Properties

Label 1078.2.i.a.901.6
Level $1078$
Weight $2$
Character 1078.901
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1078,2,Mod(901,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1078.901");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\), degree \(2\), 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: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{48})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.6
Root \(0.130526 - 0.991445i\) of defining polynomial
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.a.1011.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.937379 + 0.541196i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.937379 - 0.541196i) q^{5} -1.08239 q^{6} +1.00000i q^{8} +(-0.914214 + 1.58346i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.937379 + 0.541196i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.937379 - 0.541196i) q^{5} -1.08239 q^{6} +1.00000i q^{8} +(-0.914214 + 1.58346i) q^{9} +(-0.541196 - 0.937379i) q^{10} +(3.30518 - 0.275255i) q^{11} +(-0.937379 - 0.541196i) q^{12} -2.29610 q^{13} +1.17157 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.58346 + 0.914214i) q^{18} +(-2.77164 + 4.80062i) q^{19} -1.08239i q^{20} +(3.00000 + 1.41421i) q^{22} +(-3.12132 + 5.40629i) q^{23} +(-0.541196 - 0.937379i) q^{24} +(-1.91421 - 3.31552i) q^{25} +(-1.98848 - 1.14805i) q^{26} -5.22625i q^{27} +1.75736i q^{29} +(1.01461 + 0.585786i) q^{30} +(-1.21193 + 0.699709i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.94924 + 2.04677i) q^{33} -1.82843 q^{36} +(-3.00000 + 5.19615i) q^{37} +(-4.80062 + 2.77164i) q^{38} +(2.15232 - 1.24264i) q^{39} +(0.541196 - 0.937379i) q^{40} -4.59220 q^{41} +4.24264i q^{43} +(1.89097 + 2.72474i) q^{44} +(1.71393 - 0.989538i) q^{45} +(-5.40629 + 3.12132i) q^{46} +(-4.25151 - 2.45461i) q^{47} -1.08239i q^{48} -3.82843i q^{50} +(-1.14805 - 1.98848i) q^{52} +(-2.24264 - 3.88437i) q^{53} +(2.61313 - 4.52607i) q^{54} +(-3.24718 - 1.53073i) q^{55} -6.00000i q^{57} +(-0.878680 + 1.52192i) q^{58} +(-6.24000 + 3.60266i) q^{59} +(0.585786 + 1.01461i) q^{60} +(-2.77164 + 4.80062i) q^{61} -1.39942 q^{62} -1.00000 q^{64} +(2.15232 + 1.24264i) q^{65} +(-3.57750 + 0.297934i) q^{66} +(-5.82843 - 10.0951i) q^{67} -6.75699i q^{69} +2.00000 q^{71} +(-1.58346 - 0.914214i) q^{72} +(7.83938 + 13.5782i) q^{73} +(-5.19615 + 3.00000i) q^{74} +(3.58869 + 2.07193i) q^{75} -5.54328 q^{76} +2.48528 q^{78} +(7.34847 + 4.24264i) q^{79} +(0.937379 - 0.541196i) q^{80} +(0.0857864 + 0.148586i) q^{81} +(-3.97696 - 2.29610i) q^{82} +13.3827 q^{83} +(-2.12132 + 3.67423i) q^{86} +(-0.951076 - 1.64731i) q^{87} +(0.275255 + 3.30518i) q^{88} +(3.08669 + 1.78210i) q^{89} +1.97908 q^{90} -6.24264 q^{92} +(0.757359 - 1.31178i) q^{93} +(-2.45461 - 4.25151i) q^{94} +(5.19615 - 3.00000i) q^{95} +(0.541196 - 0.937379i) q^{96} -8.60474i q^{97} +(-2.58579 + 5.48528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 8 q^{9} + 64 q^{15} - 8 q^{16} + 48 q^{22} - 16 q^{23} - 8 q^{25} + 16 q^{36} - 48 q^{37} + 32 q^{53} - 48 q^{58} + 32 q^{60} - 16 q^{64} - 48 q^{67} + 32 q^{71} - 96 q^{78} + 24 q^{81} + 24 q^{88} - 32 q^{92} + 80 q^{93} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.937379 + 0.541196i −0.541196 + 0.312460i −0.745564 0.666435i \(-0.767820\pi\)
0.204367 + 0.978894i \(0.434486\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.937379 0.541196i −0.419209 0.242030i 0.275530 0.961292i \(-0.411147\pi\)
−0.694739 + 0.719262i \(0.744480\pi\)
\(6\) −1.08239 −0.441885
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −0.914214 + 1.58346i −0.304738 + 0.527821i
\(10\) −0.541196 0.937379i −0.171141 0.296425i
\(11\) 3.30518 0.275255i 0.996550 0.0829925i
\(12\) −0.937379 0.541196i −0.270598 0.156230i
\(13\) −2.29610 −0.636824 −0.318412 0.947952i \(-0.603149\pi\)
−0.318412 + 0.947952i \(0.603149\pi\)
\(14\) 0 0
\(15\) 1.17157 0.302499
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) −1.58346 + 0.914214i −0.373226 + 0.215482i
\(19\) −2.77164 + 4.80062i −0.635858 + 1.10134i 0.350475 + 0.936572i \(0.386020\pi\)
−0.986333 + 0.164766i \(0.947313\pi\)
\(20\) 1.08239i 0.242030i
\(21\) 0 0
\(22\) 3.00000 + 1.41421i 0.639602 + 0.301511i
\(23\) −3.12132 + 5.40629i −0.650840 + 1.12729i 0.332079 + 0.943252i \(0.392250\pi\)
−0.982919 + 0.184037i \(0.941083\pi\)
\(24\) −0.541196 0.937379i −0.110471 0.191342i
\(25\) −1.91421 3.31552i −0.382843 0.663103i
\(26\) −1.98848 1.14805i −0.389973 0.225151i
\(27\) 5.22625i 1.00579i
\(28\) 0 0
\(29\) 1.75736i 0.326333i 0.986599 + 0.163167i \(0.0521708\pi\)
−0.986599 + 0.163167i \(0.947829\pi\)
\(30\) 1.01461 + 0.585786i 0.185242 + 0.106949i
\(31\) −1.21193 + 0.699709i −0.217669 + 0.125671i −0.604871 0.796324i \(-0.706775\pi\)
0.387201 + 0.921995i \(0.373442\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −2.94924 + 2.04677i −0.513397 + 0.356297i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.82843 −0.304738
\(37\) −3.00000 + 5.19615i −0.493197 + 0.854242i −0.999969 0.00783774i \(-0.997505\pi\)
0.506772 + 0.862080i \(0.330838\pi\)
\(38\) −4.80062 + 2.77164i −0.778763 + 0.449619i
\(39\) 2.15232 1.24264i 0.344647 0.198982i
\(40\) 0.541196 0.937379i 0.0855706 0.148213i
\(41\) −4.59220 −0.717181 −0.358591 0.933495i \(-0.616743\pi\)
−0.358591 + 0.933495i \(0.616743\pi\)
\(42\) 0 0
\(43\) 4.24264i 0.646997i 0.946229 + 0.323498i \(0.104859\pi\)
−0.946229 + 0.323498i \(0.895141\pi\)
\(44\) 1.89097 + 2.72474i 0.285074 + 0.410771i
\(45\) 1.71393 0.989538i 0.255498 0.147512i
\(46\) −5.40629 + 3.12132i −0.797113 + 0.460214i
\(47\) −4.25151 2.45461i −0.620147 0.358042i 0.156779 0.987634i \(-0.449889\pi\)
−0.776926 + 0.629592i \(0.783222\pi\)
\(48\) 1.08239i 0.156230i
\(49\) 0 0
\(50\) 3.82843i 0.541421i
\(51\) 0 0
\(52\) −1.14805 1.98848i −0.159206 0.275753i
\(53\) −2.24264 3.88437i −0.308050 0.533559i 0.669885 0.742464i \(-0.266343\pi\)
−0.977936 + 0.208906i \(0.933010\pi\)
\(54\) 2.61313 4.52607i 0.355601 0.615920i
\(55\) −3.24718 1.53073i −0.437849 0.206404i
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) −0.878680 + 1.52192i −0.115376 + 0.199838i
\(59\) −6.24000 + 3.60266i −0.812378 + 0.469027i −0.847781 0.530346i \(-0.822062\pi\)
0.0354028 + 0.999373i \(0.488729\pi\)
\(60\) 0.585786 + 1.01461i 0.0756247 + 0.130986i
\(61\) −2.77164 + 4.80062i −0.354872 + 0.614656i −0.987096 0.160129i \(-0.948809\pi\)
0.632224 + 0.774786i \(0.282142\pi\)
\(62\) −1.39942 −0.177726
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 2.15232 + 1.24264i 0.266962 + 0.154131i
\(66\) −3.57750 + 0.297934i −0.440360 + 0.0366731i
\(67\) −5.82843 10.0951i −0.712056 1.23332i −0.964084 0.265597i \(-0.914431\pi\)
0.252028 0.967720i \(-0.418902\pi\)
\(68\) 0 0
\(69\) 6.75699i 0.813445i
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −1.58346 0.914214i −0.186613 0.107741i
\(73\) 7.83938 + 13.5782i 0.917530 + 1.58921i 0.803155 + 0.595771i \(0.203153\pi\)
0.114375 + 0.993438i \(0.463513\pi\)
\(74\) −5.19615 + 3.00000i −0.604040 + 0.348743i
\(75\) 3.58869 + 2.07193i 0.414386 + 0.239246i
\(76\) −5.54328 −0.635858
\(77\) 0 0
\(78\) 2.48528 0.281403
\(79\) 7.34847 + 4.24264i 0.826767 + 0.477334i 0.852745 0.522328i \(-0.174936\pi\)
−0.0259772 + 0.999663i \(0.508270\pi\)
\(80\) 0.937379 0.541196i 0.104802 0.0605076i
\(81\) 0.0857864 + 0.148586i 0.00953183 + 0.0165096i
\(82\) −3.97696 2.29610i −0.439182 0.253562i
\(83\) 13.3827 1.46894 0.734469 0.678643i \(-0.237431\pi\)
0.734469 + 0.678643i \(0.237431\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.12132 + 3.67423i −0.228748 + 0.396203i
\(87\) −0.951076 1.64731i −0.101966 0.176610i
\(88\) 0.275255 + 3.30518i 0.0293423 + 0.352334i
\(89\) 3.08669 + 1.78210i 0.327188 + 0.188902i 0.654592 0.755982i \(-0.272840\pi\)
−0.327404 + 0.944885i \(0.606174\pi\)
\(90\) 1.97908 0.208613
\(91\) 0 0
\(92\) −6.24264 −0.650840
\(93\) 0.757359 1.31178i 0.0785345 0.136026i
\(94\) −2.45461 4.25151i −0.253174 0.438510i
\(95\) 5.19615 3.00000i 0.533114 0.307794i
\(96\) 0.541196 0.937379i 0.0552356 0.0956709i
\(97\) 8.60474i 0.873679i −0.899539 0.436840i \(-0.856098\pi\)
0.899539 0.436840i \(-0.143902\pi\)
\(98\) 0 0
\(99\) −2.58579 + 5.48528i −0.259881 + 0.551292i
\(100\) 1.91421 3.31552i 0.191421 0.331552i
\(101\) 8.31492 + 14.4019i 0.827365 + 1.43304i 0.900098 + 0.435687i \(0.143494\pi\)
−0.0727333 + 0.997351i \(0.523172\pi\)
\(102\) 0 0
\(103\) −5.57717 3.21998i −0.549535 0.317274i 0.199400 0.979918i \(-0.436101\pi\)
−0.748934 + 0.662644i \(0.769434\pi\)
\(104\) 2.29610i 0.225151i
\(105\) 0 0
\(106\) 4.48528i 0.435649i
\(107\) −11.0227 6.36396i −1.06561 0.615227i −0.138628 0.990345i \(-0.544269\pi\)
−0.926977 + 0.375117i \(0.877602\pi\)
\(108\) 4.52607 2.61313i 0.435521 0.251448i
\(109\) 3.04384 1.75736i 0.291547 0.168324i −0.347093 0.937831i \(-0.612831\pi\)
0.638639 + 0.769506i \(0.279498\pi\)
\(110\) −2.04677 2.94924i −0.195152 0.281199i
\(111\) 6.49435i 0.616417i
\(112\) 0 0
\(113\) −1.41421 −0.133038 −0.0665190 0.997785i \(-0.521189\pi\)
−0.0665190 + 0.997785i \(0.521189\pi\)
\(114\) 3.00000 5.19615i 0.280976 0.486664i
\(115\) 5.85172 3.37849i 0.545676 0.315046i
\(116\) −1.52192 + 0.878680i −0.141307 + 0.0815834i
\(117\) 2.09913 3.63579i 0.194064 0.336129i
\(118\) −7.20533 −0.663304
\(119\) 0 0
\(120\) 1.17157i 0.106949i
\(121\) 10.8485 1.81954i 0.986224 0.165412i
\(122\) −4.80062 + 2.77164i −0.434628 + 0.250932i
\(123\) 4.30463 2.48528i 0.388136 0.224090i
\(124\) −1.21193 0.699709i −0.108835 0.0628357i
\(125\) 9.55582i 0.854699i
\(126\) 0 0
\(127\) 6.00000i 0.532414i −0.963916 0.266207i \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −2.29610 3.97696i −0.202160 0.350152i
\(130\) 1.24264 + 2.15232i 0.108987 + 0.188771i
\(131\) 3.44415 5.96544i 0.300917 0.521203i −0.675427 0.737427i \(-0.736041\pi\)
0.976344 + 0.216224i \(0.0693740\pi\)
\(132\) −3.24718 1.53073i −0.282630 0.133233i
\(133\) 0 0
\(134\) 11.6569i 1.00700i
\(135\) −2.82843 + 4.89898i −0.243432 + 0.421637i
\(136\) 0 0
\(137\) 8.48528 + 14.6969i 0.724947 + 1.25564i 0.958996 + 0.283420i \(0.0914689\pi\)
−0.234050 + 0.972225i \(0.575198\pi\)
\(138\) 3.37849 5.85172i 0.287596 0.498132i
\(139\) 13.3827 1.13510 0.567551 0.823338i \(-0.307891\pi\)
0.567551 + 0.823338i \(0.307891\pi\)
\(140\) 0 0
\(141\) 5.31371 0.447495
\(142\) 1.73205 + 1.00000i 0.145350 + 0.0839181i
\(143\) −7.58903 + 0.632013i −0.634627 + 0.0528516i
\(144\) −0.914214 1.58346i −0.0761845 0.131955i
\(145\) 0.951076 1.64731i 0.0789826 0.136802i
\(146\) 15.6788i 1.29758i
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) −5.82655 3.36396i −0.477330 0.275586i 0.241973 0.970283i \(-0.422205\pi\)
−0.719303 + 0.694696i \(0.755539\pi\)
\(150\) 2.07193 + 3.58869i 0.169172 + 0.293015i
\(151\) −5.19615 + 3.00000i −0.422857 + 0.244137i −0.696299 0.717752i \(-0.745171\pi\)
0.273442 + 0.961888i \(0.411838\pi\)
\(152\) −4.80062 2.77164i −0.389382 0.224810i
\(153\) 0 0
\(154\) 0 0
\(155\) 1.51472 0.121665
\(156\) 2.15232 + 1.24264i 0.172323 + 0.0994909i
\(157\) 9.98951 5.76745i 0.797250 0.460292i −0.0452587 0.998975i \(-0.514411\pi\)
0.842509 + 0.538683i \(0.181078\pi\)
\(158\) 4.24264 + 7.34847i 0.337526 + 0.584613i
\(159\) 4.20441 + 2.42742i 0.333431 + 0.192507i
\(160\) 1.08239 0.0855706
\(161\) 0 0
\(162\) 0.171573i 0.0134800i
\(163\) 4.07107 7.05130i 0.318871 0.552300i −0.661382 0.750049i \(-0.730030\pi\)
0.980253 + 0.197749i \(0.0633631\pi\)
\(164\) −2.29610 3.97696i −0.179295 0.310549i
\(165\) 3.87226 0.322481i 0.301455 0.0251051i
\(166\) 11.5897 + 6.69133i 0.899537 + 0.519348i
\(167\) 20.2710 1.56861 0.784307 0.620373i \(-0.213019\pi\)
0.784307 + 0.620373i \(0.213019\pi\)
\(168\) 0 0
\(169\) −7.72792 −0.594456
\(170\) 0 0
\(171\) −5.06774 8.77758i −0.387540 0.671238i
\(172\) −3.67423 + 2.12132i −0.280158 + 0.161749i
\(173\) −12.9071 + 22.3558i −0.981310 + 1.69968i −0.324002 + 0.946056i \(0.605029\pi\)
−0.657308 + 0.753622i \(0.728305\pi\)
\(174\) 1.90215i 0.144202i
\(175\) 0 0
\(176\) −1.41421 + 3.00000i −0.106600 + 0.226134i
\(177\) 3.89949 6.75412i 0.293104 0.507671i
\(178\) 1.78210 + 3.08669i 0.133574 + 0.231357i
\(179\) 2.82843 + 4.89898i 0.211407 + 0.366167i 0.952155 0.305616i \(-0.0988623\pi\)
−0.740748 + 0.671783i \(0.765529\pi\)
\(180\) 1.71393 + 0.989538i 0.127749 + 0.0737558i
\(181\) 20.4567i 1.52053i 0.649612 + 0.760266i \(0.274931\pi\)
−0.649612 + 0.760266i \(0.725069\pi\)
\(182\) 0 0
\(183\) 6.00000i 0.443533i
\(184\) −5.40629 3.12132i −0.398557 0.230107i
\(185\) 5.62427 3.24718i 0.413505 0.238737i
\(186\) 1.31178 0.757359i 0.0961847 0.0555323i
\(187\) 0 0
\(188\) 4.90923i 0.358042i
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 0.878680 1.52192i 0.0635790 0.110122i −0.832484 0.554049i \(-0.813082\pi\)
0.896063 + 0.443927i \(0.146415\pi\)
\(192\) 0.937379 0.541196i 0.0676495 0.0390575i
\(193\) 2.15232 1.24264i 0.154927 0.0894472i −0.420532 0.907278i \(-0.638157\pi\)
0.575459 + 0.817830i \(0.304823\pi\)
\(194\) 4.30237 7.45193i 0.308892 0.535017i
\(195\) −2.69005 −0.192638
\(196\) 0 0
\(197\) 20.4853i 1.45952i 0.683706 + 0.729758i \(0.260367\pi\)
−0.683706 + 0.729758i \(0.739633\pi\)
\(198\) −4.98200 + 3.45750i −0.354055 + 0.245714i
\(199\) 21.3518 12.3275i 1.51359 0.873870i 0.513715 0.857961i \(-0.328269\pi\)
0.999873 0.0159092i \(-0.00506428\pi\)
\(200\) 3.31552 1.91421i 0.234442 0.135355i
\(201\) 10.9269 + 6.30864i 0.770724 + 0.444977i
\(202\) 16.6298i 1.17007i
\(203\) 0 0
\(204\) 0 0
\(205\) 4.30463 + 2.48528i 0.300649 + 0.173580i
\(206\) −3.21998 5.57717i −0.224347 0.388580i
\(207\) −5.70711 9.88500i −0.396671 0.687055i
\(208\) 1.14805 1.98848i 0.0796030 0.137876i
\(209\) −7.83938 + 16.6298i −0.542261 + 1.15031i
\(210\) 0 0
\(211\) 24.7279i 1.70234i −0.524890 0.851170i \(-0.675893\pi\)
0.524890 0.851170i \(-0.324107\pi\)
\(212\) 2.24264 3.88437i 0.154025 0.266779i
\(213\) −1.87476 + 1.08239i −0.128456 + 0.0741643i
\(214\) −6.36396 11.0227i −0.435031 0.753497i
\(215\) 2.29610 3.97696i 0.156593 0.271227i
\(216\) 5.22625 0.355601
\(217\) 0 0
\(218\) 3.51472 0.238047
\(219\) −14.6969 8.48528i −0.993127 0.573382i
\(220\) −0.297934 3.57750i −0.0200867 0.241195i
\(221\) 0 0
\(222\) 3.24718 5.62427i 0.217936 0.377477i
\(223\) 7.89377i 0.528606i −0.964440 0.264303i \(-0.914858\pi\)
0.964440 0.264303i \(-0.0851419\pi\)
\(224\) 0 0
\(225\) 7.00000 0.466667
\(226\) −1.22474 0.707107i −0.0814688 0.0470360i
\(227\) −0.475538 0.823656i −0.0315626 0.0546680i 0.849813 0.527085i \(-0.176715\pi\)
−0.881375 + 0.472417i \(0.843382\pi\)
\(228\) 5.19615 3.00000i 0.344124 0.198680i
\(229\) 24.6659 + 14.2409i 1.62997 + 0.941064i 0.984100 + 0.177616i \(0.0568386\pi\)
0.645870 + 0.763447i \(0.276495\pi\)
\(230\) 6.75699 0.445542
\(231\) 0 0
\(232\) −1.75736 −0.115376
\(233\) 7.34847 + 4.24264i 0.481414 + 0.277945i 0.721006 0.692929i \(-0.243680\pi\)
−0.239591 + 0.970874i \(0.577013\pi\)
\(234\) 3.63579 2.09913i 0.237679 0.137224i
\(235\) 2.65685 + 4.60181i 0.173314 + 0.300189i
\(236\) −6.24000 3.60266i −0.406189 0.234513i
\(237\) −9.18440 −0.596591
\(238\) 0 0
\(239\) 26.4853i 1.71319i 0.515989 + 0.856595i \(0.327425\pi\)
−0.515989 + 0.856595i \(0.672575\pi\)
\(240\) −0.585786 + 1.01461i −0.0378124 + 0.0654929i
\(241\) −2.29610 3.97696i −0.147905 0.256179i 0.782548 0.622590i \(-0.213920\pi\)
−0.930453 + 0.366411i \(0.880586\pi\)
\(242\) 10.3048 + 3.84847i 0.662419 + 0.247389i
\(243\) 13.4174 + 7.74652i 0.860725 + 0.496940i
\(244\) −5.54328 −0.354872
\(245\) 0 0
\(246\) 4.97056 0.316912
\(247\) 6.36396 11.0227i 0.404929 0.701358i
\(248\) −0.699709 1.21193i −0.0444316 0.0769577i
\(249\) −12.5446 + 7.24264i −0.794983 + 0.458984i
\(250\) −4.77791 + 8.27558i −0.302182 + 0.523394i
\(251\) 12.1689i 0.768097i 0.923313 + 0.384049i \(0.125470\pi\)
−0.923313 + 0.384049i \(0.874530\pi\)
\(252\) 0 0
\(253\) −8.82843 + 18.7279i −0.555038 + 1.17741i
\(254\) 3.00000 5.19615i 0.188237 0.326036i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −19.0888 11.0209i −1.19072 0.687465i −0.232253 0.972655i \(-0.574610\pi\)
−0.958471 + 0.285191i \(0.907943\pi\)
\(258\) 4.59220i 0.285898i
\(259\) 0 0
\(260\) 2.48528i 0.154131i
\(261\) −2.78272 1.60660i −0.172246 0.0994461i
\(262\) 5.96544 3.44415i 0.368546 0.212780i
\(263\) 20.7846 12.0000i 1.28163 0.739952i 0.304487 0.952517i \(-0.401515\pi\)
0.977147 + 0.212565i \(0.0681817\pi\)
\(264\) −2.04677 2.94924i −0.125970 0.181513i
\(265\) 4.85483i 0.298230i
\(266\) 0 0
\(267\) −3.85786 −0.236097
\(268\) 5.82843 10.0951i 0.356028 0.616658i
\(269\) −3.03958 + 1.75490i −0.185327 + 0.106998i −0.589793 0.807555i \(-0.700791\pi\)
0.404466 + 0.914553i \(0.367457\pi\)
\(270\) −4.89898 + 2.82843i −0.298142 + 0.172133i
\(271\) 13.3827 23.1794i 0.812938 1.40805i −0.0978604 0.995200i \(-0.531200\pi\)
0.910799 0.412850i \(-0.135467\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 16.9706i 1.02523i
\(275\) −7.23944 10.4315i −0.436555 0.629042i
\(276\) 5.85172 3.37849i 0.352232 0.203361i
\(277\) −16.2189 + 9.36396i −0.974497 + 0.562626i −0.900604 0.434640i \(-0.856876\pi\)
−0.0738925 + 0.997266i \(0.523542\pi\)
\(278\) 11.5897 + 6.69133i 0.695105 + 0.401319i
\(279\) 2.55873i 0.153187i
\(280\) 0 0
\(281\) 12.0000i 0.715860i −0.933748 0.357930i \(-0.883483\pi\)
0.933748 0.357930i \(-0.116517\pi\)
\(282\) 4.60181 + 2.65685i 0.274034 + 0.158213i
\(283\) −11.2835 19.5436i −0.670736 1.16175i −0.977696 0.210027i \(-0.932645\pi\)
0.306960 0.951723i \(-0.400688\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) −3.24718 + 5.62427i −0.192346 + 0.333153i
\(286\) −6.88830 3.24718i −0.407314 0.192010i
\(287\) 0 0
\(288\) 1.82843i 0.107741i
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 1.64731 0.951076i 0.0967335 0.0558491i
\(291\) 4.65685 + 8.06591i 0.272990 + 0.472832i
\(292\) −7.83938 + 13.5782i −0.458765 + 0.794604i
\(293\) −0.951076 −0.0555625 −0.0277812 0.999614i \(-0.508844\pi\)
−0.0277812 + 0.999614i \(0.508844\pi\)
\(294\) 0 0
\(295\) 7.79899 0.454075
\(296\) −5.19615 3.00000i −0.302020 0.174371i
\(297\) −1.43855 17.2737i −0.0834733 1.00232i
\(298\) −3.36396 5.82655i −0.194869 0.337523i
\(299\) 7.16687 12.4134i 0.414471 0.717884i
\(300\) 4.14386i 0.239246i
\(301\) 0 0
\(302\) −6.00000 −0.345261
\(303\) −15.5885 9.00000i −0.895533 0.517036i
\(304\) −2.77164 4.80062i −0.158964 0.275334i
\(305\) 5.19615 3.00000i 0.297531 0.171780i
\(306\) 0 0
\(307\) −7.44543 −0.424933 −0.212467 0.977168i \(-0.568150\pi\)
−0.212467 + 0.977168i \(0.568150\pi\)
\(308\) 0 0
\(309\) 6.97056 0.396541
\(310\) 1.31178 + 0.757359i 0.0745044 + 0.0430151i
\(311\) −28.9174 + 16.6955i −1.63976 + 0.946714i −0.658841 + 0.752282i \(0.728953\pi\)
−0.980916 + 0.194433i \(0.937713\pi\)
\(312\) 1.24264 + 2.15232i 0.0703507 + 0.121851i
\(313\) 8.93841 + 5.16059i 0.505229 + 0.291694i 0.730870 0.682516i \(-0.239114\pi\)
−0.225641 + 0.974210i \(0.572448\pi\)
\(314\) 11.5349 0.650952
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) 11.4853 19.8931i 0.645078 1.11731i −0.339206 0.940712i \(-0.610158\pi\)
0.984284 0.176595i \(-0.0565083\pi\)
\(318\) 2.42742 + 4.20441i 0.136123 + 0.235772i
\(319\) 0.483722 + 5.80839i 0.0270832 + 0.325208i
\(320\) 0.937379 + 0.541196i 0.0524011 + 0.0302538i
\(321\) 13.7766 0.768935
\(322\) 0 0
\(323\) 0 0
\(324\) −0.0857864 + 0.148586i −0.00476591 + 0.00825480i
\(325\) 4.39523 + 7.61276i 0.243803 + 0.422280i
\(326\) 7.05130 4.07107i 0.390535 0.225476i
\(327\) −1.90215 + 3.29462i −0.105189 + 0.182193i
\(328\) 4.59220i 0.253562i
\(329\) 0 0
\(330\) 3.51472 + 1.65685i 0.193479 + 0.0912068i
\(331\) −10.2426 + 17.7408i −0.562986 + 0.975121i 0.434247 + 0.900794i \(0.357014\pi\)
−0.997234 + 0.0743275i \(0.976319\pi\)
\(332\) 6.69133 + 11.5897i 0.367234 + 0.636068i
\(333\) −5.48528 9.50079i −0.300592 0.520640i
\(334\) 17.5552 + 10.1355i 0.960576 + 0.554589i
\(335\) 12.6173i 0.689356i
\(336\) 0 0
\(337\) 26.4853i 1.44275i −0.692547 0.721373i \(-0.743512\pi\)
0.692547 0.721373i \(-0.256488\pi\)
\(338\) −6.69258 3.86396i −0.364028 0.210172i
\(339\) 1.32565 0.765367i 0.0719997 0.0415690i
\(340\) 0 0
\(341\) −3.81306 + 2.64626i −0.206489 + 0.143303i
\(342\) 10.1355i 0.548064i
\(343\) 0 0
\(344\) −4.24264 −0.228748
\(345\) −3.65685 + 6.33386i −0.196878 + 0.341003i
\(346\) −22.3558 + 12.9071i −1.20185 + 0.693891i
\(347\) −6.71807 + 3.87868i −0.360645 + 0.208218i −0.669364 0.742935i \(-0.733433\pi\)
0.308719 + 0.951153i \(0.400100\pi\)
\(348\) 0.951076 1.64731i 0.0509830 0.0883052i
\(349\) −29.0614 −1.55562 −0.777811 0.628498i \(-0.783670\pi\)
−0.777811 + 0.628498i \(0.783670\pi\)
\(350\) 0 0
\(351\) 12.0000i 0.640513i
\(352\) −2.72474 + 1.89097i −0.145229 + 0.100789i
\(353\) 1.05110 0.606854i 0.0559445 0.0322996i −0.471767 0.881723i \(-0.656384\pi\)
0.527711 + 0.849424i \(0.323050\pi\)
\(354\) 6.75412 3.89949i 0.358978 0.207256i
\(355\) −1.87476 1.08239i −0.0995018 0.0574474i
\(356\) 3.56420i 0.188902i
\(357\) 0 0
\(358\) 5.65685i 0.298974i
\(359\) 2.15232 + 1.24264i 0.113595 + 0.0655841i 0.555721 0.831369i \(-0.312442\pi\)
−0.442126 + 0.896953i \(0.645776\pi\)
\(360\) 0.989538 + 1.71393i 0.0521532 + 0.0903320i
\(361\) −5.86396 10.1567i −0.308630 0.534562i
\(362\) −10.2283 + 17.7160i −0.537589 + 0.931132i
\(363\) −9.18440 + 7.57675i −0.482056 + 0.397676i
\(364\) 0 0
\(365\) 16.9706i 0.888280i
\(366\) 3.00000 5.19615i 0.156813 0.271607i
\(367\) −9.64834 + 5.57047i −0.503639 + 0.290776i −0.730215 0.683217i \(-0.760580\pi\)
0.226576 + 0.973994i \(0.427247\pi\)
\(368\) −3.12132 5.40629i −0.162710 0.281822i
\(369\) 4.19825 7.27159i 0.218552 0.378544i
\(370\) 6.49435 0.337625
\(371\) 0 0
\(372\) 1.51472 0.0785345
\(373\) 17.7408 + 10.2426i 0.918582 + 0.530344i 0.883183 0.469029i \(-0.155396\pi\)
0.0353999 + 0.999373i \(0.488730\pi\)
\(374\) 0 0
\(375\) −5.17157 8.95743i −0.267059 0.462560i
\(376\) 2.45461 4.25151i 0.126587 0.219255i
\(377\) 4.03507i 0.207817i
\(378\) 0 0
\(379\) −11.6569 −0.598772 −0.299386 0.954132i \(-0.596782\pi\)
−0.299386 + 0.954132i \(0.596782\pi\)
\(380\) 5.19615 + 3.00000i 0.266557 + 0.153897i
\(381\) 3.24718 + 5.62427i 0.166358 + 0.288140i
\(382\) 1.52192 0.878680i 0.0778681 0.0449572i
\(383\) −12.5271 7.23252i −0.640105 0.369565i 0.144550 0.989497i \(-0.453827\pi\)
−0.784655 + 0.619933i \(0.787160\pi\)
\(384\) 1.08239 0.0552356
\(385\) 0 0
\(386\) 2.48528 0.126497
\(387\) −6.71807 3.87868i −0.341499 0.197164i
\(388\) 7.45193 4.30237i 0.378314 0.218420i
\(389\) 16.0000 + 27.7128i 0.811232 + 1.40510i 0.912002 + 0.410186i \(0.134536\pi\)
−0.100770 + 0.994910i \(0.532131\pi\)
\(390\) −2.32965 1.34502i −0.117966 0.0681080i
\(391\) 0 0
\(392\) 0 0
\(393\) 7.45584i 0.376098i
\(394\) −10.2426 + 17.7408i −0.516017 + 0.893767i
\(395\) −4.59220 7.95393i −0.231059 0.400205i
\(396\) −6.04329 + 0.503284i −0.303687 + 0.0252910i
\(397\) −1.48648 0.858221i −0.0746044 0.0430729i 0.462234 0.886758i \(-0.347048\pi\)
−0.536838 + 0.843685i \(0.680381\pi\)
\(398\) 24.6549 1.23584
\(399\) 0 0
\(400\) 3.82843 0.191421
\(401\) −0.242641 + 0.420266i −0.0121169 + 0.0209871i −0.872020 0.489470i \(-0.837190\pi\)
0.859903 + 0.510457i \(0.170524\pi\)
\(402\) 6.30864 + 10.9269i 0.314647 + 0.544984i
\(403\) 2.78272 1.60660i 0.138617 0.0800305i
\(404\) −8.31492 + 14.4019i −0.413683 + 0.716519i
\(405\) 0.185709i 0.00922796i
\(406\) 0 0
\(407\) −8.48528 + 18.0000i −0.420600 + 0.892227i
\(408\) 0 0
\(409\) 18.9259 + 32.7807i 0.935827 + 1.62090i 0.773152 + 0.634220i \(0.218679\pi\)
0.162675 + 0.986680i \(0.447988\pi\)
\(410\) 2.48528 + 4.30463i 0.122739 + 0.212591i
\(411\) −15.9079 9.18440i −0.784676 0.453033i
\(412\) 6.43996i 0.317274i
\(413\) 0 0
\(414\) 11.4142i 0.560978i
\(415\) −12.5446 7.24264i −0.615791 0.355527i
\(416\) 1.98848 1.14805i 0.0974933 0.0562878i
\(417\) −12.5446 + 7.24264i −0.614313 + 0.354674i
\(418\) −15.1040 + 10.4822i −0.738762 + 0.512700i
\(419\) 8.47343i 0.413954i −0.978346 0.206977i \(-0.933637\pi\)
0.978346 0.206977i \(-0.0663625\pi\)
\(420\) 0 0
\(421\) 17.6569 0.860542 0.430271 0.902700i \(-0.358418\pi\)
0.430271 + 0.902700i \(0.358418\pi\)
\(422\) 12.3640 21.4150i 0.601868 1.04247i
\(423\) 7.77359 4.48808i 0.377965 0.218218i
\(424\) 3.88437 2.24264i 0.188642 0.108912i
\(425\) 0 0
\(426\) −2.16478 −0.104884
\(427\) 0 0
\(428\) 12.7279i 0.615227i
\(429\) 6.77176 4.69959i 0.326944 0.226898i
\(430\) 3.97696 2.29610i 0.191786 0.110728i
\(431\) −2.15232 + 1.24264i −0.103673 + 0.0598559i −0.550940 0.834545i \(-0.685731\pi\)
0.447267 + 0.894401i \(0.352397\pi\)
\(432\) 4.52607 + 2.61313i 0.217760 + 0.125724i
\(433\) 22.6758i 1.08973i −0.838523 0.544866i \(-0.816581\pi\)
0.838523 0.544866i \(-0.183419\pi\)
\(434\) 0 0
\(435\) 2.05887i 0.0987155i
\(436\) 3.04384 + 1.75736i 0.145773 + 0.0841622i
\(437\) −17.3023 29.9685i −0.827683 1.43359i
\(438\) −8.48528 14.6969i −0.405442 0.702247i
\(439\) 3.24718 5.62427i 0.154979 0.268432i −0.778072 0.628175i \(-0.783802\pi\)
0.933051 + 0.359743i \(0.117136\pi\)
\(440\) 1.53073 3.24718i 0.0729749 0.154803i
\(441\) 0 0
\(442\) 0 0
\(443\) −11.3137 + 19.5959i −0.537531 + 0.931030i 0.461506 + 0.887137i \(0.347309\pi\)
−0.999036 + 0.0438929i \(0.986024\pi\)
\(444\) 5.62427 3.24718i 0.266916 0.154104i
\(445\) −1.92893 3.34101i −0.0914402 0.158379i
\(446\) 3.94689 6.83621i 0.186890 0.323704i
\(447\) 7.28225 0.344439
\(448\) 0 0
\(449\) −40.7279 −1.92207 −0.961035 0.276428i \(-0.910849\pi\)
−0.961035 + 0.276428i \(0.910849\pi\)
\(450\) 6.06218 + 3.50000i 0.285774 + 0.164992i
\(451\) −15.1781 + 1.26403i −0.714707 + 0.0595207i
\(452\) −0.707107 1.22474i −0.0332595 0.0576072i
\(453\) 3.24718 5.62427i 0.152566 0.264251i
\(454\) 0.951076i 0.0446362i
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) 27.2416 + 15.7279i 1.27431 + 0.735721i 0.975795 0.218685i \(-0.0701767\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(458\) 14.2409 + 24.6659i 0.665432 + 1.15256i
\(459\) 0 0
\(460\) 5.85172 + 3.37849i 0.272838 + 0.157523i
\(461\) −29.0614 −1.35352 −0.676762 0.736201i \(-0.736618\pi\)
−0.676762 + 0.736201i \(0.736618\pi\)
\(462\) 0 0
\(463\) −5.31371 −0.246949 −0.123474 0.992348i \(-0.539404\pi\)
−0.123474 + 0.992348i \(0.539404\pi\)
\(464\) −1.52192 0.878680i −0.0706533 0.0407917i
\(465\) −1.41987 + 0.819760i −0.0658447 + 0.0380155i
\(466\) 4.24264 + 7.34847i 0.196537 + 0.340411i
\(467\) −27.8663 16.0886i −1.28950 0.744493i −0.310935 0.950431i \(-0.600642\pi\)
−0.978565 + 0.205938i \(0.933976\pi\)
\(468\) 4.19825 0.194064
\(469\) 0 0
\(470\) 5.31371i 0.245103i
\(471\) −6.24264 + 10.8126i −0.287646 + 0.498217i
\(472\) −3.60266 6.24000i −0.165826 0.287219i
\(473\) 1.16781 + 14.0227i 0.0536959 + 0.644765i
\(474\) −7.95393 4.59220i −0.365336 0.210927i
\(475\) 21.2220 0.973734
\(476\) 0 0
\(477\) 8.20101 0.375498
\(478\) −13.2426 + 22.9369i −0.605704 + 1.04911i
\(479\) 4.59220 + 7.95393i 0.209823 + 0.363424i 0.951659 0.307158i \(-0.0993779\pi\)
−0.741836 + 0.670582i \(0.766045\pi\)
\(480\) −1.01461 + 0.585786i −0.0463105 + 0.0267374i
\(481\) 6.88830 11.9309i 0.314080 0.544002i
\(482\) 4.59220i 0.209169i
\(483\) 0 0
\(484\) 7.00000 + 8.48528i 0.318182 + 0.385695i
\(485\) −4.65685 + 8.06591i −0.211457 + 0.366254i
\(486\) 7.74652 + 13.4174i 0.351389 + 0.608624i
\(487\) 1.22183 + 2.11626i 0.0553662 + 0.0958971i 0.892380 0.451285i \(-0.149034\pi\)
−0.837014 + 0.547182i \(0.815701\pi\)
\(488\) −4.80062 2.77164i −0.217314 0.125466i
\(489\) 8.81298i 0.398537i
\(490\) 0 0
\(491\) 39.9411i 1.80252i −0.433281 0.901259i \(-0.642644\pi\)
0.433281 0.901259i \(-0.357356\pi\)
\(492\) 4.30463 + 2.48528i 0.194068 + 0.112045i
\(493\) 0 0
\(494\) 11.0227 6.36396i 0.495935 0.286328i
\(495\) 5.39248 3.74237i 0.242374 0.168207i
\(496\) 1.39942i 0.0628357i
\(497\) 0 0
\(498\) −14.4853 −0.649101
\(499\) −14.3137 + 24.7921i −0.640770 + 1.10985i 0.344492 + 0.938789i \(0.388051\pi\)
−0.985261 + 0.171056i \(0.945282\pi\)
\(500\) −8.27558 + 4.77791i −0.370095 + 0.213675i
\(501\) −19.0016 + 10.9706i −0.848928 + 0.490129i
\(502\) −6.08447 + 10.5386i −0.271563 + 0.470361i
\(503\) −6.49435 −0.289569 −0.144784 0.989463i \(-0.546249\pi\)
−0.144784 + 0.989463i \(0.546249\pi\)
\(504\) 0 0
\(505\) 18.0000i 0.800989i
\(506\) −17.0096 + 11.8046i −0.756169 + 0.524780i
\(507\) 7.24399 4.18232i 0.321717 0.185743i
\(508\) 5.19615 3.00000i 0.230542 0.133103i
\(509\) −28.0938 16.2200i −1.24523 0.718937i −0.275080 0.961421i \(-0.588704\pi\)
−0.970155 + 0.242485i \(0.922038\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 25.0892 + 14.4853i 1.10772 + 0.639541i
\(514\) −11.0209 19.0888i −0.486111 0.841969i
\(515\) 3.48528 + 6.03668i 0.153580 + 0.266008i
\(516\) 2.29610 3.97696i 0.101080 0.175076i
\(517\) −14.7277 6.94269i −0.647723 0.305339i
\(518\) 0 0
\(519\) 27.9411i 1.22648i
\(520\) −1.24264 + 2.15232i −0.0544934 + 0.0943853i
\(521\) −24.5522 + 14.1752i −1.07565 + 0.621028i −0.929720 0.368267i \(-0.879951\pi\)
−0.145931 + 0.989295i \(0.546618\pi\)
\(522\) −1.60660 2.78272i −0.0703190 0.121796i
\(523\) 0.475538 0.823656i 0.0207938 0.0360160i −0.855441 0.517900i \(-0.826714\pi\)
0.876235 + 0.481884i \(0.160047\pi\)
\(524\) 6.88830 0.300917
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) −0.297934 3.57750i −0.0129659 0.155691i
\(529\) −7.98528 13.8309i −0.347186 0.601344i
\(530\) −2.42742 + 4.20441i −0.105440 + 0.182628i
\(531\) 13.1744i 0.571721i
\(532\) 0 0
\(533\) 10.5442 0.456718
\(534\) −3.34101 1.92893i −0.144580 0.0834731i
\(535\) 6.88830 + 11.9309i 0.297807 + 0.515817i
\(536\) 10.0951 5.82843i 0.436043 0.251750i
\(537\) −5.30262 3.06147i −0.228825 0.132112i
\(538\) −3.50981 −0.151319
\(539\) 0 0
\(540\) −5.65685 −0.243432
\(541\) 9.50079 + 5.48528i 0.408471 + 0.235831i 0.690132 0.723683i \(-0.257552\pi\)
−0.281662 + 0.959514i \(0.590886\pi\)
\(542\) 23.1794 13.3827i 0.995642 0.574834i
\(543\) −11.0711 19.1757i −0.475105 0.822906i
\(544\) 0 0
\(545\) −3.80430 −0.162958
\(546\) 0 0
\(547\) 24.0000i 1.02617i 0.858339 + 0.513083i \(0.171497\pi\)
−0.858339 + 0.513083i \(0.828503\pi\)
\(548\) −8.48528 + 14.6969i −0.362473 + 0.627822i
\(549\) −5.06774 8.77758i −0.216286 0.374618i
\(550\) −1.05379 12.6537i −0.0449339 0.539554i
\(551\) −8.43641 4.87076i −0.359403 0.207502i
\(552\) 6.75699 0.287596
\(553\) 0 0
\(554\) −18.7279 −0.795673
\(555\) −3.51472 + 6.08767i −0.149191 + 0.258407i
\(556\) 6.69133 + 11.5897i 0.283775 + 0.491514i
\(557\) −5.19615 + 3.00000i −0.220168 + 0.127114i −0.606028 0.795443i \(-0.707238\pi\)
0.385860 + 0.922557i \(0.373905\pi\)
\(558\) 1.27937 2.21593i 0.0541599 0.0938077i
\(559\) 9.74153i 0.412023i
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 10.3923i 0.253095 0.438373i
\(563\) 13.5796 + 23.5206i 0.572313 + 0.991275i 0.996328 + 0.0856201i \(0.0272871\pi\)
−0.424015 + 0.905655i \(0.639380\pi\)
\(564\) 2.65685 + 4.60181i 0.111874 + 0.193771i
\(565\) 1.32565 + 0.765367i 0.0557707 + 0.0321992i
\(566\) 22.5671i 0.948564i
\(567\) 0 0
\(568\) 2.00000i 0.0839181i
\(569\) 25.9808 + 15.0000i 1.08917 + 0.628833i 0.933355 0.358954i \(-0.116866\pi\)
0.155815 + 0.987786i \(0.450200\pi\)
\(570\) −5.62427 + 3.24718i −0.235575 + 0.136009i
\(571\) −31.1769 + 18.0000i −1.30471 + 0.753277i −0.981209 0.192950i \(-0.938194\pi\)
−0.323505 + 0.946227i \(0.604861\pi\)
\(572\) −4.34186 6.25629i −0.181542 0.261589i
\(573\) 1.90215i 0.0794635i
\(574\) 0 0
\(575\) 23.8995 0.996678
\(576\) 0.914214 1.58346i 0.0380922 0.0659777i
\(577\) 28.7566 16.6026i 1.19715 0.691177i 0.237234 0.971453i \(-0.423759\pi\)
0.959919 + 0.280276i \(0.0904259\pi\)
\(578\) 14.7224 8.50000i 0.612372 0.353553i
\(579\) −1.34502 + 2.32965i −0.0558973 + 0.0968170i
\(580\) 1.90215 0.0789826
\(581\) 0 0
\(582\) 9.31371i 0.386066i
\(583\) −8.48153 12.2212i −0.351269 0.506152i
\(584\) −13.5782 + 7.83938i −0.561870 + 0.324396i
\(585\) −3.93535 + 2.27208i −0.162707 + 0.0939389i
\(586\) −0.823656 0.475538i −0.0340249 0.0196443i
\(587\) 37.0321i 1.52848i −0.644933 0.764239i \(-0.723115\pi\)
0.644933 0.764239i \(-0.276885\pi\)
\(588\) 0 0
\(589\) 7.75736i 0.319636i
\(590\) 6.75412 + 3.89949i 0.278063 + 0.160540i
\(591\) −11.0866 19.2025i −0.456040 0.789884i
\(592\) −3.00000 5.19615i −0.123299 0.213561i
\(593\) −14.3337 + 24.8268i −0.588616 + 1.01951i 0.405798 + 0.913963i \(0.366994\pi\)
−0.994414 + 0.105550i \(0.966340\pi\)
\(594\) 7.39104 15.6788i 0.303258 0.643307i
\(595\) 0 0
\(596\) 6.72792i 0.275586i
\(597\) −13.3431 + 23.1110i −0.546099 + 0.945871i
\(598\) 12.4134 7.16687i 0.507621 0.293075i
\(599\) 13.0000 + 22.5167i 0.531166 + 0.920006i 0.999338 + 0.0363689i \(0.0115791\pi\)
−0.468173 + 0.883637i \(0.655088\pi\)
\(600\) −2.07193 + 3.58869i −0.0845862 + 0.146508i
\(601\) 35.9497 1.46642 0.733210 0.680003i \(-0.238021\pi\)
0.733210 + 0.680003i \(0.238021\pi\)
\(602\) 0 0
\(603\) 21.3137 0.867961
\(604\) −5.19615 3.00000i −0.211428 0.122068i
\(605\) −11.1539 4.16555i −0.453469 0.169354i
\(606\) −9.00000 15.5885i −0.365600 0.633238i
\(607\) 23.1242 40.0523i 0.938582 1.62567i 0.170463 0.985364i \(-0.445474\pi\)
0.768119 0.640307i \(-0.221193\pi\)
\(608\) 5.54328i 0.224810i
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) 9.76191 + 5.63604i 0.394924 + 0.228010i
\(612\) 0 0
\(613\) 11.9142 6.87868i 0.481211 0.277827i −0.239710 0.970845i \(-0.577052\pi\)
0.720921 + 0.693017i \(0.243719\pi\)
\(614\) −6.44793 3.72271i −0.260217 0.150237i
\(615\) −5.38010 −0.216947
\(616\) 0 0
\(617\) 1.41421 0.0569341 0.0284670 0.999595i \(-0.490937\pi\)
0.0284670 + 0.999595i \(0.490937\pi\)
\(618\) 6.03668 + 3.48528i 0.242831 + 0.140199i
\(619\) −1.48648 + 0.858221i −0.0597468 + 0.0344948i −0.529576 0.848263i \(-0.677649\pi\)
0.469829 + 0.882757i \(0.344316\pi\)
\(620\) 0.757359 + 1.31178i 0.0304163 + 0.0526825i
\(621\) 28.2546 + 16.3128i 1.13382 + 0.654610i
\(622\) −33.3910 −1.33886
\(623\) 0 0
\(624\) 2.48528i 0.0994909i
\(625\) −4.39949 + 7.62015i −0.175980 + 0.304806i
\(626\) 5.16059 + 8.93841i 0.206259 + 0.357251i
\(627\) −1.65153 19.8311i −0.0659558 0.791978i
\(628\) 9.98951 + 5.76745i 0.398625 + 0.230146i
\(629\) 0 0
\(630\) 0 0
\(631\) 15.2132 0.605628 0.302814 0.953050i \(-0.402074\pi\)
0.302814 + 0.953050i \(0.402074\pi\)
\(632\) −4.24264 + 7.34847i −0.168763 + 0.292306i
\(633\) 13.3827 + 23.1794i 0.531913 + 0.921300i
\(634\) 19.8931 11.4853i 0.790056 0.456139i
\(635\) −3.24718 + 5.62427i −0.128860 + 0.223193i
\(636\) 4.85483i 0.192507i
\(637\) 0 0
\(638\) −2.48528 + 5.27208i −0.0983932 + 0.208724i
\(639\) −1.82843 + 3.16693i −0.0723315 + 0.125282i
\(640\) 0.541196 + 0.937379i 0.0213927 + 0.0370532i
\(641\) −1.39340 2.41344i −0.0550359 0.0953250i 0.837195 0.546905i \(-0.184194\pi\)
−0.892231 + 0.451580i \(0.850861\pi\)
\(642\) 11.9309 + 6.88830i 0.470875 + 0.271860i
\(643\) 5.04054i 0.198780i −0.995049 0.0993898i \(-0.968311\pi\)
0.995049 0.0993898i \(-0.0316891\pi\)
\(644\) 0 0
\(645\) 4.97056i 0.195716i
\(646\) 0 0
\(647\) 3.08669 1.78210i 0.121350 0.0700616i −0.438096 0.898928i \(-0.644347\pi\)
0.559446 + 0.828866i \(0.311014\pi\)
\(648\) −0.148586 + 0.0857864i −0.00583703 + 0.00337001i
\(649\) −19.6327 + 13.6251i −0.770650 + 0.534830i
\(650\) 8.79045i 0.344790i
\(651\) 0 0
\(652\) 8.14214 0.318871
\(653\) −10.7279 + 18.5813i −0.419816 + 0.727143i −0.995921 0.0902333i \(-0.971239\pi\)
0.576105 + 0.817376i \(0.304572\pi\)
\(654\) −3.29462 + 1.90215i −0.128830 + 0.0743800i
\(655\) −6.45695 + 3.72792i −0.252294 + 0.145662i
\(656\) 2.29610 3.97696i 0.0896477 0.155274i
\(657\) −28.6675 −1.11842
\(658\) 0 0
\(659\) 9.21320i 0.358895i 0.983768 + 0.179448i \(0.0574311\pi\)
−0.983768 + 0.179448i \(0.942569\pi\)
\(660\) 2.21541 + 3.19224i 0.0862347 + 0.124258i
\(661\) −28.9645 + 16.7227i −1.12659 + 0.650437i −0.943075 0.332580i \(-0.892081\pi\)
−0.183515 + 0.983017i \(0.558748\pi\)
\(662\) −17.7408 + 10.2426i −0.689515 + 0.398092i
\(663\) 0 0
\(664\) 13.3827i 0.519348i
\(665\) 0 0
\(666\) 10.9706i 0.425101i
\(667\) −9.50079 5.48528i −0.367872 0.212391i
\(668\) 10.1355 + 17.5552i 0.392153 + 0.679230i
\(669\) 4.27208 + 7.39946i 0.165168 + 0.286079i
\(670\) −6.30864 + 10.9269i −0.243724 + 0.422143i
\(671\) −7.83938 + 16.6298i −0.302636 + 0.641988i
\(672\) 0 0
\(673\) 45.9411i 1.77090i −0.464734 0.885450i \(-0.653850\pi\)
0.464734 0.885450i \(-0.346150\pi\)
\(674\) 13.2426 22.9369i 0.510087 0.883497i
\(675\) −17.3277 + 10.0042i −0.666944 + 0.385060i
\(676\) −3.86396 6.69258i −0.148614 0.257407i
\(677\) −9.93850 + 17.2140i −0.381968 + 0.661588i −0.991343 0.131294i \(-0.958087\pi\)
0.609376 + 0.792882i \(0.291420\pi\)
\(678\) 1.53073 0.0587875
\(679\) 0 0
\(680\) 0 0
\(681\) 0.891519 + 0.514719i 0.0341631 + 0.0197241i
\(682\) −4.62533 + 0.385197i −0.177113 + 0.0147499i
\(683\) 12.0000 + 20.7846i 0.459167 + 0.795301i 0.998917 0.0465244i \(-0.0148145\pi\)
−0.539750 + 0.841825i \(0.681481\pi\)
\(684\) 5.06774 8.77758i 0.193770 0.335619i
\(685\) 18.3688i 0.701836i
\(686\) 0 0
\(687\) −30.8284 −1.17618
\(688\) −3.67423 2.12132i −0.140079 0.0808746i
\(689\) 5.14933 + 8.91890i 0.196174 + 0.339783i
\(690\) −6.33386 + 3.65685i −0.241126 + 0.139214i
\(691\) 3.68290 + 2.12632i 0.140104 + 0.0808891i 0.568414 0.822743i \(-0.307557\pi\)
−0.428310 + 0.903632i \(0.640891\pi\)
\(692\) −25.8142 −0.981310
\(693\) 0 0
\(694\) −7.75736 −0.294465
\(695\) −12.5446 7.24264i −0.475845 0.274729i
\(696\) 1.64731 0.951076i 0.0624412 0.0360504i
\(697\) 0 0
\(698\) −25.1679 14.5307i −0.952620 0.549995i
\(699\) −9.18440 −0.347386
\(700\) 0 0
\(701\) 39.9411i 1.50856i 0.656555 + 0.754278i \(0.272013\pi\)
−0.656555 + 0.754278i \(0.727987\pi\)
\(702\) −6.00000 + 10.3923i −0.226455 + 0.392232i
\(703\) −16.6298 28.8037i −0.627206 1.08635i
\(704\) −3.30518 + 0.275255i −0.124569 + 0.0103741i
\(705\) −4.98096 2.87576i −0.187594 0.108307i
\(706\) 1.21371 0.0456785
\(707\) 0 0
\(708\) 7.79899 0.293104
\(709\) 11.6569 20.1903i 0.437782 0.758261i −0.559736 0.828671i \(-0.689097\pi\)
0.997518 + 0.0704099i \(0.0224307\pi\)
\(710\) −1.08239 1.87476i −0.0406215 0.0703584i
\(711\) −13.4361 + 7.75736i −0.503895 + 0.290924i
\(712\) −1.78210 + 3.08669i −0.0667871 + 0.115679i
\(713\) 8.73606i 0.327168i
\(714\) 0 0
\(715\) 7.45584 + 3.51472i 0.278833 + 0.131443i
\(716\) −2.82843 + 4.89898i −0.105703 + 0.183083i
\(717\) −14.3337 24.8268i −0.535303 0.927172i
\(718\) 1.24264 + 2.15232i 0.0463749 + 0.0803237i
\(719\) −20.0927 11.6006i −0.749333 0.432628i 0.0761198 0.997099i \(-0.475747\pi\)
−0.825453 + 0.564471i \(0.809080\pi\)
\(720\) 1.97908i 0.0737558i
\(721\) 0 0
\(722\) 11.7279i 0.436468i
\(723\) 4.30463 + 2.48528i 0.160091 + 0.0924286i
\(724\) −17.7160 + 10.2283i −0.658410 + 0.380133i
\(725\) 5.82655 3.36396i 0.216393 0.124934i
\(726\) −11.7423 + 1.96945i −0.435798 + 0.0730932i
\(727\) 25.9999i 0.964285i −0.876093 0.482142i \(-0.839859\pi\)
0.876093 0.482142i \(-0.160141\pi\)
\(728\) 0 0
\(729\) −17.2843 −0.640158
\(730\) 8.48528 14.6969i 0.314054 0.543958i
\(731\) 0 0
\(732\) 5.19615 3.00000i 0.192055 0.110883i
\(733\) −0.475538 + 0.823656i −0.0175644 + 0.0304224i −0.874674 0.484712i \(-0.838925\pi\)
0.857110 + 0.515134i \(0.172258\pi\)
\(734\) −11.1409 −0.411220
\(735\) 0 0
\(736\) 6.24264i 0.230107i
\(737\) −22.0428 31.7620i −0.811955 1.16997i
\(738\) 7.27159 4.19825i 0.267671 0.154540i
\(739\) −20.7846 + 12.0000i −0.764574 + 0.441427i −0.830936 0.556369i \(-0.812194\pi\)
0.0663614 + 0.997796i \(0.478861\pi\)
\(740\) 5.62427 + 3.24718i 0.206752 + 0.119369i
\(741\) 13.7766i 0.506096i
\(742\) 0 0
\(743\) 36.4264i 1.33636i 0.744002 + 0.668178i \(0.232925\pi\)
−0.744002 + 0.668178i \(0.767075\pi\)
\(744\) 1.31178 + 0.757359i 0.0480924 + 0.0277661i
\(745\) 3.64113 + 6.30661i 0.133401 + 0.231056i
\(746\) 10.2426 + 17.7408i 0.375010 + 0.649536i
\(747\) −12.2346 + 21.1910i −0.447641 + 0.775337i
\(748\) 0 0
\(749\) 0 0
\(750\) 10.3431i 0.377678i
\(751\) −9.70711 + 16.8132i −0.354217 + 0.613522i −0.986984 0.160820i \(-0.948586\pi\)
0.632766 + 0.774343i \(0.281919\pi\)
\(752\) 4.25151 2.45461i 0.155037 0.0895105i
\(753\) −6.58579 11.4069i −0.239999 0.415691i
\(754\) 2.01754 3.49448i 0.0734744 0.127261i
\(755\) 6.49435 0.236354
\(756\) 0 0
\(757\) −38.1421 −1.38630 −0.693150 0.720794i \(-0.743778\pi\)
−0.693150 + 0.720794i \(0.743778\pi\)
\(758\) −10.0951 5.82843i −0.366672 0.211698i
\(759\) −1.85989 22.3331i −0.0675099 0.810639i
\(760\) 3.00000 + 5.19615i 0.108821 + 0.188484i
\(761\) 14.3337 24.8268i 0.519597 0.899969i −0.480143 0.877190i \(-0.659415\pi\)
0.999741 0.0227789i \(-0.00725137\pi\)
\(762\) 6.49435i 0.235266i
\(763\) 0 0
\(764\) 1.75736 0.0635790
\(765\) 0 0
\(766\) −7.23252 12.5271i −0.261322 0.452622i
\(767\) 14.3277 8.27208i 0.517342 0.298687i
\(768\) 0.937379 + 0.541196i 0.0338248 + 0.0195287i
\(769\) 6.49435 0.234192 0.117096 0.993121i \(-0.462641\pi\)
0.117096 + 0.993121i \(0.462641\pi\)
\(770\) 0 0
\(771\) 23.8579 0.859220
\(772\) 2.15232 + 1.24264i 0.0774636 + 0.0447236i
\(773\) −22.2421 + 12.8415i −0.799991 + 0.461875i −0.843468 0.537179i \(-0.819490\pi\)
0.0434768 + 0.999054i \(0.486157\pi\)
\(774\) −3.87868 6.71807i −0.139416 0.241476i
\(775\) 4.63979 + 2.67878i 0.166666 + 0.0962248i
\(776\) 8.60474 0.308892
\(777\) 0 0
\(778\) 32.0000i 1.14726i
\(779\) 12.7279 22.0454i 0.456025 0.789859i
\(780\) −1.34502 2.32965i −0.0481596 0.0834149i
\(781\) 6.61037 0.550510i 0.236537 0.0196988i
\(782\) 0 0
\(783\) 9.18440 0.328224
\(784\) 0 0
\(785\) −12.4853 −0.445619
\(786\) −3.72792 + 6.45695i −0.132971 + 0.230312i
\(787\) 4.39523 + 7.61276i 0.156673 + 0.271365i 0.933667 0.358143i \(-0.116590\pi\)
−0.776994 + 0.629508i \(0.783256\pi\)
\(788\) −17.7408 + 10.2426i −0.631989 + 0.364879i
\(789\) −12.9887 + 22.4971i −0.462410 + 0.800918i
\(790\) 9.18440i 0.326766i
\(791\) 0 0
\(792\) −5.48528 2.58579i −0.194911 0.0918819i
\(793\) 6.36396 11.0227i 0.225991 0.391428i
\(794\) −0.858221 1.48648i −0.0304571 0.0527533i
\(795\) −2.62742 4.55082i −0.0931849 0.161401i
\(796\) 21.3518 + 12.3275i 0.756794 + 0.436935i
\(797\) 26.0543i 0.922892i 0.887168 + 0.461446i \(0.152669\pi\)
−0.887168 + 0.461446i \(0.847331\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 3.31552 + 1.91421i 0.117221 + 0.0676777i
\(801\) −5.64379 + 3.25844i −0.199413 + 0.115131i
\(802\) −0.420266 + 0.242641i −0.0148401 + 0.00856794i
\(803\) 29.6480 + 42.7206i 1.04626 + 1.50758i
\(804\) 12.6173i 0.444977i
\(805\) 0 0
\(806\) 3.21320 0.113180
\(807\) 1.89949 3.29002i 0.0668654 0.115814i
\(808\) −14.4019 + 8.31492i −0.506656 + 0.292518i
\(809\) 12.5446 7.24264i 0.441045 0.254638i −0.262996 0.964797i \(-0.584710\pi\)
0.704041 + 0.710159i \(0.251377\pi\)
\(810\) 0.0928546 0.160829i 0.00326258 0.00565095i
\(811\) 6.88830 0.241881 0.120940 0.992660i \(-0.461409\pi\)
0.120940 + 0.992660i \(0.461409\pi\)
\(812\) 0 0
\(813\) 28.9706i 1.01604i
\(814\) −16.3485 + 11.3458i −0.573014 + 0.397671i
\(815\) −7.63227 + 4.40649i −0.267347 + 0.154353i
\(816\) 0 0
\(817\) −20.3673 11.7591i −0.712562 0.411398i
\(818\) 37.8519i 1.32346i
\(819\) 0 0
\(820\) 4.97056i 0.173580i
\(821\) 11.9142 + 6.87868i 0.415809 + 0.240068i 0.693283 0.720666i \(-0.256164\pi\)
−0.277473 + 0.960733i \(0.589497\pi\)
\(822\) −9.18440 15.9079i −0.320343 0.554850i
\(823\) −4.39340 7.60959i −0.153144 0.265254i 0.779238 0.626729i \(-0.215607\pi\)
−0.932382 + 0.361475i \(0.882273\pi\)
\(824\) 3.21998 5.57717i 0.112173 0.194290i
\(825\) 12.4316 + 5.86030i 0.432812 + 0.204030i
\(826\) 0 0
\(827\) 16.9706i 0.590124i 0.955478 + 0.295062i \(0.0953404\pi\)
−0.955478 + 0.295062i \(0.904660\pi\)
\(828\) 5.70711 9.88500i 0.198336 0.343527i
\(829\) 19.0416 10.9937i 0.661344 0.381827i −0.131445 0.991323i \(-0.541962\pi\)
0.792789 + 0.609496i \(0.208628\pi\)
\(830\) −7.24264 12.5446i −0.251396 0.435430i
\(831\) 10.1355 17.5552i 0.351596 0.608982i
\(832\) 2.29610 0.0796030
\(833\) 0 0
\(834\) −14.4853 −0.501584
\(835\) −19.0016 10.9706i −0.657577 0.379652i
\(836\) −18.3215 + 1.52582i −0.633664 + 0.0527714i
\(837\) 3.65685 + 6.33386i 0.126399 + 0.218930i
\(838\) 4.23671 7.33820i 0.146355 0.253494i
\(839\) 27.0823i 0.934986i 0.883997 + 0.467493i \(0.154843\pi\)
−0.883997 + 0.467493i \(0.845157\pi\)
\(840\) 0 0
\(841\) 25.9117 0.893506
\(842\) 15.2913 + 8.82843i 0.526972 + 0.304248i
\(843\) 6.49435 + 11.2485i 0.223677 + 0.387421i
\(844\) 21.4150 12.3640i 0.737135 0.425585i
\(845\) 7.24399 + 4.18232i 0.249201 + 0.143876i
\(846\) 8.97616 0.308607
\(847\) 0 0
\(848\) 4.48528 0.154025
\(849\) 21.1539 + 12.2132i 0.726000 + 0.419156i
\(850\) 0 0
\(851\) −18.7279 32.4377i −0.641985 1.11195i
\(852\) −1.87476 1.08239i −0.0642282 0.0370821i
\(853\) −5.54328 −0.189798 −0.0948991 0.995487i \(-0.530253\pi\)
−0.0948991 + 0.995487i \(0.530253\pi\)
\(854\) 0 0
\(855\) 10.9706i 0.375185i
\(856\) 6.36396 11.0227i 0.217516 0.376748i
\(857\) 0.951076 + 1.64731i 0.0324881 + 0.0562711i 0.881812 0.471601i \(-0.156324\pi\)
−0.849324 + 0.527872i \(0.822990\pi\)
\(858\) 8.21431 0.684086i 0.280432 0.0233543i
\(859\) −9.98951 5.76745i −0.340838 0.196783i 0.319805 0.947483i \(-0.396383\pi\)
−0.660642 + 0.750701i \(0.729716\pi\)
\(860\) 4.59220 0.156593
\(861\) 0 0
\(862\) −2.48528 −0.0846490
\(863\) 15.3640 26.6112i 0.522995 0.905854i −0.476647 0.879095i \(-0.658148\pi\)
0.999642 0.0267595i \(-0.00851881\pi\)
\(864\) 2.61313 + 4.52607i 0.0889003 + 0.153980i
\(865\) 24.1977 13.9706i 0.822747 0.475013i
\(866\) 11.3379 19.6379i 0.385278 0.667322i
\(867\) 18.4007i 0.624919i
\(868\) 0 0
\(869\) 25.4558 + 12.0000i 0.863530 + 0.407072i
\(870\) −1.02944 + 1.78304i −0.0349012 + 0.0604506i
\(871\) 13.3827 + 23.1794i 0.453454 + 0.785405i
\(872\) 1.75736 + 3.04384i 0.0595117 + 0.103077i
\(873\) 13.6253 + 7.86657i 0.461147 + 0.266243i
\(874\) 34.6047i 1.17052i
\(875\) 0 0
\(876\) 16.9706i 0.573382i
\(877\) −46.7654 27.0000i −1.57915 0.911725i −0.994977 0.100099i \(-0.968084\pi\)
−0.584177 0.811626i \(-0.698583\pi\)
\(878\) 5.62427 3.24718i 0.189810 0.109587i
\(879\) 0.891519 0.514719i 0.0300702 0.0173610i
\(880\) 2.94924 2.04677i 0.0994189 0.0689966i
\(881\) 31.4888i 1.06089i 0.847721 + 0.530443i \(0.177974\pi\)
−0.847721 + 0.530443i \(0.822026\pi\)
\(882\) 0 0
\(883\) −42.4264 −1.42776 −0.713881 0.700267i \(-0.753064\pi\)
−0.713881 + 0.700267i \(0.753064\pi\)
\(884\) 0 0
\(885\) −7.31061 + 4.22078i −0.245743 + 0.141880i
\(886\) −19.5959 + 11.3137i −0.658338 + 0.380091i
\(887\) −4.59220 + 7.95393i −0.154191 + 0.267067i −0.932764 0.360487i \(-0.882610\pi\)
0.778573 + 0.627554i \(0.215944\pi\)
\(888\) 6.49435 0.217936
\(889\) 0 0
\(890\) 3.85786i 0.129316i
\(891\) 0.324439 + 0.467492i 0.0108691 + 0.0156616i
\(892\) 6.83621 3.94689i 0.228893 0.132151i
\(893\) 23.5673 13.6066i 0.788650 0.455328i
\(894\) 6.30661 + 3.64113i 0.210925 + 0.121777i
\(895\) 6.12293i 0.204667i
\(896\) 0 0
\(897\) 15.5147i 0.518021i
\(898\) −35.2714 20.3640i −1.17702 0.679554i
\(899\) −1.22964 2.12980i −0.0410108 0.0710328i
\(900\) 3.50000 + 6.06218i 0.116667 + 0.202073i
\(901\) 0 0
\(902\) −13.7766 6.49435i −0.458711 0.216238i
\(903\) 0 0
\(904\) 1.41421i 0.0470360i
\(905\) 11.0711 19.1757i 0.368015 0.637420i
\(906\) 5.62427 3.24718i 0.186854 0.107880i
\(907\) 0.899495 + 1.55797i 0.0298672 + 0.0517316i 0.880573 0.473911i \(-0.157158\pi\)
−0.850705 + 0.525643i \(0.823825\pi\)
\(908\) 0.475538 0.823656i 0.0157813 0.0273340i
\(909\) −30.4064 −1.00852
\(910\) 0 0
\(911\) 38.2426 1.26704 0.633518 0.773728i \(-0.281610\pi\)
0.633518 + 0.773728i \(0.281610\pi\)
\(912\) 5.19615 + 3.00000i 0.172062 + 0.0993399i
\(913\) 44.2321 3.68364i 1.46387 0.121911i
\(914\) 15.7279 + 27.2416i 0.520233 + 0.901071i
\(915\) −3.24718 + 5.62427i −0.107348 + 0.185933i
\(916\) 28.4818i 0.941064i
\(917\) 0 0
\(918\) 0 0
\(919\) 26.3500 + 15.2132i 0.869208 + 0.501837i 0.867085 0.498160i \(-0.165991\pi\)
0.00212280 + 0.999998i \(0.499324\pi\)
\(920\) 3.37849 + 5.85172i 0.111386 + 0.192926i
\(921\) 6.97919 4.02944i 0.229972 0.132774i
\(922\) −25.1679 14.5307i −0.828861 0.478543i
\(923\) −4.59220 −0.151154
\(924\) 0 0
\(925\) 22.9706 0.755267
\(926\) −4.60181 2.65685i −0.151225 0.0873096i
\(927\) 10.1974 5.88750i 0.334928 0.193371i
\(928\) −0.878680 1.52192i −0.0288441 0.0499594i
\(929\) 36.5497 + 21.1020i 1.19916 + 0.692334i 0.960367 0.278738i \(-0.0899160\pi\)
0.238790 + 0.971071i \(0.423249\pi\)
\(930\) −1.63952 −0.0537620
\(931\) 0 0
\(932\) 8.48528i 0.277945i
\(933\) 18.0711 31.3000i 0.591620 1.02472i
\(934\) −16.0886 27.8663i −0.526436 0.911814i
\(935\) 0 0
\(936\) 3.63579 + 2.09913i 0.118840 + 0.0686121i
\(937\) 35.9497 1.17443 0.587213 0.809432i \(-0.300225\pi\)
0.587213 + 0.809432i \(0.300225\pi\)
\(938\) 0 0
\(939\) −11.1716 −0.364571
\(940\) −2.65685 + 4.60181i −0.0866570 + 0.150094i
\(941\) −20.0740 34.7692i −0.654393 1.13344i −0.982046 0.188644i \(-0.939591\pi\)
0.327652 0.944798i \(-0.393742\pi\)
\(942\) −10.8126 + 6.24264i −0.352293 + 0.203396i
\(943\) 14.3337 24.8268i 0.466771 0.808470i
\(944\) 7.20533i 0.234513i
\(945\) 0 0
\(946\) −6.00000 + 12.7279i −0.195077 + 0.413820i
\(947\) 1.75736 3.04384i 0.0571065 0.0989114i −0.836059 0.548640i \(-0.815146\pi\)
0.893165 + 0.449728i \(0.148479\pi\)
\(948\) −4.59220 7.95393i −0.149148 0.258331i
\(949\) −18.0000 31.1769i −0.584305 1.01205i
\(950\) 18.3788 + 10.6110i 0.596288 + 0.344267i
\(951\) 24.8632i 0.806243i
\(952\) 0 0
\(953\) 45.9411i 1.48818i −0.668080 0.744090i \(-0.732884\pi\)
0.668080 0.744090i \(-0.267116\pi\)
\(954\) 7.10228 + 4.10051i 0.229945 + 0.132759i
\(955\) −1.64731 + 0.951076i −0.0533058 + 0.0307761i
\(956\) −22.9369 + 13.2426i −0.741833 + 0.428298i
\(957\) −3.59691 5.18288i −0.116272 0.167539i
\(958\) 9.18440i 0.296735i
\(959\) 0 0
\(960\) −1.17157 −0.0378124
\(961\) −14.5208 + 25.1508i −0.468413 + 0.811316i
\(962\) 11.9309 6.88830i 0.384667 0.222088i
\(963\) 20.1542 11.6360i 0.649460 0.374966i
\(964\) 2.29610 3.97696i 0.0739524 0.128089i
\(965\) −2.69005 −0.0865957
\(966\) 0 0
\(967\) 19.4558i 0.625658i −0.949810 0.312829i \(-0.898723\pi\)
0.949810 0.312829i \(-0.101277\pi\)
\(968\) 1.81954 + 10.8485i 0.0584821 + 0.348683i
\(969\) 0 0
\(970\) −8.06591 + 4.65685i −0.258981 + 0.149523i
\(971\) 31.3884 + 18.1221i 1.00730 + 0.581566i 0.910401 0.413728i \(-0.135774\pi\)
0.0969013 + 0.995294i \(0.469107\pi\)
\(972\) 15.4930i 0.496940i
\(973\) 0 0
\(974\) 2.44365i 0.0782996i
\(975\) −8.23999 4.75736i −0.263891 0.152357i
\(976\) −2.77164 4.80062i −0.0887180 0.153664i
\(977\) 22.1213 + 38.3153i 0.707724 + 1.22581i 0.965700 + 0.259662i \(0.0836112\pi\)
−0.257976 + 0.966151i \(0.583055\pi\)
\(978\) −4.40649 + 7.63227i −0.140904 + 0.244053i
\(979\) 10.6926 + 5.04054i 0.341737 + 0.161096i
\(980\) 0 0
\(981\) 6.42641i 0.205179i
\(982\) 19.9706 34.5900i 0.637286 1.10381i
\(983\) 38.9736 22.5014i 1.24306 0.717683i 0.273347 0.961915i \(-0.411869\pi\)
0.969717 + 0.244232i \(0.0785359\pi\)
\(984\) 2.48528 + 4.30463i 0.0792279 + 0.137227i
\(985\) 11.0866 19.2025i 0.353247 0.611842i
\(986\) 0 0
\(987\) 0 0
\(988\) 12.7279 0.404929
\(989\) −22.9369 13.2426i −0.729352 0.421091i
\(990\) 6.54121 0.544751i 0.207893 0.0173133i
\(991\) 28.7990 + 49.8813i 0.914830 + 1.58453i 0.807150 + 0.590347i \(0.201009\pi\)
0.107680 + 0.994186i \(0.465658\pi\)
\(992\) 0.699709 1.21193i 0.0222158 0.0384789i
\(993\) 22.1731i 0.703642i
\(994\) 0 0
\(995\) −26.6863 −0.846012
\(996\) −12.5446 7.24264i −0.397492 0.229492i
\(997\) −3.05020 5.28311i −0.0966009 0.167318i 0.813675 0.581320i \(-0.197464\pi\)
−0.910276 + 0.414003i \(0.864130\pi\)
\(998\) −24.7921 + 14.3137i −0.784779 + 0.453093i
\(999\) 27.1564 + 15.6788i 0.859191 + 0.496054i
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 1078.2.i.a.901.6 16
7.2 even 3 1078.2.c.a.1077.2 8
7.3 odd 6 inner 1078.2.i.a.1011.2 16
7.4 even 3 inner 1078.2.i.a.1011.3 16
7.5 odd 6 1078.2.c.a.1077.3 yes 8
7.6 odd 2 inner 1078.2.i.a.901.7 16
11.10 odd 2 inner 1078.2.i.a.901.2 16
77.10 even 6 inner 1078.2.i.a.1011.6 16
77.32 odd 6 inner 1078.2.i.a.1011.7 16
77.54 even 6 1078.2.c.a.1077.7 yes 8
77.65 odd 6 1078.2.c.a.1077.6 yes 8
77.76 even 2 inner 1078.2.i.a.901.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1078.2.c.a.1077.2 8 7.2 even 3
1078.2.c.a.1077.3 yes 8 7.5 odd 6
1078.2.c.a.1077.6 yes 8 77.65 odd 6
1078.2.c.a.1077.7 yes 8 77.54 even 6
1078.2.i.a.901.2 16 11.10 odd 2 inner
1078.2.i.a.901.3 16 77.76 even 2 inner
1078.2.i.a.901.6 16 1.1 even 1 trivial
1078.2.i.a.901.7 16 7.6 odd 2 inner
1078.2.i.a.1011.2 16 7.3 odd 6 inner
1078.2.i.a.1011.3 16 7.4 even 3 inner
1078.2.i.a.1011.6 16 77.10 even 6 inner
1078.2.i.a.1011.7 16 77.32 odd 6 inner