Properties

Label 135.2.e.a.91.1
Level $135$
Weight $2$
Character 135.91
Analytic conductor $1.078$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 135.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.07798042729\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 91.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 135.91
Dual form 135.2.e.a.46.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{7} +3.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{7} +3.00000 q^{8} -1.00000 q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.00000 - 1.73205i) q^{13} +(-1.50000 + 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} -4.00000 q^{17} -8.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{26} +3.00000 q^{28} +(-0.500000 - 0.866025i) q^{29} +(2.50000 - 4.33013i) q^{32} +(-2.00000 - 3.46410i) q^{34} -3.00000 q^{35} -4.00000 q^{37} +(-4.00000 - 6.92820i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(2.50000 - 4.33013i) q^{41} +(4.00000 + 6.92820i) q^{43} -2.00000 q^{44} +3.00000 q^{46} +(3.50000 + 6.06218i) q^{47} +(-1.00000 + 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-1.00000 - 1.73205i) q^{52} +2.00000 q^{53} +2.00000 q^{55} +(4.50000 + 7.79423i) q^{56} +(0.500000 - 0.866025i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-3.50000 - 6.06218i) q^{61} +7.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.50000 - 2.59808i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-1.50000 - 2.59808i) q^{70} -2.00000 q^{71} +4.00000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(3.00000 - 5.19615i) q^{77} +(3.00000 + 5.19615i) q^{79} -1.00000 q^{80} +5.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(2.00000 - 3.46410i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{88} +15.0000 q^{89} +6.00000 q^{91} +(-1.50000 - 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-1.00000 - 1.73205i) q^{97} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{4} - q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{4} - q^{5} + 3 q^{7} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{14} + q^{16} - 8 q^{17} - 16 q^{19} + q^{20} + 2 q^{22} + 3 q^{23} - q^{25} + 4 q^{26} + 6 q^{28} - q^{29} + 5 q^{32} - 4 q^{34} - 6 q^{35} - 8 q^{37} - 8 q^{38} - 3 q^{40} + 5 q^{41} + 8 q^{43} - 4 q^{44} + 6 q^{46} + 7 q^{47} - 2 q^{49} + q^{50} - 2 q^{52} + 4 q^{53} + 4 q^{55} + 9 q^{56} + q^{58} - 14 q^{59} - 7 q^{61} + 14 q^{64} + 2 q^{65} + 3 q^{67} - 4 q^{68} - 3 q^{70} - 4 q^{71} + 8 q^{73} - 4 q^{74} - 8 q^{76} + 6 q^{77} + 6 q^{79} - 2 q^{80} + 10 q^{82} + 9 q^{83} + 4 q^{85} - 8 q^{86} - 6 q^{88} + 30 q^{89} + 12 q^{91} - 3 q^{92} - 7 q^{94} + 8 q^{95} - 2 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(82\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 1.50000 + 2.59808i 0.566947 + 0.981981i 0.996866 + 0.0791130i \(0.0252088\pi\)
−0.429919 + 0.902867i \(0.641458\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) −1.50000 + 2.59808i −0.400892 + 0.694365i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 3.00000 0.566947
\(29\) −0.500000 0.866025i −0.0928477 0.160817i 0.815861 0.578249i \(-0.196264\pi\)
−0.908708 + 0.417432i \(0.862930\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 0 0
\(34\) −2.00000 3.46410i −0.342997 0.594089i
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) −4.00000 6.92820i −0.648886 1.12390i
\(39\) 0 0
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) 2.50000 4.33013i 0.390434 0.676252i −0.602072 0.798441i \(-0.705658\pi\)
0.992507 + 0.122189i \(0.0389915\pi\)
\(42\) 0 0
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i \(0.00388317\pi\)
−0.489398 + 0.872060i \(0.662783\pi\)
\(48\) 0 0
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 4.50000 + 7.79423i 0.601338 + 1.04155i
\(57\) 0 0
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) −7.00000 + 12.1244i −0.911322 + 1.57846i −0.0991242 + 0.995075i \(0.531604\pi\)
−0.812198 + 0.583382i \(0.801729\pi\)
\(60\) 0 0
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 0 0
\(70\) −1.50000 2.59808i −0.179284 0.310530i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −2.00000 3.46410i −0.232495 0.402694i
\(75\) 0 0
\(76\) −4.00000 + 6.92820i −0.458831 + 0.794719i
\(77\) 3.00000 5.19615i 0.341882 0.592157i
\(78\) 0 0
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 5.00000 0.552158
\(83\) 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
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) 0 0
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) −1.50000 2.59808i −0.156386 0.270868i
\(93\) 0 0
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −9.00000 15.5885i −0.895533 1.55111i −0.833143 0.553058i \(-0.813461\pi\)
−0.0623905 0.998052i \(-0.519872\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 3.00000 5.19615i 0.294174 0.509525i
\(105\) 0 0
\(106\) 1.00000 + 1.73205i 0.0971286 + 0.168232i
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 1.00000 + 1.73205i 0.0953463 + 0.165145i
\(111\) 0 0
\(112\) −1.50000 + 2.59808i −0.141737 + 0.245495i
\(113\) −4.00000 + 6.92820i −0.376288 + 0.651751i −0.990519 0.137376i \(-0.956133\pi\)
0.614231 + 0.789127i \(0.289466\pi\)
\(114\) 0 0
\(115\) 1.50000 + 2.59808i 0.139876 + 0.242272i
\(116\) −1.00000 −0.0928477
\(117\) 0 0
\(118\) −14.0000 −1.28880
\(119\) −6.00000 10.3923i −0.550019 0.952661i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 3.50000 6.06218i 0.316875 0.548844i
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.00000 −0.443678 −0.221839 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 0 0
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) −12.0000 20.7846i −1.04053 1.80225i
\(134\) 3.00000 0.259161
\(135\) 0 0
\(136\) −12.0000 −1.02899
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) −1.50000 + 2.59808i −0.126773 + 0.219578i
\(141\) 0 0
\(142\) −1.00000 1.73205i −0.0839181 0.145350i
\(143\) −4.00000 −0.334497
\(144\) 0 0
\(145\) 1.00000 0.0830455
\(146\) 2.00000 + 3.46410i 0.165521 + 0.286691i
\(147\) 0 0
\(148\) −2.00000 + 3.46410i −0.164399 + 0.284747i
\(149\) 8.50000 14.7224i 0.696347 1.20611i −0.273377 0.961907i \(-0.588141\pi\)
0.969724 0.244202i \(-0.0785259\pi\)
\(150\) 0 0
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) −24.0000 −1.94666
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) 0 0
\(156\) 0 0
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) −3.00000 + 5.19615i −0.238667 + 0.413384i
\(159\) 0 0
\(160\) 2.50000 + 4.33013i 0.197642 + 0.342327i
\(161\) 9.00000 0.709299
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −2.50000 4.33013i −0.195217 0.338126i
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) −4.50000 + 7.79423i −0.348220 + 0.603136i −0.985933 0.167139i \(-0.946547\pi\)
0.637713 + 0.770274i \(0.279881\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 0 0
\(175\) 1.50000 2.59808i 0.113389 0.196396i
\(176\) 1.00000 1.73205i 0.0753778 0.130558i
\(177\) 0 0
\(178\) 7.50000 + 12.9904i 0.562149 + 0.973670i
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 3.00000 + 5.19615i 0.222375 + 0.385164i
\(183\) 0 0
\(184\) 4.50000 7.79423i 0.331744 0.574598i
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) 0 0
\(187\) 4.00000 + 6.92820i 0.292509 + 0.506640i
\(188\) 7.00000 0.510527
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 4.00000 + 6.92820i 0.289430 + 0.501307i 0.973674 0.227946i \(-0.0732010\pi\)
−0.684244 + 0.729253i \(0.739868\pi\)
\(192\) 0 0
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) 0 0
\(196\) 1.00000 + 1.73205i 0.0714286 + 0.123718i
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) 0 0
\(202\) 9.00000 15.5885i 0.633238 1.09680i
\(203\) 1.50000 2.59808i 0.105279 0.182349i
\(204\) 0 0
\(205\) 2.50000 + 4.33013i 0.174608 + 0.302429i
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 8.00000 + 13.8564i 0.553372 + 0.958468i
\(210\) 0 0
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) 1.00000 1.73205i 0.0686803 0.118958i
\(213\) 0 0
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) 0 0
\(218\) 2.50000 + 4.33013i 0.169321 + 0.293273i
\(219\) 0 0
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) −4.00000 + 6.92820i −0.269069 + 0.466041i
\(222\) 0 0
\(223\) 9.50000 + 16.4545i 0.636167 + 1.10187i 0.986267 + 0.165161i \(0.0528144\pi\)
−0.350100 + 0.936713i \(0.613852\pi\)
\(224\) 15.0000 1.00223
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) −2.00000 3.46410i −0.132745 0.229920i 0.791989 0.610535i \(-0.209046\pi\)
−0.924734 + 0.380615i \(0.875712\pi\)
\(228\) 0 0
\(229\) −7.50000 + 12.9904i −0.495614 + 0.858429i −0.999987 0.00505719i \(-0.998390\pi\)
0.504373 + 0.863486i \(0.331724\pi\)
\(230\) −1.50000 + 2.59808i −0.0989071 + 0.171312i
\(231\) 0 0
\(232\) −1.50000 2.59808i −0.0984798 0.170572i
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) 0 0
\(235\) −7.00000 −0.456630
\(236\) 7.00000 + 12.1244i 0.455661 + 0.789228i
\(237\) 0 0
\(238\) 6.00000 10.3923i 0.388922 0.673633i
\(239\) −4.00000 + 6.92820i −0.258738 + 0.448148i −0.965904 0.258900i \(-0.916640\pi\)
0.707166 + 0.707048i \(0.249973\pi\)
\(240\) 0 0
\(241\) 5.50000 + 9.52628i 0.354286 + 0.613642i 0.986996 0.160748i \(-0.0513906\pi\)
−0.632709 + 0.774389i \(0.718057\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) −1.00000 1.73205i −0.0638877 0.110657i
\(246\) 0 0
\(247\) −8.00000 + 13.8564i −0.509028 + 0.881662i
\(248\) 0 0
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) −2.50000 4.33013i −0.156864 0.271696i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 0 0
\(259\) −6.00000 10.3923i −0.372822 0.645746i
\(260\) 2.00000 0.124035
\(261\) 0 0
\(262\) −6.00000 −0.370681
\(263\) −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i \(-0.330877\pi\)
−0.999970 + 0.00771799i \(0.997543\pi\)
\(264\) 0 0
\(265\) −1.00000 + 1.73205i −0.0614295 + 0.106399i
\(266\) 12.0000 20.7846i 0.735767 1.27439i
\(267\) 0 0
\(268\) −1.50000 2.59808i −0.0916271 0.158703i
\(269\) −25.0000 −1.52428 −0.762138 0.647414i \(-0.775850\pi\)
−0.762138 + 0.647414i \(0.775850\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −2.00000 3.46410i −0.121268 0.210042i
\(273\) 0 0
\(274\) −6.00000 + 10.3923i −0.362473 + 0.627822i
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 0 0
\(277\) −6.00000 10.3923i −0.360505 0.624413i 0.627539 0.778585i \(-0.284062\pi\)
−0.988044 + 0.154172i \(0.950729\pi\)
\(278\) 16.0000 0.959616
\(279\) 0 0
\(280\) −9.00000 −0.537853
\(281\) −7.50000 12.9904i −0.447412 0.774941i 0.550804 0.834634i \(-0.314321\pi\)
−0.998217 + 0.0596933i \(0.980988\pi\)
\(282\) 0 0
\(283\) −10.5000 + 18.1865i −0.624160 + 1.08108i 0.364542 + 0.931187i \(0.381225\pi\)
−0.988703 + 0.149890i \(0.952108\pi\)
\(284\) −1.00000 + 1.73205i −0.0593391 + 0.102778i
\(285\) 0 0
\(286\) −2.00000 3.46410i −0.118262 0.204837i
\(287\) 15.0000 0.885422
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0.500000 + 0.866025i 0.0293610 + 0.0508548i
\(291\) 0 0
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) 6.00000 10.3923i 0.350524 0.607125i −0.635818 0.771839i \(-0.719337\pi\)
0.986341 + 0.164714i \(0.0526703\pi\)
\(294\) 0 0
\(295\) −7.00000 12.1244i −0.407556 0.705907i
\(296\) −12.0000 −0.697486
\(297\) 0 0
\(298\) 17.0000 0.984784
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) 0 0
\(301\) −12.0000 + 20.7846i −0.691669 + 1.19800i
\(302\) −1.00000 + 1.73205i −0.0575435 + 0.0996683i
\(303\) 0 0
\(304\) −4.00000 6.92820i −0.229416 0.397360i
\(305\) 7.00000 0.400819
\(306\) 0 0
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) −3.00000 5.19615i −0.170941 0.296078i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) −17.0000 29.4449i −0.954815 1.65379i −0.734791 0.678294i \(-0.762720\pi\)
−0.220024 0.975494i \(-0.570614\pi\)
\(318\) 0 0
\(319\) −1.00000 + 1.73205i −0.0559893 + 0.0969762i
\(320\) −3.50000 + 6.06218i −0.195656 + 0.338886i
\(321\) 0 0
\(322\) 4.50000 + 7.79423i 0.250775 + 0.434355i
\(323\) 32.0000 1.78053
\(324\) 0 0
\(325\) −2.00000 −0.110940
\(326\) −2.00000 3.46410i −0.110770 0.191859i
\(327\) 0 0
\(328\) 7.50000 12.9904i 0.414118 0.717274i
\(329\) −10.5000 + 18.1865i −0.578884 + 1.00266i
\(330\) 0 0
\(331\) 3.00000 + 5.19615i 0.164895 + 0.285606i 0.936618 0.350352i \(-0.113938\pi\)
−0.771723 + 0.635959i \(0.780605\pi\)
\(332\) 9.00000 0.493939
\(333\) 0 0
\(334\) −9.00000 −0.492458
\(335\) 1.50000 + 2.59808i 0.0819538 + 0.141948i
\(336\) 0 0
\(337\) 4.00000 6.92820i 0.217894 0.377403i −0.736270 0.676688i \(-0.763415\pi\)
0.954164 + 0.299285i \(0.0967480\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) 0 0
\(340\) −2.00000 3.46410i −0.108465 0.187867i
\(341\) 0 0
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 12.0000 + 20.7846i 0.646997 + 1.12063i
\(345\) 0 0
\(346\) 0 0
\(347\) 2.00000 3.46410i 0.107366 0.185963i −0.807337 0.590091i \(-0.799092\pi\)
0.914702 + 0.404128i \(0.132425\pi\)
\(348\) 0 0
\(349\) 2.50000 + 4.33013i 0.133822 + 0.231786i 0.925147 0.379610i \(-0.123942\pi\)
−0.791325 + 0.611396i \(0.790608\pi\)
\(350\) 3.00000 0.160357
\(351\) 0 0
\(352\) −10.0000 −0.533002
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 0 0
\(355\) 1.00000 1.73205i 0.0530745 0.0919277i
\(356\) 7.50000 12.9904i 0.397499 0.688489i
\(357\) 0 0
\(358\) 1.00000 + 1.73205i 0.0528516 + 0.0915417i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 0 0
\(364\) 3.00000 5.19615i 0.157243 0.272352i
\(365\) −2.00000 + 3.46410i −0.104685 + 0.181319i
\(366\) 0 0
\(367\) −12.0000 20.7846i −0.626395 1.08495i −0.988269 0.152721i \(-0.951196\pi\)
0.361874 0.932227i \(-0.382137\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) 4.00000 0.207950
\(371\) 3.00000 + 5.19615i 0.155752 + 0.269771i
\(372\) 0 0
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) 0 0
\(376\) 10.5000 + 18.1865i 0.541496 + 0.937899i
\(377\) −2.00000 −0.103005
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) −4.00000 6.92820i −0.205196 0.355409i
\(381\) 0 0
\(382\) −4.00000 + 6.92820i −0.204658 + 0.354478i
\(383\) 18.0000 31.1769i 0.919757 1.59307i 0.119974 0.992777i \(-0.461719\pi\)
0.799783 0.600289i \(-0.204948\pi\)
\(384\) 0 0
\(385\) 3.00000 + 5.19615i 0.152894 + 0.264820i
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) 16.5000 + 28.5788i 0.836583 + 1.44900i 0.892735 + 0.450582i \(0.148784\pi\)
−0.0561516 + 0.998422i \(0.517883\pi\)
\(390\) 0 0
\(391\) −6.00000 + 10.3923i −0.303433 + 0.525561i
\(392\) −3.00000 + 5.19615i −0.151523 + 0.262445i
\(393\) 0 0
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) −6.00000 −0.301893
\(396\) 0 0
\(397\) 34.0000 1.70641 0.853206 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) 2.00000 + 3.46410i 0.100251 + 0.173640i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) 3.00000 0.148888
\(407\) 4.00000 + 6.92820i 0.198273 + 0.343418i
\(408\) 0 0
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −2.50000 + 4.33013i −0.123466 + 0.213850i
\(411\) 0 0
\(412\) 4.00000 + 6.92820i 0.197066 + 0.341328i
\(413\) −42.0000 −2.06668
\(414\) 0 0
\(415\) −9.00000 −0.441793
\(416\) −5.00000 8.66025i −0.245145 0.424604i
\(417\) 0 0
\(418\) −8.00000 + 13.8564i −0.391293 + 0.677739i
\(419\) 13.0000 22.5167i 0.635092 1.10001i −0.351404 0.936224i \(-0.614296\pi\)
0.986496 0.163787i \(-0.0523710\pi\)
\(420\) 0 0
\(421\) −17.0000 29.4449i −0.828529 1.43505i −0.899192 0.437555i \(-0.855845\pi\)
0.0706626 0.997500i \(-0.477489\pi\)
\(422\) 22.0000 1.07094
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0 0
\(427\) 10.5000 18.1865i 0.508131 0.880108i
\(428\) −1.50000 + 2.59808i −0.0725052 + 0.125583i
\(429\) 0 0
\(430\) −4.00000 6.92820i −0.192897 0.334108i
\(431\) 30.0000 1.44505 0.722525 0.691345i \(-0.242982\pi\)
0.722525 + 0.691345i \(0.242982\pi\)
\(432\) 0 0
\(433\) 28.0000 1.34559 0.672797 0.739827i \(-0.265093\pi\)
0.672797 + 0.739827i \(0.265093\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.50000 4.33013i 0.119728 0.207375i
\(437\) −12.0000 + 20.7846i −0.574038 + 0.994263i
\(438\) 0 0
\(439\) −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) 6.00000 0.286039
\(441\) 0 0
\(442\) −8.00000 −0.380521
\(443\) 7.50000 + 12.9904i 0.356336 + 0.617192i 0.987346 0.158583i \(-0.0506926\pi\)
−0.631010 + 0.775775i \(0.717359\pi\)
\(444\) 0 0
\(445\) −7.50000 + 12.9904i −0.355534 + 0.615803i
\(446\) −9.50000 + 16.4545i −0.449838 + 0.779142i
\(447\) 0 0
\(448\) 10.5000 + 18.1865i 0.496078 + 0.859233i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) 4.00000 + 6.92820i 0.188144 + 0.325875i
\(453\) 0 0
\(454\) 2.00000 3.46410i 0.0938647 0.162578i
\(455\) −3.00000 + 5.19615i −0.140642 + 0.243599i
\(456\) 0 0
\(457\) 10.0000 + 17.3205i 0.467780 + 0.810219i 0.999322 0.0368128i \(-0.0117205\pi\)
−0.531542 + 0.847032i \(0.678387\pi\)
\(458\) −15.0000 −0.700904
\(459\) 0 0
\(460\) 3.00000 0.139876
\(461\) 4.50000 + 7.79423i 0.209586 + 0.363013i 0.951584 0.307388i \(-0.0994551\pi\)
−0.741998 + 0.670402i \(0.766122\pi\)
\(462\) 0 0
\(463\) 18.0000 31.1769i 0.836531 1.44891i −0.0562469 0.998417i \(-0.517913\pi\)
0.892778 0.450497i \(-0.148753\pi\)
\(464\) 0.500000 0.866025i 0.0232119 0.0402042i
\(465\) 0 0
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) 9.00000 0.415581
\(470\) −3.50000 6.06218i −0.161443 0.279627i
\(471\) 0 0
\(472\) −21.0000 + 36.3731i −0.966603 + 1.67421i
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) 0 0
\(475\) 4.00000 + 6.92820i 0.183533 + 0.317888i
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) −8.00000 −0.365911
\(479\) −9.00000 15.5885i −0.411220 0.712255i 0.583803 0.811895i \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) 0 0
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) −5.50000 + 9.52628i −0.250518 + 0.433910i
\(483\) 0 0
\(484\) −3.50000 6.06218i −0.159091 0.275554i
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −10.5000 18.1865i −0.475313 0.823266i
\(489\) 0 0
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) 10.0000 17.3205i 0.451294 0.781664i −0.547173 0.837020i \(-0.684296\pi\)
0.998467 + 0.0553560i \(0.0176294\pi\)
\(492\) 0 0
\(493\) 2.00000 + 3.46410i 0.0900755 + 0.156015i
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) 0 0
\(497\) −3.00000 5.19615i −0.134568 0.233079i
\(498\) 0 0
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 0 0
\(502\) 0 0
\(503\) 7.00000 0.312115 0.156057 0.987748i \(-0.450122\pi\)
0.156057 + 0.987748i \(0.450122\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) −3.00000 5.19615i −0.133366 0.230997i
\(507\) 0 0
\(508\) −2.50000 + 4.33013i −0.110920 + 0.192118i
\(509\) 21.5000 37.2391i 0.952971 1.65059i 0.214026 0.976828i \(-0.431342\pi\)
0.738945 0.673766i \(-0.235324\pi\)
\(510\) 0 0
\(511\) 6.00000 + 10.3923i 0.265424 + 0.459728i
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) −4.00000 6.92820i −0.176261 0.305293i
\(516\) 0 0
\(517\) 7.00000 12.1244i 0.307860 0.533229i
\(518\) 6.00000 10.3923i 0.263625 0.456612i
\(519\) 0 0
\(520\) 3.00000 + 5.19615i 0.131559 + 0.227866i
\(521\) −11.0000 −0.481919 −0.240959 0.970535i \(-0.577462\pi\)
−0.240959 + 0.970535i \(0.577462\pi\)
\(522\) 0 0
\(523\) −29.0000 −1.26808 −0.634041 0.773300i \(-0.718605\pi\)
−0.634041 + 0.773300i \(0.718605\pi\)
\(524\) 3.00000 + 5.19615i 0.131056 + 0.226995i
\(525\) 0 0
\(526\) 8.00000 13.8564i 0.348817 0.604168i
\(527\) 0 0
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) −2.00000 −0.0868744
\(531\) 0 0
\(532\) −24.0000 −1.04053
\(533\) −5.00000 8.66025i −0.216574 0.375117i
\(534\) 0 0
\(535\) 1.50000 2.59808i 0.0648507 0.112325i
\(536\) 4.50000 7.79423i 0.194370 0.336659i
\(537\) 0 0
\(538\) −12.5000 21.6506i −0.538913 0.933425i
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −39.0000 −1.67674 −0.838370 0.545101i \(-0.816491\pi\)
−0.838370 + 0.545101i \(0.816491\pi\)
\(542\) −4.00000 6.92820i −0.171815 0.297592i
\(543\) 0 0
\(544\) −10.0000 + 17.3205i −0.428746 + 0.742611i
\(545\) −2.50000 + 4.33013i −0.107088 + 0.185482i
\(546\) 0 0
\(547\) 14.5000 + 25.1147i 0.619975 + 1.07383i 0.989490 + 0.144604i \(0.0461907\pi\)
−0.369514 + 0.929225i \(0.620476\pi\)
\(548\) 12.0000 0.512615
\(549\) 0 0
\(550\) −2.00000 −0.0852803
\(551\) 4.00000 + 6.92820i 0.170406 + 0.295151i
\(552\) 0 0
\(553\) −9.00000 + 15.5885i −0.382719 + 0.662889i
\(554\) 6.00000 10.3923i 0.254916 0.441527i
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) −1.50000 2.59808i −0.0633866 0.109789i
\(561\) 0 0
\(562\) 7.50000 12.9904i 0.316368 0.547966i
\(563\) −10.5000 + 18.1865i −0.442522 + 0.766471i −0.997876 0.0651433i \(-0.979250\pi\)
0.555354 + 0.831614i \(0.312583\pi\)
\(564\) 0 0
\(565\) −4.00000 6.92820i −0.168281 0.291472i
\(566\) −21.0000 −0.882696
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −2.00000 + 3.46410i −0.0836242 + 0.144841i
\(573\) 0 0
\(574\) 7.50000 + 12.9904i 0.313044 + 0.542208i
\(575\) −3.00000 −0.125109
\(576\) 0 0
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 0 0
\(580\) 0.500000 0.866025i 0.0207614 0.0359597i
\(581\) −13.5000 + 23.3827i −0.560074 + 0.970077i
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 12.0000 0.496564
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) −16.5000 28.5788i −0.681028 1.17957i −0.974668 0.223659i \(-0.928200\pi\)
0.293640 0.955916i \(-0.405133\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 7.00000 12.1244i 0.288185 0.499152i
\(591\) 0 0
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) −20.0000 −0.821302 −0.410651 0.911793i \(-0.634698\pi\)
−0.410651 + 0.911793i \(0.634698\pi\)
\(594\) 0 0
\(595\) 12.0000 0.491952
\(596\) −8.50000 14.7224i −0.348174 0.603054i
\(597\) 0 0
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) −5.00000 + 8.66025i −0.204294 + 0.353848i −0.949908 0.312531i \(-0.898823\pi\)
0.745613 + 0.666379i \(0.232157\pi\)
\(600\) 0 0
\(601\) −1.00000 1.73205i −0.0407909 0.0706518i 0.844909 0.534910i \(-0.179654\pi\)
−0.885700 + 0.464258i \(0.846321\pi\)
\(602\) −24.0000 −0.978167
\(603\) 0 0
\(604\) 2.00000 0.0813788
\(605\) 3.50000 + 6.06218i 0.142295 + 0.246463i
\(606\) 0 0
\(607\) 20.5000 35.5070i 0.832069 1.44119i −0.0643251 0.997929i \(-0.520489\pi\)
0.896394 0.443257i \(-0.146177\pi\)
\(608\) −20.0000 + 34.6410i −0.811107 + 1.40488i
\(609\) 0 0
\(610\) 3.50000 + 6.06218i 0.141711 + 0.245450i
\(611\) 14.0000 0.566379
\(612\) 0 0
\(613\) −44.0000 −1.77714 −0.888572 0.458738i \(-0.848302\pi\)
−0.888572 + 0.458738i \(0.848302\pi\)
\(614\) 3.50000 + 6.06218i 0.141249 + 0.244650i
\(615\) 0 0
\(616\) 9.00000 15.5885i 0.362620 0.628077i
\(617\) −18.0000 + 31.1769i −0.724653 + 1.25514i 0.234464 + 0.972125i \(0.424666\pi\)
−0.959117 + 0.283011i \(0.908667\pi\)
\(618\) 0 0
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 22.5000 + 38.9711i 0.901443 + 1.56135i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 7.00000 12.1244i 0.279776 0.484587i
\(627\) 0 0
\(628\) 7.00000 + 12.1244i 0.279330 + 0.483814i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 9.00000 + 15.5885i 0.358001 + 0.620076i
\(633\) 0 0
\(634\) 17.0000 29.4449i 0.675156 1.16940i
\(635\) 2.50000 4.33013i 0.0992095 0.171836i
\(636\) 0 0
\(637\) 2.00000 + 3.46410i 0.0792429 + 0.137253i
\(638\) −2.00000 −0.0791808
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.330997 + 0.943632i \(0.607385\pi\)
\(642\) 0 0
\(643\) 4.50000 7.79423i 0.177463 0.307374i −0.763548 0.645751i \(-0.776544\pi\)
0.941011 + 0.338377i \(0.109878\pi\)
\(644\) 4.50000 7.79423i 0.177325 0.307136i
\(645\) 0 0
\(646\) 16.0000 + 27.7128i 0.629512 + 1.09035i
\(647\) 17.0000 0.668339 0.334169 0.942513i \(-0.391544\pi\)
0.334169 + 0.942513i \(0.391544\pi\)
\(648\) 0 0
\(649\) 28.0000 1.09910
\(650\) −1.00000 1.73205i −0.0392232 0.0679366i
\(651\) 0 0
\(652\) −2.00000 + 3.46410i −0.0783260 + 0.135665i
\(653\) −2.00000 + 3.46410i −0.0782660 + 0.135561i −0.902502 0.430686i \(-0.858272\pi\)
0.824236 + 0.566247i \(0.191605\pi\)
\(654\) 0 0
\(655\) −3.00000 5.19615i −0.117220 0.203030i
\(656\) 5.00000 0.195217
\(657\) 0 0
\(658\) −21.0000 −0.818665
\(659\) −4.00000 6.92820i −0.155818 0.269884i 0.777539 0.628835i \(-0.216468\pi\)
−0.933357 + 0.358951i \(0.883135\pi\)
\(660\) 0 0
\(661\) 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) −3.00000 + 5.19615i −0.116598 + 0.201954i
\(663\) 0 0
\(664\) 13.5000 + 23.3827i 0.523902 + 0.907424i
\(665\) 24.0000 0.930680
\(666\) 0 0
\(667\) −3.00000 −0.116160
\(668\) 4.50000 + 7.79423i 0.174110 + 0.301568i
\(669\) 0 0
\(670\) −1.50000 + 2.59808i −0.0579501 + 0.100372i
\(671\) −7.00000 + 12.1244i −0.270232 + 0.468056i
\(672\) 0 0
\(673\) −3.00000 5.19615i −0.115642 0.200297i 0.802395 0.596794i \(-0.203559\pi\)
−0.918036 + 0.396497i \(0.870226\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) −21.0000 36.3731i −0.807096 1.39793i −0.914867 0.403755i \(-0.867705\pi\)
0.107772 0.994176i \(-0.465628\pi\)
\(678\) 0 0
\(679\) 3.00000 5.19615i 0.115129 0.199410i
\(680\) 6.00000 10.3923i 0.230089 0.398527i
\(681\) 0 0
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 7.50000 + 12.9904i 0.286351 + 0.495975i
\(687\) 0 0
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) 2.00000 3.46410i 0.0761939 0.131972i
\(690\) 0 0
\(691\) 7.00000 + 12.1244i 0.266293 + 0.461232i 0.967901 0.251330i \(-0.0808679\pi\)
−0.701609 + 0.712562i \(0.747535\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) 8.00000 + 13.8564i 0.303457 + 0.525603i
\(696\) 0 0
\(697\) −10.0000 + 17.3205i −0.378777 + 0.656061i
\(698\) −2.50000 + 4.33013i −0.0946264 + 0.163898i
\(699\) 0 0
\(700\) −1.50000 2.59808i −0.0566947 0.0981981i
\(701\) −23.0000 −0.868698 −0.434349 0.900745i \(-0.643022\pi\)
−0.434349 + 0.900745i \(0.643022\pi\)
\(702\) 0 0
\(703\) 32.0000 1.20690
\(704\) −7.00000 12.1244i −0.263822 0.456954i
\(705\) 0 0
\(706\) −12.0000 + 20.7846i −0.451626 + 0.782239i
\(707\) 27.0000 46.7654i 1.01544 1.75879i
\(708\) 0 0
\(709\) 20.5000 + 35.5070i 0.769894 + 1.33349i 0.937620 + 0.347661i \(0.113024\pi\)
−0.167727 + 0.985834i \(0.553643\pi\)
\(710\) 2.00000 0.0750587
\(711\) 0 0
\(712\) 45.0000 1.68645
\(713\) 0 0
\(714\) 0 0
\(715\) 2.00000 3.46410i 0.0747958 0.129550i
\(716\) 1.00000 1.73205i 0.0373718 0.0647298i
\(717\) 0 0
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 22.5000 + 38.9711i 0.837363 + 1.45036i
\(723\) 0 0
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) −0.500000 + 0.866025i −0.0185695 + 0.0321634i
\(726\) 0 0
\(727\) −11.5000 19.9186i −0.426511 0.738739i 0.570049 0.821611i \(-0.306924\pi\)
−0.996560 + 0.0828714i \(0.973591\pi\)
\(728\) 18.0000 0.667124
\(729\) 0 0
\(730\) −4.00000 −0.148047
\(731\) −16.0000 27.7128i −0.591781 1.02500i
\(732\) 0 0
\(733\) 17.0000 29.4449i 0.627909 1.08757i −0.360061 0.932929i \(-0.617244\pi\)
0.987971 0.154642i \(-0.0494225\pi\)
\(734\) 12.0000 20.7846i 0.442928 0.767174i
\(735\) 0 0
\(736\) −7.50000 12.9904i −0.276454 0.478832i
\(737\) −6.00000 −0.221013
\(738\) 0 0
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) −3.00000 + 5.19615i −0.110133 + 0.190757i
\(743\) −14.5000 + 25.1147i −0.531953 + 0.921370i 0.467351 + 0.884072i \(0.345209\pi\)
−0.999304 + 0.0372984i \(0.988125\pi\)
\(744\) 0 0
\(745\) 8.50000 + 14.7224i 0.311416 + 0.539388i
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) 8.00000 0.292509
\(749\) −4.50000 7.79423i −0.164426 0.284795i
\(750\) 0 0
\(751\) −5.00000 + 8.66025i −0.182453 + 0.316017i −0.942715 0.333599i \(-0.891737\pi\)
0.760263 + 0.649616i \(0.225070\pi\)
\(752\) −3.50000 + 6.06218i −0.127632 + 0.221065i
\(753\) 0 0
\(754\) −1.00000 1.73205i −0.0364179 0.0630776i
\(755\) −2.00000 −0.0727875
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) −13.0000 22.5167i −0.472181 0.817842i
\(759\) 0 0
\(760\) 12.0000 20.7846i 0.435286 0.753937i
\(761\) 7.50000 12.9904i 0.271875 0.470901i −0.697467 0.716617i \(-0.745690\pi\)
0.969342 + 0.245716i \(0.0790230\pi\)
\(762\) 0 0
\(763\) 7.50000 + 12.9904i 0.271518 + 0.470283i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) 14.0000 + 24.2487i 0.505511 + 0.875570i
\(768\) 0 0
\(769\) −2.50000 + 4.33013i −0.0901523 + 0.156148i −0.907575 0.419890i \(-0.862069\pi\)
0.817423 + 0.576038i \(0.195402\pi\)
\(770\) −3.00000 + 5.19615i −0.108112 + 0.187256i
\(771\) 0 0
\(772\) −5.00000 8.66025i −0.179954 0.311689i
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −3.00000 5.19615i −0.107694 0.186531i
\(777\) 0 0
\(778\) −16.5000 + 28.5788i −0.591554 + 1.02460i
\(779\) −20.0000 + 34.6410i −0.716574 + 1.24114i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) −12.0000 −0.429119
\(783\) 0 0
\(784\) −2.00000 −0.0714286
\(785\) −7.00000 12.1244i −0.249841 0.432737i
\(786\) 0 0
\(787\) −14.0000 + 24.2487i −0.499046 + 0.864373i −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) 6.00000 10.3923i 0.213741 0.370211i