Properties

Label 285.2.i.f.106.2
Level $285$
Weight $2$
Character 285.106
Analytic conductor $2.276$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [285,2,Mod(106,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.i (of order \(3\), degree \(2\), 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: \(2.27573645761\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 106.2
Root \(-0.690702 - 1.19633i\) of defining polynomial
Character \(\chi\) \(=\) 285.106
Dual form 285.2.i.f.121.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.690702 + 1.19633i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.0458624 + 0.0794360i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.690702 + 1.19633i) q^{6} -4.36264 q^{7} -2.88952 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.690702 - 1.19633i) q^{10} -4.31625 q^{11} +0.0917248 q^{12} +(3.18132 + 5.51021i) q^{13} +(3.01329 - 5.21916i) q^{14} +(0.500000 + 0.866025i) q^{15} +(1.90407 - 3.29794i) q^{16} +(-2.85821 + 4.95056i) q^{17} +1.38140 q^{18} +(2.97100 - 3.18954i) q^{19} -0.0917248 q^{20} +(-2.18132 + 3.77816i) q^{21} +(2.98124 - 5.16366i) q^{22} +(0.289678 + 0.501738i) q^{23} +(-1.44476 + 2.50239i) q^{24} +(-0.500000 - 0.866025i) q^{25} -8.78938 q^{26} -1.00000 q^{27} +(-0.200081 - 0.346551i) q^{28} +(1.77672 + 3.07737i) q^{29} -1.38140 q^{30} +1.18345 q^{31} +(-0.259229 - 0.448998i) q^{32} +(-2.15812 + 3.73798i) q^{33} +(-3.94834 - 6.83872i) q^{34} +(2.18132 - 3.77816i) q^{35} +(0.0458624 - 0.0794360i) q^{36} -6.54609 q^{37} +(1.76367 + 5.75732i) q^{38} +6.36264 q^{39} +(1.44476 - 2.50239i) q^{40} +(0.381403 - 0.660610i) q^{41} +(-3.01329 - 5.21916i) q^{42} +(3.18132 - 5.51021i) q^{43} +(-0.197954 - 0.342866i) q^{44} +1.00000 q^{45} -0.800326 q^{46} +(1.36632 + 2.36653i) q^{47} +(-1.90407 - 3.29794i) q^{48} +12.0327 q^{49} +1.38140 q^{50} +(2.85821 + 4.95056i) q^{51} +(-0.291806 + 0.505423i) q^{52} +(-2.56853 - 4.44882i) q^{53} +(0.690702 - 1.19633i) q^{54} +(2.15812 - 3.73798i) q^{55} +12.6059 q^{56} +(-1.27672 - 4.16773i) q^{57} -4.90874 q^{58} +(-1.91484 + 3.31660i) q^{59} +(-0.0458624 + 0.0794360i) q^{60} +(6.01053 + 10.4105i) q^{61} +(-0.817411 + 1.41580i) q^{62} +(2.18132 + 3.77816i) q^{63} +8.33247 q^{64} -6.36264 q^{65} +(-2.98124 - 5.16366i) q^{66} +(2.00213 + 3.46779i) q^{67} -0.524337 q^{68} +0.579357 q^{69} +(3.01329 + 5.21916i) q^{70} +(-1.53953 + 2.66654i) q^{71} +(1.44476 + 2.50239i) q^{72} +(-4.04320 + 7.00303i) q^{73} +(4.52140 - 7.83129i) q^{74} -1.00000 q^{75} +(0.389622 + 0.0897246i) q^{76} +18.8303 q^{77} +(-4.39469 + 7.61182i) q^{78} +(-5.66836 + 9.81790i) q^{79} +(1.90407 + 3.29794i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.526872 + 0.912569i) q^{82} +7.67889 q^{83} -0.400163 q^{84} +(-2.85821 - 4.95056i) q^{85} +(4.39469 + 7.61182i) q^{86} +3.55344 q^{87} +12.4719 q^{88} +(-4.92093 - 8.52330i) q^{89} +(-0.690702 + 1.19633i) q^{90} +(-13.8790 - 24.0391i) q^{91} +(-0.0265707 + 0.0460218i) q^{92} +(0.591725 - 1.02490i) q^{93} -3.77487 q^{94} +(1.27672 + 4.16773i) q^{95} -0.518458 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-8.31098 + 14.3950i) q^{98} +(2.15812 + 3.73798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(211\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.690702 + 1.19633i −0.488400 + 0.845933i −0.999911 0.0133433i \(-0.995753\pi\)
0.511511 + 0.859277i \(0.329086\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.0458624 + 0.0794360i 0.0229312 + 0.0397180i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0.690702 + 1.19633i 0.281978 + 0.488400i
\(7\) −4.36264 −1.64892 −0.824462 0.565917i \(-0.808522\pi\)
−0.824462 + 0.565917i \(0.808522\pi\)
\(8\) −2.88952 −1.02160
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.690702 1.19633i −0.218419 0.378313i
\(11\) −4.31625 −1.30140 −0.650699 0.759336i \(-0.725524\pi\)
−0.650699 + 0.759336i \(0.725524\pi\)
\(12\) 0.0917248 0.0264787
\(13\) 3.18132 + 5.51021i 0.882340 + 1.52826i 0.848732 + 0.528823i \(0.177366\pi\)
0.0336075 + 0.999435i \(0.489300\pi\)
\(14\) 3.01329 5.21916i 0.805334 1.39488i
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) 1.90407 3.29794i 0.476017 0.824486i
\(17\) −2.85821 + 4.95056i −0.693217 + 1.20069i 0.277561 + 0.960708i \(0.410474\pi\)
−0.970778 + 0.239979i \(0.922860\pi\)
\(18\) 1.38140 0.325600
\(19\) 2.97100 3.18954i 0.681594 0.731730i
\(20\) −0.0917248 −0.0205103
\(21\) −2.18132 + 3.77816i −0.476003 + 0.824462i
\(22\) 2.98124 5.16366i 0.635603 1.10090i
\(23\) 0.289678 + 0.501738i 0.0604021 + 0.104620i 0.894645 0.446777i \(-0.147428\pi\)
−0.834243 + 0.551397i \(0.814095\pi\)
\(24\) −1.44476 + 2.50239i −0.294910 + 0.510799i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −8.78938 −1.72374
\(27\) −1.00000 −0.192450
\(28\) −0.200081 0.346551i −0.0378118 0.0654920i
\(29\) 1.77672 + 3.07737i 0.329929 + 0.571454i 0.982497 0.186276i \(-0.0596419\pi\)
−0.652569 + 0.757730i \(0.726309\pi\)
\(30\) −1.38140 −0.252209
\(31\) 1.18345 0.212554 0.106277 0.994337i \(-0.466107\pi\)
0.106277 + 0.994337i \(0.466107\pi\)
\(32\) −0.259229 0.448998i −0.0458257 0.0793724i
\(33\) −2.15812 + 3.73798i −0.375681 + 0.650699i
\(34\) −3.94834 6.83872i −0.677134 1.17283i
\(35\) 2.18132 3.77816i 0.368711 0.638626i
\(36\) 0.0458624 0.0794360i 0.00764374 0.0132393i
\(37\) −6.54609 −1.07617 −0.538086 0.842890i \(-0.680852\pi\)
−0.538086 + 0.842890i \(0.680852\pi\)
\(38\) 1.76367 + 5.75732i 0.286105 + 0.933960i
\(39\) 6.36264 1.01884
\(40\) 1.44476 2.50239i 0.228436 0.395663i
\(41\) 0.381403 0.660610i 0.0595652 0.103170i −0.834705 0.550697i \(-0.814362\pi\)
0.894270 + 0.447527i \(0.147695\pi\)
\(42\) −3.01329 5.21916i −0.464960 0.805334i
\(43\) 3.18132 5.51021i 0.485147 0.840299i −0.514707 0.857366i \(-0.672099\pi\)
0.999854 + 0.0170666i \(0.00543274\pi\)
\(44\) −0.197954 0.342866i −0.0298426 0.0516890i
\(45\) 1.00000 0.149071
\(46\) −0.800326 −0.118002
\(47\) 1.36632 + 2.36653i 0.199298 + 0.345194i 0.948301 0.317372i \(-0.102800\pi\)
−0.749003 + 0.662567i \(0.769467\pi\)
\(48\) −1.90407 3.29794i −0.274829 0.476017i
\(49\) 12.0327 1.71895
\(50\) 1.38140 0.195360
\(51\) 2.85821 + 4.95056i 0.400229 + 0.693217i
\(52\) −0.291806 + 0.505423i −0.0404662 + 0.0700896i
\(53\) −2.56853 4.44882i −0.352814 0.611092i 0.633927 0.773393i \(-0.281442\pi\)
−0.986741 + 0.162300i \(0.948109\pi\)
\(54\) 0.690702 1.19633i 0.0939926 0.162800i
\(55\) 2.15812 3.73798i 0.291001 0.504029i
\(56\) 12.6059 1.68454
\(57\) −1.27672 4.16773i −0.169106 0.552029i
\(58\) −4.90874 −0.644549
\(59\) −1.91484 + 3.31660i −0.249291 + 0.431785i −0.963329 0.268322i \(-0.913531\pi\)
0.714038 + 0.700107i \(0.246864\pi\)
\(60\) −0.0458624 + 0.0794360i −0.00592081 + 0.0102551i
\(61\) 6.01053 + 10.4105i 0.769569 + 1.33293i 0.937797 + 0.347185i \(0.112862\pi\)
−0.168227 + 0.985748i \(0.553804\pi\)
\(62\) −0.817411 + 1.41580i −0.103811 + 0.179806i
\(63\) 2.18132 + 3.77816i 0.274821 + 0.476003i
\(64\) 8.33247 1.04156
\(65\) −6.36264 −0.789189
\(66\) −2.98124 5.16366i −0.366965 0.635603i
\(67\) 2.00213 + 3.46779i 0.244599 + 0.423658i 0.962019 0.272983i \(-0.0880104\pi\)
−0.717420 + 0.696641i \(0.754677\pi\)
\(68\) −0.524337 −0.0635852
\(69\) 0.579357 0.0697464
\(70\) 3.01329 + 5.21916i 0.360156 + 0.623809i
\(71\) −1.53953 + 2.66654i −0.182708 + 0.316460i −0.942802 0.333354i \(-0.891820\pi\)
0.760094 + 0.649814i \(0.225153\pi\)
\(72\) 1.44476 + 2.50239i 0.170266 + 0.294910i
\(73\) −4.04320 + 7.00303i −0.473221 + 0.819643i −0.999530 0.0306504i \(-0.990242\pi\)
0.526309 + 0.850293i \(0.323575\pi\)
\(74\) 4.52140 7.83129i 0.525602 0.910369i
\(75\) −1.00000 −0.115470
\(76\) 0.389622 + 0.0897246i 0.0446927 + 0.0102921i
\(77\) 18.8303 2.14591
\(78\) −4.39469 + 7.61182i −0.497601 + 0.861869i
\(79\) −5.66836 + 9.81790i −0.637741 + 1.10460i 0.348187 + 0.937425i \(0.386798\pi\)
−0.985927 + 0.167174i \(0.946536\pi\)
\(80\) 1.90407 + 3.29794i 0.212881 + 0.368721i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0.526872 + 0.912569i 0.0581833 + 0.100776i
\(83\) 7.67889 0.842868 0.421434 0.906859i \(-0.361527\pi\)
0.421434 + 0.906859i \(0.361527\pi\)
\(84\) −0.400163 −0.0436613
\(85\) −2.85821 4.95056i −0.310016 0.536963i
\(86\) 4.39469 + 7.61182i 0.473891 + 0.820804i
\(87\) 3.55344 0.380969
\(88\) 12.4719 1.32951
\(89\) −4.92093 8.52330i −0.521618 0.903468i −0.999684 0.0251445i \(-0.991995\pi\)
0.478066 0.878324i \(-0.341338\pi\)
\(90\) −0.690702 + 1.19633i −0.0728063 + 0.126104i
\(91\) −13.8790 24.0391i −1.45491 2.51998i
\(92\) −0.0265707 + 0.0460218i −0.00277019 + 0.00479811i
\(93\) 0.591725 1.02490i 0.0613590 0.106277i
\(94\) −3.77487 −0.389348
\(95\) 1.27672 + 4.16773i 0.130989 + 0.427600i
\(96\) −0.518458 −0.0529149
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) −8.31098 + 14.3950i −0.839536 + 1.45412i
\(99\) 2.15812 + 3.73798i 0.216900 + 0.375681i
\(100\) 0.0458624 0.0794360i 0.00458624 0.00794360i
\(101\) 2.24985 + 3.89685i 0.223868 + 0.387751i 0.955979 0.293434i \(-0.0947981\pi\)
−0.732111 + 0.681185i \(0.761465\pi\)
\(102\) −7.89667 −0.781887
\(103\) −16.0717 −1.58359 −0.791796 0.610785i \(-0.790854\pi\)
−0.791796 + 0.610785i \(0.790854\pi\)
\(104\) −9.19248 15.9218i −0.901397 1.56127i
\(105\) −2.18132 3.77816i −0.212875 0.368711i
\(106\) 7.09634 0.689258
\(107\) 13.6789 1.32239 0.661194 0.750215i \(-0.270050\pi\)
0.661194 + 0.750215i \(0.270050\pi\)
\(108\) −0.0458624 0.0794360i −0.00441311 0.00764374i
\(109\) 4.48337 7.76542i 0.429429 0.743792i −0.567394 0.823447i \(-0.692048\pi\)
0.996823 + 0.0796541i \(0.0253816\pi\)
\(110\) 2.98124 + 5.16366i 0.284250 + 0.492336i
\(111\) −3.27305 + 5.66908i −0.310664 + 0.538086i
\(112\) −8.30677 + 14.3878i −0.784916 + 1.35951i
\(113\) 6.42952 0.604838 0.302419 0.953175i \(-0.402206\pi\)
0.302419 + 0.953175i \(0.402206\pi\)
\(114\) 5.86782 + 1.35128i 0.549571 + 0.126559i
\(115\) −0.579357 −0.0540253
\(116\) −0.162969 + 0.282271i −0.0151313 + 0.0262082i
\(117\) 3.18132 5.51021i 0.294113 0.509419i
\(118\) −2.64517 4.58156i −0.243507 0.421767i
\(119\) 12.4693 21.5975i 1.14306 1.97984i
\(120\) −1.44476 2.50239i −0.131888 0.228436i
\(121\) 7.63001 0.693637
\(122\) −16.6059 −1.50343
\(123\) −0.381403 0.660610i −0.0343900 0.0595652i
\(124\) 0.0542759 + 0.0940086i 0.00487412 + 0.00844222i
\(125\) 1.00000 0.0894427
\(126\) −6.02657 −0.536890
\(127\) 3.09172 + 5.35502i 0.274346 + 0.475182i 0.969970 0.243225i \(-0.0782052\pi\)
−0.695624 + 0.718406i \(0.744872\pi\)
\(128\) −5.23680 + 9.07040i −0.462872 + 0.801717i
\(129\) −3.18132 5.51021i −0.280100 0.485147i
\(130\) 4.39469 7.61182i 0.385440 0.667601i
\(131\) −8.69872 + 15.0666i −0.760010 + 1.31638i 0.182834 + 0.983144i \(0.441473\pi\)
−0.942845 + 0.333233i \(0.891860\pi\)
\(132\) −0.395907 −0.0344593
\(133\) −12.9614 + 13.9148i −1.12390 + 1.20657i
\(134\) −5.53149 −0.477848
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 8.25883 14.3047i 0.708189 1.22662i
\(137\) −7.85821 13.6108i −0.671372 1.16285i −0.977515 0.210865i \(-0.932372\pi\)
0.306143 0.951985i \(-0.400961\pi\)
\(138\) −0.400163 + 0.693102i −0.0340641 + 0.0590008i
\(139\) −3.27672 5.67545i −0.277928 0.481385i 0.692942 0.720994i \(-0.256314\pi\)
−0.970870 + 0.239608i \(0.922981\pi\)
\(140\) 0.400163 0.0338199
\(141\) 2.73264 0.230130
\(142\) −2.12671 3.68357i −0.178469 0.309118i
\(143\) −13.7314 23.7834i −1.14828 1.98887i
\(144\) −3.80814 −0.317345
\(145\) −3.55344 −0.295097
\(146\) −5.58529 9.67401i −0.462242 0.800627i
\(147\) 6.01633 10.4206i 0.496219 0.859476i
\(148\) −0.300220 0.519996i −0.0246779 0.0427434i
\(149\) −2.87560 + 4.98069i −0.235578 + 0.408034i −0.959441 0.281911i \(-0.909032\pi\)
0.723862 + 0.689945i \(0.242365\pi\)
\(150\) 0.690702 1.19633i 0.0563956 0.0976800i
\(151\) −12.6673 −1.03085 −0.515425 0.856935i \(-0.672366\pi\)
−0.515425 + 0.856935i \(0.672366\pi\)
\(152\) −8.58475 + 9.21622i −0.696315 + 0.747534i
\(153\) 5.71641 0.462145
\(154\) −13.0061 + 22.5272i −1.04806 + 1.81529i
\(155\) −0.591725 + 1.02490i −0.0475285 + 0.0823217i
\(156\) 0.291806 + 0.505423i 0.0233632 + 0.0404662i
\(157\) −0.689434 + 1.19414i −0.0550228 + 0.0953024i −0.892225 0.451591i \(-0.850856\pi\)
0.837202 + 0.546894i \(0.184190\pi\)
\(158\) −7.83030 13.5625i −0.622945 1.07897i
\(159\) −5.13706 −0.407395
\(160\) 0.518458 0.0409877
\(161\) −1.26376 2.18890i −0.0995986 0.172510i
\(162\) −0.690702 1.19633i −0.0542666 0.0939926i
\(163\) −11.6120 −0.909523 −0.454762 0.890613i \(-0.650276\pi\)
−0.454762 + 0.890613i \(0.650276\pi\)
\(164\) 0.0699683 0.00546361
\(165\) −2.15812 3.73798i −0.168010 0.291001i
\(166\) −5.30382 + 9.18649i −0.411657 + 0.713010i
\(167\) 10.1557 + 17.5902i 0.785871 + 1.36117i 0.928477 + 0.371390i \(0.121119\pi\)
−0.142606 + 0.989780i \(0.545548\pi\)
\(168\) 6.30296 10.9171i 0.486284 0.842269i
\(169\) −13.7416 + 23.8012i −1.05705 + 1.83086i
\(170\) 7.89667 0.605647
\(171\) −4.24772 0.978193i −0.324831 0.0748043i
\(172\) 0.583613 0.0445000
\(173\) 6.12545 10.6096i 0.465709 0.806632i −0.533524 0.845785i \(-0.679133\pi\)
0.999233 + 0.0391527i \(0.0124659\pi\)
\(174\) −2.45437 + 4.25109i −0.186065 + 0.322274i
\(175\) 2.18132 + 3.77816i 0.164892 + 0.285602i
\(176\) −8.21843 + 14.2347i −0.619488 + 1.07298i
\(177\) 1.91484 + 3.31660i 0.143928 + 0.249291i
\(178\) 13.5956 1.01903
\(179\) −19.1840 −1.43388 −0.716941 0.697134i \(-0.754458\pi\)
−0.716941 + 0.697134i \(0.754458\pi\)
\(180\) 0.0458624 + 0.0794360i 0.00341838 + 0.00592081i
\(181\) 1.61492 + 2.79713i 0.120036 + 0.207909i 0.919782 0.392430i \(-0.128366\pi\)
−0.799746 + 0.600339i \(0.795032\pi\)
\(182\) 38.3449 2.84231
\(183\) 12.0211 0.888622
\(184\) −0.837031 1.44978i −0.0617067 0.106879i
\(185\) 3.27305 5.66908i 0.240639 0.416799i
\(186\) 0.817411 + 1.41580i 0.0599355 + 0.103811i
\(187\) 12.3367 21.3678i 0.902151 1.56257i
\(188\) −0.125325 + 0.217070i −0.00914029 + 0.0158314i
\(189\) 4.36264 0.317336
\(190\) −5.86782 1.35128i −0.425696 0.0980320i
\(191\) 27.5509 1.99352 0.996758 0.0804642i \(-0.0256403\pi\)
0.996758 + 0.0804642i \(0.0256403\pi\)
\(192\) 4.16624 7.21613i 0.300672 0.520780i
\(193\) −11.1233 + 19.2662i −0.800674 + 1.38681i 0.118499 + 0.992954i \(0.462192\pi\)
−0.919173 + 0.393854i \(0.871141\pi\)
\(194\) −1.38140 2.39266i −0.0991790 0.171783i
\(195\) −3.18132 + 5.51021i −0.227819 + 0.394594i
\(196\) 0.551847 + 0.955827i 0.0394176 + 0.0682734i
\(197\) 12.6627 0.902178 0.451089 0.892479i \(-0.351036\pi\)
0.451089 + 0.892479i \(0.351036\pi\)
\(198\) −5.96248 −0.423735
\(199\) 4.38478 + 7.59466i 0.310829 + 0.538371i 0.978542 0.206048i \(-0.0660602\pi\)
−0.667713 + 0.744418i \(0.732727\pi\)
\(200\) 1.44476 + 2.50239i 0.102160 + 0.176946i
\(201\) 4.00426 0.282438
\(202\) −6.21590 −0.437349
\(203\) −7.75120 13.4255i −0.544028 0.942284i
\(204\) −0.262168 + 0.454089i −0.0183555 + 0.0317926i
\(205\) 0.381403 + 0.660610i 0.0266384 + 0.0461390i
\(206\) 11.1008 19.2271i 0.773426 1.33961i
\(207\) 0.289678 0.501738i 0.0201340 0.0348732i
\(208\) 24.2298 1.68004
\(209\) −12.8236 + 13.7668i −0.887025 + 0.952272i
\(210\) 6.02657 0.415873
\(211\) −3.93389 + 6.81369i −0.270820 + 0.469074i −0.969072 0.246778i \(-0.920628\pi\)
0.698252 + 0.715852i \(0.253962\pi\)
\(212\) 0.235598 0.408067i 0.0161809 0.0280262i
\(213\) 1.53953 + 2.66654i 0.105487 + 0.182708i
\(214\) −9.44803 + 16.3645i −0.645854 + 1.11865i
\(215\) 3.18132 + 5.51021i 0.216964 + 0.375793i
\(216\) 2.88952 0.196607
\(217\) −5.16297 −0.350485
\(218\) 6.19334 + 10.7272i 0.419466 + 0.726536i
\(219\) 4.04320 + 7.00303i 0.273214 + 0.473221i
\(220\) 0.395907 0.0266921
\(221\) −36.3715 −2.44661
\(222\) −4.52140 7.83129i −0.303456 0.525602i
\(223\) 13.6768 23.6889i 0.915864 1.58632i 0.110232 0.993906i \(-0.464840\pi\)
0.805631 0.592417i \(-0.201826\pi\)
\(224\) 1.13092 + 1.95882i 0.0755631 + 0.130879i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) −4.44088 + 7.69183i −0.295403 + 0.511653i
\(227\) −25.0922 −1.66543 −0.832713 0.553704i \(-0.813214\pi\)
−0.832713 + 0.553704i \(0.813214\pi\)
\(228\) 0.272515 0.292560i 0.0180477 0.0193753i
\(229\) 4.98530 0.329438 0.164719 0.986341i \(-0.447328\pi\)
0.164719 + 0.986341i \(0.447328\pi\)
\(230\) 0.400163 0.693102i 0.0263860 0.0457018i
\(231\) 9.41513 16.3075i 0.619470 1.07295i
\(232\) −5.13386 8.89211i −0.337055 0.583796i
\(233\) −6.39821 + 11.0820i −0.419161 + 0.726007i −0.995855 0.0909523i \(-0.971009\pi\)
0.576695 + 0.816960i \(0.304342\pi\)
\(234\) 4.39469 + 7.61182i 0.287290 + 0.497601i
\(235\) −2.73264 −0.178258
\(236\) −0.351277 −0.0228662
\(237\) 5.66836 + 9.81790i 0.368200 + 0.637741i
\(238\) 17.2252 + 29.8349i 1.11654 + 1.93391i
\(239\) 12.8049 0.828283 0.414142 0.910212i \(-0.364082\pi\)
0.414142 + 0.910212i \(0.364082\pi\)
\(240\) 3.80814 0.245814
\(241\) 0.546395 + 0.946383i 0.0351964 + 0.0609619i 0.883087 0.469209i \(-0.155461\pi\)
−0.847891 + 0.530171i \(0.822128\pi\)
\(242\) −5.27006 + 9.12801i −0.338772 + 0.586771i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −0.551315 + 0.954905i −0.0352943 + 0.0611315i
\(245\) −6.01633 + 10.4206i −0.384369 + 0.665747i
\(246\) 1.05374 0.0671842
\(247\) 27.0267 + 6.22389i 1.71967 + 0.396017i
\(248\) −3.41960 −0.217145
\(249\) 3.83945 6.65012i 0.243315 0.421434i
\(250\) −0.690702 + 1.19633i −0.0436838 + 0.0756626i
\(251\) −3.04764 5.27867i −0.192365 0.333187i 0.753668 0.657255i \(-0.228283\pi\)
−0.946034 + 0.324068i \(0.894949\pi\)
\(252\) −0.200081 + 0.346551i −0.0126039 + 0.0218307i
\(253\) −1.25032 2.16563i −0.0786072 0.136152i
\(254\) −8.54184 −0.535963
\(255\) −5.71641 −0.357976
\(256\) 1.09835 + 1.90239i 0.0686467 + 0.118900i
\(257\) −2.31016 4.00131i −0.144104 0.249595i 0.784934 0.619579i \(-0.212697\pi\)
−0.929038 + 0.369984i \(0.879363\pi\)
\(258\) 8.78938 0.547203
\(259\) 28.5583 1.77452
\(260\) −0.291806 0.505423i −0.0180971 0.0313450i
\(261\) 1.77672 3.07737i 0.109976 0.190485i
\(262\) −12.0164 20.8131i −0.742378 1.28584i
\(263\) 15.0247 26.0236i 0.926465 1.60468i 0.137276 0.990533i \(-0.456165\pi\)
0.789189 0.614151i \(-0.210501\pi\)
\(264\) 6.23593 10.8010i 0.383795 0.664753i
\(265\) 5.13706 0.315567
\(266\) −7.69425 25.1171i −0.471765 1.54003i
\(267\) −9.84186 −0.602312
\(268\) −0.183645 + 0.318082i −0.0112179 + 0.0194300i
\(269\) 0.105639 0.182973i 0.00644095 0.0111561i −0.862787 0.505568i \(-0.831283\pi\)
0.869228 + 0.494412i \(0.164616\pi\)
\(270\) 0.690702 + 1.19633i 0.0420348 + 0.0728063i
\(271\) 3.70364 6.41489i 0.224980 0.389677i −0.731333 0.682020i \(-0.761102\pi\)
0.956313 + 0.292343i \(0.0944350\pi\)
\(272\) 10.8844 + 18.8524i 0.659966 + 1.14309i
\(273\) −27.7579 −1.67999
\(274\) 21.7107 1.31159
\(275\) 2.15812 + 3.73798i 0.130140 + 0.225409i
\(276\) 0.0265707 + 0.0460218i 0.00159937 + 0.00277019i
\(277\) −29.0668 −1.74646 −0.873229 0.487310i \(-0.837978\pi\)
−0.873229 + 0.487310i \(0.837978\pi\)
\(278\) 9.05295 0.542960
\(279\) −0.591725 1.02490i −0.0354256 0.0613590i
\(280\) −6.30296 + 10.9171i −0.376674 + 0.652419i
\(281\) −5.73796 9.93843i −0.342298 0.592877i 0.642561 0.766234i \(-0.277872\pi\)
−0.984859 + 0.173357i \(0.944539\pi\)
\(282\) −1.88744 + 3.26914i −0.112395 + 0.194674i
\(283\) 13.6662 23.6706i 0.812373 1.40707i −0.0988265 0.995105i \(-0.531509\pi\)
0.911199 0.411966i \(-0.135158\pi\)
\(284\) −0.282426 −0.0167589
\(285\) 4.24772 + 0.978193i 0.251613 + 0.0579431i
\(286\) 37.9371 2.24327
\(287\) −1.66393 + 2.88201i −0.0982185 + 0.170119i
\(288\) −0.259229 + 0.448998i −0.0152752 + 0.0264575i
\(289\) −7.83868 13.5770i −0.461099 0.798647i
\(290\) 2.45437 4.25109i 0.144125 0.249633i
\(291\) 1.00000 + 1.73205i 0.0586210 + 0.101535i
\(292\) −0.741724 −0.0434061
\(293\) 13.0211 0.760698 0.380349 0.924843i \(-0.375804\pi\)
0.380349 + 0.924843i \(0.375804\pi\)
\(294\) 8.31098 + 14.3950i 0.484706 + 0.839536i
\(295\) −1.91484 3.31660i −0.111486 0.193100i
\(296\) 18.9150 1.09941
\(297\) 4.31625 0.250454
\(298\) −3.97236 6.88034i −0.230113 0.398567i
\(299\) −1.84312 + 3.19238i −0.106590 + 0.184620i
\(300\) −0.0458624 0.0794360i −0.00264787 0.00458624i
\(301\) −13.8790 + 24.0391i −0.799971 + 1.38559i
\(302\) 8.74932 15.1543i 0.503467 0.872030i
\(303\) 4.49970 0.258501
\(304\) −4.86193 15.8713i −0.278851 0.910281i
\(305\) −12.0211 −0.688324
\(306\) −3.94834 + 6.83872i −0.225711 + 0.390943i
\(307\) −2.01267 + 3.48604i −0.114869 + 0.198959i −0.917727 0.397211i \(-0.869978\pi\)
0.802858 + 0.596170i \(0.203312\pi\)
\(308\) 0.863601 + 1.49580i 0.0492082 + 0.0852312i
\(309\) −8.03585 + 13.9185i −0.457144 + 0.791796i
\(310\) −0.817411 1.41580i −0.0464258 0.0804119i
\(311\) 15.3578 0.870860 0.435430 0.900223i \(-0.356596\pi\)
0.435430 + 0.900223i \(0.356596\pi\)
\(312\) −18.3850 −1.04084
\(313\) −10.9800 19.0179i −0.620625 1.07495i −0.989369 0.145424i \(-0.953546\pi\)
0.368744 0.929531i \(-0.379788\pi\)
\(314\) −0.952387 1.64958i −0.0537463 0.0930913i
\(315\) −4.36264 −0.245807
\(316\) −1.03986 −0.0584967
\(317\) 12.0640 + 20.8954i 0.677580 + 1.17360i 0.975708 + 0.219077i \(0.0703046\pi\)
−0.298127 + 0.954526i \(0.596362\pi\)
\(318\) 3.54817 6.14561i 0.198972 0.344629i
\(319\) −7.66877 13.2827i −0.429369 0.743689i
\(320\) −4.16624 + 7.21613i −0.232900 + 0.403394i
\(321\) 6.83945 11.8463i 0.381741 0.661194i
\(322\) 3.49154 0.194576
\(323\) 7.29826 + 23.8245i 0.406086 + 1.32563i
\(324\) −0.0917248 −0.00509582
\(325\) 3.18132 5.51021i 0.176468 0.305652i
\(326\) 8.02044 13.8918i 0.444211 0.769396i
\(327\) −4.48337 7.76542i −0.247931 0.429429i
\(328\) −1.10207 + 1.90884i −0.0608517 + 0.105398i
\(329\) −5.96076 10.3243i −0.328627 0.569199i
\(330\) 5.96248 0.328224
\(331\) −24.8416 −1.36542 −0.682710 0.730690i \(-0.739199\pi\)
−0.682710 + 0.730690i \(0.739199\pi\)
\(332\) 0.352173 + 0.609981i 0.0193280 + 0.0334771i
\(333\) 3.27305 + 5.66908i 0.179362 + 0.310664i
\(334\) −28.0582 −1.53528
\(335\) −4.00426 −0.218776
\(336\) 8.30677 + 14.3878i 0.453172 + 0.784916i
\(337\) −0.284651 + 0.493031i −0.0155059 + 0.0268571i −0.873674 0.486511i \(-0.838269\pi\)
0.858168 + 0.513368i \(0.171603\pi\)
\(338\) −18.9827 32.8790i −1.03252 1.78838i
\(339\) 3.21476 5.56813i 0.174602 0.302419i
\(340\) 0.262168 0.454089i 0.0142181 0.0246264i
\(341\) −5.10806 −0.276617
\(342\) 4.10415 4.40604i 0.221927 0.238251i
\(343\) −21.9557 −1.18550
\(344\) −9.19248 + 15.9218i −0.495625 + 0.858448i
\(345\) −0.289678 + 0.501738i −0.0155958 + 0.0270127i
\(346\) 8.46172 + 14.6561i 0.454905 + 0.787918i
\(347\) −4.68682 + 8.11782i −0.251602 + 0.435787i −0.963967 0.266022i \(-0.914291\pi\)
0.712365 + 0.701809i \(0.247624\pi\)
\(348\) 0.162969 + 0.282271i 0.00873608 + 0.0151313i
\(349\) 14.8297 0.793815 0.396907 0.917859i \(-0.370083\pi\)
0.396907 + 0.917859i \(0.370083\pi\)
\(350\) −6.02657 −0.322134
\(351\) −3.18132 5.51021i −0.169806 0.294113i
\(352\) 1.11890 + 1.93799i 0.0596375 + 0.103295i
\(353\) 31.2650 1.66407 0.832034 0.554725i \(-0.187176\pi\)
0.832034 + 0.554725i \(0.187176\pi\)
\(354\) −5.29033 −0.281178
\(355\) −1.53953 2.66654i −0.0817097 0.141525i
\(356\) 0.451372 0.781799i 0.0239226 0.0414352i
\(357\) −12.4693 21.5975i −0.659947 1.14306i
\(358\) 13.2504 22.9504i 0.700307 1.21297i
\(359\) −5.43561 + 9.41475i −0.286880 + 0.496892i −0.973063 0.230537i \(-0.925952\pi\)
0.686183 + 0.727429i \(0.259285\pi\)
\(360\) −2.88952 −0.152291
\(361\) −1.34631 18.9522i −0.0708586 0.997486i
\(362\) −4.46172 −0.234503
\(363\) 3.81500 6.60778i 0.200236 0.346819i
\(364\) 1.27305 2.20498i 0.0667258 0.115572i
\(365\) −4.04320 7.00303i −0.211631 0.366555i
\(366\) −8.30296 + 14.3812i −0.434003 + 0.751715i
\(367\) 9.36477 + 16.2203i 0.488837 + 0.846691i 0.999918 0.0128422i \(-0.00408791\pi\)
−0.511080 + 0.859533i \(0.670755\pi\)
\(368\) 2.20627 0.115010
\(369\) −0.762807 −0.0397101
\(370\) 4.52140 + 7.83129i 0.235056 + 0.407129i
\(371\) 11.2056 + 19.4086i 0.581764 + 1.00765i
\(372\) 0.108552 0.00562815
\(373\) 29.3275 1.51852 0.759259 0.650788i \(-0.225561\pi\)
0.759259 + 0.650788i \(0.225561\pi\)
\(374\) 17.0420 + 29.5176i 0.881221 + 1.52632i
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) −3.94800 6.83813i −0.203602 0.352650i
\(377\) −11.3046 + 19.5802i −0.582219 + 1.00843i
\(378\) −3.01329 + 5.21916i −0.154987 + 0.268445i
\(379\) −10.6486 −0.546980 −0.273490 0.961875i \(-0.588178\pi\)
−0.273490 + 0.961875i \(0.588178\pi\)
\(380\) −0.272515 + 0.292560i −0.0139797 + 0.0150080i
\(381\) 6.18345 0.316788
\(382\) −19.0295 + 32.9600i −0.973632 + 1.68638i
\(383\) −4.63977 + 8.03632i −0.237081 + 0.410637i −0.959876 0.280426i \(-0.909524\pi\)
0.722794 + 0.691063i \(0.242857\pi\)
\(384\) 5.23680 + 9.07040i 0.267239 + 0.462872i
\(385\) −9.41513 + 16.3075i −0.479839 + 0.831106i
\(386\) −15.3658 26.6143i −0.782098 1.35463i
\(387\) −6.36264 −0.323431
\(388\) −0.183450 −0.00931325
\(389\) −0.666237 1.15396i −0.0337796 0.0585079i 0.848641 0.528969i \(-0.177421\pi\)
−0.882421 + 0.470461i \(0.844088\pi\)
\(390\) −4.39469 7.61182i −0.222534 0.385440i
\(391\) −3.31184 −0.167487
\(392\) −34.7686 −1.75608
\(393\) 8.69872 + 15.0666i 0.438792 + 0.760010i
\(394\) −8.74613 + 15.1487i −0.440623 + 0.763182i
\(395\) −5.66836 9.81790i −0.285206 0.493992i
\(396\) −0.197954 + 0.342866i −0.00994754 + 0.0172297i
\(397\) 15.8324 27.4225i 0.794605 1.37630i −0.128485 0.991711i \(-0.541011\pi\)
0.923090 0.384584i \(-0.125655\pi\)
\(398\) −12.1143 −0.607235
\(399\) 5.56988 + 18.1823i 0.278843 + 0.910255i
\(400\) −3.80814 −0.190407
\(401\) 2.44425 4.23356i 0.122060 0.211414i −0.798520 0.601968i \(-0.794383\pi\)
0.920580 + 0.390554i \(0.127717\pi\)
\(402\) −2.76575 + 4.79041i −0.137943 + 0.238924i
\(403\) 3.76493 + 6.52106i 0.187545 + 0.324837i
\(404\) −0.206367 + 0.357438i −0.0102671 + 0.0177832i
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) 21.4151 1.06281
\(407\) 28.2546 1.40053
\(408\) −8.25883 14.3047i −0.408873 0.708189i
\(409\) 11.3941 + 19.7351i 0.563400 + 0.975837i 0.997197 + 0.0748266i \(0.0238403\pi\)
−0.433797 + 0.901011i \(0.642826\pi\)
\(410\) −1.05374 −0.0520407
\(411\) −15.7164 −0.775233
\(412\) −0.737087 1.27667i −0.0363137 0.0628972i
\(413\) 8.35377 14.4692i 0.411062 0.711980i
\(414\) 0.400163 + 0.693102i 0.0196669 + 0.0340641i
\(415\) −3.83945 + 6.65012i −0.188471 + 0.326441i
\(416\) 1.64938 2.85682i 0.0808677 0.140067i
\(417\) −6.55344 −0.320923
\(418\) −7.61243 24.8500i −0.372336 1.21545i
\(419\) 30.8809 1.50863 0.754316 0.656512i \(-0.227969\pi\)
0.754316 + 0.656512i \(0.227969\pi\)
\(420\) 0.200081 0.346551i 0.00976297 0.0169100i
\(421\) −13.2891 + 23.0174i −0.647671 + 1.12180i 0.336007 + 0.941859i \(0.390923\pi\)
−0.983678 + 0.179939i \(0.942410\pi\)
\(422\) −5.43429 9.41246i −0.264537 0.458191i
\(423\) 1.36632 2.36653i 0.0664327 0.115065i
\(424\) 7.42180 + 12.8549i 0.360434 + 0.624291i
\(425\) 5.71641 0.277287
\(426\) −4.25342 −0.206079
\(427\) −26.2218 45.4175i −1.26896 2.19791i
\(428\) 0.627347 + 1.08660i 0.0303240 + 0.0525227i
\(429\) −27.4628 −1.32591
\(430\) −8.78938 −0.423861
\(431\) −8.23718 14.2672i −0.396771 0.687228i 0.596554 0.802573i \(-0.296536\pi\)
−0.993325 + 0.115345i \(0.963203\pi\)
\(432\) −1.90407 + 3.29794i −0.0916095 + 0.158672i
\(433\) 18.4021 + 31.8733i 0.884346 + 1.53173i 0.846461 + 0.532450i \(0.178729\pi\)
0.0378851 + 0.999282i \(0.487938\pi\)
\(434\) 3.56607 6.17662i 0.171177 0.296487i
\(435\) −1.77672 + 3.07737i −0.0851873 + 0.147549i
\(436\) 0.822473 0.0393893
\(437\) 2.46095 + 0.566723i 0.117723 + 0.0271100i
\(438\) −11.1706 −0.533751
\(439\) −4.79140 + 8.29895i −0.228681 + 0.396087i −0.957417 0.288707i \(-0.906775\pi\)
0.728736 + 0.684794i \(0.240108\pi\)
\(440\) −6.23593 + 10.8010i −0.297287 + 0.514915i
\(441\) −6.01633 10.4206i −0.286492 0.496219i
\(442\) 25.1219 43.5123i 1.19492 2.06967i
\(443\) 11.1218 + 19.2635i 0.528412 + 0.915236i 0.999451 + 0.0331236i \(0.0105455\pi\)
−0.471040 + 0.882112i \(0.656121\pi\)
\(444\) −0.600439 −0.0284956
\(445\) 9.84186 0.466549
\(446\) 18.8931 + 32.7239i 0.894616 + 1.54952i
\(447\) 2.87560 + 4.98069i 0.136011 + 0.235578i
\(448\) −36.3516 −1.71745
\(449\) −0.491188 −0.0231806 −0.0115903 0.999933i \(-0.503689\pi\)
−0.0115903 + 0.999933i \(0.503689\pi\)
\(450\) −0.690702 1.19633i −0.0325600 0.0563956i
\(451\) −1.64623 + 2.85136i −0.0775180 + 0.134265i
\(452\) 0.294873 + 0.510736i 0.0138697 + 0.0240230i
\(453\) −6.33364 + 10.9702i −0.297581 + 0.515425i
\(454\) 17.3312 30.0185i 0.813394 1.40884i
\(455\) 27.7579 1.30131
\(456\) 3.68911 + 12.0427i 0.172758 + 0.563952i
\(457\) 13.2607 0.620311 0.310156 0.950686i \(-0.399619\pi\)
0.310156 + 0.950686i \(0.399619\pi\)
\(458\) −3.44336 + 5.96407i −0.160897 + 0.278683i
\(459\) 2.85821 4.95056i 0.133410 0.231072i
\(460\) −0.0265707 0.0460218i −0.00123887 0.00214578i
\(461\) −11.6867 + 20.2420i −0.544305 + 0.942763i 0.454346 + 0.890825i \(0.349873\pi\)
−0.998650 + 0.0519379i \(0.983460\pi\)
\(462\) 13.0061 + 22.5272i 0.605098 + 1.04806i
\(463\) −0.981649 −0.0456211 −0.0228105 0.999740i \(-0.507261\pi\)
−0.0228105 + 0.999740i \(0.507261\pi\)
\(464\) 13.5320 0.628207
\(465\) 0.591725 + 1.02490i 0.0274406 + 0.0475285i
\(466\) −8.83851 15.3087i −0.409436 0.709164i
\(467\) −18.8498 −0.872264 −0.436132 0.899883i \(-0.643652\pi\)
−0.436132 + 0.899883i \(0.643652\pi\)
\(468\) 0.583613 0.0269775
\(469\) −8.73457 15.1287i −0.403325 0.698579i
\(470\) 1.88744 3.26914i 0.0870610 0.150794i
\(471\) 0.689434 + 1.19414i 0.0317675 + 0.0550228i
\(472\) 5.53296 9.58337i 0.254675 0.441110i
\(473\) −13.7314 + 23.7834i −0.631369 + 1.09356i
\(474\) −15.6606 −0.719315
\(475\) −4.24772 0.978193i −0.194899 0.0448826i
\(476\) 2.28750 0.104847
\(477\) −2.56853 + 4.44882i −0.117605 + 0.203697i
\(478\) −8.84440 + 15.3189i −0.404533 + 0.700672i
\(479\) −10.0795 17.4583i −0.460546 0.797688i 0.538443 0.842662i \(-0.319013\pi\)
−0.998988 + 0.0449739i \(0.985680\pi\)
\(480\) 0.259229 0.448998i 0.0118321 0.0204939i
\(481\) −20.8252 36.0704i −0.949549 1.64467i
\(482\) −1.50958 −0.0687596
\(483\) −2.52753 −0.115007
\(484\) 0.349931 + 0.606098i 0.0159059 + 0.0275499i
\(485\) −1.00000 1.73205i −0.0454077 0.0786484i
\(486\) −1.38140 −0.0626617
\(487\) 2.79159 0.126499 0.0632494 0.997998i \(-0.479854\pi\)
0.0632494 + 0.997998i \(0.479854\pi\)
\(488\) −17.3675 30.0814i −0.786190 1.36172i
\(489\) −5.80601 + 10.0563i −0.262557 + 0.454762i
\(490\) −8.31098 14.3950i −0.375452 0.650302i
\(491\) −2.88904 + 5.00397i −0.130381 + 0.225826i −0.923823 0.382819i \(-0.874953\pi\)
0.793443 + 0.608645i \(0.208287\pi\)
\(492\) 0.0349842 0.0605943i 0.00157721 0.00273180i
\(493\) −20.3129 −0.914849
\(494\) −26.1132 + 28.0341i −1.17489 + 1.26131i
\(495\) −4.31625 −0.194001
\(496\) 2.25337 3.90295i 0.101179 0.175248i
\(497\) 6.71641 11.6332i 0.301272 0.521819i
\(498\) 5.30382 + 9.18649i 0.237670 + 0.411657i
\(499\) −6.39792 + 11.0815i −0.286410 + 0.496077i −0.972950 0.231015i \(-0.925795\pi\)
0.686540 + 0.727092i \(0.259129\pi\)
\(500\) 0.0458624 + 0.0794360i 0.00205103 + 0.00355249i
\(501\) 20.3114 0.907446
\(502\) 8.42004 0.375805
\(503\) −15.8339 27.4252i −0.706000 1.22283i −0.966329 0.257308i \(-0.917164\pi\)
0.260329 0.965520i \(-0.416169\pi\)
\(504\) −6.30296 10.9171i −0.280756 0.486284i
\(505\) −4.49970 −0.200234
\(506\) 3.45440 0.153567
\(507\) 13.7416 + 23.8012i 0.610287 + 1.05705i
\(508\) −0.283588 + 0.491189i −0.0125822 + 0.0217930i
\(509\) 2.74405 + 4.75283i 0.121628 + 0.210665i 0.920410 0.390955i \(-0.127855\pi\)
−0.798782 + 0.601621i \(0.794522\pi\)
\(510\) 3.94834 6.83872i 0.174835 0.302823i
\(511\) 17.6391 30.5517i 0.780306 1.35153i
\(512\) −23.9817 −1.05985
\(513\) −2.97100 + 3.18954i −0.131173 + 0.140822i
\(514\) 6.38252 0.281521
\(515\) 8.03585 13.9185i 0.354102 0.613323i
\(516\) 0.291806 0.505423i 0.0128461 0.0222500i
\(517\) −5.89737 10.2145i −0.259366 0.449235i
\(518\) −19.7252 + 34.1651i −0.866678 + 1.50113i
\(519\) −6.12545 10.6096i −0.268877 0.465709i
\(520\) 18.3850 0.806234
\(521\) 8.28086 0.362791 0.181396 0.983410i \(-0.441939\pi\)
0.181396 + 0.983410i \(0.441939\pi\)
\(522\) 2.45437 + 4.25109i 0.107425 + 0.186065i
\(523\) −5.77584 10.0040i −0.252560 0.437446i 0.711670 0.702514i \(-0.247939\pi\)
−0.964230 + 0.265067i \(0.914606\pi\)
\(524\) −1.59578 −0.0697118
\(525\) 4.36264 0.190401
\(526\) 20.7552 + 35.9491i 0.904970 + 1.56745i
\(527\) −3.38254 + 5.85874i −0.147346 + 0.255211i
\(528\) 8.21843 + 14.2347i 0.357661 + 0.619488i
\(529\) 11.3322 19.6279i 0.492703 0.853387i
\(530\) −3.54817 + 6.14561i −0.154123 + 0.266948i
\(531\) 3.82968 0.166194
\(532\) −1.69978 0.391436i −0.0736948 0.0169709i
\(533\) 4.85347 0.210227
\(534\) 6.79779 11.7741i 0.294169 0.509516i
\(535\) −6.83945 + 11.8463i −0.295695 + 0.512159i
\(536\) −5.78518 10.0202i −0.249882 0.432808i
\(537\) −9.59201 + 16.6139i −0.413926 + 0.716941i
\(538\) 0.145931 + 0.252759i 0.00629152 + 0.0108972i
\(539\) −51.9360 −2.23704
\(540\) 0.0917248 0.00394721
\(541\) 12.9374 + 22.4083i 0.556224 + 0.963409i 0.997807 + 0.0661881i \(0.0210837\pi\)
−0.441583 + 0.897220i \(0.645583\pi\)
\(542\) 5.11622 + 8.86155i 0.219760 + 0.380636i
\(543\) 3.22984 0.138606
\(544\) 2.96372 0.127069
\(545\) 4.48337 + 7.76542i 0.192046 + 0.332634i
\(546\) 19.1725 33.2077i 0.820506 1.42116i
\(547\) −3.20287 5.54753i −0.136945 0.237195i 0.789394 0.613887i \(-0.210395\pi\)
−0.926339 + 0.376692i \(0.877062\pi\)
\(548\) 0.720793 1.24845i 0.0307907 0.0533311i
\(549\) 6.01053 10.4105i 0.256523 0.444311i
\(550\) −5.96248 −0.254241
\(551\) 15.0940 + 3.47595i 0.643028 + 0.148080i
\(552\) −1.67406 −0.0712528
\(553\) 24.7291 42.8320i 1.05159 1.82140i
\(554\) 20.0765 34.7736i 0.852970 1.47739i
\(555\) −3.27305 5.66908i −0.138933 0.240639i
\(556\) 0.300557 0.520580i 0.0127464 0.0220775i
\(557\) 1.76281 + 3.05327i 0.0746925 + 0.129371i 0.900953 0.433918i \(-0.142869\pi\)
−0.826260 + 0.563289i \(0.809536\pi\)
\(558\) 1.63482 0.0692075
\(559\) 40.4832 1.71226
\(560\) −8.30677 14.3878i −0.351025 0.607993i
\(561\) −12.3367 21.3678i −0.520857 0.902151i
\(562\) 15.8529 0.668713
\(563\) −30.7179 −1.29461 −0.647303 0.762232i \(-0.724103\pi\)
−0.647303 + 0.762232i \(0.724103\pi\)
\(564\) 0.125325 + 0.217070i 0.00527715 + 0.00914029i
\(565\) −3.21476 + 5.56813i −0.135246 + 0.234253i
\(566\) 18.8786 + 32.6986i 0.793525 + 1.37443i
\(567\) 2.18132 3.77816i 0.0916069 0.158668i
\(568\) 4.44849 7.70501i 0.186654 0.323295i
\(569\) 9.17896 0.384802 0.192401 0.981316i \(-0.438373\pi\)
0.192401 + 0.981316i \(0.438373\pi\)
\(570\) −4.10415 + 4.40604i −0.171904 + 0.184549i
\(571\) −7.49001 −0.313447 −0.156724 0.987643i \(-0.550093\pi\)
−0.156724 + 0.987643i \(0.550093\pi\)
\(572\) 1.25951 2.18153i 0.0526627 0.0912145i
\(573\) 13.7755 23.8598i 0.575478 0.996758i
\(574\) −2.29855 3.98121i −0.0959398 0.166173i
\(575\) 0.289678 0.501738i 0.0120804 0.0209239i
\(576\) −4.16624 7.21613i −0.173593 0.300672i
\(577\) 32.6093 1.35754 0.678771 0.734350i \(-0.262513\pi\)
0.678771 + 0.734350i \(0.262513\pi\)
\(578\) 21.6568 0.900803
\(579\) 11.1233 + 19.2662i 0.462270 + 0.800674i
\(580\) −0.162969 0.282271i −0.00676694 0.0117207i
\(581\) −33.5003 −1.38983
\(582\) −2.76281 −0.114522
\(583\) 11.0864 + 19.2022i 0.459152 + 0.795275i
\(584\) 11.6829 20.2354i 0.483442 0.837346i
\(585\) 3.18132 + 5.51021i 0.131531 + 0.227819i
\(586\) −8.99367 + 15.5775i −0.371525 + 0.643500i
\(587\) 9.19474 15.9258i 0.379508 0.657326i −0.611483 0.791258i \(-0.709427\pi\)
0.990991 + 0.133931i \(0.0427601\pi\)
\(588\) 1.10369 0.0455156
\(589\) 3.51603 3.77466i 0.144875 0.155532i
\(590\) 5.29033 0.217800
\(591\) 6.33133 10.9662i 0.260436 0.451089i
\(592\) −12.4642 + 21.5886i −0.512276 + 0.887288i
\(593\) −0.208669 0.361425i −0.00856900 0.0148419i 0.861709 0.507403i \(-0.169394\pi\)
−0.870278 + 0.492561i \(0.836061\pi\)
\(594\) −2.98124 + 5.16366i −0.122322 + 0.211868i
\(595\) 12.4693 + 21.5975i 0.511193 + 0.885412i
\(596\) −0.527528 −0.0216084
\(597\) 8.76955 0.358914
\(598\) −2.54609 4.40996i −0.104118 0.180337i
\(599\) 19.4828 + 33.7452i 0.796045 + 1.37879i 0.922174 + 0.386776i \(0.126411\pi\)
−0.126129 + 0.992014i \(0.540255\pi\)
\(600\) 2.88952 0.117964
\(601\) 10.0358 0.409367 0.204683 0.978828i \(-0.434383\pi\)
0.204683 + 0.978828i \(0.434383\pi\)
\(602\) −19.1725 33.2077i −0.781411 1.35344i
\(603\) 2.00213 3.46779i 0.0815329 0.141219i
\(604\) −0.580953 1.00624i −0.0236386 0.0409433i
\(605\) −3.81500 + 6.60778i −0.155102 + 0.268644i
\(606\) −3.10795 + 5.38313i −0.126252 + 0.218675i
\(607\) −6.25423 −0.253851 −0.126926 0.991912i \(-0.540511\pi\)
−0.126926 + 0.991912i \(0.540511\pi\)
\(608\) −2.20227 0.507152i −0.0893137 0.0205677i
\(609\) −15.5024 −0.628189
\(610\) 8.30296 14.3812i 0.336177 0.582276i
\(611\) −8.69340 + 15.0574i −0.351697 + 0.609157i
\(612\) 0.262168 + 0.454089i 0.0105975 + 0.0183555i
\(613\) −14.9371 + 25.8719i −0.603306 + 1.04496i 0.389011 + 0.921233i \(0.372817\pi\)
−0.992317 + 0.123723i \(0.960517\pi\)
\(614\) −2.78031 4.81563i −0.112204 0.194343i
\(615\) 0.762807 0.0307593
\(616\) −54.4103 −2.19225
\(617\) 15.3197 + 26.5346i 0.616749 + 1.06824i 0.990075 + 0.140540i \(0.0448840\pi\)
−0.373326 + 0.927700i \(0.621783\pi\)
\(618\) −11.1008 19.2271i −0.446538 0.773426i
\(619\) 21.1480 0.850011 0.425006 0.905191i \(-0.360272\pi\)
0.425006 + 0.905191i \(0.360272\pi\)
\(620\) −0.108552 −0.00435954
\(621\) −0.289678 0.501738i −0.0116244 0.0201340i
\(622\) −10.6076 + 18.3730i −0.425328 + 0.736690i
\(623\) 21.4683 + 37.1841i 0.860108 + 1.48975i
\(624\) 12.1149 20.9836i 0.484985 0.840018i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 30.3356 1.21245
\(627\) 5.51065 + 17.9890i 0.220074 + 0.718410i
\(628\) −0.126476 −0.00504696
\(629\) 18.7101 32.4068i 0.746020 1.29214i
\(630\) 3.01329 5.21916i 0.120052 0.207936i
\(631\) 13.0124 + 22.5381i 0.518014 + 0.897227i 0.999781 + 0.0209274i \(0.00666189\pi\)
−0.481767 + 0.876299i \(0.660005\pi\)
\(632\) 16.3788 28.3690i 0.651515 1.12846i
\(633\) 3.93389 + 6.81369i 0.156358 + 0.270820i
\(634\) −33.3304 −1.32372
\(635\) −6.18345 −0.245383
\(636\) −0.235598 0.408067i −0.00934206 0.0161809i
\(637\) 38.2798 + 66.3025i 1.51670 + 2.62700i
\(638\) 21.1873 0.838815
\(639\) 3.07906 0.121806
\(640\) −5.23680 9.07040i −0.207003 0.358539i
\(641\) 9.59982 16.6274i 0.379170 0.656742i −0.611771 0.791035i \(-0.709543\pi\)
0.990942 + 0.134292i \(0.0428761\pi\)
\(642\) 9.44803 + 16.3645i 0.372884 + 0.645854i
\(643\) −4.27305 + 7.40113i −0.168513 + 0.291872i −0.937897 0.346914i \(-0.887230\pi\)
0.769385 + 0.638786i \(0.220563\pi\)
\(644\) 0.115919 0.200777i 0.00456783 0.00791172i
\(645\) 6.36264 0.250529
\(646\) −33.5429 7.72446i −1.31973 0.303915i
\(647\) −21.6966 −0.852983 −0.426492 0.904492i \(-0.640251\pi\)
−0.426492 + 0.904492i \(0.640251\pi\)
\(648\) 1.44476 2.50239i 0.0567554 0.0983033i
\(649\) 8.26493 14.3153i 0.324427 0.561924i
\(650\) 4.39469 + 7.61182i 0.172374 + 0.298560i
\(651\) −2.58148 + 4.47126i −0.101176 + 0.175243i
\(652\) −0.532555 0.922413i −0.0208565 0.0361245i
\(653\) −4.39011 −0.171798 −0.0858991 0.996304i \(-0.527376\pi\)
−0.0858991 + 0.996304i \(0.527376\pi\)
\(654\) 12.3867 0.484358
\(655\) −8.69872 15.0666i −0.339887 0.588702i
\(656\) −1.45244 2.51569i −0.0567081 0.0982213i
\(657\) 8.08640 0.315481
\(658\) 16.4684 0.642006
\(659\) 7.57327 + 13.1173i 0.295013 + 0.510977i 0.974988 0.222258i \(-0.0713428\pi\)
−0.679975 + 0.733235i \(0.738009\pi\)
\(660\) 0.197954 0.342866i 0.00770534 0.0133460i
\(661\) −3.65794 6.33574i −0.142277 0.246432i 0.786076 0.618129i \(-0.212109\pi\)
−0.928354 + 0.371698i \(0.878776\pi\)
\(662\) 17.1582 29.7188i 0.666871 1.15505i
\(663\) −18.1857 + 31.4986i −0.706276 + 1.22331i
\(664\) −22.1883 −0.861072
\(665\) −5.56988 18.1823i −0.215991 0.705080i
\(666\) −9.04280 −0.350401
\(667\) −1.02936 + 1.78290i −0.0398568 + 0.0690340i
\(668\) −0.931530 + 1.61346i −0.0360420 + 0.0624265i
\(669\) −13.6768 23.6889i −0.528774 0.915864i
\(670\) 2.76575 4.79041i 0.106850 0.185070i
\(671\) −25.9429 44.9345i −1.00152 1.73468i
\(672\) 2.26185 0.0872527
\(673\) 39.7027 1.53043 0.765213 0.643777i \(-0.222634\pi\)
0.765213 + 0.643777i \(0.222634\pi\)
\(674\) −0.393218 0.681074i −0.0151462 0.0262340i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −2.52090 −0.0969575
\(677\) −9.45197 −0.363269 −0.181634 0.983366i \(-0.558139\pi\)
−0.181634 + 0.983366i \(0.558139\pi\)
\(678\) 4.44088 + 7.69183i 0.170551 + 0.295403i
\(679\) 4.36264 7.55632i 0.167423 0.289985i
\(680\) 8.25883 + 14.3047i 0.316712 + 0.548561i
\(681\) −12.5461 + 21.7305i −0.480767 + 0.832713i
\(682\) 3.52815 6.11093i 0.135100 0.234000i
\(683\) −6.27600 −0.240145 −0.120072 0.992765i \(-0.538313\pi\)
−0.120072 + 0.992765i \(0.538313\pi\)
\(684\) −0.117107 0.382284i −0.00447770 0.0146170i
\(685\) 15.7164 0.600493
\(686\) 15.1648 26.2663i 0.578996 1.00285i
\(687\) 2.49265 4.31740i 0.0951006 0.164719i
\(688\) −12.1149 20.9836i −0.461877 0.799994i
\(689\) 16.3426 28.3063i 0.622604 1.07838i
\(690\) −0.400163 0.693102i −0.0152339 0.0263860i
\(691\) −33.8913 −1.28929 −0.644643 0.764483i \(-0.722994\pi\)
−0.644643 + 0.764483i \(0.722994\pi\)
\(692\) 1.12371 0.0427171
\(693\) −9.41513 16.3075i −0.357651 0.619470i
\(694\) −6.47439 11.2140i −0.245765 0.425677i
\(695\) 6.55344 0.248586
\(696\) −10.2677 −0.389197
\(697\) 2.18026 + 3.77632i 0.0825832 + 0.143038i
\(698\) −10.2429 + 17.7412i −0.387699 + 0.671514i
\(699\) 6.39821 + 11.0820i 0.242002 + 0.419161i
\(700\) −0.200081 + 0.346551i −0.00756237 + 0.0130984i
\(701\) −20.1520 + 34.9043i −0.761131 + 1.31832i 0.181136 + 0.983458i \(0.442022\pi\)
−0.942268 + 0.334860i \(0.891311\pi\)
\(702\) 8.78938 0.331734
\(703\) −19.4484 + 20.8790i −0.733512 + 0.787467i
\(704\) −35.9650 −1.35548
\(705\) −1.36632 + 2.36653i −0.0514585 + 0.0891288i
\(706\) −21.5948 + 37.4033i −0.812730 + 1.40769i
\(707\) −9.81529 17.0006i −0.369142 0.639373i
\(708\) −0.175638 + 0.304215i −0.00660090 + 0.0114331i
\(709\) 2.63706 + 4.56751i 0.0990367 + 0.171537i 0.911286 0.411774i \(-0.135091\pi\)
−0.812249 + 0.583310i \(0.801757\pi\)
\(710\) 4.25342 0.159628
\(711\) 11.3367 0.425161
\(712\) 14.2191 + 24.6282i 0.532884 + 0.922981i
\(713\) 0.342820 + 0.593782i 0.0128387 + 0.0222373i
\(714\) 34.4504 1.28927
\(715\) 27.4628 1.02705
\(716\) −0.879826 1.52390i −0.0328806 0.0569509i
\(717\) 6.40247 11.0894i 0.239105 0.414142i
\(718\) −7.50877 13.0056i −0.280225 0.485364i
\(719\) −11.8834 + 20.5827i −0.443176 + 0.767604i −0.997923 0.0644151i \(-0.979482\pi\)
0.554747 + 0.832019i \(0.312815\pi\)
\(720\) 1.90407 3.29794i 0.0709604 0.122907i
\(721\) 70.1151 2.61122
\(722\) 23.6030 + 11.4797i 0.878414 + 0.427231i
\(723\) 1.09279 0.0406413
\(724\) −0.148128 + 0.256566i −0.00550515 + 0.00953520i
\(725\) 1.77672 3.07737i 0.0659858 0.114291i
\(726\) 5.27006 + 9.12801i 0.195590 + 0.338772i
\(727\) 16.9225 29.3106i 0.627620 1.08707i −0.360408 0.932795i \(-0.617363\pi\)
0.988028 0.154275i \(-0.0493040\pi\)
\(728\) 40.1035 + 69.4613i 1.48634 + 2.57441i
\(729\) 1.00000 0.0370370
\(730\) 11.1706 0.413442
\(731\) 18.1857 + 31.4986i 0.672624 + 1.16502i
\(732\) 0.551315 + 0.954905i 0.0203772 + 0.0352943i
\(733\) 24.6249 0.909542 0.454771 0.890608i \(-0.349721\pi\)
0.454771 + 0.890608i \(0.349721\pi\)
\(734\) −25.8731 −0.954992
\(735\) 6.01633 + 10.4206i 0.221916 + 0.384369i
\(736\) 0.150186 0.260130i 0.00553594 0.00958853i
\(737\) −8.64168 14.9678i −0.318320 0.551347i
\(738\) 0.526872 0.912569i 0.0193944 0.0335921i
\(739\) −9.22966 + 15.9862i −0.339518 + 0.588063i −0.984342 0.176268i \(-0.943597\pi\)
0.644824 + 0.764331i \(0.276931\pi\)
\(740\) 0.600439 0.0220726
\(741\) 18.9034 20.2939i 0.694434 0.745515i
\(742\) −30.9588 −1.13653
\(743\) 4.47864 7.75723i 0.164305 0.284585i −0.772103 0.635497i \(-0.780795\pi\)
0.936408 + 0.350912i \(0.114128\pi\)
\(744\) −1.70980 + 2.96146i −0.0626842 + 0.108572i
\(745\) −2.87560 4.98069i −0.105354 0.182478i
\(746\) −20.2565 + 35.0853i −0.741644 + 1.28457i
\(747\) −3.83945 6.65012i −0.140478 0.243315i
\(748\) 2.26317 0.0827497
\(749\) −59.6761 −2.18052
\(750\) 0.690702 + 1.19633i 0.0252209 + 0.0436838i
\(751\) 14.6128 + 25.3101i 0.533228 + 0.923578i 0.999247 + 0.0388032i \(0.0123545\pi\)
−0.466019 + 0.884775i \(0.654312\pi\)
\(752\) 10.4063 0.379477
\(753\) −6.09528 −0.222124
\(754\) −15.6163 27.0482i −0.568711 0.985037i
\(755\) 6.33364 10.9702i 0.230505 0.399246i
\(756\) 0.200081 + 0.346551i 0.00727689 + 0.0126039i
\(757\) −9.33886 + 16.1754i −0.339427 + 0.587904i −0.984325 0.176364i \(-0.943566\pi\)
0.644898 + 0.764268i \(0.276900\pi\)
\(758\) 7.35499 12.7392i 0.267145 0.462709i
\(759\) −2.50065 −0.0907678
\(760\) −3.68911 12.0427i −0.133818 0.436836i
\(761\) 41.5952 1.50782 0.753912 0.656975i \(-0.228164\pi\)
0.753912 + 0.656975i \(0.228164\pi\)
\(762\) −4.27092 + 7.39745i −0.154719 + 0.267981i
\(763\) −19.5593 + 33.8778i −0.708096 + 1.22646i
\(764\) 1.26355 + 2.18854i 0.0457137 + 0.0791785i
\(765\) −2.85821 + 4.95056i −0.103339 + 0.178988i
\(766\) −6.40940 11.1014i −0.231581 0.401110i
\(767\) −24.3669 −0.879838
\(768\) 2.19670 0.0792664
\(769\) −17.6255 30.5282i −0.635590 1.10087i −0.986390 0.164424i \(-0.947424\pi\)
0.350800 0.936450i \(-0.385910\pi\)
\(770\) −13.0061 22.5272i −0.468707 0.811824i
\(771\) −4.62032 −0.166397
\(772\) −2.04057 −0.0734417
\(773\) −23.9762 41.5280i −0.862364 1.49366i −0.869641 0.493684i \(-0.835650\pi\)
0.00727780 0.999974i \(-0.497683\pi\)
\(774\) 4.39469 7.61182i 0.157964 0.273601i
\(775\) −0.591725 1.02490i −0.0212554 0.0368154i
\(776\) 2.88952 5.00479i 0.103728 0.179661i
\(777\) 14.2791 24.7322i 0.512261 0.887262i
\(778\) 1.84068 0.0659917
\(779\) −0.973891 3.17917i −0.0348933 0.113906i
\(780\) −0.583613 −0.0208967
\(781\) 6.64499 11.5095i 0.237776 0.411841i
\(782\) 2.28750 3.96206i 0.0818007 0.141683i
\(783\) −1.77672 3.07737i −0.0634948 0.109976i
\(784\) 22.9110 39.6830i 0.818250 1.41725i
\(785\) −0.689434 1.19414i −0.0246070 0.0426205i
\(786\) −24.0329 −0.857224
\(787\) −5.26074 −0.187525 −0.0937626 0.995595i \(-0.529889\pi\)
−0.0937626 + 0.995595i \(0.529889\pi\)
\(788\) 0.580741 + 1.00587i 0.0206880 + 0.0358327i
\(789\) −15.0247 26.0236i −0.534895 0.926465i
\(790\) 15.6606 0.557179
\(791\) −28.0497 −0.997333
\(792\) −6.23593 10.8010i −0.221584 0.383795i
\(793\) −38.2429 + 66.2386i −1.35804 + 2.35220i
\(794\) 21.8709 + 37.8815i 0.776170 + 1.34437i
\(795\) 2.56853 4.44882i 0.0910963 0.157783i
\(796\) −0.402193 + 0.696619i −0.0142554 + 0.0246910i
\(797\) −21.0174 −0.744474 −0.372237 0.928138i \(-0.621409\pi\)
−0.372237 + 0.928138i \(0.621409\pi\)
\(798\) −25.5992 5.89515i −0.906202 0.208686i
\(799\) −15.6209 −0.552627
\(800\) −0.259229 + 0.448998i −0.00916514 + 0.0158745i
\(801\) −4.92093 + 8.52330i −0.173873 + 0.301156i
\(802\) 3.37649 + 5.84825i 0.119228 + 0.206509i
\(803\) 17.4515 30.2268i 0.615849 1.06668i
\(804\) 0.183645 + 0.318082i 0.00647665 + 0.0112179i
\(805\) 2.52753 0.0890837
\(806\) −10.4018 −0.366387
\(807\) −0.105639 0.182973i −0.00371869 0.00644095i
\(808\) −6.50098 11.2600i −0.228704 0.396126i
\(809\) 35.3856 1.24409 0.622046 0.782981i \(-0.286302\pi\)
0.622046 + 0.782981i \(0.286302\pi\)
\(810\) 1.38140 0.0485376
\(811\) −2.67523 4.63364i −0.0939401 0.162709i 0.815226 0.579143i \(-0.196613\pi\)
−0.909166 + 0.416434i \(0.863280\pi\)
\(812\) 0.710978 1.23145i 0.0249504 0.0432154i
\(813\) −3.70364 6.41489i −0.129892 0.224980i
\(814\) −19.5155 + 33.8018i −0.684017 + 1.18475i
\(815\) 5.80601 10.0563i 0.203376 0.352257i
\(816\) 21.7689 0.762063
\(817\) −8.12332 26.5178i −0.284199 0.927740i
\(818\) −31.4796 −1.10066
\(819\) −13.8790 + 24.0391i −0.484971 + 0.839994i
\(820\) −0.0349842 + 0.0605943i −0.00122170 + 0.00211605i
\(821\) −3.81886 6.61446i −0.133279 0.230846i 0.791660 0.610962i \(-0.209217\pi\)
−0.924939 + 0.380116i \(0.875884\pi\)
\(822\) 10.8554 18.8020i 0.378624 0.655796i
\(823\) −13.7866 23.8791i −0.480570 0.832372i 0.519181 0.854664i \(-0.326237\pi\)
−0.999752 + 0.0222919i \(0.992904\pi\)
\(824\) 46.4394 1.61779
\(825\) 4.31625 0.150273
\(826\) 11.5399 + 19.9877i 0.401525 + 0.695462i
\(827\) 9.51585 + 16.4819i 0.330898 + 0.573133i 0.982688 0.185267i \(-0.0593149\pi\)
−0.651790 + 0.758400i \(0.725982\pi\)
\(828\) 0.0531414 0.00184679
\(829\) −13.7455 −0.477402 −0.238701 0.971093i \(-0.576722\pi\)
−0.238701 + 0.971093i \(0.576722\pi\)
\(830\) −5.30382 9.18649i −0.184098 0.318868i
\(831\) −14.5334 + 25.1726i −0.504159 + 0.873229i
\(832\) 26.5083 + 45.9137i 0.919009 + 1.59177i
\(833\) −34.3918 + 59.5684i −1.19161 + 2.06392i
\(834\) 4.52647 7.84008i 0.156739 0.271480i
\(835\) −20.3114 −0.702905
\(836\) −1.68170 0.387274i −0.0581629 0.0133941i
\(837\) −1.18345 −0.0409060
\(838\) −21.3295 + 36.9438i −0.736815 + 1.27620i
\(839\) −17.1800 + 29.7566i −0.593118 + 1.02731i 0.400691 + 0.916213i \(0.368770\pi\)
−0.993809 + 0.111098i \(0.964563\pi\)
\(840\) 6.30296 + 10.9171i 0.217473 + 0.376674i
\(841\) 8.18652 14.1795i 0.282294 0.488947i
\(842\) −18.3576 31.7963i −0.632644 1.09577i
\(843\) −11.4759 −0.395251
\(844\) −0.721671 −0.0248409
\(845\) −13.7416 23.8012i −0.472726 0.818786i
\(846\) 1.88744 + 3.26914i 0.0648914 + 0.112395i
\(847\) −33.2870 −1.14375
\(848\) −19.5626 −0.671783
\(849\) −13.6662 23.6706i −0.469024 0.812373i
\(850\) −3.94834 + 6.83872i −0.135427 + 0.234566i
\(851\) −1.89626 3.28442i −0.0650030 0.112589i
\(852\) −0.141213 + 0.244588i −0.00483788 + 0.00837945i
\(853\) −22.7147 + 39.3431i −0.777738 + 1.34708i 0.155505 + 0.987835i \(0.450300\pi\)
−0.933243 + 0.359247i \(0.883034\pi\)
\(854\) 72.4457 2.47904
\(855\) 2.97100 3.18954i 0.101606 0.109080i
\(856\) −39.5254 −1.35095
\(857\) −6.94674 + 12.0321i −0.237296 + 0.411009i −0.959937 0.280214i \(-0.909594\pi\)
0.722641 + 0.691223i \(0.242928\pi\)
\(858\) 18.9686 32.8545i 0.647576 1.12164i
\(859\) 1.60333 + 2.77705i 0.0547049 + 0.0947517i 0.892081 0.451875i \(-0.149245\pi\)
−0.837376 + 0.546627i \(0.815912\pi\)
\(860\) −0.291806 + 0.505423i −0.00995051 + 0.0172348i
\(861\) 1.66393 + 2.88201i 0.0567065 + 0.0982185i
\(862\) 22.7577 0.775132
\(863\) 51.7277 1.76083 0.880416 0.474201i \(-0.157263\pi\)
0.880416 + 0.474201i \(0.157263\pi\)
\(864\) 0.259229 + 0.448998i 0.00881916 + 0.0152752i
\(865\) 6.12545 + 10.6096i 0.208272 + 0.360737i
\(866\) −50.8413 −1.72766
\(867\) −15.6774 −0.532431
\(868\) −0.236786 0.410126i −0.00803705 0.0139206i
\(869\) 24.4661 42.3765i 0.829955 1.43752i
\(870\) −2.45437 4.25109i −0.0832109 0.144125i
\(871\) −12.7388 + 22.0643i −0.431639 + 0.747620i
\(872\) −12.9548 + 22.4383i −0.438704 + 0.759857i
\(873\) 2.00000 0.0676897
\(874\) −2.37777 + 2.55267i −0.0804292 + 0.0863453i
\(875\) −4.36264 −0.147484
\(876\) −0.370862 + 0.642352i −0.0125303 + 0.0217031i
\(877\) −8.51355 + 14.7459i −0.287482 + 0.497933i −0.973208 0.229926i \(-0.926151\pi\)
0.685726 + 0.727860i \(0.259485\pi\)
\(878\) −6.61885 11.4642i −0.223376 0.386898i
\(879\) 6.51053 11.2766i 0.219595 0.380349i
\(880\) −8.21843 14.2347i −0.277043 0.479853i
\(881\) 12.9112 0.434990 0.217495 0.976061i \(-0.430211\pi\)
0.217495 + 0.976061i \(0.430211\pi\)
\(882\) 16.6220 0.559690
\(883\) −12.5102 21.6684i −0.421003 0.729199i 0.575035 0.818129i \(-0.304989\pi\)
−0.996038 + 0.0889302i \(0.971655\pi\)
\(884\) −1.66808 2.88921i −0.0561038 0.0971746i
\(885\) −3.82968 −0.128733
\(886\) −30.7273 −1.03230
\(887\) −5.03634 8.72319i −0.169104 0.292896i 0.769001 0.639247i \(-0.220754\pi\)
−0.938105 + 0.346351i \(0.887421\pi\)
\(888\) 9.45752 16.3809i 0.317374 0.549707i
\(889\) −13.4881 23.3621i −0.452376 0.783539i
\(890\) −6.79779 + 11.7741i −0.227862 + 0.394669i
\(891\) 2.15812 3.73798i 0.0722999 0.125227i
\(892\) 2.50900 0.0840075
\(893\) 11.6075 + 2.67304i 0.388430 + 0.0894500i
\(894\) −7.94473 −0.265712
\(895\) 9.59201 16.6139i 0.320626 0.555340i
\(896\) 22.8463 39.5709i 0.763240 1.32197i
\(897\) 1.84312 + 3.19238i 0.0615400 + 0.106590i
\(898\) 0.339264 0.587623i 0.0113214 0.0196092i
\(899\) 2.10266 + 3.64191i 0.0701276 + 0.121465i
\(900\) −0.0917248 −0.00305749
\(901\) 29.3655 0.978307
\(902\) −2.27411 3.93887i −0.0757196 0.131150i
\(903\) 13.8790 + 24.0391i 0.461863 + 0.799971i
\(904\) −18.5782 −0.617902
\(905\) −3.22984 −0.107364
\(906\) −8.74932 15.1543i −0.290677 0.503467i
\(907\) 3.93231 6.81096i 0.130570 0.226154i −0.793326 0.608797i \(-0.791653\pi\)
0.923897 + 0.382642i \(0.124986\pi\)
\(908\) −1.15079 1.99322i −0.0381903 0.0661475i
\(909\) 2.24985 3.89685i 0.0746228 0.129250i
\(910\) −19.1725 + 33.2077i −0.635561 + 1.10082i
\(911\) −52.2665 −1.73167 −0.865833 0.500333i \(-0.833211\pi\)
−0.865833 + 0.500333i \(0.833211\pi\)
\(912\) −16.1759 3.72509i −0.535638 0.123350i
\(913\) −33.1440 −1.09691
\(914\) −9.15922 + 15.8642i −0.302960 + 0.524742i
\(915\) −6.01053 + 10.4105i −0.198702 + 0.344162i
\(916\) 0.228638 + 0.396013i 0.00755441 + 0.0130846i
\(917\) 37.9494 65.7303i 1.25320 2.17061i
\(918\) 3.94834 + 6.83872i 0.130314 + 0.225711i
\(919\) 24.2225 0.799026 0.399513 0.916728i \(-0.369179\pi\)
0.399513 + 0.916728i \(0.369179\pi\)
\(920\) 1.67406 0.0551922
\(921\) 2.01267 + 3.48604i 0.0663197 + 0.114869i
\(922\) −16.1441 27.9623i −0.531677 0.920891i
\(923\) −19.5909 −0.644844
\(924\) 1.72720 0.0568208
\(925\) 3.27305 + 5.66908i 0.107617 + 0.186398i
\(926\) 0.678026 1.17438i 0.0222813 0.0385924i
\(927\) 8.03585 + 13.9185i 0.263932 + 0.457144i
\(928\) 0.921156 1.59549i 0.0302384 0.0523745i
\(929\) 21.3993 37.0647i 0.702089 1.21605i −0.265642 0.964072i \(-0.585584\pi\)
0.967732 0.251983i \(-0.0810827\pi\)
\(930\) −1.63482 −0.0536079
\(931\) 35.7490 38.3786i 1.17163 1.25781i
\(932\) −1.17375 −0.0384474
\(933\) 7.67889 13.3002i 0.251396 0.435430i
\(934\) 13.0196 22.5506i 0.426014 0.737877i
\(935\) 12.3367 + 21.3678i 0.403454 + 0.698803i
\(936\) −9.19248 + 15.9218i −0.300466 + 0.520422i
\(937\) −5.67783 9.83429i −0.185487 0.321272i 0.758254 0.651960i \(-0.226053\pi\)
−0.943740 + 0.330687i \(0.892719\pi\)
\(938\) 24.1319 0.787935
\(939\) −21.9600 −0.716636
\(940\) −0.125325 0.217070i −0.00408766 0.00708004i
\(941\) −22.0711 38.2283i −0.719498 1.24621i −0.961199 0.275856i \(-0.911039\pi\)
0.241701 0.970351i \(-0.422295\pi\)
\(942\) −1.90477 −0.0620609
\(943\) 0.441937 0.0143915
\(944\) 7.29198 + 12.6301i 0.237334 + 0.411074i
\(945\) −2.18132 + 3.77816i −0.0709584 + 0.122904i
\(946\) −18.9686 32.8545i −0.616721 1.06819i
\(947\) 18.6191 32.2492i 0.605038 1.04796i −0.387007 0.922077i \(-0.626491\pi\)
0.992045 0.125880i \(-0.0401755\pi\)
\(948\) −0.519930 + 0.900545i −0.0168865 + 0.0292483i
\(949\) −51.4509 −1.67017
\(950\) 4.10415 4.40604i 0.133156 0.142951i
\(951\) 24.1279 0.782402
\(952\) −36.0303 + 62.4064i −1.16775 + 2.02260i
\(953\) 19.6433 34.0232i 0.636310 1.10212i −0.349926 0.936777i \(-0.613793\pi\)
0.986236 0.165344i \(-0.0528733\pi\)
\(954\) −3.54817 6.14561i −0.114876 0.198972i
\(955\) −13.7755 + 23.8598i −0.445764 + 0.772085i
\(956\) 0.587266 + 1.01717i 0.0189935 + 0.0328978i
\(957\) −15.3375 −0.495792
\(958\) 27.8478 0.899721
\(959\) 34.2826 + 59.3791i 1.10704 + 1.91745i
\(960\) 4.16624 + 7.21613i 0.134465 + 0.232900i
\(961\) −29.5994 −0.954821
\(962\) 57.5361 1.85504
\(963\) −6.83945 11.8463i −0.220398 0.381741i
\(964\) −0.0501180 + 0.0868069i −0.00161419 + 0.00279586i
\(965\) −11.1233 19.2662i −0.358072 0.620200i
\(966\) 1.74577 3.02376i 0.0561692 0.0972878i
\(967\) −10.5429 + 18.2608i −0.339037 + 0.587229i −0.984252 0.176772i \(-0.943434\pi\)
0.645215 + 0.764001i \(0.276768\pi\)
\(968\) −22.0470 −0.708618
\(969\) 24.2817 + 5.59175i 0.780041 + 0.179633i
\(970\) 2.76281 0.0887084
\(971\) 12.1226 20.9969i 0.389031 0.673822i −0.603288 0.797523i \(-0.706143\pi\)
0.992319 + 0.123701i \(0.0394765\pi\)
\(972\) −0.0458624 + 0.0794360i −0.00147104 + 0.00254791i
\(973\) 14.2952 + 24.7600i 0.458282 + 0.793768i
\(974\) −1.92815 + 3.33966i −0.0617820 + 0.107010i
\(975\) −3.18132 5.51021i −0.101884 0.176468i
\(976\) 45.7778 1.46531
\(977\) −51.4540 −1.64616 −0.823080 0.567926i \(-0.807746\pi\)
−0.823080 + 0.567926i \(0.807746\pi\)
\(978\) −8.02044 13.8918i −0.256465 0.444211i
\(979\) 21.2400 + 36.7887i 0.678832 + 1.17577i
\(980\) −1.10369 −0.0352562
\(981\) −8.96674 −0.286286
\(982\) −3.99093 6.91249i −0.127356 0.220587i
\(983\) −4.56746 + 7.91108i −0.145679 + 0.252324i −0.929626 0.368504i \(-0.879870\pi\)
0.783947 + 0.620828i \(0.213203\pi\)
\(984\) 1.10207 + 1.90884i 0.0351327 + 0.0608517i
\(985\) −6.33133 + 10.9662i −0.201733 + 0.349412i
\(986\) 14.0302 24.3010i 0.446812 0.773901i
\(987\) −11.9215 −0.379466
\(988\) 0.745111 + 2.43234i 0.0237051 + 0.0773830i
\(989\) 3.68624 0.117216
\(990\) 2.98124 5.16366i 0.0947500 0.164112i
\(991\) 8.87713 15.3756i 0.281991 0.488424i −0.689884 0.723920i \(-0.742338\pi\)
0.971875 + 0.235497i \(0.0756717\pi\)
\(992\) −0.306785 0.531367i −0.00974042 0.0168709i
\(993\) −12.4208 + 21.5135i −0.394163 + 0.682710i
\(994\) 9.27807 + 16.0701i 0.294283 + 0.509712i
\(995\) −8.76955 −0.278014
\(996\) 0.704345 0.0223180
\(997\) 28.1217 + 48.7081i 0.890622 + 1.54260i 0.839131 + 0.543929i \(0.183064\pi\)
0.0514903 + 0.998673i \(0.483603\pi\)
\(998\) −8.83810 15.3080i −0.279765 0.484568i
\(999\) 6.54609 0.207109
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 285.2.i.f.106.2 10
3.2 odd 2 855.2.k.i.676.4 10
19.7 even 3 inner 285.2.i.f.121.2 yes 10
19.8 odd 6 5415.2.a.z.1.2 5
19.11 even 3 5415.2.a.y.1.4 5
57.26 odd 6 855.2.k.i.406.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.2.i.f.106.2 10 1.1 even 1 trivial
285.2.i.f.121.2 yes 10 19.7 even 3 inner
855.2.k.i.406.4 10 57.26 odd 6
855.2.k.i.676.4 10 3.2 odd 2
5415.2.a.y.1.4 5 19.11 even 3
5415.2.a.z.1.2 5 19.8 odd 6