Properties

Label 720.2.t.c.181.6
Level $720$
Weight $2$
Character 720.181
Analytic conductor $5.749$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,2,Mod(181,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.181");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.t (of order \(4\), 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: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} - 112 x^{6} - 64 x^{5} + 112 x^{4} + 256 x^{2} - 512 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 181.6
Root \(1.21331 - 0.726558i\) of defining polynomial
Character \(\chi\) \(=\) 720.181
Dual form 720.2.t.c.541.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.376912 + 1.36306i) q^{2} +(-1.71587 + 1.02751i) q^{4} +(0.707107 + 0.707107i) q^{5} +4.50961i q^{7} +(-2.04729 - 1.95156i) q^{8} +O(q^{10})\) \(q+(0.376912 + 1.36306i) q^{2} +(-1.71587 + 1.02751i) q^{4} +(0.707107 + 0.707107i) q^{5} +4.50961i q^{7} +(-2.04729 - 1.95156i) q^{8} +(-0.697313 + 1.23035i) q^{10} +(1.64080 + 1.64080i) q^{11} +(1.51857 - 1.51857i) q^{13} +(-6.14687 + 1.69972i) q^{14} +(1.88845 - 3.52615i) q^{16} -1.45616 q^{17} +(-2.67964 + 2.67964i) q^{19} +(-1.93986 - 0.486749i) q^{20} +(-1.61808 + 2.85495i) q^{22} -2.37423i q^{23} +1.00000i q^{25} +(2.64228 + 1.49754i) q^{26} +(-4.63366 - 7.73792i) q^{28} +(-0.924966 + 0.924966i) q^{29} -7.20435 q^{31} +(5.51814 + 1.24503i) q^{32} +(-0.548843 - 1.98483i) q^{34} +(-3.18877 + 3.18877i) q^{35} +(-5.21123 - 5.21123i) q^{37} +(-4.66251 - 2.64253i) q^{38} +(-0.0676894 - 2.82762i) q^{40} +6.41166i q^{41} +(7.65800 + 7.65800i) q^{43} +(-4.50135 - 1.12947i) q^{44} +(3.23622 - 0.894875i) q^{46} +2.51027 q^{47} -13.3366 q^{49} +(-1.36306 + 0.376912i) q^{50} +(-1.04534 + 4.16603i) q^{52} +(-1.50312 - 1.50312i) q^{53} +2.32045i q^{55} +(8.80078 - 9.23248i) q^{56} +(-1.60942 - 0.912155i) q^{58} +(5.31807 + 5.31807i) q^{59} +(-1.02169 + 1.02169i) q^{61} +(-2.71541 - 9.81998i) q^{62} +(0.382800 + 7.99084i) q^{64} +2.14759 q^{65} +(5.22745 - 5.22745i) q^{67} +(2.49859 - 1.49622i) q^{68} +(-5.54838 - 3.14461i) q^{70} +1.92097i q^{71} -1.39412i q^{73} +(5.13905 - 9.06740i) q^{74} +(1.84458 - 7.35129i) q^{76} +(-7.39938 + 7.39938i) q^{77} +5.06317 q^{79} +(3.82870 - 1.15803i) q^{80} +(-8.73949 + 2.41663i) q^{82} +(2.44974 - 2.44974i) q^{83} +(-1.02966 - 1.02966i) q^{85} +(-7.55194 + 13.3247i) q^{86} +(-0.157070 - 6.56133i) q^{88} -9.36007i q^{89} +(6.84817 + 6.84817i) q^{91} +(2.43954 + 4.07388i) q^{92} +(0.946152 + 3.42166i) q^{94} -3.78959 q^{95} +18.6313 q^{97} +(-5.02671 - 18.1785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.376912 + 1.36306i 0.266517 + 0.963830i
\(3\) 0 0
\(4\) −1.71587 + 1.02751i −0.857937 + 0.513754i
\(5\) 0.707107 + 0.707107i 0.316228 + 0.316228i
\(6\) 0 0
\(7\) 4.50961i 1.70447i 0.523158 + 0.852236i \(0.324754\pi\)
−0.523158 + 0.852236i \(0.675246\pi\)
\(8\) −2.04729 1.95156i −0.723827 0.689982i
\(9\) 0 0
\(10\) −0.697313 + 1.23035i −0.220510 + 0.389070i
\(11\) 1.64080 + 1.64080i 0.494721 + 0.494721i 0.909790 0.415069i \(-0.136243\pi\)
−0.415069 + 0.909790i \(0.636243\pi\)
\(12\) 0 0
\(13\) 1.51857 1.51857i 0.421176 0.421176i −0.464432 0.885609i \(-0.653742\pi\)
0.885609 + 0.464432i \(0.153742\pi\)
\(14\) −6.14687 + 1.69972i −1.64282 + 0.454270i
\(15\) 0 0
\(16\) 1.88845 3.52615i 0.472113 0.881538i
\(17\) −1.45616 −0.353170 −0.176585 0.984285i \(-0.556505\pi\)
−0.176585 + 0.984285i \(0.556505\pi\)
\(18\) 0 0
\(19\) −2.67964 + 2.67964i −0.614752 + 0.614752i −0.944181 0.329428i \(-0.893144\pi\)
0.329428 + 0.944181i \(0.393144\pi\)
\(20\) −1.93986 0.486749i −0.433767 0.108840i
\(21\) 0 0
\(22\) −1.61808 + 2.85495i −0.344975 + 0.608678i
\(23\) 2.37423i 0.495061i −0.968880 0.247530i \(-0.920381\pi\)
0.968880 0.247530i \(-0.0796190\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) 2.64228 + 1.49754i 0.518193 + 0.293692i
\(27\) 0 0
\(28\) −4.63366 7.73792i −0.875679 1.46233i
\(29\) −0.924966 + 0.924966i −0.171762 + 0.171762i −0.787753 0.615991i \(-0.788756\pi\)
0.615991 + 0.787753i \(0.288756\pi\)
\(30\) 0 0
\(31\) −7.20435 −1.29394 −0.646970 0.762515i \(-0.723964\pi\)
−0.646970 + 0.762515i \(0.723964\pi\)
\(32\) 5.51814 + 1.24503i 0.975479 + 0.220092i
\(33\) 0 0
\(34\) −0.548843 1.98483i −0.0941259 0.340396i
\(35\) −3.18877 + 3.18877i −0.539001 + 0.539001i
\(36\) 0 0
\(37\) −5.21123 5.21123i −0.856720 0.856720i 0.134230 0.990950i \(-0.457144\pi\)
−0.990950 + 0.134230i \(0.957144\pi\)
\(38\) −4.66251 2.64253i −0.756359 0.428675i
\(39\) 0 0
\(40\) −0.0676894 2.82762i −0.0107026 0.447086i
\(41\) 6.41166i 1.00133i 0.865640 + 0.500667i \(0.166912\pi\)
−0.865640 + 0.500667i \(0.833088\pi\)
\(42\) 0 0
\(43\) 7.65800 + 7.65800i 1.16783 + 1.16783i 0.982716 + 0.185118i \(0.0592669\pi\)
0.185118 + 0.982716i \(0.440733\pi\)
\(44\) −4.50135 1.12947i −0.678604 0.170275i
\(45\) 0 0
\(46\) 3.23622 0.894875i 0.477155 0.131942i
\(47\) 2.51027 0.366161 0.183081 0.983098i \(-0.441393\pi\)
0.183081 + 0.983098i \(0.441393\pi\)
\(48\) 0 0
\(49\) −13.3366 −1.90522
\(50\) −1.36306 + 0.376912i −0.192766 + 0.0533034i
\(51\) 0 0
\(52\) −1.04534 + 4.16603i −0.144962 + 0.577724i
\(53\) −1.50312 1.50312i −0.206470 0.206470i 0.596295 0.802765i \(-0.296639\pi\)
−0.802765 + 0.596295i \(0.796639\pi\)
\(54\) 0 0
\(55\) 2.32045i 0.312889i
\(56\) 8.80078 9.23248i 1.17605 1.23374i
\(57\) 0 0
\(58\) −1.60942 0.912155i −0.211327 0.119772i
\(59\) 5.31807 + 5.31807i 0.692353 + 0.692353i 0.962749 0.270396i \(-0.0871546\pi\)
−0.270396 + 0.962749i \(0.587155\pi\)
\(60\) 0 0
\(61\) −1.02169 + 1.02169i −0.130815 + 0.130815i −0.769483 0.638668i \(-0.779486\pi\)
0.638668 + 0.769483i \(0.279486\pi\)
\(62\) −2.71541 9.81998i −0.344857 1.24714i
\(63\) 0 0
\(64\) 0.382800 + 7.99084i 0.0478499 + 0.998855i
\(65\) 2.14759 0.266375
\(66\) 0 0
\(67\) 5.22745 5.22745i 0.638635 0.638635i −0.311584 0.950219i \(-0.600859\pi\)
0.950219 + 0.311584i \(0.100859\pi\)
\(68\) 2.49859 1.49622i 0.302998 0.181443i
\(69\) 0 0
\(70\) −5.54838 3.14461i −0.663158 0.375853i
\(71\) 1.92097i 0.227978i 0.993482 + 0.113989i \(0.0363628\pi\)
−0.993482 + 0.113989i \(0.963637\pi\)
\(72\) 0 0
\(73\) 1.39412i 0.163169i −0.996666 0.0815847i \(-0.974002\pi\)
0.996666 0.0815847i \(-0.0259981\pi\)
\(74\) 5.13905 9.06740i 0.597403 1.05406i
\(75\) 0 0
\(76\) 1.84458 7.35129i 0.211587 0.843250i
\(77\) −7.39938 + 7.39938i −0.843237 + 0.843237i
\(78\) 0 0
\(79\) 5.06317 0.569651 0.284825 0.958579i \(-0.408064\pi\)
0.284825 + 0.958579i \(0.408064\pi\)
\(80\) 3.82870 1.15803i 0.428062 0.129471i
\(81\) 0 0
\(82\) −8.73949 + 2.41663i −0.965115 + 0.266872i
\(83\) 2.44974 2.44974i 0.268894 0.268894i −0.559761 0.828654i \(-0.689107\pi\)
0.828654 + 0.559761i \(0.189107\pi\)
\(84\) 0 0
\(85\) −1.02966 1.02966i −0.111682 0.111682i
\(86\) −7.55194 + 13.3247i −0.814347 + 1.43684i
\(87\) 0 0
\(88\) −0.157070 6.56133i −0.0167437 0.699440i
\(89\) 9.36007i 0.992165i −0.868275 0.496083i \(-0.834771\pi\)
0.868275 0.496083i \(-0.165229\pi\)
\(90\) 0 0
\(91\) 6.84817 + 6.84817i 0.717883 + 0.717883i
\(92\) 2.43954 + 4.07388i 0.254340 + 0.424731i
\(93\) 0 0
\(94\) 0.946152 + 3.42166i 0.0975882 + 0.352917i
\(95\) −3.78959 −0.388803
\(96\) 0 0
\(97\) 18.6313 1.89172 0.945859 0.324579i \(-0.105223\pi\)
0.945859 + 0.324579i \(0.105223\pi\)
\(98\) −5.02671 18.1785i −0.507774 1.83631i
\(99\) 0 0
\(100\) −1.02751 1.71587i −0.102751 0.171587i
\(101\) 4.84108 + 4.84108i 0.481705 + 0.481705i 0.905676 0.423971i \(-0.139364\pi\)
−0.423971 + 0.905676i \(0.639364\pi\)
\(102\) 0 0
\(103\) 9.12540i 0.899153i −0.893242 0.449576i \(-0.851575\pi\)
0.893242 0.449576i \(-0.148425\pi\)
\(104\) −6.07255 + 0.145369i −0.595463 + 0.0142546i
\(105\) 0 0
\(106\) 1.48230 2.61539i 0.143974 0.254029i
\(107\) 10.1505 + 10.1505i 0.981290 + 0.981290i 0.999828 0.0185385i \(-0.00590132\pi\)
−0.0185385 + 0.999828i \(0.505901\pi\)
\(108\) 0 0
\(109\) 1.35489 1.35489i 0.129775 0.129775i −0.639236 0.769011i \(-0.720749\pi\)
0.769011 + 0.639236i \(0.220749\pi\)
\(110\) −3.16291 + 0.874603i −0.301572 + 0.0833902i
\(111\) 0 0
\(112\) 15.9016 + 8.51618i 1.50256 + 0.804704i
\(113\) 2.56039 0.240861 0.120431 0.992722i \(-0.461572\pi\)
0.120431 + 0.992722i \(0.461572\pi\)
\(114\) 0 0
\(115\) 1.67883 1.67883i 0.156552 0.156552i
\(116\) 0.636716 2.53754i 0.0591176 0.235604i
\(117\) 0 0
\(118\) −5.24441 + 9.25329i −0.482787 + 0.851835i
\(119\) 6.56670i 0.601969i
\(120\) 0 0
\(121\) 5.61553i 0.510503i
\(122\) −1.77772 1.00754i −0.160947 0.0912188i
\(123\) 0 0
\(124\) 12.3618 7.40253i 1.11012 0.664767i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) 13.7354 1.21882 0.609409 0.792856i \(-0.291407\pi\)
0.609409 + 0.792856i \(0.291407\pi\)
\(128\) −10.7477 + 3.53362i −0.949973 + 0.312331i
\(129\) 0 0
\(130\) 0.809451 + 2.92729i 0.0709935 + 0.256741i
\(131\) −5.20726 + 5.20726i −0.454960 + 0.454960i −0.896997 0.442037i \(-0.854256\pi\)
0.442037 + 0.896997i \(0.354256\pi\)
\(132\) 0 0
\(133\) −12.0841 12.0841i −1.04783 1.04783i
\(134\) 9.09563 + 5.15505i 0.785743 + 0.445329i
\(135\) 0 0
\(136\) 2.98118 + 2.84179i 0.255634 + 0.243681i
\(137\) 22.7563i 1.94420i −0.234559 0.972102i \(-0.575365\pi\)
0.234559 0.972102i \(-0.424635\pi\)
\(138\) 0 0
\(139\) 6.28085 + 6.28085i 0.532734 + 0.532734i 0.921385 0.388651i \(-0.127059\pi\)
−0.388651 + 0.921385i \(0.627059\pi\)
\(140\) 2.19505 8.74803i 0.185515 0.739343i
\(141\) 0 0
\(142\) −2.61841 + 0.724038i −0.219732 + 0.0607599i
\(143\) 4.98336 0.416729
\(144\) 0 0
\(145\) −1.30810 −0.108632
\(146\) 1.90027 0.525460i 0.157268 0.0434874i
\(147\) 0 0
\(148\) 14.2964 + 3.58723i 1.17516 + 0.294869i
\(149\) 12.9574 + 12.9574i 1.06151 + 1.06151i 0.997980 + 0.0635329i \(0.0202368\pi\)
0.0635329 + 0.997980i \(0.479763\pi\)
\(150\) 0 0
\(151\) 14.3417i 1.16711i 0.812073 + 0.583555i \(0.198339\pi\)
−0.812073 + 0.583555i \(0.801661\pi\)
\(152\) 10.7155 0.256515i 0.869142 0.0208061i
\(153\) 0 0
\(154\) −12.8747 7.29689i −1.03747 0.588001i
\(155\) −5.09425 5.09425i −0.409180 0.409180i
\(156\) 0 0
\(157\) −2.10564 + 2.10564i −0.168049 + 0.168049i −0.786121 0.618073i \(-0.787914\pi\)
0.618073 + 0.786121i \(0.287914\pi\)
\(158\) 1.90837 + 6.90141i 0.151822 + 0.549047i
\(159\) 0 0
\(160\) 3.02155 + 4.78229i 0.238874 + 0.378073i
\(161\) 10.7068 0.843817
\(162\) 0 0
\(163\) −5.34004 + 5.34004i −0.418265 + 0.418265i −0.884605 0.466341i \(-0.845572\pi\)
0.466341 + 0.884605i \(0.345572\pi\)
\(164\) −6.58804 11.0016i −0.514439 0.859081i
\(165\) 0 0
\(166\) 4.26248 + 2.41581i 0.330833 + 0.187503i
\(167\) 16.0686i 1.24343i 0.783245 + 0.621714i \(0.213563\pi\)
−0.783245 + 0.621714i \(0.786437\pi\)
\(168\) 0 0
\(169\) 8.38787i 0.645221i
\(170\) 1.01540 1.79158i 0.0778775 0.137408i
\(171\) 0 0
\(172\) −21.0088 5.27151i −1.60191 0.401949i
\(173\) −17.1133 + 17.1133i −1.30110 + 1.30110i −0.373453 + 0.927649i \(0.621826\pi\)
−0.927649 + 0.373453i \(0.878174\pi\)
\(174\) 0 0
\(175\) −4.50961 −0.340894
\(176\) 8.88430 2.68714i 0.669679 0.202551i
\(177\) 0 0
\(178\) 12.7584 3.52792i 0.956279 0.264429i
\(179\) −1.04482 + 1.04482i −0.0780933 + 0.0780933i −0.745075 0.666981i \(-0.767586\pi\)
0.666981 + 0.745075i \(0.267586\pi\)
\(180\) 0 0
\(181\) 11.9886 + 11.9886i 0.891104 + 0.891104i 0.994627 0.103523i \(-0.0330115\pi\)
−0.103523 + 0.994627i \(0.533012\pi\)
\(182\) −6.75332 + 11.9156i −0.500589 + 0.883245i
\(183\) 0 0
\(184\) −4.63346 + 4.86074i −0.341583 + 0.358338i
\(185\) 7.36979i 0.541838i
\(186\) 0 0
\(187\) −2.38927 2.38927i −0.174721 0.174721i
\(188\) −4.30732 + 2.57933i −0.314143 + 0.188117i
\(189\) 0 0
\(190\) −1.42834 5.16544i −0.103623 0.374741i
\(191\) −0.0667471 −0.00482965 −0.00241483 0.999997i \(-0.500769\pi\)
−0.00241483 + 0.999997i \(0.500769\pi\)
\(192\) 0 0
\(193\) −1.09895 −0.0791039 −0.0395520 0.999218i \(-0.512593\pi\)
−0.0395520 + 0.999218i \(0.512593\pi\)
\(194\) 7.02234 + 25.3956i 0.504175 + 1.82329i
\(195\) 0 0
\(196\) 22.8839 13.7034i 1.63456 0.978816i
\(197\) −11.9289 11.9289i −0.849899 0.849899i 0.140222 0.990120i \(-0.455218\pi\)
−0.990120 + 0.140222i \(0.955218\pi\)
\(198\) 0 0
\(199\) 11.0397i 0.782584i −0.920267 0.391292i \(-0.872028\pi\)
0.920267 0.391292i \(-0.127972\pi\)
\(200\) 1.95156 2.04729i 0.137996 0.144765i
\(201\) 0 0
\(202\) −4.77403 + 8.42334i −0.335899 + 0.592664i
\(203\) −4.17123 4.17123i −0.292763 0.292763i
\(204\) 0 0
\(205\) −4.53373 + 4.53373i −0.316649 + 0.316649i
\(206\) 12.4385 3.43947i 0.866631 0.239639i
\(207\) 0 0
\(208\) −2.48696 8.22247i −0.172440 0.570126i
\(209\) −8.79353 −0.608261
\(210\) 0 0
\(211\) −8.59737 + 8.59737i −0.591868 + 0.591868i −0.938136 0.346268i \(-0.887449\pi\)
0.346268 + 0.938136i \(0.387449\pi\)
\(212\) 4.12364 + 1.03470i 0.283213 + 0.0710634i
\(213\) 0 0
\(214\) −10.0100 + 17.6617i −0.684266 + 1.20733i
\(215\) 10.8301i 0.738603i
\(216\) 0 0
\(217\) 32.4888i 2.20548i
\(218\) 2.35748 + 1.33613i 0.159669 + 0.0904941i
\(219\) 0 0
\(220\) −2.38428 3.98159i −0.160748 0.268439i
\(221\) −2.21128 + 2.21128i −0.148747 + 0.148747i
\(222\) 0 0
\(223\) −21.4238 −1.43465 −0.717323 0.696741i \(-0.754633\pi\)
−0.717323 + 0.696741i \(0.754633\pi\)
\(224\) −5.61460 + 24.8847i −0.375141 + 1.66268i
\(225\) 0 0
\(226\) 0.965041 + 3.48997i 0.0641936 + 0.232149i
\(227\) 8.06331 8.06331i 0.535181 0.535181i −0.386929 0.922110i \(-0.626464\pi\)
0.922110 + 0.386929i \(0.126464\pi\)
\(228\) 0 0
\(229\) 4.63169 + 4.63169i 0.306071 + 0.306071i 0.843383 0.537313i \(-0.180560\pi\)
−0.537313 + 0.843383i \(0.680560\pi\)
\(230\) 2.92112 + 1.65558i 0.192613 + 0.109166i
\(231\) 0 0
\(232\) 3.69880 0.0885445i 0.242838 0.00581323i
\(233\) 26.0672i 1.70772i −0.520502 0.853860i \(-0.674255\pi\)
0.520502 0.853860i \(-0.325745\pi\)
\(234\) 0 0
\(235\) 1.77503 + 1.77503i 0.115790 + 0.115790i
\(236\) −14.5895 3.66078i −0.949695 0.238296i
\(237\) 0 0
\(238\) 8.95082 2.47507i 0.580196 0.160435i
\(239\) −5.12209 −0.331320 −0.165660 0.986183i \(-0.552975\pi\)
−0.165660 + 0.986183i \(0.552975\pi\)
\(240\) 0 0
\(241\) 11.4987 0.740695 0.370347 0.928893i \(-0.379239\pi\)
0.370347 + 0.928893i \(0.379239\pi\)
\(242\) 7.65432 2.11656i 0.492038 0.136058i
\(243\) 0 0
\(244\) 0.703301 2.80290i 0.0450242 0.179437i
\(245\) −9.43037 9.43037i −0.602484 0.602484i
\(246\) 0 0
\(247\) 8.13847i 0.517838i
\(248\) 14.7494 + 14.0598i 0.936588 + 0.892795i
\(249\) 0 0
\(250\) −1.23035 0.697313i −0.0778140 0.0441020i
\(251\) 19.8270 + 19.8270i 1.25147 + 1.25147i 0.955061 + 0.296408i \(0.0957889\pi\)
0.296408 + 0.955061i \(0.404211\pi\)
\(252\) 0 0
\(253\) 3.89564 3.89564i 0.244917 0.244917i
\(254\) 5.17703 + 18.7222i 0.324836 + 1.17473i
\(255\) 0 0
\(256\) −8.86749 13.3179i −0.554218 0.832372i
\(257\) 24.2494 1.51264 0.756319 0.654203i \(-0.226996\pi\)
0.756319 + 0.654203i \(0.226996\pi\)
\(258\) 0 0
\(259\) 23.5006 23.5006i 1.46026 1.46026i
\(260\) −3.68499 + 2.20666i −0.228533 + 0.136851i
\(261\) 0 0
\(262\) −9.06049 5.13514i −0.559759 0.317250i
\(263\) 22.5680i 1.39160i −0.718234 0.695802i \(-0.755049\pi\)
0.718234 0.695802i \(-0.244951\pi\)
\(264\) 0 0
\(265\) 2.12574i 0.130583i
\(266\) 11.9168 21.0261i 0.730664 1.28919i
\(267\) 0 0
\(268\) −3.59840 + 14.3409i −0.219807 + 0.876010i
\(269\) 5.10558 5.10558i 0.311293 0.311293i −0.534117 0.845410i \(-0.679356\pi\)
0.845410 + 0.534117i \(0.179356\pi\)
\(270\) 0 0
\(271\) 6.67920 0.405733 0.202866 0.979206i \(-0.434974\pi\)
0.202866 + 0.979206i \(0.434974\pi\)
\(272\) −2.74989 + 5.13464i −0.166736 + 0.311333i
\(273\) 0 0
\(274\) 31.0183 8.57713i 1.87388 0.518163i
\(275\) −1.64080 + 1.64080i −0.0989441 + 0.0989441i
\(276\) 0 0
\(277\) −11.8524 11.8524i −0.712141 0.712141i 0.254842 0.966983i \(-0.417977\pi\)
−0.966983 + 0.254842i \(0.917977\pi\)
\(278\) −6.19386 + 10.9285i −0.371483 + 0.655448i
\(279\) 0 0
\(280\) 12.7514 0.305253i 0.762044 0.0182423i
\(281\) 0.477460i 0.0284829i −0.999899 0.0142414i \(-0.995467\pi\)
0.999899 0.0142414i \(-0.00453334\pi\)
\(282\) 0 0
\(283\) −0.482914 0.482914i −0.0287063 0.0287063i 0.692608 0.721314i \(-0.256462\pi\)
−0.721314 + 0.692608i \(0.756462\pi\)
\(284\) −1.97382 3.29615i −0.117124 0.195591i
\(285\) 0 0
\(286\) 1.87829 + 6.79263i 0.111065 + 0.401656i
\(287\) −28.9141 −1.70674
\(288\) 0 0
\(289\) −14.8796 −0.875271
\(290\) −0.493038 1.78302i −0.0289522 0.104703i
\(291\) 0 0
\(292\) 1.43247 + 2.39214i 0.0838290 + 0.139989i
\(293\) −7.46638 7.46638i −0.436190 0.436190i 0.454537 0.890728i \(-0.349805\pi\)
−0.890728 + 0.454537i \(0.849805\pi\)
\(294\) 0 0
\(295\) 7.52088i 0.437883i
\(296\) 0.498857 + 20.8389i 0.0289955 + 1.21124i
\(297\) 0 0
\(298\) −12.7780 + 22.5456i −0.740207 + 1.30603i
\(299\) −3.60544 3.60544i −0.208508 0.208508i
\(300\) 0 0
\(301\) −34.5346 + 34.5346i −1.99054 + 1.99054i
\(302\) −19.5486 + 5.40556i −1.12490 + 0.311055i
\(303\) 0 0
\(304\) 4.38845 + 14.5092i 0.251695 + 0.832160i
\(305\) −1.44489 −0.0827344
\(306\) 0 0
\(307\) 2.39349 2.39349i 0.136604 0.136604i −0.635498 0.772102i \(-0.719205\pi\)
0.772102 + 0.635498i \(0.219205\pi\)
\(308\) 5.09348 20.2993i 0.290228 1.15666i
\(309\) 0 0
\(310\) 5.02369 8.86386i 0.285327 0.503433i
\(311\) 20.4404i 1.15907i −0.814948 0.579534i \(-0.803235\pi\)
0.814948 0.579534i \(-0.196765\pi\)
\(312\) 0 0
\(313\) 2.46975i 0.139598i −0.997561 0.0697992i \(-0.977764\pi\)
0.997561 0.0697992i \(-0.0222359\pi\)
\(314\) −3.66376 2.07648i −0.206758 0.117182i
\(315\) 0 0
\(316\) −8.68776 + 5.20245i −0.488725 + 0.292660i
\(317\) 16.2241 16.2241i 0.911234 0.911234i −0.0851350 0.996369i \(-0.527132\pi\)
0.996369 + 0.0851350i \(0.0271322\pi\)
\(318\) 0 0
\(319\) −3.03537 −0.169948
\(320\) −5.37969 + 5.92105i −0.300734 + 0.330997i
\(321\) 0 0
\(322\) 4.03553 + 14.5941i 0.224891 + 0.813296i
\(323\) 3.90198 3.90198i 0.217112 0.217112i
\(324\) 0 0
\(325\) 1.51857 + 1.51857i 0.0842353 + 0.0842353i
\(326\) −9.29154 5.26608i −0.514611 0.291661i
\(327\) 0 0
\(328\) 12.5128 13.1265i 0.690902 0.724792i
\(329\) 11.3204i 0.624111i
\(330\) 0 0
\(331\) 3.42340 + 3.42340i 0.188167 + 0.188167i 0.794903 0.606736i \(-0.207521\pi\)
−0.606736 + 0.794903i \(0.707521\pi\)
\(332\) −1.68632 + 6.72057i −0.0925487 + 0.368839i
\(333\) 0 0
\(334\) −21.9025 + 6.05645i −1.19845 + 0.331394i
\(335\) 7.39273 0.403908
\(336\) 0 0
\(337\) −5.40017 −0.294166 −0.147083 0.989124i \(-0.546988\pi\)
−0.147083 + 0.989124i \(0.546988\pi\)
\(338\) −11.4332 + 3.16149i −0.621883 + 0.171962i
\(339\) 0 0
\(340\) 2.82475 + 0.708783i 0.153194 + 0.0384392i
\(341\) −11.8209 11.8209i −0.640139 0.640139i
\(342\) 0 0
\(343\) 28.5754i 1.54292i
\(344\) −0.733080 30.6232i −0.0395250 1.65109i
\(345\) 0 0
\(346\) −29.7767 16.8763i −1.60081 0.907276i
\(347\) 4.07531 + 4.07531i 0.218774 + 0.218774i 0.807982 0.589208i \(-0.200560\pi\)
−0.589208 + 0.807982i \(0.700560\pi\)
\(348\) 0 0
\(349\) 1.55681 1.55681i 0.0833339 0.0833339i −0.664211 0.747545i \(-0.731232\pi\)
0.747545 + 0.664211i \(0.231232\pi\)
\(350\) −1.69972 6.14687i −0.0908541 0.328564i
\(351\) 0 0
\(352\) 7.01133 + 11.0970i 0.373705 + 0.591474i
\(353\) −1.34919 −0.0718103 −0.0359052 0.999355i \(-0.511431\pi\)
−0.0359052 + 0.999355i \(0.511431\pi\)
\(354\) 0 0
\(355\) −1.35833 + 1.35833i −0.0720929 + 0.0720929i
\(356\) 9.61755 + 16.0607i 0.509729 + 0.851216i
\(357\) 0 0
\(358\) −1.81795 1.03035i −0.0960819 0.0544555i
\(359\) 23.2192i 1.22546i −0.790291 0.612732i \(-0.790071\pi\)
0.790291 0.612732i \(-0.209929\pi\)
\(360\) 0 0
\(361\) 4.63903i 0.244159i
\(362\) −11.8225 + 20.8598i −0.621379 + 1.09637i
\(363\) 0 0
\(364\) −18.7871 4.71405i −0.984714 0.247083i
\(365\) 0.985792 0.985792i 0.0515987 0.0515987i
\(366\) 0 0
\(367\) −5.16452 −0.269586 −0.134793 0.990874i \(-0.543037\pi\)
−0.134793 + 0.990874i \(0.543037\pi\)
\(368\) −8.37189 4.48362i −0.436415 0.233725i
\(369\) 0 0
\(370\) 10.0455 2.77776i 0.522239 0.144409i
\(371\) 6.77849 6.77849i 0.351922 0.351922i
\(372\) 0 0
\(373\) 18.5056 + 18.5056i 0.958185 + 0.958185i 0.999160 0.0409750i \(-0.0130464\pi\)
−0.0409750 + 0.999160i \(0.513046\pi\)
\(374\) 2.35618 4.15727i 0.121835 0.214967i
\(375\) 0 0
\(376\) −5.13926 4.89896i −0.265037 0.252645i
\(377\) 2.80926i 0.144684i
\(378\) 0 0
\(379\) −13.5254 13.5254i −0.694754 0.694754i 0.268520 0.963274i \(-0.413465\pi\)
−0.963274 + 0.268520i \(0.913465\pi\)
\(380\) 6.50246 3.89383i 0.333569 0.199749i
\(381\) 0 0
\(382\) −0.0251578 0.0909805i −0.00128718 0.00465497i
\(383\) −21.9051 −1.11930 −0.559650 0.828729i \(-0.689064\pi\)
−0.559650 + 0.828729i \(0.689064\pi\)
\(384\) 0 0
\(385\) −10.4643 −0.533310
\(386\) −0.414206 1.49793i −0.0210825 0.0762427i
\(387\) 0 0
\(388\) −31.9689 + 19.1438i −1.62298 + 0.971878i
\(389\) −4.48844 4.48844i −0.227573 0.227573i 0.584105 0.811678i \(-0.301446\pi\)
−0.811678 + 0.584105i \(0.801446\pi\)
\(390\) 0 0
\(391\) 3.45725i 0.174841i
\(392\) 27.3038 + 26.0271i 1.37905 + 1.31457i
\(393\) 0 0
\(394\) 11.7637 20.7560i 0.592646 1.04567i
\(395\) 3.58020 + 3.58020i 0.180139 + 0.180139i
\(396\) 0 0
\(397\) 11.7892 11.7892i 0.591682 0.591682i −0.346404 0.938086i \(-0.612597\pi\)
0.938086 + 0.346404i \(0.112597\pi\)
\(398\) 15.0478 4.16100i 0.754278 0.208572i
\(399\) 0 0
\(400\) 3.52615 + 1.88845i 0.176308 + 0.0944227i
\(401\) −24.9259 −1.24474 −0.622371 0.782722i \(-0.713830\pi\)
−0.622371 + 0.782722i \(0.713830\pi\)
\(402\) 0 0
\(403\) −10.9403 + 10.9403i −0.544977 + 0.544977i
\(404\) −13.2809 3.33244i −0.660751 0.165795i
\(405\) 0 0
\(406\) 4.11346 7.25784i 0.204148 0.360200i
\(407\) 17.1012i 0.847675i
\(408\) 0 0
\(409\) 21.5355i 1.06486i −0.846474 0.532430i \(-0.821279\pi\)
0.846474 0.532430i \(-0.178721\pi\)
\(410\) −7.88857 4.47094i −0.389589 0.220804i
\(411\) 0 0
\(412\) 9.37643 + 15.6581i 0.461943 + 0.771417i
\(413\) −23.9824 + 23.9824i −1.18010 + 1.18010i
\(414\) 0 0
\(415\) 3.46445 0.170063
\(416\) 10.2704 6.48903i 0.503546 0.318151i
\(417\) 0 0
\(418\) −3.31439 11.9861i −0.162112 0.586261i
\(419\) 17.2979 17.2979i 0.845060 0.845060i −0.144452 0.989512i \(-0.546142\pi\)
0.989512 + 0.144452i \(0.0461419\pi\)
\(420\) 0 0
\(421\) −19.4330 19.4330i −0.947105 0.947105i 0.0515648 0.998670i \(-0.483579\pi\)
−0.998670 + 0.0515648i \(0.983579\pi\)
\(422\) −14.9592 8.47830i −0.728203 0.412717i
\(423\) 0 0
\(424\) 0.143890 + 6.01077i 0.00698791 + 0.291909i
\(425\) 1.45616i 0.0706341i
\(426\) 0 0
\(427\) −4.60744 4.60744i −0.222970 0.222970i
\(428\) −27.8468 6.98729i −1.34603 0.337744i
\(429\) 0 0
\(430\) −14.7620 + 4.08198i −0.711888 + 0.196850i
\(431\) −28.3769 −1.36687 −0.683433 0.730013i \(-0.739514\pi\)
−0.683433 + 0.730013i \(0.739514\pi\)
\(432\) 0 0
\(433\) 9.04007 0.434438 0.217219 0.976123i \(-0.430301\pi\)
0.217219 + 0.976123i \(0.430301\pi\)
\(434\) 44.2842 12.2454i 2.12571 0.587799i
\(435\) 0 0
\(436\) −0.932664 + 3.71699i −0.0446665 + 0.178012i
\(437\) 6.36208 + 6.36208i 0.304340 + 0.304340i
\(438\) 0 0
\(439\) 28.2949i 1.35044i −0.737615 0.675221i \(-0.764048\pi\)
0.737615 0.675221i \(-0.235952\pi\)
\(440\) 4.52850 4.75063i 0.215888 0.226477i
\(441\) 0 0
\(442\) −3.84757 2.18066i −0.183010 0.103723i
\(443\) 13.1232 + 13.1232i 0.623504 + 0.623504i 0.946426 0.322922i \(-0.104665\pi\)
−0.322922 + 0.946426i \(0.604665\pi\)
\(444\) 0 0
\(445\) 6.61857 6.61857i 0.313750 0.313750i
\(446\) −8.07489 29.2020i −0.382357 1.38275i
\(447\) 0 0
\(448\) −36.0355 + 1.72628i −1.70252 + 0.0815588i
\(449\) 14.3902 0.679116 0.339558 0.940585i \(-0.389723\pi\)
0.339558 + 0.940585i \(0.389723\pi\)
\(450\) 0 0
\(451\) −10.5203 + 10.5203i −0.495380 + 0.495380i
\(452\) −4.39331 + 2.63082i −0.206644 + 0.123743i
\(453\) 0 0
\(454\) 14.0299 + 7.95163i 0.658458 + 0.373189i
\(455\) 9.68477i 0.454029i
\(456\) 0 0
\(457\) 4.54538i 0.212624i 0.994333 + 0.106312i \(0.0339042\pi\)
−0.994333 + 0.106312i \(0.966096\pi\)
\(458\) −4.56754 + 8.05902i −0.213427 + 0.376573i
\(459\) 0 0
\(460\) −1.15565 + 4.60568i −0.0538826 + 0.214741i
\(461\) −19.8046 + 19.8046i −0.922393 + 0.922393i −0.997198 0.0748050i \(-0.976167\pi\)
0.0748050 + 0.997198i \(0.476167\pi\)
\(462\) 0 0
\(463\) −14.5997 −0.678506 −0.339253 0.940695i \(-0.610174\pi\)
−0.339253 + 0.940695i \(0.610174\pi\)
\(464\) 1.51481 + 5.00833i 0.0703235 + 0.232506i
\(465\) 0 0
\(466\) 35.5312 9.82505i 1.64595 0.455137i
\(467\) −19.8105 + 19.8105i −0.916722 + 0.916722i −0.996789 0.0800671i \(-0.974487\pi\)
0.0800671 + 0.996789i \(0.474487\pi\)
\(468\) 0 0
\(469\) 23.5738 + 23.5738i 1.08853 + 1.08853i
\(470\) −1.75045 + 3.08851i −0.0807421 + 0.142462i
\(471\) 0 0
\(472\) −0.509084 21.2662i −0.0234325 0.978855i
\(473\) 25.1306i 1.15550i
\(474\) 0 0
\(475\) −2.67964 2.67964i −0.122950 0.122950i
\(476\) 6.74734 + 11.2676i 0.309264 + 0.516451i
\(477\) 0 0
\(478\) −1.93058 6.98172i −0.0883025 0.319337i
\(479\) −21.0378 −0.961243 −0.480621 0.876928i \(-0.659589\pi\)
−0.480621 + 0.876928i \(0.659589\pi\)
\(480\) 0 0
\(481\) −15.8273 −0.721661
\(482\) 4.33399 + 15.6734i 0.197408 + 0.713904i
\(483\) 0 0
\(484\) 5.77000 + 9.63555i 0.262273 + 0.437980i
\(485\) 13.1743 + 13.1743i 0.598214 + 0.598214i
\(486\) 0 0
\(487\) 10.2724i 0.465485i −0.972538 0.232743i \(-0.925230\pi\)
0.972538 0.232743i \(-0.0747699\pi\)
\(488\) 4.08561 0.0978041i 0.184947 0.00442738i
\(489\) 0 0
\(490\) 9.29976 16.4086i 0.420120 0.741265i
\(491\) 5.95681 + 5.95681i 0.268827 + 0.268827i 0.828627 0.559801i \(-0.189122\pi\)
−0.559801 + 0.828627i \(0.689122\pi\)
\(492\) 0 0
\(493\) 1.34690 1.34690i 0.0606612 0.0606612i
\(494\) −11.0932 + 3.06748i −0.499108 + 0.138013i
\(495\) 0 0
\(496\) −13.6051 + 25.4036i −0.610886 + 1.14066i
\(497\) −8.66284 −0.388581
\(498\) 0 0
\(499\) −2.81466 + 2.81466i −0.126002 + 0.126002i −0.767295 0.641294i \(-0.778398\pi\)
0.641294 + 0.767295i \(0.278398\pi\)
\(500\) 0.486749 1.93986i 0.0217681 0.0867534i
\(501\) 0 0
\(502\) −19.5524 + 34.4985i −0.872666 + 1.53974i
\(503\) 5.49759i 0.245125i −0.992461 0.122563i \(-0.960889\pi\)
0.992461 0.122563i \(-0.0391113\pi\)
\(504\) 0 0
\(505\) 6.84632i 0.304657i
\(506\) 6.77831 + 3.84169i 0.301333 + 0.170784i
\(507\) 0 0
\(508\) −23.5682 + 14.1132i −1.04567 + 0.626173i
\(509\) 4.37578 4.37578i 0.193953 0.193953i −0.603449 0.797402i \(-0.706207\pi\)
0.797402 + 0.603449i \(0.206207\pi\)
\(510\) 0 0
\(511\) 6.28693 0.278118
\(512\) 14.8109 17.1066i 0.654556 0.756013i
\(513\) 0 0
\(514\) 9.13990 + 33.0535i 0.403144 + 1.45793i
\(515\) 6.45263 6.45263i 0.284337 0.284337i
\(516\) 0 0
\(517\) 4.11887 + 4.11887i 0.181148 + 0.181148i
\(518\) 40.8904 + 23.1751i 1.79662 + 1.01826i
\(519\) 0 0
\(520\) −4.39673 4.19115i −0.192810 0.183794i
\(521\) 33.8729i 1.48400i 0.670401 + 0.741999i \(0.266122\pi\)
−0.670401 + 0.741999i \(0.733878\pi\)
\(522\) 0 0
\(523\) 27.8060 + 27.8060i 1.21587 + 1.21587i 0.969065 + 0.246804i \(0.0793803\pi\)
0.246804 + 0.969065i \(0.420620\pi\)
\(524\) 3.58450 14.2855i 0.156590 0.624065i
\(525\) 0 0
\(526\) 30.7616 8.50615i 1.34127 0.370886i
\(527\) 10.4907 0.456981
\(528\) 0 0
\(529\) 17.3630 0.754915
\(530\) 2.89751 0.801215i 0.125860 0.0348025i
\(531\) 0 0
\(532\) 33.1514 + 8.31832i 1.43730 + 0.360645i
\(533\) 9.73658 + 9.73658i 0.421738 + 0.421738i
\(534\) 0 0
\(535\) 14.3550i 0.620622i
\(536\) −20.9038 + 0.500410i −0.902907 + 0.0216144i
\(537\) 0 0
\(538\) 8.88358 + 5.03487i 0.382998 + 0.217069i
\(539\) −21.8827 21.8827i −0.942553 0.942553i
\(540\) 0 0
\(541\) 3.03066 3.03066i 0.130298 0.130298i −0.638950 0.769248i \(-0.720631\pi\)
0.769248 + 0.638950i \(0.220631\pi\)
\(542\) 2.51747 + 9.10416i 0.108135 + 0.391057i
\(543\) 0 0
\(544\) −8.03529 1.81296i −0.344510 0.0777301i
\(545\) 1.91611 0.0820771
\(546\) 0 0
\(547\) −18.4783 + 18.4783i −0.790074 + 0.790074i −0.981506 0.191432i \(-0.938687\pi\)
0.191432 + 0.981506i \(0.438687\pi\)
\(548\) 23.3823 + 39.0470i 0.998843 + 1.66801i
\(549\) 0 0
\(550\) −2.85495 1.61808i −0.121736 0.0689951i
\(551\) 4.95716i 0.211182i
\(552\) 0 0
\(553\) 22.8329i 0.970953i
\(554\) 11.6882 20.6228i 0.496585 0.876181i
\(555\) 0 0
\(556\) −17.2308 4.32353i −0.730747 0.183358i
\(557\) 30.2060 30.2060i 1.27987 1.27987i 0.339127 0.940741i \(-0.389868\pi\)
0.940741 0.339127i \(-0.110132\pi\)
\(558\) 0 0
\(559\) 23.2585 0.983729
\(560\) 5.22225 + 17.2659i 0.220680 + 0.729620i
\(561\) 0 0
\(562\) 0.650807 0.179960i 0.0274526 0.00759117i
\(563\) −2.86747 + 2.86747i −0.120850 + 0.120850i −0.764945 0.644095i \(-0.777234\pi\)
0.644095 + 0.764945i \(0.277234\pi\)
\(564\) 0 0
\(565\) 1.81047 + 1.81047i 0.0761670 + 0.0761670i
\(566\) 0.476226 0.840258i 0.0200173 0.0353187i
\(567\) 0 0
\(568\) 3.74890 3.93279i 0.157300 0.165016i
\(569\) 35.8628i 1.50345i 0.659479 + 0.751723i \(0.270777\pi\)
−0.659479 + 0.751723i \(0.729223\pi\)
\(570\) 0 0
\(571\) −17.6509 17.6509i −0.738667 0.738667i 0.233653 0.972320i \(-0.424932\pi\)
−0.972320 + 0.233653i \(0.924932\pi\)
\(572\) −8.55082 + 5.12044i −0.357528 + 0.214096i
\(573\) 0 0
\(574\) −10.8981 39.4117i −0.454876 1.64501i
\(575\) 2.37423 0.0990122
\(576\) 0 0
\(577\) 36.1387 1.50448 0.752238 0.658892i \(-0.228975\pi\)
0.752238 + 0.658892i \(0.228975\pi\)
\(578\) −5.60830 20.2818i −0.233274 0.843612i
\(579\) 0 0
\(580\) 2.24454 1.34408i 0.0931993 0.0558100i
\(581\) 11.0474 + 11.0474i 0.458322 + 0.458322i
\(582\) 0 0
\(583\) 4.93265i 0.204290i
\(584\) −2.72071 + 2.85417i −0.112584 + 0.118106i
\(585\) 0 0
\(586\) 7.36297 12.9913i 0.304161 0.536666i
\(587\) 11.4005 + 11.4005i 0.470550 + 0.470550i 0.902093 0.431542i \(-0.142030\pi\)
−0.431542 + 0.902093i \(0.642030\pi\)
\(588\) 0 0
\(589\) 19.3051 19.3051i 0.795453 0.795453i
\(590\) −10.2514 + 2.83471i −0.422045 + 0.116703i
\(591\) 0 0
\(592\) −28.2167 + 8.53441i −1.15970 + 0.350762i
\(593\) 35.0454 1.43914 0.719572 0.694418i \(-0.244338\pi\)
0.719572 + 0.694418i \(0.244338\pi\)
\(594\) 0 0
\(595\) 4.64336 4.64336i 0.190359 0.190359i
\(596\) −35.5472 8.91945i −1.45607 0.365355i
\(597\) 0 0
\(598\) 3.55550 6.27337i 0.145395 0.256537i
\(599\) 18.2753i 0.746707i 0.927689 + 0.373354i \(0.121792\pi\)
−0.927689 + 0.373354i \(0.878208\pi\)
\(600\) 0 0
\(601\) 0.480142i 0.0195854i 0.999952 + 0.00979269i \(0.00311716\pi\)
−0.999952 + 0.00979269i \(0.996883\pi\)
\(602\) −60.0893 34.0563i −2.44906 1.38803i
\(603\) 0 0
\(604\) −14.7362 24.6086i −0.599608 1.00131i
\(605\) 3.97078 3.97078i 0.161435 0.161435i
\(606\) 0 0
\(607\) −38.6107 −1.56716 −0.783581 0.621290i \(-0.786609\pi\)
−0.783581 + 0.621290i \(0.786609\pi\)
\(608\) −18.1229 + 11.4504i −0.734980 + 0.464376i
\(609\) 0 0
\(610\) −0.544598 1.96948i −0.0220501 0.0797419i
\(611\) 3.81204 3.81204i 0.154218 0.154218i
\(612\) 0 0
\(613\) −5.53592 5.53592i −0.223594 0.223594i 0.586416 0.810010i \(-0.300538\pi\)
−0.810010 + 0.586416i \(0.800538\pi\)
\(614\) 4.16461 + 2.36034i 0.168070 + 0.0952557i
\(615\) 0 0
\(616\) 29.5890 0.708322i 1.19218 0.0285391i
\(617\) 31.8836i 1.28358i −0.766879 0.641792i \(-0.778191\pi\)
0.766879 0.641792i \(-0.221809\pi\)
\(618\) 0 0
\(619\) −29.4054 29.4054i −1.18190 1.18190i −0.979251 0.202650i \(-0.935045\pi\)
−0.202650 0.979251i \(-0.564955\pi\)
\(620\) 13.9755 + 3.50671i 0.561269 + 0.140833i
\(621\) 0 0
\(622\) 27.8615 7.70422i 1.11714 0.308911i
\(623\) 42.2102 1.69112
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 3.36642 0.930878i 0.134549 0.0372054i
\(627\) 0 0
\(628\) 1.44945 5.77658i 0.0578395 0.230511i
\(629\) 7.58837 + 7.58837i 0.302568 + 0.302568i
\(630\) 0 0
\(631\) 30.7381i 1.22367i −0.790987 0.611833i \(-0.790432\pi\)
0.790987 0.611833i \(-0.209568\pi\)
\(632\) −10.3658 9.88109i −0.412328 0.393049i
\(633\) 0 0
\(634\) 28.2294 + 15.9994i 1.12113 + 0.635416i
\(635\) 9.71239 + 9.71239i 0.385424 + 0.385424i
\(636\) 0 0
\(637\) −20.2525 + 20.2525i −0.802435 + 0.802435i
\(638\) −1.14407 4.13740i −0.0452941 0.163801i
\(639\) 0 0
\(640\) −10.0984 5.10114i −0.399176 0.201640i
\(641\) −13.6348 −0.538540 −0.269270 0.963065i \(-0.586782\pi\)
−0.269270 + 0.963065i \(0.586782\pi\)
\(642\) 0 0
\(643\) 14.9224 14.9224i 0.588480 0.588480i −0.348740 0.937220i \(-0.613390\pi\)
0.937220 + 0.348740i \(0.113390\pi\)
\(644\) −18.3716 + 11.0014i −0.723942 + 0.433514i
\(645\) 0 0
\(646\) 6.78935 + 3.84794i 0.267123 + 0.151395i
\(647\) 4.87972i 0.191841i 0.995389 + 0.0959207i \(0.0305795\pi\)
−0.995389 + 0.0959207i \(0.969420\pi\)
\(648\) 0 0
\(649\) 17.4518i 0.685043i
\(650\) −1.49754 + 2.64228i −0.0587384 + 0.103639i
\(651\) 0 0
\(652\) 3.67591 14.6498i 0.143960 0.573730i
\(653\) 10.2913 10.2913i 0.402731 0.402731i −0.476463 0.879194i \(-0.658081\pi\)
0.879194 + 0.476463i \(0.158081\pi\)
\(654\) 0 0
\(655\) −7.36417 −0.287742
\(656\) 22.6085 + 12.1081i 0.882713 + 0.472743i
\(657\) 0 0
\(658\) −15.4303 + 4.26677i −0.601537 + 0.166336i
\(659\) 21.9025 21.9025i 0.853201 0.853201i −0.137325 0.990526i \(-0.543851\pi\)
0.990526 + 0.137325i \(0.0438505\pi\)
\(660\) 0 0
\(661\) 5.40595 + 5.40595i 0.210267 + 0.210267i 0.804381 0.594114i \(-0.202497\pi\)
−0.594114 + 0.804381i \(0.702497\pi\)
\(662\) −3.37599 + 5.95663i −0.131212 + 0.231511i
\(663\) 0 0
\(664\) −9.79615 + 0.234507i −0.380164 + 0.00910063i
\(665\) 17.0895i 0.662704i
\(666\) 0 0
\(667\) 2.19608 + 2.19608i 0.0850326 + 0.0850326i
\(668\) −16.5106 27.5717i −0.638816 1.06678i
\(669\) 0 0
\(670\) 2.78641 + 10.0768i 0.107648 + 0.389299i
\(671\) −3.35280 −0.129433
\(672\) 0 0
\(673\) 35.3820 1.36388 0.681938 0.731410i \(-0.261138\pi\)
0.681938 + 0.731410i \(0.261138\pi\)
\(674\) −2.03539 7.36076i −0.0784002 0.283526i
\(675\) 0 0
\(676\) −8.61861 14.3925i −0.331485 0.553559i
\(677\) −5.17061 5.17061i −0.198723 0.198723i 0.600730 0.799452i \(-0.294877\pi\)
−0.799452 + 0.600730i \(0.794877\pi\)
\(678\) 0 0
\(679\) 84.0196i 3.22438i
\(680\) 0.0985665 + 4.11746i 0.00377985 + 0.157897i
\(681\) 0 0
\(682\) 11.6572 20.5681i 0.446377 0.787593i
\(683\) −26.5989 26.5989i −1.01778 1.01778i −0.999839 0.0179409i \(-0.994289\pi\)
−0.0179409 0.999839i \(-0.505711\pi\)
\(684\) 0 0
\(685\) 16.0912 16.0912i 0.614811 0.614811i
\(686\) 38.9500 10.7704i 1.48712 0.411216i
\(687\) 0 0
\(688\) 41.4651 12.5415i 1.58084 0.478140i
\(689\) −4.56520 −0.173920
\(690\) 0 0
\(691\) −21.7989 + 21.7989i −0.829270 + 0.829270i −0.987416 0.158146i \(-0.949448\pi\)
0.158146 + 0.987416i \(0.449448\pi\)
\(692\) 11.7802 46.9484i 0.447818 1.78471i
\(693\) 0 0
\(694\) −4.01887 + 7.09093i −0.152554 + 0.269168i
\(695\) 8.88246i 0.336931i
\(696\) 0 0
\(697\) 9.33640i 0.353641i
\(698\) 2.70880 + 1.53524i 0.102530 + 0.0581099i
\(699\) 0 0
\(700\) 7.73792 4.63366i 0.292466 0.175136i
\(701\) 15.2175 15.2175i 0.574756 0.574756i −0.358698 0.933454i \(-0.616779\pi\)
0.933454 + 0.358698i \(0.116779\pi\)
\(702\) 0 0
\(703\) 27.9285 1.05334
\(704\) −12.4833 + 13.7395i −0.470482 + 0.517826i
\(705\) 0 0
\(706\) −0.508527 1.83903i −0.0191387 0.0692130i
\(707\) −21.8313 + 21.8313i −0.821052 + 0.821052i
\(708\) 0 0
\(709\) 4.87350 + 4.87350i 0.183028 + 0.183028i 0.792674 0.609646i \(-0.208688\pi\)
−0.609646 + 0.792674i \(0.708688\pi\)
\(710\) −2.36346 1.33952i −0.0886992 0.0502713i
\(711\) 0 0
\(712\) −18.2668 + 19.1628i −0.684576 + 0.718156i
\(713\) 17.1048i 0.640579i
\(714\) 0 0
\(715\) 3.52377 + 3.52377i 0.131781 + 0.131781i
\(716\) 0.719218 2.86633i 0.0268784 0.107120i
\(717\) 0 0
\(718\) 31.6492 8.75160i 1.18114 0.326607i
\(719\) −9.27351 −0.345843 −0.172922 0.984936i \(-0.555321\pi\)
−0.172922 + 0.984936i \(0.555321\pi\)
\(720\) 0 0
\(721\) 41.1520 1.53258
\(722\) −6.32328 + 1.74850i −0.235328 + 0.0650726i
\(723\) 0 0
\(724\) −32.8893 8.25254i −1.22232 0.306703i
\(725\) −0.924966 0.924966i −0.0343524 0.0343524i
\(726\) 0 0
\(727\) 10.6056i 0.393341i −0.980470 0.196670i \(-0.936987\pi\)
0.980470 0.196670i \(-0.0630129\pi\)
\(728\) −0.655557 27.3848i −0.0242965 1.01495i
\(729\) 0 0
\(730\) 1.71525 + 0.972138i 0.0634843 + 0.0359805i
\(731\) −11.1513 11.1513i −0.412445 0.412445i
\(732\) 0 0
\(733\) −29.6530 + 29.6530i −1.09526 + 1.09526i −0.100301 + 0.994957i \(0.531981\pi\)
−0.994957 + 0.100301i \(0.968019\pi\)
\(734\) −1.94657 7.03956i −0.0718492 0.259835i
\(735\) 0 0
\(736\) 2.95599 13.1013i 0.108959 0.482921i
\(737\) 17.1544 0.631892
\(738\) 0 0
\(739\) 30.8751 30.8751i 1.13576 1.13576i 0.146559 0.989202i \(-0.453180\pi\)
0.989202 0.146559i \(-0.0468197\pi\)
\(740\) 7.57252 + 12.6456i 0.278371 + 0.464863i
\(741\) 0 0
\(742\) 11.7944 + 6.68461i 0.432986 + 0.245400i
\(743\) 22.3956i 0.821617i 0.911722 + 0.410808i \(0.134753\pi\)
−0.911722 + 0.410808i \(0.865247\pi\)
\(744\) 0 0
\(745\) 18.3245i 0.671360i
\(746\) −18.2493 + 32.1993i −0.668155 + 1.17890i
\(747\) 0 0
\(748\) 6.55468 + 1.64469i 0.239663 + 0.0601359i
\(749\) −45.7749 + 45.7749i −1.67258 + 1.67258i
\(750\) 0 0
\(751\) 20.6448 0.753341 0.376670 0.926347i \(-0.377069\pi\)
0.376670 + 0.926347i \(0.377069\pi\)
\(752\) 4.74054 8.85161i 0.172870 0.322785i
\(753\) 0 0
\(754\) −3.82919 + 1.05884i −0.139451 + 0.0385608i
\(755\) −10.1411 + 10.1411i −0.369073 + 0.369073i
\(756\) 0 0
\(757\) 24.1323 + 24.1323i 0.877104 + 0.877104i 0.993234 0.116130i \(-0.0370490\pi\)
−0.116130 + 0.993234i \(0.537049\pi\)
\(758\) 13.3381 23.5339i 0.484461 0.854788i
\(759\) 0 0
\(760\) 7.75839 + 7.39562i 0.281426 + 0.268267i
\(761\) 50.1874i 1.81929i −0.415383 0.909647i \(-0.636352\pi\)
0.415383 0.909647i \(-0.363648\pi\)
\(762\) 0 0
\(763\) 6.11004 + 6.11004i 0.221198 + 0.221198i
\(764\) 0.114530 0.0685832i 0.00414354 0.00248125i
\(765\) 0 0
\(766\) −8.25631 29.8581i −0.298312 1.07882i
\(767\) 16.1517 0.583206
\(768\) 0 0
\(769\) −28.6887 −1.03454 −0.517270 0.855822i \(-0.673052\pi\)
−0.517270 + 0.855822i \(0.673052\pi\)
\(770\) −3.94412 14.2635i −0.142136 0.514020i
\(771\) 0 0
\(772\) 1.88565 1.12918i 0.0678662 0.0406400i
\(773\) 37.5957 + 37.5957i 1.35222 + 1.35222i 0.883171 + 0.469052i \(0.155404\pi\)
0.469052 + 0.883171i \(0.344596\pi\)
\(774\) 0 0
\(775\) 7.20435i 0.258788i
\(776\) −38.1436 36.3601i −1.36928 1.30525i
\(777\) 0 0
\(778\) 4.42628 7.80977i 0.158690 0.279994i
\(779\) −17.1810 17.1810i −0.615572 0.615572i
\(780\) 0 0
\(781\) −3.15194 + 3.15194i −0.112785 + 0.112785i
\(782\) −4.71245 + 1.30308i −0.168517 + 0.0465980i
\(783\) 0 0
\(784\) −25.1855 + 47.0267i −0.899481 + 1.67953i
\(785\) −2.97783 −0.106283
\(786\) 0 0
\(787\) −3.13285 + 3.13285i −0.111674 + 0.111674i −0.760736 0.649062i \(-0.775162\pi\)
0.649062 + 0.760736i \(0.275162\pi\)
\(788\) 32.7255 + 8.21145i 1.16580 + 0.292521i
\(789\) 0 0
\(790\) −3.53061 + 6.22945i −0.125614 + 0.221634i
\(791\) 11.5463i 0.410541i
\(792\) 0 0
\(793\) 3.10304i 0.110192i
\(794\) 20.5129 + 11.6259i 0.727974 + 0.412588i
\(795\) 0 0
\(796\) 11.3434 + 18.9428i 0.402056 + 0.671408i
\(797\) −0.0562195 + 0.0562195i −0.00199140 + 0.00199140i −0.708102 0.706110i \(-0.750448\pi\)
0.706110 + 0.708102i \(0.250448\pi\)
\(798\) 0 0
\(799\) −3.65536 −0.129317
\(800\) −1.24503 + 5.51814i −0.0440185 + 0.195096i
\(801\) 0 0
\(802\) −9.39488 33.9756i −0.331745 1.19972i
\(803\) 2.28748 2.28748i 0.0807233 0.0807233i
\(804\) 0 0
\(805\) 7.57088 + 7.57088i 0.266838 + 0.266838i
\(806\) −19.0359 10.7888i −0.670511 0.380020i
\(807\) 0 0
\(808\) −0.463423 19.3588i −0.0163032 0.681039i
\(809\) 3.59856i 0.126518i 0.997997 + 0.0632592i \(0.0201495\pi\)
−0.997997 + 0.0632592i \(0.979851\pi\)
\(810\) 0 0
\(811\) −7.36274 7.36274i −0.258541 0.258541i 0.565920 0.824460i \(-0.308521\pi\)
−0.824460 + 0.565920i \(0.808521\pi\)
\(812\) 11.4433 + 2.87134i 0.401581 + 0.100764i
\(813\) 0 0
\(814\) 23.3100 6.44564i 0.817014 0.225920i
\(815\) −7.55196 −0.264534
\(816\) 0 0
\(817\) −41.0414 −1.43586
\(818\) 29.3542 8.11697i 1.02634 0.283803i
\(819\) 0 0
\(820\) 3.12087 12.4378i 0.108985 0.434345i
\(821\) −14.7799 14.7799i −0.515824 0.515824i 0.400481 0.916305i \(-0.368843\pi\)
−0.916305 + 0.400481i \(0.868843\pi\)
\(822\) 0 0
\(823\) 52.7544i 1.83890i −0.393203 0.919452i \(-0.628633\pi\)
0.393203 0.919452i \(-0.371367\pi\)
\(824\) −17.8088 + 18.6824i −0.620399 + 0.650831i
\(825\) 0 0
\(826\) −41.7287 23.6502i −1.45193 0.822897i
\(827\) −16.8883 16.8883i −0.587265 0.587265i 0.349625 0.936890i \(-0.386309\pi\)
−0.936890 + 0.349625i \(0.886309\pi\)
\(828\) 0 0
\(829\) −8.55974 + 8.55974i −0.297292 + 0.297292i −0.839952 0.542660i \(-0.817417\pi\)
0.542660 + 0.839952i \(0.317417\pi\)
\(830\) 1.30579 + 4.72226i 0.0453247 + 0.163912i
\(831\) 0 0
\(832\) 12.7160 + 11.5534i 0.440847 + 0.400541i
\(833\) 19.4201 0.672868
\(834\) 0 0
\(835\) −11.3622 + 11.3622i −0.393206 + 0.393206i
\(836\) 15.0886 9.03543i 0.521850 0.312497i
\(837\) 0 0
\(838\) 30.0980 + 17.0584i 1.03972 + 0.589271i
\(839\) 17.5407i 0.605572i 0.953059 + 0.302786i \(0.0979168\pi\)
−0.953059 + 0.302786i \(0.902083\pi\)
\(840\) 0 0
\(841\) 27.2889i 0.940996i
\(842\) 19.1638 33.8129i 0.660429 1.16527i
\(843\) 0 0
\(844\) 5.91814 23.5859i 0.203711 0.811860i
\(845\) −5.93112 + 5.93112i −0.204037 + 0.204037i
\(846\) 0 0
\(847\) 25.3238 0.870137
\(848\) −8.13881 + 2.46166i −0.279488 + 0.0845337i
\(849\) 0 0
\(850\) 1.98483 0.548843i 0.0680793 0.0188252i
\(851\) −12.3726 + 12.3726i −0.424129 + 0.424129i
\(852\) 0 0
\(853\) −15.3577 15.3577i −0.525839 0.525839i 0.393490 0.919329i \(-0.371268\pi\)
−0.919329 + 0.393490i \(0.871268\pi\)
\(854\) 4.54363 8.01683i 0.155480 0.274330i
\(855\) 0 0
\(856\) −0.971684 40.5905i −0.0332115 1.38736i
\(857\) 17.9553i 0.613341i 0.951816 + 0.306671i \(0.0992150\pi\)
−0.951816 + 0.306671i \(0.900785\pi\)
\(858\) 0 0
\(859\) −33.3048 33.3048i −1.13634 1.13634i −0.989100 0.147245i \(-0.952960\pi\)
−0.147245 0.989100i \(-0.547040\pi\)
\(860\) −11.1280 18.5830i −0.379461 0.633676i
\(861\) 0 0
\(862\) −10.6956 38.6795i −0.364293 1.31743i
\(863\) 32.3557 1.10140 0.550701 0.834703i \(-0.314361\pi\)
0.550701 + 0.834703i \(0.314361\pi\)
\(864\) 0 0
\(865\) −24.2019 −0.822889
\(866\) 3.40731 + 12.3222i 0.115785 + 0.418724i
\(867\) 0 0
\(868\) 33.3825 + 55.7467i 1.13308 + 1.89217i
\(869\) 8.30766 + 8.30766i 0.281818 + 0.281818i
\(870\) 0 0
\(871\) 15.8765i 0.537956i
\(872\) −5.41803 + 0.129700i −0.183477 + 0.00439221i
\(873\) 0 0
\(874\) −6.27397 + 11.0699i −0.212220 + 0.374444i
\(875\) −3.18877 3.18877i −0.107800 0.107800i
\(876\) 0 0
\(877\) 26.2297 26.2297i 0.885714 0.885714i −0.108394 0.994108i \(-0.534571\pi\)
0.994108 + 0.108394i \(0.0345707\pi\)
\(878\) 38.5677 10.6647i 1.30160 0.359916i
\(879\) 0 0
\(880\) 8.18224 + 4.38205i 0.275823 + 0.147719i
\(881\) 47.3359 1.59479 0.797394 0.603459i \(-0.206211\pi\)
0.797394 + 0.603459i \(0.206211\pi\)
\(882\) 0 0
\(883\) 8.08371 8.08371i 0.272039 0.272039i −0.557882 0.829920i \(-0.688386\pi\)
0.829920 + 0.557882i \(0.188386\pi\)
\(884\) 1.52217 6.06640i 0.0511962 0.204035i
\(885\) 0 0
\(886\) −12.9415 + 22.8341i −0.434778 + 0.767127i
\(887\) 12.9255i 0.433994i 0.976172 + 0.216997i \(0.0696263\pi\)
−0.976172 + 0.216997i \(0.930374\pi\)
\(888\) 0 0
\(889\) 61.9412i 2.07744i
\(890\) 11.5161 + 6.52690i 0.386022 + 0.218782i
\(891\) 0 0
\(892\) 36.7606 22.0132i 1.23084 0.737055i
\(893\) −6.72664 + 6.72664i −0.225098 + 0.225098i
\(894\) 0 0
\(895\) −1.47760 −0.0493906
\(896\) −15.9352 48.4680i −0.532359 1.61920i
\(897\) 0 0
\(898\) 5.42384 + 19.6147i 0.180996 + 0.654553i
\(899\) 6.66378 6.66378i 0.222250 0.222250i
\(900\) 0 0
\(901\) 2.18878 + 2.18878i 0.0729190 + 0.0729190i
\(902\) −18.3050 10.3746i −0.609490 0.345435i
\(903\) 0 0
\(904\) −5.24186 4.99676i −0.174342 0.166190i
\(905\) 16.9544i 0.563584i
\(906\) 0 0
\(907\) 16.4991 + 16.4991i 0.547844 + 0.547844i 0.925817 0.377973i \(-0.123379\pi\)
−0.377973 + 0.925817i \(0.623379\pi\)
\(908\) −5.55051 + 22.1207i −0.184200 + 0.734103i
\(909\) 0 0
\(910\) −13.2009 + 3.65031i −0.437607 + 0.121006i
\(911\) 26.6745 0.883765 0.441883 0.897073i \(-0.354311\pi\)
0.441883 + 0.897073i \(0.354311\pi\)
\(912\) 0 0
\(913\) 8.03908 0.266055
\(914\) −6.19563 + 1.71321i −0.204933 + 0.0566678i
\(915\) 0 0
\(916\) −12.7065 3.18830i −0.419834 0.105344i
\(917\) −23.4827 23.4827i −0.775467 0.775467i
\(918\) 0 0
\(919\) 57.7425i 1.90475i 0.304932 + 0.952374i \(0.401366\pi\)
−0.304932 + 0.952374i \(0.598634\pi\)
\(920\) −6.71341 + 0.160710i −0.221334 + 0.00529846i
\(921\) 0 0
\(922\) −34.4595 19.5303i −1.13486 0.643197i
\(923\) 2.91714 + 2.91714i 0.0960188 + 0.0960188i
\(924\) 0 0
\(925\) 5.21123 5.21123i 0.171344 0.171344i
\(926\) −5.50280 19.9003i −0.180833 0.653965i
\(927\) 0 0
\(928\) −6.25571 + 3.95248i −0.205354 + 0.129747i
\(929\) −42.5386 −1.39565 −0.697823 0.716270i \(-0.745848\pi\)
−0.697823 + 0.716270i \(0.745848\pi\)
\(930\) 0 0
\(931\) 35.7372 35.7372i 1.17124 1.17124i
\(932\) 26.7843 + 44.7281i 0.877349 + 1.46512i
\(933\) 0 0
\(934\) −34.4698 19.5362i −1.12789 0.639243i
\(935\) 3.37894i 0.110503i
\(936\) 0 0
\(937\) 16.6795i 0.544894i −0.962171 0.272447i \(-0.912167\pi\)
0.962171 0.272447i \(-0.0878330\pi\)
\(938\) −23.2473 + 41.0177i −0.759050 + 1.33928i
\(939\) 0 0
\(940\) −4.86959 1.22187i −0.158829 0.0398531i
\(941\) −9.63152 + 9.63152i −0.313979 + 0.313979i −0.846449 0.532470i \(-0.821264\pi\)
0.532470 + 0.846449i \(0.321264\pi\)
\(942\) 0 0
\(943\) 15.2227 0.495721
\(944\) 28.7952 8.70938i 0.937205 0.283466i
\(945\) 0 0
\(946\) −34.2545 + 9.47200i −1.11371 + 0.307961i
\(947\) 3.44034 3.44034i 0.111796 0.111796i −0.648996 0.760792i \(-0.724811\pi\)
0.760792 + 0.648996i \(0.224811\pi\)
\(948\) 0 0
\(949\) −2.11707 2.11707i −0.0687231 0.0687231i
\(950\) 2.64253 4.66251i 0.0857350 0.151272i
\(951\) 0 0
\(952\) −12.8153 + 13.4440i −0.415347 + 0.435721i
\(953\) 17.6965i 0.573247i −0.958043 0.286623i \(-0.907467\pi\)
0.958043 0.286623i \(-0.0925328\pi\)
\(954\) 0 0
\(955\) −0.0471973 0.0471973i −0.00152727 0.00152727i
\(956\) 8.78886 5.26299i 0.284252 0.170217i
\(957\) 0 0
\(958\) −7.92940 28.6759i −0.256187 0.926475i
\(959\) 102.622 3.31384
\(960\) 0 0
\(961\) 20.9027 0.674281
\(962\) −5.96548 21.5735i −0.192335 0.695559i
\(963\) 0 0
\(964\) −19.7303 + 11.8150i −0.635470 + 0.380535i
\(965\) −0.777073 0.777073i −0.0250149 0.0250149i
\(966\) 0 0
\(967\) 15.0023i 0.482442i −0.970470 0.241221i \(-0.922452\pi\)
0.970470 0.241221i \(-0.0775479\pi\)
\(968\) −10.9591 + 11.4966i −0.352238 + 0.369516i
\(969\) 0 0
\(970\) −12.9918 + 22.9229i −0.417142 + 0.736010i
\(971\) 14.3135 + 14.3135i 0.459340 + 0.459340i 0.898439 0.439098i \(-0.144702\pi\)
−0.439098 + 0.898439i \(0.644702\pi\)
\(972\) 0 0
\(973\) −28.3241 + 28.3241i −0.908030 + 0.908030i
\(974\) 14.0019 3.87177i 0.448649 0.124060i
\(975\) 0 0
\(976\) 1.67323 + 5.53207i 0.0535587 + 0.177077i
\(977\) −48.1433 −1.54024 −0.770120 0.637900i \(-0.779804\pi\)
−0.770120 + 0.637900i \(0.779804\pi\)
\(978\) 0 0
\(979\) 15.3580 15.3580i 0.490845 0.490845i
\(980\) 25.8711 + 6.49155i 0.826422 + 0.207365i
\(981\) 0 0
\(982\) −5.87430 + 10.3647i −0.187457 + 0.330750i
\(983\) 0.791292i 0.0252383i −0.999920 0.0126191i \(-0.995983\pi\)
0.999920 0.0126191i \(-0.00401690\pi\)
\(984\) 0 0
\(985\) 16.8700i 0.537523i
\(986\) 2.34357 + 1.32824i 0.0746343 + 0.0422999i
\(987\) 0 0
\(988\) −8.36234 13.9646i −0.266042 0.444273i
\(989\) 18.1818 18.1818i 0.578149 0.578149i
\(990\) 0 0
\(991\) −60.2424 −1.91366 −0.956832 0.290643i \(-0.906131\pi\)
−0.956832 + 0.290643i \(0.906131\pi\)
\(992\) −39.7547 8.96964i −1.26221 0.284786i
\(993\) 0 0
\(994\) −3.26513 11.8080i −0.103563 0.374526i
\(995\) 7.80625 7.80625i 0.247475 0.247475i
\(996\) 0 0
\(997\) 1.15773 + 1.15773i 0.0366655 + 0.0366655i 0.725202 0.688536i \(-0.241746\pi\)
−0.688536 + 0.725202i \(0.741746\pi\)
\(998\) −4.89744 2.77568i −0.155026 0.0878626i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 720.2.t.c.181.6 16
3.2 odd 2 80.2.l.a.21.3 16
4.3 odd 2 2880.2.t.c.2161.5 16
12.11 even 2 320.2.l.a.241.1 16
15.2 even 4 400.2.q.g.149.8 16
15.8 even 4 400.2.q.h.149.1 16
15.14 odd 2 400.2.l.h.101.6 16
16.3 odd 4 2880.2.t.c.721.8 16
16.13 even 4 inner 720.2.t.c.541.6 16
24.5 odd 2 640.2.l.b.481.1 16
24.11 even 2 640.2.l.a.481.8 16
48.5 odd 4 640.2.l.b.161.1 16
48.11 even 4 640.2.l.a.161.8 16
48.29 odd 4 80.2.l.a.61.3 yes 16
48.35 even 4 320.2.l.a.81.1 16
60.23 odd 4 1600.2.q.g.49.1 16
60.47 odd 4 1600.2.q.h.49.8 16
60.59 even 2 1600.2.l.i.1201.8 16
96.29 odd 8 5120.2.a.v.1.7 8
96.35 even 8 5120.2.a.t.1.2 8
96.77 odd 8 5120.2.a.s.1.2 8
96.83 even 8 5120.2.a.u.1.7 8
240.29 odd 4 400.2.l.h.301.6 16
240.77 even 4 400.2.q.h.349.1 16
240.83 odd 4 1600.2.q.h.849.8 16
240.173 even 4 400.2.q.g.349.8 16
240.179 even 4 1600.2.l.i.401.8 16
240.227 odd 4 1600.2.q.g.849.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.2.l.a.21.3 16 3.2 odd 2
80.2.l.a.61.3 yes 16 48.29 odd 4
320.2.l.a.81.1 16 48.35 even 4
320.2.l.a.241.1 16 12.11 even 2
400.2.l.h.101.6 16 15.14 odd 2
400.2.l.h.301.6 16 240.29 odd 4
400.2.q.g.149.8 16 15.2 even 4
400.2.q.g.349.8 16 240.173 even 4
400.2.q.h.149.1 16 15.8 even 4
400.2.q.h.349.1 16 240.77 even 4
640.2.l.a.161.8 16 48.11 even 4
640.2.l.a.481.8 16 24.11 even 2
640.2.l.b.161.1 16 48.5 odd 4
640.2.l.b.481.1 16 24.5 odd 2
720.2.t.c.181.6 16 1.1 even 1 trivial
720.2.t.c.541.6 16 16.13 even 4 inner
1600.2.l.i.401.8 16 240.179 even 4
1600.2.l.i.1201.8 16 60.59 even 2
1600.2.q.g.49.1 16 60.23 odd 4
1600.2.q.g.849.1 16 240.227 odd 4
1600.2.q.h.49.8 16 60.47 odd 4
1600.2.q.h.849.8 16 240.83 odd 4
2880.2.t.c.721.8 16 16.3 odd 4
2880.2.t.c.2161.5 16 4.3 odd 2
5120.2.a.s.1.2 8 96.77 odd 8
5120.2.a.t.1.2 8 96.35 even 8
5120.2.a.u.1.7 8 96.83 even 8
5120.2.a.v.1.7 8 96.29 odd 8