Properties

Label 1638.2.bj.g.127.2
Level $1638$
Weight $2$
Character 1638.127
Analytic conductor $13.079$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + 3842 x^{4} - 3394 x^{3} + 2141 x^{2} - 832 x + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.2
Root \(0.500000 - 3.15681i\) of defining polynomial
Character \(\chi\) \(=\) 1638.127
Dual form 1638.2.bj.g.1135.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.901839i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.901839i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.450919 - 0.781015i) q^{10} +(3.75609 - 2.16858i) q^{11} +(-0.426876 - 3.58019i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.53296 + 4.38722i) q^{17} +(5.34544 + 3.08619i) q^{19} +(0.781015 + 0.450919i) q^{20} +(-2.16858 + 3.75609i) q^{22} +(-4.22559 - 7.31893i) q^{23} +4.18669 q^{25} +(2.15978 + 2.88710i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-1.09643 - 1.89907i) q^{29} -0.873062i q^{31} +(0.866025 + 0.500000i) q^{32} -5.06592i q^{34} +(-0.450919 + 0.781015i) q^{35} +(0.124973 - 0.0721531i) q^{37} -6.17238 q^{38} -0.901839 q^{40} +(3.46110 - 1.99827i) q^{41} +(3.85426 - 6.67577i) q^{43} -4.33716i q^{44} +(7.31893 + 4.22559i) q^{46} -2.92115i q^{47} +(0.500000 + 0.866025i) q^{49} +(-3.62578 + 2.09334i) q^{50} +(-3.31398 - 1.42041i) q^{52} -1.69699 q^{53} +(1.95571 + 3.38739i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(1.89907 + 1.09643i) q^{58} +(7.40394 + 4.27467i) q^{59} +(-4.16720 + 7.21780i) q^{61} +(0.436531 + 0.756094i) q^{62} -1.00000 q^{64} +(3.22876 - 0.384973i) q^{65} +(-8.99180 + 5.19142i) q^{67} +(2.53296 + 4.38722i) q^{68} -0.901839i q^{70} +(2.83932 + 1.63928i) q^{71} -0.539023i q^{73} +(-0.0721531 + 0.124973i) q^{74} +(5.34544 - 3.08619i) q^{76} +4.33716 q^{77} +6.53349 q^{79} +(0.781015 - 0.450919i) q^{80} +(-1.99827 + 3.46110i) q^{82} -13.2348i q^{83} +(-3.95656 - 2.28432i) q^{85} +7.70851i q^{86} +(2.16858 + 3.75609i) q^{88} +(6.74790 - 3.89590i) q^{89} +(1.42041 - 3.31398i) q^{91} -8.45117 q^{92} +(1.46057 + 2.52979i) q^{94} +(-2.78325 + 4.82072i) q^{95} +(10.1378 + 5.85305i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.901839i 0.403315i 0.979456 + 0.201657i \(0.0646327\pi\)
−0.979456 + 0.201657i \(0.935367\pi\)
\(6\) 0 0
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.450919 0.781015i −0.142593 0.246979i
\(11\) 3.75609 2.16858i 1.13251 0.653852i 0.187941 0.982180i \(-0.439819\pi\)
0.944564 + 0.328328i \(0.106485\pi\)
\(12\) 0 0
\(13\) −0.426876 3.58019i −0.118394 0.992967i
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.53296 + 4.38722i −0.614333 + 1.06406i 0.376168 + 0.926551i \(0.377242\pi\)
−0.990501 + 0.137505i \(0.956092\pi\)
\(18\) 0 0
\(19\) 5.34544 + 3.08619i 1.22633 + 0.708021i 0.966260 0.257570i \(-0.0829217\pi\)
0.260068 + 0.965590i \(0.416255\pi\)
\(20\) 0.781015 + 0.450919i 0.174640 + 0.100829i
\(21\) 0 0
\(22\) −2.16858 + 3.75609i −0.462343 + 0.800802i
\(23\) −4.22559 7.31893i −0.881096 1.52610i −0.850124 0.526582i \(-0.823473\pi\)
−0.0309711 0.999520i \(-0.509860\pi\)
\(24\) 0 0
\(25\) 4.18669 0.837337
\(26\) 2.15978 + 2.88710i 0.423568 + 0.566207i
\(27\) 0 0
\(28\) 0.866025 0.500000i 0.163663 0.0944911i
\(29\) −1.09643 1.89907i −0.203602 0.352649i 0.746085 0.665851i \(-0.231931\pi\)
−0.949686 + 0.313203i \(0.898598\pi\)
\(30\) 0 0
\(31\) 0.873062i 0.156807i −0.996922 0.0784033i \(-0.975018\pi\)
0.996922 0.0784033i \(-0.0249822\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 5.06592i 0.868798i
\(35\) −0.450919 + 0.781015i −0.0762193 + 0.132016i
\(36\) 0 0
\(37\) 0.124973 0.0721531i 0.0205454 0.0118619i −0.489692 0.871895i \(-0.662891\pi\)
0.510238 + 0.860034i \(0.329557\pi\)
\(38\) −6.17238 −1.00129
\(39\) 0 0
\(40\) −0.901839 −0.142593
\(41\) 3.46110 1.99827i 0.540533 0.312077i −0.204762 0.978812i \(-0.565642\pi\)
0.745295 + 0.666735i \(0.232309\pi\)
\(42\) 0 0
\(43\) 3.85426 6.67577i 0.587768 1.01804i −0.406756 0.913537i \(-0.633340\pi\)
0.994524 0.104508i \(-0.0333267\pi\)
\(44\) 4.33716i 0.653852i
\(45\) 0 0
\(46\) 7.31893 + 4.22559i 1.07912 + 0.623029i
\(47\) 2.92115i 0.426093i −0.977042 0.213047i \(-0.931661\pi\)
0.977042 0.213047i \(-0.0683387\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −3.62578 + 2.09334i −0.512762 + 0.296043i
\(51\) 0 0
\(52\) −3.31398 1.42041i −0.459566 0.196976i
\(53\) −1.69699 −0.233099 −0.116549 0.993185i \(-0.537183\pi\)
−0.116549 + 0.993185i \(0.537183\pi\)
\(54\) 0 0
\(55\) 1.95571 + 3.38739i 0.263708 + 0.456756i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 1.89907 + 1.09643i 0.249360 + 0.143968i
\(59\) 7.40394 + 4.27467i 0.963911 + 0.556514i 0.897374 0.441270i \(-0.145472\pi\)
0.0665363 + 0.997784i \(0.478805\pi\)
\(60\) 0 0
\(61\) −4.16720 + 7.21780i −0.533555 + 0.924145i 0.465676 + 0.884955i \(0.345811\pi\)
−0.999232 + 0.0391900i \(0.987522\pi\)
\(62\) 0.436531 + 0.756094i 0.0554395 + 0.0960241i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.22876 0.384973i 0.400478 0.0477501i
\(66\) 0 0
\(67\) −8.99180 + 5.19142i −1.09852 + 0.634233i −0.935833 0.352444i \(-0.885351\pi\)
−0.162691 + 0.986677i \(0.552017\pi\)
\(68\) 2.53296 + 4.38722i 0.307167 + 0.532028i
\(69\) 0 0
\(70\) 0.901839i 0.107790i
\(71\) 2.83932 + 1.63928i 0.336965 + 0.194547i 0.658929 0.752205i \(-0.271010\pi\)
−0.321964 + 0.946752i \(0.604343\pi\)
\(72\) 0 0
\(73\) 0.539023i 0.0630879i −0.999502 0.0315439i \(-0.989958\pi\)
0.999502 0.0315439i \(-0.0100424\pi\)
\(74\) −0.0721531 + 0.124973i −0.00838763 + 0.0145278i
\(75\) 0 0
\(76\) 5.34544 3.08619i 0.613164 0.354010i
\(77\) 4.33716 0.494266
\(78\) 0 0
\(79\) 6.53349 0.735075 0.367537 0.930009i \(-0.380201\pi\)
0.367537 + 0.930009i \(0.380201\pi\)
\(80\) 0.781015 0.450919i 0.0873202 0.0504143i
\(81\) 0 0
\(82\) −1.99827 + 3.46110i −0.220672 + 0.382215i
\(83\) 13.2348i 1.45271i −0.687319 0.726356i \(-0.741212\pi\)
0.687319 0.726356i \(-0.258788\pi\)
\(84\) 0 0
\(85\) −3.95656 2.28432i −0.429149 0.247769i
\(86\) 7.70851i 0.831230i
\(87\) 0 0
\(88\) 2.16858 + 3.75609i 0.231172 + 0.400401i
\(89\) 6.74790 3.89590i 0.715276 0.412965i −0.0977357 0.995212i \(-0.531160\pi\)
0.813011 + 0.582248i \(0.197827\pi\)
\(90\) 0 0
\(91\) 1.42041 3.31398i 0.148900 0.347399i
\(92\) −8.45117 −0.881096
\(93\) 0 0
\(94\) 1.46057 + 2.52979i 0.150647 + 0.260928i
\(95\) −2.78325 + 4.82072i −0.285555 + 0.494596i
\(96\) 0 0
\(97\) 10.1378 + 5.85305i 1.02934 + 0.594287i 0.916794 0.399360i \(-0.130768\pi\)
0.112541 + 0.993647i \(0.464101\pi\)
\(98\) −0.866025 0.500000i −0.0874818 0.0505076i
\(99\) 0 0
\(100\) 2.09334 3.62578i 0.209334 0.362578i
\(101\) 5.37145 + 9.30362i 0.534479 + 0.925745i 0.999188 + 0.0402814i \(0.0128254\pi\)
−0.464709 + 0.885463i \(0.653841\pi\)
\(102\) 0 0
\(103\) 4.81099 0.474041 0.237021 0.971505i \(-0.423829\pi\)
0.237021 + 0.971505i \(0.423829\pi\)
\(104\) 3.58019 0.426876i 0.351067 0.0418586i
\(105\) 0 0
\(106\) 1.46963 0.848493i 0.142743 0.0824129i
\(107\) 6.82652 + 11.8239i 0.659944 + 1.14306i 0.980630 + 0.195871i \(0.0627534\pi\)
−0.320686 + 0.947186i \(0.603913\pi\)
\(108\) 0 0
\(109\) 5.11747i 0.490165i −0.969502 0.245082i \(-0.921185\pi\)
0.969502 0.245082i \(-0.0788150\pi\)
\(110\) −3.38739 1.95571i −0.322975 0.186470i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 8.96603 15.5296i 0.843453 1.46090i −0.0435052 0.999053i \(-0.513853\pi\)
0.886958 0.461850i \(-0.152814\pi\)
\(114\) 0 0
\(115\) 6.60049 3.81080i 0.615499 0.355359i
\(116\) −2.19286 −0.203602
\(117\) 0 0
\(118\) −8.54933 −0.787030
\(119\) −4.38722 + 2.53296i −0.402175 + 0.232196i
\(120\) 0 0
\(121\) 3.90550 6.76452i 0.355045 0.614956i
\(122\) 8.33440i 0.754561i
\(123\) 0 0
\(124\) −0.756094 0.436531i −0.0678993 0.0392017i
\(125\) 8.28491i 0.741025i
\(126\) 0 0
\(127\) −9.75681 16.8993i −0.865777 1.49957i −0.866273 0.499570i \(-0.833491\pi\)
0.000496195 1.00000i \(-0.499842\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −2.60370 + 1.94777i −0.228359 + 0.170831i
\(131\) 20.6496 1.80417 0.902083 0.431562i \(-0.142037\pi\)
0.902083 + 0.431562i \(0.142037\pi\)
\(132\) 0 0
\(133\) 3.08619 + 5.34544i 0.267607 + 0.463508i
\(134\) 5.19142 8.99180i 0.448470 0.776773i
\(135\) 0 0
\(136\) −4.38722 2.53296i −0.376201 0.217200i
\(137\) −2.76224 1.59478i −0.235994 0.136251i 0.377340 0.926075i \(-0.376839\pi\)
−0.613334 + 0.789823i \(0.710172\pi\)
\(138\) 0 0
\(139\) 0.297855 0.515900i 0.0252637 0.0437581i −0.853117 0.521719i \(-0.825291\pi\)
0.878381 + 0.477961i \(0.158624\pi\)
\(140\) 0.450919 + 0.781015i 0.0381096 + 0.0660078i
\(141\) 0 0
\(142\) −3.27856 −0.275131
\(143\) −9.36733 12.5218i −0.783335 1.04713i
\(144\) 0 0
\(145\) 1.71266 0.988802i 0.142228 0.0821155i
\(146\) 0.269511 + 0.466808i 0.0223049 + 0.0386333i
\(147\) 0 0
\(148\) 0.144306i 0.0118619i
\(149\) −9.70783 5.60482i −0.795297 0.459165i 0.0465273 0.998917i \(-0.485185\pi\)
−0.841824 + 0.539752i \(0.818518\pi\)
\(150\) 0 0
\(151\) 13.0731i 1.06387i 0.846785 + 0.531935i \(0.178535\pi\)
−0.846785 + 0.531935i \(0.821465\pi\)
\(152\) −3.08619 + 5.34544i −0.250323 + 0.433572i
\(153\) 0 0
\(154\) −3.75609 + 2.16858i −0.302675 + 0.174749i
\(155\) 0.787362 0.0632424
\(156\) 0 0
\(157\) 17.9245 1.43053 0.715266 0.698853i \(-0.246306\pi\)
0.715266 + 0.698853i \(0.246306\pi\)
\(158\) −5.65817 + 3.26674i −0.450139 + 0.259888i
\(159\) 0 0
\(160\) −0.450919 + 0.781015i −0.0356483 + 0.0617447i
\(161\) 8.45117i 0.666046i
\(162\) 0 0
\(163\) 17.5958 + 10.1589i 1.37821 + 0.795710i 0.991944 0.126677i \(-0.0404312\pi\)
0.386266 + 0.922387i \(0.373765\pi\)
\(164\) 3.99654i 0.312077i
\(165\) 0 0
\(166\) 6.61742 + 11.4617i 0.513611 + 0.889601i
\(167\) 2.79770 1.61525i 0.216493 0.124992i −0.387833 0.921730i \(-0.626776\pi\)
0.604325 + 0.796738i \(0.293443\pi\)
\(168\) 0 0
\(169\) −12.6356 + 3.05660i −0.971966 + 0.235123i
\(170\) 4.56864 0.350399
\(171\) 0 0
\(172\) −3.85426 6.67577i −0.293884 0.509022i
\(173\) 4.58522 7.94183i 0.348608 0.603806i −0.637395 0.770538i \(-0.719988\pi\)
0.986002 + 0.166731i \(0.0533212\pi\)
\(174\) 0 0
\(175\) 3.62578 + 2.09334i 0.274083 + 0.158242i
\(176\) −3.75609 2.16858i −0.283126 0.163463i
\(177\) 0 0
\(178\) −3.89590 + 6.74790i −0.292010 + 0.505776i
\(179\) 8.47747 + 14.6834i 0.633636 + 1.09749i 0.986802 + 0.161929i \(0.0517717\pi\)
−0.353166 + 0.935561i \(0.614895\pi\)
\(180\) 0 0
\(181\) −2.65743 −0.197525 −0.0987626 0.995111i \(-0.531488\pi\)
−0.0987626 + 0.995111i \(0.531488\pi\)
\(182\) 0.426876 + 3.58019i 0.0316421 + 0.265382i
\(183\) 0 0
\(184\) 7.31893 4.22559i 0.539559 0.311514i
\(185\) 0.0650705 + 0.112705i 0.00478408 + 0.00828627i
\(186\) 0 0
\(187\) 21.9717i 1.60673i
\(188\) −2.52979 1.46057i −0.184504 0.106523i
\(189\) 0 0
\(190\) 5.56649i 0.403836i
\(191\) −12.2430 + 21.2056i −0.885875 + 1.53438i −0.0411671 + 0.999152i \(0.513108\pi\)
−0.844708 + 0.535228i \(0.820226\pi\)
\(192\) 0 0
\(193\) 10.6009 6.12046i 0.763072 0.440560i −0.0673254 0.997731i \(-0.521447\pi\)
0.830398 + 0.557171i \(0.188113\pi\)
\(194\) −11.7061 −0.840449
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −4.72634 + 2.72876i −0.336738 + 0.194416i −0.658829 0.752293i \(-0.728948\pi\)
0.322091 + 0.946709i \(0.395614\pi\)
\(198\) 0 0
\(199\) −6.40832 + 11.0995i −0.454274 + 0.786825i −0.998646 0.0520184i \(-0.983435\pi\)
0.544372 + 0.838844i \(0.316768\pi\)
\(200\) 4.18669i 0.296043i
\(201\) 0 0
\(202\) −9.30362 5.37145i −0.654600 0.377934i
\(203\) 2.19286i 0.153908i
\(204\) 0 0
\(205\) 1.80212 + 3.12136i 0.125865 + 0.218005i
\(206\) −4.16644 + 2.40550i −0.290290 + 0.167599i
\(207\) 0 0
\(208\) −2.88710 + 2.15978i −0.200184 + 0.149754i
\(209\) 26.7706 1.85176
\(210\) 0 0
\(211\) 9.65552 + 16.7239i 0.664713 + 1.15132i 0.979363 + 0.202110i \(0.0647797\pi\)
−0.314649 + 0.949208i \(0.601887\pi\)
\(212\) −0.848493 + 1.46963i −0.0582747 + 0.100935i
\(213\) 0 0
\(214\) −11.8239 6.82652i −0.808263 0.466651i
\(215\) 6.02046 + 3.47592i 0.410592 + 0.237056i
\(216\) 0 0
\(217\) 0.436531 0.756094i 0.0296337 0.0513270i
\(218\) 2.55874 + 4.43186i 0.173299 + 0.300163i
\(219\) 0 0
\(220\) 3.91142 0.263708
\(221\) 16.7883 + 7.19569i 1.12931 + 0.484034i
\(222\) 0 0
\(223\) −9.21079 + 5.31785i −0.616800 + 0.356110i −0.775622 0.631197i \(-0.782564\pi\)
0.158822 + 0.987307i \(0.449230\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 17.9321i 1.19282i
\(227\) −19.6776 11.3609i −1.30605 0.754047i −0.324613 0.945847i \(-0.605234\pi\)
−0.981434 + 0.191800i \(0.938567\pi\)
\(228\) 0 0
\(229\) 20.3094i 1.34208i −0.741420 0.671042i \(-0.765847\pi\)
0.741420 0.671042i \(-0.234153\pi\)
\(230\) −3.81080 + 6.60049i −0.251277 + 0.435224i
\(231\) 0 0
\(232\) 1.89907 1.09643i 0.124680 0.0719841i
\(233\) −10.6446 −0.697352 −0.348676 0.937243i \(-0.613369\pi\)
−0.348676 + 0.937243i \(0.613369\pi\)
\(234\) 0 0
\(235\) 2.63441 0.171850
\(236\) 7.40394 4.27467i 0.481955 0.278257i
\(237\) 0 0
\(238\) 2.53296 4.38722i 0.164187 0.284381i
\(239\) 0.311564i 0.0201534i −0.999949 0.0100767i \(-0.996792\pi\)
0.999949 0.0100767i \(-0.00320757\pi\)
\(240\) 0 0
\(241\) −21.9100 12.6498i −1.41135 0.814843i −0.415833 0.909441i \(-0.636510\pi\)
−0.995516 + 0.0945983i \(0.969843\pi\)
\(242\) 7.81099i 0.502110i
\(243\) 0 0
\(244\) 4.16720 + 7.21780i 0.266778 + 0.462073i
\(245\) −0.781015 + 0.450919i −0.0498972 + 0.0288082i
\(246\) 0 0
\(247\) 8.76732 20.4551i 0.557851 1.30153i
\(248\) 0.873062 0.0554395
\(249\) 0 0
\(250\) −4.14246 7.17494i −0.261992 0.453783i
\(251\) −4.02015 + 6.96311i −0.253750 + 0.439507i −0.964555 0.263881i \(-0.914997\pi\)
0.710805 + 0.703389i \(0.248331\pi\)
\(252\) 0 0
\(253\) −31.7434 18.3271i −1.99569 1.15221i
\(254\) 16.8993 + 9.75681i 1.06036 + 0.612197i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.46634 + 14.6641i 0.528116 + 0.914723i 0.999463 + 0.0327753i \(0.0104346\pi\)
−0.471347 + 0.881948i \(0.656232\pi\)
\(258\) 0 0
\(259\) 0.144306 0.00896676
\(260\) 1.28098 2.98867i 0.0794431 0.185350i
\(261\) 0 0
\(262\) −17.8831 + 10.3248i −1.10482 + 0.637869i
\(263\) 5.16045 + 8.93817i 0.318207 + 0.551151i 0.980114 0.198435i \(-0.0635859\pi\)
−0.661907 + 0.749586i \(0.730253\pi\)
\(264\) 0 0
\(265\) 1.53041i 0.0940122i
\(266\) −5.34544 3.08619i −0.327750 0.189226i
\(267\) 0 0
\(268\) 10.3828i 0.634233i
\(269\) −3.06999 + 5.31738i −0.187181 + 0.324207i −0.944309 0.329059i \(-0.893268\pi\)
0.757128 + 0.653266i \(0.226602\pi\)
\(270\) 0 0
\(271\) 9.24673 5.33860i 0.561699 0.324297i −0.192128 0.981370i \(-0.561539\pi\)
0.753827 + 0.657073i \(0.228206\pi\)
\(272\) 5.06592 0.307167
\(273\) 0 0
\(274\) 3.18956 0.192689
\(275\) 15.7256 9.07917i 0.948289 0.547495i
\(276\) 0 0
\(277\) 10.9545 18.9737i 0.658191 1.14002i −0.322892 0.946436i \(-0.604655\pi\)
0.981084 0.193585i \(-0.0620114\pi\)
\(278\) 0.595710i 0.0357283i
\(279\) 0 0
\(280\) −0.781015 0.450919i −0.0466746 0.0269476i
\(281\) 25.7719i 1.53743i −0.639594 0.768713i \(-0.720898\pi\)
0.639594 0.768713i \(-0.279102\pi\)
\(282\) 0 0
\(283\) −5.66344 9.80937i −0.336657 0.583107i 0.647145 0.762367i \(-0.275963\pi\)
−0.983802 + 0.179260i \(0.942630\pi\)
\(284\) 2.83932 1.63928i 0.168482 0.0972733i
\(285\) 0 0
\(286\) 14.3733 + 6.16055i 0.849908 + 0.364281i
\(287\) 3.99654 0.235908
\(288\) 0 0
\(289\) −4.33177 7.50285i −0.254810 0.441344i
\(290\) −0.988802 + 1.71266i −0.0580645 + 0.100571i
\(291\) 0 0
\(292\) −0.466808 0.269511i −0.0273178 0.0157720i
\(293\) −20.5646 11.8730i −1.20140 0.693626i −0.240530 0.970642i \(-0.577321\pi\)
−0.960865 + 0.277016i \(0.910655\pi\)
\(294\) 0 0
\(295\) −3.85506 + 6.67716i −0.224450 + 0.388759i
\(296\) 0.0721531 + 0.124973i 0.00419382 + 0.00726390i
\(297\) 0 0
\(298\) 11.2096 0.649357
\(299\) −24.3994 + 18.2527i −1.41105 + 1.05558i
\(300\) 0 0
\(301\) 6.67577 3.85426i 0.384785 0.222156i
\(302\) −6.53653 11.3216i −0.376135 0.651485i
\(303\) 0 0
\(304\) 6.17238i 0.354010i
\(305\) −6.50930 3.75814i −0.372721 0.215191i
\(306\) 0 0
\(307\) 6.68810i 0.381710i 0.981618 + 0.190855i \(0.0611261\pi\)
−0.981618 + 0.190855i \(0.938874\pi\)
\(308\) 2.16858 3.75609i 0.123566 0.214023i
\(309\) 0 0
\(310\) −0.681875 + 0.393681i −0.0387279 + 0.0223596i
\(311\) −9.18724 −0.520961 −0.260480 0.965479i \(-0.583881\pi\)
−0.260480 + 0.965479i \(0.583881\pi\)
\(312\) 0 0
\(313\) −17.1631 −0.970118 −0.485059 0.874481i \(-0.661202\pi\)
−0.485059 + 0.874481i \(0.661202\pi\)
\(314\) −15.5231 + 8.96225i −0.876018 + 0.505769i
\(315\) 0 0
\(316\) 3.26674 5.65817i 0.183769 0.318297i
\(317\) 3.76247i 0.211322i −0.994402 0.105661i \(-0.966304\pi\)
0.994402 0.105661i \(-0.0336958\pi\)
\(318\) 0 0
\(319\) −8.23658 4.75539i −0.461160 0.266251i
\(320\) 0.901839i 0.0504143i
\(321\) 0 0
\(322\) 4.22559 + 7.31893i 0.235483 + 0.407868i
\(323\) −27.0796 + 15.6344i −1.50675 + 0.869921i
\(324\) 0 0
\(325\) −1.78720 14.9891i −0.0991358 0.831448i
\(326\) −20.3179 −1.12530
\(327\) 0 0
\(328\) 1.99827 + 3.46110i 0.110336 + 0.191107i
\(329\) 1.46057 2.52979i 0.0805241 0.139472i
\(330\) 0 0
\(331\) −27.9083 16.1129i −1.53398 0.885643i −0.999173 0.0406683i \(-0.987051\pi\)
−0.534806 0.844975i \(-0.679615\pi\)
\(332\) −11.4617 6.61742i −0.629043 0.363178i
\(333\) 0 0
\(334\) −1.61525 + 2.79770i −0.0883827 + 0.153083i
\(335\) −4.68182 8.10916i −0.255795 0.443051i
\(336\) 0 0
\(337\) −3.01703 −0.164348 −0.0821740 0.996618i \(-0.526186\pi\)
−0.0821740 + 0.996618i \(0.526186\pi\)
\(338\) 9.41441 8.96487i 0.512077 0.487624i
\(339\) 0 0
\(340\) −3.95656 + 2.28432i −0.214575 + 0.123885i
\(341\) −1.89331 3.27931i −0.102528 0.177584i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 6.67577 + 3.85426i 0.359933 + 0.207808i
\(345\) 0 0
\(346\) 9.17044i 0.493006i
\(347\) 0.234270 0.405768i 0.0125763 0.0217828i −0.859669 0.510852i \(-0.829330\pi\)
0.872245 + 0.489069i \(0.162663\pi\)
\(348\) 0 0
\(349\) −27.9044 + 16.1106i −1.49369 + 0.862380i −0.999974 0.00724565i \(-0.997694\pi\)
−0.493712 + 0.869625i \(0.664360\pi\)
\(350\) −4.18669 −0.223788
\(351\) 0 0
\(352\) 4.33716 0.231172
\(353\) 11.3583 6.55771i 0.604540 0.349031i −0.166285 0.986078i \(-0.553177\pi\)
0.770826 + 0.637046i \(0.219844\pi\)
\(354\) 0 0
\(355\) −1.47837 + 2.56060i −0.0784635 + 0.135903i
\(356\) 7.79180i 0.412965i
\(357\) 0 0
\(358\) −14.6834 8.47747i −0.776043 0.448048i
\(359\) 4.37981i 0.231157i 0.993298 + 0.115579i \(0.0368722\pi\)
−0.993298 + 0.115579i \(0.963128\pi\)
\(360\) 0 0
\(361\) 9.54914 + 16.5396i 0.502586 + 0.870505i
\(362\) 2.30140 1.32871i 0.120959 0.0698357i
\(363\) 0 0
\(364\) −2.15978 2.88710i −0.113203 0.151325i
\(365\) 0.486112 0.0254443
\(366\) 0 0
\(367\) −12.9094 22.3597i −0.673865 1.16717i −0.976799 0.214157i \(-0.931300\pi\)
0.302934 0.953011i \(-0.402034\pi\)
\(368\) −4.22559 + 7.31893i −0.220274 + 0.381526i
\(369\) 0 0
\(370\) −0.112705 0.0650705i −0.00585928 0.00338285i
\(371\) −1.46963 0.848493i −0.0762995 0.0440515i
\(372\) 0 0
\(373\) −15.3143 + 26.5251i −0.792942 + 1.37342i 0.131196 + 0.991356i \(0.458118\pi\)
−0.924138 + 0.382059i \(0.875215\pi\)
\(374\) −10.9859 19.0281i −0.568065 0.983918i
\(375\) 0 0
\(376\) 2.92115 0.150647
\(377\) −6.33100 + 4.73609i −0.326063 + 0.243921i
\(378\) 0 0
\(379\) −33.0409 + 19.0762i −1.69720 + 0.979877i −0.748796 + 0.662801i \(0.769368\pi\)
−0.948400 + 0.317076i \(0.897299\pi\)
\(380\) 2.78325 + 4.82072i 0.142778 + 0.247298i
\(381\) 0 0
\(382\) 24.4861i 1.25282i
\(383\) 27.6783 + 15.9801i 1.41430 + 0.816544i 0.995790 0.0916693i \(-0.0292203\pi\)
0.418507 + 0.908214i \(0.362554\pi\)
\(384\) 0 0
\(385\) 3.91142i 0.199345i
\(386\) −6.12046 + 10.6009i −0.311523 + 0.539574i
\(387\) 0 0
\(388\) 10.1378 5.85305i 0.514668 0.297144i
\(389\) −5.24585 −0.265975 −0.132988 0.991118i \(-0.542457\pi\)
−0.132988 + 0.991118i \(0.542457\pi\)
\(390\) 0 0
\(391\) 42.8130 2.16514
\(392\) −0.866025 + 0.500000i −0.0437409 + 0.0252538i
\(393\) 0 0
\(394\) 2.72876 4.72634i 0.137473 0.238110i
\(395\) 5.89215i 0.296466i
\(396\) 0 0
\(397\) 21.2432 + 12.2648i 1.06617 + 0.615552i 0.927132 0.374736i \(-0.122266\pi\)
0.139035 + 0.990287i \(0.455600\pi\)
\(398\) 12.8166i 0.642440i
\(399\) 0 0
\(400\) −2.09334 3.62578i −0.104667 0.181289i
\(401\) −3.69916 + 2.13571i −0.184727 + 0.106652i −0.589512 0.807760i \(-0.700680\pi\)
0.404784 + 0.914412i \(0.367347\pi\)
\(402\) 0 0
\(403\) −3.12573 + 0.372689i −0.155704 + 0.0185650i
\(404\) 10.7429 0.534479
\(405\) 0 0
\(406\) 1.09643 + 1.89907i 0.0544149 + 0.0942493i
\(407\) 0.312940 0.542028i 0.0155119 0.0268673i
\(408\) 0 0
\(409\) −1.39990 0.808235i −0.0692208 0.0399646i 0.464990 0.885316i \(-0.346058\pi\)
−0.534211 + 0.845351i \(0.679391\pi\)
\(410\) −3.12136 1.80212i −0.154153 0.0890001i
\(411\) 0 0
\(412\) 2.40550 4.16644i 0.118510 0.205266i
\(413\) 4.27467 + 7.40394i 0.210343 + 0.364324i
\(414\) 0 0
\(415\) 11.9357 0.585900
\(416\) 1.42041 3.31398i 0.0696414 0.162481i
\(417\) 0 0
\(418\) −23.1840 + 13.3853i −1.13397 + 0.654697i
\(419\) −13.0156 22.5437i −0.635854 1.10133i −0.986334 0.164761i \(-0.947315\pi\)
0.350480 0.936570i \(-0.386018\pi\)
\(420\) 0 0
\(421\) 37.5391i 1.82954i −0.403971 0.914772i \(-0.632370\pi\)
0.403971 0.914772i \(-0.367630\pi\)
\(422\) −16.7239 9.65552i −0.814104 0.470023i
\(423\) 0 0
\(424\) 1.69699i 0.0824129i
\(425\) −10.6047 + 18.3679i −0.514404 + 0.890974i
\(426\) 0 0
\(427\) −7.21780 + 4.16720i −0.349294 + 0.201665i
\(428\) 13.6530 0.659944
\(429\) 0 0
\(430\) −6.95183 −0.335247
\(431\) −18.6662 + 10.7769i −0.899118 + 0.519106i −0.876914 0.480647i \(-0.840402\pi\)
−0.0222041 + 0.999753i \(0.507068\pi\)
\(432\) 0 0
\(433\) 1.59958 2.77056i 0.0768710 0.133145i −0.825027 0.565093i \(-0.808840\pi\)
0.901898 + 0.431948i \(0.142174\pi\)
\(434\) 0.873062i 0.0419083i
\(435\) 0 0
\(436\) −4.43186 2.55874i −0.212248 0.122541i
\(437\) 52.1638i 2.49534i
\(438\) 0 0
\(439\) 13.3114 + 23.0560i 0.635317 + 1.10040i 0.986448 + 0.164075i \(0.0524638\pi\)
−0.351131 + 0.936326i \(0.614203\pi\)
\(440\) −3.38739 + 1.95571i −0.161488 + 0.0932349i
\(441\) 0 0
\(442\) −18.1370 + 2.16252i −0.862688 + 0.102861i
\(443\) −9.09867 −0.432291 −0.216145 0.976361i \(-0.569348\pi\)
−0.216145 + 0.976361i \(0.569348\pi\)
\(444\) 0 0
\(445\) 3.51347 + 6.08551i 0.166555 + 0.288481i
\(446\) 5.31785 9.21079i 0.251808 0.436144i
\(447\) 0 0
\(448\) −0.866025 0.500000i −0.0409159 0.0236228i
\(449\) −6.08550 3.51346i −0.287192 0.165811i 0.349483 0.936943i \(-0.386357\pi\)
−0.636675 + 0.771132i \(0.719691\pi\)
\(450\) 0 0
\(451\) 8.66681 15.0114i 0.408104 0.706858i
\(452\) −8.96603 15.5296i −0.421726 0.730452i
\(453\) 0 0
\(454\) 22.7217 1.06638
\(455\) 2.98867 + 1.28098i 0.140111 + 0.0600533i
\(456\) 0 0
\(457\) −16.5853 + 9.57556i −0.775830 + 0.447926i −0.834950 0.550325i \(-0.814504\pi\)
0.0591204 + 0.998251i \(0.481170\pi\)
\(458\) 10.1547 + 17.5885i 0.474498 + 0.821855i
\(459\) 0 0
\(460\) 7.62159i 0.355359i
\(461\) 2.82026 + 1.62828i 0.131353 + 0.0758365i 0.564236 0.825613i \(-0.309171\pi\)
−0.432884 + 0.901450i \(0.642504\pi\)
\(462\) 0 0
\(463\) 21.2761i 0.988786i −0.869238 0.494393i \(-0.835390\pi\)
0.869238 0.494393i \(-0.164610\pi\)
\(464\) −1.09643 + 1.89907i −0.0509004 + 0.0881621i
\(465\) 0 0
\(466\) 9.21851 5.32231i 0.427039 0.246551i
\(467\) 3.33171 0.154173 0.0770866 0.997024i \(-0.475438\pi\)
0.0770866 + 0.997024i \(0.475438\pi\)
\(468\) 0 0
\(469\) −10.3828 −0.479435
\(470\) −2.28146 + 1.31720i −0.105236 + 0.0607580i
\(471\) 0 0
\(472\) −4.27467 + 7.40394i −0.196757 + 0.340794i
\(473\) 33.4331i 1.53725i
\(474\) 0 0
\(475\) 22.3797 + 12.9209i 1.02685 + 0.592852i
\(476\) 5.06592i 0.232196i
\(477\) 0 0
\(478\) 0.155782 + 0.269822i 0.00712530 + 0.0123414i
\(479\) 0.160402 0.0926079i 0.00732894 0.00423136i −0.496331 0.868133i \(-0.665320\pi\)
0.503660 + 0.863902i \(0.331986\pi\)
\(480\) 0 0
\(481\) −0.311670 0.416627i −0.0142109 0.0189965i
\(482\) 25.2995 1.15236
\(483\) 0 0
\(484\) −3.90550 6.76452i −0.177523 0.307478i
\(485\) −5.27851 + 9.14264i −0.239685 + 0.415146i
\(486\) 0 0
\(487\) −27.0466 15.6154i −1.22560 0.707601i −0.259494 0.965745i \(-0.583556\pi\)
−0.966106 + 0.258144i \(0.916889\pi\)
\(488\) −7.21780 4.16720i −0.326735 0.188640i
\(489\) 0 0
\(490\) 0.450919 0.781015i 0.0203705 0.0352827i
\(491\) −13.4236 23.2504i −0.605799 1.04927i −0.991925 0.126829i \(-0.959520\pi\)
0.386126 0.922446i \(-0.373813\pi\)
\(492\) 0 0
\(493\) 11.1088 0.500317
\(494\) 2.63484 + 22.0983i 0.118547 + 0.994250i
\(495\) 0 0
\(496\) −0.756094 + 0.436531i −0.0339496 + 0.0196008i
\(497\) 1.63928 + 2.83932i 0.0735317 + 0.127361i
\(498\) 0 0
\(499\) 15.2869i 0.684337i 0.939639 + 0.342168i \(0.111161\pi\)
−0.939639 + 0.342168i \(0.888839\pi\)
\(500\) 7.17494 + 4.14246i 0.320873 + 0.185256i
\(501\) 0 0
\(502\) 8.04030i 0.358856i
\(503\) −13.0551 + 22.6121i −0.582097 + 1.00822i 0.413133 + 0.910671i \(0.364434\pi\)
−0.995230 + 0.0975513i \(0.968899\pi\)
\(504\) 0 0
\(505\) −8.39036 + 4.84418i −0.373366 + 0.215563i
\(506\) 36.6541 1.62947
\(507\) 0 0
\(508\) −19.5136 −0.865777
\(509\) −14.7459 + 8.51357i −0.653602 + 0.377357i −0.789835 0.613320i \(-0.789834\pi\)
0.136233 + 0.990677i \(0.456500\pi\)
\(510\) 0 0
\(511\) 0.269511 0.466808i 0.0119225 0.0206504i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −14.6641 8.46634i −0.646807 0.373434i
\(515\) 4.33874i 0.191188i
\(516\) 0 0
\(517\) −6.33475 10.9721i −0.278602 0.482553i
\(518\) −0.124973 + 0.0721531i −0.00549099 + 0.00317023i
\(519\) 0 0
\(520\) 0.384973 + 3.22876i 0.0168822 + 0.141590i
\(521\) 18.7760 0.822593 0.411297 0.911502i \(-0.365076\pi\)
0.411297 + 0.911502i \(0.365076\pi\)
\(522\) 0 0
\(523\) 1.51624 + 2.62620i 0.0663004 + 0.114836i 0.897270 0.441482i \(-0.145547\pi\)
−0.830970 + 0.556318i \(0.812214\pi\)
\(524\) 10.3248 17.8831i 0.451042 0.781227i
\(525\) 0 0
\(526\) −8.93817 5.16045i −0.389723 0.225006i
\(527\) 3.83031 + 2.21143i 0.166851 + 0.0963315i
\(528\) 0 0
\(529\) −24.2111 + 41.9349i −1.05266 + 1.82326i
\(530\) 0.765204 + 1.32537i 0.0332383 + 0.0575705i
\(531\) 0 0
\(532\) 6.17238 0.267607
\(533\) −8.63164 11.5384i −0.373878 0.499783i
\(534\) 0 0
\(535\) −10.6632 + 6.15642i −0.461011 + 0.266165i
\(536\) −5.19142 8.99180i −0.224235 0.388387i
\(537\) 0 0
\(538\) 6.13999i 0.264714i
\(539\) 3.75609 + 2.16858i 0.161786 + 0.0934074i
\(540\) 0 0
\(541\) 6.11845i 0.263053i −0.991313 0.131526i \(-0.958012\pi\)
0.991313 0.131526i \(-0.0419878\pi\)
\(542\) −5.33860 + 9.24673i −0.229313 + 0.397181i
\(543\) 0 0
\(544\) −4.38722 + 2.53296i −0.188100 + 0.108600i
\(545\) 4.61513 0.197691
\(546\) 0 0
\(547\) −37.4754 −1.60233 −0.801166 0.598442i \(-0.795786\pi\)
−0.801166 + 0.598442i \(0.795786\pi\)
\(548\) −2.76224 + 1.59478i −0.117997 + 0.0681257i
\(549\) 0 0
\(550\) −9.07917 + 15.7256i −0.387137 + 0.670541i
\(551\) 13.5352i 0.576617i
\(552\) 0 0
\(553\) 5.65817 + 3.26674i 0.240610 + 0.138916i
\(554\) 21.9090i 0.930823i
\(555\) 0 0
\(556\) −0.297855 0.515900i −0.0126319 0.0218790i
\(557\) 7.69941 4.44526i 0.326234 0.188352i −0.327934 0.944701i \(-0.606352\pi\)
0.654168 + 0.756349i \(0.273019\pi\)
\(558\) 0 0
\(559\) −25.5458 10.9493i −1.08047 0.463104i
\(560\) 0.901839 0.0381096
\(561\) 0 0
\(562\) 12.8860 + 22.3192i 0.543562 + 0.941477i
\(563\) −8.89598 + 15.4083i −0.374921 + 0.649382i −0.990315 0.138838i \(-0.955663\pi\)
0.615394 + 0.788219i \(0.288997\pi\)
\(564\) 0 0
\(565\) 14.0052 + 8.08591i 0.589204 + 0.340177i
\(566\) 9.80937 + 5.66344i 0.412319 + 0.238052i
\(567\) 0 0
\(568\) −1.63928 + 2.83932i −0.0687826 + 0.119135i
\(569\) −5.58684 9.67669i −0.234212 0.405668i 0.724831 0.688927i \(-0.241918\pi\)
−0.959044 + 0.283259i \(0.908584\pi\)
\(570\) 0 0
\(571\) −16.7239 −0.699873 −0.349936 0.936773i \(-0.613797\pi\)
−0.349936 + 0.936773i \(0.613797\pi\)
\(572\) −15.5279 + 1.85143i −0.649253 + 0.0774122i
\(573\) 0 0
\(574\) −3.46110 + 1.99827i −0.144464 + 0.0834061i
\(575\) −17.6912 30.6421i −0.737774 1.27786i
\(576\) 0 0
\(577\) 0.798887i 0.0332581i −0.999862 0.0166291i \(-0.994707\pi\)
0.999862 0.0166291i \(-0.00529344\pi\)
\(578\) 7.50285 + 4.33177i 0.312078 + 0.180178i
\(579\) 0 0
\(580\) 1.97760i 0.0821155i
\(581\) 6.61742 11.4617i 0.274537 0.475512i
\(582\) 0 0
\(583\) −6.37404 + 3.68005i −0.263986 + 0.152412i
\(584\) 0.539023 0.0223049
\(585\) 0 0
\(586\) 23.7459 0.980935
\(587\) −6.94921 + 4.01213i −0.286825 + 0.165598i −0.636509 0.771269i \(-0.719622\pi\)
0.349684 + 0.936868i \(0.386289\pi\)
\(588\) 0 0
\(589\) 2.69444 4.66690i 0.111022 0.192296i
\(590\) 7.71012i 0.317421i
\(591\) 0 0
\(592\) −0.124973 0.0721531i −0.00513635 0.00296548i
\(593\) 4.93120i 0.202500i −0.994861 0.101250i \(-0.967716\pi\)
0.994861 0.101250i \(-0.0322842\pi\)
\(594\) 0 0
\(595\) −2.28432 3.95656i −0.0936481 0.162203i
\(596\) −9.70783 + 5.60482i −0.397648 + 0.229582i
\(597\) 0 0
\(598\) 12.0041 28.0070i 0.490886 1.14529i
\(599\) 17.8249 0.728306 0.364153 0.931339i \(-0.381358\pi\)
0.364153 + 0.931339i \(0.381358\pi\)
\(600\) 0 0
\(601\) 0.0809165 + 0.140152i 0.00330065 + 0.00571690i 0.867671 0.497139i \(-0.165616\pi\)
−0.864370 + 0.502856i \(0.832283\pi\)
\(602\) −3.85426 + 6.67577i −0.157088 + 0.272084i
\(603\) 0 0
\(604\) 11.3216 + 6.53653i 0.460670 + 0.265968i
\(605\) 6.10050 + 3.52213i 0.248021 + 0.143195i
\(606\) 0 0
\(607\) −3.09423 + 5.35937i −0.125591 + 0.217530i −0.921964 0.387276i \(-0.873416\pi\)
0.796373 + 0.604806i \(0.206749\pi\)
\(608\) 3.08619 + 5.34544i 0.125162 + 0.216786i
\(609\) 0 0
\(610\) 7.51629 0.304326
\(611\) −10.4583 + 1.24697i −0.423097 + 0.0504469i
\(612\) 0 0
\(613\) 32.2269 18.6062i 1.30163 0.751497i 0.320947 0.947097i \(-0.395999\pi\)
0.980684 + 0.195600i \(0.0626654\pi\)
\(614\) −3.34405 5.79207i −0.134955 0.233749i
\(615\) 0 0
\(616\) 4.33716i 0.174749i
\(617\) 5.78536 + 3.34018i 0.232910 + 0.134471i 0.611914 0.790924i \(-0.290400\pi\)
−0.379004 + 0.925395i \(0.623733\pi\)
\(618\) 0 0
\(619\) 23.7344i 0.953965i 0.878913 + 0.476982i \(0.158269\pi\)
−0.878913 + 0.476982i \(0.841731\pi\)
\(620\) 0.393681 0.681875i 0.0158106 0.0273848i
\(621\) 0 0
\(622\) 7.95639 4.59362i 0.319022 0.184187i
\(623\) 7.79180 0.312172
\(624\) 0 0
\(625\) 13.4618 0.538471
\(626\) 14.8637 8.58157i 0.594074 0.342989i
\(627\) 0 0
\(628\) 8.96225 15.5231i 0.357633 0.619438i
\(629\) 0.731044i 0.0291486i
\(630\) 0 0
\(631\) 19.9348 + 11.5093i 0.793590 + 0.458180i 0.841225 0.540685i \(-0.181835\pi\)
−0.0476346 + 0.998865i \(0.515168\pi\)
\(632\) 6.53349i 0.259888i
\(633\) 0 0
\(634\) 1.88124 + 3.25840i 0.0747135 + 0.129408i
\(635\) 15.2404 8.79907i 0.604798 0.349181i
\(636\) 0 0
\(637\) 2.88710 2.15978i 0.114391 0.0855737i
\(638\) 9.51078 0.376536
\(639\) 0 0
\(640\) 0.450919 + 0.781015i 0.0178242 + 0.0308723i
\(641\) −6.32539 + 10.9559i −0.249838 + 0.432732i −0.963481 0.267778i \(-0.913711\pi\)
0.713643 + 0.700510i \(0.247044\pi\)
\(642\) 0 0
\(643\) −13.1971 7.61938i −0.520445 0.300479i 0.216672 0.976244i \(-0.430480\pi\)
−0.737117 + 0.675766i \(0.763813\pi\)
\(644\) −7.31893 4.22559i −0.288406 0.166511i
\(645\) 0 0
\(646\) 15.6344 27.0796i 0.615127 1.06543i
\(647\) 14.6821 + 25.4301i 0.577213 + 0.999762i 0.995797 + 0.0915840i \(0.0291930\pi\)
−0.418585 + 0.908178i \(0.637474\pi\)
\(648\) 0 0
\(649\) 37.0799 1.45551
\(650\) 9.04233 + 12.0874i 0.354669 + 0.474106i
\(651\) 0 0
\(652\) 17.5958 10.1589i 0.689105 0.397855i
\(653\) −14.5106 25.1330i −0.567842 0.983532i −0.996779 0.0801974i \(-0.974445\pi\)
0.428937 0.903335i \(-0.358888\pi\)
\(654\) 0 0
\(655\) 18.6226i 0.727647i
\(656\) −3.46110 1.99827i −0.135133 0.0780192i
\(657\) 0 0
\(658\) 2.92115i 0.113878i
\(659\) 3.98651 6.90484i 0.155293 0.268975i −0.777873 0.628422i \(-0.783701\pi\)
0.933166 + 0.359447i \(0.117035\pi\)
\(660\) 0 0
\(661\) 3.40668 1.96685i 0.132505 0.0765015i −0.432282 0.901738i \(-0.642292\pi\)
0.564787 + 0.825237i \(0.308958\pi\)
\(662\) 32.2257 1.25249
\(663\) 0 0
\(664\) 13.2348 0.513611
\(665\) −4.82072 + 2.78325i −0.186940 + 0.107930i
\(666\) 0 0
\(667\) −9.26611 + 16.0494i −0.358785 + 0.621434i
\(668\) 3.23051i 0.124992i
\(669\) 0 0
\(670\) 8.10916 + 4.68182i 0.313284 + 0.180875i
\(671\) 36.1477i 1.39547i
\(672\) 0 0
\(673\) 18.1599 + 31.4539i 0.700014 + 1.21246i 0.968461 + 0.249166i \(0.0801563\pi\)
−0.268447 + 0.963295i \(0.586510\pi\)
\(674\) 2.61282 1.50851i 0.100642 0.0581058i
\(675\) 0 0
\(676\) −3.67069 + 12.4710i −0.141180 + 0.479654i
\(677\) 21.1068 0.811201 0.405600 0.914051i \(-0.367062\pi\)
0.405600 + 0.914051i \(0.367062\pi\)
\(678\) 0 0
\(679\) 5.85305 + 10.1378i 0.224619 + 0.389052i
\(680\) 2.28432 3.95656i 0.0875997 0.151727i
\(681\) 0 0
\(682\) 3.27931 + 1.89331i 0.125571 + 0.0724985i
\(683\) 22.8854 + 13.2129i 0.875685 + 0.505577i 0.869233 0.494402i \(-0.164613\pi\)
0.00645161 + 0.999979i \(0.497946\pi\)
\(684\) 0 0
\(685\) 1.43824 2.49110i 0.0549522 0.0951799i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) −7.70851 −0.293884
\(689\) 0.724402 + 6.07553i 0.0275975 + 0.231459i
\(690\) 0 0
\(691\) 0.675291 0.389880i 0.0256893 0.0148317i −0.487100 0.873346i \(-0.661945\pi\)
0.512790 + 0.858514i \(0.328612\pi\)
\(692\) −4.58522 7.94183i −0.174304 0.301903i
\(693\) 0 0
\(694\) 0.468540i 0.0177855i
\(695\) 0.465259 + 0.268617i 0.0176483 + 0.0101892i
\(696\) 0 0
\(697\) 20.2461i 0.766877i
\(698\) 16.1106 27.9044i 0.609795 1.05620i
\(699\) 0 0
\(700\) 3.62578 2.09334i 0.137041 0.0791209i
\(701\) −21.5491 −0.813899 −0.406950 0.913451i \(-0.633408\pi\)
−0.406950 + 0.913451i \(0.633408\pi\)
\(702\) 0 0
\(703\) 0.890713 0.0335939
\(704\) −3.75609 + 2.16858i −0.141563 + 0.0817315i
\(705\) 0 0
\(706\) −6.55771 + 11.3583i −0.246803 + 0.427474i
\(707\) 10.7429i 0.404028i
\(708\) 0 0
\(709\) −3.92952 2.26871i −0.147576 0.0852031i 0.424394 0.905478i \(-0.360487\pi\)
−0.571970 + 0.820275i \(0.693821\pi\)
\(710\) 2.95673i 0.110964i
\(711\) 0 0
\(712\) 3.89590 + 6.74790i 0.146005 + 0.252888i
\(713\) −6.38988 + 3.68920i −0.239303 + 0.138162i
\(714\) 0 0
\(715\) 11.2927 8.44782i 0.422322 0.315931i
\(716\) 16.9549 0.633636
\(717\) 0 0
\(718\) −2.18990 3.79302i −0.0817265 0.141554i
\(719\) 7.30036 12.6446i 0.272258 0.471564i −0.697182 0.716894i \(-0.745563\pi\)
0.969440 + 0.245330i \(0.0788964\pi\)
\(720\) 0 0
\(721\) 4.16644 + 2.40550i 0.155166 + 0.0895854i
\(722\) −16.5396 9.54914i −0.615540 0.355382i
\(723\) 0 0
\(724\) −1.32871 + 2.30140i −0.0493813 + 0.0855309i
\(725\) −4.59040 7.95081i −0.170483 0.295286i
\(726\) 0 0
\(727\) 30.6315 1.13606 0.568030 0.823008i \(-0.307706\pi\)
0.568030 + 0.823008i \(0.307706\pi\)
\(728\) 3.31398 + 1.42041i 0.122824 + 0.0526439i
\(729\) 0 0
\(730\) −0.420985 + 0.243056i −0.0155814 + 0.00899590i
\(731\) 19.5254 + 33.8189i 0.722171 + 1.25084i
\(732\) 0 0
\(733\) 17.7195i 0.654484i −0.944941 0.327242i \(-0.893881\pi\)
0.944941 0.327242i \(-0.106119\pi\)
\(734\) 22.3597 + 12.9094i 0.825313 + 0.476495i
\(735\) 0 0
\(736\) 8.45117i 0.311514i
\(737\) −22.5160 + 38.9989i −0.829389 + 1.43654i
\(738\) 0 0
\(739\) −9.05014 + 5.22510i −0.332915 + 0.192208i −0.657134 0.753773i \(-0.728232\pi\)
0.324220 + 0.945982i \(0.394898\pi\)
\(740\) 0.130141 0.00478408
\(741\) 0 0
\(742\) 1.69699 0.0622983
\(743\) −42.0103 + 24.2547i −1.54121 + 0.889818i −0.542447 + 0.840090i \(0.682502\pi\)
−0.998763 + 0.0497278i \(0.984165\pi\)
\(744\) 0 0
\(745\) 5.05464 8.75490i 0.185188 0.320755i
\(746\) 30.6285i 1.12139i
\(747\) 0 0
\(748\) 19.0281 + 10.9859i 0.695735 + 0.401683i
\(749\) 13.6530i 0.498871i
\(750\) 0 0
\(751\) 15.7278 + 27.2413i 0.573914 + 0.994049i 0.996159 + 0.0875667i \(0.0279091\pi\)
−0.422244 + 0.906482i \(0.638758\pi\)
\(752\) −2.52979 + 1.46057i −0.0922519 + 0.0532617i
\(753\) 0 0
\(754\) 3.11476 7.26708i 0.113433 0.264651i
\(755\) −11.7898 −0.429075
\(756\) 0 0
\(757\) −24.3442 42.1654i −0.884805 1.53253i −0.845937 0.533283i \(-0.820958\pi\)
−0.0388676 0.999244i \(-0.512375\pi\)
\(758\) 19.0762 33.0409i 0.692877 1.20010i
\(759\) 0 0
\(760\) −4.82072 2.78325i −0.174866 0.100959i
\(761\) 40.3350 + 23.2874i 1.46214 + 0.844169i 0.999110 0.0421718i \(-0.0134277\pi\)
0.463033 + 0.886341i \(0.346761\pi\)
\(762\) 0 0
\(763\) 2.55874 4.43186i 0.0926325 0.160444i
\(764\) 12.2430 + 21.2056i 0.442937 + 0.767190i
\(765\) 0 0
\(766\) −31.9602 −1.15477
\(767\) 12.1436 28.3323i 0.438479 1.02302i
\(768\) 0 0
\(769\) −24.1069 + 13.9181i −0.869315 + 0.501899i −0.867121 0.498098i \(-0.834032\pi\)
−0.00219468 + 0.999998i \(0.500699\pi\)
\(770\) −1.95571 3.38739i −0.0704789 0.122073i
\(771\) 0 0
\(772\) 12.2409i 0.440560i
\(773\) −24.6578 14.2362i −0.886880 0.512040i −0.0139594 0.999903i \(-0.504444\pi\)
−0.872921 + 0.487862i \(0.837777\pi\)
\(774\) 0 0
\(775\) 3.65524i 0.131300i
\(776\) −5.85305 + 10.1378i −0.210112 + 0.363925i
\(777\) 0 0
\(778\) 4.54304 2.62292i 0.162876 0.0940364i
\(779\) 24.6681 0.883828
\(780\) 0 0
\(781\) 14.2196 0.508819
\(782\) −37.0771 + 21.4065i −1.32587 + 0.765494i
\(783\) 0 0
\(784\) 0.500000 0.866025i 0.0178571 0.0309295i
\(785\) 16.1650i 0.576954i
\(786\) 0 0
\(787\) 13.1046 + 7.56594i 0.467128