Properties

Label 429.2.f.a.131.17
Level $429$
Weight $2$
Character 429.131
Analytic conductor $3.426$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(131,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 131.17
Character \(\chi\) \(=\) 429.131
Dual form 429.2.f.a.131.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.822598 q^{2} +(-0.0778779 - 1.73030i) q^{3} -1.32333 q^{4} -3.64046i q^{5} +(0.0640622 + 1.42334i) q^{6} -1.97039i q^{7} +2.73377 q^{8} +(-2.98787 + 0.269504i) q^{9} +O(q^{10})\) \(q-0.822598 q^{2} +(-0.0778779 - 1.73030i) q^{3} -1.32333 q^{4} -3.64046i q^{5} +(0.0640622 + 1.42334i) q^{6} -1.97039i q^{7} +2.73377 q^{8} +(-2.98787 + 0.269504i) q^{9} +2.99464i q^{10} +(-3.10754 - 1.15897i) q^{11} +(0.103058 + 2.28976i) q^{12} -1.00000i q^{13} +1.62084i q^{14} +(-6.29909 + 0.283512i) q^{15} +0.397876 q^{16} +7.48590 q^{17} +(2.45782 - 0.221694i) q^{18} +4.73844i q^{19} +4.81754i q^{20} +(-3.40936 + 0.153450i) q^{21} +(2.55625 + 0.953369i) q^{22} -1.40786i q^{23} +(-0.212900 - 4.73023i) q^{24} -8.25297 q^{25} +0.822598i q^{26} +(0.699012 + 5.14892i) q^{27} +2.60748i q^{28} -0.599024 q^{29} +(5.18162 - 0.233216i) q^{30} -3.80588 q^{31} -5.79482 q^{32} +(-1.76336 + 5.46723i) q^{33} -6.15788 q^{34} -7.17312 q^{35} +(3.95395 - 0.356644i) q^{36} +4.99572 q^{37} -3.89783i q^{38} +(-1.73030 + 0.0778779i) q^{39} -9.95217i q^{40} -9.36809 q^{41} +(2.80453 - 0.126227i) q^{42} +5.55007i q^{43} +(4.11231 + 1.53371i) q^{44} +(0.981120 + 10.8772i) q^{45} +1.15811i q^{46} -11.4369i q^{47} +(-0.0309857 - 0.688444i) q^{48} +3.11758 q^{49} +6.78887 q^{50} +(-0.582986 - 12.9528i) q^{51} +1.32333i q^{52} -7.53108i q^{53} +(-0.575006 - 4.23549i) q^{54} +(-4.21920 + 11.3129i) q^{55} -5.38658i q^{56} +(8.19892 - 0.369020i) q^{57} +0.492756 q^{58} +1.46468i q^{59} +(8.33579 - 0.375180i) q^{60} -0.106909i q^{61} +3.13070 q^{62} +(0.531027 + 5.88726i) q^{63} +3.97106 q^{64} -3.64046 q^{65} +(1.45054 - 4.49733i) q^{66} +7.88900 q^{67} -9.90634 q^{68} +(-2.43603 + 0.109642i) q^{69} +5.90059 q^{70} +5.03736i q^{71} +(-8.16814 + 0.736761i) q^{72} +0.797068i q^{73} -4.10947 q^{74} +(0.642724 + 14.2801i) q^{75} -6.27053i q^{76} +(-2.28362 + 6.12305i) q^{77} +(1.42334 - 0.0640622i) q^{78} -0.729545i q^{79} -1.44845i q^{80} +(8.85473 - 1.61049i) q^{81} +7.70617 q^{82} -1.46934 q^{83} +(4.51172 - 0.203065i) q^{84} -27.2521i q^{85} -4.56548i q^{86} +(0.0466507 + 1.03649i) q^{87} +(-8.49528 - 3.16836i) q^{88} -13.4031i q^{89} +(-0.807067 - 8.94758i) q^{90} -1.97039 q^{91} +1.86307i q^{92} +(0.296394 + 6.58530i) q^{93} +9.40796i q^{94} +17.2501 q^{95} +(0.451289 + 10.0268i) q^{96} -2.10062 q^{97} -2.56451 q^{98} +(9.59726 + 2.62537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.822598 −0.581664 −0.290832 0.956774i \(-0.593932\pi\)
−0.290832 + 0.956774i \(0.593932\pi\)
\(3\) −0.0778779 1.73030i −0.0449628 0.998989i
\(4\) −1.32333 −0.661666
\(5\) 3.64046i 1.62806i −0.580820 0.814032i \(-0.697268\pi\)
0.580820 0.814032i \(-0.302732\pi\)
\(6\) 0.0640622 + 1.42334i 0.0261533 + 0.581076i
\(7\) 1.97039i 0.744736i −0.928085 0.372368i \(-0.878546\pi\)
0.928085 0.372368i \(-0.121454\pi\)
\(8\) 2.73377 0.966532
\(9\) −2.98787 + 0.269504i −0.995957 + 0.0898347i
\(10\) 2.99464i 0.946987i
\(11\) −3.10754 1.15897i −0.936957 0.349443i
\(12\) 0.103058 + 2.28976i 0.0297504 + 0.660997i
\(13\) 1.00000i 0.277350i
\(14\) 1.62084i 0.433187i
\(15\) −6.29909 + 0.283512i −1.62642 + 0.0732024i
\(16\) 0.397876 0.0994690
\(17\) 7.48590 1.81560 0.907799 0.419406i \(-0.137762\pi\)
0.907799 + 0.419406i \(0.137762\pi\)
\(18\) 2.45782 0.221694i 0.579313 0.0522537i
\(19\) 4.73844i 1.08707i 0.839386 + 0.543536i \(0.182915\pi\)
−0.839386 + 0.543536i \(0.817085\pi\)
\(20\) 4.81754i 1.07724i
\(21\) −3.40936 + 0.153450i −0.743983 + 0.0334855i
\(22\) 2.55625 + 0.953369i 0.544995 + 0.203259i
\(23\) 1.40786i 0.293560i −0.989169 0.146780i \(-0.953109\pi\)
0.989169 0.146780i \(-0.0468909\pi\)
\(24\) −0.212900 4.73023i −0.0434580 0.965555i
\(25\) −8.25297 −1.65059
\(26\) 0.822598i 0.161325i
\(27\) 0.699012 + 5.14892i 0.134525 + 0.990910i
\(28\) 2.60748i 0.492767i
\(29\) −0.599024 −0.111236 −0.0556180 0.998452i \(-0.517713\pi\)
−0.0556180 + 0.998452i \(0.517713\pi\)
\(30\) 5.18162 0.233216i 0.946029 0.0425792i
\(31\) −3.80588 −0.683555 −0.341778 0.939781i \(-0.611029\pi\)
−0.341778 + 0.939781i \(0.611029\pi\)
\(32\) −5.79482 −1.02439
\(33\) −1.76336 + 5.46723i −0.306962 + 0.951722i
\(34\) −6.15788 −1.05607
\(35\) −7.17312 −1.21248
\(36\) 3.95395 0.356644i 0.658991 0.0594406i
\(37\) 4.99572 0.821291 0.410645 0.911795i \(-0.365303\pi\)
0.410645 + 0.911795i \(0.365303\pi\)
\(38\) 3.89783i 0.632311i
\(39\) −1.73030 + 0.0778779i −0.277070 + 0.0124704i
\(40\) 9.95217i 1.57358i
\(41\) −9.36809 −1.46305 −0.731525 0.681815i \(-0.761191\pi\)
−0.731525 + 0.681815i \(0.761191\pi\)
\(42\) 2.80453 0.126227i 0.432748 0.0194773i
\(43\) 5.55007i 0.846378i 0.906041 + 0.423189i \(0.139089\pi\)
−0.906041 + 0.423189i \(0.860911\pi\)
\(44\) 4.11231 + 1.53371i 0.619953 + 0.231215i
\(45\) 0.981120 + 10.8772i 0.146257 + 1.62148i
\(46\) 1.15811i 0.170753i
\(47\) 11.4369i 1.66824i −0.551582 0.834121i \(-0.685976\pi\)
0.551582 0.834121i \(-0.314024\pi\)
\(48\) −0.0309857 0.688444i −0.00447241 0.0993684i
\(49\) 3.11758 0.445368
\(50\) 6.78887 0.960092
\(51\) −0.582986 12.9528i −0.0816344 1.81376i
\(52\) 1.32333i 0.183513i
\(53\) 7.53108i 1.03447i −0.855843 0.517236i \(-0.826961\pi\)
0.855843 0.517236i \(-0.173039\pi\)
\(54\) −0.575006 4.23549i −0.0782484 0.576377i
\(55\) −4.21920 + 11.3129i −0.568916 + 1.52543i
\(56\) 5.38658i 0.719812i
\(57\) 8.19892 0.369020i 1.08597 0.0488779i
\(58\) 0.492756 0.0647020
\(59\) 1.46468i 0.190685i 0.995445 + 0.0953425i \(0.0303946\pi\)
−0.995445 + 0.0953425i \(0.969605\pi\)
\(60\) 8.33579 0.375180i 1.07615 0.0484356i
\(61\) 0.106909i 0.0136882i −0.999977 0.00684412i \(-0.997821\pi\)
0.999977 0.00684412i \(-0.00217857\pi\)
\(62\) 3.13070 0.397600
\(63\) 0.531027 + 5.88726i 0.0669032 + 0.741725i
\(64\) 3.97106 0.496382
\(65\) −3.64046 −0.451544
\(66\) 1.45054 4.49733i 0.178549 0.553583i
\(67\) 7.88900 0.963795 0.481898 0.876228i \(-0.339948\pi\)
0.481898 + 0.876228i \(0.339948\pi\)
\(68\) −9.90634 −1.20132
\(69\) −2.43603 + 0.109642i −0.293263 + 0.0131993i
\(70\) 5.90059 0.705256
\(71\) 5.03736i 0.597824i 0.954281 + 0.298912i \(0.0966238\pi\)
−0.954281 + 0.298912i \(0.903376\pi\)
\(72\) −8.16814 + 0.736761i −0.962624 + 0.0868282i
\(73\) 0.797068i 0.0932898i 0.998912 + 0.0466449i \(0.0148529\pi\)
−0.998912 + 0.0466449i \(0.985147\pi\)
\(74\) −4.10947 −0.477716
\(75\) 0.642724 + 14.2801i 0.0742154 + 1.64892i
\(76\) 6.27053i 0.719279i
\(77\) −2.28362 + 6.12305i −0.260243 + 0.697786i
\(78\) 1.42334 0.0640622i 0.161162 0.00725362i
\(79\) 0.729545i 0.0820802i −0.999158 0.0410401i \(-0.986933\pi\)
0.999158 0.0410401i \(-0.0130671\pi\)
\(80\) 1.44845i 0.161942i
\(81\) 8.85473 1.61049i 0.983859 0.178943i
\(82\) 7.70617 0.851004
\(83\) −1.46934 −0.161281 −0.0806404 0.996743i \(-0.525697\pi\)
−0.0806404 + 0.996743i \(0.525697\pi\)
\(84\) 4.51172 0.203065i 0.492269 0.0221562i
\(85\) 27.2521i 2.95591i
\(86\) 4.56548i 0.492308i
\(87\) 0.0466507 + 1.03649i 0.00500148 + 0.111123i
\(88\) −8.49528 3.16836i −0.905600 0.337748i
\(89\) 13.4031i 1.42072i −0.703837 0.710362i \(-0.748531\pi\)
0.703837 0.710362i \(-0.251469\pi\)
\(90\) −0.807067 8.94758i −0.0850723 0.943158i
\(91\) −1.97039 −0.206553
\(92\) 1.86307i 0.194239i
\(93\) 0.296394 + 6.58530i 0.0307346 + 0.682864i
\(94\) 9.40796i 0.970357i
\(95\) 17.2501 1.76982
\(96\) 0.451289 + 10.0268i 0.0460595 + 1.02335i
\(97\) −2.10062 −0.213286 −0.106643 0.994297i \(-0.534010\pi\)
−0.106643 + 0.994297i \(0.534010\pi\)
\(98\) −2.56451 −0.259055
\(99\) 9.59726 + 2.62537i 0.964561 + 0.263859i
\(100\) 10.9214 1.09214
\(101\) −1.50969 −0.150220 −0.0751099 0.997175i \(-0.523931\pi\)
−0.0751099 + 0.997175i \(0.523931\pi\)
\(102\) 0.479563 + 10.6550i 0.0474838 + 1.05500i
\(103\) −8.67941 −0.855208 −0.427604 0.903966i \(-0.640642\pi\)
−0.427604 + 0.903966i \(0.640642\pi\)
\(104\) 2.73377i 0.268068i
\(105\) 0.558628 + 12.4116i 0.0545165 + 1.21125i
\(106\) 6.19505i 0.601716i
\(107\) 12.0532 1.16522 0.582611 0.812751i \(-0.302031\pi\)
0.582611 + 0.812751i \(0.302031\pi\)
\(108\) −0.925026 6.81374i −0.0890106 0.655652i
\(109\) 9.00369i 0.862397i −0.902257 0.431198i \(-0.858091\pi\)
0.902257 0.431198i \(-0.141909\pi\)
\(110\) 3.47070 9.30594i 0.330918 0.887287i
\(111\) −0.389056 8.64408i −0.0369276 0.820460i
\(112\) 0.783969i 0.0740781i
\(113\) 13.1365i 1.23578i 0.786264 + 0.617891i \(0.212013\pi\)
−0.786264 + 0.617891i \(0.787987\pi\)
\(114\) −6.74441 + 0.303555i −0.631672 + 0.0284305i
\(115\) −5.12528 −0.477934
\(116\) 0.792708 0.0736011
\(117\) 0.269504 + 2.98787i 0.0249157 + 0.276229i
\(118\) 1.20484i 0.110915i
\(119\) 14.7501i 1.35214i
\(120\) −17.2202 + 0.775055i −1.57199 + 0.0707525i
\(121\) 8.31356 + 7.20310i 0.755779 + 0.654827i
\(122\) 0.0879428i 0.00796196i
\(123\) 0.729567 + 16.2096i 0.0657829 + 1.46157i
\(124\) 5.03644 0.452286
\(125\) 11.8423i 1.05921i
\(126\) −0.436822 4.84285i −0.0389152 0.431435i
\(127\) 13.8614i 1.23000i −0.788525 0.615002i \(-0.789155\pi\)
0.788525 0.615002i \(-0.210845\pi\)
\(128\) 8.32307 0.735662
\(129\) 9.60329 0.432228i 0.845522 0.0380556i
\(130\) 2.99464 0.262647
\(131\) −14.4584 −1.26323 −0.631617 0.775281i \(-0.717608\pi\)
−0.631617 + 0.775281i \(0.717608\pi\)
\(132\) 2.33351 7.23496i 0.203106 0.629722i
\(133\) 9.33656 0.809582
\(134\) −6.48948 −0.560605
\(135\) 18.7445 2.54473i 1.61327 0.219015i
\(136\) 20.4647 1.75483
\(137\) 9.16681i 0.783174i −0.920141 0.391587i \(-0.871926\pi\)
0.920141 0.391587i \(-0.128074\pi\)
\(138\) 2.00387 0.0901909i 0.170581 0.00767756i
\(139\) 6.45802i 0.547762i 0.961764 + 0.273881i \(0.0883075\pi\)
−0.961764 + 0.273881i \(0.911692\pi\)
\(140\) 9.49242 0.802256
\(141\) −19.7892 + 0.890681i −1.66655 + 0.0750089i
\(142\) 4.14372i 0.347733i
\(143\) −1.15897 + 3.10754i −0.0969182 + 0.259865i
\(144\) −1.18880 + 0.107229i −0.0990668 + 0.00893577i
\(145\) 2.18072i 0.181099i
\(146\) 0.655667i 0.0542634i
\(147\) −0.242790 5.39434i −0.0200250 0.444918i
\(148\) −6.61100 −0.543421
\(149\) 12.7811 1.04707 0.523534 0.852005i \(-0.324613\pi\)
0.523534 + 0.852005i \(0.324613\pi\)
\(150\) −0.528703 11.7468i −0.0431684 0.959121i
\(151\) 15.5506i 1.26549i −0.774361 0.632744i \(-0.781928\pi\)
0.774361 0.632744i \(-0.218072\pi\)
\(152\) 12.9538i 1.05069i
\(153\) −22.3669 + 2.01748i −1.80826 + 0.163104i
\(154\) 1.87850 5.03681i 0.151374 0.405877i
\(155\) 13.8551i 1.11287i
\(156\) 2.28976 0.103058i 0.183328 0.00825128i
\(157\) 5.77124 0.460595 0.230297 0.973120i \(-0.426030\pi\)
0.230297 + 0.973120i \(0.426030\pi\)
\(158\) 0.600122i 0.0477431i
\(159\) −13.0310 + 0.586505i −1.03343 + 0.0465128i
\(160\) 21.0958i 1.66777i
\(161\) −2.77404 −0.218625
\(162\) −7.28389 + 1.32478i −0.572276 + 0.104085i
\(163\) −16.2905 −1.27597 −0.637987 0.770047i \(-0.720233\pi\)
−0.637987 + 0.770047i \(0.720233\pi\)
\(164\) 12.3971 0.968051
\(165\) 19.9032 + 6.41945i 1.54946 + 0.499754i
\(166\) 1.20867 0.0938113
\(167\) −5.00890 −0.387600 −0.193800 0.981041i \(-0.562081\pi\)
−0.193800 + 0.981041i \(0.562081\pi\)
\(168\) −9.32039 + 0.419495i −0.719084 + 0.0323648i
\(169\) −1.00000 −0.0769231
\(170\) 22.4175i 1.71935i
\(171\) −1.27703 14.1578i −0.0976569 1.08268i
\(172\) 7.34460i 0.560020i
\(173\) −25.7966 −1.96128 −0.980640 0.195821i \(-0.937263\pi\)
−0.980640 + 0.195821i \(0.937263\pi\)
\(174\) −0.0383748 0.852615i −0.00290919 0.0646366i
\(175\) 16.2615i 1.22926i
\(176\) −1.23641 0.461127i −0.0931982 0.0347588i
\(177\) 2.53433 0.114066i 0.190492 0.00857374i
\(178\) 11.0253i 0.826384i
\(179\) 17.2616i 1.29019i 0.764101 + 0.645097i \(0.223183\pi\)
−0.764101 + 0.645097i \(0.776817\pi\)
\(180\) −1.29835 14.3942i −0.0967732 1.07288i
\(181\) 14.0884 1.04718 0.523591 0.851969i \(-0.324592\pi\)
0.523591 + 0.851969i \(0.324592\pi\)
\(182\) 1.62084 0.120144
\(183\) −0.184984 + 0.00832582i −0.0136744 + 0.000615462i
\(184\) 3.84877i 0.283735i
\(185\) 18.1867i 1.33711i
\(186\) −0.243813 5.41706i −0.0178772 0.397198i
\(187\) −23.2627 8.67595i −1.70114 0.634449i
\(188\) 15.1348i 1.10382i
\(189\) 10.1454 1.37732i 0.737967 0.100186i
\(190\) −14.1899 −1.02944
\(191\) 10.0965i 0.730558i −0.930898 0.365279i \(-0.880974\pi\)
0.930898 0.365279i \(-0.119026\pi\)
\(192\) −0.309258 6.87112i −0.0223188 0.495880i
\(193\) 23.3319i 1.67947i −0.542998 0.839734i \(-0.682711\pi\)
0.542998 0.839734i \(-0.317289\pi\)
\(194\) 1.72797 0.124061
\(195\) 0.283512 + 6.29909i 0.0203027 + 0.451087i
\(196\) −4.12559 −0.294685
\(197\) −13.5231 −0.963483 −0.481742 0.876313i \(-0.659996\pi\)
−0.481742 + 0.876313i \(0.659996\pi\)
\(198\) −7.89469 2.15962i −0.561051 0.153478i
\(199\) −14.9912 −1.06270 −0.531348 0.847154i \(-0.678314\pi\)
−0.531348 + 0.847154i \(0.678314\pi\)
\(200\) −22.5617 −1.59535
\(201\) −0.614379 13.6503i −0.0433350 0.962821i
\(202\) 1.24187 0.0873776
\(203\) 1.18031i 0.0828414i
\(204\) 0.771485 + 17.1409i 0.0540148 + 1.20010i
\(205\) 34.1042i 2.38194i
\(206\) 7.13966 0.497444
\(207\) 0.379425 + 4.20651i 0.0263719 + 0.292373i
\(208\) 0.397876i 0.0275877i
\(209\) 5.49172 14.7249i 0.379870 1.01854i
\(210\) −0.459526 10.2098i −0.0317103 0.704542i
\(211\) 18.8296i 1.29628i 0.761520 + 0.648141i \(0.224453\pi\)
−0.761520 + 0.648141i \(0.775547\pi\)
\(212\) 9.96612i 0.684476i
\(213\) 8.71614 0.392299i 0.597220 0.0268799i
\(214\) −9.91490 −0.677768
\(215\) 20.2048 1.37796
\(216\) 1.91094 + 14.0759i 0.130023 + 0.957747i
\(217\) 7.49905i 0.509068i
\(218\) 7.40641i 0.501626i
\(219\) 1.37917 0.0620740i 0.0931954 0.00419457i
\(220\) 5.58340 14.9707i 0.376433 1.00932i
\(221\) 7.48590i 0.503556i
\(222\) 0.320037 + 7.11060i 0.0214795 + 0.477233i
\(223\) −15.1932 −1.01741 −0.508704 0.860941i \(-0.669875\pi\)
−0.508704 + 0.860941i \(0.669875\pi\)
\(224\) 11.4180i 0.762900i
\(225\) 24.6588 2.22421i 1.64392 0.148281i
\(226\) 10.8061i 0.718810i
\(227\) 16.2947 1.08152 0.540759 0.841177i \(-0.318137\pi\)
0.540759 + 0.841177i \(0.318137\pi\)
\(228\) −10.8499 + 0.488336i −0.718552 + 0.0323408i
\(229\) 18.5904 1.22849 0.614244 0.789116i \(-0.289461\pi\)
0.614244 + 0.789116i \(0.289461\pi\)
\(230\) 4.21604 0.277997
\(231\) 10.7725 + 3.47450i 0.708782 + 0.228606i
\(232\) −1.63759 −0.107513
\(233\) −6.38041 −0.417995 −0.208997 0.977916i \(-0.567020\pi\)
−0.208997 + 0.977916i \(0.567020\pi\)
\(234\) −0.221694 2.45782i −0.0144926 0.160672i
\(235\) −41.6356 −2.71600
\(236\) 1.93826i 0.126170i
\(237\) −1.26233 + 0.0568154i −0.0819972 + 0.00369056i
\(238\) 12.1334i 0.786492i
\(239\) −24.6706 −1.59581 −0.797906 0.602782i \(-0.794059\pi\)
−0.797906 + 0.602782i \(0.794059\pi\)
\(240\) −2.50626 + 0.112802i −0.161778 + 0.00728137i
\(241\) 11.9918i 0.772458i −0.922403 0.386229i \(-0.873777\pi\)
0.922403 0.386229i \(-0.126223\pi\)
\(242\) −6.83872 5.92525i −0.439609 0.380890i
\(243\) −3.47621 15.1959i −0.222999 0.974819i
\(244\) 0.141476i 0.00905705i
\(245\) 11.3494i 0.725088i
\(246\) −0.600140 13.3340i −0.0382636 0.850143i
\(247\) 4.73844 0.301500
\(248\) −10.4044 −0.660678
\(249\) 0.114429 + 2.54240i 0.00725164 + 0.161118i
\(250\) 9.74146i 0.616104i
\(251\) 10.1956i 0.643544i 0.946817 + 0.321772i \(0.104278\pi\)
−0.946817 + 0.321772i \(0.895722\pi\)
\(252\) −0.702726 7.79080i −0.0442676 0.490775i
\(253\) −1.63168 + 4.37499i −0.102583 + 0.275053i
\(254\) 11.4024i 0.715450i
\(255\) −47.1543 + 2.12234i −2.95292 + 0.132906i
\(256\) −14.7887 −0.924291
\(257\) 16.6626i 1.03939i −0.854353 0.519693i \(-0.826046\pi\)
0.854353 0.519693i \(-0.173954\pi\)
\(258\) −7.89964 + 0.355550i −0.491810 + 0.0221356i
\(259\) 9.84349i 0.611645i
\(260\) 4.81754 0.298771
\(261\) 1.78981 0.161439i 0.110786 0.00999285i
\(262\) 11.8934 0.734778
\(263\) 9.52849 0.587552 0.293776 0.955874i \(-0.405088\pi\)
0.293776 + 0.955874i \(0.405088\pi\)
\(264\) −4.82062 + 14.9461i −0.296689 + 0.919870i
\(265\) −27.4166 −1.68419
\(266\) −7.68023 −0.470905
\(267\) −23.1913 + 1.04380i −1.41929 + 0.0638798i
\(268\) −10.4398 −0.637711
\(269\) 13.6704i 0.833499i −0.909021 0.416750i \(-0.863169\pi\)
0.909021 0.416750i \(-0.136831\pi\)
\(270\) −15.4191 + 2.09329i −0.938379 + 0.127393i
\(271\) 5.38915i 0.327368i 0.986513 + 0.163684i \(0.0523377\pi\)
−0.986513 + 0.163684i \(0.947662\pi\)
\(272\) 2.97846 0.180596
\(273\) 0.153450 + 3.40936i 0.00928719 + 0.206344i
\(274\) 7.54060i 0.455544i
\(275\) 25.6464 + 9.56497i 1.54654 + 0.576789i
\(276\) 3.22367 0.145092i 0.194042 0.00873352i
\(277\) 19.6645i 1.18152i 0.806846 + 0.590762i \(0.201173\pi\)
−0.806846 + 0.590762i \(0.798827\pi\)
\(278\) 5.31235i 0.318614i
\(279\) 11.3715 1.02570i 0.680792 0.0614070i
\(280\) −19.6096 −1.17190
\(281\) 15.9614 0.952180 0.476090 0.879397i \(-0.342054\pi\)
0.476090 + 0.879397i \(0.342054\pi\)
\(282\) 16.2786 0.732672i 0.969376 0.0436300i
\(283\) 13.8927i 0.825834i −0.910769 0.412917i \(-0.864510\pi\)
0.910769 0.412917i \(-0.135490\pi\)
\(284\) 6.66610i 0.395560i
\(285\) −1.34340 29.8478i −0.0795763 1.76803i
\(286\) 0.953369 2.55625i 0.0563739 0.151154i
\(287\) 18.4588i 1.08959i
\(288\) 17.3142 1.56173i 1.02025 0.0920258i
\(289\) 39.0387 2.29639
\(290\) 1.79386i 0.105339i
\(291\) 0.163592 + 3.63470i 0.00958994 + 0.213070i
\(292\) 1.05479i 0.0617267i
\(293\) 26.6897 1.55923 0.779614 0.626261i \(-0.215415\pi\)
0.779614 + 0.626261i \(0.215415\pi\)
\(294\) 0.199719 + 4.43737i 0.0116478 + 0.258793i
\(295\) 5.33211 0.310447
\(296\) 13.6571 0.793804
\(297\) 3.79525 16.8106i 0.220223 0.975450i
\(298\) −10.5137 −0.609042
\(299\) −1.40786 −0.0814189
\(300\) −0.850538 18.8973i −0.0491058 1.09104i
\(301\) 10.9358 0.630329
\(302\) 12.7919i 0.736090i
\(303\) 0.117572 + 2.61222i 0.00675431 + 0.150068i
\(304\) 1.88531i 0.108130i
\(305\) −0.389197 −0.0222853
\(306\) 18.3990 1.65958i 1.05180 0.0948716i
\(307\) 32.3856i 1.84835i 0.381974 + 0.924173i \(0.375244\pi\)
−0.381974 + 0.924173i \(0.624756\pi\)
\(308\) 3.02200 8.10283i 0.172194 0.461702i
\(309\) 0.675934 + 15.0180i 0.0384526 + 0.854343i
\(310\) 11.3972i 0.647318i
\(311\) 7.90235i 0.448101i 0.974578 + 0.224051i \(0.0719281\pi\)
−0.974578 + 0.224051i \(0.928072\pi\)
\(312\) −4.73023 + 0.212900i −0.267797 + 0.0120531i
\(313\) 31.8926 1.80268 0.901338 0.433117i \(-0.142586\pi\)
0.901338 + 0.433117i \(0.142586\pi\)
\(314\) −4.74741 −0.267912
\(315\) 21.4323 1.93319i 1.20758 0.108923i
\(316\) 0.965431i 0.0543097i
\(317\) 30.9739i 1.73966i 0.493347 + 0.869832i \(0.335773\pi\)
−0.493347 + 0.869832i \(0.664227\pi\)
\(318\) 10.7193 0.482457i 0.601107 0.0270549i
\(319\) 1.86149 + 0.694252i 0.104223 + 0.0388707i
\(320\) 14.4565i 0.808142i
\(321\) −0.938675 20.8556i −0.0523917 1.16404i
\(322\) 2.28192 0.127166
\(323\) 35.4715i 1.97369i
\(324\) −11.7178 + 2.13121i −0.650987 + 0.118401i
\(325\) 8.25297i 0.457792i
\(326\) 13.4006 0.742189
\(327\) −15.5791 + 0.701188i −0.861525 + 0.0387758i
\(328\) −25.6102 −1.41408
\(329\) −22.5351 −1.24240
\(330\) −16.3724 5.28063i −0.901268 0.290689i
\(331\) 19.6028 1.07747 0.538734 0.842476i \(-0.318903\pi\)
0.538734 + 0.842476i \(0.318903\pi\)
\(332\) 1.94442 0.106714
\(333\) −14.9266 + 1.34637i −0.817970 + 0.0737804i
\(334\) 4.12031 0.225453
\(335\) 28.7196i 1.56912i
\(336\) −1.35650 + 0.0610539i −0.0740032 + 0.00333076i
\(337\) 1.13045i 0.0615795i 0.999526 + 0.0307898i \(0.00980224\pi\)
−0.999526 + 0.0307898i \(0.990198\pi\)
\(338\) 0.822598 0.0447434
\(339\) 22.7301 1.02305i 1.23453 0.0555642i
\(340\) 36.0637i 1.95583i
\(341\) 11.8269 + 4.41091i 0.640462 + 0.238864i
\(342\) 1.05048 + 11.6462i 0.0568035 + 0.629755i
\(343\) 19.9355i 1.07642i
\(344\) 15.1726i 0.818052i
\(345\) 0.399146 + 8.86826i 0.0214893 + 0.477451i
\(346\) 21.2202 1.14081
\(347\) 5.18095 0.278128 0.139064 0.990283i \(-0.455591\pi\)
0.139064 + 0.990283i \(0.455591\pi\)
\(348\) −0.0617345 1.37162i −0.00330931 0.0735267i
\(349\) 6.62690i 0.354730i −0.984145 0.177365i \(-0.943243\pi\)
0.984145 0.177365i \(-0.0567573\pi\)
\(350\) 13.3767i 0.715015i
\(351\) 5.14892 0.699012i 0.274829 0.0373105i
\(352\) 18.0076 + 6.71604i 0.959810 + 0.357966i
\(353\) 11.0354i 0.587353i 0.955905 + 0.293677i \(0.0948789\pi\)
−0.955905 + 0.293677i \(0.905121\pi\)
\(354\) −2.08474 + 0.0938305i −0.110802 + 0.00498704i
\(355\) 18.3383 0.973297
\(356\) 17.7367i 0.940045i
\(357\) −25.5221 + 1.14871i −1.35077 + 0.0607961i
\(358\) 14.1994i 0.750460i
\(359\) −13.4125 −0.707883 −0.353941 0.935268i \(-0.615159\pi\)
−0.353941 + 0.935268i \(0.615159\pi\)
\(360\) 2.68215 + 29.7358i 0.141362 + 1.56721i
\(361\) −3.45280 −0.181726
\(362\) −11.5891 −0.609109
\(363\) 11.8161 14.9459i 0.620183 0.784457i
\(364\) 2.60748 0.136669
\(365\) 2.90170 0.151882
\(366\) 0.152167 0.00684880i 0.00795391 0.000357992i
\(367\) 26.6740 1.39237 0.696185 0.717862i \(-0.254879\pi\)
0.696185 + 0.717862i \(0.254879\pi\)
\(368\) 0.560155i 0.0292001i
\(369\) 27.9906 2.52474i 1.45713 0.131433i
\(370\) 14.9604i 0.777752i
\(371\) −14.8391 −0.770409
\(372\) −0.392228 8.71455i −0.0203360 0.451828i
\(373\) 25.5671i 1.32382i −0.749585 0.661908i \(-0.769747\pi\)
0.749585 0.661908i \(-0.230253\pi\)
\(374\) 19.1358 + 7.13682i 0.989491 + 0.369036i
\(375\) 20.4907 0.922255i 1.05814 0.0476250i
\(376\) 31.2658i 1.61241i
\(377\) 0.599024i 0.0308513i
\(378\) −8.34555 + 1.13298i −0.429249 + 0.0582744i
\(379\) −12.1517 −0.624189 −0.312095 0.950051i \(-0.601031\pi\)
−0.312095 + 0.950051i \(0.601031\pi\)
\(380\) −22.8276 −1.17103
\(381\) −23.9845 + 1.07950i −1.22876 + 0.0553045i
\(382\) 8.30537i 0.424940i
\(383\) 4.94055i 0.252450i 0.992002 + 0.126225i \(0.0402862\pi\)
−0.992002 + 0.126225i \(0.959714\pi\)
\(384\) −0.648183 14.4014i −0.0330775 0.734918i
\(385\) 22.2907 + 8.31345i 1.13604 + 0.423693i
\(386\) 19.1928i 0.976887i
\(387\) −1.49577 16.5829i −0.0760342 0.842956i
\(388\) 2.77982 0.141124
\(389\) 7.29922i 0.370085i −0.982730 0.185043i \(-0.940758\pi\)
0.982730 0.185043i \(-0.0592423\pi\)
\(390\) −0.233216 5.18162i −0.0118094 0.262381i
\(391\) 10.5391i 0.532987i
\(392\) 8.52272 0.430463
\(393\) 1.12599 + 25.0173i 0.0567986 + 1.26196i
\(394\) 11.1241 0.560424
\(395\) −2.65588 −0.133632
\(396\) −12.7004 3.47423i −0.638218 0.174587i
\(397\) 23.0312 1.15590 0.577951 0.816071i \(-0.303852\pi\)
0.577951 + 0.816071i \(0.303852\pi\)
\(398\) 12.3317 0.618132
\(399\) −0.727112 16.1550i −0.0364011 0.808763i
\(400\) −3.28366 −0.164183
\(401\) 10.2892i 0.513818i −0.966436 0.256909i \(-0.917296\pi\)
0.966436 0.256909i \(-0.0827041\pi\)
\(402\) 0.505387 + 11.2287i 0.0252064 + 0.560039i
\(403\) 3.80588i 0.189584i
\(404\) 1.99782 0.0993955
\(405\) −5.86292 32.2353i −0.291331 1.60179i
\(406\) 0.970919i 0.0481859i
\(407\) −15.5244 5.78990i −0.769515 0.286995i
\(408\) −1.59375 35.4100i −0.0789023 1.75306i
\(409\) 7.84172i 0.387748i −0.981026 0.193874i \(-0.937895\pi\)
0.981026 0.193874i \(-0.0621053\pi\)
\(410\) 28.0540i 1.38549i
\(411\) −15.8613 + 0.713892i −0.782382 + 0.0352137i
\(412\) 11.4857 0.565862
\(413\) 2.88598 0.142010
\(414\) −0.312114 3.46027i −0.0153396 0.170063i
\(415\) 5.34907i 0.262576i
\(416\) 5.79482i 0.284115i
\(417\) 11.1743 0.502937i 0.547208 0.0246290i
\(418\) −4.51748 + 12.1126i −0.220957 + 0.592449i
\(419\) 26.0909i 1.27462i −0.770606 0.637312i \(-0.780046\pi\)
0.770606 0.637312i \(-0.219954\pi\)
\(420\) −0.739250 16.4247i −0.0360717 0.801445i
\(421\) 34.5203 1.68242 0.841209 0.540710i \(-0.181844\pi\)
0.841209 + 0.540710i \(0.181844\pi\)
\(422\) 15.4892i 0.754001i
\(423\) 3.08229 + 34.1719i 0.149866 + 1.66150i
\(424\) 20.5882i 0.999851i
\(425\) −61.7809 −2.99681
\(426\) −7.16987 + 0.322704i −0.347382 + 0.0156351i
\(427\) −0.210651 −0.0101941
\(428\) −15.9503 −0.770989
\(429\) 5.46723 + 1.76336i 0.263960 + 0.0851359i
\(430\) −16.6205 −0.801509
\(431\) 20.5500 0.989858 0.494929 0.868933i \(-0.335194\pi\)
0.494929 + 0.868933i \(0.335194\pi\)
\(432\) 0.278120 + 2.04863i 0.0133811 + 0.0985648i
\(433\) −37.7944 −1.81629 −0.908143 0.418661i \(-0.862500\pi\)
−0.908143 + 0.418661i \(0.862500\pi\)
\(434\) 6.16870i 0.296107i
\(435\) 3.77330 0.169830i 0.180916 0.00814274i
\(436\) 11.9149i 0.570619i
\(437\) 6.67108 0.319121
\(438\) −1.13450 + 0.0510619i −0.0542085 + 0.00243983i
\(439\) 10.2561i 0.489496i 0.969587 + 0.244748i \(0.0787052\pi\)
−0.969587 + 0.244748i \(0.921295\pi\)
\(440\) −11.5343 + 30.9267i −0.549876 + 1.47437i
\(441\) −9.31491 + 0.840200i −0.443567 + 0.0400095i
\(442\) 6.15788i 0.292901i
\(443\) 27.2560i 1.29497i −0.762078 0.647485i \(-0.775821\pi\)
0.762078 0.647485i \(-0.224179\pi\)
\(444\) 0.514851 + 11.4390i 0.0244337 + 0.542871i
\(445\) −48.7934 −2.31303
\(446\) 12.4979 0.591791
\(447\) −0.995365 22.1151i −0.0470791 1.04601i
\(448\) 7.82452i 0.369674i
\(449\) 11.2839i 0.532519i −0.963901 0.266260i \(-0.914212\pi\)
0.963901 0.266260i \(-0.0857879\pi\)
\(450\) −20.2843 + 1.82963i −0.956210 + 0.0862496i
\(451\) 29.1117 + 10.8574i 1.37082 + 0.511253i
\(452\) 17.3840i 0.817675i
\(453\) −26.9072 + 1.21105i −1.26421 + 0.0569000i
\(454\) −13.4040 −0.629081
\(455\) 7.17312i 0.336281i
\(456\) 22.4139 1.00881i 1.04963 0.0472420i
\(457\) 32.1191i 1.50247i −0.660037 0.751233i \(-0.729459\pi\)
0.660037 0.751233i \(-0.270541\pi\)
\(458\) −15.2924 −0.714568
\(459\) 5.23273 + 38.5443i 0.244243 + 1.79909i
\(460\) 6.78245 0.316233
\(461\) −19.1961 −0.894050 −0.447025 0.894522i \(-0.647516\pi\)
−0.447025 + 0.894522i \(0.647516\pi\)
\(462\) −8.86147 2.85812i −0.412273 0.132972i
\(463\) −5.80982 −0.270005 −0.135003 0.990845i \(-0.543104\pi\)
−0.135003 + 0.990845i \(0.543104\pi\)
\(464\) −0.238337 −0.0110645
\(465\) 23.9736 1.07901i 1.11175 0.0500379i
\(466\) 5.24851 0.243133
\(467\) 0.750658i 0.0347363i 0.999849 + 0.0173681i \(0.00552873\pi\)
−0.999849 + 0.0173681i \(0.994471\pi\)
\(468\) −0.356644 3.95395i −0.0164859 0.182771i
\(469\) 15.5444i 0.717773i
\(470\) 34.2493 1.57980
\(471\) −0.449452 9.98597i −0.0207097 0.460129i
\(472\) 4.00409i 0.184303i
\(473\) 6.43239 17.2471i 0.295761 0.793021i
\(474\) 1.03839 0.0467362i 0.0476948 0.00214667i
\(475\) 39.1062i 1.79431i
\(476\) 19.5193i 0.894666i
\(477\) 2.02966 + 22.5019i 0.0929316 + 1.03029i
\(478\) 20.2940 0.928227
\(479\) 1.22846 0.0561295 0.0280648 0.999606i \(-0.491066\pi\)
0.0280648 + 0.999606i \(0.491066\pi\)
\(480\) 36.5021 1.64290i 1.66609 0.0749878i
\(481\) 4.99572i 0.227785i
\(482\) 9.86440i 0.449311i
\(483\) 0.216036 + 4.79991i 0.00982999 + 0.218404i
\(484\) −11.0016 9.53210i −0.500073 0.433277i
\(485\) 7.64724i 0.347243i
\(486\) 2.85952 + 12.5001i 0.129711 + 0.567017i
\(487\) 7.82611 0.354635 0.177317 0.984154i \(-0.443258\pi\)
0.177317 + 0.984154i \(0.443258\pi\)
\(488\) 0.292263i 0.0132301i
\(489\) 1.26867 + 28.1875i 0.0573714 + 1.27468i
\(490\) 9.33601i 0.421758i
\(491\) 16.4349 0.741698 0.370849 0.928693i \(-0.379067\pi\)
0.370849 + 0.928693i \(0.379067\pi\)
\(492\) −0.965460 21.4507i −0.0435263 0.967072i
\(493\) −4.48423 −0.201960
\(494\) −3.89783 −0.175372
\(495\) 9.55755 34.9385i 0.429580 1.57037i
\(496\) −1.51427 −0.0679926
\(497\) 9.92554 0.445221
\(498\) −0.0941291 2.09137i −0.00421802 0.0937165i
\(499\) 15.3697 0.688042 0.344021 0.938962i \(-0.388211\pi\)
0.344021 + 0.938962i \(0.388211\pi\)
\(500\) 15.6713i 0.700843i
\(501\) 0.390083 + 8.66690i 0.0174276 + 0.387208i
\(502\) 8.38692i 0.374326i
\(503\) 1.56211 0.0696510 0.0348255 0.999393i \(-0.488912\pi\)
0.0348255 + 0.999393i \(0.488912\pi\)
\(504\) 1.45171 + 16.0944i 0.0646641 + 0.716901i
\(505\) 5.49597i 0.244568i
\(506\) 1.34221 3.59885i 0.0596686 0.159989i
\(507\) 0.0778779 + 1.73030i 0.00345868 + 0.0768453i
\(508\) 18.3433i 0.813853i
\(509\) 37.2107i 1.64934i 0.565617 + 0.824668i \(0.308638\pi\)
−0.565617 + 0.824668i \(0.691362\pi\)
\(510\) 38.7891 1.74583i 1.71761 0.0773067i
\(511\) 1.57053 0.0694763
\(512\) −4.48102 −0.198035
\(513\) −24.3978 + 3.31223i −1.07719 + 0.146238i
\(514\) 13.7066i 0.604574i
\(515\) 31.5971i 1.39233i
\(516\) −12.7083 + 0.571982i −0.559454 + 0.0251801i
\(517\) −13.2550 + 35.5405i −0.582956 + 1.56307i
\(518\) 8.09724i 0.355772i
\(519\) 2.00899 + 44.6358i 0.0881847 + 1.95930i
\(520\) −9.95217 −0.436432
\(521\) 17.0742i 0.748035i 0.927422 + 0.374018i \(0.122020\pi\)
−0.927422 + 0.374018i \(0.877980\pi\)
\(522\) −1.47229 + 0.132800i −0.0644404 + 0.00581249i
\(523\) 2.84243i 0.124291i 0.998067 + 0.0621455i \(0.0197943\pi\)
−0.998067 + 0.0621455i \(0.980206\pi\)
\(524\) 19.1332 0.835839
\(525\) 28.1373 1.26641i 1.22801 0.0552709i
\(526\) −7.83812 −0.341758
\(527\) −28.4904 −1.24106
\(528\) −0.701599 + 2.17528i −0.0305332 + 0.0946668i
\(529\) 21.0179 0.913823
\(530\) 22.5528 0.979632
\(531\) −0.394737 4.37627i −0.0171301 0.189914i
\(532\) −12.3554 −0.535673
\(533\) 9.36809i 0.405777i
\(534\) 19.0771 0.858631i 0.825549 0.0371566i
\(535\) 43.8791i 1.89706i
\(536\) 21.5667 0.931539
\(537\) 29.8678 1.34430i 1.28889 0.0580108i
\(538\) 11.2452i 0.484817i
\(539\) −9.68798 3.61319i −0.417291 0.155631i
\(540\) −24.8052 + 3.36752i −1.06744 + 0.144915i
\(541\) 13.1967i 0.567371i −0.958917 0.283686i \(-0.908443\pi\)
0.958917 0.283686i \(-0.0915573\pi\)
\(542\) 4.43310i 0.190418i
\(543\) −1.09718 24.3772i −0.0470843 1.04612i
\(544\) −43.3795 −1.85988
\(545\) −32.7776 −1.40404
\(546\) −0.126227 2.80453i −0.00540203 0.120023i
\(547\) 37.9580i 1.62296i 0.584377 + 0.811482i \(0.301339\pi\)
−0.584377 + 0.811482i \(0.698661\pi\)
\(548\) 12.1307i 0.518200i
\(549\) 0.0288123 + 0.319429i 0.00122968 + 0.0136329i
\(550\) −21.0967 7.86812i −0.899565 0.335498i
\(551\) 2.83844i 0.120922i
\(552\) −6.65952 + 0.299734i −0.283448 + 0.0127575i
\(553\) −1.43749 −0.0611281
\(554\) 16.1759i 0.687250i
\(555\) −31.4685 + 1.41634i −1.33576 + 0.0601205i
\(556\) 8.54611i 0.362436i
\(557\) 27.0725 1.14710 0.573549 0.819171i \(-0.305566\pi\)
0.573549 + 0.819171i \(0.305566\pi\)
\(558\) −9.35414 + 0.843738i −0.395992 + 0.0357183i
\(559\) 5.55007 0.234743
\(560\) −2.85401 −0.120604
\(561\) −13.2003 + 40.9271i −0.557319 + 1.72794i
\(562\) −13.1298 −0.553849
\(563\) 2.39600 0.100979 0.0504896 0.998725i \(-0.483922\pi\)
0.0504896 + 0.998725i \(0.483922\pi\)
\(564\) 26.1878 1.17867i 1.10270 0.0496309i
\(565\) 47.8231 2.01193
\(566\) 11.4281i 0.480358i
\(567\) −3.17328 17.4473i −0.133265 0.732716i
\(568\) 13.7710i 0.577817i
\(569\) 36.0766 1.51241 0.756205 0.654335i \(-0.227051\pi\)
0.756205 + 0.654335i \(0.227051\pi\)
\(570\) 1.10508 + 24.5528i 0.0462867 + 1.02840i
\(571\) 2.45299i 0.102655i −0.998682 0.0513273i \(-0.983655\pi\)
0.998682 0.0513273i \(-0.0163452\pi\)
\(572\) 1.53371 4.11231i 0.0641275 0.171944i
\(573\) −17.4700 + 0.786295i −0.729819 + 0.0328480i
\(574\) 15.1841i 0.633773i
\(575\) 11.6191i 0.484548i
\(576\) −11.8650 + 1.07022i −0.494375 + 0.0445924i
\(577\) −14.3299 −0.596560 −0.298280 0.954478i \(-0.596413\pi\)
−0.298280 + 0.954478i \(0.596413\pi\)
\(578\) −32.1131 −1.33573
\(579\) −40.3712 + 1.81704i −1.67777 + 0.0755136i
\(580\) 2.88582i 0.119827i
\(581\) 2.89516i 0.120112i
\(582\) −0.134570 2.98990i −0.00557813 0.123935i
\(583\) −8.72831 + 23.4031i −0.361490 + 0.969257i
\(584\) 2.17900i 0.0901676i
\(585\) 10.8772 0.981120i 0.449718 0.0405643i
\(586\) −21.9549 −0.906947
\(587\) 34.0285i 1.40451i −0.711928 0.702253i \(-0.752178\pi\)
0.711928 0.702253i \(-0.247822\pi\)
\(588\) 0.321292 + 7.13851i 0.0132499 + 0.294387i
\(589\) 18.0339i 0.743074i
\(590\) −4.38618 −0.180576
\(591\) 1.05315 + 23.3991i 0.0433209 + 0.962509i
\(592\) 1.98768 0.0816930
\(593\) 28.3202 1.16297 0.581486 0.813557i \(-0.302472\pi\)
0.581486 + 0.813557i \(0.302472\pi\)
\(594\) −3.12197 + 13.8284i −0.128096 + 0.567384i
\(595\) −53.6972 −2.20137
\(596\) −16.9136 −0.692810
\(597\) 1.16748 + 25.9392i 0.0477818 + 1.06162i
\(598\) 1.15811 0.0473585
\(599\) 20.8985i 0.853890i −0.904278 0.426945i \(-0.859590\pi\)
0.904278 0.426945i \(-0.140410\pi\)
\(600\) 1.75706 + 39.0385i 0.0717316 + 1.59374i
\(601\) 39.0459i 1.59272i 0.604826 + 0.796358i \(0.293243\pi\)
−0.604826 + 0.796358i \(0.706757\pi\)
\(602\) −8.99576 −0.366640
\(603\) −23.5713 + 2.12612i −0.959898 + 0.0865823i
\(604\) 20.5786i 0.837331i
\(605\) 26.2226 30.2652i 1.06610 1.23046i
\(606\) −0.0967141 2.14880i −0.00392874 0.0872892i
\(607\) 0.859294i 0.0348777i −0.999848 0.0174388i \(-0.994449\pi\)
0.999848 0.0174388i \(-0.00555124\pi\)
\(608\) 27.4584i 1.11359i
\(609\) 2.04229 0.0919200i 0.0827576 0.00372479i
\(610\) 0.320152 0.0129626
\(611\) −11.4369 −0.462687
\(612\) 29.5988 2.66980i 1.19646 0.107920i
\(613\) 4.87388i 0.196854i −0.995144 0.0984271i \(-0.968619\pi\)
0.995144 0.0984271i \(-0.0313811\pi\)
\(614\) 26.6404i 1.07512i
\(615\) 59.0104 2.65596i 2.37953 0.107099i
\(616\) −6.24290 + 16.7390i −0.251533 + 0.674433i
\(617\) 26.7029i 1.07502i −0.843258 0.537510i \(-0.819365\pi\)
0.843258 0.537510i \(-0.180635\pi\)
\(618\) −0.556022 12.3538i −0.0223665 0.496941i
\(619\) −11.5826 −0.465546 −0.232773 0.972531i \(-0.574780\pi\)
−0.232773 + 0.972531i \(0.574780\pi\)
\(620\) 18.3350i 0.736350i
\(621\) 7.24898 0.984114i 0.290891 0.0394911i
\(622\) 6.50045i 0.260644i
\(623\) −26.4092 −1.05806
\(624\) −0.688444 + 0.0309857i −0.0275598 + 0.00124042i
\(625\) 1.84665 0.0738659
\(626\) −26.2348 −1.04855
\(627\) −25.9061 8.35558i −1.03459 0.333690i
\(628\) −7.63727 −0.304760
\(629\) 37.3974 1.49113
\(630\) −17.6302 + 1.59023i −0.702404 + 0.0633565i
\(631\) 11.0546 0.440078 0.220039 0.975491i \(-0.429381\pi\)
0.220039 + 0.975491i \(0.429381\pi\)
\(632\) 1.99440i 0.0793332i
\(633\) 32.5808 1.46641i 1.29497 0.0582845i
\(634\) 25.4790i 1.01190i
\(635\) −50.4621 −2.00253
\(636\) 17.2444 0.776141i 0.683784 0.0307760i
\(637\) 3.11758i 0.123523i
\(638\) −1.53126 0.571090i −0.0606230 0.0226097i
\(639\) −1.35759 15.0510i −0.0537054 0.595407i
\(640\) 30.2998i 1.19771i
\(641\) 17.4484i 0.689170i 0.938755 + 0.344585i \(0.111980\pi\)
−0.938755 + 0.344585i \(0.888020\pi\)
\(642\) 0.772152 + 17.1557i 0.0304744 + 0.677083i
\(643\) −42.6521 −1.68203 −0.841017 0.541009i \(-0.818043\pi\)
−0.841017 + 0.541009i \(0.818043\pi\)
\(644\) 3.67097 0.144657
\(645\) −1.57351 34.9604i −0.0619569 1.37656i
\(646\) 29.1788i 1.14802i
\(647\) 21.1546i 0.831675i −0.909439 0.415837i \(-0.863489\pi\)
0.909439 0.415837i \(-0.136511\pi\)
\(648\) 24.2068 4.40270i 0.950932 0.172954i
\(649\) 1.69752 4.55154i 0.0666336 0.178664i
\(650\) 6.78887i 0.266282i
\(651\) 12.9756 0.584010i 0.508554 0.0228892i
\(652\) 21.5578 0.844269
\(653\) 24.6435i 0.964375i 0.876068 + 0.482188i \(0.160158\pi\)
−0.876068 + 0.482188i \(0.839842\pi\)
\(654\) 12.8153 0.576796i 0.501118 0.0225545i
\(655\) 52.6352i 2.05663i
\(656\) −3.72734 −0.145528
\(657\) −0.214813 2.38154i −0.00838066 0.0929126i
\(658\) 18.5373 0.722660
\(659\) −0.227092 −0.00884623 −0.00442312 0.999990i \(-0.501408\pi\)
−0.00442312 + 0.999990i \(0.501408\pi\)
\(660\) −26.3386 8.49507i −1.02523 0.330670i
\(661\) 20.9415 0.814529 0.407264 0.913310i \(-0.366483\pi\)
0.407264 + 0.913310i \(0.366483\pi\)
\(662\) −16.1252 −0.626724
\(663\) −12.9528 + 0.582986i −0.503047 + 0.0226413i
\(664\) −4.01683 −0.155883
\(665\) 33.9894i 1.31805i
\(666\) 12.2785 1.10752i 0.475784 0.0429155i
\(667\) 0.843344i 0.0326544i
\(668\) 6.62844 0.256462
\(669\) 1.18321 + 26.2887i 0.0457456 + 1.01638i
\(670\) 23.6247i 0.912702i
\(671\) −0.123904 + 0.332222i −0.00478327 + 0.0128253i
\(672\) 19.7566 0.889214i 0.762129 0.0343022i
\(673\) 5.26906i 0.203107i 0.994830 + 0.101554i \(0.0323813\pi\)
−0.994830 + 0.101554i \(0.967619\pi\)
\(674\) 0.929906i 0.0358186i
\(675\) −5.76892 42.4939i −0.222046 1.63559i
\(676\) 1.32333 0.0508974
\(677\) −20.5547 −0.789979 −0.394990 0.918686i \(-0.629252\pi\)
−0.394990 + 0.918686i \(0.629252\pi\)
\(678\) −18.6978 + 0.841555i −0.718083 + 0.0323197i
\(679\) 4.13904i 0.158842i
\(680\) 74.5010i 2.85698i
\(681\) −1.26900 28.1947i −0.0486281 1.08042i
\(682\) −9.72878 3.62840i −0.372534 0.138939i
\(683\) 14.8519i 0.568293i 0.958781 + 0.284146i \(0.0917102\pi\)
−0.958781 + 0.284146i \(0.908290\pi\)
\(684\) 1.68993 + 18.7355i 0.0646163 + 0.716371i
\(685\) −33.3714 −1.27506
\(686\) 16.3989i 0.626114i
\(687\) −1.44778 32.1670i −0.0552363 1.22725i
\(688\) 2.20824i 0.0841884i
\(689\) −7.53108 −0.286911
\(690\) −0.328336 7.29501i −0.0124996 0.277716i
\(691\) −17.8137 −0.677664 −0.338832 0.940847i \(-0.610032\pi\)
−0.338832 + 0.940847i \(0.610032\pi\)
\(692\) 34.1375 1.29771
\(693\) 5.17299 18.9103i 0.196506 0.718344i
\(694\) −4.26184 −0.161777
\(695\) 23.5102 0.891792
\(696\) 0.127532 + 2.83352i 0.00483410 + 0.107404i
\(697\) −70.1286 −2.65631
\(698\) 5.45127i 0.206334i
\(699\) 0.496893 + 11.0400i 0.0187942 + 0.417572i
\(700\) 21.5194i 0.813358i
\(701\) 5.82035 0.219832 0.109916 0.993941i \(-0.464942\pi\)
0.109916 + 0.993941i \(0.464942\pi\)
\(702\) −4.23549 + 0.575006i −0.159858 + 0.0217022i
\(703\) 23.6719i 0.892803i
\(704\) −12.3402 4.60235i −0.465089 0.173458i
\(705\) 3.24249 + 72.0420i 0.122119 + 2.71326i
\(706\) 9.07767i 0.341643i
\(707\) 2.97468i 0.111874i
\(708\) −3.35377 + 0.150947i −0.126042 + 0.00567295i
\(709\) −2.80679 −0.105411 −0.0527056 0.998610i \(-0.516784\pi\)
−0.0527056 + 0.998610i \(0.516784\pi\)
\(710\) −15.0851 −0.566132
\(711\) 0.196615 + 2.17978i 0.00737365 + 0.0817483i
\(712\) 36.6409i 1.37318i
\(713\) 5.35815i 0.200664i
\(714\) 20.9944 0.944925i 0.785697 0.0353629i
\(715\) 11.3129 + 4.21920i 0.423077 + 0.157789i
\(716\) 22.8429i 0.853678i
\(717\) 1.92130 + 42.6876i 0.0717522 + 1.59420i
\(718\) 11.0331 0.411750
\(719\) 21.1094i 0.787246i −0.919272 0.393623i \(-0.871221\pi\)
0.919272 0.393623i \(-0.128779\pi\)
\(720\) 0.390364 + 4.32779i 0.0145480 + 0.161287i
\(721\) 17.1018i 0.636904i
\(722\) 2.84027 0.105704
\(723\) −20.7494 + 0.933894i −0.771677 + 0.0347319i
\(724\) −18.6437 −0.692886
\(725\) 4.94373 0.183605
\(726\) −9.71988 + 12.2945i −0.360738 + 0.456291i
\(727\) 34.0496 1.26283 0.631414 0.775446i \(-0.282475\pi\)
0.631414 + 0.775446i \(0.282475\pi\)
\(728\) −5.38658 −0.199640
\(729\) −26.0228 + 7.19831i −0.963806 + 0.266604i
\(730\) −2.38693 −0.0883442
\(731\) 41.5473i 1.53668i
\(732\) 0.244795 0.0110178i 0.00904789 0.000407231i
\(733\) 14.2555i 0.526538i 0.964722 + 0.263269i \(0.0848008\pi\)
−0.964722 + 0.263269i \(0.915199\pi\)
\(734\) −21.9420 −0.809892
\(735\) −19.6379 + 0.883869i −0.724355 + 0.0326020i
\(736\) 8.15832i 0.300720i
\(737\) −24.5154 9.14314i −0.903035 0.336792i
\(738\) −23.0250 + 2.07684i −0.847563 + 0.0764497i
\(739\) 35.2355i 1.29616i 0.761573 + 0.648079i \(0.224427\pi\)
−0.761573 + 0.648079i \(0.775573\pi\)
\(740\) 24.0671i 0.884724i
\(741\) −0.369020 8.19892i −0.0135563 0.301195i
\(742\) 12.2066 0.448120
\(743\) 46.2519 1.69682 0.848410 0.529340i \(-0.177561\pi\)
0.848410 + 0.529340i \(0.177561\pi\)
\(744\) 0.810271 + 18.0027i 0.0297060 + 0.660010i
\(745\) 46.5291i 1.70469i
\(746\) 21.0315i 0.770017i
\(747\) 4.39019 0.395993i 0.160629 0.0144886i
\(748\) 30.7843 + 11.4812i 1.12559 + 0.419793i
\(749\) 23.7494i 0.867783i
\(750\) −16.8556 + 0.758645i −0.615481 + 0.0277018i
\(751\) 17.0401 0.621802 0.310901 0.950442i \(-0.399369\pi\)
0.310901 + 0.950442i \(0.399369\pi\)
\(752\) 4.55046i 0.165938i
\(753\) 17.6415 0.794016i 0.642893 0.0289356i
\(754\) 0.492756i 0.0179451i
\(755\) −56.6113 −2.06030
\(756\) −13.4257 + 1.82266i −0.488288 + 0.0662894i
\(757\) 23.0404 0.837416 0.418708 0.908121i \(-0.362483\pi\)
0.418708 + 0.908121i \(0.362483\pi\)
\(758\) 9.99594 0.363069
\(759\) 7.69711 + 2.48257i 0.279387 + 0.0901117i
\(760\) 47.1578 1.71059
\(761\) −5.48710 −0.198907 −0.0994536 0.995042i \(-0.531709\pi\)
−0.0994536 + 0.995042i \(0.531709\pi\)
\(762\) 19.7296 0.887995i 0.714726 0.0321687i
\(763\) −17.7407 −0.642258
\(764\) 13.3610i 0.483386i
\(765\) 7.34457 + 81.4258i 0.265543 + 2.94396i
\(766\) 4.06408i 0.146841i
\(767\) 1.46468 0.0528865
\(768\) 1.15171 + 25.5888i 0.0415587 + 0.923356i
\(769\) 26.4840i 0.955036i −0.878622 0.477518i \(-0.841537\pi\)
0.878622 0.477518i \(-0.158463\pi\)
\(770\) −18.3363 6.83863i −0.660794 0.246447i
\(771\) −28.8314 + 1.29765i −1.03834 + 0.0467338i
\(772\) 30.8759i 1.11125i
\(773\) 2.30808i 0.0830159i −0.999138 0.0415080i \(-0.986784\pi\)
0.999138 0.0415080i \(-0.0132162\pi\)
\(774\) 1.23042 + 13.6411i 0.0442264 + 0.490318i
\(775\) 31.4098 1.12827
\(776\) −5.74261 −0.206148
\(777\) −17.0322 + 0.766591i −0.611026 + 0.0275013i
\(778\) 6.00432i 0.215265i
\(779\) 44.3901i 1.59044i
\(780\) −0.375180 8.33579i −0.0134336 0.298469i
\(781\) 5.83816 15.6538i 0.208906 0.560136i
\(782\) 8.66946i 0.310019i
\(783\) −0.418725 3.08433i −0.0149640 0.110225i
\(784\) 1.24041 0.0443003
\(785\) 21.0100i 0.749878i
\(786\) −0.926235 20.5792i −0.0330377 0.734035i
\(787\) 23.3910i 0.833799i −0.908953 0.416899i \(-0.863117\pi\)
0.908953 0.416899i \(-0.136883\pi\)
\(788\) 17.8956 0.637505
\(789\) −0.742059 16.4871i −0.0264180 0.586958i
\(790\) 2.18472 0.0777289
\(791\) 25.8840 0.920331
\(792\) 26.2367 + 7.17714i 0.932280 + 0.255028i
\(793\) −0.106909 −0.00379644
\(794\) −18.9454 −0.672347
\(795\) 2.13515 + 47.4389i 0.0757259 + 1.68249i
\(796\) 19.8383 0.703150
\(797\) 38.9861i 1.38096i 0.723352 + 0.690479i \(0.242600\pi\)
−0.723352 + 0.690479i \(0.757400\pi\)
\(798\) 0.598120 + 13.2891i 0.0211732 + 0.470429i
\(799\) 85.6154i 3.02886i
\(800\) 47.8245 1.69085
\(801\) 3.61219 + 40.0467i 0.127630 + 1.41498i
\(802\) 8.46387i 0.298870i
\(803\) 0.923781 2.47692i 0.0325995 0.0874086i
\(804\) 0.813028 + 18.0639i 0.0286733 + 0.637066i
\(805\) 10.0988i 0.355935i
\(806\) 3.13070i 0.110274i
\(807\) −23.6539 + 1.06462i −0.832656 + 0.0374765i
\(808\) −4.12714 −0.145192
\(809\) −35.5896 −1.25127 −0.625633 0.780118i \(-0.715159\pi\)
−0.625633 + 0.780118i \(0.715159\pi\)
\(810\) 4.82282 + 26.5167i 0.169457 + 0.931702i
\(811\) 35.0719i 1.23154i −0.787926 0.615770i \(-0.788845\pi\)
0.787926 0.615770i \(-0.211155\pi\)
\(812\) 1.56194i 0.0548134i
\(813\) 9.32485 0.419696i 0.327037 0.0147194i
\(814\) 12.7703 + 4.76276i 0.447599 + 0.166935i
\(815\) 59.3051i 2.07737i
\(816\) −0.231956 5.15362i −0.00812009 0.180413i
\(817\) −26.2987 −0.920075
\(818\) 6.45058i 0.225539i
\(819\) 5.88726 0.531027i 0.205717 0.0185556i
\(820\) 45.1312i 1.57605i
\(821\) −29.2603 −1.02119 −0.510596 0.859820i \(-0.670575\pi\)
−0.510596 + 0.859820i \(0.670575\pi\)
\(822\) 13.0475 0.587246i 0.455084 0.0204826i
\(823\) 11.3343 0.395087 0.197544 0.980294i \(-0.436704\pi\)
0.197544 + 0.980294i \(0.436704\pi\)
\(824\) −23.7275 −0.826586
\(825\) 14.5530 45.1208i 0.506669 1.57091i
\(826\) −2.37400 −0.0826021
\(827\) 44.0575 1.53203 0.766015 0.642823i \(-0.222237\pi\)
0.766015 + 0.642823i \(0.222237\pi\)
\(828\) −0.502106 5.56662i −0.0174494 0.193453i
\(829\) 0.755396 0.0262360 0.0131180 0.999914i \(-0.495824\pi\)
0.0131180 + 0.999914i \(0.495824\pi\)
\(830\) 4.40013i 0.152731i
\(831\) 34.0254 1.53143i 1.18033 0.0531246i
\(832\) 3.97106i 0.137672i
\(833\) 23.3379 0.808609
\(834\) −9.19196 + 0.413715i −0.318292 + 0.0143258i
\(835\) 18.2347i 0.631038i
\(836\) −7.26738 + 19.4859i −0.251347 + 0.673934i
\(837\) −2.66035 19.5962i −0.0919552 0.677342i
\(838\) 21.4623i 0.741404i
\(839\) 27.5172i 0.949999i −0.879986 0.474999i \(-0.842448\pi\)
0.879986 0.474999i \(-0.157552\pi\)
\(840\) 1.52716 + 33.9305i 0.0526919 + 1.17071i
\(841\) −28.6412 −0.987627
\(842\) −28.3963 −0.978603
\(843\) −1.24304 27.6181i −0.0428127 0.951217i
\(844\) 24.9178i 0.857706i
\(845\) 3.64046i 0.125236i
\(846\) −2.53548 28.1098i −0.0871718 0.966433i
\(847\) 14.1929 16.3809i 0.487674 0.562856i
\(848\) 2.99643i 0.102898i
\(849\) −24.0385 + 1.08193i −0.824999 + 0.0371318i
\(850\) 50.8208 1.74314
\(851\) 7.03329i 0.241098i
\(852\) −11.5344 + 0.519142i −0.395160 + 0.0177855i
\(853\) 43.1098i 1.47605i 0.674772 + 0.738027i \(0.264242\pi\)
−0.674772 + 0.738027i \(0.735758\pi\)
\(854\) 0.173281 0.00592956
\(855\) −51.5411 + 4.64898i −1.76267 + 0.158992i
\(856\) 32.9505 1.12623
\(857\) 8.76306 0.299340 0.149670 0.988736i \(-0.452179\pi\)
0.149670 + 0.988736i \(0.452179\pi\)
\(858\) −4.49733 1.45054i −0.153536 0.0495205i
\(859\) −3.28797 −0.112184 −0.0560921 0.998426i \(-0.517864\pi\)
−0.0560921 + 0.998426i \(0.517864\pi\)
\(860\) −26.7377 −0.911749
\(861\) 31.9392 1.43753i 1.08848 0.0489909i
\(862\) −16.9044 −0.575765
\(863\) 0.870602i 0.0296356i −0.999890 0.0148178i \(-0.995283\pi\)
0.999890 0.0148178i \(-0.00471683\pi\)
\(864\) −4.05065 29.8371i −0.137806 1.01508i
\(865\) 93.9116i 3.19309i
\(866\) 31.0896 1.05647
\(867\) −3.04025 67.5486i −0.103252 2.29407i
\(868\) 9.92374i 0.336834i
\(869\) −0.845523 + 2.26709i −0.0286824 + 0.0769057i
\(870\) −3.10391 + 0.139702i −0.105232 + 0.00473634i
\(871\) 7.88900i 0.267309i
\(872\) 24.6140i 0.833534i
\(873\) 6.27639 0.566126i 0.212423 0.0191605i
\(874\) −5.48761 −0.185621
\(875\) 23.3339 0.788831
\(876\) −1.82510 + 0.0821446i −0.0616643 + 0.00277541i
\(877\) 22.6155i 0.763671i −0.924230 0.381835i \(-0.875292\pi\)
0.924230 0.381835i \(-0.124708\pi\)
\(878\) 8.43663i 0.284722i
\(879\) −2.07854 46.1811i −0.0701073 1.55765i
\(880\) −1.67872 + 4.50112i −0.0565895 + 0.151733i
\(881\) 12.7245i 0.428699i −0.976757 0.214349i \(-0.931237\pi\)
0.976757 0.214349i \(-0.0687631\pi\)
\(882\) 7.66243 0.691147i 0.258007 0.0232721i
\(883\) −22.7173 −0.764499 −0.382250 0.924059i \(-0.624851\pi\)
−0.382250 + 0.924059i \(0.624851\pi\)
\(884\) 9.90634i 0.333186i
\(885\) −0.415254 9.22614i −0.0139586 0.310133i
\(886\) 22.4207i 0.753238i
\(887\) 4.76079 0.159852 0.0799259 0.996801i \(-0.474532\pi\)
0.0799259 + 0.996801i \(0.474532\pi\)
\(888\) −1.06359 23.6309i −0.0356917 0.793001i
\(889\) −27.3124 −0.916029
\(890\) 40.1373 1.34541
\(891\) −29.3829 5.25775i −0.984365 0.176141i
\(892\) 20.1056 0.673185
\(893\) 54.1930 1.81350
\(894\) 0.818785 + 18.1918i 0.0273843 + 0.608426i
\(895\) 62.8403 2.10052
\(896\) 16.3997i 0.547874i
\(897\) 0.109642 + 2.43603i 0.00366082 + 0.0813365i
\(898\) 9.28210i 0.309748i
\(899\) 2.27981 0.0760359
\(900\) −32.6318 + 2.94337i −1.08773 + 0.0981123i
\(901\) 56.3769i 1.87819i
\(902\) −23.9472 8.93124i −0.797355 0.297378i
\(903\) −0.851657 18.9222i −0.0283414 0.629691i
\(904\) 35.9122i 1.19442i
\(905\) 51.2883i 1.70488i
\(906\) 22.1338 0.996205i 0.735345 0.0330967i
\(907\) 35.9465 1.19358 0.596791 0.802397i \(-0.296442\pi\)
0.596791 + 0.802397i \(0.296442\pi\)
\(908\) −21.5633 −0.715605
\(909\) 4.51076 0.406868i 0.149613 0.0134950i
\(910\) 5.90059i 0.195603i
\(911\) 45.1251i 1.49506i 0.664228 + 0.747530i \(0.268760\pi\)
−0.664228 + 0.747530i \(0.731240\pi\)
\(912\) 3.26215 0.146824i 0.108021 0.00486183i
\(913\) 4.56602 + 1.70292i 0.151113 + 0.0563585i
\(914\) 26.4211i 0.873931i
\(915\) 0.0303098 + 0.673427i 0.00100201 + 0.0222628i
\(916\) −24.6013 −0.812850
\(917\) 28.4886i 0.940776i
\(918\) −4.30443 31.7065i −0.142068 1.04647i
\(919\) 8.87113i 0.292632i −0.989238 0.146316i \(-0.953258\pi\)
0.989238 0.146316i \(-0.0467416\pi\)
\(920\) −14.0113 −0.461939
\(921\) 56.0368 2.52213i 1.84648 0.0831069i
\(922\) 15.7906 0.520037
\(923\) 5.03736 0.165807
\(924\) −14.2557 4.59793i −0.468977 0.151261i
\(925\) −41.2295 −1.35562
\(926\) 4.77915 0.157052
\(927\) 25.9329 2.33914i 0.851750 0.0768274i
\(928\) 3.47124 0.113949
\(929\) 11.2355i 0.368624i −0.982868 0.184312i \(-0.940994\pi\)
0.982868 0.184312i \(-0.0590057\pi\)
\(930\) −19.7206 + 0.887591i −0.646664 + 0.0291053i
\(931\) 14.7724i 0.484147i
\(932\) 8.44341 0.276573
\(933\) 13.6734 0.615419i 0.447648 0.0201479i
\(934\) 0.617489i 0.0202049i
\(935\) −31.5845 + 84.6870i −1.03292 + 2.76956i
\(936\) 0.736761 + 8.16814i 0.0240818 + 0.266984i
\(937\) 26.9104i 0.879125i 0.898212 + 0.439562i \(0.144866\pi\)
−0.898212 + 0.439562i \(0.855134\pi\)
\(938\) 12.7868i 0.417503i
\(939\) −2.48373 55.1837i −0.0810534 1.80085i
\(940\) 55.0977 1.79709
\(941\) −24.2101 −0.789226 −0.394613 0.918847i \(-0.629121\pi\)
−0.394613 + 0.918847i \(0.629121\pi\)
\(942\) 0.369718 + 8.21443i 0.0120461 + 0.267641i
\(943\) 13.1890i 0.429493i
\(944\) 0.582760i 0.0189672i
\(945\) −5.01410 36.9338i −0.163109 1.20146i
\(946\) −5.29127 + 14.1874i −0.172034 + 0.461272i
\(947\) 55.3393i 1.79829i −0.437654 0.899144i \(-0.644190\pi\)
0.437654 0.899144i \(-0.355810\pi\)
\(948\) 1.67048 0.0751857i 0.0542548 0.00244192i
\(949\) 0.797068 0.0258739
\(950\) 32.1687i 1.04369i
\(951\) 53.5940 2.41218i 1.73791 0.0782203i
\(952\) 40.3234i 1.30689i
\(953\) −36.0891 −1.16904 −0.584520 0.811379i \(-0.698717\pi\)
−0.584520 + 0.811379i \(0.698717\pi\)
\(954\) −1.66959 18.5100i −0.0540550 0.599283i
\(955\) −36.7560 −1.18940
\(956\) 32.6475 1.05590
\(957\) 1.05630 3.27500i 0.0341452 0.105866i
\(958\) −1.01052 −0.0326486
\(959\) −18.0622 −0.583258
\(960\) −25.0140 + 1.12584i −0.807325 + 0.0363364i
\(961\) −16.5153 −0.532752
\(962\) 4.10947i 0.132494i
\(963\) −36.0133 + 3.24838i −1.16051 + 0.104677i
\(964\) 15.8691i 0.511109i
\(965\) −84.9389 −2.73428
\(966\) −0.177711 3.94840i −0.00571775 0.127038i
\(967\) 29.7325i 0.956131i 0.878324 + 0.478066i \(0.158662\pi\)
−0.878324 + 0.478066i \(0.841338\pi\)
\(968\) 22.7273 + 19.6916i 0.730484 + 0.632912i
\(969\) 61.3763 2.76244i 1.97169 0.0887425i
\(970\) 6.29060i 0.201979i
\(971\) 9.28897i 0.298097i −0.988830 0.149049i \(-0.952379\pi\)
0.988830 0.149049i \(-0.0476211\pi\)
\(972\) 4.60019 + 20.1093i 0.147551 + 0.645005i
\(973\) 12.7248 0.407938
\(974\) −6.43774 −0.206279
\(975\) 14.2801 0.642724i 0.457329 0.0205836i
\(976\) 0.0425363i 0.00136156i
\(977\) 15.8794i 0.508028i 0.967201 + 0.254014i \(0.0817510\pi\)
−0.967201 + 0.254014i \(0.918249\pi\)
\(978\) −1.04361 23.1870i −0.0333709 0.741438i
\(979\) −15.5338 + 41.6506i −0.496463 + 1.33116i
\(980\) 15.0191i 0.479766i
\(981\) 2.42653 + 26.9018i 0.0774732 + 0.858910i
\(982\) −13.5193 −0.431419
\(983\) 23.8077i 0.759346i 0.925121 + 0.379673i \(0.123964\pi\)
−0.925121 + 0.379673i \(0.876036\pi\)
\(984\) 1.99447 + 44.3132i 0.0635813 + 1.41265i
\(985\) 49.2305i 1.56861i
\(986\) 3.68872 0.117473
\(987\) 1.75499 + 38.9925i 0.0558618 + 1.24114i
\(988\) −6.27053 −0.199492
\(989\) 7.81375 0.248463
\(990\) −7.86202 + 28.7403i −0.249871 + 0.913427i
\(991\) −12.1861 −0.387103 −0.193551 0.981090i \(-0.562001\pi\)
−0.193551 + 0.981090i \(0.562001\pi\)
\(992\) 22.0544 0.700227
\(993\) −1.52663 33.9187i −0.0484460 1.07638i
\(994\) −8.16473 −0.258969
\(995\) 54.5748i 1.73014i
\(996\) −0.151428 3.36444i −0.00479817 0.106606i
\(997\) 18.0002i 0.570072i −0.958517 0.285036i \(-0.907994\pi\)
0.958517 0.285036i \(-0.0920055\pi\)
\(998\) −12.6431 −0.400210
\(999\) 3.49207 + 25.7225i 0.110484 + 0.813825i
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 429.2.f.a.131.17 48
3.2 odd 2 inner 429.2.f.a.131.32 yes 48
11.10 odd 2 inner 429.2.f.a.131.31 yes 48
33.32 even 2 inner 429.2.f.a.131.18 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.f.a.131.17 48 1.1 even 1 trivial
429.2.f.a.131.18 yes 48 33.32 even 2 inner
429.2.f.a.131.31 yes 48 11.10 odd 2 inner
429.2.f.a.131.32 yes 48 3.2 odd 2 inner