Properties

Label 450.2.l.a.379.2
Level $450$
Weight $2$
Character 450.379
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,2,Mod(19,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.l (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 379.2
Root \(0.951057 + 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 450.379
Dual form 450.2.l.a.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.951057 + 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(2.06909 + 0.847859i) q^{5} +4.07768i q^{7} +(0.587785 + 0.809017i) q^{8} +O(q^{10})\) \(q+(0.951057 + 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(2.06909 + 0.847859i) q^{5} +4.07768i q^{7} +(0.587785 + 0.809017i) q^{8} +(1.70582 + 1.44575i) q^{10} +(1.01484 - 3.12334i) q^{11} +(-5.15688 + 1.67557i) q^{13} +(-1.26007 + 3.87811i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.03353 - 2.79892i) q^{17} +(1.32292 - 0.961158i) q^{19} +(1.17557 + 1.90211i) q^{20} +(1.93033 - 2.65688i) q^{22} +(0.581542 + 0.188954i) q^{23} +(3.56227 + 3.50859i) q^{25} -5.42226 q^{26} +(-2.39680 + 3.29892i) q^{28} +(3.78173 + 2.74759i) q^{29} +(6.71737 - 4.88046i) q^{31} +1.00000i q^{32} +(-1.06909 - 3.29032i) q^{34} +(-3.45730 + 8.43710i) q^{35} +(2.28350 - 0.741955i) q^{37} +(1.55519 - 0.505311i) q^{38} +(0.530249 + 2.17229i) q^{40} +(-0.905972 - 2.78829i) q^{41} -8.64114i q^{43} +(2.65688 - 1.93033i) q^{44} +(0.494689 + 0.359413i) q^{46} +(4.06430 - 5.59403i) q^{47} -9.62750 q^{49} +(2.30371 + 4.43767i) q^{50} +(-5.15688 - 1.67557i) q^{52} +(-3.99557 + 5.49942i) q^{53} +(4.74794 - 5.60205i) q^{55} +(-3.29892 + 2.39680i) q^{56} +(2.74759 + 3.78173i) q^{58} +(-4.38081 - 13.4828i) q^{59} +(-3.88998 + 11.9721i) q^{61} +(7.89675 - 2.56581i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(-12.0907 - 0.905395i) q^{65} +(6.39169 + 8.79741i) q^{67} -3.45965i q^{68} +(-5.89529 + 6.95579i) q^{70} +(-7.33541 - 5.32949i) q^{71} +(-8.65537 - 2.81230i) q^{73} +2.40102 q^{74} +1.63522 q^{76} +(12.7360 + 4.13818i) q^{77} +(-3.31375 - 2.40758i) q^{79} +(-0.166977 + 2.22982i) q^{80} -2.93179i q^{82} +(-4.19156 - 5.76919i) q^{83} +(-1.83447 - 7.51536i) q^{85} +(2.67026 - 8.21821i) q^{86} +(3.12334 - 1.01484i) q^{88} +(1.48423 - 4.56799i) q^{89} +(-6.83245 - 21.0281i) q^{91} +(0.359413 + 0.494689i) q^{92} +(5.59403 - 4.06430i) q^{94} +(3.55217 - 0.867073i) q^{95} +(8.67557 - 11.9409i) q^{97} +(-9.15630 - 2.97506i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} - 10 q^{11} - 20 q^{13} + 2 q^{14} - 2 q^{16} - 10 q^{17} - 8 q^{19} + 10 q^{23} - 10 q^{25} - 4 q^{26} - 10 q^{28} + 22 q^{29} + 24 q^{31} + 8 q^{34} - 10 q^{35} - 20 q^{37} + 10 q^{38} - 22 q^{41} + 10 q^{46} - 10 q^{47} + 8 q^{49} + 20 q^{50} - 20 q^{52} + 30 q^{53} + 10 q^{55} - 2 q^{56} + 30 q^{58} + 20 q^{59} - 10 q^{62} + 2 q^{64} - 20 q^{65} + 10 q^{67} - 10 q^{70} - 20 q^{71} - 20 q^{73} + 4 q^{74} - 12 q^{76} + 20 q^{77} + 16 q^{79} - 70 q^{83} + 20 q^{85} + 18 q^{86} + 10 q^{88} + 34 q^{89} - 24 q^{91} - 30 q^{92} + 30 q^{94} - 30 q^{95} + 60 q^{97} - 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.951057 + 0.309017i 0.672499 + 0.218508i
\(3\) 0 0
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) 2.06909 + 0.847859i 0.925325 + 0.379174i
\(6\) 0 0
\(7\) 4.07768i 1.54122i 0.637307 + 0.770610i \(0.280048\pi\)
−0.637307 + 0.770610i \(0.719952\pi\)
\(8\) 0.587785 + 0.809017i 0.207813 + 0.286031i
\(9\) 0 0
\(10\) 1.70582 + 1.44575i 0.539427 + 0.457185i
\(11\) 1.01484 3.12334i 0.305985 0.941724i −0.673323 0.739348i \(-0.735134\pi\)
0.979308 0.202376i \(-0.0648662\pi\)
\(12\) 0 0
\(13\) −5.15688 + 1.67557i −1.43026 + 0.464720i −0.918847 0.394615i \(-0.870878\pi\)
−0.511413 + 0.859335i \(0.670878\pi\)
\(14\) −1.26007 + 3.87811i −0.336769 + 1.03647i
\(15\) 0 0
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −2.03353 2.79892i −0.493204 0.678837i 0.487771 0.872972i \(-0.337810\pi\)
−0.980975 + 0.194135i \(0.937810\pi\)
\(18\) 0 0
\(19\) 1.32292 0.961158i 0.303499 0.220505i −0.425603 0.904910i \(-0.639938\pi\)
0.729102 + 0.684405i \(0.239938\pi\)
\(20\) 1.17557 + 1.90211i 0.262866 + 0.425325i
\(21\) 0 0
\(22\) 1.93033 2.65688i 0.411548 0.566448i
\(23\) 0.581542 + 0.188954i 0.121260 + 0.0393997i 0.369018 0.929422i \(-0.379694\pi\)
−0.247758 + 0.968822i \(0.579694\pi\)
\(24\) 0 0
\(25\) 3.56227 + 3.50859i 0.712454 + 0.701719i
\(26\) −5.42226 −1.06339
\(27\) 0 0
\(28\) −2.39680 + 3.29892i −0.452953 + 0.623436i
\(29\) 3.78173 + 2.74759i 0.702249 + 0.510214i 0.880664 0.473741i \(-0.157097\pi\)
−0.178415 + 0.983955i \(0.557097\pi\)
\(30\) 0 0
\(31\) 6.71737 4.88046i 1.20648 0.876556i 0.211570 0.977363i \(-0.432142\pi\)
0.994906 + 0.100807i \(0.0321424\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −1.06909 3.29032i −0.183348 0.564286i
\(35\) −3.45730 + 8.43710i −0.584390 + 1.42613i
\(36\) 0 0
\(37\) 2.28350 0.741955i 0.375406 0.121977i −0.115236 0.993338i \(-0.536762\pi\)
0.490642 + 0.871361i \(0.336762\pi\)
\(38\) 1.55519 0.505311i 0.252285 0.0819722i
\(39\) 0 0
\(40\) 0.530249 + 2.17229i 0.0838397 + 0.343469i
\(41\) −0.905972 2.78829i −0.141489 0.435458i 0.855054 0.518539i \(-0.173524\pi\)
−0.996543 + 0.0830809i \(0.973524\pi\)
\(42\) 0 0
\(43\) 8.64114i 1.31776i −0.752247 0.658881i \(-0.771030\pi\)
0.752247 0.658881i \(-0.228970\pi\)
\(44\) 2.65688 1.93033i 0.400539 0.291009i
\(45\) 0 0
\(46\) 0.494689 + 0.359413i 0.0729379 + 0.0529925i
\(47\) 4.06430 5.59403i 0.592839 0.815973i −0.402190 0.915556i \(-0.631751\pi\)
0.995029 + 0.0995832i \(0.0317509\pi\)
\(48\) 0 0
\(49\) −9.62750 −1.37536
\(50\) 2.30371 + 4.43767i 0.325793 + 0.627582i
\(51\) 0 0
\(52\) −5.15688 1.67557i −0.715130 0.232360i
\(53\) −3.99557 + 5.49942i −0.548833 + 0.755404i −0.989853 0.142093i \(-0.954617\pi\)
0.441020 + 0.897497i \(0.354617\pi\)
\(54\) 0 0
\(55\) 4.74794 5.60205i 0.640213 0.755380i
\(56\) −3.29892 + 2.39680i −0.440836 + 0.320286i
\(57\) 0 0
\(58\) 2.74759 + 3.78173i 0.360776 + 0.496565i
\(59\) −4.38081 13.4828i −0.570333 1.75531i −0.651546 0.758609i \(-0.725879\pi\)
0.0812131 0.996697i \(-0.474121\pi\)
\(60\) 0 0
\(61\) −3.88998 + 11.9721i −0.498061 + 1.53287i 0.314070 + 0.949400i \(0.398307\pi\)
−0.812131 + 0.583475i \(0.801693\pi\)
\(62\) 7.89675 2.56581i 1.00289 0.325858i
\(63\) 0 0
\(64\) −0.309017 + 0.951057i −0.0386271 + 0.118882i
\(65\) −12.0907 0.905395i −1.49967 0.112300i
\(66\) 0 0
\(67\) 6.39169 + 8.79741i 0.780869 + 1.07477i 0.995185 + 0.0980099i \(0.0312477\pi\)
−0.214316 + 0.976764i \(0.568752\pi\)
\(68\) 3.45965i 0.419544i
\(69\) 0 0
\(70\) −5.89529 + 6.95579i −0.704622 + 0.831376i
\(71\) −7.33541 5.32949i −0.870553 0.632494i 0.0601825 0.998187i \(-0.480832\pi\)
−0.930735 + 0.365694i \(0.880832\pi\)
\(72\) 0 0
\(73\) −8.65537 2.81230i −1.01303 0.329155i −0.244972 0.969530i \(-0.578779\pi\)
−0.768062 + 0.640375i \(0.778779\pi\)
\(74\) 2.40102 0.279113
\(75\) 0 0
\(76\) 1.63522 0.187573
\(77\) 12.7360 + 4.13818i 1.45140 + 0.471589i
\(78\) 0 0
\(79\) −3.31375 2.40758i −0.372826 0.270874i 0.385556 0.922685i \(-0.374010\pi\)
−0.758382 + 0.651810i \(0.774010\pi\)
\(80\) −0.166977 + 2.22982i −0.0186686 + 0.249302i
\(81\) 0 0
\(82\) 2.93179i 0.323762i
\(83\) −4.19156 5.76919i −0.460083 0.633250i 0.514443 0.857525i \(-0.327999\pi\)
−0.974526 + 0.224274i \(0.927999\pi\)
\(84\) 0 0
\(85\) −1.83447 7.51536i −0.198977 0.815155i
\(86\) 2.67026 8.21821i 0.287942 0.886193i
\(87\) 0 0
\(88\) 3.12334 1.01484i 0.332950 0.108182i
\(89\) 1.48423 4.56799i 0.157328 0.484206i −0.841061 0.540940i \(-0.818069\pi\)
0.998389 + 0.0567336i \(0.0180686\pi\)
\(90\) 0 0
\(91\) −6.83245 21.0281i −0.716235 2.20434i
\(92\) 0.359413 + 0.494689i 0.0374714 + 0.0515749i
\(93\) 0 0
\(94\) 5.59403 4.06430i 0.576980 0.419200i
\(95\) 3.55217 0.867073i 0.364445 0.0889599i
\(96\) 0 0
\(97\) 8.67557 11.9409i 0.880871 1.21241i −0.0953083 0.995448i \(-0.530384\pi\)
0.976179 0.216967i \(-0.0696163\pi\)
\(98\) −9.15630 2.97506i −0.924926 0.300527i
\(99\) 0 0
\(100\) 0.819639 + 4.93236i 0.0819639 + 0.493236i
\(101\) 11.4846 1.14276 0.571381 0.820685i \(-0.306408\pi\)
0.571381 + 0.820685i \(0.306408\pi\)
\(102\) 0 0
\(103\) −8.20248 + 11.2897i −0.808214 + 1.11241i 0.183382 + 0.983042i \(0.441295\pi\)
−0.991596 + 0.129370i \(0.958705\pi\)
\(104\) −4.38670 3.18712i −0.430151 0.312523i
\(105\) 0 0
\(106\) −5.49942 + 3.99557i −0.534151 + 0.388084i
\(107\) 8.35405i 0.807616i 0.914844 + 0.403808i \(0.132314\pi\)
−0.914844 + 0.403808i \(0.867686\pi\)
\(108\) 0 0
\(109\) −0.164593 0.506564i −0.0157651 0.0485201i 0.942864 0.333176i \(-0.108120\pi\)
−0.958630 + 0.284656i \(0.908120\pi\)
\(110\) 6.24669 3.86067i 0.595598 0.368100i
\(111\) 0 0
\(112\) −3.87811 + 1.26007i −0.366447 + 0.119066i
\(113\) −16.3840 + 5.32350i −1.54128 + 0.500792i −0.951729 0.306938i \(-0.900695\pi\)
−0.589551 + 0.807731i \(0.700695\pi\)
\(114\) 0 0
\(115\) 1.04306 + 0.884029i 0.0972655 + 0.0824362i
\(116\) 1.44449 + 4.44569i 0.134118 + 0.412772i
\(117\) 0 0
\(118\) 14.1766i 1.30506i
\(119\) 11.4131 8.29210i 1.04624 0.760135i
\(120\) 0 0
\(121\) 0.173797 + 0.126271i 0.0157997 + 0.0114792i
\(122\) −7.39919 + 10.1841i −0.669891 + 0.922026i
\(123\) 0 0
\(124\) 8.30313 0.745643
\(125\) 4.39587 + 10.2799i 0.393179 + 0.919462i
\(126\) 0 0
\(127\) −1.09148 0.354643i −0.0968532 0.0314695i 0.260190 0.965558i \(-0.416215\pi\)
−0.357043 + 0.934088i \(0.616215\pi\)
\(128\) −0.587785 + 0.809017i −0.0519534 + 0.0715077i
\(129\) 0 0
\(130\) −11.2191 4.59731i −0.983984 0.403211i
\(131\) −5.35494 + 3.89059i −0.467864 + 0.339923i −0.796608 0.604496i \(-0.793374\pi\)
0.328745 + 0.944419i \(0.393374\pi\)
\(132\) 0 0
\(133\) 3.91930 + 5.39445i 0.339846 + 0.467758i
\(134\) 3.36031 + 10.3420i 0.290287 + 0.893410i
\(135\) 0 0
\(136\) 1.06909 3.29032i 0.0916738 0.282143i
\(137\) 7.05850 2.29345i 0.603049 0.195942i 0.00844901 0.999964i \(-0.497311\pi\)
0.594600 + 0.804022i \(0.297311\pi\)
\(138\) 0 0
\(139\) −1.63798 + 5.04119i −0.138932 + 0.427588i −0.996181 0.0873138i \(-0.972172\pi\)
0.857249 + 0.514902i \(0.172172\pi\)
\(140\) −7.75621 + 4.79360i −0.655520 + 0.405134i
\(141\) 0 0
\(142\) −5.32949 7.33541i −0.447240 0.615574i
\(143\) 17.8071i 1.48911i
\(144\) 0 0
\(145\) 5.49517 + 8.89138i 0.456349 + 0.738389i
\(146\) −7.36269 5.34931i −0.609341 0.442712i
\(147\) 0 0
\(148\) 2.28350 + 0.741955i 0.187703 + 0.0609883i
\(149\) −4.79296 −0.392655 −0.196327 0.980538i \(-0.562902\pi\)
−0.196327 + 0.980538i \(0.562902\pi\)
\(150\) 0 0
\(151\) 6.93533 0.564389 0.282195 0.959357i \(-0.408938\pi\)
0.282195 + 0.959357i \(0.408938\pi\)
\(152\) 1.55519 + 0.505311i 0.126142 + 0.0409861i
\(153\) 0 0
\(154\) 10.8339 + 7.87129i 0.873020 + 0.634286i
\(155\) 18.0368 4.40272i 1.44875 0.353635i
\(156\) 0 0
\(157\) 7.51609i 0.599849i −0.953963 0.299925i \(-0.903038\pi\)
0.953963 0.299925i \(-0.0969615\pi\)
\(158\) −2.40758 3.31375i −0.191537 0.263628i
\(159\) 0 0
\(160\) −0.847859 + 2.06909i −0.0670291 + 0.163576i
\(161\) −0.770497 + 2.37134i −0.0607236 + 0.186888i
\(162\) 0 0
\(163\) 7.95766 2.58560i 0.623292 0.202520i 0.0196905 0.999806i \(-0.493732\pi\)
0.603601 + 0.797286i \(0.293732\pi\)
\(164\) 0.905972 2.78829i 0.0707445 0.217729i
\(165\) 0 0
\(166\) −2.20363 6.78209i −0.171035 0.526392i
\(167\) −5.25731 7.23607i −0.406823 0.559944i 0.555617 0.831438i \(-0.312482\pi\)
−0.962440 + 0.271495i \(0.912482\pi\)
\(168\) 0 0
\(169\) 13.2686 9.64021i 1.02066 0.741555i
\(170\) 0.577684 7.71441i 0.0443063 0.591668i
\(171\) 0 0
\(172\) 5.07914 6.99083i 0.387280 0.533046i
\(173\) 2.22457 + 0.722807i 0.169131 + 0.0549540i 0.392358 0.919812i \(-0.371659\pi\)
−0.223228 + 0.974766i \(0.571659\pi\)
\(174\) 0 0
\(175\) −14.3069 + 14.5258i −1.08150 + 1.09805i
\(176\) 3.28408 0.247547
\(177\) 0 0
\(178\) 2.82318 3.88577i 0.211606 0.291251i
\(179\) −4.87811 3.54415i −0.364607 0.264902i 0.390364 0.920661i \(-0.372349\pi\)
−0.754971 + 0.655758i \(0.772349\pi\)
\(180\) 0 0
\(181\) −13.4112 + 9.74379i −0.996844 + 0.724250i −0.961409 0.275122i \(-0.911282\pi\)
−0.0354351 + 0.999372i \(0.511282\pi\)
\(182\) 22.1103i 1.63892i
\(183\) 0 0
\(184\) 0.188954 + 0.581542i 0.0139299 + 0.0428718i
\(185\) 5.35385 + 0.400916i 0.393623 + 0.0294759i
\(186\) 0 0
\(187\) −10.8057 + 3.51098i −0.790189 + 0.256748i
\(188\) 6.57617 2.13673i 0.479617 0.155837i
\(189\) 0 0
\(190\) 3.64625 + 0.273045i 0.264527 + 0.0198088i
\(191\) −3.08029 9.48015i −0.222882 0.685960i −0.998500 0.0547570i \(-0.982562\pi\)
0.775618 0.631203i \(-0.217438\pi\)
\(192\) 0 0
\(193\) 25.0735i 1.80483i 0.430867 + 0.902416i \(0.358208\pi\)
−0.430867 + 0.902416i \(0.641792\pi\)
\(194\) 11.9409 8.67557i 0.857307 0.622870i
\(195\) 0 0
\(196\) −7.78881 5.65890i −0.556344 0.404207i
\(197\) −15.7749 + 21.7123i −1.12391 + 1.54694i −0.324773 + 0.945792i \(0.605288\pi\)
−0.799141 + 0.601143i \(0.794712\pi\)
\(198\) 0 0
\(199\) 4.06114 0.287887 0.143943 0.989586i \(-0.454022\pi\)
0.143943 + 0.989586i \(0.454022\pi\)
\(200\) −0.744661 + 4.94424i −0.0526555 + 0.349610i
\(201\) 0 0
\(202\) 10.9225 + 3.54894i 0.768506 + 0.249703i
\(203\) −11.2038 + 15.4207i −0.786352 + 1.08232i
\(204\) 0 0
\(205\) 0.489542 6.53737i 0.0341911 0.456590i
\(206\) −11.2897 + 8.20248i −0.786594 + 0.571494i
\(207\) 0 0
\(208\) −3.18712 4.38670i −0.220987 0.304163i
\(209\) −1.65948 5.10736i −0.114789 0.353283i
\(210\) 0 0
\(211\) −1.34573 + 4.14173i −0.0926438 + 0.285128i −0.986632 0.162961i \(-0.947895\pi\)
0.893989 + 0.448090i \(0.147895\pi\)
\(212\) −6.46496 + 2.10059i −0.444015 + 0.144269i
\(213\) 0 0
\(214\) −2.58154 + 7.94517i −0.176471 + 0.543121i
\(215\) 7.32647 17.8793i 0.499661 1.21936i
\(216\) 0 0
\(217\) 19.9010 + 27.3913i 1.35097 + 1.85944i
\(218\) 0.532633i 0.0360745i
\(219\) 0 0
\(220\) 7.13397 1.74138i 0.480972 0.117404i
\(221\) 15.1764 + 11.0263i 1.02088 + 0.741711i
\(222\) 0 0
\(223\) −0.344164 0.111826i −0.0230469 0.00748840i 0.297471 0.954731i \(-0.403857\pi\)
−0.320518 + 0.947243i \(0.603857\pi\)
\(224\) −4.07768 −0.272452
\(225\) 0 0
\(226\) −17.2272 −1.14594
\(227\) 12.2284 + 3.97323i 0.811624 + 0.263713i 0.685286 0.728274i \(-0.259677\pi\)
0.126339 + 0.991987i \(0.459677\pi\)
\(228\) 0 0
\(229\) −13.3769 9.71886i −0.883968 0.642240i 0.0503302 0.998733i \(-0.483973\pi\)
−0.934298 + 0.356492i \(0.883973\pi\)
\(230\) 0.718826 + 1.16308i 0.0473980 + 0.0766915i
\(231\) 0 0
\(232\) 4.67447i 0.306894i
\(233\) −6.50714 8.95631i −0.426297 0.586747i 0.540801 0.841150i \(-0.318121\pi\)
−0.967098 + 0.254403i \(0.918121\pi\)
\(234\) 0 0
\(235\) 13.1523 8.12860i 0.857965 0.530251i
\(236\) 4.38081 13.4828i 0.285167 0.877653i
\(237\) 0 0
\(238\) 13.4169 4.35941i 0.869688 0.282579i
\(239\) −1.72654 + 5.31375i −0.111681 + 0.343718i −0.991240 0.132071i \(-0.957837\pi\)
0.879560 + 0.475789i \(0.157837\pi\)
\(240\) 0 0
\(241\) −4.59014 14.1270i −0.295677 0.909999i −0.982993 0.183641i \(-0.941212\pi\)
0.687317 0.726358i \(-0.258788\pi\)
\(242\) 0.126271 + 0.173797i 0.00811700 + 0.0111721i
\(243\) 0 0
\(244\) −10.1841 + 7.39919i −0.651971 + 0.473684i
\(245\) −19.9202 8.16276i −1.27265 0.521500i
\(246\) 0 0
\(247\) −5.21165 + 7.17322i −0.331609 + 0.456421i
\(248\) 7.89675 + 2.56581i 0.501444 + 0.162929i
\(249\) 0 0
\(250\) 1.00406 + 11.1352i 0.0635021 + 0.704250i
\(251\) 12.6802 0.800368 0.400184 0.916435i \(-0.368946\pi\)
0.400184 + 0.916435i \(0.368946\pi\)
\(252\) 0 0
\(253\) 1.18034 1.62460i 0.0742073 0.102138i
\(254\) −0.928468 0.674572i −0.0582573 0.0423264i
\(255\) 0 0
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 19.1916i 1.19714i 0.801071 + 0.598570i \(0.204264\pi\)
−0.801071 + 0.598570i \(0.795736\pi\)
\(258\) 0 0
\(259\) 3.02546 + 9.31140i 0.187993 + 0.578582i
\(260\) −9.24940 7.83921i −0.573623 0.486167i
\(261\) 0 0
\(262\) −6.29511 + 2.04541i −0.388913 + 0.126366i
\(263\) 28.0323 9.10825i 1.72855 0.561639i 0.735309 0.677732i \(-0.237037\pi\)
0.993238 + 0.116093i \(0.0370372\pi\)
\(264\) 0 0
\(265\) −12.9299 + 7.99113i −0.794279 + 0.490891i
\(266\) 2.06050 + 6.34156i 0.126337 + 0.388826i
\(267\) 0 0
\(268\) 10.8742i 0.664247i
\(269\) −17.7191 + 12.8737i −1.08035 + 0.784922i −0.977744 0.209800i \(-0.932719\pi\)
−0.102608 + 0.994722i \(0.532719\pi\)
\(270\) 0 0
\(271\) 12.2025 + 8.86562i 0.741248 + 0.538548i 0.893102 0.449855i \(-0.148524\pi\)
−0.151854 + 0.988403i \(0.548524\pi\)
\(272\) 2.03353 2.79892i 0.123301 0.169709i
\(273\) 0 0
\(274\) 7.42175 0.448364
\(275\) 14.5737 7.56555i 0.878825 0.456220i
\(276\) 0 0
\(277\) −2.45721 0.798395i −0.147639 0.0479709i 0.234265 0.972173i \(-0.424732\pi\)
−0.381904 + 0.924202i \(0.624732\pi\)
\(278\) −3.11563 + 4.28829i −0.186863 + 0.257195i
\(279\) 0 0
\(280\) −8.85790 + 2.16219i −0.529361 + 0.129215i
\(281\) −14.8843 + 10.8141i −0.887923 + 0.645113i −0.935336 0.353762i \(-0.884902\pi\)
0.0474130 + 0.998875i \(0.484902\pi\)
\(282\) 0 0
\(283\) 2.04234 + 2.81105i 0.121405 + 0.167099i 0.865394 0.501093i \(-0.167068\pi\)
−0.743989 + 0.668192i \(0.767068\pi\)
\(284\) −2.80188 8.62329i −0.166261 0.511698i
\(285\) 0 0
\(286\) −5.50271 + 16.9356i −0.325382 + 1.00142i
\(287\) 11.3698 3.69427i 0.671137 0.218066i
\(288\) 0 0
\(289\) 1.55461 4.78460i 0.0914477 0.281447i
\(290\) 2.47863 + 10.1543i 0.145550 + 0.596281i
\(291\) 0 0
\(292\) −5.34931 7.36269i −0.313045 0.430869i
\(293\) 15.8625i 0.926699i −0.886176 0.463349i \(-0.846647\pi\)
0.886176 0.463349i \(-0.153353\pi\)
\(294\) 0 0
\(295\) 2.36717 31.6114i 0.137822 1.84048i
\(296\) 1.94246 + 1.41128i 0.112903 + 0.0820291i
\(297\) 0 0
\(298\) −4.55838 1.48111i −0.264060 0.0857982i
\(299\) −3.31555 −0.191743
\(300\) 0 0
\(301\) 35.2358 2.03096
\(302\) 6.59589 + 2.14314i 0.379551 + 0.123324i
\(303\) 0 0
\(304\) 1.32292 + 0.961158i 0.0758747 + 0.0551262i
\(305\) −18.1994 + 21.4733i −1.04210 + 1.22956i
\(306\) 0 0
\(307\) 25.4122i 1.45035i 0.688565 + 0.725175i \(0.258241\pi\)
−0.688565 + 0.725175i \(0.741759\pi\)
\(308\) 7.87129 + 10.8339i 0.448508 + 0.617319i
\(309\) 0 0
\(310\) 18.5145 + 1.38644i 1.05155 + 0.0787443i
\(311\) −5.69968 + 17.5418i −0.323199 + 0.994704i 0.649048 + 0.760748i \(0.275167\pi\)
−0.972247 + 0.233957i \(0.924833\pi\)
\(312\) 0 0
\(313\) 20.8396 6.77121i 1.17793 0.382731i 0.346330 0.938113i \(-0.387428\pi\)
0.831596 + 0.555381i \(0.187428\pi\)
\(314\) 2.32260 7.14823i 0.131072 0.403398i
\(315\) 0 0
\(316\) −1.26574 3.89555i −0.0712035 0.219142i
\(317\) 3.40134 + 4.68155i 0.191039 + 0.262942i 0.893782 0.448501i \(-0.148042\pi\)
−0.702744 + 0.711443i \(0.748042\pi\)
\(318\) 0 0
\(319\) 12.4195 9.02329i 0.695358 0.505207i
\(320\) −1.44575 + 1.70582i −0.0808196 + 0.0953582i
\(321\) 0 0
\(322\) −1.46557 + 2.01719i −0.0816731 + 0.112413i
\(323\) −5.38040 1.74820i −0.299374 0.0972724i
\(324\) 0 0
\(325\) −24.2491 12.1245i −1.34510 0.672549i
\(326\) 8.36717 0.463415
\(327\) 0 0
\(328\) 1.72326 2.37186i 0.0951511 0.130964i
\(329\) 22.8107 + 16.5729i 1.25759 + 0.913695i
\(330\) 0 0
\(331\) 6.18384 4.49282i 0.339895 0.246948i −0.404723 0.914439i \(-0.632632\pi\)
0.744617 + 0.667492i \(0.232632\pi\)
\(332\) 7.13111i 0.391370i
\(333\) 0 0
\(334\) −2.76393 8.50651i −0.151236 0.465455i
\(335\) 5.76603 + 23.6219i 0.315032 + 1.29060i
\(336\) 0 0
\(337\) 3.50849 1.13998i 0.191119 0.0620985i −0.211893 0.977293i \(-0.567963\pi\)
0.403013 + 0.915194i \(0.367963\pi\)
\(338\) 15.5982 5.06816i 0.848430 0.275671i
\(339\) 0 0
\(340\) 2.93329 7.15833i 0.159080 0.388215i
\(341\) −8.42632 25.9335i −0.456311 1.40438i
\(342\) 0 0
\(343\) 10.7141i 0.578508i
\(344\) 6.99083 5.07914i 0.376920 0.273849i
\(345\) 0 0
\(346\) 1.89233 + 1.37486i 0.101732 + 0.0739129i
\(347\) 2.13673 2.94095i 0.114706 0.157879i −0.747804 0.663920i \(-0.768892\pi\)
0.862509 + 0.506041i \(0.168892\pi\)
\(348\) 0 0
\(349\) −12.2270 −0.654496 −0.327248 0.944938i \(-0.606121\pi\)
−0.327248 + 0.944938i \(0.606121\pi\)
\(350\) −18.0954 + 9.39378i −0.967241 + 0.502119i
\(351\) 0 0
\(352\) 3.12334 + 1.01484i 0.166475 + 0.0540910i
\(353\) 9.20711 12.6725i 0.490045 0.674489i −0.490351 0.871525i \(-0.663132\pi\)
0.980396 + 0.197036i \(0.0631316\pi\)
\(354\) 0 0
\(355\) −10.6590 17.2466i −0.565719 0.915353i
\(356\) 3.88577 2.82318i 0.205945 0.149628i
\(357\) 0 0
\(358\) −3.54415 4.87811i −0.187314 0.257816i
\(359\) 2.18529 + 6.72564i 0.115335 + 0.354966i 0.992017 0.126105i \(-0.0402478\pi\)
−0.876681 + 0.481071i \(0.840248\pi\)
\(360\) 0 0
\(361\) −5.04503 + 15.5270i −0.265528 + 0.817211i
\(362\) −15.7658 + 5.12261i −0.828631 + 0.269238i
\(363\) 0 0
\(364\) 6.83245 21.0281i 0.358117 1.10217i
\(365\) −15.5243 13.1574i −0.812579 0.688691i
\(366\) 0 0
\(367\) −15.7219 21.6393i −0.820676 1.12956i −0.989588 0.143932i \(-0.954025\pi\)
0.168912 0.985631i \(-0.445975\pi\)
\(368\) 0.611469i 0.0318751i
\(369\) 0 0
\(370\) 4.96792 + 2.03572i 0.258270 + 0.105832i
\(371\) −22.4249 16.2927i −1.16424 0.845872i
\(372\) 0 0
\(373\) −11.3031 3.67261i −0.585254 0.190161i 0.00139899 0.999999i \(-0.499555\pi\)
−0.586653 + 0.809839i \(0.699555\pi\)
\(374\) −11.3618 −0.587503
\(375\) 0 0
\(376\) 6.91460 0.356593
\(377\) −24.1057 7.83241i −1.24151 0.403390i
\(378\) 0 0
\(379\) −3.90398 2.83641i −0.200534 0.145696i 0.482987 0.875628i \(-0.339552\pi\)
−0.683520 + 0.729931i \(0.739552\pi\)
\(380\) 3.38342 + 1.38644i 0.173566 + 0.0711226i
\(381\) 0 0
\(382\) 9.96802i 0.510008i
\(383\) 2.82343 + 3.88612i 0.144271 + 0.198572i 0.875037 0.484056i \(-0.160837\pi\)
−0.730766 + 0.682628i \(0.760837\pi\)
\(384\) 0 0
\(385\) 22.8434 + 19.3606i 1.16421 + 0.986708i
\(386\) −7.74814 + 23.8463i −0.394370 + 1.21375i
\(387\) 0 0
\(388\) 14.0374 4.56102i 0.712639 0.231551i
\(389\) −4.15372 + 12.7838i −0.210602 + 0.648166i 0.788835 + 0.614605i \(0.210685\pi\)
−0.999437 + 0.0335605i \(0.989315\pi\)
\(390\) 0 0
\(391\) −0.653716 2.01193i −0.0330599 0.101748i
\(392\) −5.65890 7.78881i −0.285818 0.393394i
\(393\) 0 0
\(394\) −21.7123 + 15.7749i −1.09385 + 0.794727i
\(395\) −4.81516 7.79110i −0.242277 0.392013i
\(396\) 0 0
\(397\) −0.0509156 + 0.0700793i −0.00255538 + 0.00351718i −0.810293 0.586025i \(-0.800692\pi\)
0.807737 + 0.589542i \(0.200692\pi\)
\(398\) 3.86237 + 1.25496i 0.193603 + 0.0629055i
\(399\) 0 0
\(400\) −2.23607 + 4.47214i −0.111803 + 0.223607i
\(401\) −0.321141 −0.0160370 −0.00801851 0.999968i \(-0.502552\pi\)
−0.00801851 + 0.999968i \(0.502552\pi\)
\(402\) 0 0
\(403\) −26.4631 + 36.4233i −1.31822 + 1.81438i
\(404\) 9.29125 + 6.75049i 0.462257 + 0.335850i
\(405\) 0 0
\(406\) −15.4207 + 11.2038i −0.765316 + 0.556035i
\(407\) 7.88513i 0.390851i
\(408\) 0 0
\(409\) −7.48890 23.0485i −0.370302 1.13967i −0.946594 0.322429i \(-0.895501\pi\)
0.576291 0.817244i \(-0.304499\pi\)
\(410\) 2.48574 6.06613i 0.122762 0.299585i
\(411\) 0 0
\(412\) −13.2719 + 4.31230i −0.653859 + 0.212452i
\(413\) 54.9784 17.8636i 2.70531 0.879009i
\(414\) 0 0
\(415\) −3.78126 15.4908i −0.185615 0.760414i
\(416\) −1.67557 5.15688i −0.0821516 0.252837i
\(417\) 0 0
\(418\) 5.37019i 0.262665i
\(419\) −18.4661 + 13.4164i −0.902128 + 0.655434i −0.939012 0.343885i \(-0.888257\pi\)
0.0368836 + 0.999320i \(0.488257\pi\)
\(420\) 0 0
\(421\) 31.6567 + 22.9999i 1.54285 + 1.12095i 0.948514 + 0.316734i \(0.102586\pi\)
0.594339 + 0.804215i \(0.297414\pi\)
\(422\) −2.55973 + 3.52316i −0.124606 + 0.171505i
\(423\) 0 0
\(424\) −6.79766 −0.330124
\(425\) 2.57627 17.1053i 0.124967 0.829730i
\(426\) 0 0
\(427\) −48.8186 15.8621i −2.36250 0.767622i
\(428\) −4.91038 + 6.75856i −0.237352 + 0.326688i
\(429\) 0 0
\(430\) 12.4929 14.7402i 0.602461 0.710837i
\(431\) 19.9676 14.5073i 0.961806 0.698793i 0.00823646 0.999966i \(-0.497378\pi\)
0.953569 + 0.301173i \(0.0973782\pi\)
\(432\) 0 0
\(433\) −11.6839 16.0815i −0.561493 0.772829i 0.430023 0.902818i \(-0.358506\pi\)
−0.991515 + 0.129990i \(0.958506\pi\)
\(434\) 10.4626 + 32.2004i 0.502219 + 1.54567i
\(435\) 0 0
\(436\) 0.164593 0.506564i 0.00788256 0.0242600i
\(437\) 0.950949 0.308982i 0.0454901 0.0147806i
\(438\) 0 0
\(439\) −1.56742 + 4.82402i −0.0748088 + 0.230238i −0.981468 0.191626i \(-0.938624\pi\)
0.906659 + 0.421864i \(0.138624\pi\)
\(440\) 7.32292 + 0.548367i 0.349107 + 0.0261424i
\(441\) 0 0
\(442\) 11.0263 + 15.1764i 0.524469 + 0.721870i
\(443\) 10.1873i 0.484015i −0.970274 0.242008i \(-0.922194\pi\)
0.970274 0.242008i \(-0.0778059\pi\)
\(444\) 0 0
\(445\) 6.94402 8.19318i 0.329178 0.388394i
\(446\) −0.292763 0.212705i −0.0138627 0.0100719i
\(447\) 0 0
\(448\) −3.87811 1.26007i −0.183223 0.0595329i
\(449\) 10.3653 0.489169 0.244585 0.969628i \(-0.421348\pi\)
0.244585 + 0.969628i \(0.421348\pi\)
\(450\) 0 0
\(451\) −9.62822 −0.453375
\(452\) −16.3840 5.32350i −0.770640 0.250396i
\(453\) 0 0
\(454\) 10.4021 + 7.55754i 0.488193 + 0.354693i
\(455\) 3.69192 49.3020i 0.173080 2.31131i
\(456\) 0 0
\(457\) 4.06165i 0.189996i 0.995477 + 0.0949980i \(0.0302845\pi\)
−0.995477 + 0.0949980i \(0.969716\pi\)
\(458\) −9.71886 13.3769i −0.454133 0.625060i
\(459\) 0 0
\(460\) 0.324231 + 1.32829i 0.0151173 + 0.0619317i
\(461\) −2.08929 + 6.43019i −0.0973081 + 0.299484i −0.987848 0.155421i \(-0.950327\pi\)
0.890540 + 0.454905i \(0.150327\pi\)
\(462\) 0 0
\(463\) 9.24602 3.00421i 0.429699 0.139618i −0.0861791 0.996280i \(-0.527466\pi\)
0.515878 + 0.856662i \(0.327466\pi\)
\(464\) −1.44449 + 4.44569i −0.0670589 + 0.206386i
\(465\) 0 0
\(466\) −3.42101 10.5288i −0.158475 0.487736i
\(467\) −22.5722 31.0679i −1.04452 1.43765i −0.893469 0.449125i \(-0.851736\pi\)
−0.151046 0.988527i \(-0.548264\pi\)
\(468\) 0 0
\(469\) −35.8730 + 26.0633i −1.65646 + 1.20349i
\(470\) 15.0205 3.66646i 0.692844 0.169121i
\(471\) 0 0
\(472\) 8.33280 11.4691i 0.383548 0.527909i
\(473\) −26.9893 8.76934i −1.24097 0.403215i
\(474\) 0 0
\(475\) 8.08492 + 1.21768i 0.370961 + 0.0558712i
\(476\) 14.1074 0.646610
\(477\) 0 0
\(478\) −3.28408 + 4.52015i −0.150210 + 0.206747i
\(479\) −6.85832 4.98286i −0.313364 0.227673i 0.419974 0.907536i \(-0.362039\pi\)
−0.733339 + 0.679863i \(0.762039\pi\)
\(480\) 0 0
\(481\) −10.5325 + 7.65234i −0.480243 + 0.348917i
\(482\) 14.8540i 0.676581i
\(483\) 0 0
\(484\) 0.0663845 + 0.204311i 0.00301748 + 0.00928684i
\(485\) 28.0747 17.3511i 1.27481 0.787875i
\(486\) 0 0
\(487\) 27.5559 8.95344i 1.24868 0.405719i 0.391229 0.920293i \(-0.372050\pi\)
0.857446 + 0.514574i \(0.172050\pi\)
\(488\) −11.9721 + 3.88998i −0.541953 + 0.176091i
\(489\) 0 0
\(490\) −16.4228 13.9189i −0.741906 0.628793i
\(491\) 3.16018 + 9.72603i 0.142617 + 0.438930i 0.996697 0.0812121i \(-0.0258791\pi\)
−0.854080 + 0.520142i \(0.825879\pi\)
\(492\) 0 0
\(493\) 16.1720i 0.728352i
\(494\) −7.17322 + 5.21165i −0.322738 + 0.234483i
\(495\) 0 0
\(496\) 6.71737 + 4.88046i 0.301619 + 0.219139i
\(497\) 21.7320 29.9115i 0.974811 1.34171i
\(498\) 0 0
\(499\) 23.0007 1.02965 0.514827 0.857294i \(-0.327856\pi\)
0.514827 + 0.857294i \(0.327856\pi\)
\(500\) −2.48604 + 10.9004i −0.111179 + 0.487483i
\(501\) 0 0
\(502\) 12.0596 + 3.91840i 0.538246 + 0.174887i
\(503\) −11.1980 + 15.4127i −0.499293 + 0.687217i −0.982068 0.188527i \(-0.939629\pi\)
0.482775 + 0.875744i \(0.339629\pi\)
\(504\) 0 0
\(505\) 23.7627 + 9.73734i 1.05743 + 0.433306i
\(506\) 1.62460 1.18034i 0.0722222 0.0524725i
\(507\) 0 0
\(508\) −0.674572 0.928468i −0.0299293 0.0411941i
\(509\) −7.33006 22.5596i −0.324899 0.999937i −0.971486 0.237097i \(-0.923804\pi\)
0.646587 0.762840i \(-0.276196\pi\)
\(510\) 0 0
\(511\) 11.4677 35.2938i 0.507300 1.56131i
\(512\) −0.951057 + 0.309017i −0.0420312 + 0.0136568i
\(513\) 0 0
\(514\) −5.93053 + 18.2523i −0.261585 + 0.805074i
\(515\) −26.5438 + 16.4050i −1.16966 + 0.722889i
\(516\) 0 0
\(517\) −13.3475 18.3712i −0.587022 0.807966i
\(518\) 9.79059i 0.430174i
\(519\) 0 0
\(520\) −6.37425 10.3138i −0.279529 0.452288i
\(521\) 23.6577 + 17.1883i 1.03646 + 0.753034i 0.969592 0.244728i \(-0.0786985\pi\)
0.0668706 + 0.997762i \(0.478699\pi\)
\(522\) 0 0
\(523\) −18.3703 5.96888i −0.803278 0.261001i −0.121530 0.992588i \(-0.538780\pi\)
−0.681748 + 0.731587i \(0.738780\pi\)
\(524\) −6.61907 −0.289156
\(525\) 0 0
\(526\) 29.4749 1.28517
\(527\) −27.3200 8.87680i −1.19008 0.386679i
\(528\) 0 0
\(529\) −18.3049 13.2993i −0.795865 0.578230i
\(530\) −14.7665 + 3.60445i −0.641415 + 0.156567i
\(531\) 0 0
\(532\) 6.66791i 0.289091i
\(533\) 9.34397 + 12.8609i 0.404732 + 0.557066i
\(534\) 0 0
\(535\) −7.08305 + 17.2853i −0.306227 + 0.747308i
\(536\) −3.36031 + 10.3420i −0.145143 + 0.446705i
\(537\) 0 0
\(538\) −20.8300 + 6.76809i −0.898047 + 0.291793i
\(539\) −9.77034 + 30.0700i −0.420838 + 1.29521i
\(540\) 0 0
\(541\) −9.95316 30.6327i −0.427920 1.31700i −0.900170 0.435538i \(-0.856558\pi\)
0.472250 0.881464i \(-0.343442\pi\)
\(542\) 8.86562 + 12.2025i 0.380811 + 0.524141i
\(543\) 0 0
\(544\) 2.79892 2.03353i 0.120003 0.0871869i
\(545\) 0.0889378 1.18768i 0.00380968 0.0508746i
\(546\) 0 0
\(547\) −13.0871 + 18.0129i −0.559564 + 0.770174i −0.991271 0.131840i \(-0.957912\pi\)
0.431707 + 0.902014i \(0.357912\pi\)
\(548\) 7.05850 + 2.29345i 0.301524 + 0.0979712i
\(549\) 0 0
\(550\) 16.1983 2.69176i 0.690696 0.114777i
\(551\) 7.64379 0.325637
\(552\) 0 0
\(553\) 9.81736 13.5124i 0.417476 0.574607i
\(554\) −2.09023 1.51864i −0.0888052 0.0645208i
\(555\) 0 0
\(556\) −4.28829 + 3.11563i −0.181864 + 0.132132i
\(557\) 15.1565i 0.642202i 0.947045 + 0.321101i \(0.104053\pi\)
−0.947045 + 0.321101i \(0.895947\pi\)
\(558\) 0 0
\(559\) 14.4788 + 44.5613i 0.612390 + 1.88474i
\(560\) −9.09252 0.680881i −0.384229 0.0287725i
\(561\) 0 0
\(562\) −17.4975 + 5.68529i −0.738089 + 0.239820i
\(563\) −19.8019 + 6.43403i −0.834551 + 0.271162i −0.694961 0.719047i \(-0.744579\pi\)
−0.139590 + 0.990209i \(0.544579\pi\)
\(564\) 0 0
\(565\) −38.4136 2.87655i −1.61607 0.121018i
\(566\) 1.07372 + 3.30458i 0.0451320 + 0.138902i
\(567\) 0 0
\(568\) 9.06706i 0.380445i
\(569\) −11.9375 + 8.67311i −0.500446 + 0.363596i −0.809187 0.587551i \(-0.800092\pi\)
0.308741 + 0.951146i \(0.400092\pi\)
\(570\) 0 0
\(571\) 4.08805 + 2.97014i 0.171080 + 0.124297i 0.670030 0.742334i \(-0.266281\pi\)
−0.498951 + 0.866630i \(0.666281\pi\)
\(572\) −10.4668 + 14.4063i −0.437638 + 0.602356i
\(573\) 0 0
\(574\) 11.9549 0.498988
\(575\) 1.40865 + 2.71350i 0.0587446 + 0.113161i
\(576\) 0 0
\(577\) 5.22817 + 1.69873i 0.217651 + 0.0707193i 0.415813 0.909450i \(-0.363497\pi\)
−0.198162 + 0.980169i \(0.563497\pi\)
\(578\) 2.95704 4.07002i 0.122997 0.169291i
\(579\) 0 0
\(580\) −0.780532 + 10.4233i −0.0324098 + 0.432802i
\(581\) 23.5249 17.0919i 0.975978 0.709090i
\(582\) 0 0
\(583\) 13.1218 + 18.0605i 0.543447 + 0.747991i
\(584\) −2.81230 8.65537i −0.116374 0.358162i
\(585\) 0 0
\(586\) 4.90179 15.0862i 0.202491 0.623204i
\(587\) −40.3229 + 13.1017i −1.66430 + 0.540765i −0.981767 0.190088i \(-0.939123\pi\)
−0.682535 + 0.730853i \(0.739123\pi\)
\(588\) 0 0
\(589\) 4.19566 12.9129i 0.172879 0.532067i
\(590\) 12.0198 29.3327i 0.494846 1.20761i
\(591\) 0 0
\(592\) 1.41128 + 1.94246i 0.0580033 + 0.0798348i
\(593\) 6.76110i 0.277645i −0.990317 0.138822i \(-0.955668\pi\)
0.990317 0.138822i \(-0.0443317\pi\)
\(594\) 0 0
\(595\) 30.6452 7.48041i 1.25633 0.306667i
\(596\) −3.87759 2.81723i −0.158832 0.115398i
\(597\) 0 0
\(598\) −3.15327 1.02456i −0.128947 0.0418974i
\(599\) 11.7740 0.481074 0.240537 0.970640i \(-0.422676\pi\)
0.240537 + 0.970640i \(0.422676\pi\)
\(600\) 0 0
\(601\) 22.4353 0.915154 0.457577 0.889170i \(-0.348717\pi\)
0.457577 + 0.889170i \(0.348717\pi\)
\(602\) 33.5113 + 10.8885i 1.36582 + 0.443781i
\(603\) 0 0
\(604\) 5.61080 + 4.07649i 0.228300 + 0.165870i
\(605\) 0.252542 + 0.408621i 0.0102673 + 0.0166128i
\(606\) 0 0
\(607\) 33.0837i 1.34283i −0.741083 0.671413i \(-0.765688\pi\)
0.741083 0.671413i \(-0.234312\pi\)
\(608\) 0.961158 + 1.32292i 0.0389801 + 0.0536515i
\(609\) 0 0
\(610\) −23.9443 + 14.7984i −0.969475 + 0.599169i
\(611\) −11.5859 + 35.6577i −0.468715 + 1.44256i
\(612\) 0 0
\(613\) 14.5411 4.72470i 0.587311 0.190829i −0.000262331 1.00000i \(-0.500084\pi\)
0.587573 + 0.809171i \(0.300084\pi\)
\(614\) −7.85279 + 24.1684i −0.316913 + 0.975358i
\(615\) 0 0
\(616\) 4.13818 + 12.7360i 0.166732 + 0.513149i
\(617\) 6.25460 + 8.60872i 0.251801 + 0.346574i 0.916141 0.400856i \(-0.131287\pi\)
−0.664340 + 0.747430i \(0.731287\pi\)
\(618\) 0 0
\(619\) 23.3120 16.9371i 0.936987 0.680761i −0.0107068 0.999943i \(-0.503408\pi\)
0.947693 + 0.319182i \(0.103408\pi\)
\(620\) 17.1799 + 7.03988i 0.689962 + 0.282728i
\(621\) 0 0
\(622\) −10.8414 + 14.9219i −0.434702 + 0.598316i
\(623\) 18.6268 + 6.05223i 0.746268 + 0.242477i
\(624\) 0 0
\(625\) 0.379550 + 24.9971i 0.0151820 + 0.999885i
\(626\) 21.9121 0.875783
\(627\) 0 0
\(628\) 4.41785 6.08064i 0.176291 0.242644i
\(629\) −6.72024 4.88254i −0.267954 0.194680i
\(630\) 0 0
\(631\) −16.3555 + 11.8830i −0.651102 + 0.473053i −0.863646 0.504098i \(-0.831825\pi\)
0.212544 + 0.977151i \(0.431825\pi\)
\(632\) 4.09602i 0.162931i
\(633\) 0 0
\(634\) 1.78819 + 5.50349i 0.0710182 + 0.218572i
\(635\) −1.95768 1.65921i −0.0776883 0.0658437i
\(636\) 0 0
\(637\) 49.6478 16.1316i 1.96712 0.639156i
\(638\) 14.6000 4.74383i 0.578019 0.187810i
\(639\) 0 0
\(640\) −1.90211 + 1.17557i −0.0751876 + 0.0464685i
\(641\) 15.4707 + 47.6138i 0.611055 + 1.88063i 0.448053 + 0.894007i \(0.352118\pi\)
0.163002 + 0.986626i \(0.447882\pi\)
\(642\) 0 0
\(643\) 11.8080i 0.465660i −0.972517 0.232830i \(-0.925201\pi\)
0.972517 0.232830i \(-0.0747986\pi\)
\(644\) −2.01719 + 1.46557i −0.0794883 + 0.0577516i
\(645\) 0 0
\(646\) −4.57684 3.32527i −0.180073 0.130831i
\(647\) 17.0969 23.5319i 0.672148 0.925133i −0.327658 0.944796i \(-0.606260\pi\)
0.999807 + 0.0196636i \(0.00625953\pi\)
\(648\) 0 0
\(649\) −46.5571 −1.82753
\(650\) −19.3156 19.0245i −0.757619 0.746202i
\(651\) 0 0
\(652\) 7.95766 + 2.58560i 0.311646 + 0.101260i
\(653\) 14.5845 20.0738i 0.570735 0.785549i −0.421906 0.906639i \(-0.638639\pi\)
0.992642 + 0.121090i \(0.0386389\pi\)
\(654\) 0 0
\(655\) −14.3785 + 3.50976i −0.561816 + 0.137137i
\(656\) 2.37186 1.72326i 0.0926057 0.0672820i
\(657\) 0 0
\(658\) 16.5729 + 22.8107i 0.646080 + 0.889253i
\(659\) 5.92361 + 18.2310i 0.230751 + 0.710179i 0.997657 + 0.0684190i \(0.0217955\pi\)
−0.766906 + 0.641760i \(0.778205\pi\)
\(660\) 0 0
\(661\) −14.1363 + 43.5071i −0.549839 + 1.69223i 0.159359 + 0.987221i \(0.449057\pi\)
−0.709198 + 0.705010i \(0.750943\pi\)
\(662\) 7.26954 2.36202i 0.282539 0.0918024i
\(663\) 0 0
\(664\) 2.20363 6.78209i 0.0855176 0.263196i
\(665\) 3.53565 + 14.4846i 0.137107 + 0.561690i
\(666\) 0 0
\(667\) 1.68007 + 2.31241i 0.0650524 + 0.0895370i
\(668\) 8.94427i 0.346064i
\(669\) 0 0
\(670\) −1.81575 + 24.2475i −0.0701484 + 0.936764i
\(671\) 33.4454 + 24.2995i 1.29115 + 0.938072i
\(672\) 0 0
\(673\) 20.2139 + 6.56790i 0.779189 + 0.253174i 0.671494 0.741010i \(-0.265653\pi\)
0.107695 + 0.994184i \(0.465653\pi\)
\(674\) 3.68904 0.142097
\(675\) 0 0
\(676\) 16.4009 0.630804
\(677\) −41.2313 13.3968i −1.58465 0.514883i −0.621398 0.783495i \(-0.713435\pi\)
−0.963248 + 0.268613i \(0.913435\pi\)
\(678\) 0 0
\(679\) 48.6912 + 35.3762i 1.86860 + 1.35762i
\(680\) 5.00177 5.90154i 0.191809 0.226314i
\(681\) 0 0
\(682\) 27.2681i 1.04415i
\(683\) 9.15838 + 12.6054i 0.350436 + 0.482334i 0.947453 0.319895i \(-0.103648\pi\)
−0.597017 + 0.802228i \(0.703648\pi\)
\(684\) 0 0
\(685\) 16.5492 + 1.23927i 0.632313 + 0.0473499i
\(686\) 3.31085 10.1897i 0.126409 0.389046i
\(687\) 0 0
\(688\) 8.21821 2.67026i 0.313316 0.101803i
\(689\) 11.3900 35.0547i 0.433923 1.33548i
\(690\) 0 0
\(691\) 7.89660 + 24.3032i 0.300401 + 0.924539i 0.981354 + 0.192212i \(0.0615660\pi\)
−0.680953 + 0.732328i \(0.738434\pi\)
\(692\) 1.37486 + 1.89233i 0.0522643 + 0.0719357i
\(693\) 0 0
\(694\) 2.94095 2.13673i 0.111637 0.0811091i
\(695\) −7.66335 + 9.04190i −0.290688 + 0.342979i
\(696\) 0 0
\(697\) −5.96188 + 8.20582i −0.225822 + 0.310818i
\(698\) −11.6286 3.77835i −0.440148 0.143013i
\(699\) 0 0
\(700\) −20.1126 + 3.34223i −0.760185 + 0.126324i
\(701\) −24.7063 −0.933146 −0.466573 0.884483i \(-0.654511\pi\)
−0.466573 + 0.884483i \(0.654511\pi\)
\(702\) 0 0
\(703\) 2.30776 3.17636i 0.0870387 0.119799i
\(704\) 2.65688 + 1.93033i 0.100135 + 0.0727522i
\(705\) 0 0
\(706\) 12.6725 9.20711i 0.476936 0.346514i
\(707\) 46.8307i 1.76125i
\(708\) 0 0
\(709\) 6.22394 + 19.1553i 0.233745 + 0.719393i 0.997285 + 0.0736329i \(0.0234593\pi\)
−0.763541 + 0.645760i \(0.776541\pi\)
\(710\) −4.80780 19.6963i −0.180433 0.739188i
\(711\) 0 0
\(712\) 4.56799 1.48423i 0.171193 0.0556239i
\(713\) 4.82862 1.56891i 0.180833 0.0587563i
\(714\) 0 0
\(715\) −15.0979 + 36.8446i −0.564631 + 1.37791i
\(716\) −1.86327 5.73456i −0.0696337 0.214311i
\(717\) 0 0
\(718\) 7.07176i 0.263916i
\(719\) 21.0273 15.2772i 0.784187 0.569745i −0.122046 0.992524i \(-0.538945\pi\)
0.906233 + 0.422779i \(0.138945\pi\)
\(720\) 0 0
\(721\) −46.0360 33.4471i −1.71447 1.24564i
\(722\) −9.59621 + 13.2081i −0.357134 + 0.491553i
\(723\) 0 0
\(724\) −16.5771 −0.616084
\(725\) 3.83138 + 23.0562i 0.142294 + 0.856286i
\(726\) 0 0
\(727\) 32.6799 + 10.6183i 1.21203 + 0.393812i 0.844173 0.536071i \(-0.180092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(728\) 12.9961 17.8876i 0.481667 0.662958i
\(729\) 0 0
\(730\) −10.6986 17.3107i −0.395974 0.640699i
\(731\) −24.1858 + 17.5720i −0.894545 + 0.649925i
\(732\) 0 0
\(733\) 18.9570 + 26.0920i 0.700192 + 0.963731i 0.999953 + 0.00971697i \(0.00309306\pi\)
−0.299761 + 0.954014i \(0.596907\pi\)
\(734\) −8.26549 25.4385i −0.305085 0.938954i
\(735\) 0 0
\(736\) −0.188954 + 0.581542i −0.00696495 + 0.0214359i
\(737\) 33.9639 11.0355i 1.25107 0.406499i
\(738\) 0 0
\(739\) −12.7515 + 39.2451i −0.469071 + 1.44365i 0.384718 + 0.923034i \(0.374299\pi\)
−0.853789 + 0.520619i \(0.825701\pi\)
\(740\) 4.09570 + 3.47126i 0.150561 + 0.127606i
\(741\) 0 0
\(742\) −16.2927 22.4249i −0.598122 0.823244i
\(743\) 7.06997i 0.259372i −0.991555 0.129686i \(-0.958603\pi\)
0.991555 0.129686i \(-0.0413969\pi\)
\(744\) 0 0
\(745\) −9.91707 4.06375i −0.363333 0.148884i
\(746\) −9.61502 6.98572i −0.352031 0.255765i
\(747\) 0 0
\(748\) −10.8057 3.51098i −0.395095 0.128374i
\(749\) −34.0652 −1.24471
\(750\) 0 0
\(751\) −4.57240 −0.166849 −0.0834246 0.996514i \(-0.526586\pi\)
−0.0834246 + 0.996514i \(0.526586\pi\)
\(752\) 6.57617 + 2.13673i 0.239808 + 0.0779185i
\(753\) 0 0
\(754\) −20.5055 14.8981i −0.746767 0.542558i
\(755\) 14.3498 + 5.88018i 0.522244 + 0.214002i
\(756\) 0 0
\(757\) 21.1871i 0.770058i −0.922904 0.385029i \(-0.874191\pi\)
0.922904 0.385029i \(-0.125809\pi\)
\(758\) −2.83641 3.90398i −0.103023 0.141799i
\(759\) 0 0
\(760\) 2.78939 + 2.36411i 0.101182 + 0.0857554i
\(761\) 9.84246 30.2920i 0.356789 1.09808i −0.598176 0.801365i \(-0.704108\pi\)
0.954965 0.296718i \(-0.0958923\pi\)
\(762\) 0 0
\(763\) 2.06561 0.671157i 0.0747801 0.0242975i
\(764\) 3.08029 9.48015i 0.111441 0.342980i
\(765\) 0 0
\(766\) 1.48437 + 4.56841i 0.0536324 + 0.165063i
\(767\) 45.1826 + 62.1885i 1.63145 + 2.24550i
\(768\) 0 0
\(769\) −7.38487 + 5.36542i −0.266305 + 0.193482i −0.712922 0.701243i \(-0.752629\pi\)
0.446617 + 0.894725i \(0.352629\pi\)
\(770\) 15.7426 + 25.4720i 0.567323 + 0.917948i
\(771\) 0 0
\(772\) −14.7378 + 20.2849i −0.530427 + 0.730069i
\(773\) −37.1998 12.0870i −1.33798 0.434738i −0.449351 0.893355i \(-0.648345\pi\)
−0.888634 + 0.458618i \(0.848345\pi\)
\(774\) 0 0
\(775\) 41.0526 + 6.18302i 1.47465 + 0.222101i
\(776\) 14.7598 0.529845
\(777\) 0 0
\(778\) −7.90084 + 10.8746i −0.283259 + 0.389872i
\(779\) −3.87852 2.81791i −0.138962 0.100962i
\(780\) 0 0
\(781\) −24.0901 + 17.5025i −0.862010 + 0.626287i
\(782\) 2.11547i 0.0756491i
\(783\) 0 0
\(784\) −2.97506 9.15630i −0.106252 0.327011i
\(785\) 6.37258 15.5515i 0.227447 0.555056i
\(786\) 0 0
\(787\) −25.7764 + 8.37524i −0.918828 + 0.298545i −0.729986 0.683462i \(-0.760473\pi\)
−0.188842 + 0.982008i \(0.560473\pi\)
\(788\) −25.5243 + 8.29335i −0.909266 + 0.295438i
\(789\) 0 0
\(790\) −2.17191 8.89774i −0.0772731 0.316567i
\(791\) −21.7075 66.8089i −0.771831 2.37545i
\(792\) 0 0
\(793\) 68.2568i 2.42387i
\(794\) −0.0700793 + 0.0509156i −0.00248702 + 0.00180693i
\(795\) 0 0
\(796\) 3.28553 + 2.38708i 0.116453 + 0.0846077i
\(797\) 7.78292 10.7123i 0.275685 0.379448i −0.648614 0.761118i \(-0.724651\pi\)
0.924299 + 0.381670i \(0.124651\pi\)
\(798\) 0 0
\(799\) −23.9221 −0.846303
\(800\) −3.50859 + 3.56227i −0.124047 + 0.125945i
\(801\) 0 0
\(802\) −0.305423 0.0992381i −0.0107849 0.00350422i
\(803\) −17.5676 + 24.1797i −0.619946 + 0.853282i
\(804\) 0 0
\(805\) −3.60479 + 4.25325i −0.127052 + 0.149908i
\(806\) −36.4233 + 26.4631i −1.28296 + 0.932123i
\(807\) 0 0
\(808\) 6.75049 + 9.29125i 0.237481 + 0.326865i
\(809\) −2.32740 7.16299i −0.0818269 0.251837i 0.901770 0.432215i \(-0.142268\pi\)
−0.983597 + 0.180378i \(0.942268\pi\)
\(810\) 0 0
\(811\) −8.28844 + 25.5092i −0.291046 + 0.895749i 0.693475 + 0.720481i \(0.256079\pi\)
−0.984521 + 0.175267i \(0.943921\pi\)
\(812\) −18.1281 + 5.89018i −0.636172 + 0.206705i
\(813\) 0 0
\(814\) 2.43664 7.49920i 0.0854042 0.262847i
\(815\) 18.6573 + 1.39713i 0.653538 + 0.0489393i
\(816\) 0 0
\(817\) −8.30550 11.4315i −0.290573 0.399939i
\(818\) 24.2346i 0.847343i
\(819\) 0 0
\(820\) 4.23862 5.00110i 0.148019 0.174646i
\(821\) 30.1027 + 21.8709i 1.05059 + 0.763298i 0.972325 0.233634i \(-0.0750618\pi\)
0.0782654 + 0.996933i \(0.475062\pi\)
\(822\) 0 0
\(823\) 17.0656 + 5.54495i 0.594870 + 0.193285i 0.590951 0.806707i \(-0.298753\pi\)
0.00391871 + 0.999992i \(0.498753\pi\)
\(824\) −13.9549 −0.486142
\(825\) 0 0
\(826\) 57.8077 2.01139
\(827\) −16.0984 5.23070i −0.559798 0.181889i 0.0154325 0.999881i \(-0.495087\pi\)
−0.575230 + 0.817992i \(0.695087\pi\)
\(828\) 0 0
\(829\) 41.6780 + 30.2809i 1.44754 + 1.05170i 0.986399 + 0.164369i \(0.0525589\pi\)
0.461138 + 0.887328i \(0.347441\pi\)
\(830\) 1.19073 15.9011i 0.0413310 0.551936i
\(831\) 0 0
\(832\) 5.42226i 0.187983i
\(833\) 19.5778 + 26.9466i 0.678331 + 0.933643i
\(834\) 0 0
\(835\) −4.74269 19.4295i −0.164128 0.672387i
\(836\) 1.65948 5.10736i 0.0573943 0.176642i
\(837\) 0 0
\(838\) −21.7082 + 7.05342i −0.749897 + 0.243656i
\(839\) 6.86327 21.1230i 0.236946 0.729246i −0.759911 0.650027i \(-0.774757\pi\)
0.996857 0.0792188i \(-0.0252426\pi\)
\(840\) 0 0
\(841\) −2.20925 6.79938i −0.0761811 0.234461i
\(842\) 22.9999 + 31.6567i 0.792630 + 1.09096i
\(843\) 0 0
\(844\) −3.52316 + 2.55973i −0.121272 + 0.0881095i
\(845\) 35.6275 8.69656i 1.22562 0.299171i
\(846\) 0 0
\(847\) −0.514893 + 0.708689i −0.0176919 + 0.0243508i
\(848\) −6.46496 2.10059i −0.222008 0.0721347i
\(849\) 0 0
\(850\) 7.73601 15.4720i 0.265343 0.530686i
\(851\) 1.46815 0.0503275
\(852\) 0 0
\(853\) 20.8778 28.7359i 0.714843 0.983897i −0.284836 0.958576i \(-0.591939\pi\)
0.999679 0.0253210i \(-0.00806080\pi\)
\(854\) −41.5276 30.1715i −1.42104 1.03245i
\(855\) 0 0
\(856\) −6.75856 + 4.91038i −0.231003 + 0.167833i
\(857\) 35.9714i 1.22876i −0.789010 0.614380i \(-0.789406\pi\)
0.789010 0.614380i \(-0.210594\pi\)
\(858\) 0 0
\(859\) −14.5608 44.8137i −0.496809 1.52902i −0.814118 0.580700i \(-0.802779\pi\)
0.317308 0.948322i \(-0.397221\pi\)
\(860\) 16.4364 10.1583i 0.560478 0.346394i
\(861\) 0 0
\(862\) 23.4733 7.62695i 0.799505 0.259775i
\(863\) −38.4902 + 12.5062i −1.31022 + 0.425716i −0.879125 0.476590i \(-0.841872\pi\)
−0.431095 + 0.902307i \(0.641872\pi\)
\(864\) 0 0
\(865\) 3.99000 + 3.38167i 0.135664 + 0.114980i
\(866\) −6.14259 18.9050i −0.208734 0.642417i
\(867\) 0 0
\(868\) 33.8575i 1.14920i
\(869\) −10.8826 + 7.90669i −0.369168 + 0.268216i
\(870\) 0 0
\(871\) −47.7018 34.6574i −1.61631 1.17432i
\(872\) 0.313074 0.430909i 0.0106020 0.0145924i
\(873\) 0 0
\(874\) 0.999887 0.0338217
\(875\) −41.9182 + 17.9250i −1.41709 + 0.605974i
\(876\) 0 0
\(877\) −12.9166 4.19687i −0.436164 0.141718i 0.0827012 0.996574i \(-0.473645\pi\)
−0.518865 + 0.854856i \(0.673645\pi\)
\(878\) −2.98141 + 4.10355i −0.100618 + 0.138488i
\(879\) 0 0
\(880\) 6.79506 + 2.78444i 0.229061 + 0.0938633i
\(881\) 24.3625 17.7004i 0.820793 0.596341i −0.0961468 0.995367i \(-0.530652\pi\)
0.916939 + 0.399026i \(0.130652\pi\)
\(882\) 0 0
\(883\) 2.80047 + 3.85451i 0.0942433 + 0.129715i 0.853535 0.521036i \(-0.174454\pi\)
−0.759291 + 0.650751i \(0.774454\pi\)
\(884\) 5.79689 + 17.8410i 0.194970 + 0.600057i
\(885\) 0 0
\(886\) 3.14806 9.68874i 0.105761 0.325500i
\(887\) −38.4028 + 12.4778i −1.28944 + 0.418965i −0.871896 0.489692i \(-0.837109\pi\)
−0.417545 + 0.908656i \(0.637109\pi\)
\(888\) 0 0
\(889\) 1.44612 4.45071i 0.0485014 0.149272i
\(890\) 9.13599 5.64635i 0.306239 0.189266i
\(891\) 0 0
\(892\) −0.212705 0.292763i −0.00712189 0.00980244i
\(893\) 11.3069i 0.378371i
\(894\) 0 0
\(895\) −7.08831 11.4691i −0.236936 0.383370i
\(896\) −3.29892 2.39680i −0.110209 0.0800715i
\(897\) 0 0
\(898\) 9.85800 + 3.20306i 0.328966 + 0.106887i
\(899\) 38.8128 1.29448
\(900\) 0 0
\(901\) 23.5175 0.783482
\(902\) −9.15698 2.97528i −0.304894 0.0990661i
\(903\) 0 0
\(904\) −13.9371 10.1259i −0.463541 0.336782i
\(905\) −36.0103 + 8.79000i −1.19702 + 0.292189i
\(906\) 0 0
\(907\) 22.3227i 0.741214i 0.928790 + 0.370607i \(0.120850\pi\)
−0.928790 + 0.370607i \(0.879150\pi\)
\(908\) 7.55754 + 10.4021i 0.250806 + 0.345204i
\(909\) 0 0
\(910\) 18.7464 45.7481i 0.621436 1.51654i
\(911\) −0.241832 + 0.744283i −0.00801226 + 0.0246592i −0.954983 0.296661i \(-0.904127\pi\)
0.946970 + 0.321321i \(0.104127\pi\)
\(912\) 0 0
\(913\) −22.2729 + 7.23691i −0.737126 + 0.239507i
\(914\) −1.25512 + 3.86286i −0.0415156 + 0.127772i
\(915\) 0 0
\(916\) −5.10951 15.7254i −0.168823 0.519583i
\(917\) −15.8646 21.8358i −0.523896 0.721080i
\(918\) 0 0
\(919\) −1.59426 + 1.15830i −0.0525897 + 0.0382087i −0.613770 0.789485i \(-0.710348\pi\)
0.561180 + 0.827694i \(0.310348\pi\)
\(920\) −0.102102 + 1.36347i −0.00336619 + 0.0449523i
\(921\) 0 0
\(922\) −3.97407 + 5.46984i −0.130879 + 0.180140i
\(923\) 46.7577 + 15.1925i 1.53905 + 0.500067i
\(924\) 0 0
\(925\) 10.7377 + 5.36884i 0.353053 + 0.176526i
\(926\) 9.72184 0.319480
\(927\) 0 0
\(928\) −2.74759 + 3.78173i −0.0901940 + 0.124141i
\(929\) 19.1823 + 13.9368i 0.629352 + 0.457251i 0.856176 0.516685i \(-0.172834\pi\)
−0.226824 + 0.973936i \(0.572834\pi\)
\(930\) 0 0
\(931\) −12.7364 + 9.25355i −0.417419 + 0.303273i
\(932\) 11.0706i 0.362630i
\(933\) 0 0
\(934\) −11.8669 36.5225i −0.388296 1.19505i
\(935\) −25.3347 1.89716i −0.828535 0.0620437i
\(936\) 0 0
\(937\) −16.8801 + 5.48469i −0.551450 + 0.179177i −0.571471 0.820623i \(-0.693627\pi\)
0.0200205 + 0.999800i \(0.493627\pi\)
\(938\) −42.1713 + 13.7023i −1.37694 + 0.447395i
\(939\) 0 0
\(940\) 15.4183 + 1.15458i 0.502891 + 0.0376583i
\(941\) −15.3815 47.3393i −0.501422 1.54322i −0.806703 0.590956i \(-0.798750\pi\)
0.305281 0.952262i \(-0.401250\pi\)
\(942\) 0 0
\(943\) 1.79270i 0.0583783i
\(944\) 11.4691 8.33280i 0.373288 0.271210i
\(945\) 0 0
\(946\) −22.9584 16.6803i −0.746443 0.542323i
\(947\) 2.65398 3.65289i 0.0862428 0.118703i −0.763716 0.645553i \(-0.776627\pi\)
0.849958 + 0.526850i \(0.176627\pi\)
\(948\) 0 0
\(949\) 49.3469 1.60187
\(950\) 7.31293 + 3.65646i 0.237263 + 0.118631i
\(951\) 0 0
\(952\) 13.4169 + 4.35941i 0.434844 + 0.141289i
\(953\) −5.48579 + 7.55054i −0.177702 + 0.244586i −0.888572 0.458738i \(-0.848302\pi\)
0.710869 + 0.703324i \(0.248302\pi\)
\(954\) 0 0
\(955\) 1.66444 22.2269i 0.0538599 0.719247i
\(956\) −4.52015 + 3.28408i −0.146192 + 0.106215i
\(957\) 0 0
\(958\) −4.98286 6.85832i −0.160989 0.221582i
\(959\) 9.35195 + 28.7823i 0.301990 + 0.929430i
\(960\) 0 0
\(961\) 11.7247 36.0850i 0.378217 1.16403i
\(962\) −12.3817 + 4.02307i −0.399204 + 0.129709i
\(963\) 0 0
\(964\) 4.59014 14.1270i 0.147838 0.454999i
\(965\) −21.2588 + 51.8794i −0.684345 + 1.67006i
\(966\) 0 0
\(967\) −13.0799 18.0029i −0.420620 0.578934i 0.545148 0.838340i \(-0.316473\pi\)
−0.965769 + 0.259405i \(0.916473\pi\)
\(968\) 0.214825i 0.00690473i
\(969\) 0 0
\(970\) 32.0625 7.82635i 1.02946 0.251289i
\(971\) 3.55705 + 2.58435i 0.114151 + 0.0829357i 0.643396 0.765533i \(-0.277525\pi\)
−0.529245 + 0.848469i \(0.677525\pi\)
\(972\) 0 0
\(973\) −20.5564 6.67917i −0.659007 0.214124i
\(974\) 28.9739 0.928385
\(975\) 0 0
\(976\) −12.5882 −0.402940
\(977\) 14.1016 + 4.58190i 0.451151 + 0.146588i 0.525775 0.850624i \(-0.323775\pi\)
−0.0746235 + 0.997212i \(0.523775\pi\)
\(978\) 0 0
\(979\) −12.7612 9.27153i −0.407849 0.296319i
\(980\) −11.3178 18.3126i −0.361534 0.584975i
\(981\) 0 0
\(982\) 10.2266i 0.326343i
\(983\) −10.6096 14.6028i −0.338393 0.465758i 0.605578 0.795786i \(-0.292942\pi\)
−0.943971 + 0.330028i \(0.892942\pi\)
\(984\) 0 0
\(985\) −51.0486 + 31.5498i −1.62654 + 1.00526i
\(986\) 4.99744 15.3805i 0.159151 0.489816i
\(987\) 0 0
\(988\) −8.43263 + 2.73993i −0.268278 + 0.0871687i
\(989\) 1.63278 5.02519i 0.0519195 0.159792i
\(990\) 0 0
\(991\) −17.0781 52.5608i −0.542502 1.66965i −0.726856 0.686790i \(-0.759019\pi\)
0.184353 0.982860i \(-0.440981\pi\)
\(992\) 4.88046 + 6.71737i 0.154955 + 0.213277i
\(993\) 0 0
\(994\) 29.9115 21.7320i 0.948734 0.689296i
\(995\) 8.40287 + 3.44327i 0.266389 + 0.109159i
\(996\) 0 0
\(997\) −9.56346 + 13.1630i −0.302878 + 0.416875i −0.933144 0.359504i \(-0.882946\pi\)
0.630266 + 0.776379i \(0.282946\pi\)
\(998\) 21.8750 + 7.10761i 0.692440 + 0.224987i
\(999\) 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 450.2.l.a.379.2 8
3.2 odd 2 150.2.h.a.79.1 yes 8
15.2 even 4 750.2.g.c.601.1 8
15.8 even 4 750.2.g.e.601.2 8
15.14 odd 2 750.2.h.c.649.2 8
25.19 even 10 inner 450.2.l.a.19.2 8
75.8 even 20 750.2.g.e.151.2 8
75.17 even 20 750.2.g.c.151.1 8
75.38 even 20 3750.2.a.m.1.4 4
75.41 odd 10 3750.2.c.e.1249.4 8
75.44 odd 10 150.2.h.a.19.1 8
75.56 odd 10 750.2.h.c.349.2 8
75.59 odd 10 3750.2.c.e.1249.5 8
75.62 even 20 3750.2.a.o.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.h.a.19.1 8 75.44 odd 10
150.2.h.a.79.1 yes 8 3.2 odd 2
450.2.l.a.19.2 8 25.19 even 10 inner
450.2.l.a.379.2 8 1.1 even 1 trivial
750.2.g.c.151.1 8 75.17 even 20
750.2.g.c.601.1 8 15.2 even 4
750.2.g.e.151.2 8 75.8 even 20
750.2.g.e.601.2 8 15.8 even 4
750.2.h.c.349.2 8 75.56 odd 10
750.2.h.c.649.2 8 15.14 odd 2
3750.2.a.m.1.4 4 75.38 even 20
3750.2.a.o.1.1 4 75.62 even 20
3750.2.c.e.1249.4 8 75.41 odd 10
3750.2.c.e.1249.5 8 75.59 odd 10