Properties

Label 441.2.g.d.67.1
Level $441$
Weight $2$
Character 441.67
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
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] = [441,2,Mod(67,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.d.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.849814 + 1.47192i) q^{2} +(1.64400 + 0.545231i) q^{3} +(-0.444368 - 0.769668i) q^{4} +3.58836 q^{5} +(-2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 + 1.79272i) q^{9} +O(q^{10})\) \(q+(-0.849814 + 1.47192i) q^{2} +(1.64400 + 0.545231i) q^{3} +(-0.444368 - 0.769668i) q^{4} +3.58836 q^{5} +(-2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 + 1.79272i) q^{9} +(-3.04944 + 5.28179i) q^{10} -2.81089 q^{11} +(-0.310892 - 1.50761i) q^{12} +(0.500000 - 0.866025i) q^{13} +(5.89926 + 1.95649i) q^{15} +(2.49381 - 4.31941i) q^{16} +(-2.05563 + 3.56046i) q^{17} +(-4.68292 + 2.01715i) q^{18} +(-0.444368 - 0.769668i) q^{19} +(-1.59455 - 2.76185i) q^{20} +(2.38874 - 4.13741i) q^{22} +5.87636 q^{23} +(-3.10507 - 1.02980i) q^{24} +7.87636 q^{25} +(0.849814 + 1.47192i) q^{26} +(2.97710 + 4.25874i) q^{27} +(0.849814 + 1.47192i) q^{29} +(-7.89307 + 7.02059i) q^{30} +(-3.49381 - 6.05146i) q^{31} +(2.34981 + 4.07000i) q^{32} +(-4.62110 - 1.53259i) q^{33} +(-3.49381 - 6.05146i) q^{34} +(0.310892 - 2.64802i) q^{36} +(-2.38255 - 4.12669i) q^{37} +1.51052 q^{38} +(1.29418 - 1.15113i) q^{39} -6.77747 q^{40} +(-2.70582 + 4.68661i) q^{41} +(-2.60507 - 4.51212i) q^{43} +(1.24907 + 2.16345i) q^{44} +(8.63162 + 6.43292i) q^{45} +(-4.99381 + 8.64953i) q^{46} +(-1.33310 + 2.30900i) q^{47} +(6.45489 - 5.74138i) q^{48} +(-6.69344 + 11.5934i) q^{50} +(-5.32072 + 4.73259i) q^{51} -0.888736 q^{52} +(0.0618219 - 0.107079i) q^{53} +(-8.79851 + 0.762918i) q^{54} -10.0865 q^{55} +(-0.310892 - 1.50761i) q^{57} -2.88874 q^{58} +(-4.43818 - 7.68715i) q^{59} +(-1.11559 - 5.40987i) q^{60} +(1.93818 - 3.35702i) q^{61} +11.8764 q^{62} +1.98762 q^{64} +(1.79418 - 3.10761i) q^{65} +(6.18292 - 5.49948i) q^{66} +(-6.15452 - 10.6599i) q^{67} +3.65383 q^{68} +(9.66071 + 3.20397i) q^{69} -2.87636 q^{71} +(-4.54325 - 3.38597i) q^{72} +(-5.32072 + 9.21576i) q^{73} +8.09888 q^{74} +(12.9487 + 4.29443i) q^{75} +(-0.394926 + 0.684031i) q^{76} +(0.594554 + 2.88318i) q^{78} +(3.54325 - 6.13709i) q^{79} +(8.94870 - 15.4996i) q^{80} +(2.57234 + 8.62456i) q^{81} +(-4.59888 - 7.96550i) q^{82} +(-2.05563 - 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} +8.85532 q^{86} +(0.594554 + 2.88318i) q^{87} +5.30903 q^{88} +(4.80470 + 8.32199i) q^{89} +(-16.8040 + 7.23828i) q^{90} +(-2.61126 - 4.52284i) q^{92} +(-2.44437 - 11.8535i) q^{93} +(-2.26578 - 3.92445i) q^{94} +(-1.59455 - 2.76185i) q^{95} +(1.64400 + 7.97225i) q^{96} +(3.66071 + 6.34053i) q^{97} +(-6.76145 - 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} - 2 q^{3} - 3 q^{4} + 10 q^{5} - q^{6} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} - 2 q^{3} - 3 q^{4} + 10 q^{5} - q^{6} - 12 q^{8} + 8 q^{9} - 4 q^{11} + 11 q^{12} + 3 q^{13} + 11 q^{15} - 3 q^{16} - 12 q^{17} - 23 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 12 q^{25} - q^{26} + 7 q^{27} - q^{29} - 5 q^{30} - 3 q^{31} + 8 q^{32} - 5 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} - 16 q^{38} + 2 q^{39} - 42 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + 4 q^{45} - 12 q^{46} - 9 q^{47} + 14 q^{48} - 10 q^{50} + 3 q^{51} - 6 q^{52} + 18 q^{53} - 4 q^{54} + 12 q^{55} + 11 q^{57} - 18 q^{58} - 9 q^{59} + 37 q^{60} - 6 q^{61} + 36 q^{62} - 24 q^{64} + 5 q^{65} + 32 q^{66} - 12 q^{68} + 39 q^{69} + 18 q^{71} + 9 q^{72} + 3 q^{73} + 12 q^{74} + 35 q^{75} - 21 q^{76} + 10 q^{78} - 15 q^{79} + 11 q^{80} + 8 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} + 68 q^{86} + 10 q^{87} - 42 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 15 q^{93} + 24 q^{94} - 16 q^{95} - 2 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.849814 + 1.47192i −0.600909 + 1.04081i 0.391774 + 0.920061i \(0.371861\pi\)
−0.992684 + 0.120744i \(0.961472\pi\)
\(3\) 1.64400 + 0.545231i 0.949162 + 0.314789i
\(4\) −0.444368 0.769668i −0.222184 0.384834i
\(5\) 3.58836 1.60477 0.802383 0.596810i \(-0.203565\pi\)
0.802383 + 0.596810i \(0.203565\pi\)
\(6\) −2.19963 + 1.95649i −0.897994 + 0.798733i
\(7\) 0 0
\(8\) −1.88874 −0.667769
\(9\) 2.40545 + 1.79272i 0.801815 + 0.597572i
\(10\) −3.04944 + 5.28179i −0.964318 + 1.67025i
\(11\) −2.81089 −0.847516 −0.423758 0.905775i \(-0.639289\pi\)
−0.423758 + 0.905775i \(0.639289\pi\)
\(12\) −0.310892 1.50761i −0.0897469 0.435211i
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) 5.89926 + 1.95649i 1.52318 + 0.505163i
\(16\) 2.49381 4.31941i 0.623453 1.07985i
\(17\) −2.05563 + 3.56046i −0.498564 + 0.863538i −0.999999 0.00165734i \(-0.999472\pi\)
0.501435 + 0.865196i \(0.332806\pi\)
\(18\) −4.68292 + 2.01715i −1.10377 + 0.475447i
\(19\) −0.444368 0.769668i −0.101945 0.176574i 0.810541 0.585682i \(-0.199173\pi\)
−0.912486 + 0.409108i \(0.865840\pi\)
\(20\) −1.59455 2.76185i −0.356553 0.617568i
\(21\) 0 0
\(22\) 2.38874 4.13741i 0.509280 0.882099i
\(23\) 5.87636 1.22530 0.612652 0.790352i \(-0.290103\pi\)
0.612652 + 0.790352i \(0.290103\pi\)
\(24\) −3.10507 1.02980i −0.633821 0.210207i
\(25\) 7.87636 1.57527
\(26\) 0.849814 + 1.47192i 0.166662 + 0.288667i
\(27\) 2.97710 + 4.25874i 0.572943 + 0.819595i
\(28\) 0 0
\(29\) 0.849814 + 1.47192i 0.157807 + 0.273329i 0.934077 0.357071i \(-0.116224\pi\)
−0.776271 + 0.630399i \(0.782891\pi\)
\(30\) −7.89307 + 7.02059i −1.44107 + 1.28178i
\(31\) −3.49381 6.05146i −0.627507 1.08687i −0.988050 0.154131i \(-0.950742\pi\)
0.360544 0.932742i \(-0.382591\pi\)
\(32\) 2.34981 + 4.07000i 0.415392 + 0.719481i
\(33\) −4.62110 1.53259i −0.804430 0.266789i
\(34\) −3.49381 6.05146i −0.599183 1.03782i
\(35\) 0 0
\(36\) 0.310892 2.64802i 0.0518154 0.441337i
\(37\) −2.38255 4.12669i −0.391688 0.678424i 0.600984 0.799261i \(-0.294775\pi\)
−0.992672 + 0.120837i \(0.961442\pi\)
\(38\) 1.51052 0.245039
\(39\) 1.29418 1.15113i 0.207235 0.184328i
\(40\) −6.77747 −1.07161
\(41\) −2.70582 + 4.68661i −0.422578 + 0.731926i −0.996191 0.0872002i \(-0.972208\pi\)
0.573613 + 0.819126i \(0.305541\pi\)
\(42\) 0 0
\(43\) −2.60507 4.51212i −0.397270 0.688092i 0.596118 0.802897i \(-0.296709\pi\)
−0.993388 + 0.114805i \(0.963376\pi\)
\(44\) 1.24907 + 2.16345i 0.188304 + 0.326153i
\(45\) 8.63162 + 6.43292i 1.28673 + 0.958962i
\(46\) −4.99381 + 8.64953i −0.736297 + 1.27530i
\(47\) −1.33310 + 2.30900i −0.194453 + 0.336803i −0.946721 0.322055i \(-0.895627\pi\)
0.752268 + 0.658857i \(0.228960\pi\)
\(48\) 6.45489 5.74138i 0.931683 0.828697i
\(49\) 0 0
\(50\) −6.69344 + 11.5934i −0.946595 + 1.63955i
\(51\) −5.32072 + 4.73259i −0.745050 + 0.662695i
\(52\) −0.888736 −0.123245
\(53\) 0.0618219 0.107079i 0.00849190 0.0147084i −0.861748 0.507336i \(-0.830630\pi\)
0.870240 + 0.492628i \(0.163964\pi\)
\(54\) −8.79851 + 0.762918i −1.19733 + 0.103820i
\(55\) −10.0865 −1.36006
\(56\) 0 0
\(57\) −0.310892 1.50761i −0.0411787 0.199688i
\(58\) −2.88874 −0.379310
\(59\) −4.43818 7.68715i −0.577802 1.00078i −0.995731 0.0923022i \(-0.970577\pi\)
0.417929 0.908479i \(-0.362756\pi\)
\(60\) −1.11559 5.40987i −0.144023 0.698411i
\(61\) 1.93818 3.35702i 0.248158 0.429823i −0.714857 0.699271i \(-0.753508\pi\)
0.963015 + 0.269448i \(0.0868414\pi\)
\(62\) 11.8764 1.50830
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) 1.79418 3.10761i 0.222541 0.385452i
\(66\) 6.18292 5.49948i 0.761065 0.676939i
\(67\) −6.15452 10.6599i −0.751894 1.30232i −0.946904 0.321517i \(-0.895807\pi\)
0.195010 0.980801i \(-0.437526\pi\)
\(68\) 3.65383 0.443092
\(69\) 9.66071 + 3.20397i 1.16301 + 0.385713i
\(70\) 0 0
\(71\) −2.87636 −0.341361 −0.170680 0.985326i \(-0.554597\pi\)
−0.170680 + 0.985326i \(0.554597\pi\)
\(72\) −4.54325 3.38597i −0.535427 0.399040i
\(73\) −5.32072 + 9.21576i −0.622744 + 1.07862i 0.366229 + 0.930525i \(0.380649\pi\)
−0.988973 + 0.148099i \(0.952685\pi\)
\(74\) 8.09888 0.941476
\(75\) 12.9487 + 4.29443i 1.49519 + 0.495879i
\(76\) −0.394926 + 0.684031i −0.0453011 + 0.0784638i
\(77\) 0 0
\(78\) 0.594554 + 2.88318i 0.0673200 + 0.326456i
\(79\) 3.54325 6.13709i 0.398647 0.690477i −0.594912 0.803791i \(-0.702813\pi\)
0.993559 + 0.113314i \(0.0361465\pi\)
\(80\) 8.94870 15.4996i 1.00049 1.73291i
\(81\) 2.57234 + 8.62456i 0.285816 + 0.958285i
\(82\) −4.59888 7.96550i −0.507862 0.879642i
\(83\) −2.05563 3.56046i −0.225635 0.390811i 0.730875 0.682512i \(-0.239112\pi\)
−0.956510 + 0.291700i \(0.905779\pi\)
\(84\) 0 0
\(85\) −7.37636 + 12.7762i −0.800078 + 1.38578i
\(86\) 8.85532 0.954893
\(87\) 0.594554 + 2.88318i 0.0637429 + 0.309109i
\(88\) 5.30903 0.565945
\(89\) 4.80470 + 8.32199i 0.509297 + 0.882129i 0.999942 + 0.0107692i \(0.00342802\pi\)
−0.490645 + 0.871360i \(0.663239\pi\)
\(90\) −16.8040 + 7.23828i −1.77130 + 0.762981i
\(91\) 0 0
\(92\) −2.61126 4.52284i −0.272243 0.471539i
\(93\) −2.44437 11.8535i −0.253469 1.22915i
\(94\) −2.26578 3.92445i −0.233697 0.404776i
\(95\) −1.59455 2.76185i −0.163598 0.283360i
\(96\) 1.64400 + 7.97225i 0.167790 + 0.813664i
\(97\) 3.66071 + 6.34053i 0.371688 + 0.643783i 0.989825 0.142287i \(-0.0454456\pi\)
−0.618137 + 0.786070i \(0.712112\pi\)
\(98\) 0 0
\(99\) −6.76145 5.03913i −0.679551 0.506452i
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) −3.46472 −0.344753 −0.172376 0.985031i \(-0.555144\pi\)
−0.172376 + 0.985031i \(0.555144\pi\)
\(102\) −2.44437 11.8535i −0.242028 1.17367i
\(103\) 15.8764 1.56434 0.782172 0.623063i \(-0.214112\pi\)
0.782172 + 0.623063i \(0.214112\pi\)
\(104\) −0.944368 + 1.63569i −0.0926029 + 0.160393i
\(105\) 0 0
\(106\) 0.105074 + 0.181994i 0.0102057 + 0.0176768i
\(107\) 2.67673 + 4.63623i 0.258769 + 0.448201i 0.965912 0.258869i \(-0.0833498\pi\)
−0.707143 + 0.707070i \(0.750016\pi\)
\(108\) 1.95489 4.18383i 0.188109 0.402589i
\(109\) 9.43199 16.3367i 0.903421 1.56477i 0.0803973 0.996763i \(-0.474381\pi\)
0.823023 0.568008i \(-0.192286\pi\)
\(110\) 8.57165 14.8465i 0.817275 1.41556i
\(111\) −1.66690 8.08330i −0.158215 0.767233i
\(112\) 0 0
\(113\) 9.27561 16.0658i 0.872576 1.51135i 0.0132538 0.999912i \(-0.495781\pi\)
0.859322 0.511434i \(-0.170886\pi\)
\(114\) 2.48329 + 0.823583i 0.232581 + 0.0771356i
\(115\) 21.0865 1.96633
\(116\) 0.755260 1.30815i 0.0701242 0.121459i
\(117\) 2.75526 1.18682i 0.254724 0.109722i
\(118\) 15.0865 1.38883
\(119\) 0 0
\(120\) −11.1421 3.69529i −1.01713 0.337332i
\(121\) −3.09888 −0.281717
\(122\) 3.29418 + 5.70569i 0.298241 + 0.516569i
\(123\) −7.00364 + 6.22948i −0.631497 + 0.561693i
\(124\) −3.10507 + 5.37815i −0.278844 + 0.482972i
\(125\) 10.3214 0.923175
\(126\) 0 0
\(127\) 9.98762 0.886258 0.443129 0.896458i \(-0.353868\pi\)
0.443129 + 0.896458i \(0.353868\pi\)
\(128\) −6.38874 + 11.0656i −0.564690 + 0.978071i
\(129\) −1.82258 8.83828i −0.160470 0.778167i
\(130\) 3.04944 + 5.28179i 0.267454 + 0.463244i
\(131\) −16.0531 −1.40256 −0.701282 0.712884i \(-0.747389\pi\)
−0.701282 + 0.712884i \(0.747389\pi\)
\(132\) 0.873885 + 4.23774i 0.0760619 + 0.368848i
\(133\) 0 0
\(134\) 20.9208 1.80728
\(135\) 10.6829 + 15.2819i 0.919439 + 1.31526i
\(136\) 3.88255 6.72477i 0.332926 0.576644i
\(137\) −12.9876 −1.10961 −0.554804 0.831981i \(-0.687207\pi\)
−0.554804 + 0.831981i \(0.687207\pi\)
\(138\) −12.9258 + 11.4970i −1.10032 + 0.978691i
\(139\) 0.555632 0.962383i 0.0471281 0.0816283i −0.841499 0.540259i \(-0.818326\pi\)
0.888627 + 0.458630i \(0.151660\pi\)
\(140\) 0 0
\(141\) −3.45056 + 3.06914i −0.290589 + 0.258468i
\(142\) 2.44437 4.23377i 0.205127 0.355290i
\(143\) −1.40545 + 2.43430i −0.117529 + 0.203567i
\(144\) 13.7422 5.91941i 1.14518 0.493284i
\(145\) 3.04944 + 5.28179i 0.253242 + 0.438629i
\(146\) −9.04325 15.6634i −0.748425 1.29631i
\(147\) 0 0
\(148\) −2.11745 + 3.66754i −0.174054 + 0.301470i
\(149\) 8.43268 0.690832 0.345416 0.938450i \(-0.387738\pi\)
0.345416 + 0.938450i \(0.387738\pi\)
\(150\) −17.3251 + 15.4100i −1.41458 + 1.25822i
\(151\) −14.8516 −1.20861 −0.604303 0.796755i \(-0.706548\pi\)
−0.604303 + 0.796755i \(0.706548\pi\)
\(152\) 0.839294 + 1.45370i 0.0680757 + 0.117911i
\(153\) −11.3276 + 4.87933i −0.915782 + 0.394470i
\(154\) 0 0
\(155\) −12.5371 21.7148i −1.00700 1.74418i
\(156\) −1.46108 0.484566i −0.116980 0.0387964i
\(157\) 1.44437 + 2.50172i 0.115273 + 0.199659i 0.917889 0.396837i \(-0.129892\pi\)
−0.802616 + 0.596496i \(0.796559\pi\)
\(158\) 6.02221 + 10.4308i 0.479101 + 0.829828i
\(159\) 0.160018 0.142330i 0.0126902 0.0112875i
\(160\) 8.43199 + 14.6046i 0.666607 + 1.15460i
\(161\) 0 0
\(162\) −14.8807 3.54299i −1.16914 0.278363i
\(163\) 5.15452 + 8.92788i 0.403733 + 0.699286i 0.994173 0.107796i \(-0.0343792\pi\)
−0.590440 + 0.807081i \(0.701046\pi\)
\(164\) 4.80951 0.375560
\(165\) −16.5822 5.49948i −1.29092 0.428134i
\(166\) 6.98762 0.542345
\(167\) 6.07598 10.5239i 0.470174 0.814365i −0.529244 0.848469i \(-0.677525\pi\)
0.999418 + 0.0341045i \(0.0108579\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) −12.5371 21.7148i −0.961549 1.66545i
\(171\) 0.310892 2.64802i 0.0237745 0.202499i
\(172\) −2.31522 + 4.01008i −0.176534 + 0.305766i
\(173\) −3.30470 + 5.72391i −0.251252 + 0.435181i −0.963871 0.266370i \(-0.914176\pi\)
0.712619 + 0.701551i \(0.247509\pi\)
\(174\) −4.74907 1.57503i −0.360026 0.119403i
\(175\) 0 0
\(176\) −7.00983 + 12.1414i −0.528386 + 0.915191i
\(177\) −3.10507 15.0575i −0.233392 1.13179i
\(178\) −16.3324 −1.22417
\(179\) 1.92147 3.32808i 0.143617 0.248752i −0.785239 0.619193i \(-0.787460\pi\)
0.928856 + 0.370440i \(0.120793\pi\)
\(180\) 1.11559 9.50206i 0.0831515 0.708242i
\(181\) −18.5426 −1.37826 −0.689129 0.724639i \(-0.742007\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(182\) 0 0
\(183\) 5.01671 4.46218i 0.370846 0.329854i
\(184\) −11.0989 −0.818221
\(185\) −8.54944 14.8081i −0.628567 1.08871i
\(186\) 19.5247 + 6.47536i 1.43162 + 0.474796i
\(187\) 5.77816 10.0081i 0.422541 0.731862i
\(188\) 2.36955 0.172818
\(189\) 0 0
\(190\) 5.42030 0.393230
\(191\) −2.31708 + 4.01330i −0.167658 + 0.290392i −0.937596 0.347726i \(-0.886954\pi\)
0.769938 + 0.638119i \(0.220287\pi\)
\(192\) 3.26764 + 1.08371i 0.235822 + 0.0782102i
\(193\) 12.6483 + 21.9075i 0.910446 + 1.57694i 0.813435 + 0.581656i \(0.197595\pi\)
0.0970118 + 0.995283i \(0.469072\pi\)
\(194\) −12.4437 −0.893404
\(195\) 4.64400 4.13066i 0.332563 0.295803i
\(196\) 0 0
\(197\) 10.7207 0.763816 0.381908 0.924200i \(-0.375267\pi\)
0.381908 + 0.924200i \(0.375267\pi\)
\(198\) 13.1632 5.67000i 0.935466 0.402949i
\(199\) −4.38323 + 7.59199i −0.310719 + 0.538182i −0.978518 0.206160i \(-0.933903\pi\)
0.667799 + 0.744342i \(0.267237\pi\)
\(200\) −14.8764 −1.05192
\(201\) −4.30587 20.8805i −0.303713 1.47280i
\(202\) 2.94437 5.09979i 0.207165 0.358820i
\(203\) 0 0
\(204\) 6.00688 + 1.99218i 0.420566 + 0.139481i
\(205\) −9.70946 + 16.8173i −0.678138 + 1.17457i
\(206\) −13.4920 + 23.3687i −0.940029 + 1.62818i
\(207\) 14.1353 + 10.5346i 0.982468 + 0.732208i
\(208\) −2.49381 4.31941i −0.172915 0.299497i
\(209\) 1.24907 + 2.16345i 0.0864000 + 0.149649i
\(210\) 0 0
\(211\) −5.26509 + 9.11941i −0.362464 + 0.627806i −0.988366 0.152096i \(-0.951398\pi\)
0.625902 + 0.779902i \(0.284731\pi\)
\(212\) −0.109887 −0.00754705
\(213\) −4.72872 1.56828i −0.324006 0.107457i
\(214\) −9.09888 −0.621987
\(215\) −9.34795 16.1911i −0.637525 1.10423i
\(216\) −5.62296 8.04364i −0.382594 0.547300i
\(217\) 0 0
\(218\) 16.0309 + 27.7663i 1.08575 + 1.88057i
\(219\) −13.7720 + 12.2497i −0.930624 + 0.827755i
\(220\) 4.48212 + 7.76326i 0.302184 + 0.523399i
\(221\) 2.05563 + 3.56046i 0.138277 + 0.239502i
\(222\) 13.3145 + 4.41576i 0.893613 + 0.296367i
\(223\) −2.83379 4.90827i −0.189765 0.328682i 0.755407 0.655256i \(-0.227439\pi\)
−0.945172 + 0.326574i \(0.894106\pi\)
\(224\) 0 0
\(225\) 18.9462 + 14.1201i 1.26308 + 0.941338i
\(226\) 15.7651 + 27.3059i 1.04868 + 1.81636i
\(227\) 11.0989 0.736659 0.368329 0.929695i \(-0.379930\pi\)
0.368329 + 0.929695i \(0.379930\pi\)
\(228\) −1.02221 + 0.909219i −0.0676976 + 0.0602145i
\(229\) −19.6428 −1.29803 −0.649017 0.760774i \(-0.724820\pi\)
−0.649017 + 0.760774i \(0.724820\pi\)
\(230\) −17.9196 + 31.0377i −1.18158 + 2.04656i
\(231\) 0 0
\(232\) −1.60507 2.78007i −0.105378 0.182521i
\(233\) −4.48143 7.76207i −0.293588 0.508510i 0.681067 0.732221i \(-0.261516\pi\)
−0.974656 + 0.223711i \(0.928183\pi\)
\(234\) −0.594554 + 5.06410i −0.0388672 + 0.331051i
\(235\) −4.78366 + 8.28554i −0.312052 + 0.540489i
\(236\) −3.94437 + 6.83185i −0.256756 + 0.444715i
\(237\) 9.17123 8.15747i 0.595735 0.529884i
\(238\) 0 0
\(239\) −5.61126 + 9.71899i −0.362963 + 0.628670i −0.988447 0.151567i \(-0.951568\pi\)
0.625484 + 0.780237i \(0.284901\pi\)
\(240\) 23.1625 20.6022i 1.49513 1.32986i
\(241\) 6.98624 0.450023 0.225012 0.974356i \(-0.427758\pi\)
0.225012 + 0.974356i \(0.427758\pi\)
\(242\) 2.63348 4.56131i 0.169286 0.293212i
\(243\) −0.473458 + 15.5813i −0.0303723 + 0.999539i
\(244\) −3.44506 −0.220547
\(245\) 0 0
\(246\) −3.21751 15.6027i −0.205141 0.994792i
\(247\) −0.888736 −0.0565489
\(248\) 6.59888 + 11.4296i 0.419030 + 0.725781i
\(249\) −1.43818 6.97418i −0.0911408 0.441970i
\(250\) −8.77128 + 15.1923i −0.554745 + 0.960846i
\(251\) −4.62041 −0.291638 −0.145819 0.989311i \(-0.546582\pi\)
−0.145819 + 0.989311i \(0.546582\pi\)
\(252\) 0 0
\(253\) −16.5178 −1.03847
\(254\) −8.48762 + 14.7010i −0.532561 + 0.922422i
\(255\) −19.0927 + 16.9822i −1.19563 + 1.06347i
\(256\) −8.87085 15.3648i −0.554428 0.960298i
\(257\) 1.42402 0.0888277 0.0444138 0.999013i \(-0.485858\pi\)
0.0444138 + 0.999013i \(0.485858\pi\)
\(258\) 14.5581 + 4.82819i 0.906348 + 0.300590i
\(259\) 0 0
\(260\) −3.18911 −0.197780
\(261\) −0.594554 + 5.06410i −0.0368020 + 0.313460i
\(262\) 13.6421 23.6289i 0.842814 1.45980i
\(263\) 16.2632 1.00283 0.501417 0.865206i \(-0.332812\pi\)
0.501417 + 0.865206i \(0.332812\pi\)
\(264\) 8.72803 + 2.89465i 0.537173 + 0.178153i
\(265\) 0.221840 0.384237i 0.0136275 0.0236035i
\(266\) 0 0
\(267\) 3.36151 + 16.3010i 0.205721 + 0.997604i
\(268\) −5.46974 + 9.47387i −0.334118 + 0.578709i
\(269\) −9.32691 + 16.1547i −0.568672 + 0.984969i 0.428026 + 0.903767i \(0.359209\pi\)
−0.996698 + 0.0812022i \(0.974124\pi\)
\(270\) −31.5723 + 2.73763i −1.92143 + 0.166607i
\(271\) 1.98143 + 3.43194i 0.120363 + 0.208475i 0.919911 0.392127i \(-0.128261\pi\)
−0.799548 + 0.600603i \(0.794927\pi\)
\(272\) 10.2527 + 17.7582i 0.621662 + 1.07675i
\(273\) 0 0
\(274\) 11.0371 19.1168i 0.666773 1.15489i
\(275\) −22.1396 −1.33507
\(276\) −1.82691 8.85928i −0.109967 0.533266i
\(277\) −2.33379 −0.140224 −0.0701120 0.997539i \(-0.522336\pi\)
−0.0701120 + 0.997539i \(0.522336\pi\)
\(278\) 0.944368 + 1.63569i 0.0566394 + 0.0981024i
\(279\) 2.44437 20.8199i 0.146340 1.24645i
\(280\) 0 0
\(281\) −13.9975 24.2443i −0.835018 1.44629i −0.894016 0.448035i \(-0.852124\pi\)
0.0589978 0.998258i \(-0.481210\pi\)
\(282\) −1.58520 7.68715i −0.0943975 0.457763i
\(283\) 5.16002 + 8.93741i 0.306731 + 0.531274i 0.977645 0.210261i \(-0.0674314\pi\)
−0.670914 + 0.741535i \(0.734098\pi\)
\(284\) 1.27816 + 2.21384i 0.0758449 + 0.131367i
\(285\) −1.11559 5.40987i −0.0660821 0.320453i
\(286\) −2.38874 4.13741i −0.141249 0.244650i
\(287\) 0 0
\(288\) −1.64400 + 14.0027i −0.0968734 + 0.825117i
\(289\) 0.0487535 + 0.0844436i 0.00286785 + 0.00496727i
\(290\) −10.3658 −0.608703
\(291\) 2.56113 + 12.4197i 0.150136 + 0.728058i
\(292\) 9.45744 0.553455
\(293\) −15.3480 + 26.5834i −0.896637 + 1.55302i −0.0648718 + 0.997894i \(0.520664\pi\)
−0.831765 + 0.555127i \(0.812670\pi\)
\(294\) 0 0
\(295\) −15.9258 27.5843i −0.927236 1.60602i
\(296\) 4.50000 + 7.79423i 0.261557 + 0.453030i
\(297\) −8.36831 11.9709i −0.485578 0.694620i
\(298\) −7.16621 + 12.4122i −0.415127 + 0.719021i
\(299\) 2.93818 5.08907i 0.169919 0.294309i
\(300\) −2.44870 11.8745i −0.141376 0.685575i
\(301\) 0 0
\(302\) 12.6211 21.8604i 0.726262 1.25792i
\(303\) −5.69599 1.88907i −0.327226 0.108524i
\(304\) −4.43268 −0.254231
\(305\) 6.95489 12.0462i 0.398236 0.689765i
\(306\) 2.44437 20.8199i 0.139735 1.19019i
\(307\) 11.4437 0.653125 0.326563 0.945176i \(-0.394110\pi\)
0.326563 + 0.945176i \(0.394110\pi\)
\(308\) 0 0
\(309\) 26.1007 + 8.65628i 1.48482 + 0.492439i
\(310\) 42.6167 2.42047
\(311\) 5.98143 + 10.3601i 0.339176 + 0.587470i 0.984278 0.176627i \(-0.0565185\pi\)
−0.645102 + 0.764096i \(0.723185\pi\)
\(312\) −2.44437 + 2.17417i −0.138385 + 0.123088i
\(313\) −6.77197 + 11.7294i −0.382774 + 0.662985i −0.991458 0.130429i \(-0.958365\pi\)
0.608683 + 0.793413i \(0.291698\pi\)
\(314\) −4.90978 −0.277075
\(315\) 0 0
\(316\) −6.29803 −0.354292
\(317\) 14.9814 25.9486i 0.841441 1.45742i −0.0472355 0.998884i \(-0.515041\pi\)
0.888676 0.458535i \(-0.151626\pi\)
\(318\) 0.0735129 + 0.356487i 0.00412240 + 0.0199908i
\(319\) −2.38874 4.13741i −0.133744 0.231651i
\(320\) 7.13231 0.398708
\(321\) 1.87271 + 9.08138i 0.104525 + 0.506873i
\(322\) 0 0
\(323\) 3.65383 0.203304
\(324\) 5.49498 5.81233i 0.305277 0.322907i
\(325\) 3.93818 6.82112i 0.218451 0.378368i
\(326\) −17.5215 −0.970427
\(327\) 24.4134 21.7148i 1.35007 1.20083i
\(328\) 5.11058 8.85178i 0.282184 0.488758i
\(329\) 0 0
\(330\) 22.1866 19.7341i 1.22133 1.08633i
\(331\) −1.04325 + 1.80697i −0.0573423 + 0.0993198i −0.893272 0.449517i \(-0.851596\pi\)
0.835929 + 0.548837i \(0.184929\pi\)
\(332\) −1.82691 + 3.16431i −0.100265 + 0.173664i
\(333\) 1.66690 14.1978i 0.0913454 0.778032i
\(334\) 10.3269 + 17.8867i 0.565064 + 0.978719i
\(335\) −22.0846 38.2517i −1.20661 2.08992i
\(336\) 0 0
\(337\) 8.10439 14.0372i 0.441474 0.764655i −0.556325 0.830965i \(-0.687789\pi\)
0.997799 + 0.0663093i \(0.0211224\pi\)
\(338\) −20.3955 −1.10937
\(339\) 24.0087 21.3548i 1.30397 1.15983i
\(340\) 13.1113 0.711058
\(341\) 9.82072 + 17.0100i 0.531822 + 0.921143i
\(342\) 3.63348 + 2.70793i 0.196476 + 0.146428i
\(343\) 0 0
\(344\) 4.92030 + 8.52220i 0.265285 + 0.459486i
\(345\) 34.6661 + 11.4970i 1.86636 + 0.618979i
\(346\) −5.61677 9.72852i −0.301959 0.523009i
\(347\) −5.63348 9.75747i −0.302421 0.523808i 0.674263 0.738491i \(-0.264461\pi\)
−0.976684 + 0.214683i \(0.931128\pi\)
\(348\) 1.95489 1.73880i 0.104793 0.0932095i
\(349\) −0.0988844 0.171273i −0.00529316 0.00916803i 0.863367 0.504577i \(-0.168352\pi\)
−0.868660 + 0.495409i \(0.835018\pi\)
\(350\) 0 0
\(351\) 5.17673 0.448873i 0.276313 0.0239591i
\(352\) −6.60507 11.4403i −0.352052 0.609771i
\(353\) 12.5019 0.665407 0.332703 0.943032i \(-0.392039\pi\)
0.332703 + 0.943032i \(0.392039\pi\)
\(354\) 24.8022 + 8.22563i 1.31822 + 0.437187i
\(355\) −10.3214 −0.547804
\(356\) 4.27011 7.39605i 0.226315 0.391990i
\(357\) 0 0
\(358\) 3.26578 + 5.65650i 0.172602 + 0.298955i
\(359\) −10.0098 17.3375i −0.528299 0.915040i −0.999456 0.0329908i \(-0.989497\pi\)
0.471157 0.882049i \(-0.343837\pi\)
\(360\) −16.3028 12.1501i −0.859235 0.640365i
\(361\) 9.10507 15.7705i 0.479214 0.830024i
\(362\) 15.7577 27.2932i 0.828208 1.43450i
\(363\) −5.09455 1.68961i −0.267395 0.0886814i
\(364\) 0 0
\(365\) −19.0927 + 33.0695i −0.999357 + 1.73094i
\(366\) 2.30470 + 11.1762i 0.120469 + 0.584191i
\(367\) −30.0727 −1.56978 −0.784892 0.619632i \(-0.787282\pi\)
−0.784892 + 0.619632i \(0.787282\pi\)
\(368\) 14.6545 25.3824i 0.763919 1.32315i
\(369\) −14.9105 + 6.42264i −0.776208 + 0.334349i
\(370\) 29.0617 1.51085
\(371\) 0 0
\(372\) −8.03706 + 7.14867i −0.416702 + 0.370641i
\(373\) 7.01238 0.363087 0.181544 0.983383i \(-0.441891\pi\)
0.181544 + 0.983383i \(0.441891\pi\)
\(374\) 9.82072 + 17.0100i 0.507818 + 0.879566i
\(375\) 16.9684 + 5.62755i 0.876242 + 0.290606i
\(376\) 2.51788 4.36110i 0.129850 0.224906i
\(377\) 1.69963 0.0875353
\(378\) 0 0
\(379\) −19.0741 −0.979772 −0.489886 0.871787i \(-0.662962\pi\)
−0.489886 + 0.871787i \(0.662962\pi\)
\(380\) −1.41714 + 2.45455i −0.0726976 + 0.125916i
\(381\) 16.4196 + 5.44556i 0.841202 + 0.278985i
\(382\) −3.93818 6.82112i −0.201495 0.348999i
\(383\) −3.21015 −0.164031 −0.0820155 0.996631i \(-0.526136\pi\)
−0.0820155 + 0.996631i \(0.526136\pi\)
\(384\) −16.5364 + 14.7085i −0.843868 + 0.750590i
\(385\) 0 0
\(386\) −42.9949 −2.18838
\(387\) 1.82258 15.5238i 0.0926471 0.789120i
\(388\) 3.25340 5.63506i 0.165166 0.286077i
\(389\) 5.13602 0.260407 0.130203 0.991487i \(-0.458437\pi\)
0.130203 + 0.991487i \(0.458437\pi\)
\(390\) 2.13348 + 10.3459i 0.108033 + 0.523885i
\(391\) −12.0796 + 20.9225i −0.610893 + 1.05810i
\(392\) 0 0
\(393\) −26.3912 8.75264i −1.33126 0.441512i
\(394\) −9.11058 + 15.7800i −0.458984 + 0.794984i
\(395\) 12.7145 22.0221i 0.639735 1.10805i
\(396\) −0.873885 + 7.44330i −0.0439144 + 0.374040i
\(397\) 11.4691 + 19.8650i 0.575615 + 0.996995i 0.995975 + 0.0896370i \(0.0285707\pi\)
−0.420359 + 0.907358i \(0.638096\pi\)
\(398\) −7.44987 12.9036i −0.373428 0.646797i
\(399\) 0 0
\(400\) 19.6421 34.0212i 0.982107 1.70106i
\(401\) −18.2101 −0.909371 −0.454686 0.890652i \(-0.650248\pi\)
−0.454686 + 0.890652i \(0.650248\pi\)
\(402\) 34.3937 + 11.4067i 1.71540 + 0.568912i
\(403\) −6.98762 −0.348078
\(404\) 1.53961 + 2.66668i 0.0765985 + 0.132672i
\(405\) 9.23050 + 30.9481i 0.458667 + 1.53782i
\(406\) 0 0
\(407\) 6.69708 + 11.5997i 0.331962 + 0.574975i
\(408\) 10.0494 8.93861i 0.497522 0.442527i
\(409\) −7.66621 13.2783i −0.379070 0.656568i 0.611858 0.790968i \(-0.290423\pi\)
−0.990927 + 0.134400i \(0.957089\pi\)
\(410\) −16.5025 28.5831i −0.814999 1.41162i
\(411\) −21.3516 7.08125i −1.05320 0.349293i
\(412\) −7.05494 12.2195i −0.347572 0.602013i
\(413\) 0 0
\(414\) −27.5185 + 11.8535i −1.35246 + 0.582568i
\(415\) −7.37636 12.7762i −0.362091 0.627160i
\(416\) 4.69963 0.230418
\(417\) 1.43818 1.27921i 0.0704279 0.0626430i
\(418\) −4.24591 −0.207674
\(419\) 5.28435 9.15276i 0.258157 0.447142i −0.707591 0.706622i \(-0.750218\pi\)
0.965748 + 0.259481i \(0.0835513\pi\)
\(420\) 0 0
\(421\) 18.0858 + 31.3256i 0.881449 + 1.52671i 0.849731 + 0.527217i \(0.176765\pi\)
0.0317181 + 0.999497i \(0.489902\pi\)
\(422\) −8.94870 15.4996i −0.435616 0.754509i
\(423\) −7.34610 + 3.16431i −0.357179 + 0.153854i
\(424\) −0.116765 + 0.202243i −0.00567062 + 0.00982181i
\(425\) −16.1909 + 28.0434i −0.785374 + 1.36031i
\(426\) 6.32691 5.62755i 0.306540 0.272656i
\(427\) 0 0
\(428\) 2.37890 4.12038i 0.114989 0.199166i
\(429\) −3.63781 + 3.23569i −0.175635 + 0.156221i
\(430\) 31.7761 1.53238
\(431\) −17.5494 + 30.3965i −0.845327 + 1.46415i 0.0400101 + 0.999199i \(0.487261\pi\)
−0.885337 + 0.464950i \(0.846072\pi\)
\(432\) 25.8196 2.23881i 1.24224 0.107715i
\(433\) 41.1730 1.97865 0.989324 0.145731i \(-0.0465533\pi\)
0.989324 + 0.145731i \(0.0465533\pi\)
\(434\) 0 0
\(435\) 2.13348 + 10.3459i 0.102292 + 0.496047i
\(436\) −16.7651 −0.802902
\(437\) −2.61126 4.52284i −0.124914 0.216357i
\(438\) −6.32691 30.6812i −0.302312 1.46600i
\(439\) −2.33929 + 4.05178i −0.111648 + 0.193381i −0.916435 0.400184i \(-0.868946\pi\)
0.804787 + 0.593564i \(0.202280\pi\)
\(440\) 19.0507 0.908209
\(441\) 0 0
\(442\) −6.98762 −0.332367
\(443\) −15.0865 + 26.1306i −0.716781 + 1.24150i 0.245487 + 0.969400i \(0.421052\pi\)
−0.962268 + 0.272102i \(0.912281\pi\)
\(444\) −5.48074 + 4.87492i −0.260104 + 0.231353i
\(445\) 17.2410 + 29.8623i 0.817303 + 1.41561i
\(446\) 9.63279 0.456126
\(447\) 13.8633 + 4.59776i 0.655711 + 0.217466i
\(448\) 0 0
\(449\) 0.333792 0.0157526 0.00787632 0.999969i \(-0.497493\pi\)
0.00787632 + 0.999969i \(0.497493\pi\)
\(450\) −36.8843 + 15.8878i −1.73874 + 0.748959i
\(451\) 7.60576 13.1736i 0.358141 0.620319i
\(452\) −16.4871 −0.775490
\(453\) −24.4160 8.09755i −1.14716 0.380456i
\(454\) −9.43199 + 16.3367i −0.442665 + 0.766719i
\(455\) 0 0
\(456\) 0.587193 + 2.84748i 0.0274979 + 0.133346i
\(457\) 9.65452 16.7221i 0.451619 0.782227i −0.546868 0.837219i \(-0.684180\pi\)
0.998487 + 0.0549917i \(0.0175132\pi\)
\(458\) 16.6927 28.9127i 0.780001 1.35100i
\(459\) −21.2829 + 1.84544i −0.993401 + 0.0861376i
\(460\) −9.37017 16.2296i −0.436886 0.756709i
\(461\) 19.5538 + 33.8681i 0.910710 + 1.57740i 0.813064 + 0.582175i \(0.197798\pi\)
0.0976463 + 0.995221i \(0.468869\pi\)
\(462\) 0 0
\(463\) −10.9382 + 18.9455i −0.508340 + 0.880471i 0.491613 + 0.870814i \(0.336407\pi\)
−0.999953 + 0.00965741i \(0.996926\pi\)
\(464\) 8.47710 0.393539
\(465\) −8.77128 42.5347i −0.406758 1.97250i
\(466\) 15.2335 0.705680
\(467\) −6.16002 10.6695i −0.285052 0.493724i 0.687570 0.726118i \(-0.258677\pi\)
−0.972622 + 0.232394i \(0.925344\pi\)
\(468\) −2.13781 1.59325i −0.0988201 0.0736480i
\(469\) 0 0
\(470\) −8.13045 14.0823i −0.375029 0.649570i
\(471\) 1.01052 + 4.90033i 0.0465623 + 0.225795i
\(472\) 8.38255 + 14.5190i 0.385838 + 0.668291i
\(473\) 7.32258 + 12.6831i 0.336693 + 0.583169i
\(474\) 4.21331 + 20.4317i 0.193524 + 0.938457i
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) 0.340671 0.146743i 0.0155983 0.00671890i
\(478\) −9.53706 16.5187i −0.436215 0.755547i
\(479\) −13.4895 −0.616350 −0.308175 0.951330i \(-0.599718\pi\)
−0.308175 + 0.951330i \(0.599718\pi\)
\(480\) 5.89926 + 28.6073i 0.269263 + 1.30574i
\(481\) −4.76509 −0.217269
\(482\) −5.93701 + 10.2832i −0.270423 + 0.468387i
\(483\) 0 0
\(484\) 1.37704 + 2.38511i 0.0625929 + 0.108414i
\(485\) 13.1359 + 22.7521i 0.596473 + 1.03312i
\(486\) −22.5320 13.9381i −1.02207 0.632244i
\(487\) −3.77197 + 6.53324i −0.170924 + 0.296050i −0.938743 0.344617i \(-0.888009\pi\)
0.767819 + 0.640667i \(0.221342\pi\)
\(488\) −3.66071 + 6.34053i −0.165712 + 0.287022i
\(489\) 3.60624 + 17.4878i 0.163080 + 0.790826i
\(490\) 0 0
\(491\) 8.06979 13.9773i 0.364185 0.630786i −0.624460 0.781057i \(-0.714681\pi\)
0.988645 + 0.150270i \(0.0480143\pi\)
\(492\) 7.90682 + 2.62230i 0.356467 + 0.118222i
\(493\) −6.98762 −0.314707
\(494\) 0.755260 1.30815i 0.0339808 0.0588564i
\(495\) −24.2625 18.0822i −1.09052 0.812736i
\(496\) −34.8516 −1.56488
\(497\) 0 0
\(498\) 11.4876 + 3.80987i 0.514773 + 0.170724i
\(499\) −30.8654 −1.38172 −0.690862 0.722987i \(-0.742769\pi\)
−0.690862 + 0.722987i \(0.742769\pi\)
\(500\) −4.58650 7.94406i −0.205115 0.355269i
\(501\) 15.7269 13.9885i 0.702624 0.624958i
\(502\) 3.92649 6.80088i 0.175248 0.303538i
\(503\) −24.6304 −1.09822 −0.549109 0.835751i \(-0.685033\pi\)
−0.549109 + 0.835751i \(0.685033\pi\)
\(504\) 0 0
\(505\) −12.4327 −0.553247
\(506\) 14.0371 24.3129i 0.624024 1.08084i
\(507\) 4.19777 + 20.3563i 0.186429 + 0.904055i
\(508\) −4.43818 7.68715i −0.196912 0.341062i
\(509\) −13.5897 −0.602355 −0.301177 0.953568i \(-0.597380\pi\)
−0.301177 + 0.953568i \(0.597380\pi\)
\(510\) −8.77128 42.5347i −0.388399 1.88347i
\(511\) 0 0
\(512\) 4.59937 0.203265
\(513\) 1.95489 4.18383i 0.0863104 0.184720i
\(514\) −1.21015 + 2.09604i −0.0533774 + 0.0924523i
\(515\) 56.9701 2.51040
\(516\) −5.99264 + 5.33023i −0.263811 + 0.234650i
\(517\) 3.74721 6.49036i 0.164802 0.285446i
\(518\) 0 0
\(519\) −8.55377 + 7.60826i −0.375469 + 0.333966i
\(520\) −3.38874 + 5.86946i −0.148606 + 0.257393i
\(521\) −19.5865 + 33.9248i −0.858100 + 1.48627i 0.0156383 + 0.999878i \(0.495022\pi\)
−0.873739 + 0.486396i \(0.838311\pi\)
\(522\) −6.94870 5.17868i −0.304136 0.226665i
\(523\) 9.56182 + 16.5616i 0.418109 + 0.724187i 0.995749 0.0921051i \(-0.0293596\pi\)
−0.577640 + 0.816292i \(0.696026\pi\)
\(524\) 7.13348 + 12.3555i 0.311627 + 0.539754i
\(525\) 0 0
\(526\) −13.8207 + 23.9382i −0.602612 + 1.04375i
\(527\) 28.7280 1.25141
\(528\) −18.1440 + 16.1384i −0.789616 + 0.702334i
\(529\) 11.5316 0.501372
\(530\) 0.377045 + 0.653061i 0.0163778 + 0.0283671i
\(531\) 3.10507 26.4474i 0.134749 1.14772i
\(532\) 0 0
\(533\) 2.70582 + 4.68661i 0.117202 + 0.203000i
\(534\) −26.8504 8.90494i −1.16193 0.385354i
\(535\) 9.60507 + 16.6365i 0.415264 + 0.719258i
\(536\) 11.6243 + 20.1338i 0.502091 + 0.869648i
\(537\) 4.97346 4.42371i 0.214621 0.190897i
\(538\) −15.8523 27.4570i −0.683441 1.18375i
\(539\) 0 0
\(540\) 7.01485 15.0131i 0.301871 0.646061i
\(541\) −1.26509 2.19120i −0.0543906 0.0942072i 0.837548 0.546363i \(-0.183988\pi\)
−0.891939 + 0.452156i \(0.850655\pi\)
\(542\) −6.73539 −0.289310
\(543\) −30.4839 10.1100i −1.30819 0.433861i
\(544\) −19.3214 −0.828399
\(545\) 33.8454 58.6220i 1.44978 2.51109i
\(546\) 0 0
\(547\) −8.92580 15.4599i −0.381640 0.661019i 0.609657 0.792665i \(-0.291307\pi\)
−0.991297 + 0.131646i \(0.957974\pi\)
\(548\) 5.77128 + 9.99615i 0.246537 + 0.427015i
\(549\) 10.6804 4.60054i 0.455827 0.196346i
\(550\) 18.8145 32.5877i 0.802254 1.38955i
\(551\) 0.755260 1.30815i 0.0321752 0.0557290i
\(552\) −18.2465 6.05146i −0.776624 0.257567i
\(553\) 0 0
\(554\) 1.98329 3.43516i 0.0842619 0.145946i
\(555\) −5.98143 29.0058i −0.253898 1.23123i
\(556\) −0.987620 −0.0418844
\(557\) −20.6804 + 35.8195i −0.876255 + 1.51772i −0.0208360 + 0.999783i \(0.506633\pi\)
−0.855419 + 0.517936i \(0.826701\pi\)
\(558\) 28.5679 + 21.2909i 1.20938 + 0.901317i
\(559\) −5.21015 −0.220366
\(560\) 0 0
\(561\) 14.9560 13.3028i 0.631442 0.561644i
\(562\) 47.5809 2.00708
\(563\) −10.3683 17.9584i −0.436972 0.756858i 0.560482 0.828166i \(-0.310616\pi\)
−0.997454 + 0.0713087i \(0.977282\pi\)
\(564\) 3.89554 + 1.29195i 0.164032 + 0.0544011i
\(565\) 33.2843 57.6501i 1.40028 2.42536i
\(566\) −17.5402 −0.737271
\(567\) 0 0
\(568\) 5.43268 0.227950
\(569\) 0.134164 0.232379i 0.00562446 0.00974185i −0.863199 0.504863i \(-0.831543\pi\)
0.868824 + 0.495121i \(0.164876\pi\)
\(570\) 8.91095 + 2.95531i 0.373239 + 0.123785i
\(571\) −17.9684 31.1221i −0.751953 1.30242i −0.946875 0.321601i \(-0.895779\pi\)
0.194923 0.980819i \(-0.437554\pi\)
\(572\) 2.49814 0.104453
\(573\) −5.99745 + 5.33451i −0.250547 + 0.222852i
\(574\) 0 0
\(575\) 46.2843 1.93019
\(576\) 4.78111 + 3.56324i 0.199213 + 0.148468i
\(577\) 2.71565 4.70364i 0.113054 0.195815i −0.803946 0.594702i \(-0.797270\pi\)
0.917000 + 0.398887i \(0.130603\pi\)
\(578\) −0.165726 −0.00689328
\(579\) 8.84913 + 42.9122i 0.367757 + 1.78337i
\(580\) 2.71015 4.69412i 0.112533 0.194913i
\(581\) 0 0
\(582\) −20.4574 6.78468i −0.847985 0.281234i
\(583\) −0.173775 + 0.300987i −0.00719702 + 0.0124656i
\(584\) 10.0494 17.4061i 0.415849 0.720271i
\(585\) 9.88688 4.25874i 0.408772 0.176077i
\(586\) −26.0858 45.1820i −1.07760 1.86645i
\(587\) 17.5822 + 30.4532i 0.725694 + 1.25694i 0.958688 + 0.284461i \(0.0918145\pi\)
−0.232994 + 0.972478i \(0.574852\pi\)
\(588\) 0 0
\(589\) −3.10507 + 5.37815i −0.127942 + 0.221603i
\(590\) 54.1359 2.22874
\(591\) 17.6247 + 5.84524i 0.724985 + 0.240441i
\(592\) −23.7665 −0.976796
\(593\) −16.7534 29.0177i −0.687980 1.19162i −0.972490 0.232943i \(-0.925164\pi\)
0.284511 0.958673i \(-0.408169\pi\)
\(594\) 24.7317 2.14448i 1.01475 0.0879891i
\(595\) 0 0
\(596\) −3.74721 6.49036i −0.153492 0.265856i
\(597\) −11.3454 + 10.0913i −0.464337 + 0.413010i
\(598\) 4.99381 + 8.64953i 0.204212 + 0.353706i
\(599\) −3.12364 5.41031i −0.127629 0.221059i 0.795129 0.606441i \(-0.207403\pi\)
−0.922757 + 0.385381i \(0.874070\pi\)
\(600\) −24.4567 8.11105i −0.998439 0.331132i
\(601\) 11.2040 + 19.4058i 0.457019 + 0.791580i 0.998802 0.0489384i \(-0.0155838\pi\)
−0.541783 + 0.840519i \(0.682250\pi\)
\(602\) 0 0
\(603\) 4.30587 36.6752i 0.175349 1.49353i
\(604\) 6.59957 + 11.4308i 0.268533 + 0.465112i
\(605\) −11.1199 −0.452089
\(606\) 7.62110 6.77868i 0.309586 0.275365i
\(607\) −14.9505 −0.606821 −0.303411 0.952860i \(-0.598125\pi\)
−0.303411 + 0.952860i \(0.598125\pi\)
\(608\) 2.08836 3.61715i 0.0846943 0.146695i
\(609\) 0 0
\(610\) 11.8207 + 20.4741i 0.478607 + 0.828972i
\(611\) 1.33310 + 2.30900i 0.0539316 + 0.0934123i
\(612\) 8.78909 + 6.55027i 0.355278 + 0.264779i
\(613\) −17.5989 + 30.4822i −0.710812 + 1.23116i 0.253740 + 0.967272i \(0.418339\pi\)
−0.964553 + 0.263891i \(0.914994\pi\)
\(614\) −9.72500 + 16.8442i −0.392469 + 0.679776i
\(615\) −25.1316 + 22.3536i −1.01340 + 0.901386i
\(616\) 0 0
\(617\) 1.00619 1.74277i 0.0405077 0.0701614i −0.845061 0.534670i \(-0.820436\pi\)
0.885568 + 0.464509i \(0.153769\pi\)
\(618\) −34.9221 + 31.0619i −1.40477 + 1.24949i
\(619\) −39.3818 −1.58289 −0.791444 0.611242i \(-0.790670\pi\)
−0.791444 + 0.611242i \(0.790670\pi\)
\(620\) −11.1421 + 19.2987i −0.447479 + 0.775056i
\(621\) 17.4945 + 25.0259i 0.702030 + 1.00425i
\(622\) −20.3324 −0.815256
\(623\) 0 0
\(624\) −1.74474 8.46079i −0.0698455 0.338703i
\(625\) −2.34479 −0.0937918
\(626\) −11.5098 19.9356i −0.460025 0.796787i
\(627\) 0.873885 + 4.23774i 0.0348996 + 0.169239i
\(628\) 1.28366 2.22337i 0.0512237 0.0887220i
\(629\) 19.5906 0.781126
\(630\) 0 0
\(631\) 44.3832 1.76687 0.883433 0.468558i \(-0.155226\pi\)
0.883433 + 0.468558i \(0.155226\pi\)
\(632\) −6.69227 + 11.5913i −0.266204 + 0.461079i
\(633\) −13.6280 + 12.1216i −0.541663 + 0.481789i
\(634\) 25.4629 + 44.1030i 1.01126 + 1.75155i
\(635\) 35.8392 1.42224
\(636\) −0.180653 0.0599137i −0.00716337 0.00237573i
\(637\) 0 0
\(638\) 8.11993 0.321471
\(639\) −6.91892 5.15649i −0.273708 0.203988i
\(640\) −22.9251 + 39.7075i −0.906195 + 1.56957i
\(641\) −14.9862 −0.591921 −0.295961 0.955200i \(-0.595640\pi\)
−0.295961 + 0.955200i \(0.595640\pi\)
\(642\) −14.9585 4.96099i −0.590366 0.195795i
\(643\) −5.32691 + 9.22649i −0.210073 + 0.363857i −0.951737 0.306914i \(-0.900703\pi\)
0.741664 + 0.670771i \(0.234037\pi\)
\(644\) 0 0
\(645\) −6.54009 31.7150i −0.257516 1.24878i
\(646\) −3.10507 + 5.37815i −0.122168 + 0.211600i
\(647\) 1.06478 1.84424i 0.0418606 0.0725047i −0.844336 0.535814i \(-0.820005\pi\)
0.886197 + 0.463309i \(0.153338\pi\)
\(648\) −4.85848 16.2895i −0.190859 0.639913i
\(649\) 12.4752 + 21.6078i 0.489696 + 0.848178i
\(650\) 6.69344 + 11.5934i 0.262538 + 0.454730i
\(651\) 0 0
\(652\) 4.58100 7.93453i 0.179406 0.310740i
\(653\) 11.1716 0.437180 0.218590 0.975817i \(-0.429854\pi\)
0.218590 + 0.975817i \(0.429854\pi\)
\(654\) 11.2156 + 54.3882i 0.438567 + 2.12675i
\(655\) −57.6043 −2.25079
\(656\) 13.4956 + 23.3751i 0.526914 + 0.912642i
\(657\) −29.3200 + 12.6295i −1.14388 + 0.492723i
\(658\) 0 0
\(659\) 5.65452 + 9.79391i 0.220269 + 0.381517i 0.954890 0.296961i \(-0.0959733\pi\)
−0.734621 + 0.678478i \(0.762640\pi\)
\(660\) 3.13582 + 15.2066i 0.122062 + 0.591914i
\(661\) 16.1785 + 28.0220i 0.629271 + 1.08993i 0.987698 + 0.156372i \(0.0499798\pi\)
−0.358427 + 0.933558i \(0.616687\pi\)
\(662\) −1.77314 3.07117i −0.0689151 0.119364i
\(663\) 1.43818 + 6.97418i 0.0558542 + 0.270855i
\(664\) 3.88255 + 6.72477i 0.150672 + 0.260972i
\(665\) 0 0
\(666\) 19.4814 + 14.5190i 0.754890 + 0.562600i
\(667\) 4.99381 + 8.64953i 0.193361 + 0.334911i
\(668\) −10.7999 −0.417860
\(669\) −1.98260 9.61425i −0.0766518 0.371708i
\(670\) 75.0714 2.90026
\(671\) −5.44801 + 9.43623i −0.210318 + 0.364282i
\(672\) 0 0
\(673\) 12.0803 + 20.9237i 0.465662 + 0.806550i 0.999231 0.0392063i \(-0.0124830\pi\)
−0.533569 + 0.845756i \(0.679150\pi\)
\(674\) 13.7744 + 23.8580i 0.530572 + 0.918977i
\(675\) 23.4487 + 33.5434i 0.902541 + 1.29108i
\(676\) 5.33242 9.23601i 0.205093 0.355231i
\(677\) 12.5371 21.7148i 0.481838 0.834569i −0.517944 0.855414i \(-0.673303\pi\)
0.999783 + 0.0208457i \(0.00663587\pi\)
\(678\) 11.0297 + 53.4865i 0.423593 + 2.05414i
\(679\) 0 0
\(680\) 13.9320 24.1309i 0.534267 0.925378i
\(681\) 18.2465 + 6.05146i 0.699208 + 0.231892i
\(682\) −33.3832 −1.27831
\(683\) 23.8392 41.2907i 0.912182 1.57995i 0.101207 0.994865i \(-0.467729\pi\)
0.810975 0.585081i \(-0.198937\pi\)
\(684\) −2.17625 + 0.937411i −0.0832109 + 0.0358428i
\(685\) −46.6043 −1.78066
\(686\) 0 0
\(687\) −32.2927 10.7099i −1.23204 0.408607i
\(688\) −25.9862 −0.990716
\(689\) −0.0618219 0.107079i −0.00235523 0.00407937i
\(690\) −46.3825 + 41.2555i −1.76575 + 1.57057i
\(691\) −12.3400 + 21.3735i −0.469435 + 0.813085i −0.999389 0.0349408i \(-0.988876\pi\)
0.529954 + 0.848026i \(0.322209\pi\)
\(692\) 5.87402 0.223297
\(693\) 0 0
\(694\) 19.1496 0.726910
\(695\) 1.99381 3.45338i 0.0756295 0.130994i
\(696\) −1.12296 5.44556i −0.0425655 0.206413i
\(697\) −11.1243 19.2679i −0.421364 0.729824i
\(698\) 0.336134 0.0127228
\(699\) −3.13533 15.2042i −0.118589 0.575076i
\(700\) 0 0
\(701\) −29.6784 −1.12094 −0.560469 0.828175i \(-0.689379\pi\)
−0.560469 + 0.828175i \(0.689379\pi\)
\(702\) −3.73855 + 8.00119i −0.141102 + 0.301986i
\(703\) −2.11745 + 3.66754i −0.0798613 + 0.138324i
\(704\) −5.58699 −0.210567
\(705\) −12.3819 + 11.0132i −0.466328 + 0.414781i
\(706\) −10.6243 + 18.4018i −0.399849 + 0.692559i
\(707\) 0 0
\(708\) −10.2095 + 9.08094i −0.383695 + 0.341282i
\(709\) 14.6291 25.3383i 0.549406 0.951599i −0.448909 0.893577i \(-0.648187\pi\)
0.998315 0.0580220i \(-0.0184794\pi\)
\(710\) 8.77128 15.1923i 0.329180 0.570157i
\(711\) 19.5252 8.41040i 0.732251 0.315415i
\(712\) −9.07481 15.7180i −0.340093 0.589058i
\(713\) −20.5309 35.5605i −0.768887 1.33175i
\(714\) 0 0
\(715\) −5.04325 + 8.73517i −0.188607 + 0.326677i
\(716\) −3.41535 −0.127638
\(717\) −14.5240 + 12.9186i −0.542408 + 0.482452i
\(718\) 34.0260 1.26984
\(719\) 0.537063 + 0.930220i 0.0200291 + 0.0346913i 0.875866 0.482554i \(-0.160291\pi\)
−0.855837 + 0.517245i \(0.826957\pi\)
\(720\) 49.3120 21.2410i 1.83775 0.791605i
\(721\) 0 0
\(722\) 15.4752 + 26.8039i 0.575929 + 0.997538i
\(723\) 11.4854 + 3.80912i 0.427145 + 0.141663i
\(724\) 8.23972 + 14.2716i 0.306227 + 0.530400i
\(725\) 6.69344 + 11.5934i 0.248588 + 0.430567i
\(726\) 6.81639 6.06293i 0.252980 0.225016i
\(727\) 12.7163 + 22.0253i 0.471623 + 0.816875i 0.999473 0.0324628i \(-0.0103350\pi\)
−0.527850 + 0.849338i \(0.677002\pi\)
\(728\) 0 0
\(729\) −9.27375 + 25.3574i −0.343472 + 0.939163i
\(730\) −32.4505 56.2059i −1.20105 2.08027i
\(731\) 21.4203 0.792258
\(732\) −5.66366 1.87835i −0.209335 0.0694259i
\(733\) 11.3955 0.420904 0.210452 0.977604i \(-0.432506\pi\)
0.210452 + 0.977604i \(0.432506\pi\)
\(734\) 25.5562 44.2647i 0.943298 1.63384i
\(735\) 0 0
\(736\) 13.8083 + 23.9168i 0.508982 + 0.881583i
\(737\) 17.2997 + 29.9639i 0.637242 + 1.10374i
\(738\) 3.21751 27.4051i 0.118438 1.00879i
\(739\) 14.9697 25.9283i 0.550671 0.953790i −0.447556 0.894256i \(-0.647705\pi\)
0.998226 0.0595336i \(-0.0189613\pi\)
\(740\) −7.59820 + 13.1605i −0.279315 + 0.483788i
\(741\) −1.46108 0.484566i −0.0536740 0.0178010i
\(742\) 0 0
\(743\) 9.50069 16.4557i 0.348546 0.603700i −0.637445 0.770496i \(-0.720009\pi\)
0.985991 + 0.166796i \(0.0533420\pi\)
\(744\) 4.61677 + 22.3881i 0.169259 + 0.820789i
\(745\) 30.2595 1.10862
\(746\) −5.95922 + 10.3217i −0.218183 + 0.377903i
\(747\) 1.43818 12.2497i 0.0526202 0.448191i
\(748\) −10.2705 −0.375527
\(749\) 0 0
\(750\) −22.7033 + 20.1937i −0.829006 + 0.737370i
\(751\) 0.0261368 0.000953747 0.000476873 1.00000i \(-0.499848\pi\)
0.000476873 1.00000i \(0.499848\pi\)
\(752\) 6.64902 + 11.5164i 0.242465 + 0.419961i
\(753\) −7.59593 2.51919i −0.276811 0.0918044i
\(754\) −1.44437 + 2.50172i −0.0526008 + 0.0911072i
\(755\) −53.2929 −1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) 16.2095 28.0756i 0.588754 1.01975i
\(759\) −27.1552 9.00602i −0.985672 0.326898i
\(760\) 3.01169 + 5.21640i 0.109246 + 0.189219i
\(761\) 14.6428 0.530802 0.265401 0.964138i \(-0.414496\pi\)
0.265401 + 0.964138i \(0.414496\pi\)
\(762\) −21.9691 + 19.5407i −0.795855 + 0.707883i
\(763\) 0 0
\(764\) 4.11855 0.149004
\(765\) −40.6476 + 17.5088i −1.46962 + 0.633032i
\(766\) 2.72803 4.72509i 0.0985677 0.170724i
\(767\) −8.87636 −0.320507
\(768\) −6.20630 30.0963i −0.223951 1.08601i
\(769\) 24.5672 42.5517i 0.885918 1.53445i 0.0412592 0.999148i \(-0.486863\pi\)
0.844658 0.535306i \(-0.179804\pi\)
\(770\) 0 0
\(771\) 2.34108 + 0.776418i 0.0843118 + 0.0279620i
\(772\) 11.2410 19.4700i 0.404573 0.700741i
\(773\) 6.22067 10.7745i 0.223742 0.387532i −0.732199 0.681090i \(-0.761506\pi\)
0.955941 + 0.293558i \(0.0948394\pi\)
\(774\) 21.3010 + 15.8751i 0.765648 + 0.570617i
\(775\) −27.5185 47.6634i −0.988493 1.71212i
\(776\) −6.91411 11.9756i −0.248202 0.429898i
\(777\) 0 0
\(778\) −4.36467 + 7.55982i −0.156481 + 0.271033i
\(779\) 4.80951 0.172319
\(780\) −5.24288 1.73880i −0.187725 0.0622590i
\(781\) 8.08513 0.289309
\(782\) −20.5309 35.5605i −0.734183 1.27164i
\(783\) −3.73855 + 8.00119i −0.133605 + 0.285939i
\(784\) 0 0
\(785\) 5.18292 + 8.97708i 0.184986 + 0.320406i
\(786\) 35.3108 31.4077i 1.25950 1.12027i
\(787\) −16.4567 28.5038i −0.586617 1.01605i −0.994672 0.103093i \(-0.967126\pi\)
0.408055 0.912957i \(-0.366207\pi\)
\(788\) −4.76392 8.25135i −0.169708 0.293942i
\(789\) 26.7367 + 8.86722i 0.951851 + 0.315681i
\(790\) 21.6099 + 37.4294i 0.768845 + 1.33168i
\(791\) 0 0
\(792\) 12.7706 + 9.51759i 0.453783 + 0.338193i
\(793\) −1.93818 3.35702i −0.0688267 0.119211i
\(794\) −38.9862 −1.38357
\(795\) 0.574202 0.510731i 0.0203648 0.0181138i
\(796\) 7.79108 0.276147
\(797\) 13.1989 22.8612i 0.467530 0.809786i −0.531781 0.846882i \(-0.678477\pi\)
0.999312 + 0.0370953i \(0.0118105\pi\)
\(798\) 0 0
\(799\) −5.48074 9.49292i −0.193895 0.335835i
\(800\) 18.5080 + 32.0567i 0.654356 + 1.13338i
\(801\) −3.36151 + 28.6316i −0.118773 + 1.01165i
\(802\) 15.4752 26.8039i 0.546450 0.946479i
\(803\) 14.9560 25.9045i 0.527785 0.914151i
\(804\) −14.1577 + 12.5927i −0.499303 + 0.444111i
\(805\) 0 0
\(806\) 5.93818 10.2852i 0.209163 0.362282i
\(807\) −24.1414 + 21.4729i −0.849819 + 0.755883i
\(808\) 6.54394 0.230215
\(809\) −17.7960 + 30.8235i −0.625673 + 1.08370i 0.362738 + 0.931891i \(0.381842\pi\)
−0.988410 + 0.151806i \(0.951491\pi\)
\(810\) −53.3973 12.7135i −1.87619 0.446708i
\(811\) 37.8268 1.32828 0.664140 0.747608i \(-0.268798\pi\)
0.664140 + 0.747608i \(0.268798\pi\)
\(812\) 0 0
\(813\) 1.38626 + 6.72243i 0.0486184 + 0.235766i
\(814\) −22.7651 −0.797916
\(815\) 18.4963 + 32.0365i 0.647896 + 1.12219i
\(816\) 7.17309 + 34.7845i 0.251108 + 1.21770i
\(817\) −2.31522 + 4.01008i −0.0809994 + 0.140295i
\(818\) 26.0594 0.911146
\(819\) 0 0
\(820\) 17.2583 0.602686
\(821\) 9.15638 15.8593i 0.319560 0.553494i −0.660836 0.750530i \(-0.729798\pi\)
0.980396 + 0.197036i \(0.0631317\pi\)
\(822\) 28.5679 25.4101i 0.996421 0.886280i
\(823\) 18.0000 + 31.1769i 0.627441 + 1.08676i 0.988063 + 0.154047i \(0.0492308\pi\)
−0.360623 + 0.932712i \(0.617436\pi\)
\(824\) −29.9862 −1.04462
\(825\) −36.3974 12.0712i −1.26719 0.420265i
\(826\) 0 0
\(827\) −28.2115 −0.981011 −0.490505 0.871438i \(-0.663188\pi\)
−0.490505 + 0.871438i \(0.663188\pi\)
\(828\) 1.82691 15.5607i 0.0634896 0.540772i
\(829\) −5.64214 + 9.77247i −0.195960 + 0.339412i −0.947215 0.320600i \(-0.896115\pi\)
0.751255 + 0.660012i \(0.229449\pi\)
\(830\) 25.0741 0.870336
\(831\) −3.83675 1.27246i −0.133095 0.0441410i
\(832\) 0.993810 1.72133i 0.0344542 0.0596764i
\(833\) 0 0
\(834\) 0.660706 + 3.20397i 0.0228784 + 0.110944i
\(835\) 21.8028 37.7636i 0.754519 1.30686i
\(836\) 1.11009 1.92274i 0.0383934 0.0664993i
\(837\) 15.3702 32.8950i 0.531271 1.13702i
\(838\) 8.98143 + 15.5563i 0.310258 + 0.537383i
\(839\) −1.02152 1.76933i −0.0352669 0.0610840i 0.847853 0.530231i \(-0.177895\pi\)
−0.883120 + 0.469147i \(0.844561\pi\)
\(840\) 0 0
\(841\) 13.0556 22.6130i 0.450194 0.779759i
\(842\) −61.4783 −2.11868
\(843\) −9.79301 47.4894i −0.337289 1.63562i
\(844\) 9.35855 0.322135
\(845\) 21.5302 + 37.2914i 0.740661 + 1.28286i
\(846\) 1.58520 13.5019i 0.0545004 0.464206i
\(847\) 0 0
\(848\) −0.308344 0.534068i −0.0105886 0.0183400i
\(849\) 3.61009 + 17.5065i 0.123898 + 0.600821i
\(850\) −27.5185 47.6634i −0.943877 1.63484i
\(851\) −14.0007 24.2499i −0.479937 0.831276i
\(852\) 0.894237 + 4.33643i 0.0306361 + 0.148564i
\(853\) −24.2960 42.0818i −0.831878 1.44085i −0.896547 0.442948i \(-0.853933\pi\)
0.0646692 0.997907i \(-0.479401\pi\)
\(854\) 0 0
\(855\) 1.11559 9.50206i 0.0381525 0.324964i
\(856\) −5.05563 8.75661i −0.172798 0.299295i
\(857\) 44.8974 1.53367 0.766833 0.641847i \(-0.221831\pi\)
0.766833 + 0.641847i \(0.221831\pi\)
\(858\) −1.67123 8.10430i −0.0570547 0.276676i
\(859\) −29.8131 −1.01721 −0.508605 0.861000i \(-0.669838\pi\)
−0.508605 + 0.861000i \(0.669838\pi\)
\(860\) −8.30786 + 14.3896i −0.283296 + 0.490683i
\(861\) 0 0
\(862\) −29.8275 51.6628i −1.01593 1.75964i
\(863\) 21.1298 + 36.5978i 0.719265 + 1.24580i 0.961291 + 0.275534i \(0.0888548\pi\)
−0.242026 + 0.970270i \(0.577812\pi\)
\(864\) −10.3374 + 22.1240i −0.351687 + 0.752675i
\(865\) −11.8585 + 20.5395i −0.403200 + 0.698363i
\(866\) −34.9894 + 60.6034i −1.18899 + 2.05939i
\(867\) 0.0341093 + 0.165407i 0.00115841 + 0.00561751i
\(868\) 0 0
\(869\) −9.95970 + 17.2507i −0.337860 + 0.585190i
\(870\) −17.0414 5.65178i −0.577757 0.191613i
\(871\) −12.3090 −0.417076
\(872\) −17.8145 + 30.8557i −0.603276 + 1.04491i
\(873\) −2.56113 + 21.8144i −0.0866812 + 0.738306i
\(874\) 8.87636 0.300247
\(875\) 0 0
\(876\) 15.5480 + 5.15649i 0.525318 + 0.174222i
\(877\) −30.5316 −1.03098 −0.515489 0.856896i \(-0.672390\pi\)
−0.515489 + 0.856896i \(0.672390\pi\)
\(878\) −3.97593 6.88651i −0.134181 0.232409i
\(879\) −39.7261 + 35.3349i −1.33993 + 1.19182i
\(880\) −25.1538 + 43.5677i −0.847935 + 1.46867i
\(881\) 13.4079 0.451724 0.225862 0.974159i \(-0.427480\pi\)
0.225862 + 0.974159i \(0.427480\pi\)
\(882\) 0 0
\(883\) −14.1250 −0.475345 −0.237672 0.971345i \(-0.576384\pi\)
−0.237672 + 0.971345i \(0.576384\pi\)
\(884\) 1.82691 3.16431i 0.0614458 0.106427i
\(885\) −11.1421 54.0317i −0.374539 1.81626i
\(886\) −25.6414 44.4123i −0.861441 1.49206i
\(887\) 39.9432 1.34116 0.670581 0.741837i \(-0.266045\pi\)
0.670581 + 0.741837i \(0.266045\pi\)
\(888\) 3.14833 + 15.2672i 0.105651 + 0.512334i
\(889\) 0 0
\(890\) −58.6067 −1.96450
\(891\) −7.23058 24.2427i −0.242233 0.812161i
\(892\) −2.51849 + 4.36216i −0.0843254 + 0.146056i
\(893\) 2.36955 0.0792941
\(894\) −18.5488 + 16.4984i −0.620363 + 0.551790i
\(895\) 6.89493 11.9424i 0.230472 0.399189i
\(896\) 0 0
\(897\) 7.60507 6.76443i 0.253926 0.225858i
\(898\) −0.283662 + 0.491316i −0.00946591 + 0.0163954i
\(899\) 5.93818 10.2852i 0.198049 0.343031i
\(900\) 2.44870 20.8567i 0.0816233 0.695225i
\(901\) 0.254166 + 0.440229i 0.00846751 + 0.0146662i
\(902\) 12.9270 + 22.3902i 0.430421 + 0.745511i
\(903\) 0 0
\(904\) −17.5192 + 30.3441i −0.582679 + 1.00923i
\(905\) −66.5375 −2.21178
\(906\) 32.6680 29.0570i 1.08532 0.965353i
\(907\) 41.4203 1.37534 0.687669 0.726024i \(-0.258634\pi\)
0.687669 + 0.726024i \(0.258634\pi\)
\(908\) −4.93199 8.54245i −0.163674 0.283491i
\(909\) −8.33420 6.21126i −0.276428 0.206014i
\(910\) 0 0
\(911\) −0.894237 1.54886i −0.0296274 0.0513162i 0.850832 0.525439i \(-0.176099\pi\)
−0.880459 + 0.474122i \(0.842765\pi\)
\(912\) −7.28730 2.41683i −0.241307 0.0800293i
\(913\) 5.77816 + 10.0081i 0.191229 + 0.331219i
\(914\) 16.4091 + 28.4214i 0.542764 + 0.940096i
\(915\) 18.0018 16.0119i 0.595121 0.529338i
\(916\) 8.72864 + 15.1185i 0.288402 + 0.499528i
\(917\) 0 0
\(918\) 15.3702 32.8950i 0.507291 1.08570i
\(919\) 28.7341 + 49.7690i 0.947852 + 1.64173i 0.749938 + 0.661508i \(0.230083\pi\)
0.197914 + 0.980219i \(0.436583\pi\)
\(920\) −39.8268 −1.31305
\(921\) 18.8134 + 6.23945i 0.619921 + 0.205597i
\(922\) −66.4683 −2.18902
\(923\) −1.43818 + 2.49100i −0.0473382 + 0.0819922i
\(924\) 0 0
\(925\) −18.7658 32.5033i −0.617015 1.06870i
\(926\) −18.5908 32.2003i −0.610933 1.05817i
\(927\) 38.1897 + 28.4618i 1.25431 + 0.934808i
\(928\) −3.99381 + 6.91748i −0.131103 + 0.227077i
\(929\) 17.3676 30.0816i 0.569813 0.986945i −0.426771 0.904360i \(-0.640349\pi\)
0.996584 0.0825854i \(-0.0263177\pi\)
\(930\) 70.0617 + 23.2359i 2.29741 + 0.761937i
\(931\) 0 0
\(932\) −3.98281 + 6.89843i −0.130461 + 0.225965i
\(933\) 4.18478 + 20.2933i 0.137003 + 0.664373i
\(934\) 20.9395 0.685161
\(935\) 20.7341 35.9126i 0.678079 1.17447i
\(936\) −5.20396 + 2.24159i −0.170097 + 0.0732686i
\(937\) −11.6662 −0.381118 −0.190559 0.981676i \(-0.561030\pi\)
−0.190559 + 0.981676i \(0.561030\pi\)
\(938\) 0 0
\(939\) −17.5283 + 15.5908i −0.572015 + 0.508786i
\(940\) 8.50282 0.277332
\(941\) −25.1687 43.5934i −0.820475 1.42111i −0.905329 0.424712i \(-0.860375\pi\)
0.0848531 0.996393i \(-0.472958\pi\)
\(942\) −8.07165 2.67696i −0.262989 0.0872202i
\(943\) −15.9004 + 27.5402i −0.517787 + 0.896833i
\(944\) −44.2719 −1.44093
\(945\) 0 0
\(946\) −24.8913 −0.809287
\(947\) 16.1941 28.0491i 0.526238 0.911472i −0.473294 0.880904i \(-0.656935\pi\)
0.999533 0.0305673i \(-0.00973139\pi\)
\(948\) −10.3539 3.43388i −0.336280 0.111527i
\(949\) 5.32072 + 9.21576i 0.172718 + 0.299156i
\(950\) 11.8974 0.386003
\(951\) 38.7774 34.4911i 1.25744 1.11845i
\(952\) 0 0
\(953\) −12.5367 −0.406102 −0.203051 0.979168i \(-0.565086\pi\)
−0.203051 + 0.979168i \(0.565086\pi\)
\(954\) −0.0735129 + 0.626145i −0.00238007 + 0.0202722i
\(955\) −8.31453 + 14.4012i −0.269052 + 0.466012i
\(956\) 9.97386 0.322578
\(957\) −1.67123 8.10430i −0.0540231 0.261975i
\(958\) 11.4635 19.8555i 0.370370 0.641500i
\(959\) 0 0
\(960\) 11.7255 + 3.88875i 0.378438 + 0.125509i
\(961\) −8.91342 + 15.4385i −0.287530 + 0.498016i
\(962\) 4.04944 7.01384i 0.130559 0.226135i
\(963\) −1.87271 + 15.9508i −0.0603474 + 0.514008i
\(964\) −3.10446 5.37709i −0.0999880 0.173184i
\(965\) 45.3868 + 78.6122i 1.46105 + 2.53062i
\(966\) 0 0
\(967\) 28.9937 50.2186i 0.932376 1.61492i 0.153127 0.988206i \(-0.451065\pi\)
0.779248 0.626715i \(-0.215601\pi\)
\(968\) 5.85297 0.188122
\(969\) 6.00688 + 1.99218i 0.192969 + 0.0639981i
\(970\) −44.6525 −1.43370
\(971\) 14.0185 + 24.2807i 0.449875 + 0.779206i 0.998377 0.0569428i \(-0.0181353\pi\)
−0.548503 + 0.836149i \(0.684802\pi\)
\(972\) 12.2028 6.55941i 0.391405 0.210393i
\(973\) 0 0
\(974\) −6.41095 11.1041i −0.205420 0.355798i
\(975\) 10.1934 9.06668i 0.326451 0.290366i
\(976\) −9.66690 16.7436i −0.309430 0.535948i
\(977\) −4.92030 8.52220i −0.157414 0.272649i 0.776521 0.630091i \(-0.216982\pi\)
−0.933935 + 0.357442i \(0.883649\pi\)
\(978\) −28.8053 9.55328i −0.921092 0.305480i
\(979\) −13.5055 23.3922i −0.431638 0.747618i
\(980\) 0 0
\(981\) 51.9752 22.3881i 1.65944 0.714798i
\(982\) 13.7156 + 23.7562i 0.437684 + 0.758091i
\(983\) 48.6894 1.55295 0.776476 0.630147i \(-0.217005\pi\)
0.776476 + 0.630147i \(0.217005\pi\)
\(984\) 13.2280 11.7658i 0.421694 0.375081i
\(985\) 38.4697 1.22575
\(986\) 5.93818 10.2852i 0.189110 0.327548i
\(987\) 0 0
\(988\) 0.394926 + 0.684031i 0.0125643 + 0.0217619i
\(989\) −15.3083 26.5148i −0.486777 0.843123i
\(990\) 47.2343 20.3460i 1.50120 0.646639i
\(991\) −1.43199 + 2.48028i −0.0454886 + 0.0787886i −0.887873 0.460088i \(-0.847818\pi\)
0.842385 + 0.538877i \(0.181151\pi\)
\(992\) 16.4196 28.4396i 0.521323 0.902958i
\(993\) −2.70032 + 2.40183i −0.0856920 + 0.0762198i
\(994\) 0 0
\(995\) −15.7286 + 27.2428i −0.498631 + 0.863655i
\(996\) −4.72872 + 4.20602i −0.149835 + 0.133273i
\(997\) 50.8406 1.61014 0.805069 0.593181i \(-0.202128\pi\)
0.805069 + 0.593181i \(0.202128\pi\)
\(998\) 26.2298 45.4314i 0.830290 1.43810i
\(999\) 10.4814 22.4322i 0.331618 0.709724i
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 441.2.g.d.67.1 6
3.2 odd 2 1323.2.g.b.361.3 6
7.2 even 3 441.2.h.b.373.3 6
7.3 odd 6 63.2.f.b.22.1 6
7.4 even 3 441.2.f.d.148.1 6
7.5 odd 6 441.2.h.c.373.3 6
7.6 odd 2 441.2.g.e.67.1 6
9.2 odd 6 1323.2.h.e.802.1 6
9.7 even 3 441.2.h.b.214.3 6
21.2 odd 6 1323.2.h.e.226.1 6
21.5 even 6 1323.2.h.d.226.1 6
21.11 odd 6 1323.2.f.c.442.3 6
21.17 even 6 189.2.f.a.64.3 6
21.20 even 2 1323.2.g.c.361.3 6
28.3 even 6 1008.2.r.k.337.1 6
63.2 odd 6 1323.2.g.b.667.3 6
63.4 even 3 3969.2.a.m.1.3 3
63.11 odd 6 1323.2.f.c.883.3 6
63.16 even 3 inner 441.2.g.d.79.1 6
63.20 even 6 1323.2.h.d.802.1 6
63.25 even 3 441.2.f.d.295.1 6
63.31 odd 6 567.2.a.d.1.3 3
63.32 odd 6 3969.2.a.p.1.1 3
63.34 odd 6 441.2.h.c.214.3 6
63.38 even 6 189.2.f.a.127.3 6
63.47 even 6 1323.2.g.c.667.3 6
63.52 odd 6 63.2.f.b.43.1 yes 6
63.59 even 6 567.2.a.g.1.1 3
63.61 odd 6 441.2.g.e.79.1 6
84.59 odd 6 3024.2.r.g.1009.1 6
252.31 even 6 9072.2.a.bq.1.1 3
252.59 odd 6 9072.2.a.cd.1.3 3
252.115 even 6 1008.2.r.k.673.1 6
252.227 odd 6 3024.2.r.g.2017.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.f.b.22.1 6 7.3 odd 6
63.2.f.b.43.1 yes 6 63.52 odd 6
189.2.f.a.64.3 6 21.17 even 6
189.2.f.a.127.3 6 63.38 even 6
441.2.f.d.148.1 6 7.4 even 3
441.2.f.d.295.1 6 63.25 even 3
441.2.g.d.67.1 6 1.1 even 1 trivial
441.2.g.d.79.1 6 63.16 even 3 inner
441.2.g.e.67.1 6 7.6 odd 2
441.2.g.e.79.1 6 63.61 odd 6
441.2.h.b.214.3 6 9.7 even 3
441.2.h.b.373.3 6 7.2 even 3
441.2.h.c.214.3 6 63.34 odd 6
441.2.h.c.373.3 6 7.5 odd 6
567.2.a.d.1.3 3 63.31 odd 6
567.2.a.g.1.1 3 63.59 even 6
1008.2.r.k.337.1 6 28.3 even 6
1008.2.r.k.673.1 6 252.115 even 6
1323.2.f.c.442.3 6 21.11 odd 6
1323.2.f.c.883.3 6 63.11 odd 6
1323.2.g.b.361.3 6 3.2 odd 2
1323.2.g.b.667.3 6 63.2 odd 6
1323.2.g.c.361.3 6 21.20 even 2
1323.2.g.c.667.3 6 63.47 even 6
1323.2.h.d.226.1 6 21.5 even 6
1323.2.h.d.802.1 6 63.20 even 6
1323.2.h.e.226.1 6 21.2 odd 6
1323.2.h.e.802.1 6 9.2 odd 6
3024.2.r.g.1009.1 6 84.59 odd 6
3024.2.r.g.2017.1 6 252.227 odd 6
3969.2.a.m.1.3 3 63.4 even 3
3969.2.a.p.1.1 3 63.32 odd 6
9072.2.a.bq.1.1 3 252.31 even 6
9072.2.a.cd.1.3 3 252.59 odd 6