Properties

Label 1470.2.i.k.361.1
Level $1470$
Weight $2$
Character 1470.361
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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1470.361
Dual form 1470.2.i.k.961.1

$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 + 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 −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −6.00000 −1.27920
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 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 \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 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 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) −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 \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 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 \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 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 0.286064 + 0.958211i \(0.407653\pi\)
−0.972867 + 0.231367i \(0.925680\pi\)
\(54\) 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 \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) −7.00000 12.1244i −0.896258 1.55236i −0.832240 0.554416i \(-0.812942\pi\)
−0.0640184 0.997949i \(-0.520392\pi\)
\(62\) −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 0.0212861 + 0.999773i \(0.493224\pi\)
−0.876472 + 0.481452i \(0.840109\pi\)
\(68\) 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 \(-0.947534\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(74\) 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 0.998388 0.0567635i \(-0.0180781\pi\)
−0.548352 + 0.836247i \(0.684745\pi\)
\(80\) −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 \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 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 0.736644 + 0.676280i \(0.236409\pi\)
0.217354 + 0.976093i \(0.430258\pi\)
\(90\) −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 \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 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 −0.273138 0.961975i \(-0.588061\pi\)
0.969664 0.244443i \(-0.0786053\pi\)
\(102\) 0 0
\(103\) 6.00000 + 10.3923i 0.591198 + 1.02398i 0.994071 + 0.108729i \(0.0346780\pi\)
−0.402874 + 0.915255i \(0.631989\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) −2.00000 3.46410i −0.193347 0.334887i 0.753010 0.658009i \(-0.228601\pi\)
−0.946357 + 0.323122i \(0.895268\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −3.00000 + 5.19615i −0.287348 + 0.497701i −0.973176 0.230063i \(-0.926107\pi\)
0.685828 + 0.727764i \(0.259440\pi\)
\(110\) 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 −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 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 −0.996621 0.0821359i \(-0.973826\pi\)
0.569442 + 0.822031i \(0.307159\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −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 −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) −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 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) 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 \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 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 \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 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 −0.900975 0.433872i \(-0.857147\pi\)
0.826231 + 0.563331i \(0.190480\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 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 0.959558 + 0.281511i \(0.0908356\pi\)
−0.235983 + 0.971757i \(0.575831\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −11.0000 + 19.0526i −0.791797 + 1.37143i 0.133056 + 0.991109i \(0.457521\pi\)
−0.924853 + 0.380325i \(0.875812\pi\)
\(194\) 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 −0.347879 0.937539i \(-0.613098\pi\)
0.985873 0.167497i \(-0.0535685\pi\)
\(200\) 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 \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 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 0.315906 + 0.948790i \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) 5.00000 + 8.66025i 0.327561 + 0.567352i 0.982027 0.188739i \(-0.0604400\pi\)
−0.654466 + 0.756091i \(0.727107\pi\)
\(234\) 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 0.0766885 0.997055i \(-0.475565\pi\)
0.825131 0.564942i \(-0.191101\pi\)
\(242\) 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 \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 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 \(-0.0863961\pi\)
−0.713878 + 0.700270i \(0.753063\pi\)
\(258\) 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 0.352014 0.935995i \(-0.385497\pi\)
0.634588 0.772851i \(-0.281170\pi\)
\(264\) 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 0.307029 + 0.951700i \(0.400665\pi\)
−0.977711 + 0.209955i \(0.932668\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) 9.00000 + 15.5885i 0.546711 + 0.946931i 0.998497 + 0.0548050i \(0.0174537\pi\)
−0.451786 + 0.892126i \(0.649213\pi\)
\(272\) 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 −0.720473 0.693482i \(-0.756075\pi\)
0.960810 + 0.277207i \(0.0894088\pi\)
\(278\) 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 0.0640654 + 0.997946i \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) −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 \(-0.277845\pi\)
0.642627 + 0.766179i \(0.277845\pi\)
\(294\) 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 \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 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 \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 3.00000 5.19615i 0.169842 0.294174i
\(313\) −13.0000 22.5167i −0.734803 1.27272i −0.954810 0.297218i \(-0.903941\pi\)
0.220006 0.975499i \(-0.429392\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −5.00000 8.66025i −0.280828 0.486408i 0.690761 0.723083i \(-0.257276\pi\)
−0.971589 + 0.236675i \(0.923942\pi\)
\(318\) 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 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 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 −0.195507 0.980702i \(-0.562635\pi\)
0.947067 0.321037i \(-0.104031\pi\)
\(348\) 4.00000 + 6.92820i 0.214423 + 0.371391i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 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 \(-0.867282\pi\)
0.807880 + 0.589347i \(0.200615\pi\)
\(354\) −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 0.986865 + 0.161546i \(0.0516481\pi\)
−0.353529 + 0.935423i \(0.615019\pi\)
\(360\) 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 \(-0.800041\pi\)
0.913493 + 0.406855i \(0.133375\pi\)
\(368\) 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 0.950804 0.309794i \(-0.100260\pi\)
−0.743691 + 0.668523i \(0.766927\pi\)
\(374\) 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 \(-0.0502334\pi\)
−0.629890 + 0.776684i \(0.716900\pi\)
\(384\) −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 0.383076 + 0.923717i \(0.374865\pi\)
−0.991500 + 0.130105i \(0.958469\pi\)
\(390\) 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 \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) 18.0000 0.902258
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −1.00000 1.73205i −0.0499376 0.0864945i 0.839976 0.542623i \(-0.182569\pi\)
−0.889914 + 0.456129i \(0.849236\pi\)
\(402\) 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 \(-0.703879\pi\)
0.993174 + 0.116639i \(0.0372122\pi\)
\(410\) −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 \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 18.0000 0.865025 0.432512 0.901628i \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(434\) 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 \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) −6.00000 −0.286039
\(441\) 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 \(0.741317\pi\)
\(444\) −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 −0.841316 0.540544i \(-0.818219\pi\)
−0.0474665 0.998873i \(-0.515115\pi\)
\(458\) −7.00000 + 12.1244i −0.327089 + 0.566534i
\(459\) 0 0
\(460\) 0 0
\(461\) −2.00000 −0.0931493 −0.0465746 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 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 −0.0814184 0.996680i \(-0.525945\pi\)
0.903859 0.427830i \(-0.140722\pi\)
\(480\) 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 −0.969345 0.245705i \(-0.920981\pi\)
0.697459 + 0.716625i \(0.254314\pi\)
\(488\) 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 0.962472 + 0.271380i \(0.0874801\pi\)
−0.246214 + 0.969216i \(0.579187\pi\)
\(500\) −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 \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 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 −0.946111 0.323843i \(-0.895025\pi\)
0.192599 0.981278i \(-0.438308\pi\)
\(510\) 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 \(-0.819383\pi\)
0.887099 + 0.461579i \(0.152717\pi\)
\(522\) −4.00000 + 6.92820i −0.175075 + 0.303239i
\(523\) 22.0000 + 38.1051i 0.961993 + 1.66622i 0.717486 + 0.696573i \(0.245293\pi\)
0.244507 + 0.969648i \(0.421374\pi\)
\(524\) 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 0.605096 0.796152i \(-0.293135\pi\)
−0.992036 + 0.125952i \(0.959801\pi\)
\(542\) −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 −0.886433 0.462856i \(-0.846825\pi\)
0.844062 + 0.536246i \(0.180158\pi\)
\(558\) 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 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) 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 −0.998608 0.0527519i \(-0.983201\pi\)
0.453619 0.891196i \(-0.350133\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) −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 \(-0.739208\pi\)
0.974144 + 0.225927i \(0.0725410\pi\)
\(578\) −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 \(-0.270391\pi\)
0.660391 + 0.750922i \(0.270391\pi\)
\(588\) 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 \(-0.0601166\pi\)
−0.653698 + 0.756756i \(0.726783\pi\)
\(594\) −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 −0.0699877 + 0.997548i \(0.522296\pi\)
−0.828908 + 0.559385i \(0.811037\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) 12.0000 0.489490 0.244745 0.969587i \(-0.421296\pi\)
0.244745 + 0.969587i \(0.421296\pi\)
\(602\) 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 0.911621 + 0.411033i \(0.134832\pi\)
−0.0998457 + 0.995003i \(0.531835\pi\)
\(608\) 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 0.231127 + 0.972924i \(0.425759\pi\)
−0.958140 + 0.286300i \(0.907575\pi\)
\(614\) −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 \(-0.964995\pi\)
0.592025 + 0.805919i \(0.298329\pi\)
\(620\) −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 −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) 2.00000 + 3.46410i 0.0789337 + 0.136717i
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) 23.0000 39.8372i 0.904223 1.56616i 0.0822669 0.996610i \(-0.473784\pi\)
0.821956 0.569550i \(-0.192883\pi\)
\(648\) 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 0.695934 0.718106i \(-0.254991\pi\)
−0.969865 + 0.243643i \(0.921657\pi\)
\(654\) 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 \(-0.719495\pi\)
0.986260 + 0.165203i \(0.0528281\pi\)
\(662\) −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 \(-0.0277265\pi\)
−0.573444 + 0.819244i \(0.694393\pi\)
\(678\) −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 −0.539750 0.841825i \(-0.681481\pi\)
0.998917 + 0.0465244i \(0.0148145\pi\)
\(684\) 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 −0.942420 0.334431i \(-0.891456\pi\)
0.181584 0.983375i \(-0.441877\pi\)
\(692\) −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 0.846637 0.532172i \(-0.178624\pi\)
−0.884192 + 0.467123i \(0.845291\pi\)
\(710\) 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 \(-0.0702305\pi\)
−0.677409 + 0.735607i \(0.736897\pi\)
\(720\) 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 \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 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 0.881633 + 0.471935i \(0.156444\pi\)
−0.0321090 + 0.999484i \(0.510222\pi\)
\(734\) 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 −0.218698 0.975793i \(-0.570181\pi\)
0.954410 0.298498i \(-0.0964856\pi\)
\(740\) −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 −0.956963 0.290209i \(-0.906275\pi\)
0.227153 0.973859i \(-0.427058\pi\)
\(752\) 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 \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) −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 \(-0.243582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(770\) 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 \(-0.678460\pi\)
0.999314 + 0.0370420i \(0.0117935\pi\)
\(774\) −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