Properties

Label 810.2.s.a.557.6
Level $810$
Weight $2$
Character 810.557
Analytic conductor $6.468$
Analytic rank $0$
Dimension $216$
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] = [810,2,Mod(17,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([22, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.s (of order \(36\), degree \(12\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.46788256372\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 557.6
Character \(\chi\) \(=\) 810.557
Dual form 810.2.s.a.413.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.463117 - 2.18758i) q^{5} +(-1.78738 - 3.83305i) q^{7} +(0.258819 - 0.965926i) q^{8} +O(q^{10})\) \(q+(-0.819152 - 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(0.463117 - 2.18758i) q^{5} +(-1.78738 - 3.83305i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-1.63411 + 1.52633i) q^{10} +(-3.34414 - 3.98539i) q^{11} +(-0.215597 - 0.307904i) q^{13} +(-0.734411 + 4.16505i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(1.58114 + 5.90088i) q^{17} +(-2.93211 + 1.69286i) q^{19} +(2.21405 - 0.313010i) q^{20} +(0.453432 + 5.18276i) q^{22} +(1.01274 + 0.472247i) q^{23} +(-4.57105 - 2.02621i) q^{25} +0.375881i q^{26} +(2.99057 - 2.99057i) q^{28} +(1.75816 + 9.97103i) q^{29} +(-3.35678 + 1.22177i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(2.08941 - 5.74062i) q^{34} +(-9.21289 + 2.13490i) q^{35} +(5.63980 - 1.51118i) q^{37} +(3.37283 + 0.295084i) q^{38} +(-1.99318 - 1.01353i) q^{40} +(-4.77146 - 0.841337i) q^{41} +(0.570435 - 6.52010i) q^{43} +(2.60128 - 4.50554i) q^{44} +(-0.558716 - 0.967725i) q^{46} +(6.65173 - 3.10175i) q^{47} +(-6.99804 + 8.33994i) q^{49} +(2.58219 + 4.28162i) q^{50} +(0.215597 - 0.307904i) q^{52} +(-6.39299 - 6.39299i) q^{53} +(-10.2671 + 5.46988i) q^{55} +(-4.16505 + 0.734411i) q^{56} +(4.27895 - 9.17623i) q^{58} +(-2.30891 - 1.93741i) q^{59} +(-7.18421 - 2.61484i) q^{61} +(3.45049 + 0.924557i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-0.773412 + 0.329040i) q^{65} +(0.199873 - 0.139953i) q^{67} +(-5.00423 + 3.50400i) q^{68} +(8.77128 + 3.53549i) q^{70} +(-0.0530319 - 0.0306180i) q^{71} +(6.38669 + 1.71131i) q^{73} +(-5.48663 - 1.99697i) q^{74} +(-2.59360 - 2.17629i) q^{76} +(-9.29895 + 19.9417i) q^{77} +(-5.15835 + 0.909556i) q^{79} +(1.05138 + 1.97347i) q^{80} +(3.42598 + 3.42598i) q^{82} +(2.73944 - 3.91233i) q^{83} +(13.6409 - 0.726069i) q^{85} +(-4.20705 + 5.01377i) q^{86} +(-4.71511 + 2.19869i) q^{88} +(-4.63875 - 8.03454i) q^{89} +(-0.794859 + 1.37674i) q^{91} +(-0.0973907 + 1.11318i) q^{92} +(-7.22787 - 1.27447i) q^{94} +(2.34535 + 7.19823i) q^{95} +(-15.6011 - 1.36492i) q^{97} +(10.5161 - 2.81777i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.819152 0.573576i −0.579228 0.405580i
\(3\) 0 0
\(4\) 0.342020 + 0.939693i 0.171010 + 0.469846i
\(5\) 0.463117 2.18758i 0.207112 0.978317i
\(6\) 0 0
\(7\) −1.78738 3.83305i −0.675567 1.44876i −0.882457 0.470393i \(-0.844112\pi\)
0.206890 0.978364i \(-0.433666\pi\)
\(8\) 0.258819 0.965926i 0.0915064 0.341506i
\(9\) 0 0
\(10\) −1.63411 + 1.52633i −0.516751 + 0.482668i
\(11\) −3.34414 3.98539i −1.00830 1.20164i −0.979374 0.202058i \(-0.935237\pi\)
−0.0289216 0.999582i \(-0.509207\pi\)
\(12\) 0 0
\(13\) −0.215597 0.307904i −0.0597958 0.0853972i 0.788141 0.615495i \(-0.211044\pi\)
−0.847936 + 0.530098i \(0.822155\pi\)
\(14\) −0.734411 + 4.16505i −0.196280 + 1.11316i
\(15\) 0 0
\(16\) −0.766044 + 0.642788i −0.191511 + 0.160697i
\(17\) 1.58114 + 5.90088i 0.383482 + 1.43117i 0.840546 + 0.541739i \(0.182234\pi\)
−0.457065 + 0.889433i \(0.651099\pi\)
\(18\) 0 0
\(19\) −2.93211 + 1.69286i −0.672672 + 0.388368i −0.797088 0.603863i \(-0.793628\pi\)
0.124416 + 0.992230i \(0.460294\pi\)
\(20\) 2.21405 0.313010i 0.495077 0.0699912i
\(21\) 0 0
\(22\) 0.453432 + 5.18276i 0.0966721 + 1.10497i
\(23\) 1.01274 + 0.472247i 0.211170 + 0.0984704i 0.525326 0.850901i \(-0.323943\pi\)
−0.314155 + 0.949372i \(0.601721\pi\)
\(24\) 0 0
\(25\) −4.57105 2.02621i −0.914209 0.405243i
\(26\) 0.375881i 0.0737164i
\(27\) 0 0
\(28\) 2.99057 2.99057i 0.565165 0.565165i
\(29\) 1.75816 + 9.97103i 0.326483 + 1.85157i 0.499045 + 0.866576i \(0.333684\pi\)
−0.172563 + 0.984999i \(0.555205\pi\)
\(30\) 0 0
\(31\) −3.35678 + 1.22177i −0.602896 + 0.219436i −0.625392 0.780311i \(-0.715061\pi\)
0.0224959 + 0.999747i \(0.492839\pi\)
\(32\) 0.996195 0.0871557i 0.176104 0.0154071i
\(33\) 0 0
\(34\) 2.08941 5.74062i 0.358331 0.984508i
\(35\) −9.21289 + 2.13490i −1.55726 + 0.360863i
\(36\) 0 0
\(37\) 5.63980 1.51118i 0.927178 0.248436i 0.236527 0.971625i \(-0.423991\pi\)
0.690651 + 0.723188i \(0.257324\pi\)
\(38\) 3.37283 + 0.295084i 0.547145 + 0.0478690i
\(39\) 0 0
\(40\) −1.99318 1.01353i −0.315149 0.160252i
\(41\) −4.77146 0.841337i −0.745177 0.131395i −0.211848 0.977303i \(-0.567948\pi\)
−0.533329 + 0.845908i \(0.679059\pi\)
\(42\) 0 0
\(43\) 0.570435 6.52010i 0.0869905 0.994306i −0.819779 0.572680i \(-0.805904\pi\)
0.906770 0.421626i \(-0.138541\pi\)
\(44\) 2.60128 4.50554i 0.392157 0.679236i
\(45\) 0 0
\(46\) −0.558716 0.967725i −0.0823782 0.142683i
\(47\) 6.65173 3.10175i 0.970254 0.452437i 0.128152 0.991755i \(-0.459096\pi\)
0.842102 + 0.539318i \(0.181318\pi\)
\(48\) 0 0
\(49\) −6.99804 + 8.33994i −0.999721 + 1.19142i
\(50\) 2.58219 + 4.28162i 0.365177 + 0.605513i
\(51\) 0 0
\(52\) 0.215597 0.307904i 0.0298979 0.0426986i
\(53\) −6.39299 6.39299i −0.878144 0.878144i 0.115198 0.993343i \(-0.463250\pi\)
−0.993343 + 0.115198i \(0.963250\pi\)
\(54\) 0 0
\(55\) −10.2671 + 5.46988i −1.38441 + 0.737558i
\(56\) −4.16505 + 0.734411i −0.556579 + 0.0981398i
\(57\) 0 0
\(58\) 4.27895 9.17623i 0.561853 1.20490i
\(59\) −2.30891 1.93741i −0.300595 0.252229i 0.479997 0.877270i \(-0.340638\pi\)
−0.780592 + 0.625041i \(0.785082\pi\)
\(60\) 0 0
\(61\) −7.18421 2.61484i −0.919844 0.334796i −0.161668 0.986845i \(-0.551687\pi\)
−0.758176 + 0.652049i \(0.773909\pi\)
\(62\) 3.45049 + 0.924557i 0.438213 + 0.117419i
\(63\) 0 0
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) −0.773412 + 0.329040i −0.0959300 + 0.0408124i
\(66\) 0 0
\(67\) 0.199873 0.139953i 0.0244184 0.0170979i −0.561304 0.827610i \(-0.689700\pi\)
0.585722 + 0.810512i \(0.300811\pi\)
\(68\) −5.00423 + 3.50400i −0.606852 + 0.424922i
\(69\) 0 0
\(70\) 8.77128 + 3.53549i 1.04837 + 0.422572i
\(71\) −0.0530319 0.0306180i −0.00629373 0.00363369i 0.496850 0.867837i \(-0.334490\pi\)
−0.503144 + 0.864203i \(0.667823\pi\)
\(72\) 0 0
\(73\) 6.38669 + 1.71131i 0.747506 + 0.200294i 0.612412 0.790539i \(-0.290200\pi\)
0.135094 + 0.990833i \(0.456866\pi\)
\(74\) −5.48663 1.99697i −0.637808 0.232143i
\(75\) 0 0
\(76\) −2.59360 2.17629i −0.297507 0.249638i
\(77\) −9.29895 + 19.9417i −1.05971 + 2.27256i
\(78\) 0 0
\(79\) −5.15835 + 0.909556i −0.580360 + 0.102333i −0.456119 0.889919i \(-0.650761\pi\)
−0.124241 + 0.992252i \(0.539650\pi\)
\(80\) 1.05138 + 1.97347i 0.117548 + 0.220641i
\(81\) 0 0
\(82\) 3.42598 + 3.42598i 0.378336 + 0.378336i
\(83\) 2.73944 3.91233i 0.300693 0.429434i −0.640164 0.768238i \(-0.721134\pi\)
0.940857 + 0.338804i \(0.110022\pi\)
\(84\) 0 0
\(85\) 13.6409 0.726069i 1.47956 0.0787533i
\(86\) −4.20705 + 5.01377i −0.453658 + 0.540648i
\(87\) 0 0
\(88\) −4.71511 + 2.19869i −0.502633 + 0.234382i
\(89\) −4.63875 8.03454i −0.491706 0.851660i 0.508248 0.861211i \(-0.330293\pi\)
−0.999954 + 0.00955058i \(0.996960\pi\)
\(90\) 0 0
\(91\) −0.794859 + 1.37674i −0.0833238 + 0.144321i
\(92\) −0.0973907 + 1.11318i −0.0101537 + 0.116057i
\(93\) 0 0
\(94\) −7.22787 1.27447i −0.745497 0.131451i
\(95\) 2.34535 + 7.19823i 0.240628 + 0.738523i
\(96\) 0 0
\(97\) −15.6011 1.36492i −1.58405 0.138587i −0.739163 0.673527i \(-0.764779\pi\)
−0.844890 + 0.534940i \(0.820334\pi\)
\(98\) 10.5161 2.81777i 1.06228 0.284638i
\(99\) 0 0
\(100\) 0.340629 4.98838i 0.0340629 0.498838i
\(101\) 3.00976 8.26924i 0.299482 0.822820i −0.695104 0.718909i \(-0.744642\pi\)
0.994587 0.103912i \(-0.0331359\pi\)
\(102\) 0 0
\(103\) −0.00174607 0.000152761i −0.000172045 1.50520e-5i −0.0872418 0.996187i \(-0.527805\pi\)
0.0870697 + 0.996202i \(0.472250\pi\)
\(104\) −0.353213 + 0.128559i −0.0346354 + 0.0126062i
\(105\) 0 0
\(106\) 1.56996 + 8.90369i 0.152488 + 0.864803i
\(107\) 7.92458 7.92458i 0.766098 0.766098i −0.211319 0.977417i \(-0.567776\pi\)
0.977417 + 0.211319i \(0.0677759\pi\)
\(108\) 0 0
\(109\) 2.21477i 0.212137i 0.994359 + 0.106068i \(0.0338262\pi\)
−0.994359 + 0.106068i \(0.966174\pi\)
\(110\) 11.5477 + 1.40830i 1.10103 + 0.134276i
\(111\) 0 0
\(112\) 3.83305 + 1.78738i 0.362189 + 0.168892i
\(113\) 0.109693 + 1.25379i 0.0103190 + 0.117947i 0.999607 0.0280294i \(-0.00892322\pi\)
−0.989288 + 0.145976i \(0.953368\pi\)
\(114\) 0 0
\(115\) 1.50210 1.99674i 0.140071 0.186197i
\(116\) −8.76838 + 5.06243i −0.814124 + 0.470034i
\(117\) 0 0
\(118\) 0.780099 + 2.91137i 0.0718139 + 0.268013i
\(119\) 19.7923 16.6077i 1.81435 1.52242i
\(120\) 0 0
\(121\) −2.78993 + 15.8225i −0.253630 + 1.43841i
\(122\) 4.38515 + 6.26265i 0.397013 + 0.566993i
\(123\) 0 0
\(124\) −2.29618 2.73648i −0.206203 0.245743i
\(125\) −6.54944 + 9.06117i −0.585800 + 0.810456i
\(126\) 0 0
\(127\) −1.93774 + 7.23174i −0.171947 + 0.641713i 0.825105 + 0.564979i \(0.191116\pi\)
−0.997052 + 0.0767340i \(0.975551\pi\)
\(128\) 0.422618 + 0.906308i 0.0373545 + 0.0801070i
\(129\) 0 0
\(130\) 0.822272 + 0.174077i 0.0721180 + 0.0152676i
\(131\) −4.22294 11.6024i −0.368960 1.01371i −0.975758 0.218853i \(-0.929768\pi\)
0.606797 0.794856i \(-0.292454\pi\)
\(132\) 0 0
\(133\) 11.7296 + 8.21316i 1.01709 + 0.712171i
\(134\) −0.244000 −0.0210784
\(135\) 0 0
\(136\) 6.10904 0.523846
\(137\) −10.4036 7.28471i −0.888843 0.622374i 0.0374006 0.999300i \(-0.488092\pi\)
−0.926243 + 0.376926i \(0.876981\pi\)
\(138\) 0 0
\(139\) 1.49351 + 4.10338i 0.126678 + 0.348045i 0.986777 0.162082i \(-0.0518209\pi\)
−0.860099 + 0.510126i \(0.829599\pi\)
\(140\) −5.15714 7.92711i −0.435858 0.669963i
\(141\) 0 0
\(142\) 0.0258794 + 0.0554986i 0.00217175 + 0.00465734i
\(143\) −0.506132 + 1.88891i −0.0423249 + 0.157959i
\(144\) 0 0
\(145\) 22.6267 + 0.771628i 1.87905 + 0.0640802i
\(146\) −4.25011 5.06508i −0.351741 0.419189i
\(147\) 0 0
\(148\) 3.34897 + 4.78283i 0.275284 + 0.393146i
\(149\) −0.130359 + 0.739301i −0.0106794 + 0.0605659i −0.989682 0.143283i \(-0.954234\pi\)
0.979002 + 0.203849i \(0.0653452\pi\)
\(150\) 0 0
\(151\) 1.91410 1.60612i 0.155767 0.130704i −0.561573 0.827427i \(-0.689804\pi\)
0.717340 + 0.696723i \(0.245359\pi\)
\(152\) 0.876286 + 3.27034i 0.0710762 + 0.265260i
\(153\) 0 0
\(154\) 19.0553 11.0016i 1.53552 0.886534i
\(155\) 1.11814 + 7.90907i 0.0898111 + 0.635272i
\(156\) 0 0
\(157\) −0.594827 6.79890i −0.0474723 0.542611i −0.982275 0.187444i \(-0.939980\pi\)
0.934803 0.355167i \(-0.115576\pi\)
\(158\) 4.74717 + 2.21364i 0.377665 + 0.176108i
\(159\) 0 0
\(160\) 0.270694 2.21962i 0.0214003 0.175477i
\(161\) 4.72596i 0.372458i
\(162\) 0 0
\(163\) −0.670477 + 0.670477i −0.0525158 + 0.0525158i −0.732877 0.680361i \(-0.761823\pi\)
0.680361 + 0.732877i \(0.261823\pi\)
\(164\) −0.841337 4.77146i −0.0656974 0.372588i
\(165\) 0 0
\(166\) −4.48804 + 1.63351i −0.348340 + 0.126785i
\(167\) 4.99662 0.437147i 0.386650 0.0338275i 0.107826 0.994170i \(-0.465611\pi\)
0.278824 + 0.960342i \(0.410055\pi\)
\(168\) 0 0
\(169\) 4.39794 12.0832i 0.338303 0.929480i
\(170\) −11.5904 7.22934i −0.888946 0.554465i
\(171\) 0 0
\(172\) 6.32199 1.69397i 0.482047 0.129164i
\(173\) −5.65464 0.494717i −0.429915 0.0376127i −0.129855 0.991533i \(-0.541451\pi\)
−0.300060 + 0.953920i \(0.597007\pi\)
\(174\) 0 0
\(175\) 0.403616 + 21.1427i 0.0305105 + 1.59824i
\(176\) 5.12351 + 0.903414i 0.386199 + 0.0680974i
\(177\) 0 0
\(178\) −0.808587 + 9.24219i −0.0606061 + 0.692731i
\(179\) 7.12420 12.3395i 0.532488 0.922296i −0.466793 0.884367i \(-0.654591\pi\)
0.999280 0.0379289i \(-0.0120760\pi\)
\(180\) 0 0
\(181\) −6.55430 11.3524i −0.487177 0.843816i 0.512714 0.858559i \(-0.328640\pi\)
−0.999891 + 0.0147438i \(0.995307\pi\)
\(182\) 1.44077 0.671843i 0.106797 0.0498004i
\(183\) 0 0
\(184\) 0.718272 0.856003i 0.0529517 0.0631054i
\(185\) −0.693945 13.0374i −0.0510199 0.958528i
\(186\) 0 0
\(187\) 18.2297 26.0348i 1.33309 1.90385i
\(188\) 5.18972 + 5.18972i 0.378499 + 0.378499i
\(189\) 0 0
\(190\) 2.20753 7.24168i 0.160151 0.525367i
\(191\) −1.41468 + 0.249446i −0.102363 + 0.0180493i −0.224595 0.974452i \(-0.572106\pi\)
0.122232 + 0.992502i \(0.460995\pi\)
\(192\) 0 0
\(193\) 8.30860 17.8178i 0.598066 1.28256i −0.341401 0.939918i \(-0.610902\pi\)
0.939467 0.342639i \(-0.111321\pi\)
\(194\) 11.9968 + 10.0665i 0.861320 + 0.722733i
\(195\) 0 0
\(196\) −10.2305 3.72358i −0.730747 0.265970i
\(197\) −19.0913 5.11551i −1.36020 0.364465i −0.496311 0.868145i \(-0.665312\pi\)
−0.863890 + 0.503680i \(0.831979\pi\)
\(198\) 0 0
\(199\) −6.74271 3.89290i −0.477978 0.275961i 0.241596 0.970377i \(-0.422329\pi\)
−0.719573 + 0.694416i \(0.755663\pi\)
\(200\) −3.14025 + 3.89087i −0.222049 + 0.275126i
\(201\) 0 0
\(202\) −7.20849 + 5.04744i −0.507188 + 0.355137i
\(203\) 35.0770 24.5612i 2.46192 1.72386i
\(204\) 0 0
\(205\) −4.05024 + 10.0483i −0.282881 + 0.701806i
\(206\) 0.00151792 0.000876370i 0.000105758 6.10596e-5i
\(207\) 0 0
\(208\) 0.363074 + 0.0972853i 0.0251746 + 0.00674552i
\(209\) 16.5521 + 6.02446i 1.14493 + 0.416721i
\(210\) 0 0
\(211\) 0.399400 + 0.335137i 0.0274959 + 0.0230718i 0.656432 0.754385i \(-0.272065\pi\)
−0.628936 + 0.777457i \(0.716509\pi\)
\(212\) 3.82091 8.19397i 0.262421 0.562764i
\(213\) 0 0
\(214\) −11.0368 + 1.94608i −0.754459 + 0.133032i
\(215\) −13.9991 4.26745i −0.954730 0.291037i
\(216\) 0 0
\(217\) 10.6830 + 10.6830i 0.725207 + 0.725207i
\(218\) 1.27034 1.81424i 0.0860384 0.122876i
\(219\) 0 0
\(220\) −8.65156 7.77710i −0.583288 0.524332i
\(221\) 1.47602 1.75905i 0.0992876 0.118326i
\(222\) 0 0
\(223\) 7.85795 3.66422i 0.526208 0.245375i −0.141314 0.989965i \(-0.545133\pi\)
0.667522 + 0.744590i \(0.267355\pi\)
\(224\) −2.11465 3.66269i −0.141291 0.244723i
\(225\) 0 0
\(226\) 0.629291 1.08996i 0.0418598 0.0725033i
\(227\) −0.540947 + 6.18305i −0.0359039 + 0.410383i 0.956882 + 0.290479i \(0.0938145\pi\)
−0.992785 + 0.119905i \(0.961741\pi\)
\(228\) 0 0
\(229\) 23.6091 + 4.16292i 1.56013 + 0.275093i 0.886060 0.463571i \(-0.153432\pi\)
0.674073 + 0.738665i \(0.264543\pi\)
\(230\) −2.37573 + 0.774069i −0.156651 + 0.0510406i
\(231\) 0 0
\(232\) 10.0863 + 0.882439i 0.662200 + 0.0579350i
\(233\) 11.2846 3.02370i 0.739278 0.198089i 0.130521 0.991446i \(-0.458335\pi\)
0.608757 + 0.793357i \(0.291668\pi\)
\(234\) 0 0
\(235\) −3.70481 15.9877i −0.241675 1.04292i
\(236\) 1.03087 2.83230i 0.0671041 0.184367i
\(237\) 0 0
\(238\) −25.7387 + 2.25184i −1.66839 + 0.145965i
\(239\) −17.3288 + 6.30716i −1.12091 + 0.407976i −0.834983 0.550276i \(-0.814522\pi\)
−0.285923 + 0.958253i \(0.592300\pi\)
\(240\) 0 0
\(241\) 0.864030 + 4.90016i 0.0556571 + 0.315647i 0.999908 0.0135803i \(-0.00432289\pi\)
−0.944251 + 0.329227i \(0.893212\pi\)
\(242\) 11.3608 11.3608i 0.730298 0.730298i
\(243\) 0 0
\(244\) 7.64528i 0.489439i
\(245\) 15.0034 + 19.1712i 0.958533 + 1.22480i
\(246\) 0 0
\(247\) 1.15339 + 0.537835i 0.0733885 + 0.0342216i
\(248\) 0.311339 + 3.55862i 0.0197700 + 0.225973i
\(249\) 0 0
\(250\) 10.5623 3.66587i 0.668016 0.231850i
\(251\) −11.3319 + 6.54248i −0.715264 + 0.412958i −0.813007 0.582254i \(-0.802171\pi\)
0.0977433 + 0.995212i \(0.468838\pi\)
\(252\) 0 0
\(253\) −1.50465 5.61541i −0.0945962 0.353038i
\(254\) 5.73526 4.81246i 0.359862 0.301960i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −1.16005 1.65673i −0.0723622 0.103344i 0.781340 0.624106i \(-0.214537\pi\)
−0.853702 + 0.520762i \(0.825648\pi\)
\(258\) 0 0
\(259\) −15.8729 18.9166i −0.986295 1.17542i
\(260\) −0.573719 0.614231i −0.0355806 0.0380930i
\(261\) 0 0
\(262\) −3.19565 + 11.9263i −0.197428 + 0.736812i
\(263\) 4.72696 + 10.1370i 0.291477 + 0.625074i 0.996452 0.0841574i \(-0.0268198\pi\)
−0.704976 + 0.709232i \(0.749042\pi\)
\(264\) 0 0
\(265\) −16.9459 + 11.0245i −1.04098 + 0.677229i
\(266\) −4.89746 13.4556i −0.300282 0.825019i
\(267\) 0 0
\(268\) 0.199873 + 0.139953i 0.0122092 + 0.00854896i
\(269\) 9.40361 0.573348 0.286674 0.958028i \(-0.407450\pi\)
0.286674 + 0.958028i \(0.407450\pi\)
\(270\) 0 0
\(271\) −1.37745 −0.0836741 −0.0418370 0.999124i \(-0.513321\pi\)
−0.0418370 + 0.999124i \(0.513321\pi\)
\(272\) −5.00423 3.50400i −0.303426 0.212461i
\(273\) 0 0
\(274\) 4.34383 + 11.9346i 0.262420 + 0.720993i
\(275\) 7.21095 + 24.9933i 0.434837 + 1.50715i
\(276\) 0 0
\(277\) 12.2207 + 26.2073i 0.734269 + 1.57465i 0.816041 + 0.577994i \(0.196164\pi\)
−0.0817715 + 0.996651i \(0.526058\pi\)
\(278\) 1.13019 4.21794i 0.0677845 0.252975i
\(279\) 0 0
\(280\) −0.322321 + 9.45152i −0.0192624 + 0.564836i
\(281\) 20.9375 + 24.9523i 1.24903 + 1.48853i 0.805875 + 0.592085i \(0.201695\pi\)
0.443151 + 0.896447i \(0.353860\pi\)
\(282\) 0 0
\(283\) −15.0389 21.4778i −0.893970 1.27672i −0.960313 0.278924i \(-0.910022\pi\)
0.0663434 0.997797i \(-0.478867\pi\)
\(284\) 0.0106335 0.0603057i 0.000630983 0.00357848i
\(285\) 0 0
\(286\) 1.49803 1.25700i 0.0885805 0.0743279i
\(287\) 5.30353 + 19.7930i 0.313057 + 1.16835i
\(288\) 0 0
\(289\) −17.5979 + 10.1602i −1.03517 + 0.597657i
\(290\) −18.0921 13.6102i −1.06241 0.799220i
\(291\) 0 0
\(292\) 0.576273 + 6.58683i 0.0337238 + 0.385465i
\(293\) 21.1017 + 9.83988i 1.23277 + 0.574852i 0.926214 0.376999i \(-0.123044\pi\)
0.306561 + 0.951851i \(0.400822\pi\)
\(294\) 0 0
\(295\) −5.30754 + 4.15369i −0.309017 + 0.241837i
\(296\) 5.83875i 0.339371i
\(297\) 0 0
\(298\) 0.530829 0.530829i 0.0307501 0.0307501i
\(299\) −0.0729361 0.413641i −0.00421800 0.0239215i
\(300\) 0 0
\(301\) −26.0115 + 9.46740i −1.49928 + 0.545692i
\(302\) −2.48917 + 0.217774i −0.143235 + 0.0125315i
\(303\) 0 0
\(304\) 1.15798 3.18153i 0.0664148 0.182473i
\(305\) −9.04731 + 14.5051i −0.518047 + 0.830559i
\(306\) 0 0
\(307\) −14.1397 + 3.78873i −0.806997 + 0.216234i −0.638654 0.769494i \(-0.720508\pi\)
−0.168343 + 0.985728i \(0.553842\pi\)
\(308\) −21.9195 1.91770i −1.24898 0.109271i
\(309\) 0 0
\(310\) 3.62053 7.12007i 0.205632 0.404393i
\(311\) −13.9613 2.46175i −0.791672 0.139593i −0.236833 0.971550i \(-0.576109\pi\)
−0.554840 + 0.831957i \(0.687220\pi\)
\(312\) 0 0
\(313\) 0.580982 6.64066i 0.0328391 0.375352i −0.961937 0.273271i \(-0.911894\pi\)
0.994776 0.102081i \(-0.0325501\pi\)
\(314\) −3.41244 + 5.91051i −0.192575 + 0.333550i
\(315\) 0 0
\(316\) −2.61896 4.53618i −0.147328 0.255180i
\(317\) −5.98543 + 2.79105i −0.336175 + 0.156761i −0.583374 0.812204i \(-0.698268\pi\)
0.247199 + 0.968965i \(0.420490\pi\)
\(318\) 0 0
\(319\) 33.8589 40.3515i 1.89573 2.25925i
\(320\) −1.49486 + 1.66294i −0.0835654 + 0.0929614i
\(321\) 0 0
\(322\) −2.71070 + 3.87128i −0.151061 + 0.215738i
\(323\) −14.6254 14.6254i −0.813779 0.813779i
\(324\) 0 0
\(325\) 0.361623 + 1.84429i 0.0200592 + 0.102303i
\(326\) 0.933793 0.164653i 0.0517180 0.00911928i
\(327\) 0 0
\(328\) −2.04761 + 4.39112i −0.113061 + 0.242459i
\(329\) −23.7783 19.9524i −1.31094 1.10001i
\(330\) 0 0
\(331\) 8.71424 + 3.17172i 0.478978 + 0.174334i 0.570215 0.821495i \(-0.306860\pi\)
−0.0912370 + 0.995829i \(0.529082\pi\)
\(332\) 4.61333 + 1.23614i 0.253190 + 0.0678419i
\(333\) 0 0
\(334\) −4.34373 2.50785i −0.237678 0.137224i
\(335\) −0.213593 0.502053i −0.0116698 0.0274301i
\(336\) 0 0
\(337\) 28.8075 20.1713i 1.56925 1.09880i 0.619849 0.784721i \(-0.287194\pi\)
0.949397 0.314078i \(-0.101695\pi\)
\(338\) −10.5332 + 7.37545i −0.572933 + 0.401172i
\(339\) 0 0
\(340\) 5.34775 + 12.5699i 0.290022 + 0.681700i
\(341\) 16.0948 + 9.29232i 0.871581 + 0.503207i
\(342\) 0 0
\(343\) 15.8792 + 4.25483i 0.857399 + 0.229739i
\(344\) −6.15030 2.23852i −0.331602 0.120693i
\(345\) 0 0
\(346\) 4.34826 + 3.64862i 0.233764 + 0.196151i
\(347\) 7.84524 16.8242i 0.421155 0.903169i −0.575212 0.818004i \(-0.695081\pi\)
0.996367 0.0851649i \(-0.0271417\pi\)
\(348\) 0 0
\(349\) −9.68283 + 1.70734i −0.518310 + 0.0913920i −0.426683 0.904401i \(-0.640318\pi\)
−0.0916271 + 0.995793i \(0.529207\pi\)
\(350\) 11.7963 17.5506i 0.630540 0.938117i
\(351\) 0 0
\(352\) −3.67876 3.67876i −0.196079 0.196079i
\(353\) −1.87815 + 2.68228i −0.0999639 + 0.142763i −0.866018 0.500013i \(-0.833329\pi\)
0.766054 + 0.642776i \(0.222217\pi\)
\(354\) 0 0
\(355\) −0.0915394 + 0.101832i −0.00485841 + 0.00540468i
\(356\) 5.96346 7.10697i 0.316063 0.376669i
\(357\) 0 0
\(358\) −12.9134 + 6.02163i −0.682496 + 0.318253i
\(359\) 8.24511 + 14.2809i 0.435160 + 0.753719i 0.997309 0.0733169i \(-0.0233584\pi\)
−0.562149 + 0.827036i \(0.690025\pi\)
\(360\) 0 0
\(361\) −3.76848 + 6.52720i −0.198341 + 0.343537i
\(362\) −1.14249 + 13.0587i −0.0600479 + 0.686351i
\(363\) 0 0
\(364\) −1.56557 0.276051i −0.0820579 0.0144690i
\(365\) 6.70142 13.1789i 0.350768 0.689815i
\(366\) 0 0
\(367\) −32.6051 2.85258i −1.70197 0.148903i −0.805675 0.592358i \(-0.798197\pi\)
−0.896297 + 0.443455i \(0.853753\pi\)
\(368\) −1.07936 + 0.289213i −0.0562654 + 0.0150763i
\(369\) 0 0
\(370\) −6.90949 + 11.0776i −0.359207 + 0.575899i
\(371\) −13.0779 + 35.9314i −0.678973 + 1.86546i
\(372\) 0 0
\(373\) −6.17963 + 0.540647i −0.319969 + 0.0279937i −0.246009 0.969268i \(-0.579119\pi\)
−0.0739600 + 0.997261i \(0.523564\pi\)
\(374\) −29.8659 + 10.8703i −1.54433 + 0.562089i
\(375\) 0 0
\(376\) −1.27447 7.22787i −0.0657257 0.372749i
\(377\) 2.69107 2.69107i 0.138597 0.138597i
\(378\) 0 0
\(379\) 6.82213i 0.350429i 0.984530 + 0.175215i \(0.0560620\pi\)
−0.984530 + 0.175215i \(0.943938\pi\)
\(380\) −5.96196 + 4.66585i −0.305842 + 0.239353i
\(381\) 0 0
\(382\) 1.30191 + 0.607093i 0.0666117 + 0.0310616i
\(383\) −0.301009 3.44055i −0.0153808 0.175804i −0.999999 0.00108604i \(-0.999654\pi\)
0.984619 0.174718i \(-0.0559013\pi\)
\(384\) 0 0
\(385\) 39.3175 + 29.5776i 2.00381 + 1.50741i
\(386\) −17.0259 + 9.82991i −0.866596 + 0.500329i
\(387\) 0 0
\(388\) −4.05329 15.1271i −0.205775 0.767961i
\(389\) −9.14718 + 7.67539i −0.463780 + 0.389158i −0.844520 0.535525i \(-0.820114\pi\)
0.380739 + 0.924682i \(0.375669\pi\)
\(390\) 0 0
\(391\) −1.18540 + 6.72273i −0.0599482 + 0.339983i
\(392\) 6.24454 + 8.91813i 0.315397 + 0.450433i
\(393\) 0 0
\(394\) 12.7046 + 15.1407i 0.640047 + 0.762778i
\(395\) −0.399189 + 11.7056i −0.0200854 + 0.588970i
\(396\) 0 0
\(397\) 0.674193 2.51612i 0.0338368 0.126280i −0.946942 0.321406i \(-0.895845\pi\)
0.980778 + 0.195125i \(0.0625113\pi\)
\(398\) 3.29042 + 7.05634i 0.164934 + 0.353702i
\(399\) 0 0
\(400\) 4.80405 1.38604i 0.240202 0.0693020i
\(401\) −2.31034 6.34761i −0.115373 0.316984i 0.868544 0.495612i \(-0.165056\pi\)
−0.983917 + 0.178628i \(0.942834\pi\)
\(402\) 0 0
\(403\) 1.09990 + 0.770158i 0.0547899 + 0.0383643i
\(404\) 8.79994 0.437814
\(405\) 0 0
\(406\) −42.8211 −2.12518
\(407\) −24.8829 17.4232i −1.23340 0.863636i
\(408\) 0 0
\(409\) 1.32960 + 3.65304i 0.0657444 + 0.180631i 0.968215 0.250121i \(-0.0804704\pi\)
−0.902470 + 0.430752i \(0.858248\pi\)
\(410\) 9.08125 5.90799i 0.448491 0.291775i
\(411\) 0 0
\(412\) −0.000740740 0.00158852i −3.64936e−5 7.82609e-5i
\(413\) −3.29928 + 12.3131i −0.162347 + 0.605886i
\(414\) 0 0
\(415\) −7.28987 7.80463i −0.357846 0.383114i
\(416\) −0.241612 0.287942i −0.0118460 0.0141175i
\(417\) 0 0
\(418\) −10.1032 14.4288i −0.494162 0.705737i
\(419\) −2.47543 + 14.0389i −0.120933 + 0.685844i 0.862708 + 0.505703i \(0.168767\pi\)
−0.983641 + 0.180141i \(0.942344\pi\)
\(420\) 0 0
\(421\) 21.8367 18.3232i 1.06426 0.893018i 0.0697379 0.997565i \(-0.477784\pi\)
0.994520 + 0.104547i \(0.0333392\pi\)
\(422\) −0.134943 0.503615i −0.00656893 0.0245156i
\(423\) 0 0
\(424\) −7.82978 + 4.52052i −0.380248 + 0.219536i
\(425\) 4.72900 30.1769i 0.229390 1.46379i
\(426\) 0 0
\(427\) 2.81811 + 32.2112i 0.136378 + 1.55881i
\(428\) 10.1570 + 4.73630i 0.490959 + 0.228938i
\(429\) 0 0
\(430\) 9.01968 + 11.5252i 0.434968 + 0.555796i
\(431\) 38.9178i 1.87461i −0.348515 0.937303i \(-0.613314\pi\)
0.348515 0.937303i \(-0.386686\pi\)
\(432\) 0 0
\(433\) 8.50667 8.50667i 0.408804 0.408804i −0.472517 0.881321i \(-0.656655\pi\)
0.881321 + 0.472517i \(0.156655\pi\)
\(434\) −2.62347 14.8785i −0.125931 0.714189i
\(435\) 0 0
\(436\) −2.08121 + 0.757497i −0.0996717 + 0.0362775i
\(437\) −3.76891 + 0.329737i −0.180291 + 0.0157734i
\(438\) 0 0
\(439\) −12.9045 + 35.4547i −0.615896 + 1.69216i 0.100917 + 0.994895i \(0.467822\pi\)
−0.716813 + 0.697266i \(0.754400\pi\)
\(440\) 2.62618 + 11.3330i 0.125198 + 0.540278i
\(441\) 0 0
\(442\) −2.21803 + 0.594319i −0.105501 + 0.0282689i
\(443\) −37.0206 3.23888i −1.75890 0.153884i −0.838512 0.544883i \(-0.816574\pi\)
−0.920391 + 0.390999i \(0.872129\pi\)
\(444\) 0 0
\(445\) −19.7245 + 6.42671i −0.935032 + 0.304655i
\(446\) −8.53857 1.50558i −0.404313 0.0712913i
\(447\) 0 0
\(448\) −0.368608 + 4.21321i −0.0174151 + 0.199056i
\(449\) −19.5467 + 33.8559i −0.922466 + 1.59776i −0.126878 + 0.991918i \(0.540496\pi\)
−0.795587 + 0.605839i \(0.792838\pi\)
\(450\) 0 0
\(451\) 12.6034 + 21.8297i 0.593469 + 1.02792i
\(452\) −1.14066 + 0.531900i −0.0536523 + 0.0250185i
\(453\) 0 0
\(454\) 3.98957 4.75458i 0.187240 0.223144i
\(455\) 2.64361 + 2.37641i 0.123934 + 0.111408i
\(456\) 0 0
\(457\) 5.09288 7.27339i 0.238235 0.340235i −0.682175 0.731189i \(-0.738966\pi\)
0.920410 + 0.390954i \(0.127855\pi\)
\(458\) −16.9517 16.9517i −0.792100 0.792100i
\(459\) 0 0
\(460\) 2.39007 + 0.728583i 0.111438 + 0.0339704i
\(461\) 33.1532 5.84580i 1.54410 0.272266i 0.664245 0.747515i \(-0.268753\pi\)
0.879851 + 0.475249i \(0.157642\pi\)
\(462\) 0 0
\(463\) 4.18344 8.97141i 0.194421 0.416937i −0.784796 0.619755i \(-0.787232\pi\)
0.979216 + 0.202818i \(0.0650099\pi\)
\(464\) −7.75609 6.50813i −0.360067 0.302132i
\(465\) 0 0
\(466\) −10.9781 3.99571i −0.508551 0.185098i
\(467\) 7.67657 + 2.05693i 0.355229 + 0.0951834i 0.432021 0.901864i \(-0.357801\pi\)
−0.0767911 + 0.997047i \(0.524467\pi\)
\(468\) 0 0
\(469\) −0.893695 0.515975i −0.0412670 0.0238255i
\(470\) −6.13535 + 15.2213i −0.283003 + 0.702108i
\(471\) 0 0
\(472\) −2.46898 + 1.72880i −0.113644 + 0.0795745i
\(473\) −27.8927 + 19.5307i −1.28251 + 0.898023i
\(474\) 0 0
\(475\) 16.8329 1.79703i 0.772346 0.0824535i
\(476\) 22.3755 + 12.9185i 1.02558 + 0.592118i
\(477\) 0 0
\(478\) 17.8125 + 4.77286i 0.814727 + 0.218305i
\(479\) −14.8140 5.39184i −0.676867 0.246359i −0.0193652 0.999812i \(-0.506165\pi\)
−0.657502 + 0.753453i \(0.728387\pi\)
\(480\) 0 0
\(481\) −1.68122 1.41071i −0.0766571 0.0643229i
\(482\) 2.10284 4.50956i 0.0957819 0.205405i
\(483\) 0 0
\(484\) −15.8225 + 2.78993i −0.719203 + 0.126815i
\(485\) −10.2110 + 33.4966i −0.463659 + 1.52100i
\(486\) 0 0
\(487\) −6.08544 6.08544i −0.275758 0.275758i 0.555655 0.831413i \(-0.312467\pi\)
−0.831413 + 0.555655i \(0.812467\pi\)
\(488\) −4.38515 + 6.26265i −0.198506 + 0.283497i
\(489\) 0 0
\(490\) −1.29394 24.3097i −0.0584543 1.09820i
\(491\) 19.9695 23.7987i 0.901209 1.07402i −0.0956967 0.995411i \(-0.530508\pi\)
0.996906 0.0786084i \(-0.0250477\pi\)
\(492\) 0 0
\(493\) −56.0579 + 26.1402i −2.52472 + 1.17730i
\(494\) −0.636313 1.10213i −0.0286291 0.0495870i
\(495\) 0 0
\(496\) 1.78611 3.09363i 0.0801986 0.138908i
\(497\) −0.0225721 + 0.258000i −0.00101250 + 0.0115729i
\(498\) 0 0
\(499\) −12.8962 2.27395i −0.577313 0.101796i −0.122635 0.992452i \(-0.539134\pi\)
−0.454678 + 0.890656i \(0.650246\pi\)
\(500\) −10.7548 3.05536i −0.480967 0.136640i
\(501\) 0 0
\(502\) 13.0352 + 1.14043i 0.581788 + 0.0508999i
\(503\) 6.77201 1.81455i 0.301949 0.0809070i −0.104664 0.994508i \(-0.533377\pi\)
0.406613 + 0.913601i \(0.366710\pi\)
\(504\) 0 0
\(505\) −16.6958 10.4137i −0.742953 0.463405i
\(506\) −1.98833 + 5.46291i −0.0883923 + 0.242856i
\(507\) 0 0
\(508\) −7.45836 + 0.652522i −0.330911 + 0.0289510i
\(509\) 15.4656 5.62900i 0.685499 0.249501i 0.0242921 0.999705i \(-0.492267\pi\)
0.661207 + 0.750204i \(0.270045\pi\)
\(510\) 0 0
\(511\) −4.85592 27.5393i −0.214813 1.21827i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 2.02249i 0.0892083i
\(515\) −0.000474457 0.00389042i −2.09071e−5 0.000171432i
\(516\) 0 0
\(517\) −34.6060 16.1370i −1.52197 0.709706i
\(518\) 2.15221 + 24.5999i 0.0945628 + 1.08086i
\(519\) 0 0
\(520\) 0.117655 + 0.832221i 0.00515950 + 0.0364953i
\(521\) −0.953086 + 0.550265i −0.0417555 + 0.0241075i −0.520732 0.853720i \(-0.674341\pi\)
0.478977 + 0.877827i \(0.341008\pi\)
\(522\) 0 0
\(523\) −0.834549 3.11458i −0.0364923 0.136191i 0.945276 0.326271i \(-0.105792\pi\)
−0.981769 + 0.190080i \(0.939125\pi\)
\(524\) 9.45840 7.93654i 0.413192 0.346709i
\(525\) 0 0
\(526\) 1.94224 11.0150i 0.0846859 0.480278i
\(527\) −12.5170 17.8762i −0.545251 0.778699i
\(528\) 0 0
\(529\) −13.9815 16.6625i −0.607891 0.724456i
\(530\) 20.2047 + 0.689030i 0.877634 + 0.0299295i
\(531\) 0 0
\(532\) −3.70608 + 13.8313i −0.160679 + 0.599662i
\(533\) 0.769660 + 1.65054i 0.0333377 + 0.0714929i
\(534\) 0 0
\(535\) −13.6657 21.0057i −0.590819 0.908155i
\(536\) −0.0834528 0.229285i −0.00360461 0.00990359i
\(537\) 0 0
\(538\) −7.70299 5.39369i −0.332099 0.232538i
\(539\) 56.6403 2.43967
\(540\) 0 0
\(541\) 45.1758 1.94226 0.971129 0.238553i \(-0.0766732\pi\)
0.971129 + 0.238553i \(0.0766732\pi\)
\(542\) 1.12834 + 0.790072i 0.0484664 + 0.0339365i
\(543\) 0 0
\(544\) 2.08941 + 5.74062i 0.0895829 + 0.246127i
\(545\) 4.84500 + 1.02570i 0.207537 + 0.0439361i
\(546\) 0 0
\(547\) −18.1023 38.8206i −0.774000 1.65985i −0.751169 0.660110i \(-0.770510\pi\)
−0.0228315 0.999739i \(-0.507268\pi\)
\(548\) 3.28713 12.2677i 0.140419 0.524052i
\(549\) 0 0
\(550\) 8.42872 24.6094i 0.359402 1.04935i
\(551\) −22.0346 26.2599i −0.938707 1.11871i
\(552\) 0 0
\(553\) 12.7063 + 18.1465i 0.540327 + 0.771668i
\(554\) 5.02131 28.4773i 0.213335 1.20988i
\(555\) 0 0
\(556\) −3.34511 + 2.80688i −0.141864 + 0.119038i
\(557\) 5.41667 + 20.2153i 0.229512 + 0.856549i 0.980547 + 0.196286i \(0.0628882\pi\)
−0.751035 + 0.660262i \(0.770445\pi\)
\(558\) 0 0
\(559\) −2.13055 + 1.23007i −0.0901127 + 0.0520266i
\(560\) 5.68520 7.55736i 0.240243 0.319357i
\(561\) 0 0
\(562\) −2.83892 32.4490i −0.119753 1.36878i
\(563\) 33.8407 + 15.7802i 1.42621 + 0.665055i 0.973936 0.226822i \(-0.0728335\pi\)
0.452279 + 0.891877i \(0.350611\pi\)
\(564\) 0 0
\(565\) 2.79358 + 0.340691i 0.117527 + 0.0143330i
\(566\) 26.2195i 1.10209i
\(567\) 0 0
\(568\) −0.0433004 + 0.0433004i −0.00181684 + 0.00181684i
\(569\) −4.38237 24.8537i −0.183719 1.04192i −0.927591 0.373598i \(-0.878124\pi\)
0.743872 0.668322i \(-0.232987\pi\)
\(570\) 0 0
\(571\) 32.0935 11.6811i 1.34307 0.488837i 0.432292 0.901734i \(-0.357705\pi\)
0.910778 + 0.412897i \(0.135483\pi\)
\(572\) −1.94810 + 0.170437i −0.0814542 + 0.00712632i
\(573\) 0 0
\(574\) 7.00843 19.2555i 0.292526 0.803709i
\(575\) −3.67240 4.21069i −0.153149 0.175598i
\(576\) 0 0
\(577\) −22.6289 + 6.06339i −0.942052 + 0.252422i −0.696986 0.717084i \(-0.745476\pi\)
−0.245066 + 0.969506i \(0.578810\pi\)
\(578\) 20.2430 + 1.77103i 0.841998 + 0.0736653i
\(579\) 0 0
\(580\) 7.01370 + 21.5261i 0.291228 + 0.893821i
\(581\) −19.8926 3.50760i −0.825284 0.145520i
\(582\) 0 0
\(583\) −4.09950 + 46.8575i −0.169784 + 1.94064i
\(584\) 3.30600 5.72615i 0.136803 0.236950i
\(585\) 0 0
\(586\) −11.6416 20.1638i −0.480909 0.832959i
\(587\) −19.1692 + 8.93875i −0.791198 + 0.368942i −0.775831 0.630940i \(-0.782669\pi\)
−0.0153665 + 0.999882i \(0.504891\pi\)
\(588\) 0 0
\(589\) 7.77418 9.26491i 0.320330 0.381754i
\(590\) 6.73014 0.358227i 0.277075 0.0147480i
\(591\) 0 0
\(592\) −3.34897 + 4.78283i −0.137642 + 0.196573i
\(593\) 1.68491 + 1.68491i 0.0691910 + 0.0691910i 0.740855 0.671664i \(-0.234420\pi\)
−0.671664 + 0.740855i \(0.734420\pi\)
\(594\) 0 0
\(595\) −27.1646 50.9886i −1.11364 2.09033i
\(596\) −0.739301 + 0.130359i −0.0302829 + 0.00533970i
\(597\) 0 0
\(598\) −0.177509 + 0.380669i −0.00725888 + 0.0155667i
\(599\) −11.6914 9.81029i −0.477700 0.400838i 0.371894 0.928275i \(-0.378708\pi\)
−0.849594 + 0.527438i \(0.823153\pi\)
\(600\) 0 0
\(601\) 43.3179 + 15.7664i 1.76697 + 0.643126i 0.999999 + 0.00144762i \(0.000460792\pi\)
0.766974 + 0.641678i \(0.221761\pi\)
\(602\) 26.7376 + 7.16433i 1.08974 + 0.291996i
\(603\) 0 0
\(604\) 2.16392 + 1.24934i 0.0880485 + 0.0508348i
\(605\) 33.3209 + 13.4309i 1.35469 + 0.546042i
\(606\) 0 0
\(607\) 23.6505 16.5602i 0.959942 0.672159i 0.0151695 0.999885i \(-0.495171\pi\)
0.944773 + 0.327726i \(0.106282\pi\)
\(608\) −2.77341 + 1.94196i −0.112477 + 0.0787570i
\(609\) 0 0
\(610\) 15.7309 6.69255i 0.636926 0.270973i
\(611\) −2.38913 1.37937i −0.0966539 0.0558032i
\(612\) 0 0
\(613\) −26.4834 7.09621i −1.06966 0.286613i −0.319304 0.947652i \(-0.603449\pi\)
−0.750351 + 0.661039i \(0.770116\pi\)
\(614\) 13.7557 + 5.00667i 0.555135 + 0.202053i
\(615\) 0 0
\(616\) 16.8554 + 14.1434i 0.679124 + 0.569853i
\(617\) 0.481909 1.03346i 0.0194009 0.0416054i −0.896369 0.443310i \(-0.853804\pi\)
0.915769 + 0.401704i \(0.131582\pi\)
\(618\) 0 0
\(619\) 36.3650 6.41213i 1.46163 0.257725i 0.614420 0.788979i \(-0.289390\pi\)
0.847213 + 0.531254i \(0.178279\pi\)
\(620\) −7.04967 + 3.75577i −0.283121 + 0.150835i
\(621\) 0 0
\(622\) 10.0244 + 10.0244i 0.401943 + 0.401943i
\(623\) −22.5056 + 32.1414i −0.901669 + 1.28772i
\(624\) 0 0
\(625\) 16.7889 + 18.5238i 0.671556 + 0.740953i
\(626\) −4.28484 + 5.10647i −0.171257 + 0.204096i
\(627\) 0 0
\(628\) 6.18543 2.88432i 0.246826 0.115097i
\(629\) 17.8346 + 30.8904i 0.711111 + 1.23168i
\(630\) 0 0
\(631\) −23.0047 + 39.8453i −0.915802 + 1.58622i −0.110078 + 0.993923i \(0.535110\pi\)
−0.805723 + 0.592292i \(0.798223\pi\)
\(632\) −0.456515 + 5.21799i −0.0181592 + 0.207561i
\(633\) 0 0
\(634\) 6.50386 + 1.14681i 0.258301 + 0.0455455i
\(635\) 14.9226 + 7.58811i 0.592187 + 0.301125i
\(636\) 0 0
\(637\) 4.07666 + 0.356661i 0.161523 + 0.0141314i
\(638\) −50.8802 + 13.6333i −2.01437 + 0.539748i
\(639\) 0 0
\(640\) 2.17835 0.504786i 0.0861067 0.0199534i
\(641\) 2.49833 6.86411i 0.0986782 0.271116i −0.880524 0.474001i \(-0.842809\pi\)
0.979203 + 0.202885i \(0.0650317\pi\)
\(642\) 0 0
\(643\) 39.1523 3.42538i 1.54402 0.135084i 0.716925 0.697150i \(-0.245549\pi\)
0.827092 + 0.562066i \(0.189993\pi\)
\(644\) 4.44095 1.61637i 0.174998 0.0636941i
\(645\) 0 0
\(646\) 3.59164 + 20.3692i 0.141311 + 0.801415i
\(647\) 24.0132 24.0132i 0.944058 0.944058i −0.0544579 0.998516i \(-0.517343\pi\)
0.998516 + 0.0544579i \(0.0173431\pi\)
\(648\) 0 0
\(649\) 15.6809i 0.615528i
\(650\) 0.761616 1.71817i 0.0298730 0.0673922i
\(651\) 0 0
\(652\) −0.859359 0.400726i −0.0336551 0.0156936i
\(653\) 0.161787 + 1.84923i 0.00633120 + 0.0723659i 0.998703 0.0509153i \(-0.0162138\pi\)
−0.992372 + 0.123281i \(0.960658\pi\)
\(654\) 0 0
\(655\) −27.3370 + 3.86475i −1.06815 + 0.151008i
\(656\) 4.19595 2.42253i 0.163824 0.0945840i
\(657\) 0 0
\(658\) 8.03385 + 29.9828i 0.313192 + 1.16885i
\(659\) −7.92888 + 6.65312i −0.308865 + 0.259169i −0.784023 0.620732i \(-0.786835\pi\)
0.475158 + 0.879901i \(0.342391\pi\)
\(660\) 0 0
\(661\) 4.12789 23.4104i 0.160556 0.910561i −0.792972 0.609258i \(-0.791467\pi\)
0.953529 0.301303i \(-0.0974215\pi\)
\(662\) −5.31906 7.59641i −0.206731 0.295243i
\(663\) 0 0
\(664\) −3.07000 3.65868i −0.119139 0.141985i
\(665\) 23.3991 21.8558i 0.907380 0.847533i
\(666\) 0 0
\(667\) −2.92824 + 10.9283i −0.113382 + 0.423147i
\(668\) 2.11973 + 4.54577i 0.0820147 + 0.175881i
\(669\) 0 0
\(670\) −0.113000 + 0.533770i −0.00436559 + 0.0206213i
\(671\) 13.6038 + 37.3762i 0.525170 + 1.44289i
\(672\) 0 0
\(673\) 5.79958 + 4.06091i 0.223558 + 0.156537i 0.679990 0.733221i \(-0.261984\pi\)
−0.456432 + 0.889758i \(0.650873\pi\)
\(674\) −35.1675 −1.35460
\(675\) 0 0
\(676\) 12.8587 0.494566
\(677\) −19.3267 13.5327i −0.742787 0.520105i 0.139843 0.990174i \(-0.455340\pi\)
−0.882630 + 0.470068i \(0.844229\pi\)
\(678\) 0 0
\(679\) 22.6533 + 62.2395i 0.869355 + 2.38853i
\(680\) 2.82920 13.3640i 0.108495 0.512487i
\(681\) 0 0
\(682\) −7.85421 16.8434i −0.300753 0.644967i
\(683\) 12.1872 45.4832i 0.466330 1.74037i −0.186112 0.982529i \(-0.559589\pi\)
0.652442 0.757839i \(-0.273745\pi\)
\(684\) 0 0
\(685\) −20.7540 + 19.3852i −0.792970 + 0.740669i
\(686\) −10.5670 12.5933i −0.403452 0.480815i
\(687\) 0 0
\(688\) 3.75406 + 5.36136i 0.143122 + 0.204400i
\(689\) −0.590119 + 3.34673i −0.0224818 + 0.127500i
\(690\) 0 0
\(691\) 12.4777 10.4701i 0.474675 0.398300i −0.373821 0.927501i \(-0.621953\pi\)
0.848497 + 0.529201i \(0.177508\pi\)
\(692\) −1.46912 5.48283i −0.0558476 0.208426i
\(693\) 0 0
\(694\) −16.0764 + 9.28171i −0.610252 + 0.352329i
\(695\) 9.66817 1.36683i 0.366734 0.0518468i
\(696\) 0 0
\(697\) −2.57970 29.4861i −0.0977129 1.11686i
\(698\) 8.91100 + 4.15527i 0.337286 + 0.157279i
\(699\) 0 0
\(700\) −19.7296 + 7.61050i −0.745708 + 0.287650i
\(701\) 20.7744i 0.784637i −0.919829 0.392319i \(-0.871673\pi\)
0.919829 0.392319i \(-0.128327\pi\)
\(702\) 0 0
\(703\) −13.9783 + 13.9783i −0.527202 + 0.527202i
\(704\) 0.903414 + 5.12351i 0.0340487 + 0.193100i
\(705\) 0 0
\(706\) 3.07698 1.11993i 0.115804 0.0421491i
\(707\) −37.0760 + 3.24373i −1.39439 + 0.121993i
\(708\) 0 0
\(709\) 13.3009 36.5440i 0.499527 1.37244i −0.392207 0.919877i \(-0.628288\pi\)
0.891733 0.452561i \(-0.149490\pi\)
\(710\) 0.133393 0.0309111i 0.00500616 0.00116007i
\(711\) 0 0
\(712\) −8.96137 + 2.40119i −0.335842 + 0.0899885i
\(713\) −3.97652 0.347900i −0.148922 0.0130290i
\(714\) 0 0
\(715\) 3.89775 + 1.98199i 0.145768 + 0.0741223i
\(716\) 14.0319 + 2.47421i 0.524398 + 0.0924655i
\(717\) 0 0
\(718\) 1.43722 16.4275i 0.0536365 0.613067i
\(719\) −6.20709 + 10.7510i −0.231485 + 0.400945i −0.958245 0.285947i \(-0.907692\pi\)
0.726760 + 0.686891i \(0.241025\pi\)
\(720\) 0 0
\(721\) 0.00370644 + 0.00641974i 0.000138035 + 0.000239083i
\(722\) 6.83081 3.18526i 0.254216 0.118543i
\(723\) 0 0
\(724\) 8.42604 10.0418i 0.313151 0.373199i
\(725\) 12.1668 49.1405i 0.451864 1.82503i
\(726\) 0 0
\(727\) −7.81380 + 11.1593i −0.289798 + 0.413874i −0.937481 0.348035i \(-0.886849\pi\)
0.647684 + 0.761909i \(0.275738\pi\)
\(728\) 1.12410 + 1.12410i 0.0416619 + 0.0416619i
\(729\) 0 0
\(730\) −13.0486 + 6.95174i −0.482950 + 0.257295i
\(731\) 39.3763 6.94310i 1.45638 0.256800i
\(732\) 0 0
\(733\) 7.31307 15.6829i 0.270115 0.579263i −0.723725 0.690088i \(-0.757572\pi\)
0.993840 + 0.110826i \(0.0353495\pi\)
\(734\) 25.0724 + 21.0382i 0.925437 + 0.776534i
\(735\) 0 0
\(736\) 1.05004 + 0.382184i 0.0387051 + 0.0140875i
\(737\) −1.22617 0.328551i −0.0451665 0.0121023i
\(738\) 0 0
\(739\) −28.8265 16.6430i −1.06040 0.612223i −0.134858 0.990865i \(-0.543058\pi\)
−0.925543 + 0.378642i \(0.876391\pi\)
\(740\) 12.0138 5.11115i 0.441636 0.187889i
\(741\) 0 0
\(742\) 31.3222 21.9320i 1.14987 0.805151i
\(743\) 14.7359 10.3182i 0.540607 0.378537i −0.271146 0.962538i \(-0.587402\pi\)
0.811753 + 0.584001i \(0.198514\pi\)
\(744\) 0 0
\(745\) 1.55691 + 0.627553i 0.0570408 + 0.0229918i
\(746\) 5.37216 + 3.10162i 0.196689 + 0.113558i
\(747\) 0 0
\(748\) 30.6996 + 8.22594i 1.12249 + 0.300770i
\(749\) −44.5396 16.2111i −1.62744 0.592340i
\(750\) 0 0
\(751\) 15.4184 + 12.9376i 0.562627 + 0.472100i 0.879190 0.476471i \(-0.158084\pi\)
−0.316563 + 0.948571i \(0.602529\pi\)
\(752\) −3.10175 + 6.65173i −0.113109 + 0.242563i
\(753\) 0 0
\(754\) −3.74793 + 0.660860i −0.136491 + 0.0240671i
\(755\) −2.62707 4.93106i −0.0956087 0.179460i
\(756\) 0 0
\(757\) −18.5041 18.5041i −0.672541 0.672541i 0.285760 0.958301i \(-0.407754\pi\)
−0.958301 + 0.285760i \(0.907754\pi\)
\(758\) 3.91301 5.58836i 0.142127 0.202979i
\(759\) 0 0
\(760\) 7.55998 0.402397i 0.274229 0.0145965i
\(761\) −13.7056 + 16.3338i −0.496829 + 0.592098i −0.954941 0.296797i \(-0.904082\pi\)
0.458111 + 0.888895i \(0.348526\pi\)
\(762\) 0 0
\(763\) 8.48934 3.95864i 0.307335 0.143313i
\(764\) −0.718252 1.24405i −0.0259854 0.0450081i
\(765\) 0 0
\(766\) −1.72684 + 2.99098i −0.0623934 + 0.108069i
\(767\) −0.0987416 + 1.12862i −0.00356535 + 0.0407522i
\(768\) 0 0
\(769\) −13.6805 2.41225i −0.493332 0.0869878i −0.0785532 0.996910i \(-0.525030\pi\)
−0.414779 + 0.909922i \(0.636141\pi\)
\(770\) −15.2421 46.7801i −0.549286 1.68584i
\(771\) 0 0
\(772\) 19.5850 + 1.71347i 0.704880 + 0.0616690i
\(773\) 26.7372 7.16421i 0.961671 0.257679i 0.256363 0.966580i \(-0.417476\pi\)
0.705307 + 0.708902i \(0.250809\pi\)
\(774\) 0 0
\(775\) 17.8196 + 1.21680i 0.640098 + 0.0437088i
\(776\) −5.35628 + 14.7163i −0.192279 + 0.528283i
\(777\) 0 0
\(778\) 11.8954 1.04071i 0.426469 0.0373112i
\(779\) 15.4147 5.61050i 0.552289 0.201017i
\(780\) 0 0
\(781\) 0.0553214 + 0.313743i 0.00197956 + 0.0112266i
\(782\) 4.82702 4.82702i 0.172614 0.172614i
\(783\) 0 0
\(784\) 10.8870i 0.388822i
\(785\) −15.1486 1.84745i −0.540678 0.0659384i
\(786\) 0 0
\(787\) 3.50081 + 1.63245i 0.124790 + 0.0581906i 0.484011 0.875062i \(-0.339180\pi\)
−0.359220 + 0.933253i \(0.616957\pi\)
\(788\) −1.72262 19.6896i −0.0613657 0.701413i
\(789\) 0 0
\(790\) 7.04103 9.35966i 0.250508 0.333002i
\(791\) 4.60979 2.66146i 0.163905 0.0946308i
\(792\) 0 0
\(793\) 0.743773 + 2.77580i 0.0264122 + 0.0985715i
\(794\) −1.99545 + 1.67438i −0.0708160 + 0.0594217i
\(795\) 0 0
\(796\) 1.35199 7.66752i 0.0479201 0.271768i
\(797\) −7.23990 10.3397i −0.256451 0.366249i 0.670195 0.742185i \(-0.266210\pi\)
−0.926646 + 0.375935i \(0.877321\pi\)
\(798\) 0 0
\(799\) 28.8203 + 34.3467i 1.01959 + 1.21510i
\(800\) −4.73025 1.62011i −0.167239 0.0572796i
\(801\) 0 0
\(802\) −1.74832 + 6.52481i −0.0617353 + 0.230399i
\(803\) −14.5377 31.1763i −0.513026 1.10019i
\(804\) 0 0
\(805\) −10.3384 2.18867i −0.364382 0.0771406i
\(806\) −0.459240 1.26175i −0.0161761 0.0444433i
\(807\) 0 0
\(808\) −7.20849 5.04744i −0.253594 0.177568i
\(809\) −9.03399 −0.317618 −0.158809 0.987309i \(-0.550765\pi\)
−0.158809 + 0.987309i \(0.550765\pi\)
\(810\) 0 0
\(811\) −18.4143 −0.646613 −0.323307 0.946294i \(-0.604795\pi\)
−0.323307 + 0.946294i \(0.604795\pi\)
\(812\) 35.0770 + 24.5612i 1.23096 + 0.861928i
\(813\) 0 0
\(814\) 10.3893 + 28.5445i 0.364146 + 1.00048i
\(815\) 1.15622 + 1.77723i 0.0405005 + 0.0622538i
\(816\) 0 0
\(817\) 9.36501 + 20.0833i 0.327640 + 0.702627i
\(818\) 1.00616 3.75502i 0.0351794 0.131291i
\(819\) 0 0
\(820\) −10.8276 0.369249i −0.378116 0.0128947i
\(821\) 2.83979 + 3.38433i 0.0991094 + 0.118114i 0.813319 0.581818i \(-0.197658\pi\)
−0.714210 + 0.699932i \(0.753214\pi\)
\(822\) 0 0
\(823\) −23.3920 33.4072i −0.815394 1.16450i −0.983885 0.178800i \(-0.942779\pi\)
0.168492 0.985703i \(-0.446110\pi\)
\(824\) −0.000304360 0.00172611i −1.06029e−5 6.01320e-5i
\(825\) 0 0
\(826\) 9.76509 8.19389i 0.339771 0.285102i
\(827\) 0.320175 + 1.19491i 0.0111336 + 0.0415511i 0.971269 0.237984i \(-0.0764865\pi\)
−0.960136 + 0.279535i \(0.909820\pi\)
\(828\) 0 0
\(829\) 16.1883 9.34633i 0.562243 0.324611i −0.191802 0.981434i \(-0.561433\pi\)
0.754045 + 0.656822i \(0.228100\pi\)
\(830\) 1.49496 + 10.5745i 0.0518908 + 0.367045i
\(831\) 0 0
\(832\) 0.0327602 + 0.374451i 0.00113576 + 0.0129818i
\(833\) −60.2778 28.1080i −2.08850 0.973885i
\(834\) 0 0
\(835\) 1.35772 11.1330i 0.0469859 0.385272i
\(836\) 17.6143i 0.609205i
\(837\) 0 0
\(838\) 10.0801 10.0801i 0.348212 0.348212i
\(839\) −0.681446 3.86467i −0.0235261 0.133423i 0.970783 0.239961i \(-0.0771346\pi\)
−0.994309 + 0.106538i \(0.966024\pi\)
\(840\) 0 0
\(841\) −69.0793 + 25.1428i −2.38204 + 0.866993i
\(842\) −28.3974 + 2.48445i −0.978638 + 0.0856197i
\(843\) 0 0
\(844\) −0.178323 + 0.489937i −0.00613811 + 0.0168643i
\(845\) −24.3963 15.2168i −0.839259 0.523474i
\(846\) 0 0
\(847\) 65.6350 17.5869i 2.25525 0.604292i
\(848\) 9.00664 + 0.787979i 0.309289 + 0.0270593i
\(849\) 0 0
\(850\) −21.1825 + 22.0070i −0.726555 + 0.754835i
\(851\) 6.42529 + 1.13295i 0.220256 + 0.0388371i
\(852\) 0 0
\(853\) −4.22873 + 48.3346i −0.144789 + 1.65494i 0.482307 + 0.876002i \(0.339799\pi\)
−0.627096 + 0.778942i \(0.715757\pi\)
\(854\) 16.1671 28.0023i 0.553227 0.958217i
\(855\) 0 0
\(856\) −5.60352 9.70559i −0.191524 0.331730i
\(857\) 47.8835 22.3284i 1.63567 0.762725i 0.635712 0.771927i \(-0.280707\pi\)
0.999958 + 0.00920138i \(0.00292893\pi\)
\(858\) 0 0
\(859\) −15.5714 + 18.5573i −0.531291 + 0.633168i −0.963212 0.268744i \(-0.913392\pi\)
0.431921 + 0.901912i \(0.357836\pi\)
\(860\) −0.777885 14.6144i −0.0265257 0.498347i
\(861\) 0 0
\(862\) −22.3224 + 31.8796i −0.760302 + 1.08582i
\(863\) −13.3492 13.3492i −0.454411 0.454411i 0.442405 0.896816i \(-0.354126\pi\)
−0.896816 + 0.442405i \(0.854126\pi\)
\(864\) 0 0
\(865\) −3.70100 + 12.1409i −0.125838 + 0.412803i
\(866\) −11.8475 + 2.08903i −0.402594 + 0.0709881i
\(867\) 0 0
\(868\) −6.38491 + 13.6925i −0.216718 + 0.464753i
\(869\) 20.8752 + 17.5163i 0.708141 + 0.594201i
\(870\) 0 0
\(871\) −0.0861839 0.0313684i −0.00292023 0.00106288i
\(872\) 2.13931 + 0.573225i 0.0724460 + 0.0194119i
\(873\) 0 0
\(874\) 3.27644 + 1.89165i 0.110827 + 0.0639861i
\(875\) 46.4383 + 8.90859i 1.56990 + 0.301165i
\(876\) 0 0
\(877\) 3.54626 2.48312i 0.119749 0.0838489i −0.512168 0.858885i \(-0.671157\pi\)
0.631917 + 0.775036i \(0.282269\pi\)
\(878\) 30.9067 21.6411i 1.04305 0.730352i
\(879\) 0 0
\(880\) 4.34908 10.7897i 0.146607 0.363722i
\(881\) 15.2989 + 8.83285i 0.515434 + 0.297586i 0.735065 0.677997i \(-0.237152\pi\)
−0.219630 + 0.975583i \(0.570485\pi\)
\(882\) 0 0
\(883\) 52.4360 + 14.0502i 1.76461 + 0.472826i 0.987644 0.156716i \(-0.0500906\pi\)
0.776967 + 0.629542i \(0.216757\pi\)
\(884\) 2.15779 + 0.785372i 0.0725744 + 0.0264149i
\(885\) 0 0
\(886\) 28.4678 + 23.8873i 0.956393 + 0.802509i
\(887\) −11.3090 + 24.2523i −0.379721 + 0.814313i 0.619842 + 0.784727i \(0.287197\pi\)
−0.999562 + 0.0295865i \(0.990581\pi\)
\(888\) 0 0
\(889\) 31.1831 5.49843i 1.04585 0.184411i
\(890\) 19.8436 + 6.04907i 0.665159 + 0.202765i
\(891\) 0 0
\(892\) 6.13082 + 6.13082i 0.205275 + 0.205275i
\(893\) −14.2528 + 20.3551i −0.476951 + 0.681157i
\(894\) 0 0
\(895\) −23.6943 21.2994i −0.792013 0.711961i
\(896\) 2.71855 3.23984i 0.0908202 0.108235i
\(897\) 0 0
\(898\) 35.4306 16.5216i 1.18234 0.551332i
\(899\) −18.0841 31.3225i −0.603138 1.04467i
\(900\) 0 0
\(901\) 27.6160 47.8324i 0.920024 1.59353i
\(902\) 2.19691 25.1108i 0.0731491 0.836098i
\(903\) 0 0
\(904\) 1.23946 + 0.218550i 0.0412239 + 0.00726888i
\(905\) −27.8697 + 9.08060i −0.926420 + 0.301849i
\(906\) 0 0
\(907\) 3.91052 + 0.342126i 0.129847 + 0.0113601i 0.151894 0.988397i \(-0.451463\pi\)
−0.0220472 + 0.999757i \(0.507018\pi\)
\(908\) −5.99518 + 1.60640i −0.198957 + 0.0533104i
\(909\) 0 0
\(910\) −0.802467 3.46295i −0.0266015 0.114796i
\(911\) −10.6171 + 29.1702i −0.351760 + 0.966452i 0.630045 + 0.776559i \(0.283036\pi\)
−0.981805 + 0.189893i \(0.939186\pi\)
\(912\) 0 0
\(913\) −24.7532 + 2.16563i −0.819212 + 0.0716718i
\(914\) −8.34368 + 3.03685i −0.275985 + 0.100450i
\(915\) 0 0
\(916\) 4.16292 + 23.6091i 0.137547 + 0.780066i
\(917\) −36.9248 + 36.9248i −1.21936 + 1.21936i
\(918\) 0 0
\(919\) 36.3601i 1.19941i 0.800222 + 0.599705i \(0.204715\pi\)
−0.800222 + 0.599705i \(0.795285\pi\)
\(920\) −1.53993 1.96771i −0.0507701 0.0648734i
\(921\) 0 0
\(922\) −30.5105 14.2273i −1.00481 0.468550i
\(923\) 0.00200610 + 0.0229299i 6.60317e−5 + 0.000754746i
\(924\) 0 0
\(925\) −28.8418 4.51977i −0.948311 0.148609i
\(926\) −8.57266 + 4.94943i −0.281715 + 0.162648i
\(927\) 0 0
\(928\) 2.62050 + 9.77986i 0.0860223 + 0.321040i
\(929\) −23.1288 + 19.4073i −0.758830 + 0.636734i −0.937822 0.347117i \(-0.887161\pi\)
0.178992 + 0.983850i \(0.442716\pi\)
\(930\) 0 0
\(931\) 6.40073 36.3003i 0.209775 1.18969i
\(932\) 6.70090 + 9.56988i 0.219495 + 0.313472i
\(933\) 0 0
\(934\) −5.10847 6.08804i −0.167154 0.199207i
\(935\) −48.5107 51.9362i −1.58647 1.69850i
\(936\) 0 0
\(937\) 1.58532 5.91649i 0.0517901 0.193283i −0.935184 0.354162i \(-0.884766\pi\)
0.986974 + 0.160879i \(0.0514328\pi\)
\(938\) 0.436121 + 0.935264i 0.0142398 + 0.0305375i
\(939\) 0 0
\(940\) 13.7564 8.94949i 0.448684 0.291900i
\(941\) −10.4752 28.7803i −0.341481 0.938212i −0.984965 0.172753i \(-0.944734\pi\)
0.643484 0.765460i \(-0.277488\pi\)
\(942\) 0 0
\(943\) −4.43492 3.10536i −0.144421 0.101125i
\(944\) 3.01407 0.0980996
\(945\) 0 0
\(946\) 34.0508 1.10709
\(947\) −6.30587 4.41542i −0.204913 0.143482i 0.466616 0.884460i \(-0.345473\pi\)
−0.671529 + 0.740978i \(0.734362\pi\)
\(948\) 0 0
\(949\) −0.850031 2.33544i −0.0275932 0.0758116i
\(950\) −14.8194 8.18291i −0.480806 0.265489i
\(951\) 0 0
\(952\) −10.9192 23.4163i −0.353893 0.758925i
\(953\) −6.78716 + 25.3300i −0.219858 + 0.820520i 0.764542 + 0.644574i \(0.222965\pi\)
−0.984400 + 0.175946i \(0.943701\pi\)
\(954\) 0 0
\(955\) −0.109478 + 3.21025i −0.00354262 + 0.103881i
\(956\) −11.8536 14.1265i −0.383372 0.456885i
\(957\) 0 0
\(958\) 9.04225 + 12.9137i 0.292142 + 0.417222i
\(959\) −9.32739 + 52.8982i −0.301197 + 1.70817i
\(960\) 0 0
\(961\) −13.9721 + 11.7240i −0.450713 + 0.378193i
\(962\) 0.568024 + 2.11990i 0.0183138 + 0.0683482i
\(963\) 0 0
\(964\) −4.30913 + 2.48788i −0.138788 + 0.0801291i
\(965\) −35.1302 26.4275i −1.13088 0.850731i
\(966\) 0 0
\(967\) 4.09918 + 46.8539i 0.131821 + 1.50672i 0.717718 + 0.696333i \(0.245187\pi\)
−0.585898 + 0.810385i \(0.699258\pi\)
\(968\) 14.5613 + 6.79002i 0.468016 + 0.218240i
\(969\) 0 0
\(970\) 27.5773 21.5820i 0.885452 0.692957i
\(971\) 52.7240i 1.69199i 0.533188 + 0.845997i \(0.320994\pi\)
−0.533188 + 0.845997i \(0.679006\pi\)
\(972\) 0 0
\(973\) 13.0590 13.0590i 0.418653 0.418653i
\(974\) 1.49444 + 8.47537i 0.0478848 + 0.271568i
\(975\) 0 0
\(976\) 7.18421 2.61484i 0.229961 0.0836990i
\(977\) 42.1182 3.68487i 1.34748 0.117889i 0.609541 0.792755i \(-0.291354\pi\)
0.737941 + 0.674866i \(0.235798\pi\)
\(978\) 0 0
\(979\) −16.5082 + 45.3558i −0.527603 + 1.44958i
\(980\) −12.8835 + 20.6555i −0.411550 + 0.659817i
\(981\) 0 0
\(982\) −30.0084 + 8.04072i −0.957606 + 0.256590i
\(983\) −26.4689 2.31573i −0.844226 0.0738602i −0.343168 0.939274i \(-0.611500\pi\)
−0.501058 + 0.865414i \(0.667056\pi\)
\(984\) 0 0
\(985\) −20.0321 + 39.3948i −0.638277 + 1.25522i
\(986\) 60.9134 + 10.7407i 1.93988 + 0.342053i
\(987\) 0 0
\(988\) −0.110917 + 1.26778i −0.00352873 + 0.0403335i
\(989\) 3.65680 6.33377i 0.116280 0.201402i
\(990\) 0 0
\(991\) −1.05011 1.81884i −0.0333578 0.0577774i 0.848865 0.528610i \(-0.177287\pi\)
−0.882222 + 0.470833i \(0.843953\pi\)
\(992\) −3.23753 + 1.50968i −0.102792 + 0.0479325i
\(993\) 0 0
\(994\) 0.166473 0.198395i 0.00528020 0.00629269i
\(995\) −11.6387 + 12.9474i −0.368972 + 0.410459i
\(996\) 0 0
\(997\) −28.4801 + 40.6738i −0.901975 + 1.28815i 0.0551503 + 0.998478i \(0.482436\pi\)
−0.957125 + 0.289675i \(0.906453\pi\)
\(998\) 9.25966 + 9.25966i 0.293109 + 0.293109i
\(999\) 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 810.2.s.a.557.6 216
3.2 odd 2 270.2.r.a.257.18 yes 216
5.3 odd 4 inner 810.2.s.a.233.8 216
15.8 even 4 270.2.r.a.203.13 yes 216
27.2 odd 18 inner 810.2.s.a.737.8 216
27.25 even 9 270.2.r.a.137.13 yes 216
135.83 even 36 inner 810.2.s.a.413.6 216
135.133 odd 36 270.2.r.a.83.18 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.2.r.a.83.18 216 135.133 odd 36
270.2.r.a.137.13 yes 216 27.25 even 9
270.2.r.a.203.13 yes 216 15.8 even 4
270.2.r.a.257.18 yes 216 3.2 odd 2
810.2.s.a.233.8 216 5.3 odd 4 inner
810.2.s.a.413.6 216 135.83 even 36 inner
810.2.s.a.557.6 216 1.1 even 1 trivial
810.2.s.a.737.8 216 27.2 odd 18 inner