Properties

Label 1152.2.i.g.769.1
Level $1152$
Weight $2$
Character 1152.769
Analytic conductor $9.199$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.8528759163648.1
Defining polynomial: \(x^{10} - 2 x^{9} + x^{8} + 9 x^{6} - 36 x^{5} + 27 x^{4} + 27 x^{2} - 162 x + 243\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 769.1
Root \(-1.41743 - 0.995434i\) of defining polynomial
Character \(\chi\) \(=\) 1152.769
Dual form 1152.2.i.g.385.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.57079 - 0.729814i) q^{3} +(-0.115851 + 0.200661i) q^{5} +(-0.230793 - 0.399745i) q^{7} +(1.93474 + 2.29277i) q^{9} +O(q^{10})\) \(q+(-1.57079 - 0.729814i) q^{3} +(-0.115851 + 0.200661i) q^{5} +(-0.230793 - 0.399745i) q^{7} +(1.93474 + 2.29277i) q^{9} +(-0.749014 - 1.29733i) q^{11} +(1.07079 - 1.85466i) q^{13} +(0.328423 - 0.230645i) q^{15} +1.03644 q^{17} -2.94631 q^{19} +(0.0707868 + 0.796350i) q^{21} +(-0.364866 + 0.631966i) q^{23} +(2.47316 + 4.28363i) q^{25} +(-1.36578 - 5.01345i) q^{27} +(-2.33711 - 4.04800i) q^{29} +(2.73632 - 4.73945i) q^{31} +(0.229731 + 2.58447i) q^{33} +0.106951 q^{35} +2.30039 q^{37} +(-3.03553 + 2.13180i) q^{39} +(-1.84151 + 3.18959i) q^{41} +(-2.41968 - 4.19101i) q^{43} +(-0.684210 + 0.122606i) q^{45} +(-5.40881 - 9.36833i) q^{47} +(3.39347 - 5.87766i) q^{49} +(-1.62803 - 0.756411i) q^{51} -10.0430 q^{53} +0.347097 q^{55} +(4.62803 + 2.15026i) q^{57} +(2.71613 - 4.70447i) q^{59} +(-6.86526 - 11.8910i) q^{61} +(0.469996 - 1.30256i) q^{63} +(0.248104 + 0.429729i) q^{65} +(-5.58388 + 9.67156i) q^{67} +(1.03434 - 0.726400i) q^{69} -13.2942 q^{71} +4.24276 q^{73} +(-0.758546 - 8.53362i) q^{75} +(-0.345734 + 0.598829i) q^{77} +(-6.23617 - 10.8014i) q^{79} +(-1.51354 + 8.87182i) q^{81} +(3.62651 + 6.28130i) q^{83} +(-0.120073 + 0.207973i) q^{85} +(0.716820 + 8.06420i) q^{87} -11.8627 q^{89} -0.988520 q^{91} +(-7.75710 + 5.44766i) q^{93} +(0.341335 - 0.591209i) q^{95} +(-2.21479 - 3.83613i) q^{97} +(1.52532 - 4.22731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + q^{3} - 4q^{7} - q^{9} + O(q^{10}) \) \( 10q + q^{3} - 4q^{7} - q^{9} - q^{11} - 6q^{13} + 12q^{15} - 6q^{17} + 18q^{19} - 16q^{21} + 4q^{23} + q^{25} - 2q^{27} + 4q^{29} - 8q^{31} - 13q^{33} - 24q^{35} + 20q^{37} - 18q^{39} - 5q^{41} - 13q^{43} + 12q^{45} - 6q^{47} + 3q^{49} + 3q^{51} + 12q^{55} + 27q^{57} - 13q^{59} - 10q^{61} - 20q^{63} - 17q^{67} + 10q^{69} + 8q^{71} - 34q^{73} - 29q^{75} - 8q^{77} - 6q^{79} - q^{81} + 12q^{83} - 18q^{85} + 10q^{87} + 44q^{89} + 36q^{91} - 26q^{93} - 6q^{95} + 27q^{97} + 34q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(3\) −1.57079 0.729814i −0.906894 0.421358i
\(4\) 0 0
\(5\) −0.115851 + 0.200661i −0.0518103 + 0.0897381i −0.890767 0.454459i \(-0.849832\pi\)
0.838957 + 0.544198i \(0.183166\pi\)
\(6\) 0 0
\(7\) −0.230793 0.399745i −0.0872315 0.151089i 0.819108 0.573639i \(-0.194469\pi\)
−0.906340 + 0.422549i \(0.861135\pi\)
\(8\) 0 0
\(9\) 1.93474 + 2.29277i 0.644914 + 0.764255i
\(10\) 0 0
\(11\) −0.749014 1.29733i −0.225836 0.391160i 0.730734 0.682663i \(-0.239178\pi\)
−0.956570 + 0.291503i \(0.905845\pi\)
\(12\) 0 0
\(13\) 1.07079 1.85466i 0.296983 0.514389i −0.678461 0.734636i \(-0.737353\pi\)
0.975444 + 0.220247i \(0.0706863\pi\)
\(14\) 0 0
\(15\) 0.328423 0.230645i 0.0847984 0.0595523i
\(16\) 0 0
\(17\) 1.03644 0.251374 0.125687 0.992070i \(-0.459886\pi\)
0.125687 + 0.992070i \(0.459886\pi\)
\(18\) 0 0
\(19\) −2.94631 −0.675931 −0.337965 0.941159i \(-0.609739\pi\)
−0.337965 + 0.941159i \(0.609739\pi\)
\(20\) 0 0
\(21\) 0.0707868 + 0.796350i 0.0154470 + 0.173778i
\(22\) 0 0
\(23\) −0.364866 + 0.631966i −0.0760798 + 0.131774i −0.901555 0.432664i \(-0.857574\pi\)
0.825476 + 0.564438i \(0.190907\pi\)
\(24\) 0 0
\(25\) 2.47316 + 4.28363i 0.494631 + 0.856727i
\(26\) 0 0
\(27\) −1.36578 5.01345i −0.262844 0.964838i
\(28\) 0 0
\(29\) −2.33711 4.04800i −0.433991 0.751694i 0.563222 0.826306i \(-0.309562\pi\)
−0.997213 + 0.0746115i \(0.976228\pi\)
\(30\) 0 0
\(31\) 2.73632 4.73945i 0.491458 0.851230i −0.508494 0.861066i \(-0.669797\pi\)
0.999952 + 0.00983556i \(0.00313081\pi\)
\(32\) 0 0
\(33\) 0.229731 + 2.58447i 0.0399911 + 0.449899i
\(34\) 0 0
\(35\) 0.106951 0.0180780
\(36\) 0 0
\(37\) 2.30039 0.378182 0.189091 0.981960i \(-0.439446\pi\)
0.189091 + 0.981960i \(0.439446\pi\)
\(38\) 0 0
\(39\) −3.03553 + 2.13180i −0.486074 + 0.341361i
\(40\) 0 0
\(41\) −1.84151 + 3.18959i −0.287596 + 0.498131i −0.973235 0.229811i \(-0.926189\pi\)
0.685639 + 0.727941i \(0.259523\pi\)
\(42\) 0 0
\(43\) −2.41968 4.19101i −0.368998 0.639123i 0.620411 0.784277i \(-0.286966\pi\)
−0.989409 + 0.145153i \(0.953632\pi\)
\(44\) 0 0
\(45\) −0.684210 + 0.122606i −0.101996 + 0.0182771i
\(46\) 0 0
\(47\) −5.40881 9.36833i −0.788956 1.36651i −0.926607 0.376031i \(-0.877289\pi\)
0.137651 0.990481i \(-0.456045\pi\)
\(48\) 0 0
\(49\) 3.39347 5.87766i 0.484781 0.839666i
\(50\) 0 0
\(51\) −1.62803 0.756411i −0.227970 0.105919i
\(52\) 0 0
\(53\) −10.0430 −1.37951 −0.689756 0.724042i \(-0.742282\pi\)
−0.689756 + 0.724042i \(0.742282\pi\)
\(54\) 0 0
\(55\) 0.347097 0.0468026
\(56\) 0 0
\(57\) 4.62803 + 2.15026i 0.612998 + 0.284809i
\(58\) 0 0
\(59\) 2.71613 4.70447i 0.353610 0.612470i −0.633269 0.773932i \(-0.718287\pi\)
0.986879 + 0.161461i \(0.0516207\pi\)
\(60\) 0 0
\(61\) −6.86526 11.8910i −0.879007 1.52248i −0.852432 0.522838i \(-0.824873\pi\)
−0.0265746 0.999647i \(-0.508460\pi\)
\(62\) 0 0
\(63\) 0.469996 1.30256i 0.0592140 0.164107i
\(64\) 0 0
\(65\) 0.248104 + 0.429729i 0.0307736 + 0.0533014i
\(66\) 0 0
\(67\) −5.58388 + 9.67156i −0.682179 + 1.18157i 0.292135 + 0.956377i \(0.405634\pi\)
−0.974314 + 0.225192i \(0.927699\pi\)
\(68\) 0 0
\(69\) 1.03434 0.726400i 0.124520 0.0874482i
\(70\) 0 0
\(71\) −13.2942 −1.57773 −0.788866 0.614565i \(-0.789331\pi\)
−0.788866 + 0.614565i \(0.789331\pi\)
\(72\) 0 0
\(73\) 4.24276 0.496578 0.248289 0.968686i \(-0.420132\pi\)
0.248289 + 0.968686i \(0.420132\pi\)
\(74\) 0 0
\(75\) −0.758546 8.53362i −0.0875893 0.985378i
\(76\) 0 0
\(77\) −0.345734 + 0.598829i −0.0394001 + 0.0682429i
\(78\) 0 0
\(79\) −6.23617 10.8014i −0.701624 1.21525i −0.967896 0.251351i \(-0.919125\pi\)
0.266272 0.963898i \(-0.414208\pi\)
\(80\) 0 0
\(81\) −1.51354 + 8.87182i −0.168171 + 0.985758i
\(82\) 0 0
\(83\) 3.62651 + 6.28130i 0.398061 + 0.689463i 0.993487 0.113948i \(-0.0363497\pi\)
−0.595425 + 0.803411i \(0.703016\pi\)
\(84\) 0 0
\(85\) −0.120073 + 0.207973i −0.0130238 + 0.0225579i
\(86\) 0 0
\(87\) 0.716820 + 8.06420i 0.0768511 + 0.864573i
\(88\) 0 0
\(89\) −11.8627 −1.25745 −0.628724 0.777628i \(-0.716423\pi\)
−0.628724 + 0.777628i \(0.716423\pi\)
\(90\) 0 0
\(91\) −0.988520 −0.103625
\(92\) 0 0
\(93\) −7.75710 + 5.44766i −0.804373 + 0.564896i
\(94\) 0 0
\(95\) 0.341335 0.591209i 0.0350202 0.0606567i
\(96\) 0 0
\(97\) −2.21479 3.83613i −0.224878 0.389500i 0.731405 0.681943i \(-0.238865\pi\)
−0.956283 + 0.292444i \(0.905532\pi\)
\(98\) 0 0
\(99\) 1.52532 4.22731i 0.153301 0.424861i
\(100\) 0 0
\(101\) −7.47401 12.9454i −0.743692 1.28811i −0.950804 0.309794i \(-0.899740\pi\)
0.207112 0.978317i \(-0.433594\pi\)
\(102\) 0 0
\(103\) 0.0310319 0.0537488i 0.00305766 0.00529603i −0.864493 0.502646i \(-0.832360\pi\)
0.867550 + 0.497350i \(0.165693\pi\)
\(104\) 0 0
\(105\) −0.167997 0.0780541i −0.0163948 0.00761730i
\(106\) 0 0
\(107\) 11.9297 1.15329 0.576645 0.816995i \(-0.304362\pi\)
0.576645 + 0.816995i \(0.304362\pi\)
\(108\) 0 0
\(109\) 10.1328 0.970544 0.485272 0.874363i \(-0.338721\pi\)
0.485272 + 0.874363i \(0.338721\pi\)
\(110\) 0 0
\(111\) −3.61342 1.67886i −0.342971 0.159350i
\(112\) 0 0
\(113\) −0.743274 + 1.28739i −0.0699213 + 0.121107i −0.898866 0.438223i \(-0.855608\pi\)
0.828945 + 0.559330i \(0.188941\pi\)
\(114\) 0 0
\(115\) −0.0845404 0.146428i −0.00788343 0.0136545i
\(116\) 0 0
\(117\) 6.32399 1.13322i 0.584653 0.104766i
\(118\) 0 0
\(119\) −0.239204 0.414313i −0.0219278 0.0379800i
\(120\) 0 0
\(121\) 4.37796 7.58284i 0.397996 0.689349i
\(122\) 0 0
\(123\) 5.22043 3.66621i 0.470711 0.330571i
\(124\) 0 0
\(125\) −2.30459 −0.206129
\(126\) 0 0
\(127\) 16.5663 1.47002 0.735010 0.678056i \(-0.237177\pi\)
0.735010 + 0.678056i \(0.237177\pi\)
\(128\) 0 0
\(129\) 0.742144 + 8.34910i 0.0653422 + 0.735098i
\(130\) 0 0
\(131\) −1.43125 + 2.47900i −0.125049 + 0.216591i −0.921752 0.387780i \(-0.873242\pi\)
0.796703 + 0.604371i \(0.206576\pi\)
\(132\) 0 0
\(133\) 0.679988 + 1.17777i 0.0589624 + 0.102126i
\(134\) 0 0
\(135\) 1.16423 + 0.306758i 0.100201 + 0.0264015i
\(136\) 0 0
\(137\) −8.27650 14.3353i −0.707109 1.22475i −0.965925 0.258822i \(-0.916666\pi\)
0.258816 0.965927i \(-0.416668\pi\)
\(138\) 0 0
\(139\) −3.68545 + 6.38339i −0.312596 + 0.541432i −0.978923 0.204227i \(-0.934532\pi\)
0.666328 + 0.745659i \(0.267865\pi\)
\(140\) 0 0
\(141\) 1.65894 + 18.6631i 0.139708 + 1.57171i
\(142\) 0 0
\(143\) −3.20814 −0.268278
\(144\) 0 0
\(145\) 1.08303 0.0899408
\(146\) 0 0
\(147\) −9.62002 + 6.75595i −0.793446 + 0.557221i
\(148\) 0 0
\(149\) −1.06052 + 1.83688i −0.0868814 + 0.150483i −0.906191 0.422868i \(-0.861023\pi\)
0.819310 + 0.573351i \(0.194357\pi\)
\(150\) 0 0
\(151\) −1.97197 3.41555i −0.160476 0.277953i 0.774563 0.632497i \(-0.217970\pi\)
−0.935040 + 0.354543i \(0.884636\pi\)
\(152\) 0 0
\(153\) 2.00525 + 2.37632i 0.162115 + 0.192114i
\(154\) 0 0
\(155\) 0.634013 + 1.09814i 0.0509252 + 0.0882050i
\(156\) 0 0
\(157\) 5.77046 9.99472i 0.460532 0.797666i −0.538455 0.842654i \(-0.680992\pi\)
0.998987 + 0.0449886i \(0.0143252\pi\)
\(158\) 0 0
\(159\) 15.7754 + 7.32952i 1.25107 + 0.581269i
\(160\) 0 0
\(161\) 0.336834 0.0265462
\(162\) 0 0
\(163\) 0.716550 0.0561245 0.0280623 0.999606i \(-0.491066\pi\)
0.0280623 + 0.999606i \(0.491066\pi\)
\(164\) 0 0
\(165\) −0.545216 0.253317i −0.0424450 0.0197207i
\(166\) 0 0
\(167\) −4.36210 + 7.55538i −0.337550 + 0.584653i −0.983971 0.178327i \(-0.942931\pi\)
0.646422 + 0.762980i \(0.276265\pi\)
\(168\) 0 0
\(169\) 4.20683 + 7.28645i 0.323602 + 0.560496i
\(170\) 0 0
\(171\) −5.70036 6.75521i −0.435917 0.516583i
\(172\) 0 0
\(173\) 8.96809 + 15.5332i 0.681832 + 1.18097i 0.974421 + 0.224729i \(0.0721496\pi\)
−0.292590 + 0.956238i \(0.594517\pi\)
\(174\) 0 0
\(175\) 1.14157 1.97726i 0.0862949 0.149467i
\(176\) 0 0
\(177\) −7.69985 + 5.40746i −0.578756 + 0.406449i
\(178\) 0 0
\(179\) 6.66578 0.498224 0.249112 0.968475i \(-0.419861\pi\)
0.249112 + 0.968475i \(0.419861\pi\)
\(180\) 0 0
\(181\) 19.1119 1.42058 0.710290 0.703909i \(-0.248564\pi\)
0.710290 + 0.703909i \(0.248564\pi\)
\(182\) 0 0
\(183\) 2.10566 + 23.6886i 0.155655 + 1.75111i
\(184\) 0 0
\(185\) −0.266503 + 0.461598i −0.0195937 + 0.0339373i
\(186\) 0 0
\(187\) −0.776311 1.34461i −0.0567695 0.0983276i
\(188\) 0 0
\(189\) −1.68889 + 1.70303i −0.122849 + 0.123877i
\(190\) 0 0
\(191\) −1.03948 1.80042i −0.0752138 0.130274i 0.825965 0.563721i \(-0.190631\pi\)
−0.901179 + 0.433447i \(0.857297\pi\)
\(192\) 0 0
\(193\) 10.1978 17.6632i 0.734057 1.27142i −0.221079 0.975256i \(-0.570958\pi\)
0.955136 0.296168i \(-0.0957089\pi\)
\(194\) 0 0
\(195\) −0.0760965 0.856083i −0.00544938 0.0613054i
\(196\) 0 0
\(197\) −16.5458 −1.17884 −0.589419 0.807828i \(-0.700643\pi\)
−0.589419 + 0.807828i \(0.700643\pi\)
\(198\) 0 0
\(199\) 21.2942 1.50951 0.754753 0.656009i \(-0.227757\pi\)
0.754753 + 0.656009i \(0.227757\pi\)
\(200\) 0 0
\(201\) 15.8295 11.1168i 1.11653 0.784116i
\(202\) 0 0
\(203\) −1.07878 + 1.86850i −0.0757153 + 0.131143i
\(204\) 0 0
\(205\) −0.426684 0.739038i −0.0298009 0.0516166i
\(206\) 0 0
\(207\) −2.15487 + 0.386140i −0.149774 + 0.0268386i
\(208\) 0 0
\(209\) 2.20683 + 3.82234i 0.152650 + 0.264397i
\(210\) 0 0
\(211\) −10.1986 + 17.6645i −0.702101 + 1.21607i 0.265627 + 0.964076i \(0.414421\pi\)
−0.967728 + 0.251999i \(0.918912\pi\)
\(212\) 0 0
\(213\) 20.8824 + 9.70230i 1.43084 + 0.664791i
\(214\) 0 0
\(215\) 1.12129 0.0764716
\(216\) 0 0
\(217\) −2.52609 −0.171482
\(218\) 0 0
\(219\) −6.66447 3.09643i −0.450343 0.209237i
\(220\) 0 0
\(221\) 1.10981 1.92225i 0.0746539 0.129304i
\(222\) 0 0
\(223\) 2.52026 + 4.36522i 0.168769 + 0.292317i 0.937987 0.346669i \(-0.112687\pi\)
−0.769218 + 0.638986i \(0.779354\pi\)
\(224\) 0 0
\(225\) −5.03644 + 13.9581i −0.335763 + 0.930540i
\(226\) 0 0
\(227\) 8.12047 + 14.0651i 0.538975 + 0.933531i 0.998960 + 0.0456047i \(0.0145214\pi\)
−0.459985 + 0.887927i \(0.652145\pi\)
\(228\) 0 0
\(229\) −2.92453 + 5.06544i −0.193259 + 0.334734i −0.946328 0.323207i \(-0.895239\pi\)
0.753070 + 0.657941i \(0.228572\pi\)
\(230\) 0 0
\(231\) 0.980109 0.688311i 0.0644864 0.0452876i
\(232\) 0 0
\(233\) −20.7492 −1.35932 −0.679662 0.733526i \(-0.737873\pi\)
−0.679662 + 0.733526i \(0.737873\pi\)
\(234\) 0 0
\(235\) 2.50647 0.163504
\(236\) 0 0
\(237\) 1.91271 + 21.5179i 0.124244 + 1.39774i
\(238\) 0 0
\(239\) −2.09672 + 3.63163i −0.135626 + 0.234910i −0.925836 0.377925i \(-0.876638\pi\)
0.790211 + 0.612835i \(0.209971\pi\)
\(240\) 0 0
\(241\) −7.03921 12.1923i −0.453435 0.785373i 0.545161 0.838331i \(-0.316468\pi\)
−0.998597 + 0.0529581i \(0.983135\pi\)
\(242\) 0 0
\(243\) 8.85223 12.8311i 0.567871 0.823118i
\(244\) 0 0
\(245\) 0.786276 + 1.36187i 0.0502334 + 0.0870067i
\(246\) 0 0
\(247\) −3.15487 + 5.46440i −0.200740 + 0.347692i
\(248\) 0 0
\(249\) −1.11229 12.5133i −0.0704887 0.792996i
\(250\) 0 0
\(251\) 15.3752 0.970476 0.485238 0.874382i \(-0.338733\pi\)
0.485238 + 0.874382i \(0.338733\pi\)
\(252\) 0 0
\(253\) 1.09316 0.0687263
\(254\) 0 0
\(255\) 0.340391 0.239050i 0.0213161 0.0149699i
\(256\) 0 0
\(257\) 3.51288 6.08448i 0.219127 0.379540i −0.735414 0.677618i \(-0.763012\pi\)
0.954541 + 0.298078i \(0.0963456\pi\)
\(258\) 0 0
\(259\) −0.530914 0.919569i −0.0329894 0.0571393i
\(260\) 0 0
\(261\) 4.75940 13.1903i 0.294599 0.816458i
\(262\) 0 0
\(263\) 5.62093 + 9.73573i 0.346601 + 0.600331i 0.985643 0.168841i \(-0.0540024\pi\)
−0.639042 + 0.769172i \(0.720669\pi\)
\(264\) 0 0
\(265\) 1.16350 2.01523i 0.0714730 0.123795i
\(266\) 0 0
\(267\) 18.6338 + 8.65760i 1.14037 + 0.529836i
\(268\) 0 0
\(269\) 20.5678 1.25404 0.627019 0.779004i \(-0.284275\pi\)
0.627019 + 0.779004i \(0.284275\pi\)
\(270\) 0 0
\(271\) 8.25314 0.501343 0.250671 0.968072i \(-0.419349\pi\)
0.250671 + 0.968072i \(0.419349\pi\)
\(272\) 0 0
\(273\) 1.55275 + 0.721436i 0.0939769 + 0.0436633i
\(274\) 0 0
\(275\) 3.70486 6.41701i 0.223411 0.386960i
\(276\) 0 0
\(277\) 6.49837 + 11.2555i 0.390449 + 0.676278i 0.992509 0.122174i \(-0.0389864\pi\)
−0.602060 + 0.798451i \(0.705653\pi\)
\(278\) 0 0
\(279\) 16.1605 2.89587i 0.967505 0.173371i
\(280\) 0 0
\(281\) −9.29955 16.1073i −0.554765 0.960880i −0.997922 0.0644365i \(-0.979475\pi\)
0.443157 0.896444i \(-0.353858\pi\)
\(282\) 0 0
\(283\) −8.30074 + 14.3773i −0.493428 + 0.854642i −0.999971 0.00757254i \(-0.997590\pi\)
0.506544 + 0.862214i \(0.330923\pi\)
\(284\) 0 0
\(285\) −0.967636 + 0.679552i −0.0573178 + 0.0402532i
\(286\) 0 0
\(287\) 1.70003 0.100350
\(288\) 0 0
\(289\) −15.9258 −0.936811
\(290\) 0 0
\(291\) 0.679301 + 7.64212i 0.0398214 + 0.447989i
\(292\) 0 0
\(293\) −6.33729 + 10.9765i −0.370228 + 0.641254i −0.989601 0.143843i \(-0.954054\pi\)
0.619372 + 0.785098i \(0.287387\pi\)
\(294\) 0 0
\(295\) 0.629335 + 1.09004i 0.0366413 + 0.0634646i
\(296\) 0 0
\(297\) −5.48111 + 5.52701i −0.318047 + 0.320709i
\(298\) 0 0
\(299\) 0.781387 + 1.35340i 0.0451888 + 0.0782692i
\(300\) 0 0
\(301\) −1.11689 + 1.93451i −0.0643765 + 0.111503i
\(302\) 0 0
\(303\) 2.29236 + 25.7890i 0.131693 + 1.48154i
\(304\) 0 0
\(305\) 3.18140 0.182167
\(306\) 0 0
\(307\) 15.4097 0.879479 0.439740 0.898125i \(-0.355071\pi\)
0.439740 + 0.898125i \(0.355071\pi\)
\(308\) 0 0
\(309\) −0.0879711 + 0.0617804i −0.00500450 + 0.00351457i
\(310\) 0 0
\(311\) 12.7683 22.1153i 0.724022 1.25404i −0.235354 0.971910i \(-0.575625\pi\)
0.959375 0.282133i \(-0.0910419\pi\)
\(312\) 0 0
\(313\) 9.13328 + 15.8193i 0.516244 + 0.894160i 0.999822 + 0.0188591i \(0.00600341\pi\)
−0.483579 + 0.875301i \(0.660663\pi\)
\(314\) 0 0
\(315\) 0.206922 + 0.245213i 0.0116587 + 0.0138162i
\(316\) 0 0
\(317\) −5.22172 9.04428i −0.293281 0.507977i 0.681303 0.732002i \(-0.261414\pi\)
−0.974584 + 0.224024i \(0.928080\pi\)
\(318\) 0 0
\(319\) −3.50106 + 6.06402i −0.196022 + 0.339520i
\(320\) 0 0
\(321\) −18.7391 8.70649i −1.04591 0.485949i
\(322\) 0 0
\(323\) −3.05369 −0.169912
\(324\) 0 0
\(325\) 10.5929 0.587588
\(326\) 0 0
\(327\) −15.9164 7.39504i −0.880181 0.408947i
\(328\) 0 0
\(329\) −2.49663 + 4.32429i −0.137644 + 0.238406i
\(330\) 0 0
\(331\) 2.37887 + 4.12032i 0.130754 + 0.226473i 0.923968 0.382471i \(-0.124927\pi\)
−0.793213 + 0.608944i \(0.791593\pi\)
\(332\) 0 0
\(333\) 4.45066 + 5.27425i 0.243895 + 0.289027i
\(334\) 0 0
\(335\) −1.29380 2.24093i −0.0706878 0.122435i
\(336\) 0 0
\(337\) 13.7810 23.8694i 0.750700 1.30025i −0.196783 0.980447i \(-0.563050\pi\)
0.947484 0.319804i \(-0.103617\pi\)
\(338\) 0 0
\(339\) 2.10708 1.47976i 0.114441 0.0803696i
\(340\) 0 0
\(341\) −8.19818 −0.443956
\(342\) 0 0
\(343\) −6.36385 −0.343616
\(344\) 0 0
\(345\) 0.0259295 + 0.291706i 0.00139600 + 0.0157049i
\(346\) 0 0
\(347\) −10.5341 + 18.2457i −0.565502 + 0.979478i 0.431501 + 0.902113i \(0.357984\pi\)
−0.997003 + 0.0773655i \(0.975349\pi\)
\(348\) 0 0
\(349\) −17.7897 30.8126i −0.952258 1.64936i −0.740521 0.672033i \(-0.765421\pi\)
−0.211738 0.977327i \(-0.567912\pi\)
\(350\) 0 0
\(351\) −10.7607 2.83529i −0.574363 0.151336i
\(352\) 0 0
\(353\) 2.52544 + 4.37420i 0.134416 + 0.232815i 0.925374 0.379055i \(-0.123751\pi\)
−0.790958 + 0.611870i \(0.790418\pi\)
\(354\) 0 0
\(355\) 1.54015 2.66762i 0.0817428 0.141583i
\(356\) 0 0
\(357\) 0.0733665 + 0.825371i 0.00388297 + 0.0436833i
\(358\) 0 0
\(359\) −18.1271 −0.956709 −0.478355 0.878167i \(-0.658767\pi\)
−0.478355 + 0.878167i \(0.658767\pi\)
\(360\) 0 0
\(361\) −10.3192 −0.543118
\(362\) 0 0
\(363\) −12.4109 + 8.71593i −0.651403 + 0.457468i
\(364\) 0 0
\(365\) −0.491530 + 0.851355i −0.0257278 + 0.0445619i
\(366\) 0 0
\(367\) −4.83039 8.36649i −0.252145 0.436727i 0.711972 0.702208i \(-0.247803\pi\)
−0.964116 + 0.265481i \(0.914469\pi\)
\(368\) 0 0
\(369\) −10.8758 + 1.94889i −0.566174 + 0.101455i
\(370\) 0 0
\(371\) 2.31785 + 4.01464i 0.120337 + 0.208430i
\(372\) 0 0
\(373\) −16.0300 + 27.7647i −0.830001 + 1.43760i 0.0680357 + 0.997683i \(0.478327\pi\)
−0.898037 + 0.439921i \(0.855007\pi\)
\(374\) 0 0
\(375\) 3.62002 + 1.68192i 0.186937 + 0.0868541i
\(376\) 0 0
\(377\) −10.0102 −0.515551
\(378\) 0 0
\(379\) 16.0684 0.825377 0.412689 0.910872i \(-0.364590\pi\)
0.412689 + 0.910872i \(0.364590\pi\)
\(380\) 0 0
\(381\) −26.0221 12.0903i −1.33315 0.619406i
\(382\) 0 0
\(383\) −15.3129 + 26.5228i −0.782454 + 1.35525i 0.148055 + 0.988979i \(0.452699\pi\)
−0.930509 + 0.366270i \(0.880635\pi\)
\(384\) 0 0
\(385\) −0.0801076 0.138750i −0.00408266 0.00707138i
\(386\) 0 0
\(387\) 4.92754 13.6563i 0.250481 0.694188i
\(388\) 0 0
\(389\) −7.37823 12.7795i −0.374091 0.647945i 0.616099 0.787669i \(-0.288712\pi\)
−0.990191 + 0.139723i \(0.955379\pi\)
\(390\) 0 0
\(391\) −0.378162 + 0.654997i −0.0191245 + 0.0331246i
\(392\) 0 0
\(393\) 4.05740 2.84944i 0.204669 0.143735i
\(394\) 0 0
\(395\) 2.88988 0.145405
\(396\) 0 0
\(397\) 13.7032 0.687746 0.343873 0.939016i \(-0.388261\pi\)
0.343873 + 0.939016i \(0.388261\pi\)
\(398\) 0 0
\(399\) −0.208560 2.34630i −0.0104411 0.117462i
\(400\) 0 0
\(401\) 3.83939 6.65002i 0.191730 0.332086i −0.754094 0.656767i \(-0.771924\pi\)
0.945824 + 0.324681i \(0.105257\pi\)
\(402\) 0 0
\(403\) −5.86004 10.1499i −0.291909 0.505601i
\(404\) 0 0
\(405\) −1.60488 1.33152i −0.0797470 0.0661638i
\(406\) 0 0
\(407\) −1.72303 2.98437i −0.0854072 0.147930i
\(408\) 0 0
\(409\) −6.73882 + 11.6720i −0.333213 + 0.577142i −0.983140 0.182855i \(-0.941466\pi\)
0.649927 + 0.759997i \(0.274800\pi\)
\(410\) 0 0
\(411\) 2.53850 + 28.5580i 0.125215 + 1.40866i
\(412\) 0 0
\(413\) −2.50745 −0.123384
\(414\) 0 0
\(415\) −1.68055 −0.0824948
\(416\) 0 0
\(417\) 10.4477 7.33724i 0.511628 0.359306i
\(418\) 0 0
\(419\) 18.0380 31.2427i 0.881213 1.52630i 0.0312184 0.999513i \(-0.490061\pi\)
0.849994 0.526792i \(-0.176605\pi\)
\(420\) 0 0
\(421\) −2.57726 4.46394i −0.125608 0.217559i 0.796362 0.604820i \(-0.206755\pi\)
−0.921970 + 0.387260i \(0.873421\pi\)
\(422\) 0 0
\(423\) 11.0147 30.5264i 0.535555 1.48425i
\(424\) 0 0
\(425\) 2.56329 + 4.43974i 0.124338 + 0.215359i
\(426\) 0 0
\(427\) −3.16891 + 5.48871i −0.153354 + 0.265617i
\(428\) 0 0
\(429\) 5.03930 + 2.34134i 0.243300 + 0.113041i
\(430\) 0 0
\(431\) 20.7200 0.998045 0.499022 0.866589i \(-0.333693\pi\)
0.499022 + 0.866589i \(0.333693\pi\)
\(432\) 0 0
\(433\) −23.3719 −1.12318 −0.561592 0.827414i \(-0.689811\pi\)
−0.561592 + 0.827414i \(0.689811\pi\)
\(434\) 0 0
\(435\) −1.70121 0.790411i −0.0815668 0.0378973i
\(436\) 0 0
\(437\) 1.07501 1.86197i 0.0514246 0.0890701i
\(438\) 0 0
\(439\) −19.0107 32.9274i −0.907330 1.57154i −0.817759 0.575561i \(-0.804784\pi\)
−0.0895708 0.995980i \(-0.528550\pi\)
\(440\) 0 0
\(441\) 20.0416 3.59133i 0.954361 0.171016i
\(442\) 0 0
\(443\) −8.30811 14.3901i −0.394730 0.683693i 0.598336 0.801245i \(-0.295829\pi\)
−0.993067 + 0.117552i \(0.962495\pi\)
\(444\) 0 0
\(445\) 1.37432 2.38038i 0.0651488 0.112841i
\(446\) 0 0
\(447\) 3.00644 2.11136i 0.142200 0.0998640i
\(448\) 0 0
\(449\) 12.9085 0.609192 0.304596 0.952482i \(-0.401479\pi\)
0.304596 + 0.952482i \(0.401479\pi\)
\(450\) 0 0
\(451\) 5.51728 0.259798
\(452\) 0 0
\(453\) 0.604825 + 6.80427i 0.0284172 + 0.319692i
\(454\) 0 0
\(455\) 0.114521 0.198357i 0.00536884 0.00929911i
\(456\) 0 0
\(457\) 13.4943 + 23.3728i 0.631237 + 1.09333i 0.987299 + 0.158872i \(0.0507856\pi\)
−0.356063 + 0.934462i \(0.615881\pi\)
\(458\) 0 0
\(459\) −1.41555 5.19615i −0.0660721 0.242536i
\(460\) 0 0
\(461\) 10.0800 + 17.4591i 0.469474 + 0.813152i 0.999391 0.0348972i \(-0.0111104\pi\)
−0.529917 + 0.848049i \(0.677777\pi\)
\(462\) 0 0
\(463\) −17.2220 + 29.8293i −0.800373 + 1.38629i 0.118999 + 0.992894i \(0.462032\pi\)
−0.919371 + 0.393391i \(0.871302\pi\)
\(464\) 0 0
\(465\) −0.194459 2.18766i −0.00901783 0.101450i
\(466\) 0 0
\(467\) −31.6194 −1.46317 −0.731585 0.681750i \(-0.761219\pi\)
−0.731585 + 0.681750i \(0.761219\pi\)
\(468\) 0 0
\(469\) 5.15487 0.238030
\(470\) 0 0
\(471\) −16.3584 + 11.4882i −0.753757 + 0.529349i
\(472\) 0 0
\(473\) −3.62475 + 6.27825i −0.166666 + 0.288674i
\(474\) 0 0
\(475\) −7.28670 12.6209i −0.334337 0.579088i
\(476\) 0 0
\(477\) −19.4306 23.0262i −0.889667 1.05430i
\(478\) 0 0
\(479\) −3.72976 6.46014i −0.170417 0.295171i 0.768149 0.640272i \(-0.221178\pi\)
−0.938566 + 0.345100i \(0.887845\pi\)
\(480\) 0 0
\(481\) 2.46323 4.26644i 0.112314 0.194533i
\(482\) 0 0
\(483\) −0.529094 0.245826i −0.0240746 0.0111855i
\(484\) 0 0
\(485\) 1.02635 0.0466039
\(486\) 0 0
\(487\) 29.4254 1.33339 0.666697 0.745329i \(-0.267707\pi\)
0.666697 + 0.745329i \(0.267707\pi\)
\(488\) 0 0
\(489\) −1.12555 0.522948i −0.0508990 0.0236485i
\(490\) 0 0
\(491\) −14.4326 + 24.9979i −0.651332 + 1.12814i 0.331467 + 0.943467i \(0.392456\pi\)
−0.982800 + 0.184674i \(0.940877\pi\)
\(492\) 0 0
\(493\) −2.42228 4.19552i −0.109094 0.188957i
\(494\) 0 0
\(495\) 0.671544 + 0.795813i 0.0301837 + 0.0357691i
\(496\) 0 0
\(497\) 3.06821 + 5.31429i 0.137628 + 0.238379i
\(498\) 0 0
\(499\) 12.8470 22.2517i 0.575111 0.996122i −0.420918 0.907099i \(-0.638292\pi\)
0.996030 0.0890236i \(-0.0283747\pi\)
\(500\) 0 0
\(501\) 12.3660 8.68437i 0.552470 0.387989i
\(502\) 0 0
\(503\) 20.7071 0.923286 0.461643 0.887066i \(-0.347260\pi\)
0.461643 + 0.887066i \(0.347260\pi\)
\(504\) 0 0
\(505\) 3.46350 0.154124
\(506\) 0 0
\(507\) −1.29028 14.5157i −0.0573035 0.644663i
\(508\) 0 0
\(509\) 10.7631 18.6421i 0.477064 0.826299i −0.522591 0.852584i \(-0.675034\pi\)
0.999654 + 0.0262850i \(0.00836772\pi\)
\(510\) 0 0
\(511\) −0.979199 1.69602i −0.0433172 0.0750276i
\(512\) 0 0
\(513\) 4.02400 + 14.7712i 0.177664 + 0.652164i
\(514\) 0 0
\(515\) 0.00719018 + 0.0124538i 0.000316837 + 0.000548778i
\(516\) 0 0
\(517\) −8.10255 + 14.0340i −0.356350 + 0.617216i
\(518\) 0 0
\(519\) −2.75062 30.9444i −0.120739 1.35831i
\(520\) 0 0
\(521\) 22.2984 0.976911 0.488455 0.872589i \(-0.337560\pi\)
0.488455 + 0.872589i \(0.337560\pi\)
\(522\) 0 0
\(523\) −4.92665 −0.215427 −0.107714 0.994182i \(-0.534353\pi\)
−0.107714 + 0.994182i \(0.534353\pi\)
\(524\) 0 0
\(525\) −3.23620 + 2.27272i −0.141240 + 0.0991898i
\(526\) 0 0
\(527\) 2.83604 4.91217i 0.123540 0.213977i
\(528\) 0 0
\(529\) 11.2337 + 19.4574i 0.488424 + 0.845975i
\(530\) 0 0
\(531\) 16.0413 2.87450i 0.696132 0.124743i
\(532\) 0 0
\(533\) 3.94373 + 6.83075i 0.170822 + 0.295873i
\(534\) 0 0
\(535\) −1.38208 + 2.39383i −0.0597523 + 0.103494i
\(536\) 0 0
\(537\) −10.4705 4.86478i −0.451836 0.209931i
\(538\) 0 0
\(539\) −10.1670 −0.437925
\(540\) 0 0
\(541\) −22.0179 −0.946622 −0.473311 0.880895i \(-0.656941\pi\)
−0.473311 + 0.880895i \(0.656941\pi\)
\(542\) 0 0
\(543\) −30.0208 13.9482i −1.28832 0.598573i
\(544\) 0 0
\(545\) −1.17390 + 2.03325i −0.0502842 + 0.0870948i
\(546\) 0 0
\(547\) −15.2563 26.4247i −0.652311 1.12984i −0.982561 0.185943i \(-0.940466\pi\)
0.330249 0.943894i \(-0.392867\pi\)
\(548\) 0 0
\(549\) 13.9807 38.7464i 0.596682 1.65366i
\(550\) 0 0
\(551\) 6.88587 + 11.9267i 0.293348 + 0.508093i
\(552\) 0 0
\(553\) −2.87853 + 4.98575i −0.122407 + 0.212016i
\(554\) 0 0
\(555\) 0.755501 0.530573i 0.0320692 0.0225216i
\(556\) 0 0
\(557\) 34.8358 1.47604 0.738021 0.674778i \(-0.235761\pi\)
0.738021 + 0.674778i \(0.235761\pi\)
\(558\) 0 0
\(559\) −10.3639 −0.438344
\(560\) 0 0
\(561\) 0.238103 + 2.67866i 0.0100527 + 0.113093i
\(562\) 0 0
\(563\) 6.86229 11.8858i 0.289211 0.500928i −0.684411 0.729097i \(-0.739940\pi\)
0.973622 + 0.228169i \(0.0732738\pi\)
\(564\) 0 0
\(565\) −0.172219 0.298292i −0.00724529 0.0125492i
\(566\) 0 0
\(567\) 3.89578 1.44252i 0.163607 0.0605802i
\(568\) 0 0
\(569\) 14.6770 + 25.4213i 0.615291 + 1.06572i 0.990333 + 0.138708i \(0.0442950\pi\)
−0.375042 + 0.927008i \(0.622372\pi\)
\(570\) 0 0
\(571\) −1.60926 + 2.78732i −0.0673455 + 0.116646i −0.897732 0.440542i \(-0.854786\pi\)
0.830387 + 0.557188i \(0.188120\pi\)
\(572\) 0 0
\(573\) 0.318819 + 3.58671i 0.0133189 + 0.149837i
\(574\) 0 0
\(575\) −3.60948 −0.150526
\(576\) 0 0
\(577\) 0.782693 0.0325839 0.0162920 0.999867i \(-0.494814\pi\)
0.0162920 + 0.999867i \(0.494814\pi\)
\(578\) 0 0
\(579\) −28.9095 + 20.3026i −1.20144 + 0.843746i
\(580\) 0 0
\(581\) 1.67395 2.89936i 0.0694470 0.120286i
\(582\) 0 0
\(583\) 7.52235 + 13.0291i 0.311544 + 0.539610i
\(584\) 0 0
\(585\) −0.505250 + 1.40026i −0.0208895 + 0.0578936i
\(586\) 0 0
\(587\) −12.7201 22.0318i −0.525014 0.909350i −0.999576 0.0291282i \(-0.990727\pi\)
0.474562 0.880222i \(-0.342606\pi\)
\(588\) 0 0
\(589\) −8.06206 + 13.9639i −0.332192 + 0.575373i
\(590\) 0 0
\(591\) 25.9899 + 12.0753i 1.06908 + 0.496713i
\(592\) 0 0
\(593\) 44.4583 1.82569 0.912843 0.408311i \(-0.133882\pi\)
0.912843 + 0.408311i \(0.133882\pi\)
\(594\) 0 0
\(595\) 0.110848 0.00454434
\(596\) 0 0
\(597\) −33.4487 15.5408i −1.36896 0.636043i
\(598\) 0 0
\(599\) 23.7554 41.1455i 0.970618 1.68116i 0.276922 0.960892i \(-0.410686\pi\)
0.693696 0.720268i \(-0.255981\pi\)
\(600\) 0 0
\(601\) 3.61527 + 6.26183i 0.147470 + 0.255425i 0.930292 0.366821i \(-0.119554\pi\)
−0.782822 + 0.622246i \(0.786220\pi\)
\(602\) 0 0
\(603\) −32.9780 + 5.90946i −1.34297 + 0.240652i
\(604\) 0 0
\(605\) 1.01438 + 1.75697i 0.0412406 + 0.0714308i
\(606\) 0 0
\(607\) −7.00711 + 12.1367i −0.284410 + 0.492612i −0.972466 0.233045i \(-0.925131\pi\)
0.688056 + 0.725658i \(0.258464\pi\)
\(608\) 0 0
\(609\) 3.05819 2.14770i 0.123924 0.0870294i
\(610\) 0 0
\(611\) −23.1667 −0.937225
\(612\) 0 0
\(613\) −12.2357 −0.494194 −0.247097 0.968991i \(-0.579477\pi\)
−0.247097 + 0.968991i \(0.579477\pi\)
\(614\) 0 0
\(615\) 0.130869 + 1.47227i 0.00527714 + 0.0593677i
\(616\) 0 0
\(617\) 1.07716 1.86569i 0.0433647 0.0751099i −0.843528 0.537085i \(-0.819526\pi\)
0.886893 + 0.461975i \(0.152859\pi\)
\(618\) 0 0
\(619\) −5.94519 10.2974i −0.238957 0.413886i 0.721458 0.692458i \(-0.243472\pi\)
−0.960415 + 0.278572i \(0.910139\pi\)
\(620\) 0 0
\(621\) 3.66665 + 0.966111i 0.147138 + 0.0387687i
\(622\) 0 0
\(623\) 2.73784 + 4.74207i 0.109689 + 0.189987i
\(624\) 0 0
\(625\) −12.0988 + 20.9557i −0.483952 + 0.838229i
\(626\) 0 0
\(627\) −0.676861 7.61466i −0.0270312 0.304100i
\(628\) 0 0
\(629\) 2.38422 0.0950652
\(630\) 0 0
\(631\) −41.3492 −1.64609 −0.823043 0.567979i \(-0.807725\pi\)
−0.823043 + 0.567979i \(0.807725\pi\)
\(632\) 0 0
\(633\) 28.9116 20.3041i 1.14913 0.807015i
\(634\) 0 0
\(635\) −1.91923 + 3.32420i −0.0761623 + 0.131917i
\(636\) 0 0
\(637\) −7.26736 12.5874i −0.287943 0.498733i
\(638\) 0 0
\(639\) −25.7209 30.4805i −1.01750 1.20579i
\(640\) 0 0
\(641\) 12.6110 + 21.8429i 0.498106 + 0.862744i 0.999998 0.00218592i \(-0.000695802\pi\)
−0.501892 + 0.864930i \(0.667362\pi\)
\(642\) 0 0
\(643\) 7.87820 13.6454i 0.310686 0.538124i −0.667825 0.744318i \(-0.732775\pi\)
0.978511 + 0.206194i \(0.0661079\pi\)
\(644\) 0 0
\(645\) −1.76131 0.818336i −0.0693517 0.0322220i
\(646\) 0 0
\(647\) −21.8197 −0.857823 −0.428911 0.903347i \(-0.641103\pi\)
−0.428911 + 0.903347i \(0.641103\pi\)
\(648\) 0 0
\(649\) −8.13768 −0.319432
\(650\) 0 0
\(651\) 3.96796 + 1.84358i 0.155516 + 0.0722556i
\(652\) 0 0
\(653\) −12.5168 + 21.6797i −0.489819 + 0.848392i −0.999931 0.0117162i \(-0.996271\pi\)
0.510112 + 0.860108i \(0.329604\pi\)
\(654\) 0 0
\(655\) −0.331625 0.574392i −0.0129577 0.0224433i
\(656\) 0 0
\(657\) 8.20865 + 9.72766i 0.320250 + 0.379512i
\(658\) 0 0
\(659\) −14.5079 25.1285i −0.565149 0.978867i −0.997036 0.0769388i \(-0.975485\pi\)
0.431887 0.901928i \(-0.357848\pi\)
\(660\) 0 0
\(661\) −4.99232 + 8.64694i −0.194179 + 0.336327i −0.946631 0.322320i \(-0.895537\pi\)
0.752452 + 0.658647i \(0.228871\pi\)
\(662\) 0 0
\(663\) −3.14616 + 2.20948i −0.122187 + 0.0858093i
\(664\) 0 0
\(665\) −0.315110 −0.0122195
\(666\) 0 0
\(667\) 3.41093 0.132072
\(668\) 0 0
\(669\) −0.772993 8.69615i −0.0298856 0.336213i
\(670\) 0 0
\(671\) −10.2844 + 17.8130i −0.397023 + 0.687665i
\(672\) 0 0
\(673\) 2.42824 + 4.20584i 0.0936019 + 0.162123i 0.909024 0.416743i \(-0.136829\pi\)
−0.815422 + 0.578866i \(0.803495\pi\)
\(674\) 0 0
\(675\) 18.0980 18.2495i 0.696592 0.702425i
\(676\) 0 0
\(677\) −7.10559 12.3072i −0.273090 0.473006i 0.696562 0.717497i \(-0.254712\pi\)
−0.969651 + 0.244491i \(0.921379\pi\)
\(678\) 0 0
\(679\) −1.02231 + 1.77070i −0.0392328 + 0.0679533i
\(680\) 0 0
\(681\) −2.49064 28.0197i −0.0954416 1.07372i
\(682\) 0 0
\(683\) −20.7153 −0.792648 −0.396324 0.918111i \(-0.629714\pi\)
−0.396324 + 0.918111i \(0.629714\pi\)
\(684\) 0 0
\(685\) 3.83538 0.146542
\(686\) 0 0
\(687\) 8.29065 5.82236i 0.316308 0.222137i
\(688\) 0 0
\(689\) −10.7539 + 18.6263i −0.409691 + 0.709606i
\(690\) 0 0
\(691\) −6.56378 11.3688i −0.249698 0.432489i 0.713744 0.700407i \(-0.246998\pi\)
−0.963442 + 0.267917i \(0.913665\pi\)
\(692\) 0 0
\(693\) −2.04188 + 0.365893i −0.0775647 + 0.0138991i
\(694\) 0 0
\(695\) −0.853929 1.47905i −0.0323914 0.0561035i
\(696\) 0 0
\(697\) −1.90862 + 3.30583i −0.0722942 + 0.125217i
\(698\) 0 0
\(699\) 32.5925 + 15.1430i 1.23276 + 0.572762i
\(700\) 0 0
\(701\) −13.3554 −0.504426 −0.252213 0.967672i \(-0.581158\pi\)
−0.252213 + 0.967672i \(0.581158\pi\)
\(702\) 0 0
\(703\) −6.77767 −0.255625
\(704\) 0 0
\(705\) −3.93713 1.82926i −0.148281 0.0688939i
\(706\) 0 0
\(707\) −3.44989 + 5.97539i −0.129747 + 0.224728i
\(708\) 0 0
\(709\) −13.5083 23.3971i −0.507316 0.878697i −0.999964 0.00846836i \(-0.997304\pi\)
0.492648 0.870229i \(-0.336029\pi\)
\(710\) 0 0
\(711\) 12.6996 35.1959i 0.476272 1.31995i
\(712\) 0 0
\(713\) 1.99678 + 3.45852i 0.0747800 + 0.129523i
\(714\) 0 0
\(715\) 0.371667 0.643747i 0.0138996 0.0240748i
\(716\) 0 0
\(717\) 5.94391 4.17429i 0.221979 0.155892i
\(718\) 0 0
\(719\) 46.5794 1.73712 0.868559 0.495585i \(-0.165046\pi\)
0.868559 + 0.495585i \(0.165046\pi\)
\(720\) 0 0
\(721\) −0.0286478 −0.00106690
\(722\) 0 0
\(723\) 2.15901 + 24.2888i 0.0802943 + 0.903309i
\(724\) 0 0
\(725\) 11.5601 20.0227i 0.429331 0.743623i
\(726\) 0 0
\(727\) −12.5353 21.7119i −0.464910 0.805248i 0.534287 0.845303i \(-0.320580\pi\)
−0.999197 + 0.0400549i \(0.987247\pi\)
\(728\) 0 0
\(729\) −23.2693 + 13.6945i −0.861826 + 0.507203i
\(730\) 0 0
\(731\) −2.50786 4.34374i −0.0927566 0.160659i
\(732\) 0 0
\(733\) −11.8288 + 20.4881i −0.436907 + 0.756746i −0.997449 0.0713803i \(-0.977260\pi\)
0.560542 + 0.828126i \(0.310593\pi\)
\(734\) 0 0
\(735\) −0.241160 2.71304i −0.00889532 0.100072i
\(736\) 0 0
\(737\) 16.7296 0.616243
\(738\) 0 0
\(739\) 32.9834 1.21332 0.606658 0.794963i \(-0.292510\pi\)
0.606658 + 0.794963i \(0.292510\pi\)
\(740\) 0 0
\(741\) 8.94363 6.28094i 0.328553 0.230736i
\(742\) 0 0
\(743\) −5.16854 + 8.95218i −0.189615 + 0.328424i −0.945122 0.326717i \(-0.894057\pi\)
0.755507 + 0.655141i \(0.227391\pi\)
\(744\) 0 0
\(745\) −0.245726 0.425610i −0.00900271 0.0155931i
\(746\) 0 0
\(747\) −7.38519 + 20.4674i −0.270210 + 0.748865i
\(748\) 0 0
\(749\) −2.75330 4.76885i −0.100603 0.174250i
\(750\) 0 0
\(751\) −11.5268 + 19.9650i −0.420620 + 0.728535i −0.996000 0.0893513i \(-0.971521\pi\)
0.575381 + 0.817886i \(0.304854\pi\)
\(752\) 0 0
\(753\) −24.1512 11.2211i −0.880119 0.408918i
\(754\) 0 0
\(755\) 0.913821 0.0332573
\(756\) 0 0
\(757\) −4.86572 −0.176848 −0.0884239 0.996083i \(-0.528183\pi\)
−0.0884239 + 0.996083i \(0.528183\pi\)
\(758\) 0 0
\(759\) −1.71712 0.797803i −0.0623275 0.0289584i
\(760\) 0 0
\(761\) 19.3733 33.5556i 0.702283 1.21639i −0.265380 0.964144i \(-0.585497\pi\)
0.967663 0.252246i \(-0.0811694\pi\)
\(762\) 0 0
\(763\) −2.33857 4.05052i −0.0846620 0.146639i
\(764\) 0 0
\(765\) −0.709145 + 0.127075i −0.0256392 + 0.00459439i
\(766\) 0 0
\(767\) −5.81679 10.0750i −0.210032 0.363786i
\(768\) 0 0
\(769\) −14.0001 + 24.2489i −0.504858 + 0.874439i 0.495127 + 0.868821i \(0.335122\pi\)
−0.999984 + 0.00561822i \(0.998212\pi\)
\(770\) 0 0
\(771\) −9.95853 + 6.99368i −0.358648 + 0.251871i
\(772\) 0 0
\(773\) 30.9662 1.11378 0.556888 0.830588i \(-0.311995\pi\)
0.556888 + 0.830588i \(0.311995\pi\)
\(774\) 0 0
\(775\) 27.0694 0.972362
\(776\) 0 0
\(777\) 0.162837 + 1.83192i 0.00584176 + 0.0657196i
\(778\) 0 0
\(779\) 5.42567 9.39754i 0.194395 0.336702i
\(780\) 0 0
\(781\) 9.95755 + 17.2470i 0.356309 + 0.617146i
\(782\) 0 0
\(783\) −17.1025 + 17.2456i −0.611192 + 0.616309i
\(784\) 0 0
\(785\) 1.33703 + 2.31580i 0.0477207 + 0.0826546i
\(786\) 0 0
\(787\) −8.48755 + 14.7009i −0.302549 + 0.524030i −0.976713 0.214552i \(-0.931171\pi\)
0.674164 + 0.738582i \(0.264504\pi\)
\(788\) 0 0
\(789\) −1.72400 19.3950i −0.0613762 0.690480i
\(790\) 0 0
\(791\) 0.686169 0.0243974
\(792\) 0 0
\(793\) −29.4049 −1.04420
\(794\) 0 0
\(795\) −3.29835 + 2.31637i −0.116980 + 0.0821531i
\(796\) 0 0