Properties

Label 63.2.e.b.46.1
Level $63$
Weight $2$
Character 63.46
Analytic conductor $0.503$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.503057532734\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 63.46
Dual form 63.2.e.b.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(2.00000 - 3.46410i) q^{10} +(-1.00000 + 1.73205i) q^{11} +1.00000 q^{13} +(-1.00000 - 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-0.500000 - 0.866025i) q^{19} +4.00000 q^{20} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +(4.00000 - 3.46410i) q^{28} -4.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(1.00000 + 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.00000 - 1.73205i) q^{38} +10.0000 q^{41} +5.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(-3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +2.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-4.00000 - 6.92820i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-5.00000 - 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(2.50000 - 4.33013i) q^{67} +(-8.00000 + 6.92820i) q^{70} +6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} +(3.00000 - 5.19615i) q^{74} +2.00000 q^{76} +(4.00000 - 3.46410i) q^{77} +(0.500000 + 0.866025i) q^{79} +(4.00000 - 6.92820i) q^{80} +(10.0000 + 17.3205i) q^{82} -6.00000 q^{83} +(5.00000 + 8.66025i) q^{86} +(8.00000 + 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 - 10.3923i) q^{94} +(-1.00000 + 1.73205i) q^{95} -6.00000 q^{97} +(-2.00000 + 13.8564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 2q^{4} - 2q^{5} - 5q^{7} + O(q^{10}) \) \( 2q + 2q^{2} - 2q^{4} - 2q^{5} - 5q^{7} + 4q^{10} - 2q^{11} + 2q^{13} - 2q^{14} + 4q^{16} - q^{19} + 8q^{20} - 8q^{22} + q^{25} + 2q^{26} + 8q^{28} - 8q^{29} - 9q^{31} - 8q^{32} + 2q^{35} - 3q^{37} + 2q^{38} + 20q^{41} + 10q^{43} - 4q^{44} - 6q^{47} + 11q^{49} + 4q^{50} - 2q^{52} + 12q^{53} + 8q^{55} - 8q^{58} - 12q^{59} - 10q^{61} - 36q^{62} - 16q^{64} - 2q^{65} + 5q^{67} - 16q^{70} + 12q^{71} + 3q^{73} + 6q^{74} + 4q^{76} + 8q^{77} + q^{79} + 8q^{80} + 20q^{82} - 12q^{83} + 10q^{86} + 16q^{89} - 5q^{91} + 12q^{94} - 2q^{95} - 12q^{97} - 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) 0 0
\(4\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 0 0
\(9\) 0 0
\(10\) 2.00000 3.46410i 0.632456 1.09545i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) −1.00000 5.19615i −0.267261 1.38873i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 4.00000 0.894427
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) 0 0
\(28\) 4.00000 3.46410i 0.755929 0.654654i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −4.50000 + 7.79423i −0.808224 + 1.39988i 0.105869 + 0.994380i \(0.466238\pi\)
−0.914093 + 0.405505i \(0.867096\pi\)
\(32\) −4.00000 + 6.92820i −0.707107 + 1.22474i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000 + 5.19615i 0.169031 + 0.878310i
\(36\) 0 0
\(37\) −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) 0 0
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 2.00000 0.282843
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) −4.00000 6.92820i −0.525226 0.909718i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) −18.0000 −2.28600
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) 0 0
\(67\) 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i \(-0.734535\pi\)
0.977356 + 0.211604i \(0.0678686\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −8.00000 + 6.92820i −0.956183 + 0.828079i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 1.50000 2.59808i 0.175562 0.304082i −0.764794 0.644275i \(-0.777159\pi\)
0.940356 + 0.340193i \(0.110493\pi\)
\(74\) 3.00000 5.19615i 0.348743 0.604040i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 4.00000 3.46410i 0.455842 0.394771i
\(78\) 0 0
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) 4.00000 6.92820i 0.447214 0.774597i
\(81\) 0 0
\(82\) 10.0000 + 17.3205i 1.10432 + 1.91273i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.00000 + 8.66025i 0.539164 + 0.933859i
\(87\) 0 0
\(88\) 0 0
\(89\) 8.00000 + 13.8564i 0.847998 + 1.46878i 0.882992 + 0.469389i \(0.155526\pi\)
−0.0349934 + 0.999388i \(0.511141\pi\)
\(90\) 0 0
\(91\) −2.50000 0.866025i −0.262071 0.0907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 6.00000 10.3923i 0.618853 1.07188i
\(95\) −1.00000 + 1.73205i −0.102598 + 0.177705i
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) −2.00000 + 13.8564i −0.202031 + 1.39971i
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 0 0
\(103\) 3.50000 + 6.06218i 0.344865 + 0.597324i 0.985329 0.170664i \(-0.0545913\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 24.0000 2.33109
\(107\) −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) 0 0
\(109\) −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i \(-0.975180\pi\)
0.565940 + 0.824447i \(0.308513\pi\)
\(110\) 4.00000 + 6.92820i 0.381385 + 0.660578i
\(111\) 0 0
\(112\) −2.00000 10.3923i −0.188982 0.981981i
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.00000 6.92820i 0.371391 0.643268i
\(117\) 0 0
\(118\) −24.0000 −2.20938
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 10.0000 17.3205i 0.905357 1.56813i
\(123\) 0 0
\(124\) −9.00000 15.5885i −0.808224 1.39988i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −15.0000 −1.33103 −0.665517 0.746382i \(-0.731789\pi\)
−0.665517 + 0.746382i \(0.731789\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) −7.00000 12.1244i −0.611593 1.05931i −0.990972 0.134069i \(-0.957196\pi\)
0.379379 0.925241i \(-0.376138\pi\)
\(132\) 0 0
\(133\) 0.500000 + 2.59808i 0.0433555 + 0.225282i
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) −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
\(139\) −3.00000 −0.254457 −0.127228 0.991873i \(-0.540608\pi\)
−0.127228 + 0.991873i \(0.540608\pi\)
\(140\) −10.0000 3.46410i −0.845154 0.292770i
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) −1.00000 + 1.73205i −0.0836242 + 0.144841i
\(144\) 0 0
\(145\) 4.00000 + 6.92820i 0.332182 + 0.575356i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 6.00000 0.493197
\(149\) −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i \(-0.330232\pi\)
−0.999953 + 0.00974235i \(0.996899\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 10.0000 + 3.46410i 0.805823 + 0.279145i
\(155\) 18.0000 1.44579
\(156\) 0 0
\(157\) 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) −1.00000 + 1.73205i −0.0795557 + 0.137795i
\(159\) 0 0
\(160\) 16.0000 1.26491
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) −10.0000 + 17.3205i −0.780869 + 1.35250i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 14.0000 1.08335 0.541676 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) −5.00000 + 8.66025i −0.381246 + 0.660338i
\(173\) 4.00000 + 6.92820i 0.304114 + 0.526742i 0.977064 0.212947i \(-0.0683062\pi\)
−0.672949 + 0.739689i \(0.734973\pi\)
\(174\) 0 0
\(175\) −2.00000 + 1.73205i −0.151186 + 0.130931i
\(176\) −8.00000 −0.603023
\(177\) 0 0
\(178\) −16.0000 + 27.7128i −1.19925 + 2.07716i
\(179\) 1.00000 1.73205i 0.0747435 0.129460i −0.826231 0.563331i \(-0.809520\pi\)
0.900975 + 0.433872i \(0.142853\pi\)
\(180\) 0 0
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) −1.00000 5.19615i −0.0741249 0.385164i
\(183\) 0 0
\(184\) 0 0
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) 5.00000 + 8.66025i 0.361787 + 0.626634i 0.988255 0.152813i \(-0.0488333\pi\)
−0.626468 + 0.779447i \(0.715500\pi\)
\(192\) 0 0
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) −6.00000 10.3923i −0.430775 0.746124i
\(195\) 0 0
\(196\) −13.0000 + 5.19615i −0.928571 + 0.371154i
\(197\) −16.0000 −1.13995 −0.569976 0.821661i \(-0.693048\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 4.00000 0.281439
\(203\) 10.0000 + 3.46410i 0.701862 + 0.243132i
\(204\) 0 0
\(205\) −10.0000 17.3205i −0.698430 1.20972i
\(206\) −7.00000 + 12.1244i −0.487713 + 0.844744i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 12.0000 + 20.7846i 0.824163 + 1.42749i
\(213\) 0 0
\(214\) 8.00000 13.8564i 0.546869 0.947204i
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) 0 0
\(217\) 18.0000 15.5885i 1.22192 1.05821i
\(218\) −18.0000 −1.21911
\(219\) 0 0
\(220\) −4.00000 + 6.92820i −0.269680 + 0.467099i
\(221\) 0 0
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 16.0000 13.8564i 1.06904 0.925820i
\(225\) 0 0
\(226\) −10.0000 17.3205i −0.665190 1.15214i
\(227\) 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i \(-0.629553\pi\)
0.993210 0.116331i \(-0.0371134\pi\)
\(228\) 0 0
\(229\) 9.50000 + 16.4545i 0.627778 + 1.08734i 0.987997 + 0.154475i \(0.0493686\pi\)
−0.360219 + 0.932868i \(0.617298\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) −6.00000 + 10.3923i −0.391397 + 0.677919i
\(236\) −12.0000 20.7846i −0.781133 1.35296i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −7.00000 + 12.1244i −0.449977 + 0.779383i
\(243\) 0 0
\(244\) 20.0000 1.28037
\(245\) 2.00000 13.8564i 0.127775 0.885253i
\(246\) 0 0
\(247\) −0.500000 0.866025i −0.0318142 0.0551039i
\(248\) 0 0
\(249\) 0 0
\(250\) −12.0000 20.7846i −0.758947 1.31453i
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −15.0000 25.9808i −0.941184 1.63018i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 13.0000 + 22.5167i 0.810918 + 1.40455i 0.912222 + 0.409695i \(0.134365\pi\)
−0.101305 + 0.994855i \(0.532302\pi\)
\(258\) 0 0
\(259\) 1.50000 + 7.79423i 0.0932055 + 0.484310i
\(260\) 4.00000 0.248069
\(261\) 0 0
\(262\) 14.0000 24.2487i 0.864923 1.49809i
\(263\) 2.00000 3.46410i 0.123325 0.213606i −0.797752 0.602986i \(-0.793977\pi\)
0.921077 + 0.389380i \(0.127311\pi\)
\(264\) 0 0
\(265\) −24.0000 −1.47431
\(266\) −4.00000 + 3.46410i −0.245256 + 0.212398i
\(267\) 0 0
\(268\) 5.00000 + 8.66025i 0.305424 + 0.529009i
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −24.0000 −1.44989
\(275\) 1.00000 + 1.73205i 0.0603023 + 0.104447i
\(276\) 0 0
\(277\) −6.50000 + 11.2583i −0.390547 + 0.676448i −0.992522 0.122068i \(-0.961047\pi\)
0.601975 + 0.798515i \(0.294381\pi\)
\(278\) −3.00000 5.19615i −0.179928 0.311645i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.00000 0.238620 0.119310 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 0 0
\(283\) 5.50000 9.52628i 0.326941 0.566279i −0.654962 0.755662i \(-0.727315\pi\)
0.981903 + 0.189383i \(0.0606488\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) −4.00000 −0.236525
\(287\) −25.0000 8.66025i −1.47570 0.511199i
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −8.00000 + 13.8564i −0.469776 + 0.813676i
\(291\) 0 0
\(292\) 3.00000 + 5.19615i 0.175562 + 0.304082i
\(293\) −8.00000 −0.467365 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 0 0
\(298\) 12.0000 20.7846i 0.695141 1.20402i
\(299\) 0 0
\(300\) 0 0
\(301\) −12.5000 4.33013i −0.720488 0.249584i
\(302\) 32.0000 1.84139
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) −10.0000 + 17.3205i −0.572598 + 0.991769i
\(306\) 0 0
\(307\) −17.0000 −0.970241 −0.485121 0.874447i \(-0.661224\pi\)
−0.485121 + 0.874447i \(0.661224\pi\)
\(308\) 2.00000 + 10.3923i 0.113961 + 0.592157i
\(309\) 0 0
\(310\) 18.0000 + 31.1769i 1.02233 + 1.77073i
\(311\) −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) 0 0
\(313\) 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i \(-0.157669\pi\)
−0.851549 + 0.524276i \(0.824336\pi\)
\(314\) 28.0000 1.58013
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) 0 0
\(319\) 4.00000 6.92820i 0.223957 0.387905i
\(320\) 8.00000 + 13.8564i 0.447214 + 0.774597i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.500000 0.866025i 0.0277350 0.0480384i
\(326\) 4.00000 6.92820i 0.221540 0.383718i
\(327\) 0 0
\(328\) 0 0
\(329\) 3.00000 + 15.5885i 0.165395 + 0.859419i
\(330\) 0 0
\(331\) 12.5000 + 21.6506i 0.687062 + 1.19003i 0.972784 + 0.231714i \(0.0744333\pi\)
−0.285722 + 0.958313i \(0.592233\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) 0 0
\(334\) 14.0000 + 24.2487i 0.766046 + 1.32683i
\(335\) −10.0000 −0.546358
\(336\) 0 0
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) −12.0000 20.7846i −0.652714 1.13053i
\(339\) 0 0
\(340\) 0 0
\(341\) −9.00000 15.5885i −0.487377 0.844162i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) −8.00000 + 13.8564i −0.430083 + 0.744925i
\(347\) 16.0000 27.7128i 0.858925 1.48770i −0.0140303 0.999902i \(-0.504466\pi\)
0.872955 0.487800i \(-0.162201\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) −5.00000 1.73205i −0.267261 0.0925820i
\(351\) 0 0
\(352\) −8.00000 13.8564i −0.426401 0.738549i
\(353\) 17.0000 29.4449i 0.904819 1.56719i 0.0836583 0.996495i \(-0.473340\pi\)
0.821160 0.570697i \(-0.193327\pi\)
\(354\) 0 0
\(355\) −6.00000 10.3923i −0.318447 0.551566i
\(356\) −32.0000 −1.69600
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) 10.0000 + 17.3205i 0.527780 + 0.914141i 0.999476 + 0.0323801i \(0.0103087\pi\)
−0.471696 + 0.881761i \(0.656358\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 13.0000 + 22.5167i 0.683265 + 1.18345i
\(363\) 0 0
\(364\) 4.00000 3.46410i 0.209657 0.181568i
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 4.50000 7.79423i 0.234898 0.406855i −0.724345 0.689438i \(-0.757858\pi\)
0.959243 + 0.282582i \(0.0911910\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −12.0000 −0.623850
\(371\) −24.0000 + 20.7846i −1.24602 + 1.07908i
\(372\) 0 0
\(373\) −11.5000 19.9186i −0.595447 1.03135i −0.993484 0.113975i \(-0.963641\pi\)
0.398036 0.917370i \(-0.369692\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) 3.00000 0.154100 0.0770498 0.997027i \(-0.475450\pi\)
0.0770498 + 0.997027i \(0.475450\pi\)
\(380\) −2.00000 3.46410i −0.102598 0.177705i
\(381\) 0 0
\(382\) −10.0000 + 17.3205i −0.511645 + 0.886194i
\(383\) −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i \(-0.265853\pi\)
−0.977613 + 0.210411i \(0.932520\pi\)
\(384\) 0 0
\(385\) −10.0000 3.46410i −0.509647 0.176547i
\(386\) −22.0000 −1.11977
\(387\) 0 0
\(388\) 6.00000 10.3923i 0.304604 0.527589i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −16.0000 27.7128i −0.806068 1.39615i
\(395\) 1.00000 1.73205i 0.0503155 0.0871489i
\(396\) 0 0
\(397\) 4.50000 + 7.79423i 0.225849 + 0.391181i 0.956574 0.291491i \(-0.0941512\pi\)
−0.730725 + 0.682672i \(0.760818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −18.0000 31.1769i −0.898877 1.55690i −0.828932 0.559350i \(-0.811051\pi\)
−0.0699455 0.997551i \(-0.522283\pi\)
\(402\) 0 0
\(403\) −4.50000 + 7.79423i −0.224161 + 0.388258i
\(404\) 2.00000 + 3.46410i 0.0995037 + 0.172345i
\(405\) 0 0
\(406\) 4.00000 + 20.7846i 0.198517 + 1.03152i
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 20.0000 34.6410i 0.987730 1.71080i
\(411\) 0 0
\(412\) −14.0000 −0.689730
\(413\) 24.0000 20.7846i 1.18096 1.02274i
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) −4.00000 + 6.92820i −0.196116 + 0.339683i
\(417\) 0 0
\(418\) 2.00000 + 3.46410i 0.0978232 + 0.169435i
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) −7.00000 −0.341159 −0.170580 0.985344i \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(422\) 4.00000 + 6.92820i 0.194717 + 0.337260i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5.00000 + 25.9808i 0.241967 + 1.25730i
\(428\) 16.0000 0.773389
\(429\) 0 0
\(430\) 10.0000 17.3205i 0.482243 0.835269i
\(431\) −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i \(-0.976060\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(432\) 0 0
\(433\) 31.0000 1.48976 0.744882 0.667196i \(-0.232506\pi\)
0.744882 + 0.667196i \(0.232506\pi\)
\(434\) 45.0000 + 15.5885i 2.16007 + 0.748270i
\(435\) 0 0
\(436\) −9.00000 15.5885i −0.431022 0.746552i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 0 0
\(445\) 16.0000 27.7128i 0.758473 1.31371i
\(446\) 16.0000 + 27.7128i 0.757622 + 1.31224i
\(447\) 0 0
\(448\) 20.0000 + 6.92820i 0.944911 + 0.327327i
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) −10.0000 + 17.3205i −0.470882 + 0.815591i
\(452\) 10.0000 17.3205i 0.470360 0.814688i
\(453\) 0 0
\(454\) 36.0000 1.68956
\(455\) 1.00000 + 5.19615i 0.0468807 + 0.243599i
\(456\) 0 0
\(457\) 5.50000 + 9.52628i 0.257279 + 0.445621i 0.965512 0.260358i \(-0.0838407\pi\)
−0.708233 + 0.705979i \(0.750507\pi\)
\(458\) −19.0000 + 32.9090i −0.887812 + 1.53773i
\(459\) 0 0
\(460\) 0 0
\(461\) −20.0000 −0.931493 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) 0 0
\(463\) −17.0000 −0.790057 −0.395029 0.918669i \(-0.629265\pi\)
−0.395029 + 0.918669i \(0.629265\pi\)
\(464\) −8.00000 13.8564i −0.371391 0.643268i
\(465\) 0 0
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) 3.00000 + 5.19615i 0.138823 + 0.240449i 0.927052 0.374934i \(-0.122335\pi\)
−0.788228 + 0.615383i \(0.789001\pi\)
\(468\) 0 0
\(469\) −10.0000 + 8.66025i −0.461757 + 0.399893i
\(470\) −24.0000 −1.10704
\(471\) 0 0
\(472\) 0 0
\(473\) −5.00000 + 8.66025i −0.229900 + 0.398199i
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) −6.00000 10.3923i −0.274434 0.475333i
\(479\) −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i \(0.387598\pi\)
−0.985504 + 0.169654i \(0.945735\pi\)
\(480\) 0 0
\(481\) −1.50000 2.59808i −0.0683941 0.118462i
\(482\) −28.0000 −1.27537
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) 6.00000 + 10.3923i 0.272446 + 0.471890i
\(486\) 0 0
\(487\) −15.5000 + 26.8468i −0.702372 + 1.21654i 0.265260 + 0.964177i \(0.414542\pi\)
−0.967632 + 0.252367i \(0.918791\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 26.0000 10.3923i 1.17456 0.469476i
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.00000 1.73205i 0.0449921 0.0779287i
\(495\) 0 0
\(496\) −36.0000 −1.61645
\(497\) −15.0000 5.19615i −0.672842 0.233079i
\(498\) 0 0
\(499\) −18.5000 32.0429i −0.828174 1.43444i −0.899469 0.436984i \(-0.856047\pi\)
0.0712957 0.997455i \(-0.477287\pi\)
\(500\) 12.0000 20.7846i 0.536656 0.929516i
\(501\) 0 0
\(502\) 8.00000 + 13.8564i 0.357057 + 0.618442i
\(503\) 42.0000 1.87269 0.936344 0.351085i \(-0.114187\pi\)
0.936344 + 0.351085i \(0.114187\pi\)
\(504\) 0 0
\(505\) −4.00000 −0.177998
\(506\) 0 0
\(507\) 0 0
\(508\) 15.0000 25.9808i 0.665517 1.15271i
\(509\) 1.00000 + 1.73205i 0.0443242 + 0.0767718i 0.887336 0.461123i \(-0.152553\pi\)
−0.843012 + 0.537895i \(0.819220\pi\)
\(510\) 0 0
\(511\) −6.00000 + 5.19615i −0.265424 + 0.229864i
\(512\) −32.0000 −1.41421
\(513\) 0 0
\(514\) −26.0000 + 45.0333i −1.14681 + 1.98633i
\(515\) 7.00000 12.1244i 0.308457 0.534263i
\(516\) 0 0
\(517\) 12.0000 0.527759
\(518\) −12.0000 + 10.3923i −0.527250 + 0.456612i
\(519\) 0 0
\(520\) 0 0
\(521\) 6.00000 10.3923i 0.262865 0.455295i −0.704137 0.710064i \(-0.748666\pi\)
0.967002 + 0.254769i \(0.0819994\pi\)
\(522\) 0 0
\(523\) −15.5000 26.8468i −0.677768 1.17393i −0.975652 0.219326i \(-0.929614\pi\)
0.297884 0.954602i \(-0.403719\pi\)
\(524\) 28.0000 1.22319
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −24.0000 41.5692i −1.04249 1.80565i
\(531\) 0 0
\(532\) −5.00000 1.73205i −0.216777 0.0750939i
\(533\) 10.0000 0.433148
\(534\) 0 0
\(535\) −8.00000 + 13.8564i −0.345870 + 0.599065i
\(536\) 0 0
\(537\) 0 0
\(538\) 12.0000 0.517357
\(539\) −13.0000 + 5.19615i −0.559950 + 0.223814i
\(540\) 0 0
\(541\) 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i \(-0.0327407\pi\)
−0.586278 + 0.810110i \(0.699407\pi\)
\(542\) 16.0000 27.7128i 0.687259 1.19037i
\(543\) 0 0
\(544\) 0 0
\(545\) 18.0000 0.771035
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −12.0000 20.7846i −0.512615 0.887875i
\(549\) 0 0
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) 2.00000 + 3.46410i 0.0852029 + 0.147576i
\(552\) 0 0
\(553\) −0.500000 2.59808i −0.0212622 0.110481i
\(554\) −26.0000 −1.10463
\(555\) 0 0
\(556\) 3.00000 5.19615i 0.127228 0.220366i
\(557\) −1.00000 + 1.73205i −0.0423714 + 0.0733893i −0.886433 0.462856i \(-0.846825\pi\)
0.844062 + 0.536246i \(0.180158\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) −16.0000 + 13.8564i −0.676123 + 0.585540i
\(561\) 0 0
\(562\) 4.00000 + 6.92820i 0.168730 + 0.292249i
\(563\) −13.0000 + 22.5167i −0.547885 + 0.948964i 0.450535 + 0.892759i \(0.351233\pi\)
−0.998419 + 0.0562051i \(0.982100\pi\)
\(564\) 0 0
\(565\) 10.0000 + 17.3205i 0.420703 + 0.728679i
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) 0 0
\(569\) −13.0000 22.5167i −0.544988 0.943948i −0.998608 0.0527519i \(-0.983201\pi\)
0.453619 0.891196i \(-0.350133\pi\)
\(570\) 0 0
\(571\) 9.50000 16.4545i 0.397563 0.688599i −0.595862 0.803087i \(-0.703189\pi\)
0.993425 + 0.114488i \(0.0365228\pi\)
\(572\) −2.00000 3.46410i −0.0836242 0.144841i
\(573\) 0 0
\(574\) −10.0000 51.9615i −0.417392 2.16883i
\(575\) 0 0
\(576\) 0 0
\(577\) 8.50000 14.7224i 0.353860 0.612903i −0.633062 0.774101i \(-0.718202\pi\)
0.986922 + 0.161198i \(0.0515357\pi\)
\(578\) −17.0000 + 29.4449i −0.707107 + 1.22474i
\(579\) 0 0
\(580\) −16.0000 −0.664364
\(581\) 15.0000 + 5.19615i 0.622305 + 0.215573i
\(582\) 0 0
\(583\) 12.0000 + 20.7846i 0.496989 + 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) −8.00000 13.8564i −0.330477 0.572403i
\(587\) −16.0000 −0.660391 −0.330195 0.943913i \(-0.607115\pi\)
−0.330195 + 0.943913i \(0.607115\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) 24.0000 + 41.5692i 0.988064 + 1.71138i
\(591\) 0 0
\(592\) 6.00000 10.3923i 0.246598 0.427121i
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 24.0000 0.983078
\(597\) 0 0
\(598\) 0 0
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) −9.00000 −0.367118 −0.183559 0.983009i \(-0.558762\pi\)
−0.183559 + 0.983009i \(0.558762\pi\)
\(602\) −5.00000 25.9808i −0.203785 1.05890i
\(603\) 0 0
\(604\) 16.0000 + 27.7128i 0.651031 + 1.12762i
\(605\) 7.00000 12.1244i 0.284590 0.492925i
\(606\) 0 0
\(607\) −11.5000 19.9186i −0.466771 0.808470i 0.532509 0.846424i \(-0.321249\pi\)
−0.999279 + 0.0379540i \(0.987916\pi\)
\(608\) 8.00000 0.324443
\(609\) 0 0
\(610\) −40.0000 −1.61955
\(611\) −3.00000 5.19615i −0.121367 0.210214i
\(612\) 0 0
\(613\) −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i \(0.407575\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) −17.0000 29.4449i −0.686064 1.18830i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 14.5000 25.1147i 0.582804 1.00945i −0.412341 0.911030i \(-0.635289\pi\)
0.995145 0.0984169i \(-0.0313779\pi\)
\(620\) −18.0000 + 31.1769i −0.722897 + 1.25210i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) −8.00000 41.5692i −0.320513 1.66544i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) −1.00000 + 1.73205i −0.0399680 + 0.0692267i
\(627\) 0 0
\(628\) 14.0000 + 24.2487i 0.558661 + 0.967629i
\(629\) 0 0
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −24.0000 + 41.5692i −0.953162 + 1.65092i
\(635\) 15.0000 + 25.9808i 0.595257 + 1.03102i
\(636\) 0 0
\(637\) 5.50000 + 4.33013i 0.217918 + 0.171566i
\(638\) 16.0000 0.633446
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 0 0
\(643\) −19.0000 −0.749287 −0.374643 0.927169i \(-0.622235\pi\)
−0.374643 + 0.927169i \(0.622235\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.00000 1.73205i 0.0393141 0.0680939i −0.845699 0.533660i \(-0.820816\pi\)
0.885013 + 0.465566i \(0.154149\pi\)
\(648\) 0 0
\(649\) −12.0000 20.7846i −0.471041 0.815867i
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) 0 0
\(655\) −14.0000 + 24.2487i −0.547025 + 0.947476i
\(656\) 20.0000 + 34.6410i 0.780869 + 1.35250i
\(657\) 0 0
\(658\) −24.0000 + 20.7846i −0.935617 + 0.810268i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 20.5000 35.5070i 0.797358 1.38106i −0.123974 0.992286i \(-0.539564\pi\)
0.921331 0.388778i \(-0.127103\pi\)
\(662\) −25.0000 + 43.3013i −0.971653 + 1.68295i
\(663\) 0 0
\(664\) 0 0
\(665\) 4.00000 3.46410i 0.155113 0.134332i
\(666\) 0 0
\(667\) 0 0
\(668\) −14.0000 + 24.2487i −0.541676 + 0.938211i
\(669\) 0 0
\(670\) −10.0000 17.3205i −0.386334 0.669150i
\(671\) 20.0000 0.772091
\(672\) 0 0
\(673\) −41.0000 −1.58043 −0.790217 0.612827i \(-0.790032\pi\)
−0.790217 + 0.612827i \(0.790032\pi\)
\(674\) 13.0000 + 22.5167i 0.500741 + 0.867309i
\(675\) 0 0
\(676\) 12.0000 20.7846i 0.461538 0.799408i
\(677\) 6.00000 + 10.3923i 0.230599 + 0.399409i 0.957984 0.286820i \(-0.0925982\pi\)
−0.727386 + 0.686229i \(0.759265\pi\)
\(678\) 0 0
\(679\) 15.0000 + 5.19615i 0.575647 + 0.199410i
\(680\) 0 0
\(681\) 0 0
\(682\) 18.0000 31.1769i 0.689256 1.19383i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 0 0
\(685\) 24.0000 0.916993
\(686\) 17.0000 32.9090i 0.649063 1.25647i
\(687\) 0 0
\(688\) 10.0000 + 17.3205i 0.381246 + 0.660338i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) 18.5000 + 32.0429i 0.703773 + 1.21897i 0.967132 + 0.254273i \(0.0818362\pi\)
−0.263359 + 0.964698i \(0.584830\pi\)
\(692\) −16.0000 −0.608229
\(693\) 0 0
\(694\) 64.0000 2.42941
\(695\) 3.00000 + 5.19615i 0.113796 + 0.197101i
\(696\) 0 0
\(697\) 0 0
\(698\) −14.0000 24.2487i −0.529908 0.917827i
\(699\) 0 0
\(700\) −1.00000 5.19615i −0.0377964 0.196396i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −1.50000 + 2.59808i −0.0565736 + 0.0979883i
\(704\) 8.00000 13.8564i 0.301511 0.522233i
\(705\) 0 0
\(706\) 68.0000 2.55921
\(707\) −4.00000 + 3.46410i −0.150435 + 0.130281i
\(708\) 0 0
\(709\) −15.0000 25.9808i −0.563337 0.975728i −0.997202 0.0747503i \(-0.976184\pi\)
0.433865 0.900978i \(-0.357149\pi\)
\(710\) 12.0000 20.7846i 0.450352 0.780033i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) 2.00000 + 3.46410i 0.0747435 + 0.129460i
\(717\) 0 0
\(718\) −20.0000 + 34.6410i −0.746393 + 1.29279i
\(719\) −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) 0 0
\(721\) −3.50000 18.1865i −0.130347 0.677302i
\(722\) 36.0000 1.33978
\(723\) 0 0
\(724\) −13.0000 + 22.5167i −0.483141 + 0.836825i
\(725\) −2.00000 + 3.46410i −0.0742781 + 0.128654i
\(726\) 0 0
\(727\) −13.0000 −0.482143 −0.241072 0.970507i \(-0.577499\pi\)
−0.241072 + 0.970507i \(0.577499\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −6.00000 10.3923i −0.222070 0.384636i
\(731\) 0 0
\(732\) 0 0
\(733\) 7.50000 + 12.9904i 0.277019 + 0.479811i 0.970642 0.240527i \(-0.0773202\pi\)
−0.693624 + 0.720338i \(0.743987\pi\)
\(734\) 18.0000 0.664392
\(735\) 0 0
\(736\) 0 0
\(737\) 5.00000 + 8.66025i 0.184177 + 0.319005i
\(738\) 0 0
\(739\) 7.50000 12.9904i 0.275892 0.477859i −0.694468 0.719524i \(-0.744360\pi\)
0.970360 + 0.241665i \(0.0776935\pi\)
\(740\) −6.00000 10.3923i −0.220564 0.382029i
\(741\) 0 0
\(742\) −60.0000 20.7846i −2.20267 0.763027i
\(743\) −42.0000 −1.54083 −0.770415 0.637542i \(-0.779951\pi\)
−0.770415 + 0.637542i \(0.779951\pi\)
\(744\) 0 0
\(745\) −12.0000 + 20.7846i −0.439646 + 0.761489i
\(746\) 23.0000 39.8372i 0.842090 1.45854i
\(747\) 0 0
\(748\) 0 0
\(749\) 4.00000 + 20.7846i 0.146157 + 0.759453i
\(750\) 0 0
\(751\) −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i \(-0.242893\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(752\) 12.0000 20.7846i 0.437595 0.757937i
\(753\) 0 0
\(754\) −4.00000 6.92820i −0.145671 0.252310i
\(755\) −32.0000 −1.16460
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 3.00000 + 5.19615i 0.108965 + 0.188733i
\(759\) 0 0
\(760\) 0 0
\(761\) −24.0000 41.5692i −0.869999 1.50688i −0.861996 0.506915i \(-0.830786\pi\)
−0.00800331 0.999968i \(-0.502548\pi\)
\(762\) 0 0
\(763\) 18.0000 15.5885i 0.651644 0.564340i
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) −6.00000 + 10.3923i −0.216647 + 0.375244i
\(768\) 0 0
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) −4.00000 20.7846i −0.144150 0.749025i
\(771\) 0 0
\(772\) −11.0000 19.0526i −0.395899 0.685717i
\(773\) −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
\(775\) 4.50000 + 7.79423i 0.161645 + 0.279977i
\(776\) 0 0
\(777\) 0 0
\(778\) −12.0000 −0.430221
\(779\) −5.00000 8.66025i −0.179144 0.310286i
\(780\) 0 0
\(781\) −6.00000 + 10.3923i −0.214697 + 0.371866i
\(782\) 0 0
\(783\) 0 0
\(784\) −4.00000 + 27.7128i −0.142857 + 0.989743i
\(785\) −28.0000 −0.999363
\(786\) 0 0
\(787\) −20.0000 + 34.6410i −0.712923 + 1.23482i 0.250832 + 0.968031i \(0.419296\pi\)
−0.963755 + 0.266788i \(0.914038\pi\)
\(788\) 16.0000 27.7128i 0.569976 0.987228i
\(789\) 0 0
\(790\) 4.00000 0.142314
\(791\) 25.0000 + 8.66025i 0.888898 + 0.307923i
\(792\) 0 0
\(793\) −5.00000 8.66025i −0.177555