Properties

Label 1764.2.j.c.1177.1
Level $1764$
Weight $2$
Character 1764.1177
Analytic conductor $14.086$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1177.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1177
Dual form 1764.2.j.c.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(1.50000 + 2.59808i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(-1.50000 - 2.59808i) q^{13} -3.46410i q^{15} +7.00000 q^{17} +5.00000 q^{19} +(-2.00000 - 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} +5.19615i q^{27} +(0.500000 - 0.866025i) q^{29} +(1.50000 + 2.59808i) q^{31} +(-6.00000 + 3.46410i) q^{33} +11.0000 q^{37} -5.19615i q^{39} +(4.50000 + 7.79423i) q^{41} +(-2.50000 + 4.33013i) q^{43} +(3.00000 - 5.19615i) q^{45} +(-1.50000 + 2.59808i) q^{47} +(10.5000 + 6.06218i) q^{51} +3.00000 q^{53} +8.00000 q^{55} +(7.50000 + 4.33013i) q^{57} +(3.50000 + 6.06218i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-3.00000 + 5.19615i) q^{65} +(-6.50000 - 11.2583i) q^{67} -6.92820i q^{69} -8.00000 q^{71} +7.00000 q^{73} +(1.50000 - 0.866025i) q^{75} +(4.50000 - 7.79423i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-0.500000 + 0.866025i) q^{83} +(-7.00000 - 12.1244i) q^{85} +(1.50000 - 0.866025i) q^{87} +15.0000 q^{89} +5.19615i q^{93} +(-5.00000 - 8.66025i) q^{95} +(8.50000 - 14.7224i) q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} - 2q^{5} + 3q^{9} + O(q^{10}) \) \( 2q + 3q^{3} - 2q^{5} + 3q^{9} - 4q^{11} - 3q^{13} + 14q^{17} + 10q^{19} - 4q^{23} + q^{25} + q^{29} + 3q^{31} - 12q^{33} + 22q^{37} + 9q^{41} - 5q^{43} + 6q^{45} - 3q^{47} + 21q^{51} + 6q^{53} + 16q^{55} + 15q^{57} + 7q^{59} - 3q^{61} - 6q^{65} - 13q^{67} - 16q^{71} + 14q^{73} + 3q^{75} + 9q^{79} - 9q^{81} - q^{83} - 14q^{85} + 3q^{87} + 30q^{89} - 10q^{95} + 17q^{97} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 0 0
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943882i \(0.969911\pi\)
\(14\) 0 0
\(15\) 3.46410i 0.894427i
\(16\) 0 0
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 0 0
\(31\) 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i \(-0.0798387\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(32\) 0 0
\(33\) −6.00000 + 3.46410i −1.04447 + 0.603023i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11.0000 1.80839 0.904194 0.427121i \(-0.140472\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 5.19615i 0.832050i
\(40\) 0 0
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 0 0
\(43\) −2.50000 + 4.33013i −0.381246 + 0.660338i −0.991241 0.132068i \(-0.957838\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 3.00000 5.19615i 0.447214 0.774597i
\(46\) 0 0
\(47\) −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 10.5000 + 6.06218i 1.47029 + 0.848875i
\(52\) 0 0
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) 0 0
\(57\) 7.50000 + 4.33013i 0.993399 + 0.573539i
\(58\) 0 0
\(59\) 3.50000 + 6.06218i 0.455661 + 0.789228i 0.998726 0.0504625i \(-0.0160695\pi\)
−0.543065 + 0.839691i \(0.682736\pi\)
\(60\) 0 0
\(61\) −1.50000 + 2.59808i −0.192055 + 0.332650i −0.945931 0.324367i \(-0.894849\pi\)
0.753876 + 0.657017i \(0.228182\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 0 0
\(67\) −6.50000 11.2583i −0.794101 1.37542i −0.923408 0.383819i \(-0.874609\pi\)
0.129307 0.991605i \(-0.458725\pi\)
\(68\) 0 0
\(69\) 6.92820i 0.834058i
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 0 0
\(75\) 1.50000 0.866025i 0.173205 0.100000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 4.50000 7.79423i 0.506290 0.876919i −0.493684 0.869641i \(-0.664350\pi\)
0.999974 0.00727784i \(-0.00231663\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −0.500000 + 0.866025i −0.0548821 + 0.0950586i −0.892161 0.451717i \(-0.850812\pi\)
0.837279 + 0.546776i \(0.184145\pi\)
\(84\) 0 0
\(85\) −7.00000 12.1244i −0.759257 1.31507i
\(86\) 0 0
\(87\) 1.50000 0.866025i 0.160817 0.0928477i
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 5.19615i 0.538816i
\(94\) 0 0
\(95\) −5.00000 8.66025i −0.512989 0.888523i
\(96\) 0 0
\(97\) 8.50000 14.7224i 0.863044 1.49484i −0.00593185 0.999982i \(-0.501888\pi\)
0.868976 0.494854i \(-0.164778\pi\)
\(98\) 0 0
\(99\) −12.0000 −1.20605
\(100\) 0 0
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) 7.00000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) 0 0
\(111\) 16.5000 + 9.52628i 1.56611 + 0.904194i
\(112\) 0 0
\(113\) 0.500000 + 0.866025i 0.0470360 + 0.0814688i 0.888585 0.458712i \(-0.151689\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(114\) 0 0
\(115\) −4.00000 + 6.92820i −0.373002 + 0.646058i
\(116\) 0 0
\(117\) 4.50000 7.79423i 0.416025 0.720577i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 0 0
\(123\) 15.5885i 1.40556i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) −7.50000 + 4.33013i −0.660338 + 0.381246i
\(130\) 0 0
\(131\) 2.00000 + 3.46410i 0.174741 + 0.302660i 0.940072 0.340977i \(-0.110758\pi\)
−0.765331 + 0.643637i \(0.777425\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 9.00000 5.19615i 0.774597 0.447214i
\(136\) 0 0
\(137\) −7.00000 + 12.1244i −0.598050 + 1.03585i 0.395058 + 0.918656i \(0.370724\pi\)
−0.993109 + 0.117198i \(0.962609\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) −4.50000 + 2.59808i −0.378968 + 0.218797i
\(142\) 0 0
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) −2.00000 −0.166091
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 0 0
\(153\) 10.5000 + 18.1865i 0.848875 + 1.47029i
\(154\) 0 0
\(155\) 3.00000 5.19615i 0.240966 0.417365i
\(156\) 0 0
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 0 0
\(159\) 4.50000 + 2.59808i 0.356873 + 0.206041i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) 0 0
\(165\) 12.0000 + 6.92820i 0.934199 + 0.539360i
\(166\) 0 0
\(167\) −11.5000 19.9186i −0.889897 1.54135i −0.839996 0.542592i \(-0.817443\pi\)
−0.0499004 0.998754i \(-0.515890\pi\)
\(168\) 0 0
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 0 0
\(171\) 7.50000 + 12.9904i 0.573539 + 0.993399i
\(172\) 0 0
\(173\) 0.500000 0.866025i 0.0380143 0.0658427i −0.846392 0.532560i \(-0.821230\pi\)
0.884407 + 0.466717i \(0.154563\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.1244i 0.911322i
\(178\) 0 0
\(179\) −21.0000 −1.56961 −0.784807 0.619740i \(-0.787238\pi\)
−0.784807 + 0.619740i \(0.787238\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) −4.50000 + 2.59808i −0.332650 + 0.192055i
\(184\) 0 0
\(185\) −11.0000 19.0526i −0.808736 1.40077i
\(186\) 0 0
\(187\) −14.0000 + 24.2487i −1.02378 + 1.77324i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.50000 + 12.9904i −0.542681 + 0.939951i 0.456068 + 0.889945i \(0.349257\pi\)
−0.998749 + 0.0500060i \(0.984076\pi\)
\(192\) 0 0
\(193\) 0.500000 + 0.866025i 0.0359908 + 0.0623379i 0.883460 0.468507i \(-0.155208\pi\)
−0.847469 + 0.530845i \(0.821875\pi\)
\(194\) 0 0
\(195\) −9.00000 + 5.19615i −0.644503 + 0.372104i
\(196\) 0 0
\(197\) −26.0000 −1.85242 −0.926212 0.377004i \(-0.876954\pi\)
−0.926212 + 0.377004i \(0.876954\pi\)
\(198\) 0 0
\(199\) −13.0000 −0.921546 −0.460773 0.887518i \(-0.652428\pi\)
−0.460773 + 0.887518i \(0.652428\pi\)
\(200\) 0 0
\(201\) 22.5167i 1.58820i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 9.00000 15.5885i 0.628587 1.08875i
\(206\) 0 0
\(207\) 6.00000 10.3923i 0.417029 0.722315i
\(208\) 0 0
\(209\) −10.0000 + 17.3205i −0.691714 + 1.19808i
\(210\) 0 0
\(211\) 6.50000 + 11.2583i 0.447478 + 0.775055i 0.998221 0.0596196i \(-0.0189888\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 0 0
\(213\) −12.0000 6.92820i −0.822226 0.474713i
\(214\) 0 0
\(215\) 10.0000 0.681994
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.5000 + 6.06218i 0.709524 + 0.409644i
\(220\) 0 0
\(221\) −10.5000 18.1865i −0.706306 1.22336i
\(222\) 0 0
\(223\) 3.50000 6.06218i 0.234377 0.405953i −0.724714 0.689050i \(-0.758028\pi\)
0.959092 + 0.283096i \(0.0913615\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) 0 0
\(227\) 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −29.0000 −1.89985 −0.949927 0.312473i \(-0.898843\pi\)
−0.949927 + 0.312473i \(0.898843\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) 0 0
\(237\) 13.5000 7.79423i 0.876919 0.506290i
\(238\) 0 0
\(239\) 10.5000 + 18.1865i 0.679189 + 1.17639i 0.975226 + 0.221213i \(0.0710015\pi\)
−0.296037 + 0.955176i \(0.595665\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0 0
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.50000 12.9904i −0.477214 0.826558i
\(248\) 0 0
\(249\) −1.50000 + 0.866025i −0.0950586 + 0.0548821i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) 24.2487i 1.51851i
\(256\) 0 0
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) 0 0
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) −3.00000 5.19615i −0.184289 0.319197i
\(266\) 0 0
\(267\) 22.5000 + 12.9904i 1.37698 + 0.794998i
\(268\) 0 0
\(269\) −1.00000 −0.0609711 −0.0304855 0.999535i \(-0.509705\pi\)
−0.0304855 + 0.999535i \(0.509705\pi\)
\(270\) 0 0
\(271\) −3.00000 −0.182237 −0.0911185 0.995840i \(-0.529044\pi\)
−0.0911185 + 0.995840i \(0.529044\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) 0 0
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 0 0
\(279\) −4.50000 + 7.79423i −0.269408 + 0.466628i
\(280\) 0 0
\(281\) 8.50000 14.7224i 0.507067 0.878267i −0.492899 0.870087i \(-0.664063\pi\)
0.999967 0.00818015i \(-0.00260385\pi\)
\(282\) 0 0
\(283\) −0.500000 0.866025i −0.0297219 0.0514799i 0.850782 0.525519i \(-0.176129\pi\)
−0.880504 + 0.474039i \(0.842796\pi\)
\(284\) 0 0
\(285\) 17.3205i 1.02598i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) 25.5000 14.7224i 1.49484 0.863044i
\(292\) 0 0
\(293\) −13.5000 23.3827i −0.788678 1.36603i −0.926777 0.375613i \(-0.877432\pi\)
0.138098 0.990419i \(-0.455901\pi\)
\(294\) 0 0
\(295\) 7.00000 12.1244i 0.407556 0.705907i
\(296\) 0 0
\(297\) −18.0000 10.3923i −1.04447 0.603023i
\(298\) 0 0
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −3.00000 + 1.73205i −0.172345 + 0.0995037i
\(304\) 0 0
\(305\) 6.00000 0.343559
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 13.8564i 0.788263i
\(310\) 0 0
\(311\) 15.5000 + 26.8468i 0.878924 + 1.52234i 0.852523 + 0.522690i \(0.175072\pi\)
0.0264017 + 0.999651i \(0.491595\pi\)
\(312\) 0 0
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i \(-0.752000\pi\)
0.964281 + 0.264883i \(0.0853332\pi\)
\(318\) 0 0
\(319\) 2.00000 + 3.46410i 0.111979 + 0.193952i
\(320\) 0 0
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) 0 0
\(323\) 35.0000 1.94745
\(324\) 0 0
\(325\) −3.00000 −0.166410
\(326\) 0 0
\(327\) 10.5000 + 6.06218i 0.580651 + 0.335239i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 12.5000 21.6506i 0.687062 1.19003i −0.285722 0.958313i \(-0.592233\pi\)
0.972784 0.231714i \(-0.0744333\pi\)
\(332\) 0 0
\(333\) 16.5000 + 28.5788i 0.904194 + 1.56611i
\(334\) 0 0
\(335\) −13.0000 + 22.5167i −0.710266 + 1.23022i
\(336\) 0 0
\(337\) −1.50000 2.59808i −0.0817102 0.141526i 0.822274 0.569091i \(-0.192705\pi\)
−0.903985 + 0.427565i \(0.859372\pi\)
\(338\) 0 0
\(339\) 1.73205i 0.0940721i
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −12.0000 + 6.92820i −0.646058 + 0.373002i
\(346\) 0 0
\(347\) 7.50000 + 12.9904i 0.402621 + 0.697360i 0.994041 0.109003i \(-0.0347659\pi\)
−0.591420 + 0.806363i \(0.701433\pi\)
\(348\) 0 0
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 0 0
\(351\) 13.5000 7.79423i 0.720577 0.416025i
\(352\) 0 0
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 0 0
\(355\) 8.00000 + 13.8564i 0.424596 + 0.735422i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −31.0000 −1.63612 −0.818059 0.575135i \(-0.804950\pi\)
−0.818059 + 0.575135i \(0.804950\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 8.66025i 0.454545i
\(364\) 0 0
\(365\) −7.00000 12.1244i −0.366397 0.634618i
\(366\) 0 0
\(367\) −16.0000 + 27.7128i −0.835193 + 1.44660i 0.0586798 + 0.998277i \(0.481311\pi\)
−0.893873 + 0.448320i \(0.852022\pi\)
\(368\) 0 0
\(369\) −13.5000 + 23.3827i −0.702782 + 1.21725i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −11.0000 19.0526i −0.569558 0.986504i −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) 0 0
\(375\) −18.0000 10.3923i −0.929516 0.536656i
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.00000 13.8564i −0.408781 0.708029i 0.585973 0.810331i \(-0.300713\pi\)
−0.994753 + 0.102302i \(0.967379\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −15.0000 −0.762493
\(388\) 0 0
\(389\) −13.0000 + 22.5167i −0.659126 + 1.14164i 0.321716 + 0.946836i \(0.395740\pi\)
−0.980842 + 0.194804i \(0.937593\pi\)
\(390\) 0 0
\(391\) −14.0000 24.2487i −0.708010 1.22631i
\(392\) 0 0
\(393\) 6.92820i 0.349482i
\(394\) 0 0
\(395\) −18.0000 −0.905678
\(396\) 0 0
\(397\) −21.0000 −1.05396 −0.526980 0.849878i \(-0.676676\pi\)
−0.526980 + 0.849878i \(0.676676\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 0 0
\(403\) 4.50000 7.79423i 0.224161 0.388258i
\(404\) 0 0
\(405\) 18.0000 0.894427
\(406\) 0 0
\(407\) −22.0000 + 38.1051i −1.09050 + 1.88880i
\(408\) 0 0
\(409\) −11.5000 19.9186i −0.568638 0.984911i −0.996701 0.0811615i \(-0.974137\pi\)
0.428063 0.903749i \(-0.359196\pi\)
\(410\) 0 0
\(411\) −21.0000 + 12.1244i −1.03585 + 0.598050i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2.00000 0.0981761
\(416\) 0 0
\(417\) 8.66025i 0.424094i
\(418\) 0 0
\(419\) −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i \(-0.286076\pi\)
−0.989000 + 0.147918i \(0.952743\pi\)
\(420\) 0 0
\(421\) 4.50000 7.79423i 0.219317 0.379867i −0.735283 0.677761i \(-0.762951\pi\)
0.954599 + 0.297893i \(0.0962839\pi\)
\(422\) 0 0
\(423\) −9.00000 −0.437595
\(424\) 0 0
\(425\) 3.50000 6.06218i 0.169775 0.294059i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 18.0000 + 10.3923i 0.869048 + 0.501745i
\(430\) 0 0
\(431\) 39.0000 1.87856 0.939282 0.343146i \(-0.111493\pi\)
0.939282 + 0.343146i \(0.111493\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) −3.00000 1.73205i −0.143839 0.0830455i
\(436\) 0 0
\(437\) −10.0000 17.3205i −0.478365 0.828552i
\(438\) 0 0
\(439\) 10.5000 18.1865i 0.501138 0.867996i −0.498861 0.866682i \(-0.666248\pi\)
0.999999 0.00131415i \(-0.000418308\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.5000 25.1147i 0.688916 1.19324i −0.283273 0.959039i \(-0.591420\pi\)
0.972189 0.234198i \(-0.0752464\pi\)
\(444\) 0 0
\(445\) −15.0000 25.9808i −0.711068 1.23161i
\(446\) 0 0
\(447\) 10.3923i 0.491539i
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) −36.0000 −1.69517
\(452\) 0 0
\(453\) 12.0000 6.92820i 0.563809 0.325515i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15.5000 + 26.8468i −0.725059 + 1.25584i 0.233890 + 0.972263i \(0.424854\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 0 0
\(459\) 36.3731i 1.69775i
\(460\) 0 0
\(461\) −11.5000 + 19.9186i −0.535608 + 0.927701i 0.463525 + 0.886084i \(0.346584\pi\)
−0.999134 + 0.0416172i \(0.986749\pi\)
\(462\) 0 0
\(463\) 2.50000 + 4.33013i 0.116185 + 0.201238i 0.918253 0.395995i \(-0.129600\pi\)
−0.802068 + 0.597233i \(0.796267\pi\)
\(464\) 0 0
\(465\) 9.00000 5.19615i 0.417365 0.240966i
\(466\) 0 0
\(467\) 17.0000 0.786666 0.393333 0.919396i \(-0.371322\pi\)
0.393333 + 0.919396i \(0.371322\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 22.5167i 1.03751i
\(472\) 0 0
\(473\) −10.0000 17.3205i −0.459800 0.796398i
\(474\) 0 0
\(475\) 2.50000 4.33013i 0.114708 0.198680i
\(476\) 0 0
\(477\) 4.50000 + 7.79423i 0.206041 + 0.356873i
\(478\) 0 0
\(479\) 4.00000 6.92820i 0.182765 0.316558i −0.760056 0.649857i \(-0.774829\pi\)
0.942821 + 0.333300i \(0.108162\pi\)
\(480\) 0 0
\(481\) −16.5000 28.5788i −0.752335 1.30308i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −34.0000 −1.54386
\(486\) 0 0
\(487\) −1.00000 −0.0453143 −0.0226572 0.999743i \(-0.507213\pi\)
−0.0226572 + 0.999743i \(0.507213\pi\)
\(488\) 0 0
\(489\) −28.5000 16.4545i −1.28881 0.744097i
\(490\) 0 0
\(491\) 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i \(-0.101571\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(492\) 0 0
\(493\) 3.50000 6.06218i 0.157632 0.273027i
\(494\) 0 0
\(495\) 12.0000 + 20.7846i 0.539360 + 0.934199i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i \(-0.195204\pi\)
−0.907314 + 0.420455i \(0.861871\pi\)
\(500\) 0 0
\(501\) 39.8372i 1.77979i
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) 0 0
\(507\) 6.00000 3.46410i 0.266469 0.153846i
\(508\) 0 0
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 25.9808i 1.14708i
\(514\) 0 0
\(515\) −8.00000 + 13.8564i −0.352522 + 0.610586i
\(516\) 0 0
\(517\) −6.00000 10.3923i −0.263880 0.457053i
\(518\) 0 0
\(519\) 1.50000 0.866025i 0.0658427 0.0380143i
\(520\) 0 0
\(521\) 3.00000 0.131432 0.0657162 0.997838i \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) 0 0
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.5000 + 18.1865i 0.457387 + 0.792218i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) −10.5000 + 18.1865i −0.455661 + 0.789228i
\(532\) 0 0
\(533\) 13.5000 23.3827i 0.584750 1.01282i
\(534\) 0 0
\(535\) 3.00000 + 5.19615i 0.129701 + 0.224649i
\(536\) 0 0
\(537\) −31.5000 18.1865i −1.35933 0.784807i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −33.0000 −1.41878 −0.709390 0.704816i \(-0.751030\pi\)
−0.709390 + 0.704816i \(0.751030\pi\)
\(542\) 0 0
\(543\) −9.00000 5.19615i −0.386227 0.222988i
\(544\) 0 0
\(545\) −7.00000 12.1244i −0.299847 0.519350i
\(546\) 0 0
\(547\) −16.5000 + 28.5788i −0.705489 + 1.22194i 0.261026 + 0.965332i \(0.415939\pi\)
−0.966515 + 0.256611i \(0.917394\pi\)
\(548\) 0 0
\(549\) −9.00000 −0.384111
\(550\) 0 0
\(551\) 2.50000 4.33013i 0.106504 0.184470i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 38.1051i 1.61747i
\(556\) 0 0
\(557\) 11.0000 0.466085 0.233042 0.972467i \(-0.425132\pi\)
0.233042 + 0.972467i \(0.425132\pi\)
\(558\) 0 0
\(559\) 15.0000 0.634432
\(560\) 0 0
\(561\) −42.0000 + 24.2487i −1.77324 + 1.02378i
\(562\) 0 0
\(563\) −6.50000 11.2583i −0.273942 0.474482i 0.695925 0.718114i \(-0.254994\pi\)
−0.969868 + 0.243632i \(0.921661\pi\)
\(564\) 0 0
\(565\) 1.00000 1.73205i 0.0420703 0.0728679i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13.5000 + 23.3827i −0.565949 + 0.980253i 0.431011 + 0.902347i \(0.358157\pi\)
−0.996961 + 0.0779066i \(0.975176\pi\)
\(570\) 0 0
\(571\) 1.50000 + 2.59808i 0.0627730 + 0.108726i 0.895704 0.444651i \(-0.146672\pi\)
−0.832931 + 0.553377i \(0.813339\pi\)
\(572\) 0 0
\(573\) −22.5000 + 12.9904i −0.939951 + 0.542681i
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) 7.00000 0.291414 0.145707 0.989328i \(-0.453454\pi\)
0.145707 + 0.989328i \(0.453454\pi\)
\(578\) 0 0
\(579\) 1.73205i 0.0719816i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −6.00000 + 10.3923i −0.248495 + 0.430405i
\(584\) 0 0
\(585\) −18.0000 −0.744208
\(586\) 0 0
\(587\) −18.5000 + 32.0429i −0.763577 + 1.32255i 0.177419 + 0.984135i \(0.443225\pi\)
−0.940996 + 0.338418i \(0.890108\pi\)
\(588\) 0 0
\(589\) 7.50000 + 12.9904i 0.309032 + 0.535259i
\(590\) 0 0
\(591\) −39.0000 22.5167i −1.60425 0.926212i
\(592\) 0 0
\(593\) 27.0000 1.10876 0.554379 0.832265i \(-0.312956\pi\)
0.554379 + 0.832265i \(0.312956\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −19.5000 11.2583i −0.798082 0.460773i
\(598\) 0 0
\(599\) 1.50000 + 2.59808i 0.0612883 + 0.106155i 0.895042 0.445983i \(-0.147146\pi\)
−0.833753 + 0.552137i \(0.813812\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 0 0
\(603\) 19.5000 33.7750i 0.794101 1.37542i
\(604\) 0 0
\(605\) −5.00000 + 8.66025i −0.203279 + 0.352089i
\(606\) 0 0
\(607\) 24.0000 + 41.5692i 0.974130 + 1.68724i 0.682777 + 0.730627i \(0.260772\pi\)
0.291353 + 0.956616i \(0.405895\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.00000 0.364101
\(612\) 0 0
\(613\) −9.00000 −0.363507 −0.181753 0.983344i \(-0.558177\pi\)
−0.181753 + 0.983344i \(0.558177\pi\)
\(614\) 0 0
\(615\) 27.0000 15.5885i 1.08875 0.628587i
\(616\) 0 0
\(617\) −21.5000 37.2391i −0.865557 1.49919i −0.866493 0.499190i \(-0.833631\pi\)
0.000935233 1.00000i \(-0.499702\pi\)
\(618\) 0 0
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) 0 0
\(621\) 18.0000 10.3923i 0.722315 0.417029i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0 0
\(627\) −30.0000 + 17.3205i −1.19808 + 0.691714i
\(628\) 0 0
\(629\) 77.0000 3.07019
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) 22.5167i 0.894957i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −12.0000 20.7846i −0.474713 0.822226i
\(640\) 0 0
\(641\) 1.00000 1.73205i 0.0394976 0.0684119i −0.845601 0.533816i \(-0.820758\pi\)
0.885098 + 0.465404i \(0.154091\pi\)
\(642\) 0 0
\(643\) 6.50000 + 11.2583i 0.256335 + 0.443985i 0.965257 0.261301i \(-0.0841516\pi\)
−0.708922 + 0.705287i \(0.750818\pi\)
\(644\) 0 0
\(645\) 15.0000 + 8.66025i 0.590624 + 0.340997i
\(646\) 0 0
\(647\) 3.00000 0.117942 0.0589711 0.998260i \(-0.481218\pi\)
0.0589711 + 0.998260i \(0.481218\pi\)
\(648\) 0 0
\(649\) −28.0000 −1.09910
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) 0 0
\(655\) 4.00000 6.92820i 0.156293 0.270707i
\(656\) 0 0
\(657\) 10.5000 + 18.1865i 0.409644 + 0.709524i
\(658\) 0 0
\(659\) −12.5000 + 21.6506i −0.486931 + 0.843389i −0.999887 0.0150258i \(-0.995217\pi\)
0.512956 + 0.858415i \(0.328550\pi\)
\(660\) 0 0
\(661\) 8.50000 + 14.7224i 0.330612 + 0.572636i 0.982632 0.185565i \(-0.0594116\pi\)
−0.652020 + 0.758202i \(0.726078\pi\)
\(662\) 0 0
\(663\) 36.3731i 1.41261i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.00000 −0.154881
\(668\) 0 0
\(669\) 10.5000 6.06218i 0.405953 0.234377i
\(670\) 0 0
\(671\) −6.00000 10.3923i −0.231627 0.401190i
\(672\) 0 0
\(673\) 12.5000 21.6506i 0.481840 0.834571i −0.517943 0.855415i \(-0.673302\pi\)
0.999783 + 0.0208444i \(0.00663546\pi\)
\(674\) 0 0
\(675\) 4.50000 + 2.59808i 0.173205 + 0.100000i
\(676\) 0 0
\(677\) −13.5000 + 23.3827i −0.518847 + 0.898670i 0.480913 + 0.876768i \(0.340305\pi\)
−0.999760 + 0.0219013i \(0.993028\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 18.0000 10.3923i 0.689761 0.398234i
\(682\) 0 0
\(683\) −21.0000 −0.803543 −0.401771 0.915740i \(-0.631605\pi\)
−0.401771 + 0.915740i \(0.631605\pi\)
\(684\) 0 0
\(685\) 28.0000 1.06983
\(686\) 0 0
\(687\) 24.2487i 0.925146i
\(688\) 0 0
\(689\) −4.50000 7.79423i −0.171436 0.296936i
\(690\) 0 0
\(691\) −5.50000 + 9.52628i −0.209230 + 0.362397i −0.951472 0.307735i \(-0.900429\pi\)
0.742242 + 0.670132i \(0.233762\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.00000 8.66025i 0.189661 0.328502i
\(696\) 0 0
\(697\) 31.5000 + 54.5596i 1.19315 + 2.06659i
\(698\) 0 0
\(699\) −43.5000 25.1147i −1.64532 0.949927i
\(700\) 0 0
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 0 0
\(703\) 55.0000 2.07436
\(704\) 0 0
\(705\) 9.00000 + 5.19615i 0.338960 + 0.195698i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 12.5000 21.6506i 0.469447 0.813107i −0.529943 0.848034i \(-0.677787\pi\)
0.999390 + 0.0349269i \(0.0111198\pi\)
\(710\) 0 0
\(711\) 27.0000 1.01258
\(712\) 0 0
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 0 0
\(715\) −12.0000 20.7846i −0.448775 0.777300i
\(716\) 0 0
\(717\) 36.3731i 1.35838i
\(718\) 0 0
\(719\) −15.0000 −0.559406 −0.279703 0.960087i \(-0.590236\pi\)
−0.279703 + 0.960087i \(0.590236\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 15.0000 8.66025i 0.557856 0.322078i
\(724\) 0 0
\(725\) −0.500000 0.866025i −0.0185695 0.0321634i
\(726\) 0 0
\(727\) 23.5000 40.7032i 0.871567 1.50960i 0.0111912 0.999937i \(-0.496438\pi\)
0.860376 0.509661i \(-0.170229\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −17.5000 + 30.3109i −0.647261 + 1.12109i
\(732\) 0 0
\(733\) −15.0000 25.9808i −0.554038 0.959621i −0.997978 0.0635649i \(-0.979753\pi\)
0.443940 0.896056i \(-0.353580\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 52.0000 1.91544
\(738\) 0 0
\(739\) −21.0000 −0.772497 −0.386249 0.922395i \(-0.626229\pi\)
−0.386249 + 0.922395i \(0.626229\pi\)
\(740\) 0 0
\(741\) 25.9808i 0.954427i
\(742\) 0 0
\(743\) 4.50000 + 7.79423i 0.165089 + 0.285943i 0.936687 0.350168i \(-0.113876\pi\)
−0.771598 + 0.636111i \(0.780542\pi\)
\(744\) 0 0
\(745\) 6.00000 10.3923i 0.219823 0.380745i
\(746\) 0 0
\(747\) −3.00000 −0.109764
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 12.0000 + 20.7846i 0.437886 + 0.758441i 0.997526 0.0702946i \(-0.0223939\pi\)
−0.559640 + 0.828736i \(0.689061\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 0 0
\(759\) 24.0000 + 13.8564i 0.871145 + 0.502956i
\(760\) 0 0
\(761\) 1.00000 + 1.73205i 0.0362500 + 0.0627868i 0.883581 0.468278i \(-0.155125\pi\)
−0.847331 + 0.531065i \(0.821792\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 21.0000 36.3731i 0.759257 1.31507i
\(766\) 0 0
\(767\) 10.5000 18.1865i 0.379133 0.656678i
\(768\) 0 0
\(769\) 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) 0 0
\(771\) 31.1769i 1.12281i
\(772\) 0 0
\(773\) 23.0000 0.827253 0.413626 0.910447i \(-0.364262\pi\)
0.413626 + 0.910447i \(0.364262\pi\)
\(774\) 0 0
\(775\) 3.00000 0.107763
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 22.5000 + 38.9711i 0.806146 + 1.39629i
\(780\) 0 0
\(781\) 16.0000 27.7128i 0.572525 0.991642i
\(782\) 0 0
\(783\) 4.50000 + 2.59808i 0.160817 + 0.0928477i
\(784\) 0 0
\(785\) 13.0000 22.5167i 0.463990 0.803654i
\(786\) 0 0
\(787\) −10.5000 18.1865i −0.374285 0.648280i 0.615935 0.787797i \(-0.288778\pi\)
−0.990220 + 0.139517i \(0.955445\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 9.00000 0.319599
\(794\) 0 0
\(795\) 10.3923i 0.368577i
\(796\) 0 0
\(797\) −7.50000 12.9904i −0.265664 0.460143i 0.702074 0.712104i \(-0.252258\pi\)
−0.967737 + 0.251961i \(0.918924\pi\)
\(798\) 0 0
\(799\) −10.5000 + 18.1865i −0.371463 + 0.643393i