Properties

Label 891.2.e.j.595.1
Level $891$
Weight $2$
Character 891.595
Analytic conductor $7.115$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 595.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 891.595
Dual form 891.2.e.j.298.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +4.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +2.00000 q^{17} -6.00000 q^{19} +(-2.00000 - 3.46410i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-5.50000 - 9.52628i) q^{25} +2.00000 q^{26} +2.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} +(1.00000 + 1.73205i) q^{34} +8.00000 q^{35} -6.00000 q^{37} +(-3.00000 - 5.19615i) q^{38} +(6.00000 - 10.3923i) q^{40} +(5.00000 - 8.66025i) q^{41} +(-3.00000 - 5.19615i) q^{43} +1.00000 q^{44} -4.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(5.50000 - 9.52628i) q^{50} +(-1.00000 - 1.73205i) q^{52} +4.00000 q^{55} +(3.00000 + 5.19615i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(-4.00000 - 6.92820i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(1.00000 - 1.73205i) q^{68} +(4.00000 + 6.92820i) q^{70} -2.00000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(-1.00000 + 1.73205i) q^{77} +(5.00000 + 8.66025i) q^{79} +4.00000 q^{80} +10.0000 q^{82} +(-6.00000 - 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{85} +(3.00000 - 5.19615i) q^{86} +(1.50000 + 2.59808i) q^{88} +4.00000 q^{91} +(2.00000 + 3.46410i) q^{92} +(-4.00000 + 6.92820i) q^{94} +(-12.0000 + 20.7846i) q^{95} +(-1.00000 - 1.73205i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{4} + 4 q^{5} + 2 q^{7} + 6 q^{8} + O(q^{10}) \) \( 2 q + q^{2} + q^{4} + 4 q^{5} + 2 q^{7} + 6 q^{8} + 8 q^{10} + q^{11} + 2 q^{13} - 2 q^{14} + q^{16} + 4 q^{17} - 12 q^{19} - 4 q^{20} - q^{22} - 4 q^{23} - 11 q^{25} + 4 q^{26} + 4 q^{28} + 6 q^{29} - 4 q^{31} + 5 q^{32} + 2 q^{34} + 16 q^{35} - 12 q^{37} - 6 q^{38} + 12 q^{40} + 10 q^{41} - 6 q^{43} + 2 q^{44} - 8 q^{46} + 8 q^{47} + 3 q^{49} + 11 q^{50} - 2 q^{52} + 8 q^{55} + 6 q^{56} - 6 q^{58} - 4 q^{59} + 6 q^{61} - 8 q^{62} + 14 q^{64} - 8 q^{65} - 8 q^{67} + 2 q^{68} + 8 q^{70} - 4 q^{73} - 6 q^{74} - 6 q^{76} - 2 q^{77} + 10 q^{79} + 8 q^{80} + 20 q^{82} - 12 q^{83} + 8 q^{85} + 6 q^{86} + 3 q^{88} + 8 q^{91} + 4 q^{92} - 8 q^{94} - 24 q^{95} - 2 q^{97} + 6 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 0 0
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) 4.00000 1.26491
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0 0
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) −1.00000 + 1.73205i −0.267261 + 0.462910i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) −2.00000 3.46410i −0.447214 0.774597i
\(21\) 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 \(0.303595\pi\)
\(24\) 0 0
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 2.00000 0.377964
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 0 0
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) 8.00000 1.35225
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) −3.00000 5.19615i −0.486664 0.842927i
\(39\) 0 0
\(40\) 6.00000 10.3923i 0.948683 1.64317i
\(41\) 5.00000 8.66025i 0.780869 1.35250i −0.150567 0.988600i \(-0.548110\pi\)
0.931436 0.363905i \(-0.118557\pi\)
\(42\) 0 0
\(43\) −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i \(-0.317920\pi\)
−0.998828 + 0.0484030i \(0.984587\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 5.50000 9.52628i 0.777817 1.34722i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 3.00000 + 5.19615i 0.400892 + 0.694365i
\(57\) 0 0
\(58\) −3.00000 + 5.19615i −0.393919 + 0.682288i
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −4.00000 6.92820i −0.496139 0.859338i
\(66\) 0 0
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0 0
\(70\) 4.00000 + 6.92820i 0.478091 + 0.828079i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −3.00000 5.19615i −0.348743 0.604040i
\(75\) 0 0
\(76\) −3.00000 + 5.19615i −0.344124 + 0.596040i
\(77\) −1.00000 + 1.73205i −0.113961 + 0.197386i
\(78\) 0 0
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) 4.00000 0.447214
\(81\) 0 0
\(82\) 10.0000 1.10432
\(83\) −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) 0 0
\(85\) 4.00000 6.92820i 0.433861 0.751469i
\(86\) 3.00000 5.19615i 0.323498 0.560316i
\(87\) 0 0
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 2.00000 + 3.46410i 0.208514 + 0.361158i
\(93\) 0 0
\(94\) −4.00000 + 6.92820i −0.412568 + 0.714590i
\(95\) −12.0000 + 20.7846i −1.23117 + 2.13246i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) −11.0000 −1.10000
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 3.00000 5.19615i 0.294174 0.509525i
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 2.00000 + 3.46410i 0.190693 + 0.330289i
\(111\) 0 0
\(112\) −1.00000 + 1.73205i −0.0944911 + 0.163663i
\(113\) −6.00000 + 10.3923i −0.564433 + 0.977626i 0.432670 + 0.901553i \(0.357572\pi\)
−0.997102 + 0.0760733i \(0.975762\pi\)
\(114\) 0 0
\(115\) 8.00000 + 13.8564i 0.746004 + 1.29212i
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 2.00000 + 3.46410i 0.183340 + 0.317554i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −3.00000 + 5.19615i −0.271607 + 0.470438i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) −10.0000 −0.887357 −0.443678 0.896186i \(-0.646327\pi\)
−0.443678 + 0.896186i \(0.646327\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 0 0
\(130\) 4.00000 6.92820i 0.350823 0.607644i
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 0 0
\(133\) −6.00000 10.3923i −0.520266 0.901127i
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0 0
\(139\) −5.00000 + 8.66025i −0.424094 + 0.734553i −0.996335 0.0855324i \(-0.972741\pi\)
0.572241 + 0.820086i \(0.306074\pi\)
\(140\) 4.00000 6.92820i 0.338062 0.585540i
\(141\) 0 0
\(142\) 0 0
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) 24.0000 1.99309
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 0 0
\(148\) −3.00000 + 5.19615i −0.246598 + 0.427121i
\(149\) 1.00000 1.73205i 0.0819232 0.141895i −0.822153 0.569267i \(-0.807227\pi\)
0.904076 + 0.427372i \(0.140560\pi\)
\(150\) 0 0
\(151\) −7.00000 12.1244i −0.569652 0.986666i −0.996600 0.0823900i \(-0.973745\pi\)
0.426948 0.904276i \(-0.359589\pi\)
\(152\) −18.0000 −1.45999
\(153\) 0 0
\(154\) −2.00000 −0.161165
\(155\) 8.00000 + 13.8564i 0.642575 + 1.11297i
\(156\) 0 0
\(157\) 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i \(-0.702676\pi\)
0.993608 + 0.112884i \(0.0360089\pi\)
\(158\) −5.00000 + 8.66025i −0.397779 + 0.688973i
\(159\) 0 0
\(160\) −10.0000 17.3205i −0.790569 1.36931i
\(161\) −8.00000 −0.630488
\(162\) 0 0
\(163\) −20.0000 −1.56652 −0.783260 0.621694i \(-0.786445\pi\)
−0.783260 + 0.621694i \(0.786445\pi\)
\(164\) −5.00000 8.66025i −0.390434 0.676252i
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 8.00000 0.613572
\(171\) 0 0
\(172\) −6.00000 −0.457496
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) 11.0000 19.0526i 0.831522 1.44024i
\(176\) −0.500000 + 0.866025i −0.0376889 + 0.0652791i
\(177\) 0 0
\(178\) 0 0
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 2.00000 + 3.46410i 0.148250 + 0.256776i
\(183\) 0 0
\(184\) −6.00000 + 10.3923i −0.442326 + 0.766131i
\(185\) −12.0000 + 20.7846i −0.882258 + 1.52811i
\(186\) 0 0
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) −24.0000 −1.74114
\(191\) −8.00000 13.8564i −0.578860 1.00261i −0.995610 0.0935936i \(-0.970165\pi\)
0.416751 0.909021i \(-0.363169\pi\)
\(192\) 0 0
\(193\) 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i \(-0.665242\pi\)
0.999990 0.00447566i \(-0.00142465\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) 0 0
\(196\) −1.50000 2.59808i −0.107143 0.185577i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 12.0000 0.850657 0.425329 0.905039i \(-0.360158\pi\)
0.425329 + 0.905039i \(0.360158\pi\)
\(200\) −16.5000 28.5788i −1.16673 2.02083i
\(201\) 0 0
\(202\) −7.00000 + 12.1244i −0.492518 + 0.853067i
\(203\) −6.00000 + 10.3923i −0.421117 + 0.729397i
\(204\) 0 0
\(205\) −20.0000 34.6410i −1.39686 2.41943i
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) −3.00000 5.19615i −0.207514 0.359425i
\(210\) 0 0
\(211\) 3.00000 5.19615i 0.206529 0.357718i −0.744090 0.668079i \(-0.767117\pi\)
0.950619 + 0.310361i \(0.100450\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) −24.0000 −1.63679
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) −1.00000 1.73205i −0.0677285 0.117309i
\(219\) 0 0
\(220\) 2.00000 3.46410i 0.134840 0.233550i
\(221\) 2.00000 3.46410i 0.134535 0.233021i
\(222\) 0 0
\(223\) 4.00000 + 6.92820i 0.267860 + 0.463947i 0.968309 0.249756i \(-0.0803503\pi\)
−0.700449 + 0.713702i \(0.747017\pi\)
\(224\) 10.0000 0.668153
\(225\) 0 0
\(226\) −12.0000 −0.798228
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) 0 0
\(229\) −3.00000 + 5.19615i −0.198246 + 0.343371i −0.947960 0.318390i \(-0.896858\pi\)
0.749714 + 0.661762i \(0.230191\pi\)
\(230\) −8.00000 + 13.8564i −0.527504 + 0.913664i
\(231\) 0 0
\(232\) 9.00000 + 15.5885i 0.590879 + 1.02343i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 32.0000 2.08745
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) 0 0
\(238\) −2.00000 + 3.46410i −0.129641 + 0.224544i
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) 13.0000 + 22.5167i 0.837404 + 1.45043i 0.892058 + 0.451920i \(0.149261\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 0 0
\(244\) 6.00000 0.384111
\(245\) −6.00000 10.3923i −0.383326 0.663940i
\(246\) 0 0
\(247\) −6.00000 + 10.3923i −0.381771 + 0.661247i
\(248\) −6.00000 + 10.3923i −0.381000 + 0.659912i
\(249\) 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
\(253\) −4.00000 −0.251478
\(254\) −5.00000 8.66025i −0.313728 0.543393i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −4.00000 + 6.92820i −0.249513 + 0.432169i −0.963391 0.268101i \(-0.913604\pi\)
0.713878 + 0.700270i \(0.246937\pi\)
\(258\) 0 0
\(259\) −6.00000 10.3923i −0.372822 0.645746i
\(260\) −8.00000 −0.496139
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) 16.0000 + 27.7128i 0.986602 + 1.70885i 0.634588 + 0.772851i \(0.281170\pi\)
0.352014 + 0.935995i \(0.385497\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 6.00000 10.3923i 0.367884 0.637193i
\(267\) 0 0
\(268\) 4.00000 + 6.92820i 0.244339 + 0.423207i
\(269\) −16.0000 −0.975537 −0.487769 0.872973i \(-0.662189\pi\)
−0.487769 + 0.872973i \(0.662189\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) 2.00000 3.46410i 0.120824 0.209274i
\(275\) 5.50000 9.52628i 0.331662 0.574456i
\(276\) 0 0
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) −10.0000 −0.599760
\(279\) 0 0
\(280\) 24.0000 1.43427
\(281\) −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i \(-0.223942\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(282\) 0 0
\(283\) 1.00000 1.73205i 0.0594438 0.102960i −0.834772 0.550596i \(-0.814401\pi\)
0.894216 + 0.447636i \(0.147734\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.00000 + 1.73205i 0.0591312 + 0.102418i
\(287\) 20.0000 1.18056
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 12.0000 + 20.7846i 0.704664 + 1.22051i
\(291\) 0 0
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) 9.00000 15.5885i 0.525786 0.910687i −0.473763 0.880652i \(-0.657105\pi\)
0.999549 0.0300351i \(-0.00956192\pi\)
\(294\) 0 0
\(295\) 8.00000 + 13.8564i 0.465778 + 0.806751i
\(296\) −18.0000 −1.04623
\(297\) 0 0
\(298\) 2.00000 0.115857
\(299\) 4.00000 + 6.92820i 0.231326 + 0.400668i
\(300\) 0 0
\(301\) 6.00000 10.3923i 0.345834 0.599002i
\(302\) 7.00000 12.1244i 0.402805 0.697678i
\(303\) 0 0
\(304\) −3.00000 5.19615i −0.172062 0.298020i
\(305\) 24.0000 1.37424
\(306\) 0 0
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) 1.00000 + 1.73205i 0.0569803 + 0.0986928i
\(309\) 0 0
\(310\) −8.00000 + 13.8564i −0.454369 + 0.786991i
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) 0 0
\(313\) 17.0000 + 29.4449i 0.960897 + 1.66432i 0.720257 + 0.693708i \(0.244024\pi\)
0.240640 + 0.970614i \(0.422643\pi\)
\(314\) 10.0000 0.564333
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 2.00000 + 3.46410i 0.112331 + 0.194563i 0.916710 0.399554i \(-0.130835\pi\)
−0.804379 + 0.594117i \(0.797502\pi\)
\(318\) 0 0
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) 14.0000 24.2487i 0.782624 1.35554i
\(321\) 0 0
\(322\) −4.00000 6.92820i −0.222911 0.386094i
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) −22.0000 −1.22034
\(326\) −10.0000 17.3205i −0.553849 0.959294i
\(327\) 0 0
\(328\) 15.0000 25.9808i 0.828236 1.43455i
\(329\) −8.00000 + 13.8564i −0.441054 + 0.763928i
\(330\) 0 0
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 0 0
\(335\) 16.0000 + 27.7128i 0.874173 + 1.51411i
\(336\) 0 0
\(337\) −7.00000 + 12.1244i −0.381314 + 0.660456i −0.991250 0.131995i \(-0.957862\pi\)
0.609936 + 0.792451i \(0.291195\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) 0 0
\(340\) −4.00000 6.92820i −0.216930 0.375735i
\(341\) −4.00000 −0.216612
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) −9.00000 15.5885i −0.485247 0.840473i
\(345\) 0 0
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) −10.0000 + 17.3205i −0.536828 + 0.929814i 0.462244 + 0.886753i \(0.347044\pi\)
−0.999072 + 0.0430610i \(0.986289\pi\)
\(348\) 0 0
\(349\) −9.00000 15.5885i −0.481759 0.834431i 0.518022 0.855367i \(-0.326669\pi\)
−0.999781 + 0.0209364i \(0.993335\pi\)
\(350\) 22.0000 1.17595
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −12.0000 20.7846i −0.634220 1.09850i
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) 0 0
\(364\) 2.00000 3.46410i 0.104828 0.181568i
\(365\) −4.00000 + 6.92820i −0.209370 + 0.362639i
\(366\) 0 0
\(367\) −8.00000 13.8564i −0.417597 0.723299i 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) −24.0000 −1.24770
\(371\) 0 0
\(372\) 0 0
\(373\) −17.0000 + 29.4449i −0.880227 + 1.52460i −0.0291379 + 0.999575i \(0.509276\pi\)
−0.851089 + 0.525022i \(0.824057\pi\)
\(374\) −1.00000 + 1.73205i −0.0517088 + 0.0895622i
\(375\) 0 0
\(376\) 12.0000 + 20.7846i 0.618853 + 1.07188i
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 12.0000 + 20.7846i 0.615587 + 1.06623i
\(381\) 0 0
\(382\) 8.00000 13.8564i 0.409316 0.708955i
\(383\) 10.0000 17.3205i 0.510976 0.885037i −0.488943 0.872316i \(-0.662617\pi\)
0.999919 0.0127209i \(-0.00404928\pi\)
\(384\) 0 0
\(385\) 4.00000 + 6.92820i 0.203859 + 0.353094i
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) −18.0000 31.1769i −0.912636 1.58073i −0.810326 0.585980i \(-0.800710\pi\)
−0.102311 0.994753i \(-0.532624\pi\)
\(390\) 0 0
\(391\) −4.00000 + 6.92820i −0.202289 + 0.350374i
\(392\) 4.50000 7.79423i 0.227284 0.393668i
\(393\) 0 0
\(394\) 1.00000 + 1.73205i 0.0503793 + 0.0872595i
\(395\) 40.0000 2.01262
\(396\) 0 0
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) 6.00000 + 10.3923i 0.300753 + 0.520919i
\(399\) 0 0
\(400\) 5.50000 9.52628i 0.275000 0.476314i
\(401\) −14.0000 + 24.2487i −0.699127 + 1.21092i 0.269643 + 0.962960i \(0.413094\pi\)
−0.968770 + 0.247962i \(0.920239\pi\)
\(402\) 0 0
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) 14.0000 0.696526
\(405\) 0 0
\(406\) −12.0000 −0.595550
\(407\) −3.00000 5.19615i −0.148704 0.257564i
\(408\) 0 0
\(409\) −3.00000 + 5.19615i −0.148340 + 0.256933i −0.930614 0.366002i \(-0.880726\pi\)
0.782274 + 0.622935i \(0.214060\pi\)
\(410\) 20.0000 34.6410i 0.987730 1.71080i
\(411\) 0 0
\(412\) 4.00000 + 6.92820i 0.197066 + 0.341328i
\(413\) −8.00000 −0.393654
\(414\) 0 0
\(415\) −48.0000 −2.35623
\(416\) −5.00000 8.66025i −0.245145 0.424604i
\(417\) 0 0
\(418\) 3.00000 5.19615i 0.146735 0.254152i
\(419\) 16.0000 27.7128i 0.781651 1.35386i −0.149328 0.988788i \(-0.547711\pi\)
0.930979 0.365072i \(-0.118956\pi\)
\(420\) 0 0
\(421\) −17.0000 29.4449i −0.828529 1.43505i −0.899192 0.437555i \(-0.855845\pi\)
0.0706626 0.997500i \(-0.477489\pi\)
\(422\) 6.00000 0.292075
\(423\) 0 0
\(424\) 0 0
\(425\) −11.0000 19.0526i −0.533578 0.924185i
\(426\) 0 0
\(427\) −6.00000 + 10.3923i −0.290360 + 0.502919i
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 0 0
\(430\) −12.0000 20.7846i −0.578691 1.00232i
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) −4.00000 6.92820i −0.192006 0.332564i
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 12.0000 20.7846i 0.574038 0.994263i
\(438\) 0 0
\(439\) −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) 12.0000 0.572078
\(441\) 0 0
\(442\) 4.00000 0.190261
\(443\) 2.00000 + 3.46410i 0.0950229 + 0.164584i 0.909618 0.415445i \(-0.136374\pi\)
−0.814595 + 0.580030i \(0.803041\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −4.00000 + 6.92820i −0.189405 + 0.328060i
\(447\) 0 0
\(448\) 7.00000 + 12.1244i 0.330719 + 0.572822i
\(449\) −32.0000 −1.51017 −0.755087 0.655625i \(-0.772405\pi\)
−0.755087 + 0.655625i \(0.772405\pi\)
\(450\) 0 0
\(451\) 10.0000 0.470882
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 0 0
\(454\) −6.00000 + 10.3923i −0.281594 + 0.487735i
\(455\) 8.00000 13.8564i 0.375046 0.649598i
\(456\) 0 0
\(457\) 9.00000 + 15.5885i 0.421002 + 0.729197i 0.996038 0.0889312i \(-0.0283451\pi\)
−0.575036 + 0.818128i \(0.695012\pi\)
\(458\) −6.00000 −0.280362
\(459\) 0 0
\(460\) 16.0000 0.746004
\(461\) −3.00000 5.19615i −0.139724 0.242009i 0.787668 0.616100i \(-0.211288\pi\)
−0.927392 + 0.374091i \(0.877955\pi\)
\(462\) 0 0
\(463\) −8.00000 + 13.8564i −0.371792 + 0.643962i −0.989841 0.142177i \(-0.954590\pi\)
0.618050 + 0.786139i \(0.287923\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 0 0
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 0 0
\(469\) −16.0000 −0.738811
\(470\) 16.0000 + 27.7128i 0.738025 + 1.27830i
\(471\) 0 0
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) 3.00000 5.19615i 0.137940 0.238919i
\(474\) 0 0
\(475\) 33.0000 + 57.1577i 1.51414 + 2.62257i
\(476\) 4.00000 0.183340
\(477\) 0 0
\(478\) 0 0
\(479\) 16.0000 + 27.7128i 0.731059 + 1.26623i 0.956431 + 0.291958i \(0.0943068\pi\)
−0.225372 + 0.974273i \(0.572360\pi\)
\(480\) 0 0
\(481\) −6.00000 + 10.3923i −0.273576 + 0.473848i
\(482\) −13.0000 + 22.5167i −0.592134 + 1.02561i
\(483\) 0 0
\(484\) 0.500000 + 0.866025i 0.0227273 + 0.0393648i
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) 9.00000 + 15.5885i 0.407411 + 0.705656i
\(489\) 0 0
\(490\) 6.00000 10.3923i 0.271052 0.469476i
\(491\) 14.0000 24.2487i 0.631811 1.09433i −0.355370 0.934726i \(-0.615645\pi\)
0.987181 0.159603i \(-0.0510215\pi\)
\(492\) 0 0
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) −12.0000 −0.539906
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) −12.0000 + 20.7846i −0.536656 + 0.929516i
\(501\) 0 0
\(502\) 4.00000 + 6.92820i 0.178529 + 0.309221i
\(503\) −40.0000 −1.78351 −0.891756 0.452517i \(-0.850526\pi\)
−0.891756 + 0.452517i \(0.850526\pi\)
\(504\) 0 0
\(505\) 56.0000 2.49197
\(506\) −2.00000 3.46410i −0.0889108 0.153998i
\(507\) 0 0
\(508\) −5.00000 + 8.66025i −0.221839 + 0.384237i
\(509\) 12.0000 20.7846i 0.531891 0.921262i −0.467416 0.884037i \(-0.654815\pi\)
0.999307 0.0372243i \(-0.0118516\pi\)
\(510\) 0 0
\(511\) −2.00000 3.46410i −0.0884748 0.153243i
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) −8.00000 −0.352865
\(515\) 16.0000 + 27.7128i 0.705044 + 1.22117i
\(516\) 0 0
\(517\) −4.00000 + 6.92820i −0.175920 + 0.304702i
\(518\) 6.00000 10.3923i 0.263625 0.456612i
\(519\) 0 0
\(520\) −12.0000 20.7846i −0.526235 0.911465i
\(521\) −12.0000 −0.525730 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 0 0
\(523\) 38.0000 1.66162 0.830812 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) −6.00000 10.3923i −0.262111 0.453990i
\(525\) 0 0
\(526\) −16.0000 + 27.7128i −0.697633 + 1.20834i
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) 0 0
\(532\) −12.0000 −0.520266
\(533\) −10.0000 17.3205i −0.433148 0.750234i
\(534\) 0 0
\(535\) 24.0000 41.5692i 1.03761 1.79719i
\(536\) −12.0000 + 20.7846i −0.518321 + 0.897758i
\(537\) 0 0
\(538\) −8.00000 13.8564i −0.344904 0.597392i
\(539\) 3.00000 0.129219
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 1.00000 + 1.73205i 0.0429537 + 0.0743980i
\(543\) 0 0
\(544\) 5.00000 8.66025i 0.214373 0.371305i
\(545\) −4.00000 + 6.92820i −0.171341 + 0.296772i
\(546\) 0 0
\(547\) −19.0000 32.9090i −0.812381 1.40709i −0.911193 0.411980i \(-0.864837\pi\)
0.0988117 0.995106i \(-0.468496\pi\)
\(548\) −4.00000 −0.170872
\(549\) 0 0
\(550\) 11.0000 0.469042
\(551\) −18.0000 31.1769i −0.766826 1.32818i
\(552\) 0 0
\(553\) −10.0000 + 17.3205i −0.425243 + 0.736543i
\(554\) −1.00000 + 1.73205i −0.0424859 + 0.0735878i
\(555\) 0 0
\(556\) 5.00000 + 8.66025i 0.212047 + 0.367277i
\(557\) 38.0000 1.61011 0.805056 0.593199i \(-0.202135\pi\)
0.805056 + 0.593199i \(0.202135\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) 4.00000 + 6.92820i 0.169031 + 0.292770i
\(561\) 0 0
\(562\) 3.00000 5.19615i 0.126547 0.219186i
\(563\) 14.0000 24.2487i 0.590030 1.02196i −0.404198 0.914671i \(-0.632449\pi\)
0.994228 0.107290i \(-0.0342173\pi\)
\(564\) 0 0
\(565\) 24.0000 + 41.5692i 1.00969 + 1.74883i
\(566\) 2.00000 0.0840663
\(567\) 0 0
\(568\) 0 0
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) 17.0000 29.4449i 0.711428 1.23223i −0.252893 0.967494i \(-0.581382\pi\)
0.964321 0.264735i \(-0.0852845\pi\)
\(572\) 1.00000 1.73205i 0.0418121 0.0724207i
\(573\) 0 0
\(574\) 10.0000 + 17.3205i 0.417392 + 0.722944i
\(575\) 44.0000 1.83493
\(576\) 0 0
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) 0 0
\(580\) 12.0000 20.7846i 0.498273 0.863034i
\(581\) 12.0000 20.7846i 0.497844 0.862291i
\(582\) 0 0
\(583\) 0 0
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) 2.00000 + 3.46410i 0.0825488 + 0.142979i 0.904344 0.426804i \(-0.140361\pi\)
−0.821795 + 0.569783i \(0.807027\pi\)
\(588\) 0 0
\(589\) 12.0000 20.7846i 0.494451 0.856415i
\(590\) −8.00000 + 13.8564i −0.329355 + 0.570459i
\(591\) 0 0
\(592\) −3.00000 5.19615i −0.123299 0.213561i
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) 16.0000 0.655936
\(596\) −1.00000 1.73205i −0.0409616 0.0709476i
\(597\) 0 0
\(598\) −4.00000 + 6.92820i −0.163572 + 0.283315i
\(599\) 14.0000 24.2487i 0.572024 0.990775i −0.424333 0.905506i \(-0.639492\pi\)
0.996358 0.0852695i \(-0.0271751\pi\)
\(600\) 0 0
\(601\) 11.0000 + 19.0526i 0.448699 + 0.777170i 0.998302 0.0582563i \(-0.0185541\pi\)
−0.549602 + 0.835426i \(0.685221\pi\)
\(602\) 12.0000 0.489083
\(603\) 0 0
\(604\) −14.0000 −0.569652
\(605\) 2.00000 + 3.46410i 0.0813116 + 0.140836i
\(606\) 0 0
\(607\) 5.00000 8.66025i 0.202944 0.351509i −0.746532 0.665350i \(-0.768282\pi\)
0.949476 + 0.313841i \(0.101616\pi\)
\(608\) −15.0000 + 25.9808i −0.608330 + 1.05366i
\(609\) 0 0
\(610\) 12.0000 + 20.7846i 0.485866 + 0.841544i
\(611\) 16.0000 0.647291
\(612\) 0 0
\(613\) −46.0000 −1.85792 −0.928961 0.370177i \(-0.879297\pi\)
−0.928961 + 0.370177i \(0.879297\pi\)
\(614\) −11.0000 19.0526i −0.443924 0.768899i
\(615\) 0 0
\(616\) −3.00000 + 5.19615i −0.120873 + 0.209359i
\(617\) 6.00000 10.3923i 0.241551 0.418378i −0.719605 0.694383i \(-0.755677\pi\)
0.961156 + 0.276005i \(0.0890106\pi\)
\(618\) 0 0
\(619\) −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i \(-0.821334\pi\)
−0.0376891 0.999290i \(-0.512000\pi\)
\(620\) 16.0000 0.642575
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 0 0
\(624\) 0 0
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) −17.0000 + 29.4449i −0.679457 + 1.17685i
\(627\) 0 0
\(628\) −5.00000 8.66025i −0.199522 0.345582i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 4.00000 0.159237 0.0796187 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) 15.0000 + 25.9808i 0.596668 + 1.03346i
\(633\) 0 0
\(634\) −2.00000 + 3.46410i −0.0794301 + 0.137577i
\(635\) −20.0000 + 34.6410i −0.793676 + 1.37469i
\(636\) 0 0
\(637\) −3.00000 5.19615i −0.118864 0.205879i
\(638\) −6.00000 −0.237542
\(639\) 0 0
\(640\) −12.0000 −0.474342
\(641\) 12.0000 + 20.7846i 0.473972 + 0.820943i 0.999556 0.0297987i \(-0.00948663\pi\)
−0.525584 + 0.850741i \(0.676153\pi\)
\(642\) 0 0
\(643\) 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i \(-0.808201\pi\)
0.902764 + 0.430137i \(0.141535\pi\)
\(644\) −4.00000 + 6.92820i −0.157622 + 0.273009i
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 28.0000 1.10079 0.550397 0.834903i \(-0.314476\pi\)
0.550397 + 0.834903i \(0.314476\pi\)
\(648\) 0 0
\(649\) −4.00000 −0.157014
\(650\) −11.0000 19.0526i −0.431455 0.747303i
\(651\) 0 0
\(652\) −10.0000 + 17.3205i −0.391630 + 0.678323i
\(653\) 8.00000 13.8564i 0.313064 0.542243i −0.665960 0.745988i \(-0.731978\pi\)
0.979024 + 0.203744i \(0.0653112\pi\)
\(654\) 0 0
\(655\) −24.0000 41.5692i −0.937758 1.62424i
\(656\) 10.0000 0.390434
\(657\) 0 0
\(658\) −16.0000 −0.623745
\(659\) −22.0000 38.1051i −0.856998 1.48436i −0.874779 0.484523i \(-0.838993\pi\)
0.0177803 0.999842i \(-0.494340\pi\)
\(660\) 0 0
\(661\) 25.0000 43.3013i 0.972387 1.68422i 0.284087 0.958799i \(-0.408310\pi\)
0.688301 0.725426i \(-0.258357\pi\)
\(662\) 2.00000 3.46410i 0.0777322 0.134636i
\(663\) 0 0
\(664\) −18.0000 31.1769i −0.698535 1.20990i
\(665\) −48.0000 −1.86136
\(666\) 0 0
\(667\) −24.0000 −0.929284
\(668\) 0 0
\(669\) 0 0
\(670\) −16.0000 + 27.7128i −0.618134 + 1.07064i
\(671\) −3.00000 + 5.19615i −0.115814 + 0.200595i
\(672\) 0 0
\(673\) −13.0000 22.5167i −0.501113 0.867953i −0.999999 0.00128586i \(-0.999591\pi\)
0.498886 0.866668i \(-0.333743\pi\)
\(674\) −14.0000 −0.539260
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) 0 0
\(679\) 2.00000 3.46410i 0.0767530 0.132940i
\(680\) 12.0000 20.7846i 0.460179 0.797053i
\(681\) 0 0
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) −32.0000 −1.22445 −0.612223 0.790685i \(-0.709725\pi\)
−0.612223 + 0.790685i \(0.709725\pi\)
\(684\) 0 0
\(685\) −16.0000 −0.611329
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 0 0
\(688\) 3.00000 5.19615i 0.114374 0.198101i
\(689\) 0 0
\(690\) 0 0
\(691\) −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i \(-0.290887\pi\)
−0.991122 + 0.132956i \(0.957553\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −20.0000 −0.759190
\(695\) 20.0000 + 34.6410i 0.758643 + 1.31401i
\(696\) 0 0
\(697\) 10.0000 17.3205i 0.378777 0.656061i
\(698\) 9.00000 15.5885i 0.340655 0.590032i
\(699\) 0 0
\(700\) −11.0000 19.0526i −0.415761 0.720119i
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 0 0
\(703\) 36.0000 1.35777
\(704\) 3.50000 + 6.06218i 0.131911 + 0.228477i
\(705\) 0 0
\(706\) 12.0000 20.7846i 0.451626 0.782239i
\(707\) −14.0000 + 24.2487i −0.526524 + 0.911967i
\(708\) 0 0
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.00000 13.8564i −0.299602 0.518927i
\(714\) 0 0
\(715\) 4.00000 6.92820i 0.149592 0.259100i
\(716\) −12.0000 + 20.7846i −0.448461 + 0.776757i
\(717\) 0 0
\(718\) 4.00000 + 6.92820i 0.149279 + 0.258558i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) −16.0000 −0.595871
\(722\) 8.50000 + 14.7224i 0.316337 + 0.547912i
\(723\) 0 0
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 33.0000 57.1577i 1.22559 2.12278i
\(726\) 0 0
\(727\) −6.00000 10.3923i −0.222528 0.385429i 0.733047 0.680178i \(-0.238097\pi\)
−0.955575 + 0.294749i \(0.904764\pi\)
\(728\) 12.0000 0.444750
\(729\) 0 0
\(730\) −8.00000 −0.296093
\(731\) −6.00000 10.3923i −0.221918 0.384373i
\(732\) 0 0
\(733\) −3.00000 + 5.19615i −0.110808 + 0.191924i −0.916096 0.400959i \(-0.868677\pi\)
0.805289 + 0.592883i \(0.202010\pi\)
\(734\) 8.00000 13.8564i 0.295285 0.511449i
\(735\) 0 0
\(736\) 10.0000 + 17.3205i 0.368605 + 0.638442i
\(737\) −8.00000 −0.294684
\(738\) 0 0
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) 12.0000 + 20.7846i 0.441129 + 0.764057i
\(741\) 0 0
\(742\) 0 0
\(743\) 8.00000 13.8564i 0.293492 0.508342i −0.681141 0.732152i \(-0.738516\pi\)
0.974633 + 0.223810i \(0.0718494\pi\)
\(744\) 0 0
\(745\) −4.00000 6.92820i −0.146549 0.253830i
\(746\) −34.0000 −1.24483
\(747\) 0 0
\(748\) 2.00000 0.0731272
\(749\) 12.0000 + 20.7846i 0.438470 + 0.759453i
\(750\) 0 0
\(751\) 10.0000 17.3205i 0.364905 0.632034i −0.623856 0.781540i \(-0.714435\pi\)
0.988761 + 0.149505i \(0.0477681\pi\)
\(752\) −4.00000 + 6.92820i −0.145865 + 0.252646i
\(753\) 0 0
\(754\) 6.00000 + 10.3923i 0.218507 + 0.378465i
\(755\) −56.0000 −2.03805
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 2.00000 + 3.46410i 0.0726433 + 0.125822i
\(759\) 0 0
\(760\) −36.0000 + 62.3538i −1.30586 + 2.26181i
\(761\) −21.0000 + 36.3731i −0.761249 + 1.31852i 0.180957 + 0.983491i \(0.442080\pi\)
−0.942207 + 0.335032i \(0.891253\pi\)
\(762\) 0 0
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) 20.0000 0.722629
\(767\) 4.00000 + 6.92820i 0.144432 + 0.250163i
\(768\) 0 0
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) −4.00000 + 6.92820i −0.144150 + 0.249675i
\(771\) 0 0
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) 44.0000 1.58053
\(776\) −3.00000 5.19615i −0.107694 0.186531i
\(777\) 0 0
\(778\) 18.0000 31.1769i 0.645331 1.11775i
\(779\) −30.0000 + 51.9615i −1.07486 + 1.86171i
\(780\) 0 0
\(781\) 0 0
\(782\) −8.00000 −0.286079
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −20.0000 34.6410i −0.713831 1.23639i
\(786\) 0 0
\(787\) −11.0000 + 19.0526i −0.392108 + 0.679150i −0.992727 0.120384i \(-0.961587\pi\)
0.600620 + 0.799535i \(0.294921\pi\)
\(788\) 1.00000 1.73205i 0.0356235 0.0617018i
\(789\) 0 0
\(790\) 20.0000 + 34.6410i 0.711568 + 1.23247i
\(791\) −24.0000