Properties

Label 1110.2.ba.a.619.6
Level $1110$
Weight $2$
Character 1110.619
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(529,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 619.6
Character \(\chi\) \(=\) 1110.619
Dual form 1110.2.ba.a.529.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.21345 + 0.317246i) q^{5} -1.00000i q^{6} +(-1.17143 + 0.676327i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.21345 + 0.317246i) q^{5} -1.00000i q^{6} +(-1.17143 + 0.676327i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.831981 - 2.07553i) q^{10} +3.00191 q^{11} +(0.866025 + 0.500000i) q^{12} +(-1.12218 - 1.94367i) q^{13} -1.35265i q^{14} +(1.75828 - 1.38147i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.19396 - 2.06800i) q^{17} +(0.500000 + 0.866025i) q^{18} +(4.57549 - 2.64166i) q^{19} +(1.38147 + 1.75828i) q^{20} +(0.676327 - 1.17143i) q^{21} +(-1.50095 + 2.59973i) q^{22} -6.77962 q^{23} +(-0.866025 + 0.500000i) q^{24} +(4.79871 - 1.40441i) q^{25} +2.24436 q^{26} +1.00000i q^{27} +(1.17143 + 0.676327i) q^{28} +4.07927i q^{29} +(0.317246 + 2.21345i) q^{30} -4.41998i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.59973 + 1.50095i) q^{33} +(1.19396 + 2.06800i) q^{34} +(2.37834 - 1.86865i) q^{35} -1.00000 q^{36} +(3.29819 + 5.11096i) q^{37} +5.28332i q^{38} +(1.94367 + 1.12218i) q^{39} +(-2.21345 + 0.317246i) q^{40} +(2.30168 + 3.98662i) q^{41} +(0.676327 + 1.17143i) q^{42} -3.19094 q^{43} +(-1.50095 - 2.59973i) q^{44} +(-0.831981 + 2.07553i) q^{45} +(3.38981 - 5.87132i) q^{46} +12.9161i q^{47} -1.00000i q^{48} +(-2.58516 + 4.47763i) q^{49} +(-1.18310 + 4.85801i) q^{50} +2.38792i q^{51} +(-1.12218 + 1.94367i) q^{52} +(5.39612 + 3.11545i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-6.64457 + 0.952343i) q^{55} +(-1.17143 + 0.676327i) q^{56} +(-2.64166 + 4.57549i) q^{57} +(-3.53275 - 2.03964i) q^{58} +(4.19055 + 2.41941i) q^{59} +(-2.07553 - 0.831981i) q^{60} +(9.20129 - 5.31237i) q^{61} +(3.82781 + 2.20999i) q^{62} +1.35265i q^{63} +1.00000 q^{64} +(3.10051 + 3.94621i) q^{65} -3.00191i q^{66} +(-3.05897 + 1.76610i) q^{67} -2.38792 q^{68} +(5.87132 - 3.38981i) q^{69} +(0.429124 + 2.99403i) q^{70} +(6.08437 + 10.5384i) q^{71} +(0.500000 - 0.866025i) q^{72} -7.06413i q^{73} +(-6.07532 + 0.300839i) q^{74} +(-3.45360 + 3.61561i) q^{75} +(-4.57549 - 2.64166i) q^{76} +(-3.51653 + 2.03027i) q^{77} +(-1.94367 + 1.12218i) q^{78} +(0.509669 - 0.294257i) q^{79} +(0.831981 - 2.07553i) q^{80} +(-0.500000 - 0.866025i) q^{81} -4.60335 q^{82} +(3.56360 + 2.05745i) q^{83} -1.35265 q^{84} +(-1.98671 + 4.95619i) q^{85} +(1.59547 - 2.76343i) q^{86} +(-2.03964 - 3.53275i) q^{87} +3.00191 q^{88} +(14.4684 + 8.35333i) q^{89} +(-1.38147 - 1.75828i) q^{90} +(2.62912 + 1.51792i) q^{91} +(3.38981 + 5.87132i) q^{92} +(2.20999 + 3.82781i) q^{93} +(-11.1857 - 6.45806i) q^{94} +(-9.28956 + 7.29873i) q^{95} +(0.866025 + 0.500000i) q^{96} +9.59790 q^{97} +(-2.58516 - 4.47763i) q^{98} +(1.50095 - 2.59973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.21345 + 0.317246i −0.989884 + 0.141877i
\(6\) 1.00000i 0.408248i
\(7\) −1.17143 + 0.676327i −0.442760 + 0.255628i −0.704768 0.709438i \(-0.748949\pi\)
0.262008 + 0.965066i \(0.415615\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0.831981 2.07553i 0.263096 0.656339i
\(11\) 3.00191 0.905109 0.452555 0.891737i \(-0.350513\pi\)
0.452555 + 0.891737i \(0.350513\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) −1.12218 1.94367i −0.311237 0.539078i 0.667394 0.744705i \(-0.267410\pi\)
−0.978630 + 0.205627i \(0.934077\pi\)
\(14\) 1.35265i 0.361512i
\(15\) 1.75828 1.38147i 0.453986 0.356693i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.19396 2.06800i 0.289578 0.501564i −0.684131 0.729359i \(-0.739818\pi\)
0.973709 + 0.227795i \(0.0731517\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 4.57549 2.64166i 1.04969 0.606038i 0.127127 0.991886i \(-0.459424\pi\)
0.922562 + 0.385848i \(0.126091\pi\)
\(20\) 1.38147 + 1.75828i 0.308905 + 0.393163i
\(21\) 0.676327 1.17143i 0.147587 0.255628i
\(22\) −1.50095 + 2.59973i −0.320004 + 0.554264i
\(23\) −6.77962 −1.41365 −0.706824 0.707390i \(-0.749873\pi\)
−0.706824 + 0.707390i \(0.749873\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 4.79871 1.40441i 0.959742 0.280883i
\(26\) 2.24436 0.440155
\(27\) 1.00000i 0.192450i
\(28\) 1.17143 + 0.676327i 0.221380 + 0.127814i
\(29\) 4.07927i 0.757502i 0.925499 + 0.378751i \(0.123646\pi\)
−0.925499 + 0.378751i \(0.876354\pi\)
\(30\) 0.317246 + 2.21345i 0.0579209 + 0.404119i
\(31\) 4.41998i 0.793851i −0.917851 0.396926i \(-0.870077\pi\)
0.917851 0.396926i \(-0.129923\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −2.59973 + 1.50095i −0.452555 + 0.261283i
\(34\) 1.19396 + 2.06800i 0.204763 + 0.354659i
\(35\) 2.37834 1.86865i 0.402014 0.315859i
\(36\) −1.00000 −0.166667
\(37\) 3.29819 + 5.11096i 0.542220 + 0.840237i
\(38\) 5.28332i 0.857068i
\(39\) 1.94367 + 1.12218i 0.311237 + 0.179693i
\(40\) −2.21345 + 0.317246i −0.349977 + 0.0501610i
\(41\) 2.30168 + 3.98662i 0.359462 + 0.622606i 0.987871 0.155277i \(-0.0496271\pi\)
−0.628409 + 0.777883i \(0.716294\pi\)
\(42\) 0.676327 + 1.17143i 0.104360 + 0.180756i
\(43\) −3.19094 −0.486614 −0.243307 0.969949i \(-0.578232\pi\)
−0.243307 + 0.969949i \(0.578232\pi\)
\(44\) −1.50095 2.59973i −0.226277 0.391924i
\(45\) −0.831981 + 2.07553i −0.124024 + 0.309401i
\(46\) 3.38981 5.87132i 0.499800 0.865679i
\(47\) 12.9161i 1.88401i 0.335600 + 0.942005i \(0.391061\pi\)
−0.335600 + 0.942005i \(0.608939\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −2.58516 + 4.47763i −0.369309 + 0.639662i
\(50\) −1.18310 + 4.85801i −0.167315 + 0.687027i
\(51\) 2.38792i 0.334376i
\(52\) −1.12218 + 1.94367i −0.155618 + 0.269539i
\(53\) 5.39612 + 3.11545i 0.741213 + 0.427940i 0.822510 0.568750i \(-0.192573\pi\)
−0.0812969 + 0.996690i \(0.525906\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −6.64457 + 0.952343i −0.895954 + 0.128414i
\(56\) −1.17143 + 0.676327i −0.156539 + 0.0903780i
\(57\) −2.64166 + 4.57549i −0.349896 + 0.606038i
\(58\) −3.53275 2.03964i −0.463873 0.267817i
\(59\) 4.19055 + 2.41941i 0.545563 + 0.314981i 0.747330 0.664453i \(-0.231335\pi\)
−0.201768 + 0.979433i \(0.564669\pi\)
\(60\) −2.07553 0.831981i −0.267949 0.107408i
\(61\) 9.20129 5.31237i 1.17810 0.680179i 0.222529 0.974926i \(-0.428569\pi\)
0.955575 + 0.294747i \(0.0952355\pi\)
\(62\) 3.82781 + 2.20999i 0.486132 + 0.280669i
\(63\) 1.35265i 0.170418i
\(64\) 1.00000 0.125000
\(65\) 3.10051 + 3.94621i 0.384571 + 0.489467i
\(66\) 3.00191i 0.369509i
\(67\) −3.05897 + 1.76610i −0.373712 + 0.215763i −0.675079 0.737745i \(-0.735891\pi\)
0.301367 + 0.953508i \(0.402557\pi\)
\(68\) −2.38792 −0.289578
\(69\) 5.87132 3.38981i 0.706824 0.408085i
\(70\) 0.429124 + 2.99403i 0.0512901 + 0.357855i
\(71\) 6.08437 + 10.5384i 0.722082 + 1.25068i 0.960164 + 0.279438i \(0.0901481\pi\)
−0.238081 + 0.971245i \(0.576519\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 7.06413i 0.826794i −0.910551 0.413397i \(-0.864342\pi\)
0.910551 0.413397i \(-0.135658\pi\)
\(74\) −6.07532 + 0.300839i −0.706241 + 0.0349718i
\(75\) −3.45360 + 3.61561i −0.398787 + 0.417495i
\(76\) −4.57549 2.64166i −0.524845 0.303019i
\(77\) −3.51653 + 2.03027i −0.400746 + 0.231371i
\(78\) −1.94367 + 1.12218i −0.220078 + 0.127062i
\(79\) 0.509669 0.294257i 0.0573422 0.0331066i −0.471055 0.882104i \(-0.656127\pi\)
0.528397 + 0.848997i \(0.322793\pi\)
\(80\) 0.831981 2.07553i 0.0930184 0.232051i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.60335 −0.508355
\(83\) 3.56360 + 2.05745i 0.391156 + 0.225834i 0.682661 0.730735i \(-0.260823\pi\)
−0.291505 + 0.956569i \(0.594156\pi\)
\(84\) −1.35265 −0.147587
\(85\) −1.98671 + 4.95619i −0.215489 + 0.537575i
\(86\) 1.59547 2.76343i 0.172044 0.297989i
\(87\) −2.03964 3.53275i −0.218672 0.378751i
\(88\) 3.00191 0.320004
\(89\) 14.4684 + 8.35333i 1.53365 + 0.885451i 0.999189 + 0.0402561i \(0.0128174\pi\)
0.534457 + 0.845195i \(0.320516\pi\)
\(90\) −1.38147 1.75828i −0.145619 0.185339i
\(91\) 2.62912 + 1.51792i 0.275606 + 0.159121i
\(92\) 3.38981 + 5.87132i 0.353412 + 0.612127i
\(93\) 2.20999 + 3.82781i 0.229165 + 0.396926i
\(94\) −11.1857 6.45806i −1.15372 0.666098i
\(95\) −9.28956 + 7.29873i −0.953088 + 0.748834i
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) 9.59790 0.974519 0.487260 0.873257i \(-0.337997\pi\)
0.487260 + 0.873257i \(0.337997\pi\)
\(98\) −2.58516 4.47763i −0.261141 0.452309i
\(99\) 1.50095 2.59973i 0.150852 0.261283i
\(100\) −3.61561 3.45360i −0.361561 0.345360i
\(101\) −16.6462 −1.65636 −0.828180 0.560462i \(-0.810624\pi\)
−0.828180 + 0.560462i \(0.810624\pi\)
\(102\) −2.06800 1.19396i −0.204763 0.118220i
\(103\) 6.71339 0.661490 0.330745 0.943720i \(-0.392700\pi\)
0.330745 + 0.943720i \(0.392700\pi\)
\(104\) −1.12218 1.94367i −0.110039 0.190593i
\(105\) −1.12538 + 2.80747i −0.109826 + 0.273981i
\(106\) −5.39612 + 3.11545i −0.524117 + 0.302599i
\(107\) −0.170274 + 0.0983076i −0.0164610 + 0.00950376i −0.508208 0.861234i \(-0.669692\pi\)
0.491747 + 0.870738i \(0.336359\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) −11.6161 6.70656i −1.11262 0.642372i −0.173114 0.984902i \(-0.555383\pi\)
−0.939507 + 0.342530i \(0.888716\pi\)
\(110\) 2.49753 6.23054i 0.238130 0.594058i
\(111\) −5.41180 2.77713i −0.513665 0.263593i
\(112\) 1.35265i 0.127814i
\(113\) 7.24481 12.5484i 0.681535 1.18045i −0.292978 0.956119i \(-0.594646\pi\)
0.974512 0.224333i \(-0.0720204\pi\)
\(114\) −2.64166 4.57549i −0.247414 0.428534i
\(115\) 15.0063 2.15080i 1.39935 0.200564i
\(116\) 3.53275 2.03964i 0.328008 0.189375i
\(117\) −2.24436 −0.207491
\(118\) −4.19055 + 2.41941i −0.385771 + 0.222725i
\(119\) 3.23003i 0.296096i
\(120\) 1.75828 1.38147i 0.160508 0.126110i
\(121\) −1.98855 −0.180777
\(122\) 10.6247i 0.961918i
\(123\) −3.98662 2.30168i −0.359462 0.207535i
\(124\) −3.82781 + 2.20999i −0.343748 + 0.198463i
\(125\) −10.1762 + 4.63097i −0.910183 + 0.414207i
\(126\) −1.17143 0.676327i −0.104360 0.0602520i
\(127\) 8.91376 + 5.14636i 0.790968 + 0.456666i 0.840303 0.542117i \(-0.182377\pi\)
−0.0493351 + 0.998782i \(0.515710\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 2.76343 1.59547i 0.243307 0.140473i
\(130\) −4.96778 + 0.712014i −0.435703 + 0.0624477i
\(131\) 3.29183 + 1.90054i 0.287608 + 0.166051i 0.636863 0.770977i \(-0.280232\pi\)
−0.349255 + 0.937028i \(0.613565\pi\)
\(132\) 2.59973 + 1.50095i 0.226277 + 0.130641i
\(133\) −3.57325 + 6.18905i −0.309840 + 0.536659i
\(134\) 3.53219i 0.305135i
\(135\) −0.317246 2.21345i −0.0273042 0.190503i
\(136\) 1.19396 2.06800i 0.102381 0.177330i
\(137\) 10.1698i 0.868862i −0.900705 0.434431i \(-0.856950\pi\)
0.900705 0.434431i \(-0.143050\pi\)
\(138\) 6.77962i 0.577119i
\(139\) 0.463646 0.803059i 0.0393260 0.0681146i −0.845692 0.533671i \(-0.820812\pi\)
0.885018 + 0.465556i \(0.154146\pi\)
\(140\) −2.80747 1.12538i −0.237274 0.0951122i
\(141\) −6.45806 11.1857i −0.543867 0.942005i
\(142\) −12.1687 −1.02118
\(143\) −3.36868 5.83473i −0.281703 0.487924i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −1.29413 9.02926i −0.107472 0.749839i
\(146\) 6.11771 + 3.53206i 0.506306 + 0.292316i
\(147\) 5.17033i 0.426441i
\(148\) 2.77713 5.41180i 0.228278 0.444847i
\(149\) −9.05684 −0.741965 −0.370983 0.928640i \(-0.620979\pi\)
−0.370983 + 0.928640i \(0.620979\pi\)
\(150\) −1.40441 4.79871i −0.114670 0.391813i
\(151\) 5.73747 + 9.93758i 0.466908 + 0.808709i 0.999285 0.0377983i \(-0.0120344\pi\)
−0.532377 + 0.846507i \(0.678701\pi\)
\(152\) 4.57549 2.64166i 0.371121 0.214267i
\(153\) −1.19396 2.06800i −0.0965260 0.167188i
\(154\) 4.06054i 0.327208i
\(155\) 1.40222 + 9.78339i 0.112629 + 0.785821i
\(156\) 2.24436i 0.179693i
\(157\) 5.04062 + 2.91020i 0.402285 + 0.232259i 0.687469 0.726213i \(-0.258722\pi\)
−0.285184 + 0.958473i \(0.592055\pi\)
\(158\) 0.588515i 0.0468197i
\(159\) −6.23090 −0.494142
\(160\) 1.38147 + 1.75828i 0.109215 + 0.139004i
\(161\) 7.94187 4.58524i 0.625907 0.361367i
\(162\) 1.00000 0.0785674
\(163\) 2.20296 3.81563i 0.172549 0.298863i −0.766761 0.641932i \(-0.778133\pi\)
0.939310 + 0.343069i \(0.111466\pi\)
\(164\) 2.30168 3.98662i 0.179731 0.311303i
\(165\) 5.27819 4.14704i 0.410907 0.322846i
\(166\) −3.56360 + 2.05745i −0.276589 + 0.159689i
\(167\) 10.8349 + 18.7666i 0.838431 + 1.45221i 0.891206 + 0.453599i \(0.149860\pi\)
−0.0527743 + 0.998606i \(0.516806\pi\)
\(168\) 0.676327 1.17143i 0.0521798 0.0903780i
\(169\) 3.98142 6.89603i 0.306263 0.530464i
\(170\) −3.29884 4.19863i −0.253009 0.322021i
\(171\) 5.28332i 0.404026i
\(172\) 1.59547 + 2.76343i 0.121653 + 0.210710i
\(173\) −14.2574 8.23149i −1.08397 0.625829i −0.152003 0.988380i \(-0.548572\pi\)
−0.931964 + 0.362551i \(0.881906\pi\)
\(174\) 4.07927 0.309249
\(175\) −4.67152 + 4.89067i −0.353134 + 0.369700i
\(176\) −1.50095 + 2.59973i −0.113139 + 0.195962i
\(177\) −4.83883 −0.363709
\(178\) −14.4684 + 8.35333i −1.08445 + 0.626109i
\(179\) 21.2532i 1.58854i 0.607566 + 0.794269i \(0.292146\pi\)
−0.607566 + 0.794269i \(0.707854\pi\)
\(180\) 2.21345 0.317246i 0.164981 0.0236461i
\(181\) 9.22354 + 15.9756i 0.685580 + 1.18746i 0.973254 + 0.229731i \(0.0737847\pi\)
−0.287674 + 0.957728i \(0.592882\pi\)
\(182\) −2.62912 + 1.51792i −0.194883 + 0.112516i
\(183\) −5.31237 + 9.20129i −0.392701 + 0.680179i
\(184\) −6.77962 −0.499800
\(185\) −8.92181 10.2665i −0.655945 0.754809i
\(186\) −4.41998 −0.324088
\(187\) 3.58416 6.20795i 0.262100 0.453970i
\(188\) 11.1857 6.45806i 0.815800 0.471002i
\(189\) −0.676327 1.17143i −0.0491956 0.0852092i
\(190\) −1.67611 11.6944i −0.121598 0.848398i
\(191\) 8.76184i 0.633985i −0.948428 0.316992i \(-0.897327\pi\)
0.948428 0.316992i \(-0.102673\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 13.2262 0.952041 0.476020 0.879434i \(-0.342079\pi\)
0.476020 + 0.879434i \(0.342079\pi\)
\(194\) −4.79895 + 8.31202i −0.344545 + 0.596769i
\(195\) −4.65823 1.86727i −0.333583 0.133718i
\(196\) 5.17033 0.369309
\(197\) 7.32681 + 4.23013i 0.522013 + 0.301385i 0.737758 0.675065i \(-0.235885\pi\)
−0.215745 + 0.976450i \(0.569218\pi\)
\(198\) 1.50095 + 2.59973i 0.106668 + 0.184755i
\(199\) 7.72653i 0.547719i −0.961770 0.273860i \(-0.911700\pi\)
0.961770 0.273860i \(-0.0883004\pi\)
\(200\) 4.79871 1.40441i 0.339320 0.0993071i
\(201\) 1.76610 3.05897i 0.124571 0.215763i
\(202\) 8.32311 14.4160i 0.585612 1.01431i
\(203\) −2.75892 4.77859i −0.193638 0.335391i
\(204\) 2.06800 1.19396i 0.144789 0.0835940i
\(205\) −6.35938 8.09398i −0.444159 0.565308i
\(206\) −3.35670 + 5.81397i −0.233872 + 0.405078i
\(207\) −3.38981 + 5.87132i −0.235608 + 0.408085i
\(208\) 2.24436 0.155618
\(209\) 13.7352 7.93002i 0.950084 0.548531i
\(210\) −1.86865 2.37834i −0.128949 0.164121i
\(211\) −14.0101 −0.964494 −0.482247 0.876035i \(-0.660179\pi\)
−0.482247 + 0.876035i \(0.660179\pi\)
\(212\) 6.23090i 0.427940i
\(213\) −10.5384 6.08437i −0.722082 0.416894i
\(214\) 0.196615i 0.0134403i
\(215\) 7.06298 1.01231i 0.481691 0.0690391i
\(216\) 1.00000i 0.0680414i
\(217\) 2.98935 + 5.17770i 0.202930 + 0.351485i
\(218\) 11.6161 6.70656i 0.786742 0.454226i
\(219\) 3.53206 + 6.11771i 0.238675 + 0.413397i
\(220\) 4.14704 + 5.27819i 0.279593 + 0.355856i
\(221\) −5.35935 −0.360509
\(222\) 5.11096 3.29819i 0.343025 0.221360i
\(223\) 3.10337i 0.207817i −0.994587 0.103908i \(-0.966865\pi\)
0.994587 0.103908i \(-0.0331349\pi\)
\(224\) 1.17143 + 0.676327i 0.0782696 + 0.0451890i
\(225\) 1.18310 4.85801i 0.0788731 0.323867i
\(226\) 7.24481 + 12.5484i 0.481918 + 0.834706i
\(227\) 7.97179 + 13.8076i 0.529107 + 0.916439i 0.999424 + 0.0339421i \(0.0108062\pi\)
−0.470317 + 0.882497i \(0.655860\pi\)
\(228\) 5.28332 0.349896
\(229\) −6.73382 11.6633i −0.444983 0.770733i 0.553068 0.833136i \(-0.313457\pi\)
−0.998051 + 0.0624027i \(0.980124\pi\)
\(230\) −5.64052 + 14.0713i −0.371925 + 0.927832i
\(231\) 2.03027 3.51653i 0.133582 0.231371i
\(232\) 4.07927i 0.267817i
\(233\) 27.6386i 1.81067i −0.424703 0.905333i \(-0.639622\pi\)
0.424703 0.905333i \(-0.360378\pi\)
\(234\) 1.12218 1.94367i 0.0733592 0.127062i
\(235\) −4.09758 28.5892i −0.267297 1.86495i
\(236\) 4.83883i 0.314981i
\(237\) −0.294257 + 0.509669i −0.0191141 + 0.0331066i
\(238\) −2.79729 1.61502i −0.181321 0.104686i
\(239\) 11.3747 + 6.56719i 0.735768 + 0.424796i 0.820529 0.571605i \(-0.193679\pi\)
−0.0847604 + 0.996401i \(0.527012\pi\)
\(240\) 0.317246 + 2.21345i 0.0204781 + 0.142877i
\(241\) 24.8544 14.3497i 1.60101 0.924346i 0.609730 0.792610i \(-0.291278\pi\)
0.991285 0.131736i \(-0.0420553\pi\)
\(242\) 0.994274 1.72213i 0.0639143 0.110703i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −9.20129 5.31237i −0.589052 0.340089i
\(245\) 4.30162 10.7311i 0.274820 0.685588i
\(246\) 3.98662 2.30168i 0.254178 0.146750i
\(247\) −10.2690 5.92884i −0.653404 0.377243i
\(248\) 4.41998i 0.280669i
\(249\) −4.11489 −0.260771
\(250\) 1.07754 11.1283i 0.0681496 0.703815i
\(251\) 7.61640i 0.480743i 0.970681 + 0.240372i \(0.0772693\pi\)
−0.970681 + 0.240372i \(0.922731\pi\)
\(252\) 1.17143 0.676327i 0.0737933 0.0426046i
\(253\) −20.3518 −1.27951
\(254\) −8.91376 + 5.14636i −0.559299 + 0.322911i
\(255\) −0.757558 5.28554i −0.0474401 0.330993i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.86850 10.1645i 0.366067 0.634046i −0.622880 0.782317i \(-0.714037\pi\)
0.988947 + 0.148271i \(0.0473708\pi\)
\(258\) 3.19094i 0.198659i
\(259\) −7.32029 3.75649i −0.454861 0.233417i
\(260\) 1.86727 4.65823i 0.115803 0.288891i
\(261\) 3.53275 + 2.03964i 0.218672 + 0.126250i
\(262\) −3.29183 + 1.90054i −0.203370 + 0.117416i
\(263\) 12.8963 7.44568i 0.795219 0.459120i −0.0465775 0.998915i \(-0.514831\pi\)
0.841797 + 0.539795i \(0.181498\pi\)
\(264\) −2.59973 + 1.50095i −0.160002 + 0.0923773i
\(265\) −12.9324 5.18399i −0.794430 0.318450i
\(266\) −3.57325 6.18905i −0.219090 0.379475i
\(267\) −16.7067 −1.02243
\(268\) 3.05897 + 1.76610i 0.186856 + 0.107881i
\(269\) 11.5433 0.703807 0.351904 0.936036i \(-0.385534\pi\)
0.351904 + 0.936036i \(0.385534\pi\)
\(270\) 2.07553 + 0.831981i 0.126312 + 0.0506328i
\(271\) 0.336417 0.582692i 0.0204359 0.0353960i −0.855627 0.517594i \(-0.826828\pi\)
0.876062 + 0.482198i \(0.160161\pi\)
\(272\) 1.19396 + 2.06800i 0.0723945 + 0.125391i
\(273\) −3.03584 −0.183738
\(274\) 8.80728 + 5.08488i 0.532067 + 0.307189i
\(275\) 14.4053 4.21592i 0.868672 0.254230i
\(276\) −5.87132 3.38981i −0.353412 0.204042i
\(277\) 14.1902 + 24.5782i 0.852607 + 1.47676i 0.878847 + 0.477103i \(0.158313\pi\)
−0.0262400 + 0.999656i \(0.508353\pi\)
\(278\) 0.463646 + 0.803059i 0.0278077 + 0.0481643i
\(279\) −3.82781 2.20999i −0.229165 0.132309i
\(280\) 2.37834 1.86865i 0.142133 0.111673i
\(281\) −17.3856 10.0376i −1.03714 0.598791i −0.118115 0.993000i \(-0.537685\pi\)
−0.919021 + 0.394209i \(0.871018\pi\)
\(282\) 12.9161 0.769144
\(283\) 4.39309 + 7.60906i 0.261142 + 0.452312i 0.966546 0.256494i \(-0.0825675\pi\)
−0.705404 + 0.708806i \(0.749234\pi\)
\(284\) 6.08437 10.5384i 0.361041 0.625342i
\(285\) 4.39562 10.9657i 0.260374 0.649550i
\(286\) 6.73736 0.398389
\(287\) −5.39252 3.11337i −0.318310 0.183777i
\(288\) −1.00000 −0.0589256
\(289\) 5.64892 + 9.78421i 0.332289 + 0.575542i
\(290\) 8.46663 + 3.39388i 0.497178 + 0.199295i
\(291\) −8.31202 + 4.79895i −0.487260 + 0.281319i
\(292\) −6.11771 + 3.53206i −0.358012 + 0.206698i
\(293\) 18.1855 10.4994i 1.06241 0.613380i 0.136309 0.990666i \(-0.456476\pi\)
0.926097 + 0.377286i \(0.123143\pi\)
\(294\) 4.47763 + 2.58516i 0.261141 + 0.150770i
\(295\) −10.0431 4.02582i −0.584733 0.234392i
\(296\) 3.29819 + 5.11096i 0.191704 + 0.297069i
\(297\) 3.00191i 0.174188i
\(298\) 4.52842 7.84345i 0.262324 0.454359i
\(299\) 7.60795 + 13.1774i 0.439979 + 0.762066i
\(300\) 4.85801 + 1.18310i 0.280477 + 0.0683061i
\(301\) 3.73797 2.15812i 0.215453 0.124392i
\(302\) −11.4749 −0.660308
\(303\) 14.4160 8.32311i 0.828180 0.478150i
\(304\) 5.28332i 0.303019i
\(305\) −18.6813 + 14.6777i −1.06969 + 0.840444i
\(306\) 2.38792 0.136508
\(307\) 16.2086i 0.925073i 0.886600 + 0.462537i \(0.153061\pi\)
−0.886600 + 0.462537i \(0.846939\pi\)
\(308\) 3.51653 + 2.03027i 0.200373 + 0.115685i
\(309\) −5.81397 + 3.35670i −0.330745 + 0.190956i
\(310\) −9.17377 3.67734i −0.521035 0.208859i
\(311\) 2.58380 + 1.49176i 0.146514 + 0.0845899i 0.571465 0.820626i \(-0.306375\pi\)
−0.424951 + 0.905216i \(0.639709\pi\)
\(312\) 1.94367 + 1.12218i 0.110039 + 0.0635309i
\(313\) 2.25748 3.91006i 0.127600 0.221010i −0.795146 0.606418i \(-0.792606\pi\)
0.922746 + 0.385408i \(0.125939\pi\)
\(314\) −5.04062 + 2.91020i −0.284458 + 0.164232i
\(315\) −0.429124 2.99403i −0.0241784 0.168694i
\(316\) −0.509669 0.294257i −0.0286711 0.0165533i
\(317\) 5.91704 + 3.41620i 0.332334 + 0.191873i 0.656877 0.753998i \(-0.271877\pi\)
−0.324543 + 0.945871i \(0.605210\pi\)
\(318\) 3.11545 5.39612i 0.174706 0.302599i
\(319\) 12.2456i 0.685622i
\(320\) −2.21345 + 0.317246i −0.123736 + 0.0177346i
\(321\) 0.0983076 0.170274i 0.00548700 0.00950376i
\(322\) 9.17048i 0.511051i
\(323\) 12.6162i 0.701982i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −8.11474 7.75112i −0.450125 0.429955i
\(326\) 2.20296 + 3.81563i 0.122010 + 0.211328i
\(327\) 13.4131 0.741747
\(328\) 2.30168 + 3.98662i 0.127089 + 0.220124i
\(329\) −8.73552 15.1304i −0.481605 0.834164i
\(330\) 0.952343 + 6.64457i 0.0524247 + 0.365772i
\(331\) −8.89801 5.13727i −0.489079 0.282370i 0.235113 0.971968i \(-0.424454\pi\)
−0.724192 + 0.689598i \(0.757787\pi\)
\(332\) 4.11489i 0.225834i
\(333\) 6.07532 0.300839i 0.332925 0.0164859i
\(334\) −21.6698 −1.18572
\(335\) 6.21058 4.87961i 0.339320 0.266601i
\(336\) 0.676327 + 1.17143i 0.0368967 + 0.0639069i
\(337\) −17.6489 + 10.1896i −0.961395 + 0.555062i −0.896602 0.442837i \(-0.853972\pi\)
−0.0647931 + 0.997899i \(0.520639\pi\)
\(338\) 3.98142 + 6.89603i 0.216561 + 0.375095i
\(339\) 14.4896i 0.786968i
\(340\) 5.28554 0.757558i 0.286649 0.0410843i
\(341\) 13.2684i 0.718522i
\(342\) 4.57549 + 2.64166i 0.247414 + 0.142845i
\(343\) 16.4622i 0.888878i
\(344\) −3.19094 −0.172044
\(345\) −11.9205 + 9.36582i −0.641776 + 0.504239i
\(346\) 14.2574 8.23149i 0.766480 0.442528i
\(347\) 2.73199 0.146661 0.0733304 0.997308i \(-0.476637\pi\)
0.0733304 + 0.997308i \(0.476637\pi\)
\(348\) −2.03964 + 3.53275i −0.109336 + 0.189375i
\(349\) 6.08918 10.5468i 0.325946 0.564556i −0.655757 0.754972i \(-0.727650\pi\)
0.981703 + 0.190416i \(0.0609838\pi\)
\(350\) −1.89969 6.49099i −0.101543 0.346958i
\(351\) 1.94367 1.12218i 0.103746 0.0598975i
\(352\) −1.50095 2.59973i −0.0800011 0.138566i
\(353\) −12.4776 + 21.6118i −0.664115 + 1.15028i 0.315410 + 0.948956i \(0.397858\pi\)
−0.979525 + 0.201325i \(0.935475\pi\)
\(354\) 2.41941 4.19055i 0.128590 0.222725i
\(355\) −16.8107 21.3961i −0.892221 1.13559i
\(356\) 16.7067i 0.885451i
\(357\) −1.61502 2.79729i −0.0854757 0.148048i
\(358\) −18.4058 10.6266i −0.972777 0.561633i
\(359\) −32.9716 −1.74018 −0.870088 0.492897i \(-0.835938\pi\)
−0.870088 + 0.492897i \(0.835938\pi\)
\(360\) −0.831981 + 2.07553i −0.0438493 + 0.109390i
\(361\) 4.45674 7.71930i 0.234565 0.406279i
\(362\) −18.4471 −0.969557
\(363\) 1.72213 0.994274i 0.0903885 0.0521858i
\(364\) 3.03584i 0.159121i
\(365\) 2.24106 + 15.6361i 0.117303 + 0.818430i
\(366\) −5.31237 9.20129i −0.277682 0.480959i
\(367\) 25.6297 14.7973i 1.33786 0.772413i 0.351369 0.936237i \(-0.385716\pi\)
0.986490 + 0.163824i \(0.0523830\pi\)
\(368\) 3.38981 5.87132i 0.176706 0.306064i
\(369\) 4.60335 0.239641
\(370\) 13.3520 2.59326i 0.694136 0.134817i
\(371\) −8.42825 −0.437573
\(372\) 2.20999 3.82781i 0.114583 0.198463i
\(373\) 1.28458 0.741651i 0.0665129 0.0384012i −0.466375 0.884587i \(-0.654440\pi\)
0.532888 + 0.846186i \(0.321107\pi\)
\(374\) 3.58416 + 6.20795i 0.185333 + 0.321005i
\(375\) 6.49732 9.09861i 0.335520 0.469850i
\(376\) 12.9161i 0.666098i
\(377\) 7.92877 4.57768i 0.408352 0.235762i
\(378\) 1.35265 0.0695730
\(379\) −6.13208 + 10.6211i −0.314984 + 0.545568i −0.979434 0.201764i \(-0.935332\pi\)
0.664450 + 0.747333i \(0.268666\pi\)
\(380\) 10.9657 + 4.39562i 0.562527 + 0.225491i
\(381\) −10.2927 −0.527312
\(382\) 7.58798 + 4.38092i 0.388235 + 0.224147i
\(383\) −6.12268 10.6048i −0.312855 0.541880i 0.666125 0.745841i \(-0.267952\pi\)
−0.978979 + 0.203961i \(0.934619\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 7.13957 5.60951i 0.363866 0.285887i
\(386\) −6.61309 + 11.4542i −0.336597 + 0.583003i
\(387\) −1.59547 + 2.76343i −0.0811023 + 0.140473i
\(388\) −4.79895 8.31202i −0.243630 0.421979i
\(389\) 3.72965 2.15332i 0.189101 0.109177i −0.402461 0.915437i \(-0.631845\pi\)
0.591562 + 0.806260i \(0.298512\pi\)
\(390\) 3.94621 3.10051i 0.199824 0.157000i
\(391\) −8.09460 + 14.0203i −0.409361 + 0.709035i
\(392\) −2.58516 + 4.47763i −0.130570 + 0.226155i
\(393\) −3.80107 −0.191739
\(394\) −7.32681 + 4.23013i −0.369119 + 0.213111i
\(395\) −1.03477 + 0.813014i −0.0520651 + 0.0409072i
\(396\) −3.00191 −0.150852
\(397\) 3.36805i 0.169038i −0.996422 0.0845189i \(-0.973065\pi\)
0.996422 0.0845189i \(-0.0269353\pi\)
\(398\) 6.69137 + 3.86326i 0.335408 + 0.193648i
\(399\) 7.14651i 0.357773i
\(400\) −1.18310 + 4.85801i −0.0591548 + 0.242901i
\(401\) 23.8277i 1.18990i −0.803763 0.594950i \(-0.797172\pi\)
0.803763 0.594950i \(-0.202828\pi\)
\(402\) 1.76610 + 3.05897i 0.0880849 + 0.152567i
\(403\) −8.59099 + 4.96001i −0.427947 + 0.247076i
\(404\) 8.32311 + 14.4160i 0.414090 + 0.717225i
\(405\) 1.38147 + 1.75828i 0.0686457 + 0.0873696i
\(406\) 5.51784 0.273846
\(407\) 9.90087 + 15.3426i 0.490768 + 0.760506i
\(408\) 2.38792i 0.118220i
\(409\) 29.8037 + 17.2072i 1.47370 + 0.850840i 0.999561 0.0296121i \(-0.00942722\pi\)
0.474136 + 0.880452i \(0.342761\pi\)
\(410\) 10.1893 1.46039i 0.503213 0.0721237i
\(411\) 5.08488 + 8.80728i 0.250819 + 0.434431i
\(412\) −3.35670 5.81397i −0.165373 0.286434i
\(413\) −6.54526 −0.322071
\(414\) −3.38981 5.87132i −0.166600 0.288560i
\(415\) −8.54057 3.42351i −0.419240 0.168054i
\(416\) −1.12218 + 1.94367i −0.0550194 + 0.0952964i
\(417\) 0.927293i 0.0454097i
\(418\) 15.8600i 0.775740i
\(419\) 8.20896 14.2183i 0.401034 0.694611i −0.592817 0.805337i \(-0.701984\pi\)
0.993851 + 0.110726i \(0.0353176\pi\)
\(420\) 2.99403 0.429124i 0.146094 0.0209391i
\(421\) 16.8650i 0.821952i 0.911646 + 0.410976i \(0.134812\pi\)
−0.911646 + 0.410976i \(0.865188\pi\)
\(422\) 7.00504 12.1331i 0.341000 0.590630i
\(423\) 11.1857 + 6.45806i 0.543867 + 0.314002i
\(424\) 5.39612 + 3.11545i 0.262059 + 0.151300i
\(425\) 2.82514 11.6006i 0.137039 0.562709i
\(426\) 10.5384 6.08437i 0.510589 0.294789i
\(427\) −7.18579 + 12.4462i −0.347745 + 0.602312i
\(428\) 0.170274 + 0.0983076i 0.00823049 + 0.00475188i
\(429\) 5.83473 + 3.36868i 0.281703 + 0.162641i
\(430\) −2.65480 + 6.62288i −0.128026 + 0.319384i
\(431\) −20.9618 + 12.1023i −1.00969 + 0.582946i −0.911102 0.412182i \(-0.864767\pi\)
−0.0985911 + 0.995128i \(0.531434\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 27.2175i 1.30799i 0.756499 + 0.653995i \(0.226908\pi\)
−0.756499 + 0.653995i \(0.773092\pi\)
\(434\) −5.97870 −0.286987
\(435\) 5.63538 + 7.17250i 0.270196 + 0.343895i
\(436\) 13.4131i 0.642372i
\(437\) −31.0201 + 17.9094i −1.48389 + 0.856725i
\(438\) −7.06413 −0.337537
\(439\) −0.303940 + 0.175480i −0.0145063 + 0.00837519i −0.507236 0.861807i \(-0.669333\pi\)
0.492729 + 0.870183i \(0.335999\pi\)
\(440\) −6.64457 + 0.952343i −0.316767 + 0.0454012i
\(441\) 2.58516 + 4.47763i 0.123103 + 0.213221i
\(442\) 2.67968 4.64134i 0.127459 0.220766i
\(443\) 29.6858i 1.41042i 0.709001 + 0.705208i \(0.249146\pi\)
−0.709001 + 0.705208i \(0.750854\pi\)
\(444\) 0.300839 + 6.07532i 0.0142772 + 0.288322i
\(445\) −34.6751 13.8996i −1.64376 0.658906i
\(446\) 2.68760 + 1.55168i 0.127261 + 0.0734744i
\(447\) 7.84345 4.52842i 0.370983 0.214187i
\(448\) −1.17143 + 0.676327i −0.0553450 + 0.0319534i
\(449\) 17.7164 10.2286i 0.836090 0.482717i −0.0198434 0.999803i \(-0.506317\pi\)
0.855933 + 0.517086i \(0.172983\pi\)
\(450\) 3.61561 + 3.45360i 0.170442 + 0.162804i
\(451\) 6.90942 + 11.9675i 0.325352 + 0.563526i
\(452\) −14.4896 −0.681535
\(453\) −9.93758 5.73747i −0.466908 0.269570i
\(454\) −15.9436 −0.748270
\(455\) −6.30097 2.52576i −0.295394 0.118410i
\(456\) −2.64166 + 4.57549i −0.123707 + 0.214267i
\(457\) −16.1935 28.0480i −0.757502 1.31203i −0.944121 0.329599i \(-0.893086\pi\)
0.186619 0.982432i \(-0.440247\pi\)
\(458\) 13.4676 0.629301
\(459\) 2.06800 + 1.19396i 0.0965260 + 0.0557293i
\(460\) −9.36582 11.9205i −0.436684 0.555795i
\(461\) −16.5318 9.54466i −0.769964 0.444539i 0.0628977 0.998020i \(-0.479966\pi\)
−0.832862 + 0.553481i \(0.813299\pi\)
\(462\) 2.03027 + 3.51653i 0.0944568 + 0.163604i
\(463\) 9.39427 + 16.2714i 0.436589 + 0.756194i 0.997424 0.0717334i \(-0.0228531\pi\)
−0.560835 + 0.827928i \(0.689520\pi\)
\(464\) −3.53275 2.03964i −0.164004 0.0946877i
\(465\) −6.10605 7.77155i −0.283161 0.360397i
\(466\) 23.9357 + 13.8193i 1.10880 + 0.640167i
\(467\) −2.97790 −0.137801 −0.0689004 0.997624i \(-0.521949\pi\)
−0.0689004 + 0.997624i \(0.521949\pi\)
\(468\) 1.12218 + 1.94367i 0.0518728 + 0.0898463i
\(469\) 2.38892 4.13773i 0.110310 0.191062i
\(470\) 26.8077 + 10.7460i 1.23655 + 0.495675i
\(471\) −5.82040 −0.268190
\(472\) 4.19055 + 2.41941i 0.192886 + 0.111363i
\(473\) −9.57891 −0.440439
\(474\) −0.294257 0.509669i −0.0135157 0.0234099i
\(475\) 18.2465 19.1024i 0.837205 0.876480i
\(476\) 2.79729 1.61502i 0.128214 0.0740241i
\(477\) 5.39612 3.11545i 0.247071 0.142647i
\(478\) −11.3747 + 6.56719i −0.520267 + 0.300376i
\(479\) 28.9748 + 16.7286i 1.32389 + 0.764350i 0.984347 0.176239i \(-0.0563932\pi\)
0.339546 + 0.940589i \(0.389727\pi\)
\(480\) −2.07553 0.831981i −0.0947344 0.0379746i
\(481\) 6.23287 12.1460i 0.284194 0.553811i
\(482\) 28.6994i 1.30722i
\(483\) −4.58524 + 7.94187i −0.208636 + 0.361367i
\(484\) 0.994274 + 1.72213i 0.0451943 + 0.0782788i
\(485\) −21.2445 + 3.04489i −0.964661 + 0.138261i
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) −3.98263 −0.180470 −0.0902350 0.995920i \(-0.528762\pi\)
−0.0902350 + 0.995920i \(0.528762\pi\)
\(488\) 9.20129 5.31237i 0.416523 0.240479i
\(489\) 4.40591i 0.199242i
\(490\) 7.14264 + 9.09088i 0.322671 + 0.410684i
\(491\) −39.2680 −1.77214 −0.886070 0.463551i \(-0.846575\pi\)
−0.886070 + 0.463551i \(0.846575\pi\)
\(492\) 4.60335i 0.207535i
\(493\) 8.43593 + 4.87049i 0.379935 + 0.219356i
\(494\) 10.2690 5.92884i 0.462026 0.266751i
\(495\) −2.49753 + 6.23054i −0.112256 + 0.280042i
\(496\) 3.82781 + 2.20999i 0.171874 + 0.0992314i
\(497\) −14.2549 8.23005i −0.639418 0.369168i
\(498\) 2.05745 3.56360i 0.0921964 0.159689i
\(499\) −11.2105 + 6.47239i −0.501851 + 0.289744i −0.729478 0.684005i \(-0.760237\pi\)
0.227627 + 0.973749i \(0.426903\pi\)
\(500\) 9.09861 + 6.49732i 0.406902 + 0.290569i
\(501\) −18.7666 10.8349i −0.838431 0.484069i
\(502\) −6.59600 3.80820i −0.294394 0.169968i
\(503\) −3.46336 + 5.99871i −0.154424 + 0.267469i −0.932849 0.360268i \(-0.882685\pi\)
0.778425 + 0.627737i \(0.216019\pi\)
\(504\) 1.35265i 0.0602520i
\(505\) 36.8455 5.28094i 1.63961 0.234999i
\(506\) 10.1759 17.6252i 0.452374 0.783534i
\(507\) 7.96285i 0.353643i
\(508\) 10.2927i 0.456666i
\(509\) −11.5336 + 19.9767i −0.511216 + 0.885452i 0.488700 + 0.872452i \(0.337471\pi\)
−0.999916 + 0.0129996i \(0.995862\pi\)
\(510\) 4.95619 + 1.98671i 0.219464 + 0.0879728i
\(511\) 4.77766 + 8.27515i 0.211351 + 0.366071i
\(512\) 1.00000 0.0441942
\(513\) 2.64166 + 4.57549i 0.116632 + 0.202013i
\(514\) 5.86850 + 10.1645i 0.258848 + 0.448338i
\(515\) −14.8598 + 2.12980i −0.654799 + 0.0938500i
\(516\) −2.76343 1.59547i −0.121653 0.0702366i
\(517\) 38.7730i 1.70523i
\(518\) 6.91336 4.46131i 0.303756 0.196019i
\(519\) 16.4630 0.722645
\(520\) 3.10051 + 3.94621i 0.135966 + 0.173053i
\(521\) −14.6787 25.4242i −0.643084 1.11385i −0.984741 0.174029i \(-0.944321\pi\)
0.341657 0.939825i \(-0.389012\pi\)
\(522\) −3.53275 + 2.03964i −0.154624 + 0.0892724i
\(523\) 3.65507 + 6.33077i 0.159825 + 0.276825i 0.934806 0.355160i \(-0.115574\pi\)
−0.774980 + 0.631985i \(0.782240\pi\)
\(524\) 3.80107i 0.166051i
\(525\) 1.60032 6.57121i 0.0698437 0.286791i
\(526\) 14.8914i 0.649294i
\(527\) −9.14051 5.27728i −0.398167 0.229882i
\(528\) 3.00191i 0.130641i
\(529\) 22.9632 0.998400
\(530\) 10.9557 8.60778i 0.475884 0.373898i
\(531\) 4.19055 2.41941i 0.181854 0.104994i
\(532\) 7.14651 0.309840
\(533\) 5.16579 8.94741i 0.223755 0.387555i
\(534\) 8.35333 14.4684i 0.361484 0.626109i
\(535\) 0.345705 0.271618i 0.0149461 0.0117430i
\(536\) −3.05897 + 1.76610i −0.132127 + 0.0762837i
\(537\) −10.6266 18.4058i −0.458571 0.794269i
\(538\) −5.77165 + 9.99679i −0.248833 + 0.430992i
\(539\) −7.76042 + 13.4414i −0.334265 + 0.578964i
\(540\) −1.75828 + 1.38147i −0.0756643 + 0.0594489i
\(541\) 20.4675i 0.879965i −0.898006 0.439982i \(-0.854985\pi\)
0.898006 0.439982i \(-0.145015\pi\)
\(542\) 0.336417 + 0.582692i 0.0144504 + 0.0250288i
\(543\) −15.9756 9.22354i −0.685580 0.395820i
\(544\) −2.38792 −0.102381
\(545\) 27.8393 + 11.1595i 1.19250 + 0.478019i
\(546\) 1.51792 2.62912i 0.0649610 0.112516i
\(547\) −11.7724 −0.503352 −0.251676 0.967812i \(-0.580982\pi\)
−0.251676 + 0.967812i \(0.580982\pi\)
\(548\) −8.80728 + 5.08488i −0.376228 + 0.217215i
\(549\) 10.6247i 0.453452i
\(550\) −3.55155 + 14.5833i −0.151438 + 0.621834i
\(551\) 10.7760 + 18.6647i 0.459075 + 0.795141i
\(552\) 5.87132 3.38981i 0.249900 0.144280i
\(553\) −0.398029 + 0.689406i −0.0169259 + 0.0293165i
\(554\) −28.3804 −1.20577
\(555\) 12.8598 + 4.43015i 0.545867 + 0.188050i
\(556\) −0.927293 −0.0393260
\(557\) 2.72821 4.72539i 0.115598 0.200221i −0.802421 0.596759i \(-0.796455\pi\)
0.918019 + 0.396537i \(0.129788\pi\)
\(558\) 3.82781 2.20999i 0.162044 0.0935562i
\(559\) 3.58081 + 6.20214i 0.151452 + 0.262323i
\(560\) 0.429124 + 2.99403i 0.0181338 + 0.126521i
\(561\) 7.16832i 0.302647i
\(562\) 17.3856 10.0376i 0.733366 0.423409i
\(563\) −14.7884 −0.623255 −0.311627 0.950204i \(-0.600874\pi\)
−0.311627 + 0.950204i \(0.600874\pi\)
\(564\) −6.45806 + 11.1857i −0.271933 + 0.471002i
\(565\) −12.0551 + 30.0736i −0.507162 + 1.26521i
\(566\) −8.78618 −0.369311
\(567\) 1.17143 + 0.676327i 0.0491956 + 0.0284031i
\(568\) 6.08437 + 10.5384i 0.255295 + 0.442183i
\(569\) 7.17981i 0.300993i 0.988611 + 0.150497i \(0.0480873\pi\)
−0.988611 + 0.150497i \(0.951913\pi\)
\(570\) 7.29873 + 9.28956i 0.305710 + 0.389097i
\(571\) −7.05703 + 12.2231i −0.295328 + 0.511523i −0.975061 0.221937i \(-0.928762\pi\)
0.679733 + 0.733459i \(0.262096\pi\)
\(572\) −3.36868 + 5.83473i −0.140852 + 0.243962i
\(573\) 4.38092 + 7.58798i 0.183016 + 0.316992i
\(574\) 5.39252 3.11337i 0.225079 0.129950i
\(575\) −32.5334 + 9.52139i −1.35674 + 0.397070i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −6.70480 + 11.6130i −0.279124 + 0.483458i −0.971167 0.238399i \(-0.923378\pi\)
0.692043 + 0.721856i \(0.256711\pi\)
\(578\) −11.2978 −0.469928
\(579\) −11.4542 + 6.61309i −0.476020 + 0.274830i
\(580\) −7.17250 + 5.63538i −0.297822 + 0.233996i
\(581\) −5.56603 −0.230918
\(582\) 9.59790i 0.397846i
\(583\) 16.1986 + 9.35229i 0.670879 + 0.387332i
\(584\) 7.06413i 0.292316i
\(585\) 4.96778 0.712014i 0.205392 0.0294381i
\(586\) 20.9988i 0.867451i
\(587\) 11.2829 + 19.5426i 0.465697 + 0.806611i 0.999233 0.0391668i \(-0.0124704\pi\)
−0.533536 + 0.845777i \(0.679137\pi\)
\(588\) −4.47763 + 2.58516i −0.184655 + 0.106610i
\(589\) −11.6761 20.2236i −0.481104 0.833297i
\(590\) 8.50801 6.68468i 0.350269 0.275204i
\(591\) −8.46027 −0.348009
\(592\) −6.07532 + 0.300839i −0.249694 + 0.0123644i
\(593\) 1.74844i 0.0717997i 0.999355 + 0.0358998i \(0.0114297\pi\)
−0.999355 + 0.0358998i \(0.988570\pi\)
\(594\) −2.59973 1.50095i −0.106668 0.0615849i
\(595\) −1.02471 7.14951i −0.0420092 0.293101i
\(596\) 4.52842 + 7.84345i 0.185491 + 0.321280i
\(597\) 3.86326 + 6.69137i 0.158113 + 0.273860i
\(598\) −15.2159 −0.622224
\(599\) −14.3049 24.7768i −0.584481 1.01235i −0.994940 0.100472i \(-0.967965\pi\)
0.410459 0.911879i \(-0.365369\pi\)
\(600\) −3.45360 + 3.61561i −0.140993 + 0.147607i
\(601\) −6.17497 + 10.6954i −0.251882 + 0.436273i −0.964044 0.265743i \(-0.914383\pi\)
0.712162 + 0.702015i \(0.247716\pi\)
\(602\) 4.31624i 0.175917i
\(603\) 3.53219i 0.143842i
\(604\) 5.73747 9.93758i 0.233454 0.404355i
\(605\) 4.40155 0.630858i 0.178948 0.0256480i
\(606\) 16.6462i 0.676206i
\(607\) −18.1702 + 31.4717i −0.737505 + 1.27740i 0.216111 + 0.976369i \(0.430663\pi\)
−0.953616 + 0.301027i \(0.902671\pi\)
\(608\) −4.57549 2.64166i −0.185561 0.107133i
\(609\) 4.77859 + 2.75892i 0.193638 + 0.111797i
\(610\) −3.37065 23.5173i −0.136474 0.952187i
\(611\) 25.1047 14.4942i 1.01563 0.586373i
\(612\) −1.19396 + 2.06800i −0.0482630 + 0.0835940i
\(613\) 0.816507 + 0.471410i 0.0329784 + 0.0190401i 0.516399 0.856348i \(-0.327272\pi\)
−0.483420 + 0.875388i \(0.660606\pi\)
\(614\) −14.0371 8.10430i −0.566489 0.327063i
\(615\) 9.55438 + 3.82990i 0.385270 + 0.154437i
\(616\) −3.51653 + 2.03027i −0.141685 + 0.0818020i
\(617\) 8.06384 + 4.65566i 0.324638 + 0.187430i 0.653458 0.756963i \(-0.273318\pi\)
−0.328820 + 0.944393i \(0.606651\pi\)
\(618\) 6.71339i 0.270052i
\(619\) −0.187571 −0.00753912 −0.00376956 0.999993i \(-0.501200\pi\)
−0.00376956 + 0.999993i \(0.501200\pi\)
\(620\) 7.77155 6.10605i 0.312113 0.245225i
\(621\) 6.77962i 0.272057i
\(622\) −2.58380 + 1.49176i −0.103601 + 0.0598141i
\(623\) −22.5983 −0.905383
\(624\) −1.94367 + 1.12218i −0.0778092 + 0.0449232i
\(625\) 21.0552 13.4788i 0.842210 0.539150i
\(626\) 2.25748 + 3.91006i 0.0902269 + 0.156278i
\(627\) −7.93002 + 13.7352i −0.316695 + 0.548531i
\(628\) 5.82040i 0.232259i
\(629\) 14.5074 0.718380i 0.578447 0.0286437i
\(630\) 2.80747 + 1.12538i 0.111852 + 0.0448363i
\(631\) 24.8688 + 14.3580i 0.990013 + 0.571584i 0.905278 0.424820i \(-0.139662\pi\)
0.0847345 + 0.996404i \(0.472996\pi\)
\(632\) 0.509669 0.294257i 0.0202735 0.0117049i
\(633\) 12.1331 7.00504i 0.482247 0.278425i
\(634\) −5.91704 + 3.41620i −0.234995 + 0.135675i
\(635\) −21.3628 8.56335i −0.847757 0.339826i
\(636\) 3.11545 + 5.39612i 0.123536 + 0.213970i
\(637\) 11.6041 0.459770
\(638\) −10.6050 6.12280i −0.419856 0.242404i
\(639\) 12.1687 0.481388
\(640\) 0.831981 2.07553i 0.0328870 0.0820424i
\(641\) 4.13811 7.16743i 0.163446 0.283096i −0.772657 0.634824i \(-0.781072\pi\)
0.936102 + 0.351728i \(0.114406\pi\)
\(642\) 0.0983076 + 0.170274i 0.00387989 + 0.00672017i
\(643\) 14.4839 0.571189 0.285595 0.958351i \(-0.407809\pi\)
0.285595 + 0.958351i \(0.407809\pi\)
\(644\) −7.94187 4.58524i −0.312953 0.180684i
\(645\) −5.61057 + 4.40818i −0.220916 + 0.173572i
\(646\) 10.9259 + 6.30808i 0.429874 + 0.248188i
\(647\) 17.3434 + 30.0396i 0.681839 + 1.18098i 0.974419 + 0.224738i \(0.0721527\pi\)
−0.292581 + 0.956241i \(0.594514\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 12.5796 + 7.26286i 0.493794 + 0.285092i
\(650\) 10.7700 3.15201i 0.422435 0.123632i
\(651\) −5.17770 2.98935i −0.202930 0.117162i
\(652\) −4.40591 −0.172549
\(653\) −11.4681 19.8634i −0.448783 0.777315i 0.549524 0.835478i \(-0.314809\pi\)
−0.998307 + 0.0581630i \(0.981476\pi\)
\(654\) −6.70656 + 11.6161i −0.262247 + 0.454226i
\(655\) −7.88922 3.16242i −0.308257 0.123566i
\(656\) −4.60335 −0.179731
\(657\) −6.11771 3.53206i −0.238675 0.137799i
\(658\) 17.4710 0.681092
\(659\) −19.8771 34.4282i −0.774303 1.34113i −0.935186 0.354158i \(-0.884767\pi\)
0.160883 0.986974i \(-0.448566\pi\)
\(660\) −6.23054 2.49753i −0.242523 0.0972163i
\(661\) −24.3780 + 14.0746i −0.948194 + 0.547440i −0.892519 0.451009i \(-0.851064\pi\)
−0.0556746 + 0.998449i \(0.517731\pi\)
\(662\) 8.89801 5.13727i 0.345831 0.199666i
\(663\) 4.64134 2.67968i 0.180255 0.104070i
\(664\) 3.56360 + 2.05745i 0.138295 + 0.0798444i
\(665\) 5.94576 14.8328i 0.230567 0.575190i
\(666\) −2.77713 + 5.41180i −0.107611 + 0.209703i
\(667\) 27.6559i 1.07084i
\(668\) 10.8349 18.7666i 0.419216 0.726103i
\(669\) 1.55168 + 2.68760i 0.0599916 + 0.103908i
\(670\) 1.12057 + 7.81833i 0.0432915 + 0.302048i
\(671\) 27.6214 15.9472i 1.06631 0.615636i
\(672\) −1.35265 −0.0521798
\(673\) −10.4568 + 6.03721i −0.403078 + 0.232717i −0.687811 0.725890i \(-0.741428\pi\)
0.284733 + 0.958607i \(0.408095\pi\)
\(674\) 20.3792i 0.784976i
\(675\) 1.40441 + 4.79871i 0.0540559 + 0.184702i
\(676\) −7.96285 −0.306263
\(677\) 32.2867i 1.24088i −0.784254 0.620440i \(-0.786954\pi\)
0.784254 0.620440i \(-0.213046\pi\)
\(678\) −12.5484 7.24481i −0.481918 0.278235i
\(679\) −11.2433 + 6.49132i −0.431478 + 0.249114i
\(680\) −1.98671 + 4.95619i −0.0761867 + 0.190061i
\(681\) −13.8076 7.97179i −0.529107 0.305480i
\(682\) 11.4907 + 6.63418i 0.440003 + 0.254036i
\(683\) 12.6798 21.9620i 0.485178 0.840353i −0.514677 0.857384i \(-0.672088\pi\)
0.999855 + 0.0170311i \(0.00542143\pi\)
\(684\) −4.57549 + 2.64166i −0.174948 + 0.101006i
\(685\) 3.22632 + 22.5103i 0.123271 + 0.860073i
\(686\) 14.2567 + 8.23112i 0.544324 + 0.314266i
\(687\) 11.6633 + 6.73382i 0.444983 + 0.256911i
\(688\) 1.59547 2.76343i 0.0608267 0.105355i
\(689\) 13.9844i 0.532762i
\(690\) −2.15080 15.0063i −0.0818797 0.571281i
\(691\) −17.4719 + 30.2623i −0.664664 + 1.15123i 0.314712 + 0.949187i \(0.398092\pi\)
−0.979376 + 0.202045i \(0.935241\pi\)
\(692\) 16.4630i 0.625829i
\(693\) 4.06054i 0.154247i
\(694\) −1.36599 + 2.36597i −0.0518524 + 0.0898110i
\(695\) −0.771490 + 1.92462i −0.0292643 + 0.0730050i
\(696\) −2.03964 3.53275i −0.0773122 0.133909i
\(697\) 10.9924 0.416369
\(698\) 6.08918 + 10.5468i 0.230479 + 0.399201i
\(699\) 13.8193 + 23.9357i 0.522694 + 0.905333i
\(700\) 6.57121 + 1.60032i 0.248368 + 0.0604864i
\(701\) −18.2155 10.5167i −0.687990 0.397211i 0.114868 0.993381i \(-0.463355\pi\)
−0.802859 + 0.596169i \(0.796689\pi\)
\(702\) 2.24436i 0.0847079i
\(703\) 28.5923 + 14.6724i 1.07838 + 0.553382i
\(704\) 3.00191 0.113139
\(705\) 17.8432 + 22.7101i 0.672013 + 0.855314i
\(706\) −12.4776 21.6118i −0.469600 0.813371i
\(707\) 19.4999 11.2583i 0.733370 0.423411i
\(708\) 2.41941 + 4.19055i 0.0909271 + 0.157490i
\(709\) 40.1656i 1.50845i −0.656615 0.754226i \(-0.728012\pi\)
0.656615 0.754226i \(-0.271988\pi\)
\(710\) 26.9349 3.86048i 1.01085 0.144881i
\(711\) 0.588515i 0.0220710i
\(712\) 14.4684 + 8.35333i 0.542226 + 0.313054i
\(713\) 29.9657i 1.12223i
\(714\) 3.23003 0.120881
\(715\) 9.30745 + 11.8462i 0.348079 + 0.443022i
\(716\) 18.4058 10.6266i 0.687857 0.397134i
\(717\) −13.1344 −0.490512
\(718\) 16.4858 28.5543i 0.615245 1.06564i
\(719\) 26.0199 45.0677i 0.970377 1.68074i 0.275962 0.961169i \(-0.411004\pi\)
0.694416 0.719574i \(-0.255663\pi\)
\(720\) −1.38147 1.75828i −0.0514842 0.0655272i
\(721\) −7.86429 + 4.54045i −0.292881 + 0.169095i
\(722\) 4.45674 + 7.71930i 0.165863 + 0.287283i
\(723\) −14.3497 + 24.8544i −0.533671 + 0.924346i
\(724\) 9.22354 15.9756i 0.342790 0.593730i
\(725\) 5.72899 + 19.5752i 0.212769 + 0.727006i
\(726\) 1.98855i 0.0738019i
\(727\) −11.3516 19.6615i −0.421008 0.729206i 0.575031 0.818132i \(-0.304990\pi\)
−0.996038 + 0.0889253i \(0.971657\pi\)
\(728\) 2.62912 + 1.51792i 0.0974415 + 0.0562579i
\(729\) −1.00000 −0.0370370
\(730\) −14.6618 5.87722i −0.542657 0.217526i
\(731\) −3.80986 + 6.59887i −0.140913 + 0.244068i
\(732\) 10.6247 0.392701
\(733\) −26.1668 + 15.1074i −0.966494 + 0.558005i −0.898166 0.439657i \(-0.855100\pi\)
−0.0683283 + 0.997663i \(0.521767\pi\)
\(734\) 29.5946i 1.09236i
\(735\) 1.64026 + 11.4443i 0.0605021 + 0.422128i
\(736\) 3.38981 + 5.87132i 0.124950 + 0.216420i
\(737\) −9.18274 + 5.30166i −0.338251 + 0.195289i
\(738\) −2.30168 + 3.98662i −0.0847259 + 0.146750i
\(739\) −20.1078 −0.739676 −0.369838 0.929096i \(-0.620587\pi\)
−0.369838 + 0.929096i \(0.620587\pi\)
\(740\) −4.43015 + 12.8598i −0.162856 + 0.472735i
\(741\) 11.8577 0.435602
\(742\) 4.21412 7.29908i 0.154705 0.267958i
\(743\) −8.93959 + 5.16128i −0.327962 + 0.189349i −0.654936 0.755684i \(-0.727304\pi\)
0.326974 + 0.945033i \(0.393971\pi\)
\(744\) 2.20999 + 3.82781i 0.0810221 + 0.140334i
\(745\) 20.0468 2.87324i 0.734460 0.105268i
\(746\) 1.48330i 0.0543075i
\(747\) 3.56360 2.05745i 0.130385 0.0752780i
\(748\) −7.16832 −0.262100
\(749\) 0.132976 0.230322i 0.00485884 0.00841577i
\(750\) 4.63097 + 10.1762i 0.169099 + 0.371581i
\(751\) 15.2700 0.557208 0.278604 0.960406i \(-0.410128\pi\)
0.278604 + 0.960406i \(0.410128\pi\)
\(752\) −11.1857 6.45806i −0.407900 0.235501i
\(753\) −3.80820 6.59600i −0.138779 0.240372i
\(754\) 9.15535i 0.333418i
\(755\) −15.8522 20.1761i −0.576922 0.734285i
\(756\) −0.676327 + 1.17143i −0.0245978 + 0.0426046i
\(757\) 2.93517 5.08386i 0.106680 0.184776i −0.807743 0.589535i \(-0.799311\pi\)
0.914424 + 0.404759i \(0.132644\pi\)
\(758\) −6.13208 10.6211i −0.222727 0.385775i
\(759\) 17.6252 10.1759i 0.639753 0.369362i
\(760\) −9.28956 + 7.29873i −0.336968 + 0.264753i
\(761\) −13.7631 + 23.8384i −0.498911 + 0.864140i −0.999999 0.00125666i \(-0.999600\pi\)
0.501088 + 0.865396i \(0.332933\pi\)
\(762\) 5.14636 8.91376i 0.186433 0.322911i
\(763\) 18.1433 0.656832
\(764\) −7.58798 + 4.38092i −0.274523 + 0.158496i
\(765\) 3.29884 + 4.19863i 0.119270 + 0.151802i
\(766\) 12.2454 0.442443
\(767\) 10.8601i 0.392134i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) 27.2786i 0.983692i −0.870682 0.491846i \(-0.836322\pi\)
0.870682 0.491846i \(-0.163678\pi\)
\(770\) 1.28819 + 8.98780i 0.0464232 + 0.323898i
\(771\) 11.7370i 0.422698i
\(772\) −6.61309 11.4542i −0.238010 0.412246i
\(773\) −34.4624 + 19.8969i −1.23953 + 0.715642i −0.968998 0.247070i \(-0.920532\pi\)
−0.270530 + 0.962711i \(0.587199\pi\)
\(774\) −1.59547 2.76343i −0.0573480 0.0993296i
\(775\) −6.20748 21.2102i −0.222979 0.761892i
\(776\) 9.59790 0.344545
\(777\) 8.21780 0.406931i 0.294812 0.0145986i
\(778\) 4.30663i 0.154400i
\(779\) 21.0626 + 12.1605i 0.754646 + 0.435695i
\(780\) 0.712014 + 4.96778i 0.0254942 + 0.177875i
\(781\) 18.2647 + 31.6354i 0.653563 + 1.13201i
\(782\) −8.09460 14.0203i −0.289462 0.501363i
\(783\) −4.07927 −0.145781
\(784\) −2.58516 4.47763i −0.0923273 0.159916i
\(785\) −12.0804 4.84247i −0.431168 0.172835i
\(786\) 1.90054 3.29183i 0.0677899 0.117416i
\(787\) 15.7678i 0.562061i −0.959699 0.281031i \(-0.909324\pi\)
0.959699 0.281031i \(-0.0906763\pi\)
\(788\) 8.46027i 0.301385i
\(789\) −7.44568 + 12.8963i −0.265073 + 0.459120i
\(790\) −0.186704 1.30265i −0.00664263 0.0463461i
\(791\) 19.5994i 0.696876i
\(792\) 1.50095 2.59973i 0.0533341 0.0923773i
\(793\) −20.6510 11.9229i −0.733338 0.423393i
\(794\) 2.91682 + 1.68403i 0.103514 + 0.0597639i
\(795\) 13.7918 1.97673i 0.489144 0.0701072i
\(796\) −6.69137 + 3.86326i −0.237169 + 0.136930i
\(797\) −7.06082 + 12.2297i −0.250107 + 0.433198i −0.963555 0.267510i \(-0.913799\pi\)
0.713448 + 0.700708i \(0.247132\pi\)
\(798\) 6.18905 + 3.57325i 0.219090 + 0.126492i
\(799\) 26.7105 + 15.4213i 0.944951 + 0.545568i
\(800\) −3.61561 3.45360i −0.127831 0.122103i
\(801\) 14.4684 8.35333i 0.511216 0.295150i
\(802\) 20.6354 + 11.9139i 0.728661 + 0.420693i
\(803\) 21.2059i 0.748339i
\(804\) −3.53219 −0.124571
\(805\) −16.1243 + 12.6687i −0.568306 + 0.446513i
\(806\) 9.92002i 0.349418i
\(807\) −9.99679 + 5.77165i −0.351904 + 0.203172i
\(808\) −16.6462 −0.585612
\(809\) −24.2202 + 13.9835i −0.851537 + 0.491635i −0.861169 0.508319i \(-0.830267\pi\)
0.00963235 + 0.999954i \(0.496934\pi\)
\(810\) −2.21345 + 0.317246i −0.0777727 + 0.0111469i
\(811\) 24.4604 + 42.3666i 0.858919 + 1.48769i 0.872961 + 0.487791i \(0.162197\pi\)
−0.0140411 + 0.999901i \(0.504470\pi\)
\(812\) −2.75892 + 4.77859i −0.0968192 + 0.167696i
\(813\) 0.672835i 0.0235973i
\(814\) −18.2375 + 0.903091i −0.639226 + 0.0316533i
\(815\) −3.66564 + 9.14458i −0.128402 + 0.320321i
\(816\) −2.06800 1.19396i −0.0723945 0.0417970i
\(817\) −14.6001 + 8.42938i −0.510793 + 0.294907i
\(818\) −29.8037 + 17.2072i −1.04206 + 0.601634i
\(819\) 2.62912 1.51792i 0.0918688 0.0530405i
\(820\) −3.82990 + 9.55438i −0.133746 + 0.333653i
\(821\) −7.27927 12.6081i −0.254048 0.440025i 0.710588 0.703608i \(-0.248429\pi\)
−0.964637 + 0.263583i \(0.915096\pi\)
\(822\) −10.1698 −0.354711
\(823\) 13.1840 + 7.61181i 0.459567 + 0.265331i 0.711862 0.702319i \(-0.247852\pi\)
−0.252295 + 0.967650i \(0.581185\pi\)
\(824\) 6.71339 0.233872
\(825\) −10.3674 + 10.8537i −0.360946 + 0.377879i
\(826\) 3.27263 5.66836i 0.113869 0.197228i
\(827\) −6.92772 11.9992i −0.240900 0.417252i 0.720071 0.693901i \(-0.244109\pi\)
−0.960971 + 0.276649i \(0.910776\pi\)
\(828\) 6.77962 0.235608
\(829\) 18.9388 + 10.9343i 0.657770 + 0.379764i 0.791427 0.611264i \(-0.209339\pi\)
−0.133657 + 0.991028i \(0.542672\pi\)
\(830\) 7.23513 5.68459i 0.251135 0.197315i
\(831\) −24.5782 14.1902i −0.852607 0.492253i
\(832\) −1.12218 1.94367i −0.0389046 0.0673847i
\(833\) 6.17317 + 10.6922i 0.213888 + 0.370464i
\(834\) −0.803059 0.463646i −0.0278077 0.0160548i
\(835\) −29.9362 38.1017i −1.03598 1.31856i
\(836\) −13.7352 7.93002i −0.475042 0.274266i
\(837\) 4.41998 0.152777
\(838\) 8.20896 + 14.2183i 0.283574 + 0.491164i
\(839\) 14.0966 24.4161i 0.486669 0.842936i −0.513213 0.858261i \(-0.671545\pi\)
0.999883 + 0.0153252i \(0.00487836\pi\)
\(840\) −1.12538 + 2.80747i −0.0388294 + 0.0968669i
\(841\) 12.3595 0.426191
\(842\) −14.6055 8.43252i −0.503340 0.290604i
\(843\) 20.0751 0.691424
\(844\) 7.00504 + 12.1331i 0.241124 + 0.417638i
\(845\) −6.62494 + 16.5271i −0.227905 + 0.568549i
\(846\) −11.1857 + 6.45806i −0.384572 + 0.222033i
\(847\) 2.32945 1.34491i 0.0800408 0.0462116i
\(848\) −5.39612 + 3.11545i −0.185303 + 0.106985i
\(849\) −7.60906 4.39309i −0.261142 0.150771i
\(850\) 8.63380 + 8.24692i 0.296137 + 0.282867i
\(851\) −22.3605 34.6504i −0.766508 1.18780i
\(852\) 12.1687i 0.416894i
\(853\) 12.4816 21.6188i 0.427362 0.740213i −0.569275 0.822147i \(-0.692776\pi\)
0.996638 + 0.0819335i \(0.0261095\pi\)
\(854\) −7.18579 12.4462i −0.245893 0.425899i
\(855\) 1.67611 + 11.6944i 0.0573218 + 0.399939i
\(856\) −0.170274 + 0.0983076i −0.00581984 + 0.00336009i
\(857\) 25.5581 0.873047 0.436524 0.899693i \(-0.356210\pi\)
0.436524 + 0.899693i \(0.356210\pi\)
\(858\) −5.83473 + 3.36868i −0.199194 + 0.115005i
\(859\) 26.1665i 0.892789i −0.894836 0.446395i \(-0.852708\pi\)
0.894836 0.446395i \(-0.147292\pi\)
\(860\) −4.40818 5.61057i −0.150318 0.191319i
\(861\) 6.22675 0.212207
\(862\) 24.2046i 0.824411i
\(863\) −21.4938 12.4095i −0.731658 0.422423i 0.0873702 0.996176i \(-0.472154\pi\)
−0.819029 + 0.573753i \(0.805487\pi\)
\(864\) 0.866025 0.500000i 0.0294628 0.0170103i
\(865\) 34.1693 + 13.6969i 1.16179 + 0.465708i
\(866\) −23.5710 13.6087i −0.800977 0.462444i
\(867\) −9.78421 5.64892i −0.332289 0.191847i
\(868\) 2.98935 5.17770i 0.101465 0.175743i
\(869\) 1.52998 0.883334i 0.0519010 0.0299651i
\(870\) −9.02926 + 1.29413i −0.306120 + 0.0438752i
\(871\) 6.86543 + 3.96376i 0.232626 + 0.134307i
\(872\) −11.6161 6.70656i −0.393371 0.227113i
\(873\) 4.79895 8.31202i 0.162420 0.281319i
\(874\) 35.8189i 1.21159i
\(875\) 8.78863 12.3073i 0.297110 0.416062i
\(876\) 3.53206 6.11771i 0.119337 0.206698i
\(877\) 18.9348i 0.639384i −0.947522 0.319692i \(-0.896421\pi\)
0.947522 0.319692i \(-0.103579\pi\)
\(878\) 0.350960i 0.0118443i
\(879\) −10.4994 + 18.1855i −0.354135 + 0.613380i
\(880\) 2.49753 6.23054i 0.0841918 0.210031i
\(881\) 0.835883 + 1.44779i 0.0281616 + 0.0487773i 0.879763 0.475413i \(-0.157701\pi\)
−0.851601 + 0.524190i \(0.824368\pi\)
\(882\) −5.17033 −0.174094
\(883\) −19.4113 33.6214i −0.653242 1.13145i −0.982331 0.187150i \(-0.940075\pi\)
0.329089 0.944299i \(-0.393258\pi\)
\(884\) 2.67968 + 4.64134i 0.0901273 + 0.156105i
\(885\) 10.7105 1.53510i 0.360029 0.0516017i
\(886\) −25.7087 14.8429i −0.863700 0.498657i
\(887\) 54.2705i 1.82222i −0.412159 0.911112i \(-0.635225\pi\)
0.412159 0.911112i \(-0.364775\pi\)
\(888\) −5.41180 2.77713i −0.181608 0.0931942i
\(889\) −13.9225 −0.466945
\(890\) 29.3750 23.0797i 0.984652 0.773634i
\(891\) −1.50095 2.59973i −0.0502839 0.0870942i
\(892\) −2.68760 + 1.55168i −0.0899874 + 0.0519542i
\(893\) 34.1200 + 59.0976i 1.14178 + 1.97762i
\(894\) 9.05684i 0.302906i
\(895\) −6.74248 47.0428i −0.225376 1.57247i
\(896\) 1.35265i 0.0451890i
\(897\) −13.1774 7.60795i −0.439979 0.254022i
\(898\) 20.4572i 0.682664i
\(899\) 18.0303 0.601343
\(900\) −4.79871 + 1.40441i −0.159957 + 0.0468138i
\(901\) 12.8855 7.43945i 0.429278 0.247844i
\(902\) −13.8188 −0.460117
\(903\) −2.15812 + 3.73797i −0.0718177 + 0.124392i
\(904\) 7.24481 12.5484i 0.240959 0.417353i
\(905\) −25.4840 32.4351i −0.847118 1.07818i
\(906\) 9.93758 5.73747i 0.330154 0.190615i
\(907\) −7.93667 13.7467i −0.263533 0.456452i 0.703645 0.710551i \(-0.251554\pi\)
−0.967178 + 0.254099i \(0.918221\pi\)
\(908\) 7.97179 13.8076i 0.264553 0.458220i
\(909\) −8.32311 + 14.4160i −0.276060 + 0.478150i
\(910\) 5.33786 4.19392i 0.176948 0.139027i
\(911\) 54.2419i 1.79712i 0.438855 + 0.898558i \(0.355384\pi\)
−0.438855 + 0.898558i \(0.644616\pi\)
\(912\) −2.64166 4.57549i −0.0874741 0.151510i
\(913\) 10.6976 + 6.17626i 0.354039 + 0.204405i
\(914\) 32.3871 1.07127
\(915\) 8.83958 22.0519i 0.292227 0.729013i
\(916\) −6.73382 + 11.6633i −0.222492 + 0.385367i
\(917\) −5.14154 −0.169788
\(918\) −2.06800 + 1.19396i −0.0682542 + 0.0394066i
\(919\) 11.6006i 0.382667i 0.981525 + 0.191333i \(0.0612812\pi\)
−0.981525 + 0.191333i \(0.938719\pi\)
\(920\) 15.0063 2.15080i 0.494744 0.0709099i
\(921\) −8.10430 14.0371i −0.267046 0.462537i
\(922\) 16.5318 9.54466i 0.544447 0.314337i
\(923\) 13.6555 23.6521i 0.449477 0.778517i
\(924\) −4.06054 −0.133582
\(925\) 23.0050 + 19.8940i 0.756399 + 0.654110i
\(926\) −18.7885 −0.617430
\(927\) 3.35670 5.81397i 0.110248 0.190956i
\(928\) 3.53275 2.03964i 0.115968 0.0669543i
\(929\) 22.6937 + 39.3066i 0.744555 + 1.28961i 0.950402 + 0.311023i \(0.100672\pi\)
−0.205847 + 0.978584i \(0.565995\pi\)
\(930\) 9.78339 1.40222i 0.320810 0.0459806i
\(931\) 27.3165i 0.895262i
\(932\) −23.9357 + 13.8193i −0.784041 + 0.452666i
\(933\) −2.98352 −0.0976760
\(934\) 1.48895 2.57894i 0.0487200 0.0843854i
\(935\) −5.96391 + 14.8780i −0.195041 + 0.486564i
\(936\) −2.24436 −0.0733592
\(937\) −3.30744 1.90955i −0.108049 0.0623823i 0.445002 0.895530i \(-0.353203\pi\)
−0.553051 + 0.833148i \(0.686536\pi\)
\(938\) 2.38892 + 4.13773i 0.0780009 + 0.135102i
\(939\) 4.51495i 0.147340i
\(940\) −22.7101 + 17.8432i −0.740723 + 0.581981i
\(941\) 13.6763 23.6880i 0.445833 0.772206i −0.552277 0.833661i \(-0.686241\pi\)
0.998110 + 0.0614552i \(0.0195741\pi\)
\(942\) 2.91020 5.04062i 0.0948195 0.164232i
\(943\) −15.6045 27.0278i −0.508152 0.880145i
\(944\) −4.19055 + 2.41941i −0.136391 + 0.0787452i
\(945\) 1.86865 + 2.37834i 0.0607871 + 0.0773676i
\(946\) 4.78945 8.29558i 0.155719 0.269712i
\(947\) −17.8892 + 30.9851i −0.581322 + 1.00688i 0.414001 + 0.910277i \(0.364131\pi\)
−0.995323 + 0.0966032i \(0.969202\pi\)
\(948\) 0.588515 0.0191141
\(949\) −13.7304 + 7.92722i −0.445706 + 0.257328i
\(950\) 7.41997 + 25.3531i 0.240736 + 0.822564i
\(951\) −6.83240 −0.221556
\(952\) 3.23003i 0.104686i
\(953\) −2.51306 1.45091i −0.0814059 0.0469997i 0.458744 0.888568i \(-0.348299\pi\)
−0.540150 + 0.841568i \(0.681633\pi\)
\(954\) 6.23090i 0.201733i
\(955\) 2.77966 + 19.3939i 0.0899476 + 0.627572i
\(956\) 13.1344i 0.424796i
\(957\) −6.12280 10.6050i −0.197922 0.342811i
\(958\) −28.9748 + 16.7286i −0.936134 + 0.540477i
\(959\) 6.87809 + 11.9132i 0.222105 + 0.384697i
\(960\) 1.75828 1.38147i 0.0567482 0.0445867i
\(961\) 11.4638 0.369801
\(962\) 7.40233 + 11.4708i 0.238661 + 0.369835i
\(963\) 0.196615i 0.00633584i
\(964\) −24.8544 14.3497i −0.800507 0.462173i
\(965\) −29.2755 + 4.19595i −0.942410 + 0.135072i
\(966\) −4.58524 7.94187i −0.147528 0.255525i
\(967\) −26.9414 46.6639i −0.866377 1.50061i −0.865673 0.500610i \(-0.833109\pi\)
−0.000703986 1.00000i \(-0.500224\pi\)
\(968\) −1.98855 −0.0639143
\(969\) 6.30808 + 10.9259i 0.202645 + 0.350991i
\(970\) 7.98527 19.9207i 0.256392 0.639615i
\(971\) −12.2032 + 21.1365i −0.391618 + 0.678302i −0.992663 0.120913i \(-0.961418\pi\)
0.601045 + 0.799215i \(0.294751\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 1.25431i 0.0402112i
\(974\) 1.99131 3.44906i 0.0638058 0.110515i
\(975\) 10.9031 + 2.65529i 0.349180 + 0.0850375i
\(976\) 10.6247i 0.340089i
\(977\) 20.8789 36.1634i 0.667976 1.15697i −0.310493 0.950576i \(-0.600494\pi\)
0.978469 0.206393i \(-0.0661725\pi\)
\(978\) −3.81563 2.20296i −0.122010 0.0704427i
\(979\) 43.4328 + 25.0759i 1.38812 + 0.801430i
\(980\) −11.4443 + 1.64026i −0.365573 + 0.0523963i
\(981\) −11.6161 + 6.70656i −0.370874 + 0.214124i
\(982\) 19.6340 34.0071i 0.626546 1.08521i
\(983\) −0.756705 0.436884i −0.0241352 0.0139344i 0.487884 0.872909i \(-0.337769\pi\)
−0.512019 + 0.858974i \(0.671102\pi\)
\(984\) −3.98662 2.30168i −0.127089 0.0733748i
\(985\) −17.5595 7.03879i −0.559492 0.224274i
\(986\) −8.43593 + 4.87049i −0.268655 + 0.155108i
\(987\) 15.1304 + 8.73552i 0.481605 + 0.278055i
\(988\) 11.8577i 0.377243i
\(989\) 21.6333 0.687900
\(990\) −4.14704 5.27819i −0.131802 0.167752i
\(991\) 23.5804i 0.749055i 0.927216 + 0.374527i \(0.122195\pi\)
−0.927216 + 0.374527i \(0.877805\pi\)
\(992\) −3.82781 + 2.20999i −0.121533 + 0.0701672i
\(993\) 10.2745 0.326053
\(994\) 14.2549 8.23005i 0.452137 0.261041i
\(995\) 2.45121 + 17.1023i 0.0777085 + 0.542179i
\(996\) 2.05745 + 3.56360i 0.0651927 + 0.112917i
\(997\) 30.1315 52.1894i 0.954276 1.65285i 0.218258 0.975891i \(-0.429963\pi\)
0.736017 0.676963i \(-0.236704\pi\)
\(998\) 12.9448i 0.409760i
\(999\) −5.11096 + 3.29819i −0.161704 + 0.104350i
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 1110.2.ba.a.619.6 yes 36
5.4 even 2 1110.2.ba.b.619.13 yes 36
37.11 even 6 1110.2.ba.b.529.13 yes 36
185.159 even 6 inner 1110.2.ba.a.529.6 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.ba.a.529.6 36 185.159 even 6 inner
1110.2.ba.a.619.6 yes 36 1.1 even 1 trivial
1110.2.ba.b.529.13 yes 36 37.11 even 6
1110.2.ba.b.619.13 yes 36 5.4 even 2