Properties

Label 1470.2.i.r.961.1
Level $1470$
Weight $2$
Character 1470.961
Analytic conductor $11.738$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1470.961
Dual form 1470.2.i.r.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(0.500000 - 0.866025i) q^{12} -6.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} -1.00000 q^{20} -6.00000 q^{22} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(-0.500000 + 0.866025i) q^{40} +10.0000 q^{41} -6.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-1.00000 + 1.73205i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(3.00000 + 5.19615i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -6.00000 q^{55} -4.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(-7.00000 - 12.1244i) q^{67} +8.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.00000 + 5.19615i) q^{73} +(2.00000 + 3.46410i) q^{74} +(0.500000 - 0.866025i) q^{75} +4.00000 q^{76} -6.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +8.00000 q^{83} +(-3.00000 + 5.19615i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-9.00000 + 15.5885i) q^{89} +1.00000 q^{90} +(-1.00000 + 1.73205i) q^{93} +(1.00000 + 1.73205i) q^{94} +(2.00000 + 3.46410i) q^{95} +(-0.500000 + 0.866025i) q^{96} -2.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} + q^{5} + 2q^{6} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} + q^{5} + 2q^{6} - 2q^{8} - q^{9} - q^{10} - 6q^{11} + q^{12} - 12q^{13} + 2q^{15} - q^{16} + q^{18} - 4q^{19} - 2q^{20} - 12q^{22} - q^{24} - q^{25} - 6q^{26} - 2q^{27} - 16q^{29} + q^{30} + 2q^{31} + q^{32} + 6q^{33} + 2q^{36} - 4q^{37} + 4q^{38} - 6q^{39} - q^{40} + 20q^{41} - 12q^{43} - 6q^{44} + q^{45} - 2q^{47} - 2q^{48} - 2q^{50} + 6q^{52} - 10q^{53} - q^{54} - 12q^{55} - 8q^{57} - 8q^{58} - 4q^{59} - q^{60} + 14q^{61} + 4q^{62} + 2q^{64} - 6q^{65} - 6q^{66} - 14q^{67} + 16q^{71} + q^{72} + 6q^{73} + 4q^{74} + q^{75} + 8q^{76} - 12q^{78} + 8q^{79} + q^{80} - q^{81} + 10q^{82} + 16q^{83} - 6q^{86} - 8q^{87} + 6q^{88} - 18q^{89} + 2q^{90} - 2q^{93} + 2q^{94} + 4q^{95} - q^{96} - 4q^{97} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i \(-0.806886\pi\)
−0.0829925 0.996550i \(-0.526448\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −6.00000 −1.27920
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 3.00000 5.19615i 0.522233 0.904534i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) −3.00000 5.19615i −0.480384 0.832050i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) −3.00000 + 5.19615i −0.452267 + 0.783349i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 0 0
\(47\) −1.00000 + 1.73205i −0.145865 + 0.252646i −0.929695 0.368329i \(-0.879930\pi\)
0.783830 + 0.620975i \(0.213263\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 3.00000 + 5.19615i 0.416025 + 0.720577i
\(53\) −5.00000 8.66025i −0.686803 1.18958i −0.972867 0.231367i \(-0.925680\pi\)
0.286064 0.958211i \(-0.407653\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) −4.00000 + 6.92820i −0.525226 + 0.909718i
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) 7.00000 12.1244i 0.896258 1.55236i 0.0640184 0.997949i \(-0.479608\pi\)
0.832240 0.554416i \(-0.187058\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) −3.00000 5.19615i −0.369274 0.639602i
\(67\) −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i \(-0.840109\pi\)
0.0212861 0.999773i \(-0.493224\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 3.00000 + 5.19615i 0.351123 + 0.608164i 0.986447 0.164083i \(-0.0524664\pi\)
−0.635323 + 0.772246i \(0.719133\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −6.00000 −0.679366
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.00000 8.66025i 0.552158 0.956365i
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −3.00000 + 5.19615i −0.323498 + 0.560316i
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) 3.00000 + 5.19615i 0.319801 + 0.553912i
\(89\) −9.00000 + 15.5885i −0.953998 + 1.65237i −0.217354 + 0.976093i \(0.569742\pi\)
−0.736644 + 0.676280i \(0.763591\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 0 0
\(93\) −1.00000 + 1.73205i −0.103695 + 0.179605i
\(94\) 1.00000 + 1.73205i 0.103142 + 0.178647i
\(95\) 2.00000 + 3.46410i 0.205196 + 0.355409i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −7.00000 12.1244i −0.696526 1.20642i −0.969664 0.244443i \(-0.921395\pi\)
0.273138 0.961975i \(-0.411939\pi\)
\(102\) 0 0
\(103\) −6.00000 + 10.3923i −0.591198 + 1.02398i 0.402874 + 0.915255i \(0.368011\pi\)
−0.994071 + 0.108729i \(0.965322\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) −2.00000 + 3.46410i −0.193347 + 0.334887i −0.946357 0.323122i \(-0.895268\pi\)
0.753010 + 0.658009i \(0.228601\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −3.00000 5.19615i −0.287348 0.497701i 0.685828 0.727764i \(-0.259440\pi\)
−0.973176 + 0.230063i \(0.926107\pi\)
\(110\) −3.00000 + 5.19615i −0.286039 + 0.495434i
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −2.00000 + 3.46410i −0.187317 + 0.324443i
\(115\) 0 0
\(116\) 4.00000 + 6.92820i 0.371391 + 0.643268i
\(117\) 3.00000 5.19615i 0.277350 0.480384i
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) −7.00000 12.1244i −0.633750 1.09769i
\(123\) 5.00000 + 8.66025i 0.450835 + 0.780869i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −3.00000 5.19615i −0.264135 0.457496i
\(130\) 3.00000 + 5.19615i 0.263117 + 0.455733i
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0 0
\(134\) −14.0000 −1.20942
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) −5.00000 8.66025i −0.427179 0.739895i 0.569442 0.822031i \(-0.307159\pi\)
−0.996621 + 0.0821359i \(0.973826\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 4.00000 6.92820i 0.335673 0.581402i
\(143\) 18.0000 + 31.1769i 1.50524 + 2.60714i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 2.00000 3.46410i 0.162221 0.280976i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) −3.00000 + 5.19615i −0.240192 + 0.416025i
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) 5.00000 8.66025i 0.396526 0.686803i
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −1.00000 + 1.73205i −0.0783260 + 0.135665i −0.902528 0.430632i \(-0.858291\pi\)
0.824202 + 0.566296i \(0.191624\pi\)
\(164\) −5.00000 8.66025i −0.390434 0.676252i
\(165\) −3.00000 5.19615i −0.233550 0.404520i
\(166\) 4.00000 6.92820i 0.310460 0.537733i
\(167\) 18.0000 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) 3.00000 + 5.19615i 0.228748 + 0.396203i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) −8.00000 −0.606478
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) 2.00000 3.46410i 0.150329 0.260378i
\(178\) 9.00000 + 15.5885i 0.674579 + 1.16840i
\(179\) −1.00000 1.73205i −0.0747435 0.129460i 0.826231 0.563331i \(-0.190480\pi\)
−0.900975 + 0.433872i \(0.857147\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 0 0
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) 0 0
\(188\) 2.00000 0.145865
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 10.0000 17.3205i 0.723575 1.25327i −0.235983 0.971757i \(-0.575831\pi\)
0.959558 0.281511i \(-0.0908356\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −11.0000 19.0526i −0.791797 1.37143i −0.924853 0.380325i \(-0.875812\pi\)
0.133056 0.991109i \(-0.457521\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) −6.00000 −0.429669
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 3.00000 5.19615i 0.213201 0.369274i
\(199\) −9.00000 15.5885i −0.637993 1.10504i −0.985873 0.167497i \(-0.946431\pi\)
0.347879 0.937539i \(-0.386902\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 7.00000 12.1244i 0.493742 0.855186i
\(202\) −14.0000 −0.985037
\(203\) 0 0
\(204\) 0 0
\(205\) 5.00000 8.66025i 0.349215 0.604858i
\(206\) 6.00000 + 10.3923i 0.418040 + 0.724066i
\(207\) 0 0
\(208\) 3.00000 5.19615i 0.208013 0.360288i
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −5.00000 + 8.66025i −0.343401 + 0.594789i
\(213\) 4.00000 + 6.92820i 0.274075 + 0.474713i
\(214\) 2.00000 + 3.46410i 0.136717 + 0.236801i
\(215\) −3.00000 + 5.19615i −0.204598 + 0.354375i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) −3.00000 + 5.19615i −0.202721 + 0.351123i
\(220\) 3.00000 + 5.19615i 0.202260 + 0.350325i
\(221\) 0 0
\(222\) −2.00000 + 3.46410i −0.134231 + 0.232495i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 10.0000 + 17.3205i 0.663723 + 1.14960i 0.979630 + 0.200812i \(0.0643581\pi\)
−0.315906 + 0.948790i \(0.602309\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) 5.00000 8.66025i 0.327561 0.567352i −0.654466 0.756091i \(-0.727107\pi\)
0.982027 + 0.188739i \(0.0604400\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) 1.00000 + 1.73205i 0.0652328 + 0.112987i
\(236\) −2.00000 + 3.46410i −0.130189 + 0.225494i
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) −14.0000 24.2487i −0.901819 1.56200i −0.825131 0.564942i \(-0.808899\pi\)
−0.0766885 0.997055i \(-0.524435\pi\)
\(242\) 12.5000 + 21.6506i 0.803530 + 1.39176i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −14.0000 −0.896258
\(245\) 0 0
\(246\) 10.0000 0.637577
\(247\) 12.0000 20.7846i 0.763542 1.32249i
\(248\) −1.00000 1.73205i −0.0635001 0.109985i
\(249\) 4.00000 + 6.92820i 0.253490 + 0.439057i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 2.00000 3.46410i 0.125491 0.217357i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.00000 + 6.92820i −0.249513 + 0.432169i −0.963391 0.268101i \(-0.913604\pi\)
0.713878 + 0.700270i \(0.246937\pi\)
\(258\) −6.00000 −0.373544
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) −6.00000 10.3923i −0.370681 0.642039i
\(263\) 16.0000 + 27.7128i 0.986602 + 1.70885i 0.634588 + 0.772851i \(0.281170\pi\)
0.352014 + 0.935995i \(0.385497\pi\)
\(264\) −3.00000 + 5.19615i −0.184637 + 0.319801i
\(265\) −10.0000 −0.614295
\(266\) 0 0
\(267\) −18.0000 −1.10158
\(268\) −7.00000 + 12.1244i −0.427593 + 0.740613i
\(269\) 11.0000 + 19.0526i 0.670682 + 1.16166i 0.977711 + 0.209955i \(0.0673317\pi\)
−0.307029 + 0.951700i \(0.599335\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) −9.00000 + 15.5885i −0.546711 + 0.946931i 0.451786 + 0.892126i \(0.350787\pi\)
−0.998497 + 0.0548050i \(0.982546\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −10.0000 −0.604122
\(275\) −3.00000 + 5.19615i −0.180907 + 0.313340i
\(276\) 0 0
\(277\) 4.00000 + 6.92820i 0.240337 + 0.416275i 0.960810 0.277207i \(-0.0894088\pi\)
−0.720473 + 0.693482i \(0.756075\pi\)
\(278\) −4.00000 + 6.92820i −0.239904 + 0.415526i
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) −1.00000 + 1.73205i −0.0595491 + 0.103142i
\(283\) 14.0000 + 24.2487i 0.832214 + 1.44144i 0.896279 + 0.443491i \(0.146260\pi\)
−0.0640654 + 0.997946i \(0.520407\pi\)
\(284\) −4.00000 6.92820i −0.237356 0.411113i
\(285\) −2.00000 + 3.46410i −0.118470 + 0.205196i
\(286\) 36.0000 2.12872
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 4.00000 + 6.92820i 0.234888 + 0.406838i
\(291\) −1.00000 1.73205i −0.0586210 0.101535i
\(292\) 3.00000 5.19615i 0.175562 0.304082i
\(293\) −22.0000 −1.28525 −0.642627 0.766179i \(-0.722155\pi\)
−0.642627 + 0.766179i \(0.722155\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) 3.00000 + 5.19615i 0.174078 + 0.301511i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) 8.00000 0.460348
\(303\) 7.00000 12.1244i 0.402139 0.696526i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) −7.00000 12.1244i −0.400819 0.694239i
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −12.0000 −0.682656
\(310\) 1.00000 1.73205i 0.0567962 0.0983739i
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) 3.00000 + 5.19615i 0.169842 + 0.294174i
\(313\) 13.0000 22.5167i 0.734803 1.27272i −0.220006 0.975499i \(-0.570608\pi\)
0.954810 0.297218i \(-0.0960589\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) −5.00000 8.66025i −0.280386 0.485643i
\(319\) 24.0000 + 41.5692i 1.34374 + 2.32743i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 3.00000 + 5.19615i 0.166410 + 0.288231i
\(326\) 1.00000 + 1.73205i 0.0553849 + 0.0959294i
\(327\) 3.00000 5.19615i 0.165900 0.287348i
\(328\) −10.0000 −0.552158
\(329\) 0 0
\(330\) −6.00000 −0.330289
\(331\) 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) −4.00000 6.92820i −0.219529 0.380235i
\(333\) −2.00000 3.46410i −0.109599 0.189832i
\(334\) 9.00000 15.5885i 0.492458 0.852962i
\(335\) −14.0000 −0.764902
\(336\) 0 0
\(337\) −26.0000 −1.41631 −0.708155 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) 11.5000 19.9186i 0.625518 1.08343i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) 6.00000 0.323498
\(345\) 0 0
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) 14.0000 + 24.2487i 0.751559 + 1.30174i 0.947067 + 0.321037i \(0.104031\pi\)
−0.195507 + 0.980702i \(0.562635\pi\)
\(348\) −4.00000 + 6.92820i −0.214423 + 0.371391i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 6.00000 0.320256
\(352\) 3.00000 5.19615i 0.159901 0.276956i
\(353\) 2.00000 + 3.46410i 0.106449 + 0.184376i 0.914329 0.404971i \(-0.132718\pi\)
−0.807880 + 0.589347i \(0.799385\pi\)
\(354\) −2.00000 3.46410i −0.106299 0.184115i
\(355\) 4.00000 6.92820i 0.212298 0.367711i
\(356\) 18.0000 0.953998
\(357\) 0 0
\(358\) −2.00000 −0.105703
\(359\) 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i \(-0.615019\pi\)
0.986865 0.161546i \(-0.0516481\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) −5.00000 + 8.66025i −0.262794 + 0.455173i
\(363\) −25.0000 −1.31216
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 7.00000 12.1244i 0.365896 0.633750i
\(367\) −2.00000 3.46410i −0.104399 0.180825i 0.809093 0.587680i \(-0.199959\pi\)
−0.913493 + 0.406855i \(0.866625\pi\)
\(368\) 0 0
\(369\) −5.00000 + 8.66025i −0.260290 + 0.450835i
\(370\) 4.00000 0.207950
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 4.00000 6.92820i 0.207112 0.358729i −0.743691 0.668523i \(-0.766927\pi\)
0.950804 + 0.309794i \(0.100260\pi\)
\(374\) 0 0
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 1.00000 1.73205i 0.0515711 0.0893237i
\(377\) 48.0000 2.47213
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 2.00000 3.46410i 0.102598 0.177705i
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) −10.0000 17.3205i −0.511645 0.886194i
\(383\) −7.00000 + 12.1244i −0.357683 + 0.619526i −0.987573 0.157159i \(-0.949767\pi\)
0.629890 + 0.776684i \(0.283100\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −22.0000 −1.11977
\(387\) 3.00000 5.19615i 0.152499 0.264135i
\(388\) 1.00000 + 1.73205i 0.0507673 + 0.0879316i
\(389\) −12.0000 20.7846i −0.608424 1.05382i −0.991500 0.130105i \(-0.958469\pi\)
0.383076 0.923717i \(-0.374865\pi\)
\(390\) −3.00000 + 5.19615i −0.151911 + 0.263117i
\(391\) 0 0
\(392\) 0 0
\(393\) 12.0000 0.605320
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) −4.00000 6.92820i −0.201262 0.348596i
\(396\) −3.00000 5.19615i −0.150756 0.261116i
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) −18.0000 −0.902258
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −1.00000 + 1.73205i −0.0499376 + 0.0864945i −0.889914 0.456129i \(-0.849236\pi\)
0.839976 + 0.542623i \(0.182569\pi\)
\(402\) −7.00000 12.1244i −0.349128 0.604708i
\(403\) −6.00000 10.3923i −0.298881 0.517678i
\(404\) −7.00000 + 12.1244i −0.348263 + 0.603209i
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −8.00000 13.8564i −0.395575 0.685155i 0.597600 0.801795i \(-0.296121\pi\)
−0.993174 + 0.116639i \(0.962788\pi\)
\(410\) −5.00000 8.66025i −0.246932 0.427699i
\(411\) 5.00000 8.66025i 0.246632 0.427179i
\(412\) 12.0000 0.591198
\(413\) 0 0
\(414\) 0 0
\(415\) 4.00000 6.92820i 0.196352 0.340092i
\(416\) −3.00000 5.19615i −0.147087 0.254762i
\(417\) −4.00000 6.92820i −0.195881 0.339276i
\(418\) 12.0000 20.7846i 0.586939 1.01661i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 6.00000 10.3923i 0.292075 0.505889i
\(423\) −1.00000 1.73205i −0.0486217 0.0842152i
\(424\) 5.00000 + 8.66025i 0.242821 + 0.420579i
\(425\) 0 0
\(426\) 8.00000 0.387601
\(427\) 0 0
\(428\) 4.00000 0.193347
\(429\) −18.0000 + 31.1769i −0.869048 + 1.50524i
\(430\) 3.00000 + 5.19615i 0.144673 + 0.250581i
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −18.0000 −0.865025 −0.432512 0.901628i \(-0.642373\pi\)
−0.432512 + 0.901628i \(0.642373\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) −3.00000 + 5.19615i −0.143674 + 0.248851i
\(437\) 0 0
\(438\) 3.00000 + 5.19615i 0.143346 + 0.248282i
\(439\) 5.00000 8.66025i 0.238637 0.413331i −0.721686 0.692220i \(-0.756633\pi\)
0.960323 + 0.278889i \(0.0899661\pi\)
\(440\) 6.00000 0.286039
\(441\) 0 0
\(442\) 0 0
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 0 0
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0.500000 0.866025i 0.0235702 0.0408248i
\(451\) −30.0000 51.9615i −1.41264 2.44677i
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −19.0000 + 32.9090i −0.888783 + 1.53942i −0.0474665 + 0.998873i \(0.515115\pi\)
−0.841316 + 0.540544i \(0.818219\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) 0 0
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 4.00000 6.92820i 0.185695 0.321634i
\(465\) 1.00000 + 1.73205i 0.0463739 + 0.0803219i
\(466\) −5.00000 8.66025i −0.231621 0.401179i
\(467\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) 2.00000 0.0922531
\(471\) 7.00000 12.1244i 0.322543 0.558661i
\(472\) 2.00000 + 3.46410i 0.0920575 + 0.159448i
\(473\) 18.0000 + 31.1769i 0.827641 + 1.43352i
\(474\) 4.00000 6.92820i 0.183726 0.318223i
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 10.0000 0.457869
\(478\) −2.00000 + 3.46410i −0.0914779 + 0.158444i
\(479\) −18.0000 31.1769i −0.822441 1.42451i −0.903859 0.427830i \(-0.859278\pi\)
0.0814184 0.996680i \(-0.474055\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) 12.0000 20.7846i 0.547153 0.947697i
\(482\) −28.0000 −1.27537
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −6.00000 10.3923i −0.271886 0.470920i 0.697459 0.716625i \(-0.254314\pi\)
−0.969345 + 0.245705i \(0.920981\pi\)
\(488\) −7.00000 + 12.1244i −0.316875 + 0.548844i
\(489\) −2.00000 −0.0904431
\(490\) 0 0
\(491\) −22.0000 −0.992846 −0.496423 0.868081i \(-0.665354\pi\)
−0.496423 + 0.868081i \(0.665354\pi\)
\(492\) 5.00000 8.66025i 0.225417 0.390434i
\(493\) 0 0
\(494\) −12.0000 20.7846i −0.539906 0.935144i
\(495\) 3.00000 5.19615i 0.134840 0.233550i
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) 8.00000 0.358489
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 9.00000 + 15.5885i 0.402090 + 0.696441i
\(502\) 10.0000 17.3205i 0.446322 0.773052i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) −14.0000 −0.622992
\(506\) 0 0
\(507\) 11.5000 + 19.9186i 0.510733 + 0.884615i
\(508\) −2.00000 3.46410i −0.0887357 0.153695i
\(509\) 17.0000 29.4449i 0.753512 1.30512i −0.192599 0.981278i \(-0.561692\pi\)
0.946111 0.323843i \(-0.104975\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 3.46410i 0.0883022 0.152944i
\(514\) 4.00000 + 6.92820i 0.176432 + 0.305590i
\(515\) 6.00000 + 10.3923i 0.264392 + 0.457940i
\(516\) −3.00000 + 5.19615i −0.132068 + 0.228748i
\(517\) 12.0000 0.527759
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) −1.00000 1.73205i −0.0438108 0.0758825i 0.843288 0.537461i \(-0.180617\pi\)
−0.887099 + 0.461579i \(0.847283\pi\)
\(522\) −4.00000 6.92820i −0.175075 0.303239i
\(523\) −22.0000 + 38.1051i −0.961993 + 1.66622i −0.244507 + 0.969648i \(0.578626\pi\)
−0.717486 + 0.696573i \(0.754707\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 32.0000 1.39527
\(527\) 0 0
\(528\) 3.00000 + 5.19615i 0.130558 + 0.226134i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) −5.00000 + 8.66025i −0.217186 + 0.376177i
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) −60.0000 −2.59889
\(534\) −9.00000 + 15.5885i −0.389468 + 0.674579i
\(535\) 2.00000 + 3.46410i 0.0864675 + 0.149766i
\(536\) 7.00000 + 12.1244i 0.302354 + 0.523692i
\(537\) 1.00000 1.73205i 0.0431532 0.0747435i
\(538\) 22.0000 0.948487
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) −9.00000 + 15.5885i −0.386940 + 0.670200i −0.992036 0.125952i \(-0.959801\pi\)
0.605096 + 0.796152i \(0.293135\pi\)
\(542\) 9.00000 + 15.5885i 0.386583 + 0.669582i
\(543\) −5.00000 8.66025i −0.214571 0.371647i
\(544\) 0 0
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) 30.0000 1.28271 0.641354 0.767245i \(-0.278373\pi\)
0.641354 + 0.767245i \(0.278373\pi\)
\(548\) −5.00000 + 8.66025i −0.213589 + 0.369948i
\(549\) 7.00000 + 12.1244i 0.298753 + 0.517455i
\(550\) 3.00000 + 5.19615i 0.127920 + 0.221565i
\(551\) 16.0000 27.7128i 0.681623 1.18061i
\(552\) 0 0
\(553\) 0 0
\(554\) 8.00000 0.339887
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) 4.00000 + 6.92820i 0.169638 + 0.293821i
\(557\) −1.00000 1.73205i −0.0423714 0.0733893i 0.844062 0.536246i \(-0.180158\pi\)
−0.886433 + 0.462856i \(0.846825\pi\)
\(558\) −1.00000 + 1.73205i −0.0423334 + 0.0733236i
\(559\) 36.0000 1.52264
\(560\) 0 0
\(561\) 0 0
\(562\) 3.00000 5.19615i 0.126547 0.219186i
\(563\) 12.0000 + 20.7846i 0.505740 + 0.875967i 0.999978 + 0.00664037i \(0.00211371\pi\)
−0.494238 + 0.869326i \(0.664553\pi\)
\(564\) 1.00000 + 1.73205i 0.0421076 + 0.0729325i
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 28.0000 1.17693
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) −13.0000 + 22.5167i −0.544988 + 0.943948i 0.453619 + 0.891196i \(0.350133\pi\)
−0.998608 + 0.0527519i \(0.983201\pi\)
\(570\) 2.00000 + 3.46410i 0.0837708 + 0.145095i
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) 18.0000 31.1769i 0.752618 1.30357i
\(573\) 20.0000 0.835512
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −7.00000 12.1244i −0.291414 0.504744i 0.682730 0.730670i \(-0.260792\pi\)
−0.974144 + 0.225927i \(0.927459\pi\)
\(578\) −8.50000 14.7224i −0.353553 0.612372i
\(579\) 11.0000 19.0526i 0.457144 0.791797i
\(580\) 8.00000 0.332182
\(581\) 0 0
\(582\) −2.00000 −0.0829027
\(583\) −30.0000 + 51.9615i −1.24247 + 2.15203i
\(584\) −3.00000 5.19615i −0.124141 0.215018i
\(585\) −3.00000 5.19615i −0.124035 0.214834i
\(586\) −11.0000 + 19.0526i −0.454406 + 0.787054i
\(587\) −32.0000 −1.32078 −0.660391 0.750922i \(-0.729609\pi\)
−0.660391 + 0.750922i \(0.729609\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) −2.00000 + 3.46410i −0.0823387 + 0.142615i
\(591\) 3.00000 + 5.19615i 0.123404 + 0.213741i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) −8.00000 + 13.8564i −0.328521 + 0.569014i −0.982219 0.187741i \(-0.939883\pi\)
0.653698 + 0.756756i \(0.273217\pi\)
\(594\) 6.00000 0.246183
\(595\) 0 0
\(596\) 0 0
\(597\) 9.00000 15.5885i 0.368345 0.637993i
\(598\) 0 0
\(599\) −22.0000 38.1051i −0.898896 1.55693i −0.828908 0.559385i \(-0.811037\pi\)
−0.0699877 0.997548i \(-0.522296\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) −12.0000 −0.489490 −0.244745 0.969587i \(-0.578704\pi\)
−0.244745 + 0.969587i \(0.578704\pi\)
\(602\) 0 0
\(603\) 14.0000 0.570124
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) 12.5000 + 21.6506i 0.508197 + 0.880223i
\(606\) −7.00000 12.1244i −0.284356 0.492518i
\(607\) −20.0000 + 34.6410i −0.811775 + 1.40604i 0.0998457 + 0.995003i \(0.468165\pi\)
−0.911621 + 0.411033i \(0.865168\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −14.0000 −0.566843
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) 0 0
\(613\) −18.0000 31.1769i −0.727013 1.25922i −0.958140 0.286300i \(-0.907575\pi\)
0.231127 0.972924i \(-0.425759\pi\)
\(614\) 10.0000 17.3205i 0.403567 0.698999i
\(615\) 10.0000 0.403239
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) −6.00000 + 10.3923i −0.241355 + 0.418040i
\(619\) 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i \(-0.0350048\pi\)
−0.592025 + 0.805919i \(0.701671\pi\)
\(620\) −1.00000 1.73205i −0.0401610 0.0695608i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 0 0
\(624\) 6.00000 0.240192
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −13.0000 22.5167i −0.519584 0.899947i
\(627\) 12.0000 + 20.7846i 0.479234 + 0.830057i
\(628\) −7.00000 + 12.1244i −0.279330 + 0.483814i
\(629\) 0 0
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −4.00000 + 6.92820i −0.159111 + 0.275589i
\(633\) 6.00000 + 10.3923i 0.238479 + 0.413057i
\(634\) 5.00000 + 8.66025i 0.198575 + 0.343943i
\(635\) 2.00000 3.46410i 0.0793676 0.137469i
\(636\) −10.0000 −0.396526
\(637\) 0 0
\(638\) 48.0000 1.90034
\(639\) −4.00000 + 6.92820i −0.158238 + 0.274075i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) −2.00000 + 3.46410i −0.0789337 + 0.136717i
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) −23.0000 39.8372i −0.904223 1.56616i −0.821956 0.569550i \(-0.807117\pi\)
−0.0822669 0.996610i \(-0.526216\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −12.0000 + 20.7846i −0.471041 + 0.815867i
\(650\) 6.00000 0.235339
\(651\) 0 0
\(652\) 2.00000 0.0783260
\(653\) −7.00000 + 12.1244i −0.273931 + 0.474463i −0.969865 0.243643i \(-0.921657\pi\)
0.695934 + 0.718106i \(0.254991\pi\)
\(654\) −3.00000 5.19615i −0.117309 0.203186i
\(655\) −6.00000 10.3923i −0.234439 0.406061i
\(656\) −5.00000 + 8.66025i −0.195217 + 0.338126i
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −6.00000 −0.233727 −0.116863 0.993148i \(-0.537284\pi\)
−0.116863 + 0.993148i \(0.537284\pi\)
\(660\) −3.00000 + 5.19615i −0.116775 + 0.202260i
\(661\) −9.00000 15.5885i −0.350059 0.606321i 0.636200 0.771524i \(-0.280505\pi\)
−0.986260 + 0.165203i \(0.947172\pi\)
\(662\) −10.0000 17.3205i −0.388661 0.673181i
\(663\) 0 0
\(664\) −8.00000 −0.310460
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) 0 0
\(668\) −9.00000 15.5885i −0.348220 0.603136i
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) −7.00000 + 12.1244i −0.270434 + 0.468405i
\(671\) −84.0000 −3.24278
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −13.0000 + 22.5167i −0.500741 + 0.867309i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) −11.0000 + 19.0526i −0.422764 + 0.732249i −0.996209 0.0869952i \(-0.972274\pi\)
0.573444 + 0.819244i \(0.305607\pi\)
\(678\) 6.00000 0.230429
\(679\) 0 0
\(680\) 0 0
\(681\) −10.0000 + 17.3205i −0.383201 + 0.663723i
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) 12.0000 + 20.7846i 0.459167 + 0.795301i 0.998917 0.0465244i \(-0.0148145\pi\)
−0.539750 + 0.841825i \(0.681481\pi\)
\(684\) −2.00000 + 3.46410i −0.0764719 + 0.132453i
\(685\) −10.0000 −0.382080
\(686\) 0 0
\(687\) −14.0000 −0.534133
\(688\) 3.00000 5.19615i 0.114374 0.198101i
\(689\) 30.0000 + 51.9615i 1.14291 + 1.97958i
\(690\) 0 0
\(691\) 20.0000 34.6410i 0.760836 1.31781i −0.181584 0.983375i \(-0.558123\pi\)
0.942420 0.334431i \(-0.108544\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) −4.00000 + 6.92820i −0.151729 + 0.262802i
\(696\) 4.00000 + 6.92820i 0.151620 + 0.262613i
\(697\) 0 0
\(698\) −1.00000 + 1.73205i −0.0378506 + 0.0655591i
\(699\) 10.0000 0.378235
\(700\) 0 0
\(701\) 24.0000 0.906467 0.453234 0.891392i \(-0.350270\pi\)
0.453234 + 0.891392i \(0.350270\pi\)
\(702\) 3.00000 5.19615i 0.113228 0.196116i
\(703\) −8.00000 13.8564i −0.301726 0.522604i
\(704\) −3.00000 5.19615i −0.113067 0.195837i
\(705\) −1.00000 + 1.73205i −0.0376622 + 0.0652328i
\(706\) 4.00000 0.150542
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) −1.00000 + 1.73205i −0.0375558 + 0.0650485i −0.884192 0.467123i \(-0.845291\pi\)
0.846637 + 0.532172i \(0.178624\pi\)
\(710\) −4.00000 6.92820i −0.150117 0.260011i
\(711\) 4.00000 + 6.92820i 0.150012 + 0.259828i
\(712\) 9.00000 15.5885i 0.337289 0.584202i
\(713\) 0 0
\(714\) 0 0
\(715\) 36.0000 1.34632
\(716\) −1.00000 + 1.73205i −0.0373718 + 0.0647298i
\(717\) −2.00000 3.46410i −0.0746914 0.129369i
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) −8.00000 + 13.8564i −0.298350 + 0.516757i −0.975759 0.218850i \(-0.929769\pi\)
0.677409 + 0.735607i \(0.263103\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) 14.0000 24.2487i 0.520666 0.901819i
\(724\) 5.00000 + 8.66025i 0.185824 + 0.321856i
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) −12.5000 + 21.6506i −0.463919 + 0.803530i
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 0 0
\(732\) −7.00000 12.1244i −0.258727 0.448129i
\(733\) −23.0000 + 39.8372i −0.849524 + 1.47142i 0.0321090 + 0.999484i \(0.489778\pi\)
−0.881633 + 0.471935i \(0.843556\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) 0 0
\(737\) −42.0000 + 72.7461i −1.54709 + 2.67964i
\(738\) 5.00000 + 8.66025i 0.184053 + 0.318788i
\(739\) 20.0000 + 34.6410i 0.735712 + 1.27429i 0.954410 + 0.298498i \(0.0964856\pi\)
−0.218698 + 0.975793i \(0.570181\pi\)
\(740\) 2.00000 3.46410i 0.0735215 0.127343i
\(741\) 24.0000 0.881662
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 1.00000 1.73205i 0.0366618 0.0635001i
\(745\) 0 0
\(746\) −4.00000 6.92820i −0.146450 0.253660i
\(747\) −4.00000 + 6.92820i −0.146352 + 0.253490i
\(748\) 0 0
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) −20.0000 + 34.6410i −0.729810 + 1.26407i 0.227153 + 0.973859i \(0.427058\pi\)
−0.956963 + 0.290209i \(0.906275\pi\)
\(752\) −1.00000 1.73205i −0.0364662 0.0631614i
\(753\) 10.0000 + 17.3205i 0.364420 + 0.631194i
\(754\) 24.0000 41.5692i 0.874028 1.51386i
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −40.0000 −1.45382 −0.726912 0.686730i \(-0.759045\pi\)
−0.726912 + 0.686730i \(0.759045\pi\)
\(758\) 8.00000 13.8564i 0.290573 0.503287i
\(759\) 0 0
\(760\) −2.00000 3.46410i −0.0725476 0.125656i
\(761\) −3.00000 + 5.19615i −0.108750 + 0.188360i −0.915264 0.402854i \(-0.868018\pi\)
0.806514 + 0.591215i \(0.201351\pi\)
\(762\) 4.00000 0.144905
\(763\) 0 0
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) 7.00000 + 12.1244i 0.252920 + 0.438071i
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −40.0000 −1.44244 −0.721218 0.692708i \(-0.756418\pi\)
−0.721218 + 0.692708i \(0.756418\pi\)
\(770\) 0 0
\(771\) −8.00000 −0.288113
\(772\) −11.0000 + 19.0526i −0.395899 + 0.685717i
\(773\) −13.0000 22.5167i −0.467578 0.809868i 0.531736 0.846910i \(-0.321540\pi\)
−0.999314 + 0.0370420i \(0.988206\pi\)
\(774\) −3.00000 5.19615i −0.107833 0.186772i
\(775\) 1.00000 1.73205i 0.0359211 0.0622171i
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) −24.0000 −0.860442
\(779\) −20.0000 + 34.6410i −0.716574 + 1.24114i
\(780\) 3.00000 + 5.19615i 0.107417 + 0.186052i
\(781\) −24.0000 41.5692i −0.858788 1.48746i
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) −14.0000 −0.499681
\(786\) 6.00000 10.3923i 0.214013 0.370681i
\(787\) 10.0000 + 17.3205i 0.356462