Properties

Label 605.2.g.q.81.4
Level $605$
Weight $2$
Character 605.81
Analytic conductor $4.831$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(81,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
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("605.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.4
Character \(\chi\) \(=\) 605.81
Dual form 605.2.g.q.366.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.389057 + 0.282666i) q^{2} +(-0.494946 + 1.52329i) q^{3} +(-0.546569 - 1.68217i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.623145 + 0.452741i) q^{6} +(0.148607 + 0.457364i) q^{7} +(0.560059 - 1.72368i) q^{8} +(0.351618 + 0.255466i) q^{9} +O(q^{10})\) \(q+(0.389057 + 0.282666i) q^{2} +(-0.494946 + 1.52329i) q^{3} +(-0.546569 - 1.68217i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.623145 + 0.452741i) q^{6} +(0.148607 + 0.457364i) q^{7} +(0.560059 - 1.72368i) q^{8} +(0.351618 + 0.255466i) q^{9} -0.480901 q^{10} +2.83294 q^{12} +(3.87971 + 2.81878i) q^{13} +(-0.0714650 + 0.219947i) q^{14} +(-0.494946 - 1.52329i) q^{15} +(-2.15675 + 1.56697i) q^{16} +(-2.02440 + 1.47081i) q^{17} +(0.0645880 + 0.198781i) q^{18} +(-1.77913 + 5.47560i) q^{19} +(1.43094 + 1.03964i) q^{20} -0.770249 q^{21} +4.43462 q^{23} +(2.34847 + 1.70626i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.712656 + 2.19333i) q^{26} +(-4.45054 + 3.23350i) q^{27} +(0.688138 - 0.499962i) q^{28} +(2.78501 + 8.57138i) q^{29} +(0.238020 - 0.732550i) q^{30} +(-6.44956 - 4.68588i) q^{31} -4.90680 q^{32} -1.20336 q^{34} +(-0.389057 - 0.282666i) q^{35} +(0.237552 - 0.731110i) q^{36} +(1.60793 + 4.94869i) q^{37} +(-2.23995 + 1.62742i) q^{38} +(-6.21405 + 4.51478i) q^{39} +(0.560059 + 1.72368i) q^{40} +(-2.61158 + 8.03761i) q^{41} +(-0.299671 - 0.217724i) q^{42} +8.53158 q^{43} -0.434624 q^{45} +(1.72532 + 1.25352i) q^{46} +(2.96708 - 9.13174i) q^{47} +(-1.31947 - 4.06092i) q^{48} +(5.47602 - 3.97856i) q^{49} +(0.389057 - 0.282666i) q^{50} +(-1.23850 - 3.81172i) q^{51} +(2.62112 - 8.06698i) q^{52} +(-4.93542 - 3.58579i) q^{53} -2.64552 q^{54} +0.871579 q^{56} +(-7.46034 - 5.42026i) q^{57} +(-1.33931 + 4.12198i) q^{58} +(0.855586 + 2.63322i) q^{59} +(-2.29190 + 1.66516i) q^{60} +(-3.25657 + 2.36604i) q^{61} +(-1.18471 - 3.64615i) q^{62} +(-0.0645880 + 0.198781i) q^{63} +(2.40447 + 1.74695i) q^{64} -4.79559 q^{65} +7.60168 q^{67} +(3.58063 + 2.60148i) q^{68} +(-2.19490 + 6.75521i) q^{69} +(-0.0714650 - 0.219947i) q^{70} +(2.23995 - 1.62742i) q^{71} +(0.637268 - 0.463003i) q^{72} +(-1.54651 - 4.75966i) q^{73} +(-0.773253 + 2.37983i) q^{74} +(1.29579 + 0.941443i) q^{75} +10.1833 q^{76} -3.69380 q^{78} +(2.93251 + 2.13059i) q^{79} +(0.823805 - 2.53541i) q^{80} +(-2.31986 - 7.13980i) q^{81} +(-3.28802 + 2.38888i) q^{82} +(1.38713 - 1.00781i) q^{83} +(0.420994 + 1.29569i) q^{84} +(0.773253 - 2.37983i) q^{85} +(3.31927 + 2.41159i) q^{86} -14.4351 q^{87} -15.7408 q^{89} +(-0.169094 - 0.122854i) q^{90} +(-0.712656 + 2.19333i) q^{91} +(-2.42383 - 7.45977i) q^{92} +(10.3301 - 7.50527i) q^{93} +(3.73560 - 2.71407i) q^{94} +(-1.77913 - 5.47560i) q^{95} +(2.42860 - 7.47447i) q^{96} +(2.94319 + 2.13835i) q^{97} +3.25509 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.389057 + 0.282666i 0.275105 + 0.199875i 0.716779 0.697300i \(-0.245615\pi\)
−0.441675 + 0.897175i \(0.645615\pi\)
\(3\) −0.494946 + 1.52329i −0.285757 + 0.879470i 0.700413 + 0.713737i \(0.252999\pi\)
−0.986171 + 0.165733i \(0.947001\pi\)
\(4\) −0.546569 1.68217i −0.273284 0.841083i
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) −0.623145 + 0.452741i −0.254398 + 0.184831i
\(7\) 0.148607 + 0.457364i 0.0561680 + 0.172867i 0.975205 0.221305i \(-0.0710315\pi\)
−0.919037 + 0.394172i \(0.871031\pi\)
\(8\) 0.560059 1.72368i 0.198011 0.609414i
\(9\) 0.351618 + 0.255466i 0.117206 + 0.0851552i
\(10\) −0.480901 −0.152074
\(11\) 0 0
\(12\) 2.83294 0.817801
\(13\) 3.87971 + 2.81878i 1.07604 + 0.781788i 0.976988 0.213295i \(-0.0684194\pi\)
0.0990507 + 0.995082i \(0.468419\pi\)
\(14\) −0.0714650 + 0.219947i −0.0190998 + 0.0587832i
\(15\) −0.494946 1.52329i −0.127795 0.393311i
\(16\) −2.15675 + 1.56697i −0.539188 + 0.391743i
\(17\) −2.02440 + 1.47081i −0.490990 + 0.356725i −0.805565 0.592508i \(-0.798138\pi\)
0.314575 + 0.949233i \(0.398138\pi\)
\(18\) 0.0645880 + 0.198781i 0.0152235 + 0.0468532i
\(19\) −1.77913 + 5.47560i −0.408161 + 1.25619i 0.510066 + 0.860135i \(0.329621\pi\)
−0.918227 + 0.396055i \(0.870379\pi\)
\(20\) 1.43094 + 1.03964i 0.319967 + 0.232470i
\(21\) −0.770249 −0.168082
\(22\) 0 0
\(23\) 4.43462 0.924683 0.462342 0.886702i \(-0.347009\pi\)
0.462342 + 0.886702i \(0.347009\pi\)
\(24\) 2.34847 + 1.70626i 0.479379 + 0.348289i
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 0.712656 + 2.19333i 0.139763 + 0.430147i
\(27\) −4.45054 + 3.23350i −0.856506 + 0.622288i
\(28\) 0.688138 0.499962i 0.130046 0.0944839i
\(29\) 2.78501 + 8.57138i 0.517163 + 1.59167i 0.779311 + 0.626637i \(0.215569\pi\)
−0.262148 + 0.965028i \(0.584431\pi\)
\(30\) 0.238020 0.732550i 0.0434563 0.133745i
\(31\) −6.44956 4.68588i −1.15837 0.841609i −0.168803 0.985650i \(-0.553990\pi\)
−0.989572 + 0.144041i \(0.953990\pi\)
\(32\) −4.90680 −0.867409
\(33\) 0 0
\(34\) −1.20336 −0.206374
\(35\) −0.389057 0.282666i −0.0657626 0.0477794i
\(36\) 0.237552 0.731110i 0.0395920 0.121852i
\(37\) 1.60793 + 4.94869i 0.264341 + 0.813559i 0.991844 + 0.127455i \(0.0406807\pi\)
−0.727503 + 0.686105i \(0.759319\pi\)
\(38\) −2.23995 + 1.62742i −0.363368 + 0.264003i
\(39\) −6.21405 + 4.51478i −0.995045 + 0.722943i
\(40\) 0.560059 + 1.72368i 0.0885530 + 0.272538i
\(41\) −2.61158 + 8.03761i −0.407860 + 1.25526i 0.510624 + 0.859804i \(0.329415\pi\)
−0.918483 + 0.395459i \(0.870585\pi\)
\(42\) −0.299671 0.217724i −0.0462402 0.0335955i
\(43\) 8.53158 1.30105 0.650527 0.759483i \(-0.274548\pi\)
0.650527 + 0.759483i \(0.274548\pi\)
\(44\) 0 0
\(45\) −0.434624 −0.0647899
\(46\) 1.72532 + 1.25352i 0.254385 + 0.184821i
\(47\) 2.96708 9.13174i 0.432793 1.33200i −0.462538 0.886600i \(-0.653061\pi\)
0.895331 0.445401i \(-0.146939\pi\)
\(48\) −1.31947 4.06092i −0.190449 0.586143i
\(49\) 5.47602 3.97856i 0.782289 0.568366i
\(50\) 0.389057 0.282666i 0.0550210 0.0399751i
\(51\) −1.23850 3.81172i −0.173425 0.533748i
\(52\) 2.62112 8.06698i 0.363484 1.11869i
\(53\) −4.93542 3.58579i −0.677932 0.492546i 0.194739 0.980855i \(-0.437614\pi\)
−0.872671 + 0.488309i \(0.837614\pi\)
\(54\) −2.64552 −0.360009
\(55\) 0 0
\(56\) 0.871579 0.116470
\(57\) −7.46034 5.42026i −0.988147 0.717931i
\(58\) −1.33931 + 4.12198i −0.175861 + 0.541243i
\(59\) 0.855586 + 2.63322i 0.111388 + 0.342816i 0.991177 0.132549i \(-0.0423160\pi\)
−0.879789 + 0.475365i \(0.842316\pi\)
\(60\) −2.29190 + 1.66516i −0.295883 + 0.214972i
\(61\) −3.25657 + 2.36604i −0.416961 + 0.302940i −0.776414 0.630223i \(-0.782963\pi\)
0.359453 + 0.933163i \(0.382963\pi\)
\(62\) −1.18471 3.64615i −0.150458 0.463061i
\(63\) −0.0645880 + 0.198781i −0.00813732 + 0.0250441i
\(64\) 2.40447 + 1.74695i 0.300559 + 0.218369i
\(65\) −4.79559 −0.594820
\(66\) 0 0
\(67\) 7.60168 0.928693 0.464346 0.885654i \(-0.346289\pi\)
0.464346 + 0.885654i \(0.346289\pi\)
\(68\) 3.58063 + 2.60148i 0.434215 + 0.315476i
\(69\) −2.19490 + 6.75521i −0.264235 + 0.813231i
\(70\) −0.0714650 0.219947i −0.00854170 0.0262887i
\(71\) 2.23995 1.62742i 0.265834 0.193139i −0.446881 0.894593i \(-0.647465\pi\)
0.712715 + 0.701454i \(0.247465\pi\)
\(72\) 0.637268 0.463003i 0.0751028 0.0545654i
\(73\) −1.54651 4.75966i −0.181005 0.557076i 0.818852 0.574005i \(-0.194611\pi\)
−0.999857 + 0.0169292i \(0.994611\pi\)
\(74\) −0.773253 + 2.37983i −0.0898889 + 0.276649i
\(75\) 1.29579 + 0.941443i 0.149624 + 0.108709i
\(76\) 10.1833 1.16810
\(77\) 0 0
\(78\) −3.69380 −0.418240
\(79\) 2.93251 + 2.13059i 0.329933 + 0.239710i 0.740402 0.672164i \(-0.234635\pi\)
−0.410469 + 0.911874i \(0.634635\pi\)
\(80\) 0.823805 2.53541i 0.0921042 0.283468i
\(81\) −2.31986 7.13980i −0.257762 0.793311i
\(82\) −3.28802 + 2.38888i −0.363101 + 0.263808i
\(83\) 1.38713 1.00781i 0.152258 0.110622i −0.509048 0.860738i \(-0.670002\pi\)
0.661306 + 0.750116i \(0.270002\pi\)
\(84\) 0.420994 + 1.29569i 0.0459342 + 0.141371i
\(85\) 0.773253 2.37983i 0.0838711 0.258129i
\(86\) 3.31927 + 2.41159i 0.357926 + 0.260049i
\(87\) −14.4351 −1.54761
\(88\) 0 0
\(89\) −15.7408 −1.66852 −0.834262 0.551368i \(-0.814106\pi\)
−0.834262 + 0.551368i \(0.814106\pi\)
\(90\) −0.169094 0.122854i −0.0178240 0.0129499i
\(91\) −0.712656 + 2.19333i −0.0747066 + 0.229923i
\(92\) −2.42383 7.45977i −0.252702 0.777735i
\(93\) 10.3301 7.50527i 1.07118 0.778261i
\(94\) 3.73560 2.71407i 0.385298 0.279935i
\(95\) −1.77913 5.47560i −0.182535 0.561785i
\(96\) 2.42860 7.47447i 0.247868 0.762860i
\(97\) 2.94319 + 2.13835i 0.298836 + 0.217117i 0.727091 0.686541i \(-0.240872\pi\)
−0.428256 + 0.903658i \(0.640872\pi\)
\(98\) 3.25509 0.328814
\(99\) 0 0
\(100\) −1.76873 −0.176873
\(101\) −6.22818 4.52504i −0.619727 0.450258i 0.233099 0.972453i \(-0.425113\pi\)
−0.852826 + 0.522195i \(0.825113\pi\)
\(102\) 0.595597 1.83306i 0.0589729 0.181500i
\(103\) 2.81293 + 8.65732i 0.277167 + 0.853031i 0.988638 + 0.150316i \(0.0480291\pi\)
−0.711471 + 0.702715i \(0.751971\pi\)
\(104\) 7.03154 5.10872i 0.689500 0.500951i
\(105\) 0.623145 0.452741i 0.0608127 0.0441830i
\(106\) −0.906576 2.79016i −0.0880545 0.271004i
\(107\) 5.18879 15.9694i 0.501619 1.54382i −0.304762 0.952429i \(-0.598577\pi\)
0.806381 0.591396i \(-0.201423\pi\)
\(108\) 7.87182 + 5.71921i 0.757466 + 0.550331i
\(109\) 17.8817 1.71276 0.856380 0.516346i \(-0.172708\pi\)
0.856380 + 0.516346i \(0.172708\pi\)
\(110\) 0 0
\(111\) −8.33411 −0.791039
\(112\) −1.03718 0.753558i −0.0980046 0.0712045i
\(113\) −0.142930 + 0.439893i −0.0134457 + 0.0413817i −0.957554 0.288253i \(-0.906926\pi\)
0.944109 + 0.329635i \(0.106926\pi\)
\(114\) −1.37037 4.21758i −0.128347 0.395012i
\(115\) −3.58769 + 2.60661i −0.334553 + 0.243067i
\(116\) 12.8963 9.36970i 1.19739 0.869955i
\(117\) 0.644077 + 1.98227i 0.0595450 + 0.183261i
\(118\) −0.411452 + 1.26632i −0.0378772 + 0.116574i
\(119\) −0.973537 0.707316i −0.0892440 0.0648396i
\(120\) −2.90286 −0.264994
\(121\) 0 0
\(122\) −1.93579 −0.175258
\(123\) −10.9510 7.95637i −0.987418 0.717401i
\(124\) −4.35730 + 13.4104i −0.391297 + 1.20429i
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) −0.0813172 + 0.0590804i −0.00724431 + 0.00526330i
\(127\) 12.8063 9.30433i 1.13638 0.825626i 0.149766 0.988721i \(-0.452148\pi\)
0.986610 + 0.163096i \(0.0521480\pi\)
\(128\) 3.47424 + 10.6926i 0.307083 + 0.945103i
\(129\) −4.22267 + 12.9960i −0.371786 + 1.14424i
\(130\) −1.86576 1.35555i −0.163638 0.118890i
\(131\) −9.60460 −0.839158 −0.419579 0.907719i \(-0.637822\pi\)
−0.419579 + 0.907719i \(0.637822\pi\)
\(132\) 0 0
\(133\) −2.76873 −0.240080
\(134\) 2.95749 + 2.14874i 0.255488 + 0.185623i
\(135\) 1.69995 5.23192i 0.146309 0.450292i
\(136\) 1.40143 + 4.31317i 0.120172 + 0.369851i
\(137\) −3.21349 + 2.33474i −0.274547 + 0.199470i −0.716535 0.697551i \(-0.754273\pi\)
0.441988 + 0.897021i \(0.354273\pi\)
\(138\) −2.76341 + 2.00774i −0.235237 + 0.170910i
\(139\) −2.84960 8.77016i −0.241700 0.743875i −0.996162 0.0875316i \(-0.972102\pi\)
0.754462 0.656344i \(-0.227898\pi\)
\(140\) −0.262846 + 0.808955i −0.0222145 + 0.0683692i
\(141\) 12.4417 + 9.03944i 1.04778 + 0.761258i
\(142\) 1.33149 0.111736
\(143\) 0 0
\(144\) −1.15866 −0.0965550
\(145\) −7.29125 5.29740i −0.605505 0.439925i
\(146\) 0.743716 2.28892i 0.0615504 0.189433i
\(147\) 3.35016 + 10.3107i 0.276316 + 0.850414i
\(148\) 7.44567 5.40960i 0.612031 0.444666i
\(149\) 6.18907 4.49662i 0.507029 0.368378i −0.304667 0.952459i \(-0.598545\pi\)
0.811695 + 0.584081i \(0.198545\pi\)
\(150\) 0.238020 + 0.732550i 0.0194343 + 0.0598125i
\(151\) 0.887492 2.73142i 0.0722231 0.222280i −0.908429 0.418040i \(-0.862717\pi\)
0.980652 + 0.195760i \(0.0627173\pi\)
\(152\) 8.44179 + 6.13332i 0.684719 + 0.497478i
\(153\) −1.08756 −0.0879240
\(154\) 0 0
\(155\) 7.97209 0.640334
\(156\) 10.9910 + 7.98544i 0.879985 + 0.639347i
\(157\) 5.40213 16.6260i 0.431137 1.32690i −0.465857 0.884860i \(-0.654254\pi\)
0.896994 0.442043i \(-0.145746\pi\)
\(158\) 0.538665 + 1.65784i 0.0428539 + 0.131891i
\(159\) 7.90496 5.74329i 0.626904 0.455472i
\(160\) 3.96969 2.88415i 0.313831 0.228012i
\(161\) 0.659014 + 2.02824i 0.0519376 + 0.159847i
\(162\) 1.11562 3.43354i 0.0876517 0.269764i
\(163\) −10.6524 7.73940i −0.834358 0.606197i 0.0864308 0.996258i \(-0.472454\pi\)
−0.920789 + 0.390061i \(0.872454\pi\)
\(164\) 14.9480 1.16724
\(165\) 0 0
\(166\) 0.824549 0.0639974
\(167\) −12.8454 9.33274i −0.994008 0.722189i −0.0332128 0.999448i \(-0.510574\pi\)
−0.960795 + 0.277259i \(0.910574\pi\)
\(168\) −0.431385 + 1.32767i −0.0332820 + 0.102432i
\(169\) 3.08945 + 9.50835i 0.237650 + 0.731411i
\(170\) 0.973537 0.707316i 0.0746669 0.0542487i
\(171\) −2.02440 + 1.47081i −0.154810 + 0.112476i
\(172\) −4.66310 14.3515i −0.355558 1.09429i
\(173\) −7.05194 + 21.7036i −0.536149 + 1.65010i 0.205005 + 0.978761i \(0.434279\pi\)
−0.741153 + 0.671336i \(0.765721\pi\)
\(174\) −5.61608 4.08032i −0.425754 0.309328i
\(175\) 0.480901 0.0363527
\(176\) 0 0
\(177\) −4.43462 −0.333327
\(178\) −6.12408 4.44940i −0.459019 0.333497i
\(179\) −0.142930 + 0.439893i −0.0106831 + 0.0328792i −0.956256 0.292531i \(-0.905502\pi\)
0.945573 + 0.325410i \(0.105502\pi\)
\(180\) 0.237552 + 0.731110i 0.0177061 + 0.0544937i
\(181\) 2.53095 1.83884i 0.188124 0.136680i −0.489737 0.871870i \(-0.662907\pi\)
0.677861 + 0.735190i \(0.262907\pi\)
\(182\) −0.897244 + 0.651886i −0.0665082 + 0.0483210i
\(183\) −1.99233 6.13175i −0.147277 0.453272i
\(184\) 2.48365 7.64389i 0.183097 0.563515i
\(185\) −4.20961 3.05846i −0.309496 0.224862i
\(186\) 6.14050 0.450243
\(187\) 0 0
\(188\) −16.9828 −1.23860
\(189\) −2.14027 1.55500i −0.155682 0.113109i
\(190\) 0.855586 2.63322i 0.0620707 0.191034i
\(191\) −1.68011 5.17085i −0.121569 0.374150i 0.871692 0.490055i \(-0.163023\pi\)
−0.993260 + 0.115905i \(0.963023\pi\)
\(192\) −3.85119 + 2.79806i −0.277936 + 0.201932i
\(193\) −2.59432 + 1.88488i −0.186743 + 0.135677i −0.677229 0.735772i \(-0.736819\pi\)
0.490486 + 0.871449i \(0.336819\pi\)
\(194\) 0.540628 + 1.66388i 0.0388148 + 0.119460i
\(195\) 2.37356 7.30506i 0.169974 0.523126i
\(196\) −9.68563 7.03702i −0.691830 0.502644i
\(197\) −19.4048 −1.38253 −0.691267 0.722600i \(-0.742947\pi\)
−0.691267 + 0.722600i \(0.742947\pi\)
\(198\) 0 0
\(199\) 20.3509 1.44264 0.721319 0.692603i \(-0.243536\pi\)
0.721319 + 0.692603i \(0.243536\pi\)
\(200\) −1.46625 1.06529i −0.103680 0.0753277i
\(201\) −3.76242 + 11.5795i −0.265381 + 0.816758i
\(202\) −1.14404 3.52099i −0.0804944 0.247736i
\(203\) −3.50637 + 2.54753i −0.246099 + 0.178801i
\(204\) −5.73502 + 4.16674i −0.401532 + 0.291730i
\(205\) −2.61158 8.03761i −0.182400 0.561371i
\(206\) −1.35274 + 4.16331i −0.0942500 + 0.290072i
\(207\) 1.55929 + 1.13289i 0.108378 + 0.0787416i
\(208\) −12.7845 −0.886446
\(209\) 0 0
\(210\) 0.370413 0.0255610
\(211\) −5.56593 4.04388i −0.383174 0.278392i 0.379478 0.925201i \(-0.376103\pi\)
−0.762653 + 0.646808i \(0.776103\pi\)
\(212\) −3.33435 + 10.2621i −0.229004 + 0.704802i
\(213\) 1.37037 + 4.21758i 0.0938965 + 0.288984i
\(214\) 6.53276 4.74633i 0.446570 0.324452i
\(215\) −6.90219 + 5.01474i −0.470726 + 0.342002i
\(216\) 3.08098 + 9.48227i 0.209634 + 0.645187i
\(217\) 1.18471 3.64615i 0.0804230 0.247517i
\(218\) 6.95702 + 5.05457i 0.471189 + 0.342339i
\(219\) 8.01576 0.541655
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) −3.24244 2.35577i −0.217619 0.158109i
\(223\) −0.320956 + 0.987800i −0.0214928 + 0.0661480i −0.961228 0.275756i \(-0.911072\pi\)
0.939735 + 0.341904i \(0.111072\pi\)
\(224\) −0.729183 2.24420i −0.0487206 0.149947i
\(225\) 0.351618 0.255466i 0.0234412 0.0170310i
\(226\) −0.179951 + 0.130742i −0.0119702 + 0.00869684i
\(227\) 0.148607 + 0.457364i 0.00986336 + 0.0303563i 0.955867 0.293799i \(-0.0949198\pi\)
−0.946004 + 0.324156i \(0.894920\pi\)
\(228\) −5.04018 + 15.5121i −0.333794 + 1.02731i
\(229\) −10.9539 7.95849i −0.723856 0.525912i 0.163758 0.986501i \(-0.447638\pi\)
−0.887614 + 0.460588i \(0.847638\pi\)
\(230\) −2.13261 −0.140620
\(231\) 0 0
\(232\) 16.3341 1.07239
\(233\) 17.1142 + 12.4342i 1.12119 + 0.814590i 0.984389 0.176008i \(-0.0563186\pi\)
0.136799 + 0.990599i \(0.456319\pi\)
\(234\) −0.309737 + 0.953273i −0.0202482 + 0.0623174i
\(235\) 2.96708 + 9.13174i 0.193551 + 0.595689i
\(236\) 3.96188 2.87848i 0.257897 0.187373i
\(237\) −4.69693 + 3.41252i −0.305099 + 0.221667i
\(238\) −0.178827 0.550373i −0.0115916 0.0356754i
\(239\) 0.827051 2.54540i 0.0534975 0.164648i −0.920738 0.390181i \(-0.872412\pi\)
0.974236 + 0.225533i \(0.0724123\pi\)
\(240\) 3.45442 + 2.50978i 0.222982 + 0.162006i
\(241\) −4.56912 −0.294323 −0.147161 0.989112i \(-0.547014\pi\)
−0.147161 + 0.989112i \(0.547014\pi\)
\(242\) 0 0
\(243\) −4.47932 −0.287349
\(244\) 5.76000 + 4.18489i 0.368746 + 0.267910i
\(245\) −2.09165 + 6.43745i −0.133631 + 0.411274i
\(246\) −2.01157 6.19096i −0.128253 0.394721i
\(247\) −22.3370 + 16.2288i −1.42127 + 1.03261i
\(248\) −11.6891 + 8.49263i −0.742259 + 0.539282i
\(249\) 0.848631 + 2.61182i 0.0537798 + 0.165517i
\(250\) −0.148607 + 0.457364i −0.00939870 + 0.0289262i
\(251\) 9.25269 + 6.72247i 0.584025 + 0.424319i 0.840173 0.542319i \(-0.182453\pi\)
−0.256148 + 0.966638i \(0.582453\pi\)
\(252\) 0.369685 0.0232880
\(253\) 0 0
\(254\) 7.61241 0.477645
\(255\) 3.24244 + 2.35577i 0.203050 + 0.147524i
\(256\) 0.166087 0.511163i 0.0103804 0.0319477i
\(257\) −6.19415 19.0636i −0.386381 1.18916i −0.935474 0.353396i \(-0.885027\pi\)
0.549093 0.835761i \(-0.314973\pi\)
\(258\) −5.31641 + 3.86260i −0.330985 + 0.240475i
\(259\) −2.02440 + 1.47081i −0.125790 + 0.0913920i
\(260\) 2.62112 + 8.06698i 0.162555 + 0.500293i
\(261\) −1.21043 + 3.72533i −0.0749239 + 0.230592i
\(262\) −3.73674 2.71490i −0.230856 0.167727i
\(263\) −6.55852 −0.404416 −0.202208 0.979343i \(-0.564812\pi\)
−0.202208 + 0.979343i \(0.564812\pi\)
\(264\) 0 0
\(265\) 6.10051 0.374752
\(266\) −1.07720 0.782628i −0.0660471 0.0479860i
\(267\) 7.79086 23.9778i 0.476793 1.46742i
\(268\) −4.15484 12.7873i −0.253797 0.781108i
\(269\) −1.53483 + 1.11512i −0.0935803 + 0.0679901i −0.633592 0.773668i \(-0.718420\pi\)
0.540011 + 0.841658i \(0.318420\pi\)
\(270\) 2.14027 1.55500i 0.130253 0.0946340i
\(271\) 3.50861 + 10.7984i 0.213133 + 0.655956i 0.999281 + 0.0379175i \(0.0120724\pi\)
−0.786148 + 0.618038i \(0.787928\pi\)
\(272\) 2.06141 6.34436i 0.124991 0.384683i
\(273\) −2.98834 2.17116i −0.180863 0.131405i
\(274\) −1.91018 −0.115398
\(275\) 0 0
\(276\) 12.5630 0.756206
\(277\) 18.4731 + 13.4215i 1.10994 + 0.806418i 0.982654 0.185448i \(-0.0593737\pi\)
0.127285 + 0.991866i \(0.459374\pi\)
\(278\) 1.37037 4.21758i 0.0821896 0.252954i
\(279\) −1.07070 3.29528i −0.0641012 0.197283i
\(280\) −0.705122 + 0.512301i −0.0421391 + 0.0306159i
\(281\) −18.2931 + 13.2907i −1.09128 + 0.792858i −0.979614 0.200888i \(-0.935617\pi\)
−0.111662 + 0.993746i \(0.535617\pi\)
\(282\) 2.28539 + 7.03371i 0.136093 + 0.418852i
\(283\) 8.51857 26.2175i 0.506377 1.55847i −0.292067 0.956398i \(-0.594343\pi\)
0.798444 0.602069i \(-0.205657\pi\)
\(284\) −3.96188 2.87848i −0.235094 0.170806i
\(285\) 9.22149 0.546234
\(286\) 0 0
\(287\) −4.06421 −0.239903
\(288\) −1.72532 1.25352i −0.101666 0.0738643i
\(289\) −3.31838 + 10.2129i −0.195199 + 0.600760i
\(290\) −1.33931 4.12198i −0.0786472 0.242051i
\(291\) −4.71405 + 3.42495i −0.276342 + 0.200774i
\(292\) −7.16126 + 5.20296i −0.419081 + 0.304480i
\(293\) 6.75472 + 20.7889i 0.394615 + 1.21450i 0.929261 + 0.369424i \(0.120445\pi\)
−0.534646 + 0.845076i \(0.679555\pi\)
\(294\) −1.61109 + 4.95844i −0.0939609 + 0.289182i
\(295\) −2.23995 1.62742i −0.130415 0.0947521i
\(296\) 9.43050 0.548137
\(297\) 0 0
\(298\) 3.67895 0.213116
\(299\) 17.2051 + 12.5002i 0.994995 + 0.722906i
\(300\) 0.875428 2.69429i 0.0505429 0.155555i
\(301\) 1.26785 + 3.90204i 0.0730776 + 0.224910i
\(302\) 1.11737 0.811814i 0.0642972 0.0467146i
\(303\) 9.97554 7.24766i 0.573080 0.416367i
\(304\) −4.74297 14.5974i −0.272028 0.837216i
\(305\) 1.24390 3.82833i 0.0712254 0.219209i
\(306\) −0.423123 0.307417i −0.0241883 0.0175738i
\(307\) 9.80019 0.559326 0.279663 0.960098i \(-0.409777\pi\)
0.279663 + 0.960098i \(0.409777\pi\)
\(308\) 0 0
\(309\) −14.5798 −0.829418
\(310\) 3.10160 + 2.25344i 0.176159 + 0.127987i
\(311\) 3.01943 9.29284i 0.171216 0.526948i −0.828225 0.560396i \(-0.810649\pi\)
0.999440 + 0.0334480i \(0.0106488\pi\)
\(312\) 4.30181 + 13.2396i 0.243542 + 0.749545i
\(313\) 0.725814 0.527335i 0.0410254 0.0298067i −0.567084 0.823660i \(-0.691928\pi\)
0.608109 + 0.793854i \(0.291928\pi\)
\(314\) 6.80136 4.94148i 0.383823 0.278864i
\(315\) −0.0645880 0.198781i −0.00363912 0.0112001i
\(316\) 1.98119 6.09748i 0.111451 0.343010i
\(317\) 2.15864 + 1.56834i 0.121241 + 0.0880868i 0.646753 0.762699i \(-0.276126\pi\)
−0.525512 + 0.850786i \(0.676126\pi\)
\(318\) 4.69891 0.263502
\(319\) 0 0
\(320\) −2.97209 −0.166145
\(321\) 21.7579 + 15.8080i 1.21441 + 0.882318i
\(322\) −0.316921 + 0.975381i −0.0176613 + 0.0543559i
\(323\) −4.45192 13.7016i −0.247711 0.762378i
\(324\) −10.7424 + 7.80479i −0.596798 + 0.433599i
\(325\) 3.87971 2.81878i 0.215208 0.156358i
\(326\) −1.95671 6.02214i −0.108372 0.333535i
\(327\) −8.85050 + 27.2390i −0.489434 + 1.50632i
\(328\) 12.3917 + 9.00307i 0.684215 + 0.497111i
\(329\) 4.61746 0.254569
\(330\) 0 0
\(331\) 18.9744 1.04293 0.521464 0.853273i \(-0.325386\pi\)
0.521464 + 0.853273i \(0.325386\pi\)
\(332\) −2.45347 1.78255i −0.134652 0.0978303i
\(333\) −0.698843 + 2.15082i −0.0382964 + 0.117864i
\(334\) −2.35955 7.26194i −0.129109 0.397355i
\(335\) −6.14989 + 4.46815i −0.336004 + 0.244121i
\(336\) 1.66123 1.20696i 0.0906278 0.0658449i
\(337\) 1.48192 + 4.56088i 0.0807252 + 0.248447i 0.983271 0.182146i \(-0.0583044\pi\)
−0.902546 + 0.430593i \(0.858304\pi\)
\(338\) −1.48572 + 4.57257i −0.0808125 + 0.248715i
\(339\) −0.599342 0.435447i −0.0325518 0.0236502i
\(340\) −4.42590 −0.240028
\(341\) 0 0
\(342\) −1.20336 −0.0650702
\(343\) 5.35682 + 3.89196i 0.289241 + 0.210146i
\(344\) 4.77818 14.7057i 0.257622 0.792880i
\(345\) −2.19490 6.75521i −0.118169 0.363688i
\(346\) −8.87850 + 6.45060i −0.477311 + 0.346787i
\(347\) −0.209106 + 0.151924i −0.0112254 + 0.00815573i −0.593384 0.804920i \(-0.702208\pi\)
0.582158 + 0.813075i \(0.302208\pi\)
\(348\) 7.88978 + 24.2822i 0.422937 + 1.30166i
\(349\) −0.415599 + 1.27908i −0.0222465 + 0.0684677i −0.961563 0.274583i \(-0.911460\pi\)
0.939317 + 0.343051i \(0.111460\pi\)
\(350\) 0.187098 + 0.135935i 0.0100008 + 0.00726601i
\(351\) −26.3813 −1.40813
\(352\) 0 0
\(353\) 35.4537 1.88701 0.943506 0.331355i \(-0.107506\pi\)
0.943506 + 0.331355i \(0.107506\pi\)
\(354\) −1.72532 1.25352i −0.0916998 0.0666238i
\(355\) −0.855586 + 2.63322i −0.0454098 + 0.139757i
\(356\) 8.60345 + 26.4787i 0.455982 + 1.40337i
\(357\) 1.55929 1.13289i 0.0825266 0.0599591i
\(358\) −0.179951 + 0.130742i −0.00951071 + 0.00690994i
\(359\) 2.42321 + 7.45787i 0.127892 + 0.393611i 0.994417 0.105523i \(-0.0336516\pi\)
−0.866525 + 0.499134i \(0.833652\pi\)
\(360\) −0.243415 + 0.749154i −0.0128291 + 0.0394839i
\(361\) −11.4456 8.31572i −0.602400 0.437669i
\(362\) 1.50446 0.0790727
\(363\) 0 0
\(364\) 4.07906 0.213801
\(365\) 4.04881 + 2.94163i 0.211924 + 0.153972i
\(366\) 0.958111 2.94876i 0.0500813 0.154134i
\(367\) 0.329579 + 1.01434i 0.0172039 + 0.0529482i 0.959290 0.282423i \(-0.0911382\pi\)
−0.942086 + 0.335371i \(0.891138\pi\)
\(368\) −9.56438 + 6.94893i −0.498578 + 0.362238i
\(369\) −2.97161 + 2.15900i −0.154696 + 0.112393i
\(370\) −0.773253 2.37983i −0.0401995 0.123721i
\(371\) 0.906576 2.79016i 0.0470671 0.144858i
\(372\) −18.2712 13.2748i −0.947320 0.688268i
\(373\) 37.6388 1.94886 0.974431 0.224689i \(-0.0721366\pi\)
0.974431 + 0.224689i \(0.0721366\pi\)
\(374\) 0 0
\(375\) −1.60168 −0.0827104
\(376\) −14.0785 10.2286i −0.726042 0.527501i
\(377\) −13.3558 + 41.1048i −0.687857 + 2.11701i
\(378\) −0.393141 1.20996i −0.0202210 0.0622338i
\(379\) −28.4350 + 20.6592i −1.46061 + 1.06119i −0.477401 + 0.878685i \(0.658421\pi\)
−0.983205 + 0.182507i \(0.941579\pi\)
\(380\) −8.23846 + 5.98559i −0.422624 + 0.307054i
\(381\) 7.83473 + 24.1128i 0.401386 + 1.23534i
\(382\) 0.807967 2.48667i 0.0413392 0.127229i
\(383\) −0.667074 0.484658i −0.0340859 0.0247649i 0.570612 0.821220i \(-0.306706\pi\)
−0.604698 + 0.796455i \(0.706706\pi\)
\(384\) −18.0075 −0.918942
\(385\) 0 0
\(386\) −1.54213 −0.0784924
\(387\) 2.99986 + 2.17952i 0.152491 + 0.110791i
\(388\) 1.98841 6.11969i 0.100946 0.310680i
\(389\) 1.49678 + 4.60661i 0.0758896 + 0.233564i 0.981804 0.189896i \(-0.0608152\pi\)
−0.905915 + 0.423461i \(0.860815\pi\)
\(390\) 2.98834 2.17116i 0.151321 0.109941i
\(391\) −8.97747 + 6.52251i −0.454010 + 0.329858i
\(392\) −3.79089 11.6672i −0.191469 0.589280i
\(393\) 4.75376 14.6306i 0.239795 0.738014i
\(394\) −7.54957 5.48508i −0.380342 0.276334i
\(395\) −3.62478 −0.182382
\(396\) 0 0
\(397\) −7.33178 −0.367971 −0.183986 0.982929i \(-0.558900\pi\)
−0.183986 + 0.982929i \(0.558900\pi\)
\(398\) 7.91766 + 5.75252i 0.396876 + 0.288348i
\(399\) 1.37037 4.21758i 0.0686045 0.211143i
\(400\) 0.823805 + 2.53541i 0.0411903 + 0.126771i
\(401\) 25.2008 18.3094i 1.25847 0.914330i 0.259785 0.965666i \(-0.416348\pi\)
0.998681 + 0.0513367i \(0.0163482\pi\)
\(402\) −4.73694 + 3.44159i −0.236257 + 0.171651i
\(403\) −11.8140 36.3597i −0.588497 1.81121i
\(404\) −4.20774 + 12.9501i −0.209343 + 0.644290i
\(405\) 6.07348 + 4.41264i 0.301793 + 0.219266i
\(406\) −2.08428 −0.103441
\(407\) 0 0
\(408\) −7.26384 −0.359613
\(409\) −5.85089 4.25092i −0.289308 0.210194i 0.433659 0.901077i \(-0.357222\pi\)
−0.722967 + 0.690883i \(0.757222\pi\)
\(410\) 1.25591 3.86529i 0.0620250 0.190893i
\(411\) −1.96597 6.05064i −0.0969742 0.298456i
\(412\) 13.0256 9.46364i 0.641725 0.466240i
\(413\) −1.07720 + 0.782628i −0.0530053 + 0.0385106i
\(414\) 0.286423 + 0.881520i 0.0140769 + 0.0433244i
\(415\) −0.529838 + 1.63067i −0.0260087 + 0.0800467i
\(416\) −19.0370 13.8312i −0.933365 0.678130i
\(417\) 14.7699 0.723284
\(418\) 0 0
\(419\) −2.30620 −0.112665 −0.0563327 0.998412i \(-0.517941\pi\)
−0.0563327 + 0.998412i \(0.517941\pi\)
\(420\) −1.10218 0.800779i −0.0537807 0.0390740i
\(421\) 2.05125 6.31310i 0.0999718 0.307681i −0.888546 0.458788i \(-0.848284\pi\)
0.988517 + 0.151107i \(0.0482837\pi\)
\(422\) −1.02239 3.14660i −0.0497693 0.153174i
\(423\) 3.37612 2.45290i 0.164153 0.119264i
\(424\) −8.94489 + 6.49885i −0.434402 + 0.315612i
\(425\) 0.773253 + 2.37983i 0.0375083 + 0.115439i
\(426\) −0.659014 + 2.02824i −0.0319293 + 0.0982684i
\(427\) −1.56609 1.13783i −0.0757882 0.0550634i
\(428\) −29.6993 −1.43557
\(429\) 0 0
\(430\) −4.10284 −0.197857
\(431\) −26.5707 19.3047i −1.27986 0.929876i −0.280316 0.959908i \(-0.590439\pi\)
−0.999549 + 0.0300317i \(0.990439\pi\)
\(432\) 4.53189 13.9477i 0.218041 0.671060i
\(433\) 0.729904 + 2.24641i 0.0350769 + 0.107956i 0.967062 0.254541i \(-0.0819244\pi\)
−0.931985 + 0.362497i \(0.881924\pi\)
\(434\) 1.49156 1.08368i 0.0715972 0.0520184i
\(435\) 11.6782 8.48474i 0.559929 0.406812i
\(436\) −9.77361 30.0801i −0.468071 1.44057i
\(437\) −7.88978 + 24.2822i −0.377419 + 1.16158i
\(438\) 3.11859 + 2.26579i 0.149012 + 0.108264i
\(439\) −30.8847 −1.47404 −0.737022 0.675869i \(-0.763769\pi\)
−0.737022 + 0.675869i \(0.763769\pi\)
\(440\) 0 0
\(441\) 2.94185 0.140088
\(442\) −4.66868 3.39200i −0.222067 0.161341i
\(443\) −4.25665 + 13.1006i −0.202239 + 0.622429i 0.797576 + 0.603218i \(0.206115\pi\)
−0.999815 + 0.0192105i \(0.993885\pi\)
\(444\) 4.55517 + 14.0194i 0.216179 + 0.665329i
\(445\) 12.7346 9.25223i 0.603678 0.438598i
\(446\) −0.404088 + 0.293587i −0.0191341 + 0.0139017i
\(447\) 3.78639 + 11.6533i 0.179090 + 0.551183i
\(448\) −0.441672 + 1.35933i −0.0208671 + 0.0642222i
\(449\) 31.4839 + 22.8744i 1.48582 + 1.07951i 0.975623 + 0.219452i \(0.0704268\pi\)
0.510195 + 0.860059i \(0.329573\pi\)
\(450\) 0.209011 0.00985288
\(451\) 0 0
\(452\) 0.818095 0.0384800
\(453\) 3.72148 + 2.70381i 0.174850 + 0.127036i
\(454\) −0.0714650 + 0.219947i −0.00335402 + 0.0103226i
\(455\) −0.712656 2.19333i −0.0334098 0.102825i
\(456\) −13.5210 + 9.82361i −0.633181 + 0.460033i
\(457\) −1.07720 + 0.782628i −0.0503891 + 0.0366098i −0.612695 0.790320i \(-0.709914\pi\)
0.562306 + 0.826929i \(0.309914\pi\)
\(458\) −2.01210 6.19262i −0.0940194 0.289362i
\(459\) 4.25379 13.0918i 0.198550 0.611074i
\(460\) 6.34566 + 4.61039i 0.295868 + 0.214961i
\(461\) 5.73993 0.267335 0.133668 0.991026i \(-0.457325\pi\)
0.133668 + 0.991026i \(0.457325\pi\)
\(462\) 0 0
\(463\) −3.44535 −0.160119 −0.0800595 0.996790i \(-0.525511\pi\)
−0.0800595 + 0.996790i \(0.525511\pi\)
\(464\) −19.4377 14.1223i −0.902371 0.655611i
\(465\) −3.94576 + 12.1438i −0.182980 + 0.563155i
\(466\) 3.14367 + 9.67521i 0.145628 + 0.448196i
\(467\) 22.0185 15.9974i 1.01890 0.740272i 0.0528403 0.998603i \(-0.483173\pi\)
0.966056 + 0.258331i \(0.0831726\pi\)
\(468\) 2.98247 2.16689i 0.137865 0.100165i
\(469\) 1.12966 + 3.47673i 0.0521628 + 0.160541i
\(470\) −1.42687 + 4.39146i −0.0658167 + 0.202563i
\(471\) 22.6525 + 16.4580i 1.04377 + 0.758344i
\(472\) 5.01802 0.230973
\(473\) 0 0
\(474\) −2.79198 −0.128240
\(475\) 4.65783 + 3.38411i 0.213716 + 0.155274i
\(476\) −0.657718 + 2.02425i −0.0301465 + 0.0927813i
\(477\) −0.819337 2.52166i −0.0375149 0.115459i
\(478\) 1.04127 0.756527i 0.0476266 0.0346027i
\(479\) −11.3118 + 8.21851i −0.516850 + 0.375513i −0.815416 0.578876i \(-0.803492\pi\)
0.298566 + 0.954389i \(0.403492\pi\)
\(480\) 2.42860 + 7.47447i 0.110850 + 0.341161i
\(481\) −7.71095 + 23.7319i −0.351589 + 1.08208i
\(482\) −1.77765 1.29154i −0.0809696 0.0588279i
\(483\) −3.41576 −0.155423
\(484\) 0 0
\(485\) −3.63798 −0.165192
\(486\) −1.74271 1.26615i −0.0790510 0.0574339i
\(487\) −2.30333 + 7.08893i −0.104374 + 0.321230i −0.989583 0.143963i \(-0.954015\pi\)
0.885209 + 0.465194i \(0.154015\pi\)
\(488\) 2.25443 + 6.93841i 0.102053 + 0.314087i
\(489\) 17.0617 12.3960i 0.771556 0.560568i
\(490\) −2.63342 + 1.91329i −0.118966 + 0.0864338i
\(491\) −4.93673 15.1937i −0.222792 0.685682i −0.998508 0.0546007i \(-0.982611\pi\)
0.775717 0.631081i \(-0.217389\pi\)
\(492\) −7.39846 + 22.7701i −0.333548 + 1.02656i
\(493\) −18.2449 13.2557i −0.821709 0.597006i
\(494\) −13.2777 −0.597392
\(495\) 0 0
\(496\) 21.2527 0.954275
\(497\) 1.07720 + 0.782628i 0.0483188 + 0.0351057i
\(498\) −0.408107 + 1.25603i −0.0182877 + 0.0562838i
\(499\) −7.52484 23.1591i −0.336858 1.03674i −0.965799 0.259290i \(-0.916511\pi\)
0.628941 0.777453i \(-0.283489\pi\)
\(500\) 1.43094 1.03964i 0.0639934 0.0464939i
\(501\) 20.5742 14.9481i 0.919189 0.667830i
\(502\) 1.69961 + 5.23085i 0.0758572 + 0.233464i
\(503\) 8.51857 26.2175i 0.379824 1.16898i −0.560341 0.828262i \(-0.689330\pi\)
0.940166 0.340717i \(-0.110670\pi\)
\(504\) 0.306463 + 0.222658i 0.0136509 + 0.00991799i
\(505\) 7.69845 0.342577
\(506\) 0 0
\(507\) −16.0131 −0.711165
\(508\) −22.6510 16.4569i −1.00497 0.730156i
\(509\) 5.46497 16.8194i 0.242231 0.745509i −0.753849 0.657048i \(-0.771805\pi\)
0.996080 0.0884613i \(-0.0281949\pi\)
\(510\) 0.595597 + 1.83306i 0.0263735 + 0.0811693i
\(511\) 1.94707 1.41463i 0.0861335 0.0625797i
\(512\) 18.4005 13.3687i 0.813194 0.590820i
\(513\) −9.78730 30.1222i −0.432120 1.32993i
\(514\) 2.97877 9.16772i 0.131388 0.404371i
\(515\) −7.36436 5.35052i −0.324512 0.235772i
\(516\) 24.1695 1.06400
\(517\) 0 0
\(518\) −1.20336 −0.0528725
\(519\) −29.5705 21.4843i −1.29800 0.943054i
\(520\) −2.68581 + 8.26608i −0.117781 + 0.362491i
\(521\) −1.66558 5.12612i −0.0729703 0.224580i 0.907919 0.419145i \(-0.137670\pi\)
−0.980889 + 0.194566i \(0.937670\pi\)
\(522\) −1.52395 + 1.10722i −0.0667016 + 0.0484615i
\(523\) 30.4786 22.1440i 1.33274 0.968291i 0.333060 0.942906i \(-0.391919\pi\)
0.999678 0.0253853i \(-0.00808126\pi\)
\(524\) 5.24957 + 16.1565i 0.229329 + 0.705801i
\(525\) −0.238020 + 0.732550i −0.0103880 + 0.0319711i
\(526\) −2.55164 1.85387i −0.111257 0.0808327i
\(527\) 19.9486 0.868973
\(528\) 0 0
\(529\) −3.33411 −0.144961
\(530\) 2.37345 + 1.72441i 0.103096 + 0.0749036i
\(531\) −0.371858 + 1.14446i −0.0161373 + 0.0496654i
\(532\) 1.51330 + 4.65747i 0.0656101 + 0.201927i
\(533\) −32.7884 + 23.8222i −1.42022 + 1.03185i
\(534\) 9.80881 7.12652i 0.424469 0.308395i
\(535\) 5.18879 + 15.9694i 0.224331 + 0.690419i
\(536\) 4.25739 13.1029i 0.183891 0.565959i
\(537\) −0.599342 0.435447i −0.0258635 0.0187909i
\(538\) −0.912344 −0.0393339
\(539\) 0 0
\(540\) −9.73010 −0.418717
\(541\) 23.4332 + 17.0252i 1.00747 + 0.731973i 0.963678 0.267068i \(-0.0860548\pi\)
0.0437962 + 0.999040i \(0.486055\pi\)
\(542\) −1.68729 + 5.19296i −0.0724755 + 0.223057i
\(543\) 1.54840 + 4.76548i 0.0664482 + 0.204507i
\(544\) 9.93335 7.21700i 0.425889 0.309426i
\(545\) −14.4666 + 10.5106i −0.619683 + 0.450226i
\(546\) −0.548922 1.68941i −0.0234917 0.0723001i
\(547\) 6.09986 18.7734i 0.260811 0.802694i −0.731818 0.681500i \(-0.761328\pi\)
0.992629 0.121194i \(-0.0386722\pi\)
\(548\) 5.68381 + 4.12953i 0.242800 + 0.176405i
\(549\) −1.74951 −0.0746672
\(550\) 0 0
\(551\) −51.8884 −2.21052
\(552\) 10.4146 + 7.56662i 0.443273 + 0.322057i
\(553\) −0.538665 + 1.65784i −0.0229064 + 0.0704986i
\(554\) 3.39328 + 10.4434i 0.144167 + 0.443699i
\(555\) 6.74244 4.89867i 0.286201 0.207937i
\(556\) −13.1954 + 9.58699i −0.559608 + 0.406579i
\(557\) −5.15442 15.8637i −0.218400 0.672165i −0.998895 0.0470033i \(-0.985033\pi\)
0.780495 0.625162i \(-0.214967\pi\)
\(558\) 0.514901 1.58470i 0.0217975 0.0670858i
\(559\) 33.1001 + 24.0486i 1.39998 + 1.01715i
\(560\) 1.28203 0.0541756
\(561\) 0 0
\(562\) −10.8739 −0.458688
\(563\) −3.96969 2.88415i −0.167302 0.121552i 0.500984 0.865457i \(-0.332972\pi\)
−0.668286 + 0.743905i \(0.732972\pi\)
\(564\) 8.40558 25.8697i 0.353939 1.08931i
\(565\) −0.142930 0.439893i −0.00601311 0.0185065i
\(566\) 10.7250 7.79218i 0.450806 0.327530i
\(567\) 2.92074 2.12204i 0.122660 0.0891174i
\(568\) −1.55065 4.77242i −0.0650640 0.200246i
\(569\) 6.93230 21.3354i 0.290617 0.894428i −0.694041 0.719935i \(-0.744171\pi\)
0.984658 0.174493i \(-0.0558286\pi\)
\(570\) 3.58769 + 2.60661i 0.150272 + 0.109179i
\(571\) −0.195590 −0.00818520 −0.00409260 0.999992i \(-0.501303\pi\)
−0.00409260 + 0.999992i \(0.501303\pi\)
\(572\) 0 0
\(573\) 8.70826 0.363793
\(574\) −1.58121 1.14882i −0.0659984 0.0479507i
\(575\) 1.37037 4.21758i 0.0571486 0.175885i
\(576\) 0.399170 + 1.22852i 0.0166321 + 0.0511883i
\(577\) 33.3704 24.2450i 1.38923 1.00933i 0.393277 0.919420i \(-0.371341\pi\)
0.995950 0.0899127i \(-0.0286588\pi\)
\(578\) −4.17789 + 3.03541i −0.173777 + 0.126257i
\(579\) −1.58717 4.88481i −0.0659605 0.203006i
\(580\) −4.92594 + 15.1605i −0.204539 + 0.629505i
\(581\) 0.667074 + 0.484658i 0.0276749 + 0.0201070i
\(582\) −2.80215 −0.116153
\(583\) 0 0
\(584\) −9.07028 −0.375331
\(585\) −1.68622 1.22511i −0.0697165 0.0506520i
\(586\) −3.24835 + 9.99740i −0.134188 + 0.412989i
\(587\) −0.548443 1.68793i −0.0226367 0.0696685i 0.939100 0.343644i \(-0.111661\pi\)
−0.961737 + 0.273975i \(0.911661\pi\)
\(588\) 15.5133 11.2710i 0.639756 0.464810i
\(589\) 37.1326 26.9784i 1.53002 1.11163i
\(590\) −0.411452 1.26632i −0.0169392 0.0521335i
\(591\) 9.60432 29.5591i 0.395069 1.21590i
\(592\) −11.2223 8.15351i −0.461235 0.335107i
\(593\) 29.0094 1.19127 0.595636 0.803254i \(-0.296900\pi\)
0.595636 + 0.803254i \(0.296900\pi\)
\(594\) 0 0
\(595\) 1.20336 0.0493329
\(596\) −10.9468 7.95333i −0.448399 0.325781i
\(597\) −10.0726 + 31.0003i −0.412244 + 1.26876i
\(598\) 3.16036 + 9.72659i 0.129237 + 0.397750i
\(599\) −32.5768 + 23.6685i −1.33105 + 0.967067i −0.331331 + 0.943515i \(0.607498\pi\)
−0.999723 + 0.0235521i \(0.992502\pi\)
\(600\) 2.34847 1.70626i 0.0958757 0.0696578i
\(601\) 4.23221 + 13.0254i 0.172636 + 0.531318i 0.999518 0.0310577i \(-0.00988756\pi\)
−0.826882 + 0.562375i \(0.809888\pi\)
\(602\) −0.609710 + 1.87649i −0.0248499 + 0.0764802i
\(603\) 2.67289 + 1.94197i 0.108848 + 0.0790830i
\(604\) −5.07978 −0.206693
\(605\) 0 0
\(606\) 5.92972 0.240879
\(607\) 17.1142 + 12.4342i 0.694643 + 0.504688i 0.878183 0.478324i \(-0.158756\pi\)
−0.183540 + 0.983012i \(0.558756\pi\)
\(608\) 8.72985 26.8677i 0.354042 1.08963i
\(609\) −2.14515 6.60210i −0.0869259 0.267530i
\(610\) 1.56609 1.13783i 0.0634090 0.0460693i
\(611\) 37.2518 27.0650i 1.50704 1.09493i
\(612\) 0.594426 + 1.82946i 0.0240283 + 0.0739514i
\(613\) 7.18526 22.1140i 0.290210 0.893174i −0.694579 0.719417i \(-0.744409\pi\)
0.984788 0.173758i \(-0.0555909\pi\)
\(614\) 3.81283 + 2.77018i 0.153873 + 0.111796i
\(615\) 13.5362 0.545831
\(616\) 0 0
\(617\) −13.1028 −0.527501 −0.263750 0.964591i \(-0.584960\pi\)
−0.263750 + 0.964591i \(0.584960\pi\)
\(618\) −5.67239 4.12123i −0.228177 0.165780i
\(619\) 5.15076 15.8524i 0.207027 0.637163i −0.792597 0.609745i \(-0.791272\pi\)
0.999624 0.0274172i \(-0.00872827\pi\)
\(620\) −4.35730 13.4104i −0.174993 0.538574i
\(621\) −19.7365 + 14.3394i −0.791997 + 0.575419i
\(622\) 3.80150 2.76195i 0.152426 0.110744i
\(623\) −2.33919 7.19929i −0.0937177 0.288433i
\(624\) 6.32764 19.4745i 0.253308 0.779603i
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 0.431443 0.0172439
\(627\) 0 0
\(628\) −30.9204 −1.23386
\(629\) −10.5337 7.65318i −0.420006 0.305152i
\(630\) 0.0310604 0.0955941i 0.00123748 0.00380856i
\(631\) −0.823085 2.53319i −0.0327665 0.100845i 0.933336 0.359005i \(-0.116884\pi\)
−0.966102 + 0.258160i \(0.916884\pi\)
\(632\) 5.31484 3.86145i 0.211413 0.153600i
\(633\) 8.91483 6.47700i 0.354333 0.257438i
\(634\) 0.396515 + 1.22035i 0.0157476 + 0.0484662i
\(635\) −4.89157 + 15.0547i −0.194116 + 0.597428i
\(636\) −13.9818 10.1584i −0.554413 0.402805i
\(637\) 32.4601 1.28611
\(638\) 0 0
\(639\) 1.20336 0.0476041
\(640\) −9.09569 6.60841i −0.359539 0.261220i
\(641\) −0.142930 + 0.439893i −0.00564540 + 0.0173747i −0.953840 0.300317i \(-0.902908\pi\)
0.948194 + 0.317691i \(0.102908\pi\)
\(642\) 3.99666 + 12.3004i 0.157736 + 0.485460i
\(643\) 27.0714 19.6686i 1.06759 0.775652i 0.0921153 0.995748i \(-0.470637\pi\)
0.975478 + 0.220096i \(0.0706372\pi\)
\(644\) 3.05164 2.21714i 0.120251 0.0873677i
\(645\) −4.22267 12.9960i −0.166268 0.511719i
\(646\) 2.14093 6.58911i 0.0842339 0.259245i
\(647\) 32.5700 + 23.6635i 1.28046 + 0.930309i 0.999567 0.0294300i \(-0.00936921\pi\)
0.280894 + 0.959739i \(0.409369\pi\)
\(648\) −13.6060 −0.534495
\(649\) 0 0
\(650\) 2.30620 0.0904567
\(651\) 4.96777 + 3.60929i 0.194702 + 0.141459i
\(652\) −7.19670 + 22.1492i −0.281845 + 0.867429i
\(653\) 4.74297 + 14.5974i 0.185607 + 0.571239i 0.999958 0.00913312i \(-0.00290720\pi\)
−0.814352 + 0.580372i \(0.802907\pi\)
\(654\) −11.1429 + 8.09580i −0.435722 + 0.316571i
\(655\) 7.77028 5.64544i 0.303610 0.220586i
\(656\) −6.96218 21.4274i −0.271827 0.836599i
\(657\) 0.672149 2.06866i 0.0262230 0.0807062i
\(658\) 1.79645 + 1.30520i 0.0700331 + 0.0508820i
\(659\) −36.6635 −1.42821 −0.714104 0.700039i \(-0.753166\pi\)
−0.714104 + 0.700039i \(0.753166\pi\)
\(660\) 0 0
\(661\) −8.03024 −0.312340 −0.156170 0.987730i \(-0.549915\pi\)
−0.156170 + 0.987730i \(0.549915\pi\)
\(662\) 7.38213 + 5.36343i 0.286915 + 0.208456i
\(663\) 5.93935 18.2794i 0.230665 0.709915i
\(664\) −0.960272 2.95541i −0.0372658 0.114692i
\(665\) 2.23995 1.62742i 0.0868617 0.0631087i
\(666\) −0.879854 + 0.639251i −0.0340937 + 0.0247705i
\(667\) 12.3505 + 38.0108i 0.478212 + 1.47179i
\(668\) −8.67832 + 26.7091i −0.335774 + 1.03341i
\(669\) −1.34585 0.977815i −0.0520335 0.0378045i
\(670\) −3.65565 −0.141230
\(671\) 0 0
\(672\) 3.77946 0.145796
\(673\) −9.51299 6.91160i −0.366699 0.266422i 0.389142 0.921178i \(-0.372772\pi\)
−0.755841 + 0.654755i \(0.772772\pi\)
\(674\) −0.712656 + 2.19333i −0.0274505 + 0.0844839i
\(675\) 1.69995 + 5.23192i 0.0654312 + 0.201377i
\(676\) 14.3060 10.3939i 0.550232 0.399767i
\(677\) −22.0819 + 16.0435i −0.848678 + 0.616601i −0.924781 0.380499i \(-0.875752\pi\)
0.0761030 + 0.997100i \(0.475752\pi\)
\(678\) −0.110092 0.338828i −0.00422805 0.0130126i
\(679\) −0.540628 + 1.66388i −0.0207474 + 0.0638539i
\(680\) −3.66900 2.66569i −0.140700 0.102224i
\(681\) −0.770249 −0.0295160
\(682\) 0 0
\(683\) 49.5738 1.89689 0.948444 0.316945i \(-0.102657\pi\)
0.948444 + 0.316945i \(0.102657\pi\)
\(684\) 3.58063 + 2.60148i 0.136909 + 0.0994701i
\(685\) 1.22744 3.77768i 0.0468982 0.144338i
\(686\) 0.983983 + 3.02839i 0.0375686 + 0.115624i
\(687\) 17.5447 12.7470i 0.669371 0.486327i
\(688\) −18.4005 + 13.3687i −0.701512 + 0.509678i
\(689\) −9.04046 27.8237i −0.344414 1.06000i
\(690\) 1.05553 3.24859i 0.0401833 0.123672i
\(691\) 20.4886 + 14.8859i 0.779424 + 0.566285i 0.904806 0.425824i \(-0.140016\pi\)
−0.125382 + 0.992109i \(0.540016\pi\)
\(692\) 40.3635 1.53439
\(693\) 0 0
\(694\) −0.124298 −0.00471829
\(695\) 7.46034 + 5.42026i 0.282987 + 0.205602i
\(696\) −8.08450 + 24.8815i −0.306442 + 0.943132i
\(697\) −6.53495 20.1125i −0.247529 0.761816i
\(698\) −0.523246 + 0.380160i −0.0198051 + 0.0143893i
\(699\) −27.4114 + 19.9156i −1.03680 + 0.753276i
\(700\) −0.262846 0.808955i −0.00993463 0.0305756i
\(701\) 5.64125 17.3620i 0.213067 0.655753i −0.786218 0.617949i \(-0.787964\pi\)
0.999285 0.0378039i \(-0.0120362\pi\)
\(702\) −10.2638 7.45712i −0.387384 0.281451i
\(703\) −29.9578 −1.12988
\(704\) 0 0
\(705\) −15.3788 −0.579199
\(706\) 13.7935 + 10.0216i 0.519126 + 0.377167i
\(707\) 1.14404 3.52099i 0.0430261 0.132421i
\(708\) 2.42383 + 7.45977i 0.0910930 + 0.280356i
\(709\) −3.50448 + 2.54616i −0.131614 + 0.0956229i −0.651644 0.758525i \(-0.725921\pi\)
0.520031 + 0.854148i \(0.325921\pi\)
\(710\) −1.07720 + 0.782628i −0.0404264 + 0.0293715i
\(711\) 0.486830 + 1.49831i 0.0182575 + 0.0561909i
\(712\) −8.81579 + 27.1322i −0.330386 + 1.01682i
\(713\) −28.6014 20.7801i −1.07113 0.778221i
\(714\) 0.926885 0.0346878
\(715\) 0 0
\(716\) 0.818095 0.0305737
\(717\) 3.46803 + 2.51967i 0.129516 + 0.0940989i
\(718\) −1.16532 + 3.58650i −0.0434895 + 0.133847i
\(719\) −7.44747 22.9210i −0.277744 0.854807i −0.988480 0.151349i \(-0.951638\pi\)
0.710737 0.703458i \(-0.248362\pi\)
\(720\) 0.937375 0.681043i 0.0349339 0.0253810i
\(721\) −3.54153 + 2.57307i −0.131893 + 0.0958261i
\(722\) −2.10242 6.47058i −0.0782439 0.240810i
\(723\) 2.26147 6.96008i 0.0841049 0.258848i
\(724\) −4.47657 3.25242i −0.166370 0.120875i
\(725\) 9.01248 0.334715
\(726\) 0 0
\(727\) −25.1066 −0.931151 −0.465576 0.885008i \(-0.654153\pi\)
−0.465576 + 0.885008i \(0.654153\pi\)
\(728\) 3.38148 + 2.45679i 0.125326 + 0.0910545i
\(729\) 9.17661 28.2427i 0.339874 1.04603i
\(730\) 0.743716 + 2.28892i 0.0275262 + 0.0847169i
\(731\) −17.2714 + 12.5484i −0.638804 + 0.464118i
\(732\) −9.22568 + 6.70285i −0.340991 + 0.247744i
\(733\) 5.39119 + 16.5924i 0.199128 + 0.612854i 0.999904 + 0.0138888i \(0.00442110\pi\)
−0.800775 + 0.598965i \(0.795579\pi\)
\(734\) −0.158495 + 0.487798i −0.00585016 + 0.0180049i
\(735\) −8.77083 6.37238i −0.323517 0.235049i
\(736\) −21.7598 −0.802078
\(737\) 0 0
\(738\) −1.76640 −0.0650222
\(739\) −4.20704 3.05659i −0.154759 0.112439i 0.507711 0.861527i \(-0.330492\pi\)
−0.662470 + 0.749089i \(0.730492\pi\)
\(740\) −2.84399 + 8.75291i −0.104547 + 0.321764i
\(741\) −13.6655 42.0581i −0.502015 1.54504i
\(742\) 1.14139 0.829271i 0.0419019 0.0304435i
\(743\) −30.0896 + 21.8614i −1.10388 + 0.802016i −0.981689 0.190491i \(-0.938992\pi\)
−0.122191 + 0.992507i \(0.538992\pi\)
\(744\) −7.15124 22.0093i −0.262177 0.806898i
\(745\) −2.36402 + 7.27569i −0.0866108 + 0.266561i
\(746\) 14.6436 + 10.6392i 0.536141 + 0.389529i
\(747\) 0.745203 0.0272656
\(748\) 0 0
\(749\) 8.07494 0.295052
\(750\) −0.623145 0.452741i −0.0227540 0.0165318i
\(751\) 12.7998 39.3939i 0.467073 1.43750i −0.389283 0.921118i \(-0.627277\pi\)
0.856356 0.516385i \(-0.172723\pi\)
\(752\) 7.90991 + 24.3442i 0.288445 + 0.887742i
\(753\) −14.8198 + 10.7672i −0.540065 + 0.392380i
\(754\) −16.8151 + 12.2169i −0.612370 + 0.444913i
\(755\) 0.887492 + 2.73142i 0.0322991 + 0.0994065i
\(756\) −1.44596 + 4.45020i −0.0525889 + 0.161852i
\(757\) −3.16834 2.30193i −0.115155 0.0836651i 0.528717 0.848798i \(-0.322673\pi\)
−0.643872 + 0.765133i \(0.722673\pi\)
\(758\) −16.9025 −0.613926
\(759\) 0 0
\(760\) −10.4346 −0.378504
\(761\) −31.6576 23.0006i −1.14759 0.833770i −0.159428 0.987210i \(-0.550965\pi\)
−0.988158 + 0.153439i \(0.950965\pi\)
\(762\) −3.76773 + 11.5959i −0.136490 + 0.420074i
\(763\) 2.65734 + 8.17847i 0.0962023 + 0.296080i
\(764\) −7.77994 + 5.65245i −0.281468 + 0.204499i
\(765\) 0.879854 0.639251i 0.0318112 0.0231122i
\(766\) −0.122533 0.377119i −0.00442731 0.0136259i
\(767\) −4.10304 + 12.6279i −0.148152 + 0.455965i
\(768\) 0.696444 + 0.505996i 0.0251308 + 0.0182586i
\(769\) −11.6755 −0.421028 −0.210514 0.977591i \(-0.567514\pi\)
−0.210514 + 0.977591i \(0.567514\pi\)
\(770\) 0 0
\(771\) 32.1052 1.15624
\(772\) 4.58866 + 3.33386i 0.165149 + 0.119988i
\(773\) −2.39995 + 7.38629i −0.0863202 + 0.265666i −0.984895 0.173155i \(-0.944604\pi\)
0.898574 + 0.438821i \(0.144604\pi\)
\(774\) 0.551037 + 1.69592i 0.0198066 + 0.0609585i
\(775\) −6.44956 + 4.68588i −0.231675 + 0.168322i
\(776\) 5.33420 3.87552i 0.191487 0.139123i
\(777\) −1.23850 3.81172i −0.0444311 0.136745i
\(778\) −0.719801 + 2.21532i −0.0258061 + 0.0794231i
\(779\) −39.3644 28.5999i −1.41038 1.02470i
\(780\) −13.5856 −0.486444
\(781\) 0 0
\(782\) −5.33644 −0.190831
\(783\) −40.1104 29.1419i −1.43343 1.04145i
\(784\) −5.57612 + 17.1615i −0.199147 + 0.612912i
\(785\) 5.40213 + 16.6260i 0.192810 + 0.593409i
\(786\) 5.98505 4.34840i 0.213480 0.155102i
\(787\) −1.15631 + 0.840111i −0.0412181 + 0.0299467i −0.608204 0.793781i \(-0.708110\pi\)
0.566985 + 0.823728i \(0.308110\pi\)
\(788\) 10.6061 + 32.6421i 0.377825 + 1.16283i
\(789\) 3.24611 9.99051i 0.115565 0.355672i
\(790\) −1.41024 1.02460i −0.0501742 0.0364537i
\(791\) −0.222432 −0.00790876
\(792\) 0 0
\(793\) −19.3039 −0.685501
\(794\) −2.85248 2.07245i −0.101231 0.0735484i
\(795\) −3.01943 + 9.29284i −0.107088 + 0.329583i
\(796\) −11.1232 34.2336i −0.394250 1.21338i
\(797\) 29.4311 21.3829i 1.04250 0.757422i 0.0717298 0.997424i \(-0.477148\pi\)
0.970772 + 0.240002i \(0.0771481\pi\)
\(798\) 1.72532 1.25352i 0.0610757 0.0443741i
\(799\) 7.42453 + 22.8503i 0.262661 + 0.808387i
\(800\) −1.51629 + 4.66665i −0.0536088 + 0.164991i
\(801\) −5.53476 4.02124i −0.195561 0.142083i
\(802\) 14.9800 0.528962
\(803\) 0 0
\(804\) 21.5351 0.759486
\(805\) −1.72532 1.25352i −0.0608096 0.0441808i
\(806\) 5.68136 17.4854i 0.200117 0.615898i
\(807\) −0.938990 2.88991i −0.0330540 0.101730i
\(808\) −11.2879 + 8.20112i −0.397106 + 0.288514i
\(809\) 22.5501 16.3836i 0.792820 0.576018i −0.115979 0.993252i \(-0.537000\pi\)
0.908799 + 0.417234i \(0.137000\pi\)
\(810\) 1.11562 + 3.43354i 0.0391990 + 0.120642i
\(811\) −12.1071 + 37.2617i −0.425136 + 1.30843i 0.477728 + 0.878508i \(0.341461\pi\)
−0.902864 + 0.429927i \(0.858539\pi\)
\(812\) 6.20184 + 4.50590i 0.217642 + 0.158126i
\(813\) −18.1856 −0.637798
\(814\) 0 0
\(815\) 13.1671 0.461222
\(816\) 8.64400 + 6.28023i 0.302600 + 0.219852i
\(817\) −15.1788 + 46.7155i −0.531039 + 1.63437i
\(818\) −1.07474 3.30770i −0.0375773 0.115651i
\(819\) −0.810903 + 0.589155i −0.0283352 + 0.0205868i
\(820\) −12.0932 + 8.78622i −0.422312 + 0.306828i
\(821\) 4.25739 + 13.1029i 0.148584 + 0.457294i 0.997454 0.0713067i \(-0.0227169\pi\)
−0.848871 + 0.528601i \(0.822717\pi\)
\(822\) 0.945438 2.90976i 0.0329759 0.101489i
\(823\) 16.0832 + 11.6852i 0.560626 + 0.407319i 0.831688 0.555243i \(-0.187375\pi\)
−0.271062 + 0.962562i \(0.587375\pi\)
\(824\) 16.4979 0.574731
\(825\) 0 0
\(826\) −0.640313 −0.0222793
\(827\) 10.7819 + 7.83351i 0.374924 + 0.272398i 0.759250 0.650799i \(-0.225566\pi\)
−0.384326 + 0.923197i \(0.625566\pi\)
\(828\) 1.05345 3.24220i 0.0366100 0.112674i
\(829\) 15.8186 + 48.6845i 0.549401 + 1.69088i 0.710289 + 0.703910i \(0.248564\pi\)
−0.160888 + 0.986973i \(0.551436\pi\)
\(830\) −0.667074 + 0.484658i −0.0231545 + 0.0168227i
\(831\) −29.5879 + 21.4969i −1.02639 + 0.745719i
\(832\) 4.40440 + 13.5553i 0.152695 + 0.469947i
\(833\) −5.23395 + 16.1084i −0.181345 + 0.558124i
\(834\) 5.74632 + 4.17495i 0.198979 + 0.144567i
\(835\) 15.8778 0.549474
\(836\) 0 0
\(837\) 43.8558 1.51588
\(838\) −0.897244 0.651886i −0.0309948 0.0225190i
\(839\) −5.21432 + 16.0480i −0.180018 + 0.554040i −0.999827 0.0185978i \(-0.994080\pi\)
0.819809 + 0.572638i \(0.194080\pi\)
\(840\) −0.431385 1.32767i −0.0148842 0.0458088i
\(841\) −42.2508 + 30.6970i −1.45692 + 1.05852i
\(842\) 2.58255 1.87633i 0.0890007 0.0646628i
\(843\) −11.1915 34.4439i −0.385455 1.18631i
\(844\) −3.76032 + 11.5731i −0.129436 + 0.398362i
\(845\) −8.08828 5.87648i −0.278245 0.202157i
\(846\) 2.00686 0.0689972
\(847\) 0 0
\(848\) 16.2633 0.558484
\(849\) 35.7205 + 25.9525i 1.22592 + 0.890686i
\(850\) −0.371858 + 1.14446i −0.0127546 + 0.0392547i
\(851\) 7.13055 + 21.9456i 0.244432 + 0.752284i
\(852\) 6.34566 4.61039i 0.217399 0.157950i
\(853\) 4.38699 3.18734i 0.150208 0.109132i −0.510143 0.860090i \(-0.670408\pi\)
0.660351 + 0.750957i \(0.270408\pi\)
\(854\) −0.287671 0.885360i −0.00984390 0.0302964i
\(855\) 0.773253 2.37983i 0.0264447 0.0813884i
\(856\) −24.6202 17.8877i −0.841503 0.611387i
\(857\) −27.8386 −0.950947 −0.475474 0.879730i \(-0.657723\pi\)
−0.475474 + 0.879730i \(0.657723\pi\)
\(858\) 0 0
\(859\) 48.1899 1.64422 0.822109 0.569330i \(-0.192797\pi\)
0.822109 + 0.569330i \(0.192797\pi\)
\(860\) 12.2081 + 8.86974i 0.416294 + 0.302456i
\(861\) 2.01157 6.19096i 0.0685540 0.210987i
\(862\) −4.88071 15.0213i −0.166238 0.511627i
\(863\) −21.7309 + 15.7884i −0.739728 + 0.537444i −0.892626 0.450798i \(-0.851139\pi\)
0.152898 + 0.988242i \(0.451139\pi\)
\(864\) 21.8379 15.8662i 0.742941 0.539778i
\(865\) −7.05194 21.7036i −0.239773 0.737946i
\(866\) −0.351011 + 1.08030i −0.0119279 + 0.0367101i
\(867\) −13.9148 10.1097i −0.472571 0.343343i
\(868\) −6.78095 −0.230160
\(869\) 0 0
\(870\) 6.94185 0.235351
\(871\) 29.4923 + 21.4274i 0.999309 + 0.726041i
\(872\) 10.0148 30.8225i 0.339145 1.04378i
\(873\) 0.488604 + 1.50377i 0.0165367 + 0.0508948i
\(874\) −9.93335 + 7.21700i −0.336001 + 0.244119i
\(875\) −0.389057 + 0.282666i −0.0131525 + 0.00955587i
\(876\) −4.38117 13.4838i −0.148026 0.455577i
\(877\) −12.3247 + 37.9317i −0.416177 + 1.28086i 0.495017 + 0.868883i \(0.335162\pi\)
−0.911194 + 0.411978i \(0.864838\pi\)
\(878\) −12.0159 8.73005i −0.405517 0.294625i
\(879\) −35.0107 −1.18088
\(880\) 0 0
\(881\) −2.82222 −0.0950829 −0.0475415 0.998869i \(-0.515139\pi\)
−0.0475415 + 0.998869i \(0.515139\pi\)
\(882\) 1.14455 + 0.831564i 0.0385390 + 0.0280002i
\(883\) 15.6142 48.0556i 0.525460 1.61720i −0.237943 0.971279i \(-0.576473\pi\)
0.763404 0.645922i \(-0.223527\pi\)
\(884\) 6.55883 + 20.1860i 0.220597 + 0.678928i
\(885\) 3.58769 2.60661i 0.120599 0.0876201i
\(886\) −5.35918 + 3.89367i −0.180045 + 0.130811i
\(887\) 8.75120 + 26.9334i 0.293836 + 0.904336i 0.983610 + 0.180310i \(0.0577102\pi\)
−0.689773 + 0.724025i \(0.742290\pi\)
\(888\) −4.66759 + 14.3654i −0.156634 + 0.482070i
\(889\) 6.15857 + 4.47446i 0.206552 + 0.150069i
\(890\) 7.56978 0.253740
\(891\) 0 0
\(892\) 1.83707 0.0615096
\(893\) 44.7230 + 32.4931i 1.49660 + 1.08734i
\(894\) −1.82088 + 5.60409i −0.0608994 + 0.187429i
\(895\) −0.142930 0.439893i −0.00477762 0.0147040i
\(896\) −4.37413 + 3.17799i −0.146129 + 0.106169i
\(897\) −27.5570 + 20.0213i −0.920101 + 0.668493i
\(898\) 5.78321 + 17.7989i 0.192988 + 0.593957i
\(899\) 22.2024 68.3318i 0.740490 2.27899i
\(900\) −0.621919 0.451851i −0.0207306 0.0150617i
\(901\) 15.2653 0.508561
\(902\) 0 0
\(903\) −6.57144 −0.218684
\(904\) 0.678188 + 0.492732i 0.0225562 + 0.0163880i
\(905\) −0.966735 + 2.97531i −0.0321354 + 0.0989025i
\(906\) 0.683590 + 2.10387i 0.0227108 + 0.0698965i
\(907\) −41.3009 + 30.0069i −1.37138 + 0.996362i −0.373747 + 0.927531i \(0.621927\pi\)
−0.997628 + 0.0688315i \(0.978073\pi\)
\(908\) 0.688138 0.499962i 0.0228367 0.0165918i
\(909\) −1.03395 3.18217i −0.0342939 0.105546i
\(910\) 0.342717 1.05477i 0.0113610 0.0349654i
\(911\) 20.3410 + 14.7786i 0.673928 + 0.489637i 0.871338 0.490684i \(-0.163253\pi\)
−0.197410 + 0.980321i \(0.563253\pi\)
\(912\) 24.5835 0.814040
\(913\) 0 0
\(914\) −0.640313 −0.0211797
\(915\) 5.21598 + 3.78963i 0.172435 + 0.125281i
\(916\) −7.40043 + 22.7762i −0.244517 + 0.752547i
\(917\) −1.42731 4.39280i −0.0471338 0.145063i
\(918\) 5.35559 3.89106i 0.176761 0.128424i
\(919\) −20.7231 + 15.0562i −0.683591 + 0.496658i −0.874547 0.484941i \(-0.838841\pi\)
0.190956 + 0.981599i \(0.438841\pi\)
\(920\) 2.48365 + 7.64389i 0.0818835 + 0.252011i
\(921\) −4.85056 + 14.9285i −0.159832 + 0.491911i
\(922\) 2.23316 + 1.62249i 0.0735452 + 0.0534337i
\(923\) 13.2777 0.437041
\(924\) 0 0
\(925\) 5.20336 0.171085
\(926\) −1.34044 0.973885i −0.0440495 0.0320039i
\(927\) −1.22257 + 3.76268i −0.0401544 + 0.123583i
\(928\) −13.6655 42.0581i −0.448592 1.38062i
\(929\) 6.96381 5.05950i 0.228475 0.165997i −0.467658 0.883909i \(-0.654902\pi\)
0.696133 + 0.717912i \(0.254902\pi\)
\(930\) −4.96777 + 3.60929i −0.162899 + 0.118353i
\(931\) 12.0425 + 37.0629i 0.394676 + 1.21469i
\(932\) 11.5623 35.5850i 0.378735 1.16563i
\(933\) 12.6612 + 9.19890i 0.414509 + 0.301159i
\(934\) 13.0884 0.428266
\(935\) 0 0
\(936\) 3.77752 0.123472
\(937\) 4.82692 + 3.50696i 0.157689 + 0.114567i 0.663832 0.747882i \(-0.268929\pi\)
−0.506143 + 0.862450i \(0.668929\pi\)
\(938\) −0.543254 + 1.67196i −0.0177379 + 0.0545916i
\(939\) 0.444044 + 1.36663i 0.0144908 + 0.0445981i
\(940\) 13.7394 9.98225i 0.448129 0.325585i
\(941\) 18.4763 13.4238i 0.602311 0.437605i −0.244387 0.969678i \(-0.578587\pi\)
0.846699 + 0.532073i \(0.178587\pi\)
\(942\) 4.16098 + 12.8062i 0.135572 + 0.417248i
\(943\) −11.5814 + 35.6438i −0.377141 + 1.16072i
\(944\) −5.97147 4.33853i −0.194355 0.141207i
\(945\) 2.64552 0.0860586
\(946\) 0 0
\(947\) −2.30620 −0.0749415 −0.0374708 0.999298i \(-0.511930\pi\)
−0.0374708 + 0.999298i \(0.511930\pi\)
\(948\) 8.30763 + 6.03584i 0.269819 + 0.196035i
\(949\) 7.41641 22.8254i 0.240747 0.740942i
\(950\) 0.855586 + 2.63322i 0.0277589 + 0.0854330i
\(951\) −3.45744 + 2.51198i −0.112115 + 0.0814565i
\(952\) −1.76443 + 1.28193i −0.0571854 + 0.0415476i
\(953\) 8.84186 + 27.2124i 0.286416 + 0.881498i 0.985971 + 0.166919i \(0.0533817\pi\)
−0.699555 + 0.714579i \(0.746618\pi\)
\(954\) 0.394020 1.21267i 0.0127569 0.0392616i
\(955\) 4.39859 + 3.19576i 0.142335 + 0.103412i
\(956\) −4.73383 −0.153103
\(957\) 0 0
\(958\) −6.72404 −0.217244
\(959\) −1.54537 1.12278i −0.0499026 0.0362564i
\(960\) 1.47103 4.52735i 0.0474771 0.146120i
\(961\) 10.0598 + 30.9609i 0.324510 + 0.998740i
\(962\) −9.70820 + 7.05342i −0.313005 + 0.227411i
\(963\) 5.90412 4.28959i 0.190257 0.138230i
\(964\) 2.49734 + 7.68602i 0.0804339 + 0.247550i
\(965\) 0.990941 3.04980i 0.0318995 0.0981767i
\(966\) −1.32893 0.965522i −0.0427575 0.0310652i
\(967\) −31.7422 −1.02076 −0.510380 0.859949i \(-0.670495\pi\)
−0.510380 + 0.859949i \(0.670495\pi\)
\(968\) 0 0
\(969\) 23.0749 0.741274
\(970\) −1.41538 1.02834i −0.0454452 0.0330179i
\(971\) −11.4343 + 35.1913i −0.366946 + 1.12934i 0.581808 + 0.813326i \(0.302346\pi\)
−0.948754 + 0.316017i \(0.897654\pi\)
\(972\) 2.44826 + 7.53497i 0.0785279 + 0.241684i
\(973\) 3.58769 2.60661i 0.115016 0.0835640i
\(974\) −2.89993 + 2.10692i −0.0929198 + 0.0675102i
\(975\) 2.37356 + 7.30506i 0.0760147 + 0.233949i
\(976\) 3.31610 10.2059i 0.106146 0.326683i
\(977\) −27.4027 19.9092i −0.876689 0.636952i 0.0556841 0.998448i \(-0.482266\pi\)
−0.932374 + 0.361496i \(0.882266\pi\)
\(978\) 10.1419 0.324303
\(979\) 0 0
\(980\) 11.9721 0.382434
\(981\) 6.28755 + 4.56817i 0.200746 + 0.145850i
\(982\) 2.37408 7.30666i 0.0757599 0.233165i
\(983\) −11.6659 35.9039i −0.372084 1.14516i −0.945425 0.325839i \(-0.894353\pi\)
0.573342 0.819316i \(-0.305647\pi\)
\(984\) −19.8475 + 14.4200i −0.632714 + 0.459694i
\(985\) 15.6988 11.4058i 0.500205 0.363421i
\(986\) −3.35136 10.3144i −0.106729 0.328479i
\(987\) −2.28539 + 7.03371i −0.0727448 + 0.223886i
\(988\) 39.5083 + 28.7044i 1.25692 + 0.913209i
\(989\) 37.8343 1.20306
\(990\) 0 0
\(991\) −44.9354 −1.42742 −0.713710 0.700441i \(-0.752987\pi\)
−0.713710 + 0.700441i \(0.752987\pi\)
\(992\) 31.6467 + 22.9927i 1.00478 + 0.730019i
\(993\) −9.39132 + 28.9035i −0.298024 + 0.917225i
\(994\) 0.197868 + 0.608974i 0.00627598 + 0.0193155i
\(995\) −16.4642 + 11.9620i −0.521951 + 0.379220i
\(996\) 3.92968 2.85508i 0.124517 0.0904666i
\(997\) −0.122533 0.377119i −0.00388067 0.0119435i 0.949097 0.314983i \(-0.101999\pi\)
−0.952978 + 0.303039i \(0.901999\pi\)
\(998\) 3.61870 11.1372i 0.114548 0.352543i
\(999\) −23.1577 16.8251i −0.732678 0.532322i
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 605.2.g.q.81.4 24
11.2 odd 10 inner 605.2.g.q.511.4 24
11.3 even 5 inner 605.2.g.q.366.4 24
11.4 even 5 inner 605.2.g.q.251.3 24
11.5 even 5 605.2.a.m.1.3 6
11.6 odd 10 605.2.a.m.1.4 yes 6
11.7 odd 10 inner 605.2.g.q.251.4 24
11.8 odd 10 inner 605.2.g.q.366.3 24
11.9 even 5 inner 605.2.g.q.511.3 24
11.10 odd 2 inner 605.2.g.q.81.3 24
33.5 odd 10 5445.2.a.bx.1.4 6
33.17 even 10 5445.2.a.bx.1.3 6
44.27 odd 10 9680.2.a.cw.1.5 6
44.39 even 10 9680.2.a.cw.1.6 6
55.39 odd 10 3025.2.a.bg.1.3 6
55.49 even 10 3025.2.a.bg.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.a.m.1.3 6 11.5 even 5
605.2.a.m.1.4 yes 6 11.6 odd 10
605.2.g.q.81.3 24 11.10 odd 2 inner
605.2.g.q.81.4 24 1.1 even 1 trivial
605.2.g.q.251.3 24 11.4 even 5 inner
605.2.g.q.251.4 24 11.7 odd 10 inner
605.2.g.q.366.3 24 11.8 odd 10 inner
605.2.g.q.366.4 24 11.3 even 5 inner
605.2.g.q.511.3 24 11.9 even 5 inner
605.2.g.q.511.4 24 11.2 odd 10 inner
3025.2.a.bg.1.3 6 55.39 odd 10
3025.2.a.bg.1.4 6 55.49 even 10
5445.2.a.bx.1.3 6 33.17 even 10
5445.2.a.bx.1.4 6 33.5 odd 10
9680.2.a.cw.1.5 6 44.27 odd 10
9680.2.a.cw.1.6 6 44.39 even 10