Properties

Label 666.2.bs.b.89.2
Level $666$
Weight $2$
Character 666.89
Analytic conductor $5.318$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [666,2,Mod(17,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("666.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.bs (of order \(36\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 89.2
Character \(\chi\) \(=\) 666.89
Dual form 666.2.bs.b.449.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-1.52173 + 1.06553i) q^{5} +(0.800320 - 4.53884i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\) \(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(-1.52173 + 1.06553i) q^{5} +(0.800320 - 4.53884i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.928845 - 1.60881i) q^{10} +(0.382482 + 0.662479i) q^{11} +(-5.11437 + 0.447449i) q^{13} +(1.19286 + 4.45181i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(1.69790 + 0.148547i) q^{17} +(-2.29378 + 4.91902i) q^{19} +(-0.161908 + 1.85062i) q^{20} +(-0.626623 - 0.438766i) q^{22} +(-3.89704 + 1.04421i) q^{23} +(-0.529786 + 1.45557i) q^{25} +(4.44609 - 2.56695i) q^{26} +(-2.96252 - 3.53059i) q^{28} +(-9.12762 - 2.44574i) q^{29} +(1.11289 + 1.11289i) q^{31} +(0.573576 + 0.819152i) q^{32} +(-1.60160 + 0.582935i) q^{34} +(3.61838 + 7.75965i) q^{35} +(-1.35851 - 5.92912i) q^{37} -5.42754i q^{38} +(-0.635367 - 1.74566i) q^{40} +(-1.15055 - 0.965428i) q^{41} +(5.40814 - 5.40814i) q^{43} +(0.753343 + 0.132835i) q^{44} +(3.09061 - 2.59333i) q^{46} +(-4.91397 - 2.83708i) q^{47} +(-13.3827 - 4.87090i) q^{49} +(-0.135003 - 1.54310i) q^{50} +(-2.94469 + 4.20545i) q^{52} +(-8.79657 + 1.55107i) q^{53} +(-1.28792 - 0.600569i) q^{55} +(4.17704 + 1.94779i) q^{56} +(9.30605 - 1.64091i) q^{58} +(-4.19571 + 5.99209i) q^{59} +(0.804553 + 9.19608i) q^{61} +(-1.47895 - 0.538293i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(7.30592 - 6.13040i) q^{65} +(6.71231 + 1.18356i) q^{67} +(1.20518 - 1.20518i) q^{68} +(-6.55874 - 5.50344i) q^{70} +(-2.79944 - 7.69139i) q^{71} +2.36965i q^{73} +(3.73698 + 4.79947i) q^{74} +(2.29378 + 4.91902i) q^{76} +(3.31299 - 1.20583i) q^{77} +(-3.40635 - 4.86478i) q^{79} +(1.31358 + 1.31358i) q^{80} +(1.45076 + 0.388731i) q^{82} +(-6.85600 - 8.17067i) q^{83} +(-2.74203 + 1.58311i) q^{85} +(-2.61586 + 7.18702i) q^{86} +(-0.738899 + 0.197987i) q^{88} +(6.10056 + 4.27166i) q^{89} +(-2.06223 + 23.5714i) q^{91} +(-1.70506 + 3.65651i) q^{92} +(5.65258 + 0.494536i) q^{94} +(-1.75084 - 9.92951i) q^{95} +(-3.70181 - 13.8154i) q^{97} +(14.1874 - 1.24123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{36}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.906308 + 0.422618i −0.640856 + 0.298836i
\(3\) 0 0
\(4\) 0.642788 0.766044i 0.321394 0.383022i
\(5\) −1.52173 + 1.06553i −0.680538 + 0.476518i −0.862019 0.506876i \(-0.830800\pi\)
0.181480 + 0.983395i \(0.441911\pi\)
\(6\) 0 0
\(7\) 0.800320 4.53884i 0.302492 1.71552i −0.332587 0.943073i \(-0.607921\pi\)
0.635079 0.772447i \(-0.280968\pi\)
\(8\) −0.258819 + 0.965926i −0.0915064 + 0.341506i
\(9\) 0 0
\(10\) 0.928845 1.60881i 0.293727 0.508749i
\(11\) 0.382482 + 0.662479i 0.115323 + 0.199745i 0.917909 0.396792i \(-0.129876\pi\)
−0.802586 + 0.596537i \(0.796543\pi\)
\(12\) 0 0
\(13\) −5.11437 + 0.447449i −1.41847 + 0.124100i −0.770439 0.637513i \(-0.779963\pi\)
−0.648032 + 0.761613i \(0.724408\pi\)
\(14\) 1.19286 + 4.45181i 0.318805 + 1.18980i
\(15\) 0 0
\(16\) −0.173648 0.984808i −0.0434120 0.246202i
\(17\) 1.69790 + 0.148547i 0.411802 + 0.0360280i 0.291175 0.956670i \(-0.405954\pi\)
0.120627 + 0.992698i \(0.461509\pi\)
\(18\) 0 0
\(19\) −2.29378 + 4.91902i −0.526229 + 1.12850i 0.446121 + 0.894973i \(0.352805\pi\)
−0.972350 + 0.233529i \(0.924973\pi\)
\(20\) −0.161908 + 1.85062i −0.0362038 + 0.413811i
\(21\) 0 0
\(22\) −0.626623 0.438766i −0.133596 0.0935452i
\(23\) −3.89704 + 1.04421i −0.812589 + 0.217732i −0.641104 0.767454i \(-0.721523\pi\)
−0.171485 + 0.985187i \(0.554856\pi\)
\(24\) 0 0
\(25\) −0.529786 + 1.45557i −0.105957 + 0.291115i
\(26\) 4.44609 2.56695i 0.871950 0.503421i
\(27\) 0 0
\(28\) −2.96252 3.53059i −0.559863 0.667219i
\(29\) −9.12762 2.44574i −1.69496 0.454162i −0.723295 0.690539i \(-0.757373\pi\)
−0.971661 + 0.236377i \(0.924040\pi\)
\(30\) 0 0
\(31\) 1.11289 + 1.11289i 0.199881 + 0.199881i 0.799949 0.600068i \(-0.204860\pi\)
−0.600068 + 0.799949i \(0.704860\pi\)
\(32\) 0.573576 + 0.819152i 0.101395 + 0.144807i
\(33\) 0 0
\(34\) −1.60160 + 0.582935i −0.274672 + 0.0999725i
\(35\) 3.61838 + 7.75965i 0.611619 + 1.31162i
\(36\) 0 0
\(37\) −1.35851 5.92912i −0.223338 0.974741i
\(38\) 5.42754i 0.880463i
\(39\) 0 0
\(40\) −0.635367 1.74566i −0.100460 0.276013i
\(41\) −1.15055 0.965428i −0.179686 0.150775i 0.548508 0.836145i \(-0.315196\pi\)
−0.728195 + 0.685370i \(0.759640\pi\)
\(42\) 0 0
\(43\) 5.40814 5.40814i 0.824733 0.824733i −0.162049 0.986783i \(-0.551810\pi\)
0.986783 + 0.162049i \(0.0518103\pi\)
\(44\) 0.753343 + 0.132835i 0.113571 + 0.0200256i
\(45\) 0 0
\(46\) 3.09061 2.59333i 0.455686 0.382366i
\(47\) −4.91397 2.83708i −0.716777 0.413831i 0.0967885 0.995305i \(-0.469143\pi\)
−0.813565 + 0.581474i \(0.802476\pi\)
\(48\) 0 0
\(49\) −13.3827 4.87090i −1.91181 0.695843i
\(50\) −0.135003 1.54310i −0.0190924 0.218227i
\(51\) 0 0
\(52\) −2.94469 + 4.20545i −0.408355 + 0.583191i
\(53\) −8.79657 + 1.55107i −1.20830 + 0.213056i −0.741284 0.671192i \(-0.765783\pi\)
−0.467018 + 0.884248i \(0.654672\pi\)
\(54\) 0 0
\(55\) −1.28792 0.600569i −0.173664 0.0809807i
\(56\) 4.17704 + 1.94779i 0.558181 + 0.260284i
\(57\) 0 0
\(58\) 9.30605 1.64091i 1.22194 0.215462i
\(59\) −4.19571 + 5.99209i −0.546234 + 0.780104i −0.993443 0.114326i \(-0.963529\pi\)
0.447209 + 0.894430i \(0.352418\pi\)
\(60\) 0 0
\(61\) 0.804553 + 9.19608i 0.103012 + 1.17744i 0.855132 + 0.518411i \(0.173476\pi\)
−0.752119 + 0.659027i \(0.770968\pi\)
\(62\) −1.47895 0.538293i −0.187826 0.0683632i
\(63\) 0 0
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) 7.30592 6.13040i 0.906188 0.760382i
\(66\) 0 0
\(67\) 6.71231 + 1.18356i 0.820040 + 0.144595i 0.567902 0.823096i \(-0.307755\pi\)
0.252138 + 0.967691i \(0.418866\pi\)
\(68\) 1.20518 1.20518i 0.146150 0.146150i
\(69\) 0 0
\(70\) −6.55874 5.50344i −0.783919 0.657786i
\(71\) −2.79944 7.69139i −0.332232 0.912800i −0.987530 0.157430i \(-0.949679\pi\)
0.655298 0.755370i \(-0.272543\pi\)
\(72\) 0 0
\(73\) 2.36965i 0.277347i 0.990338 + 0.138673i \(0.0442838\pi\)
−0.990338 + 0.138673i \(0.955716\pi\)
\(74\) 3.73698 + 4.79947i 0.434416 + 0.557928i
\(75\) 0 0
\(76\) 2.29378 + 4.91902i 0.263114 + 0.564251i
\(77\) 3.31299 1.20583i 0.377551 0.137417i
\(78\) 0 0
\(79\) −3.40635 4.86478i −0.383245 0.547330i 0.580464 0.814286i \(-0.302871\pi\)
−0.963709 + 0.266956i \(0.913982\pi\)
\(80\) 1.31358 + 1.31358i 0.146863 + 0.146863i
\(81\) 0 0
\(82\) 1.45076 + 0.388731i 0.160210 + 0.0429281i
\(83\) −6.85600 8.17067i −0.752544 0.896847i 0.244808 0.969572i \(-0.421275\pi\)
−0.997352 + 0.0727245i \(0.976831\pi\)
\(84\) 0 0
\(85\) −2.74203 + 1.58311i −0.297415 + 0.171713i
\(86\) −2.61586 + 7.18702i −0.282075 + 0.774996i
\(87\) 0 0
\(88\) −0.738899 + 0.197987i −0.0787669 + 0.0211055i
\(89\) 6.10056 + 4.27166i 0.646658 + 0.452795i 0.850334 0.526243i \(-0.176400\pi\)
−0.203676 + 0.979038i \(0.565289\pi\)
\(90\) 0 0
\(91\) −2.06223 + 23.5714i −0.216180 + 2.47095i
\(92\) −1.70506 + 3.65651i −0.177765 + 0.381217i
\(93\) 0 0
\(94\) 5.65258 + 0.494536i 0.583019 + 0.0510075i
\(95\) −1.75084 9.92951i −0.179632 1.01875i
\(96\) 0 0
\(97\) −3.70181 13.8154i −0.375862 1.40274i −0.852081 0.523410i \(-0.824660\pi\)
0.476219 0.879327i \(-0.342007\pi\)
\(98\) 14.1874 1.24123i 1.43314 0.125384i
\(99\) 0 0
\(100\) 0.774495 + 1.34146i 0.0774495 + 0.134146i
\(101\) 3.19546 5.53469i 0.317960 0.550722i −0.662102 0.749413i \(-0.730336\pi\)
0.980062 + 0.198691i \(0.0636690\pi\)
\(102\) 0 0
\(103\) −2.61420 + 9.75634i −0.257585 + 0.961321i 0.709049 + 0.705159i \(0.249125\pi\)
−0.966634 + 0.256161i \(0.917542\pi\)
\(104\) 0.891493 5.05591i 0.0874181 0.495773i
\(105\) 0 0
\(106\) 7.31689 5.12334i 0.710679 0.497623i
\(107\) −13.2614 + 15.8043i −1.28203 + 1.52786i −0.584143 + 0.811651i \(0.698569\pi\)
−0.697885 + 0.716210i \(0.745875\pi\)
\(108\) 0 0
\(109\) −10.6648 + 4.97310i −1.02151 + 0.476336i −0.859870 0.510514i \(-0.829455\pi\)
−0.161637 + 0.986850i \(0.551677\pi\)
\(110\) 1.42107 0.135493
\(111\) 0 0
\(112\) −4.60886 −0.435496
\(113\) 16.8033 7.83553i 1.58073 0.737104i 0.583541 0.812084i \(-0.301667\pi\)
0.997185 + 0.0749795i \(0.0238891\pi\)
\(114\) 0 0
\(115\) 4.81761 5.74140i 0.449244 0.535389i
\(116\) −7.74067 + 5.42007i −0.718703 + 0.503241i
\(117\) 0 0
\(118\) 1.27023 7.20386i 0.116935 0.663169i
\(119\) 2.03310 7.58762i 0.186374 0.695556i
\(120\) 0 0
\(121\) 5.20741 9.01951i 0.473401 0.819955i
\(122\) −4.61560 7.99446i −0.417877 0.723784i
\(123\) 0 0
\(124\) 1.56787 0.137171i 0.140799 0.0123183i
\(125\) −3.14879 11.7514i −0.281636 1.05108i
\(126\) 0 0
\(127\) 0.597958 + 3.39119i 0.0530602 + 0.300919i 0.999776 0.0211499i \(-0.00673272\pi\)
−0.946716 + 0.322069i \(0.895622\pi\)
\(128\) 0.996195 + 0.0871557i 0.0880520 + 0.00770355i
\(129\) 0 0
\(130\) −4.03060 + 8.64364i −0.353507 + 0.758097i
\(131\) −0.0480530 + 0.549249i −0.00419841 + 0.0479881i −0.998005 0.0631364i \(-0.979890\pi\)
0.993806 + 0.111124i \(0.0354452\pi\)
\(132\) 0 0
\(133\) 20.4909 + 14.3479i 1.77679 + 1.24412i
\(134\) −6.58362 + 1.76407i −0.568738 + 0.152393i
\(135\) 0 0
\(136\) −0.582935 + 1.60160i −0.0499863 + 0.137336i
\(137\) 10.9115 6.29975i 0.932231 0.538224i 0.0447146 0.999000i \(-0.485762\pi\)
0.887517 + 0.460776i \(0.152429\pi\)
\(138\) 0 0
\(139\) 5.32113 + 6.34148i 0.451332 + 0.537877i 0.942950 0.332934i \(-0.108039\pi\)
−0.491618 + 0.870811i \(0.663594\pi\)
\(140\) 8.27009 + 2.21596i 0.698950 + 0.187283i
\(141\) 0 0
\(142\) 5.78768 + 5.78768i 0.485691 + 0.485691i
\(143\) −2.25258 3.21702i −0.188370 0.269021i
\(144\) 0 0
\(145\) 16.4958 6.00397i 1.36990 0.498603i
\(146\) −1.00146 2.14763i −0.0828813 0.177739i
\(147\) 0 0
\(148\) −5.41520 2.77048i −0.445127 0.227732i
\(149\) 7.29821i 0.597892i 0.954270 + 0.298946i \(0.0966351\pi\)
−0.954270 + 0.298946i \(0.903365\pi\)
\(150\) 0 0
\(151\) 3.78811 + 10.4078i 0.308272 + 0.846971i 0.992994 + 0.118166i \(0.0377016\pi\)
−0.684721 + 0.728805i \(0.740076\pi\)
\(152\) −4.15774 3.48876i −0.337237 0.282975i
\(153\) 0 0
\(154\) −2.49299 + 2.49299i −0.200891 + 0.200891i
\(155\) −2.87933 0.507703i −0.231273 0.0407797i
\(156\) 0 0
\(157\) 8.86534 7.43891i 0.707531 0.593689i −0.216374 0.976311i \(-0.569423\pi\)
0.923905 + 0.382621i \(0.124979\pi\)
\(158\) 5.14315 + 2.96940i 0.409167 + 0.236233i
\(159\) 0 0
\(160\) −1.74566 0.635367i −0.138006 0.0502302i
\(161\) 1.62062 + 18.5237i 0.127722 + 1.45987i
\(162\) 0 0
\(163\) −11.4113 + 16.2971i −0.893806 + 1.27649i 0.0665709 + 0.997782i \(0.478794\pi\)
−0.960377 + 0.278705i \(0.910095\pi\)
\(164\) −1.47912 + 0.260809i −0.115500 + 0.0203658i
\(165\) 0 0
\(166\) 9.66672 + 4.50767i 0.750283 + 0.349863i
\(167\) 15.4398 + 7.19968i 1.19477 + 0.557128i 0.915201 0.402999i \(-0.132032\pi\)
0.279565 + 0.960127i \(0.409810\pi\)
\(168\) 0 0
\(169\) 13.1541 2.31942i 1.01185 0.178417i
\(170\) 1.81607 2.59362i 0.139286 0.198921i
\(171\) 0 0
\(172\) −0.666590 7.61916i −0.0508270 0.580955i
\(173\) 19.4091 + 7.06432i 1.47564 + 0.537090i 0.949627 0.313384i \(-0.101463\pi\)
0.526017 + 0.850474i \(0.323685\pi\)
\(174\) 0 0
\(175\) 6.18262 + 3.56954i 0.467362 + 0.269832i
\(176\) 0.585997 0.491710i 0.0441712 0.0370640i
\(177\) 0 0
\(178\) −7.33427 1.29323i −0.549727 0.0969316i
\(179\) 12.2715 12.2715i 0.917214 0.917214i −0.0796123 0.996826i \(-0.525368\pi\)
0.996826 + 0.0796123i \(0.0253682\pi\)
\(180\) 0 0
\(181\) −2.13211 1.78905i −0.158478 0.132979i 0.560100 0.828425i \(-0.310763\pi\)
−0.718579 + 0.695446i \(0.755207\pi\)
\(182\) −8.09269 22.2345i −0.599870 1.64813i
\(183\) 0 0
\(184\) 4.03451i 0.297428i
\(185\) 8.38492 + 7.57499i 0.616472 + 0.556924i
\(186\) 0 0
\(187\) 0.551008 + 1.18164i 0.0402937 + 0.0864102i
\(188\) −5.33197 + 1.94068i −0.388874 + 0.141539i
\(189\) 0 0
\(190\) 5.78319 + 8.25925i 0.419557 + 0.599189i
\(191\) −6.90030 6.90030i −0.499288 0.499288i 0.411928 0.911216i \(-0.364855\pi\)
−0.911216 + 0.411928i \(0.864855\pi\)
\(192\) 0 0
\(193\) −3.43915 0.921516i −0.247555 0.0663322i 0.132908 0.991128i \(-0.457569\pi\)
−0.380463 + 0.924796i \(0.624235\pi\)
\(194\) 9.19361 + 10.9565i 0.660062 + 0.786632i
\(195\) 0 0
\(196\) −12.3336 + 7.12079i −0.880969 + 0.508628i
\(197\) −0.132447 + 0.363896i −0.00943648 + 0.0259265i −0.944321 0.329024i \(-0.893280\pi\)
0.934885 + 0.354951i \(0.115502\pi\)
\(198\) 0 0
\(199\) −4.37182 + 1.17143i −0.309910 + 0.0830402i −0.410422 0.911896i \(-0.634619\pi\)
0.100512 + 0.994936i \(0.467952\pi\)
\(200\) −1.26886 0.888464i −0.0897218 0.0628239i
\(201\) 0 0
\(202\) −0.557005 + 6.36659i −0.0391907 + 0.447952i
\(203\) −18.4058 + 39.4714i −1.29184 + 2.77035i
\(204\) 0 0
\(205\) 2.77952 + 0.243176i 0.194130 + 0.0169842i
\(206\) −1.75393 9.94706i −0.122202 0.693044i
\(207\) 0 0
\(208\) 1.32875 + 4.95897i 0.0921324 + 0.343843i
\(209\) −4.13608 + 0.361860i −0.286099 + 0.0250304i
\(210\) 0 0
\(211\) −8.83213 15.2977i −0.608029 1.05314i −0.991565 0.129611i \(-0.958627\pi\)
0.383536 0.923526i \(-0.374706\pi\)
\(212\) −4.46614 + 7.73558i −0.306736 + 0.531281i
\(213\) 0 0
\(214\) 5.33971 19.9281i 0.365015 1.36226i
\(215\) −2.46721 + 13.9922i −0.168262 + 0.954263i
\(216\) 0 0
\(217\) 5.94189 4.16056i 0.403362 0.282437i
\(218\) 7.56391 9.01432i 0.512293 0.610527i
\(219\) 0 0
\(220\) −1.28792 + 0.600569i −0.0868318 + 0.0404904i
\(221\) −8.75016 −0.588600
\(222\) 0 0
\(223\) 9.00255 0.602855 0.301428 0.953489i \(-0.402537\pi\)
0.301428 + 0.953489i \(0.402537\pi\)
\(224\) 4.17704 1.94779i 0.279090 0.130142i
\(225\) 0 0
\(226\) −11.9176 + 14.2028i −0.792745 + 0.944756i
\(227\) 13.2961 9.31000i 0.882490 0.617926i −0.0420063 0.999117i \(-0.513375\pi\)
0.924496 + 0.381191i \(0.124486\pi\)
\(228\) 0 0
\(229\) 1.05335 5.97383i 0.0696072 0.394762i −0.930021 0.367506i \(-0.880212\pi\)
0.999628 0.0272564i \(-0.00867705\pi\)
\(230\) −1.93981 + 7.23949i −0.127908 + 0.477358i
\(231\) 0 0
\(232\) 4.72480 8.18360i 0.310199 0.537280i
\(233\) 2.02597 + 3.50909i 0.132726 + 0.229888i 0.924726 0.380632i \(-0.124294\pi\)
−0.792000 + 0.610520i \(0.790960\pi\)
\(234\) 0 0
\(235\) 10.5007 0.918695i 0.684992 0.0599290i
\(236\) 1.89326 + 7.06574i 0.123241 + 0.459940i
\(237\) 0 0
\(238\) 1.36406 + 7.73594i 0.0884186 + 0.501447i
\(239\) −3.23584 0.283099i −0.209309 0.0183122i −0.0179811 0.999838i \(-0.505724\pi\)
−0.191328 + 0.981526i \(0.561279\pi\)
\(240\) 0 0
\(241\) −11.9282 + 25.5802i −0.768365 + 1.64776i −0.00654205 + 0.999979i \(0.502082\pi\)
−0.761823 + 0.647785i \(0.775695\pi\)
\(242\) −0.907712 + 10.3752i −0.0583499 + 0.666943i
\(243\) 0 0
\(244\) 7.56176 + 5.29480i 0.484092 + 0.338965i
\(245\) 25.5549 6.84742i 1.63265 0.437466i
\(246\) 0 0
\(247\) 9.53021 26.1840i 0.606393 1.66605i
\(248\) −1.36300 + 0.786931i −0.0865509 + 0.0499702i
\(249\) 0 0
\(250\) 7.82015 + 9.31969i 0.494590 + 0.589429i
\(251\) −18.5648 4.97444i −1.17180 0.313984i −0.380132 0.924932i \(-0.624122\pi\)
−0.791670 + 0.610948i \(0.790788\pi\)
\(252\) 0 0
\(253\) −2.18232 2.18232i −0.137201 0.137201i
\(254\) −1.97511 2.82075i −0.123930 0.176990i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −7.42240 15.9174i −0.462996 0.992899i −0.989741 0.142875i \(-0.954365\pi\)
0.526744 0.850024i \(-0.323413\pi\)
\(258\) 0 0
\(259\) −27.9986 + 1.42088i −1.73975 + 0.0882889i
\(260\) 9.53720i 0.591472i
\(261\) 0 0
\(262\) −0.188572 0.518096i −0.0116500 0.0320081i
\(263\) −13.0732 10.9697i −0.806130 0.676424i 0.143551 0.989643i \(-0.454148\pi\)
−0.949681 + 0.313219i \(0.898592\pi\)
\(264\) 0 0
\(265\) 11.7333 11.7333i 0.720771 0.720771i
\(266\) −24.6347 4.34377i −1.51045 0.266333i
\(267\) 0 0
\(268\) 5.22125 4.38115i 0.318939 0.267621i
\(269\) 5.55459 + 3.20694i 0.338669 + 0.195531i 0.659683 0.751544i \(-0.270690\pi\)
−0.321014 + 0.947074i \(0.604024\pi\)
\(270\) 0 0
\(271\) −9.08775 3.30767i −0.552041 0.200927i 0.0509119 0.998703i \(-0.483787\pi\)
−0.602953 + 0.797777i \(0.706009\pi\)
\(272\) −0.148547 1.69790i −0.00900699 0.102950i
\(273\) 0 0
\(274\) −7.22678 + 10.3209i −0.436585 + 0.623509i
\(275\) −1.16692 + 0.205760i −0.0703680 + 0.0124078i
\(276\) 0 0
\(277\) −25.6525 11.9620i −1.54131 0.718725i −0.548248 0.836316i \(-0.684705\pi\)
−0.993062 + 0.117591i \(0.962483\pi\)
\(278\) −7.50261 3.49852i −0.449976 0.209827i
\(279\) 0 0
\(280\) −8.43175 + 1.48675i −0.503894 + 0.0888500i
\(281\) 10.9768 15.6765i 0.654823 0.935184i −0.345171 0.938540i \(-0.612179\pi\)
0.999994 + 0.00335557i \(0.00106811\pi\)
\(282\) 0 0
\(283\) −0.198981 2.27437i −0.0118282 0.135197i 0.987984 0.154553i \(-0.0493939\pi\)
−0.999813 + 0.0193563i \(0.993838\pi\)
\(284\) −7.69139 2.79944i −0.456400 0.166116i
\(285\) 0 0
\(286\) 3.40110 + 1.96363i 0.201112 + 0.116112i
\(287\) −5.30273 + 4.44952i −0.313010 + 0.262647i
\(288\) 0 0
\(289\) −13.8809 2.44758i −0.816525 0.143975i
\(290\) −12.4129 + 12.4129i −0.728908 + 0.728908i
\(291\) 0 0
\(292\) 1.81526 + 1.52318i 0.106230 + 0.0891375i
\(293\) 0.338573 + 0.930221i 0.0197796 + 0.0543441i 0.949190 0.314705i \(-0.101906\pi\)
−0.929410 + 0.369049i \(0.879683\pi\)
\(294\) 0 0
\(295\) 13.5890i 0.791181i
\(296\) 6.07870 + 0.222347i 0.353317 + 0.0129237i
\(297\) 0 0
\(298\) −3.08436 6.61442i −0.178672 0.383163i
\(299\) 19.4637 7.08419i 1.12561 0.409690i
\(300\) 0 0
\(301\) −20.2184 28.8749i −1.16537 1.66432i
\(302\) −7.83170 7.83170i −0.450664 0.450664i
\(303\) 0 0
\(304\) 5.24260 + 1.40475i 0.300684 + 0.0805680i
\(305\) −11.0230 13.1367i −0.631174 0.752204i
\(306\) 0 0
\(307\) 23.7471 13.7104i 1.35532 0.782494i 0.366330 0.930485i \(-0.380614\pi\)
0.988989 + 0.147991i \(0.0472807\pi\)
\(308\) 1.20583 3.31299i 0.0687086 0.188775i
\(309\) 0 0
\(310\) 2.82412 0.756722i 0.160399 0.0429789i
\(311\) 3.46322 + 2.42497i 0.196381 + 0.137508i 0.667631 0.744492i \(-0.267308\pi\)
−0.471250 + 0.882000i \(0.656197\pi\)
\(312\) 0 0
\(313\) 1.70566 19.4958i 0.0964095 1.10197i −0.781748 0.623594i \(-0.785672\pi\)
0.878158 0.478371i \(-0.158773\pi\)
\(314\) −4.89091 + 10.4886i −0.276010 + 0.591906i
\(315\) 0 0
\(316\) −5.91620 0.517600i −0.332812 0.0291173i
\(317\) −2.29959 13.0416i −0.129158 0.732490i −0.978751 0.205052i \(-0.934264\pi\)
0.849593 0.527438i \(-0.176847\pi\)
\(318\) 0 0
\(319\) −1.87090 6.98231i −0.104751 0.390934i
\(320\) 1.85062 0.161908i 0.103453 0.00905095i
\(321\) 0 0
\(322\) −9.29724 16.1033i −0.518115 0.897402i
\(323\) −4.62532 + 8.01128i −0.257359 + 0.445760i
\(324\) 0 0
\(325\) 2.05822 7.68140i 0.114170 0.426087i
\(326\) 3.45474 19.5928i 0.191341 1.08515i
\(327\) 0 0
\(328\) 1.23032 0.861477i 0.0679329 0.0475671i
\(329\) −16.8098 + 20.0332i −0.926755 + 1.10446i
\(330\) 0 0
\(331\) 4.23623 1.97539i 0.232844 0.108577i −0.302695 0.953088i \(-0.597886\pi\)
0.535539 + 0.844511i \(0.320108\pi\)
\(332\) −10.6660 −0.585375
\(333\) 0 0
\(334\) −17.0359 −0.932163
\(335\) −11.4754 + 5.35109i −0.626971 + 0.292361i
\(336\) 0 0
\(337\) −11.9468 + 14.2376i −0.650784 + 0.775574i −0.986032 0.166556i \(-0.946735\pi\)
0.335248 + 0.942130i \(0.391180\pi\)
\(338\) −10.9414 + 7.66125i −0.595134 + 0.416717i
\(339\) 0 0
\(340\) −0.549809 + 3.11812i −0.0298176 + 0.169104i
\(341\) −0.311605 + 1.16293i −0.0168744 + 0.0629760i
\(342\) 0 0
\(343\) −16.6877 + 28.9039i −0.901050 + 1.56066i
\(344\) 3.82413 + 6.62359i 0.206183 + 0.357120i
\(345\) 0 0
\(346\) −20.5761 + 1.80017i −1.10618 + 0.0967780i
\(347\) 6.04031 + 22.5427i 0.324261 + 1.21016i 0.915053 + 0.403334i \(0.132149\pi\)
−0.590792 + 0.806824i \(0.701185\pi\)
\(348\) 0 0
\(349\) 3.04704 + 17.2806i 0.163104 + 0.925011i 0.950997 + 0.309199i \(0.100061\pi\)
−0.787893 + 0.615812i \(0.788828\pi\)
\(350\) −7.11191 0.622211i −0.380147 0.0332586i
\(351\) 0 0
\(352\) −0.323288 + 0.693294i −0.0172313 + 0.0369527i
\(353\) 2.09495 23.9453i 0.111503 1.27448i −0.709969 0.704233i \(-0.751291\pi\)
0.821472 0.570249i \(-0.193153\pi\)
\(354\) 0 0
\(355\) 12.4554 + 8.72135i 0.661063 + 0.462881i
\(356\) 7.19365 1.92753i 0.381263 0.102159i
\(357\) 0 0
\(358\) −5.93559 + 16.3079i −0.313706 + 0.861899i
\(359\) 9.52698 5.50040i 0.502815 0.290300i −0.227061 0.973881i \(-0.572912\pi\)
0.729875 + 0.683581i \(0.239578\pi\)
\(360\) 0 0
\(361\) −6.72240 8.01144i −0.353810 0.421655i
\(362\) 2.68843 + 0.720362i 0.141301 + 0.0378614i
\(363\) 0 0
\(364\) 16.7312 + 16.7312i 0.876951 + 0.876951i
\(365\) −2.52493 3.60597i −0.132161 0.188745i
\(366\) 0 0
\(367\) −15.0689 + 5.48462i −0.786589 + 0.286295i −0.703917 0.710282i \(-0.748567\pi\)
−0.0826716 + 0.996577i \(0.526345\pi\)
\(368\) 1.70506 + 3.65651i 0.0888823 + 0.190609i
\(369\) 0 0
\(370\) −10.8007 3.32165i −0.561499 0.172684i
\(371\) 41.1676i 2.13731i
\(372\) 0 0
\(373\) −3.24957 8.92813i −0.168256 0.462281i 0.826694 0.562652i \(-0.190219\pi\)
−0.994950 + 0.100372i \(0.967997\pi\)
\(374\) −0.998766 0.838064i −0.0516450 0.0433353i
\(375\) 0 0
\(376\) 4.01224 4.01224i 0.206916 0.206916i
\(377\) 47.7764 + 8.42426i 2.46061 + 0.433872i
\(378\) 0 0
\(379\) −14.8365 + 12.4493i −0.762102 + 0.639479i −0.938673 0.344808i \(-0.887944\pi\)
0.176571 + 0.984288i \(0.443499\pi\)
\(380\) −8.73186 5.04134i −0.447935 0.258615i
\(381\) 0 0
\(382\) 9.16999 + 3.33760i 0.469177 + 0.170767i
\(383\) 2.25137 + 25.7333i 0.115040 + 1.31491i 0.805956 + 0.591976i \(0.201652\pi\)
−0.690916 + 0.722935i \(0.742792\pi\)
\(384\) 0 0
\(385\) −3.75664 + 5.36503i −0.191456 + 0.273427i
\(386\) 3.50637 0.618268i 0.178470 0.0314690i
\(387\) 0 0
\(388\) −12.9627 6.04459i −0.658079 0.306867i
\(389\) −18.2289 8.50030i −0.924244 0.430982i −0.0985704 0.995130i \(-0.531427\pi\)
−0.825674 + 0.564148i \(0.809205\pi\)
\(390\) 0 0
\(391\) −6.77190 + 1.19407i −0.342470 + 0.0603867i
\(392\) 8.16863 11.6660i 0.412578 0.589223i
\(393\) 0 0
\(394\) −0.0337510 0.385776i −0.00170035 0.0194351i
\(395\) 10.3671 + 3.77332i 0.521626 + 0.189856i
\(396\) 0 0
\(397\) 28.8505 + 16.6568i 1.44796 + 0.835982i 0.998360 0.0572466i \(-0.0182321\pi\)
0.449603 + 0.893228i \(0.351565\pi\)
\(398\) 3.46715 2.90929i 0.173793 0.145829i
\(399\) 0 0
\(400\) 1.52546 + 0.268979i 0.0762728 + 0.0134490i
\(401\) −18.0069 + 18.0069i −0.899222 + 0.899222i −0.995367 0.0961456i \(-0.969349\pi\)
0.0961456 + 0.995367i \(0.469349\pi\)
\(402\) 0 0
\(403\) −6.18969 5.19376i −0.308330 0.258720i
\(404\) −2.18582 6.00549i −0.108749 0.298784i
\(405\) 0 0
\(406\) 43.5519i 2.16144i
\(407\) 3.40831 3.16777i 0.168944 0.157021i
\(408\) 0 0
\(409\) −7.43585 15.9462i −0.367679 0.788491i −0.999906 0.0137073i \(-0.995637\pi\)
0.632227 0.774783i \(-0.282141\pi\)
\(410\) −2.62187 + 0.954283i −0.129485 + 0.0471287i
\(411\) 0 0
\(412\) 5.79341 + 8.27385i 0.285421 + 0.407623i
\(413\) 23.8392 + 23.8392i 1.17305 + 1.17305i
\(414\) 0 0
\(415\) 19.1391 + 5.12829i 0.939499 + 0.251738i
\(416\) −3.30001 3.93280i −0.161796 0.192821i
\(417\) 0 0
\(418\) 3.59563 2.07594i 0.175868 0.101537i
\(419\) 0.504021 1.38479i 0.0246230 0.0676513i −0.926772 0.375624i \(-0.877428\pi\)
0.951395 + 0.307973i \(0.0996506\pi\)
\(420\) 0 0
\(421\) 10.9886 2.94438i 0.535550 0.143500i 0.0191003 0.999818i \(-0.493920\pi\)
0.516450 + 0.856317i \(0.327253\pi\)
\(422\) 14.4697 + 10.1318i 0.704375 + 0.493209i
\(423\) 0 0
\(424\) 0.778499 8.89828i 0.0378072 0.432139i
\(425\) −1.11575 + 2.39272i −0.0541216 + 0.116064i
\(426\) 0 0
\(427\) 42.3834 + 3.70807i 2.05108 + 0.179446i
\(428\) 3.58255 + 20.3176i 0.173169 + 0.982090i
\(429\) 0 0
\(430\) −3.67733 13.7240i −0.177336 0.661829i
\(431\) −37.3119 + 3.26437i −1.79725 + 0.157239i −0.936244 0.351352i \(-0.885722\pi\)
−0.861008 + 0.508591i \(0.830167\pi\)
\(432\) 0 0
\(433\) −13.9608 24.1808i −0.670914 1.16206i −0.977645 0.210260i \(-0.932569\pi\)
0.306732 0.951796i \(-0.400765\pi\)
\(434\) −3.62685 + 6.28190i −0.174095 + 0.301541i
\(435\) 0 0
\(436\) −3.04562 + 11.3664i −0.145859 + 0.544351i
\(437\) 3.80246 21.5648i 0.181896 1.03158i
\(438\) 0 0
\(439\) −7.11627 + 4.98287i −0.339641 + 0.237819i −0.730936 0.682446i \(-0.760916\pi\)
0.391295 + 0.920265i \(0.372027\pi\)
\(440\) 0.913445 1.08860i 0.0435468 0.0518970i
\(441\) 0 0
\(442\) 7.93034 3.69798i 0.377208 0.175895i
\(443\) −37.9608 −1.80357 −0.901785 0.432185i \(-0.857743\pi\)
−0.901785 + 0.432185i \(0.857743\pi\)
\(444\) 0 0
\(445\) −13.8350 −0.655841
\(446\) −8.15908 + 3.80464i −0.386344 + 0.180155i
\(447\) 0 0
\(448\) −2.96252 + 3.53059i −0.139966 + 0.166805i
\(449\) 13.9590 9.77422i 0.658768 0.461274i −0.195779 0.980648i \(-0.562724\pi\)
0.854547 + 0.519374i \(0.173835\pi\)
\(450\) 0 0
\(451\) 0.199510 1.13148i 0.00939455 0.0532791i
\(452\) 4.79862 17.9087i 0.225708 0.842354i
\(453\) 0 0
\(454\) −8.11574 + 14.0569i −0.380891 + 0.659722i
\(455\) −21.9778 38.0667i −1.03034 1.78459i
\(456\) 0 0
\(457\) 7.04378 0.616251i 0.329494 0.0288270i 0.0787915 0.996891i \(-0.474894\pi\)
0.250703 + 0.968064i \(0.419338\pi\)
\(458\) 1.56999 + 5.85930i 0.0733610 + 0.273787i
\(459\) 0 0
\(460\) −1.30147 7.38101i −0.0606814 0.344141i
\(461\) −19.0599 1.66753i −0.887709 0.0776645i −0.365828 0.930683i \(-0.619214\pi\)
−0.521881 + 0.853018i \(0.674770\pi\)
\(462\) 0 0
\(463\) 5.94832 12.7562i 0.276442 0.592831i −0.718244 0.695792i \(-0.755054\pi\)
0.994685 + 0.102960i \(0.0328315\pi\)
\(464\) −0.823588 + 9.41365i −0.0382341 + 0.437018i
\(465\) 0 0
\(466\) −3.31916 2.32410i −0.153757 0.107662i
\(467\) 3.56658 0.955662i 0.165042 0.0442227i −0.175352 0.984506i \(-0.556106\pi\)
0.340394 + 0.940283i \(0.389440\pi\)
\(468\) 0 0
\(469\) 10.7440 29.5189i 0.496112 1.36306i
\(470\) −9.12864 + 5.27042i −0.421073 + 0.243106i
\(471\) 0 0
\(472\) −4.70199 5.60361i −0.216426 0.257927i
\(473\) 5.65130 + 1.51426i 0.259847 + 0.0696258i
\(474\) 0 0
\(475\) −5.94479 5.94479i −0.272766 0.272766i
\(476\) −4.50560 6.43467i −0.206514 0.294933i
\(477\) 0 0
\(478\) 3.05231 1.11095i 0.139609 0.0508137i
\(479\) 15.1175 + 32.4195i 0.690734 + 1.48128i 0.867711 + 0.497070i \(0.165591\pi\)
−0.176976 + 0.984215i \(0.556632\pi\)
\(480\) 0 0
\(481\) 9.60091 + 29.7158i 0.437764 + 1.35493i
\(482\) 28.2246i 1.28560i
\(483\) 0 0
\(484\) −3.56208 9.78674i −0.161913 0.444852i
\(485\) 20.3538 + 17.0789i 0.924218 + 0.775511i
\(486\) 0 0
\(487\) 27.1187 27.1187i 1.22886 1.22886i 0.264469 0.964394i \(-0.414803\pi\)
0.964394 0.264469i \(-0.0851968\pi\)
\(488\) −9.09097 1.60298i −0.411529 0.0725636i
\(489\) 0 0
\(490\) −20.2668 + 17.0059i −0.915560 + 0.768246i
\(491\) 23.6745 + 13.6685i 1.06842 + 0.616851i 0.927748 0.373206i \(-0.121742\pi\)
0.140668 + 0.990057i \(0.455075\pi\)
\(492\) 0 0
\(493\) −15.1345 5.50851i −0.681623 0.248091i
\(494\) 2.42855 + 27.7584i 0.109266 + 1.24891i
\(495\) 0 0
\(496\) 0.902730 1.28923i 0.0405338 0.0578883i
\(497\) −37.1504 + 6.55063i −1.66643 + 0.293836i
\(498\) 0 0
\(499\) 10.9377 + 5.10035i 0.489641 + 0.228323i 0.651727 0.758453i \(-0.274045\pi\)
−0.162087 + 0.986777i \(0.551822\pi\)
\(500\) −11.0261 5.14157i −0.493104 0.229938i
\(501\) 0 0
\(502\) 18.9278 3.33747i 0.844787 0.148959i
\(503\) 20.1856 28.8280i 0.900032 1.28538i −0.0578826 0.998323i \(-0.518435\pi\)
0.957914 0.287055i \(-0.0926762\pi\)
\(504\) 0 0
\(505\) 1.03474 + 11.8272i 0.0460454 + 0.526301i
\(506\) 2.90014 + 1.05556i 0.128927 + 0.0469255i
\(507\) 0 0
\(508\) 2.98216 + 1.72175i 0.132312 + 0.0763904i
\(509\) 10.9848 9.21733i 0.486892 0.408551i −0.366019 0.930607i \(-0.619279\pi\)
0.852911 + 0.522056i \(0.174835\pi\)
\(510\) 0 0
\(511\) 10.7555 + 1.89648i 0.475794 + 0.0838953i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 13.4540 + 11.2892i 0.593428 + 0.497946i
\(515\) −6.41753 17.6320i −0.282790 0.776960i
\(516\) 0 0
\(517\) 4.34054i 0.190897i
\(518\) 24.7748 13.1205i 1.08854 0.576480i
\(519\) 0 0
\(520\) 4.03060 + 8.64364i 0.176753 + 0.379049i
\(521\) −31.2612 + 11.3782i −1.36958 + 0.498486i −0.919003 0.394252i \(-0.871004\pi\)
−0.450577 + 0.892738i \(0.648782\pi\)
\(522\) 0 0
\(523\) 13.4137 + 19.1567i 0.586538 + 0.837663i 0.997251 0.0741018i \(-0.0236090\pi\)
−0.410713 + 0.911765i \(0.634720\pi\)
\(524\) 0.389861 + 0.389861i 0.0170312 + 0.0170312i
\(525\) 0 0
\(526\) 16.4844 + 4.41698i 0.718754 + 0.192589i
\(527\) 1.72426 + 2.05489i 0.0751099 + 0.0895125i
\(528\) 0 0
\(529\) −5.82205 + 3.36136i −0.253132 + 0.146146i
\(530\) −5.67527 + 15.5927i −0.246518 + 0.677303i
\(531\) 0 0
\(532\) 24.1624 6.47430i 1.04757 0.280696i
\(533\) 6.31633 + 4.42274i 0.273591 + 0.191570i
\(534\) 0 0
\(535\) 3.34034 38.1803i 0.144416 1.65068i
\(536\) −2.88051 + 6.17727i −0.124419 + 0.266817i
\(537\) 0 0
\(538\) −6.38948 0.559007i −0.275470 0.0241005i
\(539\) −1.89178 10.7288i −0.0814846 0.462122i
\(540\) 0 0
\(541\) 0.508352 + 1.89720i 0.0218558 + 0.0815669i 0.975992 0.217805i \(-0.0698896\pi\)
−0.954137 + 0.299372i \(0.903223\pi\)
\(542\) 9.63418 0.842881i 0.413823 0.0362049i
\(543\) 0 0
\(544\) 0.852194 + 1.47604i 0.0365375 + 0.0632848i
\(545\) 10.9300 18.9314i 0.468192 0.810932i
\(546\) 0 0
\(547\) −8.68799 + 32.4240i −0.371471 + 1.38635i 0.486961 + 0.873424i \(0.338105\pi\)
−0.858432 + 0.512927i \(0.828561\pi\)
\(548\) 2.18788 12.4081i 0.0934616 0.530047i
\(549\) 0 0
\(550\) 0.970632 0.679644i 0.0413879 0.0289801i
\(551\) 32.9674 39.2890i 1.40446 1.67377i
\(552\) 0 0
\(553\) −24.8066 + 11.5675i −1.05488 + 0.491901i
\(554\) 28.3044 1.20254
\(555\) 0 0
\(556\) 8.27821 0.351074
\(557\) 22.6070 10.5418i 0.957889 0.446671i 0.120158 0.992755i \(-0.461660\pi\)
0.837731 + 0.546084i \(0.183882\pi\)
\(558\) 0 0
\(559\) −25.2394 + 30.0791i −1.06751 + 1.27221i
\(560\) 7.01344 4.91086i 0.296372 0.207522i
\(561\) 0 0
\(562\) −3.32320 + 18.8468i −0.140181 + 0.795004i
\(563\) −2.87368 + 10.7247i −0.121111 + 0.451993i −0.999671 0.0256388i \(-0.991838\pi\)
0.878560 + 0.477632i \(0.158505\pi\)
\(564\) 0 0
\(565\) −17.2212 + 29.8280i −0.724501 + 1.25487i
\(566\) 1.14153 + 1.97718i 0.0479819 + 0.0831072i
\(567\) 0 0
\(568\) 8.15386 0.713371i 0.342129 0.0299324i
\(569\) 5.37581 + 20.0628i 0.225366 + 0.841076i 0.982258 + 0.187536i \(0.0600502\pi\)
−0.756892 + 0.653540i \(0.773283\pi\)
\(570\) 0 0
\(571\) −4.08335 23.1578i −0.170883 0.969126i −0.942789 0.333389i \(-0.891808\pi\)
0.771906 0.635736i \(-0.219303\pi\)
\(572\) −3.91231 0.342283i −0.163582 0.0143116i
\(573\) 0 0
\(574\) 2.92546 6.27367i 0.122106 0.261858i
\(575\) 0.544672 6.22563i 0.0227144 0.259627i
\(576\) 0 0
\(577\) 13.1061 + 9.17696i 0.545612 + 0.382042i 0.813640 0.581369i \(-0.197483\pi\)
−0.268027 + 0.963411i \(0.586372\pi\)
\(578\) 13.6148 3.64807i 0.566300 0.151740i
\(579\) 0 0
\(580\) 6.00397 16.4958i 0.249301 0.684950i
\(581\) −42.5723 + 24.5791i −1.76620 + 1.01971i
\(582\) 0 0
\(583\) −4.39209 5.23429i −0.181902 0.216782i
\(584\) −2.28891 0.613311i −0.0947157 0.0253790i
\(585\) 0 0
\(586\) −0.699979 0.699979i −0.0289159 0.0289159i
\(587\) −13.9431 19.9128i −0.575493 0.821889i 0.420868 0.907122i \(-0.361725\pi\)
−0.996361 + 0.0852329i \(0.972837\pi\)
\(588\) 0 0
\(589\) −8.02704 + 2.92160i −0.330749 + 0.120383i
\(590\) 5.74295 + 12.3158i 0.236434 + 0.507033i
\(591\) 0 0
\(592\) −5.60314 + 2.36745i −0.230288 + 0.0973017i
\(593\) 25.3065i 1.03921i −0.854406 0.519606i \(-0.826079\pi\)
0.854406 0.519606i \(-0.173921\pi\)
\(594\) 0 0
\(595\) 4.99099 + 13.7126i 0.204611 + 0.562163i
\(596\) 5.59075 + 4.69120i 0.229006 + 0.192159i
\(597\) 0 0
\(598\) −14.6462 + 14.6462i −0.598926 + 0.598926i
\(599\) 15.5557 + 2.74289i 0.635589 + 0.112072i 0.482153 0.876087i \(-0.339855\pi\)
0.153436 + 0.988159i \(0.450966\pi\)
\(600\) 0 0
\(601\) −7.59494 + 6.37291i −0.309804 + 0.259956i −0.784411 0.620241i \(-0.787035\pi\)
0.474607 + 0.880198i \(0.342590\pi\)
\(602\) 30.5272 + 17.6249i 1.24420 + 0.718337i
\(603\) 0 0
\(604\) 10.4078 + 3.78811i 0.423486 + 0.154136i
\(605\) 1.68625 + 19.2739i 0.0685557 + 0.783595i
\(606\) 0 0
\(607\) −14.9621 + 21.3681i −0.607293 + 0.867304i −0.998597 0.0529575i \(-0.983135\pi\)
0.391304 + 0.920261i \(0.372024\pi\)
\(608\) −5.34508 + 0.942482i −0.216772 + 0.0382227i
\(609\) 0 0
\(610\) 15.5420 + 7.24736i 0.629278 + 0.293437i
\(611\) 26.4013 + 12.3111i 1.06808 + 0.498055i
\(612\) 0 0
\(613\) −15.2226 + 2.68416i −0.614837 + 0.108412i −0.472389 0.881390i \(-0.656608\pi\)
−0.142447 + 0.989802i \(0.545497\pi\)
\(614\) −15.7279 + 22.4618i −0.634727 + 0.906485i
\(615\) 0 0
\(616\) 0.307278 + 3.51220i 0.0123806 + 0.141511i
\(617\) −22.9292 8.34555i −0.923096 0.335979i −0.163626 0.986522i \(-0.552319\pi\)
−0.759469 + 0.650543i \(0.774541\pi\)
\(618\) 0 0
\(619\) 9.94091 + 5.73939i 0.399559 + 0.230685i 0.686294 0.727325i \(-0.259236\pi\)
−0.286735 + 0.958010i \(0.592570\pi\)
\(620\) −2.23972 + 1.87935i −0.0899493 + 0.0754765i
\(621\) 0 0
\(622\) −4.16358 0.734152i −0.166944 0.0294368i
\(623\) 24.2708 24.2708i 0.972388 0.972388i
\(624\) 0 0
\(625\) 11.3801 + 9.54905i 0.455205 + 0.381962i
\(626\) 6.69341 + 18.3900i 0.267522 + 0.735012i
\(627\) 0 0
\(628\) 11.5729i 0.461808i
\(629\) −1.42587 10.2689i −0.0568530 0.409446i
\(630\) 0 0
\(631\) 9.54890 + 20.4777i 0.380136 + 0.815204i 0.999546 + 0.0301361i \(0.00959408\pi\)
−0.619410 + 0.785068i \(0.712628\pi\)
\(632\) 5.58064 2.03119i 0.221986 0.0807963i
\(633\) 0 0
\(634\) 7.59576 + 10.8479i 0.301666 + 0.430824i
\(635\) −4.52333 4.52333i −0.179503 0.179503i
\(636\) 0 0
\(637\) 70.6235 + 18.9235i 2.79821 + 0.749777i
\(638\) 4.64647 + 5.53744i 0.183955 + 0.219229i
\(639\) 0 0
\(640\) −1.60881 + 0.928845i −0.0635937 + 0.0367158i
\(641\) −5.01750 + 13.7855i −0.198179 + 0.544493i −0.998481 0.0551051i \(-0.982451\pi\)
0.800301 + 0.599598i \(0.204673\pi\)
\(642\) 0 0
\(643\) −8.32101 + 2.22961i −0.328149 + 0.0879272i −0.419132 0.907925i \(-0.637666\pi\)
0.0909834 + 0.995852i \(0.470999\pi\)
\(644\) 15.2317 + 10.6654i 0.600214 + 0.420274i
\(645\) 0 0
\(646\) 0.806246 9.21543i 0.0317213 0.362576i
\(647\) 1.17711 2.52433i 0.0462771 0.0992416i −0.881810 0.471605i \(-0.843675\pi\)
0.928087 + 0.372364i \(0.121453\pi\)
\(648\) 0 0
\(649\) −5.57442 0.487698i −0.218815 0.0191438i
\(650\) 1.38091 + 7.83155i 0.0541639 + 0.307179i
\(651\) 0 0
\(652\) 5.14923 + 19.2172i 0.201659 + 0.752603i
\(653\) 22.4490 1.96403i 0.878497 0.0768585i 0.361023 0.932557i \(-0.382428\pi\)
0.517475 + 0.855699i \(0.326872\pi\)
\(654\) 0 0
\(655\) −0.512115 0.887010i −0.0200100 0.0346584i
\(656\) −0.750970 + 1.30072i −0.0293204 + 0.0507845i
\(657\) 0 0
\(658\) 6.76849 25.2603i 0.263863 0.984751i
\(659\) −2.76539 + 15.6833i −0.107724 + 0.610934i 0.882373 + 0.470551i \(0.155945\pi\)
−0.990097 + 0.140384i \(0.955166\pi\)
\(660\) 0 0
\(661\) −5.25363 + 3.67863i −0.204342 + 0.143082i −0.671269 0.741214i \(-0.734250\pi\)
0.466926 + 0.884296i \(0.345361\pi\)
\(662\) −3.00449 + 3.58062i −0.116773 + 0.139165i
\(663\) 0 0
\(664\) 9.66672 4.50767i 0.375142 0.174931i
\(665\) −46.4697 −1.80202
\(666\) 0 0
\(667\) 38.1245 1.47619
\(668\) 15.4398 7.19968i 0.597383 0.278564i
\(669\) 0 0
\(670\) 8.13882 9.69947i 0.314430 0.374723i
\(671\) −5.78448 + 4.05034i −0.223308 + 0.156362i
\(672\) 0 0
\(673\) −2.21557 + 12.5651i −0.0854040 + 0.484350i 0.911865 + 0.410491i \(0.134643\pi\)
−0.997269 + 0.0738591i \(0.976468\pi\)
\(674\) 4.81039 17.9526i 0.185289 0.691509i
\(675\) 0 0
\(676\) 6.67849 11.5675i 0.256865 0.444903i
\(677\) −14.5240 25.1563i −0.558203 0.966836i −0.997647 0.0685661i \(-0.978158\pi\)
0.439443 0.898270i \(-0.355176\pi\)
\(678\) 0 0
\(679\) −65.6683 + 5.74523i −2.52012 + 0.220482i
\(680\) −0.819479 3.05834i −0.0314256 0.117282i
\(681\) 0 0
\(682\) −0.209064 1.18566i −0.00800546 0.0454012i
\(683\) −43.6471 3.81863i −1.67011 0.146116i −0.787530 0.616277i \(-0.788640\pi\)
−0.882581 + 0.470161i \(0.844196\pi\)
\(684\) 0 0
\(685\) −9.89178 + 21.2130i −0.377946 + 0.810507i
\(686\) 2.90886 33.2484i 0.111061 1.26943i
\(687\) 0 0
\(688\) −6.26509 4.38686i −0.238854 0.167248i
\(689\) 44.2949 11.8688i 1.68750 0.452165i
\(690\) 0 0
\(691\) 7.28398 20.0126i 0.277096 0.761314i −0.720593 0.693359i \(-0.756130\pi\)
0.997688 0.0679555i \(-0.0216476\pi\)
\(692\) 17.8875 10.3273i 0.679980 0.392587i
\(693\) 0 0
\(694\) −15.0014 17.8779i −0.569444 0.678636i
\(695\) −14.8543 3.98021i −0.563457 0.150978i
\(696\) 0 0
\(697\) −1.81011 1.81011i −0.0685629 0.0685629i
\(698\) −10.0647 14.3738i −0.380953 0.544058i
\(699\) 0 0
\(700\) 6.70853 2.44171i 0.253559 0.0922878i
\(701\) −18.9227 40.5800i −0.714702 1.53268i −0.841204 0.540718i \(-0.818153\pi\)
0.126502 0.991966i \(-0.459625\pi\)
\(702\) 0 0
\(703\) 32.2816 + 6.91753i 1.21752 + 0.260900i
\(704\) 0.764965i 0.0288307i
\(705\) 0 0
\(706\) 8.22107 + 22.5872i 0.309404 + 0.850081i
\(707\) −22.5637 18.9332i −0.848595 0.712056i
\(708\) 0 0
\(709\) 15.5236 15.5236i 0.583000 0.583000i −0.352727 0.935726i \(-0.614745\pi\)
0.935726 + 0.352727i \(0.114745\pi\)
\(710\) −14.9742 2.64036i −0.561972 0.0990908i
\(711\) 0 0
\(712\) −5.70505 + 4.78710i −0.213806 + 0.179404i
\(713\) −5.49906 3.17488i −0.205941 0.118900i
\(714\) 0 0
\(715\) 6.85565 + 2.49525i 0.256387 + 0.0933171i
\(716\) −1.51254 17.2885i −0.0565264 0.646100i
\(717\) 0 0
\(718\) −6.30980 + 9.01133i −0.235480 + 0.336300i
\(719\) 13.8634 2.44448i 0.517016 0.0911638i 0.0909490 0.995856i \(-0.471010\pi\)
0.426067 + 0.904692i \(0.359899\pi\)
\(720\) 0 0
\(721\) 42.1903 + 19.6736i 1.57125 + 0.732685i
\(722\) 9.47834 + 4.41982i 0.352747 + 0.164489i
\(723\) 0 0
\(724\) −2.74098 + 0.483309i −0.101868 + 0.0179620i
\(725\) 8.39564 11.9902i 0.311806 0.445305i
\(726\) 0 0
\(727\) −0.0777661 0.888870i −0.00288418 0.0329664i 0.994616 0.103627i \(-0.0330448\pi\)
−0.997500 + 0.0706606i \(0.977489\pi\)
\(728\) −22.2345 8.09269i −0.824065 0.299935i
\(729\) 0 0
\(730\) 3.81231 + 2.20104i 0.141100 + 0.0814641i
\(731\) 9.98585 8.37913i 0.369340 0.309913i
\(732\) 0 0
\(733\) 26.1844 + 4.61701i 0.967142 + 0.170533i 0.634843 0.772641i \(-0.281065\pi\)
0.332299 + 0.943174i \(0.392176\pi\)
\(734\) 11.3391 11.3391i 0.418535 0.418535i
\(735\) 0 0
\(736\) −3.09061 2.59333i −0.113922 0.0955915i
\(737\) 1.78326 + 4.89946i 0.0656871 + 0.180474i
\(738\) 0 0
\(739\) 46.7086i 1.71820i −0.511805 0.859102i \(-0.671023\pi\)
0.511805 0.859102i \(-0.328977\pi\)
\(740\) 11.1925 1.55412i 0.411445 0.0571305i
\(741\) 0 0
\(742\) −17.3982 37.3105i −0.638707 1.36971i
\(743\) −6.10600 + 2.22240i −0.224007 + 0.0815321i −0.451586 0.892228i \(-0.649141\pi\)
0.227578 + 0.973760i \(0.426919\pi\)
\(744\) 0 0
\(745\) −7.77644 11.1059i −0.284907 0.406889i
\(746\) 6.71830 + 6.71830i 0.245975 + 0.245975i
\(747\) 0 0
\(748\) 1.25937 + 0.337447i 0.0460472 + 0.0123383i
\(749\) 61.1199 + 72.8398i 2.23327 + 2.66151i
\(750\) 0 0
\(751\) −41.9214 + 24.2034i −1.52974 + 0.883193i −0.530363 + 0.847771i \(0.677944\pi\)
−0.999372 + 0.0354225i \(0.988722\pi\)
\(752\) −1.94068 + 5.33197i −0.0707693 + 0.194437i
\(753\) 0 0
\(754\) −46.8603 + 12.5562i −1.70655 + 0.457269i
\(755\) −16.8542 11.8015i −0.613388 0.429499i
\(756\) 0 0
\(757\) 2.70655 30.9360i 0.0983711 1.12439i −0.773215 0.634144i \(-0.781352\pi\)
0.871586 0.490243i \(-0.163092\pi\)
\(758\) 8.18516 17.5531i 0.297298 0.637558i
\(759\) 0 0
\(760\) 10.0443 + 0.878764i 0.364346 + 0.0318761i
\(761\) 8.10617 + 45.9724i 0.293848 + 1.66650i 0.671846 + 0.740691i \(0.265502\pi\)
−0.377998 + 0.925807i \(0.623387\pi\)
\(762\) 0 0
\(763\) 14.0368 + 52.3861i 0.508167 + 1.89650i
\(764\) −9.72136 + 0.850509i −0.351707 + 0.0307703i
\(765\) 0 0
\(766\) −12.9158 22.3708i −0.466667 0.808291i
\(767\) 18.7772 32.5231i 0.678007 1.17434i
\(768\) 0 0
\(769\) −7.15193 + 26.6914i −0.257905 + 0.962515i 0.708546 + 0.705665i \(0.249351\pi\)
−0.966451 + 0.256850i \(0.917315\pi\)
\(770\) 1.13731 6.45000i 0.0409857 0.232442i
\(771\) 0 0
\(772\) −2.91656 + 2.04220i −0.104969 + 0.0735003i
\(773\) −27.2484 + 32.4734i −0.980057 + 1.16799i 0.00573006 + 0.999984i \(0.498176\pi\)
−0.985787 + 0.168002i \(0.946268\pi\)
\(774\) 0 0
\(775\) −2.20948 + 1.03030i −0.0793670 + 0.0370094i
\(776\) 14.3027 0.513437
\(777\) 0 0
\(778\) 20.1134 0.721101
\(779\) 7.38807 3.44511i 0.264705 0.123434i
\(780\) 0 0
\(781\) 4.02465 4.79639i 0.144013 0.171628i
\(782\) 5.63279 3.94412i 0.201428 0.141042i
\(783\) 0 0
\(784\) −2.47302 + 14.0252i −0.0883222 + 0.500900i
\(785\) −5.56431 + 20.7663i −0.198599 + 0.741180i
\(786\) 0 0
\(787\) 7.76945 13.4571i 0.276951 0.479693i −0.693674 0.720289i \(-0.744009\pi\)
0.970626 + 0.240595i \(0.0773427\pi\)
\(788\) 0.193625 + 0.335368i 0.00689760 + 0.0119470i
\(789\) 0 0
\(790\) −10.9905 + 0.961541i −0.391023 + 0.0342101i
\(791\) −22.1162 82.5386i −0.786360 2.93473i
\(792\) 0 0
\(793\) −8.22956 46.6722i −0.292240 1.65738i
\(794\) −33.1869 2.90348i −1.17776 0.103040i
\(795\) 0 0
\(796\) −1.91279 + 4.10199i −0.0677970 + 0.145391i
\(797\) 2.86500 32.7471i 0.101484 1.15996i −0.759213 0.650843i \(-0.774416\pi\)
0.860696 0.509119i \(-0.170029\pi\)
\(798\) 0 0
\(799\) −7.92200 5.54705i −0.280260 0.196240i
\(800\) −1.49621 + 0.400908i −0.0528990 + 0.0141742i
\(801\) 0 0
\(802\) 8.70975 23.9298i 0.307552 0.844992i
\(803\) −1.56984 + 0.906350i −0.0553986 + 0.0319844i
\(804\) 0 0
\(805\) −22.2037 26.4613i −0.782577 0.932639i
\(806\) 7.80474 + 2.09127i 0.274910 + 0.0736620i
\(807\) 0 0
\(808\) 4.51906 + 4.51906i 0.158980 + 0.158980i
\(809\) −6.26031 8.94065i −0.220101 0.314337i 0.693883 0.720088i \(-0.255899\pi\)
−0.913983 + 0.405752i \(0.867010\pi\)
\(810\) 0 0
\(811\) −20.0302 + 7.29041i −0.703356 + 0.256001i −0.668843 0.743403i \(-0.733210\pi\)
−0.0345131 + 0.999404i \(0.510988\pi\)
\(812\) 18.4058 + 39.4714i 0.645918 + 1.38518i
\(813\) 0 0
\(814\) −1.75022 + 4.31139i −0.0613452 + 0.151114i
\(815\) 36.9589i 1.29461i
\(816\) 0 0
\(817\) 14.1977 + 39.0078i 0.496714 + 1.36471i
\(818\) 13.4783 + 11.3097i 0.471259 + 0.395433i
\(819\) 0 0
\(820\) 1.97292 1.97292i 0.0688975 0.0688975i
\(821\) 8.08927 + 1.42636i 0.282318 + 0.0497802i 0.313014 0.949749i \(-0.398661\pi\)
−0.0306963 + 0.999529i \(0.509772\pi\)
\(822\) 0 0
\(823\) −35.0370 + 29.3995i −1.22131 + 1.02480i −0.222558 + 0.974919i \(0.571441\pi\)
−0.998755 + 0.0498838i \(0.984115\pi\)
\(824\) −8.74730 5.05025i −0.304726 0.175934i
\(825\) 0 0
\(826\) −31.6806 11.5308i −1.10231 0.401207i
\(827\) 4.49919 + 51.4260i 0.156452 + 1.78826i 0.517475 + 0.855698i \(0.326872\pi\)
−0.361023 + 0.932557i \(0.617572\pi\)
\(828\) 0 0
\(829\) −20.3619 + 29.0798i −0.707197 + 1.00998i 0.291377 + 0.956608i \(0.405886\pi\)
−0.998575 + 0.0533740i \(0.983002\pi\)
\(830\) −19.5132 + 3.44070i −0.677312 + 0.119428i
\(831\) 0 0
\(832\) 4.65290 + 2.16968i 0.161310 + 0.0752202i
\(833\) −21.9989 10.2583i −0.762218 0.355428i
\(834\) 0 0
\(835\) −31.1666 + 5.49552i −1.07857 + 0.190180i
\(836\) −2.38142 + 3.40102i −0.0823631 + 0.117627i
\(837\) 0 0
\(838\) 0.128438 + 1.46805i 0.00443681 + 0.0507130i
\(839\) 10.9056 + 3.96931i 0.376503 + 0.137036i 0.523338 0.852125i \(-0.324686\pi\)
−0.146835 + 0.989161i \(0.546909\pi\)
\(840\) 0 0
\(841\) 52.2171 + 30.1475i 1.80059 + 1.03957i
\(842\) −8.71468 + 7.31249i −0.300328 + 0.252005i
\(843\) 0 0
\(844\) −17.3959 3.06737i −0.598792 0.105583i
\(845\) −17.5455 + 17.5455i −0.603585 + 0.603585i
\(846\) 0 0
\(847\) −36.7705 30.8541i −1.26345 1.06016i
\(848\) 3.05502 + 8.39359i 0.104910 + 0.288237i
\(849\) 0 0
\(850\) 2.64008i 0.0905539i
\(851\) 11.4854 + 21.6874i 0.393715 + 0.743436i
\(852\) 0 0
\(853\) 4.66876 + 10.0122i 0.159855 + 0.342811i 0.969879 0.243586i \(-0.0783238\pi\)
−0.810024 + 0.586397i \(0.800546\pi\)
\(854\) −39.9795 + 14.5514i −1.36807 + 0.497937i
\(855\) 0 0
\(856\) −11.8335 16.9000i −0.404461 0.577630i
\(857\) −39.5995 39.5995i −1.35269 1.35269i −0.882635 0.470059i \(-0.844232\pi\)
−0.470059 0.882635i \(-0.655768\pi\)
\(858\) 0 0
\(859\) 17.8671 + 4.78747i 0.609617 + 0.163346i 0.550403 0.834899i \(-0.314474\pi\)
0.0592139 + 0.998245i \(0.481141\pi\)
\(860\) 9.13279 + 10.8840i 0.311426 + 0.371143i
\(861\) 0 0
\(862\) 32.4365 18.7272i 1.10479 0.637852i
\(863\) −15.2588 + 41.9233i −0.519417 + 1.42709i 0.351747 + 0.936095i \(0.385588\pi\)
−0.871164 + 0.490992i \(0.836634\pi\)
\(864\) 0 0
\(865\) −37.0626 + 9.93089i −1.26017 + 0.337660i
\(866\) 22.8720 + 16.0152i 0.777224 + 0.544218i
\(867\) 0 0
\(868\) 0.632202 7.22611i 0.0214583 0.245270i
\(869\) 1.91994 4.11733i 0.0651296 0.139671i
\(870\) 0 0
\(871\) −34.8588 3.04975i −1.18115 0.103337i
\(872\) −2.04338 11.5886i −0.0691976 0.392439i
\(873\) 0 0
\(874\) 5.66748 + 21.1513i 0.191705 + 0.715455i
\(875\) −55.8579 + 4.88694i −1.88834 + 0.165209i
\(876\) 0 0
\(877\) −20.9170 36.2294i −0.706319 1.22338i −0.966214 0.257743i \(-0.917021\pi\)
0.259895 0.965637i \(-0.416312\pi\)
\(878\) 4.34368 7.52347i 0.146592 0.253905i
\(879\) 0 0
\(880\) −0.367799 + 1.37265i −0.0123985 + 0.0462719i
\(881\) −2.32008 + 13.1578i −0.0781656 + 0.443299i 0.920458 + 0.390842i \(0.127816\pi\)
−0.998623 + 0.0524567i \(0.983295\pi\)
\(882\) 0 0
\(883\) 19.1640 13.4188i 0.644920 0.451578i −0.204806 0.978803i \(-0.565656\pi\)
0.849726 + 0.527225i \(0.176767\pi\)
\(884\) −5.62450 + 6.70301i −0.189172 + 0.225447i
\(885\) 0 0
\(886\) 34.4041 16.0429i 1.15583 0.538972i
\(887\) 45.4923 1.52748 0.763742 0.645522i \(-0.223360\pi\)
0.763742 + 0.645522i \(0.223360\pi\)
\(888\) 0 0
\(889\) 15.8706 0.532283
\(890\) 12.5387 5.84691i 0.420300 0.195989i
\(891\) 0 0
\(892\) 5.78673 6.89635i 0.193754 0.230907i
\(893\) 25.2272 17.6643i 0.844197 0.591113i
\(894\) 0 0
\(895\) −5.59829 + 31.7495i −0.187130 + 1.06127i
\(896\) 1.19286 4.45181i 0.0398507 0.148725i
\(897\) 0 0
\(898\) −8.52042 + 14.7578i −0.284330 + 0.492474i
\(899\) −7.43619 12.8799i −0.248011 0.429567i
\(900\) 0 0
\(901\) −15.1661 + 1.32686i −0.505257 + 0.0442042i
\(902\) 0.297365 + 1.10978i 0.00990118 + 0.0369517i
\(903\) 0 0
\(904\) 3.21951 + 18.2588i 0.107079 + 0.607278i
\(905\) 5.15077 + 0.450634i 0.171217 + 0.0149796i
\(906\) 0 0
\(907\) 18.2216 39.0764i 0.605039 1.29751i −0.330340 0.943862i \(-0.607163\pi\)
0.935379 0.353648i \(-0.115059\pi\)
\(908\) 1.41467 16.1697i 0.0469474 0.536611i
\(909\) 0 0
\(910\) 36.0063 + 25.2119i 1.19360 + 0.835766i
\(911\) −3.38314 + 0.906510i −0.112088 + 0.0300340i −0.314427 0.949282i \(-0.601812\pi\)
0.202339 + 0.979316i \(0.435146\pi\)
\(912\) 0 0
\(913\) 2.79059 7.66709i 0.0923552 0.253744i
\(914\) −6.12340 + 3.53534i −0.202544 + 0.116939i
\(915\) 0 0
\(916\) −3.89914 4.64682i −0.128831 0.153535i
\(917\) 2.45449 + 0.657680i 0.0810545 + 0.0217185i
\(918\) 0 0
\(919\) −13.8897 13.8897i −0.458180 0.458180i 0.439878 0.898058i \(-0.355022\pi\)
−0.898058 + 0.439878i \(0.855022\pi\)
\(920\) 4.29888 + 6.13944i 0.141730 + 0.202411i
\(921\) 0 0
\(922\) 17.9789 6.54378i 0.592103 0.215508i
\(923\) 17.7589 + 38.0840i 0.584540 + 1.25355i
\(924\) 0 0
\(925\) 9.34999 + 1.16375i 0.307426 + 0.0382638i
\(926\) 14.0749i 0.462531i
\(927\) 0 0
\(928\) −3.23196 8.87973i −0.106094 0.291491i
\(929\) 1.52848 + 1.28255i 0.0501479 + 0.0420791i 0.667517 0.744594i \(-0.267357\pi\)
−0.617369 + 0.786674i \(0.711802\pi\)
\(930\) 0 0
\(931\) 54.6570 54.6570i 1.79131 1.79131i
\(932\) 3.99039 + 0.703613i 0.130710 + 0.0230476i
\(933\) 0 0
\(934\) −2.82854 + 2.37342i −0.0925526 + 0.0776608i
\(935\) −2.09756 1.21102i −0.0685974 0.0396047i
\(936\) 0 0
\(937\) −31.1706 11.3452i −1.01830 0.370630i −0.221684 0.975119i \(-0.571155\pi\)
−0.796614 + 0.604488i \(0.793378\pi\)
\(938\) 2.73785 + 31.2938i 0.0893941 + 1.02178i
\(939\) 0 0
\(940\) 6.04598 8.63455i 0.197198 0.281628i
\(941\) 2.39309 0.421966i 0.0780125 0.0137557i −0.134506 0.990913i \(-0.542945\pi\)
0.212518 + 0.977157i \(0.431834\pi\)
\(942\) 0 0
\(943\) 5.49185 + 2.56089i 0.178839 + 0.0833942i
\(944\) 6.62963 + 3.09145i 0.215776 + 0.100618i
\(945\) 0 0
\(946\) −5.76177 + 1.01596i −0.187331 + 0.0330316i
\(947\) −17.9402 + 25.6213i −0.582979 + 0.832581i −0.996977 0.0776973i \(-0.975243\pi\)
0.413998 + 0.910278i \(0.364132\pi\)
\(948\) 0 0
\(949\) −1.06030 12.1193i −0.0344188 0.393408i
\(950\) 7.90019 + 2.87543i 0.256316 + 0.0932914i
\(951\) 0 0
\(952\) 6.80287 + 3.92764i 0.220482 + 0.127296i
\(953\) −10.4418 + 8.76171i −0.338243 + 0.283820i −0.796049 0.605233i \(-0.793080\pi\)
0.457805 + 0.889052i \(0.348636\pi\)
\(954\) 0 0
\(955\) 17.8529 + 3.14794i 0.577705 + 0.101865i
\(956\) −2.29682 + 2.29682i −0.0742846 + 0.0742846i
\(957\) 0 0
\(958\) −27.4021 22.9931i −0.885323 0.742874i
\(959\) −19.8609 54.5673i −0.641341 1.76207i
\(960\) 0 0
\(961\) 28.5230i 0.920095i
\(962\) −21.2598 22.8742i −0.685445 0.737493i
\(963\) 0 0
\(964\) 11.9282 + 25.5802i 0.384182 + 0.823882i
\(965\) 6.21535 2.26220i 0.200079 0.0728229i
\(966\) 0 0
\(967\) −10.0857 14.4039i −0.324336 0.463199i 0.623562 0.781774i \(-0.285685\pi\)
−0.947898 + 0.318574i \(0.896796\pi\)
\(968\) 7.36440 + 7.36440i 0.236701 + 0.236701i
\(969\) 0 0
\(970\) −25.6646 6.87682i −0.824042 0.220801i
\(971\) 36.6117 + 43.6321i 1.17492 + 1.40022i 0.898380 + 0.439219i \(0.144745\pi\)
0.276544 + 0.961001i \(0.410811\pi\)
\(972\) 0 0
\(973\) 33.0416 19.0765i 1.05926 0.611566i
\(974\) −13.1170 + 36.0387i −0.420296 + 1.15475i
\(975\) 0 0
\(976\) 8.91666 2.38921i 0.285415 0.0764768i
\(977\) −35.4126 24.7961i −1.13295 0.793299i −0.152157 0.988356i \(-0.548622\pi\)
−0.980792 + 0.195057i \(0.937511\pi\)
\(978\) 0 0
\(979\) −0.496527 + 5.67533i −0.0158691 + 0.181384i
\(980\) 11.1810 23.9777i 0.357163 0.765938i
\(981\) 0 0
\(982\) −27.2330 2.38258i −0.869039 0.0760310i
\(983\) 8.37067 + 47.4725i 0.266983 + 1.51414i 0.763328 + 0.646011i \(0.223564\pi\)
−0.496345 + 0.868125i \(0.665325\pi\)
\(984\) 0 0
\(985\) −0.186192 0.694877i −0.00593256 0.0221406i
\(986\) 16.0445 1.40371i 0.510961 0.0447033i
\(987\) 0 0
\(988\) −13.9322 24.1313i −0.443244 0.767720i
\(989\) −15.4285 + 26.7230i −0.490598 + 0.849740i
\(990\) 0 0
\(991\) 3.01622 11.2567i 0.0958135 0.357581i −0.901328 0.433137i \(-0.857407\pi\)
0.997142 + 0.0755563i \(0.0240732\pi\)
\(992\) −0.273298 + 1.54995i −0.00867723 + 0.0492110i
\(993\) 0 0
\(994\) 30.9013 21.6373i 0.980130 0.686295i
\(995\) 5.40455 6.44089i 0.171336 0.204190i
\(996\) 0 0
\(997\) −27.2229 + 12.6942i −0.862157 + 0.402031i −0.802830 0.596208i \(-0.796673\pi\)
−0.0593274 + 0.998239i \(0.518896\pi\)
\(998\) −12.0685 −0.382020
\(999\) 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 666.2.bs.b.89.2 96
3.2 odd 2 inner 666.2.bs.b.89.7 yes 96
37.5 odd 36 inner 666.2.bs.b.449.7 yes 96
111.5 even 36 inner 666.2.bs.b.449.2 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
666.2.bs.b.89.2 96 1.1 even 1 trivial
666.2.bs.b.89.7 yes 96 3.2 odd 2 inner
666.2.bs.b.449.2 yes 96 111.5 even 36 inner
666.2.bs.b.449.7 yes 96 37.5 odd 36 inner