Properties

Label 1470.2.n.a.79.2
Level $1470$
Weight $2$
Character 1470.79
Analytic conductor $11.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(79,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.79
Dual form 1470.2.n.a.949.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.23205 + 0.133975i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-0.866025 - 0.500000i) q^{12} +6.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.00000 - 1.00000i) q^{20} -2.00000i q^{22} +(-3.46410 - 2.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.96410 - 4.59808i) q^{25} +(-3.00000 + 5.19615i) q^{26} +1.00000i q^{27} +(1.86603 - 1.23205i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(-1.73205 - 1.00000i) q^{37} +(-3.00000 - 5.19615i) q^{39} +(-1.23205 - 1.86603i) q^{40} -2.00000 q^{41} +4.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(0.133975 + 2.23205i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(-6.92820 - 4.00000i) q^{47} -1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +(1.00000 - 1.73205i) q^{51} +(-5.19615 + 3.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.00000 + 2.00000i) q^{55} +(-5.00000 - 8.66025i) q^{59} +(2.23205 - 0.133975i) q^{60} +(1.00000 - 1.73205i) q^{61} -8.00000i q^{62} -1.00000 q^{64} +(-7.39230 - 11.1962i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-6.92820 + 4.00000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +4.00000 q^{69} +12.0000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(0.598076 + 4.96410i) q^{75} -6.00000i q^{78} +(-0.133975 - 2.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.73205 - 1.00000i) q^{82} -4.00000i q^{83} +(2.00000 - 4.00000i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(1.73205 - 1.00000i) q^{88} +(5.00000 - 8.66025i) q^{89} +(-1.00000 + 2.00000i) q^{90} -4.00000i q^{92} +(6.92820 + 4.00000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(0.500000 - 0.866025i) q^{96} +8.00000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 4 q^{5} - 4 q^{6} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 4 q^{15} - 2 q^{16} - 8 q^{20} - 2 q^{24} - 6 q^{25} - 12 q^{26} + 4 q^{30} - 16 q^{31} - 8 q^{34} + 4 q^{36} - 12 q^{39} + 2 q^{40} - 8 q^{41} + 4 q^{44} + 4 q^{45} - 8 q^{46} + 16 q^{50} + 4 q^{51} - 2 q^{54} + 16 q^{55} - 20 q^{59} + 2 q^{60} + 4 q^{61} - 4 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{69} + 48 q^{71} - 4 q^{74} - 8 q^{75} - 4 q^{80} - 2 q^{81} + 8 q^{85} - 8 q^{86} + 20 q^{89} - 4 q^{90} - 16 q^{94} + 2 q^{96} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.86603 + 1.23205i −0.834512 + 0.550990i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −2.23205 + 0.133975i −0.705836 + 0.0423665i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 6.00000i 1.66410i 0.554700 + 0.832050i \(0.312833\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 1.00000 2.00000i 0.258199 0.516398i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.73205 + 1.00000i −0.420084 + 0.242536i −0.695113 0.718900i \(-0.744646\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) −2.00000 1.00000i −0.447214 0.223607i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) −3.46410 2.00000i −0.722315 0.417029i 0.0932891 0.995639i \(-0.470262\pi\)
−0.815604 + 0.578610i \(0.803595\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 1.96410 4.59808i 0.392820 0.919615i
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.86603 1.23205i 0.340688 0.224941i
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 1.73205 + 1.00000i 0.301511 + 0.174078i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −1.73205 1.00000i −0.284747 0.164399i 0.350823 0.936442i \(-0.385902\pi\)
−0.635571 + 0.772043i \(0.719235\pi\)
\(38\) 0 0
\(39\) −3.00000 5.19615i −0.480384 0.832050i
\(40\) −1.23205 1.86603i −0.194804 0.295045i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) 0.133975 + 2.23205i 0.0199718 + 0.332734i
\(46\) −2.00000 3.46410i −0.294884 0.510754i
\(47\) −6.92820 4.00000i −1.01058 0.583460i −0.0992202 0.995066i \(-0.531635\pi\)
−0.911362 + 0.411606i \(0.864968\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 1.00000 1.73205i 0.140028 0.242536i
\(52\) −5.19615 + 3.00000i −0.720577 + 0.416025i
\(53\) −5.19615 + 3.00000i −0.713746 + 0.412082i −0.812447 0.583036i \(-0.801865\pi\)
0.0987002 + 0.995117i \(0.468532\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 4.00000 + 2.00000i 0.539360 + 0.269680i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.00000 8.66025i −0.650945 1.12747i −0.982894 0.184172i \(-0.941040\pi\)
0.331949 0.943297i \(-0.392294\pi\)
\(60\) 2.23205 0.133975i 0.288157 0.0172960i
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −7.39230 11.1962i −0.916903 1.38871i
\(66\) 1.00000 + 1.73205i 0.123091 + 0.213201i
\(67\) −6.92820 + 4.00000i −0.846415 + 0.488678i −0.859440 0.511237i \(-0.829187\pi\)
0.0130248 + 0.999915i \(0.495854\pi\)
\(68\) −1.73205 1.00000i −0.210042 0.121268i
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) −3.46410 + 2.00000i −0.405442 + 0.234082i −0.688830 0.724923i \(-0.741875\pi\)
0.283387 + 0.959006i \(0.408542\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0.598076 + 4.96410i 0.0690599 + 0.573205i
\(76\) 0 0
\(77\) 0 0
\(78\) 6.00000i 0.679366i
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) −0.133975 2.23205i −0.0149788 0.249551i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.73205 1.00000i −0.191273 0.110432i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 0 0
\(85\) 2.00000 4.00000i 0.216930 0.433861i
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) 1.73205 1.00000i 0.184637 0.106600i
\(89\) 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) −1.00000 + 2.00000i −0.105409 + 0.210819i
\(91\) 0 0
\(92\) 4.00000i 0.417029i
\(93\) 6.92820 + 4.00000i 0.718421 + 0.414781i
\(94\) −4.00000 6.92820i −0.412568 0.714590i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 8.00000i 0.812277i 0.913812 + 0.406138i \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 4.96410 0.598076i 0.496410 0.0598076i
\(101\) −4.00000 6.92820i −0.398015 0.689382i 0.595466 0.803380i \(-0.296967\pi\)
−0.993481 + 0.113998i \(0.963634\pi\)
\(102\) 1.73205 1.00000i 0.171499 0.0990148i
\(103\) 12.1244 + 7.00000i 1.19465 + 0.689730i 0.959357 0.282194i \(-0.0910623\pi\)
0.235291 + 0.971925i \(0.424396\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −10.3923 6.00000i −1.00466 0.580042i −0.0950377 0.995474i \(-0.530297\pi\)
−0.909624 + 0.415432i \(0.863630\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 2.46410 + 3.73205i 0.234943 + 0.355837i
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 8.92820 0.535898i 0.832559 0.0499728i
\(116\) 0 0
\(117\) 5.19615 + 3.00000i 0.480384 + 0.277350i
\(118\) 10.0000i 0.920575i
\(119\) 0 0
\(120\) 2.00000 + 1.00000i 0.182574 + 0.0912871i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 1.73205 1.00000i 0.156813 0.0905357i
\(123\) 1.73205 1.00000i 0.156174 0.0901670i
\(124\) 4.00000 6.92820i 0.359211 0.622171i
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) −0.803848 13.3923i −0.0705021 1.17458i
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −1.23205 1.86603i −0.106038 0.160602i
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −15.5885 + 9.00000i −1.33181 + 0.768922i −0.985577 0.169226i \(-0.945873\pi\)
−0.346235 + 0.938148i \(0.612540\pi\)
\(138\) 3.46410 + 2.00000i 0.294884 + 0.170251i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 10.3923 + 6.00000i 0.872103 + 0.503509i
\(143\) 10.3923 6.00000i 0.869048 0.501745i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) −10.0000 + 17.3205i −0.819232 + 1.41895i 0.0870170 + 0.996207i \(0.472267\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(150\) −1.96410 + 4.59808i −0.160368 + 0.375431i
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 16.0000 + 8.00000i 1.28515 + 0.642575i
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) −19.0526 + 11.0000i −1.52056 + 0.877896i −0.520854 + 0.853646i \(0.674386\pi\)
−0.999706 + 0.0242497i \(0.992280\pi\)
\(158\) 0 0
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 13.8564 + 8.00000i 1.08532 + 0.626608i 0.932326 0.361619i \(-0.117776\pi\)
0.152992 + 0.988227i \(0.451109\pi\)
\(164\) −1.00000 1.73205i −0.0780869 0.135250i
\(165\) −4.46410 + 0.267949i −0.347530 + 0.0208598i
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 0 0
\(169\) −23.0000 −1.76923
\(170\) 3.73205 2.46410i 0.286235 0.188988i
\(171\) 0 0
\(172\) −3.46410 + 2.00000i −0.264135 + 0.152499i
\(173\) 12.1244 + 7.00000i 0.921798 + 0.532200i 0.884208 0.467093i \(-0.154699\pi\)
0.0375896 + 0.999293i \(0.488032\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) 8.66025 + 5.00000i 0.650945 + 0.375823i
\(178\) 8.66025 5.00000i 0.649113 0.374766i
\(179\) 5.00000 + 8.66025i 0.373718 + 0.647298i 0.990134 0.140122i \(-0.0447496\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(180\) −1.86603 + 1.23205i −0.139085 + 0.0918316i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) 4.46410 0.267949i 0.328207 0.0197000i
\(186\) 4.00000 + 6.92820i 0.293294 + 0.508001i
\(187\) 3.46410 + 2.00000i 0.253320 + 0.146254i
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) 0 0
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 3.46410 2.00000i 0.249351 0.143963i −0.370116 0.928986i \(-0.620682\pi\)
0.619467 + 0.785022i \(0.287349\pi\)
\(194\) −4.00000 + 6.92820i −0.287183 + 0.497416i
\(195\) 12.0000 + 6.00000i 0.859338 + 0.429669i
\(196\) 0 0
\(197\) 22.0000i 1.56744i 0.621117 + 0.783718i \(0.286679\pi\)
−0.621117 + 0.783718i \(0.713321\pi\)
\(198\) −1.73205 1.00000i −0.123091 0.0710669i
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 4.59808 + 1.96410i 0.325133 + 0.138883i
\(201\) 4.00000 6.92820i 0.282138 0.488678i
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 3.73205 2.46410i 0.260658 0.172100i
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) −3.46410 + 2.00000i −0.240772 + 0.139010i
\(208\) −5.19615 3.00000i −0.360288 0.208013i
\(209\) 0 0
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −5.19615 3.00000i −0.356873 0.206041i
\(213\) −10.3923 + 6.00000i −0.712069 + 0.411113i
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −4.92820 7.46410i −0.336101 0.509048i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 10.0000i 0.677285i
\(219\) 2.00000 3.46410i 0.135147 0.234082i
\(220\) 0.267949 + 4.46410i 0.0180651 + 0.300970i
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) 1.73205 + 1.00000i 0.116248 + 0.0671156i
\(223\) 26.0000i 1.74109i 0.492090 + 0.870544i \(0.336233\pi\)
−0.492090 + 0.870544i \(0.663767\pi\)
\(224\) 0 0
\(225\) −3.00000 4.00000i −0.200000 0.266667i
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 24.2487 14.0000i 1.60944 0.929213i 0.619949 0.784642i \(-0.287153\pi\)
0.989494 0.144571i \(-0.0461801\pi\)
\(228\) 0 0
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 8.00000 + 4.00000i 0.527504 + 0.263752i
\(231\) 0 0
\(232\) 0 0
\(233\) −12.1244 7.00000i −0.794293 0.458585i 0.0471787 0.998886i \(-0.484977\pi\)
−0.841472 + 0.540301i \(0.818310\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 17.8564 1.07180i 1.16482 0.0699163i
\(236\) 5.00000 8.66025i 0.325472 0.563735i
\(237\) 0 0
\(238\) 0 0
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 1.23205 + 1.86603i 0.0795285 + 0.120451i
\(241\) 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i \(0.0839937\pi\)
−0.256814 + 0.966461i \(0.582673\pi\)
\(242\) 6.06218 3.50000i 0.389692 0.224989i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) 6.92820 4.00000i 0.439941 0.254000i
\(249\) 2.00000 + 3.46410i 0.126745 + 0.219529i
\(250\) −3.76795 + 10.5263i −0.238306 + 0.665740i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 0 0
\(253\) 8.00000i 0.502956i
\(254\) −1.00000 + 1.73205i −0.0627456 + 0.108679i
\(255\) 0.267949 + 4.46410i 0.0167796 + 0.279553i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −15.5885 9.00000i −0.972381 0.561405i −0.0724199 0.997374i \(-0.523072\pi\)
−0.899961 + 0.435970i \(0.856405\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) 6.00000 12.0000i 0.372104 0.744208i
\(261\) 0 0
\(262\) −15.5885 + 9.00000i −0.963058 + 0.556022i
\(263\) 3.46410 2.00000i 0.213606 0.123325i −0.389380 0.921077i \(-0.627311\pi\)
0.602986 + 0.797752i \(0.293977\pi\)
\(264\) −1.00000 + 1.73205i −0.0615457 + 0.106600i
\(265\) 6.00000 12.0000i 0.368577 0.737154i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) −6.92820 4.00000i −0.423207 0.244339i
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) −0.133975 2.23205i −0.00815343 0.135838i
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) −9.92820 + 1.19615i −0.598693 + 0.0721307i
\(276\) 2.00000 + 3.46410i 0.120386 + 0.208514i
\(277\) 1.73205 1.00000i 0.104069 0.0600842i −0.447062 0.894503i \(-0.647530\pi\)
0.551131 + 0.834419i \(0.314196\pi\)
\(278\) −17.3205 10.0000i −1.03882 0.599760i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 6.92820 + 4.00000i 0.412568 + 0.238197i
\(283\) 13.8564 8.00000i 0.823678 0.475551i −0.0280052 0.999608i \(-0.508916\pi\)
0.851683 + 0.524057i \(0.175582\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) 0 0
\(291\) −4.00000 6.92820i −0.234484 0.406138i
\(292\) −3.46410 2.00000i −0.202721 0.117041i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) 0 0
\(295\) 20.0000 + 10.0000i 1.16445 + 0.582223i
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 1.73205 1.00000i 0.100504 0.0580259i
\(298\) −17.3205 + 10.0000i −1.00335 + 0.579284i
\(299\) 12.0000 20.7846i 0.693978 1.20201i
\(300\) −4.00000 + 3.00000i −0.230940 + 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 6.92820 + 4.00000i 0.398015 + 0.229794i
\(304\) 0 0
\(305\) 0.267949 + 4.46410i 0.0153427 + 0.255614i
\(306\) −1.00000 + 1.73205i −0.0571662 + 0.0990148i
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 0 0
\(309\) −14.0000 −0.796432
\(310\) 9.85641 + 14.9282i 0.559806 + 0.847865i
\(311\) 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i \(-0.0561621\pi\)
−0.644246 + 0.764818i \(0.722829\pi\)
\(312\) 5.19615 3.00000i 0.294174 0.169842i
\(313\) 3.46410 + 2.00000i 0.195803 + 0.113047i 0.594696 0.803951i \(-0.297272\pi\)
−0.398894 + 0.916997i \(0.630606\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) 0 0
\(317\) −1.73205 1.00000i −0.0972817 0.0561656i 0.450570 0.892741i \(-0.351221\pi\)
−0.547852 + 0.836576i \(0.684554\pi\)
\(318\) 5.19615 3.00000i 0.291386 0.168232i
\(319\) 0 0
\(320\) 1.86603 1.23205i 0.104314 0.0688737i
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 27.5885 + 11.7846i 1.53033 + 0.653693i
\(326\) 8.00000 + 13.8564i 0.443079 + 0.767435i
\(327\) −8.66025 5.00000i −0.478913 0.276501i
\(328\) 2.00000i 0.110432i
\(329\) 0 0
\(330\) −4.00000 2.00000i −0.220193 0.110096i
\(331\) 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i \(-0.762773\pi\)
0.954765 + 0.297361i \(0.0961066\pi\)
\(332\) 3.46410 2.00000i 0.190117 0.109764i
\(333\) −1.73205 + 1.00000i −0.0949158 + 0.0547997i
\(334\) 6.00000 10.3923i 0.328305 0.568642i
\(335\) 8.00000 16.0000i 0.437087 0.874173i
\(336\) 0 0
\(337\) 28.0000i 1.52526i −0.646837 0.762629i \(-0.723908\pi\)
0.646837 0.762629i \(-0.276092\pi\)
\(338\) −19.9186 11.5000i −1.08343 0.625518i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 4.46410 0.267949i 0.242100 0.0145316i
\(341\) −8.00000 + 13.8564i −0.433224 + 0.750366i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) −7.46410 + 4.92820i −0.401854 + 0.265326i
\(346\) 7.00000 + 12.1244i 0.376322 + 0.651809i
\(347\) 10.3923 6.00000i 0.557888 0.322097i −0.194409 0.980921i \(-0.562279\pi\)
0.752297 + 0.658824i \(0.228946\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) 1.73205 + 1.00000i 0.0923186 + 0.0533002i
\(353\) −12.1244 + 7.00000i −0.645314 + 0.372572i −0.786659 0.617388i \(-0.788191\pi\)
0.141344 + 0.989960i \(0.454858\pi\)
\(354\) 5.00000 + 8.66025i 0.265747 + 0.460287i
\(355\) −22.3923 + 14.7846i −1.18846 + 0.784686i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 10.0000i 0.528516i
\(359\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) −2.23205 + 0.133975i −0.117639 + 0.00706108i
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) −1.73205 1.00000i −0.0910346 0.0525588i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 4.00000 8.00000i 0.209370 0.418739i
\(366\) −1.00000 + 1.73205i −0.0522708 + 0.0905357i
\(367\) −1.73205 + 1.00000i −0.0904123 + 0.0521996i −0.544524 0.838745i \(-0.683290\pi\)
0.454112 + 0.890945i \(0.349957\pi\)
\(368\) 3.46410 2.00000i 0.180579 0.104257i
\(369\) −1.00000 + 1.73205i −0.0520579 + 0.0901670i
\(370\) 4.00000 + 2.00000i 0.207950 + 0.103975i
\(371\) 0 0
\(372\) 8.00000i 0.414781i
\(373\) 5.19615 + 3.00000i 0.269047 + 0.155334i 0.628454 0.777847i \(-0.283688\pi\)
−0.359408 + 0.933181i \(0.617021\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) −7.23205 8.52628i −0.373461 0.440295i
\(376\) 4.00000 6.92820i 0.206284 0.357295i
\(377\) 0 0
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −1.00000 1.73205i −0.0512316 0.0887357i
\(382\) −10.3923 + 6.00000i −0.531717 + 0.306987i
\(383\) −13.8564 8.00000i −0.708029 0.408781i 0.102302 0.994753i \(-0.467379\pi\)
−0.810331 + 0.585973i \(0.800713\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) 3.46410 + 2.00000i 0.176090 + 0.101666i
\(388\) −6.92820 + 4.00000i −0.351726 + 0.203069i
\(389\) 10.0000 + 17.3205i 0.507020 + 0.878185i 0.999967 + 0.00812520i \(0.00258636\pi\)
−0.492947 + 0.870059i \(0.664080\pi\)
\(390\) 7.39230 + 11.1962i 0.374324 + 0.566939i
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 18.0000i 0.907980i
\(394\) −11.0000 + 19.0526i −0.554172 + 0.959854i
\(395\) 0 0
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) 1.73205 + 1.00000i 0.0869291 + 0.0501886i 0.542834 0.839840i \(-0.317351\pi\)
−0.455905 + 0.890028i \(0.650684\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −11.0000 + 19.0526i −0.549314 + 0.951439i 0.449008 + 0.893528i \(0.351777\pi\)
−0.998322 + 0.0579116i \(0.981556\pi\)
\(402\) 6.92820 4.00000i 0.345547 0.199502i
\(403\) 41.5692 24.0000i 2.07071 1.19553i
\(404\) 4.00000 6.92820i 0.199007 0.344691i
\(405\) 2.00000 + 1.00000i 0.0993808 + 0.0496904i
\(406\) 0 0
\(407\) 4.00000i 0.198273i
\(408\) 1.73205 + 1.00000i 0.0857493 + 0.0495074i
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 4.46410 0.267949i 0.220466 0.0132331i
\(411\) 9.00000 15.5885i 0.443937 0.768922i
\(412\) 14.0000i 0.689730i
\(413\) 0 0
\(414\) −4.00000 −0.196589
\(415\) 4.92820 + 7.46410i 0.241916 + 0.366398i
\(416\) −3.00000 5.19615i −0.147087 0.254762i
\(417\) 17.3205 10.0000i 0.848189 0.489702i
\(418\) 0 0
\(419\) −10.0000 −0.488532 −0.244266 0.969708i \(-0.578547\pi\)
−0.244266 + 0.969708i \(0.578547\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 10.3923 + 6.00000i 0.505889 + 0.292075i
\(423\) −6.92820 + 4.00000i −0.336861 + 0.194487i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 1.19615 + 9.92820i 0.0580219 + 0.481589i
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) −6.00000 + 10.3923i −0.289683 + 0.501745i
\(430\) −0.535898 8.92820i −0.0258433 0.430556i
\(431\) −16.0000 27.7128i −0.770693 1.33488i −0.937184 0.348836i \(-0.886577\pi\)
0.166491 0.986043i \(-0.446756\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 4.00000i 0.192228i −0.995370 0.0961139i \(-0.969359\pi\)
0.995370 0.0961139i \(-0.0306413\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.00000 + 8.66025i −0.239457 + 0.414751i
\(437\) 0 0
\(438\) 3.46410 2.00000i 0.165521 0.0955637i
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) −2.00000 + 4.00000i −0.0953463 + 0.190693i
\(441\) 0 0
\(442\) 12.0000i 0.570782i
\(443\) 31.1769 + 18.0000i 1.48126 + 0.855206i 0.999774 0.0212481i \(-0.00676401\pi\)
0.481486 + 0.876454i \(0.340097\pi\)
\(444\) 1.00000 + 1.73205i 0.0474579 + 0.0821995i
\(445\) 1.33975 + 22.3205i 0.0635100 + 1.05809i
\(446\) −13.0000 + 22.5167i −0.615568 + 1.06619i
\(447\) 20.0000i 0.945968i
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −0.598076 4.96410i −0.0281936 0.234010i
\(451\) 2.00000 + 3.46410i 0.0941763 + 0.163118i
\(452\) 5.19615 3.00000i 0.244406 0.141108i
\(453\) −6.92820 4.00000i −0.325515 0.187936i
\(454\) 28.0000 1.31411
\(455\) 0 0
\(456\) 0 0
\(457\) −27.7128 16.0000i −1.29635 0.748448i −0.316579 0.948566i \(-0.602534\pi\)
−0.979772 + 0.200118i \(0.935868\pi\)
\(458\) 8.66025 5.00000i 0.404667 0.233635i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) 4.92820 + 7.46410i 0.229779 + 0.348016i
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 6.00000i 0.278844i −0.990233 0.139422i \(-0.955476\pi\)
0.990233 0.139422i \(-0.0445244\pi\)
\(464\) 0 0
\(465\) −17.8564 + 1.07180i −0.828071 + 0.0497034i
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) 10.3923 + 6.00000i 0.480899 + 0.277647i 0.720791 0.693153i \(-0.243779\pi\)
−0.239892 + 0.970799i \(0.577112\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 0 0
\(470\) 16.0000 + 8.00000i 0.738025 + 0.369012i
\(471\) 11.0000 19.0526i 0.506853 0.877896i
\(472\) 8.66025 5.00000i 0.398621 0.230144i
\(473\) 6.92820 4.00000i 0.318559 0.183920i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) −17.3205 10.0000i −0.792222 0.457389i
\(479\) −10.0000 17.3205i −0.456912 0.791394i 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) 0.133975 + 2.23205i 0.00611508 + 0.101879i
\(481\) 6.00000 10.3923i 0.273576 0.473848i
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −9.85641 14.9282i −0.447556 0.677855i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −15.5885 + 9.00000i −0.706380 + 0.407829i −0.809719 0.586817i \(-0.800381\pi\)
0.103339 + 0.994646i \(0.467047\pi\)
\(488\) 1.73205 + 1.00000i 0.0784063 + 0.0452679i
\(489\) −16.0000 −0.723545
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 1.73205 + 1.00000i 0.0780869 + 0.0450835i
\(493\) 0 0
\(494\) 0 0
\(495\) 3.73205 2.46410i 0.167743 0.110753i
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 4.00000i 0.179244i
\(499\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(500\) −8.52628 + 7.23205i −0.381307 + 0.323427i
\(501\) 6.00000 + 10.3923i 0.268060 + 0.464294i
\(502\) 15.5885 + 9.00000i 0.695747 + 0.401690i
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 0 0
\(505\) 16.0000 + 8.00000i 0.711991 + 0.355995i
\(506\) −4.00000 + 6.92820i −0.177822 + 0.307996i
\(507\) 19.9186 11.5000i 0.884615 0.510733i
\(508\) −1.73205 + 1.00000i −0.0768473 + 0.0443678i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) −2.00000 + 4.00000i −0.0885615 + 0.177123i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −9.00000 15.5885i −0.396973 0.687577i
\(515\) −31.2487 + 1.87564i −1.37698 + 0.0826508i
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 16.0000i 0.703679i
\(518\) 0 0
\(519\) −14.0000 −0.614532
\(520\) 11.1962 7.39230i 0.490984 0.324174i
\(521\) 11.0000 + 19.0526i 0.481919 + 0.834708i 0.999785 0.0207541i \(-0.00660670\pi\)
−0.517866 + 0.855462i \(0.673273\pi\)
\(522\) 0 0
\(523\) −13.8564 8.00000i −0.605898 0.349816i 0.165460 0.986216i \(-0.447089\pi\)
−0.771358 + 0.636401i \(0.780422\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) 4.00000 0.174408
\(527\) 13.8564 + 8.00000i 0.603595 + 0.348485i
\(528\) −1.73205 + 1.00000i −0.0753778 + 0.0435194i
\(529\) −3.50000 6.06218i −0.152174 0.263573i
\(530\) 11.1962 7.39230i 0.486330 0.321101i
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) −5.00000 + 8.66025i −0.216371 + 0.374766i
\(535\) 26.7846 1.60770i 1.15800 0.0695067i
\(536\) −4.00000 6.92820i −0.172774 0.299253i
\(537\) −8.66025 5.00000i −0.373718 0.215766i
\(538\) 0 0
\(539\) 0 0
\(540\) 1.00000 2.00000i 0.0430331 0.0860663i
\(541\) 19.0000 32.9090i 0.816874 1.41487i −0.0911008 0.995842i \(-0.529039\pi\)
0.907975 0.419025i \(-0.137628\pi\)
\(542\) −6.92820 + 4.00000i −0.297592 + 0.171815i
\(543\) 1.73205 1.00000i 0.0743294 0.0429141i
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) −20.0000 10.0000i −0.856706 0.428353i
\(546\) 0 0
\(547\) 28.0000i 1.19719i −0.801050 0.598597i \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) −15.5885 9.00000i −0.665906 0.384461i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) −9.19615 3.92820i −0.392125 0.167499i
\(551\) 0 0
\(552\) 4.00000i 0.170251i
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) −3.73205 + 2.46410i −0.158417 + 0.104595i
\(556\) −10.0000 17.3205i −0.424094 0.734553i
\(557\) −15.5885 + 9.00000i −0.660504 + 0.381342i −0.792469 0.609912i \(-0.791205\pi\)
0.131965 + 0.991254i \(0.457871\pi\)
\(558\) −6.92820 4.00000i −0.293294 0.169334i
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) −15.5885 9.00000i −0.657559 0.379642i
\(563\) −38.1051 + 22.0000i −1.60594 + 0.927189i −0.615673 + 0.788002i \(0.711116\pi\)
−0.990266 + 0.139188i \(0.955551\pi\)
\(564\) 4.00000 + 6.92820i 0.168430 + 0.291730i
\(565\) 7.39230 + 11.1962i 0.310997 + 0.471026i
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i \(-0.900553\pi\)
0.741981 + 0.670421i \(0.233886\pi\)
\(570\) 0 0
\(571\) 4.00000 + 6.92820i 0.167395 + 0.289936i 0.937503 0.347977i \(-0.113131\pi\)
−0.770108 + 0.637913i \(0.779798\pi\)
\(572\) 10.3923 + 6.00000i 0.434524 + 0.250873i
\(573\) 12.0000i 0.501307i
\(574\) 0 0
\(575\) −16.0000 + 12.0000i −0.667246 + 0.500435i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −27.7128 + 16.0000i −1.15370 + 0.666089i −0.949786 0.312900i \(-0.898699\pi\)
−0.203913 + 0.978989i \(0.565366\pi\)
\(578\) −11.2583 + 6.50000i −0.468285 + 0.270364i
\(579\) −2.00000 + 3.46410i −0.0831172 + 0.143963i
\(580\) 0 0
\(581\) 0 0
\(582\) 8.00000i 0.331611i
\(583\) 10.3923 + 6.00000i 0.430405 + 0.248495i
\(584\) −2.00000 3.46410i −0.0827606 0.143346i
\(585\) −13.3923 + 0.803848i −0.553704 + 0.0332350i
\(586\) −3.00000 + 5.19615i −0.123929 + 0.214651i
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 12.3205 + 18.6603i 0.507227 + 0.768231i
\(591\) −11.0000 19.0526i −0.452480 0.783718i
\(592\) 1.73205 1.00000i 0.0711868 0.0410997i
\(593\) −5.19615 3.00000i −0.213380 0.123195i 0.389501 0.921026i \(-0.372647\pi\)
−0.602881 + 0.797831i \(0.705981\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) −20.0000 −0.819232
\(597\) 0 0
\(598\) 20.7846 12.0000i 0.849946 0.490716i
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) −4.96410 + 0.598076i −0.202659 + 0.0244164i
\(601\) −2.00000 −0.0815817 −0.0407909 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 0 0
\(603\) 8.00000i 0.325785i
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) 0.937822 + 15.6244i 0.0381279 + 0.635220i
\(606\) 4.00000 + 6.92820i 0.162489 + 0.281439i
\(607\) 19.0526 + 11.0000i 0.773320 + 0.446476i 0.834058 0.551678i \(-0.186012\pi\)
−0.0607380 + 0.998154i \(0.519345\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −2.00000 + 4.00000i −0.0809776 + 0.161955i
\(611\) 24.0000 41.5692i 0.970936 1.68171i
\(612\) −1.73205 + 1.00000i −0.0700140 + 0.0404226i
\(613\) −22.5167 + 13.0000i −0.909439 + 0.525065i −0.880251 0.474509i \(-0.842626\pi\)
−0.0291886 + 0.999574i \(0.509292\pi\)
\(614\) 6.00000 10.3923i 0.242140 0.419399i
\(615\) −2.00000 + 4.00000i −0.0806478 + 0.161296i
\(616\) 0 0
\(617\) 2.00000i 0.0805170i 0.999189 + 0.0402585i \(0.0128181\pi\)
−0.999189 + 0.0402585i \(0.987182\pi\)
\(618\) −12.1244 7.00000i −0.487713 0.281581i
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 1.07180 + 17.8564i 0.0430444 + 0.717131i
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 6.00000 0.240192
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) 2.00000 + 3.46410i 0.0799361 + 0.138453i
\(627\) 0 0
\(628\) −19.0526 11.0000i −0.760280 0.438948i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 0 0
\(633\) −10.3923 + 6.00000i −0.413057 + 0.238479i
\(634\) −1.00000 1.73205i −0.0397151 0.0687885i
\(635\) −2.46410 3.73205i −0.0977849 0.148102i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 10.3923i 0.237356 0.411113i
\(640\) 2.23205 0.133975i 0.0882296 0.00529581i
\(641\) −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) 10.3923 + 6.00000i 0.410152 + 0.236801i
\(643\) 24.0000i 0.946468i −0.880937 0.473234i \(-0.843087\pi\)
0.880937 0.473234i \(-0.156913\pi\)
\(644\) 0 0
\(645\) 8.00000 + 4.00000i 0.315000 + 0.157500i
\(646\) 0 0
\(647\) 41.5692 24.0000i 1.63425 0.943537i 0.651494 0.758654i \(-0.274142\pi\)
0.982760 0.184884i \(-0.0591909\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −10.0000 + 17.3205i −0.392534 + 0.679889i
\(650\) 18.0000 + 24.0000i 0.706018 + 0.941357i
\(651\) 0 0
\(652\) 16.0000i 0.626608i
\(653\) 22.5167 + 13.0000i 0.881145 + 0.508729i 0.871036 0.491220i \(-0.163449\pi\)
0.0101092 + 0.999949i \(0.496782\pi\)
\(654\) −5.00000 8.66025i −0.195515 0.338643i
\(655\) −2.41154 40.1769i −0.0942268 1.56984i
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) 50.0000 1.94772 0.973862 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) −2.46410 3.73205i −0.0959150 0.145270i
\(661\) 1.00000 + 1.73205i 0.0388955 + 0.0673690i 0.884818 0.465937i \(-0.154283\pi\)
−0.845922 + 0.533306i \(0.820949\pi\)
\(662\) 6.92820 4.00000i 0.269272 0.155464i
\(663\) 10.3923 + 6.00000i 0.403604 + 0.233021i
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 10.3923 6.00000i 0.402090 0.232147i
\(669\) −13.0000 22.5167i −0.502609 0.870544i
\(670\) 14.9282 9.85641i 0.576727 0.380786i
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) 14.0000 24.2487i 0.539260 0.934025i
\(675\) 4.59808 + 1.96410i 0.176980 + 0.0755983i
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) 1.73205 + 1.00000i 0.0665681 + 0.0384331i 0.532915 0.846169i \(-0.321097\pi\)
−0.466347 + 0.884602i \(0.654430\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) 4.00000 + 2.00000i 0.153393 + 0.0766965i
\(681\) −14.0000 + 24.2487i −0.536481 + 0.929213i
\(682\) −13.8564 + 8.00000i −0.530589 + 0.306336i
\(683\) 3.46410 2.00000i 0.132550 0.0765279i −0.432259 0.901750i \(-0.642283\pi\)
0.564809 + 0.825222i \(0.308950\pi\)
\(684\) 0 0
\(685\) 18.0000 36.0000i 0.687745 1.37549i
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) −3.46410 2.00000i −0.132068 0.0762493i
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) −8.92820 + 0.535898i −0.339891 + 0.0204013i
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 37.3205 24.6410i 1.41565 0.934687i
\(696\) 0 0
\(697\) 3.46410 2.00000i 0.131212 0.0757554i
\(698\) 8.66025 + 5.00000i 0.327795 + 0.189253i
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) 32.0000 1.20862 0.604312 0.796748i \(-0.293448\pi\)
0.604312 + 0.796748i \(0.293448\pi\)
\(702\) −5.19615 3.00000i −0.196116 0.113228i
\(703\) 0 0
\(704\) 1.00000 + 1.73205i 0.0376889 + 0.0652791i
\(705\) −14.9282 + 9.85641i −0.562229 + 0.371214i
\(706\) −14.0000 −0.526897
\(707\) 0 0
\(708\) 10.0000i 0.375823i
\(709\) 15.0000 25.9808i 0.563337 0.975728i −0.433865 0.900978i \(-0.642851\pi\)
0.997202 0.0747503i \(-0.0238160\pi\)
\(710\) −26.7846 + 1.60770i −1.00521 + 0.0603357i
\(711\) 0 0
\(712\) 8.66025 + 5.00000i 0.324557 + 0.187383i
\(713\) 32.0000i 1.19841i
\(714\) 0 0
\(715\) −12.0000 + 24.0000i −0.448775 + 0.897549i
\(716\) −5.00000 + 8.66025i −0.186859 + 0.323649i
\(717\) 17.3205 10.0000i 0.646846 0.373457i
\(718\) 0 0
\(719\) 20.0000 34.6410i 0.745874 1.29189i −0.203911 0.978989i \(-0.565365\pi\)
0.949785 0.312903i \(-0.101301\pi\)
\(720\) −2.00000 1.00000i −0.0745356 0.0372678i
\(721\) 0 0
\(722\) 19.0000i 0.707107i
\(723\) −19.0526 11.0000i −0.708572 0.409094i
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 0 0
\(726\) −3.50000 + 6.06218i −0.129897 + 0.224989i
\(727\) 18.0000i 0.667583i 0.942647 + 0.333792i \(0.108328\pi\)
−0.942647 + 0.333792i \(0.891672\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 7.46410 4.92820i 0.276259 0.182401i
\(731\) −4.00000 6.92820i −0.147945 0.256249i
\(732\) −1.73205 + 1.00000i −0.0640184 + 0.0369611i
\(733\) 12.1244 + 7.00000i 0.447823 + 0.258551i 0.706910 0.707303i \(-0.250088\pi\)
−0.259087 + 0.965854i \(0.583422\pi\)
\(734\) −2.00000 −0.0738213
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 13.8564 + 8.00000i 0.510407 + 0.294684i
\(738\) −1.73205 + 1.00000i −0.0637577 + 0.0368105i
\(739\) 20.0000 + 34.6410i 0.735712 + 1.27429i 0.954410 + 0.298498i \(0.0964856\pi\)
−0.218698 + 0.975793i \(0.570181\pi\)
\(740\) 2.46410 + 3.73205i 0.0905822 + 0.137193i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000i 0.880475i 0.897881 + 0.440237i \(0.145106\pi\)
−0.897881 + 0.440237i \(0.854894\pi\)
\(744\) −4.00000 + 6.92820i −0.146647 + 0.254000i
\(745\) −2.67949 44.6410i −0.0981690 1.63552i
\(746\) 3.00000 + 5.19615i 0.109838 + 0.190245i
\(747\) −3.46410 2.00000i −0.126745 0.0731762i
\(748\) 4.00000i 0.146254i
\(749\) 0 0
\(750\) −2.00000 11.0000i −0.0730297 0.401663i
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 6.92820 4.00000i 0.252646 0.145865i
\(753\) −15.5885 + 9.00000i −0.568075 + 0.327978i
\(754\) 0 0
\(755\) −16.0000 8.00000i −0.582300 0.291150i
\(756\) 0 0
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) −17.3205 10.0000i −0.629109 0.363216i
\(759\) −4.00000 6.92820i −0.145191 0.251478i
\(760\) 0 0
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) −2.46410 3.73205i −0.0890898 0.134933i
\(766\) −8.00000 13.8564i −0.289052 0.500652i
\(767\) 51.9615 30.0000i 1.87622 1.08324i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 3.46410 + 2.00000i 0.124676 + 0.0719816i
\(773\) −46.7654 + 27.0000i −1.68203 + 0.971123i −0.721726 + 0.692179i \(0.756651\pi\)
−0.960307 + 0.278944i \(0.910016\pi\)
\(774\) 2.00000 + 3.46410i 0.0718885 + 0.124515i
\(775\) −39.7128 + 4.78461i −1.42653 + 0.171868i
\(776\) −8.00000 −0.287183
\(777\) 0 0
\(778\) 20.0000i 0.717035i
\(779\) 0 0
\(780\) 0.803848 + 13.3923i 0.0287824 + 0.479521i
\(781\) −12.0000 20.7846i −0.429394 0.743732i
\(782\) 6.92820 + 4.00000i 0.247752 + 0.143040i
\(783\) 0 0
\(784\) 0 0
\(785\) 22.0000 44.0000i 0.785214 1.57043i
\(786\) 9.00000 15.5885i 0.321019 0.556022i
\(787\) −27.7128 + 16.0000i −0.987855 + 0.570338i −0.904632 0.426193i \(-0.859855\pi\)
−0.0832226 + 0.996531i \(0.526521\pi\)
\(788\) −19.0526 + 11.0000i −0.678719 + 0.391859i
\(789\) −2.00000 + 3.46410i −0.0712019 + 0.123325i
\(790\) 0 0
\(791\) 0 0
\(792\) 2.00000i 0.0710669i
\(793\) 10.3923 + 6.00000i 0.369042 + 0.213066i
\(794\) 1.00000 + 1.73205i 0.0354887 + 0.0614682i
\(795\) 0.803848 + 13.3923i 0.0285095 + 0.474976i
\(796\) 0 0
\(797\) 2.00000i 0.0708436i −0.999372 0.0354218i \(-0.988723\pi\)
0.999372 0.0354218i \(-0.0112775\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 0.598076 + 4.96410i 0.0211452 + 0.175507i
\(801\) −5.00000 8.66025i −0.176666 0.305995i
\(802\) −19.0526 + 11.0000i −0.672769 + 0.388424i
\(803\) 6.92820 + 4.00000i 0.244491 + 0.141157i
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) 48.0000 1.69073
\(807\) 0 0
\(808\) 6.92820 4.00000i 0.243733 0.140720i
\(809\) −15.0000 25.9808i −0.527372 0.913435i −0.999491 0.0319002i \(-0.989844\pi\)
0.472119 0.881535i \(-0.343489\pi\)
\(810\) 1.23205 + 1.86603i 0.0432899 + 0.0655654i
\(811\) −52.0000 −1.82597 −0.912983 0.407997i \(-0.866228\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 0 0
\(813\) 8.00000i 0.280572i
\(814\) −2.00000 + 3.46410i −0.0701000 + 0.121417i
\(815\) −35.7128 + 2.14359i −1.25097 + 0.0750868i
\(816\) 1.00000 + 1.73205i 0.0350070 + 0.0606339i
\(817\) 0 0
\(818\) 10.0000i 0.349642i
\(819\) 0 0
\(820\) 4.00000 + 2.00000i 0.139686 + 0.0698430i
\(821\) 4.00000 6.92820i 0.139601 0.241796i −0.787745 0.616002i \(-0.788751\pi\)
0.927346 + 0.374206i \(0.122085\pi\)
\(822\) 15.5885 9.00000i 0.543710 0.313911i
\(823\) −5.19615 + 3.00000i −0.181126 + 0.104573i −0.587822 0.808990i \(-0.700014\pi\)
0.406695 + 0.913564i \(0.366681\pi\)
\(824\) −7.00000 + 12.1244i −0.243857 + 0.422372i
\(825\) 8.00000 6.00000i 0.278524 0.208893i
\(826\) 0 0
\(827\) 28.0000i 0.973655i −0.873498 0.486828i \(-0.838154\pi\)
0.873498 0.486828i \(-0.161846\pi\)
\(828\) −3.46410 2.00000i −0.120386 0.0695048i
\(829\) 15.0000 + 25.9808i 0.520972 + 0.902349i 0.999703 + 0.0243876i \(0.00776357\pi\)
−0.478731 + 0.877962i \(0.658903\pi\)
\(830\) 0.535898 + 8.92820i 0.0186013 + 0.309902i
\(831\) −1.00000 + 1.73205i −0.0346896 + 0.0600842i
\(832\) 6.00000i 0.208013i
\(833\) 0 0
\(834\) 20.0000 0.692543
\(835\) 14.7846 + 22.3923i 0.511643 + 0.774918i
\(836\) 0 0
\(837\) 6.92820 4.00000i 0.239474 0.138260i
\(838\) −8.66025 5.00000i −0.299164 0.172722i
\(839\) 40.0000 1.38095 0.690477 0.723355i \(-0.257401\pi\)
0.690477 + 0.723355i \(0.257401\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 19.0526 + 11.0000i 0.656595 + 0.379085i
\(843\) 15.5885 9.00000i 0.536895 0.309976i
\(844\) 6.00000 + 10.3923i 0.206529 + 0.357718i
\(845\) 42.9186 28.3372i 1.47644 0.974828i
\(846\) −8.00000 −0.275046
\(847\) 0 0
\(848\) 6.00000i 0.206041i
\(849\) −8.00000 + 13.8564i −0.274559 + 0.475551i
\(850\) −3.92820 + 9.19615i −0.134736 + 0.315425i
\(851\) 4.00000 + 6.92820i 0.137118 + 0.237496i
\(852\) −10.3923 6.00000i −0.356034 0.205557i
\(853\) 14.0000i 0.479351i −0.970853 0.239675i \(-0.922959\pi\)
0.970853 0.239675i \(-0.0770410\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 6.00000 10.3923i 0.205076 0.355202i
\(857\) −36.3731 + 21.0000i −1.24248 + 0.717346i −0.969599 0.244701i \(-0.921310\pi\)
−0.272882 + 0.962048i \(0.587977\pi\)
\(858\) −10.3923 + 6.00000i −0.354787 + 0.204837i
\(859\) −10.0000 + 17.3205i −0.341196 + 0.590968i −0.984655 0.174512i \(-0.944165\pi\)
0.643459 + 0.765480i \(0.277499\pi\)
\(860\) 4.00000 8.00000i 0.136399 0.272798i
\(861\) 0 0
\(862\) 32.0000i 1.08992i
\(863\) 31.1769 + 18.0000i 1.06127 + 0.612727i 0.925785 0.378052i \(-0.123406\pi\)
0.135490 + 0.990779i \(0.456739\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) −31.2487 + 1.87564i −1.06249 + 0.0637738i
\(866\) 2.00000 3.46410i 0.0679628 0.117715i
\(867\) 13.0000i 0.441503i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −24.0000 41.5692i −0.813209 1.40852i
\(872\) −8.66025 + 5.00000i −0.293273 + 0.169321i
\(873\) 6.92820 + 4.00000i 0.234484 + 0.135379i
\(874\) 0 0
\(875\) 0 0
\(876\) 4.00000 0.135147
\(877\) −19.0526 11.0000i −0.643359 0.371444i 0.142548 0.989788i \(-0.454470\pi\)
−0.785907 + 0.618344i \(0.787804\pi\)
\(878\) 0 0
\(879\) −3.00000 5.19615i −0.101187 0.175262i
\(880\) −3.73205 + 2.46410i −0.125807 + 0.0830648i
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) 24.0000i 0.807664i 0.914833 + 0.403832i \(0.132322\pi\)
−0.914833 + 0.403832i \(0.867678\pi\)
\(884\) 6.00000 10.3923i 0.201802 0.349531i
\(885\) −22.3205 + 1.33975i −0.750296 + 0.0450351i
\(886\) 18.0000 + 31.1769i 0.604722 + 1.04741i
\(887\) 10.3923 + 6.00000i 0.348939 + 0.201460i 0.664218 0.747539i \(-0.268765\pi\)
−0.315279 + 0.948999i \(0.602098\pi\)
\(888\) 2.00000i 0.0671156i
\(889\) 0 0
\(890\) −10.0000 + 20.0000i −0.335201 + 0.670402i
\(891\) −1.00000 + 1.73205i −0.0335013 + 0.0580259i
\(892\) −22.5167 + 13.0000i −0.753914 + 0.435272i
\(893\) 0 0
\(894\) 10.0000 17.3205i 0.334450 0.579284i
\(895\) −20.0000 10.0000i −0.668526 0.334263i
\(896\) 0 0
\(897\) 24.0000i 0.801337i
\(898\) −25.9808 15.0000i −0.866989 0.500556i
\(899\) 0 0
\(900\) 1.96410 4.59808i 0.0654701 0.153269i
\(901\) 6.00000 10.3923i 0.199889 0.346218i
\(902\) 4.00000i 0.133185i
\(903\) 0 0
\(904\) 6.00000 0.199557
\(905\) 3.73205 2.46410i 0.124058 0.0819095i
\(906\) −4.00000 6.92820i −0.132891 0.230174i
\(907\) 10.3923 6.00000i 0.345071 0.199227i −0.317441 0.948278i \(-0.602824\pi\)
0.662512 + 0.749051i \(0.269490\pi\)
\(908\) 24.2487 + 14.0000i 0.804722 + 0.464606i
\(909\) −8.00000 −0.265343
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 0 0
\(913\) −6.92820 + 4.00000i −0.229290 + 0.132381i
\(914\) −16.0000 27.7128i −0.529233 0.916658i
\(915\) −2.46410 3.73205i −0.0814607 0.123378i
\(916\) 10.0000 0.330409
\(917\) 0 0
\(918\) 2.00000i 0.0660098i
\(919\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(920\) 0.535898 + 8.92820i 0.0176680 + 0.294354i
\(921\) 6.00000 + 10.3923i 0.197707 + 0.342438i
\(922\) −10.3923 6.00000i −0.342252 0.197599i
\(923\) 72.0000i 2.36991i
\(924\) 0 0
\(925\) −8.00000 + 6.00000i −0.263038 + 0.197279i
\(926\) 3.00000 5.19615i 0.0985861 0.170756i
\(927\) 12.1244 7.00000i 0.398216 0.229910i
\(928\) 0 0
\(929\) −15.0000 + 25.9808i −0.492134 + 0.852401i −0.999959 0.00905914i \(-0.997116\pi\)
0.507825 + 0.861460i \(0.330450\pi\)
\(930\) −16.0000 8.00000i −0.524661 0.262330i
\(931\) 0 0
\(932\) 14.0000i 0.458585i
\(933\) −10.3923 6.00000i −0.340229 0.196431i
\(934\) 6.00000 + 10.3923i 0.196326 + 0.340047i
\(935\) −8.92820 + 0.535898i −0.291983 + 0.0175258i
\(936\) −3.00000 + 5.19615i −0.0980581 + 0.169842i
\(937\) 8.00000i 0.261349i 0.991425 + 0.130674i \(0.0417142\pi\)
−0.991425 + 0.130674i \(0.958286\pi\)
\(938\) 0 0
\(939\) −4.00000 −0.130535
\(940\) 9.85641 + 14.9282i 0.321481 + 0.486904i
\(941\) −14.0000 24.2487i −0.456387 0.790485i 0.542380 0.840133i \(-0.317523\pi\)
−0.998767 + 0.0496480i \(0.984190\pi\)
\(942\) 19.0526 11.0000i 0.620766 0.358399i
\(943\) 6.92820 + 4.00000i 0.225613 + 0.130258i
\(944\) 10.0000 0.325472
\(945\) 0 0
\(946\) 8.00000 0.260102
\(947\) −10.3923 6.00000i −0.337705 0.194974i 0.321552 0.946892i \(-0.395796\pi\)
−0.659256 + 0.751918i \(0.729129\pi\)
\(948\) 0 0
\(949\) −12.0000 20.7846i −0.389536 0.674697i
\(950\) 0 0
\(951\) 2.00000 0.0648544
\(952\) 0 0
\(953\) 46.0000i 1.49009i −0.667016 0.745043i \(-0.732429\pi\)
0.667016 0.745043i \(-0.267571\pi\)
\(954\) −3.00000 + 5.19615i −0.0971286 + 0.168232i
\(955\) −1.60770 26.7846i −0.0520238 0.866730i
\(956\) −10.0000 17.3205i −0.323423 0.560185i
\(957\) 0 0
\(958\) 20.0000i 0.646171i
\(959\) 0 0
\(960\) −1.00000 + 2.00000i −0.0322749 + 0.0645497i
\(961\) −16.5000 + 28.5788i −0.532258 + 0.921898i
\(962\) 10.3923 6.00000i 0.335061 0.193448i
\(963\) −10.3923 + 6.00000i −0.334887 + 0.193347i
\(964\) −11.0000 + 19.0526i −0.354286 + 0.613642i
\(965\) −4.00000 + 8.00000i −0.128765 + 0.257529i
\(966\) 0 0
\(967\) 38.0000i 1.22200i −0.791632 0.610999i \(-0.790768\pi\)
0.791632 0.610999i \(-0.209232\pi\)
\(968\) 6.06218 + 3.50000i 0.194846 + 0.112494i
\(969\) 0 0
\(970\) −1.07180 17.8564i −0.0344133 0.573335i
\(971\) −9.00000 + 15.5885i −0.288824 + 0.500257i −0.973529 0.228562i \(-0.926597\pi\)
0.684706 + 0.728820i \(0.259931\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 0 0
\(974\) −18.0000 −0.576757
\(975\) −29.7846 + 3.58846i −0.953871 + 0.114923i
\(976\) 1.00000 + 1.73205i 0.0320092 + 0.0554416i
\(977\) 36.3731 21.0000i 1.16368 0.671850i 0.211495 0.977379i \(-0.432167\pi\)
0.952183 + 0.305530i \(0.0988335\pi\)
\(978\) −13.8564 8.00000i −0.443079 0.255812i
\(979\) −20.0000 −0.639203
\(980\) 0 0
\(981\) 10.0000 0.319275
\(982\) −15.5885 9.00000i −0.497448 0.287202i
\(983\) 13.8564 8.00000i 0.441951 0.255160i −0.262474 0.964939i \(-0.584538\pi\)
0.704425 + 0.709779i \(0.251205\pi\)
\(984\) 1.00000 + 1.73205i 0.0318788 + 0.0552158i
\(985\) −27.1051 41.0526i −0.863641 1.30804i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 8.00000 13.8564i 0.254385 0.440608i
\(990\) 4.46410 0.267949i 0.141878 0.00851598i
\(991\) 4.00000 + 6.92820i 0.127064 + 0.220082i 0.922538 0.385906i \(-0.126111\pi\)
−0.795474 + 0.605988i \(0.792778\pi\)
\(992\) 6.92820 + 4.00000i 0.219971 + 0.127000i
\(993\) 8.00000i 0.253872i
\(994\) 0 0
\(995\) 0 0
\(996\) −2.00000 + 3.46410i −0.0633724 + 0.109764i
\(997\) 15.5885 9.00000i 0.493691 0.285033i −0.232413 0.972617i \(-0.574662\pi\)
0.726105 + 0.687584i \(0.241329\pi\)
\(998\) 0 0
\(999\) 1.00000 1.73205i 0.0316386 0.0547997i
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 1470.2.n.a.79.2 4
5.4 even 2 inner 1470.2.n.a.79.1 4
7.2 even 3 1470.2.g.g.589.1 2
7.3 odd 6 1470.2.n.h.949.1 4
7.4 even 3 inner 1470.2.n.a.949.1 4
7.5 odd 6 30.2.c.a.19.1 2
7.6 odd 2 1470.2.n.h.79.2 4
21.5 even 6 90.2.c.a.19.2 2
28.19 even 6 240.2.f.a.49.1 2
35.2 odd 12 7350.2.a.cc.1.1 1
35.4 even 6 inner 1470.2.n.a.949.2 4
35.9 even 6 1470.2.g.g.589.2 2
35.12 even 12 150.2.a.c.1.1 1
35.19 odd 6 30.2.c.a.19.2 yes 2
35.23 odd 12 7350.2.a.bg.1.1 1
35.24 odd 6 1470.2.n.h.949.2 4
35.33 even 12 150.2.a.a.1.1 1
35.34 odd 2 1470.2.n.h.79.1 4
56.5 odd 6 960.2.f.h.769.1 2
56.19 even 6 960.2.f.i.769.2 2
63.5 even 6 810.2.i.b.379.1 4
63.40 odd 6 810.2.i.e.379.2 4
63.47 even 6 810.2.i.b.109.2 4
63.61 odd 6 810.2.i.e.109.1 4
84.47 odd 6 720.2.f.f.289.2 2
105.47 odd 12 450.2.a.b.1.1 1
105.68 odd 12 450.2.a.f.1.1 1
105.89 even 6 90.2.c.a.19.1 2
112.5 odd 12 3840.2.d.y.2689.1 2
112.19 even 12 3840.2.d.x.2689.2 2
112.61 odd 12 3840.2.d.g.2689.2 2
112.75 even 12 3840.2.d.j.2689.1 2
140.19 even 6 240.2.f.a.49.2 2
140.47 odd 12 1200.2.a.g.1.1 1
140.103 odd 12 1200.2.a.m.1.1 1
168.5 even 6 2880.2.f.e.1729.1 2
168.131 odd 6 2880.2.f.c.1729.1 2
280.19 even 6 960.2.f.i.769.1 2
280.117 even 12 4800.2.a.l.1.1 1
280.173 even 12 4800.2.a.cg.1.1 1
280.187 odd 12 4800.2.a.cj.1.1 1
280.229 odd 6 960.2.f.h.769.2 2
280.243 odd 12 4800.2.a.m.1.1 1
315.124 odd 6 810.2.i.e.109.2 4
315.194 even 6 810.2.i.b.379.2 4
315.229 odd 6 810.2.i.e.379.1 4
315.299 even 6 810.2.i.b.109.1 4
420.47 even 12 3600.2.a.bg.1.1 1
420.299 odd 6 720.2.f.f.289.1 2
420.383 even 12 3600.2.a.o.1.1 1
560.19 even 12 3840.2.d.j.2689.2 2
560.229 odd 12 3840.2.d.g.2689.1 2
560.299 even 12 3840.2.d.x.2689.1 2
560.509 odd 12 3840.2.d.y.2689.2 2
840.299 odd 6 2880.2.f.c.1729.2 2
840.509 even 6 2880.2.f.e.1729.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.2.c.a.19.1 2 7.5 odd 6
30.2.c.a.19.2 yes 2 35.19 odd 6
90.2.c.a.19.1 2 105.89 even 6
90.2.c.a.19.2 2 21.5 even 6
150.2.a.a.1.1 1 35.33 even 12
150.2.a.c.1.1 1 35.12 even 12
240.2.f.a.49.1 2 28.19 even 6
240.2.f.a.49.2 2 140.19 even 6
450.2.a.b.1.1 1 105.47 odd 12
450.2.a.f.1.1 1 105.68 odd 12
720.2.f.f.289.1 2 420.299 odd 6
720.2.f.f.289.2 2 84.47 odd 6
810.2.i.b.109.1 4 315.299 even 6
810.2.i.b.109.2 4 63.47 even 6
810.2.i.b.379.1 4 63.5 even 6
810.2.i.b.379.2 4 315.194 even 6
810.2.i.e.109.1 4 63.61 odd 6
810.2.i.e.109.2 4 315.124 odd 6
810.2.i.e.379.1 4 315.229 odd 6
810.2.i.e.379.2 4 63.40 odd 6
960.2.f.h.769.1 2 56.5 odd 6
960.2.f.h.769.2 2 280.229 odd 6
960.2.f.i.769.1 2 280.19 even 6
960.2.f.i.769.2 2 56.19 even 6
1200.2.a.g.1.1 1 140.47 odd 12
1200.2.a.m.1.1 1 140.103 odd 12
1470.2.g.g.589.1 2 7.2 even 3
1470.2.g.g.589.2 2 35.9 even 6
1470.2.n.a.79.1 4 5.4 even 2 inner
1470.2.n.a.79.2 4 1.1 even 1 trivial
1470.2.n.a.949.1 4 7.4 even 3 inner
1470.2.n.a.949.2 4 35.4 even 6 inner
1470.2.n.h.79.1 4 35.34 odd 2
1470.2.n.h.79.2 4 7.6 odd 2
1470.2.n.h.949.1 4 7.3 odd 6
1470.2.n.h.949.2 4 35.24 odd 6
2880.2.f.c.1729.1 2 168.131 odd 6
2880.2.f.c.1729.2 2 840.299 odd 6
2880.2.f.e.1729.1 2 168.5 even 6
2880.2.f.e.1729.2 2 840.509 even 6
3600.2.a.o.1.1 1 420.383 even 12
3600.2.a.bg.1.1 1 420.47 even 12
3840.2.d.g.2689.1 2 560.229 odd 12
3840.2.d.g.2689.2 2 112.61 odd 12
3840.2.d.j.2689.1 2 112.75 even 12
3840.2.d.j.2689.2 2 560.19 even 12
3840.2.d.x.2689.1 2 560.299 even 12
3840.2.d.x.2689.2 2 112.19 even 12
3840.2.d.y.2689.1 2 112.5 odd 12
3840.2.d.y.2689.2 2 560.509 odd 12
4800.2.a.l.1.1 1 280.117 even 12
4800.2.a.m.1.1 1 280.243 odd 12
4800.2.a.cg.1.1 1 280.173 even 12
4800.2.a.cj.1.1 1 280.187 odd 12
7350.2.a.bg.1.1 1 35.23 odd 12
7350.2.a.cc.1.1 1 35.2 odd 12