Properties

Label 450.2.p.d.257.1
Level $450$
Weight $2$
Character 450.257
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 257.1
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 450.257
Dual form 450.2.p.d.443.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(-0.448288 + 1.67303i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(-0.448288 + 1.67303i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(3.00000 - 1.73205i) q^{11} +(-0.448288 + 1.67303i) q^{12} +(0.896575 + 3.34607i) q^{13} +(0.866025 - 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-4.24264 + 4.24264i) q^{17} +(2.89778 - 0.776457i) q^{18} +2.00000i q^{19} -3.00000 q^{21} +(-3.34607 + 0.896575i) q^{22} +(2.89778 - 0.776457i) q^{23} +(0.866025 - 1.50000i) q^{24} -3.46410i q^{26} +(-3.67423 - 3.67423i) q^{27} +(-1.22474 + 1.22474i) q^{28} +(-4.33013 - 7.50000i) q^{29} +(-5.00000 + 8.66025i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(4.24264 + 4.24264i) q^{33} +(5.19615 - 3.00000i) q^{34} -3.00000 q^{36} +(2.44949 + 2.44949i) q^{37} +(0.517638 - 1.93185i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(7.50000 + 4.33013i) q^{41} +(2.89778 + 0.776457i) q^{42} +(-10.0382 - 2.68973i) q^{43} +3.46410 q^{44} -3.00000 q^{46} +(-2.89778 - 0.776457i) q^{47} +(-1.22474 + 1.22474i) q^{48} +(3.46410 + 2.00000i) q^{49} +(-9.00000 - 5.19615i) q^{51} +(-0.896575 + 3.34607i) q^{52} +(2.59808 + 4.50000i) q^{54} +(1.50000 - 0.866025i) q^{56} +(-3.34607 + 0.896575i) q^{57} +(2.24144 + 8.36516i) q^{58} +(-3.46410 + 6.00000i) q^{59} +(6.50000 + 11.2583i) q^{61} +(7.07107 - 7.07107i) q^{62} +(-1.34486 - 5.01910i) q^{63} +1.00000i q^{64} +(-3.00000 - 5.19615i) q^{66} +(11.7112 - 3.13801i) q^{67} +(-5.79555 + 1.55291i) q^{68} +(2.59808 + 4.50000i) q^{69} -3.46410i q^{71} +(2.89778 + 0.776457i) q^{72} +(9.79796 - 9.79796i) q^{73} +(-1.73205 - 3.00000i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(1.55291 + 5.79555i) q^{77} +(5.79555 - 1.55291i) q^{78} +(3.46410 - 2.00000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(-6.12372 - 6.12372i) q^{82} +(0.776457 - 2.89778i) q^{83} +(-2.59808 - 1.50000i) q^{84} +(9.00000 + 5.19615i) q^{86} +(10.6066 - 10.6066i) q^{87} +(-3.34607 - 0.896575i) q^{88} +1.73205 q^{89} -6.00000 q^{91} +(2.89778 + 0.776457i) q^{92} +(-16.7303 - 4.48288i) q^{93} +(2.59808 + 1.50000i) q^{94} +(1.50000 - 0.866025i) q^{96} +(1.79315 - 6.69213i) q^{97} +(-2.82843 - 2.82843i) q^{98} +(-5.19615 + 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 24 q^{11} + 4 q^{16} - 24 q^{21} - 40 q^{31} - 24 q^{36} + 60 q^{41} - 24 q^{46} - 72 q^{51} + 12 q^{56} + 52 q^{61} - 24 q^{66} - 8 q^{76} + 36 q^{81} + 72 q^{86} - 48 q^{91} + 12 q^{96}+O(q^{100}) \) 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
\(7\) −0.448288 + 1.67303i −0.169437 + 0.632347i 0.827996 + 0.560734i \(0.189481\pi\)
−0.997433 + 0.0716124i \(0.977186\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −2.59808 + 1.50000i −0.866025 + 0.500000i
\(10\) 0 0
\(11\) 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i \(-0.491766\pi\)
0.878668 + 0.477432i \(0.158432\pi\)
\(12\) −0.448288 + 1.67303i −0.129410 + 0.482963i
\(13\) 0.896575 + 3.34607i 0.248665 + 0.928032i 0.971506 + 0.237016i \(0.0761695\pi\)
−0.722840 + 0.691015i \(0.757164\pi\)
\(14\) 0.866025 1.50000i 0.231455 0.400892i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −4.24264 + 4.24264i −1.02899 + 1.02899i −0.0294245 + 0.999567i \(0.509367\pi\)
−0.999567 + 0.0294245i \(0.990633\pi\)
\(18\) 2.89778 0.776457i 0.683013 0.183013i
\(19\) 2.00000i 0.458831i 0.973329 + 0.229416i \(0.0736815\pi\)
−0.973329 + 0.229416i \(0.926318\pi\)
\(20\) 0 0
\(21\) −3.00000 −0.654654
\(22\) −3.34607 + 0.896575i −0.713384 + 0.191151i
\(23\) 2.89778 0.776457i 0.604228 0.161903i 0.0562805 0.998415i \(-0.482076\pi\)
0.547948 + 0.836512i \(0.315409\pi\)
\(24\) 0.866025 1.50000i 0.176777 0.306186i
\(25\) 0 0
\(26\) 3.46410i 0.679366i
\(27\) −3.67423 3.67423i −0.707107 0.707107i
\(28\) −1.22474 + 1.22474i −0.231455 + 0.231455i
\(29\) −4.33013 7.50000i −0.804084 1.39272i −0.916907 0.399100i \(-0.869323\pi\)
0.112823 0.993615i \(-0.464011\pi\)
\(30\) 0 0
\(31\) −5.00000 + 8.66025i −0.898027 + 1.55543i −0.0680129 + 0.997684i \(0.521666\pi\)
−0.830014 + 0.557743i \(0.811667\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) 4.24264 + 4.24264i 0.738549 + 0.738549i
\(34\) 5.19615 3.00000i 0.891133 0.514496i
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 2.44949 + 2.44949i 0.402694 + 0.402694i 0.879181 0.476488i \(-0.158090\pi\)
−0.476488 + 0.879181i \(0.658090\pi\)
\(38\) 0.517638 1.93185i 0.0839720 0.313388i
\(39\) −5.19615 + 3.00000i −0.832050 + 0.480384i
\(40\) 0 0
\(41\) 7.50000 + 4.33013i 1.17130 + 0.676252i 0.953987 0.299849i \(-0.0969363\pi\)
0.217317 + 0.976101i \(0.430270\pi\)
\(42\) 2.89778 + 0.776457i 0.447137 + 0.119810i
\(43\) −10.0382 2.68973i −1.53081 0.410179i −0.607527 0.794299i \(-0.707838\pi\)
−0.923283 + 0.384120i \(0.874505\pi\)
\(44\) 3.46410 0.522233
\(45\) 0 0
\(46\) −3.00000 −0.442326
\(47\) −2.89778 0.776457i −0.422684 0.113258i 0.0412058 0.999151i \(-0.486880\pi\)
−0.463890 + 0.885893i \(0.653547\pi\)
\(48\) −1.22474 + 1.22474i −0.176777 + 0.176777i
\(49\) 3.46410 + 2.00000i 0.494872 + 0.285714i
\(50\) 0 0
\(51\) −9.00000 5.19615i −1.26025 0.727607i
\(52\) −0.896575 + 3.34607i −0.124333 + 0.464016i
\(53\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) 2.59808 + 4.50000i 0.353553 + 0.612372i
\(55\) 0 0
\(56\) 1.50000 0.866025i 0.200446 0.115728i
\(57\) −3.34607 + 0.896575i −0.443197 + 0.118754i
\(58\) 2.24144 + 8.36516i 0.294315 + 1.09840i
\(59\) −3.46410 + 6.00000i −0.450988 + 0.781133i −0.998448 0.0556984i \(-0.982261\pi\)
0.547460 + 0.836832i \(0.315595\pi\)
\(60\) 0 0
\(61\) 6.50000 + 11.2583i 0.832240 + 1.44148i 0.896258 + 0.443533i \(0.146275\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 7.07107 7.07107i 0.898027 0.898027i
\(63\) −1.34486 5.01910i −0.169437 0.632347i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −3.00000 5.19615i −0.369274 0.639602i
\(67\) 11.7112 3.13801i 1.43075 0.383369i 0.541468 0.840721i \(-0.317869\pi\)
0.889286 + 0.457352i \(0.151202\pi\)
\(68\) −5.79555 + 1.55291i −0.702814 + 0.188319i
\(69\) 2.59808 + 4.50000i 0.312772 + 0.541736i
\(70\) 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
\(73\) 9.79796 9.79796i 1.14676 1.14676i 0.159579 0.987185i \(-0.448986\pi\)
0.987185 0.159579i \(-0.0510137\pi\)
\(74\) −1.73205 3.00000i −0.201347 0.348743i
\(75\) 0 0
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) 1.55291 + 5.79555i 0.176971 + 0.660465i
\(78\) 5.79555 1.55291i 0.656217 0.175833i
\(79\) 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
\(82\) −6.12372 6.12372i −0.676252 0.676252i
\(83\) 0.776457 2.89778i 0.0852272 0.318072i −0.910130 0.414323i \(-0.864018\pi\)
0.995357 + 0.0962507i \(0.0306850\pi\)
\(84\) −2.59808 1.50000i −0.283473 0.163663i
\(85\) 0 0
\(86\) 9.00000 + 5.19615i 0.970495 + 0.560316i
\(87\) 10.6066 10.6066i 1.13715 1.13715i
\(88\) −3.34607 0.896575i −0.356692 0.0955753i
\(89\) 1.73205 0.183597 0.0917985 0.995778i \(-0.470738\pi\)
0.0917985 + 0.995778i \(0.470738\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 2.89778 + 0.776457i 0.302114 + 0.0809513i
\(93\) −16.7303 4.48288i −1.73485 0.464853i
\(94\) 2.59808 + 1.50000i 0.267971 + 0.154713i
\(95\) 0 0
\(96\) 1.50000 0.866025i 0.153093 0.0883883i
\(97\) 1.79315 6.69213i 0.182067 0.679483i −0.813173 0.582023i \(-0.802261\pi\)
0.995239 0.0974602i \(-0.0310719\pi\)
\(98\) −2.82843 2.82843i −0.285714 0.285714i
\(99\) −5.19615 + 9.00000i −0.522233 + 0.904534i
\(100\) 0 0
\(101\) 12.0000 6.92820i 1.19404 0.689382i 0.234823 0.972038i \(-0.424549\pi\)
0.959221 + 0.282656i \(0.0912155\pi\)
\(102\) 7.34847 + 7.34847i 0.727607 + 0.727607i
\(103\) −0.896575 3.34607i −0.0883422 0.329698i 0.907584 0.419871i \(-0.137925\pi\)
−0.995926 + 0.0901732i \(0.971258\pi\)
\(104\) 1.73205 3.00000i 0.169842 0.294174i
\(105\) 0 0
\(106\) 0 0
\(107\) 2.12132 2.12132i 0.205076 0.205076i −0.597095 0.802171i \(-0.703678\pi\)
0.802171 + 0.597095i \(0.203678\pi\)
\(108\) −1.34486 5.01910i −0.129410 0.482963i
\(109\) 5.00000i 0.478913i −0.970907 0.239457i \(-0.923031\pi\)
0.970907 0.239457i \(-0.0769693\pi\)
\(110\) 0 0
\(111\) −3.00000 + 5.19615i −0.284747 + 0.493197i
\(112\) −1.67303 + 0.448288i −0.158087 + 0.0423592i
\(113\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(114\) 3.46410 0.324443
\(115\) 0 0
\(116\) 8.66025i 0.804084i
\(117\) −7.34847 7.34847i −0.679366 0.679366i
\(118\) 4.89898 4.89898i 0.450988 0.450988i
\(119\) −5.19615 9.00000i −0.476331 0.825029i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) −3.36465 12.5570i −0.304621 1.13686i
\(123\) −3.88229 + 14.4889i −0.350054 + 1.30642i
\(124\) −8.66025 + 5.00000i −0.777714 + 0.449013i
\(125\) 0 0
\(126\) 5.19615i 0.462910i
\(127\) −3.67423 3.67423i −0.326036 0.326036i 0.525041 0.851077i \(-0.324050\pi\)
−0.851077 + 0.525041i \(0.824050\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) 18.0000i 1.58481i
\(130\) 0 0
\(131\) −6.00000 3.46410i −0.524222 0.302660i 0.214438 0.976738i \(-0.431208\pi\)
−0.738661 + 0.674078i \(0.764541\pi\)
\(132\) 1.55291 + 5.79555i 0.135164 + 0.504438i
\(133\) −3.34607 0.896575i −0.290141 0.0777430i
\(134\) −12.1244 −1.04738
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) 11.5911 + 3.10583i 0.990295 + 0.265349i 0.717375 0.696688i \(-0.245344\pi\)
0.272921 + 0.962037i \(0.412010\pi\)
\(138\) −1.34486 5.01910i −0.114482 0.427254i
\(139\) 3.46410 + 2.00000i 0.293821 + 0.169638i 0.639664 0.768655i \(-0.279074\pi\)
−0.345843 + 0.938293i \(0.612407\pi\)
\(140\) 0 0
\(141\) 5.19615i 0.437595i
\(142\) −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
\(146\) −12.0000 + 6.92820i −0.993127 + 0.573382i
\(147\) −1.79315 + 6.69213i −0.147897 + 0.551958i
\(148\) 0.896575 + 3.34607i 0.0736980 + 0.275045i
\(149\) 2.59808 4.50000i 0.212843 0.368654i −0.739760 0.672870i \(-0.765061\pi\)
0.952603 + 0.304216i \(0.0983945\pi\)
\(150\) 0 0
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) 1.41421 1.41421i 0.114708 0.114708i
\(153\) 4.65874 17.3867i 0.376637 1.40563i
\(154\) 6.00000i 0.483494i
\(155\) 0 0
\(156\) −6.00000 −0.480384
\(157\) 20.0764 5.37945i 1.60227 0.429327i 0.656543 0.754288i \(-0.272018\pi\)
0.945727 + 0.324961i \(0.105351\pi\)
\(158\) −3.86370 + 1.03528i −0.307380 + 0.0823622i
\(159\) 0 0
\(160\) 0 0
\(161\) 5.19615i 0.409514i
\(162\) −6.36396 + 6.36396i −0.500000 + 0.500000i
\(163\) 12.2474 12.2474i 0.959294 0.959294i −0.0399091 0.999203i \(-0.512707\pi\)
0.999203 + 0.0399091i \(0.0127068\pi\)
\(164\) 4.33013 + 7.50000i 0.338126 + 0.585652i
\(165\) 0 0
\(166\) −1.50000 + 2.59808i −0.116423 + 0.201650i
\(167\) 2.32937 + 8.69333i 0.180252 + 0.672710i 0.995597 + 0.0937349i \(0.0298806\pi\)
−0.815345 + 0.578975i \(0.803453\pi\)
\(168\) 2.12132 + 2.12132i 0.163663 + 0.163663i
\(169\) 0.866025 0.500000i 0.0666173 0.0384615i
\(170\) 0 0
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) −7.34847 7.34847i −0.560316 0.560316i
\(173\) −6.21166 + 23.1822i −0.472264 + 1.76251i 0.159344 + 0.987223i \(0.449062\pi\)
−0.631607 + 0.775288i \(0.717605\pi\)
\(174\) −12.9904 + 7.50000i −0.984798 + 0.568574i
\(175\) 0 0
\(176\) 3.00000 + 1.73205i 0.226134 + 0.130558i
\(177\) −11.5911 3.10583i −0.871241 0.233448i
\(178\) −1.67303 0.448288i −0.125399 0.0336006i
\(179\) 24.2487 1.81243 0.906217 0.422813i \(-0.138957\pi\)
0.906217 + 0.422813i \(0.138957\pi\)
\(180\) 0 0
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 5.79555 + 1.55291i 0.429595 + 0.115110i
\(183\) −15.9217 + 15.9217i −1.17696 + 1.17696i
\(184\) −2.59808 1.50000i −0.191533 0.110581i
\(185\) 0 0
\(186\) 15.0000 + 8.66025i 1.09985 + 0.635001i
\(187\) −5.37945 + 20.0764i −0.393385 + 1.46813i
\(188\) −2.12132 2.12132i −0.154713 0.154713i
\(189\) 7.79423 4.50000i 0.566947 0.327327i
\(190\) 0 0
\(191\) −15.0000 + 8.66025i −1.08536 + 0.626634i −0.932338 0.361588i \(-0.882235\pi\)
−0.153024 + 0.988222i \(0.548901\pi\)
\(192\) −1.67303 + 0.448288i −0.120741 + 0.0323524i
\(193\) 4.48288 + 16.7303i 0.322685 + 1.20428i 0.916619 + 0.399762i \(0.130907\pi\)
−0.593934 + 0.804513i \(0.702426\pi\)
\(194\) −3.46410 + 6.00000i −0.248708 + 0.430775i
\(195\) 0 0
\(196\) 2.00000 + 3.46410i 0.142857 + 0.247436i
\(197\) −8.48528 + 8.48528i −0.604551 + 0.604551i −0.941517 0.336966i \(-0.890599\pi\)
0.336966 + 0.941517i \(0.390599\pi\)
\(198\) 7.34847 7.34847i 0.522233 0.522233i
\(199\) 10.0000i 0.708881i 0.935079 + 0.354441i \(0.115329\pi\)
−0.935079 + 0.354441i \(0.884671\pi\)
\(200\) 0 0
\(201\) 10.5000 + 18.1865i 0.740613 + 1.28278i
\(202\) −13.3843 + 3.58630i −0.941713 + 0.252331i
\(203\) 14.4889 3.88229i 1.01692 0.272483i
\(204\) −5.19615 9.00000i −0.363803 0.630126i
\(205\) 0 0
\(206\) 3.46410i 0.241355i
\(207\) −6.36396 + 6.36396i −0.442326 + 0.442326i
\(208\) −2.44949 + 2.44949i −0.169842 + 0.169842i
\(209\) 3.46410 + 6.00000i 0.239617 + 0.415029i
\(210\) 0 0
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) 0 0
\(213\) 5.79555 1.55291i 0.397105 0.106404i
\(214\) −2.59808 + 1.50000i −0.177601 + 0.102538i
\(215\) 0 0
\(216\) 5.19615i 0.353553i
\(217\) −12.2474 12.2474i −0.831411 0.831411i
\(218\) −1.29410 + 4.82963i −0.0876472 + 0.327104i
\(219\) 20.7846 + 12.0000i 1.40449 + 0.810885i
\(220\) 0 0
\(221\) −18.0000 10.3923i −1.21081 0.699062i
\(222\) 4.24264 4.24264i 0.284747 0.284747i
\(223\) −15.0573 4.03459i −1.00831 0.270176i −0.283387 0.959005i \(-0.591458\pi\)
−0.724923 + 0.688829i \(0.758125\pi\)
\(224\) 1.73205 0.115728
\(225\) 0 0
\(226\) 0 0
\(227\) −23.1822 6.21166i −1.53866 0.412282i −0.612826 0.790218i \(-0.709967\pi\)
−0.925832 + 0.377936i \(0.876634\pi\)
\(228\) −3.34607 0.896575i −0.221599 0.0593772i
\(229\) −4.33013 2.50000i −0.286143 0.165205i 0.350058 0.936728i \(-0.386162\pi\)
−0.636201 + 0.771523i \(0.719495\pi\)
\(230\) 0 0
\(231\) −9.00000 + 5.19615i −0.592157 + 0.341882i
\(232\) −2.24144 + 8.36516i −0.147158 + 0.549200i
\(233\) 4.24264 + 4.24264i 0.277945 + 0.277945i 0.832288 0.554343i \(-0.187031\pi\)
−0.554343 + 0.832288i \(0.687031\pi\)
\(234\) 5.19615 + 9.00000i 0.339683 + 0.588348i
\(235\) 0 0
\(236\) −6.00000 + 3.46410i −0.390567 + 0.225494i
\(237\) 4.89898 + 4.89898i 0.318223 + 0.318223i
\(238\) 2.68973 + 10.0382i 0.174349 + 0.650680i
\(239\) −10.3923 + 18.0000i −0.672222 + 1.16432i 0.305050 + 0.952336i \(0.401327\pi\)
−0.977273 + 0.211987i \(0.932007\pi\)
\(240\) 0 0
\(241\) −8.50000 14.7224i −0.547533 0.948355i −0.998443 0.0557856i \(-0.982234\pi\)
0.450910 0.892570i \(-0.351100\pi\)
\(242\) −0.707107 + 0.707107i −0.0454545 + 0.0454545i
\(243\) 15.0573 + 4.03459i 0.965926 + 0.258819i
\(244\) 13.0000i 0.832240i
\(245\) 0 0
\(246\) 7.50000 12.9904i 0.478183 0.828236i
\(247\) −6.69213 + 1.79315i −0.425810 + 0.114095i
\(248\) 9.65926 2.58819i 0.613364 0.164350i
\(249\) 5.19615 0.329293
\(250\) 0 0
\(251\) 10.3923i 0.655956i 0.944685 + 0.327978i \(0.106367\pi\)
−0.944685 + 0.327978i \(0.893633\pi\)
\(252\) 1.34486 5.01910i 0.0847184 0.316173i
\(253\) 7.34847 7.34847i 0.461994 0.461994i
\(254\) 2.59808 + 4.50000i 0.163018 + 0.282355i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(258\) −4.65874 + 17.3867i −0.290041 + 1.08245i
\(259\) −5.19615 + 3.00000i −0.322873 + 0.186411i
\(260\) 0 0
\(261\) 22.5000 + 12.9904i 1.39272 + 0.804084i
\(262\) 4.89898 + 4.89898i 0.302660 + 0.302660i
\(263\) 6.21166 23.1822i 0.383027 1.42948i −0.458226 0.888836i \(-0.651515\pi\)
0.841253 0.540641i \(-0.181818\pi\)
\(264\) 6.00000i 0.369274i
\(265\) 0 0
\(266\) 3.00000 + 1.73205i 0.183942 + 0.106199i
\(267\) 0.776457 + 2.89778i 0.0475184 + 0.177341i
\(268\) 11.7112 + 3.13801i 0.715377 + 0.191685i
\(269\) 1.73205 0.105605 0.0528025 0.998605i \(-0.483185\pi\)
0.0528025 + 0.998605i \(0.483185\pi\)
\(270\) 0 0
\(271\) −10.0000 −0.607457 −0.303728 0.952759i \(-0.598232\pi\)
−0.303728 + 0.952759i \(0.598232\pi\)
\(272\) −5.79555 1.55291i −0.351407 0.0941593i
\(273\) −2.68973 10.0382i −0.162790 0.607539i
\(274\) −10.3923 6.00000i −0.627822 0.362473i
\(275\) 0 0
\(276\) 5.19615i 0.312772i
\(277\) −2.68973 + 10.0382i −0.161610 + 0.603137i 0.836838 + 0.547450i \(0.184401\pi\)
−0.998448 + 0.0556866i \(0.982265\pi\)
\(278\) −2.82843 2.82843i −0.169638 0.169638i
\(279\) 30.0000i 1.79605i
\(280\) 0 0
\(281\) 4.50000 2.59808i 0.268447 0.154988i −0.359734 0.933055i \(-0.617133\pi\)
0.628182 + 0.778067i \(0.283799\pi\)
\(282\) −1.34486 + 5.01910i −0.0800854 + 0.298883i
\(283\) 1.34486 + 5.01910i 0.0799438 + 0.298354i 0.994309 0.106537i \(-0.0339761\pi\)
−0.914365 + 0.404891i \(0.867309\pi\)
\(284\) 1.73205 3.00000i 0.102778 0.178017i
\(285\) 0 0
\(286\) −6.00000 10.3923i −0.354787 0.614510i
\(287\) −10.6066 + 10.6066i −0.626088 + 0.626088i
\(288\) 2.12132 + 2.12132i 0.125000 + 0.125000i
\(289\) 19.0000i 1.11765i
\(290\) 0 0
\(291\) 12.0000 0.703452
\(292\) 13.3843 3.58630i 0.783255 0.209872i
\(293\) −28.9778 + 7.76457i −1.69290 + 0.453611i −0.971136 0.238528i \(-0.923335\pi\)
−0.721764 + 0.692139i \(0.756668\pi\)
\(294\) 3.46410 6.00000i 0.202031 0.349927i
\(295\) 0 0
\(296\) 3.46410i 0.201347i
\(297\) −17.3867 4.65874i −1.00888 0.270328i
\(298\) −3.67423 + 3.67423i −0.212843 + 0.212843i
\(299\) 5.19615 + 9.00000i 0.300501 + 0.520483i
\(300\) 0 0
\(301\) 9.00000 15.5885i 0.518751 0.898504i
\(302\) 2.58819 + 9.65926i 0.148934 + 0.555828i
\(303\) 16.9706 + 16.9706i 0.974933 + 0.974933i
\(304\) −1.73205 + 1.00000i −0.0993399 + 0.0573539i
\(305\) 0 0
\(306\) −9.00000 + 15.5885i −0.514496 + 0.891133i
\(307\) 3.67423 + 3.67423i 0.209700 + 0.209700i 0.804140 0.594440i \(-0.202626\pi\)
−0.594440 + 0.804140i \(0.702626\pi\)
\(308\) −1.55291 + 5.79555i −0.0884855 + 0.330232i
\(309\) 5.19615 3.00000i 0.295599 0.170664i
\(310\) 0 0
\(311\) −21.0000 12.1244i −1.19080 0.687509i −0.232313 0.972641i \(-0.574629\pi\)
−0.958488 + 0.285132i \(0.907963\pi\)
\(312\) 5.79555 + 1.55291i 0.328109 + 0.0879165i
\(313\) 3.34607 + 0.896575i 0.189131 + 0.0506774i 0.352141 0.935947i \(-0.385454\pi\)
−0.163010 + 0.986624i \(0.552120\pi\)
\(314\) −20.7846 −1.17294
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 5.79555 + 1.55291i 0.325511 + 0.0872204i 0.417874 0.908505i \(-0.362775\pi\)
−0.0923631 + 0.995725i \(0.529442\pi\)
\(318\) 0 0
\(319\) −25.9808 15.0000i −1.45464 0.839839i
\(320\) 0 0
\(321\) 4.50000 + 2.59808i 0.251166 + 0.145010i
\(322\) 1.34486 5.01910i 0.0749463 0.279703i
\(323\) −8.48528 8.48528i −0.472134 0.472134i
\(324\) 7.79423 4.50000i 0.433013 0.250000i
\(325\) 0 0
\(326\) −15.0000 + 8.66025i −0.830773 + 0.479647i
\(327\) 8.36516 2.24144i 0.462595 0.123952i
\(328\) −2.24144 8.36516i −0.123763 0.461889i
\(329\) 2.59808 4.50000i 0.143237 0.248093i
\(330\) 0 0
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) 2.12132 2.12132i 0.116423 0.116423i
\(333\) −10.0382 2.68973i −0.550090 0.147396i
\(334\) 9.00000i 0.492458i
\(335\) 0 0
\(336\) −1.50000 2.59808i −0.0818317 0.141737i
\(337\) 13.3843 3.58630i 0.729087 0.195358i 0.124864 0.992174i \(-0.460150\pi\)
0.604223 + 0.796815i \(0.293484\pi\)
\(338\) −0.965926 + 0.258819i −0.0525394 + 0.0140779i
\(339\) 0 0
\(340\) 0 0
\(341\) 34.6410i 1.87592i
\(342\) 1.55291 + 5.79555i 0.0839720 + 0.313388i
\(343\) −13.4722 + 13.4722i −0.727430 + 0.727430i
\(344\) 5.19615 + 9.00000i 0.280158 + 0.485247i
\(345\) 0 0
\(346\) 12.0000 20.7846i 0.645124 1.11739i
\(347\) −3.10583 11.5911i −0.166730 0.622243i −0.997813 0.0660960i \(-0.978946\pi\)
0.831084 0.556147i \(-0.187721\pi\)
\(348\) 14.4889 3.88229i 0.776686 0.208112i
\(349\) −0.866025 + 0.500000i −0.0463573 + 0.0267644i −0.523000 0.852333i \(-0.675187\pi\)
0.476642 + 0.879097i \(0.341854\pi\)
\(350\) 0 0
\(351\) 9.00000 15.5885i 0.480384 0.832050i
\(352\) −2.44949 2.44949i −0.130558 0.130558i
\(353\) 6.21166 23.1822i 0.330613 1.23387i −0.577934 0.816083i \(-0.696141\pi\)
0.908547 0.417782i \(-0.137192\pi\)
\(354\) 10.3923 + 6.00000i 0.552345 + 0.318896i
\(355\) 0 0
\(356\) 1.50000 + 0.866025i 0.0794998 + 0.0458993i
\(357\) 12.7279 12.7279i 0.673633 0.673633i
\(358\) −23.4225 6.27603i −1.23792 0.331698i
\(359\) −17.3205 −0.914141 −0.457071 0.889430i \(-0.651101\pi\)
−0.457071 + 0.889430i \(0.651101\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) −6.76148 1.81173i −0.355376 0.0952226i
\(363\) 1.67303 + 0.448288i 0.0878114 + 0.0235290i
\(364\) −5.19615 3.00000i −0.272352 0.157243i
\(365\) 0 0
\(366\) 19.5000 11.2583i 1.01928 0.588482i
\(367\) −0.896575 + 3.34607i −0.0468009 + 0.174663i −0.985370 0.170427i \(-0.945485\pi\)
0.938569 + 0.345091i \(0.112152\pi\)
\(368\) 2.12132 + 2.12132i 0.110581 + 0.110581i
\(369\) −25.9808 −1.35250
\(370\) 0 0
\(371\) 0 0
\(372\) −12.2474 12.2474i −0.635001 0.635001i
\(373\) 3.58630 + 13.3843i 0.185692 + 0.693011i 0.994481 + 0.104913i \(0.0334564\pi\)
−0.808790 + 0.588098i \(0.799877\pi\)
\(374\) 10.3923 18.0000i 0.537373 0.930758i
\(375\) 0 0
\(376\) 1.50000 + 2.59808i 0.0773566 + 0.133986i
\(377\) 21.2132 21.2132i 1.09254 1.09254i
\(378\) −8.69333 + 2.32937i −0.447137 + 0.119810i
\(379\) 8.00000i 0.410932i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) 0 0
\(381\) 4.50000 7.79423i 0.230542 0.399310i
\(382\) 16.7303 4.48288i 0.855998 0.229364i
\(383\) 23.1822 6.21166i 1.18456 0.317401i 0.387824 0.921733i \(-0.373227\pi\)
0.796732 + 0.604333i \(0.206560\pi\)
\(384\) 1.73205 0.0883883
\(385\) 0 0
\(386\) 17.3205i 0.881591i
\(387\) 30.1146 8.06918i 1.53081 0.410179i
\(388\) 4.89898 4.89898i 0.248708 0.248708i
\(389\) 12.9904 + 22.5000i 0.658638 + 1.14080i 0.980968 + 0.194168i \(0.0622006\pi\)
−0.322330 + 0.946627i \(0.604466\pi\)
\(390\) 0 0
\(391\) −9.00000 + 15.5885i −0.455150 + 0.788342i
\(392\) −1.03528 3.86370i −0.0522893 0.195146i
\(393\) 3.10583 11.5911i 0.156668 0.584694i
\(394\) 10.3923 6.00000i 0.523557 0.302276i
\(395\) 0 0
\(396\) −9.00000 + 5.19615i −0.452267 + 0.261116i
\(397\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) 2.58819 9.65926i 0.129734 0.484175i
\(399\) 6.00000i 0.300376i
\(400\) 0 0
\(401\) −18.0000 10.3923i −0.898877 0.518967i −0.0220414 0.999757i \(-0.507017\pi\)
−0.876836 + 0.480790i \(0.840350\pi\)
\(402\) −5.43520 20.2844i −0.271083 1.01170i
\(403\) −33.4607 8.96575i −1.66679 0.446616i
\(404\) 13.8564 0.689382
\(405\) 0 0
\(406\) −15.0000 −0.744438
\(407\) 11.5911 + 3.10583i 0.574550 + 0.153950i
\(408\) 2.68973 + 10.0382i 0.133161 + 0.496965i
\(409\) −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
\(411\) 20.7846i 1.02523i
\(412\) 0.896575 3.34607i 0.0441711 0.164849i
\(413\) −8.48528 8.48528i −0.417533 0.417533i
\(414\) 7.79423 4.50000i 0.383065 0.221163i
\(415\) 0 0
\(416\) 3.00000 1.73205i 0.147087 0.0849208i
\(417\) −1.79315 + 6.69213i −0.0878110 + 0.327715i
\(418\) −1.79315 6.69213i −0.0877059 0.327323i
\(419\) −5.19615 + 9.00000i −0.253849 + 0.439679i −0.964582 0.263783i \(-0.915030\pi\)
0.710734 + 0.703461i \(0.248363\pi\)
\(420\) 0 0
\(421\) −5.00000 8.66025i −0.243685 0.422075i 0.718076 0.695965i \(-0.245023\pi\)
−0.961761 + 0.273890i \(0.911690\pi\)
\(422\) −15.5563 + 15.5563i −0.757271 + 0.757271i
\(423\) 8.69333 2.32937i 0.422684 0.113258i
\(424\) 0 0
\(425\) 0 0
\(426\) −6.00000 −0.290701
\(427\) −21.7494 + 5.82774i −1.05253 + 0.282024i
\(428\) 2.89778 0.776457i 0.140069 0.0375315i
\(429\) −10.3923 + 18.0000i −0.501745 + 0.869048i
\(430\) 0 0
\(431\) 6.92820i 0.333720i 0.985981 + 0.166860i \(0.0533628\pi\)
−0.985981 + 0.166860i \(0.946637\pi\)
\(432\) 1.34486 5.01910i 0.0647048 0.241481i
\(433\) −7.34847 + 7.34847i −0.353145 + 0.353145i −0.861278 0.508133i \(-0.830336\pi\)
0.508133 + 0.861278i \(0.330336\pi\)
\(434\) 8.66025 + 15.0000i 0.415705 + 0.720023i
\(435\) 0 0
\(436\) 2.50000 4.33013i 0.119728 0.207375i
\(437\) 1.55291 + 5.79555i 0.0742860 + 0.277239i
\(438\) −16.9706 16.9706i −0.810885 0.810885i
\(439\) −17.3205 + 10.0000i −0.826663 + 0.477274i −0.852709 0.522387i \(-0.825042\pi\)
0.0260459 + 0.999661i \(0.491708\pi\)
\(440\) 0 0
\(441\) −12.0000 −0.571429
\(442\) 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 \(0.151918\pi\)
\(444\) −5.19615 + 3.00000i −0.246598 + 0.142374i
\(445\) 0 0
\(446\) 13.5000 + 7.79423i 0.639244 + 0.369067i
\(447\) 8.69333 + 2.32937i 0.411181 + 0.110175i
\(448\) −1.67303 0.448288i −0.0790434 0.0211796i
\(449\) −13.8564 −0.653924 −0.326962 0.945037i \(-0.606025\pi\)
−0.326962 + 0.945037i \(0.606025\pi\)
\(450\) 0 0
\(451\) 30.0000 1.41264
\(452\) 0 0
\(453\) 12.2474 12.2474i 0.575435 0.575435i
\(454\) 20.7846 + 12.0000i 0.975470 + 0.563188i
\(455\) 0 0
\(456\) 3.00000 + 1.73205i 0.140488 + 0.0811107i
\(457\) 8.06918 30.1146i 0.377460 1.40870i −0.472256 0.881461i \(-0.656560\pi\)
0.849717 0.527240i \(-0.176773\pi\)
\(458\) 3.53553 + 3.53553i 0.165205 + 0.165205i
\(459\) 31.1769 1.45521
\(460\) 0 0
\(461\) 10.5000 6.06218i 0.489034 0.282344i −0.235140 0.971962i \(-0.575555\pi\)
0.724174 + 0.689618i \(0.242221\pi\)
\(462\) 10.0382 2.68973i 0.467019 0.125137i
\(463\) −4.48288 16.7303i −0.208337 0.777524i −0.988406 0.151831i \(-0.951483\pi\)
0.780069 0.625693i \(-0.215184\pi\)
\(464\) 4.33013 7.50000i 0.201021 0.348179i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 25.4558 25.4558i 1.17796 1.17796i 0.197692 0.980264i \(-0.436655\pi\)
0.980264 0.197692i \(-0.0633445\pi\)
\(468\) −2.68973 10.0382i −0.124333 0.464016i
\(469\) 21.0000i 0.969690i
\(470\) 0 0
\(471\) 18.0000 + 31.1769i 0.829396 + 1.43656i
\(472\) 6.69213 1.79315i 0.308030 0.0825365i
\(473\) −34.7733 + 9.31749i −1.59888 + 0.428418i
\(474\) −3.46410 6.00000i −0.159111 0.275589i
\(475\) 0 0
\(476\) 10.3923i 0.476331i
\(477\) 0 0
\(478\) 14.6969 14.6969i 0.672222 0.672222i
\(479\) −13.8564 24.0000i −0.633115 1.09659i −0.986911 0.161265i \(-0.948443\pi\)
0.353796 0.935323i \(-0.384891\pi\)
\(480\) 0 0
\(481\) −6.00000 + 10.3923i −0.273576 + 0.473848i
\(482\) 4.39992 + 16.4207i 0.200411 + 0.747944i
\(483\) −8.69333 + 2.32937i −0.395560 + 0.105990i
\(484\) 0.866025 0.500000i 0.0393648 0.0227273i
\(485\) 0 0
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) 17.1464 + 17.1464i 0.776979 + 0.776979i 0.979316 0.202337i \(-0.0648537\pi\)
−0.202337 + 0.979316i \(0.564854\pi\)
\(488\) 3.36465 12.5570i 0.152310 0.568430i
\(489\) 25.9808 + 15.0000i 1.17489 + 0.678323i
\(490\) 0 0
\(491\) 12.0000 + 6.92820i 0.541552 + 0.312665i 0.745708 0.666273i \(-0.232111\pi\)
−0.204155 + 0.978938i \(0.565445\pi\)
\(492\) −10.6066 + 10.6066i −0.478183 + 0.478183i
\(493\) 50.1910 + 13.4486i 2.26049 + 0.605696i
\(494\) 6.92820 0.311715
\(495\) 0 0
\(496\) −10.0000 −0.449013
\(497\) 5.79555 + 1.55291i 0.259966 + 0.0696577i
\(498\) −5.01910 1.34486i −0.224911 0.0602648i
\(499\) 38.1051 + 22.0000i 1.70582 + 0.984855i 0.939599 + 0.342277i \(0.111198\pi\)
0.766220 + 0.642578i \(0.222135\pi\)
\(500\) 0 0
\(501\) −13.5000 + 7.79423i −0.603136 + 0.348220i
\(502\) 2.68973 10.0382i 0.120048 0.448027i
\(503\) −6.36396 6.36396i −0.283755 0.283755i 0.550850 0.834605i \(-0.314304\pi\)
−0.834605 + 0.550850i \(0.814304\pi\)
\(504\) −2.59808 + 4.50000i −0.115728 + 0.200446i
\(505\) 0 0
\(506\) −9.00000 + 5.19615i −0.400099 + 0.230997i
\(507\) 1.22474 + 1.22474i 0.0543928 + 0.0543928i
\(508\) −1.34486 5.01910i −0.0596687 0.222686i
\(509\) 2.59808 4.50000i 0.115158 0.199459i −0.802685 0.596403i \(-0.796596\pi\)
0.917843 + 0.396944i \(0.129929\pi\)
\(510\) 0 0
\(511\) 12.0000 + 20.7846i 0.530849 + 0.919457i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 7.34847 7.34847i 0.324443 0.324443i
\(514\) 0 0
\(515\) 0 0
\(516\) 9.00000 15.5885i 0.396203 0.686244i
\(517\) −10.0382 + 2.68973i −0.441479 + 0.118294i
\(518\) 5.79555 1.55291i 0.254642 0.0682311i
\(519\) −41.5692 −1.82469
\(520\) 0 0
\(521\) 5.19615i 0.227648i 0.993501 + 0.113824i \(0.0363099\pi\)
−0.993501 + 0.113824i \(0.963690\pi\)
\(522\) −18.3712 18.3712i −0.804084 0.804084i
\(523\) −8.57321 + 8.57321i −0.374880 + 0.374880i −0.869251 0.494371i \(-0.835399\pi\)
0.494371 + 0.869251i \(0.335399\pi\)
\(524\) −3.46410 6.00000i −0.151330 0.262111i
\(525\) 0 0
\(526\) −12.0000 + 20.7846i −0.523225 + 0.906252i
\(527\) −15.5291 57.9555i −0.676460 2.52458i
\(528\) −1.55291 + 5.79555i −0.0675819 + 0.252219i
\(529\) −12.1244 + 7.00000i −0.527146 + 0.304348i
\(530\) 0 0
\(531\) 20.7846i 0.901975i
\(532\) −2.44949 2.44949i −0.106199 0.106199i
\(533\) −7.76457 + 28.9778i −0.336321 + 1.25517i
\(534\) 3.00000i 0.129823i
\(535\) 0 0
\(536\) −10.5000 6.06218i −0.453531 0.261846i
\(537\) 10.8704 + 40.5689i 0.469092 + 1.75068i
\(538\) −1.67303 0.448288i −0.0721296 0.0193271i
\(539\) 13.8564 0.596838
\(540\) 0 0
\(541\) −43.0000 −1.84871 −0.924357 0.381528i \(-0.875398\pi\)
−0.924357 + 0.381528i \(0.875398\pi\)
\(542\) 9.65926 + 2.58819i 0.414901 + 0.111172i
\(543\) 3.13801 + 11.7112i 0.134665 + 0.502577i
\(544\) 5.19615 + 3.00000i 0.222783 + 0.128624i
\(545\) 0 0
\(546\) 10.3923i 0.444750i
\(547\) 0.448288 1.67303i 0.0191674 0.0715337i −0.955680 0.294408i \(-0.904877\pi\)
0.974847 + 0.222875i \(0.0715441\pi\)
\(548\) 8.48528 + 8.48528i 0.362473 + 0.362473i
\(549\) −33.7750 19.5000i −1.44148 0.832240i
\(550\) 0 0
\(551\) 15.0000 8.66025i 0.639021 0.368939i
\(552\) 1.34486 5.01910i 0.0572412 0.213627i
\(553\) 1.79315 + 6.69213i 0.0762525 + 0.284578i
\(554\) 5.19615 9.00000i 0.220763 0.382373i
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −25.4558 + 25.4558i −1.07860 + 1.07860i −0.0819634 + 0.996635i \(0.526119\pi\)
−0.996635 + 0.0819634i \(0.973881\pi\)
\(558\) −7.76457 + 28.9778i −0.328701 + 1.22673i
\(559\) 36.0000i 1.52264i
\(560\) 0 0
\(561\) −36.0000 −1.51992
\(562\) −5.01910 + 1.34486i −0.211718 + 0.0567296i
\(563\) 20.2844 5.43520i 0.854887 0.229066i 0.195346 0.980734i \(-0.437417\pi\)
0.659542 + 0.751668i \(0.270750\pi\)
\(564\) 2.59808 4.50000i 0.109399 0.189484i
\(565\) 0 0
\(566\) 5.19615i 0.218411i
\(567\) 11.0227 + 11.0227i 0.462910 + 0.462910i
\(568\) −2.44949 + 2.44949i −0.102778 + 0.102778i
\(569\) −3.46410 6.00000i −0.145223 0.251533i 0.784233 0.620466i \(-0.213057\pi\)
−0.929456 + 0.368933i \(0.879723\pi\)
\(570\) 0 0
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) 3.10583 + 11.5911i 0.129861 + 0.484649i
\(573\) −21.2132 21.2132i −0.886194 0.886194i
\(574\) 12.9904 7.50000i 0.542208 0.313044i
\(575\) 0 0
\(576\) −1.50000 2.59808i −0.0625000 0.108253i
\(577\) −24.4949 24.4949i −1.01974 1.01974i −0.999801 0.0199346i \(-0.993654\pi\)
−0.0199346 0.999801i \(-0.506346\pi\)
\(578\) −4.91756 + 18.3526i −0.204544 + 0.763367i
\(579\) −25.9808 + 15.0000i −1.07972 + 0.623379i
\(580\) 0 0
\(581\) 4.50000 + 2.59808i 0.186691 + 0.107786i
\(582\) −11.5911 3.10583i −0.480467 0.128741i
\(583\) 0 0
\(584\) −13.8564 −0.573382
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 2.89778 + 0.776457i 0.119604 + 0.0320478i 0.318125 0.948049i \(-0.396947\pi\)
−0.198520 + 0.980097i \(0.563614\pi\)
\(588\) −4.89898 + 4.89898i −0.202031 + 0.202031i
\(589\) −17.3205 10.0000i −0.713679 0.412043i
\(590\) 0 0
\(591\) −18.0000 10.3923i −0.740421 0.427482i
\(592\) −0.896575 + 3.34607i −0.0368490 + 0.137522i
\(593\) −12.7279 12.7279i −0.522673 0.522673i 0.395705 0.918378i \(-0.370500\pi\)
−0.918378 + 0.395705i \(0.870500\pi\)
\(594\) 15.5885 + 9.00000i 0.639602 + 0.369274i
\(595\) 0 0
\(596\) 4.50000 2.59808i 0.184327 0.106421i
\(597\) −16.7303 + 4.48288i −0.684727 + 0.183472i
\(598\) −2.68973 10.0382i −0.109991 0.410492i
\(599\) 13.8564 24.0000i 0.566157 0.980613i −0.430784 0.902455i \(-0.641763\pi\)
0.996941 0.0781581i \(-0.0249039\pi\)
\(600\) 0 0
\(601\) 19.0000 + 32.9090i 0.775026 + 1.34238i 0.934780 + 0.355228i \(0.115597\pi\)
−0.159754 + 0.987157i \(0.551070\pi\)
\(602\) −12.7279 + 12.7279i −0.518751 + 0.518751i
\(603\) −25.7196 + 25.7196i −1.04738 + 1.04738i
\(604\) 10.0000i 0.406894i
\(605\) 0 0
\(606\) −12.0000 20.7846i −0.487467 0.844317i
\(607\) −38.4797 + 10.3106i −1.56184 + 0.418495i −0.933247 0.359235i \(-0.883038\pi\)
−0.628598 + 0.777730i \(0.716371\pi\)
\(608\) 1.93185 0.517638i 0.0783469 0.0209930i
\(609\) 12.9904 + 22.5000i 0.526397 + 0.911746i
\(610\) 0 0
\(611\) 10.3923i 0.420428i
\(612\) 12.7279 12.7279i 0.514496 0.514496i
\(613\) 12.2474 12.2474i 0.494670 0.494670i −0.415104 0.909774i \(-0.636255\pi\)
0.909774 + 0.415104i \(0.136255\pi\)
\(614\) −2.59808 4.50000i −0.104850 0.181605i
\(615\) 0 0
\(616\) 3.00000 5.19615i 0.120873 0.209359i
\(617\) 9.31749 + 34.7733i 0.375108 + 1.39992i 0.853187 + 0.521605i \(0.174666\pi\)
−0.478079 + 0.878317i \(0.658667\pi\)
\(618\) −5.79555 + 1.55291i −0.233131 + 0.0624674i
\(619\) 19.0526 11.0000i 0.765787 0.442127i −0.0655827 0.997847i \(-0.520891\pi\)
0.831370 + 0.555720i \(0.187557\pi\)
\(620\) 0 0
\(621\) −13.5000 7.79423i −0.541736 0.312772i
\(622\) 17.1464 + 17.1464i 0.687509 + 0.687509i
\(623\) −0.776457 + 2.89778i −0.0311081 + 0.116097i
\(624\) −5.19615 3.00000i −0.208013 0.120096i
\(625\) 0 0
\(626\) −3.00000 1.73205i −0.119904 0.0692267i
\(627\) −8.48528 + 8.48528i −0.338869 + 0.338869i
\(628\) 20.0764 + 5.37945i 0.801135 + 0.214664i
\(629\) −20.7846 −0.828737
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −3.86370 1.03528i −0.153690 0.0411811i
\(633\) 36.8067 + 9.86233i 1.46294 + 0.391992i
\(634\) −5.19615 3.00000i −0.206366 0.119145i
\(635\) 0 0
\(636\) 0 0
\(637\) −3.58630 + 13.3843i −0.142094 + 0.530304i
\(638\) 21.2132 + 21.2132i 0.839839 + 0.839839i
\(639\) 5.19615 + 9.00000i 0.205557 + 0.356034i
\(640\) 0 0
\(641\) 28.5000 16.4545i 1.12568 0.649913i 0.182837 0.983143i \(-0.441472\pi\)
0.942845 + 0.333230i \(0.108139\pi\)
\(642\) −3.67423 3.67423i −0.145010 0.145010i
\(643\) −1.34486 5.01910i −0.0530362 0.197934i 0.934324 0.356424i \(-0.116004\pi\)
−0.987361 + 0.158490i \(0.949337\pi\)
\(644\) −2.59808 + 4.50000i −0.102379 + 0.177325i
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) 14.8492 14.8492i 0.583784 0.583784i −0.352157 0.935941i \(-0.614552\pi\)
0.935941 + 0.352157i \(0.114552\pi\)
\(648\) −8.69333 + 2.32937i −0.341506 + 0.0915064i
\(649\) 24.0000i 0.942082i
\(650\) 0 0
\(651\) 15.0000 25.9808i 0.587896 1.01827i
\(652\) 16.7303 4.48288i 0.655210 0.175563i
\(653\) 17.3867 4.65874i 0.680393 0.182311i 0.0979610 0.995190i \(-0.468768\pi\)
0.582432 + 0.812880i \(0.302101\pi\)
\(654\) −8.66025 −0.338643
\(655\) 0 0
\(656\) 8.66025i 0.338126i
\(657\) −10.7589 + 40.1528i −0.419745 + 1.56651i
\(658\) −3.67423 + 3.67423i −0.143237 + 0.143237i
\(659\) −10.3923 18.0000i −0.404827 0.701180i 0.589475 0.807787i \(-0.299335\pi\)
−0.994301 + 0.106606i \(0.966001\pi\)
\(660\) 0 0
\(661\) −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) 2.07055 + 7.72741i 0.0804743 + 0.300334i
\(663\) 9.31749 34.7733i 0.361861 1.35048i
\(664\) −2.59808 + 1.50000i −0.100825 + 0.0582113i
\(665\) 0 0
\(666\) 9.00000 + 5.19615i 0.348743 + 0.201347i
\(667\) −18.3712 18.3712i −0.711335 0.711335i
\(668\) −2.32937 + 8.69333i −0.0901261 + 0.336355i
\(669\) 27.0000i 1.04388i
\(670\) 0 0
\(671\) 39.0000 + 22.5167i 1.50558 + 0.869246i
\(672\) 0.776457 + 2.89778i 0.0299525 + 0.111784i
\(673\) 36.8067 + 9.86233i 1.41879 + 0.380165i 0.885056 0.465485i \(-0.154120\pi\)
0.533739 + 0.845649i \(0.320787\pi\)
\(674\) −13.8564 −0.533729
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) −5.79555 1.55291i −0.222741 0.0596833i 0.145722 0.989326i \(-0.453449\pi\)
−0.368464 + 0.929642i \(0.620116\pi\)
\(678\) 0 0
\(679\) 10.3923 + 6.00000i 0.398820 + 0.230259i
\(680\) 0 0
\(681\) 41.5692i 1.59294i
\(682\) 8.96575 33.4607i 0.343316 1.28127i
\(683\) 8.48528 + 8.48528i 0.324680 + 0.324680i 0.850559 0.525879i \(-0.176264\pi\)
−0.525879 + 0.850559i \(0.676264\pi\)
\(684\) 6.00000i 0.229416i
\(685\) 0 0
\(686\) 16.5000 9.52628i 0.629973 0.363715i
\(687\) 2.24144 8.36516i 0.0855162 0.319151i
\(688\) −2.68973 10.0382i −0.102545 0.382703i
\(689\) 0 0
\(690\) 0 0
\(691\) 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i \(-0.118041\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) −16.9706 + 16.9706i −0.645124 + 0.645124i
\(693\) −12.7279 12.7279i −0.483494 0.483494i
\(694\) 12.0000i 0.455514i
\(695\) 0 0
\(696\) −15.0000 −0.568574
\(697\) −50.1910 + 13.4486i −1.90112 + 0.509403i
\(698\) 0.965926 0.258819i 0.0365608 0.00979645i
\(699\) −5.19615 + 9.00000i −0.196537 + 0.340411i
\(700\) 0 0
\(701\) 12.1244i 0.457931i −0.973435 0.228965i \(-0.926466\pi\)
0.973435 0.228965i \(-0.0735342\pi\)
\(702\) −12.7279 + 12.7279i −0.480384 + 0.480384i
\(703\) −4.89898 + 4.89898i −0.184769 + 0.184769i
\(704\) 1.73205 + 3.00000i 0.0652791 + 0.113067i
\(705\) 0 0
\(706\) −12.0000 + 20.7846i −0.451626 + 0.782239i
\(707\) 6.21166 + 23.1822i 0.233613 + 0.871857i
\(708\) −8.48528 8.48528i −0.318896 0.318896i
\(709\) 35.5070 20.5000i 1.33349 0.769894i 0.347661 0.937620i \(-0.386976\pi\)
0.985834 + 0.167727i \(0.0536426\pi\)
\(710\) 0 0
\(711\) −6.00000 + 10.3923i −0.225018 + 0.389742i
\(712\) −1.22474 1.22474i −0.0458993 0.0458993i
\(713\) −7.76457 + 28.9778i −0.290785 + 1.08523i
\(714\) −15.5885 + 9.00000i −0.583383 + 0.336817i
\(715\) 0 0
\(716\) 21.0000 + 12.1244i 0.784807 + 0.453108i
\(717\) −34.7733 9.31749i −1.29863 0.347968i
\(718\) 16.7303 + 4.48288i 0.624370 + 0.167299i
\(719\) 6.92820 0.258378 0.129189 0.991620i \(-0.458763\pi\)
0.129189 + 0.991620i \(0.458763\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) −14.4889 3.88229i −0.539221 0.144484i
\(723\) 20.8207 20.8207i 0.774329 0.774329i
\(724\) 6.06218 + 3.50000i 0.225299 + 0.130076i
\(725\) 0 0
\(726\) −1.50000 0.866025i −0.0556702 0.0321412i
\(727\) −1.34486 + 5.01910i −0.0498782 + 0.186148i −0.986370 0.164541i \(-0.947386\pi\)
0.936492 + 0.350689i \(0.114052\pi\)
\(728\) 4.24264 + 4.24264i 0.157243 + 0.157243i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 54.0000 31.1769i 1.99726 1.15312i
\(732\) −21.7494 + 5.82774i −0.803882 + 0.215399i
\(733\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(734\) 1.73205 3.00000i 0.0639312 0.110732i
\(735\) 0 0
\(736\) −1.50000 2.59808i −0.0552907 0.0957664i
\(737\) 29.6985 29.6985i 1.09396 1.09396i
\(738\) 25.0955 + 6.72432i 0.923778 + 0.247525i
\(739\) 4.00000i 0.147142i −0.997290 0.0735712i \(-0.976560\pi\)
0.997290 0.0735712i \(-0.0234396\pi\)
\(740\) 0 0
\(741\) −6.00000 10.3923i −0.220416 0.381771i
\(742\) 0 0
\(743\) −26.0800 + 6.98811i −0.956782 + 0.256369i −0.703238 0.710955i \(-0.748263\pi\)
−0.253544 + 0.967324i \(0.581596\pi\)
\(744\) 8.66025 + 15.0000i 0.317500 + 0.549927i
\(745\) 0 0
\(746\) 13.8564i 0.507319i
\(747\) 2.32937 + 8.69333i 0.0852272 + 0.318072i
\(748\) −14.6969 + 14.6969i −0.537373 + 0.537373i
\(749\) 2.59808 + 4.50000i 0.0949316 + 0.164426i
\(750\) 0 0
\(751\) 1.00000 1.73205i 0.0364905 0.0632034i −0.847203 0.531269i \(-0.821715\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(752\) −0.776457 2.89778i −0.0283145 0.105671i
\(753\) −17.3867 + 4.65874i −0.633605 + 0.169774i
\(754\) −25.9808 + 15.0000i −0.946164 + 0.546268i
\(755\) 0 0
\(756\) 9.00000 0.327327
\(757\) 31.8434 + 31.8434i 1.15737 + 1.15737i 0.985040 + 0.172327i \(0.0551286\pi\)
0.172327 + 0.985040i \(0.444871\pi\)
\(758\) 2.07055 7.72741i 0.0752058 0.280672i
\(759\) 15.5885 + 9.00000i 0.565825 + 0.326679i
\(760\) 0 0
\(761\) −34.5000 19.9186i −1.25062 0.722048i −0.279391 0.960178i \(-0.590132\pi\)
−0.971233 + 0.238129i \(0.923466\pi\)
\(762\) −6.36396 + 6.36396i −0.230542 + 0.230542i
\(763\) 8.36516 + 2.24144i 0.302839 + 0.0811455i
\(764\) −17.3205 −0.626634
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) −23.1822 6.21166i −0.837061 0.224290i
\(768\) −1.67303 0.448288i −0.0603704 0.0161762i
\(769\) 19.9186 + 11.5000i 0.718283 + 0.414701i 0.814120 0.580696i \(-0.197220\pi\)
−0.0958377 + 0.995397i \(0.530553\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.48288 + 16.7303i −0.161342 + 0.602138i
\(773\) 25.4558 + 25.4558i 0.915583 + 0.915583i 0.996704 0.0811212i \(-0.0258501\pi\)
−0.0811212 + 0.996704i \(0.525850\pi\)
\(774\) −31.1769 −1.12063
\(775\) 0 0
\(776\) −6.00000 + 3.46410i −0.215387 + 0.124354i
\(777\) −7.34847 7.34847i −0.263625 0.263625i
\(778\) −6.72432 25.0955i −0.241078 0.899717i
\(779\) −8.66025 + 15.0000i −0.310286 + 0.537431i
\(780\) 0 0
\(781\) −6.00000 10.3923i −0.214697 0.371866i
\(782\) 12.7279 12.7279i 0.455150 0.455150i
\(783\) −11.6469 + 43.4667i −0.416225 + 1.55337i
\(784\) 4.00000i 0.142857i
\(785\) 0 0
\(786\) −6.00000 + 10.3923i −0.214013 + 0.370681i
\(787\) −3.34607 + 0.896575i −0.119274 + 0.0319595i −0.317962 0.948103i \(-0.602999\pi\)
0.198688 + 0.980063i \(0.436332\pi\)
\(788\) −11.5911 + 3.10583i −0.412916 + 0.110641i
\(789\) 41.5692 1.47990
\(790\) 0 0
\(791\) 0 0
\(792\) 10.0382 2.68973i 0.356692 0.0955753i
\(793\) −31.8434 + 31.8434i −1.13079 + 1.13079i
\(794\) 0 0
\(795\) 0 0
\(796\) −5.00000 + 8.66025i −0.177220 + 0.306955i
\(797\) −10.8704 40.5689i −0.385049 1.43702i −0.838089 0.545533i \(-0.816327\pi\)
0.453040 0.891490i \(-0.350340\pi\)
\(798\) −1.55291 + 5.79555i −0.0549726 + 0.205160i
\(799\) 15.5885 9.00000i 0.551480 0.318397i
\(800\) 0 0
\(801\) −4.50000 + 2.59808i −0.159000 + 0.0917985i
\(802\) 14.6969 + 14.6969i 0.518967 + 0.518967i
\(803\) 12.4233 46.3644i 0.438409 1.63617i
\(804\) 21.0000i 0.740613i
\(805\) 0 0
\(806\) 30.0000 + 17.3205i 1.05670 + 0.610089i
\(807\) 0.776457 + 2.89778i 0.0273326 + 0.102007i
\(808\) −13.3843 3.58630i −0.470857 0.126166i
\(809\) −6.92820 −0.243583 −0.121791 0.992556i \(-0.538864\pi\)
−0.121791 + 0.992556i \(0.538864\pi\)
\(810\) 0 0
\(811\) 4.00000 0.140459 0.0702295 0.997531i \(-0.477627\pi\)
0.0702295 + 0.997531i \(0.477627\pi\)
\(812\) 14.4889 + 3.88229i 0.508460 + 0.136242i
\(813\) −4.48288 16.7303i −0.157221 0.586758i
\(814\) −10.3923 6.00000i −0.364250 0.210300i
\(815\) 0 0
\(816\) 10.3923i 0.363803i
\(817\) 5.37945 20.0764i 0.188203 0.702384i
\(818\) 1.41421 + 1.41421i 0.0494468 + 0.0494468i
\(819\) 15.5885 9.00000i 0.544705 0.314485i
\(820\) 0 0
\(821\) −16.5000 + 9.52628i −0.575854 + 0.332469i −0.759484 0.650526i \(-0.774548\pi\)
0.183630 + 0.982995i \(0.441215\pi\)
\(822\) 5.37945 20.0764i 0.187630 0.700245i
\(823\) −7.62089 28.4416i −0.265648 0.991410i −0.961853 0.273567i \(-0.911796\pi\)
0.696205 0.717843i \(-0.254870\pi\)
\(824\) −1.73205 + 3.00000i −0.0603388 + 0.104510i
\(825\) 0 0
\(826\) 6.00000 + 10.3923i 0.208767 + 0.361595i
\(827\) −31.8198 + 31.8198i −1.10648 + 1.10648i −0.112874 + 0.993609i \(0.536006\pi\)
−0.993609 + 0.112874i \(0.963994\pi\)
\(828\) −8.69333 + 2.32937i −0.302114 + 0.0809513i
\(829\) 29.0000i 1.00721i 0.863934 + 0.503606i \(0.167994\pi\)
−0.863934 + 0.503606i \(0.832006\pi\)
\(830\) 0 0
\(831\) −18.0000 −0.624413
\(832\) −3.34607 + 0.896575i −0.116004 + 0.0310832i
\(833\) −23.1822 + 6.21166i −0.803216 + 0.215221i
\(834\) 3.46410 6.00000i 0.119952 0.207763i
\(835\) 0 0
\(836\) 6.92820i 0.239617i
\(837\) 50.1910 13.4486i 1.73485 0.464853i
\(838\) 7.34847 7.34847i 0.253849 0.253849i
\(839\) −19.0526 33.0000i −0.657767 1.13929i −0.981192 0.193033i \(-0.938168\pi\)
0.323425 0.946254i \(-0.395166\pi\)
\(840\) 0 0
\(841\) −23.0000 + 39.8372i −0.793103 + 1.37370i
\(842\) 2.58819 + 9.65926i 0.0891949 + 0.332880i
\(843\) 6.36396 + 6.36396i 0.219186 + 0.219186i
\(844\) 19.0526 11.0000i 0.655816 0.378636i
\(845\) 0 0
\(846\) −9.00000 −0.309426
\(847\) 1.22474 + 1.22474i 0.0420827 + 0.0420827i
\(848\) 0 0
\(849\) −7.79423 + 4.50000i −0.267497 + 0.154440i
\(850\) 0 0
\(851\) 9.00000 + 5.19615i 0.308516 + 0.178122i
\(852\) 5.79555 + 1.55291i 0.198552 + 0.0532020i
\(853\) 16.7303 + 4.48288i 0.572835 + 0.153491i 0.533597 0.845739i \(-0.320840\pi\)
0.0392388 + 0.999230i \(0.487507\pi\)
\(854\) 22.5167 0.770504
\(855\) 0 0
\(856\) −3.00000 −0.102538
\(857\) 40.5689 + 10.8704i 1.38581 + 0.371326i 0.873227 0.487314i \(-0.162023\pi\)
0.512580 + 0.858640i \(0.328690\pi\)
\(858\) 14.6969 14.6969i 0.501745 0.501745i
\(859\) −19.0526 11.0000i −0.650065 0.375315i 0.138416 0.990374i \(-0.455799\pi\)
−0.788481 + 0.615059i \(0.789132\pi\)
\(860\) 0 0
\(861\) −22.5000 12.9904i −0.766798 0.442711i
\(862\) 1.79315 6.69213i 0.0610750 0.227935i
\(863\) −10.6066 10.6066i −0.361053 0.361053i 0.503148 0.864201i \(-0.332175\pi\)
−0.864201 + 0.503148i \(0.832175\pi\)
\(864\) −2.59808 + 4.50000i −0.0883883 + 0.153093i
\(865\) 0 0
\(866\) 9.00000 5.19615i 0.305832 0.176572i
\(867\) 31.7876 8.51747i 1.07956 0.289268i
\(868\) −4.48288 16.7303i −0.152159 0.567864i
\(869\) 6.92820 12.0000i 0.235023 0.407072i
\(870\) 0 0
\(871\) 21.0000 + 36.3731i 0.711558 + 1.23245i
\(872\) −3.53553 + 3.53553i −0.119728 + 0.119728i
\(873\) 5.37945 + 20.0764i 0.182067 + 0.679483i
\(874\) 6.00000i 0.202953i
\(875\) 0 0
\(876\) 12.0000 + 20.7846i 0.405442 + 0.702247i
\(877\) 16.7303 4.48288i 0.564943 0.151376i 0.0349667 0.999388i \(-0.488867\pi\)
0.529976 + 0.848012i \(0.322201\pi\)
\(878\) 19.3185 5.17638i 0.651968 0.174694i
\(879\) −25.9808 45.0000i −0.876309 1.51781i
\(880\) 0 0
\(881\) 1.73205i 0.0583543i −0.999574 0.0291771i \(-0.990711\pi\)
0.999574 0.0291771i \(-0.00928869\pi\)
\(882\) 11.5911 + 3.10583i 0.390293 + 0.104579i
\(883\) −30.6186 + 30.6186i −1.03040 + 1.03040i −0.0308754 + 0.999523i \(0.509830\pi\)
−0.999523 + 0.0308754i \(0.990170\pi\)
\(884\) −10.3923 18.0000i −0.349531 0.605406i
\(885\) 0 0
\(886\) 4.50000 7.79423i 0.151180 0.261852i
\(887\) −6.21166 23.1822i −0.208567 0.778383i −0.988333 0.152311i \(-0.951328\pi\)
0.779766 0.626072i \(-0.215338\pi\)
\(888\) 5.79555 1.55291i 0.194486 0.0521124i
\(889\) 7.79423 4.50000i 0.261410 0.150925i
\(890\) 0 0
\(891\) 31.1769i 1.04447i
\(892\) −11.0227 11.0227i −0.369067 0.369067i
\(893\) 1.55291 5.79555i 0.0519663 0.193941i
\(894\) −7.79423 4.50000i −0.260678 0.150503i
\(895\) 0 0
\(896\) 1.50000 + 0.866025i 0.0501115 + 0.0289319i
\(897\) −12.7279 + 12.7279i −0.424973 + 0.424973i
\(898\) 13.3843 + 3.58630i 0.446639 + 0.119676i
\(899\) 86.6025 2.88836
\(900\) 0 0
\(901\) 0 0
\(902\) −28.9778 7.76457i −0.964854 0.258532i
\(903\) 30.1146 + 8.06918i 1.00215 + 0.268525i
\(904\) 0 0
\(905\) 0 0
\(906\) −15.0000 + 8.66025i −0.498342 + 0.287718i
\(907\) 2.24144 8.36516i 0.0744257 0.277761i −0.918677 0.395010i \(-0.870741\pi\)
0.993102 + 0.117250i \(0.0374077\pi\)
\(908\) −16.9706 16.9706i −0.563188 0.563188i
\(909\) −20.7846 + 36.0000i −0.689382 + 1.19404i
\(910\) 0 0
\(911\) −48.0000 + 27.7128i −1.59031 + 0.918166i −0.597058 + 0.802198i \(0.703664\pi\)
−0.993253 + 0.115968i \(0.963003\pi\)
\(912\) −2.44949 2.44949i −0.0811107 0.0811107i
\(913\) −2.68973 10.0382i −0.0890170 0.332216i
\(914\) −15.5885 + 27.0000i −0.515620 + 0.893081i
\(915\) 0 0
\(916\) −2.50000 4.33013i −0.0826023 0.143071i
\(917\) 8.48528 8.48528i 0.280209 0.280209i
\(918\) −30.1146 8.06918i −0.993929 0.266323i
\(919\) 40.0000i 1.31948i −0.751495 0.659739i \(-0.770667\pi\)
0.751495 0.659739i \(-0.229333\pi\)
\(920\) 0 0
\(921\) −4.50000 + 7.79423i −0.148280 + 0.256829i
\(922\) −11.7112 + 3.13801i −0.385689 + 0.103345i
\(923\) 11.5911 3.10583i 0.381526 0.102230i
\(924\) −10.3923 −0.341882
\(925\) 0 0
\(926\) 17.3205i 0.569187i
\(927\) 7.34847 + 7.34847i 0.241355 + 0.241355i
\(928\) −6.12372 + 6.12372i −0.201021 + 0.201021i
\(929\) 3.46410 + 6.00000i 0.113653 + 0.196854i 0.917241 0.398333i \(-0.130411\pi\)
−0.803587 + 0.595187i \(0.797078\pi\)
\(930\) 0 0
\(931\) −4.00000 + 6.92820i −0.131095 + 0.227063i
\(932\) 1.55291 + 5.79555i 0.0508674 + 0.189840i
\(933\) 10.8704 40.5689i 0.355881 1.32817i
\(934\) −31.1769 + 18.0000i −1.02014 + 0.588978i
\(935\) 0 0
\(936\) 10.3923i 0.339683i
\(937\) 9.79796 + 9.79796i 0.320085 + 0.320085i 0.848800 0.528714i \(-0.177326\pi\)
−0.528714 + 0.848800i \(0.677326\pi\)
\(938\) 5.43520 20.2844i 0.177466 0.662311i
\(939\) 6.00000i 0.195803i
\(940\) 0 0
\(941\) −4.50000 2.59808i −0.146696 0.0846949i 0.424856 0.905261i \(-0.360325\pi\)
−0.571551 + 0.820566i \(0.693658\pi\)
\(942\) −9.31749 34.7733i −0.303580 1.13298i
\(943\) 25.0955 + 6.72432i 0.817222 + 0.218974i
\(944\) −6.92820 −0.225494
\(945\) 0 0
\(946\) 36.0000 1.17046
\(947\) 26.0800 + 6.98811i 0.847486 + 0.227083i 0.656328 0.754476i \(-0.272109\pi\)
0.191158 + 0.981559i \(0.438776\pi\)
\(948\) 1.79315 + 6.69213i 0.0582388 + 0.217350i
\(949\) 41.5692 + 24.0000i 1.34939 + 0.779073i
\(950\) 0 0
\(951\) 10.3923i 0.336994i
\(952\) −2.68973 + 10.0382i −0.0871745 + 0.325340i
\(953\) −29.6985 29.6985i −0.962028 0.962028i 0.0372767 0.999305i \(-0.488132\pi\)
−0.999305 + 0.0372767i \(0.988132\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −18.0000 + 10.3923i −0.582162 + 0.336111i
\(957\) 13.4486 50.1910i 0.434733 1.62244i
\(958\) 7.17260 + 26.7685i 0.231736 + 0.864852i
\(959\) −10.3923 + 18.0000i −0.335585 + 0.581250i
\(960\) 0 0
\(961\) −34.5000 59.7558i −1.11290 1.92760i
\(962\) 8.48528 8.48528i 0.273576 0.273576i
\(963\) −2.32937 + 8.69333i −0.0750629 + 0.280139i
\(964\) 17.0000i 0.547533i
\(965\) 0 0
\(966\) 9.00000 0.289570
\(967\) 51.8640 13.8969i 1.66783 0.446895i 0.703309 0.710885i \(-0.251705\pi\)
0.964525 + 0.263990i \(0.0850385\pi\)
\(968\) −0.965926 + 0.258819i −0.0310460 + 0.00831876i
\(969\) 10.3923 18.0000i 0.333849 0.578243i
\(970\) 0 0
\(971\) 38.1051i 1.22285i −0.791302 0.611426i \(-0.790596\pi\)
0.791302 0.611426i \(-0.209404\pi\)
\(972\) 11.0227 + 11.0227i 0.353553 + 0.353553i
\(973\) −4.89898 + 4.89898i −0.157054 + 0.157054i
\(974\) −12.1244 21.0000i −0.388489 0.672883i
\(975\) 0 0
\(976\) −6.50000 + 11.2583i −0.208060 + 0.360370i
\(977\) 10.8704 + 40.5689i 0.347775 + 1.29791i 0.889337 + 0.457253i \(0.151167\pi\)
−0.541562 + 0.840661i \(0.682167\pi\)
\(978\) −21.2132 21.2132i −0.678323 0.678323i
\(979\) 5.19615 3.00000i 0.166070 0.0958804i
\(980\) 0 0
\(981\) 7.50000 + 12.9904i 0.239457 + 0.414751i
\(982\) −9.79796 9.79796i −0.312665 0.312665i
\(983\) 2.32937 8.69333i 0.0742954 0.277274i −0.918777 0.394776i \(-0.870822\pi\)
0.993073 + 0.117502i \(0.0374887\pi\)
\(984\) 12.9904 7.50000i 0.414118 0.239091i
\(985\) 0 0
\(986\) −45.0000 25.9808i −1.43309 0.827396i
\(987\) 8.69333 + 2.32937i 0.276712 + 0.0741447i
\(988\) −6.69213 1.79315i −0.212905 0.0570477i
\(989\) −31.1769 −0.991368
\(990\) 0 0
\(991\) 20.0000 0.635321 0.317660 0.948205i \(-0.397103\pi\)
0.317660 + 0.948205i \(0.397103\pi\)
\(992\) 9.65926 + 2.58819i 0.306682 + 0.0821751i
\(993\) 9.79796 9.79796i 0.310929 0.310929i
\(994\) −5.19615 3.00000i −0.164812 0.0951542i
\(995\) 0 0
\(996\) 4.50000 + 2.59808i 0.142588 + 0.0823232i
\(997\) 10.7589 40.1528i 0.340738 1.27165i −0.556775 0.830663i \(-0.687961\pi\)
0.897513 0.440988i \(-0.145372\pi\)
\(998\) −31.1127 31.1127i −0.984855 0.984855i
\(999\) 18.0000i 0.569495i
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.d.257.1 8
3.2 odd 2 1350.2.q.b.557.2 8
5.2 odd 4 inner 450.2.p.d.293.2 yes 8
5.3 odd 4 inner 450.2.p.d.293.1 yes 8
5.4 even 2 inner 450.2.p.d.257.2 yes 8
9.2 odd 6 inner 450.2.p.d.407.1 yes 8
9.7 even 3 1350.2.q.b.1007.2 8
15.2 even 4 1350.2.q.b.1043.1 8
15.8 even 4 1350.2.q.b.1043.2 8
15.14 odd 2 1350.2.q.b.557.1 8
45.2 even 12 inner 450.2.p.d.443.2 yes 8
45.7 odd 12 1350.2.q.b.143.1 8
45.29 odd 6 inner 450.2.p.d.407.2 yes 8
45.34 even 6 1350.2.q.b.1007.1 8
45.38 even 12 inner 450.2.p.d.443.1 yes 8
45.43 odd 12 1350.2.q.b.143.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.p.d.257.1 8 1.1 even 1 trivial
450.2.p.d.257.2 yes 8 5.4 even 2 inner
450.2.p.d.293.1 yes 8 5.3 odd 4 inner
450.2.p.d.293.2 yes 8 5.2 odd 4 inner
450.2.p.d.407.1 yes 8 9.2 odd 6 inner
450.2.p.d.407.2 yes 8 45.29 odd 6 inner
450.2.p.d.443.1 yes 8 45.38 even 12 inner
450.2.p.d.443.2 yes 8 45.2 even 12 inner
1350.2.q.b.143.1 8 45.7 odd 12
1350.2.q.b.143.2 8 45.43 odd 12
1350.2.q.b.557.1 8 15.14 odd 2
1350.2.q.b.557.2 8 3.2 odd 2
1350.2.q.b.1007.1 8 45.34 even 6
1350.2.q.b.1007.2 8 9.7 even 3
1350.2.q.b.1043.1 8 15.2 even 4
1350.2.q.b.1043.2 8 15.8 even 4