Properties

Label 350.2.j.f.249.1
Level $350$
Weight $2$
Character 350.249
Analytic conductor $2.795$
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] = [350,2,Mod(149,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("350.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.j (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: \(2.79476407074\)
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 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 249.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 350.249
Dual form 350.2.j.f.149.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-2.59808 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-2.59808 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(3.00000 + 5.19615i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-2.59808 + 1.50000i) q^{12} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-5.19615 - 3.00000i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-7.50000 - 2.59808i) q^{21} +2.00000i q^{22} +(2.59808 - 1.50000i) q^{23} +(1.50000 - 2.59808i) q^{24} -9.00000i q^{27} +(0.866025 - 2.50000i) q^{28} -9.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.19615 + 3.00000i) q^{33} +4.00000 q^{34} +6.00000 q^{36} +(3.46410 - 2.00000i) q^{37} +(5.19615 + 3.00000i) q^{38} -7.00000 q^{41} +(7.79423 - 1.50000i) q^{42} -5.00000i q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-6.92820 + 4.00000i) q^{47} +3.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(6.00000 + 10.3923i) q^{51} +(1.73205 + 1.00000i) q^{53} +(4.50000 + 7.79423i) q^{54} +(0.500000 + 2.59808i) q^{56} +18.0000i q^{57} +(7.79423 - 4.50000i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-0.500000 - 0.866025i) q^{61} +4.00000i q^{62} +(10.3923 + 12.0000i) q^{63} -1.00000 q^{64} +(3.00000 - 5.19615i) q^{66} +(-7.79423 - 4.50000i) q^{67} +(-3.46410 + 2.00000i) q^{68} -9.00000 q^{69} +2.00000 q^{71} +(-5.19615 + 3.00000i) q^{72} +(3.46410 + 2.00000i) q^{73} +(-2.00000 + 3.46410i) q^{74} -6.00000 q^{76} +(1.73205 - 5.00000i) q^{77} +(5.00000 + 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(6.06218 - 3.50000i) q^{82} -7.00000i q^{83} +(-6.00000 + 5.19615i) q^{84} +(2.50000 + 4.33013i) q^{86} +(23.3827 + 13.5000i) q^{87} +(1.73205 + 1.00000i) q^{88} +(0.500000 + 0.866025i) q^{89} -3.00000i q^{92} +(-10.3923 + 6.00000i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-1.50000 - 2.59808i) q^{96} -14.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} + 12 q^{6} + 12 q^{9} + 4 q^{11} - 8 q^{14} - 2 q^{16} - 12 q^{19} - 30 q^{21} + 6 q^{24} - 36 q^{29} + 8 q^{31} + 16 q^{34} + 24 q^{36} - 28 q^{41} - 4 q^{44} - 6 q^{46} + 26 q^{49} + 24 q^{51} + 18 q^{54} + 2 q^{56} + 20 q^{59} - 2 q^{61} - 4 q^{64} + 12 q^{66} - 36 q^{69} + 8 q^{71} - 8 q^{74} - 24 q^{76} + 20 q^{79} - 18 q^{81} - 24 q^{84} + 10 q^{86} + 2 q^{89} + 16 q^{94} - 6 q^{96} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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
\(3\) −2.59808 1.50000i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 3.00000 1.22474
\(7\) 2.59808 0.500000i 0.981981 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 3.00000 + 5.19615i 1.00000 + 1.73205i
\(10\) 0 0
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) −2.59808 + 1.50000i −0.750000 + 0.433013i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.46410 2.00000i −0.840168 0.485071i 0.0171533 0.999853i \(-0.494540\pi\)
−0.857321 + 0.514782i \(0.827873\pi\)
\(18\) −5.19615 3.00000i −1.22474 0.707107i
\(19\) −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i \(-0.925047\pi\)
0.284157 0.958778i \(-0.408286\pi\)
\(20\) 0 0
\(21\) −7.50000 2.59808i −1.63663 0.566947i
\(22\) 2.00000i 0.426401i
\(23\) 2.59808 1.50000i 0.541736 0.312772i −0.204046 0.978961i \(-0.565409\pi\)
0.745782 + 0.666190i \(0.232076\pi\)
\(24\) 1.50000 2.59808i 0.306186 0.530330i
\(25\) 0 0
\(26\) 0 0
\(27\) 9.00000i 1.73205i
\(28\) 0.866025 2.50000i 0.163663 0.472456i
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −5.19615 + 3.00000i −0.904534 + 0.522233i
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 6.00000 1.00000
\(37\) 3.46410 2.00000i 0.569495 0.328798i −0.187453 0.982274i \(-0.560023\pi\)
0.756948 + 0.653476i \(0.226690\pi\)
\(38\) 5.19615 + 3.00000i 0.842927 + 0.486664i
\(39\) 0 0
\(40\) 0 0
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 7.79423 1.50000i 1.20268 0.231455i
\(43\) 5.00000i 0.762493i −0.924473 0.381246i \(-0.875495\pi\)
0.924473 0.381246i \(-0.124505\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 0 0
\(46\) −1.50000 + 2.59808i −0.221163 + 0.383065i
\(47\) −6.92820 + 4.00000i −1.01058 + 0.583460i −0.911362 0.411606i \(-0.864968\pi\)
−0.0992202 + 0.995066i \(0.531635\pi\)
\(48\) 3.00000i 0.433013i
\(49\) 6.50000 2.59808i 0.928571 0.371154i
\(50\) 0 0
\(51\) 6.00000 + 10.3923i 0.840168 + 1.45521i
\(52\) 0 0
\(53\) 1.73205 + 1.00000i 0.237915 + 0.137361i 0.614218 0.789136i \(-0.289471\pi\)
−0.376303 + 0.926497i \(0.622805\pi\)
\(54\) 4.50000 + 7.79423i 0.612372 + 1.06066i
\(55\) 0 0
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) 18.0000i 2.38416i
\(58\) 7.79423 4.50000i 1.02343 0.590879i
\(59\) 5.00000 8.66025i 0.650945 1.12747i −0.331949 0.943297i \(-0.607706\pi\)
0.982894 0.184172i \(-0.0589603\pi\)
\(60\) 0 0
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 10.3923 + 12.0000i 1.30931 + 1.51186i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) −7.79423 4.50000i −0.952217 0.549762i −0.0584478 0.998290i \(-0.518615\pi\)
−0.893769 + 0.448528i \(0.851948\pi\)
\(68\) −3.46410 + 2.00000i −0.420084 + 0.242536i
\(69\) −9.00000 −1.08347
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −5.19615 + 3.00000i −0.612372 + 0.353553i
\(73\) 3.46410 + 2.00000i 0.405442 + 0.234082i 0.688830 0.724923i \(-0.258125\pi\)
−0.283387 + 0.959006i \(0.591458\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 1.73205 5.00000i 0.197386 0.569803i
\(78\) 0 0
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 6.06218 3.50000i 0.669456 0.386510i
\(83\) 7.00000i 0.768350i −0.923260 0.384175i \(-0.874486\pi\)
0.923260 0.384175i \(-0.125514\pi\)
\(84\) −6.00000 + 5.19615i −0.654654 + 0.566947i
\(85\) 0 0
\(86\) 2.50000 + 4.33013i 0.269582 + 0.466930i
\(87\) 23.3827 + 13.5000i 2.50689 + 1.44735i
\(88\) 1.73205 + 1.00000i 0.184637 + 0.106600i
\(89\) 0.500000 + 0.866025i 0.0529999 + 0.0917985i 0.891308 0.453398i \(-0.149788\pi\)
−0.838308 + 0.545197i \(0.816455\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.00000i 0.312772i
\(93\) −10.3923 + 6.00000i −1.07763 + 0.622171i
\(94\) 4.00000 6.92820i 0.412568 0.714590i
\(95\) 0 0
\(96\) −1.50000 2.59808i −0.153093 0.265165i
\(97\) 14.0000i 1.42148i −0.703452 0.710742i \(-0.748359\pi\)
0.703452 0.710742i \(-0.251641\pi\)
\(98\) −4.33013 + 5.50000i −0.437409 + 0.555584i
\(99\) 12.0000 1.20605
\(100\) 0 0
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) −10.3923 6.00000i −1.02899 0.594089i
\(103\) 0.866025 0.500000i 0.0853320 0.0492665i −0.456727 0.889607i \(-0.650978\pi\)
0.542059 + 0.840341i \(0.317645\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −2.59808 + 1.50000i −0.251166 + 0.145010i −0.620298 0.784366i \(-0.712988\pi\)
0.369132 + 0.929377i \(0.379655\pi\)
\(108\) −7.79423 4.50000i −0.750000 0.433013i
\(109\) −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i \(-0.975180\pi\)
0.565940 + 0.824447i \(0.308513\pi\)
\(110\) 0 0
\(111\) −12.0000 −1.13899
\(112\) −1.73205 2.00000i −0.163663 0.188982i
\(113\) 2.00000i 0.188144i 0.995565 + 0.0940721i \(0.0299884\pi\)
−0.995565 + 0.0940721i \(0.970012\pi\)
\(114\) −9.00000 15.5885i −0.842927 1.45999i
\(115\) 0 0
\(116\) −4.50000 + 7.79423i −0.417815 + 0.723676i
\(117\) 0 0
\(118\) 10.0000i 0.920575i
\(119\) −10.0000 3.46410i −0.916698 0.317554i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0.866025 + 0.500000i 0.0784063 + 0.0452679i
\(123\) 18.1865 + 10.5000i 1.63982 + 0.946753i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 0 0
\(126\) −15.0000 5.19615i −1.33631 0.462910i
\(127\) 16.0000i 1.41977i −0.704317 0.709885i \(-0.748747\pi\)
0.704317 0.709885i \(-0.251253\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −7.50000 + 12.9904i −0.660338 + 1.14374i
\(130\) 0 0
\(131\) −4.00000 6.92820i −0.349482 0.605320i 0.636676 0.771132i \(-0.280309\pi\)
−0.986157 + 0.165812i \(0.946976\pi\)
\(132\) 6.00000i 0.522233i
\(133\) −10.3923 12.0000i −0.901127 1.04053i
\(134\) 9.00000 0.777482
\(135\) 0 0
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) 7.79423 4.50000i 0.663489 0.383065i
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 24.0000 2.02116
\(142\) −1.73205 + 1.00000i −0.145350 + 0.0839181i
\(143\) 0 0
\(144\) 3.00000 5.19615i 0.250000 0.433013i
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) −20.7846 3.00000i −1.71429 0.247436i
\(148\) 4.00000i 0.328798i
\(149\) 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i \(-0.127452\pi\)
−0.798019 + 0.602632i \(0.794119\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 5.19615 3.00000i 0.421464 0.243332i
\(153\) 24.0000i 1.94029i
\(154\) 1.00000 + 5.19615i 0.0805823 + 0.418718i
\(155\) 0 0
\(156\) 0 0
\(157\) 8.66025 + 5.00000i 0.691164 + 0.399043i 0.804048 0.594565i \(-0.202676\pi\)
−0.112884 + 0.993608i \(0.536009\pi\)
\(158\) −8.66025 5.00000i −0.688973 0.397779i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) 0 0
\(161\) 6.00000 5.19615i 0.472866 0.409514i
\(162\) 9.00000i 0.707107i
\(163\) −3.46410 + 2.00000i −0.271329 + 0.156652i −0.629492 0.777007i \(-0.716737\pi\)
0.358162 + 0.933659i \(0.383403\pi\)
\(164\) −3.50000 + 6.06218i −0.273304 + 0.473377i
\(165\) 0 0
\(166\) 3.50000 + 6.06218i 0.271653 + 0.470516i
\(167\) 21.0000i 1.62503i 0.582941 + 0.812514i \(0.301902\pi\)
−0.582941 + 0.812514i \(0.698098\pi\)
\(168\) 2.59808 7.50000i 0.200446 0.578638i
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 18.0000 31.1769i 1.37649 2.38416i
\(172\) −4.33013 2.50000i −0.330169 0.190623i
\(173\) 6.92820 4.00000i 0.526742 0.304114i −0.212947 0.977064i \(-0.568306\pi\)
0.739689 + 0.672949i \(0.234973\pi\)
\(174\) −27.0000 −2.04686
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) −25.9808 + 15.0000i −1.95283 + 1.12747i
\(178\) −0.866025 0.500000i −0.0649113 0.0374766i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) 3.00000i 0.221766i
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) 0 0
\(186\) 6.00000 10.3923i 0.439941 0.762001i
\(187\) −6.92820 + 4.00000i −0.506640 + 0.292509i
\(188\) 8.00000i 0.583460i
\(189\) −4.50000 23.3827i −0.327327 1.70084i
\(190\) 0 0
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 2.59808 + 1.50000i 0.187500 + 0.108253i
\(193\) −22.5167 13.0000i −1.62078 0.935760i −0.986710 0.162488i \(-0.948048\pi\)
−0.634074 0.773272i \(-0.718619\pi\)
\(194\) 7.00000 + 12.1244i 0.502571 + 0.870478i
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) −10.3923 + 6.00000i −0.738549 + 0.426401i
\(199\) −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 0 0
\(201\) 13.5000 + 23.3827i 0.952217 + 1.64929i
\(202\) 3.00000i 0.211079i
\(203\) −23.3827 + 4.50000i −1.64114 + 0.315838i
\(204\) 12.0000 0.840168
\(205\) 0 0
\(206\) −0.500000 + 0.866025i −0.0348367 + 0.0603388i
\(207\) 15.5885 + 9.00000i 1.08347 + 0.625543i
\(208\) 0 0
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) −26.0000 −1.78991 −0.894957 0.446153i \(-0.852794\pi\)
−0.894957 + 0.446153i \(0.852794\pi\)
\(212\) 1.73205 1.00000i 0.118958 0.0686803i
\(213\) −5.19615 3.00000i −0.356034 0.205557i
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) 0 0
\(216\) 9.00000 0.612372
\(217\) 3.46410 10.0000i 0.235159 0.678844i
\(218\) 9.00000i 0.609557i
\(219\) −6.00000 10.3923i −0.405442 0.702247i
\(220\) 0 0
\(221\) 0 0
\(222\) 10.3923 6.00000i 0.697486 0.402694i
\(223\) 28.0000i 1.87502i 0.347960 + 0.937509i \(0.386874\pi\)
−0.347960 + 0.937509i \(0.613126\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) 0 0
\(226\) −1.00000 1.73205i −0.0665190 0.115214i
\(227\) −3.46410 2.00000i −0.229920 0.132745i 0.380615 0.924734i \(-0.375712\pi\)
−0.610535 + 0.791989i \(0.709046\pi\)
\(228\) 15.5885 + 9.00000i 1.03237 + 0.596040i
\(229\) 11.0000 + 19.0526i 0.726900 + 1.25903i 0.958187 + 0.286143i \(0.0923732\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) −12.0000 + 10.3923i −0.789542 + 0.683763i
\(232\) 9.00000i 0.590879i
\(233\) 20.7846 12.0000i 1.36165 0.786146i 0.371802 0.928312i \(-0.378740\pi\)
0.989843 + 0.142166i \(0.0454066\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −5.00000 8.66025i −0.325472 0.563735i
\(237\) 30.0000i 1.94871i
\(238\) 10.3923 2.00000i 0.673633 0.129641i
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) −6.06218 3.50000i −0.389692 0.224989i
\(243\) 0 0
\(244\) −1.00000 −0.0640184
\(245\) 0 0
\(246\) −21.0000 −1.33891
\(247\) 0 0
\(248\) 3.46410 + 2.00000i 0.219971 + 0.127000i
\(249\) −10.5000 + 18.1865i −0.665410 + 1.15252i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 15.5885 3.00000i 0.981981 0.188982i
\(253\) 6.00000i 0.377217i
\(254\) 8.00000 + 13.8564i 0.501965 + 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.92820 + 4.00000i −0.432169 + 0.249513i −0.700270 0.713878i \(-0.746937\pi\)
0.268101 + 0.963391i \(0.413604\pi\)
\(258\) 15.0000i 0.933859i
\(259\) 8.00000 6.92820i 0.497096 0.430498i
\(260\) 0 0
\(261\) −27.0000 46.7654i −1.67126 2.89470i
\(262\) 6.92820 + 4.00000i 0.428026 + 0.247121i
\(263\) −4.33013 2.50000i −0.267007 0.154157i 0.360520 0.932752i \(-0.382599\pi\)
−0.627527 + 0.778595i \(0.715933\pi\)
\(264\) −3.00000 5.19615i −0.184637 0.319801i
\(265\) 0 0
\(266\) 15.0000 + 5.19615i 0.919709 + 0.318597i
\(267\) 3.00000i 0.183597i
\(268\) −7.79423 + 4.50000i −0.476108 + 0.274881i
\(269\) 1.50000 2.59808i 0.0914566 0.158408i −0.816668 0.577108i \(-0.804181\pi\)
0.908124 + 0.418701i \(0.137514\pi\)
\(270\) 0 0
\(271\) 3.00000 + 5.19615i 0.182237 + 0.315644i 0.942642 0.333805i \(-0.108333\pi\)
−0.760405 + 0.649449i \(0.775000\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) −4.50000 + 7.79423i −0.270868 + 0.469157i
\(277\) 10.3923 + 6.00000i 0.624413 + 0.360505i 0.778585 0.627539i \(-0.215938\pi\)
−0.154172 + 0.988044i \(0.549271\pi\)
\(278\) −12.1244 + 7.00000i −0.727171 + 0.419832i
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) −20.7846 + 12.0000i −1.23771 + 0.714590i
\(283\) 3.46410 + 2.00000i 0.205919 + 0.118888i 0.599414 0.800439i \(-0.295400\pi\)
−0.393494 + 0.919327i \(0.628734\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) −18.1865 + 3.50000i −1.07352 + 0.206598i
\(288\) 6.00000i 0.353553i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) −21.0000 + 36.3731i −1.23104 + 2.13223i
\(292\) 3.46410 2.00000i 0.202721 0.117041i
\(293\) 28.0000i 1.63578i 0.575376 + 0.817889i \(0.304856\pi\)
−0.575376 + 0.817889i \(0.695144\pi\)
\(294\) 19.5000 7.79423i 1.13726 0.454569i
\(295\) 0 0
\(296\) 2.00000 + 3.46410i 0.116248 + 0.201347i
\(297\) −15.5885 9.00000i −0.904534 0.522233i
\(298\) −2.59808 1.50000i −0.150503 0.0868927i
\(299\) 0 0
\(300\) 0 0
\(301\) −2.50000 12.9904i −0.144098 0.748753i
\(302\) 16.0000i 0.920697i
\(303\) 7.79423 4.50000i 0.447767 0.258518i
\(304\) −3.00000 + 5.19615i −0.172062 + 0.298020i
\(305\) 0 0
\(306\) 12.0000 + 20.7846i 0.685994 + 1.18818i
\(307\) 7.00000i 0.399511i −0.979846 0.199756i \(-0.935985\pi\)
0.979846 0.199756i \(-0.0640148\pi\)
\(308\) −3.46410 4.00000i −0.197386 0.227921i
\(309\) −3.00000 −0.170664
\(310\) 0 0
\(311\) 9.00000 15.5885i 0.510343 0.883940i −0.489585 0.871956i \(-0.662852\pi\)
0.999928 0.0119847i \(-0.00381495\pi\)
\(312\) 0 0
\(313\) 6.92820 4.00000i 0.391605 0.226093i −0.291250 0.956647i \(-0.594071\pi\)
0.682855 + 0.730554i \(0.260738\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 27.7128 16.0000i 1.55651 0.898650i 0.558920 0.829222i \(-0.311216\pi\)
0.997587 0.0694277i \(-0.0221173\pi\)
\(318\) 5.19615 + 3.00000i 0.291386 + 0.168232i
\(319\) −9.00000 + 15.5885i −0.503903 + 0.872786i
\(320\) 0 0
\(321\) 9.00000 0.502331
\(322\) −2.59808 + 7.50000i −0.144785 + 0.417959i
\(323\) 24.0000i 1.33540i
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) 0 0
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) 23.3827 13.5000i 1.29307 0.746552i
\(328\) 7.00000i 0.386510i
\(329\) −16.0000 + 13.8564i −0.882109 + 0.763928i
\(330\) 0 0
\(331\) 16.0000 + 27.7128i 0.879440 + 1.52323i 0.851957 + 0.523612i \(0.175416\pi\)
0.0274825 + 0.999622i \(0.491251\pi\)
\(332\) −6.06218 3.50000i −0.332705 0.192087i
\(333\) 20.7846 + 12.0000i 1.13899 + 0.657596i
\(334\) −10.5000 18.1865i −0.574534 0.995123i
\(335\) 0 0
\(336\) 1.50000 + 7.79423i 0.0818317 + 0.425210i
\(337\) 26.0000i 1.41631i 0.706057 + 0.708155i \(0.250472\pi\)
−0.706057 + 0.708155i \(0.749528\pi\)
\(338\) −11.2583 + 6.50000i −0.612372 + 0.353553i
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 0 0
\(341\) −4.00000 6.92820i −0.216612 0.375183i
\(342\) 36.0000i 1.94666i
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 5.00000 0.269582
\(345\) 0 0
\(346\) −4.00000 + 6.92820i −0.215041 + 0.372463i
\(347\) 16.4545 + 9.50000i 0.883323 + 0.509987i 0.871753 0.489946i \(-0.162984\pi\)
0.0115703 + 0.999933i \(0.496317\pi\)
\(348\) 23.3827 13.5000i 1.25344 0.723676i
\(349\) 35.0000 1.87351 0.936754 0.349990i \(-0.113815\pi\)
0.936754 + 0.349990i \(0.113815\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.73205 1.00000i 0.0923186 0.0533002i
\(353\) 15.5885 + 9.00000i 0.829690 + 0.479022i 0.853746 0.520689i \(-0.174325\pi\)
−0.0240566 + 0.999711i \(0.507658\pi\)
\(354\) 15.0000 25.9808i 0.797241 1.38086i
\(355\) 0 0
\(356\) 1.00000 0.0529999
\(357\) 20.7846 + 24.0000i 1.10004 + 1.27021i
\(358\) 12.0000i 0.634220i
\(359\) −2.00000 3.46410i −0.105556 0.182828i 0.808409 0.588621i \(-0.200329\pi\)
−0.913965 + 0.405793i \(0.866996\pi\)
\(360\) 0 0
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −6.06218 + 3.50000i −0.318621 + 0.183956i
\(363\) 21.0000i 1.10221i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.50000 2.59808i −0.0784063 0.135804i
\(367\) −9.52628 5.50000i −0.497268 0.287098i 0.230317 0.973116i \(-0.426024\pi\)
−0.727585 + 0.686018i \(0.759357\pi\)
\(368\) −2.59808 1.50000i −0.135434 0.0781929i
\(369\) −21.0000 36.3731i −1.09322 1.89351i
\(370\) 0 0
\(371\) 5.00000 + 1.73205i 0.259587 + 0.0899236i
\(372\) 12.0000i 0.622171i
\(373\) −3.46410 + 2.00000i −0.179364 + 0.103556i −0.586994 0.809591i \(-0.699689\pi\)
0.407630 + 0.913147i \(0.366355\pi\)
\(374\) 4.00000 6.92820i 0.206835 0.358249i
\(375\) 0 0
\(376\) −4.00000 6.92820i −0.206284 0.357295i
\(377\) 0 0
\(378\) 15.5885 + 18.0000i 0.801784 + 0.925820i
\(379\) −30.0000 −1.54100 −0.770498 0.637442i \(-0.779993\pi\)
−0.770498 + 0.637442i \(0.779993\pi\)
\(380\) 0 0
\(381\) −24.0000 + 41.5692i −1.22956 + 2.12966i
\(382\) −15.5885 9.00000i −0.797575 0.460480i
\(383\) 12.9904 7.50000i 0.663777 0.383232i −0.129937 0.991522i \(-0.541478\pi\)
0.793715 + 0.608290i \(0.208144\pi\)
\(384\) −3.00000 −0.153093
\(385\) 0 0
\(386\) 26.0000 1.32337
\(387\) 25.9808 15.0000i 1.32068 0.762493i
\(388\) −12.1244 7.00000i −0.615521 0.355371i
\(389\) 13.0000 22.5167i 0.659126 1.14164i −0.321716 0.946836i \(-0.604260\pi\)
0.980842 0.194804i \(-0.0624070\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 2.59808 + 6.50000i 0.131223 + 0.328300i
\(393\) 24.0000i 1.21064i
\(394\) 1.00000 + 1.73205i 0.0503793 + 0.0872595i
\(395\) 0 0
\(396\) 6.00000 10.3923i 0.301511 0.522233i
\(397\) −19.0526 + 11.0000i −0.956221 + 0.552074i −0.895008 0.446051i \(-0.852830\pi\)
−0.0612128 + 0.998125i \(0.519497\pi\)
\(398\) 4.00000i 0.200502i
\(399\) 9.00000 + 46.7654i 0.450564 + 2.34120i
\(400\) 0 0
\(401\) −15.5000 26.8468i −0.774033 1.34066i −0.935336 0.353760i \(-0.884903\pi\)
0.161303 0.986905i \(-0.448430\pi\)
\(402\) −23.3827 13.5000i −1.16622 0.673319i
\(403\) 0 0
\(404\) 1.50000 + 2.59808i 0.0746278 + 0.129259i
\(405\) 0 0
\(406\) 18.0000 15.5885i 0.893325 0.773642i
\(407\) 8.00000i 0.396545i
\(408\) −10.3923 + 6.00000i −0.514496 + 0.297044i
\(409\) 1.50000 2.59808i 0.0741702 0.128467i −0.826555 0.562856i \(-0.809703\pi\)
0.900725 + 0.434389i \(0.143036\pi\)
\(410\) 0 0
\(411\) −18.0000 31.1769i −0.887875 1.53784i
\(412\) 1.00000i 0.0492665i
\(413\) 8.66025 25.0000i 0.426143 1.23017i
\(414\) −18.0000 −0.884652
\(415\) 0 0
\(416\) 0 0
\(417\) −36.3731 21.0000i −1.78120 1.02837i
\(418\) 10.3923 6.00000i 0.508304 0.293470i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −19.0000 −0.926003 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 22.5167 13.0000i 1.09609 0.632830i
\(423\) −41.5692 24.0000i −2.02116 1.16692i
\(424\) −1.00000 + 1.73205i −0.0485643 + 0.0841158i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) −1.73205 2.00000i −0.0838198 0.0967868i
\(428\) 3.00000i 0.145010i
\(429\) 0 0
\(430\) 0 0
\(431\) 15.0000 25.9808i 0.722525 1.25145i −0.237460 0.971397i \(-0.576315\pi\)
0.959985 0.280052i \(-0.0903517\pi\)
\(432\) −7.79423 + 4.50000i −0.375000 + 0.216506i
\(433\) 14.0000i 0.672797i 0.941720 + 0.336399i \(0.109209\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) 2.00000 + 10.3923i 0.0960031 + 0.498847i
\(435\) 0 0
\(436\) 4.50000 + 7.79423i 0.215511 + 0.373276i
\(437\) −15.5885 9.00000i −0.745697 0.430528i
\(438\) 10.3923 + 6.00000i 0.496564 + 0.286691i
\(439\) −10.0000 17.3205i −0.477274 0.826663i 0.522387 0.852709i \(-0.325042\pi\)
−0.999661 + 0.0260459i \(0.991708\pi\)
\(440\) 0 0
\(441\) 33.0000 + 25.9808i 1.57143 + 1.23718i
\(442\) 0 0
\(443\) 26.8468 15.5000i 1.27553 0.736427i 0.299506 0.954094i \(-0.403178\pi\)
0.976023 + 0.217667i \(0.0698447\pi\)
\(444\) −6.00000 + 10.3923i −0.284747 + 0.493197i
\(445\) 0 0
\(446\) −14.0000 24.2487i −0.662919 1.14821i
\(447\) 9.00000i 0.425685i
\(448\) −2.59808 + 0.500000i −0.122748 + 0.0236228i
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) −7.00000 + 12.1244i −0.329617 + 0.570914i
\(452\) 1.73205 + 1.00000i 0.0814688 + 0.0470360i
\(453\) −41.5692 + 24.0000i −1.95309 + 1.12762i
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) −18.0000 −0.842927
\(457\) 27.7128 16.0000i 1.29635 0.748448i 0.316579 0.948566i \(-0.397466\pi\)
0.979772 + 0.200118i \(0.0641325\pi\)
\(458\) −19.0526 11.0000i −0.890268 0.513996i
\(459\) −18.0000 + 31.1769i −0.840168 + 1.45521i
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 5.19615 15.0000i 0.241747 0.697863i
\(463\) 19.0000i 0.883005i −0.897260 0.441502i \(-0.854446\pi\)
0.897260 0.441502i \(-0.145554\pi\)
\(464\) 4.50000 + 7.79423i 0.208907 + 0.361838i
\(465\) 0 0
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) 11.2583 6.50000i 0.520973 0.300784i −0.216359 0.976314i \(-0.569418\pi\)
0.737333 + 0.675530i \(0.236085\pi\)
\(468\) 0 0
\(469\) −22.5000 7.79423i −1.03895 0.359904i
\(470\) 0 0
\(471\) −15.0000 25.9808i −0.691164 1.19713i
\(472\) 8.66025 + 5.00000i 0.398621 + 0.230144i
\(473\) −8.66025 5.00000i −0.398199 0.229900i
\(474\) 15.0000 + 25.9808i 0.688973 + 1.19334i
\(475\) 0 0
\(476\) −8.00000 + 6.92820i −0.366679 + 0.317554i
\(477\) 12.0000i 0.549442i
\(478\) 13.8564 8.00000i 0.633777 0.365911i
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 10.0000i 0.455488i
\(483\) −23.3827 + 4.50000i −1.06395 + 0.204757i
\(484\) 7.00000 0.318182
\(485\) 0 0
\(486\) 0 0
\(487\) −13.8564 8.00000i −0.627894 0.362515i 0.152042 0.988374i \(-0.451415\pi\)
−0.779936 + 0.625859i \(0.784748\pi\)
\(488\) 0.866025 0.500000i 0.0392031 0.0226339i
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 18.1865 10.5000i 0.819912 0.473377i
\(493\) 31.1769 + 18.0000i 1.40414 + 0.810679i
\(494\) 0 0
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 5.19615 1.00000i 0.233079 0.0448561i
\(498\) 21.0000i 0.941033i
\(499\) −9.00000 15.5885i −0.402895 0.697835i 0.591179 0.806541i \(-0.298663\pi\)
−0.994074 + 0.108705i \(0.965329\pi\)
\(500\) 0 0
\(501\) 31.5000 54.5596i 1.40732 2.43754i
\(502\) 0 0
\(503\) 21.0000i 0.936344i −0.883637 0.468172i \(-0.844913\pi\)
0.883637 0.468172i \(-0.155087\pi\)
\(504\) −12.0000 + 10.3923i −0.534522 + 0.462910i
\(505\) 0 0
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) −33.7750 19.5000i −1.50000 0.866025i
\(508\) −13.8564 8.00000i −0.614779 0.354943i
\(509\) 0.500000 + 0.866025i 0.0221621 + 0.0383859i 0.876894 0.480684i \(-0.159612\pi\)
−0.854732 + 0.519070i \(0.826278\pi\)
\(510\) 0 0
\(511\) 10.0000 + 3.46410i 0.442374 + 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) −46.7654 + 27.0000i −2.06474 + 1.19208i
\(514\) 4.00000 6.92820i 0.176432 0.305590i
\(515\) 0 0
\(516\) 7.50000 + 12.9904i 0.330169 + 0.571870i
\(517\) 16.0000i 0.703679i
\(518\) −3.46410 + 10.0000i −0.152204 + 0.439375i
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) −19.0000 + 32.9090i −0.832405 + 1.44177i 0.0637207 + 0.997968i \(0.479703\pi\)
−0.896126 + 0.443800i \(0.853630\pi\)
\(522\) 46.7654 + 27.0000i 2.04686 + 1.18176i
\(523\) −17.3205 + 10.0000i −0.757373 + 0.437269i −0.828352 0.560208i \(-0.810721\pi\)
0.0709788 + 0.997478i \(0.477388\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) 5.00000 0.218010
\(527\) −13.8564 + 8.00000i −0.603595 + 0.348485i
\(528\) 5.19615 + 3.00000i 0.226134 + 0.130558i
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) 0 0
\(531\) 60.0000 2.60378
\(532\) −15.5885 + 3.00000i −0.675845 + 0.130066i
\(533\) 0 0
\(534\) 1.50000 + 2.59808i 0.0649113 + 0.112430i
\(535\) 0 0
\(536\) 4.50000 7.79423i 0.194370 0.336659i
\(537\) −31.1769 + 18.0000i −1.34538 + 0.776757i
\(538\) 3.00000i 0.129339i
\(539\) 2.00000 13.8564i 0.0861461 0.596838i
\(540\) 0 0
\(541\) −1.50000 2.59808i −0.0644900 0.111700i 0.831978 0.554809i \(-0.187209\pi\)
−0.896468 + 0.443109i \(0.853875\pi\)
\(542\) −5.19615 3.00000i −0.223194 0.128861i
\(543\) −18.1865 10.5000i −0.780459 0.450598i
\(544\) −2.00000 3.46410i −0.0857493 0.148522i
\(545\) 0 0
\(546\) 0 0
\(547\) 33.0000i 1.41098i 0.708721 + 0.705489i \(0.249273\pi\)
−0.708721 + 0.705489i \(0.750727\pi\)
\(548\) 10.3923 6.00000i 0.443937 0.256307i
\(549\) 3.00000 5.19615i 0.128037 0.221766i
\(550\) 0 0
\(551\) 27.0000 + 46.7654i 1.15024 + 1.99227i
\(552\) 9.00000i 0.383065i
\(553\) 17.3205 + 20.0000i 0.736543 + 0.850487i
\(554\) −12.0000 −0.509831
\(555\) 0 0
\(556\) 7.00000 12.1244i 0.296866 0.514187i
\(557\) −1.73205 1.00000i −0.0733893 0.0423714i 0.462856 0.886433i \(-0.346825\pi\)
−0.536246 + 0.844062i \(0.680158\pi\)
\(558\) −20.7846 + 12.0000i −0.879883 + 0.508001i
\(559\) 0 0
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) −1.73205 + 1.00000i −0.0730622 + 0.0421825i
\(563\) −14.7224 8.50000i −0.620477 0.358232i 0.156578 0.987666i \(-0.449954\pi\)
−0.777055 + 0.629433i \(0.783287\pi\)
\(564\) 12.0000 20.7846i 0.505291 0.875190i
\(565\) 0 0
\(566\) −4.00000 −0.168133
\(567\) −7.79423 + 22.5000i −0.327327 + 0.944911i
\(568\) 2.00000i 0.0839181i
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) 15.0000 25.9808i 0.627730 1.08726i −0.360276 0.932846i \(-0.617317\pi\)
0.988006 0.154415i \(-0.0493493\pi\)
\(572\) 0 0
\(573\) 54.0000i 2.25588i
\(574\) 14.0000 12.1244i 0.584349 0.506061i
\(575\) 0 0
\(576\) −3.00000 5.19615i −0.125000 0.216506i
\(577\) 8.66025 + 5.00000i 0.360531 + 0.208153i 0.669314 0.742980i \(-0.266588\pi\)
−0.308783 + 0.951133i \(0.599922\pi\)
\(578\) 0.866025 + 0.500000i 0.0360219 + 0.0207973i
\(579\) 39.0000 + 67.5500i 1.62078 + 2.80728i
\(580\) 0 0
\(581\) −3.50000 18.1865i −0.145204 0.754505i
\(582\) 42.0000i 1.74096i
\(583\) 3.46410 2.00000i 0.143468 0.0828315i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) 0 0
\(586\) −14.0000 24.2487i −0.578335 1.00171i
\(587\) 28.0000i 1.15568i 0.816149 + 0.577842i \(0.196105\pi\)
−0.816149 + 0.577842i \(0.803895\pi\)
\(588\) −12.9904 + 16.5000i −0.535714 + 0.680449i
\(589\) −24.0000 −0.988903
\(590\) 0 0
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) −3.46410 2.00000i −0.142374 0.0821995i
\(593\) −5.19615 + 3.00000i −0.213380 + 0.123195i −0.602881 0.797831i \(-0.705981\pi\)
0.389501 + 0.921026i \(0.372647\pi\)
\(594\) 18.0000 0.738549
\(595\) 0 0
\(596\) 3.00000 0.122885
\(597\) 10.3923 6.00000i 0.425329 0.245564i
\(598\) 0 0
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 8.66025 + 10.0000i 0.352966 + 0.407570i
\(603\) 54.0000i 2.19905i
\(604\) −8.00000 13.8564i −0.325515 0.563809i
\(605\) 0 0
\(606\) −4.50000 + 7.79423i −0.182800 + 0.316619i
\(607\) −0.866025 + 0.500000i −0.0351509 + 0.0202944i −0.517472 0.855700i \(-0.673127\pi\)
0.482322 + 0.875994i \(0.339794\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 67.5000 + 23.3827i 2.73524 + 0.947514i
\(610\) 0 0
\(611\) 0 0
\(612\) −20.7846 12.0000i −0.840168 0.485071i
\(613\) −10.3923 6.00000i −0.419741 0.242338i 0.275225 0.961380i \(-0.411248\pi\)
−0.694967 + 0.719042i \(0.744581\pi\)
\(614\) 3.50000 + 6.06218i 0.141249 + 0.244650i
\(615\) 0 0
\(616\) 5.00000 + 1.73205i 0.201456 + 0.0697863i
\(617\) 44.0000i 1.77137i −0.464283 0.885687i \(-0.653688\pi\)
0.464283 0.885687i \(-0.346312\pi\)
\(618\) 2.59808 1.50000i 0.104510 0.0603388i
\(619\) −23.0000 + 39.8372i −0.924448 + 1.60119i −0.132002 + 0.991250i \(0.542140\pi\)
−0.792446 + 0.609941i \(0.791193\pi\)
\(620\) 0 0
\(621\) −13.5000 23.3827i −0.541736 0.938315i
\(622\) 18.0000i 0.721734i
\(623\) 1.73205 + 2.00000i 0.0693932 + 0.0801283i
\(624\) 0 0
\(625\) 0 0
\(626\) −4.00000 + 6.92820i −0.159872 + 0.276907i
\(627\) 31.1769 + 18.0000i 1.24509 + 0.718851i
\(628\) 8.66025 5.00000i 0.345582 0.199522i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) −8.66025 + 5.00000i −0.344486 + 0.198889i
\(633\) 67.5500 + 39.0000i 2.68487 + 1.55011i
\(634\) −16.0000 + 27.7128i −0.635441 + 1.10062i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 18.0000i 0.712627i
\(639\) 6.00000 + 10.3923i 0.237356 + 0.411113i
\(640\) 0 0
\(641\) −2.50000 + 4.33013i −0.0987441 + 0.171030i −0.911165 0.412042i \(-0.864816\pi\)
0.812421 + 0.583071i \(0.198149\pi\)
\(642\) −7.79423 + 4.50000i −0.307614 + 0.177601i
\(643\) 28.0000i 1.10421i 0.833774 + 0.552106i \(0.186176\pi\)
−0.833774 + 0.552106i \(0.813824\pi\)
\(644\) −1.50000 7.79423i −0.0591083 0.307136i
\(645\) 0 0
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) −9.52628 5.50000i −0.374517 0.216227i 0.300913 0.953652i \(-0.402709\pi\)
−0.675430 + 0.737424i \(0.736042\pi\)
\(648\) −7.79423 4.50000i −0.306186 0.176777i
\(649\) −10.0000 17.3205i −0.392534 0.679889i
\(650\) 0 0
\(651\) −24.0000 + 20.7846i −0.940634 + 0.814613i
\(652\) 4.00000i 0.156652i
\(653\) −3.46410 + 2.00000i −0.135561 + 0.0782660i −0.566247 0.824236i \(-0.691605\pi\)
0.430686 + 0.902502i \(0.358272\pi\)
\(654\) −13.5000 + 23.3827i −0.527892 + 0.914335i
\(655\) 0 0
\(656\) 3.50000 + 6.06218i 0.136652 + 0.236688i
\(657\) 24.0000i 0.936329i
\(658\) 6.92820 20.0000i 0.270089 0.779681i
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) 0 0
\(661\) 5.50000 9.52628i 0.213925 0.370529i −0.739014 0.673690i \(-0.764708\pi\)
0.952940 + 0.303160i \(0.0980418\pi\)
\(662\) −27.7128 16.0000i −1.07709 0.621858i
\(663\) 0 0
\(664\) 7.00000 0.271653
\(665\) 0 0
\(666\) −24.0000 −0.929981
\(667\) −23.3827 + 13.5000i −0.905381 + 0.522722i
\(668\) 18.1865 + 10.5000i 0.703658 + 0.406257i
\(669\) 42.0000 72.7461i 1.62381 2.81253i
\(670\) 0 0
\(671\) −2.00000 −0.0772091
\(672\) −5.19615 6.00000i −0.200446 0.231455i
\(673\) 16.0000i 0.616755i 0.951264 + 0.308377i \(0.0997859\pi\)
−0.951264 + 0.308377i \(0.900214\pi\)
\(674\) −13.0000 22.5167i −0.500741 0.867309i
\(675\) 0 0
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) 41.5692 24.0000i 1.59763 0.922395i 0.605693 0.795698i \(-0.292896\pi\)
0.991941 0.126697i \(-0.0404375\pi\)
\(678\) 6.00000i 0.230429i
\(679\) −7.00000 36.3731i −0.268635 1.39587i
\(680\) 0 0
\(681\) 6.00000 + 10.3923i 0.229920 + 0.398234i
\(682\) 6.92820 + 4.00000i 0.265295 + 0.153168i
\(683\) 32.0429 + 18.5000i 1.22609 + 0.707883i 0.966209 0.257758i \(-0.0829838\pi\)
0.259880 + 0.965641i \(0.416317\pi\)
\(684\) −18.0000 31.1769i −0.688247 1.19208i
\(685\) 0 0
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 66.0000i 2.51806i
\(688\) −4.33013 + 2.50000i −0.165085 + 0.0953116i
\(689\) 0 0
\(690\) 0 0
\(691\) −11.0000 19.0526i −0.418460 0.724793i 0.577325 0.816514i \(-0.304097\pi\)
−0.995785 + 0.0917209i \(0.970763\pi\)
\(692\) 8.00000i 0.304114i
\(693\) 31.1769 6.00000i 1.18431 0.227921i
\(694\) −19.0000 −0.721230
\(695\) 0 0
\(696\) −13.5000 + 23.3827i −0.511716 + 0.886318i
\(697\) 24.2487 + 14.0000i 0.918485 + 0.530288i
\(698\) −30.3109 + 17.5000i −1.14728 + 0.662385i
\(699\) −72.0000 −2.72329
\(700\) 0 0
\(701\) −47.0000 −1.77517 −0.887583 0.460648i \(-0.847617\pi\)
−0.887583 + 0.460648i \(0.847617\pi\)
\(702\) 0 0
\(703\) −20.7846 12.0000i −0.783906 0.452589i
\(704\) −1.00000 + 1.73205i −0.0376889 + 0.0652791i
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) −2.59808 + 7.50000i −0.0977107 + 0.282067i
\(708\) 30.0000i 1.12747i
\(709\) −5.50000 9.52628i −0.206557 0.357767i 0.744071 0.668101i \(-0.232892\pi\)
−0.950628 + 0.310334i \(0.899559\pi\)
\(710\) 0 0
\(711\) −30.0000 + 51.9615i −1.12509 + 1.94871i
\(712\) −0.866025 + 0.500000i −0.0324557 + 0.0187383i
\(713\) 12.0000i 0.449404i
\(714\) −30.0000 10.3923i −1.12272 0.388922i
\(715\) 0 0
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 41.5692 + 24.0000i 1.55243 + 0.896296i
\(718\) 3.46410 + 2.00000i 0.129279 + 0.0746393i
\(719\) −3.00000 5.19615i −0.111881 0.193784i 0.804648 0.593753i \(-0.202354\pi\)
−0.916529 + 0.399969i \(0.869021\pi\)
\(720\) 0 0
\(721\) 2.00000 1.73205i 0.0744839 0.0645049i
\(722\) 17.0000i 0.632674i
\(723\) 25.9808 15.0000i 0.966235 0.557856i
\(724\) 3.50000 6.06218i 0.130076 0.225299i
\(725\) 0 0
\(726\) 10.5000 + 18.1865i 0.389692 + 0.674966i
\(727\) 21.0000i 0.778847i 0.921059 + 0.389423i \(0.127326\pi\)
−0.921059 + 0.389423i \(0.872674\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) 2.59808 + 1.50000i 0.0960277 + 0.0554416i
\(733\) 19.0526 11.0000i 0.703722 0.406294i −0.105010 0.994471i \(-0.533487\pi\)
0.808732 + 0.588177i \(0.200154\pi\)
\(734\) 11.0000 0.406017
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −15.5885 + 9.00000i −0.574208 + 0.331519i
\(738\) 36.3731 + 21.0000i 1.33891 + 0.773021i
\(739\) −1.00000 + 1.73205i −0.0367856 + 0.0637145i −0.883832 0.467804i \(-0.845045\pi\)
0.847046 + 0.531519i \(0.178379\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −5.19615 + 1.00000i −0.190757 + 0.0367112i
\(743\) 9.00000i 0.330178i 0.986279 + 0.165089i \(0.0527911\pi\)
−0.986279 + 0.165089i \(0.947209\pi\)
\(744\) −6.00000 10.3923i −0.219971 0.381000i
\(745\) 0 0
\(746\) 2.00000 3.46410i 0.0732252 0.126830i
\(747\) 36.3731 21.0000i 1.33082 0.768350i
\(748\) 8.00000i 0.292509i
\(749\) −6.00000 + 5.19615i −0.219235 + 0.189863i
\(750\) 0 0
\(751\) 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i \(-0.143415\pi\)
−0.827225 + 0.561870i \(0.810082\pi\)
\(752\) 6.92820 + 4.00000i 0.252646 + 0.145865i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −22.5000 7.79423i −0.818317 0.283473i
\(757\) 16.0000i 0.581530i −0.956795 0.290765i \(-0.906090\pi\)
0.956795 0.290765i \(-0.0939098\pi\)
\(758\) 25.9808 15.0000i 0.943664 0.544825i
\(759\) −9.00000 + 15.5885i −0.326679 + 0.565825i
\(760\) 0 0
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) 48.0000i 1.73886i
\(763\) −7.79423 + 22.5000i −0.282170 + 0.814555i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) −7.50000 + 12.9904i −0.270986 + 0.469362i
\(767\) 0 0
\(768\) 2.59808 1.50000i 0.0937500 0.0541266i
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 24.0000 0.864339
\(772\) −22.5167 + 13.0000i −0.810392 + 0.467880i
\(773\) −20.7846 12.0000i −0.747570 0.431610i 0.0772449 0.997012i \(-0.475388\pi\)
−0.824815 + 0.565402i \(0.808721\pi\)
\(774\) −15.0000 + 25.9808i −0.539164 + 0.933859i
\(775\) 0 0
\(776\) 14.0000 0.502571
\(777\) −31.1769 + 6.00000i −1.11847 + 0.215249i
\(778\) 26.0000i 0.932145i
\(779\) 21.0000 + 36.3731i 0.752403 + 1.30320i
\(780\) 0 0
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) 10.3923 6.00000i 0.371628 0.214560i
\(783\) 81.0000i 2.89470i
\(784\) −5.50000 4.33013i −0.196429 0.154647i
\(785\) 0 0
\(786\) −12.0000 20.7846i −0.428026 0.741362i
\(787\) 26.8468 + 15.5000i 0.956985 + 0.552515i 0.895244 0.445577i \(-0.147001\pi\)
0.0617409 + 0.998092i \(0.480335\pi\)
\(788\) −1.73205 1.00000i −0.0617018 0.0356235i
\(789\) 7.50000 + 12.9904i 0.267007 + 0.462470i
\(790\) 0 0
\(791\) 1.00000 + 5.19615i 0.0355559 + 0.184754i
\(792\) 12.0000i 0.426401i
\(793\) 0 0
\(794\) 11.0000 19.0526i 0.390375 0.676150i
\(795\) 0 0
\(796\) 2.00000 + 3.46410i 0.0708881 + 0.122782i
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) −31.1769 36.0000i −1.10365 1.27439i
\(799\) 32.0000 1.13208
\(800\) 0 0
\(801\) −3.00000 + 5.19615i −0.106000 + 0.183597i
\(802\) 26.8468 + 15.5000i 0.947993 + 0.547324i
\(803\) 6.92820 4.00000i 0.244491 0.141157i
\(804\) 27.0000 0.952217
\(805\) 0 0
\(806\) 0 0
\(807\) −7.79423 + 4.50000i −0.274370 + 0.158408i
\(808\) −2.59808 1.50000i −0.0914000 0.0527698i
\(809\) −25.5000 + 44.1673i −0.896532 + 1.55284i −0.0646355 + 0.997909i \(0.520588\pi\)
−0.831897 + 0.554930i \(0.812745\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) −7.79423 + 22.5000i −0.273524 + 0.789595i
\(813\) 18.0000i 0.631288i
\(814\) 4.00000 + 6.92820i 0.140200 + 0.242833i
\(815\) 0 0
\(816\) 6.00000 10.3923i 0.210042 0.363803i
\(817\) −25.9808 + 15.0000i −0.908952 + 0.524784i
\(818\) 3.00000i 0.104893i
\(819\) 0 0
\(820\) 0 0
\(821\) 9.00000 + 15.5885i 0.314102 + 0.544041i 0.979246 0.202674i \(-0.0649632\pi\)
−0.665144 + 0.746715i \(0.731630\pi\)
\(822\) 31.1769 + 18.0000i 1.08742 + 0.627822i
\(823\) −16.4545 9.50000i −0.573567 0.331149i 0.185006 0.982737i \(-0.440770\pi\)
−0.758573 + 0.651588i \(0.774103\pi\)
\(824\) 0.500000 + 0.866025i 0.0174183 + 0.0301694i
\(825\) 0 0
\(826\) 5.00000 + 25.9808i 0.173972 + 0.903986i
\(827\) 19.0000i 0.660695i 0.943859 + 0.330347i \(0.107166\pi\)
−0.943859 + 0.330347i \(0.892834\pi\)
\(828\) 15.5885 9.00000i 0.541736 0.312772i
\(829\) −23.0000 + 39.8372i −0.798823 + 1.38360i 0.121560 + 0.992584i \(0.461210\pi\)
−0.920383 + 0.391018i \(0.872123\pi\)
\(830\) 0 0
\(831\) −18.0000 31.1769i −0.624413 1.08152i
\(832\) 0 0
\(833\) −27.7128 4.00000i −0.960192 0.138592i
\(834\) 42.0000 1.45434
\(835\) 0 0
\(836\) −6.00000 + 10.3923i −0.207514 + 0.359425i
\(837\) −31.1769 18.0000i −1.07763 0.622171i
\(838\) 0 0
\(839\) −14.0000 −0.483334 −0.241667 0.970359i \(-0.577694\pi\)
−0.241667 + 0.970359i \(0.577694\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) 16.4545 9.50000i 0.567059 0.327392i
\(843\) −5.19615 3.00000i −0.178965 0.103325i
\(844\) −13.0000 + 22.5167i −0.447478 + 0.775055i
\(845\) 0 0
\(846\) 48.0000 1.65027
\(847\) 12.1244 + 14.0000i 0.416598 + 0.481046i
\(848\) 2.00000i 0.0686803i
\(849\) −6.00000 10.3923i −0.205919 0.356663i
\(850\) 0 0
\(851\) 6.00000 10.3923i 0.205677 0.356244i
\(852\) −5.19615 + 3.00000i −0.178017 + 0.102778i
\(853\) 14.0000i 0.479351i 0.970853 + 0.239675i \(0.0770410\pi\)
−0.970853 + 0.239675i \(0.922959\pi\)
\(854\) 2.50000 + 0.866025i 0.0855482 + 0.0296348i
\(855\) 0 0
\(856\) −1.50000 2.59808i −0.0512689 0.0888004i
\(857\) −15.5885 9.00000i −0.532492 0.307434i 0.209539 0.977800i \(-0.432804\pi\)
−0.742030 + 0.670366i \(0.766137\pi\)
\(858\) 0 0
\(859\) −24.0000 41.5692i −0.818869 1.41832i −0.906516 0.422172i \(-0.861268\pi\)
0.0876464 0.996152i \(-0.472065\pi\)
\(860\) 0 0
\(861\) 52.5000 + 18.1865i 1.78920 + 0.619795i
\(862\) 30.0000i 1.02180i
\(863\) −9.52628 + 5.50000i −0.324278 + 0.187222i −0.653298 0.757101i \(-0.726615\pi\)
0.329020 + 0.944323i \(0.393282\pi\)
\(864\) 4.50000 7.79423i 0.153093 0.265165i
\(865\) 0 0
\(866\) −7.00000 12.1244i −0.237870 0.412002i
\(867\) 3.00000i 0.101885i
\(868\) −6.92820 8.00000i −0.235159 0.271538i
\(869\) 20.0000 0.678454
\(870\) 0 0
\(871\) 0 0
\(872\) −7.79423 4.50000i −0.263946 0.152389i
\(873\) 72.7461 42.0000i 2.46208 1.42148i
\(874\) 18.0000 0.608859
\(875\) 0 0
\(876\) −12.0000 −0.405442
\(877\) −32.9090 + 19.0000i −1.11126 + 0.641584i −0.939155 0.343495i \(-0.888389\pi\)
−0.172102 + 0.985079i \(0.555056\pi\)
\(878\) 17.3205 + 10.0000i 0.584539 + 0.337484i
\(879\) 42.0000 72.7461i 1.41662 2.45367i
\(880\) 0 0
\(881\) −7.00000 −0.235836 −0.117918 0.993023i \(-0.537622\pi\)
−0.117918 + 0.993023i \(0.537622\pi\)
\(882\) −41.5692 6.00000i −1.39971 0.202031i
\(883\) 12.0000i 0.403832i −0.979403 0.201916i \(-0.935283\pi\)
0.979403 0.201916i \(-0.0647168\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −15.5000 + 26.8468i −0.520733 + 0.901935i
\(887\) −25.1147 + 14.5000i −0.843270 + 0.486862i −0.858375 0.513024i \(-0.828525\pi\)
0.0151042 + 0.999886i \(0.495192\pi\)
\(888\) 12.0000i 0.402694i
\(889\) −8.00000 41.5692i −0.268311 1.39419i
\(890\) 0 0
\(891\) 9.00000 + 15.5885i 0.301511 + 0.522233i
\(892\) 24.2487 + 14.0000i 0.811907 + 0.468755i
\(893\) 41.5692 + 24.0000i 1.39106 + 0.803129i
\(894\) 4.50000 + 7.79423i 0.150503 + 0.260678i
\(895\) 0 0
\(896\) 2.00000 1.73205i 0.0668153 0.0578638i
\(897\) 0 0
\(898\) −28.5788 + 16.5000i −0.953688 + 0.550612i
\(899\) −18.0000 + 31.1769i −0.600334 + 1.03981i
\(900\) 0 0
\(901\) −4.00000 6.92820i −0.133259 0.230812i
\(902\) 14.0000i 0.466149i
\(903\) −12.9904 + 37.5000i −0.432293 + 1.24792i
\(904\) −2.00000 −0.0665190
\(905\) 0 0
\(906\) 24.0000 41.5692i 0.797347 1.38104i
\(907\) 4.33013 + 2.50000i 0.143780 + 0.0830111i 0.570164 0.821531i \(-0.306880\pi\)
−0.426385 + 0.904542i \(0.640213\pi\)
\(908\) −3.46410 + 2.00000i −0.114960 + 0.0663723i
\(909\) −18.0000 −0.597022
\(910\) 0 0
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) 15.5885 9.00000i 0.516185 0.298020i
\(913\) −12.1244 7.00000i −0.401258 0.231666i
\(914\) −16.0000 + 27.7128i −0.529233 + 0.916658i
\(915\) 0 0
\(916\) 22.0000 0.726900
\(917\) −13.8564 16.0000i −0.457579 0.528367i
\(918\) 36.0000i 1.18818i
\(919\) 19.0000 + 32.9090i 0.626752 + 1.08557i 0.988199 + 0.153174i \(0.0489495\pi\)
−0.361447 + 0.932393i \(0.617717\pi\)
\(920\) 0 0
\(921\) −10.5000 + 18.1865i −0.345987 + 0.599267i
\(922\) 12.1244 7.00000i 0.399294 0.230533i
\(923\) 0 0
\(924\) 3.00000 + 15.5885i 0.0986928 + 0.512823i
\(925\) 0 0
\(926\) 9.50000 + 16.4545i 0.312189 + 0.540728i
\(927\) 5.19615 + 3.00000i 0.170664 + 0.0985329i
\(928\) −7.79423 4.50000i −0.255858 0.147720i
\(929\) 21.5000 + 37.2391i 0.705392 + 1.22177i 0.966550 + 0.256479i \(0.0825624\pi\)
−0.261158 + 0.965296i \(0.584104\pi\)
\(930\) 0 0
\(931\) −33.0000 25.9808i −1.08153 0.851485i
\(932\) 24.0000i 0.786146i
\(933\) −46.7654 + 27.0000i −1.53103 + 0.883940i
\(934\) −6.50000 + 11.2583i −0.212686 + 0.368384i
\(935\) 0 0
\(936\) 0 0
\(937\) 28.0000i 0.914720i 0.889282 + 0.457360i \(0.151205\pi\)
−0.889282 + 0.457360i \(0.848795\pi\)
\(938\) 23.3827 4.50000i 0.763472 0.146930i
\(939\) −24.0000 −0.783210
\(940\) 0 0
\(941\) 23.0000 39.8372i 0.749779 1.29865i −0.198150 0.980172i \(-0.563493\pi\)
0.947929 0.318483i \(-0.103173\pi\)
\(942\) 25.9808 + 15.0000i 0.846499 + 0.488726i
\(943\) −18.1865 + 10.5000i −0.592235 + 0.341927i
\(944\) −10.0000 −0.325472
\(945\) 0 0
\(946\) 10.0000 0.325128
\(947\) 21.6506 12.5000i 0.703551 0.406195i −0.105118 0.994460i \(-0.533522\pi\)
0.808669 + 0.588264i \(0.200189\pi\)
\(948\) −25.9808 15.0000i −0.843816 0.487177i
\(949\) 0 0
\(950\) 0 0
\(951\) −96.0000 −3.11301
\(952\) 3.46410 10.0000i 0.112272 0.324102i
\(953\) 12.0000i 0.388718i −0.980930 0.194359i \(-0.937737\pi\)
0.980930 0.194359i \(-0.0622627\pi\)
\(954\) −6.00000 10.3923i −0.194257 0.336463i
\(955\) 0 0
\(956\) −8.00000 + 13.8564i −0.258738 + 0.448148i
\(957\) 46.7654 27.0000i 1.51171 0.872786i
\(958\) 24.0000i 0.775405i
\(959\) 30.0000 + 10.3923i 0.968751 + 0.335585i
\(960\) 0 0
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) 0 0
\(963\) −15.5885 9.00000i −0.502331 0.290021i
\(964\) 5.00000 + 8.66025i 0.161039 + 0.278928i
\(965\) 0 0
\(966\) 18.0000 15.5885i 0.579141 0.501550i
\(967\) 37.0000i 1.18984i −0.803785 0.594920i \(-0.797184\pi\)
0.803785 0.594920i \(-0.202816\pi\)
\(968\) −6.06218 + 3.50000i −0.194846 + 0.112494i
\(969\) 36.0000 62.3538i 1.15649 2.00309i
\(970\) 0 0
\(971\) 24.0000 + 41.5692i 0.770197 + 1.33402i 0.937455 + 0.348107i \(0.113175\pi\)
−0.167258 + 0.985913i \(0.553491\pi\)
\(972\) 0 0
\(973\) 36.3731 7.00000i 1.16607 0.224410i
\(974\) 16.0000 0.512673
\(975\) 0 0
\(976\) −0.500000 + 0.866025i −0.0160046 + 0.0277208i
\(977\) −25.9808 15.0000i −0.831198 0.479893i 0.0230645 0.999734i \(-0.492658\pi\)
−0.854263 + 0.519841i \(0.825991\pi\)
\(978\) −10.3923 + 6.00000i −0.332309 + 0.191859i
\(979\) 2.00000 0.0639203
\(980\) 0 0
\(981\) −54.0000 −1.72409
\(982\) 10.3923 6.00000i 0.331632 0.191468i
\(983\) −14.7224 8.50000i −0.469573 0.271108i 0.246488 0.969146i \(-0.420723\pi\)
−0.716061 + 0.698038i \(0.754057\pi\)
\(984\) −10.5000 + 18.1865i −0.334728 + 0.579766i
\(985\) 0 0
\(986\) −36.0000 −1.14647
\(987\) 62.3538 12.0000i 1.98474 0.381964i
\(988\) 0 0
\(989\) −7.50000 12.9904i −0.238486 0.413070i
\(990\) 0 0
\(991\) −20.0000 + 34.6410i −0.635321 + 1.10041i 0.351126 + 0.936328i \(0.385799\pi\)
−0.986447 + 0.164080i \(0.947534\pi\)
\(992\) 3.46410 2.00000i 0.109985 0.0635001i
\(993\) 96.0000i 3.04647i
\(994\) −4.00000 + 3.46410i −0.126872 + 0.109875i
\(995\) 0 0
\(996\) 10.5000 + 18.1865i 0.332705 + 0.576262i
\(997\) −39.8372 23.0000i −1.26166 0.728417i −0.288261 0.957552i \(-0.593077\pi\)
−0.973395 + 0.229135i \(0.926410\pi\)
\(998\) 15.5885 + 9.00000i 0.493444 + 0.284890i
\(999\) −18.0000 31.1769i −0.569495 0.986394i
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 350.2.j.f.249.1 4
5.2 odd 4 70.2.e.a.11.1 2
5.3 odd 4 350.2.e.l.151.1 2
5.4 even 2 inner 350.2.j.f.249.2 4
7.2 even 3 inner 350.2.j.f.149.2 4
7.3 odd 6 2450.2.c.a.99.1 2
7.4 even 3 2450.2.c.s.99.1 2
15.2 even 4 630.2.k.f.361.1 2
20.7 even 4 560.2.q.i.81.1 2
35.2 odd 12 70.2.e.a.51.1 yes 2
35.3 even 12 2450.2.a.q.1.1 1
35.4 even 6 2450.2.c.s.99.2 2
35.9 even 6 inner 350.2.j.f.149.1 4
35.12 even 12 490.2.e.f.471.1 2
35.17 even 12 490.2.a.e.1.1 1
35.18 odd 12 2450.2.a.b.1.1 1
35.23 odd 12 350.2.e.l.51.1 2
35.24 odd 6 2450.2.c.a.99.2 2
35.27 even 4 490.2.e.f.361.1 2
35.32 odd 12 490.2.a.k.1.1 1
105.2 even 12 630.2.k.f.541.1 2
105.17 odd 12 4410.2.a.h.1.1 1
105.32 even 12 4410.2.a.r.1.1 1
140.67 even 12 3920.2.a.b.1.1 1
140.87 odd 12 3920.2.a.bk.1.1 1
140.107 even 12 560.2.q.i.401.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.e.a.11.1 2 5.2 odd 4
70.2.e.a.51.1 yes 2 35.2 odd 12
350.2.e.l.51.1 2 35.23 odd 12
350.2.e.l.151.1 2 5.3 odd 4
350.2.j.f.149.1 4 35.9 even 6 inner
350.2.j.f.149.2 4 7.2 even 3 inner
350.2.j.f.249.1 4 1.1 even 1 trivial
350.2.j.f.249.2 4 5.4 even 2 inner
490.2.a.e.1.1 1 35.17 even 12
490.2.a.k.1.1 1 35.32 odd 12
490.2.e.f.361.1 2 35.27 even 4
490.2.e.f.471.1 2 35.12 even 12
560.2.q.i.81.1 2 20.7 even 4
560.2.q.i.401.1 2 140.107 even 12
630.2.k.f.361.1 2 15.2 even 4
630.2.k.f.541.1 2 105.2 even 12
2450.2.a.b.1.1 1 35.18 odd 12
2450.2.a.q.1.1 1 35.3 even 12
2450.2.c.a.99.1 2 7.3 odd 6
2450.2.c.a.99.2 2 35.24 odd 6
2450.2.c.s.99.1 2 7.4 even 3
2450.2.c.s.99.2 2 35.4 even 6
3920.2.a.b.1.1 1 140.67 even 12
3920.2.a.bk.1.1 1 140.87 odd 12
4410.2.a.h.1.1 1 105.17 odd 12
4410.2.a.r.1.1 1 105.32 even 12