Properties

Label 507.2.j.c.316.1
Level $507$
Weight $2$
Character 507.316
Analytic conductor $4.048$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
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: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 507.316
Dual form 507.2.j.c.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} +(3.00000 - 1.73205i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} +(3.00000 - 1.73205i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} +1.00000 q^{12} +6.00000 q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} -1.73205i q^{18} +(-3.00000 + 1.73205i) q^{19} -3.46410i q^{21} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 - 0.866025i) q^{24} +5.00000 q^{25} -1.00000 q^{27} +(3.00000 + 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} +3.46410i q^{31} +(4.50000 - 2.59808i) q^{32} +(-3.00000 + 1.73205i) q^{33} +10.3923i q^{34} +(0.500000 - 0.866025i) q^{36} +(6.00000 + 3.46410i) q^{37} -6.00000 q^{38} +(-6.00000 - 3.46410i) q^{41} +(3.00000 - 5.19615i) q^{42} +(2.00000 + 3.46410i) q^{43} -3.46410i q^{44} -3.46410i q^{47} +(-2.50000 - 4.33013i) q^{48} +(2.50000 - 4.33013i) q^{49} +(7.50000 + 4.33013i) q^{50} +6.00000 q^{51} +6.00000 q^{53} +(-1.50000 - 0.866025i) q^{54} +(-3.00000 - 5.19615i) q^{56} +3.46410i q^{57} +(-9.00000 + 5.19615i) q^{58} +(-9.00000 + 5.19615i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-3.00000 + 5.19615i) q^{62} +(-3.00000 - 1.73205i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(-9.00000 - 5.19615i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 + 1.73205i) q^{71} +(-1.50000 + 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{74} +(2.50000 - 4.33013i) q^{75} +(-3.00000 - 1.73205i) q^{76} -12.0000 q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-6.00000 - 10.3923i) q^{82} +3.46410i q^{83} +(3.00000 - 1.73205i) q^{84} +6.92820i q^{86} +(3.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-6.00000 - 3.46410i) q^{89} +(3.00000 + 1.73205i) q^{93} +(3.00000 - 5.19615i) q^{94} -5.19615i q^{96} +(12.0000 - 6.92820i) q^{97} +(7.50000 - 4.33013i) q^{98} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 6 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 6 q^{7} - q^{9} - 6 q^{11} + 2 q^{12} + 12 q^{14} + 5 q^{16} + 6 q^{17} - 6 q^{19} - 6 q^{22} - 3 q^{24} + 10 q^{25} - 2 q^{27} + 6 q^{28} - 6 q^{29} + 9 q^{32} - 6 q^{33} + q^{36} + 12 q^{37} - 12 q^{38} - 12 q^{41} + 6 q^{42} + 4 q^{43} - 5 q^{48} + 5 q^{49} + 15 q^{50} + 12 q^{51} + 12 q^{53} - 3 q^{54} - 6 q^{56} - 18 q^{58} - 18 q^{59} + 2 q^{61} - 6 q^{62} - 6 q^{63} - 2 q^{64} - 12 q^{66} - 18 q^{67} - 6 q^{68} - 6 q^{71} - 3 q^{72} + 12 q^{74} + 5 q^{75} - 6 q^{76} - 24 q^{77} - 16 q^{79} - q^{81} - 12 q^{82} + 6 q^{84} + 6 q^{87} - 6 q^{88} - 12 q^{89} + 6 q^{93} + 6 q^{94} + 24 q^{97} + 15 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 + 0.866025i 1.06066 + 0.612372i 0.925615 0.378467i \(-0.123549\pi\)
0.135045 + 0.990839i \(0.456882\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) 3.00000 1.73205i 1.13389 0.654654i 0.188982 0.981981i \(-0.439481\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 1.73205i 0.612372i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.00000 1.73205i −0.904534 0.522233i −0.0258656 0.999665i \(-0.508234\pi\)
−0.878668 + 0.477432i \(0.841568\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 6.00000 1.60357
\(15\) 0 0
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 1.73205i 0.408248i
\(19\) −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i \(-0.796740\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 3.46410i 0.755929i
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) 5.00000 1.00000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 3.00000 + 1.73205i 0.566947 + 0.327327i
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) 4.50000 2.59808i 0.795495 0.459279i
\(33\) −3.00000 + 1.73205i −0.522233 + 0.301511i
\(34\) 10.3923i 1.78227i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 6.00000 + 3.46410i 0.986394 + 0.569495i 0.904194 0.427121i \(-0.140472\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 0 0
\(41\) −6.00000 3.46410i −0.937043 0.541002i −0.0480106 0.998847i \(-0.515288\pi\)
−0.889032 + 0.457845i \(0.848621\pi\)
\(42\) 3.00000 5.19615i 0.462910 0.801784i
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 3.46410i 0.522233i
\(45\) 0 0
\(46\) 0 0
\(47\) 3.46410i 0.505291i −0.967559 0.252646i \(-0.918699\pi\)
0.967559 0.252646i \(-0.0813007\pi\)
\(48\) −2.50000 4.33013i −0.360844 0.625000i
\(49\) 2.50000 4.33013i 0.357143 0.618590i
\(50\) 7.50000 + 4.33013i 1.06066 + 0.612372i
\(51\) 6.00000 0.840168
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.50000 0.866025i −0.204124 0.117851i
\(55\) 0 0
\(56\) −3.00000 5.19615i −0.400892 0.694365i
\(57\) 3.46410i 0.458831i
\(58\) −9.00000 + 5.19615i −1.18176 + 0.682288i
\(59\) −9.00000 + 5.19615i −1.17170 + 0.676481i −0.954080 0.299552i \(-0.903163\pi\)
−0.217620 + 0.976034i \(0.569829\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) −3.00000 + 5.19615i −0.381000 + 0.659912i
\(63\) −3.00000 1.73205i −0.377964 0.218218i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −6.00000 −0.738549
\(67\) −9.00000 5.19615i −1.09952 0.634811i −0.163429 0.986555i \(-0.552255\pi\)
−0.936096 + 0.351744i \(0.885589\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 + 1.73205i −0.356034 + 0.205557i −0.667340 0.744753i \(-0.732567\pi\)
0.311305 + 0.950310i \(0.399234\pi\)
\(72\) −1.50000 + 0.866025i −0.176777 + 0.102062i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 6.00000 + 10.3923i 0.697486 + 1.20808i
\(75\) 2.50000 4.33013i 0.288675 0.500000i
\(76\) −3.00000 1.73205i −0.344124 0.198680i
\(77\) −12.0000 −1.36753
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −6.00000 10.3923i −0.662589 1.14764i
\(83\) 3.46410i 0.380235i 0.981761 + 0.190117i \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) 3.00000 1.73205i 0.327327 0.188982i
\(85\) 0 0
\(86\) 6.92820i 0.747087i
\(87\) 3.00000 + 5.19615i 0.321634 + 0.557086i
\(88\) −3.00000 + 5.19615i −0.319801 + 0.553912i
\(89\) −6.00000 3.46410i −0.635999 0.367194i 0.147073 0.989126i \(-0.453015\pi\)
−0.783072 + 0.621932i \(0.786348\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 3.00000 + 1.73205i 0.311086 + 0.179605i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) 5.19615i 0.530330i
\(97\) 12.0000 6.92820i 1.21842 0.703452i 0.253837 0.967247i \(-0.418307\pi\)
0.964579 + 0.263795i \(0.0849741\pi\)
\(98\) 7.50000 4.33013i 0.757614 0.437409i
\(99\) 3.46410i 0.348155i
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 9.00000 + 5.19615i 0.891133 + 0.514496i
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 9.00000 + 5.19615i 0.874157 + 0.504695i
\(107\) −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
\(109\) 6.92820i 0.663602i −0.943349 0.331801i \(-0.892344\pi\)
0.943349 0.331801i \(-0.107656\pi\)
\(110\) 0 0
\(111\) 6.00000 3.46410i 0.569495 0.328798i
\(112\) 17.3205i 1.63663i
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) −3.00000 + 5.19615i −0.280976 + 0.486664i
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) −18.0000 −1.65703
\(119\) 18.0000 + 10.3923i 1.65006 + 0.952661i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 3.46410i 0.313625i
\(123\) −6.00000 + 3.46410i −0.541002 + 0.312348i
\(124\) −3.00000 + 1.73205i −0.269408 + 0.155543i
\(125\) 0 0
\(126\) −3.00000 5.19615i −0.267261 0.462910i
\(127\) 4.00000 6.92820i 0.354943 0.614779i −0.632166 0.774833i \(-0.717834\pi\)
0.987108 + 0.160055i \(0.0511671\pi\)
\(128\) −10.5000 6.06218i −0.928078 0.535826i
\(129\) 4.00000 0.352180
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −3.00000 1.73205i −0.261116 0.150756i
\(133\) −6.00000 + 10.3923i −0.520266 + 0.901127i
\(134\) −9.00000 15.5885i −0.777482 1.34664i
\(135\) 0 0
\(136\) 9.00000 5.19615i 0.771744 0.445566i
\(137\) 18.0000 10.3923i 1.53784 0.887875i 0.538879 0.842383i \(-0.318848\pi\)
0.998965 0.0454914i \(-0.0144854\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) −3.00000 1.73205i −0.252646 0.145865i
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) −5.00000 −0.416667
\(145\) 0 0
\(146\) 0 0
\(147\) −2.50000 4.33013i −0.206197 0.357143i
\(148\) 6.92820i 0.569495i
\(149\) −12.0000 + 6.92820i −0.983078 + 0.567581i −0.903198 0.429224i \(-0.858787\pi\)
−0.0798802 + 0.996804i \(0.525454\pi\)
\(150\) 7.50000 4.33013i 0.612372 0.353553i
\(151\) 10.3923i 0.845714i −0.906196 0.422857i \(-0.861027\pi\)
0.906196 0.422857i \(-0.138973\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) 3.00000 5.19615i 0.242536 0.420084i
\(154\) −18.0000 10.3923i −1.45048 0.837436i
\(155\) 0 0
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −12.0000 6.92820i −0.954669 0.551178i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) 0 0
\(162\) −1.50000 + 0.866025i −0.117851 + 0.0680414i
\(163\) −3.00000 + 1.73205i −0.234978 + 0.135665i −0.612866 0.790186i \(-0.709984\pi\)
0.377888 + 0.925851i \(0.376650\pi\)
\(164\) 6.92820i 0.541002i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 15.0000 + 8.66025i 1.16073 + 0.670151i 0.951480 0.307711i \(-0.0995628\pi\)
0.209255 + 0.977861i \(0.432896\pi\)
\(168\) −6.00000 −0.462910
\(169\) 0 0
\(170\) 0 0
\(171\) 3.00000 + 1.73205i 0.229416 + 0.132453i
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) 10.3923i 0.787839i
\(175\) 15.0000 8.66025i 1.13389 0.654654i
\(176\) −15.0000 + 8.66025i −1.13067 + 0.652791i
\(177\) 10.3923i 0.781133i
\(178\) −6.00000 10.3923i −0.449719 0.778936i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 0 0
\(186\) 3.00000 + 5.19615i 0.219971 + 0.381000i
\(187\) 20.7846i 1.51992i
\(188\) 3.00000 1.73205i 0.218797 0.126323i
\(189\) −3.00000 + 1.73205i −0.218218 + 0.125988i
\(190\) 0 0
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 24.0000 1.72310
\(195\) 0 0
\(196\) 5.00000 0.357143
\(197\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) −3.00000 + 5.19615i −0.213201 + 0.369274i
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 8.66025i 0.612372i
\(201\) −9.00000 + 5.19615i −0.634811 + 0.366508i
\(202\) −9.00000 + 5.19615i −0.633238 + 0.365600i
\(203\) 20.7846i 1.45879i
\(204\) 3.00000 + 5.19615i 0.210042 + 0.363803i
\(205\) 0 0
\(206\) 12.0000 + 6.92820i 0.836080 + 0.482711i
\(207\) 0 0
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 10.0000 17.3205i 0.688428 1.19239i −0.283918 0.958849i \(-0.591634\pi\)
0.972346 0.233544i \(-0.0750324\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 3.46410i 0.237356i
\(214\) −18.0000 + 10.3923i −1.23045 + 0.710403i
\(215\) 0 0
\(216\) 1.73205i 0.117851i
\(217\) 6.00000 + 10.3923i 0.407307 + 0.705476i
\(218\) 6.00000 10.3923i 0.406371 0.703856i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 12.0000 0.805387
\(223\) −3.00000 1.73205i −0.200895 0.115987i 0.396178 0.918174i \(-0.370336\pi\)
−0.597073 + 0.802187i \(0.703670\pi\)
\(224\) 9.00000 15.5885i 0.601338 1.04155i
\(225\) −2.50000 4.33013i −0.166667 0.288675i
\(226\) 10.3923i 0.691286i
\(227\) 15.0000 8.66025i 0.995585 0.574801i 0.0886460 0.996063i \(-0.471746\pi\)
0.906939 + 0.421262i \(0.138413\pi\)
\(228\) −3.00000 + 1.73205i −0.198680 + 0.114708i
\(229\) 6.92820i 0.457829i 0.973447 + 0.228914i \(0.0735176\pi\)
−0.973447 + 0.228914i \(0.926482\pi\)
\(230\) 0 0
\(231\) −6.00000 + 10.3923i −0.394771 + 0.683763i
\(232\) 9.00000 + 5.19615i 0.590879 + 0.341144i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −9.00000 5.19615i −0.585850 0.338241i
\(237\) −4.00000 + 6.92820i −0.259828 + 0.450035i
\(238\) 18.0000 + 31.1769i 1.16677 + 2.02090i
\(239\) 10.3923i 0.672222i 0.941822 + 0.336111i \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) 0 0
\(241\) −12.0000 + 6.92820i −0.772988 + 0.446285i −0.833939 0.551856i \(-0.813920\pi\)
0.0609515 + 0.998141i \(0.480586\pi\)
\(242\) 1.73205i 0.111340i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −1.00000 + 1.73205i −0.0640184 + 0.110883i
\(245\) 0 0
\(246\) −12.0000 −0.765092
\(247\) 0 0
\(248\) 6.00000 0.381000
\(249\) 3.00000 + 1.73205i 0.190117 + 0.109764i
\(250\) 0 0
\(251\) 6.00000 + 10.3923i 0.378717 + 0.655956i 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) 3.46410i 0.218218i
\(253\) 0 0
\(254\) 12.0000 6.92820i 0.752947 0.434714i
\(255\) 0 0
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 6.00000 + 3.46410i 0.373544 + 0.215666i
\(259\) 24.0000 1.49129
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) −18.0000 10.3923i −1.11204 0.642039i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) 0 0
\(266\) −18.0000 + 10.3923i −1.10365 + 0.637193i
\(267\) −6.00000 + 3.46410i −0.367194 + 0.212000i
\(268\) 10.3923i 0.634811i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) 9.00000 + 5.19615i 0.546711 + 0.315644i 0.747794 0.663930i \(-0.231113\pi\)
−0.201083 + 0.979574i \(0.564446\pi\)
\(272\) 30.0000 1.81902
\(273\) 0 0
\(274\) 36.0000 2.17484
\(275\) −15.0000 8.66025i −0.904534 0.522233i
\(276\) 0 0
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 6.92820i 0.415526i
\(279\) 3.00000 1.73205i 0.179605 0.103695i
\(280\) 0 0
\(281\) 6.92820i 0.413302i −0.978415 0.206651i \(-0.933744\pi\)
0.978415 0.206651i \(-0.0662565\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) −3.00000 1.73205i −0.178017 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) −4.50000 2.59808i −0.265165 0.153093i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 13.8564i 0.812277i
\(292\) 0 0
\(293\) −24.0000 + 13.8564i −1.40209 + 0.809500i −0.994607 0.103711i \(-0.966928\pi\)
−0.407487 + 0.913211i \(0.633595\pi\)
\(294\) 8.66025i 0.505076i
\(295\) 0 0
\(296\) 6.00000 10.3923i 0.348743 0.604040i
\(297\) 3.00000 + 1.73205i 0.174078 + 0.100504i
\(298\) −24.0000 −1.39028
\(299\) 0 0
\(300\) 5.00000 0.288675
\(301\) 12.0000 + 6.92820i 0.691669 + 0.399335i
\(302\) 9.00000 15.5885i 0.517892 0.897015i
\(303\) 3.00000 + 5.19615i 0.172345 + 0.298511i
\(304\) 17.3205i 0.993399i
\(305\) 0 0
\(306\) 9.00000 5.19615i 0.514496 0.297044i
\(307\) 10.3923i 0.593120i 0.955014 + 0.296560i \(0.0958395\pi\)
−0.955014 + 0.296560i \(0.904160\pi\)
\(308\) −6.00000 10.3923i −0.341882 0.592157i
\(309\) 4.00000 6.92820i 0.227552 0.394132i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 21.0000 + 12.1244i 1.18510 + 0.684217i
\(315\) 0 0
\(316\) −4.00000 6.92820i −0.225018 0.389742i
\(317\) 13.8564i 0.778253i −0.921184 0.389127i \(-0.872777\pi\)
0.921184 0.389127i \(-0.127223\pi\)
\(318\) 9.00000 5.19615i 0.504695 0.291386i
\(319\) 18.0000 10.3923i 1.00781 0.581857i
\(320\) 0 0
\(321\) 6.00000 + 10.3923i 0.334887 + 0.580042i
\(322\) 0 0
\(323\) −18.0000 10.3923i −1.00155 0.578243i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) −6.00000 3.46410i −0.331801 0.191565i
\(328\) −6.00000 + 10.3923i −0.331295 + 0.573819i
\(329\) −6.00000 10.3923i −0.330791 0.572946i
\(330\) 0 0
\(331\) −3.00000 + 1.73205i −0.164895 + 0.0952021i −0.580176 0.814491i \(-0.697016\pi\)
0.415282 + 0.909693i \(0.363683\pi\)
\(332\) −3.00000 + 1.73205i −0.164646 + 0.0950586i
\(333\) 6.92820i 0.379663i
\(334\) 15.0000 + 25.9808i 0.820763 + 1.42160i
\(335\) 0 0
\(336\) −15.0000 8.66025i −0.818317 0.472456i
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 3.00000 + 5.19615i 0.162221 + 0.280976i
\(343\) 6.92820i 0.374088i
\(344\) 6.00000 3.46410i 0.323498 0.186772i
\(345\) 0 0
\(346\) 31.1769i 1.67608i
\(347\) −18.0000 31.1769i −0.966291 1.67366i −0.706107 0.708105i \(-0.749550\pi\)
−0.260184 0.965559i \(-0.583783\pi\)
\(348\) −3.00000 + 5.19615i −0.160817 + 0.278543i
\(349\) −6.00000 3.46410i −0.321173 0.185429i 0.330743 0.943721i \(-0.392701\pi\)
−0.651915 + 0.758292i \(0.726034\pi\)
\(350\) 30.0000 1.60357
\(351\) 0 0
\(352\) −18.0000 −0.959403
\(353\) 30.0000 + 17.3205i 1.59674 + 0.921878i 0.992110 + 0.125370i \(0.0400119\pi\)
0.604629 + 0.796507i \(0.293321\pi\)
\(354\) −9.00000 + 15.5885i −0.478345 + 0.828517i
\(355\) 0 0
\(356\) 6.92820i 0.367194i
\(357\) 18.0000 10.3923i 0.952661 0.550019i
\(358\) 18.0000 10.3923i 0.951330 0.549250i
\(359\) 17.3205i 0.914141i −0.889430 0.457071i \(-0.848899\pi\)
0.889430 0.457071i \(-0.151101\pi\)
\(360\) 0 0
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) −15.0000 8.66025i −0.788382 0.455173i
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 0 0
\(366\) 3.00000 + 1.73205i 0.156813 + 0.0905357i
\(367\) 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i \(-0.696206\pi\)
0.995697 + 0.0926670i \(0.0295392\pi\)
\(368\) 0 0
\(369\) 6.92820i 0.360668i
\(370\) 0 0
\(371\) 18.0000 10.3923i 0.934513 0.539542i
\(372\) 3.46410i 0.179605i
\(373\) −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) 18.0000 31.1769i 0.930758 1.61212i
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) 0 0
\(378\) −6.00000 −0.308607
\(379\) 15.0000 + 8.66025i 0.770498 + 0.444847i 0.833052 0.553194i \(-0.186591\pi\)
−0.0625541 + 0.998042i \(0.519925\pi\)
\(380\) 0 0
\(381\) −4.00000 6.92820i −0.204926 0.354943i
\(382\) 41.5692i 2.12687i
\(383\) −3.00000 + 1.73205i −0.153293 + 0.0885037i −0.574684 0.818375i \(-0.694875\pi\)
0.421392 + 0.906879i \(0.361542\pi\)
\(384\) −10.5000 + 6.06218i −0.535826 + 0.309359i
\(385\) 0 0
\(386\) 0 0
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) 12.0000 + 6.92820i 0.609208 + 0.351726i
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −7.50000 4.33013i −0.378807 0.218704i
\(393\) −6.00000 + 10.3923i −0.302660 + 0.524222i
\(394\) 0 0
\(395\) 0 0
\(396\) −3.00000 + 1.73205i −0.150756 + 0.0870388i
\(397\) 30.0000 17.3205i 1.50566 0.869291i 0.505678 0.862722i \(-0.331242\pi\)
0.999978 0.00656933i \(-0.00209110\pi\)
\(398\) 27.7128i 1.38912i
\(399\) 6.00000 + 10.3923i 0.300376 + 0.520266i
\(400\) 12.5000 21.6506i 0.625000 1.08253i
\(401\) 6.00000 + 3.46410i 0.299626 + 0.172989i 0.642275 0.766475i \(-0.277991\pi\)
−0.342649 + 0.939463i \(0.611324\pi\)
\(402\) −18.0000 −0.897758
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) −18.0000 + 31.1769i −0.893325 + 1.54728i
\(407\) −12.0000 20.7846i −0.594818 1.03025i
\(408\) 10.3923i 0.514496i
\(409\) −24.0000 + 13.8564i −1.18672 + 0.685155i −0.957560 0.288233i \(-0.906932\pi\)
−0.229163 + 0.973388i \(0.573599\pi\)
\(410\) 0 0
\(411\) 20.7846i 1.02523i
\(412\) 4.00000 + 6.92820i 0.197066 + 0.341328i
\(413\) −18.0000 + 31.1769i −0.885722 + 1.53412i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.00000 0.195881
\(418\) 18.0000 + 10.3923i 0.880409 + 0.508304i
\(419\) 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) 34.6410i 1.68830i 0.536107 + 0.844150i \(0.319894\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 30.0000 17.3205i 1.46038 0.843149i
\(423\) −3.00000 + 1.73205i −0.145865 + 0.0842152i
\(424\) 10.3923i 0.504695i
\(425\) 15.0000 + 25.9808i 0.727607 + 1.26025i
\(426\) −3.00000 + 5.19615i −0.145350 + 0.251754i
\(427\) 6.00000 + 3.46410i 0.290360 + 0.167640i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −21.0000 12.1244i −1.01153 0.584010i −0.0998939 0.994998i \(-0.531850\pi\)
−0.911641 + 0.410988i \(0.865184\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) −17.0000 29.4449i −0.816968 1.41503i −0.907906 0.419173i \(-0.862320\pi\)
0.0909384 0.995857i \(-0.471013\pi\)
\(434\) 20.7846i 0.997693i
\(435\) 0 0
\(436\) 6.00000 3.46410i 0.287348 0.165900i
\(437\) 0 0
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) −5.00000 −0.238095
\(442\) 0 0
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 6.00000 + 3.46410i 0.284747 + 0.164399i
\(445\) 0 0
\(446\) −3.00000 5.19615i −0.142054 0.246045i
\(447\) 13.8564i 0.655386i
\(448\) −3.00000 + 1.73205i −0.141737 + 0.0818317i
\(449\) −6.00000 + 3.46410i −0.283158 + 0.163481i −0.634852 0.772634i \(-0.718939\pi\)
0.351694 + 0.936115i \(0.385606\pi\)
\(450\) 8.66025i 0.408248i
\(451\) 12.0000 + 20.7846i 0.565058 + 0.978709i
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) −9.00000 5.19615i −0.422857 0.244137i
\(454\) 30.0000 1.40797
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −24.0000 13.8564i −1.12267 0.648175i −0.180591 0.983558i \(-0.557801\pi\)
−0.942082 + 0.335383i \(0.891134\pi\)
\(458\) −6.00000 + 10.3923i −0.280362 + 0.485601i
\(459\) −3.00000 5.19615i −0.140028 0.242536i
\(460\) 0 0
\(461\) 12.0000 6.92820i 0.558896 0.322679i −0.193806 0.981040i \(-0.562083\pi\)
0.752702 + 0.658361i \(0.228750\pi\)
\(462\) −18.0000 + 10.3923i −0.837436 + 0.483494i
\(463\) 17.3205i 0.804952i 0.915430 + 0.402476i \(0.131850\pi\)
−0.915430 + 0.402476i \(0.868150\pi\)
\(464\) 15.0000 + 25.9808i 0.696358 + 1.20613i
\(465\) 0 0
\(466\) −9.00000 5.19615i −0.416917 0.240707i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −36.0000 −1.66233
\(470\) 0 0
\(471\) 7.00000 12.1244i 0.322543 0.558661i
\(472\) 9.00000 + 15.5885i 0.414259 + 0.717517i
\(473\) 13.8564i 0.637118i
\(474\) −12.0000 + 6.92820i −0.551178 + 0.318223i
\(475\) −15.0000 + 8.66025i −0.688247 + 0.397360i
\(476\) 20.7846i 0.952661i
\(477\) −3.00000 5.19615i −0.137361 0.237915i
\(478\) −9.00000 + 15.5885i −0.411650 + 0.712999i
\(479\) −9.00000 5.19615i −0.411220 0.237418i 0.280094 0.959973i \(-0.409635\pi\)
−0.691314 + 0.722554i \(0.742968\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −24.0000 −1.09317
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.0227273 + 0.0393648i
\(485\) 0 0
\(486\) 1.73205i 0.0785674i
\(487\) −33.0000 + 19.0526i −1.49537 + 0.863354i −0.999986 0.00531860i \(-0.998307\pi\)
−0.495387 + 0.868672i \(0.664974\pi\)
\(488\) 3.00000 1.73205i 0.135804 0.0784063i
\(489\) 3.46410i 0.156652i
\(490\) 0 0
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) −6.00000 3.46410i −0.270501 0.156174i
\(493\) −36.0000 −1.62136
\(494\) 0 0
\(495\) 0 0
\(496\) 15.0000 + 8.66025i 0.673520 + 0.388857i
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) 3.00000 + 5.19615i 0.134433 + 0.232845i
\(499\) 10.3923i 0.465223i 0.972570 + 0.232612i \(0.0747271\pi\)
−0.972570 + 0.232612i \(0.925273\pi\)
\(500\) 0 0
\(501\) 15.0000 8.66025i 0.670151 0.386912i
\(502\) 20.7846i 0.927663i
\(503\) −12.0000 20.7846i −0.535054 0.926740i −0.999161 0.0409609i \(-0.986958\pi\)
0.464107 0.885779i \(-0.346375\pi\)
\(504\) −3.00000 + 5.19615i −0.133631 + 0.231455i
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) −36.0000 20.7846i −1.59567 0.921262i −0.992308 0.123796i \(-0.960493\pi\)
−0.603364 0.797466i \(-0.706173\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) 3.00000 1.73205i 0.132453 0.0764719i
\(514\) −27.0000 + 15.5885i −1.19092 + 0.687577i
\(515\) 0 0
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) −6.00000 + 10.3923i −0.263880 + 0.457053i
\(518\) 36.0000 + 20.7846i 1.58175 + 0.913223i
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 9.00000 + 5.19615i 0.393919 + 0.227429i
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) −6.00000 10.3923i −0.262111 0.453990i
\(525\) 17.3205i 0.755929i
\(526\) 36.0000 20.7846i 1.56967 0.906252i
\(527\) −18.0000 + 10.3923i −0.784092 + 0.452696i
\(528\) 17.3205i 0.753778i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 9.00000 + 5.19615i 0.390567 + 0.225494i
\(532\) −12.0000 −0.520266
\(533\) 0 0
\(534\) −12.0000 −0.519291
\(535\) 0 0
\(536\) −9.00000 + 15.5885i −0.388741 + 0.673319i
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) 10.3923i 0.448044i
\(539\) −15.0000 + 8.66025i −0.646096 + 0.373024i
\(540\) 0 0
\(541\) 6.92820i 0.297867i −0.988847 0.148933i \(-0.952416\pi\)
0.988847 0.148933i \(-0.0475840\pi\)
\(542\) 9.00000 + 15.5885i 0.386583 + 0.669582i
\(543\) −5.00000 + 8.66025i −0.214571 + 0.371647i
\(544\) 27.0000 + 15.5885i 1.15762 + 0.668350i
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 18.0000 + 10.3923i 0.768922 + 0.443937i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) −15.0000 25.9808i −0.639602 1.10782i
\(551\) 20.7846i 0.885454i
\(552\) 0 0
\(553\) −24.0000 + 13.8564i −1.02058 + 0.589234i
\(554\) 17.3205i 0.735878i
\(555\) 0 0
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 12.0000 + 6.92820i 0.508456 + 0.293557i 0.732199 0.681091i \(-0.238494\pi\)
−0.223743 + 0.974648i \(0.571827\pi\)
\(558\) 6.00000 0.254000
\(559\) 0 0
\(560\) 0 0
\(561\) −18.0000 10.3923i −0.759961 0.438763i
\(562\) 6.00000 10.3923i 0.253095 0.438373i
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) 3.46410i 0.145865i
\(565\) 0 0
\(566\) −6.00000 + 3.46410i −0.252199 + 0.145607i
\(567\) 3.46410i 0.145479i
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) −36.0000 20.7846i −1.50261 0.867533i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −28.5000 + 16.4545i −1.18544 + 0.684416i
\(579\) 0 0
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) 12.0000 20.7846i 0.497416 0.861550i
\(583\) −18.0000 10.3923i −0.745484 0.430405i
\(584\) 0 0
\(585\) 0 0
\(586\) −48.0000 −1.98286
\(587\) 9.00000 + 5.19615i 0.371470 + 0.214468i 0.674100 0.738640i \(-0.264532\pi\)
−0.302631 + 0.953108i \(0.597865\pi\)
\(588\) 2.50000 4.33013i 0.103098 0.178571i
\(589\) −6.00000 10.3923i −0.247226 0.428207i
\(590\) 0 0
\(591\) 0 0
\(592\) 30.0000 17.3205i 1.23299 0.711868i
\(593\) 6.92820i 0.284507i −0.989830 0.142254i \(-0.954565\pi\)
0.989830 0.142254i \(-0.0454349\pi\)
\(594\) 3.00000 + 5.19615i 0.123091 + 0.213201i
\(595\) 0 0
\(596\) −12.0000 6.92820i −0.491539 0.283790i
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −7.50000 4.33013i −0.306186 0.176777i
\(601\) −5.00000 + 8.66025i −0.203954 + 0.353259i −0.949799 0.312861i \(-0.898713\pi\)
0.745845 + 0.666120i \(0.232046\pi\)
\(602\) 12.0000 + 20.7846i 0.489083 + 0.847117i
\(603\) 10.3923i 0.423207i
\(604\) 9.00000 5.19615i 0.366205 0.211428i
\(605\) 0 0
\(606\) 10.3923i 0.422159i
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) −9.00000 + 15.5885i −0.364998 + 0.632195i
\(609\) 18.0000 + 10.3923i 0.729397 + 0.421117i
\(610\) 0 0
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) −18.0000 10.3923i −0.727013 0.419741i 0.0903153 0.995913i \(-0.471213\pi\)
−0.817328 + 0.576172i \(0.804546\pi\)
\(614\) −9.00000 + 15.5885i −0.363210 + 0.629099i
\(615\) 0 0
\(616\) 20.7846i 0.837436i
\(617\) 6.00000 3.46410i 0.241551 0.139459i −0.374338 0.927292i \(-0.622130\pi\)
0.615889 + 0.787833i \(0.288797\pi\)
\(618\) 12.0000 6.92820i 0.482711 0.278693i
\(619\) 31.1769i 1.25311i −0.779379 0.626553i \(-0.784465\pi\)
0.779379 0.626553i \(-0.215535\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −24.0000 −0.961540
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 15.0000 + 8.66025i 0.599521 + 0.346133i
\(627\) 6.00000 10.3923i 0.239617 0.415029i
\(628\) 7.00000 + 12.1244i 0.279330 + 0.483814i
\(629\) 41.5692i 1.65747i
\(630\) 0 0
\(631\) −33.0000 + 19.0526i −1.31371 + 0.758470i −0.982708 0.185160i \(-0.940720\pi\)
−0.331001 + 0.943630i \(0.607386\pi\)
\(632\) 13.8564i 0.551178i
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) 12.0000 20.7846i 0.476581 0.825462i
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 36.0000 1.42525
\(639\) 3.00000 + 1.73205i 0.118678 + 0.0685189i
\(640\) 0 0
\(641\) 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i \(-0.128860\pi\)
−0.800678 + 0.599095i \(0.795527\pi\)
\(642\) 20.7846i 0.820303i
\(643\) 9.00000 5.19615i 0.354925 0.204916i −0.311927 0.950106i \(-0.600974\pi\)
0.666852 + 0.745190i \(0.267641\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −18.0000 31.1769i −0.708201 1.22664i
\(647\) 12.0000 20.7846i 0.471769 0.817127i −0.527710 0.849425i \(-0.676949\pi\)
0.999478 + 0.0322975i \(0.0102824\pi\)
\(648\) 1.50000 + 0.866025i 0.0589256 + 0.0340207i
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) −3.00000 1.73205i −0.117489 0.0678323i
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) −6.00000 10.3923i −0.234619 0.406371i
\(655\) 0 0
\(656\) −30.0000 + 17.3205i −1.17130 + 0.676252i
\(657\) 0 0
\(658\) 20.7846i 0.810268i
\(659\) −6.00000 10.3923i −0.233727 0.404827i 0.725175 0.688565i \(-0.241759\pi\)
−0.958902 + 0.283738i \(0.908425\pi\)
\(660\) 0 0
\(661\) −18.0000 10.3923i −0.700119 0.404214i 0.107273 0.994230i \(-0.465788\pi\)
−0.807392 + 0.590016i \(0.799121\pi\)
\(662\) −6.00000 −0.233197
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 6.00000 10.3923i 0.232495 0.402694i
\(667\) 0 0
\(668\) 17.3205i 0.670151i
\(669\) −3.00000 + 1.73205i −0.115987 + 0.0669650i
\(670\) 0 0
\(671\) 6.92820i 0.267460i
\(672\) −9.00000 15.5885i −0.347183 0.601338i
\(673\) 23.0000 39.8372i 0.886585 1.53561i 0.0426985 0.999088i \(-0.486405\pi\)
0.843886 0.536522i \(-0.180262\pi\)
\(674\) −21.0000 12.1244i −0.808890 0.467013i
\(675\) −5.00000 −0.192450
\(676\) 0 0
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 9.00000 + 5.19615i 0.345643 + 0.199557i
\(679\) 24.0000 41.5692i 0.921035 1.59528i
\(680\) 0 0
\(681\) 17.3205i 0.663723i
\(682\) 18.0000 10.3923i 0.689256 0.397942i
\(683\) 27.0000 15.5885i 1.03313 0.596476i 0.115248 0.993337i \(-0.463234\pi\)
0.917879 + 0.396861i \(0.129901\pi\)
\(684\) 3.46410i 0.132453i
\(685\) 0 0
\(686\) −6.00000 + 10.3923i −0.229081 + 0.396780i
\(687\) 6.00000 + 3.46410i 0.228914 + 0.132164i
\(688\) 20.0000 0.762493
\(689\) 0 0
\(690\) 0 0
\(691\) 39.0000 + 22.5167i 1.48363 + 0.856574i 0.999827 0.0186028i \(-0.00592180\pi\)
0.483803 + 0.875177i \(0.339255\pi\)
\(692\) −9.00000 + 15.5885i −0.342129 + 0.592584i
\(693\) 6.00000 + 10.3923i 0.227921 + 0.394771i
\(694\) 62.3538i 2.36692i
\(695\) 0 0
\(696\) 9.00000 5.19615i 0.341144 0.196960i
\(697\) 41.5692i 1.57455i
\(698\) −6.00000 10.3923i −0.227103 0.393355i
\(699\) −3.00000 + 5.19615i −0.113470 + 0.196537i
\(700\) 15.0000 + 8.66025i 0.566947 + 0.327327i
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 3.00000 + 1.73205i 0.113067 + 0.0652791i
\(705\) 0 0
\(706\) 30.0000 + 51.9615i 1.12906 + 1.95560i
\(707\) 20.7846i 0.781686i
\(708\) −9.00000 + 5.19615i −0.338241 + 0.195283i
\(709\) 6.00000 3.46410i 0.225335 0.130097i −0.383083 0.923714i \(-0.625138\pi\)
0.608418 + 0.793617i \(0.291804\pi\)
\(710\) 0 0
\(711\) 4.00000 + 6.92820i 0.150012 + 0.259828i
\(712\) −6.00000 + 10.3923i −0.224860 + 0.389468i
\(713\) 0 0
\(714\) 36.0000 1.34727
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 9.00000 + 5.19615i 0.336111 + 0.194054i
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) −12.0000 20.7846i −0.447524 0.775135i 0.550700 0.834703i \(-0.314361\pi\)
−0.998224 + 0.0595683i \(0.981028\pi\)
\(720\) 0 0
\(721\) 24.0000 13.8564i 0.893807 0.516040i
\(722\) −10.5000 + 6.06218i −0.390770 + 0.225611i
\(723\) 13.8564i 0.515325i
\(724\) −5.00000 8.66025i −0.185824 0.321856i
\(725\) −15.0000 + 25.9808i −0.557086 + 0.964901i
\(726\) 1.50000 + 0.866025i 0.0556702 + 0.0321412i
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 1.00000 + 1.73205i 0.0369611 + 0.0640184i
\(733\) 34.6410i 1.27950i −0.768585 0.639748i \(-0.779039\pi\)
0.768585 0.639748i \(-0.220961\pi\)
\(734\) 24.0000 13.8564i 0.885856 0.511449i
\(735\) 0 0
\(736\) 0 0
\(737\) 18.0000 + 31.1769i 0.663039 + 1.14842i
\(738\) −6.00000 + 10.3923i −0.220863 + 0.382546i
\(739\) −33.0000 19.0526i −1.21392 0.700860i −0.250313 0.968165i \(-0.580533\pi\)
−0.963612 + 0.267305i \(0.913867\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 36.0000 1.32160
\(743\) 3.00000 + 1.73205i 0.110059 + 0.0635428i 0.554019 0.832504i \(-0.313093\pi\)
−0.443960 + 0.896047i \(0.646427\pi\)
\(744\) 3.00000 5.19615i 0.109985 0.190500i
\(745\) 0 0
\(746\) 38.1051i 1.39513i
\(747\) 3.00000 1.73205i 0.109764 0.0633724i
\(748\) 18.0000 10.3923i 0.658145 0.379980i
\(749\) 41.5692i 1.51891i
\(750\) 0 0
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) −15.0000 8.66025i −0.546994 0.315807i
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) 0 0
\(756\) −3.00000 1.73205i −0.109109 0.0629941i
\(757\) −11.0000 + 19.0526i −0.399802 + 0.692477i −0.993701 0.112062i \(-0.964254\pi\)
0.593899 + 0.804539i \(0.297588\pi\)
\(758\) 15.0000 + 25.9808i 0.544825 + 0.943664i
\(759\) 0 0
\(760\) 0 0
\(761\) 42.0000 24.2487i 1.52250 0.879015i 0.522852 0.852423i \(-0.324868\pi\)
0.999646 0.0265919i \(-0.00846546\pi\)
\(762\) 13.8564i 0.501965i
\(763\) −12.0000 20.7846i −0.434429 0.752453i
\(764\) 12.0000 20.7846i 0.434145 0.751961i
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) 0 0
\(768\) −19.0000 −0.685603
\(769\) 24.0000 + 13.8564i 0.865462 + 0.499675i 0.865838 0.500325i \(-0.166786\pi\)
−0.000375472 1.00000i \(0.500120\pi\)
\(770\) 0 0
\(771\) 9.00000 + 15.5885i 0.324127 + 0.561405i
\(772\) 0 0
\(773\) 12.0000 6.92820i 0.431610 0.249190i −0.268422 0.963301i \(-0.586502\pi\)
0.700032 + 0.714111i \(0.253169\pi\)
\(774\) 6.00000 3.46410i 0.215666 0.124515i
\(775\) 17.3205i 0.622171i
\(776\) −12.0000 20.7846i −0.430775 0.746124i
\(777\) 12.0000 20.7846i 0.430498 0.745644i
\(778\) −27.0000 15.5885i −0.967997 0.558873i
\(779\) 24.0000 0.859889
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) 3.00000 5.19615i 0.107211 0.185695i
\(784\) −12.5000 21.6506i −0.446429 0.773237i
\(785\) 0