Properties

Label 1638.2.j.i.235.1
Level $1638$
Weight $2$
Character 1638.235
Analytic conductor $13.079$
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] = [1638,2,Mod(235,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.235");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.j (of order \(3\), degree \(2\), 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: \(13.0794958511\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1638.235
Dual form 1638.2.j.i.1171.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-2.50000 + 4.33013i) q^{11} -1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.50000 - 6.06218i) q^{17} +(-3.50000 - 6.06218i) q^{19} -5.00000 q^{22} +(1.00000 + 1.73205i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(2.00000 - 1.73205i) q^{28} +9.00000 q^{29} +(0.500000 - 0.866025i) q^{32} +7.00000 q^{34} +(-2.00000 - 3.46410i) q^{37} +(3.50000 - 6.06218i) q^{38} -4.00000 q^{41} +2.00000 q^{43} +(-2.50000 - 4.33013i) q^{44} +(-1.00000 + 1.73205i) q^{46} +(-1.50000 - 2.59808i) q^{47} +(5.50000 + 4.33013i) q^{49} +5.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(0.500000 - 0.866025i) q^{53} +(2.50000 + 0.866025i) q^{56} +(4.50000 + 7.79423i) q^{58} +(3.50000 - 6.06218i) q^{59} +(-6.50000 - 11.2583i) q^{61} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{67} +(3.50000 + 6.06218i) q^{68} -9.00000 q^{71} +(5.00000 - 8.66025i) q^{73} +(2.00000 - 3.46410i) q^{74} +7.00000 q^{76} +(10.0000 - 8.66025i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-2.00000 - 3.46410i) q^{82} -16.0000 q^{83} +(1.00000 + 1.73205i) q^{86} +(2.50000 - 4.33013i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(2.50000 + 0.866025i) q^{91} -2.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +6.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - 5 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} - 5 q^{7} - 2 q^{8} - 5 q^{11} - 2 q^{13} - q^{14} - q^{16} + 7 q^{17} - 7 q^{19} - 10 q^{22} + 2 q^{23} + 5 q^{25} - q^{26} + 4 q^{28} + 18 q^{29} + q^{32} + 14 q^{34} - 4 q^{37} + 7 q^{38} - 8 q^{41} + 4 q^{43} - 5 q^{44} - 2 q^{46} - 3 q^{47} + 11 q^{49} + 10 q^{50} + q^{52} + q^{53} + 5 q^{56} + 9 q^{58} + 7 q^{59} - 13 q^{61} + 2 q^{64} - 3 q^{67} + 7 q^{68} - 18 q^{71} + 10 q^{73} + 4 q^{74} + 14 q^{76} + 20 q^{77} - 14 q^{79} - 4 q^{82} - 32 q^{83} + 2 q^{86} + 5 q^{88} - 12 q^{89} + 5 q^{91} - 4 q^{92} + 3 q^{94} + 12 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.50000 6.06218i 0.848875 1.47029i −0.0333386 0.999444i \(-0.510614\pi\)
0.882213 0.470850i \(-0.156053\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −5.00000 −1.06600
\(23\) 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i \(-0.0998038\pi\)
−0.742732 + 0.669588i \(0.766471\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) −0.500000 0.866025i −0.0980581 0.169842i
\(27\) 0 0
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 7.00000 1.20049
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 3.50000 6.06218i 0.567775 0.983415i
\(39\) 0 0
\(40\) 0 0
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −2.50000 4.33013i −0.376889 0.652791i
\(45\) 0 0
\(46\) −1.00000 + 1.73205i −0.147442 + 0.255377i
\(47\) −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i \(-0.236880\pi\)
−0.954441 + 0.298401i \(0.903547\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) 0.500000 0.866025i 0.0686803 0.118958i −0.829640 0.558298i \(-0.811454\pi\)
0.898321 + 0.439340i \(0.144788\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 0 0
\(58\) 4.50000 + 7.79423i 0.590879 + 1.02343i
\(59\) 3.50000 6.06218i 0.455661 0.789228i −0.543065 0.839691i \(-0.682736\pi\)
0.998726 + 0.0504625i \(0.0160695\pi\)
\(60\) 0 0
\(61\) −6.50000 11.2583i −0.832240 1.44148i −0.896258 0.443533i \(-0.853725\pi\)
0.0640184 0.997949i \(-0.479608\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) 3.50000 + 6.06218i 0.424437 + 0.735147i
\(69\) 0 0
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i \(-0.634347\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) 0 0
\(76\) 7.00000 0.802955
\(77\) 10.0000 8.66025i 1.13961 0.986928i
\(78\) 0 0
\(79\) −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −2.00000 3.46410i −0.220863 0.382546i
\(83\) −16.0000 −1.75623 −0.878114 0.478451i \(-0.841198\pi\)
−0.878114 + 0.478451i \(0.841198\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 0 0
\(88\) 2.50000 4.33013i 0.266501 0.461593i
\(89\) −6.00000 10.3923i −0.635999 1.10158i −0.986303 0.164946i \(-0.947255\pi\)
0.350304 0.936636i \(-0.386078\pi\)
\(90\) 0 0
\(91\) 2.50000 + 0.866025i 0.262071 + 0.0907841i
\(92\) −2.00000 −0.208514
\(93\) 0 0
\(94\) 1.50000 2.59808i 0.154713 0.267971i
\(95\) 0 0
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) 0 0
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) 0 0
\(109\) −4.00000 + 6.92820i −0.383131 + 0.663602i −0.991508 0.130046i \(-0.958487\pi\)
0.608377 + 0.793648i \(0.291821\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) −1.00000 −0.0940721 −0.0470360 0.998893i \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.50000 + 7.79423i −0.417815 + 0.723676i
\(117\) 0 0
\(118\) 7.00000 0.644402
\(119\) −14.0000 + 12.1244i −1.28338 + 1.11144i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 6.50000 11.2583i 0.588482 1.01928i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 22.0000 1.95218 0.976092 0.217357i \(-0.0697436\pi\)
0.976092 + 0.217357i \(0.0697436\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 9.00000 + 15.5885i 0.786334 + 1.36197i 0.928199 + 0.372084i \(0.121357\pi\)
−0.141865 + 0.989886i \(0.545310\pi\)
\(132\) 0 0
\(133\) 3.50000 + 18.1865i 0.303488 + 1.57697i
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) −3.50000 + 6.06218i −0.300123 + 0.519827i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.50000 7.79423i −0.377632 0.654077i
\(143\) 2.50000 4.33013i 0.209061 0.362103i
\(144\) 0 0
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 0 0
\(151\) 8.50000 14.7224i 0.691720 1.19809i −0.279554 0.960130i \(-0.590186\pi\)
0.971274 0.237964i \(-0.0764802\pi\)
\(152\) 3.50000 + 6.06218i 0.283887 + 0.491708i
\(153\) 0 0
\(154\) 12.5000 + 4.33013i 1.00728 + 0.348932i
\(155\) 0 0
\(156\) 0 0
\(157\) −5.50000 + 9.52628i −0.438948 + 0.760280i −0.997609 0.0691164i \(-0.977982\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 7.00000 12.1244i 0.556890 0.964562i
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 5.19615i −0.0788110 0.409514i
\(162\) 0 0
\(163\) −6.50000 11.2583i −0.509119 0.881820i −0.999944 0.0105623i \(-0.996638\pi\)
0.490825 0.871258i \(-0.336695\pi\)
\(164\) 2.00000 3.46410i 0.156174 0.270501i
\(165\) 0 0
\(166\) −8.00000 13.8564i −0.620920 1.07547i
\(167\) 5.00000 0.386912 0.193456 0.981109i \(-0.438030\pi\)
0.193456 + 0.981109i \(0.438030\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −6.50000 11.2583i −0.494186 0.855955i 0.505792 0.862656i \(-0.331200\pi\)
−0.999978 + 0.00670064i \(0.997867\pi\)
\(174\) 0 0
\(175\) −10.0000 + 8.66025i −0.755929 + 0.654654i
\(176\) 5.00000 0.376889
\(177\) 0 0
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) −5.00000 + 8.66025i −0.373718 + 0.647298i −0.990134 0.140122i \(-0.955250\pi\)
0.616417 + 0.787420i \(0.288584\pi\)
\(180\) 0 0
\(181\) −11.0000 −0.817624 −0.408812 0.912619i \(-0.634057\pi\)
−0.408812 + 0.912619i \(0.634057\pi\)
\(182\) 0.500000 + 2.59808i 0.0370625 + 0.192582i
\(183\) 0 0
\(184\) −1.00000 1.73205i −0.0737210 0.127688i
\(185\) 0 0
\(186\) 0 0
\(187\) 17.5000 + 30.3109i 1.27973 + 2.21655i
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 0 0
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0 0
\(193\) 4.00000 6.92820i 0.287926 0.498703i −0.685388 0.728178i \(-0.740368\pi\)
0.973315 + 0.229475i \(0.0737008\pi\)
\(194\) 3.00000 + 5.19615i 0.215387 + 0.373062i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 0 0
\(199\) −9.00000 + 15.5885i −0.637993 + 1.10504i 0.347879 + 0.937539i \(0.386902\pi\)
−0.985873 + 0.167497i \(0.946431\pi\)
\(200\) −2.50000 + 4.33013i −0.176777 + 0.306186i
\(201\) 0 0
\(202\) −6.00000 −0.422159
\(203\) −22.5000 7.79423i −1.57919 0.547048i
\(204\) 0 0
\(205\) 0 0
\(206\) −5.00000 + 8.66025i −0.348367 + 0.603388i
\(207\) 0 0
\(208\) 0.500000 + 0.866025i 0.0346688 + 0.0600481i
\(209\) 35.0000 2.42100
\(210\) 0 0
\(211\) −26.0000 −1.78991 −0.894957 0.446153i \(-0.852794\pi\)
−0.894957 + 0.446153i \(0.852794\pi\)
\(212\) 0.500000 + 0.866025i 0.0343401 + 0.0594789i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −8.00000 −0.541828
\(219\) 0 0
\(220\) 0 0
\(221\) −3.50000 + 6.06218i −0.235435 + 0.407786i
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 0 0
\(226\) −0.500000 0.866025i −0.0332595 0.0576072i
\(227\) 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) 0 0
\(229\) −9.00000 15.5885i −0.594737 1.03011i −0.993584 0.113097i \(-0.963923\pi\)
0.398847 0.917017i \(-0.369410\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i \(-0.197997\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.50000 + 6.06218i 0.227831 + 0.394614i
\(237\) 0 0
\(238\) −17.5000 6.06218i −1.13436 0.392953i
\(239\) 1.00000 0.0646846 0.0323423 0.999477i \(-0.489703\pi\)
0.0323423 + 0.999477i \(0.489703\pi\)
\(240\) 0 0
\(241\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) 7.00000 12.1244i 0.449977 0.779383i
\(243\) 0 0
\(244\) 13.0000 0.832240
\(245\) 0 0
\(246\) 0 0
\(247\) 3.50000 + 6.06218i 0.222700 + 0.385727i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) −10.0000 −0.628695
\(254\) 11.0000 + 19.0526i 0.690201 + 1.19546i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.00000 12.1244i −0.436648 0.756297i 0.560781 0.827964i \(-0.310501\pi\)
−0.997429 + 0.0716680i \(0.977168\pi\)
\(258\) 0 0
\(259\) 2.00000 + 10.3923i 0.124274 + 0.645746i
\(260\) 0 0
\(261\) 0 0
\(262\) −9.00000 + 15.5885i −0.556022 + 0.963058i
\(263\) −2.00000 + 3.46410i −0.123325 + 0.213606i −0.921077 0.389380i \(-0.872689\pi\)
0.797752 + 0.602986i \(0.206023\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −14.0000 + 12.1244i −0.858395 + 0.743392i
\(267\) 0 0
\(268\) −1.50000 2.59808i −0.0916271 0.158703i
\(269\) 11.5000 19.9186i 0.701167 1.21446i −0.266890 0.963727i \(-0.585996\pi\)
0.968057 0.250730i \(-0.0806708\pi\)
\(270\) 0 0
\(271\) −1.50000 2.59808i −0.0911185 0.157822i 0.816864 0.576831i \(-0.195711\pi\)
−0.907982 + 0.419009i \(0.862378\pi\)
\(272\) −7.00000 −0.424437
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) 12.5000 + 21.6506i 0.753778 + 1.30558i
\(276\) 0 0
\(277\) −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i \(0.360033\pi\)
−0.996484 + 0.0837823i \(0.973300\pi\)
\(278\) 8.00000 + 13.8564i 0.479808 + 0.831052i
\(279\) 0 0
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 0 0
\(283\) 5.00000 8.66025i 0.297219 0.514799i −0.678280 0.734804i \(-0.737274\pi\)
0.975499 + 0.220005i \(0.0706075\pi\)
\(284\) 4.50000 7.79423i 0.267026 0.462502i
\(285\) 0 0
\(286\) 5.00000 0.295656
\(287\) 10.0000 + 3.46410i 0.590281 + 0.204479i
\(288\) 0 0
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) 0 0
\(291\) 0 0
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2.00000 + 3.46410i 0.116248 + 0.201347i
\(297\) 0 0
\(298\) −5.00000 + 8.66025i −0.289642 + 0.501675i
\(299\) −1.00000 1.73205i −0.0578315 0.100167i
\(300\) 0 0
\(301\) −5.00000 1.73205i −0.288195 0.0998337i
\(302\) 17.0000 0.978240
\(303\) 0 0
\(304\) −3.50000 + 6.06218i −0.200739 + 0.347690i
\(305\) 0 0
\(306\) 0 0
\(307\) 19.0000 1.08439 0.542194 0.840254i \(-0.317594\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) 2.50000 + 12.9904i 0.142451 + 0.740196i
\(309\) 0 0
\(310\) 0 0
\(311\) 10.0000 17.3205i 0.567048 0.982156i −0.429808 0.902920i \(-0.641419\pi\)
0.996856 0.0792356i \(-0.0252479\pi\)
\(312\) 0 0
\(313\) 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i \(-0.112429\pi\)
−0.768699 + 0.639611i \(0.779095\pi\)
\(314\) −11.0000 −0.620766
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) 13.0000 + 22.5167i 0.730153 + 1.26466i 0.956818 + 0.290689i \(0.0938844\pi\)
−0.226665 + 0.973973i \(0.572782\pi\)
\(318\) 0 0
\(319\) −22.5000 + 38.9711i −1.25976 + 2.18197i
\(320\) 0 0
\(321\) 0 0
\(322\) 4.00000 3.46410i 0.222911 0.193047i
\(323\) −49.0000 −2.72643
\(324\) 0 0
\(325\) −2.50000 + 4.33013i −0.138675 + 0.240192i
\(326\) 6.50000 11.2583i 0.360002 0.623541i
\(327\) 0 0
\(328\) 4.00000 0.220863
\(329\) 1.50000 + 7.79423i 0.0826977 + 0.429710i
\(330\) 0 0
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) 8.00000 13.8564i 0.439057 0.760469i
\(333\) 0 0
\(334\) 2.50000 + 4.33013i 0.136794 + 0.236934i
\(335\) 0 0
\(336\) 0 0
\(337\) −33.0000 −1.79762 −0.898812 0.438334i \(-0.855569\pi\)
−0.898812 + 0.438334i \(0.855569\pi\)
\(338\) 0.500000 + 0.866025i 0.0271964 + 0.0471056i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) 6.50000 11.2583i 0.349442 0.605252i
\(347\) −8.00000 + 13.8564i −0.429463 + 0.743851i −0.996826 0.0796169i \(-0.974630\pi\)
0.567363 + 0.823468i \(0.307964\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −12.5000 4.33013i −0.668153 0.231455i
\(351\) 0 0
\(352\) 2.50000 + 4.33013i 0.133250 + 0.230797i
\(353\) 1.00000 1.73205i 0.0532246 0.0921878i −0.838186 0.545385i \(-0.816383\pi\)
0.891410 + 0.453197i \(0.149717\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 12.0000 0.635999
\(357\) 0 0
\(358\) −10.0000 −0.528516
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −5.50000 9.52628i −0.289074 0.500690i
\(363\) 0 0
\(364\) −2.00000 + 1.73205i −0.104828 + 0.0907841i
\(365\) 0 0
\(366\) 0 0
\(367\) −1.00000 + 1.73205i −0.0521996 + 0.0904123i −0.890945 0.454112i \(-0.849957\pi\)
0.838745 + 0.544524i \(0.183290\pi\)
\(368\) 1.00000 1.73205i 0.0521286 0.0902894i
\(369\) 0 0
\(370\) 0 0
\(371\) −2.00000 + 1.73205i −0.103835 + 0.0899236i
\(372\) 0 0
\(373\) 10.5000 + 18.1865i 0.543669 + 0.941663i 0.998689 + 0.0511818i \(0.0162988\pi\)
−0.455020 + 0.890481i \(0.650368\pi\)
\(374\) −17.5000 + 30.3109i −0.904903 + 1.56734i
\(375\) 0 0
\(376\) 1.50000 + 2.59808i 0.0773566 + 0.133986i
\(377\) −9.00000 −0.463524
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 6.00000 10.3923i 0.306987 0.531717i
\(383\) 4.00000 + 6.92820i 0.204390 + 0.354015i 0.949938 0.312437i \(-0.101145\pi\)
−0.745548 + 0.666452i \(0.767812\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8.00000 0.407189
\(387\) 0 0
\(388\) −3.00000 + 5.19615i −0.152302 + 0.263795i
\(389\) −11.5000 + 19.9186i −0.583073 + 1.00991i 0.412039 + 0.911166i \(0.364817\pi\)
−0.995113 + 0.0987463i \(0.968517\pi\)
\(390\) 0 0
\(391\) 14.0000 0.708010
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) 0 0
\(394\) −11.0000 19.0526i −0.554172 0.959854i
\(395\) 0 0
\(396\) 0 0
\(397\) 1.00000 + 1.73205i 0.0501886 + 0.0869291i 0.890028 0.455905i \(-0.150684\pi\)
−0.839840 + 0.542834i \(0.817351\pi\)
\(398\) −18.0000 −0.902258
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −19.0000 32.9090i −0.948815 1.64340i −0.747927 0.663781i \(-0.768951\pi\)
−0.200888 0.979614i \(-0.564383\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −3.00000 5.19615i −0.149256 0.258518i
\(405\) 0 0
\(406\) −4.50000 23.3827i −0.223331 1.16046i
\(407\) 20.0000 0.991363
\(408\) 0 0
\(409\) 2.00000 3.46410i 0.0988936 0.171289i −0.812333 0.583193i \(-0.801803\pi\)
0.911227 + 0.411905i \(0.135136\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −10.0000 −0.492665
\(413\) −14.0000 + 12.1244i −0.688895 + 0.596601i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) 17.5000 + 30.3109i 0.855953 + 1.48255i
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) −13.0000 22.5167i −0.632830 1.09609i
\(423\) 0 0
\(424\) −0.500000 + 0.866025i −0.0242821 + 0.0420579i
\(425\) −17.5000 30.3109i −0.848875 1.47029i
\(426\) 0 0
\(427\) 6.50000 + 33.7750i 0.314557 + 1.63449i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.00000 + 13.8564i −0.385346 + 0.667440i −0.991817 0.127666i \(-0.959251\pi\)
0.606471 + 0.795106i \(0.292585\pi\)
\(432\) 0 0
\(433\) −11.0000 −0.528626 −0.264313 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.00000 6.92820i −0.191565 0.331801i
\(437\) 7.00000 12.1244i 0.334855 0.579987i
\(438\) 0 0
\(439\) 11.0000 + 19.0526i 0.525001 + 0.909329i 0.999576 + 0.0291138i \(0.00926853\pi\)
−0.474575 + 0.880215i \(0.657398\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −7.00000 −0.332956
\(443\) −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.500000 0.866025i −0.0236757 0.0410075i
\(447\) 0 0
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) −4.00000 −0.188772 −0.0943858 0.995536i \(-0.530089\pi\)
−0.0943858 + 0.995536i \(0.530089\pi\)
\(450\) 0 0
\(451\) 10.0000 17.3205i 0.470882 0.815591i
\(452\) 0.500000 0.866025i 0.0235180 0.0407344i
\(453\) 0 0
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 0 0
\(457\) 5.00000 + 8.66025i 0.233890 + 0.405110i 0.958950 0.283577i \(-0.0915211\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) 9.00000 15.5885i 0.420542 0.728401i
\(459\) 0 0
\(460\) 0 0
\(461\) 8.00000 0.372597 0.186299 0.982493i \(-0.440351\pi\)
0.186299 + 0.982493i \(0.440351\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) −4.50000 7.79423i −0.208907 0.361838i
\(465\) 0 0
\(466\) 1.50000 2.59808i 0.0694862 0.120354i
\(467\) −3.00000 5.19615i −0.138823 0.240449i 0.788228 0.615383i \(-0.210999\pi\)
−0.927052 + 0.374934i \(0.877665\pi\)
\(468\) 0 0
\(469\) 6.00000 5.19615i 0.277054 0.239936i
\(470\) 0 0
\(471\) 0 0
\(472\) −3.50000 + 6.06218i −0.161101 + 0.279034i
\(473\) −5.00000 + 8.66025i −0.229900 + 0.398199i
\(474\) 0 0
\(475\) −35.0000 −1.60591
\(476\) −3.50000 18.1865i −0.160422 0.833578i
\(477\) 0 0
\(478\) 0.500000 + 0.866025i 0.0228695 + 0.0396111i
\(479\) −5.50000 + 9.52628i −0.251301 + 0.435267i −0.963884 0.266321i \(-0.914192\pi\)
0.712583 + 0.701588i \(0.247525\pi\)
\(480\) 0 0
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) 0 0
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) 0 0
\(487\) 2.50000 4.33013i 0.113286 0.196217i −0.803807 0.594890i \(-0.797196\pi\)
0.917093 + 0.398673i \(0.130529\pi\)
\(488\) 6.50000 + 11.2583i 0.294241 + 0.509641i
\(489\) 0 0
\(490\) 0 0
\(491\) 22.0000 0.992846 0.496423 0.868081i \(-0.334646\pi\)
0.496423 + 0.868081i \(0.334646\pi\)
\(492\) 0 0
\(493\) 31.5000 54.5596i 1.41869 2.45724i
\(494\) −3.50000 + 6.06218i −0.157472 + 0.272750i
\(495\) 0 0
\(496\) 0 0
\(497\) 22.5000 + 7.79423i 1.00926 + 0.349619i
\(498\) 0 0
\(499\) −20.0000 34.6410i −0.895323 1.55074i −0.833404 0.552664i \(-0.813611\pi\)
−0.0619186 0.998081i \(-0.519722\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −9.00000 15.5885i −0.401690 0.695747i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −5.00000 8.66025i −0.222277 0.384995i
\(507\) 0 0
\(508\) −11.0000 + 19.0526i −0.488046 + 0.845321i
\(509\) 12.0000 + 20.7846i 0.531891 + 0.921262i 0.999307 + 0.0372243i \(0.0118516\pi\)
−0.467416 + 0.884037i \(0.654815\pi\)
\(510\) 0 0
\(511\) −20.0000 + 17.3205i −0.884748 + 0.766214i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 7.00000 12.1244i 0.308757 0.534782i
\(515\) 0 0
\(516\) 0 0
\(517\) 15.0000 0.659699
\(518\) −8.00000 + 6.92820i −0.351500 + 0.304408i
\(519\) 0 0
\(520\) 0 0
\(521\) −19.0000 + 32.9090i −0.832405 + 1.44177i 0.0637207 + 0.997968i \(0.479703\pi\)
−0.896126 + 0.443800i \(0.853630\pi\)
\(522\) 0 0
\(523\) −13.0000 22.5167i −0.568450 0.984585i −0.996719 0.0809336i \(-0.974210\pi\)
0.428269 0.903651i \(-0.359124\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) −4.00000 −0.174408
\(527\) 0 0
\(528\) 0 0
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 0 0
\(531\) 0 0
\(532\) −17.5000 6.06218i −0.758721 0.262829i
\(533\) 4.00000 0.173259
\(534\) 0 0
\(535\) 0 0
\(536\) 1.50000 2.59808i 0.0647901 0.112220i
\(537\) 0 0
\(538\) 23.0000 0.991600
\(539\) −32.5000 + 12.9904i −1.39987 + 0.559535i
\(540\) 0 0
\(541\) −8.00000 13.8564i −0.343947 0.595733i 0.641215 0.767361i \(-0.278431\pi\)
−0.985162 + 0.171628i \(0.945097\pi\)
\(542\) 1.50000 2.59808i 0.0644305 0.111597i
\(543\) 0 0
\(544\) −3.50000 6.06218i −0.150061 0.259914i
\(545\) 0 0
\(546\) 0 0
\(547\) −38.0000 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) 0 0
\(550\) −12.5000 + 21.6506i −0.533002 + 0.923186i
\(551\) −31.5000 54.5596i −1.34195 2.32432i
\(552\) 0 0
\(553\) 7.00000 + 36.3731i 0.297670 + 1.54674i
\(554\) −19.0000 −0.807233
\(555\) 0 0
\(556\) −8.00000 + 13.8564i −0.339276 + 0.587643i
\(557\) 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) 0 0
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) 12.0000 + 20.7846i 0.506189 + 0.876746i
\(563\) −6.00000 + 10.3923i −0.252870 + 0.437983i −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 10.0000 0.420331
\(567\) 0 0
\(568\) 9.00000 0.377632
\(569\) −15.5000 26.8468i −0.649794 1.12548i −0.983172 0.182683i \(-0.941522\pi\)
0.333378 0.942793i \(-0.391811\pi\)
\(570\) 0 0
\(571\) 16.0000 27.7128i 0.669579 1.15975i −0.308443 0.951243i \(-0.599808\pi\)
0.978022 0.208502i \(-0.0668588\pi\)
\(572\) 2.50000 + 4.33013i 0.104530 + 0.181052i
\(573\) 0 0
\(574\) 2.00000 + 10.3923i 0.0834784 + 0.433766i
\(575\) 10.0000 0.417029
\(576\) 0 0
\(577\) 7.00000 12.1244i 0.291414 0.504744i −0.682730 0.730670i \(-0.739208\pi\)
0.974144 + 0.225927i \(0.0725410\pi\)
\(578\) 16.0000 27.7128i 0.665512 1.15270i
\(579\) 0 0
\(580\) 0 0
\(581\) 40.0000 + 13.8564i 1.65948 + 0.574861i
\(582\) 0 0
\(583\) 2.50000 + 4.33013i 0.103539 + 0.179336i
\(584\) −5.00000 + 8.66025i −0.206901 + 0.358364i
\(585\) 0 0
\(586\) 15.0000 + 25.9808i 0.619644 + 1.07326i
\(587\) 45.0000 1.85735 0.928674 0.370896i \(-0.120949\pi\)
0.928674 + 0.370896i \(0.120949\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 0 0
\(598\) 1.00000 1.73205i 0.0408930 0.0708288i
\(599\) −8.00000 + 13.8564i −0.326871 + 0.566157i −0.981889 0.189456i \(-0.939328\pi\)
0.655018 + 0.755613i \(0.272661\pi\)
\(600\) 0 0
\(601\) 25.0000 1.01977 0.509886 0.860242i \(-0.329688\pi\)
0.509886 + 0.860242i \(0.329688\pi\)
\(602\) −1.00000 5.19615i −0.0407570 0.211779i
\(603\) 0 0
\(604\) 8.50000 + 14.7224i 0.345860 + 0.599047i
\(605\) 0 0
\(606\) 0 0
\(607\) 7.00000 + 12.1244i 0.284121 + 0.492112i 0.972396 0.233338i \(-0.0749648\pi\)
−0.688274 + 0.725450i \(0.741632\pi\)
\(608\) −7.00000 −0.283887
\(609\) 0 0
\(610\) 0 0
\(611\) 1.50000 + 2.59808i 0.0606835 + 0.105107i
\(612\) 0 0
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) 9.50000 + 16.4545i 0.383389 + 0.664049i
\(615\) 0 0
\(616\) −10.0000 + 8.66025i −0.402911 + 0.348932i
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 20.0000 0.801927
\(623\) 6.00000 + 31.1769i 0.240385 + 1.24908i
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −3.00000 + 5.19615i −0.119904 + 0.207680i
\(627\) 0 0
\(628\) −5.50000 9.52628i −0.219474 0.380140i
\(629\) −28.0000 −1.11643
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 7.00000 + 12.1244i 0.278445 + 0.482281i
\(633\) 0 0
\(634\) −13.0000 + 22.5167i −0.516296 + 0.894251i
\(635\) 0 0
\(636\) 0 0
\(637\) −5.50000 4.33013i −0.217918 0.171566i
\(638\) −45.0000 −1.78157
\(639\) 0 0
\(640\) 0 0
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 0 0
\(643\) −9.00000 −0.354925 −0.177463 0.984128i \(-0.556789\pi\)
−0.177463 + 0.984128i \(0.556789\pi\)
\(644\) 5.00000 + 1.73205i 0.197028 + 0.0682524i
\(645\) 0 0
\(646\) −24.5000 42.4352i −0.963940 1.66959i
\(647\) −3.00000 + 5.19615i −0.117942 + 0.204282i −0.918952 0.394369i \(-0.870963\pi\)
0.801010 + 0.598651i \(0.204296\pi\)
\(648\) 0 0
\(649\) 17.5000 + 30.3109i 0.686935 + 1.18981i
\(650\) −5.00000 −0.196116
\(651\) 0 0
\(652\) 13.0000 0.509119
\(653\) −11.0000 19.0526i −0.430463 0.745584i 0.566450 0.824096i \(-0.308316\pi\)
−0.996913 + 0.0785119i \(0.974983\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 2.00000 + 3.46410i 0.0780869 + 0.135250i
\(657\) 0 0
\(658\) −6.00000 + 5.19615i −0.233904 + 0.202567i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 2.00000 3.46410i 0.0777910 0.134738i −0.824506 0.565854i \(-0.808547\pi\)
0.902297 + 0.431116i \(0.141880\pi\)
\(662\) 2.00000 3.46410i 0.0777322 0.134636i
\(663\) 0 0
\(664\) 16.0000 0.620920
\(665\) 0 0
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) −2.50000 + 4.33013i −0.0967279 + 0.167538i
\(669\) 0 0
\(670\) 0 0
\(671\) 65.0000 2.50930
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) −16.5000 28.5788i −0.635556 1.10082i
\(675\) 0 0
\(676\) −0.500000 + 0.866025i −0.0192308 + 0.0333087i
\(677\) 12.5000 + 21.6506i 0.480414 + 0.832102i 0.999748 0.0224702i \(-0.00715308\pi\)
−0.519333 + 0.854572i \(0.673820\pi\)
\(678\) 0 0
\(679\) −15.0000 5.19615i −0.575647 0.199410i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −20.0000 + 34.6410i −0.765279 + 1.32550i 0.174820 + 0.984600i \(0.444066\pi\)
−0.940099 + 0.340901i \(0.889268\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) −0.500000 + 0.866025i −0.0190485 + 0.0329929i
\(690\) 0 0
\(691\) −2.50000 4.33013i −0.0951045 0.164726i 0.814548 0.580097i \(-0.196985\pi\)
−0.909652 + 0.415371i \(0.863652\pi\)
\(692\) 13.0000 0.494186
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 0 0
\(696\) 0 0
\(697\) −14.0000 + 24.2487i −0.530288 + 0.918485i
\(698\) 1.00000 + 1.73205i 0.0378506 + 0.0655591i
\(699\) 0 0
\(700\) −2.50000 12.9904i −0.0944911 0.490990i
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) −14.0000 + 24.2487i −0.528020 + 0.914557i
\(704\) −2.50000 + 4.33013i −0.0942223 + 0.163198i
\(705\) 0 0
\(706\) 2.00000 0.0752710
\(707\) 12.0000 10.3923i 0.451306 0.390843i
\(708\) 0 0
\(709\) 23.0000 + 39.8372i 0.863783 + 1.49612i 0.868250 + 0.496126i \(0.165245\pi\)
−0.00446726 + 0.999990i \(0.501422\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.00000 + 10.3923i 0.224860 + 0.389468i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −5.00000 8.66025i −0.186859 0.323649i
\(717\) 0 0
\(718\) 0 0
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) 0 0
\(721\) −5.00000 25.9808i −0.186210 0.967574i
\(722\) −30.0000 −1.11648
\(723\) 0 0
\(724\) 5.50000 9.52628i 0.204406 0.354041i
\(725\) 22.5000 38.9711i 0.835629 1.44735i
\(726\) 0 0
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) −2.50000 0.866025i −0.0926562 0.0320970i
\(729\) 0 0
\(730\) 0 0
\(731\) 7.00000 12.1244i 0.258904 0.448435i
\(732\) 0 0
\(733\) −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) −2.00000 −0.0738213
\(735\) 0 0
\(736\) 2.00000 0.0737210
\(737\) −7.50000 12.9904i −0.276266 0.478507i
\(738\) 0 0
\(739\) 14.0000 24.2487i 0.514998 0.892003i −0.484850 0.874597i \(-0.661126\pi\)
0.999849 0.0174060i \(-0.00554079\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.50000 0.866025i −0.0917779 0.0317928i
\(743\) 5.00000 0.183432 0.0917161 0.995785i \(-0.470765\pi\)
0.0917161 + 0.995785i \(0.470765\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −10.5000 + 18.1865i −0.384432 + 0.665856i
\(747\) 0 0
\(748\) −35.0000 −1.27973
\(749\) 0 0
\(750\) 0 0
\(751\) −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) −4.50000 7.79423i −0.163880 0.283849i
\(755\) 0 0
\(756\) 0 0
\(757\) 29.0000 1.05402 0.527011 0.849858i \(-0.323312\pi\)
0.527011 + 0.849858i \(0.323312\pi\)
\(758\) −2.00000 3.46410i −0.0726433 0.125822i
\(759\) 0 0
\(760\) 0 0
\(761\) −4.00000 6.92820i −0.145000 0.251147i 0.784373 0.620289i \(-0.212985\pi\)
−0.929373 + 0.369142i \(0.879652\pi\)
\(762\) 0 0
\(763\) 16.0000 13.8564i 0.579239 0.501636i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) −4.00000 + 6.92820i −0.144526 + 0.250326i
\(767\) −3.50000 + 6.06218i −0.126378 + 0.218893i
\(768\) 0 0
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.00000 + 6.92820i 0.143963 + 0.249351i
\(773\) −17.0000 + 29.4449i −0.611448 + 1.05906i 0.379549 + 0.925172i \(0.376079\pi\)
−0.990997 + 0.133887i \(0.957254\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) −23.0000 −0.824590
\(779\) 14.0000 + 24.2487i 0.501602 + 0.868800i
\(780\) 0 0
\(781\) 22.5000 38.9711i 0.805113 1.39450i
\(782\) 7.00000 + 12.1244i 0.250319 + 0.433566i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 0 0
\(786\) 0 0
\(787\) −8.50000 + 14.7224i −0.302992 + 0.524798i −0.976812 0.214097i \(-0.931319\pi\)
0.673820 + 0.738896i