Properties

Label 1470.2.i.g.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: \( x^{2} - x + 1 \) Copy content Toggle raw display
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.g.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +1.00000 q^{20} +2.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(-4.00000 + 6.92820i) q^{37} +(1.00000 + 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -2.00000 q^{41} -2.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-5.00000 + 8.66025i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(1.00000 + 1.73205i) q^{53} +(0.500000 - 0.866025i) q^{54} +2.00000 q^{55} +(-2.00000 - 3.46410i) q^{59} +(0.500000 + 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(0.500000 - 0.866025i) q^{75} -2.00000 q^{78} +(-8.00000 + 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +16.0000 q^{83} -4.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(-1.00000 - 1.73205i) q^{88} +(-7.00000 + 12.1244i) q^{89} +1.00000 q^{90} +8.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-5.00000 - 8.66025i) q^{94} +(0.500000 - 0.866025i) q^{96} +6.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{8} - q^{9} - q^{10} - 2 q^{11} + q^{12} + 4 q^{13} - 2 q^{15} - q^{16} + 4 q^{17} - q^{18} + 2 q^{20} + 4 q^{22} - 8 q^{23} + q^{24} - q^{25} - 2 q^{26} - 2 q^{27} + q^{30} + 2 q^{31} - q^{32} + 2 q^{33} - 8 q^{34} + 2 q^{36} - 8 q^{37} + 2 q^{39} - q^{40} - 4 q^{41} - 4 q^{43} - 2 q^{44} - q^{45} - 8 q^{46} - 10 q^{47} - 2 q^{48} + 2 q^{50} - 4 q^{51} - 2 q^{52} + 2 q^{53} + q^{54} + 4 q^{55} - 4 q^{59} + q^{60} + 10 q^{61} - 4 q^{62} + 2 q^{64} - 2 q^{65} + 2 q^{66} - 2 q^{67} + 4 q^{68} - 16 q^{69} - 24 q^{71} - q^{72} - 10 q^{73} - 8 q^{74} + q^{75} - 4 q^{78} - 16 q^{79} - q^{80} - q^{81} + 2 q^{82} + 32 q^{83} - 8 q^{85} + 2 q^{86} - 2 q^{88} - 14 q^{89} + 2 q^{90} + 16 q^{92} - 2 q^{93} - 10 q^{94} + q^{96} + 12 q^{97} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 2.00000 0.426401
\(23\) −4.00000 + 6.92820i −0.834058 + 1.44463i 0.0607377 + 0.998154i \(0.480655\pi\)
−0.894795 + 0.446476i \(0.852679\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 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
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) −4.00000 −0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −4.00000 + 6.92820i −0.657596 + 1.13899i 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) 0 0
\(39\) 1.00000 + 1.73205i 0.160128 + 0.277350i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) −4.00000 6.92820i −0.589768 1.02151i
\(47\) −5.00000 + 8.66025i −0.729325 + 1.26323i 0.227844 + 0.973698i \(0.426832\pi\)
−0.957169 + 0.289530i \(0.906501\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −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
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 1.00000 + 1.73205i 0.123091 + 0.213201i
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −5.00000 8.66025i −0.585206 1.01361i −0.994850 0.101361i \(-0.967680\pi\)
0.409644 0.912245i \(-0.365653\pi\)
\(74\) −4.00000 6.92820i −0.464991 0.805387i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −8.00000 + 13.8564i −0.900070 + 1.55897i −0.0726692 + 0.997356i \(0.523152\pi\)
−0.827401 + 0.561611i \(0.810182\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) 16.0000 1.75623 0.878114 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) 0 0
\(88\) −1.00000 1.73205i −0.106600 0.184637i
\(89\) −7.00000 + 12.1244i −0.741999 + 1.28518i 0.209585 + 0.977790i \(0.432789\pi\)
−0.951584 + 0.307389i \(0.900545\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) −1.00000 + 1.73205i −0.103695 + 0.179605i
\(94\) −5.00000 8.66025i −0.515711 0.893237i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) −2.00000 3.46410i −0.198030 0.342997i
\(103\) 10.0000 17.3205i 0.985329 1.70664i 0.344865 0.938652i \(-0.387925\pi\)
0.640464 0.767988i \(-0.278742\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −1.00000 + 1.73205i −0.0953463 + 0.165145i
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) −4.00000 6.92820i −0.373002 0.646058i
\(116\) 0 0
\(117\) −1.00000 + 1.73205i −0.0924500 + 0.160128i
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 5.00000 + 8.66025i 0.452679 + 0.784063i
\(123\) −1.00000 1.73205i −0.0901670 0.156174i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.00000 1.73205i −0.0880451 0.152499i
\(130\) −1.00000 1.73205i −0.0877058 0.151911i
\(131\) −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) −2.00000 −0.174078
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) 4.00000 6.92820i 0.340503 0.589768i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −10.0000 −0.842152
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) −2.00000 3.46410i −0.167248 0.289683i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 8.00000 13.8564i 0.655386 1.13516i −0.326411 0.945228i \(-0.605840\pi\)
0.981797 0.189933i \(-0.0608272\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 1.00000 1.73205i 0.0800641 0.138675i
\(157\) 5.00000 + 8.66025i 0.399043 + 0.691164i 0.993608 0.112884i \(-0.0360089\pi\)
−0.594565 + 0.804048i \(0.702676\pi\)
\(158\) −8.00000 13.8564i −0.636446 1.10236i
\(159\) −1.00000 + 1.73205i −0.0793052 + 0.137361i
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 5.00000 8.66025i 0.391630 0.678323i −0.601035 0.799223i \(-0.705245\pi\)
0.992665 + 0.120900i \(0.0385779\pi\)
\(164\) 1.00000 + 1.73205i 0.0780869 + 0.135250i
\(165\) 1.00000 + 1.73205i 0.0778499 + 0.134840i
\(166\) −8.00000 + 13.8564i −0.620920 + 1.07547i
\(167\) 18.0000 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) 0 0
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) 2.00000 3.46410i 0.150329 0.260378i
\(178\) −7.00000 12.1244i −0.524672 0.908759i
\(179\) 1.00000 + 1.73205i 0.0747435 + 0.129460i 0.900975 0.433872i \(-0.142853\pi\)
−0.826231 + 0.563331i \(0.809520\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) −4.00000 + 6.92820i −0.294884 + 0.510754i
\(185\) −4.00000 6.92820i −0.294086 0.509372i
\(186\) −1.00000 1.73205i −0.0733236 0.127000i
\(187\) 4.00000 6.92820i 0.292509 0.506640i
\(188\) 10.0000 0.729325
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 9.00000 + 15.5885i 0.647834 + 1.12208i 0.983639 + 0.180150i \(0.0576584\pi\)
−0.335805 + 0.941932i \(0.609008\pi\)
\(194\) −3.00000 + 5.19615i −0.215387 + 0.373062i
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −1.00000 + 1.73205i −0.0710669 + 0.123091i
\(199\) −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 1.00000 1.73205i 0.0705346 0.122169i
\(202\) −14.0000 −0.985037
\(203\) 0 0
\(204\) 4.00000 0.280056
\(205\) 1.00000 1.73205i 0.0698430 0.120972i
\(206\) 10.0000 + 17.3205i 0.696733 + 1.20678i
\(207\) −4.00000 6.92820i −0.278019 0.481543i
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 1.00000 1.73205i 0.0686803 0.118958i
\(213\) −6.00000 10.3923i −0.411113 0.712069i
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) 1.00000 1.73205i 0.0681994 0.118125i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) 5.00000 8.66025i 0.337869 0.585206i
\(220\) −1.00000 1.73205i −0.0674200 0.116775i
\(221\) 4.00000 + 6.92820i 0.269069 + 0.466041i
\(222\) 4.00000 6.92820i 0.268462 0.464991i
\(223\) 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
\(226\) 7.00000 12.1244i 0.465633 0.806500i
\(227\) 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
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) 0 0
\(233\) 7.00000 12.1244i 0.458585 0.794293i −0.540301 0.841472i \(-0.681690\pi\)
0.998886 + 0.0471787i \(0.0150230\pi\)
\(234\) −1.00000 1.73205i −0.0653720 0.113228i
\(235\) −5.00000 8.66025i −0.326164 0.564933i
\(236\) −2.00000 + 3.46410i −0.130189 + 0.225494i
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) 10.0000 + 17.3205i 0.644157 + 1.11571i 0.984496 + 0.175409i \(0.0561248\pi\)
−0.340339 + 0.940303i \(0.610542\pi\)
\(242\) 3.50000 + 6.06218i 0.224989 + 0.389692i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) 8.00000 + 13.8564i 0.506979 + 0.878114i
\(250\) −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
\(253\) 16.0000 1.00591
\(254\) 6.00000 10.3923i 0.376473 0.652071i
\(255\) −2.00000 3.46410i −0.125245 0.216930i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i \(-0.955440\pi\)
0.615948 + 0.787787i \(0.288773\pi\)
\(258\) 2.00000 0.124515
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 0 0
\(262\) −6.00000 10.3923i −0.370681 0.642039i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 1.00000 1.73205i 0.0615457 0.106600i
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) −14.0000 −0.856786
\(268\) −1.00000 + 1.73205i −0.0610847 + 0.105802i
\(269\) 5.00000 + 8.66025i 0.304855 + 0.528025i 0.977229 0.212187i \(-0.0680585\pi\)
−0.672374 + 0.740212i \(0.734725\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) 7.00000 12.1244i 0.425220 0.736502i −0.571221 0.820796i \(-0.693530\pi\)
0.996441 + 0.0842940i \(0.0268635\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 4.00000 + 6.92820i 0.240772 + 0.417029i
\(277\) 14.0000 + 24.2487i 0.841178 + 1.45696i 0.888899 + 0.458103i \(0.151471\pi\)
−0.0477206 + 0.998861i \(0.515196\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) 14.0000 0.835170 0.417585 0.908638i \(-0.362877\pi\)
0.417585 + 0.908638i \(0.362877\pi\)
\(282\) 5.00000 8.66025i 0.297746 0.515711i
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) −5.00000 + 8.66025i −0.292603 + 0.506803i
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) −4.00000 + 6.92820i −0.232495 + 0.402694i
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) 8.00000 + 13.8564i 0.463428 + 0.802680i
\(299\) −8.00000 + 13.8564i −0.462652 + 0.801337i
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) 0 0
\(303\) −7.00000 + 12.1244i −0.402139 + 0.696526i
\(304\) 0 0
\(305\) 5.00000 + 8.66025i 0.286299 + 0.495885i
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 20.0000 1.13776
\(310\) 1.00000 1.73205i 0.0567962 0.0983739i
\(311\) 10.0000 + 17.3205i 0.567048 + 0.982156i 0.996856 + 0.0792356i \(0.0252479\pi\)
−0.429808 + 0.902920i \(0.641419\pi\)
\(312\) 1.00000 + 1.73205i 0.0566139 + 0.0980581i
\(313\) 13.0000 22.5167i 0.734803 1.27272i −0.220006 0.975499i \(-0.570608\pi\)
0.954810 0.297218i \(-0.0960589\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) −1.00000 1.73205i −0.0560772 0.0971286i
\(319\) 0 0
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) 5.00000 + 8.66025i 0.276924 + 0.479647i
\(327\) −1.00000 + 1.73205i −0.0553001 + 0.0957826i
\(328\) −2.00000 −0.110432
\(329\) 0 0
\(330\) −2.00000 −0.110096
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −8.00000 13.8564i −0.439057 0.760469i
\(333\) −4.00000 6.92820i −0.219199 0.379663i
\(334\) −9.00000 + 15.5885i −0.492458 + 0.852962i
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) −7.00000 12.1244i −0.380188 0.658505i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 2.00000 3.46410i 0.108306 0.187592i
\(342\) 0 0
\(343\) 0 0
\(344\) −2.00000 −0.107833
\(345\) 4.00000 6.92820i 0.215353 0.373002i
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) 2.00000 + 3.46410i 0.107366 + 0.185963i 0.914702 0.404128i \(-0.132425\pi\)
−0.807337 + 0.590091i \(0.799092\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) −1.00000 + 1.73205i −0.0533002 + 0.0923186i
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 2.00000 + 3.46410i 0.106299 + 0.184115i
\(355\) 6.00000 10.3923i 0.318447 0.551566i
\(356\) 14.0000 0.741999
\(357\) 0 0
\(358\) −2.00000 −0.105703
\(359\) 10.0000 17.3205i 0.527780 0.914141i −0.471696 0.881761i \(-0.656358\pi\)
0.999476 0.0323801i \(-0.0103087\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) 11.0000 19.0526i 0.578147 1.00138i
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) −5.00000 + 8.66025i −0.261354 + 0.452679i
\(367\) 14.0000 + 24.2487i 0.730794 + 1.26577i 0.956544 + 0.291587i \(0.0941834\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(368\) −4.00000 6.92820i −0.208514 0.361158i
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) 8.00000 0.415900
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 18.0000 31.1769i 0.932005 1.61428i 0.152115 0.988363i \(-0.451392\pi\)
0.779890 0.625917i \(-0.215275\pi\)
\(374\) 4.00000 + 6.92820i 0.206835 + 0.358249i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) −5.00000 + 8.66025i −0.257855 + 0.446619i
\(377\) 0 0
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 0 0
\(381\) −6.00000 10.3923i −0.307389 0.532414i
\(382\) 0 0
\(383\) −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
\(386\) −18.0000 −0.916176
\(387\) 1.00000 1.73205i 0.0508329 0.0880451i
\(388\) −3.00000 5.19615i −0.152302 0.263795i
\(389\) 12.0000 + 20.7846i 0.608424 + 1.05382i 0.991500 + 0.130105i \(0.0415314\pi\)
−0.383076 + 0.923717i \(0.625135\pi\)
\(390\) 1.00000 1.73205i 0.0506370 0.0877058i
\(391\) −32.0000 −1.61831
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) −8.00000 13.8564i −0.402524 0.697191i
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) 10.0000 0.501255
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 7.00000 12.1244i 0.349563 0.605461i −0.636609 0.771187i \(-0.719663\pi\)
0.986172 + 0.165726i \(0.0529966\pi\)
\(402\) 1.00000 + 1.73205i 0.0498755 + 0.0863868i
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) 7.00000 12.1244i 0.348263 0.603209i
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 16.0000 0.793091
\(408\) −2.00000 + 3.46410i −0.0990148 + 0.171499i
\(409\) 16.0000 + 27.7128i 0.791149 + 1.37031i 0.925256 + 0.379344i \(0.123850\pi\)
−0.134107 + 0.990967i \(0.542817\pi\)
\(410\) 1.00000 + 1.73205i 0.0493865 + 0.0855399i
\(411\) −1.00000 + 1.73205i −0.0493264 + 0.0854358i
\(412\) −20.0000 −0.985329
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) −8.00000 + 13.8564i −0.392705 + 0.680184i
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) −2.00000 3.46410i −0.0979404 0.169638i
\(418\) 0 0
\(419\) 36.0000 1.75872 0.879358 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) 0 0
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) 2.00000 3.46410i 0.0973585 0.168630i
\(423\) −5.00000 8.66025i −0.243108 0.421076i
\(424\) 1.00000 + 1.73205i 0.0485643 + 0.0841158i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 2.00000 3.46410i 0.0965609 0.167248i
\(430\) 1.00000 + 1.73205i 0.0482243 + 0.0835269i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 38.0000 1.82616 0.913082 0.407777i \(-0.133696\pi\)
0.913082 + 0.407777i \(0.133696\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 0 0
\(438\) 5.00000 + 8.66025i 0.238909 + 0.413803i
\(439\) 13.0000 22.5167i 0.620456 1.07466i −0.368945 0.929451i \(-0.620281\pi\)
0.989401 0.145210i \(-0.0463858\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) −8.00000 −0.380521
\(443\) −14.0000 + 24.2487i −0.665160 + 1.15209i 0.314082 + 0.949396i \(0.398303\pi\)
−0.979242 + 0.202695i \(0.935030\pi\)
\(444\) 4.00000 + 6.92820i 0.189832 + 0.328798i
\(445\) −7.00000 12.1244i −0.331832 0.574750i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 16.0000 0.756774
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) 2.00000 + 3.46410i 0.0941763 + 0.163118i
\(452\) 7.00000 + 12.1244i 0.329252 + 0.570282i
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 0 0
\(457\) 21.0000 36.3731i 0.982339 1.70146i 0.329125 0.944286i \(-0.393246\pi\)
0.653213 0.757174i \(-0.273421\pi\)
\(458\) −5.00000 8.66025i −0.233635 0.404667i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) −4.00000 + 6.92820i −0.186501 + 0.323029i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) −1.00000 1.73205i −0.0463739 0.0803219i
\(466\) 7.00000 + 12.1244i 0.324269 + 0.561650i
\(467\) −4.00000 + 6.92820i −0.185098 + 0.320599i −0.943610 0.331061i \(-0.892594\pi\)
0.758512 + 0.651660i \(0.225927\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) 10.0000 0.461266
\(471\) −5.00000 + 8.66025i −0.230388 + 0.399043i
\(472\) −2.00000 3.46410i −0.0920575 0.159448i
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) 8.00000 13.8564i 0.367452 0.636446i
\(475\) 0 0
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 4.00000 6.92820i 0.182956 0.316889i
\(479\) −2.00000 3.46410i −0.0913823 0.158279i 0.816711 0.577047i \(-0.195795\pi\)
−0.908093 + 0.418769i \(0.862462\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) −8.00000 + 13.8564i −0.364769 + 0.631798i
\(482\) −20.0000 −0.910975
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) −3.00000 + 5.19615i −0.136223 + 0.235945i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −14.0000 24.2487i −0.634401 1.09881i −0.986642 0.162905i \(-0.947914\pi\)
0.352241 0.935909i \(-0.385420\pi\)
\(488\) 5.00000 8.66025i 0.226339 0.392031i
\(489\) 10.0000 0.452216
\(490\) 0 0
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) −1.00000 + 1.73205i −0.0450835 + 0.0780869i
\(493\) 0 0
\(494\) 0 0
\(495\) −1.00000 + 1.73205i −0.0449467 + 0.0778499i
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) −16.0000 −0.716977
\(499\) −20.0000 + 34.6410i −0.895323 + 1.55074i −0.0619186 + 0.998081i \(0.519722\pi\)
−0.833404 + 0.552664i \(0.813611\pi\)
\(500\) −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
\(506\) −8.00000 + 13.8564i −0.355643 + 0.615992i
\(507\) −4.50000 7.79423i −0.199852 0.346154i
\(508\) 6.00000 + 10.3923i 0.266207 + 0.461084i
\(509\) −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) 4.00000 0.177123
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −6.00000 10.3923i −0.264649 0.458385i
\(515\) 10.0000 + 17.3205i 0.440653 + 0.763233i
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 20.0000 0.879599
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) −1.00000 + 1.73205i −0.0438529 + 0.0759555i
\(521\) −15.0000 25.9808i −0.657162 1.13824i −0.981347 0.192244i \(-0.938423\pi\)
0.324185 0.945994i \(-0.394910\pi\)
\(522\) 0 0
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 0 0
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) 1.00000 + 1.73205i 0.0435194 + 0.0753778i
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) 1.00000 1.73205i 0.0434372 0.0752355i
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) −4.00000 −0.173259
\(534\) 7.00000 12.1244i 0.302920 0.524672i
\(535\) −6.00000 10.3923i −0.259403 0.449299i
\(536\) −1.00000 1.73205i −0.0431934 0.0748132i
\(537\) −1.00000 + 1.73205i −0.0431532 + 0.0747435i
\(538\) −10.0000 −0.431131
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) 7.00000 + 12.1244i 0.300676 + 0.520786i
\(543\) −11.0000 19.0526i −0.472055 0.817624i
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) −14.0000 −0.598597 −0.299298 0.954160i \(-0.596753\pi\)
−0.299298 + 0.954160i \(0.596753\pi\)
\(548\) 1.00000 1.73205i 0.0427179 0.0739895i
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) −1.00000 1.73205i −0.0426401 0.0738549i
\(551\) 0 0
\(552\) −8.00000 −0.340503
\(553\) 0 0
\(554\) −28.0000 −1.18961
\(555\) 4.00000 6.92820i 0.169791 0.294086i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) 1.00000 1.73205i 0.0423334 0.0733236i
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) −7.00000 + 12.1244i −0.295277 + 0.511435i
\(563\) −12.0000 20.7846i −0.505740 0.875967i −0.999978 0.00664037i \(-0.997886\pi\)
0.494238 0.869326i \(-0.335447\pi\)
\(564\) 5.00000 + 8.66025i 0.210538 + 0.364662i
\(565\) 7.00000 12.1244i 0.294492 0.510075i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) 19.0000 32.9090i 0.796521 1.37962i −0.125347 0.992113i \(-0.540004\pi\)
0.921869 0.387503i \(-0.126662\pi\)
\(570\) 0 0
\(571\) −6.00000 10.3923i −0.251092 0.434904i 0.712735 0.701434i \(-0.247456\pi\)
−0.963827 + 0.266529i \(0.914123\pi\)
\(572\) −2.00000 + 3.46410i −0.0836242 + 0.144841i
\(573\) 0 0
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 1.00000 + 1.73205i 0.0416305 + 0.0721062i 0.886090 0.463513i \(-0.153411\pi\)
−0.844459 + 0.535620i \(0.820078\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) −9.00000 + 15.5885i −0.374027 + 0.647834i
\(580\) 0 0
\(581\) 0 0
\(582\) −6.00000 −0.248708
\(583\) 2.00000 3.46410i 0.0828315 0.143468i
\(584\) −5.00000 8.66025i −0.206901 0.358364i
\(585\) −1.00000 1.73205i −0.0413449 0.0716115i
\(586\) −15.0000 + 25.9808i −0.619644 + 1.07326i
\(587\) −16.0000 −0.660391 −0.330195 0.943913i \(-0.607115\pi\)
−0.330195 + 0.943913i \(0.607115\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −2.00000 + 3.46410i −0.0823387 + 0.142615i
\(591\) 9.00000 + 15.5885i 0.370211 + 0.641223i
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) 10.0000 17.3205i 0.410651 0.711268i −0.584310 0.811530i \(-0.698635\pi\)
0.994961 + 0.100262i \(0.0319682\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) −16.0000 −0.655386
\(597\) 5.00000 8.66025i 0.204636 0.354441i
\(598\) −8.00000 13.8564i −0.327144 0.566631i
\(599\) −16.0000 27.7128i −0.653742 1.13231i −0.982208 0.187799i \(-0.939865\pi\)
0.328465 0.944516i \(-0.393469\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) 4.00000 0.163163 0.0815817 0.996667i \(-0.474003\pi\)
0.0815817 + 0.996667i \(0.474003\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) 0 0
\(605\) 3.50000 + 6.06218i 0.142295 + 0.246463i
\(606\) −7.00000 12.1244i −0.284356 0.492518i
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) −10.0000 + 17.3205i −0.404557 + 0.700713i
\(612\) 2.00000 + 3.46410i 0.0808452 + 0.140028i
\(613\) 4.00000 + 6.92820i 0.161558 + 0.279827i 0.935428 0.353518i \(-0.115015\pi\)
−0.773869 + 0.633345i \(0.781681\pi\)
\(614\) 10.0000 17.3205i 0.403567 0.698999i
\(615\) 2.00000 0.0806478
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) −10.0000 + 17.3205i −0.402259 + 0.696733i
\(619\) 12.0000 + 20.7846i 0.482321 + 0.835404i 0.999794 0.0202954i \(-0.00646066\pi\)
−0.517473 + 0.855699i \(0.673127\pi\)
\(620\) 1.00000 + 1.73205i 0.0401610 + 0.0695608i
\(621\) 4.00000 6.92820i 0.160514 0.278019i
\(622\) −20.0000 −0.801927
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 13.0000 + 22.5167i 0.519584 + 0.899947i
\(627\) 0 0
\(628\) 5.00000 8.66025i 0.199522 0.345582i
\(629\) −32.0000 −1.27592
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) −8.00000 + 13.8564i −0.318223 + 0.551178i
\(633\) −2.00000 3.46410i −0.0794929 0.137686i
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 6.00000 10.3923i 0.238103 0.412406i
\(636\) 2.00000 0.0793052
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 10.3923i 0.237356 0.411113i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −21.0000 36.3731i −0.829450 1.43665i −0.898470 0.439034i \(-0.855321\pi\)
0.0690201 0.997615i \(-0.478013\pi\)
\(642\) 6.00000 10.3923i 0.236801 0.410152i
\(643\) −36.0000 −1.41970 −0.709851 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) 0 0
\(645\) 2.00000 0.0787499
\(646\) 0 0
\(647\) 1.00000 + 1.73205i 0.0393141 + 0.0680939i 0.885013 0.465566i \(-0.154149\pi\)
−0.845699 + 0.533660i \(0.820816\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −4.00000 + 6.92820i −0.157014 + 0.271956i
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) −10.0000 −0.391630
\(653\) −1.00000 + 1.73205i −0.0391330 + 0.0677804i −0.884929 0.465727i \(-0.845793\pi\)
0.845796 + 0.533507i \(0.179126\pi\)
\(654\) −1.00000 1.73205i −0.0391031 0.0677285i
\(655\) −6.00000 10.3923i −0.234439 0.406061i
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) 10.0000 0.390137
\(658\) 0 0
\(659\) −34.0000 −1.32445 −0.662226 0.749304i \(-0.730388\pi\)
−0.662226 + 0.749304i \(0.730388\pi\)
\(660\) 1.00000 1.73205i 0.0389249 0.0674200i
\(661\) 13.0000 + 22.5167i 0.505641 + 0.875797i 0.999979 + 0.00652642i \(0.00207744\pi\)
−0.494337 + 0.869270i \(0.664589\pi\)
\(662\) 2.00000 + 3.46410i 0.0777322 + 0.134636i
\(663\) −4.00000 + 6.92820i −0.155347 + 0.269069i
\(664\) 16.0000 0.620920
\(665\) 0 0
\(666\) 8.00000 0.309994
\(667\) 0 0
\(668\) −9.00000 15.5885i −0.348220 0.603136i
\(669\) 8.00000 + 13.8564i 0.309298 + 0.535720i
\(670\) −1.00000 + 1.73205i −0.0386334 + 0.0669150i
\(671\) −20.0000 −0.772091
\(672\) 0 0
\(673\) 10.0000 0.385472 0.192736 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) 1.00000 1.73205i 0.0385186 0.0667161i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −13.0000 + 22.5167i −0.499631 + 0.865386i −1.00000 0.000426509i \(-0.999864\pi\)
0.500369 + 0.865812i \(0.333198\pi\)
\(678\) 14.0000 0.537667
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) −6.00000 + 10.3923i −0.229920 + 0.398234i
\(682\) 2.00000 + 3.46410i 0.0765840 + 0.132647i
\(683\) −12.0000 20.7846i −0.459167 0.795301i 0.539750 0.841825i \(-0.318519\pi\)
−0.998917 + 0.0465244i \(0.985185\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 1.00000 1.73205i 0.0381246 0.0660338i
\(689\) 2.00000 + 3.46410i 0.0761939 + 0.131972i
\(690\) 4.00000 + 6.92820i 0.152277 + 0.263752i
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) 0 0
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) −5.00000 + 8.66025i −0.189253 + 0.327795i
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) 16.0000 0.604312 0.302156 0.953259i \(-0.402294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(702\) 1.00000 1.73205i 0.0377426 0.0653720i
\(703\) 0 0
\(704\) −1.00000 1.73205i −0.0376889 0.0652791i
\(705\) 5.00000 8.66025i 0.188311 0.326164i
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) −21.0000 + 36.3731i −0.788672 + 1.36602i 0.138109 + 0.990417i \(0.455897\pi\)
−0.926781 + 0.375602i \(0.877436\pi\)
\(710\) 6.00000 + 10.3923i 0.225176 + 0.390016i
\(711\) −8.00000 13.8564i −0.300023 0.519656i
\(712\) −7.00000 + 12.1244i −0.262336 + 0.454379i
\(713\) −16.0000 −0.599205
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) 1.00000 1.73205i 0.0373718 0.0647298i
\(717\) −4.00000 6.92820i −0.149383 0.258738i
\(718\) 10.0000 + 17.3205i 0.373197 + 0.646396i
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) −19.0000 −0.707107
\(723\) −10.0000 + 17.3205i −0.371904 + 0.644157i
\(724\) 11.0000 + 19.0526i 0.408812 + 0.708083i
\(725\) 0 0
\(726\) −3.50000 + 6.06218i −0.129897 + 0.224989i
\(727\) 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
\(730\) −5.00000 + 8.66025i −0.185058 + 0.320530i
\(731\) −4.00000 6.92820i −0.147945 0.256249i
\(732\) −5.00000 8.66025i −0.184805 0.320092i
\(733\) −15.0000 + 25.9808i −0.554038 + 0.959621i 0.443940 + 0.896056i \(0.353580\pi\)
−0.997978 + 0.0635649i \(0.979753\pi\)
\(734\) −28.0000 −1.03350
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) −2.00000 + 3.46410i −0.0736709 + 0.127602i
\(738\) 1.00000 + 1.73205i 0.0368105 + 0.0637577i
\(739\) −24.0000 41.5692i −0.882854 1.52915i −0.848153 0.529751i \(-0.822285\pi\)
−0.0347009 0.999398i \(-0.511048\pi\)
\(740\) −4.00000 + 6.92820i −0.147043 + 0.254686i
\(741\) 0 0
\(742\) 0 0
\(743\) −48.0000 −1.76095 −0.880475 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) −1.00000 + 1.73205i −0.0366618 + 0.0635001i
\(745\) 8.00000 + 13.8564i 0.293097 + 0.507659i
\(746\) 18.0000 + 31.1769i 0.659027 + 1.14147i
\(747\) −8.00000 + 13.8564i −0.292705 + 0.506979i
\(748\) −8.00000 −0.292509
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) 4.00000 6.92820i 0.145962 0.252814i −0.783769 0.621052i \(-0.786706\pi\)
0.929731 + 0.368238i \(0.120039\pi\)
\(752\) −5.00000 8.66025i −0.182331 0.315807i
\(753\) −10.0000 17.3205i −0.364420 0.631194i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −20.0000 −0.726912 −0.363456 0.931611i \(-0.618403\pi\)
−0.363456 + 0.931611i \(0.618403\pi\)
\(758\) −4.00000 + 6.92820i −0.145287 + 0.251644i
\(759\) 8.00000 + 13.8564i 0.290382 + 0.502956i
\(760\) 0 0
\(761\) 15.0000 25.9808i 0.543750 0.941802i −0.454935 0.890525i \(-0.650337\pi\)
0.998684 0.0512772i \(-0.0163292\pi\)
\(762\) 12.0000 0.434714
\(763\) 0 0
\(764\) 0 0
\(765\) 2.00000 3.46410i 0.0723102 0.125245i
\(766\) −7.00000 12.1244i −0.252920 0.438071i
\(767\) −4.00000 6.92820i −0.144432 0.250163i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 16.0000 0.576975 0.288487 0.957484i \(-0.406848\pi\)
0.288487 + 0.957484i \(0.406848\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) 9.00000 15.5885i 0.323917 0.561041i
\(773\) −15.0000 25.9808i −0.539513 0.934463i −0.998930 0.0462427i \(-0.985275\pi\)
0.459418 0.888220i \(-0.348058\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) 1.00000 1.73205i 0.0359211 0.0622171i
\(776\) 6.00000 0.215387
\(777\) 0 0
\(778\) −24.0000 −0.860442
\(779\) 0 0
\(780\) 1.00000 + 1.73205i 0.0358057 + 0.0620174i
\(781\) 12.0000 + 20.7846i 0.429394 + 0.743732i
\(782\) 16.0000 27.7128i 0.572159 0.991008i
\(783\) 0 0
\(784\) 0 0
\(785\) −10.0000 −0.356915