Properties

Label 666.2.bs.b.557.1
Level $666$
Weight $2$
Character 666.557
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 557.1
Character \(\chi\) \(=\) 666.557
Dual form 666.2.bs.b.611.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0871557 + 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-3.66235 - 1.70778i) q^{5} +(-0.294498 + 0.107188i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\) \(q+(-0.0871557 + 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-3.66235 - 1.70778i) q^{5} +(-0.294498 + 0.107188i) q^{7} +(0.258819 - 0.965926i) q^{8} +(2.02048 - 3.49957i) q^{10} +(0.875768 + 1.51687i) q^{11} +(1.84986 + 2.64187i) q^{13} +(-0.0811133 - 0.302719i) q^{14} +(0.939693 + 0.342020i) q^{16} +(0.590940 - 0.843949i) q^{17} +(5.81418 - 0.508675i) q^{19} +(3.31015 + 2.31779i) q^{20} +(-1.58743 + 0.740231i) q^{22} +(2.42008 - 0.648460i) q^{23} +(7.28233 + 8.67874i) q^{25} +(-2.79304 + 1.61256i) q^{26} +(0.308637 - 0.0544210i) q^{28} +(2.34207 + 0.627556i) q^{29} +(0.925955 + 0.925955i) q^{31} +(-0.422618 + 0.906308i) q^{32} +(0.789234 + 0.662246i) q^{34} +(1.26161 + 0.110376i) q^{35} +(5.99877 + 1.00737i) q^{37} +5.83639i q^{38} +(-2.59747 + 3.09555i) q^{40} +(0.370837 - 2.10312i) q^{41} +(4.14796 - 4.14796i) q^{43} +(-0.599060 - 1.64590i) q^{44} +(0.435068 + 2.46739i) q^{46} +(3.98978 + 2.30350i) q^{47} +(-5.28707 + 4.43638i) q^{49} +(-9.28041 + 6.49821i) q^{50} +(-1.36300 - 2.92296i) q^{52} +(-2.72394 + 7.48397i) q^{53} +(-0.616877 - 7.05093i) q^{55} +(0.0273144 + 0.312205i) q^{56} +(-0.829292 + 2.27846i) q^{58} +(-0.432400 - 0.927286i) q^{59} +(0.131194 - 0.0918629i) q^{61} +(-1.00313 + 0.841729i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-2.26309 - 12.8346i) q^{65} +(-5.46909 - 15.0262i) q^{67} +(-0.728512 + 0.728512i) q^{68} +(-0.219912 + 1.24719i) q^{70} +(-8.74807 + 10.4255i) q^{71} -11.4937i q^{73} +(-1.52636 + 5.88814i) q^{74} +(-5.81418 - 0.508675i) q^{76} +(-0.420503 - 0.352844i) q^{77} +(-0.448415 + 0.961629i) q^{79} +(-2.85738 - 2.85738i) q^{80} +(2.06280 + 0.552725i) q^{82} +(8.03449 - 1.41670i) q^{83} +(-3.60550 + 2.08164i) q^{85} +(3.77066 + 4.49370i) q^{86} +(1.69185 - 0.453331i) q^{88} +(12.5101 - 5.83354i) q^{89} +(-0.827957 - 0.579742i) q^{91} +(-2.49592 + 0.218365i) q^{92} +(-2.64247 + 3.77383i) q^{94} +(-22.1622 - 8.06640i) q^{95} +(2.88852 + 10.7801i) q^{97} +(-3.95870 - 5.65361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0871557 + 0.996195i −0.0616284 + 0.704416i
\(3\) 0 0
\(4\) −0.984808 0.173648i −0.492404 0.0868241i
\(5\) −3.66235 1.70778i −1.63785 0.763742i −0.637871 0.770143i \(-0.720185\pi\)
−0.999980 + 0.00640061i \(0.997963\pi\)
\(6\) 0 0
\(7\) −0.294498 + 0.107188i −0.111310 + 0.0405134i −0.397075 0.917786i \(-0.629975\pi\)
0.285765 + 0.958300i \(0.407752\pi\)
\(8\) 0.258819 0.965926i 0.0915064 0.341506i
\(9\) 0 0
\(10\) 2.02048 3.49957i 0.638931 1.10666i
\(11\) 0.875768 + 1.51687i 0.264054 + 0.457355i 0.967315 0.253577i \(-0.0816070\pi\)
−0.703261 + 0.710931i \(0.748274\pi\)
\(12\) 0 0
\(13\) 1.84986 + 2.64187i 0.513058 + 0.732723i 0.989188 0.146652i \(-0.0468496\pi\)
−0.476130 + 0.879375i \(0.657961\pi\)
\(14\) −0.0811133 0.302719i −0.0216784 0.0809051i
\(15\) 0 0
\(16\) 0.939693 + 0.342020i 0.234923 + 0.0855050i
\(17\) 0.590940 0.843949i 0.143324 0.204688i −0.741072 0.671426i \(-0.765682\pi\)
0.884395 + 0.466738i \(0.154571\pi\)
\(18\) 0 0
\(19\) 5.81418 0.508675i 1.33386 0.116698i 0.602190 0.798353i \(-0.294295\pi\)
0.731674 + 0.681655i \(0.238739\pi\)
\(20\) 3.31015 + 2.31779i 0.740173 + 0.518275i
\(21\) 0 0
\(22\) −1.58743 + 0.740231i −0.338441 + 0.157818i
\(23\) 2.42008 0.648460i 0.504623 0.135213i 0.00247802 0.999997i \(-0.499211\pi\)
0.502144 + 0.864784i \(0.332545\pi\)
\(24\) 0 0
\(25\) 7.28233 + 8.67874i 1.45647 + 1.73575i
\(26\) −2.79304 + 1.61256i −0.547761 + 0.316250i
\(27\) 0 0
\(28\) 0.308637 0.0544210i 0.0583268 0.0102846i
\(29\) 2.34207 + 0.627556i 0.434911 + 0.116534i 0.469631 0.882863i \(-0.344387\pi\)
−0.0347193 + 0.999397i \(0.511054\pi\)
\(30\) 0 0
\(31\) 0.925955 + 0.925955i 0.166306 + 0.166306i 0.785354 0.619047i \(-0.212481\pi\)
−0.619047 + 0.785354i \(0.712481\pi\)
\(32\) −0.422618 + 0.906308i −0.0747091 + 0.160214i
\(33\) 0 0
\(34\) 0.789234 + 0.662246i 0.135352 + 0.113574i
\(35\) 1.26161 + 0.110376i 0.213250 + 0.0186570i
\(36\) 0 0
\(37\) 5.99877 + 1.00737i 0.986191 + 0.165610i
\(38\) 5.83639i 0.946787i
\(39\) 0 0
\(40\) −2.59747 + 3.09555i −0.410697 + 0.489449i
\(41\) 0.370837 2.10312i 0.0579150 0.328453i −0.942061 0.335443i \(-0.891114\pi\)
0.999976 + 0.00699040i \(0.00222513\pi\)
\(42\) 0 0
\(43\) 4.14796 4.14796i 0.632559 0.632559i −0.316151 0.948709i \(-0.602390\pi\)
0.948709 + 0.316151i \(0.102390\pi\)
\(44\) −0.599060 1.64590i −0.0903117 0.248129i
\(45\) 0 0
\(46\) 0.435068 + 2.46739i 0.0641473 + 0.363797i
\(47\) 3.98978 + 2.30350i 0.581969 + 0.336000i 0.761916 0.647676i \(-0.224259\pi\)
−0.179946 + 0.983676i \(0.557592\pi\)
\(48\) 0 0
\(49\) −5.28707 + 4.43638i −0.755296 + 0.633769i
\(50\) −9.28041 + 6.49821i −1.31245 + 0.918986i
\(51\) 0 0
\(52\) −1.36300 2.92296i −0.189014 0.405342i
\(53\) −2.72394 + 7.48397i −0.374162 + 1.02800i 0.599573 + 0.800320i \(0.295337\pi\)
−0.973735 + 0.227683i \(0.926885\pi\)
\(54\) 0 0
\(55\) −0.616877 7.05093i −0.0831797 0.950748i
\(56\) 0.0273144 + 0.312205i 0.00365004 + 0.0417202i
\(57\) 0 0
\(58\) −0.829292 + 2.27846i −0.108891 + 0.299177i
\(59\) −0.432400 0.927286i −0.0562937 0.120722i 0.876149 0.482041i \(-0.160104\pi\)
−0.932442 + 0.361319i \(0.882327\pi\)
\(60\) 0 0
\(61\) 0.131194 0.0918629i 0.0167976 0.0117618i −0.565147 0.824990i \(-0.691181\pi\)
0.581945 + 0.813228i \(0.302292\pi\)
\(62\) −1.00313 + 0.841729i −0.127398 + 0.106900i
\(63\) 0 0
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) −2.26309 12.8346i −0.280701 1.59194i
\(66\) 0 0
\(67\) −5.46909 15.0262i −0.668156 1.83574i −0.535406 0.844595i \(-0.679841\pi\)
−0.132750 0.991150i \(-0.542381\pi\)
\(68\) −0.728512 + 0.728512i −0.0883451 + 0.0883451i
\(69\) 0 0
\(70\) −0.219912 + 1.24719i −0.0262846 + 0.149067i
\(71\) −8.74807 + 10.4255i −1.03821 + 1.23729i −0.0673223 + 0.997731i \(0.521446\pi\)
−0.970883 + 0.239554i \(0.922999\pi\)
\(72\) 0 0
\(73\) 11.4937i 1.34524i −0.739987 0.672621i \(-0.765169\pi\)
0.739987 0.672621i \(-0.234831\pi\)
\(74\) −1.52636 + 5.88814i −0.177436 + 0.684483i
\(75\) 0 0
\(76\) −5.81418 0.508675i −0.666932 0.0583490i
\(77\) −0.420503 0.352844i −0.0479207 0.0402103i
\(78\) 0 0
\(79\) −0.448415 + 0.961629i −0.0504506 + 0.108192i −0.929917 0.367769i \(-0.880122\pi\)
0.879467 + 0.475961i \(0.157900\pi\)
\(80\) −2.85738 2.85738i −0.319465 0.319465i
\(81\) 0 0
\(82\) 2.06280 + 0.552725i 0.227798 + 0.0610383i
\(83\) 8.03449 1.41670i 0.881900 0.155503i 0.285681 0.958325i \(-0.407780\pi\)
0.596219 + 0.802822i \(0.296669\pi\)
\(84\) 0 0
\(85\) −3.60550 + 2.08164i −0.391072 + 0.225785i
\(86\) 3.77066 + 4.49370i 0.406601 + 0.484568i
\(87\) 0 0
\(88\) 1.69185 0.453331i 0.180352 0.0483252i
\(89\) 12.5101 5.83354i 1.32606 0.618354i 0.374907 0.927062i \(-0.377674\pi\)
0.951157 + 0.308708i \(0.0998967\pi\)
\(90\) 0 0
\(91\) −0.827957 0.579742i −0.0867935 0.0607734i
\(92\) −2.49592 + 0.218365i −0.260218 + 0.0227661i
\(93\) 0 0
\(94\) −2.64247 + 3.77383i −0.272550 + 0.389241i
\(95\) −22.1622 8.06640i −2.27380 0.827595i
\(96\) 0 0
\(97\) 2.88852 + 10.7801i 0.293285 + 1.09455i 0.942570 + 0.334009i \(0.108401\pi\)
−0.649285 + 0.760545i \(0.724932\pi\)
\(98\) −3.95870 5.65361i −0.399889 0.571101i
\(99\) 0 0
\(100\) −5.66464 9.81145i −0.566464 0.981145i
\(101\) 3.85019 6.66872i 0.383108 0.663562i −0.608397 0.793633i \(-0.708187\pi\)
0.991505 + 0.130071i \(0.0415204\pi\)
\(102\) 0 0
\(103\) −5.13479 + 19.1633i −0.505946 + 1.88822i −0.0488373 + 0.998807i \(0.515552\pi\)
−0.457109 + 0.889411i \(0.651115\pi\)
\(104\) 3.03063 1.10306i 0.297178 0.108164i
\(105\) 0 0
\(106\) −7.21809 3.36585i −0.701083 0.326920i
\(107\) 16.2662 + 2.86817i 1.57251 + 0.277277i 0.890818 0.454360i \(-0.150132\pi\)
0.681695 + 0.731636i \(0.261243\pi\)
\(108\) 0 0
\(109\) −1.12456 + 12.8538i −0.107713 + 1.23117i 0.729380 + 0.684109i \(0.239809\pi\)
−0.837093 + 0.547060i \(0.815747\pi\)
\(110\) 7.07787 0.674848
\(111\) 0 0
\(112\) −0.313398 −0.0296133
\(113\) −1.19803 + 13.6936i −0.112701 + 1.28818i 0.703617 + 0.710579i \(0.251567\pi\)
−0.816318 + 0.577602i \(0.803988\pi\)
\(114\) 0 0
\(115\) −9.97061 1.75809i −0.929764 0.163943i
\(116\) −2.19751 1.02472i −0.204034 0.0951427i
\(117\) 0 0
\(118\) 0.961443 0.349937i 0.0885080 0.0322143i
\(119\) −0.0835688 + 0.311883i −0.00766074 + 0.0285903i
\(120\) 0 0
\(121\) 3.96606 6.86942i 0.360551 0.624493i
\(122\) 0.0800790 + 0.138701i 0.00725001 + 0.0125574i
\(123\) 0 0
\(124\) −0.751097 1.07268i −0.0674505 0.0963293i
\(125\) −6.61965 24.7049i −0.592079 2.20967i
\(126\) 0 0
\(127\) −7.99824 2.91112i −0.709729 0.258320i −0.0381699 0.999271i \(-0.512153\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(128\) 0.573576 0.819152i 0.0506975 0.0724035i
\(129\) 0 0
\(130\) 12.9830 1.13587i 1.13868 0.0996220i
\(131\) 5.93708 + 4.15719i 0.518725 + 0.363215i 0.803429 0.595400i \(-0.203006\pi\)
−0.284704 + 0.958615i \(0.591895\pi\)
\(132\) 0 0
\(133\) −1.65774 + 0.773016i −0.143744 + 0.0670290i
\(134\) 15.4457 4.13866i 1.33431 0.357526i
\(135\) 0 0
\(136\) −0.662246 0.789234i −0.0567871 0.0676762i
\(137\) 12.4532 7.18988i 1.06395 0.614273i 0.137429 0.990512i \(-0.456116\pi\)
0.926523 + 0.376239i \(0.122783\pi\)
\(138\) 0 0
\(139\) 4.78219 0.843229i 0.405620 0.0715217i 0.0328839 0.999459i \(-0.489531\pi\)
0.372736 + 0.927937i \(0.378420\pi\)
\(140\) −1.22327 0.327775i −0.103385 0.0277020i
\(141\) 0 0
\(142\) −9.62343 9.62343i −0.807580 0.807580i
\(143\) −2.38734 + 5.11967i −0.199639 + 0.428128i
\(144\) 0 0
\(145\) −7.50574 6.29806i −0.623318 0.523026i
\(146\) 11.4500 + 1.00175i 0.947610 + 0.0829051i
\(147\) 0 0
\(148\) −5.73270 2.03374i −0.471225 0.167172i
\(149\) 1.17334i 0.0961241i 0.998844 + 0.0480620i \(0.0153045\pi\)
−0.998844 + 0.0480620i \(0.984695\pi\)
\(150\) 0 0
\(151\) −0.451815 + 0.538453i −0.0367682 + 0.0438187i −0.784115 0.620615i \(-0.786883\pi\)
0.747347 + 0.664434i \(0.231327\pi\)
\(152\) 1.01348 5.74772i 0.0822040 0.466202i
\(153\) 0 0
\(154\) 0.388150 0.388150i 0.0312780 0.0312780i
\(155\) −1.80984 4.97249i −0.145370 0.399400i
\(156\) 0 0
\(157\) −1.01497 5.75619i −0.0810036 0.459394i −0.998148 0.0608382i \(-0.980623\pi\)
0.917144 0.398556i \(-0.130488\pi\)
\(158\) −0.918888 0.530520i −0.0731028 0.0422059i
\(159\) 0 0
\(160\) 3.09555 2.59747i 0.244725 0.205348i
\(161\) −0.643202 + 0.450375i −0.0506914 + 0.0354945i
\(162\) 0 0
\(163\) 7.98612 + 17.1263i 0.625521 + 1.34143i 0.922295 + 0.386487i \(0.126312\pi\)
−0.296774 + 0.954948i \(0.595911\pi\)
\(164\) −0.730407 + 2.00678i −0.0570352 + 0.156703i
\(165\) 0 0
\(166\) 0.711055 + 8.12739i 0.0551885 + 0.630808i
\(167\) −2.15983 24.6870i −0.167133 1.91034i −0.366512 0.930413i \(-0.619448\pi\)
0.199379 0.979922i \(-0.436107\pi\)
\(168\) 0 0
\(169\) 0.888752 2.44183i 0.0683656 0.187833i
\(170\) −1.75948 3.77321i −0.134946 0.289392i
\(171\) 0 0
\(172\) −4.80523 + 3.36466i −0.366396 + 0.256553i
\(173\) 7.73952 6.49423i 0.588425 0.493747i −0.299277 0.954166i \(-0.596745\pi\)
0.887702 + 0.460419i \(0.152301\pi\)
\(174\) 0 0
\(175\) −3.07489 1.77529i −0.232440 0.134199i
\(176\) 0.304151 + 1.72493i 0.0229262 + 0.130021i
\(177\) 0 0
\(178\) 4.72102 + 12.9709i 0.353855 + 0.972209i
\(179\) −15.9537 + 15.9537i −1.19244 + 1.19244i −0.216057 + 0.976381i \(0.569320\pi\)
−0.976381 + 0.216057i \(0.930680\pi\)
\(180\) 0 0
\(181\) 2.79647 15.8595i 0.207860 1.17883i −0.685016 0.728528i \(-0.740205\pi\)
0.892876 0.450303i \(-0.148684\pi\)
\(182\) 0.649697 0.774278i 0.0481587 0.0573933i
\(183\) 0 0
\(184\) 2.50546i 0.184705i
\(185\) −20.2492 13.9339i −1.48875 1.02444i
\(186\) 0 0
\(187\) 1.79769 + 0.157277i 0.131460 + 0.0115013i
\(188\) −3.52917 2.96132i −0.257391 0.215977i
\(189\) 0 0
\(190\) 9.96727 21.3749i 0.723102 1.55070i
\(191\) −4.91016 4.91016i −0.355287 0.355287i 0.506785 0.862072i \(-0.330834\pi\)
−0.862072 + 0.506785i \(0.830834\pi\)
\(192\) 0 0
\(193\) 7.21131 + 1.93226i 0.519081 + 0.139087i 0.508842 0.860860i \(-0.330074\pi\)
0.0102397 + 0.999948i \(0.496741\pi\)
\(194\) −10.9908 + 1.93798i −0.789096 + 0.139139i
\(195\) 0 0
\(196\) 5.97712 3.45089i 0.426937 0.246492i
\(197\) 14.2648 + 17.0001i 1.01632 + 1.21121i 0.977276 + 0.211971i \(0.0679882\pi\)
0.0390483 + 0.999237i \(0.487567\pi\)
\(198\) 0 0
\(199\) −14.2006 + 3.80504i −1.00665 + 0.269732i −0.724230 0.689558i \(-0.757805\pi\)
−0.282423 + 0.959290i \(0.591138\pi\)
\(200\) 10.2678 4.78796i 0.726045 0.338560i
\(201\) 0 0
\(202\) 6.30778 + 4.41675i 0.443814 + 0.310762i
\(203\) −0.757001 + 0.0662290i −0.0531310 + 0.00464836i
\(204\) 0 0
\(205\) −4.94980 + 7.06905i −0.345709 + 0.493724i
\(206\) −18.6429 6.78545i −1.29891 0.472765i
\(207\) 0 0
\(208\) 0.834725 + 3.11524i 0.0578778 + 0.216003i
\(209\) 5.86347 + 8.37390i 0.405584 + 0.579235i
\(210\) 0 0
\(211\) −13.2618 22.9700i −0.912977 1.58132i −0.809836 0.586656i \(-0.800444\pi\)
−0.103141 0.994667i \(-0.532889\pi\)
\(212\) 3.98214 6.89727i 0.273494 0.473706i
\(213\) 0 0
\(214\) −4.27495 + 15.9543i −0.292230 + 1.09062i
\(215\) −22.2751 + 8.10747i −1.51915 + 0.552925i
\(216\) 0 0
\(217\) −0.371943 0.173440i −0.0252491 0.0117739i
\(218\) −12.7069 2.24056i −0.860617 0.151750i
\(219\) 0 0
\(220\) −0.616877 + 7.05093i −0.0415898 + 0.475374i
\(221\) 3.32276 0.223513
\(222\) 0 0
\(223\) −17.1123 −1.14592 −0.572962 0.819582i \(-0.694206\pi\)
−0.572962 + 0.819582i \(0.694206\pi\)
\(224\) 0.0273144 0.312205i 0.00182502 0.0208601i
\(225\) 0 0
\(226\) −13.5370 2.38695i −0.900470 0.158777i
\(227\) 10.2733 + 4.79050i 0.681860 + 0.317957i 0.732506 0.680760i \(-0.238350\pi\)
−0.0506464 + 0.998717i \(0.516128\pi\)
\(228\) 0 0
\(229\) 19.2576 7.00919i 1.27258 0.463180i 0.384606 0.923081i \(-0.374337\pi\)
0.887970 + 0.459901i \(0.152115\pi\)
\(230\) 2.62039 9.77944i 0.172784 0.644837i
\(231\) 0 0
\(232\) 1.21234 2.09984i 0.0795943 0.137861i
\(233\) −6.61145 11.4514i −0.433131 0.750205i 0.564010 0.825768i \(-0.309258\pi\)
−0.997141 + 0.0755632i \(0.975925\pi\)
\(234\) 0 0
\(235\) −10.6781 15.2499i −0.696561 0.994793i
\(236\) 0.264810 + 0.988284i 0.0172377 + 0.0643318i
\(237\) 0 0
\(238\) −0.303413 0.110433i −0.0196673 0.00715832i
\(239\) −10.0129 + 14.2999i −0.647678 + 0.924981i −0.999940 0.0109208i \(-0.996524\pi\)
0.352262 + 0.935901i \(0.385413\pi\)
\(240\) 0 0
\(241\) −15.6164 + 1.36625i −1.00594 + 0.0880082i −0.578200 0.815895i \(-0.696245\pi\)
−0.427738 + 0.903903i \(0.640689\pi\)
\(242\) 6.49762 + 4.54968i 0.417683 + 0.292465i
\(243\) 0 0
\(244\) −0.145152 + 0.0676857i −0.00929243 + 0.00433313i
\(245\) 26.9394 7.21840i 1.72110 0.461167i
\(246\) 0 0
\(247\) 12.0993 + 14.4193i 0.769858 + 0.917481i
\(248\) 1.13406 0.654749i 0.0720128 0.0415766i
\(249\) 0 0
\(250\) 25.1878 4.44129i 1.59302 0.280892i
\(251\) 3.37176 + 0.903459i 0.212823 + 0.0570258i 0.363655 0.931534i \(-0.381529\pi\)
−0.150832 + 0.988559i \(0.548195\pi\)
\(252\) 0 0
\(253\) 3.10306 + 3.10306i 0.195088 + 0.195088i
\(254\) 3.59714 7.71408i 0.225704 0.484025i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) 21.6111 + 1.89072i 1.34806 + 0.117940i 0.738208 0.674574i \(-0.235673\pi\)
0.609854 + 0.792514i \(0.291228\pi\)
\(258\) 0 0
\(259\) −1.87460 + 0.346331i −0.116482 + 0.0215199i
\(260\) 13.0326i 0.808247i
\(261\) 0 0
\(262\) −4.65882 + 5.55217i −0.287823 + 0.343014i
\(263\) −4.61211 + 26.1566i −0.284395 + 1.61288i 0.423044 + 0.906109i \(0.360961\pi\)
−0.707439 + 0.706774i \(0.750150\pi\)
\(264\) 0 0
\(265\) 22.7570 22.7570i 1.39795 1.39795i
\(266\) −0.625593 1.71880i −0.0383576 0.105387i
\(267\) 0 0
\(268\) 2.77673 + 15.7476i 0.169616 + 0.961940i
\(269\) −14.0963 8.13848i −0.859465 0.496212i 0.00436832 0.999990i \(-0.498610\pi\)
−0.863833 + 0.503778i \(0.831943\pi\)
\(270\) 0 0
\(271\) −10.8508 + 9.10492i −0.659140 + 0.553084i −0.909829 0.414983i \(-0.863787\pi\)
0.250689 + 0.968068i \(0.419343\pi\)
\(272\) 0.843949 0.590940i 0.0511719 0.0358310i
\(273\) 0 0
\(274\) 6.07715 + 13.0325i 0.367134 + 0.787321i
\(275\) −6.78693 + 18.6469i −0.409267 + 1.12445i
\(276\) 0 0
\(277\) −1.93687 22.1386i −0.116375 1.33018i −0.799849 0.600202i \(-0.795087\pi\)
0.683473 0.729975i \(-0.260469\pi\)
\(278\) 0.423225 + 4.83748i 0.0253833 + 0.290133i
\(279\) 0 0
\(280\) 0.433143 1.19005i 0.0258852 0.0711191i
\(281\) 10.5355 + 22.5933i 0.628492 + 1.34781i 0.920256 + 0.391316i \(0.127980\pi\)
−0.291764 + 0.956490i \(0.594242\pi\)
\(282\) 0 0
\(283\) 1.47386 1.03201i 0.0876118 0.0613464i −0.528950 0.848653i \(-0.677414\pi\)
0.616562 + 0.787307i \(0.288525\pi\)
\(284\) 10.4255 8.74807i 0.618643 0.519103i
\(285\) 0 0
\(286\) −4.89212 2.82446i −0.289277 0.167014i
\(287\) 0.116220 + 0.659114i 0.00686023 + 0.0389063i
\(288\) 0 0
\(289\) 5.45130 + 14.9773i 0.320665 + 0.881019i
\(290\) 6.92827 6.92827i 0.406842 0.406842i
\(291\) 0 0
\(292\) −1.99587 + 11.3191i −0.116799 + 0.662402i
\(293\) 4.15142 4.94747i 0.242528 0.289034i −0.631025 0.775763i \(-0.717365\pi\)
0.873553 + 0.486729i \(0.161810\pi\)
\(294\) 0 0
\(295\) 4.13449i 0.240719i
\(296\) 2.52564 5.53364i 0.146800 0.321636i
\(297\) 0 0
\(298\) −1.16888 0.102264i −0.0677113 0.00592397i
\(299\) 6.18996 + 5.19399i 0.357975 + 0.300376i
\(300\) 0 0
\(301\) −0.776952 + 1.66618i −0.0447828 + 0.0960370i
\(302\) −0.497025 0.497025i −0.0286006 0.0286006i
\(303\) 0 0
\(304\) 5.63752 + 1.51057i 0.323334 + 0.0866371i
\(305\) −0.637359 + 0.112384i −0.0364950 + 0.00643506i
\(306\) 0 0
\(307\) −1.76388 + 1.01838i −0.100670 + 0.0581218i −0.549490 0.835500i \(-0.685178\pi\)
0.448820 + 0.893622i \(0.351845\pi\)
\(308\) 0.352844 + 0.420503i 0.0201051 + 0.0239604i
\(309\) 0 0
\(310\) 5.11131 1.36957i 0.290303 0.0777864i
\(311\) 1.45635 0.679106i 0.0825819 0.0385086i −0.380888 0.924621i \(-0.624382\pi\)
0.463470 + 0.886112i \(0.346604\pi\)
\(312\) 0 0
\(313\) 4.27359 + 2.99240i 0.241557 + 0.169140i 0.688086 0.725629i \(-0.258451\pi\)
−0.446529 + 0.894769i \(0.647340\pi\)
\(314\) 5.82275 0.509424i 0.328597 0.0287485i
\(315\) 0 0
\(316\) 0.608588 0.869154i 0.0342357 0.0488937i
\(317\) −7.73134 2.81398i −0.434235 0.158049i 0.115648 0.993290i \(-0.463106\pi\)
−0.549883 + 0.835242i \(0.685328\pi\)
\(318\) 0 0
\(319\) 1.09919 + 4.10222i 0.0615426 + 0.229680i
\(320\) 2.31779 + 3.31015i 0.129569 + 0.185043i
\(321\) 0 0
\(322\) −0.392602 0.680007i −0.0218789 0.0378953i
\(323\) 3.00653 5.20747i 0.167288 0.289751i
\(324\) 0 0
\(325\) −9.45684 + 35.2934i −0.524571 + 1.95773i
\(326\) −17.7572 + 6.46308i −0.983478 + 0.357957i
\(327\) 0 0
\(328\) −1.93548 0.902529i −0.106869 0.0498339i
\(329\) −1.42189 0.250717i −0.0783913 0.0138225i
\(330\) 0 0
\(331\) −2.45856 + 28.1015i −0.135135 + 1.54460i 0.561685 + 0.827351i \(0.310153\pi\)
−0.696819 + 0.717247i \(0.745402\pi\)
\(332\) −8.15844 −0.447752
\(333\) 0 0
\(334\) 24.7813 1.35597
\(335\) −5.63175 + 64.3712i −0.307695 + 3.51697i
\(336\) 0 0
\(337\) −22.6775 3.99865i −1.23532 0.217820i −0.482412 0.875945i \(-0.660239\pi\)
−0.752909 + 0.658124i \(0.771350\pi\)
\(338\) 2.35508 + 1.09819i 0.128099 + 0.0597336i
\(339\) 0 0
\(340\) 3.91220 1.42392i 0.212169 0.0772232i
\(341\) −0.593636 + 2.21548i −0.0321472 + 0.119975i
\(342\) 0 0
\(343\) 2.17839 3.77309i 0.117622 0.203728i
\(344\) −2.93305 5.08020i −0.158140 0.273906i
\(345\) 0 0
\(346\) 5.79497 + 8.27608i 0.311540 + 0.444925i
\(347\) −6.39126 23.8525i −0.343101 1.28047i −0.894815 0.446437i \(-0.852693\pi\)
0.551714 0.834033i \(-0.313974\pi\)
\(348\) 0 0
\(349\) 25.1954 + 9.17038i 1.34868 + 0.490879i 0.912535 0.408998i \(-0.134122\pi\)
0.436144 + 0.899877i \(0.356344\pi\)
\(350\) 2.03653 2.90846i 0.108857 0.155464i
\(351\) 0 0
\(352\) −1.74487 + 0.152656i −0.0930019 + 0.00813661i
\(353\) −12.3033 8.61485i −0.654837 0.458522i 0.198347 0.980132i \(-0.436443\pi\)
−0.853184 + 0.521610i \(0.825332\pi\)
\(354\) 0 0
\(355\) 49.8430 23.2422i 2.64539 1.23357i
\(356\) −13.3330 + 3.57256i −0.706647 + 0.189346i
\(357\) 0 0
\(358\) −14.5026 17.2835i −0.766484 0.913460i
\(359\) −23.5938 + 13.6219i −1.24523 + 0.718935i −0.970155 0.242487i \(-0.922037\pi\)
−0.275077 + 0.961422i \(0.588704\pi\)
\(360\) 0 0
\(361\) 14.8346 2.61574i 0.780768 0.137670i
\(362\) 15.5555 + 4.16808i 0.817577 + 0.219069i
\(363\) 0 0
\(364\) 0.714707 + 0.714707i 0.0374608 + 0.0374608i
\(365\) −19.6288 + 42.0941i −1.02742 + 2.20330i
\(366\) 0 0
\(367\) −13.5860 11.4000i −0.709185 0.595077i 0.215185 0.976573i \(-0.430964\pi\)
−0.924370 + 0.381496i \(0.875409\pi\)
\(368\) 2.49592 + 0.218365i 0.130109 + 0.0113831i
\(369\) 0 0
\(370\) 15.6457 18.9577i 0.813382 0.985565i
\(371\) 2.49599i 0.129585i
\(372\) 0 0
\(373\) 9.42680 11.2344i 0.488101 0.581696i −0.464632 0.885504i \(-0.653813\pi\)
0.952733 + 0.303807i \(0.0982579\pi\)
\(374\) −0.313358 + 1.77714i −0.0162034 + 0.0918938i
\(375\) 0 0
\(376\) 3.25764 3.25764i 0.168000 0.168000i
\(377\) 2.67458 + 7.34834i 0.137748 + 0.378459i
\(378\) 0 0
\(379\) −0.762761 4.32583i −0.0391804 0.222203i 0.958930 0.283641i \(-0.0915425\pi\)
−0.998111 + 0.0614380i \(0.980431\pi\)
\(380\) 20.4248 + 11.7923i 1.04777 + 0.604931i
\(381\) 0 0
\(382\) 5.31943 4.46353i 0.272166 0.228374i
\(383\) −4.43745 + 3.10714i −0.226743 + 0.158767i −0.681428 0.731885i \(-0.738641\pi\)
0.454685 + 0.890652i \(0.349752\pi\)
\(384\) 0 0
\(385\) 0.937447 + 2.01036i 0.0477767 + 0.102458i
\(386\) −2.55342 + 7.01546i −0.129966 + 0.357077i
\(387\) 0 0
\(388\) −0.972692 11.1179i −0.0493809 0.564427i
\(389\) −0.979381 11.1944i −0.0496566 0.567578i −0.979746 0.200244i \(-0.935826\pi\)
0.930089 0.367333i \(-0.119729\pi\)
\(390\) 0 0
\(391\) 0.882857 2.42563i 0.0446480 0.122669i
\(392\) 2.91682 + 6.25514i 0.147322 + 0.315932i
\(393\) 0 0
\(394\) −18.1787 + 12.7289i −0.915829 + 0.641270i
\(395\) 3.28450 2.75602i 0.165261 0.138671i
\(396\) 0 0
\(397\) −2.68748 1.55162i −0.134881 0.0778736i 0.431041 0.902332i \(-0.358146\pi\)
−0.565922 + 0.824459i \(0.691480\pi\)
\(398\) −2.55289 14.4782i −0.127965 0.725726i
\(399\) 0 0
\(400\) 3.87484 + 10.6460i 0.193742 + 0.532302i
\(401\) −25.4721 + 25.4721i −1.27201 + 1.27201i −0.326984 + 0.945030i \(0.606032\pi\)
−0.945030 + 0.326984i \(0.893968\pi\)
\(402\) 0 0
\(403\) −0.733369 + 4.15914i −0.0365317 + 0.207182i
\(404\) −4.94971 + 5.89883i −0.246257 + 0.293478i
\(405\) 0 0
\(406\) 0.759892i 0.0377128i
\(407\) 3.72548 + 9.98159i 0.184665 + 0.494769i
\(408\) 0 0
\(409\) −0.121186 0.0106024i −0.00599227 0.000524256i 0.0841592 0.996452i \(-0.473180\pi\)
−0.0901515 + 0.995928i \(0.528735\pi\)
\(410\) −6.61075 5.54708i −0.326482 0.273951i
\(411\) 0 0
\(412\) 8.38446 17.9805i 0.413073 0.885837i
\(413\) 0.226735 + 0.226735i 0.0111569 + 0.0111569i
\(414\) 0 0
\(415\) −31.8445 8.53271i −1.56318 0.418854i
\(416\) −3.17613 + 0.560038i −0.155723 + 0.0274581i
\(417\) 0 0
\(418\) −8.85307 + 5.11132i −0.433018 + 0.250003i
\(419\) −14.6325 17.4383i −0.714844 0.851918i 0.279275 0.960211i \(-0.409906\pi\)
−0.994119 + 0.108293i \(0.965461\pi\)
\(420\) 0 0
\(421\) 16.8669 4.51948i 0.822045 0.220266i 0.176804 0.984246i \(-0.443424\pi\)
0.645240 + 0.763980i \(0.276757\pi\)
\(422\) 24.0385 11.2093i 1.17017 0.545661i
\(423\) 0 0
\(424\) 6.52395 + 4.56812i 0.316831 + 0.221848i
\(425\) 11.6278 1.01730i 0.564033 0.0493465i
\(426\) 0 0
\(427\) −0.0287896 + 0.0411158i −0.00139323 + 0.00198974i
\(428\) −15.5210 5.64919i −0.750238 0.273064i
\(429\) 0 0
\(430\) −6.13522 22.8969i −0.295866 1.10419i
\(431\) −13.6040 19.4285i −0.655281 0.935838i 0.344715 0.938707i \(-0.387976\pi\)
−0.999996 + 0.00286932i \(0.999087\pi\)
\(432\) 0 0
\(433\) 18.6294 + 32.2671i 0.895273 + 1.55066i 0.833466 + 0.552570i \(0.186353\pi\)
0.0618070 + 0.998088i \(0.480314\pi\)
\(434\) 0.205197 0.355412i 0.00984977 0.0170603i
\(435\) 0 0
\(436\) 3.33951 12.4632i 0.159934 0.596880i
\(437\) 13.7410 5.00130i 0.657319 0.239245i
\(438\) 0 0
\(439\) −7.37435 3.43872i −0.351959 0.164121i 0.238595 0.971119i \(-0.423313\pi\)
−0.590554 + 0.806998i \(0.701091\pi\)
\(440\) −6.97034 1.22906i −0.332298 0.0585931i
\(441\) 0 0
\(442\) −0.289598 + 3.31012i −0.0137748 + 0.157446i
\(443\) 13.8127 0.656259 0.328130 0.944633i \(-0.393582\pi\)
0.328130 + 0.944633i \(0.393582\pi\)
\(444\) 0 0
\(445\) −55.7786 −2.64416
\(446\) 1.49143 17.0472i 0.0706214 0.807207i
\(447\) 0 0
\(448\) 0.308637 + 0.0544210i 0.0145817 + 0.00257115i
\(449\) −14.8097 6.90586i −0.698912 0.325908i 0.0404829 0.999180i \(-0.487110\pi\)
−0.739395 + 0.673272i \(0.764888\pi\)
\(450\) 0 0
\(451\) 3.51494 1.27933i 0.165512 0.0602414i
\(452\) 3.55769 13.2775i 0.167340 0.624521i
\(453\) 0 0
\(454\) −5.66764 + 9.81664i −0.265996 + 0.460718i
\(455\) 2.04219 + 3.53718i 0.0957395 + 0.165826i
\(456\) 0 0
\(457\) −3.10859 4.43953i −0.145414 0.207672i 0.739837 0.672786i \(-0.234902\pi\)
−0.885251 + 0.465113i \(0.846014\pi\)
\(458\) 5.30411 + 19.7952i 0.247845 + 0.924969i
\(459\) 0 0
\(460\) 9.51385 + 3.46276i 0.443585 + 0.161452i
\(461\) 2.14790 3.06752i 0.100038 0.142869i −0.766013 0.642826i \(-0.777762\pi\)
0.866050 + 0.499957i \(0.166651\pi\)
\(462\) 0 0
\(463\) 20.6921 1.81032i 0.961642 0.0841328i 0.404489 0.914543i \(-0.367449\pi\)
0.557153 + 0.830410i \(0.311894\pi\)
\(464\) 1.98619 + 1.39074i 0.0922065 + 0.0645637i
\(465\) 0 0
\(466\) 11.9840 5.58824i 0.555149 0.258870i
\(467\) 7.39003 1.98015i 0.341970 0.0916305i −0.0837469 0.996487i \(-0.526689\pi\)
0.425717 + 0.904857i \(0.360022\pi\)
\(468\) 0 0
\(469\) 3.22127 + 3.83896i 0.148744 + 0.177267i
\(470\) 16.1225 9.30833i 0.743676 0.429361i
\(471\) 0 0
\(472\) −1.00760 + 0.177668i −0.0463787 + 0.00817781i
\(473\) 9.92459 + 2.65929i 0.456333 + 0.122274i
\(474\) 0 0
\(475\) 46.7554 + 46.7554i 2.14529 + 2.14529i
\(476\) 0.136457 0.292633i 0.00625450 0.0134128i
\(477\) 0 0
\(478\) −13.3728 11.2211i −0.611656 0.513240i
\(479\) −0.917985 0.0803133i −0.0419438 0.00366961i 0.0661645 0.997809i \(-0.478924\pi\)
−0.108108 + 0.994139i \(0.534479\pi\)
\(480\) 0 0
\(481\) 8.43553 + 17.7115i 0.384627 + 0.807573i
\(482\) 15.6760i 0.714023i
\(483\) 0 0
\(484\) −5.09867 + 6.07636i −0.231758 + 0.276198i
\(485\) 7.83128 44.4134i 0.355600 2.01671i
\(486\) 0 0
\(487\) 21.8338 21.8338i 0.989385 0.989385i −0.0105593 0.999944i \(-0.503361\pi\)
0.999944 + 0.0105593i \(0.00336121\pi\)
\(488\) −0.0547773 0.150499i −0.00247965 0.00681278i
\(489\) 0 0
\(490\) 4.84301 + 27.4661i 0.218785 + 1.24079i
\(491\) −2.71120 1.56531i −0.122355 0.0706416i 0.437574 0.899183i \(-0.355838\pi\)
−0.559928 + 0.828541i \(0.689171\pi\)
\(492\) 0 0
\(493\) 1.91365 1.60574i 0.0861863 0.0723189i
\(494\) −15.4190 + 10.7965i −0.693733 + 0.485757i
\(495\) 0 0
\(496\) 0.553418 + 1.18681i 0.0248492 + 0.0532893i
\(497\) 1.45879 4.00799i 0.0654357 0.179783i
\(498\) 0 0
\(499\) −1.81759 20.7751i −0.0813664 0.930022i −0.921687 0.387933i \(-0.873189\pi\)
0.840321 0.542089i \(-0.182366\pi\)
\(500\) 2.22913 + 25.4790i 0.0996895 + 1.13946i
\(501\) 0 0
\(502\) −1.19389 + 3.28018i −0.0532859 + 0.146402i
\(503\) 3.11236 + 6.67447i 0.138773 + 0.297600i 0.963396 0.268083i \(-0.0863902\pi\)
−0.824623 + 0.565683i \(0.808612\pi\)
\(504\) 0 0
\(505\) −25.4894 + 17.8479i −1.13426 + 0.794220i
\(506\) −3.36170 + 2.82081i −0.149446 + 0.125400i
\(507\) 0 0
\(508\) 7.37122 + 4.25577i 0.327045 + 0.188819i
\(509\) 3.70917 + 21.0358i 0.164406 + 0.932394i 0.949675 + 0.313238i \(0.101414\pi\)
−0.785268 + 0.619156i \(0.787475\pi\)
\(510\) 0 0
\(511\) 1.23200 + 3.38488i 0.0545003 + 0.149738i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) −3.76706 + 21.3640i −0.166158 + 0.942328i
\(515\) 51.5321 61.4136i 2.27078 2.70621i
\(516\) 0 0
\(517\) 8.06932i 0.354888i
\(518\) −0.181630 1.89765i −0.00798038 0.0833781i
\(519\) 0 0
\(520\) −12.9830 1.13587i −0.569342 0.0498110i
\(521\) −11.1679 9.37098i −0.489275 0.410550i 0.364492 0.931207i \(-0.381243\pi\)
−0.853766 + 0.520656i \(0.825687\pi\)
\(522\) 0 0
\(523\) −1.60056 + 3.43241i −0.0699875 + 0.150089i −0.938189 0.346123i \(-0.887498\pi\)
0.868202 + 0.496211i \(0.165276\pi\)
\(524\) −5.12499 5.12499i −0.223886 0.223886i
\(525\) 0 0
\(526\) −25.6551 6.87425i −1.11861 0.299732i
\(527\) 1.32864 0.234276i 0.0578766 0.0102052i
\(528\) 0 0
\(529\) −14.4823 + 8.36135i −0.629664 + 0.363537i
\(530\) 20.6870 + 24.6538i 0.898586 + 1.07089i
\(531\) 0 0
\(532\) 1.76679 0.473409i 0.0765999 0.0205249i
\(533\) 6.24218 2.91077i 0.270379 0.126080i
\(534\) 0 0
\(535\) −54.6743 38.2833i −2.36377 1.65513i
\(536\) −15.9297 + 1.39367i −0.688059 + 0.0601973i
\(537\) 0 0
\(538\) 9.33609 13.3333i 0.402507 0.574840i
\(539\) −11.3597 4.13458i −0.489296 0.178089i
\(540\) 0 0
\(541\) 4.66754 + 17.4195i 0.200673 + 0.748923i 0.990725 + 0.135883i \(0.0433870\pi\)
−0.790052 + 0.613040i \(0.789946\pi\)
\(542\) −8.12456 11.6031i −0.348980 0.498395i
\(543\) 0 0
\(544\) 0.515136 + 0.892241i 0.0220863 + 0.0382545i
\(545\) 26.0700 45.1545i 1.11671 1.93421i
\(546\) 0 0
\(547\) −0.783509 + 2.92410i −0.0335004 + 0.125025i −0.980651 0.195764i \(-0.937281\pi\)
0.947151 + 0.320789i \(0.103948\pi\)
\(548\) −13.5125 + 4.91816i −0.577227 + 0.210094i
\(549\) 0 0
\(550\) −17.9845 8.38629i −0.766860 0.357592i
\(551\) 13.9364 + 2.45737i 0.593712 + 0.104687i
\(552\) 0 0
\(553\) 0.0289817 0.331262i 0.00123243 0.0140867i
\(554\) 22.2231 0.944170
\(555\) 0 0
\(556\) −4.85596 −0.205939
\(557\) 0.227391 2.59909i 0.00963485 0.110127i −0.989854 0.142086i \(-0.954619\pi\)
0.999489 + 0.0319591i \(0.0101746\pi\)
\(558\) 0 0
\(559\) 18.6315 + 3.28524i 0.788030 + 0.138951i
\(560\) 1.14777 + 0.535215i 0.0485022 + 0.0226169i
\(561\) 0 0
\(562\) −23.4256 + 8.52622i −0.988149 + 0.359657i
\(563\) 8.62275 32.1805i 0.363406 1.35625i −0.506164 0.862437i \(-0.668937\pi\)
0.869569 0.493811i \(-0.164396\pi\)
\(564\) 0 0
\(565\) 27.7732 48.1046i 1.16843 2.02377i
\(566\) 0.899625 + 1.55820i 0.0378140 + 0.0654958i
\(567\) 0 0
\(568\) 7.80614 + 11.1483i 0.327538 + 0.467773i
\(569\) 1.56364 + 5.83560i 0.0655514 + 0.244641i 0.990925 0.134415i \(-0.0429155\pi\)
−0.925374 + 0.379056i \(0.876249\pi\)
\(570\) 0 0
\(571\) −18.7956 6.84105i −0.786572 0.286289i −0.0826618 0.996578i \(-0.526342\pi\)
−0.703910 + 0.710289i \(0.748564\pi\)
\(572\) 3.24009 4.62733i 0.135475 0.193478i
\(573\) 0 0
\(574\) −0.666735 + 0.0583318i −0.0278290 + 0.00243472i
\(575\) 23.2517 + 16.2810i 0.969661 + 0.678964i
\(576\) 0 0
\(577\) 26.7644 12.4805i 1.11422 0.519568i 0.223764 0.974643i \(-0.428165\pi\)
0.890453 + 0.455075i \(0.150388\pi\)
\(578\) −15.3954 + 4.12520i −0.640366 + 0.171586i
\(579\) 0 0
\(580\) 6.29806 + 7.50574i 0.261513 + 0.311659i
\(581\) −2.21429 + 1.27842i −0.0918640 + 0.0530377i
\(582\) 0 0
\(583\) −13.7378 + 2.42234i −0.568961 + 0.100323i
\(584\) −11.1021 2.97480i −0.459409 0.123098i
\(585\) 0 0
\(586\) 4.56682 + 4.56682i 0.188654 + 0.188654i
\(587\) 4.39523 9.42560i 0.181410 0.389036i −0.794482 0.607288i \(-0.792258\pi\)
0.975893 + 0.218252i \(0.0700353\pi\)
\(588\) 0 0
\(589\) 5.85468 + 4.91266i 0.241238 + 0.202423i
\(590\) −4.11875 0.360344i −0.169566 0.0148351i
\(591\) 0 0
\(592\) 5.29246 + 2.99832i 0.217519 + 0.123230i
\(593\) 28.4921i 1.17003i −0.811022 0.585016i \(-0.801088\pi\)
0.811022 0.585016i \(-0.198912\pi\)
\(594\) 0 0
\(595\) 0.838685 0.999506i 0.0343827 0.0409757i
\(596\) 0.203749 1.15552i 0.00834588 0.0473319i
\(597\) 0 0
\(598\) −5.71372 + 5.71372i −0.233651 + 0.233651i
\(599\) 4.43933 + 12.1970i 0.181386 + 0.498354i 0.996747 0.0805993i \(-0.0256834\pi\)
−0.815360 + 0.578954i \(0.803461\pi\)
\(600\) 0 0
\(601\) −8.34511 47.3275i −0.340404 1.93053i −0.365424 0.930841i \(-0.619076\pi\)
0.0250202 0.999687i \(-0.492035\pi\)
\(602\) −1.59212 0.919213i −0.0648901 0.0374643i
\(603\) 0 0
\(604\) 0.538453 0.451815i 0.0219093 0.0183841i
\(605\) −26.2566 + 18.3850i −1.06748 + 0.747458i
\(606\) 0 0
\(607\) −17.4240 37.3659i −0.707219 1.51664i −0.849944 0.526873i \(-0.823364\pi\)
0.142726 0.989762i \(-0.454413\pi\)
\(608\) −1.99616 + 5.48441i −0.0809551 + 0.222422i
\(609\) 0 0
\(610\) −0.0564064 0.644728i −0.00228383 0.0261043i
\(611\) 1.29498 + 14.8016i 0.0523891 + 0.598810i
\(612\) 0 0
\(613\) −5.00311 + 13.7459i −0.202074 + 0.555193i −0.998791 0.0491591i \(-0.984346\pi\)
0.796717 + 0.604352i \(0.206568\pi\)
\(614\) −0.860769 1.84593i −0.0347378 0.0744955i
\(615\) 0 0
\(616\) −0.449655 + 0.314852i −0.0181171 + 0.0126857i
\(617\) −3.19202 + 2.67842i −0.128506 + 0.107829i −0.704775 0.709431i \(-0.748952\pi\)
0.576270 + 0.817260i \(0.304508\pi\)
\(618\) 0 0
\(619\) −8.32867 4.80856i −0.334758 0.193272i 0.323194 0.946333i \(-0.395243\pi\)
−0.657951 + 0.753060i \(0.728577\pi\)
\(620\) 0.918880 + 5.21123i 0.0369031 + 0.209288i
\(621\) 0 0
\(622\) 0.549593 + 1.50999i 0.0220367 + 0.0605452i
\(623\) −3.05890 + 3.05890i −0.122552 + 0.122552i
\(624\) 0 0
\(625\) −8.11047 + 45.9968i −0.324419 + 1.83987i
\(626\) −3.35348 + 3.99652i −0.134032 + 0.159733i
\(627\) 0 0
\(628\) 5.84499i 0.233240i
\(629\) 4.39508 4.46736i 0.175243 0.178125i
\(630\) 0 0
\(631\) −10.7081 0.936833i −0.426281 0.0372947i −0.128003 0.991774i \(-0.540857\pi\)
−0.298278 + 0.954479i \(0.596412\pi\)
\(632\) 0.812804 + 0.682024i 0.0323316 + 0.0271294i
\(633\) 0 0
\(634\) 3.47710 7.45666i 0.138093 0.296142i
\(635\) 24.3208 + 24.3208i 0.965140 + 0.965140i
\(636\) 0 0
\(637\) −21.5007 5.76109i −0.851888 0.228263i
\(638\) −4.18241 + 0.737471i −0.165583 + 0.0291968i
\(639\) 0 0
\(640\) −3.49957 + 2.02048i −0.138333 + 0.0798663i
\(641\) −23.8550 28.4293i −0.942216 1.12289i −0.992264 0.124143i \(-0.960382\pi\)
0.0500484 0.998747i \(-0.484062\pi\)
\(642\) 0 0
\(643\) −22.4858 + 6.02506i −0.886755 + 0.237605i −0.673319 0.739352i \(-0.735132\pi\)
−0.213436 + 0.976957i \(0.568465\pi\)
\(644\) 0.711637 0.331842i 0.0280424 0.0130764i
\(645\) 0 0
\(646\) 4.92562 + 3.44895i 0.193796 + 0.135697i
\(647\) 31.4432 2.75092i 1.23616 0.108150i 0.549728 0.835344i \(-0.314731\pi\)
0.686432 + 0.727194i \(0.259176\pi\)
\(648\) 0 0
\(649\) 1.02789 1.46798i 0.0403483 0.0576234i
\(650\) −34.3349 12.4969i −1.34673 0.490168i
\(651\) 0 0
\(652\) −4.89084 18.2529i −0.191540 0.714838i
\(653\) −3.88391 5.54680i −0.151989 0.217063i 0.735936 0.677051i \(-0.236743\pi\)
−0.887925 + 0.459988i \(0.847854\pi\)
\(654\) 0 0
\(655\) −14.6441 25.3643i −0.572192 0.991065i
\(656\) 1.06778 1.84945i 0.0416899 0.0722091i
\(657\) 0 0
\(658\) 0.373689 1.39463i 0.0145679 0.0543682i
\(659\) −38.6771 + 14.0773i −1.50665 + 0.548374i −0.957772 0.287530i \(-0.907166\pi\)
−0.548875 + 0.835905i \(0.684944\pi\)
\(660\) 0 0
\(661\) 15.8222 + 7.37804i 0.615414 + 0.286972i 0.705222 0.708987i \(-0.250847\pi\)
−0.0898076 + 0.995959i \(0.528625\pi\)
\(662\) −27.7803 4.89841i −1.07971 0.190382i
\(663\) 0 0
\(664\) 0.711055 8.12739i 0.0275943 0.315404i
\(665\) 7.39135 0.286624
\(666\) 0 0
\(667\) 6.07495 0.235223
\(668\) −2.15983 + 24.6870i −0.0835664 + 0.955168i
\(669\) 0 0
\(670\) −63.6354 11.2206i −2.45845 0.433491i
\(671\) 0.254240 + 0.118554i 0.00981481 + 0.00457672i
\(672\) 0 0
\(673\) 8.98287 3.26950i 0.346264 0.126030i −0.163033 0.986621i \(-0.552128\pi\)
0.509297 + 0.860591i \(0.329905\pi\)
\(674\) 5.95991 22.2427i 0.229567 0.856756i
\(675\) 0 0
\(676\) −1.29927 + 2.25040i −0.0499719 + 0.0865538i
\(677\) −13.3132 23.0591i −0.511667 0.886234i −0.999909 0.0135252i \(-0.995695\pi\)
0.488241 0.872709i \(-0.337639\pi\)
\(678\) 0 0
\(679\) −2.00616 2.86510i −0.0769895 0.109952i
\(680\) 1.07754 + 4.02142i 0.0413216 + 0.154214i
\(681\) 0 0
\(682\) −2.15531 0.784468i −0.0825311 0.0300388i
\(683\) 1.76416 2.51949i 0.0675039 0.0964056i −0.783981 0.620785i \(-0.786814\pi\)
0.851485 + 0.524380i \(0.175703\pi\)
\(684\) 0 0
\(685\) −57.8868 + 5.06443i −2.21174 + 0.193502i
\(686\) 3.56887 + 2.49895i 0.136260 + 0.0954104i
\(687\) 0 0
\(688\) 5.31650 2.47912i 0.202690 0.0945157i
\(689\) −24.8106 + 6.64798i −0.945209 + 0.253268i
\(690\) 0 0
\(691\) 11.4621 + 13.6600i 0.436039 + 0.519651i 0.938654 0.344859i \(-0.112073\pi\)
−0.502616 + 0.864510i \(0.667629\pi\)
\(692\) −8.74965 + 5.05161i −0.332612 + 0.192034i
\(693\) 0 0
\(694\) 24.3188 4.28806i 0.923128 0.162772i
\(695\) −18.9541 5.07873i −0.718969 0.192647i
\(696\) 0 0
\(697\) −1.55579 1.55579i −0.0589296 0.0589296i
\(698\) −11.3314 + 24.3003i −0.428900 + 0.919779i
\(699\) 0 0
\(700\) 2.71990 + 2.28227i 0.102802 + 0.0862615i
\(701\) −28.8141 2.52091i −1.08829 0.0952133i −0.471142 0.882058i \(-0.656158\pi\)
−0.617152 + 0.786844i \(0.711713\pi\)
\(702\) 0 0
\(703\) 35.3903 + 2.80560i 1.33477 + 0.105815i
\(704\) 1.75154i 0.0660135i
\(705\) 0 0
\(706\) 9.65437 11.5056i 0.363347 0.433020i
\(707\) −0.419062 + 2.37662i −0.0157604 + 0.0893819i
\(708\) 0 0
\(709\) 0.829801 0.829801i 0.0311638 0.0311638i −0.691353 0.722517i \(-0.742985\pi\)
0.722517 + 0.691353i \(0.242985\pi\)
\(710\) 18.8096 + 51.6790i 0.705913 + 1.93948i
\(711\) 0 0
\(712\) −2.39692 13.5936i −0.0898285 0.509443i
\(713\) 2.84133 + 1.64045i 0.106409 + 0.0614351i
\(714\) 0 0
\(715\) 17.4865 14.6729i 0.653959 0.548737i
\(716\) 18.4817 12.9410i 0.690693 0.483629i
\(717\) 0 0
\(718\) −11.5137 24.6912i −0.429688 0.921468i
\(719\) 8.63325 23.7197i 0.321966 0.884594i −0.668110 0.744062i \(-0.732896\pi\)
0.990076 0.140532i \(-0.0448813\pi\)
\(720\) 0 0
\(721\) −0.541900 6.19394i −0.0201814 0.230674i
\(722\) 1.31287 + 15.0061i 0.0488598 + 0.558470i
\(723\) 0 0
\(724\) −5.50796 + 15.1330i −0.204702 + 0.562414i
\(725\) 11.6093 + 24.8963i 0.431159 + 0.924624i
\(726\) 0 0
\(727\) −0.559460 + 0.391738i −0.0207492 + 0.0145288i −0.583905 0.811822i \(-0.698476\pi\)
0.563156 + 0.826351i \(0.309587\pi\)
\(728\) −0.774278 + 0.649697i −0.0286967 + 0.0240794i
\(729\) 0 0
\(730\) −40.2231 23.2228i −1.48873 0.859516i
\(731\) −1.04947 5.95187i −0.0388162 0.220138i
\(732\) 0 0
\(733\) 2.99002 + 8.21501i 0.110439 + 0.303428i 0.982584 0.185819i \(-0.0594938\pi\)
−0.872145 + 0.489247i \(0.837272\pi\)
\(734\) 12.5408 12.5408i 0.462888 0.462888i
\(735\) 0 0
\(736\) −0.435068 + 2.46739i −0.0160368 + 0.0909493i
\(737\) 18.0032 21.4554i 0.663157 0.790320i
\(738\) 0 0
\(739\) 28.5466i 1.05010i 0.851071 + 0.525051i \(0.175954\pi\)
−0.851071 + 0.525051i \(0.824046\pi\)
\(740\) 17.5220 + 17.2385i 0.644120 + 0.633698i
\(741\) 0 0
\(742\) 2.48649 + 0.217540i 0.0912819 + 0.00798613i
\(743\) −16.8230 14.1161i −0.617174 0.517871i 0.279740 0.960076i \(-0.409752\pi\)
−0.896914 + 0.442205i \(0.854196\pi\)
\(744\) 0 0
\(745\) 2.00381 4.29719i 0.0734140 0.157437i
\(746\) 10.3701 + 10.3701i 0.379675 + 0.379675i
\(747\) 0 0
\(748\) −1.74307 0.467054i −0.0637329 0.0170772i
\(749\) −5.09779 + 0.898879i −0.186269 + 0.0328443i
\(750\) 0 0
\(751\) 16.9423 9.78162i 0.618232 0.356937i −0.157948 0.987447i \(-0.550488\pi\)
0.776180 + 0.630511i \(0.217155\pi\)
\(752\) 2.96132 + 3.52917i 0.107988 + 0.128695i
\(753\) 0 0
\(754\) −7.55348 + 2.02395i −0.275081 + 0.0737079i
\(755\) 2.57426 1.20040i 0.0936870 0.0436870i
\(756\) 0 0
\(757\) 18.6066 + 13.0285i 0.676269 + 0.473529i 0.860564 0.509342i \(-0.170111\pi\)
−0.184295 + 0.982871i \(0.559000\pi\)
\(758\) 4.37585 0.382837i 0.158938 0.0139053i
\(759\) 0 0
\(760\) −13.5276 + 19.3193i −0.490696 + 0.700786i
\(761\) 28.8549 + 10.5023i 1.04599 + 0.380709i 0.807147 0.590350i \(-0.201010\pi\)
0.238841 + 0.971059i \(0.423232\pi\)
\(762\) 0 0
\(763\) −1.04660 3.90595i −0.0378893 0.141405i
\(764\) 3.98293 + 5.68821i 0.144097 + 0.205792i
\(765\) 0 0
\(766\) −2.70857 4.69137i −0.0978644 0.169506i
\(767\) 1.64989 2.85769i 0.0595741 0.103185i
\(768\) 0 0
\(769\) −10.4223 + 38.8967i −0.375839 + 1.40265i 0.476276 + 0.879296i \(0.341986\pi\)
−0.852115 + 0.523355i \(0.824680\pi\)
\(770\) −2.08442 + 0.758665i −0.0751171 + 0.0273404i
\(771\) 0 0
\(772\) −6.76622 3.15514i −0.243522 0.113556i
\(773\) 17.6601 + 3.11395i 0.635189 + 0.112001i 0.481965 0.876191i \(-0.339923\pi\)
0.153224 + 0.988191i \(0.451034\pi\)
\(774\) 0 0
\(775\) −1.29301 + 14.7792i −0.0464465 + 0.530886i
\(776\) 11.1604 0.400634
\(777\) 0 0
\(778\) 11.2371 0.402871
\(779\) 1.08631 12.4166i 0.0389211 0.444870i
\(780\) 0 0
\(781\) −23.4755 4.13937i −0.840020 0.148118i
\(782\) 2.33945 + 1.09090i 0.0836586 + 0.0390107i
\(783\) 0 0
\(784\) −6.48555 + 2.36055i −0.231627 + 0.0843053i
\(785\) −6.11313 + 22.8145i −0.218187 + 0.814285i
\(786\) 0 0
\(787\) −7.44633 + 12.8974i −0.265433 + 0.459744i −0.967677 0.252193i \(-0.918848\pi\)
0.702244 + 0.711936i \(0.252182\pi\)
\(788\) −11.0960 19.2189i −0.395280 0.684645i
\(789\) 0 0
\(790\) 2.45927 + 3.51221i 0.0874970 + 0.124959i
\(791\) −1.11497 4.16114i −0.0396439 0.147953i
\(792\) 0 0
\(793\) 0.485380 + 0.176664i 0.0172363 + 0.00627352i
\(794\) 1.77994 2.54202i 0.0631679 0.0902131i
\(795\) 0 0
\(796\) 14.6456 1.28132i 0.519099 0.0454153i
\(797\) −16.3333 11.4367i −0.578555 0.405108i 0.247343 0.968928i \(-0.420442\pi\)
−0.825898 + 0.563820i \(0.809331\pi\)
\(798\) 0 0
\(799\) 4.30176 2.00594i 0.152185 0.0709651i
\(800\) −10.9433 + 2.93224i −0.386902 + 0.103670i
\(801\) 0 0
\(802\) −23.1551 27.5952i −0.817635 0.974419i
\(803\) 17.4346 10.0659i 0.615252 0.355216i
\(804\) 0 0
\(805\) 3.12477 0.550981i 0.110134 0.0194195i
\(806\) −4.07940 1.09307i −0.143691 0.0385018i
\(807\) 0 0
\(808\) −5.44499 5.44499i −0.191554 0.191554i
\(809\) −11.0839 + 23.7695i −0.389690 + 0.835693i 0.609393 + 0.792869i \(0.291413\pi\)
−0.999083 + 0.0428242i \(0.986364\pi\)
\(810\) 0 0
\(811\) 27.0775 + 22.7207i 0.950819 + 0.797832i 0.979435 0.201759i \(-0.0646657\pi\)
−0.0286164 + 0.999590i \(0.509110\pi\)
\(812\) 0.757001 + 0.0662290i 0.0265655 + 0.00232418i
\(813\) 0 0
\(814\) −10.2683 + 2.84135i −0.359904 + 0.0995891i
\(815\) 76.3609i 2.67481i
\(816\) 0 0
\(817\) 22.0070 26.2270i 0.769929 0.917566i
\(818\) 0.0211241 0.119801i 0.000738588 0.00418874i
\(819\) 0 0
\(820\) 6.10213 6.10213i 0.213096 0.213096i
\(821\) 15.6204 + 42.9166i 0.545154 + 1.49780i 0.840179 + 0.542309i \(0.182450\pi\)
−0.295025 + 0.955490i \(0.595328\pi\)
\(822\) 0 0
\(823\) 2.60357 + 14.7656i 0.0907549 + 0.514696i 0.995966 + 0.0897339i \(0.0286016\pi\)
−0.905211 + 0.424963i \(0.860287\pi\)
\(824\) 17.1814 + 9.91966i 0.598541 + 0.345568i
\(825\) 0 0
\(826\) −0.245634 + 0.206111i −0.00854669 + 0.00717152i
\(827\) 35.6153 24.9381i 1.23846 0.867182i 0.243747 0.969839i \(-0.421623\pi\)
0.994717 + 0.102657i \(0.0327343\pi\)
\(828\) 0 0
\(829\) −8.51185 18.2537i −0.295629 0.633978i 0.701251 0.712915i \(-0.252625\pi\)
−0.996880 + 0.0789367i \(0.974847\pi\)
\(830\) 11.2757 30.9796i 0.391384 1.07532i
\(831\) 0 0
\(832\) −0.281089 3.21286i −0.00974499 0.111386i
\(833\) 0.619739 + 7.08365i 0.0214727 + 0.245434i
\(834\) 0 0
\(835\) −34.2499 + 94.1008i −1.18527 + 3.25649i
\(836\) −4.32027 9.26486i −0.149420 0.320432i
\(837\) 0 0
\(838\) 18.6473 13.0570i 0.644159 0.451045i
\(839\) −13.2259 + 11.0978i −0.456607 + 0.383139i −0.841881 0.539663i \(-0.818552\pi\)
0.385274 + 0.922802i \(0.374107\pi\)
\(840\) 0 0
\(841\) −20.0233 11.5604i −0.690458 0.398636i
\(842\) 3.03224 + 17.1967i 0.104498 + 0.592636i
\(843\) 0 0
\(844\) 9.07158 + 24.9240i 0.312257 + 0.857918i
\(845\) −7.42502 + 7.42502i −0.255428 + 0.255428i
\(846\) 0 0
\(847\) −0.431674 + 2.44814i −0.0148325 + 0.0841192i
\(848\) −5.11934 + 6.10099i −0.175799 + 0.209509i
\(849\) 0 0
\(850\) 11.6722i 0.400355i
\(851\) 15.1708 1.45204i 0.520047 0.0497754i
\(852\) 0 0
\(853\) 0.0642643 + 0.00562239i 0.00220037 + 0.000192507i 0.0882559 0.996098i \(-0.471871\pi\)
−0.0860555 + 0.996290i \(0.527426\pi\)
\(854\) −0.0384502 0.0322636i −0.00131574 0.00110404i
\(855\) 0 0
\(856\) 6.98044 14.9696i 0.238587 0.511651i
\(857\) 26.4642 + 26.4642i 0.903998 + 0.903998i 0.995779 0.0917808i \(-0.0292559\pi\)
−0.0917808 + 0.995779i \(0.529256\pi\)
\(858\) 0 0
\(859\) −11.4826 3.07676i −0.391782 0.104978i 0.0575496 0.998343i \(-0.481671\pi\)
−0.449332 + 0.893365i \(0.648338\pi\)
\(860\) 23.3445 4.11627i 0.796042 0.140364i
\(861\) 0 0
\(862\) 20.5402 11.8589i 0.699603 0.403916i
\(863\) 2.31209 + 2.75544i 0.0787045 + 0.0937964i 0.803960 0.594684i \(-0.202723\pi\)
−0.725255 + 0.688480i \(0.758278\pi\)
\(864\) 0 0
\(865\) −39.4355 + 10.5667i −1.34085 + 0.359279i
\(866\) −33.7680 + 15.7463i −1.14748 + 0.535080i
\(867\) 0 0
\(868\) 0.336175 + 0.235392i 0.0114105 + 0.00798973i
\(869\) −1.85138 + 0.161975i −0.0628037 + 0.00549461i
\(870\) 0 0
\(871\) 29.5803 42.2450i 1.00229 1.43142i
\(872\) 12.1247 + 4.41305i 0.410596 + 0.149445i
\(873\) 0 0
\(874\) 3.78466 + 14.1246i 0.128018 + 0.477770i
\(875\) 4.59754 + 6.56597i 0.155425 + 0.221970i
\(876\) 0 0
\(877\) −19.0667 33.0245i −0.643836 1.11516i −0.984569 0.174997i \(-0.944008\pi\)
0.340733 0.940160i \(-0.389325\pi\)
\(878\) 4.06835 7.04659i 0.137300 0.237811i
\(879\) 0 0
\(880\) 1.83189 6.83670i 0.0617529 0.230465i
\(881\) −19.4881 + 7.09310i −0.656572 + 0.238973i −0.648756 0.760997i \(-0.724710\pi\)
−0.00781619 + 0.999969i \(0.502488\pi\)
\(882\) 0 0
\(883\) 43.7825 + 20.4161i 1.47340 + 0.687057i 0.982859 0.184361i \(-0.0590215\pi\)
0.490541 + 0.871418i \(0.336799\pi\)
\(884\) −3.27228 0.576991i −0.110059 0.0194063i
\(885\) 0 0
\(886\) −1.20385 + 13.7601i −0.0404442 + 0.462279i
\(887\) −4.29206 −0.144113 −0.0720566 0.997401i \(-0.522956\pi\)
−0.0720566 + 0.997401i \(0.522956\pi\)
\(888\) 0 0
\(889\) 2.66750 0.0894651
\(890\) 4.86142 55.5663i 0.162955 1.86259i
\(891\) 0 0
\(892\) 16.8523 + 2.97152i 0.564257 + 0.0994937i
\(893\) 24.3690 + 11.3635i 0.815479 + 0.380264i
\(894\) 0 0
\(895\) 85.6735 31.1826i 2.86375 1.04232i
\(896\) −0.0811133 + 0.302719i −0.00270981 + 0.0101131i
\(897\) 0 0
\(898\) 8.17033 14.1514i 0.272648 0.472239i
\(899\) 1.58756 + 2.74974i 0.0529482 + 0.0917089i
\(900\) 0 0
\(901\) 4.70641 + 6.72145i 0.156793 + 0.223924i
\(902\) 0.968118 + 3.61306i 0.0322348 + 0.120302i
\(903\) 0 0
\(904\) 12.9169 + 4.70136i 0.429609 + 0.156365i
\(905\) −37.3262 + 53.3074i −1.24077 + 1.77200i
\(906\) 0 0
\(907\) −30.3538 + 2.65562i −1.00788 + 0.0881783i −0.579123 0.815240i \(-0.696605\pi\)
−0.428759 + 0.903419i \(0.641049\pi\)
\(908\) −9.28532 6.50165i −0.308144 0.215765i
\(909\) 0 0
\(910\) −3.70171 + 1.72614i −0.122711 + 0.0572209i
\(911\) 17.3137 4.63920i 0.573630 0.153704i 0.0396690 0.999213i \(-0.487370\pi\)
0.533961 + 0.845509i \(0.320703\pi\)
\(912\) 0 0
\(913\) 9.18530 + 10.9466i 0.303989 + 0.362280i
\(914\) 4.69356 2.70983i 0.155249 0.0896332i
\(915\) 0 0
\(916\) −20.1821 + 3.55866i −0.666837 + 0.117581i
\(917\) −2.19406 0.587896i −0.0724542 0.0194140i
\(918\) 0 0
\(919\) 22.1656 + 22.1656i 0.731176 + 0.731176i 0.970853 0.239677i \(-0.0770415\pi\)
−0.239677 + 0.970853i \(0.577042\pi\)
\(920\) −4.27877 + 9.17585i −0.141067 + 0.302519i
\(921\) 0 0
\(922\) 2.86865 + 2.40708i 0.0944738 + 0.0792730i
\(923\) −43.7257 3.82550i −1.43925 0.125918i
\(924\) 0 0
\(925\) 34.9423 + 59.3977i 1.14890 + 1.95298i
\(926\) 20.7711i 0.682581i
\(927\) 0 0
\(928\) −1.55856 + 1.85742i −0.0511622 + 0.0609728i
\(929\) 2.32904 13.2086i 0.0764132 0.433361i −0.922468 0.386073i \(-0.873831\pi\)
0.998881 0.0472874i \(-0.0150577\pi\)
\(930\) 0 0
\(931\) −28.4833 + 28.4833i −0.933503 + 0.933503i
\(932\) 4.52250 + 12.4255i 0.148139 + 0.407010i
\(933\) 0 0
\(934\) 1.32853 + 7.53449i 0.0434709 + 0.246536i
\(935\) −6.31517 3.64606i −0.206528 0.119239i
\(936\) 0 0
\(937\) 16.8627 14.1495i 0.550880 0.462243i −0.324359 0.945934i \(-0.605148\pi\)
0.875239 + 0.483691i \(0.160704\pi\)
\(938\) −4.10510 + 2.87443i −0.134036 + 0.0938533i
\(939\) 0 0
\(940\) 7.86774 + 16.8724i 0.256617 + 0.550318i
\(941\) 1.66861 4.58447i 0.0543951 0.149449i −0.909519 0.415662i \(-0.863550\pi\)
0.963914 + 0.266212i \(0.0857722\pi\)
\(942\) 0 0
\(943\) −0.466333 5.33021i −0.0151859 0.173575i
\(944\) −0.0891731 1.01925i −0.00290234 0.0331739i
\(945\) 0 0
\(946\) −3.51415 + 9.65505i −0.114255 + 0.313913i
\(947\) −20.8015 44.6090i −0.675959 1.44960i −0.882093 0.471075i \(-0.843866\pi\)
0.206135 0.978524i \(-0.433912\pi\)
\(948\) 0 0
\(949\) 30.3650 21.2618i 0.985690 0.690187i
\(950\) −50.6525 + 42.5025i −1.64338 + 1.37896i
\(951\) 0 0
\(952\) 0.279627 + 0.161442i 0.00906275 + 0.00523238i
\(953\) 9.77644 + 55.4449i 0.316690 + 1.79604i 0.562583 + 0.826741i \(0.309808\pi\)
−0.245893 + 0.969297i \(0.579081\pi\)
\(954\) 0 0
\(955\) 9.59724 + 26.3682i 0.310559 + 0.853255i
\(956\) 12.3439 12.3439i 0.399230 0.399230i
\(957\) 0 0
\(958\) 0.160015 0.907492i 0.00516986 0.0293197i
\(959\) −2.89678 + 3.45224i −0.0935418 + 0.111479i
\(960\) 0 0
\(961\) 29.2852i 0.944684i
\(962\) −18.3793 + 6.85978i −0.592571 + 0.221168i
\(963\) 0 0
\(964\) 15.6164 + 1.36625i 0.502969 + 0.0440041i
\(965\) −23.1104 19.3919i −0.743951 0.624249i
\(966\) 0 0
\(967\) 21.4989 46.1045i 0.691357 1.48262i −0.175716 0.984441i \(-0.556224\pi\)
0.867074 0.498180i \(-0.165998\pi\)
\(968\) −5.60886 5.60886i −0.180276 0.180276i
\(969\) 0 0
\(970\) 43.5619 + 11.6724i 1.39869 + 0.374777i
\(971\) −54.2677 + 9.56886i −1.74153 + 0.307079i −0.951880 0.306472i \(-0.900851\pi\)
−0.789654 + 0.613552i \(0.789740\pi\)
\(972\) 0 0
\(973\) −1.31796 + 0.760924i −0.0422518 + 0.0243941i
\(974\) 19.8478 + 23.6537i 0.635964 + 0.757913i
\(975\) 0 0
\(976\) 0.154701 0.0414519i 0.00495185 0.00132684i
\(977\) 23.7018 11.0523i 0.758286 0.353595i −0.00471738 0.999989i \(-0.501502\pi\)
0.763004 + 0.646394i \(0.223724\pi\)
\(978\) 0 0
\(979\) 19.8047 + 13.8674i 0.632959 + 0.443203i
\(980\) −27.7836 + 2.43075i −0.887516 + 0.0776476i
\(981\) 0 0
\(982\) 1.79565 2.56446i 0.0573016 0.0818351i
\(983\) −47.4957 17.2870i −1.51488 0.551371i −0.555016 0.831840i \(-0.687288\pi\)
−0.959863 + 0.280469i \(0.909510\pi\)
\(984\) 0 0
\(985\) −23.2101 86.6214i −0.739537 2.75999i
\(986\) 1.43284 + 2.04631i 0.0456311 + 0.0651679i
\(987\) 0 0
\(988\) −9.41156 16.3013i −0.299422 0.518613i
\(989\) 7.34864 12.7282i 0.233673 0.404734i
\(990\) 0 0
\(991\) −10.2293 + 38.1762i −0.324944 + 1.21271i 0.589424 + 0.807824i \(0.299355\pi\)
−0.914368 + 0.404883i \(0.867312\pi\)
\(992\) −1.23053 + 0.447875i −0.0390692 + 0.0142200i
\(993\) 0 0
\(994\) 3.86560 + 1.80256i 0.122609 + 0.0571737i
\(995\) 58.5056 + 10.3161i 1.85475 + 0.327043i
\(996\) 0 0
\(997\) 1.75339 20.0413i 0.0555304 0.634715i −0.916527 0.399972i \(-0.869020\pi\)
0.972058 0.234743i \(-0.0754247\pi\)
\(998\) 20.8545 0.660137
\(999\) 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.557.1 96
3.2 odd 2 inner 666.2.bs.b.557.8 yes 96
37.19 odd 36 inner 666.2.bs.b.611.8 yes 96
111.56 even 36 inner 666.2.bs.b.611.1 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
666.2.bs.b.557.1 96 1.1 even 1 trivial
666.2.bs.b.557.8 yes 96 3.2 odd 2 inner
666.2.bs.b.611.1 yes 96 111.56 even 36 inner
666.2.bs.b.611.8 yes 96 37.19 odd 36 inner