Properties

Label 567.2.ba.a.143.13
Level $567$
Weight $2$
Character 567.143
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
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] = [567,2,Mod(143,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([7, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.ba (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 143.13
Character \(\chi\) \(=\) 567.143
Dual form 567.2.ba.a.341.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.159953 - 0.190625i) q^{2} +(0.336544 + 1.90863i) q^{4} +(-1.62936 + 1.36719i) q^{5} +(2.64099 - 0.158668i) q^{7} +(0.848674 + 0.489982i) q^{8} +O(q^{10})\) \(q+(0.159953 - 0.190625i) q^{2} +(0.336544 + 1.90863i) q^{4} +(-1.62936 + 1.36719i) q^{5} +(2.64099 - 0.158668i) q^{7} +(0.848674 + 0.489982i) q^{8} +0.529283i q^{10} +(0.919336 - 1.09562i) q^{11} +(-1.30709 + 3.59121i) q^{13} +(0.392189 - 0.528818i) q^{14} +(-3.41324 + 1.24232i) q^{16} -0.218194 q^{17} -2.96748i q^{19} +(-3.15782 - 2.64972i) q^{20} +(-0.0618021 - 0.350497i) q^{22} +(-2.64486 + 7.26669i) q^{23} +(-0.0826545 + 0.468757i) q^{25} +(0.475500 + 0.823590i) q^{26} +(1.19165 + 4.98728i) q^{28} +(1.78349 + 4.90009i) q^{29} +(3.81477 - 0.672647i) q^{31} +(-0.979478 + 2.69109i) q^{32} +(-0.0349009 + 0.0415932i) q^{34} +(-4.08618 + 3.86926i) q^{35} +(-3.00625 + 5.20699i) q^{37} +(-0.565677 - 0.474659i) q^{38} +(-2.05269 + 0.361945i) q^{40} +(-10.0627 - 3.66253i) q^{41} +(1.29579 - 7.34878i) q^{43} +(2.40054 + 1.38595i) q^{44} +(0.962159 + 1.66651i) q^{46} +(1.01967 - 5.78285i) q^{47} +(6.94965 - 0.838080i) q^{49} +(0.0761360 + 0.0907353i) q^{50} +(-7.29419 - 1.28616i) q^{52} +(12.1036 + 6.98800i) q^{53} +3.04206i q^{55} +(2.31908 + 1.15938i) q^{56} +(1.21936 + 0.443809i) q^{58} +(1.48515 + 0.540550i) q^{59} +(4.18950 + 0.738722i) q^{61} +(0.481963 - 0.834784i) q^{62} +(-3.27598 - 5.67416i) q^{64} +(-2.78015 - 7.63839i) q^{65} +(11.4276 - 9.58891i) q^{67} +(-0.0734317 - 0.416452i) q^{68} +(0.0839802 + 1.39783i) q^{70} +(4.29452 - 2.47944i) q^{71} +(-2.13740 + 1.23403i) q^{73} +(0.511721 + 1.40594i) q^{74} +(5.66384 - 0.998688i) q^{76} +(2.25412 - 3.03939i) q^{77} +(-2.98202 - 2.50221i) q^{79} +(3.86290 - 6.69073i) q^{80} +(-2.30773 + 1.33237i) q^{82} +(-0.141502 + 0.0515026i) q^{83} +(0.355515 - 0.298313i) q^{85} +(-1.19360 - 1.42247i) q^{86} +(1.31705 - 0.479367i) q^{88} -6.80542 q^{89} +(-2.88221 + 9.69173i) q^{91} +(-14.7595 - 2.60251i) q^{92} +(-0.939256 - 1.11936i) q^{94} +(4.05712 + 4.83509i) q^{95} +(-12.2644 - 2.16255i) q^{97} +(0.951861 - 1.45883i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{18}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.159953 0.190625i 0.113104 0.134792i −0.706522 0.707691i \(-0.749737\pi\)
0.819626 + 0.572899i \(0.194181\pi\)
\(3\) 0 0
\(4\) 0.336544 + 1.90863i 0.168272 + 0.954317i
\(5\) −1.62936 + 1.36719i −0.728670 + 0.611427i −0.929769 0.368144i \(-0.879993\pi\)
0.201099 + 0.979571i \(0.435549\pi\)
\(6\) 0 0
\(7\) 2.64099 0.158668i 0.998200 0.0599708i
\(8\) 0.848674 + 0.489982i 0.300052 + 0.173235i
\(9\) 0 0
\(10\) 0.529283i 0.167374i
\(11\) 0.919336 1.09562i 0.277190 0.330342i −0.609431 0.792839i \(-0.708602\pi\)
0.886621 + 0.462497i \(0.153046\pi\)
\(12\) 0 0
\(13\) −1.30709 + 3.59121i −0.362522 + 0.996021i 0.615613 + 0.788049i \(0.288909\pi\)
−0.978135 + 0.207972i \(0.933314\pi\)
\(14\) 0.392189 0.528818i 0.104817 0.141333i
\(15\) 0 0
\(16\) −3.41324 + 1.24232i −0.853310 + 0.310580i
\(17\) −0.218194 −0.0529198 −0.0264599 0.999650i \(-0.508423\pi\)
−0.0264599 + 0.999650i \(0.508423\pi\)
\(18\) 0 0
\(19\) 2.96748i 0.680788i −0.940283 0.340394i \(-0.889440\pi\)
0.940283 0.340394i \(-0.110560\pi\)
\(20\) −3.15782 2.64972i −0.706109 0.592496i
\(21\) 0 0
\(22\) −0.0618021 0.350497i −0.0131762 0.0747262i
\(23\) −2.64486 + 7.26669i −0.551491 + 1.51521i 0.280184 + 0.959946i \(0.409604\pi\)
−0.831675 + 0.555262i \(0.812618\pi\)
\(24\) 0 0
\(25\) −0.0826545 + 0.468757i −0.0165309 + 0.0937514i
\(26\) 0.475500 + 0.823590i 0.0932532 + 0.161519i
\(27\) 0 0
\(28\) 1.19165 + 4.98728i 0.225200 + 0.942508i
\(29\) 1.78349 + 4.90009i 0.331185 + 0.909924i 0.987804 + 0.155702i \(0.0497638\pi\)
−0.656619 + 0.754223i \(0.728014\pi\)
\(30\) 0 0
\(31\) 3.81477 0.672647i 0.685153 0.120811i 0.179774 0.983708i \(-0.442463\pi\)
0.505380 + 0.862897i \(0.331352\pi\)
\(32\) −0.979478 + 2.69109i −0.173149 + 0.475723i
\(33\) 0 0
\(34\) −0.0349009 + 0.0415932i −0.00598545 + 0.00713318i
\(35\) −4.08618 + 3.86926i −0.690691 + 0.654025i
\(36\) 0 0
\(37\) −3.00625 + 5.20699i −0.494225 + 0.856023i −0.999978 0.00665534i \(-0.997882\pi\)
0.505753 + 0.862679i \(0.331215\pi\)
\(38\) −0.565677 0.474659i −0.0917649 0.0769999i
\(39\) 0 0
\(40\) −2.05269 + 0.361945i −0.324559 + 0.0572285i
\(41\) −10.0627 3.66253i −1.57153 0.571990i −0.598190 0.801354i \(-0.704113\pi\)
−0.973341 + 0.229364i \(0.926335\pi\)
\(42\) 0 0
\(43\) 1.29579 7.34878i 0.197606 1.12068i −0.711053 0.703139i \(-0.751781\pi\)
0.908659 0.417540i \(-0.137108\pi\)
\(44\) 2.40054 + 1.38595i 0.361894 + 0.208940i
\(45\) 0 0
\(46\) 0.962159 + 1.66651i 0.141863 + 0.245713i
\(47\) 1.01967 5.78285i 0.148735 0.843515i −0.815558 0.578675i \(-0.803570\pi\)
0.964292 0.264840i \(-0.0853191\pi\)
\(48\) 0 0
\(49\) 6.94965 0.838080i 0.992807 0.119726i
\(50\) 0.0761360 + 0.0907353i 0.0107673 + 0.0128319i
\(51\) 0 0
\(52\) −7.29419 1.28616i −1.01152 0.178359i
\(53\) 12.1036 + 6.98800i 1.66255 + 0.959875i 0.971490 + 0.237080i \(0.0761904\pi\)
0.691063 + 0.722795i \(0.257143\pi\)
\(54\) 0 0
\(55\) 3.04206i 0.410192i
\(56\) 2.31908 + 1.15938i 0.309901 + 0.154929i
\(57\) 0 0
\(58\) 1.21936 + 0.443809i 0.160109 + 0.0582750i
\(59\) 1.48515 + 0.540550i 0.193350 + 0.0703736i 0.436880 0.899520i \(-0.356083\pi\)
−0.243530 + 0.969893i \(0.578306\pi\)
\(60\) 0 0
\(61\) 4.18950 + 0.738722i 0.536410 + 0.0945836i 0.435290 0.900291i \(-0.356646\pi\)
0.101121 + 0.994874i \(0.467757\pi\)
\(62\) 0.481963 0.834784i 0.0612093 0.106018i
\(63\) 0 0
\(64\) −3.27598 5.67416i −0.409497 0.709270i
\(65\) −2.78015 7.63839i −0.344835 0.947426i
\(66\) 0 0
\(67\) 11.4276 9.58891i 1.39611 1.17147i 0.433308 0.901246i \(-0.357346\pi\)
0.962797 0.270226i \(-0.0870983\pi\)
\(68\) −0.0734317 0.416452i −0.00890490 0.0505022i
\(69\) 0 0
\(70\) 0.0839802 + 1.39783i 0.0100376 + 0.167073i
\(71\) 4.29452 2.47944i 0.509666 0.294256i −0.223031 0.974811i \(-0.571595\pi\)
0.732696 + 0.680556i \(0.238262\pi\)
\(72\) 0 0
\(73\) −2.13740 + 1.23403i −0.250164 + 0.144432i −0.619839 0.784729i \(-0.712802\pi\)
0.369676 + 0.929161i \(0.379469\pi\)
\(74\) 0.511721 + 1.40594i 0.0594864 + 0.163438i
\(75\) 0 0
\(76\) 5.66384 0.998688i 0.649687 0.114557i
\(77\) 2.25412 3.03939i 0.256880 0.346371i
\(78\) 0 0
\(79\) −2.98202 2.50221i −0.335503 0.281521i 0.459435 0.888212i \(-0.348052\pi\)
−0.794938 + 0.606691i \(0.792497\pi\)
\(80\) 3.86290 6.69073i 0.431885 0.748047i
\(81\) 0 0
\(82\) −2.30773 + 1.33237i −0.254847 + 0.147136i
\(83\) −0.141502 + 0.0515026i −0.0155319 + 0.00565315i −0.349774 0.936834i \(-0.613742\pi\)
0.334243 + 0.942487i \(0.391520\pi\)
\(84\) 0 0
\(85\) 0.355515 0.298313i 0.0385610 0.0323566i
\(86\) −1.19360 1.42247i −0.128709 0.153389i
\(87\) 0 0
\(88\) 1.31705 0.479367i 0.140398 0.0511007i
\(89\) −6.80542 −0.721373 −0.360686 0.932687i \(-0.617458\pi\)
−0.360686 + 0.932687i \(0.617458\pi\)
\(90\) 0 0
\(91\) −2.88221 + 9.69173i −0.302137 + 1.01597i
\(92\) −14.7595 2.60251i −1.53879 0.271330i
\(93\) 0 0
\(94\) −0.939256 1.11936i −0.0968769 0.115453i
\(95\) 4.05712 + 4.83509i 0.416252 + 0.496069i
\(96\) 0 0
\(97\) −12.2644 2.16255i −1.24526 0.219573i −0.488092 0.872792i \(-0.662307\pi\)
−0.757169 + 0.653219i \(0.773418\pi\)
\(98\) 0.951861 1.45883i 0.0961525 0.147364i
\(99\) 0 0
\(100\) −0.922502 −0.0922502
\(101\) 7.87176 2.86509i 0.783269 0.285087i 0.0807341 0.996736i \(-0.474274\pi\)
0.702535 + 0.711649i \(0.252051\pi\)
\(102\) 0 0
\(103\) 0.137771 + 0.164189i 0.0135750 + 0.0161781i 0.772789 0.634663i \(-0.218861\pi\)
−0.759214 + 0.650841i \(0.774417\pi\)
\(104\) −2.86892 + 2.40731i −0.281321 + 0.236056i
\(105\) 0 0
\(106\) 3.26809 1.18949i 0.317425 0.115533i
\(107\) 15.3166 8.84302i 1.48071 0.854887i 0.480946 0.876750i \(-0.340293\pi\)
0.999761 + 0.0218632i \(0.00695982\pi\)
\(108\) 0 0
\(109\) −0.476343 + 0.825050i −0.0456254 + 0.0790255i −0.887936 0.459967i \(-0.847861\pi\)
0.842311 + 0.538992i \(0.181195\pi\)
\(110\) 0.579894 + 0.486589i 0.0552907 + 0.0463944i
\(111\) 0 0
\(112\) −8.81722 + 3.82252i −0.833149 + 0.361194i
\(113\) 13.8921 2.44955i 1.30686 0.230434i 0.523510 0.852020i \(-0.324622\pi\)
0.783346 + 0.621586i \(0.213511\pi\)
\(114\) 0 0
\(115\) −5.62554 15.4560i −0.524584 1.44128i
\(116\) −8.75226 + 5.05312i −0.812627 + 0.469170i
\(117\) 0 0
\(118\) 0.340597 0.196644i 0.0313545 0.0181025i
\(119\) −0.576248 + 0.0346203i −0.0528245 + 0.00317364i
\(120\) 0 0
\(121\) 1.55492 + 8.81840i 0.141356 + 0.801673i
\(122\) 0.810944 0.680463i 0.0734194 0.0616062i
\(123\) 0 0
\(124\) 2.56767 + 7.05463i 0.230584 + 0.633524i
\(125\) −5.82364 10.0868i −0.520882 0.902194i
\(126\) 0 0
\(127\) −2.41898 + 4.18980i −0.214650 + 0.371785i −0.953164 0.302453i \(-0.902194\pi\)
0.738514 + 0.674238i \(0.235528\pi\)
\(128\) −7.24623 1.27771i −0.640482 0.112934i
\(129\) 0 0
\(130\) −1.90076 0.691822i −0.166708 0.0606768i
\(131\) −3.37090 1.22691i −0.294517 0.107195i 0.190536 0.981680i \(-0.438977\pi\)
−0.485053 + 0.874485i \(0.661200\pi\)
\(132\) 0 0
\(133\) −0.470844 7.83709i −0.0408274 0.679562i
\(134\) 3.71217i 0.320683i
\(135\) 0 0
\(136\) −0.185175 0.106911i −0.0158787 0.00916755i
\(137\) 3.52128 + 0.620896i 0.300843 + 0.0530467i 0.322032 0.946729i \(-0.395634\pi\)
−0.0211891 + 0.999775i \(0.506745\pi\)
\(138\) 0 0
\(139\) 3.85722 + 4.59686i 0.327165 + 0.389900i 0.904405 0.426674i \(-0.140315\pi\)
−0.577240 + 0.816574i \(0.695870\pi\)
\(140\) −8.76018 6.49684i −0.740371 0.549084i
\(141\) 0 0
\(142\) 0.214279 1.21524i 0.0179819 0.101981i
\(143\) 2.73295 + 4.73360i 0.228540 + 0.395844i
\(144\) 0 0
\(145\) −9.60530 5.54562i −0.797677 0.460539i
\(146\) −0.106648 + 0.604829i −0.00882623 + 0.0500560i
\(147\) 0 0
\(148\) −10.9500 3.98546i −0.900081 0.327603i
\(149\) 5.49324 0.968607i 0.450024 0.0793514i 0.0559572 0.998433i \(-0.482179\pi\)
0.394067 + 0.919082i \(0.371068\pi\)
\(150\) 0 0
\(151\) 1.21887 + 1.02275i 0.0991903 + 0.0832306i 0.691034 0.722822i \(-0.257155\pi\)
−0.591844 + 0.806053i \(0.701600\pi\)
\(152\) 1.45401 2.51843i 0.117936 0.204271i
\(153\) 0 0
\(154\) −0.218831 0.915852i −0.0176339 0.0738015i
\(155\) −5.29598 + 6.31151i −0.425384 + 0.506952i
\(156\) 0 0
\(157\) 8.46292 23.2517i 0.675414 1.85569i 0.188947 0.981987i \(-0.439493\pi\)
0.486467 0.873699i \(-0.338285\pi\)
\(158\) −0.953968 + 0.168210i −0.0758936 + 0.0133821i
\(159\) 0 0
\(160\) −2.08332 5.72388i −0.164701 0.452513i
\(161\) −5.83205 + 19.6109i −0.459630 + 1.54555i
\(162\) 0 0
\(163\) −6.48707 11.2359i −0.508107 0.880066i −0.999956 0.00938604i \(-0.997012\pi\)
0.491849 0.870680i \(-0.336321\pi\)
\(164\) 3.60388 20.4386i 0.281416 1.59599i
\(165\) 0 0
\(166\) −0.0128161 + 0.0352119i −0.000994721 + 0.00273297i
\(167\) 1.43124 + 8.11696i 0.110753 + 0.628110i 0.988766 + 0.149473i \(0.0477577\pi\)
−0.878013 + 0.478637i \(0.841131\pi\)
\(168\) 0 0
\(169\) −1.22969 1.03183i −0.0945915 0.0793717i
\(170\) 0.115486i 0.00885740i
\(171\) 0 0
\(172\) 14.4622 1.10273
\(173\) 22.1228 8.05204i 1.68197 0.612186i 0.688389 0.725342i \(-0.258318\pi\)
0.993577 + 0.113156i \(0.0360960\pi\)
\(174\) 0 0
\(175\) −0.143913 + 1.25110i −0.0108788 + 0.0945740i
\(176\) −1.77680 + 4.88173i −0.133932 + 0.367974i
\(177\) 0 0
\(178\) −1.08855 + 1.29728i −0.0815903 + 0.0972355i
\(179\) 8.34763i 0.623931i −0.950093 0.311965i \(-0.899013\pi\)
0.950093 0.311965i \(-0.100987\pi\)
\(180\) 0 0
\(181\) 3.60525 + 2.08149i 0.267976 + 0.154716i 0.627967 0.778240i \(-0.283887\pi\)
−0.359992 + 0.932956i \(0.617220\pi\)
\(182\) 1.38647 + 2.09965i 0.102772 + 0.155636i
\(183\) 0 0
\(184\) −5.80517 + 4.87111i −0.427963 + 0.359103i
\(185\) −2.22069 12.5942i −0.163268 0.925941i
\(186\) 0 0
\(187\) −0.200593 + 0.239058i −0.0146688 + 0.0174816i
\(188\) 11.3805 0.830009
\(189\) 0 0
\(190\) 1.57064 0.113946
\(191\) −0.621752 + 0.740976i −0.0449884 + 0.0536151i −0.788069 0.615586i \(-0.788919\pi\)
0.743081 + 0.669201i \(0.233364\pi\)
\(192\) 0 0
\(193\) −1.25034 7.09105i −0.0900017 0.510425i −0.996165 0.0874966i \(-0.972113\pi\)
0.906163 0.422928i \(-0.138998\pi\)
\(194\) −2.37397 + 1.99200i −0.170441 + 0.143017i
\(195\) 0 0
\(196\) 3.93845 + 12.9823i 0.281318 + 0.927306i
\(197\) −6.90426 3.98617i −0.491908 0.284003i 0.233458 0.972367i \(-0.424996\pi\)
−0.725366 + 0.688364i \(0.758329\pi\)
\(198\) 0 0
\(199\) 4.27232i 0.302857i −0.988468 0.151428i \(-0.951613\pi\)
0.988468 0.151428i \(-0.0483873\pi\)
\(200\) −0.299829 + 0.357323i −0.0212011 + 0.0252665i
\(201\) 0 0
\(202\) 0.712958 1.95884i 0.0501635 0.137823i
\(203\) 5.48766 + 12.6581i 0.385158 + 0.888425i
\(204\) 0 0
\(205\) 21.4031 7.79009i 1.49486 0.544084i
\(206\) 0.0533356 0.00371607
\(207\) 0 0
\(208\) 13.8815i 0.962507i
\(209\) −3.25124 2.72811i −0.224893 0.188708i
\(210\) 0 0
\(211\) 3.70699 + 21.0234i 0.255199 + 1.44731i 0.795560 + 0.605875i \(0.207177\pi\)
−0.540361 + 0.841433i \(0.681712\pi\)
\(212\) −9.26415 + 25.4530i −0.636264 + 1.74812i
\(213\) 0 0
\(214\) 0.764235 4.33419i 0.0522420 0.296279i
\(215\) 7.93589 + 13.7454i 0.541223 + 0.937426i
\(216\) 0 0
\(217\) 9.96805 2.38174i 0.676675 0.161683i
\(218\) 0.0810826 + 0.222773i 0.00549161 + 0.0150881i
\(219\) 0 0
\(220\) −5.80618 + 1.02379i −0.391453 + 0.0690237i
\(221\) 0.285199 0.783579i 0.0191846 0.0527092i
\(222\) 0 0
\(223\) −7.92110 + 9.44000i −0.530436 + 0.632149i −0.963015 0.269447i \(-0.913159\pi\)
0.432579 + 0.901596i \(0.357604\pi\)
\(224\) −2.15980 + 7.26256i −0.144308 + 0.485250i
\(225\) 0 0
\(226\) 1.75514 3.03999i 0.116750 0.202217i
\(227\) 14.3018 + 12.0006i 0.949245 + 0.796511i 0.979170 0.203041i \(-0.0650825\pi\)
−0.0299253 + 0.999552i \(0.509527\pi\)
\(228\) 0 0
\(229\) −19.1244 + 3.37215i −1.26378 + 0.222838i −0.765078 0.643937i \(-0.777300\pi\)
−0.498699 + 0.866775i \(0.666189\pi\)
\(230\) −3.84613 1.39988i −0.253607 0.0923052i
\(231\) 0 0
\(232\) −0.887358 + 5.03246i −0.0582579 + 0.330397i
\(233\) −11.4205 6.59360i −0.748179 0.431961i 0.0768565 0.997042i \(-0.475512\pi\)
−0.825036 + 0.565081i \(0.808845\pi\)
\(234\) 0 0
\(235\) 6.24485 + 10.8164i 0.407369 + 0.705584i
\(236\) −0.531894 + 3.01652i −0.0346234 + 0.196359i
\(237\) 0 0
\(238\) −0.0855733 + 0.115385i −0.00554689 + 0.00747929i
\(239\) −10.0464 11.9729i −0.649849 0.774460i 0.336043 0.941847i \(-0.390911\pi\)
−0.985891 + 0.167387i \(0.946467\pi\)
\(240\) 0 0
\(241\) 6.39561 + 1.12772i 0.411978 + 0.0726428i 0.375796 0.926702i \(-0.377369\pi\)
0.0361818 + 0.999345i \(0.488480\pi\)
\(242\) 1.92972 + 1.11413i 0.124047 + 0.0716187i
\(243\) 0 0
\(244\) 8.24483i 0.527821i
\(245\) −10.1776 + 10.8670i −0.650225 + 0.694269i
\(246\) 0 0
\(247\) 10.6568 + 3.87877i 0.678079 + 0.246801i
\(248\) 3.56708 + 1.29831i 0.226510 + 0.0824429i
\(249\) 0 0
\(250\) −2.85432 0.503293i −0.180523 0.0318310i
\(251\) −11.9045 + 20.6191i −0.751403 + 1.30147i 0.195740 + 0.980656i \(0.437289\pi\)
−0.947143 + 0.320812i \(0.896044\pi\)
\(252\) 0 0
\(253\) 5.53002 + 9.57828i 0.347670 + 0.602182i
\(254\) 0.411757 + 1.13129i 0.0258359 + 0.0709836i
\(255\) 0 0
\(256\) 8.63555 7.24609i 0.539722 0.452881i
\(257\) −5.27488 29.9153i −0.329038 1.86607i −0.479631 0.877470i \(-0.659230\pi\)
0.150594 0.988596i \(-0.451881\pi\)
\(258\) 0 0
\(259\) −7.11331 + 14.2286i −0.441999 + 0.884122i
\(260\) 13.6433 7.87694i 0.846119 0.488507i
\(261\) 0 0
\(262\) −0.773067 + 0.446330i −0.0477602 + 0.0275744i
\(263\) 5.29060 + 14.5358i 0.326232 + 0.896316i 0.989056 + 0.147540i \(0.0471356\pi\)
−0.662824 + 0.748775i \(0.730642\pi\)
\(264\) 0 0
\(265\) −29.2749 + 5.16196i −1.79835 + 0.317097i
\(266\) −1.56926 1.16382i −0.0962175 0.0713581i
\(267\) 0 0
\(268\) 22.1476 + 18.5840i 1.35288 + 1.13520i
\(269\) 0.343714 0.595329i 0.0209566 0.0362979i −0.855357 0.518039i \(-0.826662\pi\)
0.876314 + 0.481741i \(0.159995\pi\)
\(270\) 0 0
\(271\) 6.24649 3.60641i 0.379447 0.219074i −0.298131 0.954525i \(-0.596363\pi\)
0.677578 + 0.735451i \(0.263030\pi\)
\(272\) 0.744748 0.271066i 0.0451570 0.0164358i
\(273\) 0 0
\(274\) 0.681599 0.571929i 0.0411769 0.0345515i
\(275\) 0.437593 + 0.521503i 0.0263879 + 0.0314478i
\(276\) 0 0
\(277\) −11.6791 + 4.25083i −0.701727 + 0.255408i −0.668148 0.744028i \(-0.732913\pi\)
−0.0335789 + 0.999436i \(0.510691\pi\)
\(278\) 1.49325 0.0895593
\(279\) 0 0
\(280\) −5.36371 + 1.28159i −0.320543 + 0.0765896i
\(281\) −2.05517 0.362382i −0.122601 0.0216179i 0.112011 0.993707i \(-0.464271\pi\)
−0.234612 + 0.972089i \(0.575382\pi\)
\(282\) 0 0
\(283\) 13.0108 + 15.5056i 0.773410 + 0.921714i 0.998616 0.0525970i \(-0.0167499\pi\)
−0.225206 + 0.974311i \(0.572305\pi\)
\(284\) 6.17764 + 7.36222i 0.366575 + 0.436867i
\(285\) 0 0
\(286\) 1.33949 + 0.236188i 0.0792055 + 0.0139661i
\(287\) −27.1566 8.07606i −1.60301 0.476715i
\(288\) 0 0
\(289\) −16.9524 −0.997199
\(290\) −2.59354 + 0.943970i −0.152298 + 0.0554318i
\(291\) 0 0
\(292\) −3.07464 3.66421i −0.179929 0.214432i
\(293\) 21.6520 18.1682i 1.26493 1.06140i 0.269786 0.962920i \(-0.413047\pi\)
0.995139 0.0984780i \(-0.0313974\pi\)
\(294\) 0 0
\(295\) −3.15887 + 1.14973i −0.183916 + 0.0669401i
\(296\) −5.10266 + 2.94602i −0.296586 + 0.171234i
\(297\) 0 0
\(298\) 0.694022 1.20208i 0.0402036 0.0696347i
\(299\) −22.6391 18.9965i −1.30925 1.09859i
\(300\) 0 0
\(301\) 2.25615 19.6136i 0.130042 1.13051i
\(302\) 0.389925 0.0687543i 0.0224377 0.00395637i
\(303\) 0 0
\(304\) 3.68656 + 10.1287i 0.211439 + 0.580923i
\(305\) −7.83616 + 4.52421i −0.448697 + 0.259055i
\(306\) 0 0
\(307\) 1.71807 0.991927i 0.0980553 0.0566122i −0.450170 0.892943i \(-0.648637\pi\)
0.548226 + 0.836330i \(0.315303\pi\)
\(308\) 6.55969 + 3.27939i 0.373773 + 0.186861i
\(309\) 0 0
\(310\) 0.356021 + 2.01909i 0.0202206 + 0.114677i
\(311\) −10.4064 + 8.73204i −0.590095 + 0.495149i −0.888245 0.459371i \(-0.848075\pi\)
0.298150 + 0.954519i \(0.403631\pi\)
\(312\) 0 0
\(313\) 5.00633 + 13.7548i 0.282974 + 0.777466i 0.997004 + 0.0773503i \(0.0246460\pi\)
−0.714030 + 0.700116i \(0.753132\pi\)
\(314\) −3.07868 5.33243i −0.173740 0.300927i
\(315\) 0 0
\(316\) 3.77222 6.53368i 0.212204 0.367548i
\(317\) −18.6192 3.28307i −1.04576 0.184395i −0.375728 0.926730i \(-0.622607\pi\)
−0.670029 + 0.742335i \(0.733719\pi\)
\(318\) 0 0
\(319\) 7.00827 + 2.55080i 0.392388 + 0.142817i
\(320\) 13.0954 + 4.76633i 0.732055 + 0.266446i
\(321\) 0 0
\(322\) 2.80547 + 4.24857i 0.156343 + 0.236763i
\(323\) 0.647487i 0.0360271i
\(324\) 0 0
\(325\) −1.57537 0.909538i −0.0873856 0.0504521i
\(326\) −3.17948 0.560628i −0.176095 0.0310503i
\(327\) 0 0
\(328\) −6.74539 8.03884i −0.372452 0.443871i
\(329\) 1.77539 15.4342i 0.0978805 0.850917i
\(330\) 0 0
\(331\) 2.05674 11.6643i 0.113049 0.641130i −0.874649 0.484756i \(-0.838908\pi\)
0.987698 0.156374i \(-0.0499806\pi\)
\(332\) −0.145921 0.252743i −0.00800847 0.0138711i
\(333\) 0 0
\(334\) 1.77623 + 1.02551i 0.0971909 + 0.0561132i
\(335\) −5.50977 + 31.2475i −0.301031 + 1.70723i
\(336\) 0 0
\(337\) 19.6990 + 7.16984i 1.07307 + 0.390566i 0.817324 0.576178i \(-0.195456\pi\)
0.255747 + 0.966744i \(0.417679\pi\)
\(338\) −0.393386 + 0.0693646i −0.0213974 + 0.00377294i
\(339\) 0 0
\(340\) 0.689016 + 0.578153i 0.0373671 + 0.0313548i
\(341\) 2.77009 4.79794i 0.150009 0.259823i
\(342\) 0 0
\(343\) 18.2210 3.31605i 0.983840 0.179050i
\(344\) 4.70047 5.60181i 0.253433 0.302029i
\(345\) 0 0
\(346\) 2.00370 5.50512i 0.107719 0.295957i
\(347\) 30.1613 5.31825i 1.61914 0.285499i 0.710697 0.703499i \(-0.248380\pi\)
0.908447 + 0.418000i \(0.137269\pi\)
\(348\) 0 0
\(349\) 6.58819 + 18.1009i 0.352658 + 0.968919i 0.981513 + 0.191397i \(0.0613017\pi\)
−0.628855 + 0.777523i \(0.716476\pi\)
\(350\) 0.215471 + 0.227551i 0.0115174 + 0.0121631i
\(351\) 0 0
\(352\) 2.04795 + 3.54715i 0.109156 + 0.189064i
\(353\) −3.20406 + 18.1711i −0.170535 + 0.967152i 0.772637 + 0.634848i \(0.218937\pi\)
−0.943172 + 0.332304i \(0.892174\pi\)
\(354\) 0 0
\(355\) −3.60743 + 9.91132i −0.191462 + 0.526038i
\(356\) −2.29032 12.9890i −0.121387 0.688418i
\(357\) 0 0
\(358\) −1.59127 1.33523i −0.0841011 0.0705692i
\(359\) 0.779690i 0.0411504i 0.999788 + 0.0205752i \(0.00654976\pi\)
−0.999788 + 0.0205752i \(0.993450\pi\)
\(360\) 0 0
\(361\) 10.1940 0.536528
\(362\) 0.973456 0.354309i 0.0511637 0.0186221i
\(363\) 0 0
\(364\) −19.4679 2.23939i −1.02040 0.117376i
\(365\) 1.79543 4.93291i 0.0939771 0.258200i
\(366\) 0 0
\(367\) 15.9909 19.0572i 0.834717 0.994777i −0.165247 0.986252i \(-0.552842\pi\)
0.999964 0.00852445i \(-0.00271345\pi\)
\(368\) 28.0887i 1.46423i
\(369\) 0 0
\(370\) −2.75597 1.59116i −0.143276 0.0827205i
\(371\) 33.0742 + 16.5348i 1.71712 + 0.858443i
\(372\) 0 0
\(373\) −18.4215 + 15.4574i −0.953827 + 0.800356i −0.979938 0.199303i \(-0.936132\pi\)
0.0261111 + 0.999659i \(0.491688\pi\)
\(374\) 0.0134848 + 0.0764763i 0.000697284 + 0.00395449i
\(375\) 0 0
\(376\) 3.69886 4.40813i 0.190754 0.227332i
\(377\) −19.9284 −1.02637
\(378\) 0 0
\(379\) −30.5872 −1.57116 −0.785579 0.618761i \(-0.787635\pi\)
−0.785579 + 0.618761i \(0.787635\pi\)
\(380\) −7.86301 + 9.37077i −0.403364 + 0.480710i
\(381\) 0 0
\(382\) 0.0417971 + 0.237043i 0.00213853 + 0.0121282i
\(383\) −27.5758 + 23.1388i −1.40906 + 1.18234i −0.452149 + 0.891942i \(0.649342\pi\)
−0.956907 + 0.290396i \(0.906213\pi\)
\(384\) 0 0
\(385\) 0.482678 + 8.03406i 0.0245995 + 0.409454i
\(386\) −1.55173 0.895891i −0.0789809 0.0455997i
\(387\) 0 0
\(388\) 24.1360i 1.22532i
\(389\) −15.6823 + 18.6895i −0.795125 + 0.947593i −0.999510 0.0312973i \(-0.990036\pi\)
0.204385 + 0.978891i \(0.434481\pi\)
\(390\) 0 0
\(391\) 0.577092 1.58555i 0.0291848 0.0801845i
\(392\) 6.30863 + 2.69395i 0.318634 + 0.136065i
\(393\) 0 0
\(394\) −1.86422 + 0.678522i −0.0939183 + 0.0341835i
\(395\) 8.27977 0.416600
\(396\) 0 0
\(397\) 6.76334i 0.339443i −0.985492 0.169721i \(-0.945713\pi\)
0.985492 0.169721i \(-0.0542867\pi\)
\(398\) −0.814412 0.683373i −0.0408228 0.0342544i
\(399\) 0 0
\(400\) −0.300226 1.70266i −0.0150113 0.0851332i
\(401\) −0.329299 + 0.904741i −0.0164444 + 0.0451806i −0.947643 0.319331i \(-0.896542\pi\)
0.931199 + 0.364512i \(0.118764\pi\)
\(402\) 0 0
\(403\) −2.57064 + 14.5788i −0.128053 + 0.726224i
\(404\) 8.11759 + 14.0601i 0.403865 + 0.699515i
\(405\) 0 0
\(406\) 3.29072 + 0.978623i 0.163316 + 0.0485682i
\(407\) 2.94113 + 8.08068i 0.145786 + 0.400545i
\(408\) 0 0
\(409\) −28.6167 + 5.04589i −1.41500 + 0.249503i −0.828294 0.560294i \(-0.810688\pi\)
−0.586709 + 0.809798i \(0.699577\pi\)
\(410\) 1.93851 5.32602i 0.0957363 0.263033i
\(411\) 0 0
\(412\) −0.267011 + 0.318212i −0.0131547 + 0.0156772i
\(413\) 4.00803 + 1.19194i 0.197222 + 0.0586516i
\(414\) 0 0
\(415\) 0.160144 0.277377i 0.00786114 0.0136159i
\(416\) −8.38400 7.03501i −0.411060 0.344920i
\(417\) 0 0
\(418\) −1.04009 + 0.183397i −0.0508727 + 0.00897022i
\(419\) 22.8869 + 8.33016i 1.11810 + 0.406955i 0.833958 0.551828i \(-0.186069\pi\)
0.284141 + 0.958782i \(0.408292\pi\)
\(420\) 0 0
\(421\) 2.03579 11.5455i 0.0992181 0.562694i −0.894155 0.447758i \(-0.852223\pi\)
0.993373 0.114936i \(-0.0366663\pi\)
\(422\) 4.60053 + 2.65611i 0.223950 + 0.129298i
\(423\) 0 0
\(424\) 6.84799 + 11.8611i 0.332568 + 0.576024i
\(425\) 0.0180347 0.102280i 0.000874812 0.00496130i
\(426\) 0 0
\(427\) 11.1816 + 1.28622i 0.541117 + 0.0622444i
\(428\) 22.0328 + 26.2576i 1.06499 + 1.26921i
\(429\) 0 0
\(430\) 3.88958 + 0.685839i 0.187572 + 0.0330741i
\(431\) −22.9443 13.2469i −1.10519 0.638082i −0.167610 0.985853i \(-0.553605\pi\)
−0.937579 + 0.347772i \(0.886938\pi\)
\(432\) 0 0
\(433\) 23.5474i 1.13161i −0.824538 0.565807i \(-0.808565\pi\)
0.824538 0.565807i \(-0.191435\pi\)
\(434\) 1.14040 2.28113i 0.0547412 0.109498i
\(435\) 0 0
\(436\) −1.73503 0.631499i −0.0830928 0.0302433i
\(437\) 21.5638 + 7.84857i 1.03154 + 0.375448i
\(438\) 0 0
\(439\) 4.11182 + 0.725025i 0.196247 + 0.0346036i 0.270907 0.962605i \(-0.412676\pi\)
−0.0746608 + 0.997209i \(0.523787\pi\)
\(440\) −1.49056 + 2.58172i −0.0710595 + 0.123079i
\(441\) 0 0
\(442\) −0.103751 0.179702i −0.00493494 0.00854757i
\(443\) −0.830398 2.28150i −0.0394534 0.108397i 0.918402 0.395649i \(-0.129480\pi\)
−0.957855 + 0.287252i \(0.907258\pi\)
\(444\) 0 0
\(445\) 11.0884 9.30431i 0.525643 0.441066i
\(446\) 0.532494 + 3.01992i 0.0252143 + 0.142997i
\(447\) 0 0
\(448\) −9.55213 14.4656i −0.451296 0.683435i
\(449\) −10.0967 + 5.82936i −0.476495 + 0.275104i −0.718955 0.695057i \(-0.755379\pi\)
0.242460 + 0.970161i \(0.422046\pi\)
\(450\) 0 0
\(451\) −13.2637 + 7.65783i −0.624565 + 0.360593i
\(452\) 9.35057 + 25.6905i 0.439814 + 1.20838i
\(453\) 0 0
\(454\) 4.57525 0.806740i 0.214727 0.0378622i
\(455\) −8.55431 19.7318i −0.401032 0.925041i
\(456\) 0 0
\(457\) −16.2729 13.6546i −0.761213 0.638734i 0.177229 0.984170i \(-0.443287\pi\)
−0.938442 + 0.345436i \(0.887731\pi\)
\(458\) −2.41620 + 4.18498i −0.112902 + 0.195551i
\(459\) 0 0
\(460\) 27.6067 15.9387i 1.28717 0.743147i
\(461\) 25.2929 9.20586i 1.17801 0.428760i 0.322510 0.946566i \(-0.395473\pi\)
0.855498 + 0.517806i \(0.173251\pi\)
\(462\) 0 0
\(463\) 18.3826 15.4248i 0.854311 0.716852i −0.106424 0.994321i \(-0.533940\pi\)
0.960735 + 0.277469i \(0.0894956\pi\)
\(464\) −12.1749 14.5095i −0.565208 0.673588i
\(465\) 0 0
\(466\) −3.08365 + 1.12236i −0.142847 + 0.0519922i
\(467\) −6.18976 −0.286428 −0.143214 0.989692i \(-0.545744\pi\)
−0.143214 + 0.989692i \(0.545744\pi\)
\(468\) 0 0
\(469\) 28.6588 27.1374i 1.32334 1.25309i
\(470\) 3.06076 + 0.539695i 0.141183 + 0.0248943i
\(471\) 0 0
\(472\) 0.995547 + 1.18645i 0.0458238 + 0.0546106i
\(473\) −6.86022 8.17569i −0.315433 0.375918i
\(474\) 0 0
\(475\) 1.39103 + 0.245276i 0.0638248 + 0.0112540i
\(476\) −0.260010 1.08819i −0.0119175 0.0498773i
\(477\) 0 0
\(478\) −3.88929 −0.177892
\(479\) −15.1479 + 5.51338i −0.692124 + 0.251913i −0.664044 0.747693i \(-0.731161\pi\)
−0.0280796 + 0.999606i \(0.508939\pi\)
\(480\) 0 0
\(481\) −14.7699 17.6021i −0.673450 0.802586i
\(482\) 1.23797 1.03878i 0.0563881 0.0473152i
\(483\) 0 0
\(484\) −16.3078 + 5.93555i −0.741263 + 0.269798i
\(485\) 22.9397 13.2442i 1.04164 0.601390i
\(486\) 0 0
\(487\) −13.0260 + 22.5617i −0.590265 + 1.02237i 0.403931 + 0.914789i \(0.367643\pi\)
−0.994196 + 0.107580i \(0.965690\pi\)
\(488\) 3.19356 + 2.67971i 0.144566 + 0.121305i
\(489\) 0 0
\(490\) 0.443582 + 3.67833i 0.0200390 + 0.166170i
\(491\) −10.3899 + 1.83203i −0.468892 + 0.0826783i −0.403102 0.915155i \(-0.632068\pi\)
−0.0657902 + 0.997833i \(0.520957\pi\)
\(492\) 0 0
\(493\) −0.389146 1.06917i −0.0175263 0.0481530i
\(494\) 2.44399 1.41104i 0.109960 0.0634857i
\(495\) 0 0
\(496\) −12.1851 + 7.03507i −0.547127 + 0.315884i
\(497\) 10.9484 7.22958i 0.491101 0.324291i
\(498\) 0 0
\(499\) −1.40174 7.94964i −0.0627503 0.355875i −0.999974 0.00714726i \(-0.997725\pi\)
0.937224 0.348728i \(-0.113386\pi\)
\(500\) 17.2922 14.5098i 0.773329 0.648900i
\(501\) 0 0
\(502\) 2.02637 + 5.56739i 0.0904411 + 0.248485i
\(503\) −15.6629 27.1289i −0.698373 1.20962i −0.969030 0.246941i \(-0.920575\pi\)
0.270658 0.962676i \(-0.412759\pi\)
\(504\) 0 0
\(505\) −8.90877 + 15.4304i −0.396435 + 0.686646i
\(506\) 2.71041 + 0.477918i 0.120492 + 0.0212460i
\(507\) 0 0
\(508\) −8.81089 3.20690i −0.390920 0.142283i
\(509\) −38.0919 13.8643i −1.68840 0.614526i −0.693974 0.720000i \(-0.744142\pi\)
−0.994422 + 0.105474i \(0.966364\pi\)
\(510\) 0 0
\(511\) −5.44905 + 3.59819i −0.241052 + 0.159175i
\(512\) 17.5212i 0.774336i
\(513\) 0 0
\(514\) −6.54634 3.77953i −0.288747 0.166708i
\(515\) −0.448957 0.0791632i −0.0197834 0.00348835i
\(516\) 0 0
\(517\) −5.39839 6.43355i −0.237421 0.282947i
\(518\) 1.57453 + 3.63189i 0.0691808 + 0.159576i
\(519\) 0 0
\(520\) 1.38324 7.84473i 0.0606590 0.344014i
\(521\) −11.7007 20.2662i −0.512616 0.887878i −0.999893 0.0146299i \(-0.995343\pi\)
0.487277 0.873248i \(-0.337990\pi\)
\(522\) 0 0
\(523\) 12.1378 + 7.00778i 0.530751 + 0.306429i 0.741322 0.671149i \(-0.234199\pi\)
−0.210571 + 0.977578i \(0.567532\pi\)
\(524\) 1.20726 6.84672i 0.0527395 0.299100i
\(525\) 0 0
\(526\) 3.61714 + 1.31653i 0.157715 + 0.0574035i
\(527\) −0.832360 + 0.146768i −0.0362582 + 0.00639329i
\(528\) 0 0
\(529\) −28.1904 23.6546i −1.22567 1.02846i
\(530\) −3.69863 + 6.40621i −0.160658 + 0.278268i
\(531\) 0 0
\(532\) 14.7997 3.53619i 0.641647 0.153313i
\(533\) 26.3058 31.3500i 1.13943 1.35792i
\(534\) 0 0
\(535\) −12.8660 + 35.3491i −0.556246 + 1.52827i
\(536\) 14.3967 2.53853i 0.621843 0.109648i
\(537\) 0 0
\(538\) −0.0585066 0.160745i −0.00252240 0.00693023i
\(539\) 5.47084 8.38466i 0.235646 0.361153i
\(540\) 0 0
\(541\) −11.9247 20.6542i −0.512683 0.887993i −0.999892 0.0147075i \(-0.995318\pi\)
0.487209 0.873285i \(-0.338015\pi\)
\(542\) 0.311675 1.76759i 0.0133876 0.0759247i
\(543\) 0 0
\(544\) 0.213716 0.587180i 0.00916300 0.0251751i
\(545\) −0.351870 1.99555i −0.0150724 0.0854801i
\(546\) 0 0
\(547\) −0.534982 0.448903i −0.0228742 0.0191937i 0.631279 0.775556i \(-0.282530\pi\)
−0.654153 + 0.756362i \(0.726975\pi\)
\(548\) 6.92978i 0.296026i
\(549\) 0 0
\(550\) 0.169406 0.00722350
\(551\) 14.5409 5.29247i 0.619465 0.225467i
\(552\) 0 0
\(553\) −8.27250 6.13516i −0.351782 0.260894i
\(554\) −1.05779 + 2.90626i −0.0449413 + 0.123475i
\(555\) 0 0
\(556\) −7.47559 + 8.90906i −0.317036 + 0.377828i
\(557\) 11.1225i 0.471276i 0.971841 + 0.235638i \(0.0757180\pi\)
−0.971841 + 0.235638i \(0.924282\pi\)
\(558\) 0 0
\(559\) 24.6973 + 14.2590i 1.04458 + 0.603090i
\(560\) 9.14027 18.2831i 0.386247 0.772601i
\(561\) 0 0
\(562\) −0.397811 + 0.333803i −0.0167806 + 0.0140806i
\(563\) −1.95102 11.0648i −0.0822256 0.466325i −0.997921 0.0644512i \(-0.979470\pi\)
0.915695 0.401873i \(-0.131641\pi\)
\(564\) 0 0
\(565\) −19.2861 + 22.9843i −0.811373 + 0.966957i
\(566\) 5.03688 0.211716
\(567\) 0 0
\(568\) 4.85953 0.203901
\(569\) 23.2352 27.6906i 0.974069 1.16085i −0.0128961 0.999917i \(-0.504105\pi\)
0.986965 0.160934i \(-0.0514505\pi\)
\(570\) 0 0
\(571\) 3.46989 + 19.6787i 0.145210 + 0.823528i 0.967198 + 0.254023i \(0.0817540\pi\)
−0.821988 + 0.569505i \(0.807135\pi\)
\(572\) −8.11495 + 6.80925i −0.339303 + 0.284709i
\(573\) 0 0
\(574\) −5.88330 + 3.88494i −0.245564 + 0.162154i
\(575\) −3.18770 1.84042i −0.132936 0.0767508i
\(576\) 0 0
\(577\) 30.5734i 1.27279i 0.771365 + 0.636393i \(0.219574\pi\)
−0.771365 + 0.636393i \(0.780426\pi\)
\(578\) −2.71159 + 3.23155i −0.112787 + 0.134415i
\(579\) 0 0
\(580\) 7.35196 20.1993i 0.305273 0.838732i
\(581\) −0.365534 + 0.158470i −0.0151649 + 0.00657443i
\(582\) 0 0
\(583\) 18.7834 6.83661i 0.777930 0.283144i
\(584\) −2.41861 −0.100083
\(585\) 0 0
\(586\) 7.03349i 0.290551i
\(587\) −23.6386 19.8352i −0.975671 0.818685i 0.00775999 0.999970i \(-0.497530\pi\)
−0.983431 + 0.181285i \(0.941974\pi\)
\(588\) 0 0
\(589\) −1.99607 11.3203i −0.0822467 0.466444i
\(590\) −0.286104 + 0.786064i −0.0117787 + 0.0323617i
\(591\) 0 0
\(592\) 3.79234 21.5074i 0.155864 0.883950i
\(593\) 15.8362 + 27.4292i 0.650316 + 1.12638i 0.983046 + 0.183358i \(0.0586968\pi\)
−0.332730 + 0.943022i \(0.607970\pi\)
\(594\) 0 0
\(595\) 0.891579 0.844250i 0.0365512 0.0346109i
\(596\) 3.69743 + 10.1586i 0.151453 + 0.416113i
\(597\) 0 0
\(598\) −7.24240 + 1.27703i −0.296164 + 0.0522217i
\(599\) 5.08335 13.9664i 0.207700 0.570651i −0.791478 0.611198i \(-0.790688\pi\)
0.999178 + 0.0405469i \(0.0129100\pi\)
\(600\) 0 0
\(601\) 11.0892 13.2156i 0.452338 0.539075i −0.490890 0.871221i \(-0.663328\pi\)
0.943228 + 0.332146i \(0.107773\pi\)
\(602\) −3.37798 3.56735i −0.137676 0.145394i
\(603\) 0 0
\(604\) −1.54186 + 2.67058i −0.0627374 + 0.108664i
\(605\) −14.5900 12.2424i −0.593166 0.497726i
\(606\) 0 0
\(607\) −40.0370 + 7.05960i −1.62505 + 0.286540i −0.910645 0.413191i \(-0.864414\pi\)
−0.714406 + 0.699731i \(0.753303\pi\)
\(608\) 7.98578 + 2.90659i 0.323866 + 0.117878i
\(609\) 0 0
\(610\) −0.390993 + 2.21743i −0.0158308 + 0.0897812i
\(611\) 19.4346 + 11.2206i 0.786240 + 0.453936i
\(612\) 0 0
\(613\) −14.0624 24.3568i −0.567975 0.983761i −0.996766 0.0803574i \(-0.974394\pi\)
0.428792 0.903403i \(-0.358939\pi\)
\(614\) 0.0857247 0.486169i 0.00345957 0.0196202i
\(615\) 0 0
\(616\) 3.40226 1.47498i 0.137081 0.0594286i
\(617\) −2.77984 3.31289i −0.111912 0.133372i 0.707180 0.707033i \(-0.249967\pi\)
−0.819092 + 0.573661i \(0.805523\pi\)
\(618\) 0 0
\(619\) 15.2309 + 2.68562i 0.612182 + 0.107944i 0.471139 0.882059i \(-0.343843\pi\)
0.141044 + 0.990003i \(0.454954\pi\)
\(620\) −13.8287 7.98399i −0.555373 0.320645i
\(621\) 0 0
\(622\) 3.38045i 0.135544i
\(623\) −17.9730 + 1.07980i −0.720074 + 0.0432613i
\(624\) 0 0
\(625\) 21.0430 + 7.65903i 0.841720 + 0.306361i
\(626\) 3.42279 + 1.24579i 0.136802 + 0.0497919i
\(627\) 0 0
\(628\) 47.2271 + 8.32741i 1.88457 + 0.332300i
\(629\) 0.655946 1.13613i 0.0261543 0.0453006i
\(630\) 0 0
\(631\) −17.0661 29.5593i −0.679389 1.17674i −0.975165 0.221479i \(-0.928911\pi\)
0.295776 0.955257i \(-0.404422\pi\)
\(632\) −1.30472 3.58470i −0.0518991 0.142592i
\(633\) 0 0
\(634\) −3.60404 + 3.02415i −0.143135 + 0.120104i
\(635\) −1.78688 10.1339i −0.0709101 0.402151i
\(636\) 0 0
\(637\) −6.07411 + 26.0531i −0.240665 + 1.03226i
\(638\) 1.60724 0.927943i 0.0636314 0.0367376i
\(639\) 0 0
\(640\) 13.5536 7.82515i 0.535751 0.309316i
\(641\) 1.13498 + 3.11832i 0.0448289 + 0.123166i 0.960087 0.279702i \(-0.0902356\pi\)
−0.915258 + 0.402868i \(0.868013\pi\)
\(642\) 0 0
\(643\) 24.9953 4.40734i 0.985717 0.173808i 0.342521 0.939510i \(-0.388719\pi\)
0.643196 + 0.765702i \(0.277608\pi\)
\(644\) −39.3927 4.53133i −1.55229 0.178559i
\(645\) 0 0
\(646\) 0.123427 + 0.103568i 0.00485618 + 0.00407482i
\(647\) 0.170073 0.294574i 0.00668625 0.0115809i −0.862663 0.505779i \(-0.831205\pi\)
0.869349 + 0.494198i \(0.164538\pi\)
\(648\) 0 0
\(649\) 1.95759 1.13021i 0.0768420 0.0443648i
\(650\) −0.425366 + 0.154821i −0.0166842 + 0.00607256i
\(651\) 0 0
\(652\) 19.2621 16.1628i 0.754362 0.632985i
\(653\) 18.0690 + 21.5337i 0.707093 + 0.842680i 0.993309 0.115485i \(-0.0368421\pi\)
−0.286217 + 0.958165i \(0.592398\pi\)
\(654\) 0 0
\(655\) 7.16981 2.60960i 0.280148 0.101965i
\(656\) 38.8965 1.51865
\(657\) 0 0
\(658\) −2.65817 2.80719i −0.103626 0.109436i
\(659\) −29.0041 5.11420i −1.12984 0.199221i −0.422682 0.906278i \(-0.638911\pi\)
−0.707157 + 0.707057i \(0.750022\pi\)
\(660\) 0 0
\(661\) −0.521355 0.621326i −0.0202783 0.0241668i 0.755810 0.654791i \(-0.227243\pi\)
−0.776088 + 0.630624i \(0.782799\pi\)
\(662\) −1.89453 2.25782i −0.0736332 0.0877526i
\(663\) 0 0
\(664\) −0.145325 0.0256247i −0.00563969 0.000994430i
\(665\) 11.4820 + 12.1257i 0.445252 + 0.470214i
\(666\) 0 0
\(667\) −40.3245 −1.56137
\(668\) −15.0106 + 5.46342i −0.580779 + 0.211386i
\(669\) 0 0
\(670\) 5.07525 + 6.04844i 0.196074 + 0.233672i
\(671\) 4.66091 3.91097i 0.179933 0.150981i
\(672\) 0 0
\(673\) 12.2309 4.45168i 0.471466 0.171600i −0.0953502 0.995444i \(-0.530397\pi\)
0.566816 + 0.823844i \(0.308175\pi\)
\(674\) 4.51767 2.60828i 0.174014 0.100467i
\(675\) 0 0
\(676\) 1.55554 2.69428i 0.0598286 0.103626i
\(677\) 10.0934 + 8.46940i 0.387922 + 0.325506i 0.815803 0.578330i \(-0.196295\pi\)
−0.427881 + 0.903835i \(0.640740\pi\)
\(678\) 0 0
\(679\) −32.7333 3.76529i −1.25619 0.144499i
\(680\) 0.447885 0.0789741i 0.0171756 0.00302852i
\(681\) 0 0
\(682\) −0.471522 1.29550i −0.0180555 0.0496071i
\(683\) 5.41536 3.12656i 0.207213 0.119635i −0.392802 0.919623i \(-0.628494\pi\)
0.600016 + 0.799988i \(0.295161\pi\)
\(684\) 0 0
\(685\) −6.58629 + 3.80260i −0.251649 + 0.145290i
\(686\) 2.28239 4.00379i 0.0871419 0.152865i
\(687\) 0 0
\(688\) 4.70669 + 26.6929i 0.179441 + 1.01766i
\(689\) −40.9158 + 34.3324i −1.55877 + 1.30796i
\(690\) 0 0
\(691\) 1.78729 + 4.91054i 0.0679918 + 0.186806i 0.969035 0.246923i \(-0.0794196\pi\)
−0.901043 + 0.433729i \(0.857197\pi\)
\(692\) 22.8137 + 39.5145i 0.867246 + 1.50211i
\(693\) 0 0
\(694\) 3.81061 6.60018i 0.144649 0.250539i
\(695\) −12.5696 2.21635i −0.476791 0.0840711i
\(696\) 0 0
\(697\) 2.19562 + 0.799141i 0.0831651 + 0.0302696i
\(698\) 4.50429 + 1.63943i 0.170490 + 0.0620533i
\(699\) 0 0
\(700\) −2.43632 + 0.146371i −0.0920842 + 0.00553232i
\(701\) 21.7945i 0.823166i 0.911372 + 0.411583i \(0.135024\pi\)
−0.911372 + 0.411583i \(0.864976\pi\)
\(702\) 0 0
\(703\) 15.4517 + 8.92101i 0.582770 + 0.336462i
\(704\) −9.22845 1.62723i −0.347810 0.0613284i
\(705\) 0 0
\(706\) 2.95137 + 3.51731i 0.111076 + 0.132376i
\(707\) 20.3346 8.81566i 0.764763 0.331547i
\(708\) 0 0
\(709\) 3.00042 17.0162i 0.112683 0.639059i −0.875188 0.483783i \(-0.839262\pi\)
0.987871 0.155276i \(-0.0496265\pi\)
\(710\) 1.31233 + 2.27302i 0.0492507 + 0.0853048i
\(711\) 0 0
\(712\) −5.77558 3.33453i −0.216449 0.124967i
\(713\) −5.20161 + 29.4998i −0.194802 + 1.10478i
\(714\) 0 0
\(715\) −10.9247 3.97626i −0.408560 0.148704i
\(716\) 15.9326 2.80934i 0.595428 0.104990i
\(717\) 0 0
\(718\) 0.148628 + 0.124714i 0.00554676 + 0.00465429i
\(719\) −12.1162 + 20.9858i −0.451857 + 0.782639i −0.998501 0.0547260i \(-0.982571\pi\)
0.546645 + 0.837365i \(0.315905\pi\)
\(720\) 0 0
\(721\) 0.389904 + 0.411763i 0.0145208 + 0.0153348i
\(722\) 1.63057 1.94324i 0.0606836 0.0723199i
\(723\) 0 0
\(724\) −2.75948 + 7.58160i −0.102555 + 0.281768i
\(725\) −2.44437 + 0.431008i −0.0907815 + 0.0160072i
\(726\) 0 0
\(727\) −4.28953 11.7854i −0.159090 0.437095i 0.834380 0.551189i \(-0.185826\pi\)
−0.993470 + 0.114094i \(0.963604\pi\)
\(728\) −7.19483 + 6.81289i −0.266658 + 0.252502i
\(729\) 0 0
\(730\) −0.653150 1.13129i −0.0241742 0.0418709i
\(731\) −0.282733 + 1.60346i −0.0104573 + 0.0593060i
\(732\) 0 0
\(733\) −6.22901 + 17.1141i −0.230074 + 0.632123i −0.999982 0.00603225i \(-0.998080\pi\)
0.769908 + 0.638155i \(0.220302\pi\)
\(734\) −1.07498 6.09652i −0.0396783 0.225027i
\(735\) 0 0
\(736\) −16.9648 14.2351i −0.625329 0.524713i
\(737\) 21.3358i 0.785913i
\(738\) 0 0
\(739\) −48.3570 −1.77884 −0.889420 0.457092i \(-0.848891\pi\)
−0.889420 + 0.457092i \(0.848891\pi\)
\(740\) 23.2903 8.47696i 0.856167 0.311619i
\(741\) 0 0
\(742\) 8.44227 3.65997i 0.309925 0.134362i
\(743\) −11.3965 + 31.3117i −0.418098 + 1.14872i 0.534682 + 0.845053i \(0.320431\pi\)
−0.952780 + 0.303662i \(0.901791\pi\)
\(744\) 0 0
\(745\) −7.62617 + 9.08852i −0.279401 + 0.332978i
\(746\) 5.98406i 0.219092i
\(747\) 0 0
\(748\) −0.523782 0.302406i −0.0191514 0.0110570i
\(749\) 39.0478 25.7846i 1.42677 0.942147i
\(750\) 0 0
\(751\) 25.3577 21.2776i 0.925314 0.776430i −0.0496563 0.998766i \(-0.515813\pi\)
0.974970 + 0.222336i \(0.0713682\pi\)
\(752\) 3.70375 + 21.0050i 0.135062 + 0.765974i
\(753\) 0 0
\(754\) −3.18762 + 3.79886i −0.116086 + 0.138346i
\(755\) −3.38427 −0.123166
\(756\) 0 0
\(757\) 37.7148 1.37077 0.685384 0.728182i \(-0.259635\pi\)
0.685384 + 0.728182i \(0.259635\pi\)
\(758\) −4.89253 + 5.83069i −0.177705 + 0.211780i
\(759\) 0 0
\(760\) 1.07407 + 6.09133i 0.0389605 + 0.220956i
\(761\) −4.49229 + 3.76948i −0.162845 + 0.136644i −0.720569 0.693383i \(-0.756119\pi\)
0.557724 + 0.830027i \(0.311675\pi\)
\(762\) 0 0
\(763\) −1.12711 + 2.25453i −0.0408040 + 0.0816194i
\(764\) −1.62350 0.937327i −0.0587361 0.0339113i
\(765\) 0 0
\(766\) 8.95777i 0.323657i
\(767\) −3.88245 + 4.62692i −0.140187 + 0.167069i
\(768\) 0 0
\(769\) 6.33820 17.4141i 0.228561 0.627967i −0.771404 0.636346i \(-0.780445\pi\)
0.999965 + 0.00837935i \(0.00266726\pi\)
\(770\) 1.60870 + 1.19307i 0.0579735 + 0.0429951i
\(771\) 0 0
\(772\) 13.1134 4.77289i 0.471962 0.171780i
\(773\) 6.32723 0.227575 0.113787 0.993505i \(-0.463702\pi\)
0.113787 + 0.993505i \(0.463702\pi\)
\(774\) 0 0
\(775\) 1.84380i 0.0662312i
\(776\) −9.34888 7.84464i −0.335605 0.281606i
\(777\) 0 0
\(778\) 1.05424 + 5.97889i 0.0377963 + 0.214354i
\(779\) −10.8685 + 29.8609i −0.389404 + 1.06988i
\(780\) 0 0
\(781\) 1.23157 6.98460i 0.0440692 0.249929i
\(782\) −0.209937 0.363622i −0.00750733 0.0130031i
\(783\) 0 0
\(784\) −22.6797 + 11.4942i −0.809988 + 0.410509i
\(785\) 18.0004 + 49.4557i 0.642462 + 1.76515i
\(786\) 0 0
\(787\) 46.5890 8.21490i 1.66072 0.292830i 0.736998 0.675895i \(-0.236243\pi\)
0.923721 + 0.383065i \(0.125132\pi\)
\(788\) 5.28456 14.5192i 0.188255 0.517226i
\(789\) 0 0
\(790\) 1.32438 1.57833i 0.0471192 0.0561545i
\(791\) 36.3002 8.67345i 1.29068 0.308392i
\(792\) 0 0
\(793\) −8.12896 + 14.0798i −0.288668 + 0.499987i
\(794\) −1.28926 1.08182i −0.0457542 0.0383924i
\(795\) 0 0
\(796\) 8.15429 1.43782i 0.289021 0.0509622i
\(797\) −14.8436 5.40264i −0.525788 0.191371i 0.0654686 0.997855i \(-0.479146\pi\)
−0.591257 + 0.806483i \(0.701368\pi\)
\(798\) 0 0
\(799\) −0.222486 + 1.26178i −0.00787100 + 0.0446386i
\(800\) −1.18051 0.681568i −0.0417374 0.0240971i
\(801\) 0 0
\(802\) 0.119794 + 0.207489i 0.00423007 + 0.00732669i
\(803\) −0.612960 + 3.47627i −0.0216309 + 0.122675i
\(804\) 0 0
\(805\) −17.3094 39.9266i −0.610075 1.40723i
\(806\) 2.36791 + 2.82197i 0.0834061 + 0.0993995i
\(807\) 0 0
\(808\) 8.08440 + 1.42550i 0.284408 + 0.0501488i
\(809\) −43.3139 25.0073i −1.52284 0.879210i −0.999635 0.0269998i \(-0.991405\pi\)
−0.523200 0.852210i \(-0.675262\pi\)
\(810\) 0 0
\(811\) 43.1499i 1.51520i 0.652720 + 0.757600i \(0.273628\pi\)
−0.652720 + 0.757600i \(0.726372\pi\)
\(812\) −22.3129 + 14.7339i −0.783028 + 0.517060i
\(813\) 0 0
\(814\) 2.01083 + 0.731880i 0.0704794 + 0.0256524i
\(815\) 25.9314 + 9.43826i 0.908338 + 0.330608i
\(816\) 0 0
\(817\) −21.8074 3.84523i −0.762944 0.134528i
\(818\) −3.61546 + 6.26216i −0.126412 + 0.218951i
\(819\) 0 0
\(820\) 22.0715 + 38.2290i 0.770770 + 1.33501i
\(821\) −10.3629 28.4718i −0.361667 0.993671i −0.978440 0.206531i \(-0.933783\pi\)
0.616773 0.787141i \(-0.288440\pi\)
\(822\) 0 0
\(823\) 16.6545 13.9748i 0.580539 0.487130i −0.304585 0.952485i \(-0.598518\pi\)
0.885124 + 0.465355i \(0.154073\pi\)
\(824\) 0.0364730 + 0.206849i 0.00127060 + 0.00720592i
\(825\) 0 0
\(826\) 0.868312 0.573376i 0.0302124 0.0199503i
\(827\) −6.80237 + 3.92735i −0.236541 + 0.136567i −0.613586 0.789628i \(-0.710274\pi\)
0.377045 + 0.926195i \(0.376940\pi\)
\(828\) 0 0
\(829\) −3.51679 + 2.03042i −0.122143 + 0.0705193i −0.559827 0.828610i \(-0.689132\pi\)
0.437684 + 0.899129i \(0.355799\pi\)
\(830\) −0.0272595 0.0748947i −0.000946190 0.00259963i
\(831\) 0 0
\(832\) 24.6591 4.34806i 0.854900 0.150742i
\(833\) −1.51637 + 0.182864i −0.0525391 + 0.00633586i
\(834\) 0 0
\(835\) −13.4294 11.2686i −0.464745 0.389967i
\(836\) 4.11279 7.12355i 0.142244 0.246373i
\(837\) 0 0
\(838\) 5.24878 3.03038i 0.181316 0.104683i
\(839\) 16.0171 5.82975i 0.552971 0.201265i −0.0503948 0.998729i \(-0.516048\pi\)
0.603366 + 0.797464i \(0.293826\pi\)
\(840\) 0 0
\(841\) 1.38521 1.16233i 0.0477660 0.0400804i
\(842\) −1.87523 2.23482i −0.0646248 0.0770169i
\(843\) 0 0
\(844\) −38.8783 + 14.1506i −1.33825 + 0.487082i
\(845\) 3.41431 0.117456
\(846\) 0 0
\(847\) 5.50573 + 23.0426i 0.189179 + 0.791752i
\(848\) −49.9937 8.81524i −1.71679 0.302717i
\(849\) 0 0
\(850\) −0.0166124 0.0197979i −0.000569801 0.000679062i
\(851\) −29.8864 35.6172i −1.02449 1.22094i
\(852\) 0 0
\(853\) 23.9922 + 4.23048i 0.821478 + 0.144849i 0.568563 0.822640i \(-0.307500\pi\)
0.252915 + 0.967488i \(0.418611\pi\)
\(854\) 2.03373 1.92577i 0.0695927 0.0658983i
\(855\) 0 0
\(856\) 17.3317 0.592385
\(857\) −50.7585 + 18.4746i −1.73388 + 0.631079i −0.998895 0.0470070i \(-0.985032\pi\)
−0.734982 + 0.678087i \(0.762809\pi\)
\(858\) 0 0
\(859\) 17.6336 + 21.0149i 0.601652 + 0.717021i 0.977800 0.209539i \(-0.0671962\pi\)
−0.376149 + 0.926559i \(0.622752\pi\)
\(860\) −23.5641 + 19.7726i −0.803529 + 0.674241i
\(861\) 0 0
\(862\) −6.19522 + 2.25488i −0.211010 + 0.0768014i
\(863\) 13.4069 7.74047i 0.456376 0.263489i −0.254143 0.967167i \(-0.581793\pi\)
0.710519 + 0.703678i \(0.248460\pi\)
\(864\) 0 0
\(865\) −25.0372 + 43.3658i −0.851292 + 1.47448i
\(866\) −4.48872 3.76648i −0.152533 0.127990i
\(867\) 0 0
\(868\) 7.90054 + 18.2238i 0.268162 + 0.618556i
\(869\) −5.48295 + 0.966792i −0.185996 + 0.0327962i
\(870\) 0 0
\(871\) 19.4988 + 53.5725i 0.660691 + 1.81523i
\(872\) −0.808520 + 0.466799i −0.0273799 + 0.0158078i
\(873\) 0 0
\(874\) 4.94534 2.85519i 0.167278 0.0965783i
\(875\) −16.9806 25.7152i −0.574050 0.869333i
\(876\) 0 0
\(877\) 6.31884 + 35.8359i 0.213372 + 1.21009i 0.883709 + 0.468036i \(0.155038\pi\)
−0.670337 + 0.742057i \(0.733851\pi\)
\(878\) 0.795908 0.667846i 0.0268606 0.0225387i
\(879\) 0 0
\(880\) −3.77921 10.3833i −0.127397 0.350021i
\(881\) 16.4076 + 28.4188i 0.552787 + 0.957455i 0.998072 + 0.0620663i \(0.0197690\pi\)
−0.445285 + 0.895389i \(0.646898\pi\)
\(882\) 0 0
\(883\) −4.24994 + 7.36111i −0.143022 + 0.247721i −0.928633 0.370999i \(-0.879015\pi\)
0.785611 + 0.618720i \(0.212349\pi\)
\(884\) 1.59155 + 0.280633i 0.0535295 + 0.00943870i
\(885\) 0 0
\(886\) −0.567736 0.206639i −0.0190735 0.00694218i
\(887\) 7.44027 + 2.70804i 0.249820 + 0.0909270i 0.463895 0.885890i \(-0.346452\pi\)
−0.214075 + 0.976817i \(0.568674\pi\)
\(888\) 0 0
\(889\) −5.72372 + 11.4490i −0.191967 + 0.383988i
\(890\) 3.60199i 0.120739i
\(891\) 0 0
\(892\) −20.6833 11.9415i −0.692528 0.399831i
\(893\) −17.1605 3.02586i −0.574255 0.101257i
\(894\) 0 0
\(895\) 11.4128 + 13.6012i 0.381488 + 0.454640i
\(896\) −19.3399 2.22466i −0.646102 0.0743208i
\(897\) 0 0
\(898\) −0.503787 + 2.85712i −0.0168116 + 0.0953433i
\(899\) 10.0996 + 17.4931i 0.336842 + 0.583427i
\(900\) 0 0
\(901\) −2.64092 1.52474i −0.0879819 0.0507964i
\(902\) −0.661808 + 3.75330i −0.0220358 + 0.124971i
\(903\) 0 0
\(904\) 12.9901 + 4.72800i 0.432044 + 0.157251i
\(905\) −8.72002 + 1.53758i −0.289863 + 0.0511107i
\(906\) 0 0
\(907\) −28.2444 23.6999i −0.937840 0.786941i 0.0393684 0.999225i \(-0.487465\pi\)
−0.977208 + 0.212284i \(0.931910\pi\)
\(908\) −18.0917 + 31.3357i −0.600393 + 1.03991i
\(909\) 0 0
\(910\) −5.12967 1.52550i −0.170047 0.0505699i
\(911\) 3.62967 4.32568i 0.120256 0.143316i −0.702557 0.711627i \(-0.747959\pi\)
0.822814 + 0.568311i \(0.192403\pi\)
\(912\) 0 0
\(913\) −0.0736607 + 0.202381i −0.00243781 + 0.00669784i
\(914\) −5.20581 + 0.917924i −0.172193 + 0.0303622i
\(915\) 0 0
\(916\) −12.8724 35.3666i −0.425316 1.16855i
\(917\) −9.09719 2.70540i −0.300416 0.0893401i
\(918\) 0 0
\(919\) 10.6179 + 18.3908i 0.350253 + 0.606655i 0.986294 0.165000i \(-0.0527624\pi\)
−0.636041 + 0.771655i \(0.719429\pi\)
\(920\) 2.79894 15.8736i 0.0922782 0.523336i
\(921\) 0 0
\(922\) 2.29082 6.29397i 0.0754441 0.207281i
\(923\) 3.29085 + 18.6634i 0.108320 + 0.614312i
\(924\) 0 0
\(925\) −2.19233 1.83958i −0.0720834 0.0604851i
\(926\) 5.97143i 0.196233i
\(927\) 0 0
\(928\) −14.9335 −0.490216
\(929\) 37.4072 13.6151i 1.22729 0.446697i 0.354621 0.935010i \(-0.384610\pi\)
0.872668 + 0.488314i \(0.162388\pi\)
\(930\) 0 0
\(931\) −2.48699 20.6230i −0.0815078 0.675891i
\(932\) 8.74129 24.0165i 0.286331 0.786687i
\(933\) 0 0
\(934\) −0.990073 + 1.17992i −0.0323962 + 0.0386083i
\(935\) 0.663760i 0.0217073i
\(936\) 0 0
\(937\) −2.26157 1.30572i −0.0738824 0.0426560i 0.462604 0.886565i \(-0.346915\pi\)
−0.536486 + 0.843909i \(0.680249\pi\)
\(938\) −0.589002 9.80380i −0.0192316 0.320105i
\(939\) 0 0
\(940\) −18.5429 + 15.5593i −0.604802 + 0.507489i
\(941\) 5.15868 + 29.2563i 0.168168 + 0.953730i 0.945737 + 0.324932i \(0.105341\pi\)
−0.777569 + 0.628798i \(0.783547\pi\)
\(942\) 0 0
\(943\) 53.2288 63.4357i 1.73337 2.06575i
\(944\) −5.74070 −0.186844
\(945\) 0 0
\(946\) −2.65581 −0.0863477
\(947\) 11.1333 13.2682i 0.361784 0.431158i −0.554193 0.832388i \(-0.686973\pi\)
0.915977 + 0.401231i \(0.131417\pi\)
\(948\) 0 0
\(949\) −1.63787 9.28883i −0.0531676 0.301528i
\(950\) 0.269256 0.225932i 0.00873581 0.00733021i
\(951\) 0 0
\(952\) −0.506010 0.252970i −0.0163999 0.00819880i
\(953\) 16.8568 + 9.73226i 0.546044 + 0.315259i 0.747525 0.664234i \(-0.231242\pi\)
−0.201481 + 0.979492i \(0.564575\pi\)
\(954\) 0 0
\(955\) 2.05737i 0.0665748i
\(956\) 19.4707 23.2043i 0.629728 0.750481i
\(957\) 0 0
\(958\) −1.37197 + 3.76945i −0.0443262 + 0.121785i
\(959\) 9.39817 + 1.08107i 0.303483 + 0.0349095i
\(960\) 0 0
\(961\) −15.0304 + 5.47063i −0.484853 + 0.176472i
\(962\) −5.71790 −0.184352
\(963\) 0 0
\(964\) 12.5864i 0.405381i
\(965\) 11.7321 + 9.84438i 0.377669 + 0.316902i
\(966\) 0 0
\(967\) 3.08674 + 17.5057i 0.0992627 + 0.562947i 0.993357 + 0.115069i \(0.0367089\pi\)
−0.894095 + 0.447878i \(0.852180\pi\)
\(968\) −3.00124 + 8.24583i −0.0964634 + 0.265031i
\(969\) 0 0
\(970\) 1.14460 6.49134i 0.0367509 0.208424i
\(971\) −15.6634 27.1298i −0.502662 0.870636i −0.999995 0.00307625i \(-0.999021\pi\)
0.497334 0.867559i \(-0.334313\pi\)
\(972\) 0 0
\(973\) 10.9163 + 11.5282i 0.349959 + 0.369578i
\(974\) 2.21727 + 6.09191i 0.0710461 + 0.195197i
\(975\) 0 0
\(976\) −15.2175 + 2.68326i −0.487100 + 0.0858889i
\(977\) 0.0731353 0.200938i 0.00233980 0.00642856i −0.938517 0.345232i \(-0.887800\pi\)
0.940857 + 0.338804i \(0.110022\pi\)
\(978\) 0 0
\(979\) −6.25646 + 7.45616i −0.199957 + 0.238300i
\(980\) −24.1664 15.7681i −0.771967 0.503695i
\(981\) 0 0
\(982\) −1.31268 + 2.27362i −0.0418892 + 0.0725543i
\(983\) 14.8906 + 12.4947i 0.474935 + 0.398518i 0.848591 0.529049i \(-0.177451\pi\)
−0.373656 + 0.927568i \(0.621896\pi\)
\(984\) 0 0
\(985\) 16.6994 2.94455i 0.532086 0.0938210i
\(986\) −0.266056 0.0968364i −0.00847295 0.00308390i
\(987\) 0 0
\(988\) −3.81667 + 21.6454i −0.121424 + 0.688632i
\(989\) 49.9741 + 28.8526i 1.58908 + 0.917458i
\(990\) 0 0
\(991\) 14.0834 + 24.3931i 0.447373 + 0.774872i 0.998214 0.0597375i \(-0.0190264\pi\)
−0.550841 + 0.834610i \(0.685693\pi\)
\(992\) −1.92633 + 10.9248i −0.0611610 + 0.346861i
\(993\) 0 0
\(994\) 0.373090 3.24343i 0.0118337 0.102875i
\(995\) 5.84108 + 6.96113i 0.185175 + 0.220683i
\(996\) 0 0
\(997\) −32.9869 5.81648i −1.04471 0.184210i −0.375144 0.926966i \(-0.622407\pi\)
−0.669561 + 0.742757i \(0.733518\pi\)
\(998\) −1.73961 1.00437i −0.0550665 0.0317927i
\(999\) 0 0
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 567.2.ba.a.143.13 132
3.2 odd 2 189.2.ba.a.101.10 132
7.5 odd 6 567.2.bd.a.467.10 132
21.5 even 6 189.2.bd.a.47.13 yes 132
27.4 even 9 189.2.bd.a.185.13 yes 132
27.23 odd 18 567.2.bd.a.17.10 132
189.131 even 18 inner 567.2.ba.a.341.13 132
189.166 odd 18 189.2.ba.a.131.10 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.ba.a.101.10 132 3.2 odd 2
189.2.ba.a.131.10 yes 132 189.166 odd 18
189.2.bd.a.47.13 yes 132 21.5 even 6
189.2.bd.a.185.13 yes 132 27.4 even 9
567.2.ba.a.143.13 132 1.1 even 1 trivial
567.2.ba.a.341.13 132 189.131 even 18 inner
567.2.bd.a.17.10 132 27.23 odd 18
567.2.bd.a.467.10 132 7.5 odd 6