Properties

Label 882.2.e.e.655.1
Level $882$
Weight $2$
Character 882.655
Analytic conductor $7.043$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(373,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.373");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.e (of order \(3\), 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: \(7.04280545828\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 655.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.655
Dual form 882.2.e.e.373.1

$q$-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 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-3.00000 - 5.19615i) q^{13} -3.46410i q^{15} +1.00000 q^{16} +(-2.50000 + 4.33013i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(1.00000 - 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} -5.19615i q^{27} +(2.00000 - 3.46410i) q^{29} +3.46410i q^{30} +6.00000 q^{31} -1.00000 q^{32} +(-1.50000 - 0.866025i) q^{33} +(2.50000 - 4.33013i) q^{34} +(1.50000 - 2.59808i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-9.00000 - 5.19615i) q^{39} +(-1.00000 + 1.73205i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(2.00000 - 3.46410i) q^{46} +(1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{50} +8.66025i q^{51} +(-3.00000 - 5.19615i) q^{52} +(-6.00000 + 10.3923i) q^{53} +5.19615i q^{54} -2.00000 q^{55} +(-10.5000 - 6.06218i) q^{57} +(-2.00000 + 3.46410i) q^{58} +7.00000 q^{59} -3.46410i q^{60} +12.0000 q^{61} -6.00000 q^{62} +1.00000 q^{64} -12.0000 q^{65} +(1.50000 + 0.866025i) q^{66} +13.0000 q^{67} +(-2.50000 + 4.33013i) q^{68} +6.92820i q^{69} -8.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(0.500000 - 0.866025i) q^{73} +(1.00000 + 1.73205i) q^{74} +(1.50000 + 0.866025i) q^{75} +(-3.50000 - 6.06218i) q^{76} +(9.00000 + 5.19615i) q^{78} -6.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(8.00000 - 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} +(-0.500000 + 0.866025i) q^{86} -6.92820i q^{87} +(0.500000 + 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 + 5.19615i) q^{90} +(-2.00000 + 3.46410i) q^{92} +(9.00000 - 5.19615i) q^{93} -14.0000 q^{95} +(-1.50000 + 0.866025i) q^{96} +(-2.50000 + 4.33013i) q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{6} - 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{16} - 5 q^{17} - 3 q^{18} - 7 q^{19} + 2 q^{20} + q^{22} - 4 q^{23} - 3 q^{24}+ \cdots - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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 −0.707107
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 1.00000 0.500000
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) −1.50000 + 0.866025i −0.612372 + 0.353553i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −1.00000 + 1.73205i −0.316228 + 0.547723i
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 1.50000 0.866025i 0.433013 0.250000i
\(13\) −3.00000 5.19615i −0.832050 1.44115i −0.896410 0.443227i \(-0.853834\pi\)
0.0643593 0.997927i \(-0.479500\pi\)
\(14\) 0 0
\(15\) 3.46410i 0.894427i
\(16\) 1.00000 0.250000
\(17\) −2.50000 + 4.33013i −0.606339 + 1.05021i 0.385499 + 0.922708i \(0.374029\pi\)
−0.991838 + 0.127502i \(0.959304\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) 0 0
\(22\) 0.500000 + 0.866025i 0.106600 + 0.184637i
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 3.00000 + 5.19615i 0.588348 + 1.01905i
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 2.00000 3.46410i 0.371391 0.643268i −0.618389 0.785872i \(-0.712214\pi\)
0.989780 + 0.142605i \(0.0455477\pi\)
\(30\) 3.46410i 0.632456i
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.50000 0.866025i −0.261116 0.150756i
\(34\) 2.50000 4.33013i 0.428746 0.742611i
\(35\) 0 0
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 3.50000 + 6.06218i 0.567775 + 0.983415i
\(39\) −9.00000 5.19615i −1.44115 0.832050i
\(40\) −1.00000 + 1.73205i −0.158114 + 0.273861i
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) −3.00000 5.19615i −0.447214 0.774597i
\(46\) 2.00000 3.46410i 0.294884 0.510754i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.50000 0.866025i 0.216506 0.125000i
\(49\) 0 0
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) 8.66025i 1.21268i
\(52\) −3.00000 5.19615i −0.416025 0.720577i
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 5.19615i 0.707107i
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) −10.5000 6.06218i −1.39076 0.802955i
\(58\) −2.00000 + 3.46410i −0.262613 + 0.454859i
\(59\) 7.00000 0.911322 0.455661 0.890153i \(-0.349403\pi\)
0.455661 + 0.890153i \(0.349403\pi\)
\(60\) 3.46410i 0.447214i
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −12.0000 −1.48842
\(66\) 1.50000 + 0.866025i 0.184637 + 0.106600i
\(67\) 13.0000 1.58820 0.794101 0.607785i \(-0.207942\pi\)
0.794101 + 0.607785i \(0.207942\pi\)
\(68\) −2.50000 + 4.33013i −0.303170 + 0.525105i
\(69\) 6.92820i 0.834058i
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) 0.500000 0.866025i 0.0585206 0.101361i −0.835281 0.549823i \(-0.814695\pi\)
0.893801 + 0.448463i \(0.148028\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 1.50000 + 0.866025i 0.173205 + 0.100000i
\(76\) −3.50000 6.06218i −0.401478 0.695379i
\(77\) 0 0
\(78\) 9.00000 + 5.19615i 1.01905 + 0.588348i
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) 1.00000 1.73205i 0.111803 0.193649i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) 8.00000 13.8564i 0.878114 1.52094i 0.0247060 0.999695i \(-0.492135\pi\)
0.853408 0.521243i \(-0.174532\pi\)
\(84\) 0 0
\(85\) 5.00000 + 8.66025i 0.542326 + 0.939336i
\(86\) −0.500000 + 0.866025i −0.0539164 + 0.0933859i
\(87\) 6.92820i 0.742781i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 3.00000 + 5.19615i 0.316228 + 0.547723i
\(91\) 0 0
\(92\) −2.00000 + 3.46410i −0.208514 + 0.361158i
\(93\) 9.00000 5.19615i 0.933257 0.538816i
\(94\) 0 0
\(95\) −14.0000 −1.43637
\(96\) −1.50000 + 0.866025i −0.153093 + 0.0883883i
\(97\) −2.50000 + 4.33013i −0.253837 + 0.439658i −0.964579 0.263795i \(-0.915026\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −2.00000 3.46410i −0.199007 0.344691i 0.749199 0.662344i \(-0.230438\pi\)
−0.948207 + 0.317653i \(0.897105\pi\)
\(102\) 8.66025i 0.857493i
\(103\) 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i \(-0.591062\pi\)
0.971925 0.235291i \(-0.0756043\pi\)
\(104\) 3.00000 + 5.19615i 0.294174 + 0.509525i
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i \(-0.212988\pi\)
−0.929377 + 0.369132i \(0.879655\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 2.00000 0.190693
\(111\) −3.00000 1.73205i −0.284747 0.164399i
\(112\) 0 0
\(113\) 5.00000 + 8.66025i 0.470360 + 0.814688i 0.999425 0.0338931i \(-0.0107906\pi\)
−0.529065 + 0.848581i \(0.677457\pi\)
\(114\) 10.5000 + 6.06218i 0.983415 + 0.567775i
\(115\) 4.00000 + 6.92820i 0.373002 + 0.646058i
\(116\) 2.00000 3.46410i 0.185695 0.321634i
\(117\) −18.0000 −1.66410
\(118\) −7.00000 −0.644402
\(119\) 0 0
\(120\) 3.46410i 0.316228i
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) −12.0000 −1.08643
\(123\) 4.50000 + 2.59808i 0.405751 + 0.234261i
\(124\) 6.00000 0.538816
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.73205i 0.152499i
\(130\) 12.0000 1.05247
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) −1.50000 0.866025i −0.130558 0.0753778i
\(133\) 0 0
\(134\) −13.0000 −1.12303
\(135\) −9.00000 5.19615i −0.774597 0.447214i
\(136\) 2.50000 4.33013i 0.214373 0.371305i
\(137\) 9.50000 + 16.4545i 0.811640 + 1.40580i 0.911716 + 0.410822i \(0.134758\pi\)
−0.100076 + 0.994980i \(0.531909\pi\)
\(138\) 6.92820i 0.589768i
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.00000 0.671345
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) −4.00000 6.92820i −0.332182 0.575356i
\(146\) −0.500000 + 0.866025i −0.0413803 + 0.0716728i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 12.0000 20.7846i 0.983078 1.70274i 0.332896 0.942964i \(-0.391974\pi\)
0.650183 0.759778i \(-0.274692\pi\)
\(150\) −1.50000 0.866025i −0.122474 0.0707107i
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) 3.50000 + 6.06218i 0.283887 + 0.491708i
\(153\) 7.50000 + 12.9904i 0.606339 + 1.05021i
\(154\) 0 0
\(155\) 6.00000 10.3923i 0.481932 0.834730i
\(156\) −9.00000 5.19615i −0.720577 0.416025i
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 6.00000 0.477334
\(159\) 20.7846i 1.64833i
\(160\) −1.00000 + 1.73205i −0.0790569 + 0.136931i
\(161\) 0 0
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) 1.50000 + 2.59808i 0.117130 + 0.202876i
\(165\) −3.00000 + 1.73205i −0.233550 + 0.134840i
\(166\) −8.00000 + 13.8564i −0.620920 + 1.07547i
\(167\) 10.0000 + 17.3205i 0.773823 + 1.34030i 0.935454 + 0.353450i \(0.114991\pi\)
−0.161630 + 0.986851i \(0.551675\pi\)
\(168\) 0 0
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) −5.00000 8.66025i −0.383482 0.664211i
\(171\) −21.0000 −1.60591
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 6.92820i 0.525226i
\(175\) 0 0
\(176\) −0.500000 0.866025i −0.0376889 0.0652791i
\(177\) 10.5000 6.06218i 0.789228 0.455661i
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −12.0000 + 20.7846i −0.896922 + 1.55351i −0.0655145 + 0.997852i \(0.520869\pi\)
−0.831408 + 0.555663i \(0.812464\pi\)
\(180\) −3.00000 5.19615i −0.223607 0.387298i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 18.0000 10.3923i 1.33060 0.768221i
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) −4.00000 −0.294086
\(186\) −9.00000 + 5.19615i −0.659912 + 0.381000i
\(187\) 5.00000 0.365636
\(188\) 0 0
\(189\) 0 0
\(190\) 14.0000 1.01567
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 1.50000 0.866025i 0.108253 0.0625000i
\(193\) 17.0000 1.22369 0.611843 0.790979i \(-0.290428\pi\)
0.611843 + 0.790979i \(0.290428\pi\)
\(194\) 2.50000 4.33013i 0.179490 0.310885i
\(195\) −18.0000 + 10.3923i −1.28901 + 0.744208i
\(196\) 0 0
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 3.00000 0.213201
\(199\) 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i \(-0.668055\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 19.5000 11.2583i 1.37542 0.794101i
\(202\) 2.00000 + 3.46410i 0.140720 + 0.243733i
\(203\) 0 0
\(204\) 8.66025i 0.606339i
\(205\) 6.00000 0.419058
\(206\) −7.00000 + 12.1244i −0.487713 + 0.844744i
\(207\) 6.00000 + 10.3923i 0.417029 + 0.722315i
\(208\) −3.00000 5.19615i −0.208013 0.360288i
\(209\) −3.50000 + 6.06218i −0.242100 + 0.419330i
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −6.00000 + 10.3923i −0.412082 + 0.713746i
\(213\) −12.0000 + 6.92820i −0.822226 + 0.474713i
\(214\) 1.50000 + 2.59808i 0.102538 + 0.177601i
\(215\) −1.00000 1.73205i −0.0681994 0.118125i
\(216\) 5.19615i 0.353553i
\(217\) 0 0
\(218\) −1.00000 + 1.73205i −0.0677285 + 0.117309i
\(219\) 1.73205i 0.117041i
\(220\) −2.00000 −0.134840
\(221\) 30.0000 2.01802
\(222\) 3.00000 + 1.73205i 0.201347 + 0.116248i
\(223\) −2.00000 + 3.46410i −0.133930 + 0.231973i −0.925188 0.379509i \(-0.876093\pi\)
0.791258 + 0.611482i \(0.209426\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) −5.00000 8.66025i −0.332595 0.576072i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) −10.5000 6.06218i −0.695379 0.401478i
\(229\) −13.0000 + 22.5167i −0.859064 + 1.48794i 0.0137585 + 0.999905i \(0.495620\pi\)
−0.872823 + 0.488037i \(0.837713\pi\)
\(230\) −4.00000 6.92820i −0.263752 0.456832i
\(231\) 0 0
\(232\) −2.00000 + 3.46410i −0.131306 + 0.227429i
\(233\) 14.5000 + 25.1147i 0.949927 + 1.64532i 0.745573 + 0.666424i \(0.232176\pi\)
0.204354 + 0.978897i \(0.434491\pi\)
\(234\) 18.0000 1.17670
\(235\) 0 0
\(236\) 7.00000 0.455661
\(237\) −9.00000 + 5.19615i −0.584613 + 0.337526i
\(238\) 0 0
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) 3.46410i 0.223607i
\(241\) 11.5000 + 19.9186i 0.740780 + 1.28307i 0.952141 + 0.305661i \(0.0988773\pi\)
−0.211360 + 0.977408i \(0.567789\pi\)
\(242\) −5.00000 + 8.66025i −0.321412 + 0.556702i
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) 12.0000 0.768221
\(245\) 0 0
\(246\) −4.50000 2.59808i −0.286910 0.165647i
\(247\) −21.0000 + 36.3731i −1.33620 + 2.31436i
\(248\) −6.00000 −0.381000
\(249\) 27.7128i 1.75623i
\(250\) −12.0000 −0.758947
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 12.0000 0.752947
\(255\) 15.0000 + 8.66025i 0.939336 + 0.542326i
\(256\) 1.00000 0.0625000
\(257\) −7.50000 + 12.9904i −0.467837 + 0.810318i −0.999325 0.0367485i \(-0.988300\pi\)
0.531487 + 0.847066i \(0.321633\pi\)
\(258\) 1.73205i 0.107833i
\(259\) 0 0
\(260\) −12.0000 −0.744208
\(261\) −6.00000 10.3923i −0.371391 0.643268i
\(262\) 2.00000 3.46410i 0.123560 0.214013i
\(263\) −9.00000 15.5885i −0.554964 0.961225i −0.997906 0.0646755i \(-0.979399\pi\)
0.442943 0.896550i \(-0.353935\pi\)
\(264\) 1.50000 + 0.866025i 0.0923186 + 0.0533002i
\(265\) 12.0000 + 20.7846i 0.737154 + 1.27679i
\(266\) 0 0
\(267\) −9.00000 5.19615i −0.550791 0.317999i
\(268\) 13.0000 0.794101
\(269\) 10.0000 17.3205i 0.609711 1.05605i −0.381577 0.924337i \(-0.624619\pi\)
0.991288 0.131713i \(-0.0420477\pi\)
\(270\) 9.00000 + 5.19615i 0.547723 + 0.316228i
\(271\) −3.00000 5.19615i −0.182237 0.315644i 0.760405 0.649449i \(-0.225000\pi\)
−0.942642 + 0.333805i \(0.891667\pi\)
\(272\) −2.50000 + 4.33013i −0.151585 + 0.262553i
\(273\) 0 0
\(274\) −9.50000 16.4545i −0.573916 0.994052i
\(275\) 0.500000 0.866025i 0.0301511 0.0522233i
\(276\) 6.92820i 0.417029i
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) 2.50000 + 4.33013i 0.149940 + 0.259704i
\(279\) 9.00000 15.5885i 0.538816 0.933257i
\(280\) 0 0
\(281\) −11.0000 + 19.0526i −0.656205 + 1.13658i 0.325385 + 0.945582i \(0.394506\pi\)
−0.981590 + 0.190999i \(0.938827\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −8.00000 −0.474713
\(285\) −21.0000 + 12.1244i −1.24393 + 0.718185i
\(286\) 3.00000 5.19615i 0.177394 0.307255i
\(287\) 0 0
\(288\) −1.50000 + 2.59808i −0.0883883 + 0.153093i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) 4.00000 + 6.92820i 0.234888 + 0.406838i
\(291\) 8.66025i 0.507673i
\(292\) 0.500000 0.866025i 0.0292603 0.0506803i
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) 0 0
\(295\) 7.00000 12.1244i 0.407556 0.705907i
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) −4.50000 + 2.59808i −0.261116 + 0.150756i
\(298\) −12.0000 + 20.7846i −0.695141 + 1.20402i
\(299\) 24.0000 1.38796
\(300\) 1.50000 + 0.866025i 0.0866025 + 0.0500000i
\(301\) 0 0
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) −6.00000 3.46410i −0.344691 0.199007i
\(304\) −3.50000 6.06218i −0.200739 0.347690i
\(305\) 12.0000 20.7846i 0.687118 1.19012i
\(306\) −7.50000 12.9904i −0.428746 0.742611i
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 0 0
\(309\) 24.2487i 1.37946i
\(310\) −6.00000 + 10.3923i −0.340777 + 0.590243i
\(311\) −2.00000 −0.113410 −0.0567048 0.998391i \(-0.518059\pi\)
−0.0567048 + 0.998391i \(0.518059\pi\)
\(312\) 9.00000 + 5.19615i 0.509525 + 0.294174i
\(313\) 17.0000 0.960897 0.480448 0.877023i \(-0.340474\pi\)
0.480448 + 0.877023i \(0.340474\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) −6.00000 −0.337526
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 20.7846i 1.16554i
\(319\) −4.00000 −0.223957
\(320\) 1.00000 1.73205i 0.0559017 0.0968246i
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) 0 0
\(323\) 35.0000 1.94745
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) 3.00000 5.19615i 0.166410 0.288231i
\(326\) −2.00000 3.46410i −0.110770 0.191859i
\(327\) 3.46410i 0.191565i
\(328\) −1.50000 2.59808i −0.0828236 0.143455i
\(329\) 0 0
\(330\) 3.00000 1.73205i 0.165145 0.0953463i
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 8.00000 13.8564i 0.439057 0.760469i
\(333\) −6.00000 −0.328798
\(334\) −10.0000 17.3205i −0.547176 0.947736i
\(335\) 13.0000 22.5167i 0.710266 1.23022i
\(336\) 0 0
\(337\) 4.50000 + 7.79423i 0.245131 + 0.424579i 0.962168 0.272456i \(-0.0878358\pi\)
−0.717038 + 0.697034i \(0.754502\pi\)
\(338\) 11.5000 19.9186i 0.625518 1.08343i
\(339\) 15.0000 + 8.66025i 0.814688 + 0.470360i
\(340\) 5.00000 + 8.66025i 0.271163 + 0.469668i
\(341\) −3.00000 5.19615i −0.162459 0.281387i
\(342\) 21.0000 1.13555
\(343\) 0 0
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) 12.0000 + 6.92820i 0.646058 + 0.373002i
\(346\) 2.00000 0.107521
\(347\) −3.00000 −0.161048 −0.0805242 0.996753i \(-0.525659\pi\)
−0.0805242 + 0.996753i \(0.525659\pi\)
\(348\) 6.92820i 0.371391i
\(349\) −7.00000 + 12.1244i −0.374701 + 0.649002i −0.990282 0.139072i \(-0.955588\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) 0 0
\(351\) −27.0000 + 15.5885i −1.44115 + 0.832050i
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −7.50000 12.9904i −0.399185 0.691408i 0.594441 0.804139i \(-0.297373\pi\)
−0.993626 + 0.112731i \(0.964040\pi\)
\(354\) −10.5000 + 6.06218i −0.558069 + 0.322201i
\(355\) −8.00000 + 13.8564i −0.424596 + 0.735422i
\(356\) −3.00000 5.19615i −0.159000 0.275396i
\(357\) 0 0
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) −1.00000 1.73205i −0.0527780 0.0914141i 0.838429 0.545010i \(-0.183474\pi\)
−0.891207 + 0.453596i \(0.850141\pi\)
\(360\) 3.00000 + 5.19615i 0.158114 + 0.273861i
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) 17.3205i 0.909091i
\(364\) 0 0
\(365\) −1.00000 1.73205i −0.0523424 0.0906597i
\(366\) −18.0000 + 10.3923i −0.940875 + 0.543214i
\(367\) −11.0000 19.0526i −0.574195 0.994535i −0.996129 0.0879086i \(-0.971982\pi\)
0.421933 0.906627i \(-0.361352\pi\)
\(368\) −2.00000 + 3.46410i −0.104257 + 0.180579i
\(369\) 9.00000 0.468521
\(370\) 4.00000 0.207950
\(371\) 0 0
\(372\) 9.00000 5.19615i 0.466628 0.269408i
\(373\) −11.0000 + 19.0526i −0.569558 + 0.986504i 0.427051 + 0.904227i \(0.359552\pi\)
−0.996610 + 0.0822766i \(0.973781\pi\)
\(374\) −5.00000 −0.258544
\(375\) 18.0000 10.3923i 0.929516 0.536656i
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) −17.0000 −0.873231 −0.436616 0.899648i \(-0.643823\pi\)
−0.436616 + 0.899648i \(0.643823\pi\)
\(380\) −14.0000 −0.718185
\(381\) −18.0000 + 10.3923i −0.922168 + 0.532414i
\(382\) −12.0000 −0.613973
\(383\) 2.00000 3.46410i 0.102195 0.177007i −0.810394 0.585886i \(-0.800747\pi\)
0.912589 + 0.408879i \(0.134080\pi\)
\(384\) −1.50000 + 0.866025i −0.0765466 + 0.0441942i
\(385\) 0 0
\(386\) −17.0000 −0.865277
\(387\) −1.50000 2.59808i −0.0762493 0.132068i
\(388\) −2.50000 + 4.33013i −0.126918 + 0.219829i
\(389\) −4.00000 6.92820i −0.202808 0.351274i 0.746624 0.665246i \(-0.231673\pi\)
−0.949432 + 0.313972i \(0.898340\pi\)
\(390\) 18.0000 10.3923i 0.911465 0.526235i
\(391\) −10.0000 17.3205i −0.505722 0.875936i
\(392\) 0 0
\(393\) 6.92820i 0.349482i
\(394\) −10.0000 −0.503793
\(395\) −6.00000 + 10.3923i −0.301893 + 0.522894i
\(396\) −3.00000 −0.150756
\(397\) 9.00000 + 15.5885i 0.451697 + 0.782362i 0.998492 0.0549046i \(-0.0174855\pi\)
−0.546795 + 0.837267i \(0.684152\pi\)
\(398\) −7.00000 + 12.1244i −0.350878 + 0.607739i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −4.50000 + 7.79423i −0.224719 + 0.389225i −0.956235 0.292599i \(-0.905480\pi\)
0.731516 + 0.681824i \(0.238813\pi\)
\(402\) −19.5000 + 11.2583i −0.972572 + 0.561514i
\(403\) −18.0000 31.1769i −0.896644 1.55303i
\(404\) −2.00000 3.46410i −0.0995037 0.172345i
\(405\) −18.0000 −0.894427
\(406\) 0 0
\(407\) −1.00000 + 1.73205i −0.0495682 + 0.0858546i
\(408\) 8.66025i 0.428746i
\(409\) −11.0000 −0.543915 −0.271957 0.962309i \(-0.587671\pi\)
−0.271957 + 0.962309i \(0.587671\pi\)
\(410\) −6.00000 −0.296319
\(411\) 28.5000 + 16.4545i 1.40580 + 0.811640i
\(412\) 7.00000 12.1244i 0.344865 0.597324i
\(413\) 0 0
\(414\) −6.00000 10.3923i −0.294884 0.510754i
\(415\) −16.0000 27.7128i −0.785409 1.36037i
\(416\) 3.00000 + 5.19615i 0.147087 + 0.254762i
\(417\) −7.50000 4.33013i −0.367277 0.212047i
\(418\) 3.50000 6.06218i 0.171191 0.296511i
\(419\) −6.00000 10.3923i −0.293119 0.507697i 0.681426 0.731887i \(-0.261360\pi\)
−0.974546 + 0.224189i \(0.928027\pi\)
\(420\) 0 0
\(421\) 6.00000 10.3923i 0.292422 0.506490i −0.681960 0.731390i \(-0.738872\pi\)
0.974382 + 0.224900i \(0.0722054\pi\)
\(422\) −8.00000 13.8564i −0.389434 0.674519i
\(423\) 0 0
\(424\) 6.00000 10.3923i 0.291386 0.504695i
\(425\) −5.00000 −0.242536
\(426\) 12.0000 6.92820i 0.581402 0.335673i
\(427\) 0 0
\(428\) −1.50000 2.59808i −0.0725052 0.125583i
\(429\) 10.3923i 0.501745i
\(430\) 1.00000 + 1.73205i 0.0482243 + 0.0835269i
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 25.0000 1.20142 0.600712 0.799466i \(-0.294884\pi\)
0.600712 + 0.799466i \(0.294884\pi\)
\(434\) 0 0
\(435\) −12.0000 6.92820i −0.575356 0.332182i
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 28.0000 1.33942
\(438\) 1.73205i 0.0827606i
\(439\) 24.0000 1.14546 0.572729 0.819745i \(-0.305885\pi\)
0.572729 + 0.819745i \(0.305885\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) −30.0000 −1.42695
\(443\) 7.00000 0.332580 0.166290 0.986077i \(-0.446821\pi\)
0.166290 + 0.986077i \(0.446821\pi\)
\(444\) −3.00000 1.73205i −0.142374 0.0821995i
\(445\) −12.0000 −0.568855
\(446\) 2.00000 3.46410i 0.0947027 0.164030i
\(447\) 41.5692i 1.96616i
\(448\) 0 0
\(449\) 17.0000 0.802280 0.401140 0.916017i \(-0.368614\pi\)
0.401140 + 0.916017i \(0.368614\pi\)
\(450\) −3.00000 −0.141421
\(451\) 1.50000 2.59808i 0.0706322 0.122339i
\(452\) 5.00000 + 8.66025i 0.235180 + 0.407344i
\(453\) −15.0000 8.66025i −0.704761 0.406894i
\(454\) −1.50000 2.59808i −0.0703985 0.121934i
\(455\) 0 0
\(456\) 10.5000 + 6.06218i 0.491708 + 0.283887i
\(457\) 1.00000 0.0467780 0.0233890 0.999726i \(-0.492554\pi\)
0.0233890 + 0.999726i \(0.492554\pi\)
\(458\) 13.0000 22.5167i 0.607450 1.05213i
\(459\) 22.5000 + 12.9904i 1.05021 + 0.606339i
\(460\) 4.00000 + 6.92820i 0.186501 + 0.323029i
\(461\) 7.00000 12.1244i 0.326023 0.564688i −0.655696 0.755025i \(-0.727625\pi\)
0.981719 + 0.190337i \(0.0609581\pi\)
\(462\) 0 0
\(463\) 4.00000 + 6.92820i 0.185896 + 0.321981i 0.943878 0.330294i \(-0.107148\pi\)
−0.757982 + 0.652275i \(0.773815\pi\)
\(464\) 2.00000 3.46410i 0.0928477 0.160817i
\(465\) 20.7846i 0.963863i
\(466\) −14.5000 25.1147i −0.671700 1.16342i
\(467\) −6.50000 11.2583i −0.300784 0.520973i 0.675530 0.737333i \(-0.263915\pi\)
−0.976314 + 0.216359i \(0.930582\pi\)
\(468\) −18.0000 −0.832050
\(469\) 0 0
\(470\) 0 0
\(471\) −3.00000 + 1.73205i −0.138233 + 0.0798087i
\(472\) −7.00000 −0.322201
\(473\) −1.00000 −0.0459800
\(474\) 9.00000 5.19615i 0.413384 0.238667i
\(475\) 3.50000 6.06218i 0.160591 0.278152i
\(476\) 0 0
\(477\) 18.0000 + 31.1769i 0.824163 + 1.42749i
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) −10.0000 17.3205i −0.456912 0.791394i 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) 3.46410i 0.158114i
\(481\) −6.00000 + 10.3923i −0.273576 + 0.473848i
\(482\) −11.5000 19.9186i −0.523811 0.907267i
\(483\) 0 0
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) 5.00000 + 8.66025i 0.227038 + 0.393242i
\(486\) 13.5000 + 7.79423i 0.612372 + 0.353553i
\(487\) 5.00000 8.66025i 0.226572 0.392434i −0.730218 0.683214i \(-0.760582\pi\)
0.956790 + 0.290780i \(0.0939149\pi\)
\(488\) −12.0000 −0.543214
\(489\) 6.00000 + 3.46410i 0.271329 + 0.156652i
\(490\) 0 0
\(491\) −16.5000 28.5788i −0.744635 1.28974i −0.950365 0.311136i \(-0.899290\pi\)
0.205731 0.978609i \(-0.434043\pi\)
\(492\) 4.50000 + 2.59808i 0.202876 + 0.117130i
\(493\) 10.0000 + 17.3205i 0.450377 + 0.780076i
\(494\) 21.0000 36.3731i 0.944835 1.63650i
\(495\) −3.00000 + 5.19615i −0.134840 + 0.233550i
\(496\) 6.00000 0.269408
\(497\) 0 0
\(498\) 27.7128i 1.24184i
\(499\) 14.5000 25.1147i 0.649109 1.12429i −0.334227 0.942493i \(-0.608475\pi\)
0.983336 0.181797i \(-0.0581915\pi\)
\(500\) 12.0000 0.536656
\(501\) 30.0000 + 17.3205i 1.34030 + 0.773823i
\(502\) 3.00000 0.133897
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.355995
\(506\) −4.00000 −0.177822
\(507\) 39.8372i 1.76923i
\(508\) −12.0000 −0.532414
\(509\) 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) −15.0000 8.66025i −0.664211 0.383482i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −31.5000 + 18.1865i −1.39076 + 0.802955i
\(514\) 7.50000 12.9904i 0.330811 0.572981i
\(515\) −14.0000 24.2487i −0.616914 1.06853i
\(516\) 1.73205i 0.0762493i
\(517\) 0 0
\(518\) 0 0
\(519\) −3.00000 + 1.73205i −0.131685 + 0.0760286i
\(520\) 12.0000 0.526235
\(521\) −4.50000 + 7.79423i −0.197149 + 0.341471i −0.947603 0.319451i \(-0.896501\pi\)
0.750454 + 0.660922i \(0.229835\pi\)
\(522\) 6.00000 + 10.3923i 0.262613 + 0.454859i
\(523\) −14.0000 24.2487i −0.612177 1.06032i −0.990873 0.134801i \(-0.956961\pi\)
0.378695 0.925521i \(-0.376373\pi\)
\(524\) −2.00000 + 3.46410i −0.0873704 + 0.151330i
\(525\) 0 0
\(526\) 9.00000 + 15.5885i 0.392419 + 0.679689i
\(527\) −15.0000 + 25.9808i −0.653410 + 1.13174i
\(528\) −1.50000 0.866025i −0.0652791 0.0376889i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −12.0000 20.7846i −0.521247 0.902826i
\(531\) 10.5000 18.1865i 0.455661 0.789228i
\(532\) 0 0
\(533\) 9.00000 15.5885i 0.389833 0.675211i
\(534\) 9.00000 + 5.19615i 0.389468 + 0.224860i
\(535\) −6.00000 −0.259403
\(536\) −13.0000 −0.561514
\(537\) 41.5692i 1.79384i
\(538\) −10.0000 + 17.3205i −0.431131 + 0.746740i
\(539\) 0 0
\(540\) −9.00000 5.19615i −0.387298 0.223607i
\(541\) 12.0000 + 20.7846i 0.515920 + 0.893600i 0.999829 + 0.0184818i \(0.00588327\pi\)
−0.483909 + 0.875118i \(0.660783\pi\)
\(542\) 3.00000 + 5.19615i 0.128861 + 0.223194i
\(543\) 0 0
\(544\) 2.50000 4.33013i 0.107187 0.185653i
\(545\) −2.00000 3.46410i −0.0856706 0.148386i
\(546\) 0 0
\(547\) 10.5000 18.1865i 0.448948 0.777600i −0.549370 0.835579i \(-0.685132\pi\)
0.998318 + 0.0579790i \(0.0184657\pi\)
\(548\) 9.50000 + 16.4545i 0.405820 + 0.702901i
\(549\) 18.0000 31.1769i 0.768221 1.33060i
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) −28.0000 −1.19284
\(552\) 6.92820i 0.294884i
\(553\) 0 0
\(554\) 1.00000 + 1.73205i 0.0424859 + 0.0735878i
\(555\) −6.00000 + 3.46410i −0.254686 + 0.147043i
\(556\) −2.50000 4.33013i −0.106024 0.183638i
\(557\) 14.0000 24.2487i 0.593199 1.02745i −0.400599 0.916253i \(-0.631198\pi\)
0.993798 0.111198i \(-0.0354686\pi\)
\(558\) −9.00000 + 15.5885i −0.381000 + 0.659912i
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) 7.50000 4.33013i 0.316650 0.182818i
\(562\) 11.0000 19.0526i 0.464007 0.803684i
\(563\) −31.0000 −1.30649 −0.653247 0.757145i \(-0.726594\pi\)
−0.653247 + 0.757145i \(0.726594\pi\)
\(564\) 0 0
\(565\) 20.0000 0.841406
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) −15.0000 −0.628833 −0.314416 0.949285i \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) 21.0000 12.1244i 0.879593 0.507833i
\(571\) −33.0000 −1.38101 −0.690504 0.723329i \(-0.742611\pi\)
−0.690504 + 0.723329i \(0.742611\pi\)
\(572\) −3.00000 + 5.19615i −0.125436 + 0.217262i
\(573\) 18.0000 10.3923i 0.751961 0.434145i
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −17.5000 + 30.3109i −0.728535 + 1.26186i 0.228968 + 0.973434i \(0.426465\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) 25.5000 14.7224i 1.05974 0.611843i
\(580\) −4.00000 6.92820i −0.166091 0.287678i
\(581\) 0 0
\(582\) 8.66025i 0.358979i
\(583\) 12.0000 0.496989
\(584\) −0.500000 + 0.866025i −0.0206901 + 0.0358364i
\(585\) −18.0000 + 31.1769i −0.744208 + 1.28901i
\(586\) 0 0
\(587\) −23.5000 + 40.7032i −0.969949 + 1.68000i −0.274263 + 0.961655i \(0.588434\pi\)
−0.695686 + 0.718346i \(0.744900\pi\)
\(588\) 0 0
\(589\) −21.0000 36.3731i −0.865290 1.49873i
\(590\) −7.00000 + 12.1244i −0.288185 + 0.499152i
\(591\) 15.0000 8.66025i 0.617018 0.356235i
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 4.50000 2.59808i 0.184637 0.106600i
\(595\) 0 0
\(596\) 12.0000 20.7846i 0.491539 0.851371i
\(597\) 24.2487i 0.992434i
\(598\) −24.0000 −0.981433
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −1.50000 0.866025i −0.0612372 0.0353553i
\(601\) −9.50000 + 16.4545i −0.387513 + 0.671192i −0.992114 0.125336i \(-0.959999\pi\)
0.604601 + 0.796528i \(0.293332\pi\)
\(602\) 0 0
\(603\) 19.5000 33.7750i 0.794101 1.37542i
\(604\) −5.00000 8.66025i −0.203447 0.352381i
\(605\) −10.0000 17.3205i −0.406558 0.704179i
\(606\) 6.00000 + 3.46410i 0.243733 + 0.140720i
\(607\) −12.0000 + 20.7846i −0.487065 + 0.843621i −0.999889 0.0148722i \(-0.995266\pi\)
0.512824 + 0.858494i \(0.328599\pi\)
\(608\) 3.50000 + 6.06218i 0.141944 + 0.245854i
\(609\) 0 0
\(610\) −12.0000 + 20.7846i −0.485866 + 0.841544i
\(611\) 0 0
\(612\) 7.50000 + 12.9904i 0.303170 + 0.525105i
\(613\) −21.0000 + 36.3731i −0.848182 + 1.46909i 0.0346469 + 0.999400i \(0.488969\pi\)
−0.882829 + 0.469695i \(0.844364\pi\)
\(614\) 7.00000 0.282497
\(615\) 9.00000 5.19615i 0.362915 0.209529i
\(616\) 0 0
\(617\) 8.50000 + 14.7224i 0.342197 + 0.592703i 0.984840 0.173463i \(-0.0554956\pi\)
−0.642643 + 0.766165i \(0.722162\pi\)
\(618\) 24.2487i 0.975426i
\(619\) 18.5000 + 32.0429i 0.743578 + 1.28791i 0.950856 + 0.309633i \(0.100206\pi\)
−0.207279 + 0.978282i \(0.566461\pi\)
\(620\) 6.00000 10.3923i 0.240966 0.417365i
\(621\) 18.0000 + 10.3923i 0.722315 + 0.417029i
\(622\) 2.00000 0.0801927
\(623\) 0 0
\(624\) −9.00000 5.19615i −0.360288 0.208013i
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) −17.0000 −0.679457
\(627\) 12.1244i 0.484200i
\(628\) −2.00000 −0.0798087
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 6.00000 0.238667
\(633\) 24.0000 + 13.8564i 0.953914 + 0.550743i
\(634\) 6.00000 0.238290
\(635\) −12.0000 + 20.7846i −0.476205 + 0.824812i
\(636\) 20.7846i 0.824163i
\(637\) 0 0
\(638\) 4.00000 0.158362
\(639\) −12.0000 + 20.7846i −0.474713 + 0.822226i
\(640\) −1.00000 + 1.73205i −0.0395285 + 0.0684653i
\(641\) −0.500000 0.866025i −0.0197488 0.0342059i 0.855982 0.517005i \(-0.172953\pi\)
−0.875731 + 0.482800i \(0.839620\pi\)
\(642\) 4.50000 + 2.59808i 0.177601 + 0.102538i
\(643\) −3.50000 6.06218i −0.138027 0.239069i 0.788723 0.614749i \(-0.210743\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 0 0
\(645\) −3.00000 1.73205i −0.118125 0.0681994i
\(646\) −35.0000 −1.37706
\(647\) 6.00000 10.3923i 0.235884 0.408564i −0.723645 0.690172i \(-0.757535\pi\)
0.959529 + 0.281609i \(0.0908680\pi\)
\(648\) 4.50000 + 7.79423i 0.176777 + 0.306186i
\(649\) −3.50000 6.06218i −0.137387 0.237961i
\(650\) −3.00000 + 5.19615i −0.117670 + 0.203810i
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 3.46410i 0.135457i
\(655\) 4.00000 + 6.92820i 0.156293 + 0.270707i
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) −1.50000 2.59808i −0.0585206 0.101361i
\(658\) 0 0
\(659\) −8.00000 + 13.8564i −0.311636 + 0.539769i −0.978717 0.205216i \(-0.934210\pi\)
0.667081 + 0.744985i \(0.267544\pi\)
\(660\) −3.00000 + 1.73205i −0.116775 + 0.0674200i
\(661\) −28.0000 −1.08907 −0.544537 0.838737i \(-0.683295\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(662\) −8.00000 −0.310929
\(663\) 45.0000 25.9808i 1.74766 1.00901i
\(664\) −8.00000 + 13.8564i −0.310460 + 0.537733i
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 8.00000 + 13.8564i 0.309761 + 0.536522i
\(668\) 10.0000 + 17.3205i 0.386912 + 0.670151i
\(669\) 6.92820i 0.267860i
\(670\) −13.0000 + 22.5167i −0.502234 + 0.869894i
\(671\) −6.00000 10.3923i −0.231627 0.401190i
\(672\) 0 0
\(673\) −7.00000 + 12.1244i −0.269830 + 0.467360i −0.968818 0.247774i \(-0.920301\pi\)
0.698988 + 0.715134i \(0.253634\pi\)
\(674\) −4.50000 7.79423i −0.173334 0.300222i
\(675\) 4.50000 2.59808i 0.173205 0.100000i
\(676\) −11.5000 + 19.9186i −0.442308 + 0.766099i
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) −15.0000 8.66025i −0.576072 0.332595i
\(679\) 0 0
\(680\) −5.00000 8.66025i −0.191741 0.332106i
\(681\) 4.50000 + 2.59808i 0.172440 + 0.0995585i
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) −19.5000 + 33.7750i −0.746147 + 1.29236i 0.203510 + 0.979073i \(0.434765\pi\)
−0.949657 + 0.313291i \(0.898568\pi\)
\(684\) −21.0000 −0.802955
\(685\) 38.0000 1.45191
\(686\) 0 0
\(687\) 45.0333i 1.71813i
\(688\) 0.500000 0.866025i 0.0190623 0.0330169i
\(689\) 72.0000 2.74298
\(690\) −12.0000 6.92820i −0.456832 0.263752i
\(691\) −32.0000 −1.21734 −0.608669 0.793424i \(-0.708296\pi\)
−0.608669 + 0.793424i \(0.708296\pi\)
\(692\) −2.00000 −0.0760286
\(693\) 0 0
\(694\) 3.00000 0.113878
\(695\) −10.0000 −0.379322
\(696\) 6.92820i 0.262613i
\(697\) −15.0000 −0.568166
\(698\) 7.00000 12.1244i 0.264954 0.458914i
\(699\) 43.5000 + 25.1147i 1.64532 + 0.949927i
\(700\) 0 0
\(701\) 8.00000 0.302156 0.151078 0.988522i \(-0.451726\pi\)
0.151078 + 0.988522i \(0.451726\pi\)
\(702\) 27.0000 15.5885i 1.01905 0.588348i
\(703\) −7.00000 + 12.1244i −0.264010 + 0.457279i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) 7.50000 + 12.9904i 0.282266 + 0.488899i
\(707\) 0 0
\(708\) 10.5000 6.06218i 0.394614 0.227831i
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) 8.00000 13.8564i 0.300235 0.520022i
\(711\) −9.00000 + 15.5885i −0.337526 + 0.584613i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) −12.0000 + 20.7846i −0.449404 + 0.778390i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) −12.0000 + 20.7846i −0.448461 + 0.776757i
\(717\) −9.00000 5.19615i −0.336111 0.194054i
\(718\) 1.00000 + 1.73205i 0.0373197 + 0.0646396i
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) −3.00000 5.19615i −0.111803 0.193649i
\(721\) 0 0
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) 34.5000 + 19.9186i 1.28307 + 0.740780i
\(724\) 0 0
\(725\) 4.00000 0.148556
\(726\) 17.3205i 0.642824i
\(727\) −7.00000 + 12.1244i −0.259616 + 0.449667i −0.966139 0.258022i \(-0.916929\pi\)
0.706523 + 0.707690i \(0.250263\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 1.00000 + 1.73205i 0.0370117 + 0.0641061i
\(731\) 2.50000 + 4.33013i 0.0924658 + 0.160156i
\(732\) 18.0000 10.3923i 0.665299 0.384111i
\(733\) −9.00000 + 15.5885i −0.332423 + 0.575773i −0.982986 0.183679i \(-0.941199\pi\)
0.650564 + 0.759452i \(0.274533\pi\)
\(734\) 11.0000 + 19.0526i 0.406017 + 0.703243i
\(735\) 0 0
\(736\) 2.00000 3.46410i 0.0737210 0.127688i
\(737\) −6.50000 11.2583i −0.239431 0.414706i
\(738\) −9.00000 −0.331295
\(739\) 16.5000 28.5788i 0.606962 1.05129i −0.384776 0.923010i \(-0.625721\pi\)
0.991738 0.128279i \(-0.0409454\pi\)
\(740\) −4.00000 −0.147043
\(741\) 72.7461i 2.67240i
\(742\) 0 0
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) −9.00000 + 5.19615i −0.329956 + 0.190500i
\(745\) −24.0000 41.5692i −0.879292 1.52298i
\(746\) 11.0000 19.0526i 0.402739 0.697564i
\(747\) −24.0000 41.5692i −0.878114 1.52094i
\(748\) 5.00000 0.182818
\(749\) 0 0
\(750\) −18.0000 + 10.3923i −0.657267 + 0.379473i
\(751\) 9.00000 15.5885i 0.328415 0.568831i −0.653783 0.756682i \(-0.726819\pi\)
0.982197 + 0.187851i \(0.0601523\pi\)
\(752\) 0 0
\(753\) −4.50000 + 2.59808i −0.163989 + 0.0946792i
\(754\) 24.0000 0.874028
\(755\) −20.0000 −0.727875
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) 17.0000 0.617468
\(759\) 6.00000 3.46410i 0.217786 0.125739i
\(760\) 14.0000 0.507833
\(761\) 5.00000 8.66025i 0.181250 0.313934i −0.761057 0.648686i \(-0.775319\pi\)
0.942306 + 0.334752i \(0.108652\pi\)
\(762\) 18.0000 10.3923i 0.652071 0.376473i
\(763\) 0 0
\(764\) 12.0000 0.434145
\(765\) 30.0000 1.08465
\(766\) −2.00000 + 3.46410i −0.0722629 + 0.125163i
\(767\) −21.0000 36.3731i −0.758266 1.31336i
\(768\) 1.50000 0.866025i 0.0541266 0.0312500i
\(769\) 11.0000 + 19.0526i 0.396670 + 0.687053i 0.993313 0.115454i \(-0.0368323\pi\)
−0.596643 + 0.802507i \(0.703499\pi\)
\(770\) 0 0
\(771\) 25.9808i 0.935674i
\(772\) 17.0000 0.611843
\(773\) −26.0000 + 45.0333i −0.935155 + 1.61974i −0.160798 + 0.986987i \(0.551407\pi\)
−0.774357 + 0.632749i \(0.781927\pi\)
\(774\) 1.50000 + 2.59808i 0.0539164 + 0.0933859i
\(775\) 3.00000 + 5.19615i 0.107763 + 0.186651i
\(776\) 2.50000 4.33013i 0.0897448 0.155443i
\(777\) 0 0
\(778\) 4.00000 + 6.92820i 0.143407 + 0.248388i
\(779\) 10.5000 18.1865i 0.376202 0.651600i
\(780\) −18.0000 + 10.3923i −0.644503 + 0.372104i
\(781\) 4.00000 + 6.92820i 0.143131 + 0.247911i
\(782\) 10.0000 + 17.3205i 0.357599 + 0.619380i
\(783\) −18.0000 10.3923i −0.643268 0.371391i
\(784\) 0 0
\(785\) −2.00000 + 3.46410i −0.0713831 + 0.123639i
\(786\) 6.92820i 0.247121i
\(787\) 12.0000 0.427754 0.213877 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(788\) 10.0000 0.356235
\(789\) −27.0000 15.5885i −0.961225 0.554964i
\(790\) 6.00000 10.3923i 0.213470 0.369742i
\(791\) 0 0
\(792\) 3.00000 0.106600
\(793\) −36.0000 62.3538i −1.27840 2.21425i
\(794\) −9.00000 15.5885i −0.319398 0.553214i
\(795\) 36.0000 + 20.7846i 1.27679 + 0.737154i
\(796\) 7.00000 12.1244i 0.248108 0.429736i
\(797\) −6.00000 10.3923i −0.212531 0.368114i 0.739975 0.672634i \(-0.234837\pi\)
−0.952506 + 0.304520i \(0.901504\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) −18.0000 −0.635999
\(802\) 4.50000 7.79423i 0.158901 0.275224i
\(803\) −1.00000 −0.0352892
\(804\) 19.5000 11.2583i 0.687712 0.397051i
\(805\) 0 0
\(806\) 18.0000 + 31.1769i 0.634023 + 1.09816i
\(807\) 34.6410i 1.21942i
\(808\) 2.00000 + 3.46410i 0.0703598 + 0.121867i
\(809\) 21.5000 37.2391i 0.755900 1.30926i −0.189026 0.981972i \(-0.560533\pi\)
0.944926 0.327285i \(-0.106134\pi\)
\(810\) 18.0000 0.632456
\(811\) −31.0000 −1.08856 −0.544279 0.838905i \(-0.683197\pi\)
−0.544279 + 0.838905i \(0.683197\pi\)
\(812\) 0 0
\(813\) −9.00000 5.19615i −0.315644 0.182237i
\(814\) 1.00000 1.73205i 0.0350500 0.0607083i
\(815\) 8.00000 0.280228
\(816\) 8.66025i 0.303170i
\(817\) −7.00000 −0.244899
\(818\) 11.0000 0.384606
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 46.0000 1.60541 0.802706 0.596376i \(-0.203393\pi\)
0.802706 + 0.596376i \(0.203393\pi\)
\(822\) −28.5000 16.4545i −0.994052 0.573916i
\(823\) 34.0000 1.18517 0.592583 0.805510i \(-0.298108\pi\)
0.592583 + 0.805510i \(0.298108\pi\)
\(824\) −7.00000 + 12.1244i −0.243857 + 0.422372i
\(825\) 1.73205i 0.0603023i
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 6.00000 + 10.3923i 0.208514 + 0.361158i
\(829\) 2.00000 3.46410i 0.0694629 0.120313i −0.829202 0.558949i \(-0.811205\pi\)
0.898665 + 0.438636i \(0.144538\pi\)
\(830\) 16.0000 + 27.7128i 0.555368 + 0.961926i
\(831\) −3.00000 1.73205i −0.104069 0.0600842i
\(832\) −3.00000 5.19615i −0.104006 0.180144i
\(833\) 0 0
\(834\) 7.50000 + 4.33013i 0.259704 + 0.149940i
\(835\) 40.0000 1.38426
\(836\) −3.50000 + 6.06218i −0.121050 + 0.209665i
\(837\) 31.1769i 1.07763i
\(838\) 6.00000 + 10.3923i 0.207267 + 0.358996i
\(839\) −10.0000 + 17.3205i −0.345238 + 0.597970i −0.985397 0.170272i \(-0.945535\pi\)
0.640159 + 0.768243i \(0.278869\pi\)
\(840\) 0 0
\(841\) 6.50000 + 11.2583i 0.224138 + 0.388218i
\(842\) −6.00000 + 10.3923i −0.206774 + 0.358142i
\(843\) 38.1051i 1.31241i
\(844\) 8.00000 + 13.8564i 0.275371 + 0.476957i
\(845\) 23.0000 + 39.8372i 0.791224 + 1.37044i
\(846\) 0 0
\(847\) 0 0
\(848\) −6.00000 + 10.3923i −0.206041 + 0.356873i
\(849\) −6.00000 + 3.46410i −0.205919 + 0.118888i
\(850\) 5.00000 0.171499
\(851\) 8.00000 0.274236
\(852\) −12.0000 + 6.92820i −0.411113 + 0.237356i
\(853\) 22.0000 38.1051i 0.753266 1.30469i −0.192966 0.981205i \(-0.561811\pi\)
0.946232 0.323489i \(-0.104856\pi\)
\(854\) 0 0
\(855\) −21.0000 + 36.3731i −0.718185 + 1.24393i
\(856\) 1.50000 + 2.59808i 0.0512689 + 0.0888004i
\(857\) 15.0000 + 25.9808i 0.512390 + 0.887486i 0.999897 + 0.0143666i \(0.00457319\pi\)
−0.487507 + 0.873119i \(0.662093\pi\)
\(858\) 10.3923i 0.354787i
\(859\) 14.5000 25.1147i 0.494734 0.856904i −0.505248 0.862974i \(-0.668599\pi\)
0.999982 + 0.00607046i \(0.00193230\pi\)
\(860\) −1.00000 1.73205i −0.0340997 0.0590624i
\(861\) 0 0
\(862\) 0 0
\(863\) −19.0000 32.9090i −0.646768 1.12023i −0.983890 0.178774i \(-0.942787\pi\)
0.337123 0.941461i \(-0.390546\pi\)
\(864\) 5.19615i 0.176777i
\(865\) −2.00000 + 3.46410i −0.0680020 + 0.117783i
\(866\) −25.0000 −0.849535
\(867\) −12.0000 6.92820i −0.407541 0.235294i
\(868\) 0 0
\(869\) 3.00000 + 5.19615i 0.101768 + 0.176267i
\(870\) 12.0000 + 6.92820i 0.406838 + 0.234888i
\(871\) −39.0000 67.5500i −1.32146 2.28884i
\(872\) −1.00000 + 1.73205i −0.0338643 + 0.0586546i
\(873\) 7.50000 + 12.9904i 0.253837 + 0.439658i
\(874\) −28.0000 −0.947114
\(875\) 0 0
\(876\) 1.73205i 0.0585206i
\(877\) −8.00000 + 13.8564i −0.270141 + 0.467898i −0.968898 0.247462i \(-0.920404\pi\)
0.698757 + 0.715359i \(0.253737\pi\)
\(878\) −24.0000 −0.809961
\(879\) 0 0
\(880\) −2.00000 −0.0674200
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 0 0
\(883\) 53.0000 1.78359 0.891796 0.452438i \(-0.149446\pi\)
0.891796 + 0.452438i \(0.149446\pi\)
\(884\) 30.0000 1.00901
\(885\) 24.2487i 0.815112i
\(886\) −7.00000 −0.235170
\(887\) −3.00000 + 5.19615i −0.100730 + 0.174470i −0.911986 0.410222i \(-0.865451\pi\)
0.811256 + 0.584692i \(0.198785\pi\)
\(888\) 3.00000 + 1.73205i 0.100673 + 0.0581238i
\(889\) 0 0
\(890\) 12.0000 0.402241
\(891\) −4.50000 + 7.79423i −0.150756 + 0.261116i
\(892\) −2.00000 + 3.46410i −0.0669650 + 0.115987i
\(893\) 0 0
\(894\) 41.5692i 1.39028i
\(895\) 24.0000 + 41.5692i 0.802232 + 1.38951i
\(896\) 0 0
\(897\) 36.0000 20.7846i 1.20201 0.693978i
\(898\) −17.0000 −0.567297
\(899\) 12.0000 20.7846i 0.400222 0.693206i
\(900\) 3.00000 0.100000
\(901\) −30.0000 51.9615i −0.999445 1.73109i
\(902\) −1.50000 + 2.59808i −0.0499445 + 0.0865065i
\(903\) 0 0
\(904\) −5.00000 8.66025i −0.166298 0.288036i
\(905\) 0 0
\(906\) 15.0000 + 8.66025i 0.498342 + 0.287718i
\(907\) 13.5000 + 23.3827i 0.448260 + 0.776409i 0.998273 0.0587469i \(-0.0187105\pi\)
−0.550013 + 0.835156i \(0.685377\pi\)
\(908\) 1.50000 + 2.59808i 0.0497792 + 0.0862202i
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(912\) −10.5000 6.06218i −0.347690 0.200739i
\(913\) −16.0000 −0.529523
\(914\) −1.00000 −0.0330771
\(915\) 41.5692i 1.37424i
\(916\) −13.0000 + 22.5167i −0.429532 + 0.743971i
\(917\) 0 0
\(918\) −22.5000 12.9904i −0.742611 0.428746i
\(919\) −8.00000 13.8564i −0.263896 0.457081i 0.703378 0.710816i \(-0.251674\pi\)
−0.967274 + 0.253735i \(0.918341\pi\)
\(920\) −4.00000 6.92820i −0.131876 0.228416i
\(921\) −10.5000 + 6.06218i −0.345987 + 0.199756i
\(922\) −7.00000 + 12.1244i −0.230533 + 0.399294i
\(923\) 24.0000 + 41.5692i 0.789970 + 1.36827i
\(924\) 0 0
\(925\) 1.00000 1.73205i 0.0328798 0.0569495i
\(926\) −4.00000 6.92820i −0.131448 0.227675i
\(927\) −21.0000 36.3731i −0.689730 1.19465i
\(928\) −2.00000 + 3.46410i −0.0656532 + 0.113715i
\(929\) 18.0000 0.590561 0.295280 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) 20.7846i 0.681554i
\(931\) 0 0
\(932\) 14.5000 + 25.1147i 0.474963 + 0.822661i
\(933\) −3.00000 + 1.73205i −0.0982156 + 0.0567048i
\(934\) 6.50000 + 11.2583i 0.212686 + 0.368384i
\(935\) 5.00000 8.66025i 0.163517 0.283221i
\(936\) 18.0000 0.588348
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 0 0
\(939\) 25.5000 14.7224i 0.832161 0.480448i
\(940\) 0 0
\(941\) −20.0000 −0.651981 −0.325991 0.945373i \(-0.605698\pi\)
−0.325991 + 0.945373i \(0.605698\pi\)
\(942\) 3.00000 1.73205i 0.0977453 0.0564333i
\(943\) −12.0000 −0.390774
\(944\) 7.00000 0.227831
\(945\) 0 0
\(946\) 1.00000 0.0325128
\(947\) −37.0000 −1.20234 −0.601169 0.799122i \(-0.705298\pi\)
−0.601169 + 0.799122i \(0.705298\pi\)
\(948\) −9.00000 + 5.19615i −0.292306 + 0.168763i
\(949\) −6.00000 −0.194768
\(950\) −3.50000 + 6.06218i −0.113555 + 0.196683i
\(951\) −9.00000 + 5.19615i −0.291845 + 0.168497i
\(952\) 0 0
\(953\) −35.0000 −1.13376 −0.566881 0.823800i \(-0.691850\pi\)
−0.566881 + 0.823800i \(0.691850\pi\)
\(954\) −18.0000 31.1769i −0.582772 1.00939i
\(955\) 12.0000 20.7846i 0.388311 0.672574i
\(956\) −3.00000 5.19615i −0.0970269 0.168056i
\(957\) −6.00000 + 3.46410i −0.193952 + 0.111979i
\(958\) 10.0000 + 17.3205i 0.323085 + 0.559600i
\(959\) 0 0
\(960\) 3.46410i 0.111803i
\(961\) 5.00000 0.161290
\(962\) 6.00000 10.3923i 0.193448 0.335061i
\(963\) −9.00000 −0.290021
\(964\) 11.5000 + 19.9186i 0.370390 + 0.641534i
\(965\) 17.0000 29.4449i 0.547249 0.947864i
\(966\) 0 0
\(967\) −7.00000 12.1244i −0.225105 0.389893i 0.731246 0.682114i \(-0.238939\pi\)
−0.956351 + 0.292221i \(0.905606\pi\)
\(968\) −5.00000 + 8.66025i −0.160706 + 0.278351i
\(969\) 52.5000 30.3109i 1.68654 0.973726i
\(970\) −5.00000 8.66025i −0.160540 0.278064i
\(971\) −6.00000 10.3923i −0.192549 0.333505i 0.753545 0.657396i \(-0.228342\pi\)
−0.946094 + 0.323891i \(0.895009\pi\)
\(972\) −13.5000 7.79423i −0.433013 0.250000i
\(973\) 0 0
\(974\) −5.00000 + 8.66025i −0.160210 + 0.277492i
\(975\) 10.3923i 0.332820i
\(976\) 12.0000 0.384111
\(977\) −15.0000 −0.479893 −0.239946 0.970786i \(-0.577130\pi\)
−0.239946 + 0.970786i \(0.577130\pi\)
\(978\) −6.00000 3.46410i −0.191859 0.110770i
\(979\) −3.00000 + 5.19615i −0.0958804 + 0.166070i
\(980\) 0 0
\(981\) −3.00000 5.19615i −0.0957826 0.165900i
\(982\) 16.5000 + 28.5788i 0.526536 + 0.911987i
\(983\) −30.0000 51.9615i −0.956851 1.65732i −0.730073 0.683369i \(-0.760514\pi\)
−0.226778 0.973946i \(-0.572819\pi\)
\(984\) −4.50000 2.59808i −0.143455 0.0828236i
\(985\) 10.0000 17.3205i 0.318626 0.551877i
\(986\) −10.0000 17.3205i −0.318465 0.551597i
\(987\) 0 0
\(988\) −21.0000 + 36.3731i −0.668099 + 1.15718i
\(989\) 2.00000 + 3.46410i 0.0635963 + 0.110152i
\(990\) 3.00000 5.19615i 0.0953463 0.165145i
\(991\) 14.0000 24.2487i 0.444725 0.770286i −0.553308 0.832977i \(-0.686635\pi\)
0.998033 + 0.0626908i \(0.0199682\pi\)
\(992\) −6.00000 −0.190500
\(993\) 12.0000 6.92820i 0.380808 0.219860i
\(994\) 0 0
\(995\) −14.0000 24.2487i −0.443830 0.768736i
\(996\) 27.7128i 0.878114i
\(997\) 1.00000 + 1.73205i 0.0316703 + 0.0548546i 0.881426 0.472322i \(-0.156584\pi\)
−0.849756 + 0.527176i \(0.823251\pi\)
\(998\) −14.5000 + 25.1147i −0.458989 + 0.794993i
\(999\) −9.00000 + 5.19615i −0.284747 + 0.164399i
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 882.2.e.e.655.1 2
3.2 odd 2 2646.2.e.h.2125.1 2
7.2 even 3 882.2.h.g.79.1 2
7.3 odd 6 126.2.f.b.43.1 2
7.4 even 3 882.2.f.f.295.1 2
7.5 odd 6 882.2.h.h.79.1 2
7.6 odd 2 882.2.e.a.655.1 2
9.4 even 3 882.2.h.g.67.1 2
9.5 odd 6 2646.2.h.c.361.1 2
21.2 odd 6 2646.2.h.c.667.1 2
21.5 even 6 2646.2.h.b.667.1 2
21.11 odd 6 2646.2.f.b.883.1 2
21.17 even 6 378.2.f.b.127.1 2
21.20 even 2 2646.2.e.i.2125.1 2
28.3 even 6 1008.2.r.a.673.1 2
63.4 even 3 882.2.f.f.589.1 2
63.5 even 6 2646.2.e.i.1549.1 2
63.11 odd 6 7938.2.a.bb.1.1 1
63.13 odd 6 882.2.h.h.67.1 2
63.23 odd 6 2646.2.e.h.1549.1 2
63.25 even 3 7938.2.a.e.1.1 1
63.31 odd 6 126.2.f.b.85.1 yes 2
63.32 odd 6 2646.2.f.b.1765.1 2
63.38 even 6 1134.2.a.f.1.1 1
63.40 odd 6 882.2.e.a.373.1 2
63.41 even 6 2646.2.h.b.361.1 2
63.52 odd 6 1134.2.a.c.1.1 1
63.58 even 3 inner 882.2.e.e.373.1 2
63.59 even 6 378.2.f.b.253.1 2
84.59 odd 6 3024.2.r.c.2017.1 2
252.31 even 6 1008.2.r.a.337.1 2
252.59 odd 6 3024.2.r.c.1009.1 2
252.115 even 6 9072.2.a.t.1.1 1
252.227 odd 6 9072.2.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.f.b.43.1 2 7.3 odd 6
126.2.f.b.85.1 yes 2 63.31 odd 6
378.2.f.b.127.1 2 21.17 even 6
378.2.f.b.253.1 2 63.59 even 6
882.2.e.a.373.1 2 63.40 odd 6
882.2.e.a.655.1 2 7.6 odd 2
882.2.e.e.373.1 2 63.58 even 3 inner
882.2.e.e.655.1 2 1.1 even 1 trivial
882.2.f.f.295.1 2 7.4 even 3
882.2.f.f.589.1 2 63.4 even 3
882.2.h.g.67.1 2 9.4 even 3
882.2.h.g.79.1 2 7.2 even 3
882.2.h.h.67.1 2 63.13 odd 6
882.2.h.h.79.1 2 7.5 odd 6
1008.2.r.a.337.1 2 252.31 even 6
1008.2.r.a.673.1 2 28.3 even 6
1134.2.a.c.1.1 1 63.52 odd 6
1134.2.a.f.1.1 1 63.38 even 6
2646.2.e.h.1549.1 2 63.23 odd 6
2646.2.e.h.2125.1 2 3.2 odd 2
2646.2.e.i.1549.1 2 63.5 even 6
2646.2.e.i.2125.1 2 21.20 even 2
2646.2.f.b.883.1 2 21.11 odd 6
2646.2.f.b.1765.1 2 63.32 odd 6
2646.2.h.b.361.1 2 63.41 even 6
2646.2.h.b.667.1 2 21.5 even 6
2646.2.h.c.361.1 2 9.5 odd 6
2646.2.h.c.667.1 2 21.2 odd 6
3024.2.r.c.1009.1 2 252.59 odd 6
3024.2.r.c.2017.1 2 84.59 odd 6
7938.2.a.e.1.1 1 63.25 even 3
7938.2.a.bb.1.1 1 63.11 odd 6
9072.2.a.f.1.1 1 252.227 odd 6
9072.2.a.t.1.1 1 252.115 even 6