Properties

Label 450.2.p.b.257.2
Level $450$
Weight $2$
Character 450.257
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,2,Mod(257,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.p (of order \(12\), degree \(4\), 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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 257.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 450.257
Dual form 450.2.p.b.443.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.73205i q^{6} +(0.707107 + 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.73205i q^{6} +(0.707107 + 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-1.50000 + 0.866025i) q^{11} +(-0.448288 + 1.67303i) q^{12} +(1.79315 + 6.69213i) q^{13} +(0.500000 + 0.866025i) q^{16} +(2.12132 - 2.12132i) q^{17} +(-2.89778 + 0.776457i) q^{18} -4.00000i q^{19} +(-1.67303 + 0.448288i) q^{22} +(5.79555 - 1.55291i) q^{23} +(-0.866025 + 1.50000i) q^{24} +6.92820i q^{26} +(-3.67423 - 3.67423i) q^{27} +(-1.73205 - 3.00000i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-2.12132 - 2.12132i) q^{33} +(2.59808 - 1.50000i) q^{34} -3.00000 q^{36} +(-4.89898 - 4.89898i) q^{37} +(1.03528 - 3.86370i) q^{38} +(-10.3923 + 6.00000i) q^{39} +(-6.00000 - 3.46410i) q^{41} +(8.36516 + 2.24144i) q^{43} -1.73205 q^{44} +6.00000 q^{46} +(11.5911 + 3.10583i) q^{47} +(-1.22474 + 1.22474i) q^{48} +(6.06218 + 3.50000i) q^{49} +(4.50000 + 2.59808i) q^{51} +(-1.79315 + 6.69213i) q^{52} +(-8.48528 - 8.48528i) q^{53} +(-2.59808 - 4.50000i) q^{54} +(6.69213 - 1.79315i) q^{57} +(-0.896575 - 3.34607i) q^{58} +(4.33013 - 7.50000i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-2.82843 + 2.82843i) q^{62} +1.00000i q^{64} +(-1.50000 - 2.59808i) q^{66} +(3.34607 - 0.896575i) q^{67} +(2.89778 - 0.776457i) q^{68} +(5.19615 + 9.00000i) q^{69} -3.46410i q^{71} +(-2.89778 - 0.776457i) q^{72} +(-4.89898 + 4.89898i) q^{73} +(-3.46410 - 6.00000i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-11.5911 + 3.10583i) q^{78} +(3.46410 - 2.00000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(-4.89898 - 4.89898i) q^{82} +(2.32937 - 8.69333i) q^{83} +(7.50000 + 4.33013i) q^{86} +(4.24264 - 4.24264i) q^{87} +(-1.67303 - 0.448288i) q^{88} +1.73205 q^{89} +(5.79555 + 1.55291i) q^{92} +(-6.69213 - 1.79315i) q^{93} +(10.3923 + 6.00000i) q^{94} +(-1.50000 + 0.866025i) q^{96} +(-4.03459 + 15.0573i) q^{97} +(4.94975 + 4.94975i) q^{98} +(2.59808 - 4.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{11} + 4 q^{16} - 16 q^{31} - 24 q^{36} - 48 q^{41} + 48 q^{46} + 36 q^{51} - 32 q^{61} - 12 q^{66} + 16 q^{76} + 36 q^{81} + 60 q^{86} - 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.683013 + 0.183013i
\(3\) 0.448288 + 1.67303i 0.258819 + 0.965926i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.73205i 0.707107i
\(7\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.59808 + 1.50000i −0.866025 + 0.500000i
\(10\) 0 0
\(11\) −1.50000 + 0.866025i −0.452267 + 0.261116i −0.708787 0.705422i \(-0.750757\pi\)
0.256520 + 0.966539i \(0.417424\pi\)
\(12\) −0.448288 + 1.67303i −0.129410 + 0.482963i
\(13\) 1.79315 + 6.69213i 0.497331 + 1.85606i 0.516565 + 0.856248i \(0.327210\pi\)
−0.0192343 + 0.999815i \(0.506123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 2.12132 2.12132i 0.514496 0.514496i −0.401405 0.915901i \(-0.631478\pi\)
0.915901 + 0.401405i \(0.131478\pi\)
\(18\) −2.89778 + 0.776457i −0.683013 + 0.183013i
\(19\) 4.00000i 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.67303 + 0.448288i −0.356692 + 0.0955753i
\(23\) 5.79555 1.55291i 1.20846 0.323805i 0.402300 0.915508i \(-0.368211\pi\)
0.806156 + 0.591703i \(0.201544\pi\)
\(24\) −0.866025 + 1.50000i −0.176777 + 0.306186i
\(25\) 0 0
\(26\) 6.92820i 1.35873i
\(27\) −3.67423 3.67423i −0.707107 0.707107i
\(28\) 0 0
\(29\) −1.73205 3.00000i −0.321634 0.557086i 0.659192 0.751975i \(-0.270899\pi\)
−0.980825 + 0.194889i \(0.937565\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0.258819 + 0.965926i 0.0457532 + 0.170753i
\(33\) −2.12132 2.12132i −0.369274 0.369274i
\(34\) 2.59808 1.50000i 0.445566 0.257248i
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) −4.89898 4.89898i −0.805387 0.805387i 0.178545 0.983932i \(-0.442861\pi\)
−0.983932 + 0.178545i \(0.942861\pi\)
\(38\) 1.03528 3.86370i 0.167944 0.626775i
\(39\) −10.3923 + 6.00000i −1.66410 + 0.960769i
\(40\) 0 0
\(41\) −6.00000 3.46410i −0.937043 0.541002i −0.0480106 0.998847i \(-0.515288\pi\)
−0.889032 + 0.457845i \(0.848621\pi\)
\(42\) 0 0
\(43\) 8.36516 + 2.24144i 1.27568 + 0.341816i 0.832203 0.554472i \(-0.187080\pi\)
0.443473 + 0.896288i \(0.353746\pi\)
\(44\) −1.73205 −0.261116
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 11.5911 + 3.10583i 1.69074 + 0.453032i 0.970580 0.240779i \(-0.0774030\pi\)
0.720157 + 0.693811i \(0.244070\pi\)
\(48\) −1.22474 + 1.22474i −0.176777 + 0.176777i
\(49\) 6.06218 + 3.50000i 0.866025 + 0.500000i
\(50\) 0 0
\(51\) 4.50000 + 2.59808i 0.630126 + 0.363803i
\(52\) −1.79315 + 6.69213i −0.248665 + 0.928032i
\(53\) −8.48528 8.48528i −1.16554 1.16554i −0.983243 0.182300i \(-0.941646\pi\)
−0.182300 0.983243i \(-0.558354\pi\)
\(54\) −2.59808 4.50000i −0.353553 0.612372i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.69213 1.79315i 0.886394 0.237509i
\(58\) −0.896575 3.34607i −0.117726 0.439360i
\(59\) 4.33013 7.50000i 0.563735 0.976417i −0.433432 0.901186i \(-0.642697\pi\)
0.997166 0.0752304i \(-0.0239692\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) −2.82843 + 2.82843i −0.359211 + 0.359211i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −1.50000 2.59808i −0.184637 0.319801i
\(67\) 3.34607 0.896575i 0.408787 0.109534i −0.0485648 0.998820i \(-0.515465\pi\)
0.457352 + 0.889286i \(0.348798\pi\)
\(68\) 2.89778 0.776457i 0.351407 0.0941593i
\(69\) 5.19615 + 9.00000i 0.625543 + 1.08347i
\(70\) 0 0
\(71\) 3.46410i 0.411113i −0.978645 0.205557i \(-0.934100\pi\)
0.978645 0.205557i \(-0.0659005\pi\)
\(72\) −2.89778 0.776457i −0.341506 0.0915064i
\(73\) −4.89898 + 4.89898i −0.573382 + 0.573382i −0.933072 0.359690i \(-0.882883\pi\)
0.359690 + 0.933072i \(0.382883\pi\)
\(74\) −3.46410 6.00000i −0.402694 0.697486i
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) 0 0
\(78\) −11.5911 + 3.10583i −1.31243 + 0.351666i
\(79\) 3.46410 2.00000i 0.389742 0.225018i −0.292306 0.956325i \(-0.594423\pi\)
0.682048 + 0.731307i \(0.261089\pi\)
\(80\) 0 0
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) −4.89898 4.89898i −0.541002 0.541002i
\(83\) 2.32937 8.69333i 0.255682 0.954217i −0.712028 0.702151i \(-0.752223\pi\)
0.967710 0.252066i \(-0.0811101\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 7.50000 + 4.33013i 0.808746 + 0.466930i
\(87\) 4.24264 4.24264i 0.454859 0.454859i
\(88\) −1.67303 0.448288i −0.178346 0.0477876i
\(89\) 1.73205 0.183597 0.0917985 0.995778i \(-0.470738\pi\)
0.0917985 + 0.995778i \(0.470738\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.79555 + 1.55291i 0.604228 + 0.161903i
\(93\) −6.69213 1.79315i −0.693942 0.185941i
\(94\) 10.3923 + 6.00000i 1.07188 + 0.618853i
\(95\) 0 0
\(96\) −1.50000 + 0.866025i −0.153093 + 0.0883883i
\(97\) −4.03459 + 15.0573i −0.409651 + 1.52884i 0.385664 + 0.922639i \(0.373972\pi\)
−0.795314 + 0.606197i \(0.792694\pi\)
\(98\) 4.94975 + 4.94975i 0.500000 + 0.500000i
\(99\) 2.59808 4.50000i 0.261116 0.452267i
\(100\) 0 0
\(101\) 12.0000 6.92820i 1.19404 0.689382i 0.234823 0.972038i \(-0.424549\pi\)
0.959221 + 0.282656i \(0.0912155\pi\)
\(102\) 3.67423 + 3.67423i 0.363803 + 0.363803i
\(103\) 1.79315 + 6.69213i 0.176684 + 0.659395i 0.996259 + 0.0864221i \(0.0275434\pi\)
−0.819574 + 0.572973i \(0.805790\pi\)
\(104\) −3.46410 + 6.00000i −0.339683 + 0.588348i
\(105\) 0 0
\(106\) −6.00000 10.3923i −0.582772 1.00939i
\(107\) −8.48528 + 8.48528i −0.820303 + 0.820303i −0.986151 0.165848i \(-0.946964\pi\)
0.165848 + 0.986151i \(0.446964\pi\)
\(108\) −1.34486 5.01910i −0.129410 0.482963i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) 0 0
\(111\) 6.00000 10.3923i 0.569495 0.986394i
\(112\) 0 0
\(113\) −2.89778 + 0.776457i −0.272600 + 0.0730429i −0.392529 0.919739i \(-0.628400\pi\)
0.119929 + 0.992782i \(0.461733\pi\)
\(114\) 6.92820 0.648886
\(115\) 0 0
\(116\) 3.46410i 0.321634i
\(117\) −14.6969 14.6969i −1.35873 1.35873i
\(118\) 6.12372 6.12372i 0.563735 0.563735i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.00000 + 6.92820i −0.363636 + 0.629837i
\(122\) −2.07055 7.72741i −0.187459 0.699607i
\(123\) 3.10583 11.5911i 0.280043 1.04514i
\(124\) −3.46410 + 2.00000i −0.311086 + 0.179605i
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) −0.258819 + 0.965926i −0.0228766 + 0.0853766i
\(129\) 15.0000i 1.32068i
\(130\) 0 0
\(131\) −15.0000 8.66025i −1.31056 0.756650i −0.328368 0.944550i \(-0.606499\pi\)
−0.982188 + 0.187900i \(0.939832\pi\)
\(132\) −0.776457 2.89778i −0.0675819 0.252219i
\(133\) 0 0
\(134\) 3.46410 0.299253
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) −17.3867 4.65874i −1.48544 0.398023i −0.577247 0.816569i \(-0.695873\pi\)
−0.908196 + 0.418546i \(0.862540\pi\)
\(138\) 2.68973 + 10.0382i 0.228965 + 0.854508i
\(139\) 11.2583 + 6.50000i 0.954919 + 0.551323i 0.894606 0.446857i \(-0.147457\pi\)
0.0603135 + 0.998179i \(0.480790\pi\)
\(140\) 0 0
\(141\) 20.7846i 1.75038i
\(142\) 0.896575 3.34607i 0.0752389 0.280796i
\(143\) −8.48528 8.48528i −0.709575 0.709575i
\(144\) −2.59808 1.50000i −0.216506 0.125000i
\(145\) 0 0
\(146\) −6.00000 + 3.46410i −0.496564 + 0.286691i
\(147\) −3.13801 + 11.7112i −0.258819 + 0.965926i
\(148\) −1.79315 6.69213i −0.147396 0.550090i
\(149\) 5.19615 9.00000i 0.425685 0.737309i −0.570799 0.821090i \(-0.693366\pi\)
0.996484 + 0.0837813i \(0.0266997\pi\)
\(150\) 0 0
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) 2.82843 2.82843i 0.229416 0.229416i
\(153\) −2.32937 + 8.69333i −0.188319 + 0.702814i
\(154\) 0 0
\(155\) 0 0
\(156\) −12.0000 −0.960769
\(157\) 6.69213 1.79315i 0.534090 0.143109i 0.0183138 0.999832i \(-0.494170\pi\)
0.515776 + 0.856723i \(0.327504\pi\)
\(158\) 3.86370 1.03528i 0.307380 0.0823622i
\(159\) 10.3923 18.0000i 0.824163 1.42749i
\(160\) 0 0
\(161\) 0 0
\(162\) 6.36396 6.36396i 0.500000 0.500000i
\(163\) −1.22474 + 1.22474i −0.0959294 + 0.0959294i −0.753443 0.657513i \(-0.771608\pi\)
0.657513 + 0.753443i \(0.271608\pi\)
\(164\) −3.46410 6.00000i −0.270501 0.468521i
\(165\) 0 0
\(166\) 4.50000 7.79423i 0.349268 0.604949i
\(167\) 1.55291 + 5.79555i 0.120168 + 0.448474i 0.999621 0.0275115i \(-0.00875830\pi\)
−0.879453 + 0.475985i \(0.842092\pi\)
\(168\) 0 0
\(169\) −30.3109 + 17.5000i −2.33161 + 1.34615i
\(170\) 0 0
\(171\) 6.00000 + 10.3923i 0.458831 + 0.794719i
\(172\) 6.12372 + 6.12372i 0.466930 + 0.466930i
\(173\) −4.65874 + 17.3867i −0.354198 + 1.32188i 0.527294 + 0.849683i \(0.323207\pi\)
−0.881491 + 0.472200i \(0.843460\pi\)
\(174\) 5.19615 3.00000i 0.393919 0.227429i
\(175\) 0 0
\(176\) −1.50000 0.866025i −0.113067 0.0652791i
\(177\) 14.4889 + 3.88229i 1.08905 + 0.291810i
\(178\) 1.67303 + 0.448288i 0.125399 + 0.0336006i
\(179\) −12.1244 −0.906217 −0.453108 0.891455i \(-0.649685\pi\)
−0.453108 + 0.891455i \(0.649685\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 9.79796 9.79796i 0.724286 0.724286i
\(184\) 5.19615 + 3.00000i 0.383065 + 0.221163i
\(185\) 0 0
\(186\) −6.00000 3.46410i −0.439941 0.254000i
\(187\) −1.34486 + 5.01910i −0.0983461 + 0.367033i
\(188\) 8.48528 + 8.48528i 0.618853 + 0.618853i
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 1.73205i 0.217072 0.125327i −0.387522 0.921861i \(-0.626669\pi\)
0.604594 + 0.796534i \(0.293335\pi\)
\(192\) −1.67303 + 0.448288i −0.120741 + 0.0323524i
\(193\) −1.34486 5.01910i −0.0968054 0.361283i 0.900482 0.434894i \(-0.143214\pi\)
−0.997287 + 0.0736115i \(0.976548\pi\)
\(194\) −7.79423 + 13.5000i −0.559593 + 0.969244i
\(195\) 0 0
\(196\) 3.50000 + 6.06218i 0.250000 + 0.433013i
\(197\) 4.24264 4.24264i 0.302276 0.302276i −0.539628 0.841904i \(-0.681435\pi\)
0.841904 + 0.539628i \(0.181435\pi\)
\(198\) 3.67423 3.67423i 0.261116 0.261116i
\(199\) 26.0000i 1.84309i −0.388270 0.921546i \(-0.626927\pi\)
0.388270 0.921546i \(-0.373073\pi\)
\(200\) 0 0
\(201\) 3.00000 + 5.19615i 0.211604 + 0.366508i
\(202\) 13.3843 3.58630i 0.941713 0.252331i
\(203\) 0 0
\(204\) 2.59808 + 4.50000i 0.181902 + 0.315063i
\(205\) 0 0
\(206\) 6.92820i 0.482711i
\(207\) −12.7279 + 12.7279i −0.884652 + 0.884652i
\(208\) −4.89898 + 4.89898i −0.339683 + 0.339683i
\(209\) 3.46410 + 6.00000i 0.239617 + 0.415029i
\(210\) 0 0
\(211\) −11.5000 + 19.9186i −0.791693 + 1.37125i 0.133226 + 0.991086i \(0.457467\pi\)
−0.924918 + 0.380166i \(0.875867\pi\)
\(212\) −3.10583 11.5911i −0.213309 0.796081i
\(213\) 5.79555 1.55291i 0.397105 0.106404i
\(214\) −10.3923 + 6.00000i −0.710403 + 0.410152i
\(215\) 0 0
\(216\) 5.19615i 0.353553i
\(217\) 0 0
\(218\) 0.517638 1.93185i 0.0350589 0.130842i
\(219\) −10.3923 6.00000i −0.702247 0.405442i
\(220\) 0 0
\(221\) 18.0000 + 10.3923i 1.21081 + 0.699062i
\(222\) 8.48528 8.48528i 0.569495 0.569495i
\(223\) −3.34607 0.896575i −0.224069 0.0600391i 0.145038 0.989426i \(-0.453670\pi\)
−0.369107 + 0.929387i \(0.620336\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.00000 −0.199557
\(227\) 2.89778 + 0.776457i 0.192332 + 0.0515353i 0.353699 0.935359i \(-0.384924\pi\)
−0.161367 + 0.986894i \(0.551590\pi\)
\(228\) 6.69213 + 1.79315i 0.443197 + 0.118754i
\(229\) −17.3205 10.0000i −1.14457 0.660819i −0.197013 0.980401i \(-0.563124\pi\)
−0.947559 + 0.319582i \(0.896457\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.896575 3.34607i 0.0588631 0.219680i
\(233\) 6.36396 + 6.36396i 0.416917 + 0.416917i 0.884140 0.467223i \(-0.154745\pi\)
−0.467223 + 0.884140i \(0.654745\pi\)
\(234\) −10.3923 18.0000i −0.679366 1.17670i
\(235\) 0 0
\(236\) 7.50000 4.33013i 0.488208 0.281867i
\(237\) 4.89898 + 4.89898i 0.318223 + 0.318223i
\(238\) 0 0
\(239\) −5.19615 + 9.00000i −0.336111 + 0.582162i −0.983698 0.179830i \(-0.942445\pi\)
0.647586 + 0.761992i \(0.275778\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) −5.65685 + 5.65685i −0.363636 + 0.363636i
\(243\) 15.0573 + 4.03459i 0.965926 + 0.258819i
\(244\) 8.00000i 0.512148i
\(245\) 0 0
\(246\) 6.00000 10.3923i 0.382546 0.662589i
\(247\) 26.7685 7.17260i 1.70324 0.456382i
\(248\) −3.86370 + 1.03528i −0.245345 + 0.0657401i
\(249\) 15.5885 0.987878
\(250\) 0 0
\(251\) 10.3923i 0.655956i 0.944685 + 0.327978i \(0.106367\pi\)
−0.944685 + 0.327978i \(0.893633\pi\)
\(252\) 0 0
\(253\) −7.34847 + 7.34847i −0.461994 + 0.461994i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.776457 2.89778i −0.0484341 0.180758i 0.937471 0.348063i \(-0.113160\pi\)
−0.985905 + 0.167304i \(0.946494\pi\)
\(258\) −3.88229 + 14.4889i −0.241701 + 0.902039i
\(259\) 0 0
\(260\) 0 0
\(261\) 9.00000 + 5.19615i 0.557086 + 0.321634i
\(262\) −12.2474 12.2474i −0.756650 0.756650i
\(263\) −6.21166 + 23.1822i −0.383027 + 1.42948i 0.458226 + 0.888836i \(0.348485\pi\)
−0.841253 + 0.540641i \(0.818182\pi\)
\(264\) 3.00000i 0.184637i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.776457 + 2.89778i 0.0475184 + 0.177341i
\(268\) 3.34607 + 0.896575i 0.204393 + 0.0547671i
\(269\) 6.92820 0.422420 0.211210 0.977441i \(-0.432260\pi\)
0.211210 + 0.977441i \(0.432260\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 2.89778 + 0.776457i 0.175704 + 0.0470796i
\(273\) 0 0
\(274\) −15.5885 9.00000i −0.941733 0.543710i
\(275\) 0 0
\(276\) 10.3923i 0.625543i
\(277\) −0.896575 + 3.34607i −0.0538700 + 0.201046i −0.987616 0.156891i \(-0.949853\pi\)
0.933746 + 0.357936i \(0.116520\pi\)
\(278\) 9.19239 + 9.19239i 0.551323 + 0.551323i
\(279\) 12.0000i 0.718421i
\(280\) 0 0
\(281\) −18.0000 + 10.3923i −1.07379 + 0.619953i −0.929214 0.369541i \(-0.879515\pi\)
−0.144575 + 0.989494i \(0.546182\pi\)
\(282\) −5.37945 + 20.0764i −0.320342 + 1.19553i
\(283\) −8.51747 31.7876i −0.506311 1.88958i −0.454120 0.890941i \(-0.650046\pi\)
−0.0521913 0.998637i \(-0.516621\pi\)
\(284\) 1.73205 3.00000i 0.102778 0.178017i
\(285\) 0 0
\(286\) −6.00000 10.3923i −0.354787 0.614510i
\(287\) 0 0
\(288\) −2.12132 2.12132i −0.125000 0.125000i
\(289\) 8.00000i 0.470588i
\(290\) 0 0
\(291\) −27.0000 −1.58277
\(292\) −6.69213 + 1.79315i −0.391627 + 0.104936i
\(293\) −11.5911 + 3.10583i −0.677160 + 0.181444i −0.580978 0.813919i \(-0.697330\pi\)
−0.0961820 + 0.995364i \(0.530663\pi\)
\(294\) −6.06218 + 10.5000i −0.353553 + 0.612372i
\(295\) 0 0
\(296\) 6.92820i 0.402694i
\(297\) 8.69333 + 2.32937i 0.504438 + 0.135164i
\(298\) 7.34847 7.34847i 0.425685 0.425685i
\(299\) 20.7846 + 36.0000i 1.20201 + 2.08193i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.517638 + 1.93185i 0.0297867 + 0.111166i
\(303\) 16.9706 + 16.9706i 0.974933 + 0.974933i
\(304\) 3.46410 2.00000i 0.198680 0.114708i
\(305\) 0 0
\(306\) −4.50000 + 7.79423i −0.257248 + 0.445566i
\(307\) −15.9217 15.9217i −0.908698 0.908698i 0.0874688 0.996167i \(-0.472122\pi\)
−0.996167 + 0.0874688i \(0.972122\pi\)
\(308\) 0 0
\(309\) −10.3923 + 6.00000i −0.591198 + 0.341328i
\(310\) 0 0
\(311\) −3.00000 1.73205i −0.170114 0.0982156i 0.412525 0.910946i \(-0.364647\pi\)
−0.582640 + 0.812731i \(0.697980\pi\)
\(312\) −11.5911 3.10583i −0.656217 0.175833i
\(313\) 1.67303 + 0.448288i 0.0945654 + 0.0253387i 0.305791 0.952099i \(-0.401079\pi\)
−0.211226 + 0.977437i \(0.567746\pi\)
\(314\) 6.92820 0.390981
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) −28.9778 7.76457i −1.62755 0.436102i −0.674346 0.738416i \(-0.735574\pi\)
−0.953208 + 0.302314i \(0.902241\pi\)
\(318\) 14.6969 14.6969i 0.824163 0.824163i
\(319\) 5.19615 + 3.00000i 0.290929 + 0.167968i
\(320\) 0 0
\(321\) −18.0000 10.3923i −1.00466 0.580042i
\(322\) 0 0
\(323\) −8.48528 8.48528i −0.472134 0.472134i
\(324\) 7.79423 4.50000i 0.433013 0.250000i
\(325\) 0 0
\(326\) −1.50000 + 0.866025i −0.0830773 + 0.0479647i
\(327\) 3.34607 0.896575i 0.185038 0.0495807i
\(328\) −1.79315 6.69213i −0.0990102 0.369511i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.500000 + 0.866025i 0.0274825 + 0.0476011i 0.879440 0.476011i \(-0.157918\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 6.36396 6.36396i 0.349268 0.349268i
\(333\) 20.0764 + 5.37945i 1.10018 + 0.294792i
\(334\) 6.00000i 0.328305i
\(335\) 0 0
\(336\) 0 0
\(337\) −8.36516 + 2.24144i −0.455679 + 0.122099i −0.479356 0.877621i \(-0.659130\pi\)
0.0236762 + 0.999720i \(0.492463\pi\)
\(338\) −33.8074 + 9.05867i −1.83888 + 0.492727i
\(339\) −2.59808 4.50000i −0.141108 0.244406i
\(340\) 0 0
\(341\) 6.92820i 0.375183i
\(342\) 3.10583 + 11.5911i 0.167944 + 0.626775i
\(343\) 0 0
\(344\) 4.33013 + 7.50000i 0.233465 + 0.404373i
\(345\) 0 0
\(346\) −9.00000 + 15.5885i −0.483843 + 0.838041i
\(347\) 5.43520 + 20.2844i 0.291777 + 1.08893i 0.943744 + 0.330678i \(0.107278\pi\)
−0.651967 + 0.758248i \(0.726056\pi\)
\(348\) 5.79555 1.55291i 0.310674 0.0832449i
\(349\) −8.66025 + 5.00000i −0.463573 + 0.267644i −0.713545 0.700609i \(-0.752912\pi\)
0.249973 + 0.968253i \(0.419578\pi\)
\(350\) 0 0
\(351\) 18.0000 31.1769i 0.960769 1.66410i
\(352\) −1.22474 1.22474i −0.0652791 0.0652791i
\(353\) −2.32937 + 8.69333i −0.123980 + 0.462699i −0.999801 0.0199361i \(-0.993654\pi\)
0.875821 + 0.482635i \(0.160320\pi\)
\(354\) 12.9904 + 7.50000i 0.690431 + 0.398621i
\(355\) 0 0
\(356\) 1.50000 + 0.866025i 0.0794998 + 0.0458993i
\(357\) 0 0
\(358\) −11.7112 3.13801i −0.618958 0.165849i
\(359\) 13.8564 0.731313 0.365657 0.930750i \(-0.380844\pi\)
0.365657 + 0.930750i \(0.380844\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) −1.93185 0.517638i −0.101536 0.0272065i
\(363\) −13.3843 3.58630i −0.702492 0.188232i
\(364\) 0 0
\(365\) 0 0
\(366\) 12.0000 6.92820i 0.627250 0.362143i
\(367\) 6.27603 23.4225i 0.327606 1.22264i −0.584060 0.811710i \(-0.698537\pi\)
0.911666 0.410932i \(-0.134797\pi\)
\(368\) 4.24264 + 4.24264i 0.221163 + 0.221163i
\(369\) 20.7846 1.08200
\(370\) 0 0
\(371\) 0 0
\(372\) −4.89898 4.89898i −0.254000 0.254000i
\(373\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(374\) −2.59808 + 4.50000i −0.134343 + 0.232689i
\(375\) 0 0
\(376\) 6.00000 + 10.3923i 0.309426 + 0.535942i
\(377\) 16.9706 16.9706i 0.874028 0.874028i
\(378\) 0 0
\(379\) 19.0000i 0.975964i −0.872854 0.487982i \(-0.837733\pi\)
0.872854 0.487982i \(-0.162267\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 3.34607 0.896575i 0.171200 0.0458728i
\(383\) 28.9778 7.76457i 1.48070 0.396751i 0.574111 0.818777i \(-0.305348\pi\)
0.906584 + 0.422026i \(0.138681\pi\)
\(384\) −1.73205 −0.0883883
\(385\) 0 0
\(386\) 5.19615i 0.264477i
\(387\) −25.0955 + 6.72432i −1.27568 + 0.341816i
\(388\) −11.0227 + 11.0227i −0.559593 + 0.559593i
\(389\) 5.19615 + 9.00000i 0.263455 + 0.456318i 0.967158 0.254177i \(-0.0818045\pi\)
−0.703702 + 0.710495i \(0.748471\pi\)
\(390\) 0 0
\(391\) 9.00000 15.5885i 0.455150 0.788342i
\(392\) 1.81173 + 6.76148i 0.0915064 + 0.341506i
\(393\) 7.76457 28.9778i 0.391671 1.46174i
\(394\) 5.19615 3.00000i 0.261778 0.151138i
\(395\) 0 0
\(396\) 4.50000 2.59808i 0.226134 0.130558i
\(397\) −2.44949 2.44949i −0.122936 0.122936i 0.642962 0.765898i \(-0.277705\pi\)
−0.765898 + 0.642962i \(0.777705\pi\)
\(398\) 6.72930 25.1141i 0.337309 1.25885i
\(399\) 0 0
\(400\) 0 0
\(401\) 22.5000 + 12.9904i 1.12360 + 0.648709i 0.942317 0.334723i \(-0.108643\pi\)
0.181280 + 0.983432i \(0.441976\pi\)
\(402\) 1.55291 + 5.79555i 0.0774523 + 0.289056i
\(403\) −26.7685 7.17260i −1.33344 0.357293i
\(404\) 13.8564 0.689382
\(405\) 0 0
\(406\) 0 0
\(407\) 11.5911 + 3.10583i 0.574550 + 0.153950i
\(408\) 1.34486 + 5.01910i 0.0665807 + 0.248482i
\(409\) −1.73205 1.00000i −0.0856444 0.0494468i 0.456566 0.889689i \(-0.349079\pi\)
−0.542211 + 0.840243i \(0.682412\pi\)
\(410\) 0 0
\(411\) 31.1769i 1.53784i
\(412\) −1.79315 + 6.69213i −0.0883422 + 0.329698i
\(413\) 0 0
\(414\) −15.5885 + 9.00000i −0.766131 + 0.442326i
\(415\) 0 0
\(416\) −6.00000 + 3.46410i −0.294174 + 0.169842i
\(417\) −5.82774 + 21.7494i −0.285386 + 1.06507i
\(418\) 1.79315 + 6.69213i 0.0877059 + 0.327323i
\(419\) −2.59808 + 4.50000i −0.126924 + 0.219839i −0.922484 0.386037i \(-0.873844\pi\)
0.795559 + 0.605876i \(0.207177\pi\)
\(420\) 0 0
\(421\) −14.0000 24.2487i −0.682318 1.18181i −0.974272 0.225377i \(-0.927639\pi\)
0.291953 0.956433i \(-0.405695\pi\)
\(422\) −16.2635 + 16.2635i −0.791693 + 0.791693i
\(423\) −34.7733 + 9.31749i −1.69074 + 0.453032i
\(424\) 12.0000i 0.582772i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) 0 0
\(428\) −11.5911 + 3.10583i −0.560277 + 0.150126i
\(429\) 10.3923 18.0000i 0.501745 0.869048i
\(430\) 0 0
\(431\) 24.2487i 1.16802i −0.811747 0.584010i \(-0.801483\pi\)
0.811747 0.584010i \(-0.198517\pi\)
\(432\) 1.34486 5.01910i 0.0647048 0.241481i
\(433\) 20.8207 20.8207i 1.00058 1.00058i 0.000577367 1.00000i \(-0.499816\pi\)
1.00000 0.000577367i \(-0.000183782\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) −6.21166 23.1822i −0.297144 1.10896i
\(438\) −8.48528 8.48528i −0.405442 0.405442i
\(439\) 8.66025 5.00000i 0.413331 0.238637i −0.278889 0.960323i \(-0.589966\pi\)
0.692220 + 0.721686i \(0.256633\pi\)
\(440\) 0 0
\(441\) −21.0000 −1.00000
\(442\) 14.6969 + 14.6969i 0.699062 + 0.699062i
\(443\) −2.32937 + 8.69333i −0.110672 + 0.413033i −0.998927 0.0463181i \(-0.985251\pi\)
0.888255 + 0.459351i \(0.151918\pi\)
\(444\) 10.3923 6.00000i 0.493197 0.284747i
\(445\) 0 0
\(446\) −3.00000 1.73205i −0.142054 0.0820150i
\(447\) 17.3867 + 4.65874i 0.822361 + 0.220351i
\(448\) 0 0
\(449\) −34.6410 −1.63481 −0.817405 0.576063i \(-0.804588\pi\)
−0.817405 + 0.576063i \(0.804588\pi\)
\(450\) 0 0
\(451\) 12.0000 0.565058
\(452\) −2.89778 0.776457i −0.136300 0.0365215i
\(453\) −2.44949 + 2.44949i −0.115087 + 0.115087i
\(454\) 2.59808 + 1.50000i 0.121934 + 0.0703985i
\(455\) 0 0
\(456\) 6.00000 + 3.46410i 0.280976 + 0.162221i
\(457\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(458\) −14.1421 14.1421i −0.660819 0.660819i
\(459\) −15.5885 −0.727607
\(460\) 0 0
\(461\) 15.0000 8.66025i 0.698620 0.403348i −0.108213 0.994128i \(-0.534513\pi\)
0.806833 + 0.590779i \(0.201180\pi\)
\(462\) 0 0
\(463\) 0.896575 + 3.34607i 0.0416674 + 0.155505i 0.983625 0.180227i \(-0.0576832\pi\)
−0.941958 + 0.335732i \(0.891016\pi\)
\(464\) 1.73205 3.00000i 0.0804084 0.139272i
\(465\) 0 0
\(466\) 4.50000 + 7.79423i 0.208458 + 0.361061i
\(467\) 10.6066 10.6066i 0.490815 0.490815i −0.417748 0.908563i \(-0.637180\pi\)
0.908563 + 0.417748i \(0.137180\pi\)
\(468\) −5.37945 20.0764i −0.248665 0.928032i
\(469\) 0 0
\(470\) 0 0
\(471\) 6.00000 + 10.3923i 0.276465 + 0.478852i
\(472\) 8.36516 2.24144i 0.385038 0.103171i
\(473\) −14.4889 + 3.88229i −0.666200 + 0.178508i
\(474\) 3.46410 + 6.00000i 0.159111 + 0.275589i
\(475\) 0 0
\(476\) 0 0
\(477\) 34.7733 + 9.31749i 1.59216 + 0.426618i
\(478\) −7.34847 + 7.34847i −0.336111 + 0.336111i
\(479\) −3.46410 6.00000i −0.158279 0.274147i 0.775969 0.630771i \(-0.217261\pi\)
−0.934248 + 0.356624i \(0.883928\pi\)
\(480\) 0 0
\(481\) 24.0000 41.5692i 1.09431 1.89539i
\(482\) 2.58819 + 9.65926i 0.117889 + 0.439967i
\(483\) 0 0
\(484\) −6.92820 + 4.00000i −0.314918 + 0.181818i
\(485\) 0 0
\(486\) 13.5000 + 7.79423i 0.612372 + 0.353553i
\(487\) 12.2474 + 12.2474i 0.554985 + 0.554985i 0.927875 0.372890i \(-0.121633\pi\)
−0.372890 + 0.927875i \(0.621633\pi\)
\(488\) 2.07055 7.72741i 0.0937295 0.349803i
\(489\) −2.59808 1.50000i −0.117489 0.0678323i
\(490\) 0 0
\(491\) −19.5000 11.2583i −0.880023 0.508081i −0.00935679 0.999956i \(-0.502978\pi\)
−0.870666 + 0.491875i \(0.836312\pi\)
\(492\) 8.48528 8.48528i 0.382546 0.382546i
\(493\) −10.0382 2.68973i −0.452098 0.121139i
\(494\) 27.7128 1.24686
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 15.0573 + 4.03459i 0.674733 + 0.180794i
\(499\) 4.33013 + 2.50000i 0.193843 + 0.111915i 0.593780 0.804627i \(-0.297635\pi\)
−0.399937 + 0.916542i \(0.630968\pi\)
\(500\) 0 0
\(501\) −9.00000 + 5.19615i −0.402090 + 0.232147i
\(502\) −2.68973 + 10.0382i −0.120048 + 0.448027i
\(503\) 16.9706 + 16.9706i 0.756680 + 0.756680i 0.975717 0.219037i \(-0.0702914\pi\)
−0.219037 + 0.975717i \(0.570291\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −9.00000 + 5.19615i −0.400099 + 0.230997i
\(507\) −42.8661 42.8661i −1.90375 1.90375i
\(508\) 0 0
\(509\) 15.5885 27.0000i 0.690946 1.19675i −0.280582 0.959830i \(-0.590527\pi\)
0.971528 0.236924i \(-0.0761392\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −14.6969 + 14.6969i −0.648886 + 0.648886i
\(514\) 3.00000i 0.132324i
\(515\) 0 0
\(516\) −7.50000 + 12.9904i −0.330169 + 0.571870i
\(517\) −20.0764 + 5.37945i −0.882959 + 0.236588i
\(518\) 0 0
\(519\) −31.1769 −1.36851
\(520\) 0 0
\(521\) 5.19615i 0.227648i −0.993501 0.113824i \(-0.963690\pi\)
0.993501 0.113824i \(-0.0363099\pi\)
\(522\) 7.34847 + 7.34847i 0.321634 + 0.321634i
\(523\) 18.3712 18.3712i 0.803315 0.803315i −0.180297 0.983612i \(-0.557706\pi\)
0.983612 + 0.180297i \(0.0577059\pi\)
\(524\) −8.66025 15.0000i −0.378325 0.655278i
\(525\) 0 0
\(526\) −12.0000 + 20.7846i −0.523225 + 0.906252i
\(527\) 3.10583 + 11.5911i 0.135292 + 0.504917i
\(528\) 0.776457 2.89778i 0.0337910 0.126110i
\(529\) 11.2583 6.50000i 0.489493 0.282609i
\(530\) 0 0
\(531\) 25.9808i 1.12747i
\(532\) 0 0
\(533\) 12.4233 46.3644i 0.538113 2.00827i
\(534\) 3.00000i 0.129823i
\(535\) 0 0
\(536\) 3.00000 + 1.73205i 0.129580 + 0.0748132i
\(537\) −5.43520 20.2844i −0.234546 0.875338i
\(538\) 6.69213 + 1.79315i 0.288518 + 0.0773082i
\(539\) −12.1244 −0.522233
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) 7.72741 + 2.07055i 0.331921 + 0.0889378i
\(543\) −0.896575 3.34607i −0.0384757 0.143593i
\(544\) 2.59808 + 1.50000i 0.111392 + 0.0643120i
\(545\) 0 0
\(546\) 0 0
\(547\) 4.48288 16.7303i 0.191674 0.715337i −0.801429 0.598090i \(-0.795926\pi\)
0.993103 0.117247i \(-0.0374069\pi\)
\(548\) −12.7279 12.7279i −0.543710 0.543710i
\(549\) 20.7846 + 12.0000i 0.887066 + 0.512148i
\(550\) 0 0
\(551\) −12.0000 + 6.92820i −0.511217 + 0.295151i
\(552\) −2.68973 + 10.0382i −0.114482 + 0.427254i
\(553\) 0 0
\(554\) −1.73205 + 3.00000i −0.0735878 + 0.127458i
\(555\) 0 0
\(556\) 6.50000 + 11.2583i 0.275661 + 0.477460i
\(557\) 4.24264 4.24264i 0.179766 0.179766i −0.611488 0.791254i \(-0.709429\pi\)
0.791254 + 0.611488i \(0.209429\pi\)
\(558\) 3.10583 11.5911i 0.131480 0.490691i
\(559\) 60.0000i 2.53773i
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) −20.0764 + 5.37945i −0.846871 + 0.226919i
\(563\) 20.2844 5.43520i 0.854887 0.229066i 0.195346 0.980734i \(-0.437417\pi\)
0.659542 + 0.751668i \(0.270750\pi\)
\(564\) −10.3923 + 18.0000i −0.437595 + 0.757937i
\(565\) 0 0
\(566\) 32.9090i 1.38327i
\(567\) 0 0
\(568\) 2.44949 2.44949i 0.102778 0.102778i
\(569\) −16.4545 28.5000i −0.689808 1.19478i −0.971900 0.235395i \(-0.924362\pi\)
0.282092 0.959387i \(-0.408972\pi\)
\(570\) 0 0
\(571\) −8.50000 + 14.7224i −0.355714 + 0.616115i −0.987240 0.159240i \(-0.949096\pi\)
0.631526 + 0.775355i \(0.282429\pi\)
\(572\) −3.10583 11.5911i −0.129861 0.484649i
\(573\) 4.24264 + 4.24264i 0.177239 + 0.177239i
\(574\) 0 0
\(575\) 0 0
\(576\) −1.50000 2.59808i −0.0625000 0.108253i
\(577\) 14.6969 + 14.6969i 0.611842 + 0.611842i 0.943426 0.331584i \(-0.107583\pi\)
−0.331584 + 0.943426i \(0.607583\pi\)
\(578\) −2.07055 + 7.72741i −0.0861236 + 0.321418i
\(579\) 7.79423 4.50000i 0.323917 0.187014i
\(580\) 0 0
\(581\) 0 0
\(582\) −26.0800 6.98811i −1.08105 0.289667i
\(583\) 20.0764 + 5.37945i 0.831479 + 0.222794i
\(584\) −6.92820 −0.286691
\(585\) 0 0
\(586\) −12.0000 −0.495715
\(587\) −26.0800 6.98811i −1.07644 0.288430i −0.323301 0.946296i \(-0.604793\pi\)
−0.753135 + 0.657866i \(0.771459\pi\)
\(588\) −8.57321 + 8.57321i −0.353553 + 0.353553i
\(589\) 13.8564 + 8.00000i 0.570943 + 0.329634i
\(590\) 0 0
\(591\) 9.00000 + 5.19615i 0.370211 + 0.213741i
\(592\) 1.79315 6.69213i 0.0736980 0.275045i
\(593\) 14.8492 + 14.8492i 0.609785 + 0.609785i 0.942890 0.333105i \(-0.108096\pi\)
−0.333105 + 0.942890i \(0.608096\pi\)
\(594\) 7.79423 + 4.50000i 0.319801 + 0.184637i
\(595\) 0 0
\(596\) 9.00000 5.19615i 0.368654 0.212843i
\(597\) 43.4988 11.6555i 1.78029 0.477027i
\(598\) 10.7589 + 40.1528i 0.439964 + 1.64197i
\(599\) −22.5167 + 39.0000i −0.920006 + 1.59350i −0.120603 + 0.992701i \(0.538483\pi\)
−0.799402 + 0.600796i \(0.794850\pi\)
\(600\) 0 0
\(601\) −9.50000 16.4545i −0.387513 0.671192i 0.604601 0.796528i \(-0.293332\pi\)
−0.992114 + 0.125336i \(0.959999\pi\)
\(602\) 0 0
\(603\) −7.34847 + 7.34847i −0.299253 + 0.299253i
\(604\) 2.00000i 0.0813788i
\(605\) 0 0
\(606\) 12.0000 + 20.7846i 0.487467 + 0.844317i
\(607\) 6.69213 1.79315i 0.271625 0.0727818i −0.120435 0.992721i \(-0.538429\pi\)
0.392061 + 0.919939i \(0.371762\pi\)
\(608\) 3.86370 1.03528i 0.156694 0.0419860i
\(609\) 0 0
\(610\) 0 0
\(611\) 83.1384i 3.36342i
\(612\) −6.36396 + 6.36396i −0.257248 + 0.257248i
\(613\) −17.1464 + 17.1464i −0.692538 + 0.692538i −0.962790 0.270252i \(-0.912893\pi\)
0.270252 + 0.962790i \(0.412893\pi\)
\(614\) −11.2583 19.5000i −0.454349 0.786956i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.98811 + 26.0800i 0.281331 + 1.04994i 0.951479 + 0.307714i \(0.0995639\pi\)
−0.670148 + 0.742227i \(0.733769\pi\)
\(618\) −11.5911 + 3.10583i −0.466263 + 0.124935i
\(619\) 32.0429 18.5000i 1.28791 0.743578i 0.309633 0.950856i \(-0.399794\pi\)
0.978282 + 0.207279i \(0.0664606\pi\)
\(620\) 0 0
\(621\) −27.0000 15.5885i −1.08347 0.625543i
\(622\) −2.44949 2.44949i −0.0982156 0.0982156i
\(623\) 0 0
\(624\) −10.3923 6.00000i −0.416025 0.240192i
\(625\) 0 0
\(626\) 1.50000 + 0.866025i 0.0599521 + 0.0346133i
\(627\) −8.48528 + 8.48528i −0.338869 + 0.338869i
\(628\) 6.69213 + 1.79315i 0.267045 + 0.0715545i
\(629\) −20.7846 −0.828737
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) 3.86370 + 1.03528i 0.153690 + 0.0411811i
\(633\) −38.4797 10.3106i −1.52943 0.409810i
\(634\) −25.9808 15.0000i −1.03183 0.595726i
\(635\) 0 0
\(636\) 18.0000 10.3923i 0.713746 0.412082i
\(637\) −12.5521 + 46.8449i −0.497331 + 1.85606i
\(638\) 4.24264 + 4.24264i 0.167968 + 0.167968i
\(639\) 5.19615 + 9.00000i 0.205557 + 0.356034i
\(640\) 0 0
\(641\) −16.5000 + 9.52628i −0.651711 + 0.376265i −0.789111 0.614250i \(-0.789459\pi\)
0.137401 + 0.990516i \(0.456125\pi\)
\(642\) −14.6969 14.6969i −0.580042 0.580042i
\(643\) 12.1038 + 45.1719i 0.477326 + 1.78141i 0.612376 + 0.790566i \(0.290214\pi\)
−0.135050 + 0.990839i \(0.543120\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 8.48528 8.48528i 0.333591 0.333591i −0.520358 0.853948i \(-0.674201\pi\)
0.853948 + 0.520358i \(0.174201\pi\)
\(648\) 8.69333 2.32937i 0.341506 0.0915064i
\(649\) 15.0000i 0.588802i
\(650\) 0 0
\(651\) 0 0
\(652\) −1.67303 + 0.448288i −0.0655210 + 0.0175563i
\(653\) 46.3644 12.4233i 1.81438 0.486162i 0.818314 0.574771i \(-0.194909\pi\)
0.996066 + 0.0886092i \(0.0282422\pi\)
\(654\) 3.46410 0.135457
\(655\) 0 0
\(656\) 6.92820i 0.270501i
\(657\) 5.37945 20.0764i 0.209872 0.783255i
\(658\) 0 0
\(659\) −7.79423 13.5000i −0.303620 0.525885i 0.673333 0.739339i \(-0.264862\pi\)
−0.976953 + 0.213454i \(0.931529\pi\)
\(660\) 0 0
\(661\) −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) 0.258819 + 0.965926i 0.0100593 + 0.0375418i
\(663\) −9.31749 + 34.7733i −0.361861 + 1.35048i
\(664\) 7.79423 4.50000i 0.302475 0.174634i
\(665\) 0 0
\(666\) 18.0000 + 10.3923i 0.697486 + 0.402694i
\(667\) −14.6969 14.6969i −0.569068 0.569068i
\(668\) −1.55291 + 5.79555i −0.0600841 + 0.224237i
\(669\) 6.00000i 0.231973i
\(670\) 0 0
\(671\) 12.0000 + 6.92820i 0.463255 + 0.267460i
\(672\) 0 0
\(673\) 46.8449 + 12.5521i 1.80574 + 0.483846i 0.994850 0.101355i \(-0.0323177\pi\)
0.810888 + 0.585201i \(0.198984\pi\)
\(674\) −8.66025 −0.333581
\(675\) 0 0
\(676\) −35.0000 −1.34615
\(677\) −5.79555 1.55291i −0.222741 0.0596833i 0.145722 0.989326i \(-0.453449\pi\)
−0.368464 + 0.929642i \(0.620116\pi\)
\(678\) −1.34486 5.01910i −0.0516492 0.192757i
\(679\) 0 0
\(680\) 0 0
\(681\) 5.19615i 0.199117i
\(682\) 1.79315 6.69213i 0.0686633 0.256255i
\(683\) −8.48528 8.48528i −0.324680 0.324680i 0.525879 0.850559i \(-0.323736\pi\)
−0.850559 + 0.525879i \(0.823736\pi\)
\(684\) 12.0000i 0.458831i
\(685\) 0 0
\(686\) 0 0
\(687\) 8.96575 33.4607i 0.342065 1.27660i
\(688\) 2.24144 + 8.36516i 0.0854540 + 0.318919i
\(689\) 41.5692 72.0000i 1.58366 2.74298i
\(690\) 0 0
\(691\) 17.5000 + 30.3109i 0.665731 + 1.15308i 0.979086 + 0.203445i \(0.0652137\pi\)
−0.313355 + 0.949636i \(0.601453\pi\)
\(692\) −12.7279 + 12.7279i −0.483843 + 0.483843i
\(693\) 0 0
\(694\) 21.0000i 0.797149i
\(695\) 0 0
\(696\) 6.00000 0.227429
\(697\) −20.0764 + 5.37945i −0.760448 + 0.203761i
\(698\) −9.65926 + 2.58819i −0.365608 + 0.0979645i
\(699\) −7.79423 + 13.5000i −0.294805 + 0.510617i
\(700\) 0 0
\(701\) 27.7128i 1.04670i −0.852118 0.523349i \(-0.824682\pi\)
0.852118 0.523349i \(-0.175318\pi\)
\(702\) 25.4558 25.4558i 0.960769 0.960769i
\(703\) −19.5959 + 19.5959i −0.739074 + 0.739074i
\(704\) −0.866025 1.50000i −0.0326396 0.0565334i
\(705\) 0 0
\(706\) −4.50000 + 7.79423i −0.169360 + 0.293340i
\(707\) 0 0
\(708\) 10.6066 + 10.6066i 0.398621 + 0.398621i
\(709\) 6.92820 4.00000i 0.260194 0.150223i −0.364229 0.931309i \(-0.618667\pi\)
0.624423 + 0.781086i \(0.285334\pi\)
\(710\) 0 0
\(711\) −6.00000 + 10.3923i −0.225018 + 0.389742i
\(712\) 1.22474 + 1.22474i 0.0458993 + 0.0458993i
\(713\) −6.21166 + 23.1822i −0.232628 + 0.868181i
\(714\) 0 0
\(715\) 0 0
\(716\) −10.5000 6.06218i −0.392403 0.226554i
\(717\) −17.3867 4.65874i −0.649317 0.173984i
\(718\) 13.3843 + 3.58630i 0.499496 + 0.133840i
\(719\) −34.6410 −1.29189 −0.645946 0.763383i \(-0.723537\pi\)
−0.645946 + 0.763383i \(0.723537\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.89778 + 0.776457i 0.107844 + 0.0288967i
\(723\) −12.2474 + 12.2474i −0.455488 + 0.455488i
\(724\) −1.73205 1.00000i −0.0643712 0.0371647i
\(725\) 0 0
\(726\) −12.0000 6.92820i −0.445362 0.257130i
\(727\) 0.896575 3.34607i 0.0332521 0.124099i −0.947305 0.320334i \(-0.896205\pi\)
0.980557 + 0.196235i \(0.0628716\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 22.5000 12.9904i 0.832193 0.480467i
\(732\) 13.3843 3.58630i 0.494697 0.132554i
\(733\) −5.37945 20.0764i −0.198695 0.741538i −0.991279 0.131777i \(-0.957932\pi\)
0.792585 0.609762i \(-0.208735\pi\)
\(734\) 12.1244 21.0000i 0.447518 0.775124i
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) −4.24264 + 4.24264i −0.156280 + 0.156280i
\(738\) 20.0764 + 5.37945i 0.739022 + 0.198020i
\(739\) 41.0000i 1.50821i 0.656754 + 0.754105i \(0.271929\pi\)
−0.656754 + 0.754105i \(0.728071\pi\)
\(740\) 0 0
\(741\) 24.0000 + 41.5692i 0.881662 + 1.52708i
\(742\) 0 0
\(743\) −23.1822 + 6.21166i −0.850473 + 0.227884i −0.657625 0.753345i \(-0.728439\pi\)
−0.192848 + 0.981229i \(0.561772\pi\)
\(744\) −3.46410 6.00000i −0.127000 0.219971i
\(745\) 0 0
\(746\) 0 0
\(747\) 6.98811 + 26.0800i 0.255682 + 0.954217i
\(748\) −3.67423 + 3.67423i −0.134343 + 0.134343i
\(749\) 0 0
\(750\) 0 0
\(751\) 19.0000 32.9090i 0.693320 1.20087i −0.277424 0.960748i \(-0.589481\pi\)
0.970744 0.240118i \(-0.0771860\pi\)
\(752\) 3.10583 + 11.5911i 0.113258 + 0.422684i
\(753\) −17.3867 + 4.65874i −0.633605 + 0.169774i
\(754\) 20.7846 12.0000i 0.756931 0.437014i
\(755\) 0 0
\(756\) 0 0
\(757\) 29.3939 + 29.3939i 1.06834 + 1.06834i 0.997487 + 0.0708518i \(0.0225717\pi\)
0.0708518 + 0.997487i \(0.477428\pi\)
\(758\) 4.91756 18.3526i 0.178614 0.666596i
\(759\) −15.5885 9.00000i −0.565825 0.326679i
\(760\) 0 0
\(761\) 46.5000 + 26.8468i 1.68562 + 0.973195i 0.957802 + 0.287429i \(0.0928005\pi\)
0.727822 + 0.685766i \(0.240533\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 3.46410 0.125327
\(765\) 0 0
\(766\) 30.0000 1.08394
\(767\) 57.9555 + 15.5291i 2.09265 + 0.560725i
\(768\) −1.67303 0.448288i −0.0603704 0.0161762i
\(769\) −11.2583 6.50000i −0.405986 0.234396i 0.283078 0.959097i \(-0.408645\pi\)
−0.689063 + 0.724701i \(0.741978\pi\)
\(770\) 0 0
\(771\) 4.50000 2.59808i 0.162064 0.0935674i
\(772\) 1.34486 5.01910i 0.0484027 0.180641i
\(773\) 4.24264 + 4.24264i 0.152597 + 0.152597i 0.779277 0.626680i \(-0.215587\pi\)
−0.626680 + 0.779277i \(0.715587\pi\)
\(774\) −25.9808 −0.933859
\(775\) 0 0
\(776\) −13.5000 + 7.79423i −0.484622 + 0.279797i
\(777\) 0 0
\(778\) 2.68973 + 10.0382i 0.0964314 + 0.359887i
\(779\) −13.8564 + 24.0000i −0.496457 + 0.859889i
\(780\) 0 0
\(781\) 3.00000 + 5.19615i 0.107348 + 0.185933i
\(782\) 12.7279 12.7279i 0.455150 0.455150i
\(783\) −4.65874 + 17.3867i −0.166490 + 0.621349i
\(784\) 7.00000i 0.250000i
\(785\) 0 0
\(786\) 15.0000 25.9808i 0.535032 0.926703i
\(787\) −50.1910 + 13.4486i −1.78912 + 0.479392i −0.992195 0.124693i \(-0.960205\pi\)
−0.796920 + 0.604085i \(0.793539\pi\)
\(788\) 5.79555 1.55291i 0.206458 0.0553203i
\(789\) −41.5692 −1.47990
\(790\) 0 0
\(791\) 0 0
\(792\) 5.01910 1.34486i 0.178346 0.0477876i
\(793\) 39.1918 39.1918i 1.39174 1.39174i
\(794\) −1.73205 3.00000i −0.0614682 0.106466i
\(795\) 0 0
\(796\) 13.0000 22.5167i 0.460773 0.798082i
\(797\) 6.21166 + 23.1822i 0.220028 + 0.821156i 0.984336 + 0.176304i \(0.0564143\pi\)
−0.764308 + 0.644852i \(0.776919\pi\)
\(798\) 0 0
\(799\) 31.1769 18.0000i 1.10296 0.636794i
\(800\) 0 0
\(801\) −4.50000 + 2.59808i −0.159000 + 0.0917985i
\(802\) 18.3712 + 18.3712i 0.648709 + 0.648709i
\(803\) 3.10583 11.5911i 0.109602 0.409041i
\(804\) 6.00000i 0.211604i
\(805\) 0 0
\(806\) −24.0000 13.8564i −0.845364 0.488071i
\(807\) 3.10583 + 11.5911i 0.109330 + 0.408026i
\(808\) 13.3843 + 3.58630i 0.470857 + 0.126166i
\(809\) 8.66025 0.304478 0.152239 0.988344i \(-0.451352\pi\)
0.152239 + 0.988344i \(0.451352\pi\)
\(810\) 0 0
\(811\) −29.0000 −1.01833 −0.509164 0.860670i \(-0.670045\pi\)
−0.509164 + 0.860670i \(0.670045\pi\)
\(812\) 0 0
\(813\) 3.58630 + 13.3843i 0.125777 + 0.469407i
\(814\) 10.3923 + 6.00000i 0.364250 + 0.210300i
\(815\) 0 0
\(816\) 5.19615i 0.181902i
\(817\) 8.96575 33.4607i 0.313672 1.17064i
\(818\) −1.41421 1.41421i −0.0494468 0.0494468i
\(819\) 0 0
\(820\) 0 0
\(821\) −30.0000 + 17.3205i −1.04701 + 0.604490i −0.921810 0.387642i \(-0.873290\pi\)
−0.125197 + 0.992132i \(0.539956\pi\)
\(822\) 8.06918 30.1146i 0.281445 1.05037i
\(823\) −1.79315 6.69213i −0.0625053 0.233273i 0.927605 0.373562i \(-0.121864\pi\)
−0.990111 + 0.140289i \(0.955197\pi\)
\(824\) −3.46410 + 6.00000i −0.120678 + 0.209020i
\(825\) 0 0
\(826\) 0 0
\(827\) −23.3345 + 23.3345i −0.811421 + 0.811421i −0.984847 0.173426i \(-0.944516\pi\)
0.173426 + 0.984847i \(0.444516\pi\)
\(828\) −17.3867 + 4.65874i −0.604228 + 0.161903i
\(829\) 16.0000i 0.555703i −0.960624 0.277851i \(-0.910378\pi\)
0.960624 0.277851i \(-0.0896223\pi\)
\(830\) 0 0
\(831\) −6.00000 −0.208138
\(832\) −6.69213 + 1.79315i −0.232008 + 0.0621663i
\(833\) 20.2844 5.43520i 0.702814 0.188319i
\(834\) −11.2583 + 19.5000i −0.389844 + 0.675230i
\(835\) 0 0
\(836\) 6.92820i 0.239617i
\(837\) 20.0764 5.37945i 0.693942 0.185941i
\(838\) −3.67423 + 3.67423i −0.126924 + 0.126924i
\(839\) −3.46410 6.00000i −0.119594 0.207143i 0.800013 0.599983i \(-0.204826\pi\)
−0.919607 + 0.392840i \(0.871493\pi\)
\(840\) 0 0
\(841\) 8.50000 14.7224i 0.293103 0.507670i
\(842\) −7.24693 27.0459i −0.249746 0.932064i
\(843\) −25.4558 25.4558i −0.876746 0.876746i
\(844\) −19.9186 + 11.5000i −0.685626 + 0.395846i
\(845\) 0 0
\(846\) −36.0000 −1.23771
\(847\) 0 0
\(848\) 3.10583 11.5911i 0.106655 0.398040i
\(849\) 49.3634 28.5000i 1.69415 0.978117i
\(850\) 0 0
\(851\) −36.0000 20.7846i −1.23406 0.712487i
\(852\) 5.79555 + 1.55291i 0.198552 + 0.0532020i
\(853\) −16.7303 4.48288i −0.572835 0.153491i −0.0392388 0.999230i \(-0.512493\pi\)
−0.533597 + 0.845739i \(0.679160\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) 2.89778 + 0.776457i 0.0989862 + 0.0265233i 0.307972 0.951395i \(-0.400350\pi\)
−0.208986 + 0.977919i \(0.567016\pi\)
\(858\) 14.6969 14.6969i 0.501745 0.501745i
\(859\) 27.7128 + 16.0000i 0.945549 + 0.545913i 0.891695 0.452636i \(-0.149516\pi\)
0.0538535 + 0.998549i \(0.482850\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 6.27603 23.4225i 0.213762 0.797772i
\(863\) −33.9411 33.9411i −1.15537 1.15537i −0.985460 0.169910i \(-0.945652\pi\)
−0.169910 0.985460i \(-0.554348\pi\)
\(864\) 2.59808 4.50000i 0.0883883 0.153093i
\(865\) 0 0
\(866\) 25.5000 14.7224i 0.866525 0.500289i
\(867\) −13.3843 + 3.58630i −0.454553 + 0.121797i
\(868\) 0 0
\(869\) −3.46410 + 6.00000i −0.117512 + 0.203536i
\(870\) 0 0
\(871\) 12.0000 + 20.7846i 0.406604 + 0.704260i
\(872\) 1.41421 1.41421i 0.0478913 0.0478913i
\(873\) −12.1038 45.1719i −0.409651 1.52884i
\(874\) 24.0000i 0.811812i
\(875\) 0 0
\(876\) −6.00000 10.3923i −0.202721 0.351123i
\(877\) −20.0764 + 5.37945i −0.677932 + 0.181651i −0.581325 0.813671i \(-0.697466\pi\)
−0.0966065 + 0.995323i \(0.530799\pi\)
\(878\) 9.65926 2.58819i 0.325984 0.0873472i
\(879\) −10.3923 18.0000i −0.350524 0.607125i
\(880\) 0 0
\(881\) 34.6410i 1.16709i 0.812082 + 0.583543i \(0.198334\pi\)
−0.812082 + 0.583543i \(0.801666\pi\)
\(882\) −20.2844 5.43520i −0.683013 0.183013i
\(883\) −18.3712 + 18.3712i −0.618239 + 0.618239i −0.945080 0.326840i \(-0.894016\pi\)
0.326840 + 0.945080i \(0.394016\pi\)
\(884\) 10.3923 + 18.0000i 0.349531 + 0.605406i
\(885\) 0 0
\(886\) −4.50000 + 7.79423i −0.151180 + 0.261852i
\(887\) −10.8704 40.5689i −0.364992 1.36217i −0.867431 0.497557i \(-0.834230\pi\)
0.502439 0.864613i \(-0.332436\pi\)
\(888\) 11.5911 3.10583i 0.388972 0.104225i
\(889\) 0 0
\(890\) 0 0
\(891\) 15.5885i 0.522233i
\(892\) −2.44949 2.44949i −0.0820150 0.0820150i
\(893\) 12.4233 46.3644i 0.415730 1.55153i
\(894\) 15.5885 + 9.00000i 0.521356 + 0.301005i
\(895\) 0 0
\(896\) 0 0
\(897\) −50.9117 + 50.9117i −1.69989 + 1.69989i
\(898\) −33.4607 8.96575i −1.11660 0.299191i
\(899\) 13.8564 0.462137
\(900\) 0 0
\(901\) −36.0000 −1.19933
\(902\) 11.5911 + 3.10583i 0.385942 + 0.103413i
\(903\) 0 0
\(904\) −2.59808 1.50000i −0.0864107 0.0498893i
\(905\) 0 0
\(906\) −3.00000 + 1.73205i −0.0996683 + 0.0575435i
\(907\) 2.24144 8.36516i 0.0744257 0.277761i −0.918677 0.395010i \(-0.870741\pi\)
0.993102 + 0.117250i \(0.0374077\pi\)
\(908\) 2.12132 + 2.12132i 0.0703985 + 0.0703985i
\(909\) −20.7846 + 36.0000i −0.689382 + 1.19404i
\(910\) 0 0
\(911\) 33.0000 19.0526i 1.09334 0.631239i 0.158875 0.987299i \(-0.449213\pi\)
0.934463 + 0.356059i \(0.115880\pi\)
\(912\) 4.89898 + 4.89898i 0.162221 + 0.162221i
\(913\) 4.03459 + 15.0573i 0.133525 + 0.498324i
\(914\) 0 0
\(915\) 0 0
\(916\) −10.0000 17.3205i −0.330409 0.572286i
\(917\) 0 0
\(918\) −15.0573 4.03459i −0.496965 0.133161i
\(919\) 34.0000i 1.12156i −0.827966 0.560778i \(-0.810502\pi\)
0.827966 0.560778i \(-0.189498\pi\)
\(920\) 0 0
\(921\) 19.5000 33.7750i 0.642547 1.11292i
\(922\) 16.7303 4.48288i 0.550984 0.147636i
\(923\) 23.1822 6.21166i 0.763052 0.204459i
\(924\) 0 0
\(925\) 0 0
\(926\) 3.46410i 0.113837i
\(927\) −14.6969 14.6969i −0.482711 0.482711i
\(928\) 2.44949 2.44949i 0.0804084 0.0804084i
\(929\) −17.3205 30.0000i −0.568267 0.984268i −0.996737 0.0807121i \(-0.974281\pi\)
0.428470 0.903556i \(-0.359053\pi\)
\(930\) 0 0
\(931\) 14.0000 24.2487i 0.458831 0.794719i
\(932\) 2.32937 + 8.69333i 0.0763011 + 0.284760i
\(933\) 1.55291 5.79555i 0.0508401 0.189738i
\(934\) 12.9904 7.50000i 0.425058 0.245407i
\(935\) 0 0
\(936\) 20.7846i 0.679366i
\(937\) −3.67423 3.67423i −0.120032 0.120032i 0.644539 0.764571i \(-0.277049\pi\)
−0.764571 + 0.644539i \(0.777049\pi\)
\(938\) 0 0
\(939\) 3.00000i 0.0979013i
\(940\) 0 0
\(941\) −18.0000 10.3923i −0.586783 0.338779i 0.177041 0.984203i \(-0.443347\pi\)
−0.763825 + 0.645424i \(0.776681\pi\)
\(942\) 3.10583 + 11.5911i 0.101193 + 0.377659i
\(943\) −40.1528 10.7589i −1.30755 0.350358i
\(944\) 8.66025 0.281867
\(945\) 0 0
\(946\) −15.0000 −0.487692
\(947\) 14.4889 + 3.88229i 0.470826 + 0.126157i 0.486427 0.873721i \(-0.338300\pi\)
−0.0156019 + 0.999878i \(0.504966\pi\)
\(948\) 1.79315 + 6.69213i 0.0582388 + 0.217350i
\(949\) −41.5692 24.0000i −1.34939 0.779073i
\(950\) 0 0
\(951\) 51.9615i 1.68497i
\(952\) 0 0
\(953\) −14.8492 14.8492i −0.481014 0.481014i 0.424441 0.905455i \(-0.360471\pi\)
−0.905455 + 0.424441i \(0.860471\pi\)
\(954\) 31.1769 + 18.0000i 1.00939 + 0.582772i
\(955\) 0 0
\(956\) −9.00000 + 5.19615i −0.291081 + 0.168056i
\(957\) −2.68973 + 10.0382i −0.0869465 + 0.324489i
\(958\) −1.79315 6.69213i −0.0579341 0.216213i
\(959\) 0 0
\(960\) 0 0
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) 33.9411 33.9411i 1.09431 1.09431i
\(963\) 9.31749 34.7733i 0.300252 1.12055i
\(964\) 10.0000i 0.322078i
\(965\) 0 0
\(966\) 0 0
\(967\) −13.3843 + 3.58630i −0.430409 + 0.115328i −0.467518 0.883984i \(-0.654852\pi\)
0.0371092 + 0.999311i \(0.488185\pi\)
\(968\) −7.72741 + 2.07055i −0.248368 + 0.0665501i
\(969\) 10.3923 18.0000i 0.333849 0.578243i
\(970\) 0 0
\(971\) 12.1244i 0.389089i −0.980894 0.194545i \(-0.937677\pi\)
0.980894 0.194545i \(-0.0623229\pi\)
\(972\) 11.0227 + 11.0227i 0.353553 + 0.353553i
\(973\) 0 0
\(974\) 8.66025 + 15.0000i 0.277492 + 0.480631i
\(975\) 0 0
\(976\) 4.00000 6.92820i 0.128037 0.221766i
\(977\) −1.55291 5.79555i −0.0496821 0.185416i 0.936625 0.350332i \(-0.113931\pi\)
−0.986308 + 0.164916i \(0.947265\pi\)
\(978\) −2.12132 2.12132i −0.0678323 0.0678323i
\(979\) −2.59808 + 1.50000i −0.0830349 + 0.0479402i
\(980\) 0 0
\(981\) 3.00000 + 5.19615i 0.0957826 + 0.165900i
\(982\) −15.9217 15.9217i −0.508081 0.508081i
\(983\) −10.8704 + 40.5689i −0.346712 + 1.29395i 0.543888 + 0.839158i \(0.316952\pi\)
−0.890600 + 0.454788i \(0.849715\pi\)
\(984\) 10.3923 6.00000i 0.331295 0.191273i
\(985\) 0 0
\(986\) −9.00000 5.19615i −0.286618 0.165479i
\(987\) 0 0
\(988\) 26.7685 + 7.17260i 0.851620 + 0.228191i
\(989\) 51.9615 1.65228
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) −3.86370 1.03528i −0.122673 0.0328701i
\(993\) −1.22474 + 1.22474i −0.0388661 + 0.0388661i
\(994\) 0 0
\(995\) 0 0
\(996\) 13.5000 + 7.79423i 0.427764 + 0.246970i
\(997\) −2.68973 + 10.0382i −0.0851845 + 0.317913i −0.995349 0.0963340i \(-0.969288\pi\)
0.910165 + 0.414247i \(0.135955\pi\)
\(998\) 3.53553 + 3.53553i 0.111915 + 0.111915i
\(999\) 36.0000i 1.13899i
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 450.2.p.b.257.2 yes 8
3.2 odd 2 1350.2.q.e.557.1 8
5.2 odd 4 inner 450.2.p.b.293.1 yes 8
5.3 odd 4 inner 450.2.p.b.293.2 yes 8
5.4 even 2 inner 450.2.p.b.257.1 8
9.2 odd 6 inner 450.2.p.b.407.2 yes 8
9.7 even 3 1350.2.q.e.1007.1 8
15.2 even 4 1350.2.q.e.1043.2 8
15.8 even 4 1350.2.q.e.1043.1 8
15.14 odd 2 1350.2.q.e.557.2 8
45.2 even 12 inner 450.2.p.b.443.1 yes 8
45.7 odd 12 1350.2.q.e.143.2 8
45.29 odd 6 inner 450.2.p.b.407.1 yes 8
45.34 even 6 1350.2.q.e.1007.2 8
45.38 even 12 inner 450.2.p.b.443.2 yes 8
45.43 odd 12 1350.2.q.e.143.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.p.b.257.1 8 5.4 even 2 inner
450.2.p.b.257.2 yes 8 1.1 even 1 trivial
450.2.p.b.293.1 yes 8 5.2 odd 4 inner
450.2.p.b.293.2 yes 8 5.3 odd 4 inner
450.2.p.b.407.1 yes 8 45.29 odd 6 inner
450.2.p.b.407.2 yes 8 9.2 odd 6 inner
450.2.p.b.443.1 yes 8 45.2 even 12 inner
450.2.p.b.443.2 yes 8 45.38 even 12 inner
1350.2.q.e.143.1 8 45.43 odd 12
1350.2.q.e.143.2 8 45.7 odd 12
1350.2.q.e.557.1 8 3.2 odd 2
1350.2.q.e.557.2 8 15.14 odd 2
1350.2.q.e.1007.1 8 9.7 even 3
1350.2.q.e.1007.2 8 45.34 even 6
1350.2.q.e.1043.1 8 15.8 even 4
1350.2.q.e.1043.2 8 15.2 even 4