Properties

Label 735.2.y.g.128.6
Level $735$
Weight $2$
Character 735.128
Analytic conductor $5.869$
Analytic rank $0$
Dimension $48$
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] = [735,2,Mod(128,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.128");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.y (of order \(12\), 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: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 128.6
Character \(\chi\) \(=\) 735.128
Dual form 735.2.y.g.557.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.355526 + 0.0952630i) q^{2} +(1.73147 - 0.0448327i) q^{3} +(-1.61473 + 0.932263i) q^{4} +(1.32690 + 1.79982i) q^{5} +(-0.611312 + 0.180884i) q^{6} +(1.00579 - 1.00579i) q^{8} +(2.99598 - 0.155253i) q^{9} +O(q^{10})\) \(q+(-0.355526 + 0.0952630i) q^{2} +(1.73147 - 0.0448327i) q^{3} +(-1.61473 + 0.932263i) q^{4} +(1.32690 + 1.79982i) q^{5} +(-0.611312 + 0.180884i) q^{6} +(1.00579 - 1.00579i) q^{8} +(2.99598 - 0.155253i) q^{9} +(-0.643203 - 0.513478i) q^{10} +(2.93366 - 1.69375i) q^{11} +(-2.75406 + 1.68658i) q^{12} +(-1.59420 - 1.59420i) q^{13} +(2.37818 + 3.05684i) q^{15} +(1.60275 - 2.77605i) q^{16} +(-0.0514941 + 0.192179i) q^{17} +(-1.05036 + 0.340602i) q^{18} +(6.36261 + 3.67345i) q^{19} +(-3.82048 - 1.66919i) q^{20} +(-0.881641 + 0.881641i) q^{22} +(0.810540 + 3.02498i) q^{23} +(1.69641 - 1.78660i) q^{24} +(-1.47868 + 4.77635i) q^{25} +(0.718647 + 0.414911i) q^{26} +(5.18049 - 0.403134i) q^{27} -9.49165 q^{29} +(-1.13671 - 0.860235i) q^{30} +(0.461291 + 0.798980i) q^{31} +(-1.04166 + 3.88752i) q^{32} +(5.00361 - 3.06420i) q^{33} -0.0732300i q^{34} +(-4.69295 + 3.04373i) q^{36} +(2.16525 + 8.08083i) q^{37} +(-2.61202 - 0.699888i) q^{38} +(-2.83178 - 2.68883i) q^{39} +(3.14483 + 0.475658i) q^{40} +1.39256i q^{41} +(0.864526 + 0.864526i) q^{43} +(-3.15804 + 5.46988i) q^{44} +(4.25479 + 5.18621i) q^{45} +(-0.576337 - 0.998245i) q^{46} +(0.889755 - 0.238409i) q^{47} +(2.65066 - 4.87851i) q^{48} +(0.0707006 - 1.83898i) q^{50} +(-0.0805446 + 0.335060i) q^{51} +(4.06040 + 1.08798i) q^{52} +(-8.93528 - 2.39420i) q^{53} +(-1.80340 + 0.636833i) q^{54} +(6.94110 + 3.03262i) q^{55} +(11.1814 + 6.07522i) q^{57} +(3.37453 - 0.904203i) q^{58} +(-3.12516 - 5.41293i) q^{59} +(-6.68989 - 2.71888i) q^{60} +(0.916307 - 1.58709i) q^{61} +(-0.240114 - 0.240114i) q^{62} +4.92967i q^{64} +(0.753925 - 4.98460i) q^{65} +(-1.48701 + 1.56606i) q^{66} +(1.11399 + 0.298494i) q^{67} +(-0.0960121 - 0.358322i) q^{68} +(1.53904 + 5.20132i) q^{69} -9.77651i q^{71} +(2.85719 - 3.16949i) q^{72} +(1.75973 - 6.56741i) q^{73} +(-1.53961 - 2.66668i) q^{74} +(-2.34616 + 8.33640i) q^{75} -13.6985 q^{76} +(1.26292 + 0.686187i) q^{78} +(-2.95931 - 1.70856i) q^{79} +(7.12308 - 0.798875i) q^{80} +(8.95179 - 0.930269i) q^{81} +(-0.132659 - 0.495092i) q^{82} +(6.26911 - 6.26911i) q^{83} +(-0.414214 + 0.162321i) q^{85} +(-0.389719 - 0.225004i) q^{86} +(-16.4345 + 0.425536i) q^{87} +(1.24709 - 4.65422i) q^{88} +(6.18833 - 10.7185i) q^{89} +(-2.00674 - 1.43851i) q^{90} +(-4.12888 - 4.12888i) q^{92} +(0.834532 + 1.36273i) q^{93} +(-0.293620 + 0.169521i) q^{94} +(1.83099 + 16.3258i) q^{95} +(-1.62931 + 6.77783i) q^{96} +(6.71326 - 6.71326i) q^{97} +(8.52622 - 5.52990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{3} - 16 q^{10} + 16 q^{12} + 16 q^{13} - 32 q^{15} + 16 q^{16} + 20 q^{18} + 16 q^{22} + 16 q^{25} + 32 q^{27} - 20 q^{30} + 28 q^{33} + 32 q^{36} + 16 q^{37} + 64 q^{40} - 80 q^{43} + 20 q^{45} + 64 q^{46} - 32 q^{48} + 20 q^{51} - 80 q^{55} + 8 q^{57} - 40 q^{58} - 32 q^{60} + 32 q^{61} - 16 q^{66} - 24 q^{67} + 8 q^{72} + 32 q^{73} - 60 q^{75} - 64 q^{76} + 120 q^{78} - 52 q^{81} - 80 q^{82} + 48 q^{85} + 4 q^{87} - 96 q^{88} + 48 q^{90} + 76 q^{93} - 96 q^{96} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.355526 + 0.0952630i −0.251395 + 0.0673611i −0.382316 0.924032i \(-0.624873\pi\)
0.130921 + 0.991393i \(0.458207\pi\)
\(3\) 1.73147 0.0448327i 0.999665 0.0258842i
\(4\) −1.61473 + 0.932263i −0.807363 + 0.466132i
\(5\) 1.32690 + 1.79982i 0.593407 + 0.804903i
\(6\) −0.611312 + 0.180884i −0.249567 + 0.0738457i
\(7\) 0 0
\(8\) 1.00579 1.00579i 0.355602 0.355602i
\(9\) 2.99598 0.155253i 0.998660 0.0517510i
\(10\) −0.643203 0.513478i −0.203399 0.162376i
\(11\) 2.93366 1.69375i 0.884531 0.510684i 0.0123815 0.999923i \(-0.496059\pi\)
0.872150 + 0.489239i \(0.162725\pi\)
\(12\) −2.75406 + 1.68658i −0.795028 + 0.486873i
\(13\) −1.59420 1.59420i −0.442151 0.442151i 0.450583 0.892734i \(-0.351216\pi\)
−0.892734 + 0.450583i \(0.851216\pi\)
\(14\) 0 0
\(15\) 2.37818 + 3.05684i 0.614042 + 0.789273i
\(16\) 1.60275 2.77605i 0.400689 0.694013i
\(17\) −0.0514941 + 0.192179i −0.0124891 + 0.0466101i −0.971889 0.235439i \(-0.924347\pi\)
0.959400 + 0.282049i \(0.0910140\pi\)
\(18\) −1.05036 + 0.340602i −0.247572 + 0.0802808i
\(19\) 6.36261 + 3.67345i 1.45968 + 0.842748i 0.998995 0.0448148i \(-0.0142698\pi\)
0.460687 + 0.887563i \(0.347603\pi\)
\(20\) −3.82048 1.66919i −0.854286 0.373243i
\(21\) 0 0
\(22\) −0.881641 + 0.881641i −0.187966 + 0.187966i
\(23\) 0.810540 + 3.02498i 0.169009 + 0.630752i 0.997495 + 0.0707408i \(0.0225363\pi\)
−0.828485 + 0.560011i \(0.810797\pi\)
\(24\) 1.69641 1.78660i 0.346278 0.364687i
\(25\) −1.47868 + 4.77635i −0.295736 + 0.955270i
\(26\) 0.718647 + 0.414911i 0.140938 + 0.0813707i
\(27\) 5.18049 0.403134i 0.996986 0.0775831i
\(28\) 0 0
\(29\) −9.49165 −1.76256 −0.881278 0.472598i \(-0.843316\pi\)
−0.881278 + 0.472598i \(0.843316\pi\)
\(30\) −1.13671 0.860235i −0.207533 0.157057i
\(31\) 0.461291 + 0.798980i 0.0828503 + 0.143501i 0.904473 0.426531i \(-0.140264\pi\)
−0.821623 + 0.570031i \(0.806931\pi\)
\(32\) −1.04166 + 3.88752i −0.184141 + 0.687224i
\(33\) 5.00361 3.06420i 0.871016 0.533409i
\(34\) 0.0732300i 0.0125588i
\(35\) 0 0
\(36\) −4.69295 + 3.04373i −0.782159 + 0.507289i
\(37\) 2.16525 + 8.08083i 0.355965 + 1.32848i 0.879266 + 0.476332i \(0.158034\pi\)
−0.523300 + 0.852148i \(0.675299\pi\)
\(38\) −2.61202 0.699888i −0.423725 0.113537i
\(39\) −2.83178 2.68883i −0.453447 0.430558i
\(40\) 3.14483 + 0.475658i 0.497242 + 0.0752082i
\(41\) 1.39256i 0.217481i 0.994070 + 0.108741i \(0.0346818\pi\)
−0.994070 + 0.108741i \(0.965318\pi\)
\(42\) 0 0
\(43\) 0.864526 + 0.864526i 0.131839 + 0.131839i 0.769947 0.638108i \(-0.220283\pi\)
−0.638108 + 0.769947i \(0.720283\pi\)
\(44\) −3.15804 + 5.46988i −0.476092 + 0.824616i
\(45\) 4.25479 + 5.18621i 0.634266 + 0.773115i
\(46\) −0.576337 0.998245i −0.0849762 0.147183i
\(47\) 0.889755 0.238409i 0.129784 0.0347755i −0.193342 0.981131i \(-0.561933\pi\)
0.323126 + 0.946356i \(0.395266\pi\)
\(48\) 2.65066 4.87851i 0.382591 0.704152i
\(49\) 0 0
\(50\) 0.0707006 1.83898i 0.00999858 0.260071i
\(51\) −0.0805446 + 0.335060i −0.0112785 + 0.0469178i
\(52\) 4.06040 + 1.08798i 0.563077 + 0.150876i
\(53\) −8.93528 2.39420i −1.22736 0.328869i −0.413806 0.910365i \(-0.635801\pi\)
−0.813549 + 0.581496i \(0.802468\pi\)
\(54\) −1.80340 + 0.636833i −0.245411 + 0.0866621i
\(55\) 6.94110 + 3.03262i 0.935938 + 0.408918i
\(56\) 0 0
\(57\) 11.1814 + 6.07522i 1.48101 + 0.804683i
\(58\) 3.37453 0.904203i 0.443098 0.118728i
\(59\) −3.12516 5.41293i −0.406861 0.704704i 0.587675 0.809097i \(-0.300043\pi\)
−0.994536 + 0.104393i \(0.966710\pi\)
\(60\) −6.68989 2.71888i −0.863660 0.351006i
\(61\) 0.916307 1.58709i 0.117321 0.203206i −0.801384 0.598150i \(-0.795903\pi\)
0.918705 + 0.394944i \(0.129236\pi\)
\(62\) −0.240114 0.240114i −0.0304945 0.0304945i
\(63\) 0 0
\(64\) 4.92967i 0.616209i
\(65\) 0.753925 4.98460i 0.0935129 0.618264i
\(66\) −1.48701 + 1.56606i −0.183038 + 0.192769i
\(67\) 1.11399 + 0.298494i 0.136096 + 0.0364668i 0.326224 0.945292i \(-0.394224\pi\)
−0.190128 + 0.981759i \(0.560890\pi\)
\(68\) −0.0960121 0.358322i −0.0116432 0.0434529i
\(69\) 1.53904 + 5.20132i 0.185279 + 0.626166i
\(70\) 0 0
\(71\) 9.77651i 1.16026i −0.814524 0.580129i \(-0.803002\pi\)
0.814524 0.580129i \(-0.196998\pi\)
\(72\) 2.85719 3.16949i 0.336723 0.373528i
\(73\) 1.75973 6.56741i 0.205961 0.768658i −0.783193 0.621778i \(-0.786410\pi\)
0.989154 0.146879i \(-0.0469229\pi\)
\(74\) −1.53961 2.66668i −0.178976 0.309995i
\(75\) −2.34616 + 8.33640i −0.270911 + 0.962604i
\(76\) −13.6985 −1.57133
\(77\) 0 0
\(78\) 1.26292 + 0.686187i 0.142997 + 0.0776954i
\(79\) −2.95931 1.70856i −0.332948 0.192228i 0.324201 0.945988i \(-0.394905\pi\)
−0.657149 + 0.753760i \(0.728238\pi\)
\(80\) 7.12308 0.798875i 0.796384 0.0893170i
\(81\) 8.95179 0.930269i 0.994644 0.103363i
\(82\) −0.132659 0.495092i −0.0146498 0.0546737i
\(83\) 6.26911 6.26911i 0.688124 0.688124i −0.273693 0.961817i \(-0.588245\pi\)
0.961817 + 0.273693i \(0.0882453\pi\)
\(84\) 0 0
\(85\) −0.414214 + 0.162321i −0.0449278 + 0.0176062i
\(86\) −0.389719 0.225004i −0.0420245 0.0242628i
\(87\) −16.4345 + 0.425536i −1.76197 + 0.0456223i
\(88\) 1.24709 4.65422i 0.132941 0.496141i
\(89\) 6.18833 10.7185i 0.655962 1.13616i −0.325690 0.945477i \(-0.605596\pi\)
0.981652 0.190683i \(-0.0610703\pi\)
\(90\) −2.00674 1.43851i −0.211529 0.151632i
\(91\) 0 0
\(92\) −4.12888 4.12888i −0.430465 0.430465i
\(93\) 0.834532 + 1.36273i 0.0865370 + 0.141308i
\(94\) −0.293620 + 0.169521i −0.0302845 + 0.0174848i
\(95\) 1.83099 + 16.3258i 0.187856 + 1.67499i
\(96\) −1.62931 + 6.77783i −0.166291 + 0.691760i
\(97\) 6.71326 6.71326i 0.681628 0.681628i −0.278739 0.960367i \(-0.589916\pi\)
0.960367 + 0.278739i \(0.0899164\pi\)
\(98\) 0 0
\(99\) 8.52622 5.52990i 0.856918 0.555775i
\(100\) −2.06515 9.09102i −0.206515 0.909102i
\(101\) 10.7840 6.22616i 1.07305 0.619526i 0.144037 0.989572i \(-0.453992\pi\)
0.929013 + 0.370047i \(0.120658\pi\)
\(102\) −0.00328310 0.126796i −0.000325075 0.0125546i
\(103\) −13.3724 + 3.58311i −1.31762 + 0.353055i −0.848085 0.529861i \(-0.822244\pi\)
−0.469533 + 0.882915i \(0.655578\pi\)
\(104\) −3.20687 −0.314459
\(105\) 0 0
\(106\) 3.40481 0.330704
\(107\) −7.12882 + 1.91016i −0.689169 + 0.184662i −0.586374 0.810040i \(-0.699445\pi\)
−0.102795 + 0.994703i \(0.532779\pi\)
\(108\) −7.98925 + 5.48053i −0.768766 + 0.527364i
\(109\) 5.78212 3.33831i 0.553826 0.319752i −0.196838 0.980436i \(-0.563067\pi\)
0.750664 + 0.660684i \(0.229734\pi\)
\(110\) −2.75664 0.416944i −0.262835 0.0397541i
\(111\) 4.11135 + 13.8946i 0.390233 + 1.31882i
\(112\) 0 0
\(113\) −8.23451 + 8.23451i −0.774637 + 0.774637i −0.978913 0.204276i \(-0.934516\pi\)
0.204276 + 0.978913i \(0.434516\pi\)
\(114\) −4.55401 1.09473i −0.426522 0.102531i
\(115\) −4.36890 + 5.47266i −0.407402 + 0.510328i
\(116\) 15.3264 8.84872i 1.42302 0.821583i
\(117\) −5.02369 4.52868i −0.464440 0.418677i
\(118\) 1.62673 + 1.62673i 0.149752 + 0.149752i
\(119\) 0 0
\(120\) 5.46651 + 0.682597i 0.499022 + 0.0623123i
\(121\) 0.237567 0.411478i 0.0215970 0.0374071i
\(122\) −0.174580 + 0.651543i −0.0158058 + 0.0589879i
\(123\) 0.0624322 + 2.41118i 0.00562932 + 0.217408i
\(124\) −1.48972 0.860089i −0.133781 0.0772383i
\(125\) −10.5586 + 3.67638i −0.944391 + 0.328825i
\(126\) 0 0
\(127\) 1.88180 1.88180i 0.166983 0.166983i −0.618669 0.785652i \(-0.712328\pi\)
0.785652 + 0.618669i \(0.212328\pi\)
\(128\) −2.55293 9.52767i −0.225649 0.842135i
\(129\) 1.53566 + 1.45814i 0.135207 + 0.128382i
\(130\) 0.206808 + 1.84398i 0.0181382 + 0.161728i
\(131\) 7.76894 + 4.48540i 0.678776 + 0.391891i 0.799394 0.600808i \(-0.205154\pi\)
−0.120618 + 0.992699i \(0.538488\pi\)
\(132\) −5.22282 + 9.61252i −0.454588 + 0.836663i
\(133\) 0 0
\(134\) −0.424489 −0.0366703
\(135\) 7.59955 + 8.78902i 0.654065 + 0.756438i
\(136\) 0.141500 + 0.245084i 0.0121335 + 0.0210158i
\(137\) −2.37747 + 8.87285i −0.203121 + 0.758059i 0.786893 + 0.617090i \(0.211688\pi\)
−0.990014 + 0.140969i \(0.954978\pi\)
\(138\) −1.04266 1.70259i −0.0887575 0.144934i
\(139\) 1.83916i 0.155995i 0.996954 + 0.0779976i \(0.0248526\pi\)
−0.996954 + 0.0779976i \(0.975147\pi\)
\(140\) 0 0
\(141\) 1.52990 0.452688i 0.128840 0.0381232i
\(142\) 0.931340 + 3.47581i 0.0781563 + 0.291683i
\(143\) −7.37700 1.97666i −0.616896 0.165297i
\(144\) 4.37083 8.56583i 0.364236 0.713819i
\(145\) −12.5945 17.0832i −1.04591 1.41869i
\(146\) 2.50253i 0.207110i
\(147\) 0 0
\(148\) −11.0297 11.0297i −0.906640 0.906640i
\(149\) 0.493614 0.854964i 0.0404384 0.0700414i −0.845098 0.534612i \(-0.820458\pi\)
0.885536 + 0.464570i \(0.153791\pi\)
\(150\) 0.0399696 3.18731i 0.00326351 0.260243i
\(151\) 4.35542 + 7.54381i 0.354439 + 0.613907i 0.987022 0.160586i \(-0.0513385\pi\)
−0.632583 + 0.774493i \(0.718005\pi\)
\(152\) 10.0942 2.70474i 0.818749 0.219383i
\(153\) −0.124439 + 0.583758i −0.0100603 + 0.0471940i
\(154\) 0 0
\(155\) −0.825930 + 1.89040i −0.0663403 + 0.151841i
\(156\) 7.07925 + 1.70177i 0.566793 + 0.136251i
\(157\) 7.18947 + 1.92641i 0.573782 + 0.153744i 0.534031 0.845465i \(-0.320677\pi\)
0.0397515 + 0.999210i \(0.487343\pi\)
\(158\) 1.21487 + 0.325524i 0.0966502 + 0.0258973i
\(159\) −15.5785 3.74490i −1.23546 0.296990i
\(160\) −8.37901 + 3.28355i −0.662419 + 0.259588i
\(161\) 0 0
\(162\) −3.09398 + 1.18351i −0.243086 + 0.0929853i
\(163\) −19.3308 + 5.17967i −1.51411 + 0.405703i −0.917796 0.397052i \(-0.870033\pi\)
−0.596309 + 0.802755i \(0.703367\pi\)
\(164\) −1.29823 2.24860i −0.101375 0.175586i
\(165\) 12.1543 + 4.93970i 0.946209 + 0.384555i
\(166\) −1.63162 + 2.82605i −0.126638 + 0.219344i
\(167\) −17.4876 17.4876i −1.35323 1.35323i −0.882018 0.471215i \(-0.843816\pi\)
−0.471215 0.882018i \(-0.656184\pi\)
\(168\) 0 0
\(169\) 7.91707i 0.609005i
\(170\) 0.131801 0.0971688i 0.0101086 0.00745250i
\(171\) 19.6326 + 10.0178i 1.50134 + 0.766079i
\(172\) −2.20194 0.590008i −0.167896 0.0449877i
\(173\) −3.98116 14.8579i −0.302682 1.12962i −0.934922 0.354852i \(-0.884531\pi\)
0.632241 0.774772i \(-0.282135\pi\)
\(174\) 5.80236 1.71689i 0.439876 0.130157i
\(175\) 0 0
\(176\) 10.8587i 0.818502i
\(177\) −5.65380 9.23222i −0.424965 0.693936i
\(178\) −1.17904 + 4.40023i −0.0883726 + 0.329811i
\(179\) −8.82622 15.2875i −0.659703 1.14264i −0.980693 0.195556i \(-0.937349\pi\)
0.320990 0.947083i \(-0.395984\pi\)
\(180\) −11.7052 4.40773i −0.872457 0.328533i
\(181\) 11.9237 0.886282 0.443141 0.896452i \(-0.353864\pi\)
0.443141 + 0.896452i \(0.353864\pi\)
\(182\) 0 0
\(183\) 1.51541 2.78908i 0.112022 0.206175i
\(184\) 3.85774 + 2.22727i 0.284397 + 0.164196i
\(185\) −11.6709 + 14.6195i −0.858065 + 1.07485i
\(186\) −0.426516 0.404986i −0.0312736 0.0296950i
\(187\) 0.174436 + 0.651004i 0.0127560 + 0.0476061i
\(188\) −1.21445 + 1.21445i −0.0885729 + 0.0885729i
\(189\) 0 0
\(190\) −2.20621 5.62983i −0.160055 0.408431i
\(191\) −15.4022 8.89245i −1.11446 0.643435i −0.174480 0.984661i \(-0.555825\pi\)
−0.939981 + 0.341226i \(0.889158\pi\)
\(192\) 0.221010 + 8.53558i 0.0159500 + 0.616002i
\(193\) 5.24857 19.5879i 0.377801 1.40997i −0.471409 0.881915i \(-0.656254\pi\)
0.849210 0.528056i \(-0.177079\pi\)
\(194\) −1.74721 + 3.02626i −0.125443 + 0.217273i
\(195\) 1.08193 8.66449i 0.0774783 0.620477i
\(196\) 0 0
\(197\) −4.10678 4.10678i −0.292596 0.292596i 0.545509 0.838105i \(-0.316336\pi\)
−0.838105 + 0.545509i \(0.816336\pi\)
\(198\) −2.50450 + 2.77826i −0.177987 + 0.197442i
\(199\) −11.6175 + 6.70739i −0.823546 + 0.475474i −0.851638 0.524131i \(-0.824390\pi\)
0.0280920 + 0.999605i \(0.491057\pi\)
\(200\) 3.31677 + 6.29127i 0.234531 + 0.444860i
\(201\) 1.94223 + 0.466890i 0.136994 + 0.0329319i
\(202\) −3.24088 + 3.24088i −0.228027 + 0.228027i
\(203\) 0 0
\(204\) −0.182307 0.616119i −0.0127640 0.0431370i
\(205\) −2.50635 + 1.84779i −0.175051 + 0.129055i
\(206\) 4.41289 2.54778i 0.307460 0.177512i
\(207\) 2.89800 + 8.93694i 0.201425 + 0.621160i
\(208\) −6.98068 + 1.87047i −0.484023 + 0.129694i
\(209\) 24.8876 1.72151
\(210\) 0 0
\(211\) 8.11525 0.558677 0.279338 0.960193i \(-0.409885\pi\)
0.279338 + 0.960193i \(0.409885\pi\)
\(212\) 16.6601 4.46405i 1.14422 0.306592i
\(213\) −0.438307 16.9277i −0.0300323 1.15987i
\(214\) 2.35251 1.35823i 0.160815 0.0928464i
\(215\) −0.408850 + 2.70313i −0.0278833 + 0.184352i
\(216\) 4.80504 5.61598i 0.326941 0.382119i
\(217\) 0 0
\(218\) −1.73768 + 1.73768i −0.117690 + 0.117690i
\(219\) 2.75249 11.4502i 0.185996 0.773731i
\(220\) −14.0352 + 1.57409i −0.946252 + 0.106125i
\(221\) 0.388462 0.224279i 0.0261308 0.0150866i
\(222\) −2.78534 4.54825i −0.186940 0.305259i
\(223\) 11.5431 + 11.5431i 0.772984 + 0.772984i 0.978627 0.205643i \(-0.0659285\pi\)
−0.205643 + 0.978627i \(0.565928\pi\)
\(224\) 0 0
\(225\) −3.68856 + 14.5394i −0.245904 + 0.969294i
\(226\) 2.14314 3.71203i 0.142559 0.246920i
\(227\) 2.57893 9.62471i 0.171170 0.638815i −0.826002 0.563666i \(-0.809390\pi\)
0.997172 0.0751483i \(-0.0239430\pi\)
\(228\) −23.7185 + 0.614140i −1.57080 + 0.0406724i
\(229\) 4.15793 + 2.40058i 0.274764 + 0.158635i 0.631051 0.775742i \(-0.282624\pi\)
−0.356287 + 0.934377i \(0.615957\pi\)
\(230\) 1.03192 2.36187i 0.0680426 0.155737i
\(231\) 0 0
\(232\) −9.54665 + 9.54665i −0.626768 + 0.626768i
\(233\) 5.22651 + 19.5056i 0.342400 + 1.27785i 0.895620 + 0.444820i \(0.146732\pi\)
−0.553220 + 0.833035i \(0.686601\pi\)
\(234\) 2.21747 + 1.13149i 0.144960 + 0.0739680i
\(235\) 1.60971 + 1.28505i 0.105006 + 0.0838275i
\(236\) 10.0926 + 5.82694i 0.656969 + 0.379301i
\(237\) −5.20055 2.82564i −0.337812 0.183545i
\(238\) 0 0
\(239\) 12.8618 0.831961 0.415981 0.909373i \(-0.363438\pi\)
0.415981 + 0.909373i \(0.363438\pi\)
\(240\) 12.2976 1.70258i 0.793806 0.109901i
\(241\) −8.09281 14.0172i −0.521304 0.902924i −0.999693 0.0247765i \(-0.992113\pi\)
0.478389 0.878148i \(-0.341221\pi\)
\(242\) −0.0452627 + 0.168923i −0.00290960 + 0.0108588i
\(243\) 15.4581 2.01207i 0.991635 0.129074i
\(244\) 3.41696i 0.218748i
\(245\) 0 0
\(246\) −0.251892 0.851289i −0.0160601 0.0542762i
\(247\) −4.28704 15.9995i −0.272778 1.01802i
\(248\) 1.26757 + 0.339645i 0.0804910 + 0.0215675i
\(249\) 10.5737 11.1358i 0.670082 0.705705i
\(250\) 3.40364 2.31289i 0.215265 0.146280i
\(251\) 8.02862i 0.506762i 0.967367 + 0.253381i \(0.0815426\pi\)
−0.967367 + 0.253381i \(0.918457\pi\)
\(252\) 0 0
\(253\) 7.50140 + 7.50140i 0.471609 + 0.471609i
\(254\) −0.489763 + 0.848294i −0.0307304 + 0.0532267i
\(255\) −0.709921 + 0.299625i −0.0444570 + 0.0187633i
\(256\) −3.11440 5.39430i −0.194650 0.337144i
\(257\) −22.6908 + 6.07998i −1.41541 + 0.379259i −0.883854 0.467763i \(-0.845060\pi\)
−0.531558 + 0.847022i \(0.678393\pi\)
\(258\) −0.684874 0.372116i −0.0426384 0.0231669i
\(259\) 0 0
\(260\) 3.42958 + 8.75163i 0.212693 + 0.542753i
\(261\) −28.4368 + 1.47361i −1.76019 + 0.0912140i
\(262\) −3.18936 0.854585i −0.197039 0.0527964i
\(263\) −18.9005 5.06438i −1.16546 0.312283i −0.376313 0.926493i \(-0.622808\pi\)
−0.789143 + 0.614210i \(0.789475\pi\)
\(264\) 1.95065 8.11455i 0.120054 0.499416i
\(265\) −7.54709 19.2587i −0.463614 1.18305i
\(266\) 0 0
\(267\) 10.2344 18.8362i 0.626334 1.15276i
\(268\) −2.07707 + 0.556549i −0.126877 + 0.0339967i
\(269\) −5.73161 9.92745i −0.349463 0.605287i 0.636691 0.771119i \(-0.280303\pi\)
−0.986154 + 0.165832i \(0.946969\pi\)
\(270\) −3.53911 2.40077i −0.215383 0.146106i
\(271\) 4.21138 7.29432i 0.255823 0.443099i −0.709296 0.704911i \(-0.750987\pi\)
0.965119 + 0.261813i \(0.0843202\pi\)
\(272\) 0.450965 + 0.450965i 0.0273438 + 0.0273438i
\(273\) 0 0
\(274\) 3.38102i 0.204255i
\(275\) 3.75199 + 16.5167i 0.226253 + 0.995994i
\(276\) −7.33414 6.96392i −0.441463 0.419179i
\(277\) −17.3905 4.65976i −1.04489 0.279978i −0.304752 0.952432i \(-0.598574\pi\)
−0.740139 + 0.672454i \(0.765240\pi\)
\(278\) −0.175203 0.653868i −0.0105080 0.0392164i
\(279\) 1.50606 + 2.32211i 0.0901656 + 0.139021i
\(280\) 0 0
\(281\) 4.41251i 0.263228i 0.991301 + 0.131614i \(0.0420160\pi\)
−0.991301 + 0.131614i \(0.957984\pi\)
\(282\) −0.500793 + 0.306685i −0.0298218 + 0.0182628i
\(283\) −0.758575 + 2.83104i −0.0450926 + 0.168288i −0.984800 0.173691i \(-0.944431\pi\)
0.939708 + 0.341979i \(0.111097\pi\)
\(284\) 9.11428 + 15.7864i 0.540833 + 0.936751i
\(285\) 3.90224 + 28.1856i 0.231149 + 1.66957i
\(286\) 2.81102 0.166219
\(287\) 0 0
\(288\) −2.51724 + 11.8087i −0.148330 + 0.695832i
\(289\) 14.6882 + 8.48021i 0.864009 + 0.498836i
\(290\) 6.10506 + 4.87375i 0.358502 + 0.286197i
\(291\) 11.3228 11.9248i 0.663756 0.699043i
\(292\) 3.28107 + 12.2451i 0.192010 + 0.716591i
\(293\) −7.37595 + 7.37595i −0.430908 + 0.430908i −0.888937 0.458029i \(-0.848555\pi\)
0.458029 + 0.888937i \(0.348555\pi\)
\(294\) 0 0
\(295\) 5.59552 12.8071i 0.325784 0.745660i
\(296\) 10.3054 + 5.94985i 0.598992 + 0.345828i
\(297\) 14.5150 9.95710i 0.842245 0.577770i
\(298\) −0.0940462 + 0.350985i −0.00544795 + 0.0203320i
\(299\) 3.53025 6.11457i 0.204160 0.353615i
\(300\) −3.98332 15.6482i −0.229977 0.903452i
\(301\) 0 0
\(302\) −2.26711 2.26711i −0.130458 0.130458i
\(303\) 18.3931 11.2639i 1.05665 0.647093i
\(304\) 20.3954 11.7753i 1.16976 0.675359i
\(305\) 4.07232 0.456723i 0.233180 0.0261519i
\(306\) −0.0113692 0.219396i −0.000649932 0.0125420i
\(307\) −11.3608 + 11.3608i −0.648396 + 0.648396i −0.952605 0.304209i \(-0.901608\pi\)
0.304209 + 0.952605i \(0.401608\pi\)
\(308\) 0 0
\(309\) −22.9932 + 6.80357i −1.30804 + 0.387042i
\(310\) 0.113554 0.750769i 0.00644946 0.0426408i
\(311\) −7.74479 + 4.47145i −0.439167 + 0.253553i −0.703244 0.710949i \(-0.748266\pi\)
0.264078 + 0.964501i \(0.414933\pi\)
\(312\) −5.55260 + 0.143773i −0.314354 + 0.00813952i
\(313\) 6.18089 1.65617i 0.349365 0.0936120i −0.0798692 0.996805i \(-0.525450\pi\)
0.429234 + 0.903193i \(0.358784\pi\)
\(314\) −2.73956 −0.154602
\(315\) 0 0
\(316\) 6.37130 0.358414
\(317\) 2.43772 0.653184i 0.136916 0.0366865i −0.189710 0.981840i \(-0.560755\pi\)
0.326626 + 0.945154i \(0.394088\pi\)
\(318\) 5.89532 0.152647i 0.330593 0.00855999i
\(319\) −27.8453 + 16.0765i −1.55904 + 0.900110i
\(320\) −8.87251 + 6.54117i −0.495988 + 0.365663i
\(321\) −12.2577 + 3.62699i −0.684158 + 0.202439i
\(322\) 0 0
\(323\) −1.03360 + 1.03360i −0.0575108 + 0.0575108i
\(324\) −13.5874 + 9.84756i −0.754858 + 0.547086i
\(325\) 9.97175 5.25713i 0.553133 0.291613i
\(326\) 6.37918 3.68302i 0.353310 0.203984i
\(327\) 9.86190 6.03941i 0.545364 0.333980i
\(328\) 1.40063 + 1.40063i 0.0773368 + 0.0773368i
\(329\) 0 0
\(330\) −4.79173 0.598339i −0.263776 0.0329375i
\(331\) 1.80929 3.13378i 0.0994474 0.172248i −0.812009 0.583645i \(-0.801626\pi\)
0.911456 + 0.411397i \(0.134959\pi\)
\(332\) −4.27844 + 15.9674i −0.234810 + 0.876322i
\(333\) 7.74162 + 23.8738i 0.424238 + 1.30828i
\(334\) 7.88323 + 4.55139i 0.431351 + 0.249041i
\(335\) 0.940923 + 2.40106i 0.0514081 + 0.131184i
\(336\) 0 0
\(337\) −17.0941 + 17.0941i −0.931175 + 0.931175i −0.997779 0.0666042i \(-0.978784\pi\)
0.0666042 + 0.997779i \(0.478784\pi\)
\(338\) 0.754203 + 2.81473i 0.0410233 + 0.153101i
\(339\) −13.8886 + 14.6270i −0.754327 + 0.794428i
\(340\) 0.517515 0.648261i 0.0280662 0.0351569i
\(341\) 2.70654 + 1.56262i 0.146567 + 0.0846207i
\(342\) −7.93421 1.69133i −0.429033 0.0914565i
\(343\) 0 0
\(344\) 1.73907 0.0937644
\(345\) −7.31927 + 9.67162i −0.394056 + 0.520703i
\(346\) 2.83081 + 4.90311i 0.152185 + 0.263593i
\(347\) 2.00792 7.49364i 0.107791 0.402280i −0.890856 0.454285i \(-0.849895\pi\)
0.998647 + 0.0520055i \(0.0165613\pi\)
\(348\) 26.1405 16.0084i 1.40128 0.858141i
\(349\) 14.8272i 0.793681i −0.917888 0.396841i \(-0.870107\pi\)
0.917888 0.396841i \(-0.129893\pi\)
\(350\) 0 0
\(351\) −8.90140 7.61605i −0.475122 0.406515i
\(352\) 3.52862 + 13.1690i 0.188076 + 0.701909i
\(353\) 10.3213 + 2.76558i 0.549346 + 0.147197i 0.522807 0.852451i \(-0.324885\pi\)
0.0265388 + 0.999648i \(0.491551\pi\)
\(354\) 2.88956 + 2.74370i 0.153578 + 0.145826i
\(355\) 17.5959 12.9724i 0.933895 0.688506i
\(356\) 23.0766i 1.22306i
\(357\) 0 0
\(358\) 4.59428 + 4.59428i 0.242815 + 0.242815i
\(359\) 3.04752 5.27846i 0.160842 0.278587i −0.774329 0.632783i \(-0.781912\pi\)
0.935171 + 0.354197i \(0.115246\pi\)
\(360\) 9.49570 + 0.936819i 0.500467 + 0.0493747i
\(361\) 17.4885 + 30.2910i 0.920448 + 1.59426i
\(362\) −4.23919 + 1.13589i −0.222807 + 0.0597009i
\(363\) 0.392893 0.723114i 0.0206215 0.0379536i
\(364\) 0 0
\(365\) 14.1551 5.54710i 0.740913 0.290348i
\(366\) −0.273070 + 1.13595i −0.0142736 + 0.0593773i
\(367\) 4.81870 + 1.29117i 0.251534 + 0.0673984i 0.382383 0.924004i \(-0.375104\pi\)
−0.130849 + 0.991402i \(0.541770\pi\)
\(368\) 9.69660 + 2.59820i 0.505470 + 0.135440i
\(369\) 0.216199 + 4.17208i 0.0112549 + 0.217190i
\(370\) 2.75663 6.30942i 0.143310 0.328011i
\(371\) 0 0
\(372\) −2.61796 1.42243i −0.135735 0.0737496i
\(373\) 9.65902 2.58813i 0.500125 0.134008i 6.70928e−5 1.00000i \(-0.499979\pi\)
0.500058 + 0.865992i \(0.333312\pi\)
\(374\) −0.124033 0.214832i −0.00641360 0.0111087i
\(375\) −18.1171 + 6.83891i −0.935563 + 0.353160i
\(376\) 0.655120 1.13470i 0.0337852 0.0585177i
\(377\) 15.1316 + 15.1316i 0.779315 + 0.779315i
\(378\) 0 0
\(379\) 21.4715i 1.10292i 0.834202 + 0.551459i \(0.185929\pi\)
−0.834202 + 0.551459i \(0.814071\pi\)
\(380\) −18.1765 24.6548i −0.932436 1.26476i
\(381\) 3.17391 3.34264i 0.162604 0.171249i
\(382\) 6.32299 + 1.69424i 0.323513 + 0.0866849i
\(383\) 5.36443 + 20.0203i 0.274110 + 1.02299i 0.956436 + 0.291943i \(0.0943018\pi\)
−0.682326 + 0.731048i \(0.739032\pi\)
\(384\) −4.84748 16.3824i −0.247372 0.836012i
\(385\) 0 0
\(386\) 7.46402i 0.379909i
\(387\) 2.72432 + 2.45588i 0.138485 + 0.124840i
\(388\) −4.58156 + 17.0986i −0.232593 + 0.868050i
\(389\) −6.81615 11.8059i −0.345592 0.598583i 0.639869 0.768484i \(-0.278989\pi\)
−0.985461 + 0.169901i \(0.945655\pi\)
\(390\) 0.440752 + 3.18352i 0.0223183 + 0.161204i
\(391\) −0.623074 −0.0315102
\(392\) 0 0
\(393\) 13.6528 + 7.41804i 0.688692 + 0.374190i
\(394\) 1.85129 + 1.06884i 0.0932667 + 0.0538476i
\(395\) −0.851612 7.59329i −0.0428492 0.382060i
\(396\) −8.61220 + 16.8780i −0.432780 + 0.848149i
\(397\) 8.99077 + 33.5540i 0.451234 + 1.68403i 0.698931 + 0.715189i \(0.253660\pi\)
−0.247697 + 0.968838i \(0.579674\pi\)
\(398\) 3.49137 3.49137i 0.175007 0.175007i
\(399\) 0 0
\(400\) 10.8894 + 11.7602i 0.544472 + 0.588011i
\(401\) 13.4243 + 7.75055i 0.670380 + 0.387044i 0.796221 0.605006i \(-0.206829\pi\)
−0.125841 + 0.992050i \(0.540163\pi\)
\(402\) −0.734991 + 0.0190310i −0.0366580 + 0.000949180i
\(403\) 0.538342 2.00912i 0.0268167 0.100081i
\(404\) −11.6088 + 20.1071i −0.577561 + 1.00036i
\(405\) 13.5524 + 14.8772i 0.673426 + 0.739255i
\(406\) 0 0
\(407\) 20.0390 + 20.0390i 0.993296 + 0.993296i
\(408\) 0.255990 + 0.418013i 0.0126734 + 0.0206947i
\(409\) 27.7487 16.0207i 1.37208 0.792172i 0.380893 0.924619i \(-0.375617\pi\)
0.991190 + 0.132447i \(0.0422834\pi\)
\(410\) 0.715048 0.895699i 0.0353137 0.0442354i
\(411\) −3.71873 + 15.4697i −0.183431 + 0.763062i
\(412\) 18.2523 18.2523i 0.899226 0.899226i
\(413\) 0 0
\(414\) −1.88167 2.90124i −0.0924792 0.142588i
\(415\) 19.6017 + 2.96477i 0.962210 + 0.145535i
\(416\) 7.85809 4.53687i 0.385275 0.222438i
\(417\) 0.0824543 + 3.18444i 0.00403780 + 0.155943i
\(418\) −8.84820 + 2.37087i −0.432780 + 0.115963i
\(419\) 5.95062 0.290707 0.145353 0.989380i \(-0.453568\pi\)
0.145353 + 0.989380i \(0.453568\pi\)
\(420\) 0 0
\(421\) −10.6388 −0.518504 −0.259252 0.965810i \(-0.583476\pi\)
−0.259252 + 0.965810i \(0.583476\pi\)
\(422\) −2.88518 + 0.773083i −0.140449 + 0.0376331i
\(423\) 2.62867 0.852406i 0.127810 0.0414454i
\(424\) −11.3951 + 6.57898i −0.553396 + 0.319504i
\(425\) −0.841768 0.530124i −0.0408318 0.0257148i
\(426\) 1.76842 + 5.97650i 0.0856801 + 0.289563i
\(427\) 0 0
\(428\) 9.73032 9.73032i 0.470333 0.470333i
\(429\) −12.8617 3.09180i −0.620968 0.149273i
\(430\) −0.112151 0.999981i −0.00540840 0.0482234i
\(431\) −9.76349 + 5.63695i −0.470291 + 0.271523i −0.716361 0.697729i \(-0.754194\pi\)
0.246071 + 0.969252i \(0.420860\pi\)
\(432\) 7.18394 15.0274i 0.345637 0.723008i
\(433\) −9.75098 9.75098i −0.468602 0.468602i 0.432859 0.901462i \(-0.357505\pi\)
−0.901462 + 0.432859i \(0.857505\pi\)
\(434\) 0 0
\(435\) −22.5728 29.0145i −1.08228 1.39114i
\(436\) −6.22436 + 10.7809i −0.298093 + 0.516312i
\(437\) −5.95496 + 22.2242i −0.284865 + 1.06313i
\(438\) 0.112195 + 4.33305i 0.00536088 + 0.207041i
\(439\) 24.6276 + 14.2188i 1.17541 + 0.678625i 0.954949 0.296770i \(-0.0959096\pi\)
0.220464 + 0.975395i \(0.429243\pi\)
\(440\) 10.0315 3.93113i 0.478233 0.187409i
\(441\) 0 0
\(442\) −0.116743 + 0.116743i −0.00555290 + 0.00555290i
\(443\) −7.03213 26.2443i −0.334106 1.24690i −0.904835 0.425763i \(-0.860006\pi\)
0.570728 0.821139i \(-0.306661\pi\)
\(444\) −19.5922 18.6032i −0.929804 0.882868i
\(445\) 27.5026 3.08451i 1.30375 0.146220i
\(446\) −5.20351 3.00425i −0.246393 0.142255i
\(447\) 0.816347 1.50247i 0.0386119 0.0710646i
\(448\) 0 0
\(449\) −2.40628 −0.113559 −0.0567796 0.998387i \(-0.518083\pi\)
−0.0567796 + 0.998387i \(0.518083\pi\)
\(450\) −0.0736894 5.52053i −0.00347375 0.260240i
\(451\) 2.35865 + 4.08529i 0.111064 + 0.192369i
\(452\) 5.61975 20.9732i 0.264331 0.986496i
\(453\) 7.87949 + 12.8666i 0.370211 + 0.604527i
\(454\) 3.66752i 0.172125i
\(455\) 0 0
\(456\) 17.3566 5.13572i 0.812796 0.240502i
\(457\) 2.27517 + 8.49105i 0.106428 + 0.397194i 0.998503 0.0546923i \(-0.0174178\pi\)
−0.892075 + 0.451887i \(0.850751\pi\)
\(458\) −1.70694 0.457373i −0.0797601 0.0213716i
\(459\) −0.189291 + 1.01634i −0.00883535 + 0.0474386i
\(460\) 1.95262 12.9098i 0.0910414 0.601924i
\(461\) 35.4227i 1.64980i −0.565278 0.824900i \(-0.691231\pi\)
0.565278 0.824900i \(-0.308769\pi\)
\(462\) 0 0
\(463\) −20.0869 20.0869i −0.933519 0.933519i 0.0644045 0.997924i \(-0.479485\pi\)
−0.997924 + 0.0644045i \(0.979485\pi\)
\(464\) −15.2128 + 26.3493i −0.706236 + 1.22324i
\(465\) −1.34532 + 3.31021i −0.0623878 + 0.153507i
\(466\) −3.71632 6.43686i −0.172155 0.298182i
\(467\) −7.93069 + 2.12502i −0.366989 + 0.0983343i −0.437600 0.899170i \(-0.644172\pi\)
0.0706117 + 0.997504i \(0.477505\pi\)
\(468\) 12.3338 + 2.62918i 0.570130 + 0.121534i
\(469\) 0 0
\(470\) −0.694711 0.303524i −0.0320446 0.0140005i
\(471\) 12.5347 + 3.01320i 0.577569 + 0.138841i
\(472\) −8.58756 2.30103i −0.395275 0.105914i
\(473\) 4.00051 + 1.07193i 0.183944 + 0.0492876i
\(474\) 2.11811 + 0.509170i 0.0972881 + 0.0233870i
\(475\) −26.9540 + 24.9582i −1.23673 + 1.14516i
\(476\) 0 0
\(477\) −27.1416 5.78575i −1.24273 0.264911i
\(478\) −4.57271 + 1.22525i −0.209151 + 0.0560418i
\(479\) 20.1914 + 34.9726i 0.922571 + 1.59794i 0.795422 + 0.606056i \(0.207249\pi\)
0.127149 + 0.991884i \(0.459417\pi\)
\(480\) −14.3608 + 6.06103i −0.655477 + 0.276647i
\(481\) 9.43060 16.3343i 0.429998 0.744779i
\(482\) 4.21252 + 4.21252i 0.191875 + 0.191875i
\(483\) 0 0
\(484\) 0.885900i 0.0402682i
\(485\) 20.9904 + 3.17482i 0.953127 + 0.144161i
\(486\) −5.30407 + 2.18792i −0.240597 + 0.0992462i
\(487\) −27.0450 7.24668i −1.22552 0.328378i −0.412690 0.910872i \(-0.635411\pi\)
−0.812835 + 0.582493i \(0.802077\pi\)
\(488\) −0.674670 2.51790i −0.0305409 0.113980i
\(489\) −33.2385 + 9.83510i −1.50310 + 0.444759i
\(490\) 0 0
\(491\) 36.6924i 1.65590i 0.560798 + 0.827952i \(0.310494\pi\)
−0.560798 + 0.827952i \(0.689506\pi\)
\(492\) −2.34866 3.83519i −0.105886 0.172904i
\(493\) 0.488764 1.82409i 0.0220128 0.0821530i
\(494\) 3.04831 + 5.27983i 0.137150 + 0.237551i
\(495\) 21.2662 + 8.00803i 0.955846 + 0.359934i
\(496\) 2.95735 0.132789
\(497\) 0 0
\(498\) −2.69840 + 4.96636i −0.120918 + 0.222548i
\(499\) 6.60386 + 3.81274i 0.295629 + 0.170682i 0.640478 0.767977i \(-0.278736\pi\)
−0.344849 + 0.938658i \(0.612070\pi\)
\(500\) 13.6219 15.7797i 0.609191 0.705692i
\(501\) −31.0633 29.4953i −1.38781 1.31775i
\(502\) −0.764830 2.85438i −0.0341360 0.127397i
\(503\) 15.7533 15.7533i 0.702406 0.702406i −0.262521 0.964926i \(-0.584554\pi\)
0.964926 + 0.262521i \(0.0845538\pi\)
\(504\) 0 0
\(505\) 25.5152 + 11.1478i 1.13541 + 0.496070i
\(506\) −3.38155 1.95234i −0.150328 0.0867921i
\(507\) −0.354943 13.7082i −0.0157636 0.608801i
\(508\) −1.28426 + 4.79292i −0.0569798 + 0.212651i
\(509\) 7.20456 12.4787i 0.319336 0.553107i −0.661013 0.750374i \(-0.729873\pi\)
0.980350 + 0.197267i \(0.0632067\pi\)
\(510\) 0.223852 0.174154i 0.00991235 0.00771166i
\(511\) 0 0
\(512\) 15.5706 + 15.5706i 0.688130 + 0.688130i
\(513\) 34.4423 + 16.4653i 1.52067 + 0.726961i
\(514\) 7.48797 4.32318i 0.330280 0.190687i
\(515\) −24.1927 19.3134i −1.06606 0.851049i
\(516\) −3.83904 0.922862i −0.169005 0.0406267i
\(517\) 2.20643 2.20643i 0.0970387 0.0970387i
\(518\) 0 0
\(519\) −7.55938 25.5475i −0.331820 1.12141i
\(520\) −4.25519 5.77178i −0.186602 0.253109i
\(521\) −21.9841 + 12.6925i −0.963140 + 0.556069i −0.897138 0.441750i \(-0.854358\pi\)
−0.0660022 + 0.997819i \(0.521024\pi\)
\(522\) 9.96965 3.23288i 0.436360 0.141499i
\(523\) −21.9198 + 5.87340i −0.958486 + 0.256826i −0.703960 0.710240i \(-0.748586\pi\)
−0.254527 + 0.967066i \(0.581920\pi\)
\(524\) −16.7263 −0.730692
\(525\) 0 0
\(526\) 7.20208 0.314026
\(527\) −0.177300 + 0.0475075i −0.00772333 + 0.00206946i
\(528\) −0.486822 18.8014i −0.0211862 0.818228i
\(529\) 11.4251 6.59627i 0.496742 0.286794i
\(530\) 4.51783 + 6.12803i 0.196242 + 0.266184i
\(531\) −10.2033 15.7318i −0.442785 0.682704i
\(532\) 0 0
\(533\) 2.22002 2.22002i 0.0961595 0.0961595i
\(534\) −1.84420 + 7.67173i −0.0798062 + 0.331988i
\(535\) −12.8972 10.2960i −0.557593 0.445134i
\(536\) 1.42067 0.820225i 0.0613637 0.0354283i
\(537\) −15.9677 26.0741i −0.689058 1.12518i
\(538\) 2.98346 + 2.98346i 0.128626 + 0.128626i
\(539\) 0 0
\(540\) −20.4649 7.10708i −0.880668 0.305840i
\(541\) 13.4713 23.3330i 0.579178 1.00316i −0.416396 0.909183i \(-0.636707\pi\)
0.995574 0.0939817i \(-0.0299595\pi\)
\(542\) −0.802377 + 2.99451i −0.0344650 + 0.128625i
\(543\) 20.6455 0.534571i 0.885985 0.0229407i
\(544\) −0.693459 0.400369i −0.0297318 0.0171657i
\(545\) 13.6806 + 5.97716i 0.586013 + 0.256033i
\(546\) 0 0
\(547\) 17.9286 17.9286i 0.766572 0.766572i −0.210929 0.977501i \(-0.567649\pi\)
0.977501 + 0.210929i \(0.0676489\pi\)
\(548\) −4.43286 16.5437i −0.189362 0.706710i
\(549\) 2.49884 4.89715i 0.106648 0.209005i
\(550\) −2.90736 5.51469i −0.123970 0.235147i
\(551\) −60.3917 34.8671i −2.57277 1.48539i
\(552\) 6.77942 + 3.68350i 0.288551 + 0.156780i
\(553\) 0 0
\(554\) 6.62667 0.281540
\(555\) −19.5525 + 25.8365i −0.829956 + 1.09670i
\(556\) −1.71458 2.96973i −0.0727142 0.125945i
\(557\) −1.88849 + 7.04793i −0.0800177 + 0.298630i −0.994324 0.106393i \(-0.966070\pi\)
0.914306 + 0.405023i \(0.132737\pi\)
\(558\) −0.756656 0.682099i −0.0320318 0.0288756i
\(559\) 2.75645i 0.116585i
\(560\) 0 0
\(561\) 0.331217 + 1.11937i 0.0139840 + 0.0472600i
\(562\) −0.420349 1.56876i −0.0177313 0.0661743i
\(563\) −31.7666 8.51184i −1.33880 0.358731i −0.482813 0.875723i \(-0.660385\pi\)
−0.855990 + 0.516992i \(0.827052\pi\)
\(564\) −2.04834 + 2.15723i −0.0862506 + 0.0908359i
\(565\) −25.7470 3.89425i −1.08318 0.163832i
\(566\) 1.07877i 0.0453442i
\(567\) 0 0
\(568\) −9.83316 9.83316i −0.412590 0.412590i
\(569\) 22.5957 39.1369i 0.947260 1.64070i 0.196098 0.980584i \(-0.437173\pi\)
0.751162 0.660118i \(-0.229494\pi\)
\(570\) −4.07239 9.64898i −0.170574 0.404151i
\(571\) −7.62340 13.2041i −0.319029 0.552575i 0.661256 0.750160i \(-0.270024\pi\)
−0.980286 + 0.197585i \(0.936690\pi\)
\(572\) 13.7546 3.68554i 0.575109 0.154100i
\(573\) −27.0671 14.7065i −1.13074 0.614372i
\(574\) 0 0
\(575\) −15.6469 0.601553i −0.652520 0.0250865i
\(576\) 0.765346 + 14.7692i 0.0318894 + 0.615383i
\(577\) −8.36250 2.24072i −0.348135 0.0932826i 0.0805142 0.996753i \(-0.474344\pi\)
−0.428649 + 0.903471i \(0.641010\pi\)
\(578\) −6.02987 1.61570i −0.250810 0.0672042i
\(579\) 8.20957 34.1512i 0.341178 1.41928i
\(580\) 36.2627 + 15.8434i 1.50573 + 0.657862i
\(581\) 0 0
\(582\) −2.88958 + 5.31822i −0.119777 + 0.220447i
\(583\) −30.2682 + 8.11035i −1.25358 + 0.335896i
\(584\) −4.83554 8.37540i −0.200096 0.346576i
\(585\) 1.48487 15.0508i 0.0613918 0.622275i
\(586\) 1.91969 3.32500i 0.0793016 0.137354i
\(587\) 3.77086 + 3.77086i 0.155640 + 0.155640i 0.780632 0.624992i \(-0.214898\pi\)
−0.624992 + 0.780632i \(0.714898\pi\)
\(588\) 0 0
\(589\) 6.77812i 0.279288i
\(590\) −0.769309 + 5.08631i −0.0316720 + 0.209400i
\(591\) −7.29489 6.92665i −0.300071 0.284924i
\(592\) 25.9032 + 6.94074i 1.06461 + 0.285262i
\(593\) 3.06735 + 11.4475i 0.125961 + 0.470093i 0.999872 0.0159927i \(-0.00509085\pi\)
−0.873911 + 0.486086i \(0.838424\pi\)
\(594\) −4.21191 + 4.92275i −0.172817 + 0.201983i
\(595\) 0 0
\(596\) 1.84071i 0.0753985i
\(597\) −19.8147 + 12.1345i −0.810962 + 0.496632i
\(598\) −0.672604 + 2.51019i −0.0275048 + 0.102649i
\(599\) 3.37794 + 5.85076i 0.138019 + 0.239056i 0.926747 0.375687i \(-0.122593\pi\)
−0.788728 + 0.614743i \(0.789260\pi\)
\(600\) 6.02495 + 10.7445i 0.245968 + 0.438640i
\(601\) −21.2564 −0.867068 −0.433534 0.901137i \(-0.642734\pi\)
−0.433534 + 0.901137i \(0.642734\pi\)
\(602\) 0 0
\(603\) 3.38385 + 0.721331i 0.137801 + 0.0293749i
\(604\) −14.0656 8.12080i −0.572322 0.330431i
\(605\) 1.05581 0.118413i 0.0429249 0.00481416i
\(606\) −5.46619 + 5.75678i −0.222049 + 0.233853i
\(607\) −0.997386 3.72230i −0.0404827 0.151083i 0.942726 0.333568i \(-0.108253\pi\)
−0.983209 + 0.182485i \(0.941586\pi\)
\(608\) −20.9083 + 20.9083i −0.847944 + 0.847944i
\(609\) 0 0
\(610\) −1.40431 + 0.550318i −0.0568588 + 0.0222817i
\(611\) −1.79852 1.03837i −0.0727602 0.0420081i
\(612\) −0.343281 1.05862i −0.0138763 0.0427921i
\(613\) 5.71850 21.3417i 0.230968 0.861985i −0.748957 0.662619i \(-0.769445\pi\)
0.979925 0.199366i \(-0.0638884\pi\)
\(614\) 2.95680 5.12133i 0.119327 0.206680i
\(615\) −4.25683 + 3.31175i −0.171652 + 0.133543i
\(616\) 0 0
\(617\) 5.47009 + 5.47009i 0.220218 + 0.220218i 0.808590 0.588373i \(-0.200231\pi\)
−0.588373 + 0.808590i \(0.700231\pi\)
\(618\) 7.52656 4.60925i 0.302763 0.185411i
\(619\) −37.2349 + 21.4976i −1.49660 + 0.864060i −0.999992 0.00391818i \(-0.998753\pi\)
−0.496603 + 0.867978i \(0.665419\pi\)
\(620\) −0.428702 3.82247i −0.0172171 0.153514i
\(621\) 5.41847 + 15.3441i 0.217436 + 0.615738i
\(622\) 2.32751 2.32751i 0.0933247 0.0933247i
\(623\) 0 0
\(624\) −12.0030 + 3.55162i −0.480504 + 0.142179i
\(625\) −20.6270 14.1254i −0.825080 0.565015i
\(626\) −2.03970 + 1.17762i −0.0815227 + 0.0470672i
\(627\) 43.0922 1.11578i 1.72094 0.0445599i
\(628\) −13.4050 + 3.59185i −0.534916 + 0.143330i
\(629\) −1.66446 −0.0663664
\(630\) 0 0
\(631\) −38.0091 −1.51312 −0.756560 0.653925i \(-0.773121\pi\)
−0.756560 + 0.653925i \(0.773121\pi\)
\(632\) −4.69491 + 1.25800i −0.186754 + 0.0500405i
\(633\) 14.0513 0.363828i 0.558490 0.0144609i
\(634\) −0.804448 + 0.464448i −0.0319487 + 0.0184456i
\(635\) 5.88384 + 0.889936i 0.233493 + 0.0353160i
\(636\) 28.6463 8.47629i 1.13590 0.336107i
\(637\) 0 0
\(638\) 8.36823 8.36823i 0.331301 0.331301i
\(639\) −1.51783 29.2902i −0.0600445 1.15870i
\(640\) 13.7606 17.2371i 0.543935 0.681355i
\(641\) −26.6744 + 15.4005i −1.05357 + 0.608282i −0.923648 0.383242i \(-0.874808\pi\)
−0.129927 + 0.991524i \(0.541474\pi\)
\(642\) 4.01242 2.45720i 0.158357 0.0969778i
\(643\) 6.17366 + 6.17366i 0.243465 + 0.243465i 0.818282 0.574817i \(-0.194927\pi\)
−0.574817 + 0.818282i \(0.694927\pi\)
\(644\) 0 0
\(645\) −0.586724 + 4.69871i −0.0231022 + 0.185012i
\(646\) 0.269007 0.465934i 0.0105839 0.0183319i
\(647\) 8.57582 32.0054i 0.337150 1.25826i −0.564369 0.825523i \(-0.690880\pi\)
0.901519 0.432739i \(-0.142453\pi\)
\(648\) 8.06800 9.93932i 0.316941 0.390453i
\(649\) −18.3363 10.5865i −0.719762 0.415555i
\(650\) −3.04441 + 2.81899i −0.119412 + 0.110570i
\(651\) 0 0
\(652\) 26.3851 26.3851i 1.03332 1.03332i
\(653\) 6.29299 + 23.4857i 0.246264 + 0.919068i 0.972744 + 0.231881i \(0.0744881\pi\)
−0.726481 + 0.687187i \(0.758845\pi\)
\(654\) −2.93083 + 3.08664i −0.114605 + 0.120697i
\(655\) 2.23570 + 19.9343i 0.0873560 + 0.778899i
\(656\) 3.86582 + 2.23193i 0.150935 + 0.0871423i
\(657\) 4.25252 19.9490i 0.165906 0.778286i
\(658\) 0 0
\(659\) 0.0375362 0.00146220 0.000731101 1.00000i \(-0.499767\pi\)
0.000731101 1.00000i \(0.499767\pi\)
\(660\) −24.2309 + 3.35472i −0.943188 + 0.130582i
\(661\) 9.84684 + 17.0552i 0.382998 + 0.663371i 0.991489 0.130189i \(-0.0415584\pi\)
−0.608492 + 0.793560i \(0.708225\pi\)
\(662\) −0.344716 + 1.28650i −0.0133978 + 0.0500011i
\(663\) 0.662556 0.405748i 0.0257315 0.0157579i
\(664\) 12.6109i 0.489396i
\(665\) 0 0
\(666\) −5.02664 7.75029i −0.194778 0.300318i
\(667\) −7.69337 28.7120i −0.297888 1.11173i
\(668\) 44.5408 + 11.9347i 1.72334 + 0.461766i
\(669\) 20.5041 + 19.4691i 0.792733 + 0.752717i
\(670\) −0.563254 0.764003i −0.0217604 0.0295160i
\(671\) 6.20798i 0.239656i
\(672\) 0 0
\(673\) −4.33276 4.33276i −0.167016 0.167016i 0.618651 0.785666i \(-0.287680\pi\)
−0.785666 + 0.618651i \(0.787680\pi\)
\(674\) 4.44897 7.70584i 0.171368 0.296818i
\(675\) −5.73478 + 25.3399i −0.220732 + 0.975335i
\(676\) 7.38079 + 12.7839i 0.283877 + 0.491689i
\(677\) 4.98104 1.33467i 0.191437 0.0512954i −0.161827 0.986819i \(-0.551739\pi\)
0.353264 + 0.935524i \(0.385072\pi\)
\(678\) 3.54436 6.52335i 0.136120 0.250528i
\(679\) 0 0
\(680\) −0.253352 + 0.579876i −0.00971559 + 0.0222372i
\(681\) 4.03385 16.7805i 0.154577 0.643031i
\(682\) −1.11111 0.297720i −0.0425465 0.0114003i
\(683\) 46.1083 + 12.3547i 1.76429 + 0.472739i 0.987579 0.157122i \(-0.0502217\pi\)
0.776708 + 0.629861i \(0.216888\pi\)
\(684\) −41.0404 + 2.12673i −1.56922 + 0.0813176i
\(685\) −19.1242 + 7.49436i −0.730697 + 0.286345i
\(686\) 0 0
\(687\) 7.30696 + 3.97013i 0.278778 + 0.151470i
\(688\) 3.78559 1.01435i 0.144324 0.0386716i
\(689\) 10.4278 + 18.0614i 0.397267 + 0.688086i
\(690\) 1.68084 4.13577i 0.0639887 0.157446i
\(691\) −6.10922 + 10.5815i −0.232406 + 0.402539i −0.958516 0.285040i \(-0.907993\pi\)
0.726110 + 0.687579i \(0.241326\pi\)
\(692\) 20.2799 + 20.2799i 0.770928 + 0.770928i
\(693\) 0 0
\(694\) 2.85547i 0.108392i
\(695\) −3.31014 + 2.44037i −0.125561 + 0.0925686i
\(696\) −16.1017 + 16.9577i −0.610335 + 0.642782i
\(697\) −0.267620 0.0717086i −0.0101368 0.00271616i
\(698\) 1.41248 + 5.27145i 0.0534632 + 0.199527i
\(699\) 9.92404 + 33.5391i 0.375362 + 1.26856i
\(700\) 0 0
\(701\) 21.7907i 0.823024i −0.911404 0.411512i \(-0.865001\pi\)
0.911404 0.411512i \(-0.134999\pi\)
\(702\) 3.89021 + 1.85973i 0.146826 + 0.0701911i
\(703\) −15.9079 + 59.3691i −0.599978 + 2.23915i
\(704\) 8.34962 + 14.4620i 0.314688 + 0.545056i
\(705\) 2.84477 + 2.15286i 0.107140 + 0.0810814i
\(706\) −3.93294 −0.148018
\(707\) 0 0
\(708\) 17.7362 + 9.63670i 0.666567 + 0.362169i
\(709\) 12.2649 + 7.08112i 0.460617 + 0.265937i 0.712304 0.701872i \(-0.247652\pi\)
−0.251687 + 0.967809i \(0.580985\pi\)
\(710\) −5.02002 + 6.28828i −0.188398 + 0.235995i
\(711\) −9.13129 4.65936i −0.342450 0.174740i
\(712\) −4.55642 17.0048i −0.170759 0.637282i
\(713\) −2.04300 + 2.04300i −0.0765110 + 0.0765110i
\(714\) 0 0
\(715\) −6.23090 15.9001i −0.233023 0.594629i
\(716\) 28.5039 + 16.4567i 1.06524 + 0.615016i
\(717\) 22.2698 0.576629i 0.831683 0.0215346i
\(718\) −0.580632 + 2.16695i −0.0216690 + 0.0808698i
\(719\) −19.6576 + 34.0480i −0.733106 + 1.26978i 0.222443 + 0.974946i \(0.428597\pi\)
−0.955549 + 0.294831i \(0.904737\pi\)
\(720\) 21.2166 3.49929i 0.790695 0.130411i
\(721\) 0 0
\(722\) −9.10324 9.10324i −0.338787 0.338787i
\(723\) −14.6409 23.9075i −0.544500 0.889128i
\(724\) −19.2535 + 11.1160i −0.715551 + 0.413124i
\(725\) 14.0351 45.3354i 0.521251 1.68372i
\(726\) −0.0707978 + 0.294514i −0.00262755 + 0.0109304i
\(727\) −10.0141 + 10.0141i −0.371403 + 0.371403i −0.867988 0.496585i \(-0.834587\pi\)
0.496585 + 0.867988i \(0.334587\pi\)
\(728\) 0 0
\(729\) 26.6750 4.17686i 0.987962 0.154699i
\(730\) −4.50409 + 3.32060i −0.166704 + 0.122901i
\(731\) −0.210661 + 0.121625i −0.00779159 + 0.00449848i
\(732\) 0.153191 + 5.91636i 0.00566212 + 0.218675i
\(733\) −41.7644 + 11.1907i −1.54260 + 0.413339i −0.927106 0.374799i \(-0.877712\pi\)
−0.615498 + 0.788139i \(0.711045\pi\)
\(734\) −1.83618 −0.0677745
\(735\) 0 0
\(736\) −12.6040 −0.464589
\(737\) 3.77365 1.01115i 0.139004 0.0372461i
\(738\) −0.474309 1.46269i −0.0174596 0.0538423i
\(739\) 13.9513 8.05476i 0.513205 0.296299i −0.220945 0.975286i \(-0.570914\pi\)
0.734150 + 0.678987i \(0.237581\pi\)
\(740\) 5.21617 34.4869i 0.191750 1.26776i
\(741\) −8.14019 27.5104i −0.299037 1.01062i
\(742\) 0 0
\(743\) 23.1679 23.1679i 0.849946 0.849946i −0.140180 0.990126i \(-0.544768\pi\)
0.990126 + 0.140180i \(0.0447681\pi\)
\(744\) 2.20999 + 0.531257i 0.0810222 + 0.0194768i
\(745\) 2.19375 0.246036i 0.0803729 0.00901407i
\(746\) −3.18748 + 1.84029i −0.116702 + 0.0673780i
\(747\) 17.8088 19.7554i 0.651591 0.722813i
\(748\) −0.888574 0.888574i −0.0324895 0.0324895i
\(749\) 0 0
\(750\) 5.78961 4.15730i 0.211407 0.151803i
\(751\) −14.3770 + 24.9017i −0.524625 + 0.908677i 0.474964 + 0.880005i \(0.342461\pi\)
−0.999589 + 0.0286715i \(0.990872\pi\)
\(752\) 0.764222 2.85212i 0.0278683 0.104006i
\(753\) 0.359944 + 13.9013i 0.0131171 + 0.506592i
\(754\) −6.82115 3.93819i −0.248412 0.143420i
\(755\) −7.79827 + 17.8488i −0.283808 + 0.649585i
\(756\) 0 0
\(757\) −1.29026 + 1.29026i −0.0468952 + 0.0468952i −0.730166 0.683270i \(-0.760557\pi\)
0.683270 + 0.730166i \(0.260557\pi\)
\(758\) −2.04544 7.63369i −0.0742938 0.277268i
\(759\) 13.3248 + 12.6521i 0.483658 + 0.459244i
\(760\) 18.2620 + 14.5788i 0.662433 + 0.528829i
\(761\) 29.4421 + 16.9984i 1.06728 + 0.616193i 0.927436 0.373981i \(-0.122008\pi\)
0.139841 + 0.990174i \(0.455341\pi\)
\(762\) −0.809978 + 1.49075i −0.0293424 + 0.0540043i
\(763\) 0 0
\(764\) 33.1604 1.19970
\(765\) −1.21577 + 0.550620i −0.0439564 + 0.0199077i
\(766\) −3.81439 6.60672i −0.137820 0.238711i
\(767\) −3.64716 + 13.6114i −0.131691 + 0.491479i
\(768\) −5.63434 9.20045i −0.203312 0.331993i
\(769\) 21.4206i 0.772448i 0.922405 + 0.386224i \(0.126221\pi\)
−0.922405 + 0.386224i \(0.873779\pi\)
\(770\) 0 0
\(771\) −39.0158 + 11.5446i −1.40512 + 0.415768i
\(772\) 9.78610 + 36.5222i 0.352209 + 1.31446i
\(773\) 12.9845 + 3.47919i 0.467021 + 0.125138i 0.484653 0.874707i \(-0.338946\pi\)
−0.0176318 + 0.999845i \(0.505613\pi\)
\(774\) −1.20252 0.613604i −0.0432238 0.0220555i
\(775\) −4.49831 + 1.02185i −0.161584 + 0.0367060i
\(776\) 13.5043i 0.484777i
\(777\) 0 0
\(778\) 3.54798 + 3.54798i 0.127201 + 0.127201i
\(779\) −5.11550 + 8.86031i −0.183282 + 0.317454i
\(780\) 6.33057 + 14.9994i 0.226671 + 0.537066i
\(781\) −16.5590 28.6810i −0.592526 1.02629i
\(782\) 0.221519 0.0593559i 0.00792151 0.00212256i
\(783\) −49.1714 + 3.82640i −1.75724 + 0.136745i
\(784\) 0 0
\(785\) 6.07251 + 15.4959i 0.216737 + 0.553072i
\(786\) −5.56059 1.33670i −0.198340 0.0476786i
\(787\) 7.79736 + 2.08930i 0.277946 + 0.0744754i 0.395099 0.918638i \(-0.370710\pi\)
−0.117153 + 0.993114i \(0.537377\pi\)
\(788\) 10.4599 + 2.80273i 0.372619 + 0.0998431i
\(789\) −32.9527 7.92146i −1.17315 0.282011i
\(790\) 1.02613 + 2.61849i 0.0365081 + 0.0931616i
\(791\) 0 0
\(792\) 3.01369 14.1376i 0.107087 0.502356i
\(793\) −3.99091 + 1.06936i −0.141721 + 0.0379741i
\(794\) −6.39291 11.0728i −0.226876 0.392960i
\(795\) −13.9310 33.0076i −0.494081 1.17066i
\(796\) 12.5061 21.6612i 0.443267 0.767761i
\(797\) 7.78096 + 7.78096i 0.275616 + 0.275616i 0.831356 0.555740i \(-0.187565\pi\)
−0.555740 + 0.831356i \(0.687565\pi\)
\(798\) 0 0
\(799\) 0.183268i 0.00648357i
\(800\) −17.0279 10.7237i −0.602027 0.379141i
\(801\) 16.8760 33.0732i 0.596286 1.16858i
\(802\) −5.51105 1.47668i −0.194602 0.0521434i
\(803\) −5.96109 22.2471i −0.210362 0.785083i
\(804\) −3.57144 + 1.05677i −0.125955 + 0.0372694i
\(805\) 0 0
\(806\) 0.765579i 0.0269664i
\(807\) −10.3692 16.9321i −0.365013 0.596039i
\(808\) 4.58427 17.1087i 0.161274 0.601883i
\(809\) 14.3936 + 24.9304i 0.506051 + 0.876506i 0.999975 + 0.00700090i \(0.00222847\pi\)
−0.493925 + 0.869505i \(0.664438\pi\)
\(810\) −6.23549 3.99819i −0.219093 0.140482i
\(811\) 9.83136 0.345226 0.172613 0.984990i \(-0.444779\pi\)
0.172613 + 0.984990i \(0.444779\pi\)
\(812\) 0 0
\(813\) 6.96485 12.8187i 0.244268 0.449572i
\(814\) −9.03336 5.21542i −0.316619 0.182800i
\(815\) −34.9725 27.9190i −1.22503 0.977960i
\(816\) 0.801051 + 0.760615i 0.0280424 + 0.0266269i
\(817\) 2.32484 + 8.67644i 0.0813360 + 0.303550i
\(818\) −8.33920 + 8.33920i −0.291573 + 0.291573i
\(819\) 0 0
\(820\) 2.32445 5.32025i 0.0811734 0.185791i
\(821\) −29.9149 17.2714i −1.04404 0.602775i −0.123063 0.992399i \(-0.539272\pi\)
−0.920974 + 0.389624i \(0.872605\pi\)
\(822\) −0.151580 5.85413i −0.00528696 0.204186i
\(823\) −4.37251 + 16.3184i −0.152416 + 0.568825i 0.846896 + 0.531758i \(0.178468\pi\)
−0.999313 + 0.0370675i \(0.988198\pi\)
\(824\) −9.84596 + 17.0537i −0.343000 + 0.594094i
\(825\) 7.23695 + 28.4299i 0.251958 + 0.989804i
\(826\) 0 0
\(827\) −20.8624 20.8624i −0.725457 0.725457i 0.244254 0.969711i \(-0.421457\pi\)
−0.969711 + 0.244254i \(0.921457\pi\)
\(828\) −13.0111 11.7290i −0.452165 0.407611i
\(829\) 30.0070 17.3245i 1.04219 0.601706i 0.121734 0.992563i \(-0.461154\pi\)
0.920452 + 0.390856i \(0.127821\pi\)
\(830\) −7.25136 + 0.813262i −0.251698 + 0.0282287i
\(831\) −30.3200 7.28858i −1.05179 0.252838i
\(832\) 7.85887 7.85887i 0.272457 0.272457i
\(833\) 0 0
\(834\) −0.332674 1.12430i −0.0115196 0.0389313i
\(835\) 8.27022 54.6788i 0.286203 1.89224i
\(836\) −40.1867 + 23.2018i −1.38989 + 0.802451i
\(837\) 2.71181 + 3.95314i 0.0937339 + 0.136641i
\(838\) −2.11560 + 0.566873i −0.0730822 + 0.0195823i
\(839\) −10.9282 −0.377283 −0.188642 0.982046i \(-0.560408\pi\)
−0.188642 + 0.982046i \(0.560408\pi\)
\(840\) 0 0
\(841\) 61.0915 2.10660
\(842\) 3.78238 1.01348i 0.130349 0.0349270i
\(843\) 0.197825 + 7.64013i 0.00681344 + 0.263140i
\(844\) −13.1039 + 7.56555i −0.451055 + 0.260417i
\(845\) 14.2493 10.5051i 0.490190 0.361388i
\(846\) −0.853360 + 0.553468i −0.0293391 + 0.0190286i
\(847\) 0 0
\(848\) −20.9675 + 20.9675i −0.720027 + 0.720027i
\(849\) −1.18653 + 4.93587i −0.0407215 + 0.169399i
\(850\) 0.349772 + 0.108284i 0.0119971 + 0.00371410i
\(851\) −22.6893 + 13.0997i −0.777779 + 0.449051i
\(852\) 16.4889 + 26.9251i 0.564899 + 0.922438i
\(853\) 8.08267 + 8.08267i 0.276745 + 0.276745i 0.831808 0.555063i \(-0.187306\pi\)
−0.555063 + 0.831808i \(0.687306\pi\)
\(854\) 0 0
\(855\) 8.02025 + 48.6276i 0.274287 + 1.66303i
\(856\) −5.24890 + 9.09135i −0.179404 + 0.310736i
\(857\) 5.24115 19.5603i 0.179034 0.668166i −0.816795 0.576928i \(-0.804251\pi\)
0.995829 0.0912372i \(-0.0290821\pi\)
\(858\) 4.86720 0.126026i 0.166163 0.00430244i
\(859\) 21.7038 + 12.5307i 0.740525 + 0.427542i 0.822260 0.569112i \(-0.192713\pi\)
−0.0817353 + 0.996654i \(0.526046\pi\)
\(860\) −1.85984 4.74597i −0.0634202 0.161836i
\(861\) 0 0
\(862\) 2.93418 2.93418i 0.0999387 0.0999387i
\(863\) 12.0115 + 44.8273i 0.408875 + 1.52594i 0.796796 + 0.604248i \(0.206526\pi\)
−0.387922 + 0.921692i \(0.626807\pi\)
\(864\) −3.82911 + 20.5592i −0.130269 + 0.699438i
\(865\) 21.4589 26.8803i 0.729624 0.913956i
\(866\) 4.39564 + 2.53782i 0.149370 + 0.0862387i
\(867\) 25.8123 + 14.0247i 0.876631 + 0.476304i
\(868\) 0 0
\(869\) −11.5755 −0.392671
\(870\) 10.7892 + 8.16505i 0.365789 + 0.276821i
\(871\) −1.30007 2.25178i −0.0440511 0.0762988i
\(872\) 2.45797 9.17327i 0.0832374 0.310646i
\(873\) 19.0705 21.1550i 0.645440 0.715990i
\(874\) 8.46858i 0.286454i
\(875\) 0 0
\(876\) 6.23006 + 21.0550i 0.210494 + 0.711381i
\(877\) 5.59615 + 20.8851i 0.188968 + 0.705240i 0.993746 + 0.111663i \(0.0356178\pi\)
−0.804778 + 0.593576i \(0.797716\pi\)
\(878\) −10.1103 2.70904i −0.341206 0.0914258i
\(879\) −12.4406 + 13.1019i −0.419609 + 0.441917i
\(880\) 19.5436 14.4083i 0.658814 0.485705i
\(881\) 29.1988i 0.983734i −0.870670 0.491867i \(-0.836315\pi\)
0.870670 0.491867i \(-0.163685\pi\)
\(882\) 0 0
\(883\) −24.7944 24.7944i −0.834397 0.834397i 0.153718 0.988115i \(-0.450875\pi\)
−0.988115 + 0.153718i \(0.950875\pi\)
\(884\) −0.418174 + 0.724298i −0.0140647 + 0.0243608i
\(885\) 9.11430 22.4260i 0.306374 0.753842i
\(886\) 5.00021 + 8.66062i 0.167985 + 0.290959i
\(887\) 25.3441 6.79094i 0.850973 0.228018i 0.193131 0.981173i \(-0.438136\pi\)
0.657843 + 0.753156i \(0.271469\pi\)
\(888\) 18.1103 + 9.83997i 0.607743 + 0.330208i
\(889\) 0 0
\(890\) −9.48407 + 3.71661i −0.317907 + 0.124581i
\(891\) 24.6859 17.8912i 0.827007 0.599377i
\(892\) −29.4002 7.87776i −0.984392 0.263767i
\(893\) 6.53694 + 1.75157i 0.218750 + 0.0586140i
\(894\) −0.147103 + 0.611937i −0.00491985 + 0.0204662i
\(895\) 15.8031 36.1705i 0.528240 1.20905i
\(896\) 0 0
\(897\) 5.83839 10.7455i 0.194938 0.358781i
\(898\) 0.855494 0.229229i 0.0285482 0.00764947i
\(899\) −4.37842 7.58364i −0.146028 0.252928i
\(900\) −7.59855 26.9159i −0.253285 0.897196i
\(901\) 0.920228 1.59388i 0.0306572 0.0530999i
\(902\) −1.22774 1.22774i −0.0408792 0.0408792i
\(903\) 0 0
\(904\) 16.5644i 0.550925i
\(905\) 15.8215 + 21.4605i 0.525926 + 0.713370i
\(906\) −4.02708 3.82380i −0.133791 0.127037i
\(907\) −4.63366 1.24159i −0.153858 0.0412262i 0.181068 0.983471i \(-0.442045\pi\)
−0.334926 + 0.942244i \(0.608711\pi\)
\(908\) 4.80849 + 17.9455i 0.159575 + 0.595543i
\(909\) 31.3421 20.3277i 1.03955 0.674227i
\(910\) 0 0
\(911\) 16.2139i 0.537190i 0.963253 + 0.268595i \(0.0865592\pi\)
−0.963253 + 0.268595i \(0.913441\pi\)
\(912\) 34.7861 21.3029i 1.15188 0.705411i
\(913\) 7.77313 29.0097i 0.257253 0.960081i
\(914\) −1.61776 2.80205i −0.0535109 0.0926836i
\(915\) 7.03063 0.973376i 0.232425 0.0321788i
\(916\) −8.95190 −0.295779
\(917\) 0 0
\(918\) −0.0295215 0.379367i −0.000974354 0.0125210i
\(919\) 4.80348 + 2.77329i 0.158452 + 0.0914823i 0.577129 0.816653i \(-0.304173\pi\)
−0.418677 + 0.908135i \(0.637506\pi\)
\(920\) 1.11016 + 9.89859i 0.0366008 + 0.326347i
\(921\) −19.1616 + 20.1803i −0.631396 + 0.664962i
\(922\) 3.37447 + 12.5937i 0.111132 + 0.414752i
\(923\) −15.5857 + 15.5857i −0.513009 + 0.513009i
\(924\) 0 0
\(925\) −41.7986 1.60697i −1.37433 0.0528368i
\(926\) 9.05498 + 5.22789i 0.297565 + 0.171799i
\(927\) −39.5070 + 12.8110i −1.29758 + 0.420769i
\(928\) 9.88706 36.8990i 0.324559 1.21127i
\(929\) 6.39892 11.0833i 0.209942 0.363630i −0.741754 0.670672i \(-0.766006\pi\)
0.951696 + 0.307042i \(0.0993392\pi\)
\(930\) 0.162957 1.30503i 0.00534357 0.0427935i
\(931\) 0 0
\(932\) −26.6237 26.6237i −0.872090 0.872090i
\(933\) −13.2094 + 8.08941i −0.432456 + 0.264835i
\(934\) 2.61713 1.51100i 0.0856352 0.0494415i
\(935\) −0.940229 + 1.17777i −0.0307488 + 0.0385172i
\(936\) −9.60771 + 0.497876i −0.314038 + 0.0162736i
\(937\) −24.4148 + 24.4148i −0.797598 + 0.797598i −0.982716 0.185119i \(-0.940733\pi\)
0.185119 + 0.982716i \(0.440733\pi\)
\(938\) 0 0
\(939\) 10.6278 3.14471i 0.346825 0.102624i
\(940\) −3.79724 0.574336i −0.123852 0.0187328i
\(941\) 3.22540 1.86219i 0.105145 0.0607055i −0.446505 0.894781i \(-0.647332\pi\)
0.551650 + 0.834075i \(0.313998\pi\)
\(942\) −4.74347 + 0.122822i −0.154551 + 0.00400175i
\(943\) −4.21246 + 1.12873i −0.137177 + 0.0367564i
\(944\) −20.0354 −0.652098
\(945\) 0 0
\(946\) −1.52440 −0.0495626
\(947\) −46.9322 + 12.5754i −1.52509 + 0.408647i −0.921414 0.388582i \(-0.872965\pi\)
−0.603677 + 0.797229i \(0.706298\pi\)
\(948\) 11.0317 0.285642i 0.358294 0.00927723i
\(949\) −13.2751 + 7.66439i −0.430929 + 0.248797i
\(950\) 7.20525 11.4410i 0.233769 0.371195i
\(951\) 4.19155 1.24026i 0.135920 0.0402181i
\(952\) 0 0
\(953\) −21.7199 + 21.7199i −0.703578 + 0.703578i −0.965177 0.261599i \(-0.915750\pi\)
0.261599 + 0.965177i \(0.415750\pi\)
\(954\) 10.2007 0.528606i 0.330261 0.0171143i
\(955\) −4.43234 39.5204i −0.143427 1.27885i
\(956\) −20.7683 + 11.9906i −0.671695 + 0.387803i
\(957\) −47.4925 + 29.0843i −1.53521 + 0.940162i
\(958\) −10.5102 10.5102i −0.339569 0.339569i
\(959\) 0 0
\(960\) −15.0692 + 11.7236i −0.486357 + 0.378378i
\(961\) 15.0744 26.1097i 0.486272 0.842247i
\(962\) −1.79677 + 6.70565i −0.0579303 + 0.216199i
\(963\) −21.0612 + 6.82958i −0.678689 + 0.220080i
\(964\) 26.1353 + 15.0893i 0.841763 + 0.485992i
\(965\) 42.2190 16.5447i 1.35908 0.532594i
\(966\) 0 0
\(967\) −42.1187 + 42.1187i −1.35445 + 1.35445i −0.473831 + 0.880616i \(0.657129\pi\)
−0.880616 + 0.473831i \(0.842871\pi\)
\(968\) −0.174919 0.652806i −0.00562211 0.0209820i
\(969\) −1.74330 + 1.83598i −0.0560029 + 0.0589801i
\(970\) −7.76510 + 0.870880i −0.249322 + 0.0279623i
\(971\) −23.7650 13.7207i −0.762655 0.440319i 0.0675934 0.997713i \(-0.478468\pi\)
−0.830248 + 0.557394i \(0.811801\pi\)
\(972\) −23.0848 + 17.6599i −0.740444 + 0.566442i
\(973\) 0 0
\(974\) 10.3055 0.330211
\(975\) 17.0301 9.54963i 0.545400 0.305833i
\(976\) −2.93723 5.08744i −0.0940185 0.162845i
\(977\) 14.8450 55.4023i 0.474933 1.77248i −0.146715 0.989179i \(-0.546870\pi\)
0.621648 0.783297i \(-0.286463\pi\)
\(978\) 10.8802 6.66303i 0.347912 0.213060i
\(979\) 41.9259i 1.33996i
\(980\) 0 0
\(981\) 16.8048 10.8992i 0.536537 0.347984i
\(982\) −3.49543 13.0451i −0.111544 0.416286i
\(983\) 23.2674 + 6.23449i 0.742116 + 0.198849i 0.610018 0.792387i \(-0.291162\pi\)
0.132098 + 0.991237i \(0.457829\pi\)
\(984\) 2.48794 + 2.36235i 0.0793127 + 0.0753091i
\(985\) 1.94217 12.8407i 0.0618827 0.409140i
\(986\) 0.695074i 0.0221357i
\(987\) 0 0
\(988\) 21.8381 + 21.8381i 0.694763 + 0.694763i
\(989\) −1.91444 + 3.31591i −0.0608756 + 0.105440i
\(990\) −8.32357 0.821180i −0.264540 0.0260988i
\(991\) −11.2380 19.4648i −0.356986 0.618319i 0.630469 0.776214i \(-0.282862\pi\)
−0.987456 + 0.157895i \(0.949529\pi\)
\(992\) −3.58656 + 0.961016i −0.113873 + 0.0305123i
\(993\) 2.99223 5.50716i 0.0949556 0.174764i
\(994\) 0 0
\(995\) −27.4874 12.0094i −0.871408 0.380724i
\(996\) −6.69213 + 27.8388i −0.212048 + 0.882107i
\(997\) 43.4825 + 11.6511i 1.37710 + 0.368994i 0.870068 0.492931i \(-0.164074\pi\)
0.507036 + 0.861925i \(0.330741\pi\)
\(998\) −2.71106 0.726425i −0.0858170 0.0229946i
\(999\) 14.4747 + 40.9898i 0.457960 + 1.29686i
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 735.2.y.g.128.6 48
3.2 odd 2 inner 735.2.y.g.128.7 48
5.2 odd 4 inner 735.2.y.g.422.6 48
7.2 even 3 735.2.j.h.638.7 24
7.3 odd 6 735.2.y.j.263.7 48
7.4 even 3 inner 735.2.y.g.263.7 48
7.5 odd 6 105.2.j.a.8.7 yes 24
7.6 odd 2 735.2.y.j.128.6 48
15.2 even 4 inner 735.2.y.g.422.7 48
21.2 odd 6 735.2.j.h.638.6 24
21.5 even 6 105.2.j.a.8.6 24
21.11 odd 6 inner 735.2.y.g.263.6 48
21.17 even 6 735.2.y.j.263.6 48
21.20 even 2 735.2.y.j.128.7 48
35.2 odd 12 735.2.j.h.197.6 24
35.12 even 12 105.2.j.a.92.6 yes 24
35.17 even 12 735.2.y.j.557.7 48
35.19 odd 6 525.2.j.b.218.6 24
35.27 even 4 735.2.y.j.422.6 48
35.32 odd 12 inner 735.2.y.g.557.7 48
35.33 even 12 525.2.j.b.407.7 24
105.2 even 12 735.2.j.h.197.7 24
105.17 odd 12 735.2.y.j.557.6 48
105.32 even 12 inner 735.2.y.g.557.6 48
105.47 odd 12 105.2.j.a.92.7 yes 24
105.62 odd 4 735.2.y.j.422.7 48
105.68 odd 12 525.2.j.b.407.6 24
105.89 even 6 525.2.j.b.218.7 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.j.a.8.6 24 21.5 even 6
105.2.j.a.8.7 yes 24 7.5 odd 6
105.2.j.a.92.6 yes 24 35.12 even 12
105.2.j.a.92.7 yes 24 105.47 odd 12
525.2.j.b.218.6 24 35.19 odd 6
525.2.j.b.218.7 24 105.89 even 6
525.2.j.b.407.6 24 105.68 odd 12
525.2.j.b.407.7 24 35.33 even 12
735.2.j.h.197.6 24 35.2 odd 12
735.2.j.h.197.7 24 105.2 even 12
735.2.j.h.638.6 24 21.2 odd 6
735.2.j.h.638.7 24 7.2 even 3
735.2.y.g.128.6 48 1.1 even 1 trivial
735.2.y.g.128.7 48 3.2 odd 2 inner
735.2.y.g.263.6 48 21.11 odd 6 inner
735.2.y.g.263.7 48 7.4 even 3 inner
735.2.y.g.422.6 48 5.2 odd 4 inner
735.2.y.g.422.7 48 15.2 even 4 inner
735.2.y.g.557.6 48 105.32 even 12 inner
735.2.y.g.557.7 48 35.32 odd 12 inner
735.2.y.j.128.6 48 7.6 odd 2
735.2.y.j.128.7 48 21.20 even 2
735.2.y.j.263.6 48 21.17 even 6
735.2.y.j.263.7 48 7.3 odd 6
735.2.y.j.422.6 48 35.27 even 4
735.2.y.j.422.7 48 105.62 odd 4
735.2.y.j.557.6 48 105.17 odd 12
735.2.y.j.557.7 48 35.17 even 12