Properties

Label 324.3.f.c.271.1
Level $324$
Weight $3$
Character 324.271
Analytic conductor $8.828$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(55,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.55");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.f (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: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 324.271
Dual form 324.3.f.c.55.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-3.50000 + 6.06218i) q^{5} +(7.50000 - 4.33013i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-3.50000 + 6.06218i) q^{5} +(7.50000 - 4.33013i) q^{7} +8.00000 q^{8} +(-7.00000 - 12.1244i) q^{10} +(-7.50000 + 4.33013i) q^{11} +(-10.0000 + 17.3205i) q^{13} +17.3205i q^{14} +(-8.00000 + 13.8564i) q^{16} -8.00000 q^{17} -10.3923i q^{19} +28.0000 q^{20} -17.3205i q^{22} +(-3.00000 - 1.73205i) q^{23} +(-12.0000 - 20.7846i) q^{25} +(-20.0000 - 34.6410i) q^{26} +(-30.0000 - 17.3205i) q^{28} +(-5.00000 - 8.66025i) q^{29} +(-46.5000 - 26.8468i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(8.00000 - 13.8564i) q^{34} +60.6218i q^{35} -10.0000 q^{37} +(18.0000 + 10.3923i) q^{38} +(-28.0000 + 48.4974i) q^{40} +(25.0000 - 43.3013i) q^{41} +(-15.0000 + 8.66025i) q^{43} +(30.0000 + 17.3205i) q^{44} +(6.00000 - 3.46410i) q^{46} +(-75.0000 + 43.3013i) q^{47} +(13.0000 - 22.5167i) q^{49} +48.0000 q^{50} +80.0000 q^{52} -47.0000 q^{53} -60.6218i q^{55} +(60.0000 - 34.6410i) q^{56} +20.0000 q^{58} +(-30.0000 - 17.3205i) q^{59} +(32.0000 + 55.4256i) q^{61} +(93.0000 - 53.6936i) q^{62} +64.0000 q^{64} +(-70.0000 - 121.244i) q^{65} +(75.0000 + 43.3013i) q^{67} +(16.0000 + 27.7128i) q^{68} +(-105.000 - 60.6218i) q^{70} -55.0000 q^{73} +(10.0000 - 17.3205i) q^{74} +(-36.0000 + 20.7846i) q^{76} +(-37.5000 + 64.9519i) q^{77} +(-6.00000 + 3.46410i) q^{79} +(-56.0000 - 96.9948i) q^{80} +(50.0000 + 86.6025i) q^{82} +(-25.5000 + 14.7224i) q^{83} +(28.0000 - 48.4974i) q^{85} -34.6410i q^{86} +(-60.0000 + 34.6410i) q^{88} +10.0000 q^{89} +173.205i q^{91} +13.8564i q^{92} -173.205i q^{94} +(63.0000 + 36.3731i) q^{95} +(12.5000 + 21.6506i) q^{97} +(26.0000 + 45.0333i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 4 q^{4} - 7 q^{5} + 15 q^{7} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 4 q^{4} - 7 q^{5} + 15 q^{7} + 16 q^{8} - 14 q^{10} - 15 q^{11} - 20 q^{13} - 16 q^{16} - 16 q^{17} + 56 q^{20} - 6 q^{23} - 24 q^{25} - 40 q^{26} - 60 q^{28} - 10 q^{29} - 93 q^{31} - 32 q^{32} + 16 q^{34} - 20 q^{37} + 36 q^{38} - 56 q^{40} + 50 q^{41} - 30 q^{43} + 60 q^{44} + 12 q^{46} - 150 q^{47} + 26 q^{49} + 96 q^{50} + 160 q^{52} - 94 q^{53} + 120 q^{56} + 40 q^{58} - 60 q^{59} + 64 q^{61} + 186 q^{62} + 128 q^{64} - 140 q^{65} + 150 q^{67} + 32 q^{68} - 210 q^{70} - 110 q^{73} + 20 q^{74} - 72 q^{76} - 75 q^{77} - 12 q^{79} - 112 q^{80} + 100 q^{82} - 51 q^{83} + 56 q^{85} - 120 q^{88} + 20 q^{89} + 126 q^{95} + 25 q^{97} + 52 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.500000 0.866025i
\(5\) −3.50000 + 6.06218i −0.700000 + 1.21244i 0.268466 + 0.963289i \(0.413483\pi\)
−0.968466 + 0.249146i \(0.919850\pi\)
\(6\) 0 0
\(7\) 7.50000 4.33013i 1.07143 0.618590i 0.142857 0.989743i \(-0.454371\pi\)
0.928571 + 0.371154i \(0.121038\pi\)
\(8\) 8.00000 1.00000
\(9\) 0 0
\(10\) −7.00000 12.1244i −0.700000 1.21244i
\(11\) −7.50000 + 4.33013i −0.681818 + 0.393648i −0.800540 0.599280i \(-0.795454\pi\)
0.118722 + 0.992928i \(0.462120\pi\)
\(12\) 0 0
\(13\) −10.0000 + 17.3205i −0.769231 + 1.33235i 0.168750 + 0.985659i \(0.446027\pi\)
−0.937981 + 0.346688i \(0.887306\pi\)
\(14\) 17.3205i 1.23718i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(17\) −8.00000 −0.470588 −0.235294 0.971924i \(-0.575605\pi\)
−0.235294 + 0.971924i \(0.575605\pi\)
\(18\) 0 0
\(19\) 10.3923i 0.546963i −0.961877 0.273482i \(-0.911825\pi\)
0.961877 0.273482i \(-0.0881753\pi\)
\(20\) 28.0000 1.40000
\(21\) 0 0
\(22\) 17.3205i 0.787296i
\(23\) −3.00000 1.73205i −0.130435 0.0753066i 0.433363 0.901220i \(-0.357327\pi\)
−0.563798 + 0.825913i \(0.690660\pi\)
\(24\) 0 0
\(25\) −12.0000 20.7846i −0.480000 0.831384i
\(26\) −20.0000 34.6410i −0.769231 1.33235i
\(27\) 0 0
\(28\) −30.0000 17.3205i −1.07143 0.618590i
\(29\) −5.00000 8.66025i −0.172414 0.298629i 0.766849 0.641827i \(-0.221823\pi\)
−0.939263 + 0.343198i \(0.888490\pi\)
\(30\) 0 0
\(31\) −46.5000 26.8468i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(32\) −16.0000 27.7128i −0.500000 0.866025i
\(33\) 0 0
\(34\) 8.00000 13.8564i 0.235294 0.407541i
\(35\) 60.6218i 1.73205i
\(36\) 0 0
\(37\) −10.0000 −0.270270 −0.135135 0.990827i \(-0.543147\pi\)
−0.135135 + 0.990827i \(0.543147\pi\)
\(38\) 18.0000 + 10.3923i 0.473684 + 0.273482i
\(39\) 0 0
\(40\) −28.0000 + 48.4974i −0.700000 + 1.21244i
\(41\) 25.0000 43.3013i 0.609756 1.05613i −0.381524 0.924359i \(-0.624601\pi\)
0.991280 0.131770i \(-0.0420659\pi\)
\(42\) 0 0
\(43\) −15.0000 + 8.66025i −0.348837 + 0.201401i −0.664173 0.747579i \(-0.731216\pi\)
0.315336 + 0.948980i \(0.397883\pi\)
\(44\) 30.0000 + 17.3205i 0.681818 + 0.393648i
\(45\) 0 0
\(46\) 6.00000 3.46410i 0.130435 0.0753066i
\(47\) −75.0000 + 43.3013i −1.59574 + 0.921304i −0.603450 + 0.797401i \(0.706208\pi\)
−0.992294 + 0.123903i \(0.960459\pi\)
\(48\) 0 0
\(49\) 13.0000 22.5167i 0.265306 0.459524i
\(50\) 48.0000 0.960000
\(51\) 0 0
\(52\) 80.0000 1.53846
\(53\) −47.0000 −0.886792 −0.443396 0.896326i \(-0.646227\pi\)
−0.443396 + 0.896326i \(0.646227\pi\)
\(54\) 0 0
\(55\) 60.6218i 1.10221i
\(56\) 60.0000 34.6410i 1.07143 0.618590i
\(57\) 0 0
\(58\) 20.0000 0.344828
\(59\) −30.0000 17.3205i −0.508475 0.293568i 0.223732 0.974651i \(-0.428176\pi\)
−0.732206 + 0.681083i \(0.761509\pi\)
\(60\) 0 0
\(61\) 32.0000 + 55.4256i 0.524590 + 0.908617i 0.999590 + 0.0286310i \(0.00911476\pi\)
−0.475000 + 0.879986i \(0.657552\pi\)
\(62\) 93.0000 53.6936i 1.50000 0.866025i
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) −70.0000 121.244i −1.07692 1.86529i
\(66\) 0 0
\(67\) 75.0000 + 43.3013i 1.11940 + 0.646288i 0.941248 0.337715i \(-0.109654\pi\)
0.178155 + 0.984003i \(0.442987\pi\)
\(68\) 16.0000 + 27.7128i 0.235294 + 0.407541i
\(69\) 0 0
\(70\) −105.000 60.6218i −1.50000 0.866025i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −55.0000 −0.753425 −0.376712 0.926330i \(-0.622945\pi\)
−0.376712 + 0.926330i \(0.622945\pi\)
\(74\) 10.0000 17.3205i 0.135135 0.234061i
\(75\) 0 0
\(76\) −36.0000 + 20.7846i −0.473684 + 0.273482i
\(77\) −37.5000 + 64.9519i −0.487013 + 0.843531i
\(78\) 0 0
\(79\) −6.00000 + 3.46410i −0.0759494 + 0.0438494i −0.537494 0.843268i \(-0.680629\pi\)
0.461544 + 0.887117i \(0.347296\pi\)
\(80\) −56.0000 96.9948i −0.700000 1.21244i
\(81\) 0 0
\(82\) 50.0000 + 86.6025i 0.609756 + 1.05613i
\(83\) −25.5000 + 14.7224i −0.307229 + 0.177379i −0.645686 0.763603i \(-0.723428\pi\)
0.338457 + 0.940982i \(0.390095\pi\)
\(84\) 0 0
\(85\) 28.0000 48.4974i 0.329412 0.570558i
\(86\) 34.6410i 0.402803i
\(87\) 0 0
\(88\) −60.0000 + 34.6410i −0.681818 + 0.393648i
\(89\) 10.0000 0.112360 0.0561798 0.998421i \(-0.482108\pi\)
0.0561798 + 0.998421i \(0.482108\pi\)
\(90\) 0 0
\(91\) 173.205i 1.90335i
\(92\) 13.8564i 0.150613i
\(93\) 0 0
\(94\) 173.205i 1.84261i
\(95\) 63.0000 + 36.3731i 0.663158 + 0.382874i
\(96\) 0 0
\(97\) 12.5000 + 21.6506i 0.128866 + 0.223202i 0.923237 0.384230i \(-0.125533\pi\)
−0.794372 + 0.607432i \(0.792200\pi\)
\(98\) 26.0000 + 45.0333i 0.265306 + 0.459524i
\(99\) 0 0
\(100\) −48.0000 + 83.1384i −0.480000 + 0.831384i
\(101\) 77.5000 + 134.234i 0.767327 + 1.32905i 0.939008 + 0.343896i \(0.111747\pi\)
−0.171681 + 0.985153i \(0.554920\pi\)
\(102\) 0 0
\(103\) 120.000 + 69.2820i 1.16505 + 0.672641i 0.952509 0.304511i \(-0.0984931\pi\)
0.212540 + 0.977152i \(0.431826\pi\)
\(104\) −80.0000 + 138.564i −0.769231 + 1.33235i
\(105\) 0 0
\(106\) 47.0000 81.4064i 0.443396 0.767985i
\(107\) 129.904i 1.21405i 0.794681 + 0.607027i \(0.207638\pi\)
−0.794681 + 0.607027i \(0.792362\pi\)
\(108\) 0 0
\(109\) 134.000 1.22936 0.614679 0.788777i \(-0.289286\pi\)
0.614679 + 0.788777i \(0.289286\pi\)
\(110\) 105.000 + 60.6218i 0.954545 + 0.551107i
\(111\) 0 0
\(112\) 138.564i 1.23718i
\(113\) 37.0000 64.0859i 0.327434 0.567132i −0.654568 0.756003i \(-0.727150\pi\)
0.982002 + 0.188871i \(0.0604829\pi\)
\(114\) 0 0
\(115\) 21.0000 12.1244i 0.182609 0.105429i
\(116\) −20.0000 + 34.6410i −0.172414 + 0.298629i
\(117\) 0 0
\(118\) 60.0000 34.6410i 0.508475 0.293568i
\(119\) −60.0000 + 34.6410i −0.504202 + 0.291101i
\(120\) 0 0
\(121\) −23.0000 + 39.8372i −0.190083 + 0.329233i
\(122\) −128.000 −1.04918
\(123\) 0 0
\(124\) 214.774i 1.73205i
\(125\) −7.00000 −0.0560000
\(126\) 0 0
\(127\) 25.9808i 0.204573i 0.994755 + 0.102286i \(0.0326158\pi\)
−0.994755 + 0.102286i \(0.967384\pi\)
\(128\) −64.0000 + 110.851i −0.500000 + 0.866025i
\(129\) 0 0
\(130\) 280.000 2.15385
\(131\) −142.500 82.2724i −1.08779 0.628034i −0.154800 0.987946i \(-0.549473\pi\)
−0.932986 + 0.359912i \(0.882807\pi\)
\(132\) 0 0
\(133\) −45.0000 77.9423i −0.338346 0.586032i
\(134\) −150.000 + 86.6025i −1.11940 + 0.646288i
\(135\) 0 0
\(136\) −64.0000 −0.470588
\(137\) 31.0000 + 53.6936i 0.226277 + 0.391924i 0.956702 0.291070i \(-0.0940111\pi\)
−0.730425 + 0.682993i \(0.760678\pi\)
\(138\) 0 0
\(139\) −150.000 86.6025i −1.07914 0.623040i −0.148473 0.988916i \(-0.547436\pi\)
−0.930663 + 0.365877i \(0.880769\pi\)
\(140\) 210.000 121.244i 1.50000 0.866025i
\(141\) 0 0
\(142\) 0 0
\(143\) 173.205i 1.21122i
\(144\) 0 0
\(145\) 70.0000 0.482759
\(146\) 55.0000 95.2628i 0.376712 0.652485i
\(147\) 0 0
\(148\) 20.0000 + 34.6410i 0.135135 + 0.234061i
\(149\) −57.5000 + 99.5929i −0.385906 + 0.668409i −0.991894 0.127065i \(-0.959444\pi\)
0.605988 + 0.795473i \(0.292778\pi\)
\(150\) 0 0
\(151\) −37.5000 + 21.6506i −0.248344 + 0.143382i −0.619006 0.785386i \(-0.712464\pi\)
0.370662 + 0.928768i \(0.379131\pi\)
\(152\) 83.1384i 0.546963i
\(153\) 0 0
\(154\) −75.0000 129.904i −0.487013 0.843531i
\(155\) 325.500 187.928i 2.10000 1.21244i
\(156\) 0 0
\(157\) −10.0000 + 17.3205i −0.0636943 + 0.110322i −0.896114 0.443824i \(-0.853622\pi\)
0.832420 + 0.554146i \(0.186955\pi\)
\(158\) 13.8564i 0.0876988i
\(159\) 0 0
\(160\) 224.000 1.40000
\(161\) −30.0000 −0.186335
\(162\) 0 0
\(163\) 103.923i 0.637565i −0.947828 0.318782i \(-0.896726\pi\)
0.947828 0.318782i \(-0.103274\pi\)
\(164\) −200.000 −1.21951
\(165\) 0 0
\(166\) 58.8897i 0.354757i
\(167\) 213.000 + 122.976i 1.27545 + 0.736381i 0.976008 0.217734i \(-0.0698665\pi\)
0.299441 + 0.954115i \(0.403200\pi\)
\(168\) 0 0
\(169\) −115.500 200.052i −0.683432 1.18374i
\(170\) 56.0000 + 96.9948i 0.329412 + 0.570558i
\(171\) 0 0
\(172\) 60.0000 + 34.6410i 0.348837 + 0.201401i
\(173\) −63.5000 109.985i −0.367052 0.635753i 0.622051 0.782977i \(-0.286300\pi\)
−0.989103 + 0.147224i \(0.952966\pi\)
\(174\) 0 0
\(175\) −180.000 103.923i −1.02857 0.593846i
\(176\) 138.564i 0.787296i
\(177\) 0 0
\(178\) −10.0000 + 17.3205i −0.0561798 + 0.0973062i
\(179\) 233.827i 1.30630i −0.757231 0.653148i \(-0.773448\pi\)
0.757231 0.653148i \(-0.226552\pi\)
\(180\) 0 0
\(181\) 56.0000 0.309392 0.154696 0.987962i \(-0.450560\pi\)
0.154696 + 0.987962i \(0.450560\pi\)
\(182\) −300.000 173.205i −1.64835 0.951676i
\(183\) 0 0
\(184\) −24.0000 13.8564i −0.130435 0.0753066i
\(185\) 35.0000 60.6218i 0.189189 0.327685i
\(186\) 0 0
\(187\) 60.0000 34.6410i 0.320856 0.185246i
\(188\) 300.000 + 173.205i 1.59574 + 0.921304i
\(189\) 0 0
\(190\) −126.000 + 72.7461i −0.663158 + 0.382874i
\(191\) −30.0000 + 17.3205i −0.157068 + 0.0906833i −0.576474 0.817116i \(-0.695572\pi\)
0.419406 + 0.907799i \(0.362238\pi\)
\(192\) 0 0
\(193\) −32.5000 + 56.2917i −0.168394 + 0.291667i −0.937855 0.347027i \(-0.887191\pi\)
0.769462 + 0.638693i \(0.220525\pi\)
\(194\) −50.0000 −0.257732
\(195\) 0 0
\(196\) −104.000 −0.530612
\(197\) 253.000 1.28426 0.642132 0.766594i \(-0.278050\pi\)
0.642132 + 0.766594i \(0.278050\pi\)
\(198\) 0 0
\(199\) 129.904i 0.652783i 0.945235 + 0.326391i \(0.105833\pi\)
−0.945235 + 0.326391i \(0.894167\pi\)
\(200\) −96.0000 166.277i −0.480000 0.831384i
\(201\) 0 0
\(202\) −310.000 −1.53465
\(203\) −75.0000 43.3013i −0.369458 0.213307i
\(204\) 0 0
\(205\) 175.000 + 303.109i 0.853659 + 1.47858i
\(206\) −240.000 + 138.564i −1.16505 + 0.672641i
\(207\) 0 0
\(208\) −160.000 277.128i −0.769231 1.33235i
\(209\) 45.0000 + 77.9423i 0.215311 + 0.372930i
\(210\) 0 0
\(211\) 129.000 + 74.4782i 0.611374 + 0.352977i 0.773503 0.633792i \(-0.218503\pi\)
−0.162129 + 0.986770i \(0.551836\pi\)
\(212\) 94.0000 + 162.813i 0.443396 + 0.767985i
\(213\) 0 0
\(214\) −225.000 129.904i −1.05140 0.607027i
\(215\) 121.244i 0.563924i
\(216\) 0 0
\(217\) −465.000 −2.14286
\(218\) −134.000 + 232.095i −0.614679 + 1.06466i
\(219\) 0 0
\(220\) −210.000 + 121.244i −0.954545 + 0.551107i
\(221\) 80.0000 138.564i 0.361991 0.626987i
\(222\) 0 0
\(223\) 30.0000 17.3205i 0.134529 0.0776704i −0.431225 0.902244i \(-0.641918\pi\)
0.565754 + 0.824574i \(0.308585\pi\)
\(224\) −240.000 138.564i −1.07143 0.618590i
\(225\) 0 0
\(226\) 74.0000 + 128.172i 0.327434 + 0.567132i
\(227\) 78.0000 45.0333i 0.343612 0.198385i −0.318256 0.948005i \(-0.603097\pi\)
0.661868 + 0.749620i \(0.269764\pi\)
\(228\) 0 0
\(229\) −73.0000 + 126.440i −0.318777 + 0.552138i −0.980233 0.197846i \(-0.936606\pi\)
0.661456 + 0.749984i \(0.269939\pi\)
\(230\) 48.4974i 0.210858i
\(231\) 0 0
\(232\) −40.0000 69.2820i −0.172414 0.298629i
\(233\) 334.000 1.43348 0.716738 0.697342i \(-0.245634\pi\)
0.716738 + 0.697342i \(0.245634\pi\)
\(234\) 0 0
\(235\) 606.218i 2.57965i
\(236\) 138.564i 0.587136i
\(237\) 0 0
\(238\) 138.564i 0.582202i
\(239\) 15.0000 + 8.66025i 0.0627615 + 0.0362354i 0.531052 0.847339i \(-0.321797\pi\)
−0.468291 + 0.883574i \(0.655130\pi\)
\(240\) 0 0
\(241\) −67.0000 116.047i −0.278008 0.481524i 0.692881 0.721052i \(-0.256341\pi\)
−0.970890 + 0.239527i \(0.923008\pi\)
\(242\) −46.0000 79.6743i −0.190083 0.329233i
\(243\) 0 0
\(244\) 128.000 221.703i 0.524590 0.908617i
\(245\) 91.0000 + 157.617i 0.371429 + 0.643333i
\(246\) 0 0
\(247\) 180.000 + 103.923i 0.728745 + 0.420741i
\(248\) −372.000 214.774i −1.50000 0.866025i
\(249\) 0 0
\(250\) 7.00000 12.1244i 0.0280000 0.0484974i
\(251\) 207.846i 0.828072i 0.910260 + 0.414036i \(0.135881\pi\)
−0.910260 + 0.414036i \(0.864119\pi\)
\(252\) 0 0
\(253\) 30.0000 0.118577
\(254\) −45.0000 25.9808i −0.177165 0.102286i
\(255\) 0 0
\(256\) −128.000 221.703i −0.500000 0.866025i
\(257\) −134.000 + 232.095i −0.521401 + 0.903093i 0.478289 + 0.878202i \(0.341257\pi\)
−0.999690 + 0.0248904i \(0.992076\pi\)
\(258\) 0 0
\(259\) −75.0000 + 43.3013i −0.289575 + 0.167186i
\(260\) −280.000 + 484.974i −1.07692 + 1.86529i
\(261\) 0 0
\(262\) 285.000 164.545i 1.08779 0.628034i
\(263\) 375.000 216.506i 1.42586 0.823218i 0.429065 0.903274i \(-0.358843\pi\)
0.996790 + 0.0800555i \(0.0255098\pi\)
\(264\) 0 0
\(265\) 164.500 284.922i 0.620755 1.07518i
\(266\) 180.000 0.676692
\(267\) 0 0
\(268\) 346.410i 1.29258i
\(269\) −350.000 −1.30112 −0.650558 0.759457i \(-0.725465\pi\)
−0.650558 + 0.759457i \(0.725465\pi\)
\(270\) 0 0
\(271\) 36.3731i 0.134218i 0.997746 + 0.0671090i \(0.0213775\pi\)
−0.997746 + 0.0671090i \(0.978622\pi\)
\(272\) 64.0000 110.851i 0.235294 0.407541i
\(273\) 0 0
\(274\) −124.000 −0.452555
\(275\) 180.000 + 103.923i 0.654545 + 0.377902i
\(276\) 0 0
\(277\) 260.000 + 450.333i 0.938628 + 1.62575i 0.768033 + 0.640410i \(0.221236\pi\)
0.170595 + 0.985341i \(0.445431\pi\)
\(278\) 300.000 173.205i 1.07914 0.623040i
\(279\) 0 0
\(280\) 484.974i 1.73205i
\(281\) 220.000 + 381.051i 0.782918 + 1.35605i 0.930235 + 0.366965i \(0.119603\pi\)
−0.147317 + 0.989089i \(0.547064\pi\)
\(282\) 0 0
\(283\) −285.000 164.545i −1.00707 0.581430i −0.0967355 0.995310i \(-0.530840\pi\)
−0.910332 + 0.413880i \(0.864173\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 300.000 + 173.205i 1.04895 + 0.605612i
\(287\) 433.013i 1.50876i
\(288\) 0 0
\(289\) −225.000 −0.778547
\(290\) −70.0000 + 121.244i −0.241379 + 0.418081i
\(291\) 0 0
\(292\) 110.000 + 190.526i 0.376712 + 0.652485i
\(293\) 109.000 188.794i 0.372014 0.644347i −0.617862 0.786287i \(-0.712001\pi\)
0.989875 + 0.141940i \(0.0453341\pi\)
\(294\) 0 0
\(295\) 210.000 121.244i 0.711864 0.410995i
\(296\) −80.0000 −0.270270
\(297\) 0 0
\(298\) −115.000 199.186i −0.385906 0.668409i
\(299\) 60.0000 34.6410i 0.200669 0.115856i
\(300\) 0 0
\(301\) −75.0000 + 129.904i −0.249169 + 0.431574i
\(302\) 86.6025i 0.286763i
\(303\) 0 0
\(304\) 144.000 + 83.1384i 0.473684 + 0.273482i
\(305\) −448.000 −1.46885
\(306\) 0 0
\(307\) 207.846i 0.677023i 0.940962 + 0.338512i \(0.109923\pi\)
−0.940962 + 0.338512i \(0.890077\pi\)
\(308\) 300.000 0.974026
\(309\) 0 0
\(310\) 751.710i 2.42487i
\(311\) −255.000 147.224i −0.819936 0.473390i 0.0304586 0.999536i \(-0.490303\pi\)
−0.850394 + 0.526146i \(0.823637\pi\)
\(312\) 0 0
\(313\) −242.500 420.022i −0.774760 1.34192i −0.934929 0.354835i \(-0.884537\pi\)
0.160169 0.987090i \(-0.448796\pi\)
\(314\) −20.0000 34.6410i −0.0636943 0.110322i
\(315\) 0 0
\(316\) 24.0000 + 13.8564i 0.0759494 + 0.0438494i
\(317\) −108.500 187.928i −0.342271 0.592831i 0.642583 0.766216i \(-0.277863\pi\)
−0.984854 + 0.173385i \(0.944530\pi\)
\(318\) 0 0
\(319\) 75.0000 + 43.3013i 0.235110 + 0.135741i
\(320\) −224.000 + 387.979i −0.700000 + 1.21244i
\(321\) 0 0
\(322\) 30.0000 51.9615i 0.0931677 0.161371i
\(323\) 83.1384i 0.257395i
\(324\) 0 0
\(325\) 480.000 1.47692
\(326\) 180.000 + 103.923i 0.552147 + 0.318782i
\(327\) 0 0
\(328\) 200.000 346.410i 0.609756 1.05613i
\(329\) −375.000 + 649.519i −1.13982 + 1.97422i
\(330\) 0 0
\(331\) −375.000 + 216.506i −1.13293 + 0.654098i −0.944670 0.328021i \(-0.893618\pi\)
−0.188260 + 0.982119i \(0.560285\pi\)
\(332\) 102.000 + 58.8897i 0.307229 + 0.177379i
\(333\) 0 0
\(334\) −426.000 + 245.951i −1.27545 + 0.736381i
\(335\) −525.000 + 303.109i −1.56716 + 0.904803i
\(336\) 0 0
\(337\) 155.000 268.468i 0.459941 0.796641i −0.539017 0.842295i \(-0.681204\pi\)
0.998957 + 0.0456545i \(0.0145373\pi\)
\(338\) 462.000 1.36686
\(339\) 0 0
\(340\) −224.000 −0.658824
\(341\) 465.000 1.36364
\(342\) 0 0
\(343\) 199.186i 0.580717i
\(344\) −120.000 + 69.2820i −0.348837 + 0.201401i
\(345\) 0 0
\(346\) 254.000 0.734104
\(347\) −187.500 108.253i −0.540346 0.311969i 0.204873 0.978789i \(-0.434322\pi\)
−0.745219 + 0.666820i \(0.767655\pi\)
\(348\) 0 0
\(349\) −37.0000 64.0859i −0.106017 0.183627i 0.808136 0.588996i \(-0.200477\pi\)
−0.914153 + 0.405369i \(0.867143\pi\)
\(350\) 360.000 207.846i 1.02857 0.593846i
\(351\) 0 0
\(352\) 240.000 + 138.564i 0.681818 + 0.393648i
\(353\) −197.000 341.214i −0.558074 0.966612i −0.997657 0.0684103i \(-0.978207\pi\)
0.439584 0.898202i \(-0.355126\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −20.0000 34.6410i −0.0561798 0.0973062i
\(357\) 0 0
\(358\) 405.000 + 233.827i 1.13128 + 0.653148i
\(359\) 571.577i 1.59214i 0.605207 + 0.796068i \(0.293090\pi\)
−0.605207 + 0.796068i \(0.706910\pi\)
\(360\) 0 0
\(361\) 253.000 0.700831
\(362\) −56.0000 + 96.9948i −0.154696 + 0.267942i
\(363\) 0 0
\(364\) 600.000 346.410i 1.64835 0.951676i
\(365\) 192.500 333.420i 0.527397 0.913479i
\(366\) 0 0
\(367\) −487.500 + 281.458i −1.32834 + 0.766916i −0.985043 0.172311i \(-0.944877\pi\)
−0.343295 + 0.939228i \(0.611543\pi\)
\(368\) 48.0000 27.7128i 0.130435 0.0753066i
\(369\) 0 0
\(370\) 70.0000 + 121.244i 0.189189 + 0.327685i
\(371\) −352.500 + 203.516i −0.950135 + 0.548561i
\(372\) 0 0
\(373\) 20.0000 34.6410i 0.0536193 0.0928714i −0.837970 0.545716i \(-0.816258\pi\)
0.891589 + 0.452845i \(0.149591\pi\)
\(374\) 138.564i 0.370492i
\(375\) 0 0
\(376\) −600.000 + 346.410i −1.59574 + 0.921304i
\(377\) 200.000 0.530504
\(378\) 0 0
\(379\) 685.892i 1.80974i 0.425686 + 0.904871i \(0.360033\pi\)
−0.425686 + 0.904871i \(0.639967\pi\)
\(380\) 290.985i 0.765749i
\(381\) 0 0
\(382\) 69.2820i 0.181367i
\(383\) 312.000 + 180.133i 0.814621 + 0.470322i 0.848558 0.529102i \(-0.177471\pi\)
−0.0339368 + 0.999424i \(0.510804\pi\)
\(384\) 0 0
\(385\) −262.500 454.663i −0.681818 1.18094i
\(386\) −65.0000 112.583i −0.168394 0.291667i
\(387\) 0 0
\(388\) 50.0000 86.6025i 0.128866 0.223202i
\(389\) −237.500 411.362i −0.610540 1.05749i −0.991150 0.132750i \(-0.957619\pi\)
0.380610 0.924736i \(-0.375714\pi\)
\(390\) 0 0
\(391\) 24.0000 + 13.8564i 0.0613811 + 0.0354384i
\(392\) 104.000 180.133i 0.265306 0.459524i
\(393\) 0 0
\(394\) −253.000 + 438.209i −0.642132 + 1.11221i
\(395\) 48.4974i 0.122778i
\(396\) 0 0
\(397\) 260.000 0.654912 0.327456 0.944866i \(-0.393809\pi\)
0.327456 + 0.944866i \(0.393809\pi\)
\(398\) −225.000 129.904i −0.565327 0.326391i
\(399\) 0 0
\(400\) 384.000 0.960000
\(401\) 370.000 640.859i 0.922693 1.59815i 0.127464 0.991843i \(-0.459316\pi\)
0.795230 0.606308i \(-0.207350\pi\)
\(402\) 0 0
\(403\) 930.000 536.936i 2.30769 1.33235i
\(404\) 310.000 536.936i 0.767327 1.32905i
\(405\) 0 0
\(406\) 150.000 86.6025i 0.369458 0.213307i
\(407\) 75.0000 43.3013i 0.184275 0.106391i
\(408\) 0 0
\(409\) −329.500 + 570.711i −0.805623 + 1.39538i 0.110246 + 0.993904i \(0.464836\pi\)
−0.915869 + 0.401476i \(0.868497\pi\)
\(410\) −700.000 −1.70732
\(411\) 0 0
\(412\) 554.256i 1.34528i
\(413\) −300.000 −0.726392
\(414\) 0 0
\(415\) 206.114i 0.496660i
\(416\) 640.000 1.53846
\(417\) 0 0
\(418\) −180.000 −0.430622
\(419\) 510.000 + 294.449i 1.21718 + 0.702741i 0.964315 0.264759i \(-0.0852924\pi\)
0.252869 + 0.967500i \(0.418626\pi\)
\(420\) 0 0
\(421\) 248.000 + 429.549i 0.589074 + 1.02031i 0.994354 + 0.106113i \(0.0338405\pi\)
−0.405280 + 0.914192i \(0.632826\pi\)
\(422\) −258.000 + 148.956i −0.611374 + 0.352977i
\(423\) 0 0
\(424\) −376.000 −0.886792
\(425\) 96.0000 + 166.277i 0.225882 + 0.391240i
\(426\) 0 0
\(427\) 480.000 + 277.128i 1.12412 + 0.649012i
\(428\) 450.000 259.808i 1.05140 0.607027i
\(429\) 0 0
\(430\) 210.000 + 121.244i 0.488372 + 0.281962i
\(431\) 571.577i 1.32616i 0.748547 + 0.663082i \(0.230752\pi\)
−0.748547 + 0.663082i \(0.769248\pi\)
\(432\) 0 0
\(433\) −235.000 −0.542725 −0.271363 0.962477i \(-0.587474\pi\)
−0.271363 + 0.962477i \(0.587474\pi\)
\(434\) 465.000 805.404i 1.07143 1.85577i
\(435\) 0 0
\(436\) −268.000 464.190i −0.614679 1.06466i
\(437\) −18.0000 + 31.1769i −0.0411899 + 0.0713431i
\(438\) 0 0
\(439\) 358.500 206.980i 0.816629 0.471481i −0.0326238 0.999468i \(-0.510386\pi\)
0.849253 + 0.527987i \(0.177053\pi\)
\(440\) 484.974i 1.10221i
\(441\) 0 0
\(442\) 160.000 + 277.128i 0.361991 + 0.626987i
\(443\) −498.000 + 287.520i −1.12415 + 0.649030i −0.942458 0.334325i \(-0.891492\pi\)
−0.181695 + 0.983355i \(0.558159\pi\)
\(444\) 0 0
\(445\) −35.0000 + 60.6218i −0.0786517 + 0.136229i
\(446\) 69.2820i 0.155341i
\(447\) 0 0
\(448\) 480.000 277.128i 1.07143 0.618590i
\(449\) −470.000 −1.04677 −0.523385 0.852096i \(-0.675331\pi\)
−0.523385 + 0.852096i \(0.675331\pi\)
\(450\) 0 0
\(451\) 433.013i 0.960117i
\(452\) −296.000 −0.654867
\(453\) 0 0
\(454\) 180.133i 0.396769i
\(455\) −1050.00 606.218i −2.30769 1.33235i
\(456\) 0 0
\(457\) 162.500 + 281.458i 0.355580 + 0.615882i 0.987217 0.159382i \(-0.0509501\pi\)
−0.631637 + 0.775264i \(0.717617\pi\)
\(458\) −146.000 252.879i −0.318777 0.552138i
\(459\) 0 0
\(460\) −84.0000 48.4974i −0.182609 0.105429i
\(461\) −327.500 567.247i −0.710412 1.23047i −0.964703 0.263342i \(-0.915175\pi\)
0.254290 0.967128i \(-0.418158\pi\)
\(462\) 0 0
\(463\) 142.500 + 82.2724i 0.307775 + 0.177694i 0.645931 0.763396i \(-0.276470\pi\)
−0.338155 + 0.941090i \(0.609803\pi\)
\(464\) 160.000 0.344828
\(465\) 0 0
\(466\) −334.000 + 578.505i −0.716738 + 1.24143i
\(467\) 57.1577i 0.122393i −0.998126 0.0611967i \(-0.980508\pi\)
0.998126 0.0611967i \(-0.0194917\pi\)
\(468\) 0 0
\(469\) 750.000 1.59915
\(470\) 1050.00 + 606.218i 2.23404 + 1.28983i
\(471\) 0 0
\(472\) −240.000 138.564i −0.508475 0.293568i
\(473\) 75.0000 129.904i 0.158562 0.274638i
\(474\) 0 0
\(475\) −216.000 + 124.708i −0.454737 + 0.262542i
\(476\) 240.000 + 138.564i 0.504202 + 0.291101i
\(477\) 0 0
\(478\) −30.0000 + 17.3205i −0.0627615 + 0.0362354i
\(479\) 285.000 164.545i 0.594990 0.343517i −0.172078 0.985083i \(-0.555048\pi\)
0.767068 + 0.641566i \(0.221715\pi\)
\(480\) 0 0
\(481\) 100.000 173.205i 0.207900 0.360094i
\(482\) 268.000 0.556017
\(483\) 0 0
\(484\) 184.000 0.380165
\(485\) −175.000 −0.360825
\(486\) 0 0
\(487\) 519.615i 1.06697i −0.845809 0.533486i \(-0.820882\pi\)
0.845809 0.533486i \(-0.179118\pi\)
\(488\) 256.000 + 443.405i 0.524590 + 0.908617i
\(489\) 0 0
\(490\) −364.000 −0.742857
\(491\) −187.500 108.253i −0.381874 0.220475i 0.296759 0.954952i \(-0.404094\pi\)
−0.678633 + 0.734477i \(0.737427\pi\)
\(492\) 0 0
\(493\) 40.0000 + 69.2820i 0.0811359 + 0.140532i
\(494\) −360.000 + 207.846i −0.728745 + 0.420741i
\(495\) 0 0
\(496\) 744.000 429.549i 1.50000 0.866025i
\(497\) 0 0
\(498\) 0 0
\(499\) 39.0000 + 22.5167i 0.0781563 + 0.0451236i 0.538569 0.842581i \(-0.318965\pi\)
−0.460413 + 0.887705i \(0.652299\pi\)
\(500\) 14.0000 + 24.2487i 0.0280000 + 0.0484974i
\(501\) 0 0
\(502\) −360.000 207.846i −0.717131 0.414036i
\(503\) 384.515i 0.764444i 0.924071 + 0.382222i \(0.124841\pi\)
−0.924071 + 0.382222i \(0.875159\pi\)
\(504\) 0 0
\(505\) −1085.00 −2.14851
\(506\) −30.0000 + 51.9615i −0.0592885 + 0.102691i
\(507\) 0 0
\(508\) 90.0000 51.9615i 0.177165 0.102286i
\(509\) −132.500 + 229.497i −0.260314 + 0.450878i −0.966325 0.257323i \(-0.917160\pi\)
0.706011 + 0.708201i \(0.250493\pi\)
\(510\) 0 0
\(511\) −412.500 + 238.157i −0.807241 + 0.466061i
\(512\) 512.000 1.00000
\(513\) 0 0
\(514\) −268.000 464.190i −0.521401 0.903093i
\(515\) −840.000 + 484.974i −1.63107 + 0.941698i
\(516\) 0 0
\(517\) 375.000 649.519i 0.725338 1.25632i
\(518\) 173.205i 0.334373i
\(519\) 0 0
\(520\) −560.000 969.948i −1.07692 1.86529i
\(521\) −380.000 −0.729367 −0.364683 0.931132i \(-0.618823\pi\)
−0.364683 + 0.931132i \(0.618823\pi\)
\(522\) 0 0
\(523\) 623.538i 1.19223i −0.802898 0.596117i \(-0.796709\pi\)
0.802898 0.596117i \(-0.203291\pi\)
\(524\) 658.179i 1.25607i
\(525\) 0 0
\(526\) 866.025i 1.64644i
\(527\) 372.000 + 214.774i 0.705882 + 0.407541i
\(528\) 0 0
\(529\) −258.500 447.735i −0.488658 0.846380i
\(530\) 329.000 + 569.845i 0.620755 + 1.07518i
\(531\) 0 0
\(532\) −180.000 + 311.769i −0.338346 + 0.586032i
\(533\) 500.000 + 866.025i 0.938086 + 1.62481i
\(534\) 0 0
\(535\) −787.500 454.663i −1.47196 0.849838i
\(536\) 600.000 + 346.410i 1.11940 + 0.646288i
\(537\) 0 0
\(538\) 350.000 606.218i 0.650558 1.12680i
\(539\) 225.167i 0.417749i
\(540\) 0 0
\(541\) −532.000 −0.983364 −0.491682 0.870775i \(-0.663618\pi\)
−0.491682 + 0.870775i \(0.663618\pi\)
\(542\) −63.0000 36.3731i −0.116236 0.0671090i
\(543\) 0 0
\(544\) 128.000 + 221.703i 0.235294 + 0.407541i
\(545\) −469.000 + 812.332i −0.860550 + 1.49052i
\(546\) 0 0
\(547\) −780.000 + 450.333i −1.42596 + 0.823278i −0.996799 0.0799498i \(-0.974524\pi\)
−0.429161 + 0.903228i \(0.641191\pi\)
\(548\) 124.000 214.774i 0.226277 0.391924i
\(549\) 0 0
\(550\) −360.000 + 207.846i −0.654545 + 0.377902i
\(551\) −90.0000 + 51.9615i −0.163339 + 0.0943040i
\(552\) 0 0
\(553\) −30.0000 + 51.9615i −0.0542495 + 0.0939630i
\(554\) −1040.00 −1.87726
\(555\) 0 0
\(556\) 692.820i 1.24608i
\(557\) −89.0000 −0.159785 −0.0798923 0.996804i \(-0.525458\pi\)
−0.0798923 + 0.996804i \(0.525458\pi\)
\(558\) 0 0
\(559\) 346.410i 0.619696i
\(560\) −840.000 484.974i −1.50000 0.866025i
\(561\) 0 0
\(562\) −880.000 −1.56584
\(563\) 262.500 + 151.554i 0.466252 + 0.269191i 0.714670 0.699462i \(-0.246577\pi\)
−0.248417 + 0.968653i \(0.579910\pi\)
\(564\) 0 0
\(565\) 259.000 + 448.601i 0.458407 + 0.793984i
\(566\) 570.000 329.090i 1.00707 0.581430i
\(567\) 0 0
\(568\) 0 0
\(569\) −50.0000 86.6025i −0.0878735 0.152201i 0.818739 0.574166i \(-0.194674\pi\)
−0.906612 + 0.421965i \(0.861340\pi\)
\(570\) 0 0
\(571\) −294.000 169.741i −0.514886 0.297270i 0.219954 0.975510i \(-0.429409\pi\)
−0.734840 + 0.678241i \(0.762743\pi\)
\(572\) −600.000 + 346.410i −1.04895 + 0.605612i
\(573\) 0 0
\(574\) 750.000 + 433.013i 1.30662 + 0.754378i
\(575\) 83.1384i 0.144589i
\(576\) 0 0
\(577\) −730.000 −1.26516 −0.632582 0.774493i \(-0.718005\pi\)
−0.632582 + 0.774493i \(0.718005\pi\)
\(578\) 225.000 389.711i 0.389273 0.674241i
\(579\) 0 0
\(580\) −140.000 242.487i −0.241379 0.418081i
\(581\) −127.500 + 220.836i −0.219449 + 0.380097i
\(582\) 0 0
\(583\) 352.500 203.516i 0.604631 0.349084i
\(584\) −440.000 −0.753425
\(585\) 0 0
\(586\) 218.000 + 377.587i 0.372014 + 0.644347i
\(587\) 694.500 400.970i 1.18313 0.683083i 0.226397 0.974035i \(-0.427305\pi\)
0.956738 + 0.290952i \(0.0939720\pi\)
\(588\) 0 0
\(589\) −279.000 + 483.242i −0.473684 + 0.820445i
\(590\) 484.974i 0.821990i
\(591\) 0 0
\(592\) 80.0000 138.564i 0.135135 0.234061i
\(593\) 982.000 1.65599 0.827993 0.560738i \(-0.189483\pi\)
0.827993 + 0.560738i \(0.189483\pi\)
\(594\) 0 0
\(595\) 484.974i 0.815083i
\(596\) 460.000 0.771812
\(597\) 0 0
\(598\) 138.564i 0.231712i
\(599\) 195.000 + 112.583i 0.325543 + 0.187952i 0.653860 0.756615i \(-0.273148\pi\)
−0.328318 + 0.944567i \(0.606482\pi\)
\(600\) 0 0
\(601\) −125.500 217.372i −0.208819 0.361684i 0.742524 0.669819i \(-0.233629\pi\)
−0.951343 + 0.308135i \(0.900295\pi\)
\(602\) −150.000 259.808i −0.249169 0.431574i
\(603\) 0 0
\(604\) 150.000 + 86.6025i 0.248344 + 0.143382i
\(605\) −161.000 278.860i −0.266116 0.460926i
\(606\) 0 0
\(607\) −330.000 190.526i −0.543657 0.313881i 0.202903 0.979199i \(-0.434963\pi\)
−0.746560 + 0.665318i \(0.768296\pi\)
\(608\) −288.000 + 166.277i −0.473684 + 0.273482i
\(609\) 0 0
\(610\) 448.000 775.959i 0.734426 1.27206i
\(611\) 1732.05i 2.83478i
\(612\) 0 0
\(613\) 650.000 1.06036 0.530179 0.847885i \(-0.322125\pi\)
0.530179 + 0.847885i \(0.322125\pi\)
\(614\) −360.000 207.846i −0.586319 0.338512i
\(615\) 0 0
\(616\) −300.000 + 519.615i −0.487013 + 0.843531i
\(617\) 379.000 656.447i 0.614263 1.06393i −0.376251 0.926518i \(-0.622787\pi\)
0.990513 0.137416i \(-0.0438798\pi\)
\(618\) 0 0
\(619\) −150.000 + 86.6025i −0.242326 + 0.139907i −0.616245 0.787554i \(-0.711347\pi\)
0.373919 + 0.927461i \(0.378014\pi\)
\(620\) −1302.00 751.710i −2.10000 1.21244i
\(621\) 0 0
\(622\) 510.000 294.449i 0.819936 0.473390i
\(623\) 75.0000 43.3013i 0.120385 0.0695044i
\(624\) 0 0
\(625\) 324.500 562.050i 0.519200 0.899281i
\(626\) 970.000 1.54952
\(627\) 0 0
\(628\) 80.0000 0.127389
\(629\) 80.0000 0.127186
\(630\) 0 0
\(631\) 119.512i 0.189400i 0.995506 + 0.0947001i \(0.0301892\pi\)
−0.995506 + 0.0947001i \(0.969811\pi\)
\(632\) −48.0000 + 27.7128i −0.0759494 + 0.0438494i
\(633\) 0 0
\(634\) 434.000 0.684543
\(635\) −157.500 90.9327i −0.248031 0.143201i
\(636\) 0 0
\(637\) 260.000 + 450.333i 0.408163 + 0.706960i
\(638\) −150.000 + 86.6025i −0.235110 + 0.135741i
\(639\) 0 0
\(640\) −448.000 775.959i −0.700000 1.21244i
\(641\) −455.000 788.083i −0.709828 1.22946i −0.964921 0.262542i \(-0.915439\pi\)
0.255092 0.966917i \(-0.417894\pi\)
\(642\) 0 0
\(643\) 30.0000 + 17.3205i 0.0466563 + 0.0269370i 0.523147 0.852243i \(-0.324758\pi\)
−0.476490 + 0.879180i \(0.658091\pi\)
\(644\) 60.0000 + 103.923i 0.0931677 + 0.161371i
\(645\) 0 0
\(646\) −144.000 83.1384i −0.222910 0.128697i
\(647\) 914.523i 1.41348i 0.707472 + 0.706741i \(0.249835\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(648\) 0 0
\(649\) 300.000 0.462250
\(650\) −480.000 + 831.384i −0.738462 + 1.27905i
\(651\) 0 0
\(652\) −360.000 + 207.846i −0.552147 + 0.318782i
\(653\) −51.5000 + 89.2006i −0.0788668 + 0.136601i −0.902761 0.430142i \(-0.858464\pi\)
0.823894 + 0.566743i \(0.191797\pi\)
\(654\) 0 0
\(655\) 997.500 575.907i 1.52290 0.879247i
\(656\) 400.000 + 692.820i 0.609756 + 1.05613i
\(657\) 0 0
\(658\) −750.000 1299.04i −1.13982 1.97422i
\(659\) −52.5000 + 30.3109i −0.0796662 + 0.0459953i −0.539304 0.842111i \(-0.681313\pi\)
0.459638 + 0.888106i \(0.347979\pi\)
\(660\) 0 0
\(661\) −289.000 + 500.563i −0.437216 + 0.757281i −0.997474 0.0710377i \(-0.977369\pi\)
0.560257 + 0.828319i \(0.310702\pi\)
\(662\) 866.025i 1.30820i
\(663\) 0 0
\(664\) −204.000 + 117.779i −0.307229 + 0.177379i
\(665\) 630.000 0.947368
\(666\) 0 0
\(667\) 34.6410i 0.0519356i
\(668\) 983.805i 1.47276i
\(669\) 0 0
\(670\) 1212.44i 1.80961i
\(671\) −480.000 277.128i −0.715350 0.413008i
\(672\) 0 0
\(673\) −422.500 731.791i −0.627786 1.08736i −0.987995 0.154486i \(-0.950628\pi\)
0.360209 0.932872i \(-0.382705\pi\)
\(674\) 310.000 + 536.936i 0.459941 + 0.796641i
\(675\) 0 0
\(676\) −462.000 + 800.207i −0.683432 + 1.18374i
\(677\) 577.000 + 999.393i 0.852290 + 1.47621i 0.879137 + 0.476569i \(0.158120\pi\)
−0.0268475 + 0.999640i \(0.508547\pi\)
\(678\) 0 0
\(679\) 187.500 + 108.253i 0.276141 + 0.159430i
\(680\) 224.000 387.979i 0.329412 0.570558i
\(681\) 0 0
\(682\) −465.000 + 805.404i −0.681818 + 1.18094i
\(683\) 187.061i 0.273882i 0.990579 + 0.136941i \(0.0437271\pi\)
−0.990579 + 0.136941i \(0.956273\pi\)
\(684\) 0 0
\(685\) −434.000 −0.633577
\(686\) −345.000 199.186i −0.502915 0.290358i
\(687\) 0 0
\(688\) 277.128i 0.402803i
\(689\) 470.000 814.064i 0.682148 1.18152i
\(690\) 0 0
\(691\) 426.000 245.951i 0.616498 0.355935i −0.159006 0.987278i \(-0.550829\pi\)
0.775504 + 0.631342i \(0.217496\pi\)
\(692\) −254.000 + 439.941i −0.367052 + 0.635753i
\(693\) 0 0
\(694\) 375.000 216.506i 0.540346 0.311969i
\(695\) 1050.00 606.218i 1.51079 0.872256i
\(696\) 0 0
\(697\) −200.000 + 346.410i −0.286944 + 0.497002i
\(698\) 148.000 0.212034
\(699\) 0 0
\(700\) 831.384i 1.18769i
\(701\) −215.000 −0.306705 −0.153352 0.988172i \(-0.549007\pi\)
−0.153352 + 0.988172i \(0.549007\pi\)
\(702\) 0 0
\(703\) 103.923i 0.147828i
\(704\) −480.000 + 277.128i −0.681818 + 0.393648i
\(705\) 0 0
\(706\) 788.000 1.11615
\(707\) 1162.50 + 671.170i 1.64427 + 0.949321i
\(708\) 0 0
\(709\) 266.000 + 460.726i 0.375176 + 0.649824i 0.990353 0.138565i \(-0.0442488\pi\)
−0.615177 + 0.788389i \(0.710916\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 80.0000 0.112360
\(713\) 93.0000 + 161.081i 0.130435 + 0.225920i
\(714\) 0 0
\(715\) 1050.00 + 606.218i 1.46853 + 0.847857i
\(716\) −810.000 + 467.654i −1.13128 + 0.653148i
\(717\) 0 0
\(718\) −990.000 571.577i −1.37883 0.796068i
\(719\) 1143.15i 1.58992i −0.606661 0.794961i \(-0.707491\pi\)
0.606661 0.794961i \(-0.292509\pi\)
\(720\) 0 0
\(721\) 1200.00 1.66436
\(722\) −253.000 + 438.209i −0.350416 + 0.606937i
\(723\) 0 0
\(724\) −112.000 193.990i −0.154696 0.267942i
\(725\) −120.000 + 207.846i −0.165517 + 0.286684i
\(726\) 0 0
\(727\) −1072.50 + 619.208i −1.47524 + 0.851731i −0.999610 0.0279146i \(-0.991113\pi\)
−0.475630 + 0.879645i \(0.657780\pi\)
\(728\) 1385.64i 1.90335i
\(729\) 0 0
\(730\) 385.000 + 666.840i 0.527397 + 0.913479i
\(731\) 120.000 69.2820i 0.164159 0.0947771i
\(732\) 0 0
\(733\) −475.000 + 822.724i −0.648022 + 1.12241i 0.335573 + 0.942014i \(0.391070\pi\)
−0.983595 + 0.180392i \(0.942263\pi\)
\(734\) 1125.83i 1.53383i
\(735\) 0 0
\(736\) 110.851i 0.150613i
\(737\) −750.000 −1.01764
\(738\) 0 0
\(739\) 581.969i 0.787509i 0.919216 + 0.393754i \(0.128824\pi\)
−0.919216 + 0.393754i \(0.871176\pi\)
\(740\) −280.000 −0.378378
\(741\) 0 0
\(742\) 814.064i 1.09712i
\(743\) −750.000 433.013i −1.00942 0.582790i −0.0983991 0.995147i \(-0.531372\pi\)
−0.911022 + 0.412357i \(0.864706\pi\)
\(744\) 0 0
\(745\) −402.500 697.150i −0.540268 0.935772i
\(746\) 40.0000 + 69.2820i 0.0536193 + 0.0928714i
\(747\) 0 0
\(748\) −240.000 138.564i −0.320856 0.185246i
\(749\) 562.500 + 974.279i 0.751001 + 1.30077i
\(750\) 0 0
\(751\) 151.500 + 87.4686i 0.201731 + 0.116469i 0.597463 0.801897i \(-0.296176\pi\)
−0.395732 + 0.918366i \(0.629509\pi\)
\(752\) 1385.64i 1.84261i
\(753\) 0 0
\(754\) −200.000 + 346.410i −0.265252 + 0.459430i
\(755\) 303.109i 0.401469i
\(756\) 0 0
\(757\) 830.000 1.09643 0.548217 0.836336i \(-0.315307\pi\)
0.548217 + 0.836336i \(0.315307\pi\)
\(758\) −1188.00 685.892i −1.56728 0.904871i
\(759\) 0 0
\(760\) 504.000 + 290.985i 0.663158 + 0.382874i
\(761\) 280.000 484.974i 0.367937 0.637285i −0.621306 0.783568i \(-0.713398\pi\)
0.989243 + 0.146283i \(0.0467309\pi\)
\(762\) 0 0
\(763\) 1005.00 580.237i 1.31717 0.760468i
\(764\) 120.000 + 69.2820i 0.157068 + 0.0906833i
\(765\) 0 0
\(766\) −624.000 + 360.267i −0.814621 + 0.470322i
\(767\) 600.000 346.410i 0.782269 0.451643i
\(768\) 0 0
\(769\) 165.500 286.654i 0.215215 0.372763i −0.738124 0.674665i \(-0.764288\pi\)
0.953339 + 0.301902i \(0.0976216\pi\)
\(770\) 1050.00 1.36364
\(771\) 0 0
\(772\) 260.000 0.336788
\(773\) 298.000 0.385511 0.192755 0.981247i \(-0.438258\pi\)
0.192755 + 0.981247i \(0.438258\pi\)
\(774\) 0 0
\(775\) 1288.65i 1.66277i
\(776\) 100.000 + 173.205i 0.128866 + 0.223202i
\(777\) 0 0
\(778\) 950.000 1.22108
\(779\) −450.000 259.808i −0.577664 0.333514i
\(780\) 0 0
\(781\) 0 0
\(782\) −48.0000 + 27.7128i −0.0613811 + 0.0354384i
\(783\) 0 0
\(784\) 208.000 + 360.267i 0.265306 + 0.459524i
\(785\) −70.0000 121.244i −0.0891720 0.154450i
\(786\) 0 0
\(787\) −960.000 554.256i −1.21982 0.704265i −0.254942 0.966956i \(-0.582056\pi\)
−0.964880 + 0.262692i \(0.915390\pi\)
\(788\) −506.000 876.418i −0.642132 1.11221i
\(789\) 0 0
\(790\) 84.0000 + 48.4974i 0.106329 + 0.0613891i
\(791\) 640.859i 0.810188i
\(792\) 0 0
\(793\) −1280.00 −1.61412
\(794\) −260.000 + 450.333i −0.327456 + 0.567170i
\(795\) 0 0
\(796\) 450.000 259.808i 0.565327 0.326391i
\(797\) −651.500 + 1128.43i −0.817440 + 1.41585i 0.0901219 + 0.995931i \(0.471274\pi\)
−0.907562 + 0.419918i \(0.862059\pi\)
\(798\) 0 0
\(799\) 600.000 346.410i 0.750939 0.433555i
\(800\) −384.000 + 665.108i −0.480000 + 0.831384i
\(801\) 0 0
\(802\) 740.000 + 1281.72i 0.922693 + 1.59815i
\(803\) 412.500 238.157i 0.513699 0.296584i
\(804\) 0 0
\(805\) 105.000 181.865i 0.130435 0.225920i
\(806\) 2147.74i 2.66469i
\(807\) 0 0
\(808\) 620.000 + 1073.87i 0.767327 + 1.32905i
\(809\) −170.000 −0.210136 −0.105068 0.994465i \(-0.533506\pi\)
−0.105068 + 0.994465i \(0.533506\pi\)
\(810\) 0 0
\(811\) 779.423i 0.961064i 0.876977 + 0.480532i \(0.159556\pi\)
−0.876977 + 0.480532i \(0.840444\pi\)
\(812\) 346.410i 0.426613i
\(813\) 0 0
\(814\) 173.205i 0.212783i
\(815\) 630.000 + 363.731i 0.773006 + 0.446295i
\(816\) 0 0
\(817\) 90.0000 + 155.885i 0.110159 + 0.190801i
\(818\) −659.000 1141.42i −0.805623 1.39538i
\(819\) 0 0
\(820\) 700.000 1212.44i 0.853659 1.47858i
\(821\) −545.000 943.968i −0.663825 1.14978i −0.979603 0.200945i \(-0.935599\pi\)
0.315778 0.948833i \(-0.397735\pi\)
\(822\) 0 0
\(823\) 817.500 + 471.984i 0.993317 + 0.573492i 0.906264 0.422712i \(-0.138922\pi\)
0.0870530 + 0.996204i \(0.472255\pi\)
\(824\) 960.000 + 554.256i 1.16505 + 0.672641i
\(825\) 0 0
\(826\) 300.000 519.615i 0.363196 0.629074i
\(827\) 83.1384i 0.100530i 0.998736 + 0.0502651i \(0.0160066\pi\)
−0.998736 + 0.0502651i \(0.983993\pi\)
\(828\) 0 0
\(829\) 542.000 0.653800 0.326900 0.945059i \(-0.393996\pi\)
0.326900 + 0.945059i \(0.393996\pi\)
\(830\) 357.000 + 206.114i 0.430120 + 0.248330i
\(831\) 0 0
\(832\) −640.000 + 1108.51i −0.769231 + 1.33235i
\(833\) −104.000 + 180.133i −0.124850 + 0.216246i
\(834\) 0 0
\(835\) −1491.00 + 860.829i −1.78563 + 1.03093i
\(836\) 180.000 311.769i 0.215311 0.372930i
\(837\) 0 0
\(838\) −1020.00 + 588.897i −1.21718 + 0.702741i
\(839\) 600.000 346.410i 0.715137 0.412885i −0.0978231 0.995204i \(-0.531188\pi\)
0.812960 + 0.582319i \(0.197855\pi\)
\(840\) 0 0
\(841\) 370.500 641.725i 0.440547 0.763050i
\(842\) −992.000 −1.17815
\(843\) 0 0
\(844\) 595.825i 0.705954i
\(845\) 1617.00 1.91361
\(846\) 0 0
\(847\) 398.372i 0.470333i
\(848\) 376.000 651.251i 0.443396 0.767985i
\(849\) 0 0
\(850\) −384.000 −0.451765
\(851\) 30.0000 + 17.3205i 0.0352526 + 0.0203531i
\(852\) 0 0
\(853\) −145.000 251.147i −0.169988 0.294428i 0.768427 0.639937i \(-0.221040\pi\)
−0.938415 + 0.345509i \(0.887706\pi\)
\(854\) −960.000 + 554.256i −1.12412 + 0.649012i
\(855\) 0 0
\(856\) 1039.23i 1.21405i
\(857\) 184.000 + 318.697i 0.214702 + 0.371876i 0.953180 0.302402i \(-0.0977885\pi\)
−0.738478 + 0.674278i \(0.764455\pi\)
\(858\) 0 0
\(859\) −924.000 533.472i −1.07567 0.621038i −0.145944 0.989293i \(-0.546622\pi\)
−0.929725 + 0.368255i \(0.879955\pi\)
\(860\) −420.000 + 242.487i −0.488372 + 0.281962i
\(861\) 0 0
\(862\) −990.000 571.577i −1.14849 0.663082i
\(863\) 1018.45i 1.18012i −0.807358 0.590061i \(-0.799104\pi\)
0.807358 0.590061i \(-0.200896\pi\)
\(864\) 0 0
\(865\) 889.000 1.02775
\(866\) 235.000 407.032i 0.271363 0.470014i
\(867\) 0 0
\(868\) 930.000 + 1610.81i 1.07143 + 1.85577i
\(869\) 30.0000 51.9615i 0.0345224 0.0597946i
\(870\) 0 0
\(871\) −1500.00 + 866.025i −1.72216 + 0.994289i
\(872\) 1072.00 1.22936
\(873\) 0 0
\(874\) −36.0000 62.3538i −0.0411899 0.0713431i
\(875\) −52.5000 + 30.3109i −0.0600000 + 0.0346410i
\(876\) 0 0
\(877\) 665.000 1151.81i 0.758267 1.31336i −0.185467 0.982651i \(-0.559380\pi\)
0.943734 0.330706i \(-0.107287\pi\)
\(878\) 827.920i 0.942962i
\(879\) 0 0
\(880\) 840.000 + 484.974i 0.954545 + 0.551107i
\(881\) 1060.00 1.20318 0.601589 0.798806i \(-0.294534\pi\)
0.601589 + 0.798806i \(0.294534\pi\)
\(882\) 0 0
\(883\) 1506.88i 1.70655i −0.521461 0.853275i \(-0.674613\pi\)
0.521461 0.853275i \(-0.325387\pi\)
\(884\) −640.000 −0.723982
\(885\) 0 0
\(886\) 1150.08i 1.29806i
\(887\) 618.000 + 356.802i 0.696731 + 0.402258i 0.806129 0.591740i \(-0.201559\pi\)
−0.109398 + 0.993998i \(0.534892\pi\)
\(888\) 0 0
\(889\) 112.500 + 194.856i 0.126547 + 0.219185i
\(890\) −70.0000 121.244i −0.0786517 0.136229i
\(891\) 0 0
\(892\) −120.000 69.2820i −0.134529 0.0776704i
\(893\) 450.000 + 779.423i 0.503919 + 0.872814i
\(894\) 0 0
\(895\) 1417.50 + 818.394i 1.58380 + 0.914407i
\(896\) 1108.51i 1.23718i
\(897\) 0 0
\(898\) 470.000 814.064i 0.523385 0.906530i
\(899\) 536.936i 0.597259i
\(900\) 0 0
\(901\) 376.000 0.417314
\(902\) −750.000 433.013i −0.831486 0.480058i
\(903\) 0 0
\(904\) 296.000 512.687i 0.327434 0.567132i
\(905\) −196.000 + 339.482i −0.216575 + 0.375118i
\(906\) 0 0
\(907\) 1155.00 666.840i 1.27343 0.735215i 0.297797 0.954629i \(-0.403748\pi\)
0.975632 + 0.219415i \(0.0704147\pi\)
\(908\) −312.000 180.133i −0.343612 0.198385i
\(909\) 0 0
\(910\) 2100.00 1212.44i 2.30769 1.33235i
\(911\) −1335.00 + 770.763i −1.46542 + 0.846062i −0.999253 0.0386335i \(-0.987700\pi\)
−0.466169 + 0.884696i \(0.654366\pi\)
\(912\) 0 0
\(913\) 127.500 220.836i 0.139650 0.241880i
\(914\) −650.000 −0.711160
\(915\) 0 0
\(916\) 584.000 0.637555
\(917\) −1425.00 −1.55398
\(918\) 0 0
\(919\) 909.327i 0.989474i −0.869043 0.494737i \(-0.835264\pi\)
0.869043 0.494737i \(-0.164736\pi\)
\(920\) 168.000 96.9948i 0.182609 0.105429i
\(921\) 0 0
\(922\) 1310.00 1.42082
\(923\) 0 0
\(924\) 0 0
\(925\) 120.000 + 207.846i 0.129730 + 0.224698i
\(926\) −285.000 + 164.545i −0.307775 + 0.177694i
\(927\) 0 0
\(928\) −160.000 + 277.128i −0.172414 + 0.298629i
\(929\) 670.000 + 1160.47i 0.721206 + 1.24916i 0.960517 + 0.278222i \(0.0897450\pi\)
−0.239311 + 0.970943i \(0.576922\pi\)
\(930\) 0 0
\(931\) −234.000 135.100i −0.251343 0.145113i
\(932\) −668.000 1157.01i −0.716738 1.24143i
\(933\) 0 0
\(934\) 99.0000 + 57.1577i 0.105996 + 0.0611967i
\(935\) 484.974i 0.518689i
\(936\) 0 0
\(937\) −1225.00 −1.30736 −0.653682 0.756769i \(-0.726777\pi\)
−0.653682 + 0.756769i \(0.726777\pi\)
\(938\) −750.000 + 1299.04i −0.799574 + 1.38490i
\(939\) 0 0
\(940\) −2100.00 + 1212.44i −2.23404 + 1.28983i
\(941\) −57.5000 + 99.5929i −0.0611052 + 0.105837i −0.894960 0.446147i \(-0.852796\pi\)
0.833854 + 0.551984i \(0.186129\pi\)
\(942\) 0 0
\(943\) −150.000 + 86.6025i −0.159067 + 0.0918373i
\(944\) 480.000 277.128i 0.508475 0.293568i
\(945\) 0 0
\(946\) 150.000 + 259.808i 0.158562 + 0.274638i
\(947\) 595.500 343.812i 0.628828 0.363054i −0.151470 0.988462i \(-0.548401\pi\)
0.780298 + 0.625408i \(0.215067\pi\)
\(948\) 0 0
\(949\) 550.000 952.628i 0.579557 1.00382i
\(950\) 498.831i 0.525085i
\(951\) 0 0
\(952\) −480.000 + 277.128i −0.504202 + 0.291101i
\(953\) −44.0000 −0.0461700 −0.0230850 0.999734i \(-0.507349\pi\)
−0.0230850 + 0.999734i \(0.507349\pi\)
\(954\) 0 0
\(955\) 242.487i 0.253913i
\(956\) 69.2820i 0.0724707i
\(957\) 0 0
\(958\) 658.179i 0.687035i
\(959\) 465.000 + 268.468i 0.484880 + 0.279946i
\(960\) 0 0
\(961\) 961.000 + 1664.50i 1.00000 + 1.73205i
\(962\) 200.000 + 346.410i 0.207900 + 0.360094i
\(963\) 0 0
\(964\) −268.000 + 464.190i −0.278008 + 0.481524i
\(965\) −227.500 394.042i −0.235751 0.408333i
\(966\) 0 0
\(967\) −217.500 125.574i −0.224922 0.129859i 0.383305 0.923622i \(-0.374786\pi\)
−0.608227 + 0.793763i \(0.708119\pi\)
\(968\) −184.000 + 318.697i −0.190083 + 0.329233i
\(969\) 0 0
\(970\) 175.000 303.109i 0.180412 0.312483i
\(971\) 337.750i 0.347837i 0.984760 + 0.173919i \(0.0556430\pi\)
−0.984760 + 0.173919i \(0.944357\pi\)
\(972\) 0 0
\(973\) −1500.00 −1.54162
\(974\) 900.000 + 519.615i 0.924025 + 0.533486i
\(975\) 0 0
\(976\) −1024.00 −1.04918
\(977\) −173.000 + 299.645i −0.177073 + 0.306699i −0.940877 0.338749i \(-0.889996\pi\)
0.763804 + 0.645448i \(0.223329\pi\)
\(978\) 0 0
\(979\) −75.0000 + 43.3013i −0.0766088 + 0.0442301i
\(980\) 364.000 630.466i 0.371429 0.643333i
\(981\) 0 0
\(982\) 375.000 216.506i 0.381874 0.220475i
\(983\) −687.000 + 396.640i −0.698881 + 0.403499i −0.806931 0.590646i \(-0.798873\pi\)
0.108050 + 0.994146i \(0.465539\pi\)
\(984\) 0 0
\(985\) −885.500 + 1533.73i −0.898985 + 1.55709i
\(986\) −160.000 −0.162272
\(987\) 0 0
\(988\) 831.384i 0.841482i
\(989\) 60.0000 0.0606673
\(990\) 0 0
\(991\) 1054.82i 1.06440i 0.846619 + 0.532199i \(0.178634\pi\)
−0.846619 + 0.532199i \(0.821366\pi\)
\(992\) 1718.19i 1.73205i
\(993\) 0 0
\(994\) 0 0
\(995\) −787.500 454.663i −0.791457 0.456948i
\(996\) 0 0
\(997\) −130.000 225.167i −0.130391 0.225844i 0.793436 0.608653i \(-0.208290\pi\)
−0.923827 + 0.382809i \(0.874957\pi\)
\(998\) −78.0000 + 45.0333i −0.0781563 + 0.0451236i
\(999\) 0 0
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 324.3.f.c.271.1 2
3.2 odd 2 324.3.f.h.271.1 2
4.3 odd 2 324.3.f.i.271.1 2
9.2 odd 6 324.3.f.b.55.1 2
9.4 even 3 108.3.d.a.55.1 2
9.5 odd 6 108.3.d.b.55.2 yes 2
9.7 even 3 324.3.f.i.55.1 2
12.11 even 2 324.3.f.b.271.1 2
36.7 odd 6 inner 324.3.f.c.55.1 2
36.11 even 6 324.3.f.h.55.1 2
36.23 even 6 108.3.d.b.55.1 yes 2
36.31 odd 6 108.3.d.a.55.2 yes 2
72.5 odd 6 1728.3.g.f.703.2 2
72.13 even 6 1728.3.g.a.703.2 2
72.59 even 6 1728.3.g.f.703.1 2
72.67 odd 6 1728.3.g.a.703.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.d.a.55.1 2 9.4 even 3
108.3.d.a.55.2 yes 2 36.31 odd 6
108.3.d.b.55.1 yes 2 36.23 even 6
108.3.d.b.55.2 yes 2 9.5 odd 6
324.3.f.b.55.1 2 9.2 odd 6
324.3.f.b.271.1 2 12.11 even 2
324.3.f.c.55.1 2 36.7 odd 6 inner
324.3.f.c.271.1 2 1.1 even 1 trivial
324.3.f.h.55.1 2 36.11 even 6
324.3.f.h.271.1 2 3.2 odd 2
324.3.f.i.55.1 2 9.7 even 3
324.3.f.i.271.1 2 4.3 odd 2
1728.3.g.a.703.1 2 72.67 odd 6
1728.3.g.a.703.2 2 72.13 even 6
1728.3.g.f.703.1 2 72.59 even 6
1728.3.g.f.703.2 2 72.5 odd 6