Properties

Label 1134.2.h.p.109.1
Level $1134$
Weight $2$
Character 1134.109
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.109
Dual form 1134.2.h.p.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{10} +3.00000 q^{11} +(2.00000 - 3.46410i) q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +4.00000 q^{25} +(-2.00000 - 3.46410i) q^{26} +(-0.500000 + 2.59808i) q^{28} +(-4.50000 - 7.79423i) q^{29} +(0.500000 + 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.00000 - 5.19615i) q^{35} +(-4.00000 - 6.92820i) q^{37} +4.00000 q^{38} -3.00000 q^{40} +(5.00000 + 8.66025i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(3.00000 - 5.19615i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{50} -4.00000 q^{52} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(2.00000 + 1.73205i) q^{56} -9.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-7.50000 + 2.59808i) q^{70} -6.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} -8.00000 q^{74} +(2.00000 - 3.46410i) q^{76} +(-6.00000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(4.50000 + 7.79423i) q^{83} +10.0000 q^{86} -3.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(0.500000 + 0.866025i) q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + 6q^{5} - 4q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + 6q^{5} - 4q^{7} - 2q^{8} + 3q^{10} + 6q^{11} + 4q^{13} - 5q^{14} - q^{16} + 4q^{19} - 3q^{20} + 3q^{22} + 8q^{25} - 4q^{26} - q^{28} - 9q^{29} + q^{31} + q^{32} - 12q^{35} - 8q^{37} + 8q^{38} - 6q^{40} + 10q^{43} - 3q^{44} + 6q^{47} + 2q^{49} + 4q^{50} - 8q^{52} + 3q^{53} + 18q^{55} + 4q^{56} - 18q^{58} - 3q^{59} + 10q^{61} + 2q^{62} + 2q^{64} + 12q^{65} + 10q^{67} - 15q^{70} - 12q^{71} - 2q^{73} - 16q^{74} + 4q^{76} - 12q^{77} + q^{79} - 3q^{80} + 9q^{83} + 20q^{86} - 6q^{88} - 6q^{89} - 20q^{91} - 6q^{94} + 12q^{95} + q^{97} + 13q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 2.00000 3.46410i 0.554700 0.960769i −0.443227 0.896410i \(-0.646166\pi\)
0.997927 0.0643593i \(-0.0205004\pi\)
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 0 0
\(16\) −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 0
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) −1.50000 2.59808i −0.335410 0.580948i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −2.00000 3.46410i −0.392232 0.679366i
\(27\) 0 0
\(28\) −0.500000 + 2.59808i −0.0944911 + 0.490990i
\(29\) −4.50000 7.79423i −0.835629 1.44735i −0.893517 0.449029i \(-0.851770\pi\)
0.0578882 0.998323i \(-0.481563\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) −6.00000 5.19615i −1.01419 0.878310i
\(36\) 0 0
\(37\) −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) −1.50000 2.59808i −0.226134 0.391675i
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 2.00000 3.46410i 0.282843 0.489898i
\(51\) 0 0
\(52\) −4.00000 −0.554700
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) 0 0
\(58\) −9.00000 −1.18176
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 1.00000 0.127000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 0 0
\(67\) 5.00000 + 8.66025i 0.610847 + 1.05802i 0.991098 + 0.133135i \(0.0425044\pi\)
−0.380251 + 0.924883i \(0.624162\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −7.50000 + 2.59808i −0.896421 + 0.310530i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) −6.00000 5.19615i −0.683763 0.592157i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) 0 0
\(82\) 0 0
\(83\) 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 10.0000 1.07833
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) −10.0000 + 3.46410i −1.04828 + 0.363137i
\(92\) 0 0
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 6.00000 + 10.3923i 0.615587 + 1.06623i
\(96\) 0 0
\(97\) 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 6.50000 + 2.59808i 0.656599 + 0.262445i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −2.00000 + 3.46410i −0.196116 + 0.339683i
\(105\) 0 0
\(106\) −1.50000 2.59808i −0.145693 0.252347i
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) 4.50000 7.79423i 0.429058 0.743151i
\(111\) 0 0
\(112\) 2.50000 0.866025i 0.236228 0.0818317i
\(113\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.50000 + 7.79423i −0.417815 + 0.723676i
\(117\) 0 0
\(118\) −3.00000 −0.276172
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −5.00000 8.66025i −0.452679 0.784063i
\(123\) 0 0
\(124\) 0.500000 0.866025i 0.0449013 0.0777714i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −6.00000 10.3923i −0.526235 0.911465i
\(131\) −9.00000 −0.786334 −0.393167 0.919467i \(-0.628621\pi\)
−0.393167 + 0.919467i \(0.628621\pi\)
\(132\) 0 0
\(133\) 2.00000 10.3923i 0.173422 0.901127i
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 0 0
\(139\) −1.00000 + 1.73205i −0.0848189 + 0.146911i −0.905314 0.424743i \(-0.860365\pi\)
0.820495 + 0.571654i \(0.193698\pi\)
\(140\) −1.50000 + 7.79423i −0.126773 + 0.658733i
\(141\) 0 0
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) 6.00000 10.3923i 0.501745 0.869048i
\(144\) 0 0
\(145\) −13.5000 23.3827i −1.12111 1.94183i
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) 0 0
\(148\) −4.00000 + 6.92820i −0.328798 + 0.569495i
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) −2.00000 3.46410i −0.162221 0.280976i
\(153\) 0 0
\(154\) −7.50000 + 2.59808i −0.604367 + 0.209359i
\(155\) 1.50000 + 2.59808i 0.120483 + 0.208683i
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −0.500000 0.866025i −0.0397779 0.0688973i
\(159\) 0 0
\(160\) 1.50000 + 2.59808i 0.118585 + 0.205396i
\(161\) 0 0
\(162\) 0 0
\(163\) 8.00000 + 13.8564i 0.626608 + 1.08532i 0.988227 + 0.152992i \(0.0488907\pi\)
−0.361619 + 0.932326i \(0.617776\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 9.00000 0.698535
\(167\) −3.00000 + 5.19615i −0.232147 + 0.402090i −0.958440 0.285295i \(-0.907908\pi\)
0.726293 + 0.687386i \(0.241242\pi\)
\(168\) 0 0
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) 0 0
\(171\) 0 0
\(172\) 5.00000 8.66025i 0.381246 0.660338i
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 0 0
\(175\) −8.00000 6.92820i −0.604743 0.523723i
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −2.00000 + 10.3923i −0.148250 + 0.770329i
\(183\) 0 0
\(184\) 0 0
\(185\) −12.0000 20.7846i −0.882258 1.52811i
\(186\) 0 0
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0 0
\(193\) 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i \(0.0730182\pi\)
−0.289980 + 0.957033i \(0.593649\pi\)
\(194\) 1.00000 0.0717958
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) −4.00000 −0.282843
\(201\) 0 0
\(202\) −9.00000 + 15.5885i −0.633238 + 1.09680i
\(203\) −4.50000 + 23.3827i −0.315838 + 1.64114i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 6.00000 + 10.3923i 0.415029 + 0.718851i
\(210\) 0 0
\(211\) −7.00000 + 12.1244i −0.481900 + 0.834675i −0.999784 0.0207756i \(-0.993386\pi\)
0.517884 + 0.855451i \(0.326720\pi\)
\(212\) −3.00000 −0.206041
\(213\) 0 0
\(214\) 3.00000 0.205076
\(215\) 15.0000 + 25.9808i 1.02299 + 1.77187i
\(216\) 0 0
\(217\) 0.500000 2.59808i 0.0339422 0.176369i
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) 0 0
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) 0 0
\(222\) 0 0
\(223\) 9.50000 + 16.4545i 0.636167 + 1.10187i 0.986267 + 0.165161i \(0.0528144\pi\)
−0.350100 + 0.936713i \(0.613852\pi\)
\(224\) 0.500000 2.59808i 0.0334077 0.173591i
\(225\) 0 0
\(226\) 0 0
\(227\) −27.0000 −1.79205 −0.896026 0.444001i \(-0.853559\pi\)
−0.896026 + 0.444001i \(0.853559\pi\)
\(228\) 0 0
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.50000 + 7.79423i 0.295439 + 0.511716i
\(233\) 12.0000 + 20.7846i 0.786146 + 1.36165i 0.928312 + 0.371802i \(0.121260\pi\)
−0.142166 + 0.989843i \(0.545407\pi\)
\(234\) 0 0
\(235\) 9.00000 15.5885i 0.587095 1.01688i
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) 0 0
\(238\) 0 0
\(239\) 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157 −0.0322078 0.999481i \(-0.510254\pi\)
−0.0322078 + 0.999481i \(0.510254\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) 3.00000 + 20.7846i 0.191663 + 1.32788i
\(246\) 0 0
\(247\) 16.0000 1.01806
\(248\) −0.500000 0.866025i −0.0317500 0.0549927i
\(249\) 0 0
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 2.50000 4.33013i 0.156864 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) −4.00000 + 20.7846i −0.248548 + 1.29149i
\(260\) −12.0000 −0.744208
\(261\) 0 0
\(262\) −4.50000 + 7.79423i −0.278011 + 0.481529i
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) 0 0
\(265\) 4.50000 7.79423i 0.276433 0.478796i
\(266\) −8.00000 6.92820i −0.490511 0.424795i
\(267\) 0 0
\(268\) 5.00000 8.66025i 0.305424 0.529009i
\(269\) −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i \(0.387814\pi\)
−0.985389 + 0.170321i \(0.945520\pi\)
\(270\) 0 0
\(271\) −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i \(-0.275099\pi\)
−0.983312 + 0.181928i \(0.941766\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 9.00000 15.5885i 0.543710 0.941733i
\(275\) 12.0000 0.723627
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 1.00000 + 1.73205i 0.0599760 + 0.103882i
\(279\) 0 0
\(280\) 6.00000 + 5.19615i 0.358569 + 0.310530i
\(281\) −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i \(-0.223942\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) −6.00000 10.3923i −0.354787 0.614510i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −27.0000 −1.58549
\(291\) 0 0
\(292\) 2.00000 0.117041
\(293\) −16.5000 + 28.5788i −0.963940 + 1.66959i −0.251505 + 0.967856i \(0.580925\pi\)
−0.712436 + 0.701737i \(0.752408\pi\)
\(294\) 0 0
\(295\) −4.50000 7.79423i −0.262000 0.453798i
\(296\) 4.00000 + 6.92820i 0.232495 + 0.402694i
\(297\) 0 0
\(298\) 9.00000 15.5885i 0.521356 0.903015i
\(299\) 0 0
\(300\) 0 0
\(301\) 5.00000 25.9808i 0.288195 1.49751i
\(302\) −0.500000 + 0.866025i −0.0287718 + 0.0498342i
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) 15.0000 25.9808i 0.858898 1.48765i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) −1.50000 + 7.79423i −0.0854704 + 0.444117i
\(309\) 0 0
\(310\) 3.00000 0.170389
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0 0
\(313\) 15.5000 26.8468i 0.876112 1.51747i 0.0205381 0.999789i \(-0.493462\pi\)
0.855574 0.517681i \(-0.173205\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) −4.50000 + 7.79423i −0.252745 + 0.437767i −0.964281 0.264883i \(-0.914667\pi\)
0.711535 + 0.702650i \(0.248000\pi\)
\(318\) 0 0
\(319\) −13.5000 23.3827i −0.755855 1.30918i
\(320\) 3.00000 0.167705
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 8.00000 13.8564i 0.443760 0.768615i
\(326\) 16.0000 0.886158
\(327\) 0 0
\(328\) 0 0
\(329\) −15.0000 + 5.19615i −0.826977 + 0.286473i
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) 4.50000 7.79423i 0.246970 0.427764i
\(333\) 0 0
\(334\) 3.00000 + 5.19615i 0.164153 + 0.284321i
\(335\) 15.0000 + 25.9808i 0.819538 + 1.41948i
\(336\) 0 0
\(337\) 3.50000 6.06218i 0.190657 0.330228i −0.754811 0.655942i \(-0.772271\pi\)
0.945468 + 0.325714i \(0.105605\pi\)
\(338\) −3.00000 −0.163178
\(339\) 0 0
\(340\) 0 0
\(341\) 1.50000 + 2.59808i 0.0812296 + 0.140694i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −5.00000 8.66025i −0.269582 0.466930i
\(345\) 0 0
\(346\) 9.00000 + 15.5885i 0.483843 + 0.838041i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) −13.0000 22.5167i −0.695874 1.20529i −0.969885 0.243563i \(-0.921684\pi\)
0.274011 0.961727i \(-0.411649\pi\)
\(350\) −10.0000 + 3.46410i −0.534522 + 0.185164i
\(351\) 0 0
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 0 0
\(355\) −18.0000 −0.955341
\(356\) −3.00000 + 5.19615i −0.159000 + 0.275396i
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) −15.0000 25.9808i −0.791670 1.37121i −0.924932 0.380131i \(-0.875879\pi\)
0.133263 0.991081i \(-0.457455\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 4.00000 6.92820i 0.210235 0.364138i
\(363\) 0 0
\(364\) 8.00000 + 6.92820i 0.419314 + 0.363137i
\(365\) −3.00000 + 5.19615i −0.157027 + 0.271979i
\(366\) 0 0
\(367\) −19.0000 −0.991792 −0.495896 0.868382i \(-0.665160\pi\)
−0.495896 + 0.868382i \(0.665160\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −24.0000 −1.24770
\(371\) −7.50000 + 2.59808i −0.389381 + 0.134885i
\(372\) 0 0
\(373\) 8.00000 0.414224 0.207112 0.978317i \(-0.433593\pi\)
0.207112 + 0.978317i \(0.433593\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −36.0000 −1.85409
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 6.00000 10.3923i 0.307794 0.533114i
\(381\) 0 0
\(382\) 0 0
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) −18.0000 15.5885i −0.917365 0.794461i
\(386\) 19.0000 0.967075
\(387\) 0 0
\(388\) 0.500000 0.866025i 0.0253837 0.0439658i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) 0 0
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 1.50000 2.59808i 0.0754732 0.130723i
\(396\) 0 0
\(397\) 2.00000 + 3.46410i 0.100377 + 0.173858i 0.911840 0.410546i \(-0.134662\pi\)
−0.811463 + 0.584404i \(0.801328\pi\)
\(398\) 10.0000 + 17.3205i 0.501255 + 0.868199i
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 24.0000 1.19850 0.599251 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) 0 0
\(403\) 4.00000 0.199254
\(404\) 9.00000 + 15.5885i 0.447767 + 0.775555i
\(405\) 0 0
\(406\) 18.0000 + 15.5885i 0.893325 + 0.773642i
\(407\) −12.0000 20.7846i −0.594818 1.03025i
\(408\) 0 0
\(409\) 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i \(0.0454247\pi\)
−0.371750 + 0.928333i \(0.621242\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 6.92820i −0.197066 0.341328i
\(413\) −1.50000 + 7.79423i −0.0738102 + 0.383529i
\(414\) 0 0
\(415\) 13.5000 + 23.3827i 0.662689 + 1.14781i
\(416\) 4.00000 0.196116
\(417\) 0 0
\(418\) 12.0000 0.586939
\(419\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(420\) 0 0
\(421\) 11.0000 + 19.0526i 0.536107 + 0.928565i 0.999109 + 0.0422075i \(0.0134391\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 7.00000 + 12.1244i 0.340755 + 0.590204i
\(423\) 0 0
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) 0 0
\(426\) 0 0
\(427\) −25.0000 + 8.66025i −1.20983 + 0.419099i
\(428\) 1.50000 2.59808i 0.0725052 0.125583i
\(429\) 0 0
\(430\) 30.0000 1.44673
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) −2.00000 1.73205i −0.0960031 0.0831411i
\(435\) 0 0
\(436\) 14.0000 0.670478
\(437\) 0 0
\(438\) 0 0
\(439\) −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i \(0.481332\pi\)
−0.893843 + 0.448379i \(0.852001\pi\)
\(440\) −9.00000 −0.429058
\(441\) 0 0
\(442\) 0 0
\(443\) 16.5000 28.5788i 0.783939 1.35782i −0.145692 0.989330i \(-0.546541\pi\)
0.929631 0.368492i \(-0.120126\pi\)
\(444\) 0 0
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) 19.0000 0.899676
\(447\) 0 0
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −13.5000 + 23.3827i −0.633586 + 1.09740i
\(455\) −30.0000 + 10.3923i −1.40642 + 0.487199i
\(456\) 0 0
\(457\) 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) −2.00000 + 3.46410i −0.0934539 + 0.161867i
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i \(-0.920465\pi\)
0.270326 0.962769i \(-0.412869\pi\)
\(462\) 0 0
\(463\) −4.00000 + 6.92820i −0.185896 + 0.321981i −0.943878 0.330294i \(-0.892852\pi\)
0.757982 + 0.652275i \(0.226185\pi\)
\(464\) 9.00000 0.417815
\(465\) 0 0
\(466\) 24.0000 1.11178
\(467\) −18.0000 31.1769i −0.832941 1.44270i −0.895696 0.444667i \(-0.853322\pi\)
0.0627555 0.998029i \(-0.480011\pi\)
\(468\) 0 0
\(469\) 5.00000 25.9808i 0.230879 1.19968i
\(470\) −9.00000 15.5885i −0.415139 0.719042i
\(471\) 0 0
\(472\) 1.50000 + 2.59808i 0.0690431 + 0.119586i
\(473\) 15.0000 + 25.9808i 0.689701 + 1.19460i
\(474\) 0 0
\(475\) 8.00000 + 13.8564i 0.367065 + 0.635776i
\(476\) 0 0
\(477\) 0 0
\(478\) −12.0000 20.7846i −0.548867 0.950666i
\(479\) −18.0000 −0.822441 −0.411220 0.911536i \(-0.634897\pi\)
−0.411220 + 0.911536i \(0.634897\pi\)
\(480\) 0 0
\(481\) −32.0000 −1.45907
\(482\) −0.500000 + 0.866025i −0.0227744 + 0.0394464i
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 1.50000 + 2.59808i 0.0681115 + 0.117973i
\(486\) 0 0
\(487\) −20.5000 + 35.5070i −0.928944 + 1.60898i −0.143851 + 0.989599i \(0.545949\pi\)
−0.785093 + 0.619378i \(0.787385\pi\)
\(488\) −5.00000 + 8.66025i −0.226339 + 0.392031i
\(489\) 0 0
\(490\) 19.5000 + 7.79423i 0.880920 + 0.352107i
\(491\) 16.5000 28.5788i 0.744635 1.28974i −0.205731 0.978609i \(-0.565957\pi\)
0.950365 0.311136i \(-0.100710\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 8.00000 13.8564i 0.359937 0.623429i
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 12.0000 + 10.3923i 0.538274 + 0.466159i
\(498\) 0 0
\(499\) 2.00000 0.0895323 0.0447661 0.998997i \(-0.485746\pi\)
0.0447661 + 0.998997i \(0.485746\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) 0 0
\(502\) 13.5000 23.3827i 0.602534 1.04362i
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −54.0000 −2.40297
\(506\) 0 0
\(507\) 0 0
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) −3.00000 −0.132973 −0.0664863 0.997787i \(-0.521179\pi\)
−0.0664863 + 0.997787i \(0.521179\pi\)
\(510\) 0 0
\(511\) 5.00000 1.73205i 0.221187 0.0766214i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 3.00000 5.19615i 0.132324 0.229192i
\(515\) 24.0000 1.05757
\(516\) 0 0
\(517\) 9.00000 15.5885i 0.395820 0.685580i
\(518\) 16.0000 + 13.8564i 0.703000 + 0.608816i
\(519\) 0 0
\(520\) −6.00000 + 10.3923i −0.263117 + 0.455733i
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) 0 0
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) 4.50000 + 7.79423i 0.196583 + 0.340492i
\(525\) 0 0
\(526\) −3.00000 + 5.19615i −0.130806 + 0.226563i
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) −4.50000 7.79423i −0.195468 0.338560i
\(531\) 0 0
\(532\) −10.0000 + 3.46410i −0.433555 + 0.150188i
\(533\) 0 0
\(534\) 0 0
\(535\) 4.50000 + 7.79423i 0.194552 + 0.336974i
\(536\) −5.00000 8.66025i −0.215967 0.374066i
\(537\) 0 0
\(538\) 10.5000 + 18.1865i 0.452687 + 0.784077i
\(539\) 3.00000 + 20.7846i 0.129219 + 0.895257i
\(540\) 0 0
\(541\) −13.0000 22.5167i −0.558914 0.968067i −0.997587 0.0694205i \(-0.977885\pi\)
0.438674 0.898646i \(-0.355448\pi\)
\(542\) −11.0000 −0.472490
\(543\) 0 0
\(544\) 0 0
\(545\) −21.0000 + 36.3731i −0.899541 + 1.55805i
\(546\) 0 0
\(547\) −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i \(-0.221375\pi\)
−0.938779 + 0.344519i \(0.888042\pi\)
\(548\) −9.00000 15.5885i −0.384461 0.665906i
\(549\) 0 0
\(550\) 6.00000 10.3923i 0.255841 0.443129i
\(551\) 18.0000 31.1769i 0.766826 1.32818i
\(552\) 0 0
\(553\) −2.50000 + 0.866025i −0.106311 + 0.0368271i
\(554\) 4.00000 6.92820i 0.169944 0.294351i
\(555\) 0 0
\(556\) 2.00000 0.0848189
\(557\) −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i \(-0.853578\pi\)
0.832496 + 0.554031i \(0.186911\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) 7.50000 2.59808i 0.316933 0.109789i
\(561\) 0 0
\(562\) −6.00000 −0.253095
\(563\) −19.5000 33.7750i −0.821827 1.42345i −0.904320 0.426855i \(-0.859622\pi\)
0.0824933 0.996592i \(-0.473712\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i \(-0.561165\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(570\) 0 0
\(571\) 17.0000 + 29.4449i 0.711428 + 1.23223i 0.964321 + 0.264735i \(0.0852845\pi\)
−0.252893 + 0.967494i \(0.581382\pi\)
\(572\) −12.0000 −0.501745
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −11.5000 + 19.9186i −0.478751 + 0.829222i −0.999703 0.0243645i \(-0.992244\pi\)
0.520952 + 0.853586i \(0.325577\pi\)
\(578\) 17.0000 0.707107
\(579\) 0 0
\(580\) −13.5000 + 23.3827i −0.560557 + 0.970913i
\(581\) 4.50000 23.3827i 0.186691 0.970077i
\(582\) 0 0
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 1.00000 1.73205i 0.0413803 0.0716728i
\(585\) 0 0
\(586\) 16.5000 + 28.5788i 0.681609 + 1.18058i
\(587\) −10.5000 18.1865i −0.433381 0.750639i 0.563781 0.825925i \(-0.309346\pi\)
−0.997162 + 0.0752860i \(0.976013\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) −9.00000 −0.370524
\(591\) 0 0
\(592\) 8.00000 0.328798
\(593\) −12.0000 20.7846i −0.492781 0.853522i 0.507184 0.861838i \(-0.330686\pi\)
−0.999965 + 0.00831589i \(0.997353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.00000 15.5885i −0.368654 0.638528i
\(597\) 0 0
\(598\) 0 0
\(599\) 9.00000 + 15.5885i 0.367730 + 0.636927i 0.989210 0.146503i \(-0.0468017\pi\)
−0.621480 + 0.783430i \(0.713468\pi\)
\(600\) 0 0
\(601\) −5.50000 9.52628i −0.224350 0.388585i 0.731774 0.681547i \(-0.238692\pi\)
−0.956124 + 0.292962i \(0.905359\pi\)
\(602\) −20.0000 17.3205i −0.815139 0.705931i
\(603\) 0 0
\(604\) 0.500000 + 0.866025i 0.0203447 + 0.0352381i
\(605\) −6.00000 −0.243935
\(606\) 0 0
\(607\) −7.00000 −0.284121 −0.142061 0.989858i \(-0.545373\pi\)
−0.142061 + 0.989858i \(0.545373\pi\)
\(608\) −2.00000 + 3.46410i −0.0811107 + 0.140488i
\(609\) 0 0
\(610\) −15.0000 25.9808i −0.607332 1.05193i
\(611\) −12.0000 20.7846i −0.485468 0.840855i
\(612\) 0 0
\(613\) 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) 0 0
\(616\) 6.00000 + 5.19615i 0.241747 + 0.209359i
\(617\) 3.00000 5.19615i 0.120775 0.209189i −0.799298 0.600935i \(-0.794795\pi\)
0.920074 + 0.391745i \(0.128129\pi\)
\(618\) 0 0
\(619\) −34.0000 −1.36658 −0.683288 0.730149i \(-0.739451\pi\)
−0.683288 + 0.730149i \(0.739451\pi\)
\(620\) 1.50000 2.59808i 0.0602414 0.104341i
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) −3.00000 + 15.5885i −0.120192 + 0.624538i
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −15.5000 26.8468i −0.619505 1.07301i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 0 0
\(630\) 0 0
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) −0.500000 + 0.866025i −0.0198889 + 0.0344486i
\(633\) 0 0
\(634\) 4.50000 + 7.79423i 0.178718 + 0.309548i
\(635\) 15.0000 0.595257
\(636\) 0 0
\(637\) 26.0000 + 10.3923i 1.03016 + 0.411758i
\(638\) −27.0000 −1.06894
\(639\) 0 0
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 0 0
\(643\) 17.0000 29.4449i 0.670415 1.16119i −0.307372 0.951589i \(-0.599450\pi\)
0.977787 0.209603i \(-0.0672170\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i \(-0.718214\pi\)
0.986916 + 0.161233i \(0.0515470\pi\)
\(648\) 0 0
\(649\) −4.50000 7.79423i −0.176640 0.305950i
\(650\) −8.00000 13.8564i −0.313786 0.543493i
\(651\) 0 0
\(652\) 8.00000 13.8564i 0.313304 0.542659i
\(653\) 3.00000 0.117399 0.0586995 0.998276i \(-0.481305\pi\)
0.0586995 + 0.998276i \(0.481305\pi\)
\(654\) 0 0
\(655\) −27.0000 −1.05498
\(656\) 0 0
\(657\) 0 0
\(658\) −3.00000 + 15.5885i −0.116952 + 0.607701i
\(659\) 12.0000 + 20.7846i 0.467454 + 0.809653i 0.999309 0.0371821i \(-0.0118382\pi\)
−0.531855 + 0.846836i \(0.678505\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 10.0000 + 17.3205i 0.388661 + 0.673181i
\(663\) 0 0
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) 6.00000 31.1769i 0.232670 1.20899i
\(666\) 0 0
\(667\) 0 0
\(668\) 6.00000 0.232147
\(669\) 0 0
\(670\) 30.0000 1.15900
\(671\) 15.0000 25.9808i 0.579069 1.00298i
\(672\) 0 0
\(673\) −14.5000 25.1147i −0.558934 0.968102i −0.997586 0.0694449i \(-0.977877\pi\)
0.438652 0.898657i \(-0.355456\pi\)
\(674\) −3.50000 6.06218i −0.134815 0.233506i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) 16.5000 28.5788i 0.634147 1.09837i −0.352549 0.935793i \(-0.614685\pi\)
0.986695 0.162581i \(-0.0519817\pi\)
\(678\) 0 0
\(679\) 0.500000 2.59808i 0.0191882 0.0997050i
\(680\) 0 0
\(681\) 0 0
\(682\) 3.00000 0.114876
\(683\) −16.5000 + 28.5788i −0.631355 + 1.09354i 0.355920 + 0.934516i \(0.384168\pi\)
−0.987275 + 0.159022i \(0.949166\pi\)
\(684\) 0 0
\(685\) 54.0000 2.06323
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 0 0
\(688\) −10.0000 −0.381246
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −3.00000 + 5.19615i −0.113796 + 0.197101i
\(696\) 0 0
\(697\) 0 0
\(698\) −26.0000 −0.984115
\(699\) 0 0
\(700\) −2.00000 + 10.3923i −0.0755929 + 0.392792i
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) 0 0
\(703\) 16.0000 27.7128i 0.603451 1.04521i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) 12.0000 20.7846i 0.451626 0.782239i
\(707\) 36.0000 + 31.1769i 1.35392 + 1.17253i
\(708\) 0 0
\(709\) 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) −9.00000 + 15.5885i −0.337764 + 0.585024i
\(711\) 0 0
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) 18.0000 31.1769i 0.673162 1.16595i
\(716\) 12.0000 0.448461
\(717\) 0 0
\(718\) −30.0000 −1.11959
\(719\) 9.00000 + 15.5885i 0.335643 + 0.581351i 0.983608 0.180319i \(-0.0577130\pi\)
−0.647965 + 0.761670i \(0.724380\pi\)
\(720\) 0 0
\(721\) −16.0000 13.8564i −0.595871 0.516040i
\(722\) −1.50000 2.59808i −0.0558242 0.0966904i
\(723\) 0 0
\(724\) −4.00000 6.92820i −0.148659 0.257485i
\(725\) −18.0000 31.1769i −0.668503 1.15788i
\(726\) 0 0
\(727\) 6.50000 + 11.2583i 0.241072 + 0.417548i 0.961020 0.276479i \(-0.0891678\pi\)
−0.719948 + 0.694028i \(0.755834\pi\)
\(728\) 10.0000 3.46410i 0.370625 0.128388i
\(729\) 0 0
\(730\) 3.00000 + 5.19615i 0.111035 + 0.192318i
\(731\) 0 0
\(732\) 0 0
\(733\) −10.0000 −0.369358 −0.184679 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) −9.50000 + 16.4545i −0.350651 + 0.607346i
\(735\) 0 0
\(736\) 0 0
\(737\) 15.0000 + 25.9808i 0.552532 + 0.957014i
\(738\) 0 0
\(739\) −25.0000 + 43.3013i −0.919640 + 1.59286i −0.119677 + 0.992813i \(0.538186\pi\)
−0.799962 + 0.600050i \(0.795147\pi\)
\(740\) −12.0000 + 20.7846i −0.441129 + 0.764057i
\(741\) 0 0
\(742\) −1.50000 + 7.79423i −0.0550667 + 0.286135i
\(743\) −21.0000 + 36.3731i −0.770415 + 1.33440i 0.166920 + 0.985970i \(0.446618\pi\)
−0.937336 + 0.348428i \(0.886716\pi\)
\(744\) 0 0
\(745\) 54.0000 1.97841
\(746\) 4.00000 6.92820i 0.146450 0.253660i
\(747\) 0 0
\(748\) 0 0
\(749\) 1.50000 7.79423i 0.0548088 0.284795i
\(750\) 0 0
\(751\) −7.00000 −0.255434 −0.127717 0.991811i \(-0.540765\pi\)
−0.127717 + 0.991811i \(0.540765\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −18.0000 + 31.1769i −0.655521 + 1.13540i
\(755\) −3.00000 −0.109181
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 4.00000 6.92820i 0.145287 0.251644i
\(759\) 0 0
\(760\) −6.00000 10.3923i −0.217643 0.376969i
\(761\) 12.0000 0.435000 0.217500 0.976060i \(-0.430210\pi\)
0.217500 + 0.976060i \(0.430210\pi\)
\(762\) 0 0
\(763\) 35.0000 12.1244i 1.26709 0.438931i
\(764\) 0 0
\(765\) 0 0
\(766\) 9.00000 15.5885i 0.325183 0.563234i
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) 9.50000 16.4545i 0.342579 0.593364i −0.642332 0.766426i \(-0.722033\pi\)
0.984911 + 0.173063i \(0.0553663\pi\)
\(770\) −22.5000 + 7.79423i −0.810844 + 0.280885i
\(771\) 0 0
\(772\) 9.50000 16.4545i 0.341912 0.592210i
\(773\) −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i \(-0.867747\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(774\) 0 0
\(775\) 2.00000 + 3.46410i 0.0718421 + 0.124434i
\(776\) −0.500000 0.866025i −0.0179490 0.0310885i
\(777\) 0 0
\(778\) −3.00000 + 5.19615i −0.107555 + 0.186291i
\(779\) 0 0
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 0 0
\(783\) 0 0
\(784\) −6.50000 2.59808i −0.232143 0.0927884i
\(785\) 6.00000 + 10.3923i 0.214149 + 0.370917i
\(786\) 0 0
\(787\) −25.0000 43.3013i −0.891154 1.54352i −0.838494 0.544911i \(-0.816563\pi\)
−0.0526599 0.998613i \(-0.516770\pi\)
\(788\) −3.00000 5.19615i −0.106871 0.185105i
\(789\) 0 0
\(790\) −1.50000 2.59808i −0.0533676 0.0924354i
\(791\) 0 0
\(792\) 0 0