Properties

Label 804.2.o.c.641.1
Level 804
Weight 2
Character 804.641
Analytic conductor 6.420
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 641.1
Root \(-1.22474 - 0.707107i\)
Character \(\chi\) = 804.641
Dual form 804.2.o.c.365.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.41421i) q^{3} -2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.41421i) q^{3} -2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 - 2.82843i) q^{9} +(-1.72474 - 2.98735i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 + 2.82843i) q^{15} +(2.17423 + 1.25529i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(0.724745 - 7.86566i) q^{21} +(-8.17423 - 4.71940i) q^{23} -1.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +(7.62372 - 4.40156i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(-5.94949 - 0.548188i) q^{33} +(-7.89898 + 4.56048i) q^{35} +(-0.0505103 + 0.0874863i) q^{37} +(8.17423 - 3.76588i) q^{39} +(0.724745 + 1.25529i) q^{41} -12.5851i q^{43} +(2.00000 + 5.65685i) q^{45} +(-2.72474 + 1.57313i) q^{47} +(6.89898 - 11.9494i) q^{49} +(3.94949 - 1.81954i) q^{51} +6.00000 q^{53} +(3.44949 + 5.97469i) q^{55} +(2.17423 + 4.71940i) q^{57} +6.29253i q^{59} +(-0.398979 - 0.230351i) q^{61} +(-10.3990 - 8.89060i) q^{63} +(-9.00000 - 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-14.8485 + 6.84072i) q^{69} +(3.82577 - 2.20881i) q^{71} +(-1.94949 + 3.37662i) q^{73} +(-1.00000 + 1.41421i) q^{75} +(-13.6237 - 7.86566i) q^{77} +(-9.39898 + 5.42650i) q^{79} +(-7.00000 + 5.65685i) q^{81} +(7.07321 + 4.08372i) q^{83} +(-4.34847 - 2.51059i) q^{85} +(1.39898 - 15.1831i) q^{87} +16.0492i q^{89} +23.6969 q^{91} +(-0.275255 + 2.98735i) q^{93} +(3.00000 - 5.19615i) q^{95} +(-2.84847 - 1.64456i) q^{97} +(-6.72474 + 7.86566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} - 8q^{5} + 6q^{7} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} - 8q^{5} + 6q^{7} - 4q^{9} - 2q^{11} + 18q^{13} - 8q^{15} - 6q^{17} - 6q^{19} - 2q^{21} - 18q^{23} - 4q^{25} - 20q^{27} + 6q^{29} - 6q^{31} - 14q^{33} - 12q^{35} - 10q^{37} + 18q^{39} - 2q^{41} + 8q^{45} - 6q^{47} + 8q^{49} + 6q^{51} + 24q^{53} + 4q^{55} - 6q^{57} + 18q^{61} - 22q^{63} - 36q^{65} + 32q^{67} - 30q^{69} + 30q^{71} + 2q^{73} - 4q^{75} - 30q^{77} - 18q^{79} - 28q^{81} - 6q^{83} + 12q^{85} - 14q^{87} + 36q^{91} - 6q^{93} + 12q^{95} + 18q^{97} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 0 0
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) 3.94949 2.28024i 1.49277 0.861849i 0.492801 0.870142i \(-0.335973\pi\)
0.999966 + 0.00829261i \(0.00263965\pi\)
\(8\) 0 0
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 0 0
\(11\) −1.72474 2.98735i −0.520030 0.900719i −0.999729 0.0232854i \(-0.992587\pi\)
0.479699 0.877433i \(-0.340746\pi\)
\(12\) 0 0
\(13\) 4.50000 + 2.59808i 1.24808 + 0.720577i 0.970725 0.240192i \(-0.0772105\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −2.00000 + 2.82843i −0.516398 + 0.730297i
\(16\) 0 0
\(17\) 2.17423 + 1.25529i 0.527329 + 0.304454i 0.739928 0.672686i \(-0.234859\pi\)
−0.212599 + 0.977140i \(0.568193\pi\)
\(18\) 0 0
\(19\) −1.50000 + 2.59808i −0.344124 + 0.596040i −0.985194 0.171442i \(-0.945157\pi\)
0.641071 + 0.767482i \(0.278491\pi\)
\(20\) 0 0
\(21\) 0.724745 7.86566i 0.158152 1.71643i
\(22\) 0 0
\(23\) −8.17423 4.71940i −1.70445 0.984062i −0.941135 0.338031i \(-0.890239\pi\)
−0.763311 0.646032i \(-0.776427\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 0 0
\(29\) 7.62372 4.40156i 1.41569 0.817349i 0.419774 0.907629i \(-0.362109\pi\)
0.995916 + 0.0902798i \(0.0287761\pi\)
\(30\) 0 0
\(31\) −1.50000 + 0.866025i −0.269408 + 0.155543i −0.628619 0.777714i \(-0.716379\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) −5.94949 0.548188i −1.03567 0.0954273i
\(34\) 0 0
\(35\) −7.89898 + 4.56048i −1.33517 + 0.770861i
\(36\) 0 0
\(37\) −0.0505103 + 0.0874863i −0.00830384 + 0.0143827i −0.870147 0.492791i \(-0.835977\pi\)
0.861844 + 0.507174i \(0.169310\pi\)
\(38\) 0 0
\(39\) 8.17423 3.76588i 1.30893 0.603024i
\(40\) 0 0
\(41\) 0.724745 + 1.25529i 0.113186 + 0.196044i 0.917053 0.398765i \(-0.130561\pi\)
−0.803867 + 0.594809i \(0.797228\pi\)
\(42\) 0 0
\(43\) 12.5851i 1.91920i −0.281362 0.959602i \(-0.590786\pi\)
0.281362 0.959602i \(-0.409214\pi\)
\(44\) 0 0
\(45\) 2.00000 + 5.65685i 0.298142 + 0.843274i
\(46\) 0 0
\(47\) −2.72474 + 1.57313i −0.397445 + 0.229465i −0.685381 0.728185i \(-0.740364\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(48\) 0 0
\(49\) 6.89898 11.9494i 0.985568 1.70705i
\(50\) 0 0
\(51\) 3.94949 1.81954i 0.553039 0.254786i
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 3.44949 + 5.97469i 0.465129 + 0.805627i
\(56\) 0 0
\(57\) 2.17423 + 4.71940i 0.287984 + 0.625099i
\(58\) 0 0
\(59\) 6.29253i 0.819217i 0.912261 + 0.409609i \(0.134335\pi\)
−0.912261 + 0.409609i \(0.865665\pi\)
\(60\) 0 0
\(61\) −0.398979 0.230351i −0.0510841 0.0294934i 0.474240 0.880395i \(-0.342723\pi\)
−0.525325 + 0.850902i \(0.676056\pi\)
\(62\) 0 0
\(63\) −10.3990 8.89060i −1.31015 1.12011i
\(64\) 0 0
\(65\) −9.00000 5.19615i −1.11631 0.644503i
\(66\) 0 0
\(67\) 8.00000 1.73205i 0.977356 0.211604i
\(68\) 0 0
\(69\) −14.8485 + 6.84072i −1.78755 + 0.823526i
\(70\) 0 0
\(71\) 3.82577 2.20881i 0.454035 0.262137i −0.255498 0.966810i \(-0.582239\pi\)
0.709533 + 0.704672i \(0.248906\pi\)
\(72\) 0 0
\(73\) −1.94949 + 3.37662i −0.228171 + 0.395203i −0.957266 0.289209i \(-0.906608\pi\)
0.729095 + 0.684412i \(0.239941\pi\)
\(74\) 0 0
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 0 0
\(77\) −13.6237 7.86566i −1.55257 0.896375i
\(78\) 0 0
\(79\) −9.39898 + 5.42650i −1.05747 + 0.610529i −0.924731 0.380622i \(-0.875710\pi\)
−0.132737 + 0.991151i \(0.542377\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) 7.07321 + 4.08372i 0.776386 + 0.448247i 0.835148 0.550025i \(-0.185382\pi\)
−0.0587619 + 0.998272i \(0.518715\pi\)
\(84\) 0 0
\(85\) −4.34847 2.51059i −0.471658 0.272312i
\(86\) 0 0
\(87\) 1.39898 15.1831i 0.149986 1.62780i
\(88\) 0 0
\(89\) 16.0492i 1.70121i 0.525807 + 0.850604i \(0.323763\pi\)
−0.525807 + 0.850604i \(0.676237\pi\)
\(90\) 0 0
\(91\) 23.6969 2.48411
\(92\) 0 0
\(93\) −0.275255 + 2.98735i −0.0285426 + 0.309773i
\(94\) 0 0
\(95\) 3.00000 5.19615i 0.307794 0.533114i
\(96\) 0 0
\(97\) −2.84847 1.64456i −0.289218 0.166980i 0.348371 0.937357i \(-0.386735\pi\)
−0.637589 + 0.770377i \(0.720068\pi\)
\(98\) 0 0
\(99\) −6.72474 + 7.86566i −0.675862 + 0.790529i
\(100\) 0 0
\(101\) 4.27526 + 7.40496i 0.425404 + 0.736821i 0.996458 0.0840913i \(-0.0267988\pi\)
−0.571054 + 0.820912i \(0.693465\pi\)
\(102\) 0 0
\(103\) −2.94949 5.10867i −0.290622 0.503372i 0.683335 0.730105i \(-0.260529\pi\)
−0.973957 + 0.226733i \(0.927195\pi\)
\(104\) 0 0
\(105\) −1.44949 + 15.7313i −0.141456 + 1.53522i
\(106\) 0 0
\(107\) 2.19275i 0.211981i −0.994367 0.105991i \(-0.966199\pi\)
0.994367 0.105991i \(-0.0338014\pi\)
\(108\) 0 0
\(109\) 11.9494i 1.14454i 0.820064 + 0.572272i \(0.193938\pi\)
−0.820064 + 0.572272i \(0.806062\pi\)
\(110\) 0 0
\(111\) 0.0732141 + 0.158919i 0.00694917 + 0.0150839i
\(112\) 0 0
\(113\) 5.72474 + 9.91555i 0.538539 + 0.932776i 0.998983 + 0.0450878i \(0.0143568\pi\)
−0.460444 + 0.887689i \(0.652310\pi\)
\(114\) 0 0
\(115\) 16.3485 + 9.43879i 1.52450 + 0.880172i
\(116\) 0 0
\(117\) 2.84847 15.3260i 0.263341 1.41689i
\(118\) 0 0
\(119\) 11.4495 1.04957
\(120\) 0 0
\(121\) −0.449490 + 0.778539i −0.0408627 + 0.0707763i
\(122\) 0 0
\(123\) 2.50000 + 0.230351i 0.225417 + 0.0207700i
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −5.39898 9.35131i −0.479082 0.829794i 0.520630 0.853782i \(-0.325697\pi\)
−0.999712 + 0.0239879i \(0.992364\pi\)
\(128\) 0 0
\(129\) −17.7980 12.5851i −1.56702 1.10805i
\(130\) 0 0
\(131\) 0.635674i 0.0555391i −0.999614 0.0277696i \(-0.991160\pi\)
0.999614 0.0277696i \(-0.00884046\pi\)
\(132\) 0 0
\(133\) 13.6814i 1.18633i
\(134\) 0 0
\(135\) 10.0000 + 2.82843i 0.860663 + 0.243432i
\(136\) 0 0
\(137\) 18.8990 1.61465 0.807324 0.590108i \(-0.200915\pi\)
0.807324 + 0.590108i \(0.200915\pi\)
\(138\) 0 0
\(139\) 21.0703i 1.78716i 0.448901 + 0.893581i \(0.351816\pi\)
−0.448901 + 0.893581i \(0.648184\pi\)
\(140\) 0 0
\(141\) −0.500000 + 5.42650i −0.0421076 + 0.456994i
\(142\) 0 0
\(143\) 17.9241i 1.49889i
\(144\) 0 0
\(145\) −15.2474 + 8.80312i −1.26623 + 0.731059i
\(146\) 0 0
\(147\) −10.0000 21.7060i −0.824786 1.79028i
\(148\) 0 0
\(149\) 7.84961i 0.643065i −0.946899 0.321532i \(-0.895802\pi\)
0.946899 0.321532i \(-0.104198\pi\)
\(150\) 0 0
\(151\) 5.39898 9.35131i 0.439363 0.760999i −0.558278 0.829654i \(-0.688538\pi\)
0.997640 + 0.0686556i \(0.0218710\pi\)
\(152\) 0 0
\(153\) 1.37628 7.40496i 0.111265 0.598655i
\(154\) 0 0
\(155\) 3.00000 1.73205i 0.240966 0.139122i
\(156\) 0 0
\(157\) 2.05051 3.55159i 0.163649 0.283448i −0.772526 0.634983i \(-0.781007\pi\)
0.936175 + 0.351536i \(0.114340\pi\)
\(158\) 0 0
\(159\) 6.00000 8.48528i 0.475831 0.672927i
\(160\) 0 0
\(161\) −43.0454 −3.39245
\(162\) 0 0
\(163\) 8.29796 + 14.3725i 0.649946 + 1.12574i 0.983135 + 0.182880i \(0.0585420\pi\)
−0.333189 + 0.942860i \(0.608125\pi\)
\(164\) 0 0
\(165\) 11.8990 + 1.09638i 0.926334 + 0.0853528i
\(166\) 0 0
\(167\) −4.92679 + 2.84448i −0.381246 + 0.220113i −0.678360 0.734729i \(-0.737309\pi\)
0.297114 + 0.954842i \(0.403976\pi\)
\(168\) 0 0
\(169\) 7.00000 + 12.1244i 0.538462 + 0.932643i
\(170\) 0 0
\(171\) 8.84847 + 1.64456i 0.676659 + 0.125763i
\(172\) 0 0
\(173\) −1.62372 0.937458i −0.123449 0.0712736i 0.437004 0.899460i \(-0.356040\pi\)
−0.560453 + 0.828186i \(0.689373\pi\)
\(174\) 0 0
\(175\) −3.94949 + 2.28024i −0.298553 + 0.172370i
\(176\) 0 0
\(177\) 8.89898 + 6.29253i 0.668888 + 0.472975i
\(178\) 0 0
\(179\) 25.5959 1.91313 0.956564 0.291521i \(-0.0941614\pi\)
0.956564 + 0.291521i \(0.0941614\pi\)
\(180\) 0 0
\(181\) 5.94949 + 10.3048i 0.442222 + 0.765951i 0.997854 0.0654772i \(-0.0208570\pi\)
−0.555632 + 0.831428i \(0.687524\pi\)
\(182\) 0 0
\(183\) −0.724745 + 0.333891i −0.0535747 + 0.0246820i
\(184\) 0 0
\(185\) 0.101021 0.174973i 0.00742718 0.0128642i
\(186\) 0 0
\(187\) 8.66025i 0.633300i
\(188\) 0 0
\(189\) −22.9722 + 5.81577i −1.67098 + 0.423035i
\(190\) 0 0
\(191\) −6.27526 + 10.8691i −0.454062 + 0.786458i −0.998634 0.0522563i \(-0.983359\pi\)
0.544572 + 0.838714i \(0.316692\pi\)
\(192\) 0 0
\(193\) −3.10102 −0.223216 −0.111608 0.993752i \(-0.535600\pi\)
−0.111608 + 0.993752i \(0.535600\pi\)
\(194\) 0 0
\(195\) −16.3485 + 7.53177i −1.17074 + 0.539361i
\(196\) 0 0
\(197\) −10.6237 18.4008i −0.756909 1.31100i −0.944420 0.328742i \(-0.893375\pi\)
0.187511 0.982263i \(-0.439958\pi\)
\(198\) 0 0
\(199\) 5.50000 9.52628i 0.389885 0.675300i −0.602549 0.798082i \(-0.705848\pi\)
0.992434 + 0.122782i \(0.0391815\pi\)
\(200\) 0 0
\(201\) 5.55051 13.0458i 0.391503 0.920177i
\(202\) 0 0
\(203\) 20.0732 34.7678i 1.40886 2.44022i
\(204\) 0 0
\(205\) −1.44949 2.51059i −0.101237 0.175347i
\(206\) 0 0
\(207\) −5.17423 + 27.8396i −0.359634 + 1.93499i
\(208\) 0 0
\(209\) 10.3485 0.715819
\(210\) 0 0
\(211\) −1.94949 + 3.37662i −0.134208 + 0.232456i −0.925295 0.379249i \(-0.876182\pi\)
0.791086 + 0.611704i \(0.209516\pi\)
\(212\) 0 0
\(213\) 0.702041 7.61926i 0.0481031 0.522063i
\(214\) 0 0
\(215\) 25.1701i 1.71659i
\(216\) 0 0
\(217\) −3.94949 + 6.84072i −0.268109 + 0.464378i
\(218\) 0 0
\(219\) 2.82577 + 6.13361i 0.190948 + 0.414471i
\(220\) 0 0
\(221\) 6.52270 + 11.2977i 0.438765 + 0.759962i
\(222\) 0 0
\(223\) −8.69694 −0.582390 −0.291195 0.956664i \(-0.594053\pi\)
−0.291195 + 0.956664i \(0.594053\pi\)
\(224\) 0 0
\(225\) 1.00000 + 2.82843i 0.0666667 + 0.188562i
\(226\) 0 0
\(227\) −8.42168 + 4.86226i −0.558967 + 0.322720i −0.752731 0.658329i \(-0.771264\pi\)
0.193764 + 0.981048i \(0.437930\pi\)
\(228\) 0 0
\(229\) 5.84847 + 3.37662i 0.386478 + 0.223133i 0.680633 0.732625i \(-0.261705\pi\)
−0.294155 + 0.955758i \(0.595038\pi\)
\(230\) 0 0
\(231\) −24.7474 + 11.4012i −1.62826 + 0.750144i
\(232\) 0 0
\(233\) 11.7247 + 20.3079i 0.768114 + 1.33041i 0.938585 + 0.345049i \(0.112138\pi\)
−0.170471 + 0.985363i \(0.554529\pi\)
\(234\) 0 0
\(235\) 5.44949 3.14626i 0.355486 0.205240i
\(236\) 0 0
\(237\) −1.72474 + 18.7187i −0.112034 + 1.21591i
\(238\) 0 0
\(239\) 6.62372 + 11.4726i 0.428453 + 0.742103i 0.996736 0.0807307i \(-0.0257254\pi\)
−0.568283 + 0.822833i \(0.692392\pi\)
\(240\) 0 0
\(241\) 4.00000 0.257663 0.128831 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) 0 0
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 0 0
\(245\) −13.7980 + 23.8988i −0.881519 + 1.52684i
\(246\) 0 0
\(247\) −13.5000 + 7.79423i −0.858984 + 0.495935i
\(248\) 0 0
\(249\) 12.8485 5.91931i 0.814239 0.375121i
\(250\) 0 0
\(251\) −7.07321 + 12.2512i −0.446457 + 0.773287i −0.998152 0.0607591i \(-0.980648\pi\)
0.551695 + 0.834046i \(0.313981\pi\)
\(252\) 0 0
\(253\) 32.5590i 2.04697i
\(254\) 0 0
\(255\) −7.89898 + 3.63907i −0.494653 + 0.227888i
\(256\) 0 0
\(257\) 4.07321 2.35167i 0.254080 0.146693i −0.367551 0.930003i \(-0.619804\pi\)
0.621631 + 0.783310i \(0.286470\pi\)
\(258\) 0 0
\(259\) 0.460702i 0.0286266i
\(260\) 0 0
\(261\) −20.0732 17.1616i −1.24250 1.06228i
\(262\) 0 0
\(263\) 14.7778i 0.911239i 0.890175 + 0.455619i \(0.150582\pi\)
−0.890175 + 0.455619i \(0.849418\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 22.6969 + 16.0492i 1.38903 + 0.982193i
\(268\) 0 0
\(269\) 28.6342i 1.74586i −0.487846 0.872929i \(-0.662217\pi\)
0.487846 0.872929i \(-0.337783\pi\)
\(270\) 0 0
\(271\) 4.09978i 0.249044i 0.992217 + 0.124522i \(0.0397397\pi\)
−0.992217 + 0.124522i \(0.960260\pi\)
\(272\) 0 0
\(273\) 23.6969 33.5125i 1.43420 2.02827i
\(274\) 0 0
\(275\) 1.72474 + 2.98735i 0.104006 + 0.180144i
\(276\) 0 0
\(277\) 6.20204 0.372645 0.186322 0.982489i \(-0.440343\pi\)
0.186322 + 0.982489i \(0.440343\pi\)
\(278\) 0 0
\(279\) 3.94949 + 3.37662i 0.236450 + 0.202153i
\(280\) 0 0
\(281\) 1.27526 2.20881i 0.0760753 0.131766i −0.825478 0.564434i \(-0.809094\pi\)
0.901553 + 0.432668i \(0.142428\pi\)
\(282\) 0 0
\(283\) 11.7980 0.701316 0.350658 0.936504i \(-0.385958\pi\)
0.350658 + 0.936504i \(0.385958\pi\)
\(284\) 0 0
\(285\) −4.34847 9.43879i −0.257581 0.559106i
\(286\) 0 0
\(287\) 5.72474 + 3.30518i 0.337921 + 0.195099i
\(288\) 0 0
\(289\) −5.34847 9.26382i −0.314616 0.544931i
\(290\) 0 0
\(291\) −5.17423 + 2.38378i −0.303319 + 0.139740i
\(292\) 0 0
\(293\) 12.2993i 0.718534i 0.933235 + 0.359267i \(0.116973\pi\)
−0.933235 + 0.359267i \(0.883027\pi\)
\(294\) 0 0
\(295\) 12.5851i 0.732730i
\(296\) 0 0
\(297\) 4.39898 + 17.3759i 0.255255 + 1.00825i
\(298\) 0 0
\(299\) −24.5227 42.4746i −1.41818 2.45637i
\(300\) 0 0
\(301\) −28.6969 49.7046i −1.65406 2.86492i
\(302\) 0 0
\(303\) 14.7474 + 1.35884i 0.847219 + 0.0780630i
\(304\) 0 0
\(305\) 0.797959 + 0.460702i 0.0456910 + 0.0263797i
\(306\) 0 0
\(307\) 15.2980 26.4968i 0.873101 1.51225i 0.0143283 0.999897i \(-0.495439\pi\)
0.858772 0.512357i \(-0.171228\pi\)
\(308\) 0 0
\(309\) −10.1742 0.937458i −0.578792 0.0533301i
\(310\) 0 0
\(311\) −33.7980 −1.91651 −0.958253 0.285921i \(-0.907701\pi\)
−0.958253 + 0.285921i \(0.907701\pi\)
\(312\) 0 0
\(313\) 22.9774i 1.29876i 0.760465 + 0.649379i \(0.224971\pi\)
−0.760465 + 0.649379i \(0.775029\pi\)
\(314\) 0 0
\(315\) 20.7980 + 17.7812i 1.17183 + 1.00186i
\(316\) 0 0
\(317\) −25.3207 14.6189i −1.42215 0.821079i −0.425668 0.904880i \(-0.639961\pi\)
−0.996483 + 0.0838009i \(0.973294\pi\)
\(318\) 0 0
\(319\) −26.2980 15.1831i −1.47240 0.850092i
\(320\) 0 0
\(321\) −3.10102 2.19275i −0.173082 0.122388i
\(322\) 0 0
\(323\) −6.52270 + 3.76588i −0.362933 + 0.209539i
\(324\) 0 0
\(325\) −4.50000 2.59808i −0.249615 0.144115i
\(326\) 0 0
\(327\) 16.8990 + 11.9494i 0.934516 + 0.660802i
\(328\) 0 0
\(329\) −7.17423 + 12.4261i −0.395528 + 0.685075i
\(330\) 0 0
\(331\) 27.0959 15.6438i 1.48933 0.859863i 0.489401 0.872059i \(-0.337216\pi\)
0.999926 + 0.0121961i \(0.00388222\pi\)
\(332\) 0 0
\(333\) 0.297959 + 0.0553782i 0.0163281 + 0.00303471i
\(334\) 0 0
\(335\) −16.0000 + 3.46410i −0.874173 + 0.189264i
\(336\) 0 0
\(337\) −11.0505 6.38002i −0.601960 0.347542i 0.167852 0.985812i \(-0.446317\pi\)
−0.769812 + 0.638271i \(0.779650\pi\)
\(338\) 0 0
\(339\) 19.7474 + 1.81954i 1.07253 + 0.0988237i
\(340\) 0 0
\(341\) 5.17423 + 2.98735i 0.280201 + 0.161774i
\(342\) 0 0
\(343\) 31.0019i 1.67395i
\(344\) 0 0
\(345\) 29.6969 13.6814i 1.59883 0.736584i
\(346\) 0 0
\(347\) −11.0732 19.1794i −0.594441 1.02960i −0.993625 0.112732i \(-0.964040\pi\)
0.399184 0.916871i \(-0.369293\pi\)
\(348\) 0 0
\(349\) 21.7980 1.16682 0.583409 0.812179i \(-0.301718\pi\)
0.583409 + 0.812179i \(0.301718\pi\)
\(350\) 0 0
\(351\) −18.8258 19.3543i −1.00485 1.03306i
\(352\) 0 0
\(353\) 4.17423 7.22999i 0.222172 0.384813i −0.733295 0.679910i \(-0.762019\pi\)
0.955467 + 0.295097i \(0.0953520\pi\)
\(354\) 0 0
\(355\) −7.65153 + 4.41761i −0.406101 + 0.234463i
\(356\) 0 0
\(357\) 11.4495 16.1920i 0.605971 0.856973i
\(358\) 0 0
\(359\) 20.4347i 1.07850i −0.842146 0.539250i \(-0.818708\pi\)
0.842146 0.539250i \(-0.181292\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) 0 0
\(363\) 0.651531 + 1.41421i 0.0341965 + 0.0742270i
\(364\) 0 0
\(365\) 3.89898 6.75323i 0.204082 0.353480i
\(366\) 0 0
\(367\) 13.5000 7.79423i 0.704694 0.406855i −0.104399 0.994535i \(-0.533292\pi\)
0.809093 + 0.587680i \(0.199959\pi\)
\(368\) 0 0
\(369\) 2.82577 3.30518i 0.147103 0.172061i
\(370\) 0 0
\(371\) 23.6969 13.6814i 1.23028 0.710305i
\(372\) 0 0
\(373\) −9.39898 + 5.42650i −0.486661 + 0.280974i −0.723188 0.690651i \(-0.757324\pi\)
0.236527 + 0.971625i \(0.423991\pi\)
\(374\) 0 0
\(375\) 12.0000 16.9706i 0.619677 0.876356i
\(376\) 0 0
\(377\) 45.7423 2.35585
\(378\) 0 0
\(379\) −30.3990 17.5509i −1.56149 0.901527i −0.997107 0.0760147i \(-0.975780\pi\)
−0.564384 0.825512i \(-0.690886\pi\)
\(380\) 0 0
\(381\) −18.6237 1.71600i −0.954122 0.0879132i
\(382\) 0 0
\(383\) −5.07321 + 8.78706i −0.259229 + 0.448998i −0.966036 0.258409i \(-0.916802\pi\)
0.706806 + 0.707407i \(0.250135\pi\)
\(384\) 0 0
\(385\) 27.2474 + 15.7313i 1.38866 + 0.801742i
\(386\) 0 0
\(387\) −35.5959 + 12.5851i −1.80944 + 0.639734i
\(388\) 0 0
\(389\) −17.9722 10.3763i −0.911226 0.526097i −0.0304008 0.999538i \(-0.509678\pi\)
−0.880826 + 0.473441i \(0.843012\pi\)
\(390\) 0 0
\(391\) −11.8485 20.5222i −0.599203 1.03785i
\(392\) 0 0
\(393\) −0.898979 0.635674i −0.0453475 0.0320655i
\(394\) 0 0
\(395\) 18.7980 10.8530i 0.945828 0.546074i
\(396\) 0 0
\(397\) 2.69694 0.135355 0.0676777 0.997707i \(-0.478441\pi\)
0.0676777 + 0.997707i \(0.478441\pi\)
\(398\) 0 0
\(399\) 19.3485 + 13.6814i 0.968635 + 0.684928i
\(400\) 0 0
\(401\) −14.8990 −0.744020 −0.372010 0.928229i \(-0.621331\pi\)
−0.372010 + 0.928229i \(0.621331\pi\)
\(402\) 0 0
\(403\) −9.00000 −0.448322
\(404\) 0 0
\(405\) 14.0000 11.3137i 0.695666 0.562183i
\(406\) 0 0
\(407\) 0.348469 0.0172730
\(408\) 0 0
\(409\) −16.5000 + 9.52628i −0.815872 + 0.471044i −0.848991 0.528407i \(-0.822789\pi\)
0.0331186 + 0.999451i \(0.489456\pi\)
\(410\) 0 0
\(411\) 18.8990 26.7272i 0.932218 1.31836i
\(412\) 0 0
\(413\) 14.3485 + 24.8523i 0.706042 + 1.22290i
\(414\) 0 0
\(415\) −14.1464 8.16744i −0.694421 0.400924i
\(416\) 0 0
\(417\) 29.7980 + 21.0703i 1.45921 + 1.03182i
\(418\) 0 0
\(419\) 19.3207 + 11.1548i 0.943876 + 0.544947i 0.891173 0.453663i \(-0.149883\pi\)
0.0527029 + 0.998610i \(0.483216\pi\)
\(420\) 0 0
\(421\) −6.50000 + 11.2583i −0.316791 + 0.548697i −0.979817 0.199899i \(-0.935939\pi\)
0.663026 + 0.748596i \(0.269272\pi\)
\(422\) 0 0
\(423\) 7.17423 + 6.13361i 0.348823 + 0.298226i
\(424\) 0 0
\(425\) −2.17423 1.25529i −0.105466 0.0608907i
\(426\) 0 0
\(427\) −2.10102 −0.101676
\(428\) 0 0
\(429\) −25.3485 17.9241i −1.22384 0.865382i
\(430\) 0 0
\(431\) 18.7702 10.8370i 0.904126 0.521998i 0.0255898 0.999673i \(-0.491854\pi\)
0.878537 + 0.477675i \(0.158520\pi\)
\(432\) 0 0
\(433\) −13.5000 + 7.79423i −0.648769 + 0.374567i −0.787984 0.615695i \(-0.788875\pi\)
0.139216 + 0.990262i \(0.455542\pi\)
\(434\) 0 0
\(435\) −2.79796 + 30.3663i −0.134152 + 1.45595i
\(436\) 0 0
\(437\) 24.5227 14.1582i 1.17308 0.677278i
\(438\) 0 0
\(439\) −14.3990 + 24.9398i −0.687226 + 1.19031i 0.285506 + 0.958377i \(0.407838\pi\)
−0.972732 + 0.231933i \(0.925495\pi\)
\(440\) 0 0
\(441\) −40.6969 7.56388i −1.93795 0.360185i
\(442\) 0 0
\(443\) 4.37628 + 7.57993i 0.207923 + 0.360133i 0.951060 0.309006i \(-0.0999963\pi\)
−0.743137 + 0.669139i \(0.766663\pi\)
\(444\) 0 0
\(445\) 32.0983i 1.52161i
\(446\) 0 0
\(447\) −11.1010 7.84961i −0.525060 0.371274i
\(448\) 0 0
\(449\) −6.82577 + 3.94086i −0.322128 + 0.185981i −0.652341 0.757926i \(-0.726213\pi\)
0.330213 + 0.943907i \(0.392879\pi\)
\(450\) 0 0
\(451\) 2.50000 4.33013i 0.117720 0.203898i
\(452\) 0 0
\(453\) −7.82577 16.9866i −0.367687 0.798101i
\(454\) 0 0
\(455\) −47.3939 −2.22186
\(456\) 0 0
\(457\) −11.1969 19.3937i −0.523771 0.907197i −0.999617 0.0276691i \(-0.991192\pi\)
0.475846 0.879528i \(-0.342142\pi\)
\(458\) 0 0
\(459\) −9.09592 9.35131i −0.424561 0.436482i
\(460\) 0 0
\(461\) 14.4279i 0.671973i 0.941867 + 0.335986i \(0.109070\pi\)
−0.941867 + 0.335986i \(0.890930\pi\)
\(462\) 0 0
\(463\) 22.1969 + 12.8154i 1.03158 + 0.595583i 0.917437 0.397882i \(-0.130255\pi\)
0.114143 + 0.993464i \(0.463588\pi\)
\(464\) 0 0
\(465\) 0.550510 5.97469i 0.0255293 0.277070i
\(466\) 0 0
\(467\) 27.8258 + 16.0652i 1.28762 + 0.743409i 0.978230 0.207525i \(-0.0665408\pi\)
0.309393 + 0.950934i \(0.399874\pi\)
\(468\) 0 0
\(469\) 27.6464 25.0826i 1.27659 1.15821i
\(470\) 0 0
\(471\) −2.97219 6.45145i −0.136951 0.297267i
\(472\) 0 0
\(473\) −37.5959 + 21.7060i −1.72866 + 0.998044i
\(474\) 0 0
\(475\) 1.50000 2.59808i 0.0688247 0.119208i
\(476\) 0 0
\(477\) −6.00000 16.9706i −0.274721 0.777029i
\(478\) 0 0
\(479\) 15.2753 + 8.81917i 0.697944 + 0.402958i 0.806581 0.591123i \(-0.201315\pi\)
−0.108637 + 0.994081i \(0.534649\pi\)
\(480\) 0 0
\(481\) −0.454592 + 0.262459i −0.0207276 + 0.0119671i
\(482\) 0 0
\(483\) −43.0454 + 60.8754i −1.95863 + 2.76993i
\(484\) 0 0
\(485\) 5.69694 + 3.28913i 0.258685 + 0.149352i
\(486\) 0 0
\(487\) −18.3990 10.6227i −0.833737 0.481358i 0.0213932 0.999771i \(-0.493190\pi\)
−0.855131 + 0.518413i \(0.826523\pi\)
\(488\) 0 0
\(489\) 28.6237 + 2.63740i 1.29441 + 0.119267i
\(490\) 0 0
\(491\) 22.9774i 1.03695i −0.855092 0.518477i \(-0.826499\pi\)
0.855092 0.518477i \(-0.173501\pi\)
\(492\) 0 0
\(493\) 22.1010 0.995380
\(494\) 0 0
\(495\) 13.4495 15.7313i 0.604510 0.707070i
\(496\) 0 0
\(497\) 10.0732 17.4473i 0.451845 0.782619i
\(498\) 0 0
\(499\) 6.39898 + 3.69445i 0.286458 + 0.165386i 0.636343 0.771406i \(-0.280446\pi\)
−0.349886 + 0.936792i \(0.613780\pi\)
\(500\) 0 0
\(501\) −0.904082 + 9.81201i −0.0403914 + 0.438368i
\(502\) 0 0
\(503\) −14.8258 25.6790i −0.661048 1.14497i −0.980341 0.197313i \(-0.936779\pi\)
0.319292 0.947656i \(-0.396555\pi\)
\(504\) 0 0
\(505\) −8.55051 14.8099i −0.380493 0.659033i
\(506\) 0 0
\(507\) 24.1464 + 2.22486i 1.07238 + 0.0988095i
\(508\) 0 0
\(509\) 2.82843i 0.125368i −0.998033 0.0626839i \(-0.980034\pi\)
0.998033 0.0626839i \(-0.0199660\pi\)
\(510\) 0 0
\(511\) 17.7812i 0.786594i
\(512\) 0 0
\(513\) 11.1742 10.8691i 0.493355 0.479881i
\(514\) 0 0
\(515\) 5.89898 + 10.2173i 0.259940 + 0.450229i
\(516\) 0 0
\(517\) 9.39898 + 5.42650i 0.413367 + 0.238657i
\(518\) 0 0
\(519\) −2.94949 + 1.35884i −0.129468 + 0.0596463i
\(520\) 0 0
\(521\) −28.2929 −1.23953 −0.619766 0.784786i \(-0.712773\pi\)
−0.619766 + 0.784786i \(0.712773\pi\)
\(522\) 0 0
\(523\) −11.6464 + 20.1722i −0.509263 + 0.882069i 0.490680 + 0.871340i \(0.336749\pi\)
−0.999942 + 0.0107289i \(0.996585\pi\)
\(524\) 0 0
\(525\) −0.724745 + 7.86566i −0.0316305 + 0.343286i
\(526\) 0 0
\(527\) −4.34847 −0.189422
\(528\) 0 0
\(529\) 33.0454 + 57.2363i 1.43676 + 2.48854i
\(530\) 0 0
\(531\) 17.7980 6.29253i 0.772366 0.273072i
\(532\) 0 0
\(533\) 7.53177i 0.326237i
\(534\) 0 0
\(535\) 4.38551i 0.189602i
\(536\) 0 0
\(537\) 25.5959 36.1981i 1.10455 1.56206i
\(538\) 0 0
\(539\) −47.5959 −2.05010
\(540\) 0 0
\(541\) 17.8920i 0.769236i −0.923076 0.384618i \(-0.874333\pi\)
0.923076 0.384618i \(-0.125667\pi\)
\(542\) 0 0
\(543\) 20.5227 + 1.89097i 0.880714 + 0.0811493i
\(544\) 0 0
\(545\) 23.8988i 1.02371i
\(546\) 0 0
\(547\) 3.15153 1.81954i 0.134750 0.0777978i −0.431110 0.902300i \(-0.641878\pi\)
0.565859 + 0.824502i \(0.308544\pi\)
\(548\) 0 0
\(549\) −0.252551 + 1.35884i −0.0107786 + 0.0579937i
\(550\) 0 0
\(551\) 26.4094i 1.12508i
\(552\) 0 0
\(553\) −24.7474 + 42.8638i −1.05237 + 1.82276i
\(554\) 0 0
\(555\) −0.146428 0.317837i −0.00621553 0.0134914i
\(556\) 0 0
\(557\) −10.0732 + 5.81577i −0.426816 + 0.246422i −0.697989 0.716108i \(-0.745922\pi\)
0.271173 + 0.962531i \(0.412588\pi\)
\(558\) 0 0
\(559\) 32.6969 56.6328i 1.38293 2.39531i
\(560\) 0 0
\(561\) −12.2474 8.66025i −0.517088 0.365636i
\(562\) 0 0
\(563\) −26.2929 −1.10811 −0.554056 0.832479i \(-0.686921\pi\)
−0.554056 + 0.832479i \(0.686921\pi\)
\(564\) 0 0
\(565\) −11.4495 19.8311i −0.481684 0.834301i
\(566\) 0 0
\(567\) −14.7474 + 38.3034i −0.619335 + 1.60859i
\(568\) 0 0
\(569\) 8.42168 4.86226i 0.353055 0.203837i −0.312975 0.949761i \(-0.601326\pi\)
0.666030 + 0.745925i \(0.267992\pi\)
\(570\) 0 0
\(571\) −4.15153 7.19066i −0.173736 0.300920i 0.765987 0.642856i \(-0.222251\pi\)
−0.939723 + 0.341936i \(0.888917\pi\)
\(572\) 0 0
\(573\) 9.09592 + 19.7436i 0.379987 + 0.824801i
\(574\) 0 0
\(575\) 8.17423 + 4.71940i 0.340889 + 0.196812i
\(576\) 0 0
\(577\) −12.1515 + 7.01569i −0.505875 + 0.292067i −0.731136 0.682231i \(-0.761010\pi\)
0.225262 + 0.974298i \(0.427676\pi\)
\(578\) 0 0
\(579\) −3.10102 + 4.38551i −0.128874 + 0.182255i
\(580\) 0 0
\(581\) 37.2474 1.54528
\(582\) 0 0
\(583\) −10.3485 17.9241i −0.428590 0.742339i
\(584\) 0 0
\(585\) −5.69694 + 30.6520i −0.235539 + 1.26730i
\(586\) 0 0
\(587\) −10.7247 + 18.5758i −0.442658 + 0.766705i −0.997886 0.0649926i \(-0.979298\pi\)
0.555228 + 0.831698i \(0.312631\pi\)
\(588\) 0 0
\(589\) 5.19615i 0.214104i
\(590\) 0 0
\(591\) −36.6464 3.37662i −1.50743 0.138895i
\(592\) 0 0
\(593\) 14.9722 25.9326i 0.614834 1.06492i −0.375579 0.926790i \(-0.622556\pi\)
0.990414 0.138134i \(-0.0441105\pi\)
\(594\) 0 0
\(595\) −22.8990 −0.938767
\(596\) 0 0
\(597\) −7.97219 17.3045i −0.326280 0.708224i
\(598\) 0 0
\(599\) 0.825765 + 1.43027i 0.0337399 + 0.0584391i 0.882402 0.470496i \(-0.155925\pi\)
−0.848662 + 0.528935i \(0.822592\pi\)
\(600\) 0 0
\(601\) 8.39898 14.5475i 0.342602 0.593403i −0.642313 0.766442i \(-0.722025\pi\)
0.984915 + 0.173039i \(0.0553586\pi\)
\(602\) 0 0
\(603\) −12.8990 20.8954i −0.525287 0.850925i
\(604\) 0 0
\(605\) 0.898979 1.55708i 0.0365487 0.0633042i
\(606\) 0 0
\(607\) 4.84847 + 8.39780i 0.196793 + 0.340856i 0.947487 0.319795i \(-0.103614\pi\)
−0.750694 + 0.660650i \(0.770281\pi\)
\(608\) 0 0
\(609\) −29.0959 63.1556i −1.17903 2.55920i
\(610\) 0 0
\(611\) −16.3485 −0.661388
\(612\) 0 0
\(613\) −16.1969 + 28.0539i −0.654188 + 1.13309i 0.327908 + 0.944709i \(0.393656\pi\)
−0.982097 + 0.188378i \(0.939677\pi\)
\(614\) 0 0
\(615\) −5.00000 0.460702i −0.201619 0.0185773i
\(616\) 0 0
\(617\) 12.8708i 0.518158i 0.965856 + 0.259079i \(0.0834191\pi\)
−0.965856 + 0.259079i \(0.916581\pi\)
\(618\) 0 0
\(619\) 1.94949 3.37662i 0.0783566 0.135718i −0.824184 0.566322i \(-0.808366\pi\)
0.902541 + 0.430604i \(0.141699\pi\)
\(620\) 0 0
\(621\) 34.1969 + 35.1571i 1.37228 + 1.41081i
\(622\) 0 0
\(623\) 36.5959 + 63.3860i 1.46618 + 2.53951i
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 10.3485 14.6349i 0.413278 0.584463i
\(628\) 0 0
\(629\) −0.219642 + 0.126811i −0.00875771 + 0.00505627i
\(630\) 0 0
\(631\) −20.5454 11.8619i −0.817900 0.472215i 0.0317919 0.999495i \(-0.489879\pi\)
−0.849692 + 0.527280i \(0.823212\pi\)
\(632\) 0 0
\(633\) 2.82577 + 6.13361i 0.112314 + 0.243789i
\(634\) 0 0
\(635\) 10.7980 + 18.7026i 0.428504 + 0.742191i
\(636\) 0 0
\(637\) 62.0908 35.8481i 2.46013 1.42036i
\(638\) 0 0
\(639\) −10.0732 8.61209i −0.398490 0.340689i
\(640\) 0 0
\(641\) 0.522704 + 0.905350i 0.0206456 + 0.0357592i 0.876164 0.482014i \(-0.160095\pi\)
−0.855518 + 0.517773i \(0.826761\pi\)
\(642\) 0 0
\(643\) −49.1918 −1.93994 −0.969968 0.243231i \(-0.921793\pi\)
−0.969968 + 0.243231i \(0.921793\pi\)
\(644\) 0 0
\(645\) 35.5959 + 25.1701i 1.40159 + 0.991072i
\(646\) 0 0
\(647\) 7.17423 12.4261i 0.282048 0.488522i −0.689841 0.723961i \(-0.742320\pi\)
0.971889 + 0.235439i \(0.0756528\pi\)
\(648\) 0 0
\(649\) 18.7980 10.8530i 0.737884 0.426018i
\(650\) 0 0
\(651\) 5.72474 + 12.4261i 0.224370 + 0.487019i
\(652\) 0 0
\(653\) 2.62372 4.54442i 0.102674 0.177837i −0.810111 0.586276i \(-0.800593\pi\)
0.912786 + 0.408439i \(0.133927\pi\)
\(654\) 0 0
\(655\) 1.27135i 0.0496757i
\(656\) 0 0
\(657\) 11.5000 + 2.13737i 0.448658 + 0.0833869i
\(658\) 0 0
\(659\) −3.27526 + 1.89097i −0.127586 + 0.0736617i −0.562435 0.826842i \(-0.690135\pi\)
0.434849 + 0.900504i \(0.356802\pi\)
\(660\) 0 0
\(661\) 2.47848i 0.0964018i 0.998838 + 0.0482009i \(0.0153488\pi\)
−0.998838 + 0.0482009i \(0.984651\pi\)
\(662\) 0 0
\(663\) 22.5000 + 2.07316i 0.873828 + 0.0805148i
\(664\) 0 0
\(665\) 27.3629i 1.06109i
\(666\) 0 0
\(667\) −83.0908 −3.21729
\(668\) 0 0
\(669\) −8.69694 + 12.2993i −0.336243 + 0.475520i
\(670\) 0 0
\(671\) 1.58919i 0.0613499i
\(672\) 0 0
\(673\) 18.2419i 0.703174i 0.936155 + 0.351587i \(0.114358\pi\)
−0.936155 + 0.351587i \(0.885642\pi\)
\(674\) 0 0
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) 0 0
\(677\) −19.7247 34.1643i −0.758084 1.31304i −0.943827 0.330441i \(-0.892803\pi\)
0.185743 0.982598i \(-0.440531\pi\)
\(678\) 0 0
\(679\) −15.0000 −0.575647
\(680\) 0 0
\(681\) −1.54541 + 16.7723i −0.0592202 + 0.642717i
\(682\) 0 0
\(683\) −8.82577 + 15.2867i −0.337709 + 0.584928i −0.984001 0.178161i \(-0.942985\pi\)
0.646293 + 0.763090i \(0.276318\pi\)
\(684\) 0 0
\(685\) −37.7980 −1.44419
\(686\) 0 0
\(687\) 10.6237 4.89437i 0.405320 0.186732i
\(688\) 0 0
\(689\) 27.0000 + 15.5885i 1.02862 + 0.593873i
\(690\) 0 0
\(691\) 20.6464 + 35.7607i 0.785427 + 1.36040i 0.928744 + 0.370723i \(0.120890\pi\)
−0.143316 + 0.989677i \(0.545777\pi\)
\(692\) 0 0
\(693\) −8.62372 + 46.3994i −0.327588 + 1.76257i
\(694\) 0 0
\(695\) 42.1407i 1.59849i
\(696\) 0 0
\(697\) 3.63907i 0.137840i
\(698\) 0 0
\(699\) 40.4444 + 3.72656i 1.52975 + 0.140951i
\(700\) 0 0
\(701\) 14.1742 + 24.5505i 0.535353 + 0.927259i 0.999146 + 0.0413156i \(0.0131549\pi\)
−0.463793 + 0.885944i \(0.653512\pi\)
\(702\) 0 0
\(703\) −0.151531 0.262459i −0.00571509 0.00989883i
\(704\) 0 0
\(705\) 1.00000 10.8530i 0.0376622 0.408748i
\(706\) 0 0
\(707\) 33.7702 + 19.4972i 1.27006 + 0.733268i
\(708\) 0 0
\(709\) −11.7474 + 20.3472i −0.441185 + 0.764154i −0.997778 0.0666310i \(-0.978775\pi\)
0.556593 + 0.830785i \(0.312108\pi\)
\(710\) 0 0
\(711\) 24.7474 + 21.1578i 0.928102 + 0.793480i
\(712\) 0 0
\(713\) 16.3485 0.612255
\(714\) 0 0
\(715\) 35.8481i 1.34064i
\(716\) 0 0
\(717\) 22.8485 + 2.10527i 0.853292 + 0.0786226i
\(718\) 0 0
\(719\) −41.6691 24.0577i −1.55400 0.897200i −0.997810 0.0661425i \(-0.978931\pi\)
−0.556186 0.831058i \(-0.687736\pi\)
\(720\) 0 0
\(721\) −23.2980 13.4511i −0.867661 0.500945i
\(722\) 0 0
\(723\) 4.00000 5.65685i 0.148762 0.210381i
\(724\) 0 0
\(725\) −7.62372 + 4.40156i −0.283138 + 0.163470i
\(726\) 0 0
\(727\) −12.8939 7.44428i −0.478207 0.276093i 0.241462 0.970410i \(-0.422373\pi\)
−0.719669 + 0.694317i \(0.755707\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) 15.7980 27.3629i 0.584309 1.01205i
\(732\) 0 0
\(733\) 18.9495 10.9405i 0.699915 0.404096i −0.107401 0.994216i \(-0.534253\pi\)
0.807316 + 0.590120i \(0.200919\pi\)
\(734\) 0 0
\(735\) 20.0000 + 43.4120i 0.737711 + 1.60128i
\(736\) 0 0
\(737\) −18.9722 20.9114i −0.698850 0.770282i
\(738\) 0 0
\(739\) −2.35357 1.35884i −0.0865775 0.0499856i 0.456086 0.889936i \(-0.349251\pi\)
−0.542664 + 0.839950i \(0.682584\pi\)
\(740\) 0 0
\(741\) −2.47730 + 26.8861i −0.0910057 + 0.987686i
\(742\) 0 0
\(743\) 8.72474 + 5.03723i 0.320080 + 0.184798i 0.651428 0.758710i \(-0.274170\pi\)
−0.331348 + 0.943508i \(0.607504\pi\)
\(744\) 0 0
\(745\) 15.6992i 0.575175i
\(746\) 0 0
\(747\) 4.47730 24.0898i 0.163816 0.881399i
\(748\) 0 0
\(749\) −5.00000 8.66025i −0.182696 0.316439i
\(750\) 0 0
\(751\) −43.3939 −1.58347 −0.791733 0.610868i \(-0.790821\pi\)
−0.791733 + 0.610868i \(0.790821\pi\)
\(752\) 0 0
\(753\) 10.2526 + 22.2542i 0.373624 + 0.810988i
\(754\) 0 0
\(755\) −10.7980 + 18.7026i −0.392978 + 0.680658i
\(756\) 0 0
\(757\) −21.9495 + 12.6725i −0.797768 + 0.460591i −0.842690 0.538399i \(-0.819029\pi\)
0.0449222 + 0.998990i \(0.485696\pi\)
\(758\) 0 0
\(759\) 46.0454 + 32.5590i 1.67134 + 1.18182i
\(760\) 0 0
\(761\) 23.6130i 0.855972i 0.903785 + 0.427986i \(0.140777\pi\)
−0.903785 + 0.427986i \(0.859223\pi\)
\(762\) 0 0
\(763\) 27.2474 + 47.1940i 0.986424 + 1.70854i
\(764\) 0 0
\(765\) −2.75255 + 14.8099i −0.0995187 + 0.535454i
\(766\) 0 0
\(767\) −16.3485 + 28.3164i −0.590309 + 1.02245i
\(768\) 0 0
\(769\) 13.7474 7.93709i 0.495746 0.286219i −0.231209 0.972904i \(-0.574268\pi\)
0.726955 + 0.686685i \(0.240935\pi\)
\(770\) 0 0
\(771\) 0.747449 8.11207i 0.0269187 0.292149i
\(772\) 0 0
\(773\) 23.9722 13.8404i 0.862220 0.497803i −0.00253516 0.999997i \(-0.500807\pi\)
0.864755 + 0.502194i \(0.167474\pi\)
\(774\) 0 0
\(775\) 1.50000 0.866025i 0.0538816 0.0311086i
\(776\) 0 0
\(777\) 0.651531 + 0.460702i 0.0233735 + 0.0165276i
\(778\) 0 0
\(779\) −4.34847 −0.155800
\(780\) 0 0
\(781\) −13.1969 7.61926i −0.472224 0.272638i
\(782\) 0 0
\(783\) −44.3434 + 11.2262i −1.58470 + 0.401192i
\(784\) 0 0
\(785\) −4.10102 + 7.10318i −0.146372 + 0.253523i
\(786\) 0 0
\(787\) −15.6464 9.03347i −0.557735 0.322008i 0.194501 0.980902i \(-0.437691\pi\)
−0.752236 + 0.658894i \(0.771025\pi\)
\(788\) 0 0
\(789\) 20.8990 + 14.7778i 0.744023 + 0.526104i
\(790\) 0 0
\(791\) 45.2196 + 26.1076i 1.60783 + 0.928278i
\(792\) 0 0
\(793\) −1.19694 2.07316i −0.0425045 0.0736200i
\(794\) 0 0
\(795\) −12.0000 + 16.9706i −0.425596 + 0.601884i
\(796\) 0 0
\(797\) −3.82577 + 2.20881i −0.135516 + 0.0782399i −0.566225 0.824251i \(-0.691597\pi\)
0.430709 + 0.902491i \(0.358263\pi\)
\(798\) 0 0
\(799\) −7.89898 −0.279446
\(800\) 0 0
\(801\) 45.3939 16.0492i