Properties

Label 1134.2.h.p.541.1
Level $1134$
Weight $2$
Character 1134.541
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 541.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.541
Dual form 1134.2.h.p.109.1

$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

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

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 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) −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 0.0578882 + 0.998323i \(0.481563\pi\)
−0.893517 + 0.449029i \(0.851770\pi\)
\(30\) 0 0
\(31\) 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(32\) 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 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 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 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 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 −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 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 −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) 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 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −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 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) 0 0
\(82\) 0 0
\(83\) 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i \(-0.668890\pi\)
0.999976 + 0.00698436i \(0.00222321\pi\)
\(84\) 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 −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 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 −0.839525 0.543321i \(-0.817167\pi\)
0.890292 + 0.455389i \(0.150500\pi\)
\(98\) 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 −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(114\) 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 0.820495 0.571654i \(-0.193698\pi\)
−0.905314 + 0.424743i \(0.860365\pi\)
\(140\) −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 −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) −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 −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 9.00000 0.698535
\(167\) −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i \(-0.241242\pi\)
−0.958440 + 0.285295i \(0.907908\pi\)
\(168\) 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 −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 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 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0 0
\(193\) 9.50000 16.4545i 0.683825 1.18442i −0.289980 0.957033i \(-0.593649\pi\)
0.973805 0.227387i \(-0.0730182\pi\)
\(194\) 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 −0.965272 0.261245i \(-0.915867\pi\)
0.256391 0.966573i \(-0.417466\pi\)
\(200\) −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 0.517884 0.855451i \(-0.326720\pi\)
−0.999784 + 0.0207756i \(0.993386\pi\)
\(212\) −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 −0.350100 0.936713i \(-0.613852\pi\)
0.986267 0.165161i \(-0.0528144\pi\)
\(224\) 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 −0.142166 0.989843i \(-0.545407\pi\)
0.928312 0.371802i \(-0.121260\pi\)
\(234\) 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 0.934109 + 0.356988i \(0.116196\pi\)
−0.157893 + 0.987456i \(0.550470\pi\)
\(240\) 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 −0.985389 0.170321i \(-0.945520\pi\)
0.345192 0.938532i \(-0.387814\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) 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 −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) 0 0
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 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 −0.712436 0.701737i \(-0.752408\pi\)
−0.251505 0.967856i \(-0.580925\pi\)
\(294\) 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 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) 15.5000 + 26.8468i 0.876112 + 1.51747i 0.855574 + 0.517681i \(0.173205\pi\)
0.0205381 + 0.999789i \(0.493462\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) −4.50000 7.79423i −0.252745 0.437767i 0.711535 0.702650i \(-0.248000\pi\)
−0.964281 + 0.264883i \(0.914667\pi\)
\(318\) 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 −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 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 0.945468 0.325714i \(-0.105605\pi\)
−0.754811 + 0.655942i \(0.772271\pi\)
\(338\) −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 −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) −13.0000 + 22.5167i −0.695874 + 1.20529i 0.274011 + 0.961727i \(0.411649\pi\)
−0.969885 + 0.243563i \(0.921684\pi\)
\(350\) −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 0.133263 + 0.991081i \(0.457455\pi\)
−0.924932 + 0.380131i \(0.875879\pi\)
\(360\) 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 −0.811463 0.584404i \(-0.801328\pi\)
0.911840 + 0.410546i \(0.134662\pi\)
\(398\) 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 −0.371750 0.928333i \(-0.621242\pi\)
0.989835 0.142222i \(-0.0454247\pi\)
\(410\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) 11.0000 19.0526i 0.536107 0.928565i −0.463002 0.886357i \(-0.653228\pi\)
0.999109 0.0422075i \(-0.0134391\pi\)
\(422\) 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 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 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 −0.893843 0.448379i \(-0.852001\pi\)
0.0586141 0.998281i \(-0.481332\pi\)
\(440\) −9.00000 −0.429058
\(441\) 0 0
\(442\) 0 0
\(443\) 16.5000 + 28.5788i 0.783939 + 1.35782i 0.929631 + 0.368492i \(0.120126\pi\)
−0.145692 + 0.989330i \(0.546541\pi\)
\(444\) 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 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) −2.00000 3.46410i −0.0934539 0.161867i
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 + 25.9808i −0.698620 + 1.21004i 0.270326 + 0.962769i \(0.412869\pi\)
−0.968945 + 0.247276i \(0.920465\pi\)
\(462\) 0 0
\(463\) −4.00000 6.92820i −0.185896 0.321981i 0.757982 0.652275i \(-0.226185\pi\)
−0.943878 + 0.330294i \(0.892852\pi\)
\(464\) 9.00000 0.417815
\(465\) 0 0
\(466\) 24.0000 1.11178
\(467\) −18.0000 + 31.1769i −0.832941 + 1.44270i 0.0627555 + 0.998029i \(0.480011\pi\)
−0.895696 + 0.444667i \(0.853322\pi\)
\(468\) 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 −0.785093 0.619378i \(-0.787385\pi\)
−0.143851 0.989599i \(-0.545949\pi\)
\(488\) −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 0.950365 + 0.311136i \(0.100710\pi\)
−0.205731 + 0.978609i \(0.565957\pi\)
\(492\) 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 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 0 0
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) 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 0.438674 + 0.898646i \(0.355448\pi\)
−0.997587 + 0.0694205i \(0.977885\pi\)
\(542\) −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 −0.938779 0.344519i \(-0.888042\pi\)
0.767752 + 0.640747i \(0.221375\pi\)
\(548\) −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 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) 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 0.0824933 + 0.996592i \(0.473712\pi\)
−0.904320 + 0.426855i \(0.859622\pi\)
\(564\) 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 0.945573 + 0.325409i \(0.105502\pi\)
−0.190974 + 0.981595i \(0.561165\pi\)
\(570\) 0 0
\(571\) 17.0000 29.4449i 0.711428 1.23223i −0.252893 0.967494i \(-0.581382\pi\)
0.964321 0.264735i \(-0.0852845\pi\)
\(572\) −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 0.520952 0.853586i \(-0.325577\pi\)
−0.999703 + 0.0243645i \(0.992244\pi\)
\(578\) 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 −0.997162 0.0752860i \(-0.976013\pi\)
0.563781 + 0.825925i \(0.309346\pi\)
\(588\) 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 −0.999965 0.00831589i \(-0.997353\pi\)
0.507184 + 0.861838i \(0.330686\pi\)
\(594\) 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 −0.621480 0.783430i \(-0.713468\pi\)
0.989210 + 0.146503i \(0.0468017\pi\)
\(600\) 0 0
\(601\) −5.50000 + 9.52628i −0.224350 + 0.388585i −0.956124 0.292962i \(-0.905359\pi\)
0.731774 + 0.681547i \(0.238692\pi\)
\(602\) −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 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) 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 0.920074 0.391745i \(-0.128129\pi\)
−0.799298 + 0.600935i \(0.794795\pi\)
\(618\) 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 0.977787 + 0.209603i \(0.0672170\pi\)
−0.307372 + 0.951589i \(0.599450\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) 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 −0.531855 0.846836i \(-0.678505\pi\)
0.999309 + 0.0371821i \(0.0118382\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) 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 0.438652 + 0.898657i \(0.355456\pi\)
−0.997586 + 0.0694449i \(0.977877\pi\)
\(674\) −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 0.986695 + 0.162581i \(0.0519817\pi\)
−0.352549 + 0.935793i \(0.614685\pi\)
\(678\) 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 −0.987275 0.159022i \(-0.949166\pi\)
0.355920 0.934516i \(-0.384168\pi\)
\(684\) 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 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 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 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) −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 −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 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 −0.719948 0.694028i \(-0.755834\pi\)
0.961020 + 0.276479i \(0.0891678\pi\)
\(728\) 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 −0.799962 0.600050i \(-0.795147\pi\)
−0.119677 0.992813i \(-0.538186\pi\)
\(740\) −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 −0.937336 0.348428i \(-0.886716\pi\)
0.166920 0.985970i \(-0.446618\pi\)
\(744\) 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 0.984911 0.173063i \(-0.0553663\pi\)
−0.642332 + 0.766426i \(0.722033\pi\)
\(770\) −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 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) 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 −0.0526599 + 0.998613i \(0.516770\pi\)
−0.838494 + 0.544911i \(0.816563\pi\)
\(788\) −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