Properties

Label 735.2.y.g.128.7
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 128.7
Character \(\chi\) \(=\) 735.128
Dual form 735.2.y.g.557.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.355526 - 0.0952630i) q^{2} +(-1.47708 - 0.904561i) q^{3} +(-1.61473 + 0.932263i) q^{4} +(-1.32690 - 1.79982i) q^{5} +(-0.611312 - 0.180884i) q^{6} +(-1.00579 + 1.00579i) q^{8} +(1.36354 + 2.67222i) q^{9} +O(q^{10})\) \(q+(0.355526 - 0.0952630i) q^{2} +(-1.47708 - 0.904561i) 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} +(1.36354 + 2.67222i) q^{9} +(-0.643203 - 0.513478i) q^{10} +(-2.93366 + 1.69375i) q^{11} +(3.22837 + 0.0835917i) q^{12} +(-1.59420 - 1.59420i) q^{13} +(0.331892 + 3.85874i) q^{15} +(1.60275 - 2.77605i) q^{16} +(0.0514941 - 0.192179i) q^{17} +(0.739337 + 0.820150i) 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} +(2.39544 - 0.575837i) q^{24} +(-1.47868 + 4.77635i) q^{25} +(-0.718647 - 0.414911i) q^{26} +(0.403134 - 5.18049i) q^{27} +9.49165 q^{29} +(0.485591 + 1.34027i) q^{30} +(0.461291 + 0.798980i) q^{31} +(1.04166 - 3.88752i) q^{32} +(5.86535 + 0.151871i) q^{33} -0.0732300i q^{34} +(-4.69295 - 3.04373i) q^{36} +(2.16525 + 8.08083i) q^{37} +(2.61202 + 0.699888i) q^{38} +(0.912709 + 3.79681i) q^{39} +(3.14483 + 0.475658i) q^{40} -1.39256i q^{41} +(0.864526 + 0.864526i) q^{43} +(3.15804 - 5.46988i) q^{44} +(3.00023 - 5.99988i) q^{45} +(-0.576337 - 0.998245i) q^{46} +(-0.889755 + 0.238409i) q^{47} +(-4.87851 + 2.65066i) q^{48} +(-0.0707006 + 1.83898i) q^{50} +(-0.249898 + 0.237284i) q^{51} +(4.06040 + 1.08798i) q^{52} +(8.93528 + 2.39420i) q^{53} +(-0.350184 - 1.88020i) q^{54} +(6.94110 + 3.03262i) q^{55} +(-6.07522 - 11.1814i) q^{57} +(3.37453 - 0.904203i) q^{58} +(3.12516 + 5.41293i) q^{59} +(-4.13327 - 5.92140i) q^{60} +(0.916307 - 1.58709i) q^{61} +(0.240114 + 0.240114i) q^{62} +4.92967i q^{64} +(-0.753925 + 4.98460i) q^{65} +(2.09975 - 0.504757i) q^{66} +(1.11399 + 0.298494i) q^{67} +(0.0960121 + 0.358322i) q^{68} +(-1.53904 + 5.20132i) q^{69} +9.77651i q^{71} +(-4.05914 - 1.31627i) q^{72} +(1.75973 - 6.56741i) q^{73} +(1.53961 + 2.66668i) q^{74} +(6.50463 - 5.71750i) q^{75} -13.6985 q^{76} +(0.686187 + 1.26292i) q^{78} +(-2.95931 - 1.70856i) q^{79} +(-7.12308 + 0.798875i) q^{80} +(-5.28153 + 7.28735i) 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} +(-14.0199 - 8.58578i) q^{87} +(1.24709 - 4.65422i) q^{88} +(-6.18833 + 10.7185i) q^{89} +(0.495095 - 2.41893i) q^{90} +(4.12888 + 4.12888i) q^{92} +(0.0413618 - 1.59742i) q^{93} +(-0.293620 + 0.169521i) q^{94} +(-1.83099 - 16.3258i) q^{95} +(-5.05512 + 4.79994i) 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 −0.130921 0.991393i \(-0.541793\pi\)
0.382316 + 0.924032i \(0.375127\pi\)
\(3\) −1.47708 0.904561i −0.852793 0.522249i
\(4\) −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
\(9\) 1.36354 + 2.67222i 0.454512 + 0.890740i
\(10\) −0.643203 0.513478i −0.203399 0.162376i
\(11\) −2.93366 + 1.69375i −0.884531 + 0.510684i −0.872150 0.489239i \(-0.837275\pi\)
−0.0123815 + 0.999923i \(0.503941\pi\)
\(12\) 3.22837 + 0.0835917i 0.931951 + 0.0241308i
\(13\) −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
\(15\) 0.331892 + 3.85874i 0.0856941 + 0.996321i
\(16\) 1.60275 2.77605i 0.400689 0.694013i
\(17\) 0.0514941 0.192179i 0.0124891 0.0466101i −0.959400 0.282049i \(-0.908986\pi\)
0.971889 + 0.235439i \(0.0756527\pi\)
\(18\) 0.739337 + 0.820150i 0.174263 + 0.193311i
\(19\) 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 \(-0.977464\pi\)
0.828485 0.560011i \(-0.189203\pi\)
\(24\) 2.39544 0.575837i 0.488968 0.117542i
\(25\) −1.47868 + 4.77635i −0.295736 + 0.955270i
\(26\) −0.718647 0.414911i −0.140938 0.0813707i
\(27\) 0.403134 5.18049i 0.0775831 0.996986i
\(28\) 0 0
\(29\) 9.49165 1.76256 0.881278 0.472598i \(-0.156684\pi\)
0.881278 + 0.472598i \(0.156684\pi\)
\(30\) 0.485591 + 1.34027i 0.0886564 + 0.244698i
\(31\) 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
\(33\) 5.86535 + 0.151871i 1.02103 + 0.0264373i
\(34\) 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
\(39\) 0.912709 + 3.79681i 0.146150 + 0.607976i
\(40\) 3.14483 + 0.475658i 0.497242 + 0.0752082i
\(41\) 1.39256i 0.217481i −0.994070 0.108741i \(-0.965318\pi\)
0.994070 0.108741i \(-0.0346818\pi\)
\(42\) 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
\(45\) 3.00023 5.99988i 0.447248 0.894410i
\(46\) −0.576337 0.998245i −0.0849762 0.147183i
\(47\) −0.889755 + 0.238409i −0.129784 + 0.0347755i −0.323126 0.946356i \(-0.604734\pi\)
0.193342 + 0.981131i \(0.438067\pi\)
\(48\) −4.87851 + 2.65066i −0.704152 + 0.382591i
\(49\) 0 0
\(50\) −0.0707006 + 1.83898i −0.00999858 + 0.260071i
\(51\) −0.249898 + 0.237284i −0.0349928 + 0.0332264i
\(52\) 4.06040 + 1.08798i 0.563077 + 0.150876i
\(53\) 8.93528 + 2.39420i 1.22736 + 0.328869i 0.813549 0.581496i \(-0.197532\pi\)
0.413806 + 0.910365i \(0.364199\pi\)
\(54\) −0.350184 1.88020i −0.0476540 0.255863i
\(55\) 6.94110 + 3.03262i 0.935938 + 0.408918i
\(56\) 0 0
\(57\) −6.07522 11.1814i −0.804683 1.48101i
\(58\) 3.37453 0.904203i 0.443098 0.118728i
\(59\) 3.12516 + 5.41293i 0.406861 + 0.704704i 0.994536 0.104393i \(-0.0332900\pi\)
−0.587675 + 0.809097i \(0.699957\pi\)
\(60\) −4.13327 5.92140i −0.533603 0.764449i
\(61\) 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
\(66\) 2.09975 0.504757i 0.258462 0.0621313i
\(67\) 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 \(0.196998\pi\)
−0.814524 + 0.580129i \(0.803002\pi\)
\(72\) −4.05914 1.31627i −0.478374 0.155124i
\(73\) 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
\(75\) 6.50463 5.71750i 0.751090 0.660200i
\(76\) −13.6985 −1.57133
\(77\) 0 0
\(78\) 0.686187 + 1.26292i 0.0776954 + 0.142997i
\(79\) −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
\(81\) −5.28153 + 7.28735i −0.586837 + 0.809705i
\(82\) −0.132659 0.495092i −0.0146498 0.0546737i
\(83\) −6.26911 + 6.26911i −0.688124 + 0.688124i −0.961817 0.273693i \(-0.911755\pi\)
0.273693 + 0.961817i \(0.411755\pi\)
\(84\) 0 0
\(85\) −0.414214 + 0.162321i −0.0449278 + 0.0176062i
\(86\) 0.389719 + 0.225004i 0.0420245 + 0.0242628i
\(87\) −14.0199 8.58578i −1.50310 0.920493i
\(88\) 1.24709 4.65422i 0.132941 0.496141i
\(89\) −6.18833 + 10.7185i −0.655962 + 1.13616i 0.325690 + 0.945477i \(0.394404\pi\)
−0.981652 + 0.190683i \(0.938930\pi\)
\(90\) 0.495095 2.41893i 0.0521876 0.254977i
\(91\) 0 0
\(92\) 4.12888 + 4.12888i 0.430465 + 0.430465i
\(93\) 0.0413618 1.59742i 0.00428902 0.165645i
\(94\) −0.293620 + 0.169521i −0.0302845 + 0.0174848i
\(95\) −1.83099 16.3258i −0.187856 1.67499i
\(96\) −5.05512 + 4.79994i −0.515936 + 0.489892i
\(97\) 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 −0.929013 0.370047i \(-0.879342\pi\)
−0.144037 + 0.989572i \(0.546008\pi\)
\(102\) −0.0662410 + 0.108167i −0.00655884 + 0.0107101i
\(103\) −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 0.102795 0.994703i \(-0.467221\pi\)
0.586374 + 0.810040i \(0.300555\pi\)
\(108\) 4.17863 + 8.74090i 0.402089 + 0.841094i
\(109\) 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 −0.204276 0.978913i \(-0.565484\pi\)
0.978913 + 0.204276i \(0.0654841\pi\)
\(114\) −3.22507 3.39652i −0.302056 0.318113i
\(115\) −4.36890 + 5.47266i −0.407402 + 0.510328i
\(116\) −15.3264 + 8.84872i −1.42302 + 0.821583i
\(117\) 2.08630 6.43380i 0.192879 0.594805i
\(118\) 1.62673 + 1.62673i 0.149752 + 0.149752i
\(119\) 0 0
\(120\) −4.21491 3.54728i −0.384767 0.323821i
\(121\) 0.237567 0.411478i 0.0215970 0.0374071i
\(122\) 0.174580 0.651543i 0.0158058 0.0589879i
\(123\) −1.25966 + 2.05692i −0.113579 + 0.185467i
\(124\) −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
\(129\) −0.494958 2.05899i −0.0435786 0.181284i
\(130\) 0.206808 + 1.84398i 0.0181382 + 0.161728i
\(131\) −7.76894 4.48540i −0.678776 0.391891i 0.120618 0.992699i \(-0.461512\pi\)
−0.799394 + 0.600808i \(0.794846\pi\)
\(132\) −9.61252 + 5.22282i −0.836663 + 0.454588i
\(133\) 0 0
\(134\) 0.424489 0.0366703
\(135\) −9.85885 + 6.14842i −0.848515 + 0.529172i
\(136\) 0.141500 + 0.245084i 0.0121335 + 0.0210158i
\(137\) 2.37747 8.87285i 0.203121 0.758059i −0.786893 0.617090i \(-0.788312\pi\)
0.990014 0.140969i \(-0.0450218\pi\)
\(138\) −0.0516774 + 1.99582i −0.00439908 + 0.169895i
\(139\) 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
\(144\) 9.60364 + 0.497665i 0.800304 + 0.0414721i
\(145\) −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 −0.885536 0.464570i \(-0.846209\pi\)
0.845098 + 0.534612i \(0.179542\pi\)
\(150\) 1.76790 2.65237i 0.144349 0.216565i
\(151\) 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
\(153\) 0.583758 0.124439i 0.0471940 0.0100603i
\(154\) 0 0
\(155\) 0.825930 1.89040i 0.0663403 0.151841i
\(156\) −5.01340 5.27992i −0.401393 0.422732i
\(157\) 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
\(159\) −11.0324 11.6189i −0.874929 0.921442i
\(160\) −8.37901 + 3.28355i −0.662419 + 0.259588i
\(161\) 0 0
\(162\) −1.18351 + 3.09398i −0.0929853 + 0.243086i
\(163\) −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
\(165\) −7.50939 10.7581i −0.584605 0.837515i
\(166\) −1.63162 + 2.82605i −0.126638 + 0.219344i
\(167\) 17.4876 + 17.4876i 1.35323 + 1.35323i 0.882018 + 0.471215i \(0.156184\pi\)
0.471215 + 0.882018i \(0.343816\pi\)
\(168\) 0 0
\(169\) 7.91707i 0.609005i
\(170\) −0.131801 + 0.0971688i −0.0101086 + 0.00745250i
\(171\) −1.14063 + 22.0112i −0.0872260 + 1.68324i
\(172\) −2.20194 0.590008i −0.167896 0.0449877i
\(173\) 3.98116 + 14.8579i 0.302682 + 1.12962i 0.934922 + 0.354852i \(0.115469\pi\)
−0.632241 + 0.774772i \(0.717865\pi\)
\(174\) −5.80236 1.71689i −0.439876 0.130157i
\(175\) 0 0
\(176\) 10.8587i 0.818502i
\(177\) 0.280218 10.8222i 0.0210625 0.813449i
\(178\) −1.17904 + 4.40023i −0.0883726 + 0.329811i
\(179\) 8.82622 + 15.2875i 0.659703 + 1.14264i 0.980693 + 0.195556i \(0.0626511\pi\)
−0.320990 + 0.947083i \(0.604016\pi\)
\(180\) 0.748912 + 12.4852i 0.0558206 + 0.930590i
\(181\) 11.9237 0.886282 0.443141 0.896452i \(-0.353864\pi\)
0.443141 + 0.896452i \(0.353864\pi\)
\(182\) 0 0
\(183\) −2.78908 + 1.51541i −0.206175 + 0.112022i
\(184\) 3.85774 + 2.22727i 0.284397 + 0.164196i
\(185\) 11.6709 14.6195i 0.858065 1.07485i
\(186\) −0.137470 0.571866i −0.0100798 0.0419313i
\(187\) 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 0.939981 0.341226i \(-0.110842\pi\)
0.174480 + 0.984661i \(0.444175\pi\)
\(192\) 4.45919 7.28152i 0.321814 0.525499i
\(193\) 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
\(195\) 5.62249 6.68069i 0.402635 0.478414i
\(196\) 0 0
\(197\) 4.10678 + 4.10678i 0.292596 + 0.292596i 0.838105 0.545509i \(-0.183664\pi\)
−0.545509 + 0.838105i \(0.683664\pi\)
\(198\) −3.55809 1.15379i −0.252862 0.0819963i
\(199\) −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
\(201\) −1.37545 1.44858i −0.0970170 0.102175i
\(202\) −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
\(207\) 6.97821 6.29061i 0.485019 0.437228i
\(208\) −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
\(213\) 8.84346 14.4407i 0.605944 0.989461i
\(214\) 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
\(219\) −8.53990 + 8.10882i −0.577073 + 0.547943i
\(220\) −14.0352 + 1.57409i −0.946252 + 0.106125i
\(221\) −0.388462 + 0.224279i −0.0261308 + 0.0150866i
\(222\) 0.138049 5.33157i 0.00926527 0.357832i
\(223\) 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
\(225\) −14.7797 + 2.56137i −0.985313 + 0.170758i
\(226\) 2.14314 3.71203i 0.142559 0.246920i
\(227\) −2.57893 + 9.62471i −0.171170 + 0.638815i 0.826002 + 0.563666i \(0.190610\pi\)
−0.997172 + 0.0751483i \(0.976057\pi\)
\(228\) 20.2338 + 12.3911i 1.34002 + 0.820623i
\(229\) 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 \(-0.853268\pi\)
0.553220 0.833035i \(-0.313399\pi\)
\(234\) 0.128832 2.48613i 0.00842203 0.162523i
\(235\) 1.60971 + 1.28505i 0.105006 + 0.0838275i
\(236\) −10.0926 5.82694i −0.656969 0.379301i
\(237\) 2.82564 + 5.20055i 0.183545 + 0.337812i
\(238\) 0 0
\(239\) −12.8618 −0.831961 −0.415981 0.909373i \(-0.636562\pi\)
−0.415981 + 0.909373i \(0.636562\pi\)
\(240\) 11.2440 + 5.26326i 0.725797 + 0.339742i
\(241\) −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
\(243\) 14.3931 5.98653i 0.923318 0.384036i
\(244\) 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
\(249\) 14.9308 3.58919i 0.946199 0.227455i
\(250\) 3.40364 2.31289i 0.215265 0.146280i
\(251\) 8.02862i 0.506762i −0.967367 0.253381i \(-0.918457\pi\)
0.967367 0.253381i \(-0.0815426\pi\)
\(252\) 0 0
\(253\) 7.50140 + 7.50140i 0.471609 + 0.471609i
\(254\) 0.489763 0.848294i 0.0307304 0.0532267i
\(255\) 0.758657 + 0.134920i 0.0475089 + 0.00844899i
\(256\) −3.11440 5.39430i −0.194650 0.337144i
\(257\) 22.6908 6.07998i 1.41541 0.379259i 0.531558 0.847022i \(-0.321607\pi\)
0.883854 + 0.467763i \(0.154940\pi\)
\(258\) −0.372116 0.684874i −0.0231669 0.0426384i
\(259\) 0 0
\(260\) −3.42958 8.75163i −0.212693 0.542753i
\(261\) 12.9422 + 25.3638i 0.801103 + 1.56998i
\(262\) −3.18936 0.854585i −0.197039 0.0527964i
\(263\) 18.9005 + 5.06438i 1.16546 + 0.312283i 0.789143 0.614210i \(-0.210525\pi\)
0.376313 + 0.926493i \(0.377192\pi\)
\(264\) −6.05209 + 5.74658i −0.372480 + 0.353678i
\(265\) −7.54709 19.2587i −0.463614 1.18305i
\(266\) 0 0
\(267\) 18.8362 10.2344i 1.15276 0.626334i
\(268\) −2.07707 + 0.556549i −0.126877 + 0.0339967i
\(269\) 5.73161 + 9.92745i 0.349463 + 0.605287i 0.986154 0.165832i \(-0.0530308\pi\)
−0.636691 + 0.771119i \(0.719697\pi\)
\(270\) −2.91936 + 3.12511i −0.177667 + 0.190188i
\(271\) 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
\(276\) −2.36386 9.83351i −0.142288 0.591908i
\(277\) −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 \(-0.957984\pi\)
0.991301 0.131614i \(-0.0420160\pi\)
\(282\) 0.587042 + 0.0152002i 0.0349579 + 0.000905158i
\(283\) −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
\(285\) −12.0632 + 25.7708i −0.714562 + 1.52653i
\(286\) 2.81102 0.166219
\(287\) 0 0
\(288\) 11.8087 2.51724i 0.695832 0.148330i
\(289\) 14.6882 + 8.48021i 0.864009 + 0.498836i
\(290\) −6.10506 4.87375i −0.358502 0.286197i
\(291\) −15.9886 + 3.84347i −0.937267 + 0.225308i
\(292\) 3.28107 + 12.2451i 0.192010 + 0.716591i
\(293\) 7.37595 7.37595i 0.430908 0.430908i −0.458029 0.888937i \(-0.651445\pi\)
0.888937 + 0.458029i \(0.151445\pi\)
\(294\) 0 0
\(295\) 5.59552 12.8071i 0.325784 0.745660i
\(296\) −10.3054 5.94985i −0.598992 0.345828i
\(297\) 7.59179 + 15.8806i 0.440520 + 0.921486i
\(298\) −0.0940462 + 0.350985i −0.00544795 + 0.0203320i
\(299\) −3.53025 + 6.11457i −0.204160 + 0.353615i
\(300\) −5.17299 + 15.2962i −0.298663 + 0.883128i
\(301\) 0 0
\(302\) 2.26711 + 2.26711i 0.130458 + 0.130458i
\(303\) 21.5608 + 0.558270i 1.23864 + 0.0320718i
\(304\) 20.3954 11.7753i 1.16976 0.675359i
\(305\) −4.07232 + 0.456723i −0.233180 + 0.0261519i
\(306\) 0.195687 0.0998518i 0.0111867 0.00570815i
\(307\) −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 −0.264078 0.964501i \(-0.585067\pi\)
0.703244 + 0.710949i \(0.251734\pi\)
\(312\) −4.73681 2.90081i −0.268169 0.164226i
\(313\) 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 −0.326626 0.945154i \(-0.605912\pi\)
0.189710 + 0.981840i \(0.439245\pi\)
\(318\) −5.02917 3.07986i −0.282022 0.172710i
\(319\) −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
\(324\) 1.73451 16.6909i 0.0963617 0.927270i
\(325\) 9.97175 5.25713i 0.553133 0.291613i
\(326\) −6.37918 + 3.68302i −0.353310 + 0.203984i
\(327\) −11.5604 0.299330i −0.639289 0.0165530i
\(328\) 1.40063 + 1.40063i 0.0773368 + 0.0773368i
\(329\) 0 0
\(330\) −3.69463 3.10941i −0.203383 0.171167i
\(331\) 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
\(333\) −18.6414 + 16.8045i −1.02154 + 0.920883i
\(334\) 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
\(339\) −19.6116 + 4.71442i −1.06516 + 0.256052i
\(340\) 0.517515 0.648261i 0.0280662 0.0351569i
\(341\) −2.70654 1.56262i −0.146567 0.0846207i
\(342\) 1.69133 + 7.93421i 0.0914565 + 0.429033i
\(343\) 0 0
\(344\) −1.73907 −0.0937644
\(345\) 11.4036 4.13163i 0.613948 0.222439i
\(346\) 2.83081 + 4.90311i 0.152185 + 0.263593i
\(347\) −2.00792 + 7.49364i −0.107791 + 0.402280i −0.998647 0.0520055i \(-0.983439\pi\)
0.890856 + 0.454285i \(0.150105\pi\)
\(348\) 30.6426 + 0.793423i 1.64262 + 0.0425320i
\(349\) 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 −0.0265388 0.999648i \(-0.508449\pi\)
−0.522807 + 0.852451i \(0.675115\pi\)
\(354\) −0.931333 3.87428i −0.0494998 0.205916i
\(355\) 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 −0.935171 0.354197i \(-0.884754\pi\)
0.774329 + 0.632783i \(0.218088\pi\)
\(360\) 3.01703 + 9.05226i 0.159011 + 0.477096i
\(361\) 17.4885 + 30.2910i 0.920448 + 1.59426i
\(362\) 4.23919 1.13589i 0.222807 0.0597009i
\(363\) −0.723114 + 0.392893i −0.0379536 + 0.0206215i
\(364\) 0 0
\(365\) −14.1551 + 5.54710i −0.740913 + 0.290348i
\(366\) −0.847230 + 0.804463i −0.0442854 + 0.0420499i
\(367\) 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
\(369\) 3.72123 1.89881i 0.193719 0.0988479i
\(370\) 2.75663 6.30942i 0.143310 0.328011i
\(371\) 0 0
\(372\) 1.42243 + 2.61796i 0.0737496 + 0.135735i
\(373\) 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
\(375\) −18.9214 4.12061i −0.977099 0.212787i
\(376\) 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
\(381\) −4.48177 + 1.07737i −0.229608 + 0.0551951i
\(382\) 6.32299 + 1.69424i 0.323513 + 0.0866849i
\(383\) −5.36443 20.0203i −0.274110 1.02299i −0.956436 0.291943i \(-0.905698\pi\)
0.682326 0.731048i \(-0.260968\pi\)
\(384\) 4.84748 16.3824i 0.247372 0.836012i
\(385\) 0 0
\(386\) 7.46402i 0.379909i
\(387\) −1.13139 + 3.48902i −0.0575119 + 0.177357i
\(388\) −4.58156 + 17.0986i −0.232593 + 0.868050i
\(389\) 6.81615 + 11.8059i 0.345592 + 0.598583i 0.985461 0.169901i \(-0.0543447\pi\)
−0.639869 + 0.768484i \(0.721011\pi\)
\(390\) 1.36252 2.91077i 0.0689938 0.147393i
\(391\) −0.623074 −0.0315102
\(392\) 0 0
\(393\) 7.41804 + 13.6528i 0.374190 + 0.688692i
\(394\) 1.85129 + 1.06884i 0.0932667 + 0.0538476i
\(395\) 0.851612 + 7.59329i 0.0428492 + 0.382060i
\(396\) 18.9228 + 0.980589i 0.950908 + 0.0492765i
\(397\) 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 0.125841 0.992050i \(-0.459837\pi\)
−0.796221 + 0.605006i \(0.793171\pi\)
\(402\) −0.627005 0.383977i −0.0312722 0.0191510i
\(403\) 0.538342 2.00912i 0.0268167 0.100081i
\(404\) 11.6088 20.1071i 0.577561 1.00036i
\(405\) 20.1239 0.163776i 0.999967 0.00813810i
\(406\) 0 0
\(407\) −20.0390 20.0390i −0.993296 0.993296i
\(408\) 0.0126876 0.490005i 0.000628130 0.0242588i
\(409\) 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
\(411\) −11.5378 + 10.9553i −0.569116 + 0.540387i
\(412\) 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
\(417\) 1.66363 2.71658i 0.0814683 0.133032i
\(418\) −8.84820 + 2.37087i −0.432780 + 0.115963i
\(419\) −5.95062 −0.290707 −0.145353 0.989380i \(-0.546432\pi\)
−0.145353 + 0.989380i \(0.546432\pi\)
\(420\) 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
\(423\) −1.85030 2.05254i −0.0899644 0.0997980i
\(424\) −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
\(429\) −9.10842 9.59264i −0.439758 0.463137i
\(430\) −0.112151 0.999981i −0.00540840 0.0482234i
\(431\) 9.76349 5.63695i 0.470291 0.271523i −0.246071 0.969252i \(-0.579140\pi\)
0.716361 + 0.697729i \(0.245806\pi\)
\(432\) −13.7352 9.42218i −0.660835 0.453325i
\(433\) −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
\(435\) 3.15020 + 36.6258i 0.151041 + 1.75607i
\(436\) −6.22436 + 10.7809i −0.298093 + 0.516312i
\(437\) 5.95496 22.2242i 0.284865 1.06313i
\(438\) −2.26369 + 3.69643i −0.108163 + 0.176622i
\(439\) 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 \(0.139994\pi\)
−0.570728 + 0.821139i \(0.693339\pi\)
\(444\) 6.31475 + 26.2689i 0.299685 + 1.24667i
\(445\) 27.5026 3.08451i 1.30375 0.146220i
\(446\) 5.20351 + 3.00425i 0.246393 + 0.142255i
\(447\) 1.50247 0.816347i 0.0710646 0.0386119i
\(448\) 0 0
\(449\) 2.40628 0.113559 0.0567796 0.998387i \(-0.481917\pi\)
0.0567796 + 0.998387i \(0.481917\pi\)
\(450\) −5.01057 + 2.31859i −0.236200 + 0.109299i
\(451\) 2.35865 + 4.08529i 0.111064 + 0.192369i
\(452\) −5.61975 + 20.9732i −0.264331 + 0.986496i
\(453\) 0.390530 15.0826i 0.0183487 0.708641i
\(454\) 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
\(459\) −0.974820 0.344238i −0.0455007 0.0160677i
\(460\) 1.95262 12.9098i 0.0910414 0.601924i
\(461\) 35.4227i 1.64980i 0.565278 + 0.824900i \(0.308769\pi\)
−0.565278 + 0.824900i \(0.691231\pi\)
\(462\) 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
\(465\) −2.92995 + 2.04518i −0.135873 + 0.0948427i
\(466\) −3.71632 6.43686i −0.172155 0.298182i
\(467\) 7.93069 2.12502i 0.366989 0.0983343i −0.0706117 0.997504i \(-0.522495\pi\)
0.437600 + 0.899170i \(0.355828\pi\)
\(468\) 2.62918 + 12.3338i 0.121534 + 0.570130i
\(469\) 0 0
\(470\) 0.694711 + 0.303524i 0.0320446 + 0.0140005i
\(471\) −8.87687 9.34879i −0.409025 0.430769i
\(472\) −8.58756 2.30103i −0.395275 0.105914i
\(473\) −4.00051 1.07193i −0.183944 0.0492876i
\(474\) 1.50001 + 1.57975i 0.0688978 + 0.0725605i
\(475\) −26.9540 + 24.9582i −1.23673 + 1.14516i
\(476\) 0 0
\(477\) 5.78575 + 27.1416i 0.264911 + 1.24273i
\(478\) −4.57271 + 1.22525i −0.209151 + 0.0560418i
\(479\) −20.1914 34.9726i −0.922571 1.59794i −0.795422 0.606056i \(-0.792751\pi\)
−0.127149 0.991884i \(-0.540583\pi\)
\(480\) 15.3466 + 2.72925i 0.700475 + 0.124573i
\(481\) 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
\(486\) 4.54683 3.49950i 0.206248 0.158740i
\(487\) −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 \(-0.689506\pi\)
0.560798 0.827952i \(-0.310494\pi\)
\(492\) 0.116406 4.49570i 0.00524801 0.202682i
\(493\) 0.488764 1.82409i 0.0220128 0.0821530i
\(494\) −3.04831 5.27983i −0.137150 0.237551i
\(495\) 1.36063 + 22.6832i 0.0611559 + 1.01954i
\(496\) 2.95735 0.132789
\(497\) 0 0
\(498\) 4.96636 2.69840i 0.222548 0.120918i
\(499\) 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
\(501\) −10.0120 41.6493i −0.447304 1.86075i
\(502\) −0.764830 2.85438i −0.0341360 0.127397i
\(503\) −15.7533 + 15.7533i −0.702406 + 0.702406i −0.964926 0.262521i \(-0.915446\pi\)
0.262521 + 0.964926i \(0.415446\pi\)
\(504\) 0 0
\(505\) 25.5152 + 11.1478i 1.13541 + 0.496070i
\(506\) 3.38155 + 1.95234i 0.150328 + 0.0867921i
\(507\) −7.16148 + 11.6942i −0.318052 + 0.519356i
\(508\) −1.28426 + 4.79292i −0.0569798 + 0.212651i
\(509\) −7.20456 + 12.4787i −0.319336 + 0.553107i −0.980350 0.197267i \(-0.936793\pi\)
0.661013 + 0.750374i \(0.270127\pi\)
\(510\) 0.282575 0.0243044i 0.0125126 0.00107622i
\(511\) 0 0
\(512\) −15.5706 15.5706i −0.688130 0.688130i
\(513\) 21.5953 31.4805i 0.953454 1.38990i
\(514\) 7.48797 4.32318i 0.330280 0.190687i
\(515\) 24.1927 + 19.3134i 1.06606 + 0.851049i
\(516\) 2.71874 + 2.86328i 0.119686 + 0.126049i
\(517\) 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 0.0660022 0.997819i \(-0.478976\pi\)
0.897138 + 0.441750i \(0.145642\pi\)
\(522\) 7.01753 + 7.78458i 0.307149 + 0.340722i
\(523\) −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
\(528\) 9.82232 16.0391i 0.427462 0.698013i
\(529\) 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
\(534\) 5.72181 5.43298i 0.247607 0.235108i
\(535\) −12.8972 10.2960i −0.557593 0.445134i
\(536\) −1.42067 + 0.820225i −0.0613637 + 0.0354283i
\(537\) 0.791406 30.5647i 0.0341517 1.31896i
\(538\) 2.98346 + 2.98346i 0.128626 + 0.128626i
\(539\) 0 0
\(540\) 10.1874 19.1191i 0.438396 0.822753i
\(541\) 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
\(543\) −17.6123 10.7857i −0.755815 0.462859i
\(544\) −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
\(549\) 5.49048 + 0.284519i 0.234328 + 0.0121430i
\(550\) −2.90736 5.51469i −0.123970 0.235147i
\(551\) 60.3917 + 34.8671i 2.57277 + 1.48539i
\(552\) −3.68350 6.77942i −0.156780 0.288551i
\(553\) 0 0
\(554\) −6.62667 −0.281540
\(555\) −30.4632 + 11.0371i −1.29309 + 0.468499i
\(556\) −1.71458 2.96973i −0.0727142 0.125945i
\(557\) 1.88849 7.04793i 0.0800177 0.298630i −0.914306 0.405023i \(-0.867263\pi\)
0.994324 + 0.106393i \(0.0339301\pi\)
\(558\) −0.314234 + 0.969043i −0.0133026 + 0.0410229i
\(559\) 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 0.855990 0.516992i \(-0.172948\pi\)
0.482813 + 0.875723i \(0.339615\pi\)
\(564\) −2.89239 + 0.695297i −0.121791 + 0.0292773i
\(565\) −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 \(0.562827\pi\)
−0.751162 + 0.660118i \(0.770506\pi\)
\(570\) −1.83378 + 10.3114i −0.0768084 + 0.431896i
\(571\) −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
\(573\) −14.7065 27.0671i −0.614372 1.13074i
\(574\) 0 0
\(575\) 15.6469 + 0.601553i 0.652520 + 0.0250865i
\(576\) −13.1732 + 6.72179i −0.548882 + 0.280075i
\(577\) −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
\(579\) −25.4711 + 24.1853i −1.05854 + 1.00511i
\(580\) 36.2627 + 15.8434i 1.50573 + 0.657862i
\(581\) 0 0
\(582\) −5.31822 + 2.88958i −0.220447 + 0.119777i
\(583\) −30.2682 + 8.11035i −1.25358 + 0.335896i
\(584\) 4.83554 + 8.37540i 0.200096 + 0.346576i
\(585\) −14.3480 + 4.78203i −0.593215 + 0.197713i
\(586\) 1.91969 3.32500i 0.0793016 0.137354i
\(587\) −3.77086 3.77086i −0.155640 0.155640i 0.624992 0.780632i \(-0.285102\pi\)
−0.780632 + 0.624992i \(0.785102\pi\)
\(588\) 0 0
\(589\) 6.77812i 0.279288i
\(590\) 0.769309 5.08631i 0.0316720 0.209400i
\(591\) −2.35121 9.78088i −0.0967159 0.402332i
\(592\) 25.9032 + 6.94074i 1.06461 + 0.285262i
\(593\) −3.06735 11.4475i −0.125961 0.470093i 0.873911 0.486086i \(-0.161576\pi\)
−0.999872 + 0.0159927i \(0.994909\pi\)
\(594\) 4.21191 + 4.92275i 0.172817 + 0.201983i
\(595\) 0 0
\(596\) 1.84071i 0.0753985i
\(597\) 23.2273 + 0.601420i 0.950630 + 0.0246145i
\(598\) −0.672604 + 2.51019i −0.0275048 + 0.102649i
\(599\) −3.37794 5.85076i −0.138019 0.239056i 0.788728 0.614743i \(-0.210740\pi\)
−0.926747 + 0.375687i \(0.877407\pi\)
\(600\) −0.791696 + 12.2929i −0.0323209 + 0.501857i
\(601\) −21.2564 −0.867068 −0.433534 0.901137i \(-0.642734\pi\)
−0.433534 + 0.901137i \(0.642734\pi\)
\(602\) 0 0
\(603\) 0.721331 + 3.38385i 0.0293749 + 0.137801i
\(604\) −14.0656 8.12080i −0.572322 0.330431i
\(605\) −1.05581 + 0.118413i −0.0429249 + 0.00481416i
\(606\) 7.71861 1.85547i 0.313547 0.0753732i
\(607\) −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
\(612\) −0.826599 + 0.745151i −0.0334133 + 0.0301209i
\(613\) 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
\(615\) 5.37352 0.462179i 0.216681 0.0186369i
\(616\) 0 0
\(617\) −5.47009 5.47009i −0.220218 0.220218i 0.588373 0.808590i \(-0.299769\pi\)
−0.808590 + 0.588373i \(0.799769\pi\)
\(618\) 8.82281 + 0.228448i 0.354906 + 0.00918951i
\(619\) −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
\(621\) −15.9976 + 2.97953i −0.641963 + 0.119564i
\(622\) 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
\(627\) 36.7610 + 22.5124i 1.46809 + 0.899058i
\(628\) −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
\(633\) −11.9869 7.34074i −0.476436 0.291768i
\(634\) −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
\(639\) −26.1250 + 13.3306i −1.03349 + 0.527352i
\(640\) 13.7606 17.2371i 0.543935 0.681355i
\(641\) 26.6744 15.4005i 1.05357 0.608282i 0.129927 0.991524i \(-0.458526\pi\)
0.923648 + 0.383242i \(0.125192\pi\)
\(642\) −4.70345 0.121786i −0.185630 0.00480650i
\(643\) 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
\(645\) −3.04905 + 3.62291i −0.120056 + 0.142652i
\(646\) 0.269007 0.465934i 0.0105839 0.0183319i
\(647\) −8.57582 + 32.0054i −0.337150 + 1.25826i 0.564369 + 0.825523i \(0.309120\pi\)
−0.901519 + 0.432739i \(0.857547\pi\)
\(648\) −2.01743 12.6417i −0.0792523 0.496613i
\(649\) −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 \(-0.925512\pi\)
0.726481 0.687187i \(-0.241155\pi\)
\(654\) −4.13853 + 0.994854i −0.161829 + 0.0389019i
\(655\) 2.23570 + 19.9343i 0.0873560 + 0.778899i
\(656\) −3.86582 2.23193i −0.150935 0.0871423i
\(657\) 19.9490 4.25252i 0.778286 0.165906i
\(658\) 0 0
\(659\) −0.0375362 −0.00146220 −0.000731101 1.00000i \(-0.500233\pi\)
−0.000731101 1.00000i \(0.500233\pi\)
\(660\) 22.1550 + 10.3706i 0.862381 + 0.403676i
\(661\) 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
\(663\) 0.776664 + 0.0201100i 0.0301631 + 0.000781009i
\(664\) 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
\(669\) −6.60866 27.4916i −0.255506 1.06289i
\(670\) −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
\(675\) 24.1477 + 9.58580i 0.929446 + 0.368958i
\(676\) 7.38079 + 12.7839i 0.283877 + 0.491689i
\(677\) −4.98104 + 1.33467i −0.191437 + 0.0512954i −0.353264 0.935524i \(-0.614928\pi\)
0.161827 + 0.986819i \(0.448261\pi\)
\(678\) −6.52335 + 3.54436i −0.250528 + 0.136120i
\(679\) 0 0
\(680\) 0.253352 0.579876i 0.00971559 0.0222372i
\(681\) 12.5154 11.8837i 0.479593 0.455384i
\(682\) −1.11111 0.297720i −0.0425465 0.0114003i
\(683\) −46.1083 12.3547i −1.76429 0.472739i −0.776708 0.629861i \(-0.783112\pi\)
−0.987579 + 0.157122i \(0.949778\pi\)
\(684\) −18.6784 36.6054i −0.714187 1.39964i
\(685\) −19.1242 + 7.49436i −0.730697 + 0.286345i
\(686\) 0 0
\(687\) −3.97013 7.30696i −0.151470 0.278778i
\(688\) 3.78559 1.01435i 0.144324 0.0386716i
\(689\) −10.4278 18.0614i −0.397267 0.688086i
\(690\) 3.66068 2.55524i 0.139360 0.0972764i
\(691\) −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
\(696\) 22.7367 5.46564i 0.861833 0.207175i
\(697\) −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 \(0.134999\pi\)
−0.911404 + 0.411512i \(0.865001\pi\)
\(702\) −2.43915 + 3.55568i −0.0920599 + 0.134200i
\(703\) −15.9079 + 59.3691i −0.599978 + 2.23915i
\(704\) −8.34962 14.4620i −0.314688 0.545056i
\(705\) −1.21526 3.35420i −0.0457693 0.126327i
\(706\) −3.93294 −0.148018
\(707\) 0 0
\(708\) 9.63670 + 17.7362i 0.362169 + 0.666567i
\(709\) 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
\(711\) 0.530517 10.2376i 0.0198959 0.383940i
\(712\) −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
\(717\) 18.9979 + 11.6343i 0.709491 + 0.434491i
\(718\) −0.580632 + 2.16695i −0.0216690 + 0.0808698i
\(719\) 19.6576 34.0480i 0.733106 1.26978i −0.222443 0.974946i \(-0.571403\pi\)
0.955549 0.294831i \(-0.0952635\pi\)
\(720\) −11.8474 17.9451i −0.441525 0.668776i
\(721\) 0 0
\(722\) 9.10324 + 9.10324i 0.338787 + 0.338787i
\(723\) −0.725644 + 28.0249i −0.0269870 + 1.04226i
\(724\) −19.2535 + 11.1160i −0.715551 + 0.413124i
\(725\) −14.0351 + 45.3354i −0.521251 + 1.68372i
\(726\) −0.219658 + 0.208570i −0.00815226 + 0.00774075i
\(727\) −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
\(732\) 3.09085 5.04712i 0.114241 0.186547i
\(733\) −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
\(738\) 1.14211 1.02957i 0.0420416 0.0378990i
\(739\) 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 −0.990126 0.140180i \(-0.955232\pi\)
0.140180 + 0.990126i \(0.455232\pi\)
\(744\) 1.56508 + 1.64828i 0.0573785 + 0.0604289i
\(745\) 2.19375 0.246036i 0.0803729 0.00901407i
\(746\) 3.18748 1.84029i 0.116702 0.0673780i
\(747\) −25.3006 8.20428i −0.925701 0.300179i
\(748\) −0.888574 0.888574i −0.0324895 0.0324895i
\(749\) 0 0
\(750\) −7.11961 + 0.337528i −0.259971 + 0.0123248i
\(751\) −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
\(753\) −7.26238 + 11.8589i −0.264656 + 0.432163i
\(754\) −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
\(759\) −4.29470 17.8657i −0.155888 0.648482i
\(760\) 18.2620 + 14.5788i 0.662433 + 0.528829i
\(761\) −29.4421 16.9984i −1.06728 0.616193i −0.139841 0.990174i \(-0.544659\pi\)
−0.927436 + 0.373981i \(0.877992\pi\)
\(762\) −1.49075 + 0.809978i −0.0540043 + 0.0293424i
\(763\) 0 0
\(764\) −33.1604 −1.19970
\(765\) −0.998555 0.885539i −0.0361028 0.0320167i
\(766\) −3.81439 6.60672i −0.137820 0.238711i
\(767\) 3.64716 13.6114i 0.131691 0.491479i
\(768\) −0.279254 + 10.7850i −0.0100767 + 0.389170i
\(769\) 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 0.0176318 0.999845i \(-0.494387\pi\)
−0.484653 + 0.874707i \(0.661054\pi\)
\(774\) −0.0698652 + 1.34822i −0.00251125 + 0.0484607i
\(775\) −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
\(780\) −2.85062 + 16.0291i −0.102069 + 0.573935i
\(781\) −16.5590 28.6810i −0.592526 1.02629i
\(782\) −0.221519 + 0.0593559i −0.00792151 + 0.00212256i
\(783\) 3.82640 49.1714i 0.136745 1.75724i
\(784\) 0 0
\(785\) −6.07251 15.4959i −0.216737 0.553072i
\(786\) 3.93791 + 4.14726i 0.140461 + 0.147928i
\(787\) 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
\(789\) −23.3366 24.5772i −0.830803 0.874971i
\(790\) 1.02613 + 2.61849i 0.0365081 + 0.0931616i
\(791\) 0 0
\(792\) 14.1376 3.01369i 0.502356 0.107087i
\(793\) −3.99091 + 1.06936i −0.141721 + 0.0379741i
\(794\) 6.39291 + 11.0728i 0.226876 + 0.392960i
\(795\) −6.27305 + 35.2735i −0.222482 + 1.25102i
\(796\) 12.5061 21.6612i 0.443267 0.767761i
\(797\) −7.78096 7.78096i −0.275616 0.275616i 0.555740 0.831356i \(-0.312435\pi\)
−0.831356 + 0.555740i \(0.812435\pi\)
\(798\) 0 0
\(799\) 0.183268i 0.00648357i
\(800\) 17.0279 + 10.7237i 0.602027 + 0.379141i
\(801\) −37.0803 1.92151i −1.31017 0.0678934i
\(802\) −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
\(807\) 0.513927 19.8482i 0.0180911 0.698691i
\(808\) 4.58427 17.1087i 0.161274 0.601883i
\(809\) −14.3936 24.9304i −0.506051 0.876506i −0.999975 0.00700090i \(-0.997772\pi\)
0.493925 0.869505i \(-0.335562\pi\)
\(810\) 7.13899 1.97529i 0.250838 0.0694047i
\(811\) 9.83136 0.345226 0.172613 0.984990i \(-0.444779\pi\)
0.172613 + 0.984990i \(0.444779\pi\)
\(812\) 0 0
\(813\) −12.8187 + 6.96485i −0.449572 + 0.244268i
\(814\) −9.03336 5.21542i −0.316619 0.182800i
\(815\) 34.9725 + 27.9190i 1.22503 + 0.977960i
\(816\) 0.258187 + 1.07404i 0.00903834 + 0.0375989i
\(817\) 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 0.920974 0.389624i \(-0.127395\pi\)
0.123063 + 0.992399i \(0.460728\pi\)
\(822\) −3.05834 + 4.99403i −0.106672 + 0.174187i
\(823\) −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
\(825\) −9.39837 + 27.7904i −0.327209 + 0.967537i
\(826\) 0 0
\(827\) 20.8624 + 20.8624i 0.725457 + 0.725457i 0.969711 0.244254i \(-0.0785431\pi\)
−0.244254 + 0.969711i \(0.578543\pi\)
\(828\) −5.40340 + 16.6631i −0.187781 + 0.579084i
\(829\) 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
\(831\) 21.4721 + 22.6136i 0.744858 + 0.784456i
\(832\) 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
\(837\) 4.32507 2.06762i 0.149496 0.0714674i
\(838\) −2.11560 + 0.566873i −0.0730822 + 0.0195823i
\(839\) 10.9282 0.377283 0.188642 0.982046i \(-0.439592\pi\)
0.188642 + 0.982046i \(0.439592\pi\)
\(840\) 0 0
\(841\) 61.0915 2.10660
\(842\) −3.78238 + 1.01348i −0.130349 + 0.0349270i
\(843\) −3.99139 + 6.51763i −0.137471 + 0.224479i
\(844\) −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
\(849\) 3.68133 3.49550i 0.126343 0.119965i
\(850\) 0.349772 + 0.108284i 0.0119971 + 0.00371410i
\(851\) 22.6893 13.0997i 0.777779 0.449051i
\(852\) −0.817235 + 31.5622i −0.0279980 + 1.08130i
\(853\) 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
\(855\) 41.1296 27.1537i 1.40660 0.928636i
\(856\) −5.24890 + 9.09135i −0.179404 + 0.310736i
\(857\) −5.24115 + 19.5603i −0.179034 + 0.668166i 0.816795 + 0.576928i \(0.195749\pi\)
−0.995829 + 0.0912372i \(0.970918\pi\)
\(858\) −4.15210 2.54274i −0.141750 0.0868077i
\(859\) 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 \(-0.793474\pi\)
0.387922 0.921692i \(-0.373193\pi\)
\(864\) −19.7194 6.96349i −0.670866 0.236903i
\(865\) 21.4589 26.8803i 0.729624 0.913956i
\(866\) −4.39564 2.53782i −0.149370 0.0862387i
\(867\) −14.0247 25.8123i −0.476304 0.876631i
\(868\) 0 0
\(869\) 11.5755 0.392671
\(870\) 4.60906 + 12.7213i 0.156262 + 0.431294i
\(871\) −1.30007 2.25178i −0.0440511 0.0762988i
\(872\) −2.45797 + 9.17327i −0.0832374 + 0.310646i
\(873\) 27.0931 + 8.78554i 0.916962 + 0.297345i
\(874\) 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
\(879\) −17.5669 + 4.22288i −0.592516 + 0.142434i
\(880\) 19.5436 14.4083i 0.658814 0.485705i
\(881\) 29.1988i 0.983734i 0.870670 + 0.491867i \(0.163685\pi\)
−0.870670 + 0.491867i \(0.836315\pi\)
\(882\) 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
\(885\) −19.8499 + 13.8557i −0.667246 + 0.465753i
\(886\) 5.00021 + 8.66062i 0.167985 + 0.290959i
\(887\) −25.3441 + 6.79094i −0.850973 + 0.228018i −0.657843 0.753156i \(-0.728531\pi\)
−0.193131 + 0.981173i \(0.561864\pi\)
\(888\) 9.83997 + 18.1103i 0.330208 + 0.607743i
\(889\) 0 0
\(890\) 9.48407 3.71661i 0.317907 0.124581i
\(891\) 3.15128 30.3242i 0.105572 1.01590i
\(892\) −29.4002 7.87776i −0.984392 0.263767i
\(893\) −6.53694 1.75157i −0.218750 0.0586140i
\(894\) 0.456402 0.433363i 0.0152643 0.0144938i
\(895\) 15.8031 36.1705i 0.528240 1.20905i
\(896\) 0 0
\(897\) 10.7455 5.83839i 0.358781 0.194938i
\(898\) 0.855494 0.229229i 0.0285482 0.00764947i
\(899\) 4.37842 + 7.58364i 0.146028 + 0.252928i
\(900\) 21.4773 17.9145i 0.715910 0.597149i
\(901\) 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
\(906\) −1.29797 5.39945i −0.0431220 0.179385i
\(907\) −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 \(-0.913441\pi\)
0.963253 0.268595i \(-0.0865592\pi\)
\(912\) −40.7771 1.05584i −1.35027 0.0349622i
\(913\) 7.77313 29.0097i 0.257253 0.960081i
\(914\) 1.61776 + 2.80205i 0.0535109 + 0.0926836i
\(915\) 6.42828 + 3.00905i 0.212512 + 0.0994760i
\(916\) −8.95190 −0.295779
\(917\) 0 0
\(918\) −0.379367 0.0295215i −0.0125210 0.000974354i
\(919\) 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
\(921\) 27.0574 6.50429i 0.891572 0.214324i
\(922\) 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
\(927\) −27.8086 30.8482i −0.913353 1.01319i
\(928\) 9.88706 36.8990i 0.324559 1.21127i
\(929\) −6.39892 + 11.0833i −0.209942 + 0.363630i −0.951696 0.307042i \(-0.900661\pi\)
0.741754 + 0.670672i \(0.233994\pi\)
\(930\) −0.846846 + 1.00623i −0.0277692 + 0.0329956i
\(931\) 0 0
\(932\) 26.6237 + 26.6237i 0.872090 + 0.872090i
\(933\) −15.4844 0.400935i −0.506936 0.0131260i
\(934\) 2.61713 1.51100i 0.0856352 0.0494415i
\(935\) 0.940229 1.17777i 0.0307488 0.0385172i
\(936\) 4.37268 + 8.56946i 0.142926 + 0.280102i
\(937\) −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 −0.551650 0.834075i \(-0.686002\pi\)
0.446505 + 0.894781i \(0.352668\pi\)
\(942\) −4.04655 2.47810i −0.131844 0.0807409i
\(943\) −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 0.603677 0.797229i \(-0.293702\pi\)
0.921414 + 0.388582i \(0.127035\pi\)
\(948\) −9.41093 5.76323i −0.305653 0.187181i
\(949\) −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 −0.261599 0.965177i \(-0.584250\pi\)
0.965177 + 0.261599i \(0.0842497\pi\)
\(954\) 4.64258 + 9.09839i 0.150309 + 0.294571i
\(955\) −4.43234 39.5204i −0.143427 1.27885i
\(956\) 20.7683 11.9906i 0.671695 0.387803i
\(957\) 55.6719 + 1.44150i 1.79962 + 0.0465972i
\(958\) −10.5102 10.5102i −0.339569 0.339569i
\(959\) 0 0
\(960\) −19.0223 + 1.63612i −0.613942 + 0.0528055i
\(961\) 15.0744 26.1097i 0.486272 0.842247i
\(962\) 1.79677 6.70565i 0.0579303 0.216199i
\(963\) 14.8248 + 16.4452i 0.477722 + 0.529939i
\(964\) 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
\(969\) −2.46165 + 0.591754i −0.0790797 + 0.0190099i
\(970\) −7.76510 + 0.870880i −0.249322 + 0.0279623i
\(971\) 23.7650 + 13.7207i 0.762655 + 0.440319i 0.830248 0.557394i \(-0.188199\pi\)
−0.0675934 + 0.997713i \(0.521532\pi\)
\(972\) −17.6599 + 23.0848i −0.566442 + 0.740444i
\(973\) 0 0
\(974\) −10.3055 −0.330211
\(975\) −19.4845 1.25485i −0.624003 0.0401873i
\(976\) −2.93723 5.08744i −0.0940185 0.162845i
\(977\) −14.8450 + 55.4023i −0.474933 + 1.77248i 0.146715 + 0.989179i \(0.453130\pi\)
−0.621648 + 0.783297i \(0.713537\pi\)
\(978\) 12.7541 + 0.330239i 0.407830 + 0.0105599i
\(979\) 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 −0.132098 0.991237i \(-0.542171\pi\)
−0.610018 + 0.792387i \(0.708838\pi\)
\(984\) −0.801887 3.33580i −0.0255632 0.106341i
\(985\) 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
\(990\) 2.64461 + 7.93487i 0.0840514 + 0.252187i
\(991\) −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
\(993\) −5.50716 + 2.99223i −0.174764 + 0.0949556i
\(994\) 0 0
\(995\) 27.4874 + 12.0094i 0.871408 + 0.380724i
\(996\) −20.7631 + 19.7150i −0.657903 + 0.624692i
\(997\) 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
\(999\) 42.7355 7.95941i 1.35209 0.251825i
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.128.7 48
3.2 odd 2 inner 735.2.y.g.128.6 48
5.2 odd 4 inner 735.2.y.g.422.7 48
7.2 even 3 735.2.j.h.638.6 24
7.3 odd 6 735.2.y.j.263.6 48
7.4 even 3 inner 735.2.y.g.263.6 48
7.5 odd 6 105.2.j.a.8.6 24
7.6 odd 2 735.2.y.j.128.7 48
15.2 even 4 inner 735.2.y.g.422.6 48
21.2 odd 6 735.2.j.h.638.7 24
21.5 even 6 105.2.j.a.8.7 yes 24
21.11 odd 6 inner 735.2.y.g.263.7 48
21.17 even 6 735.2.y.j.263.7 48
21.20 even 2 735.2.y.j.128.6 48
35.2 odd 12 735.2.j.h.197.7 24
35.12 even 12 105.2.j.a.92.7 yes 24
35.17 even 12 735.2.y.j.557.6 48
35.19 odd 6 525.2.j.b.218.7 24
35.27 even 4 735.2.y.j.422.7 48
35.32 odd 12 inner 735.2.y.g.557.6 48
35.33 even 12 525.2.j.b.407.6 24
105.2 even 12 735.2.j.h.197.6 24
105.17 odd 12 735.2.y.j.557.7 48
105.32 even 12 inner 735.2.y.g.557.7 48
105.47 odd 12 105.2.j.a.92.6 yes 24
105.62 odd 4 735.2.y.j.422.6 48
105.68 odd 12 525.2.j.b.407.7 24
105.89 even 6 525.2.j.b.218.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.j.a.8.6 24 7.5 odd 6
105.2.j.a.8.7 yes 24 21.5 even 6
105.2.j.a.92.6 yes 24 105.47 odd 12
105.2.j.a.92.7 yes 24 35.12 even 12
525.2.j.b.218.6 24 105.89 even 6
525.2.j.b.218.7 24 35.19 odd 6
525.2.j.b.407.6 24 35.33 even 12
525.2.j.b.407.7 24 105.68 odd 12
735.2.j.h.197.6 24 105.2 even 12
735.2.j.h.197.7 24 35.2 odd 12
735.2.j.h.638.6 24 7.2 even 3
735.2.j.h.638.7 24 21.2 odd 6
735.2.y.g.128.6 48 3.2 odd 2 inner
735.2.y.g.128.7 48 1.1 even 1 trivial
735.2.y.g.263.6 48 7.4 even 3 inner
735.2.y.g.263.7 48 21.11 odd 6 inner
735.2.y.g.422.6 48 15.2 even 4 inner
735.2.y.g.422.7 48 5.2 odd 4 inner
735.2.y.g.557.6 48 35.32 odd 12 inner
735.2.y.g.557.7 48 105.32 even 12 inner
735.2.y.j.128.6 48 21.20 even 2
735.2.y.j.128.7 48 7.6 odd 2
735.2.y.j.263.6 48 7.3 odd 6
735.2.y.j.263.7 48 21.17 even 6
735.2.y.j.422.6 48 105.62 odd 4
735.2.y.j.422.7 48 35.27 even 4
735.2.y.j.557.6 48 35.17 even 12
735.2.y.j.557.7 48 105.17 odd 12