1 24
11.5 even 5 847.2.n.e.487.1 24
11.6 odd 10 847.2.n.d.487.3 24
11.7 odd 10 847.2.n.d.753.3 24
11.8 odd 10 847.2.n.d.130.1 24
11.9 even 5 847.2.n.e.81.3 24
11.10 odd 2 847.2.e.d.606.1 6
21.2 odd 6 693.2.i.g.100.1 6
21.11 odd 6 4851.2.a.bo.1.3 3
21.17 even 6 4851.2.a.bn.1.3 3
28.3 even 6 8624.2.a.ck.1.2 3
28.11 odd 6 8624.2.a.cl.1.2 3
28.23 odd 6 1232.2.q.k.177.2 6
77.2 odd 30 847.2.n.d.807.3 24
77.9 even 15 847.2.n.e.807.1 24
77.10 even 6 5929.2.a.w.1.3 3
77.16 even 15 847.2.n.e.366.3 24
77.30 odd 30 847.2.n.d.9.3 24
77.32 odd 6 5929.2.a.v.1.3 3
77.37 even 15 847.2.n.e.632.3 24
77.51 odd 30 847.2.n.d.632.1 24
77.58 even 15 847.2.n.e.9.1 24
77.65 odd 6 847.2.e.d.485.1 6
77.72 odd 30 847.2.n.d.366.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.e.b.23.3 6 7.2 even 3 inner
77.2.e.b.67.3 yes 6 1.1 even 1 trivial
539.2.a.h.1.1 3 7.4 even 3
539.2.a.i.1.1 3 7.3 odd 6
539.2.e.l.67.3 6 7.6 odd 2
539.2.e.l.177.3 6 7.5 odd 6
693.2.i.g.100.1 6 21.2 odd 6
693.2.i.g.298.1 6 3.2 odd 2
847.2.e.d.485.1 6 77.65 odd 6
847.2.e.d.606.1 6 11.10 odd 2
847.2.n.d.9.3 24 77.30 odd 30
847.2.n.d.81.1 24 11.2 odd 10
847.2.n.d.130.1 24 11.8 odd 10
847.2.n.d.366.1 24 77.72 odd 30
847.2.n.d.487.3 24 11.6 odd 10
847.2.n.d.632.1 24 77.51 odd 30
847.2.n.d.753.3 24 11.7 odd 10
847.2.n.d.807.3 24 77.2 odd 30
847.2.n.e.9.1 24 77.58 even 15
847.2.n.e.81.3 24 11.9 even 5
847.2.n.e.130.3 24 11.3 even 5
847.2.n.e.366.3 24 77.16 even 15
847.2.n.e.487.1 24 11.5 even 5
847.2.n.e.632.3 24 77.37 even 15
847.2.n.e.753.1 24 11.4 even 5
847.2.n.e.807.1 24 77.9 even 15
1232.2.q.k.177.2 6 28.23 odd 6
1232.2.q.k.529.2 6 4.3 odd 2
4851.2.a.bn.1.3 3 21.17 even 6
4851.2.a.bo.1.3 3 21.11 odd 6
5929.2.a.v.1.3 3 77.32 odd 6
5929.2.a.w.1.3 3 77.10 even 6
8624.2.a.ck.1.2 3 28.3 even 6
8624.2.a.cl.1.2 3 28.11 odd 6