Properties

Label 216.2.n.b.37.3
Level $216$
Weight $2$
Character 216.37
Analytic conductor $1.725$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + 64 x^{2} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 37.3
Root \(0.587625 + 1.28635i\) of defining polynomial
Character \(\chi\) \(=\) 216.37
Dual form 216.2.n.b.181.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.820200 - 1.15207i) q^{2} +(-0.654545 + 1.88986i) q^{4} +(-1.97542 - 1.14051i) q^{5} +(-0.907824 - 1.57240i) q^{7} +(2.71411 - 0.795980i) q^{8} +O(q^{10})\) \(q+(-0.820200 - 1.15207i) q^{2} +(-0.654545 + 1.88986i) q^{4} +(-1.97542 - 1.14051i) q^{5} +(-0.907824 - 1.57240i) q^{7} +(2.71411 - 0.795980i) q^{8} +(0.306290 + 3.21128i) q^{10} +(-4.24153 + 2.44885i) q^{11} +(-4.00895 - 2.31457i) q^{13} +(-1.06692 + 2.33556i) q^{14} +(-3.14314 - 2.47400i) q^{16} -1.92788 q^{17} +2.12907i q^{19} +(3.44841 - 2.98676i) q^{20} +(6.30015 + 2.87801i) q^{22} +(1.15765 - 2.00511i) q^{23} +(0.101535 + 0.175863i) q^{25} +(0.621589 + 6.51702i) q^{26} +(3.56582 - 0.686457i) q^{28} +(3.16440 - 1.82697i) q^{29} +(-2.65800 + 4.60379i) q^{31} +(-0.272218 + 5.65030i) q^{32} +(1.58125 + 2.22106i) q^{34} +4.14154i q^{35} -7.98438i q^{37} +(2.45284 - 1.74626i) q^{38} +(-6.26935 - 1.52308i) q^{40} +(2.36240 - 4.09180i) q^{41} +(2.20800 - 1.27479i) q^{43} +(-1.85171 - 9.61877i) q^{44} +(-3.25953 + 0.310892i) q^{46} +(2.02005 + 3.49884i) q^{47} +(1.85171 - 3.20726i) q^{49} +(0.119328 - 0.261218i) q^{50} +(6.99825 - 6.06137i) q^{52} -8.95958i q^{53} +11.1718 q^{55} +(-3.71554 - 3.54506i) q^{56} +(-4.70024 - 2.14714i) q^{58} +(3.05255 + 1.76239i) q^{59} +(-1.71675 + 0.991165i) q^{61} +(7.48399 - 0.713818i) q^{62} +(6.73283 - 4.32076i) q^{64} +(5.27959 + 9.14451i) q^{65} +(7.72723 + 4.46132i) q^{67} +(1.26188 - 3.64342i) q^{68} +(4.77135 - 3.39689i) q^{70} -13.3561 q^{71} -11.5592 q^{73} +(-9.19859 + 6.54879i) q^{74} +(-4.02364 - 1.39357i) q^{76} +(7.70112 + 4.44625i) q^{77} +(-4.97330 - 8.61401i) q^{79} +(3.38742 + 8.47198i) q^{80} +(-6.65170 + 0.634435i) q^{82} +(3.12153 - 1.80221i) q^{83} +(3.80838 + 2.19877i) q^{85} +(-3.27965 - 1.49820i) q^{86} +(-9.56276 + 10.0226i) q^{88} -2.49965 q^{89} +8.40489i q^{91} +(3.03164 + 3.50023i) q^{92} +(2.37407 - 5.19699i) q^{94} +(2.42823 - 4.20582i) q^{95} +(6.99370 + 12.1134i) q^{97} +(-5.21376 + 0.497285i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{2} - q^{4} + 6q^{7} + 2q^{8} + O(q^{10}) \) \( 16q - q^{2} - q^{4} + 6q^{7} + 2q^{8} - 16q^{10} - 16q^{14} - 9q^{16} + 28q^{17} + 8q^{20} + q^{22} + 10q^{23} + 2q^{25} - 28q^{26} + 4q^{28} - 10q^{31} - 11q^{32} + q^{34} - 23q^{38} + 6q^{40} + 8q^{41} - 18q^{44} - 20q^{46} - 6q^{47} + 18q^{49} + 23q^{50} - 8q^{52} - 4q^{55} - 10q^{56} - 14q^{58} + 52q^{62} + 26q^{64} + 14q^{65} + 39q^{68} - 72q^{71} - 44q^{73} + 38q^{74} + 5q^{76} - 30q^{79} + 96q^{80} + 38q^{82} - 7q^{86} + 31q^{88} - 64q^{89} + 30q^{92} - 12q^{94} - 44q^{95} - 66q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.820200 1.15207i −0.579969 0.814639i
\(3\) 0 0
\(4\) −0.654545 + 1.88986i −0.327272 + 0.944930i
\(5\) −1.97542 1.14051i −0.883437 0.510052i −0.0116467 0.999932i \(-0.503707\pi\)
−0.871790 + 0.489880i \(0.837041\pi\)
\(6\) 0 0
\(7\) −0.907824 1.57240i −0.343125 0.594311i 0.641886 0.766800i \(-0.278152\pi\)
−0.985011 + 0.172490i \(0.944819\pi\)
\(8\) 2.71411 0.795980i 0.959584 0.281421i
\(9\) 0 0
\(10\) 0.306290 + 3.21128i 0.0968573 + 1.01550i
\(11\) −4.24153 + 2.44885i −1.27887 + 0.738355i −0.976640 0.214880i \(-0.931064\pi\)
−0.302228 + 0.953236i \(0.597730\pi\)
\(12\) 0 0
\(13\) −4.00895 2.31457i −1.11188 0.641946i −0.172567 0.984998i \(-0.555206\pi\)
−0.939317 + 0.343052i \(0.888539\pi\)
\(14\) −1.06692 + 2.33556i −0.285146 + 0.624205i
\(15\) 0 0
\(16\) −3.14314 2.47400i −0.785786 0.618499i
\(17\) −1.92788 −0.467579 −0.233790 0.972287i \(-0.575113\pi\)
−0.233790 + 0.972287i \(0.575113\pi\)
\(18\) 0 0
\(19\) 2.12907i 0.488442i 0.969720 + 0.244221i \(0.0785322\pi\)
−0.969720 + 0.244221i \(0.921468\pi\)
\(20\) 3.44841 2.98676i 0.771088 0.667860i
\(21\) 0 0
\(22\) 6.30015 + 2.87801i 1.34320 + 0.613593i
\(23\) 1.15765 2.00511i 0.241387 0.418094i −0.719723 0.694261i \(-0.755731\pi\)
0.961109 + 0.276168i \(0.0890645\pi\)
\(24\) 0 0
\(25\) 0.101535 + 0.175863i 0.0203069 + 0.0351726i
\(26\) 0.621589 + 6.51702i 0.121904 + 1.27809i
\(27\) 0 0
\(28\) 3.56582 0.686457i 0.673877 0.129728i
\(29\) 3.16440 1.82697i 0.587615 0.339260i −0.176539 0.984294i \(-0.556490\pi\)
0.764154 + 0.645034i \(0.223157\pi\)
\(30\) 0 0
\(31\) −2.65800 + 4.60379i −0.477391 + 0.826865i −0.999664 0.0259130i \(-0.991751\pi\)
0.522273 + 0.852778i \(0.325084\pi\)
\(32\) −0.272218 + 5.65030i −0.0481218 + 0.998841i
\(33\) 0 0
\(34\) 1.58125 + 2.22106i 0.271181 + 0.380908i
\(35\) 4.14154i 0.700048i
\(36\) 0 0
\(37\) 7.98438i 1.31262i −0.754489 0.656312i \(-0.772115\pi\)
0.754489 0.656312i \(-0.227885\pi\)
\(38\) 2.45284 1.74626i 0.397904 0.283281i
\(39\) 0 0
\(40\) −6.26935 1.52308i −0.991272 0.240820i
\(41\) 2.36240 4.09180i 0.368946 0.639033i −0.620455 0.784242i \(-0.713052\pi\)
0.989401 + 0.145209i \(0.0463855\pi\)
\(42\) 0 0
\(43\) 2.20800 1.27479i 0.336717 0.194404i −0.322102 0.946705i \(-0.604390\pi\)
0.658819 + 0.752301i \(0.271056\pi\)
\(44\) −1.85171 9.61877i −0.279156 1.45008i
\(45\) 0 0
\(46\) −3.25953 + 0.310892i −0.480592 + 0.0458386i
\(47\) 2.02005 + 3.49884i 0.294655 + 0.510358i 0.974905 0.222623i \(-0.0714619\pi\)
−0.680249 + 0.732981i \(0.738129\pi\)
\(48\) 0 0
\(49\) 1.85171 3.20726i 0.264530 0.458179i
\(50\) 0.119328 0.261218i 0.0168756 0.0369418i
\(51\) 0 0
\(52\) 6.99825 6.06137i 0.970483 0.840561i
\(53\) 8.95958i 1.23069i −0.788257 0.615347i \(-0.789016\pi\)
0.788257 0.615347i \(-0.210984\pi\)
\(54\) 0 0
\(55\) 11.1718 1.50640
\(56\) −3.71554 3.54506i −0.496509 0.473728i
\(57\) 0 0
\(58\) −4.70024 2.14714i −0.617172 0.281934i
\(59\) 3.05255 + 1.76239i 0.397408 + 0.229444i 0.685365 0.728200i \(-0.259643\pi\)
−0.287957 + 0.957643i \(0.592976\pi\)
\(60\) 0 0
\(61\) −1.71675 + 0.991165i −0.219807 + 0.126906i −0.605861 0.795571i \(-0.707171\pi\)
0.386054 + 0.922476i \(0.373838\pi\)
\(62\) 7.48399 0.713818i 0.950468 0.0906550i
\(63\) 0 0
\(64\) 6.73283 4.32076i 0.841604 0.540095i
\(65\) 5.27959 + 9.14451i 0.654852 + 1.13424i
\(66\) 0 0
\(67\) 7.72723 + 4.46132i 0.944031 + 0.545036i 0.891222 0.453568i \(-0.149849\pi\)
0.0528093 + 0.998605i \(0.483182\pi\)
\(68\) 1.26188 3.64342i 0.153026 0.441830i
\(69\) 0 0
\(70\) 4.77135 3.39689i 0.570286 0.406006i
\(71\) −13.3561 −1.58508 −0.792539 0.609821i \(-0.791241\pi\)
−0.792539 + 0.609821i \(0.791241\pi\)
\(72\) 0 0
\(73\) −11.5592 −1.35290 −0.676450 0.736489i \(-0.736482\pi\)
−0.676450 + 0.736489i \(0.736482\pi\)
\(74\) −9.19859 + 6.54879i −1.06931 + 0.761281i
\(75\) 0 0
\(76\) −4.02364 1.39357i −0.461543 0.159854i
\(77\) 7.70112 + 4.44625i 0.877625 + 0.506697i
\(78\) 0 0
\(79\) −4.97330 8.61401i −0.559540 0.969151i −0.997535 0.0701739i \(-0.977645\pi\)
0.437995 0.898977i \(-0.355689\pi\)
\(80\) 3.38742 + 8.47198i 0.378725 + 0.947196i
\(81\) 0 0
\(82\) −6.65170 + 0.634435i −0.734558 + 0.0700616i
\(83\) 3.12153 1.80221i 0.342632 0.197819i −0.318803 0.947821i \(-0.603281\pi\)
0.661435 + 0.750002i \(0.269948\pi\)
\(84\) 0 0
\(85\) 3.80838 + 2.19877i 0.413077 + 0.238490i
\(86\) −3.27965 1.49820i −0.353654 0.161555i
\(87\) 0 0
\(88\) −9.56276 + 10.0226i −1.01939 + 1.06841i
\(89\) −2.49965 −0.264962 −0.132481 0.991186i \(-0.542294\pi\)
−0.132481 + 0.991186i \(0.542294\pi\)
\(90\) 0 0
\(91\) 8.40489i 0.881072i
\(92\) 3.03164 + 3.50023i 0.316070 + 0.364924i
\(93\) 0 0
\(94\) 2.37407 5.19699i 0.244866 0.536029i
\(95\) 2.42823 4.20582i 0.249131 0.431508i
\(96\) 0 0
\(97\) 6.99370 + 12.1134i 0.710103 + 1.22993i 0.964818 + 0.262918i \(0.0846849\pi\)
−0.254715 + 0.967016i \(0.581982\pi\)
\(98\) −5.21376 + 0.497285i −0.526670 + 0.0502334i
\(99\) 0 0
\(100\) −0.398816 + 0.0767760i −0.0398816 + 0.00767760i
\(101\) −1.13087 + 0.652911i −0.112526 + 0.0649671i −0.555207 0.831712i \(-0.687361\pi\)
0.442681 + 0.896679i \(0.354028\pi\)
\(102\) 0 0
\(103\) −3.22312 + 5.58261i −0.317584 + 0.550071i −0.979983 0.199080i \(-0.936205\pi\)
0.662400 + 0.749151i \(0.269538\pi\)
\(104\) −12.7231 3.09096i −1.24760 0.303094i
\(105\) 0 0
\(106\) −10.3221 + 7.34865i −1.00257 + 0.713764i
\(107\) 3.10427i 0.300101i −0.988678 0.150051i \(-0.952056\pi\)
0.988678 0.150051i \(-0.0479437\pi\)
\(108\) 0 0
\(109\) 18.0837i 1.73210i 0.499955 + 0.866051i \(0.333350\pi\)
−0.499955 + 0.866051i \(0.666650\pi\)
\(110\) −9.16307 12.8707i −0.873665 1.22717i
\(111\) 0 0
\(112\) −1.03668 + 7.18822i −0.0979574 + 0.679223i
\(113\) 1.41718 2.45463i 0.133317 0.230913i −0.791636 0.610993i \(-0.790770\pi\)
0.924953 + 0.380080i \(0.124104\pi\)
\(114\) 0 0
\(115\) −4.57370 + 2.64063i −0.426500 + 0.246240i
\(116\) 1.38147 + 7.17611i 0.128267 + 0.666285i
\(117\) 0 0
\(118\) −0.473298 4.96227i −0.0435706 0.456814i
\(119\) 1.75018 + 3.03139i 0.160438 + 0.277887i
\(120\) 0 0
\(121\) 6.49370 11.2474i 0.590337 1.02249i
\(122\) 2.54997 + 1.16487i 0.230863 + 0.105462i
\(123\) 0 0
\(124\) −6.96074 8.03663i −0.625093 0.721711i
\(125\) 10.9419i 0.978674i
\(126\) 0 0
\(127\) −7.44962 −0.661047 −0.330523 0.943798i \(-0.607225\pi\)
−0.330523 + 0.943798i \(0.607225\pi\)
\(128\) −10.5001 4.21283i −0.928086 0.372365i
\(129\) 0 0
\(130\) 6.20483 13.5828i 0.544200 1.19129i
\(131\) −3.12153 1.80221i −0.272729 0.157460i 0.357398 0.933952i \(-0.383664\pi\)
−0.630127 + 0.776492i \(0.716997\pi\)
\(132\) 0 0
\(133\) 3.34774 1.93282i 0.290286 0.167597i
\(134\) −1.19811 12.5615i −0.103501 1.08515i
\(135\) 0 0
\(136\) −5.23248 + 1.53455i −0.448682 + 0.131587i
\(137\) −5.88147 10.1870i −0.502488 0.870335i −0.999996 0.00287543i \(-0.999085\pi\)
0.497508 0.867460i \(-0.334249\pi\)
\(138\) 0 0
\(139\) −11.0400 6.37395i −0.936400 0.540631i −0.0475703 0.998868i \(-0.515148\pi\)
−0.888830 + 0.458237i \(0.848481\pi\)
\(140\) −7.82693 2.71082i −0.661496 0.229106i
\(141\) 0 0
\(142\) 10.9547 + 15.3872i 0.919296 + 1.29127i
\(143\) 22.6721 1.89594
\(144\) 0 0
\(145\) −8.33472 −0.692161
\(146\) 9.48083 + 13.3170i 0.784639 + 1.10212i
\(147\) 0 0
\(148\) 15.0894 + 5.22613i 1.24034 + 0.429586i
\(149\) −6.59790 3.80930i −0.540521 0.312070i 0.204769 0.978810i \(-0.434356\pi\)
−0.745290 + 0.666740i \(0.767689\pi\)
\(150\) 0 0
\(151\) 2.26988 + 3.93155i 0.184720 + 0.319945i 0.943482 0.331423i \(-0.107529\pi\)
−0.758762 + 0.651368i \(0.774195\pi\)
\(152\) 1.69470 + 5.77854i 0.137458 + 0.468701i
\(153\) 0 0
\(154\) −1.19406 12.5191i −0.0962201 1.00882i
\(155\) 10.5014 6.06296i 0.843489 0.486989i
\(156\) 0 0
\(157\) 11.4105 + 6.58787i 0.910659 + 0.525769i 0.880643 0.473780i \(-0.157111\pi\)
0.0300161 + 0.999549i \(0.490444\pi\)
\(158\) −5.84486 + 12.7948i −0.464992 + 1.01790i
\(159\) 0 0
\(160\) 6.98198 10.8513i 0.551974 0.857869i
\(161\) −4.20377 −0.331303
\(162\) 0 0
\(163\) 20.5911i 1.61282i −0.591358 0.806409i \(-0.701408\pi\)
0.591358 0.806409i \(-0.298592\pi\)
\(164\) 6.18664 + 7.14288i 0.483095 + 0.557765i
\(165\) 0 0
\(166\) −4.63656 2.11805i −0.359867 0.164393i
\(167\) −2.53912 + 4.39789i −0.196483 + 0.340319i −0.947386 0.320094i \(-0.896285\pi\)
0.750903 + 0.660413i \(0.229619\pi\)
\(168\) 0 0
\(169\) 4.21446 + 7.29967i 0.324190 + 0.561513i
\(170\) −0.590490 6.19096i −0.0452885 0.474825i
\(171\) 0 0
\(172\) 0.963939 + 5.00722i 0.0734997 + 0.381797i
\(173\) −11.0398 + 6.37385i −0.839343 + 0.484595i −0.857041 0.515248i \(-0.827700\pi\)
0.0176977 + 0.999843i \(0.494366\pi\)
\(174\) 0 0
\(175\) 0.184351 0.319306i 0.0139356 0.0241372i
\(176\) 19.3902 + 2.79644i 1.46159 + 0.210790i
\(177\) 0 0
\(178\) 2.05021 + 2.87978i 0.153670 + 0.215849i
\(179\) 8.82019i 0.659252i −0.944112 0.329626i \(-0.893077\pi\)
0.944112 0.329626i \(-0.106923\pi\)
\(180\) 0 0
\(181\) 15.4369i 1.14741i −0.819061 0.573707i \(-0.805505\pi\)
0.819061 0.573707i \(-0.194495\pi\)
\(182\) 9.68305 6.89369i 0.717755 0.510994i
\(183\) 0 0
\(184\) 1.54597 6.36356i 0.113970 0.469128i
\(185\) −9.10628 + 15.7725i −0.669507 + 1.15962i
\(186\) 0 0
\(187\) 8.17715 4.72108i 0.597972 0.345239i
\(188\) −7.93453 + 1.52748i −0.578685 + 0.111403i
\(189\) 0 0
\(190\) −6.83704 + 0.652112i −0.496011 + 0.0473092i
\(191\) −4.81698 8.34326i −0.348545 0.603697i 0.637446 0.770495i \(-0.279991\pi\)
−0.985991 + 0.166797i \(0.946657\pi\)
\(192\) 0 0
\(193\) 3.49335 6.05066i 0.251457 0.435536i −0.712470 0.701702i \(-0.752424\pi\)
0.963927 + 0.266166i \(0.0857570\pi\)
\(194\) 8.21934 17.9927i 0.590114 1.29180i
\(195\) 0 0
\(196\) 4.84924 + 5.59876i 0.346374 + 0.399912i
\(197\) 4.31842i 0.307675i 0.988096 + 0.153837i \(0.0491632\pi\)
−0.988096 + 0.153837i \(0.950837\pi\)
\(198\) 0 0
\(199\) 5.90649 0.418700 0.209350 0.977841i \(-0.432865\pi\)
0.209350 + 0.977841i \(0.432865\pi\)
\(200\) 0.415560 + 0.396493i 0.0293845 + 0.0280363i
\(201\) 0 0
\(202\) 1.67974 + 0.767333i 0.118186 + 0.0539894i
\(203\) −5.74544 3.31713i −0.403251 0.232817i
\(204\) 0 0
\(205\) −9.33350 + 5.38870i −0.651880 + 0.376363i
\(206\) 9.07518 0.865585i 0.632298 0.0603082i
\(207\) 0 0
\(208\) 6.87447 + 17.1932i 0.476659 + 1.19213i
\(209\) −5.21376 9.03050i −0.360644 0.624653i
\(210\) 0 0
\(211\) −15.8781 9.16723i −1.09309 0.631098i −0.158696 0.987328i \(-0.550729\pi\)
−0.934399 + 0.356229i \(0.884062\pi\)
\(212\) 16.9324 + 5.86445i 1.16292 + 0.402772i
\(213\) 0 0
\(214\) −3.57635 + 2.54612i −0.244474 + 0.174049i
\(215\) −5.81565 −0.396624
\(216\) 0 0
\(217\) 9.65199 0.655220
\(218\) 20.8337 14.8322i 1.41104 1.00457i
\(219\) 0 0
\(220\) −7.31241 + 21.1131i −0.493003 + 1.42344i
\(221\) 7.72877 + 4.46221i 0.519893 + 0.300161i
\(222\) 0 0
\(223\) −2.63263 4.55986i −0.176294 0.305350i 0.764314 0.644844i \(-0.223078\pi\)
−0.940608 + 0.339494i \(0.889744\pi\)
\(224\) 9.13165 4.70145i 0.610134 0.314129i
\(225\) 0 0
\(226\) −3.99029 + 0.380591i −0.265430 + 0.0253166i
\(227\) −1.53638 + 0.887027i −0.101973 + 0.0588741i −0.550119 0.835086i \(-0.685418\pi\)
0.448146 + 0.893960i \(0.352084\pi\)
\(228\) 0 0
\(229\) −3.30687 1.90922i −0.218524 0.126165i 0.386742 0.922188i \(-0.373600\pi\)
−0.605267 + 0.796023i \(0.706934\pi\)
\(230\) 6.79354 + 3.10339i 0.447953 + 0.204632i
\(231\) 0 0
\(232\) 7.13432 7.47740i 0.468391 0.490915i
\(233\) 20.3207 1.33125 0.665627 0.746284i \(-0.268164\pi\)
0.665627 + 0.746284i \(0.268164\pi\)
\(234\) 0 0
\(235\) 9.21558i 0.601158i
\(236\) −5.32870 + 4.61533i −0.346869 + 0.300432i
\(237\) 0 0
\(238\) 2.05689 4.50268i 0.133328 0.291865i
\(239\) −8.69811 + 15.0656i −0.562634 + 0.974510i 0.434632 + 0.900608i \(0.356879\pi\)
−0.997266 + 0.0739020i \(0.976455\pi\)
\(240\) 0 0
\(241\) −6.85611 11.8751i −0.441641 0.764944i 0.556171 0.831068i \(-0.312270\pi\)
−0.997811 + 0.0661240i \(0.978937\pi\)
\(242\) −18.2840 + 1.74391i −1.17534 + 0.112103i
\(243\) 0 0
\(244\) −0.749475 3.89317i −0.0479802 0.249235i
\(245\) −7.31583 + 4.22379i −0.467391 + 0.269848i
\(246\) 0 0
\(247\) 4.92788 8.53534i 0.313553 0.543090i
\(248\) −3.54959 + 14.6109i −0.225399 + 0.927795i
\(249\) 0 0
\(250\) 12.6059 8.97455i 0.797266 0.567601i
\(251\) 4.50751i 0.284512i −0.989830 0.142256i \(-0.954564\pi\)
0.989830 0.142256i \(-0.0454356\pi\)
\(252\) 0 0
\(253\) 11.3396i 0.712916i
\(254\) 6.11018 + 8.58250i 0.383387 + 0.538514i
\(255\) 0 0
\(256\) 3.75869 + 15.5522i 0.234918 + 0.972015i
\(257\) 4.11258 7.12320i 0.256536 0.444333i −0.708776 0.705434i \(-0.750752\pi\)
0.965311 + 0.261101i \(0.0840856\pi\)
\(258\) 0 0
\(259\) −12.5546 + 7.24842i −0.780106 + 0.450395i
\(260\) −20.7376 + 3.99219i −1.28609 + 0.247585i
\(261\) 0 0
\(262\) 0.483993 + 5.07440i 0.0299012 + 0.313498i
\(263\) −2.51376 4.35395i −0.155005 0.268476i 0.778056 0.628195i \(-0.216206\pi\)
−0.933061 + 0.359719i \(0.882873\pi\)
\(264\) 0 0
\(265\) −10.2185 + 17.6990i −0.627718 + 1.08724i
\(266\) −4.97257 2.27155i −0.304888 0.139277i
\(267\) 0 0
\(268\) −13.4891 + 11.6832i −0.823977 + 0.713668i
\(269\) 23.1577i 1.41195i 0.708236 + 0.705976i \(0.249491\pi\)
−0.708236 + 0.705976i \(0.750509\pi\)
\(270\) 0 0
\(271\) 20.9367 1.27181 0.635906 0.771766i \(-0.280627\pi\)
0.635906 + 0.771766i \(0.280627\pi\)
\(272\) 6.05960 + 4.76956i 0.367417 + 0.289197i
\(273\) 0 0
\(274\) −6.91220 + 15.1313i −0.417581 + 0.914113i
\(275\) −0.861323 0.497285i −0.0519398 0.0299874i
\(276\) 0 0
\(277\) 19.2687 11.1248i 1.15775 0.668425i 0.206983 0.978345i \(-0.433636\pi\)
0.950763 + 0.309920i \(0.100302\pi\)
\(278\) 1.71175 + 17.9468i 0.102664 + 1.07638i
\(279\) 0 0
\(280\) 3.29658 + 11.2406i 0.197008 + 0.671755i
\(281\) 9.28029 + 16.0739i 0.553616 + 0.958890i 0.998010 + 0.0630590i \(0.0200856\pi\)
−0.444394 + 0.895831i \(0.646581\pi\)
\(282\) 0 0
\(283\) 1.75962 + 1.01592i 0.104599 + 0.0603901i 0.551387 0.834250i \(-0.314099\pi\)
−0.446788 + 0.894640i \(0.647432\pi\)
\(284\) 8.74217 25.2412i 0.518752 1.49779i
\(285\) 0 0
\(286\) −18.5957 26.1199i −1.09958 1.54450i
\(287\) −8.57859 −0.506378
\(288\) 0 0
\(289\) −13.2833 −0.781370
\(290\) 6.83613 + 9.60220i 0.401432 + 0.563861i
\(291\) 0 0
\(292\) 7.56600 21.8452i 0.442766 1.27840i
\(293\) −29.5484 17.0598i −1.72623 0.996642i −0.904057 0.427411i \(-0.859426\pi\)
−0.822178 0.569231i \(-0.807241\pi\)
\(294\) 0 0
\(295\) −4.02005 6.96294i −0.234057 0.405398i
\(296\) −6.35541 21.6705i −0.369401 1.25957i
\(297\) 0 0
\(298\) 1.02300 + 10.7256i 0.0592611 + 0.621320i
\(299\) −9.28192 + 5.35892i −0.536787 + 0.309914i
\(300\) 0 0
\(301\) −4.00895 2.31457i −0.231072 0.133410i
\(302\) 2.66767 5.83972i 0.153507 0.336038i
\(303\) 0 0
\(304\) 5.26731 6.69197i 0.302101 0.383811i
\(305\) 4.52174 0.258914
\(306\) 0 0
\(307\) 4.77588i 0.272574i 0.990669 + 0.136287i \(0.0435169\pi\)
−0.990669 + 0.136287i \(0.956483\pi\)
\(308\) −13.4435 + 11.6438i −0.766015 + 0.663466i
\(309\) 0 0
\(310\) −15.5982 7.12549i −0.885917 0.404701i
\(311\) 11.1771 19.3592i 0.633793 1.09776i −0.352976 0.935632i \(-0.614830\pi\)
0.986769 0.162130i \(-0.0518364\pi\)
\(312\) 0 0
\(313\) 1.22411 + 2.12022i 0.0691907 + 0.119842i 0.898545 0.438881i \(-0.144625\pi\)
−0.829355 + 0.558723i \(0.811292\pi\)
\(314\) −1.76920 18.5491i −0.0998420 1.04679i
\(315\) 0 0
\(316\) 19.5345 3.76059i 1.09890 0.211550i
\(317\) 14.2886 8.24953i 0.802528 0.463340i −0.0418263 0.999125i \(-0.513318\pi\)
0.844354 + 0.535785i \(0.179984\pi\)
\(318\) 0 0
\(319\) −8.94793 + 15.4983i −0.500988 + 0.867737i
\(320\) −18.2281 + 0.856461i −1.01898 + 0.0478776i
\(321\) 0 0
\(322\) 3.44793 + 4.84305i 0.192146 + 0.269893i
\(323\) 4.10459i 0.228385i
\(324\) 0 0
\(325\) 0.940035i 0.0521438i
\(326\) −23.7224 + 16.8888i −1.31386 + 0.935385i
\(327\) 0 0
\(328\) 3.15484 12.9861i 0.174197 0.717035i
\(329\) 3.66771 6.35266i 0.202207 0.350233i
\(330\) 0 0
\(331\) −0.329200 + 0.190064i −0.0180945 + 0.0104469i −0.509020 0.860755i \(-0.669992\pi\)
0.490925 + 0.871202i \(0.336659\pi\)
\(332\) 1.36275 + 7.07888i 0.0747909 + 0.388504i
\(333\) 0 0
\(334\) 7.14928 0.681893i 0.391191 0.0373115i
\(335\) −10.1764 17.6260i −0.555994 0.963010i
\(336\) 0 0
\(337\) −2.51872 + 4.36255i −0.137203 + 0.237643i −0.926437 0.376450i \(-0.877145\pi\)
0.789234 + 0.614093i \(0.210478\pi\)
\(338\) 4.95305 10.8426i 0.269410 0.589757i
\(339\) 0 0
\(340\) −6.64812 + 5.75811i −0.360545 + 0.312277i
\(341\) 26.0361i 1.40994i
\(342\) 0 0
\(343\) −19.4337 −1.04932
\(344\) 4.97806 5.21745i 0.268399 0.281306i
\(345\) 0 0
\(346\) 16.3980 + 7.49086i 0.881563 + 0.402711i
\(347\) 8.40337 + 4.85169i 0.451116 + 0.260452i 0.708302 0.705910i \(-0.249462\pi\)
−0.257185 + 0.966362i \(0.582795\pi\)
\(348\) 0 0
\(349\) −26.1239 + 15.0827i −1.39838 + 0.807356i −0.994223 0.107333i \(-0.965769\pi\)
−0.404158 + 0.914689i \(0.632436\pi\)
\(350\) −0.519068 + 0.0495084i −0.0277454 + 0.00264633i
\(351\) 0 0
\(352\) −12.6821 24.6325i −0.675958 1.31292i
\(353\) −13.2376 22.9282i −0.704565 1.22034i −0.966848 0.255352i \(-0.917809\pi\)
0.262283 0.964991i \(-0.415525\pi\)
\(354\) 0 0
\(355\) 26.3840 + 15.2328i 1.40032 + 0.808473i
\(356\) 1.63613 4.72399i 0.0867148 0.250371i
\(357\) 0 0
\(358\) −10.1615 + 7.23431i −0.537052 + 0.382345i
\(359\) 23.4619 1.23827 0.619135 0.785285i \(-0.287483\pi\)
0.619135 + 0.785285i \(0.287483\pi\)
\(360\) 0 0
\(361\) 14.4671 0.761424
\(362\) −17.7844 + 12.6613i −0.934727 + 0.665464i
\(363\) 0 0
\(364\) −15.8841 5.50138i −0.832551 0.288350i
\(365\) 22.8343 + 13.1834i 1.19520 + 0.690050i
\(366\) 0 0
\(367\) 9.62599 + 16.6727i 0.502472 + 0.870308i 0.999996 + 0.00285720i \(0.000909476\pi\)
−0.497524 + 0.867450i \(0.665757\pi\)
\(368\) −8.59928 + 3.43832i −0.448269 + 0.179235i
\(369\) 0 0
\(370\) 25.6401 2.44553i 1.33296 0.127137i
\(371\) −14.0880 + 8.13373i −0.731414 + 0.422282i
\(372\) 0 0
\(373\) −9.09206 5.24930i −0.470769 0.271799i 0.245793 0.969322i \(-0.420952\pi\)
−0.716562 + 0.697524i \(0.754285\pi\)
\(374\) −12.1459 5.54844i −0.628051 0.286903i
\(375\) 0 0
\(376\) 8.26766 + 7.88832i 0.426372 + 0.406809i
\(377\) −16.9146 −0.871145
\(378\) 0 0
\(379\) 35.5203i 1.82455i 0.409574 + 0.912277i \(0.365677\pi\)
−0.409574 + 0.912277i \(0.634323\pi\)
\(380\) 6.35902 + 7.34191i 0.326211 + 0.376632i
\(381\) 0 0
\(382\) −5.66116 + 12.3927i −0.289650 + 0.634064i
\(383\) −18.0395 + 31.2453i −0.921774 + 1.59656i −0.125105 + 0.992144i \(0.539927\pi\)
−0.796669 + 0.604416i \(0.793407\pi\)
\(384\) 0 0
\(385\) −10.1420 17.5664i −0.516884 0.895269i
\(386\) −9.83605 + 0.938156i −0.500642 + 0.0477509i
\(387\) 0 0
\(388\) −27.4704 + 5.28833i −1.39460 + 0.268474i
\(389\) 17.5243 10.1177i 0.888519 0.512987i 0.0150612 0.999887i \(-0.495206\pi\)
0.873458 + 0.486900i \(0.161872\pi\)
\(390\) 0 0
\(391\) −2.23181 + 3.86560i −0.112867 + 0.195492i
\(392\) 2.47284 10.1788i 0.124897 0.514106i
\(393\) 0 0
\(394\) 4.97513 3.54197i 0.250644 0.178442i
\(395\) 22.6884i 1.14158i
\(396\) 0 0
\(397\) 3.99499i 0.200503i 0.994962 + 0.100251i \(0.0319647\pi\)
−0.994962 + 0.100251i \(0.968035\pi\)
\(398\) −4.84450 6.80471i −0.242833 0.341089i
\(399\) 0 0
\(400\) 0.115947 0.803959i 0.00579733 0.0401979i
\(401\) −14.0124 + 24.2702i −0.699747 + 1.21200i 0.268807 + 0.963194i \(0.413371\pi\)
−0.968554 + 0.248803i \(0.919963\pi\)
\(402\) 0 0
\(403\) 21.3116 12.3042i 1.06161 0.612918i
\(404\) −0.493702 2.56455i −0.0245626 0.127591i
\(405\) 0 0
\(406\) 0.890832 + 9.33988i 0.0442112 + 0.463531i
\(407\) 19.5525 + 33.8660i 0.969183 + 1.67867i
\(408\) 0 0
\(409\) 8.22481 14.2458i 0.406691 0.704409i −0.587826 0.808987i \(-0.700016\pi\)
0.994517 + 0.104579i \(0.0333494\pi\)
\(410\) 13.8635 + 6.33307i 0.684670 + 0.312768i
\(411\) 0 0
\(412\) −8.44068 9.74532i −0.415842 0.480118i
\(413\) 6.39976i 0.314912i
\(414\) 0 0
\(415\) −8.22179 −0.403592
\(416\) 14.1693 22.0217i 0.694708 1.07970i
\(417\) 0 0
\(418\) −6.12747 + 13.4135i −0.299704 + 0.656074i
\(419\) 20.5573 + 11.8688i 1.00429 + 0.579827i 0.909515 0.415672i \(-0.136453\pi\)
0.0947752 + 0.995499i \(0.469787\pi\)
\(420\) 0 0
\(421\) 25.9420 14.9776i 1.26433 0.729963i 0.290424 0.956898i \(-0.406204\pi\)
0.973910 + 0.226935i \(0.0728704\pi\)
\(422\) 2.46190 + 25.8117i 0.119844 + 1.25649i
\(423\) 0 0
\(424\) −7.13165 24.3173i −0.346343 1.18095i
\(425\) −0.195746 0.339043i −0.00949509 0.0164460i
\(426\) 0 0
\(427\) 3.11701 + 1.79961i 0.150843 + 0.0870891i
\(428\) 5.86664 + 2.03188i 0.283575 + 0.0982148i
\(429\) 0 0
\(430\) 4.76999 + 6.70005i 0.230030 + 0.323105i
\(431\) 11.0367 0.531621 0.265810 0.964025i \(-0.414360\pi\)
0.265810 + 0.964025i \(0.414360\pi\)
\(432\) 0 0
\(433\) 34.9394 1.67908 0.839541 0.543297i \(-0.182824\pi\)
0.839541 + 0.543297i \(0.182824\pi\)
\(434\) −7.91656 11.1198i −0.380007 0.533767i
\(435\) 0 0
\(436\) −34.1756 11.8366i −1.63672 0.566869i
\(437\) 4.26901 + 2.46472i 0.204215 + 0.117903i
\(438\) 0 0
\(439\) −6.58518 11.4059i −0.314293 0.544372i 0.664994 0.746849i \(-0.268434\pi\)
−0.979287 + 0.202477i \(0.935101\pi\)
\(440\) 30.3214 8.89249i 1.44552 0.423933i
\(441\) 0 0
\(442\) −1.19835 12.5640i −0.0569996 0.597609i
\(443\) 23.6849 13.6745i 1.12530 0.649694i 0.182554 0.983196i \(-0.441564\pi\)
0.942749 + 0.333502i \(0.108230\pi\)
\(444\) 0 0
\(445\) 4.93787 + 2.85088i 0.234077 + 0.135145i
\(446\) −3.09400 + 6.77298i −0.146505 + 0.320710i
\(447\) 0 0
\(448\) −12.9062 6.66420i −0.609760 0.314854i
\(449\) 13.8225 0.652323 0.326161 0.945314i \(-0.394245\pi\)
0.326161 + 0.945314i \(0.394245\pi\)
\(450\) 0 0
\(451\) 23.1407i 1.08965i
\(452\) 3.71130 + 4.28495i 0.174565 + 0.201547i
\(453\) 0 0
\(454\) 2.28206 + 1.04248i 0.107102 + 0.0489259i
\(455\) 9.58588 16.6032i 0.449393 0.778371i
\(456\) 0 0
\(457\) −2.86205 4.95722i −0.133881 0.231889i 0.791288 0.611443i \(-0.209411\pi\)
−0.925170 + 0.379554i \(0.876077\pi\)
\(458\) 0.512731 + 5.37570i 0.0239584 + 0.251190i
\(459\) 0 0
\(460\) −1.99672 10.3721i −0.0930977 0.483600i
\(461\) 19.3717 11.1843i 0.902231 0.520903i 0.0243074 0.999705i \(-0.492262\pi\)
0.877923 + 0.478801i \(0.158929\pi\)
\(462\) 0 0
\(463\) 18.5733 32.1699i 0.863174 1.49506i −0.00567564 0.999984i \(-0.501807\pi\)
0.868849 0.495077i \(-0.164860\pi\)
\(464\) −14.4661 2.08629i −0.671571 0.0968537i
\(465\) 0 0
\(466\) −16.6671 23.4110i −0.772086 1.08449i
\(467\) 22.6850i 1.04974i 0.851184 + 0.524868i \(0.175885\pi\)
−0.851184 + 0.524868i \(0.824115\pi\)
\(468\) 0 0
\(469\) 16.2004i 0.748063i
\(470\) −10.6170 + 7.55862i −0.489727 + 0.348653i
\(471\) 0 0
\(472\) 9.68780 + 2.35356i 0.445917 + 0.108331i
\(473\) −6.24353 + 10.8141i −0.287078 + 0.497233i
\(474\) 0 0
\(475\) −0.374425 + 0.216174i −0.0171798 + 0.00991875i
\(476\) −6.87447 + 1.32340i −0.315091 + 0.0606582i
\(477\) 0 0
\(478\) 24.4908 2.33592i 1.12018 0.106842i
\(479\) −13.1576 22.7897i −0.601188 1.04129i −0.992641 0.121091i \(-0.961361\pi\)
0.391453 0.920198i \(-0.371973\pi\)
\(480\) 0 0
\(481\) −18.4804 + 32.0090i −0.842634 + 1.45948i
\(482\) −8.05763 + 17.6387i −0.367015 + 0.803421i
\(483\) 0 0
\(484\) 17.0056 + 19.6341i 0.772984 + 0.892460i
\(485\) 31.9056i 1.44876i
\(486\) 0 0
\(487\) −24.0388 −1.08930 −0.544652 0.838662i \(-0.683338\pi\)
−0.544652 + 0.838662i \(0.683338\pi\)
\(488\) −3.87050 + 4.05663i −0.175209 + 0.183635i
\(489\) 0 0
\(490\) 10.8666 + 4.96401i 0.490901 + 0.224251i
\(491\) −27.2256 15.7187i −1.22867 0.709374i −0.261920 0.965090i \(-0.584356\pi\)
−0.966752 + 0.255715i \(0.917689\pi\)
\(492\) 0 0
\(493\) −6.10058 + 3.52217i −0.274756 + 0.158631i
\(494\) −13.8752 + 1.32340i −0.624274 + 0.0595428i
\(495\) 0 0
\(496\) 19.7442 7.89449i 0.886542 0.354473i
\(497\) 12.1250 + 21.0011i 0.543881 + 0.942029i
\(498\) 0 0
\(499\) 5.08156 + 2.93384i 0.227482 + 0.131337i 0.609410 0.792855i \(-0.291406\pi\)
−0.381928 + 0.924192i \(0.624740\pi\)
\(500\) −20.6787 7.16197i −0.924779 0.320293i
\(501\) 0 0
\(502\) −5.19298 + 3.69706i −0.231774 + 0.165008i
\(503\) −32.4317 −1.44606 −0.723029 0.690818i \(-0.757251\pi\)
−0.723029 + 0.690818i \(0.757251\pi\)
\(504\) 0 0
\(505\) 2.97861 0.132546
\(506\) 13.0641 9.30076i 0.580769 0.413469i
\(507\) 0 0
\(508\) 4.87611 14.0787i 0.216342 0.624643i
\(509\) 13.6855 + 7.90133i 0.606599 + 0.350220i 0.771633 0.636068i \(-0.219440\pi\)
−0.165034 + 0.986288i \(0.552773\pi\)
\(510\) 0 0
\(511\) 10.4937 + 18.1756i 0.464214 + 0.804042i
\(512\) 14.8344 17.0862i 0.655596 0.755112i
\(513\) 0 0
\(514\) −11.5796 + 1.10445i −0.510753 + 0.0487153i
\(515\) 12.7341 7.35202i 0.561130 0.323969i
\(516\) 0 0
\(517\) −17.1362 9.89361i −0.753650 0.435120i
\(518\) 18.6480 + 8.51870i 0.819346 + 0.374290i
\(519\) 0 0
\(520\) 21.6083 + 20.6168i 0.947585 + 0.904107i
\(521\) −5.50310 −0.241095 −0.120548 0.992708i \(-0.538465\pi\)
−0.120548 + 0.992708i \(0.538465\pi\)
\(522\) 0 0
\(523\) 38.5894i 1.68740i −0.536818 0.843698i \(-0.680374\pi\)
0.536818 0.843698i \(-0.319626\pi\)
\(524\) 5.44911 4.71962i 0.238046 0.206178i
\(525\) 0 0
\(526\) −2.95429 + 6.46714i −0.128813 + 0.281981i
\(527\) 5.12430 8.87555i 0.223218 0.386625i
\(528\) 0 0
\(529\) 8.81970 + 15.2762i 0.383465 + 0.664181i
\(530\) 28.7717 2.74423i 1.24976 0.119202i
\(531\) 0 0
\(532\) 1.46151 + 7.59189i 0.0633647 + 0.329150i
\(533\) −18.9415 + 10.9359i −0.820449 + 0.473686i
\(534\) 0 0
\(535\) −3.54046 + 6.13225i −0.153067 + 0.265120i
\(536\) 24.5237 + 5.95781i 1.05926 + 0.257338i
\(537\) 0 0
\(538\) 26.6794 18.9940i 1.15023 0.818888i
\(539\) 18.1382i 0.781268i
\(540\) 0 0
\(541\) 22.5666i 0.970214i −0.874455 0.485107i \(-0.838781\pi\)
0.874455 0.485107i \(-0.161219\pi\)
\(542\) −17.1723 24.1206i −0.737612 1.03607i
\(543\) 0 0
\(544\) 0.524803 10.8931i 0.0225008 0.467037i
\(545\) 20.6246 35.7229i 0.883463 1.53020i
\(546\) 0 0
\(547\) −11.2679 + 6.50552i −0.481780 + 0.278156i −0.721158 0.692770i \(-0.756390\pi\)
0.239378 + 0.970927i \(0.423057\pi\)
\(548\) 23.1017 4.44731i 0.986856 0.189980i
\(549\) 0 0
\(550\) 0.133548 + 1.40018i 0.00569452 + 0.0597039i
\(551\) 3.88974 + 6.73723i 0.165709 + 0.287016i
\(552\) 0 0
\(553\) −9.02976 + 15.6400i −0.383985 + 0.665081i
\(554\) −28.6208 13.0744i −1.21598 0.555479i
\(555\) 0 0
\(556\) 19.2720 16.6920i 0.817316 0.707899i
\(557\) 5.73693i 0.243081i −0.992586 0.121541i \(-0.961217\pi\)
0.992586 0.121541i \(-0.0387835\pi\)
\(558\) 0 0
\(559\) −11.8024 −0.499186
\(560\) 10.2461 13.0174i 0.432979 0.550087i
\(561\) 0 0
\(562\) 10.9067 23.8754i 0.460069 1.00712i
\(563\) −13.2510 7.65045i −0.558462 0.322428i 0.194066 0.980988i \(-0.437832\pi\)
−0.752528 + 0.658560i \(0.771166\pi\)
\(564\) 0 0
\(565\) −5.59908 + 3.23263i −0.235555 + 0.135998i
\(566\) −0.272830 2.86047i −0.0114679 0.120235i
\(567\) 0 0
\(568\) −36.2500 + 10.6312i −1.52102 + 0.446075i
\(569\) −6.63095 11.4851i −0.277984 0.481482i 0.692900 0.721034i \(-0.256333\pi\)
−0.970884 + 0.239552i \(0.922999\pi\)
\(570\) 0 0
\(571\) 23.4262 + 13.5251i 0.980357 + 0.566009i 0.902378 0.430946i \(-0.141820\pi\)
0.0779788 + 0.996955i \(0.475153\pi\)
\(572\) −14.8399 + 42.8471i −0.620488 + 1.79153i
\(573\) 0 0
\(574\) 7.03616 + 9.88317i 0.293684 + 0.412515i
\(575\) 0.470166 0.0196073
\(576\) 0 0
\(577\) −4.78434 −0.199174 −0.0995872 0.995029i \(-0.531752\pi\)
−0.0995872 + 0.995029i \(0.531752\pi\)
\(578\) 10.8949 + 15.3033i 0.453170 + 0.636534i
\(579\) 0 0
\(580\) 5.45544 15.7514i 0.226525 0.654043i
\(581\) −5.66760 3.27219i −0.235132 0.135753i
\(582\) 0 0
\(583\) 21.9406 + 38.0023i 0.908689 + 1.57390i
\(584\) −31.3729 + 9.20087i −1.29822 + 0.380735i
\(585\) 0 0
\(586\) 4.58148 + 48.0343i 0.189259 + 1.98428i
\(587\) −37.0796 + 21.4079i −1.53044 + 0.883598i −0.531095 + 0.847312i \(0.678219\pi\)
−0.999341 + 0.0362861i \(0.988447\pi\)
\(588\) 0 0
\(589\) −9.80179 5.65906i −0.403876 0.233178i
\(590\) −4.72457 + 10.3424i −0.194507 + 0.425790i
\(591\) 0 0
\(592\) −19.7533 + 25.0961i −0.811857 + 1.03144i
\(593\) 0.825572 0.0339022 0.0169511 0.999856i \(-0.494604\pi\)
0.0169511 + 0.999856i \(0.494604\pi\)
\(594\) 0 0
\(595\) 7.98438i 0.327328i
\(596\) 11.5177 9.97575i 0.471782 0.408623i
\(597\) 0 0
\(598\) 13.7869 + 6.29807i 0.563788 + 0.257547i
\(599\) 0.961228 1.66490i 0.0392747 0.0680258i −0.845720 0.533627i \(-0.820829\pi\)
0.884995 + 0.465601i \(0.154162\pi\)
\(600\) 0 0
\(601\) −21.5937 37.4014i −0.880825 1.52563i −0.850425 0.526096i \(-0.823655\pi\)
−0.0303994 0.999538i \(-0.509678\pi\)
\(602\) 0.621589 + 6.51702i 0.0253341 + 0.265614i
\(603\) 0 0
\(604\) −8.91581 + 1.71638i −0.362779 + 0.0698386i
\(605\) −25.6556 + 14.8123i −1.04305 + 0.602205i
\(606\) 0 0
\(607\) 20.5078 35.5206i 0.832386 1.44174i −0.0637546 0.997966i \(-0.520307\pi\)
0.896141 0.443770i \(-0.146359\pi\)
\(608\) −12.0299 0.579571i −0.487876 0.0235047i
\(609\) 0 0
\(610\) −3.70873 5.20937i −0.150162 0.210921i
\(611\) 18.7022i 0.756611i
\(612\) 0 0
\(613\) 5.05878i 0.204322i 0.994768 + 0.102161i \(0.0325757\pi\)
−0.994768 + 0.102161i \(0.967424\pi\)
\(614\) 5.50216 3.91717i 0.222049 0.158084i
\(615\) 0 0
\(616\) 24.4409 + 5.93768i 0.984750 + 0.239236i
\(617\) 16.0739 27.8408i 0.647112 1.12083i −0.336698 0.941613i \(-0.609310\pi\)
0.983809 0.179217i \(-0.0573566\pi\)
\(618\) 0 0
\(619\) −27.3562 + 15.7941i −1.09954 + 0.634820i −0.936100 0.351734i \(-0.885592\pi\)
−0.163440 + 0.986553i \(0.552259\pi\)
\(620\) 4.58454 + 23.8146i 0.184120 + 0.956416i
\(621\) 0 0
\(622\) −31.4707 + 3.00165i −1.26186 + 0.120355i
\(623\) 2.26924 + 3.93044i 0.0909153 + 0.157470i
\(624\) 0 0
\(625\) 12.9871 22.4942i 0.519482 0.899770i
\(626\) 1.43863 3.14927i 0.0574993 0.125870i
\(627\) 0 0
\(628\) −19.9189 + 17.2522i −0.794849 + 0.688440i
\(629\) 15.3929i 0.613756i
\(630\) 0 0
\(631\) −15.4885 −0.616586 −0.308293 0.951292i \(-0.599758\pi\)
−0.308293 + 0.951292i \(0.599758\pi\)
\(632\) −20.3547 19.4207i −0.809665 0.772516i
\(633\) 0 0
\(634\) −21.2236 9.69525i −0.842896 0.385048i
\(635\) 14.7162 + 8.49638i 0.583993 + 0.337168i
\(636\) 0 0
\(637\) −14.8468 + 8.57182i −0.588253 + 0.339628i
\(638\) 25.1942 2.40301i 0.997449 0.0951361i
\(639\) 0 0
\(640\) 15.9374 + 20.2976i 0.629980 + 0.802334i
\(641\) 15.2248 + 26.3701i 0.601344 + 1.04156i 0.992618 + 0.121284i \(0.0387011\pi\)
−0.391274 + 0.920274i \(0.627966\pi\)
\(642\) 0 0
\(643\) −14.5911 8.42419i −0.575418 0.332218i 0.183893 0.982946i \(-0.441130\pi\)
−0.759310 + 0.650729i \(0.774463\pi\)
\(644\) 2.75155 7.94454i 0.108426 0.313059i
\(645\) 0 0
\(646\) −4.72878 + 3.36658i −0.186051 + 0.132456i
\(647\) −18.6734 −0.734126 −0.367063 0.930196i \(-0.619637\pi\)
−0.367063 + 0.930196i \(0.619637\pi\)
\(648\) 0 0
\(649\) −17.2633 −0.677644
\(650\) −1.08299 + 0.771017i −0.0424783 + 0.0302418i
\(651\) 0 0
\(652\) 38.9143 + 13.4778i 1.52400 + 0.527831i
\(653\) −31.4276 18.1448i −1.22986 0.710059i −0.262858 0.964834i \(-0.584665\pi\)
−0.967000 + 0.254775i \(0.917999\pi\)
\(654\) 0 0
\(655\) 4.11089 + 7.12028i 0.160626 + 0.278212i
\(656\) −17.5485 + 7.01655i −0.685153 + 0.273950i
\(657\) 0 0
\(658\) −10.3270 + 0.984980i −0.402588 + 0.0383985i
\(659\) −19.3088 + 11.1480i −0.752166 + 0.434263i −0.826476 0.562972i \(-0.809658\pi\)
0.0743103 + 0.997235i \(0.476324\pi\)
\(660\) 0 0
\(661\) 5.19793 + 3.00103i 0.202176 + 0.116726i 0.597670 0.801742i \(-0.296093\pi\)
−0.395494 + 0.918469i \(0.629427\pi\)
\(662\) 0.488978 + 0.223373i 0.0190047 + 0.00868162i
\(663\) 0 0
\(664\) 7.03765 7.37609i 0.273114 0.286248i
\(665\) −8.81762 −0.341933
\(666\) 0 0
\(667\) 8.45996i 0.327571i
\(668\) −6.64943 7.67720i −0.257274 0.297040i
\(669\) 0 0
\(670\) −11.9598 + 26.1807i −0.462046 + 1.01145i
\(671\) 4.85442 8.40810i 0.187403 0.324591i
\(672\) 0 0
\(673\) −3.70444 6.41629i −0.142796 0.247330i 0.785753 0.618541i \(-0.212276\pi\)
−0.928548 + 0.371211i \(0.878943\pi\)
\(674\) 7.09183 0.676414i 0.273167 0.0260545i
\(675\) 0 0
\(676\) −16.5539 + 3.18679i −0.636689 + 0.122569i
\(677\) −8.57613 + 4.95143i −0.329607 + 0.190299i −0.655667 0.755050i \(-0.727612\pi\)
0.326059 + 0.945349i \(0.394279\pi\)
\(678\) 0 0
\(679\) 12.6981 21.9938i 0.487309 0.844043i
\(680\) 12.0865 + 2.93632i 0.463498 + 0.112603i
\(681\) 0 0
\(682\) −29.9955 + 21.3548i −1.14859 + 0.817719i
\(683\) 39.0736i 1.49511i −0.664200 0.747555i \(-0.731228\pi\)
0.664200 0.747555i \(-0.268772\pi\)
\(684\) 0 0
\(685\) 26.8316i 1.02518i
\(686\) 15.9395 + 22.3890i 0.608572 + 0.854815i
\(687\) 0 0
\(688\) −10.0939 1.45574i −0.384826 0.0554994i
\(689\) −20.7376 + 35.9185i −0.790039 + 1.36839i
\(690\) 0 0
\(691\) 2.07502 1.19801i 0.0789375 0.0455746i −0.460012 0.887913i \(-0.652155\pi\)
0.538949 + 0.842338i \(0.318821\pi\)
\(692\) −4.81962 25.0357i −0.183215 0.951715i
\(693\) 0 0
\(694\) −1.30294 13.6606i −0.0494590 0.518551i
\(695\) 14.5391 + 25.1825i 0.551500 + 0.955227i
\(696\) 0 0
\(697\) −4.55443 + 7.88850i −0.172511 + 0.298798i
\(698\) 38.8032 + 17.7259i 1.46872 + 0.670934i
\(699\) 0 0
\(700\) 0.482777 + 0.557398i 0.0182472 + 0.0210677i
\(701\) 30.9184i 1.16777i 0.811836 + 0.583885i \(0.198468\pi\)
−0.811836 + 0.583885i \(0.801532\pi\)
\(702\) 0 0
\(703\) 16.9993 0.641141
\(704\) −17.9766 + 34.8143i −0.677519 + 1.31211i
\(705\) 0 0
\(706\) −15.5575 + 34.0563i −0.585513 + 1.28173i
\(707\) 2.05327 + 1.18546i 0.0772212 + 0.0445837i
\(708\) 0 0
\(709\) −4.46959 + 2.58052i −0.167859 + 0.0969133i −0.581576 0.813492i \(-0.697564\pi\)
0.413717 + 0.910406i \(0.364230\pi\)
\(710\) −4.09084 42.8902i −0.153526 1.60964i
\(711\) 0 0
\(712\) −6.78434 + 1.98967i −0.254254 + 0.0745661i
\(713\) 6.15406 + 10.6591i 0.230471 + 0.399188i
\(714\) 0 0
\(715\) −44.7870 25.8578i −1.67494 0.967027i
\(716\) 16.6689 + 5.77320i 0.622947 + 0.215755i
\(717\) 0 0
\(718\) −19.2434 27.0298i −0.718158 1.00874i
\(719\) −14.7871 −0.551465 −0.275733 0.961234i \(-0.588920\pi\)
−0.275733 + 0.961234i \(0.588920\pi\)
\(720\) 0 0
\(721\) 11.7041 0.435884
\(722\) −11.8659 16.6671i −0.441602 0.620286i
\(723\) 0 0
\(724\) 29.1735 + 10.1041i 1.08423 + 0.375517i
\(725\) 0.642593 + 0.371001i 0.0238653 + 0.0137786i
\(726\) 0 0
\(727\) −1.06681 1.84777i −0.0395658 0.0685299i 0.845564 0.533873i \(-0.179264\pi\)
−0.885130 + 0.465344i \(0.845931\pi\)
\(728\) 6.69012 + 22.8118i 0.247952 + 0.845463i
\(729\) 0 0
\(730\) −3.54046 37.1198i −0.131038 1.37386i
\(731\) −4.25675 + 2.45764i −0.157442 + 0.0908990i
\(732\) 0 0
\(733\) 22.2298 + 12.8344i 0.821076 + 0.474048i 0.850787 0.525510i \(-0.176125\pi\)
−0.0297113 + 0.999559i \(0.509459\pi\)
\(734\) 11.3129 24.7648i 0.417568 0.914085i
\(735\) 0 0
\(736\) 11.0143 + 7.08689i 0.405993 + 0.261226i
\(737\) −43.7003 −1.60972
\(738\) 0 0
\(739\) 5.46282i 0.200953i 0.994939 + 0.100476i \(0.0320367\pi\)
−0.994939 + 0.100476i \(0.967963\pi\)
\(740\) −23.8474 27.5334i −0.876649 1.01215i
\(741\) 0 0
\(742\) 20.9257 + 9.55916i 0.768205 + 0.350928i
\(743\) 16.8170 29.1279i 0.616955 1.06860i −0.373083 0.927798i \(-0.621699\pi\)
0.990038 0.140800i \(-0.0449674\pi\)
\(744\) 0 0
\(745\) 8.68910 + 15.0500i 0.318344 + 0.551388i
\(746\) 1.40972 + 14.7802i 0.0516137 + 0.541141i
\(747\) 0 0
\(748\) 3.56987 + 18.5438i 0.130527 + 0.678029i
\(749\) −4.88115 + 2.81813i −0.178353 + 0.102972i
\(750\) 0 0
\(751\) −12.6727 + 21.9498i −0.462435 + 0.800961i −0.999082 0.0428462i \(-0.986357\pi\)
0.536647 + 0.843807i \(0.319691\pi\)
\(752\) 2.30679 15.9949i 0.0841198 0.583276i
\(753\) 0 0
\(754\) 13.8733 + 19.4868i 0.505237 + 0.709669i
\(755\) 10.3553i 0.376868i
\(756\) 0 0
\(757\) 3.95103i 0.143603i −0.997419 0.0718014i \(-0.977125\pi\)
0.997419 0.0718014i \(-0.0228748\pi\)
\(758\) 40.9219 29.1337i 1.48635 1.05818i
\(759\) 0 0
\(760\) 3.24275 13.3479i 0.117627 0.484179i
\(761\) 23.3979 40.5264i 0.848175 1.46908i −0.0346607 0.999399i \(-0.511035\pi\)
0.882835 0.469682i \(-0.155632\pi\)
\(762\) 0 0
\(763\) 28.4347 16.4168i 1.02941 0.594328i
\(764\) 18.9205 3.64239i 0.684521 0.131777i
\(765\) 0 0
\(766\) 50.7928 4.84459i 1.83522 0.175042i
\(767\) −8.15835 14.1307i −0.294581 0.510229i
\(768\) 0 0
\(769\) 2.60083 4.50478i 0.0937885 0.162446i −0.815314 0.579019i \(-0.803436\pi\)
0.909102 + 0.416573i \(0.136769\pi\)
\(770\) −11.9194 + 26.0923i −0.429544 + 0.940302i
\(771\) 0 0
\(772\) 9.14835 + 10.5624i 0.329256 + 0.380148i
\(773\) 38.8477i 1.39725i 0.715486 + 0.698627i \(0.246205\pi\)
−0.715486 + 0.698627i \(0.753795\pi\)
\(774\) 0 0
\(775\) −1.07952 −0.0387773
\(776\) 28.6238 + 27.3104i 1.02753 + 0.980387i
\(777\) 0 0
\(778\) −26.0298 11.8908i −0.933212 0.426306i
\(779\) 8.71173 + 5.02972i 0.312130 + 0.180209i
\(780\) 0 0
\(781\) 56.6503 32.7071i 2.02711 1.17035i
\(782\) 6.28399 0.599362i 0.224715 0.0214332i
\(783\) 0 0
\(784\) −13.7549 + 5.49974i −0.491247 + 0.196419i
\(785\) −15.0271 26.0277i −0.536340 0.928968i
\(786\) 0 0
\(787\) −40.8579 23.5893i −1.45643 0.840869i −0.457595 0.889161i \(-0.651289\pi\)
−0.998833 + 0.0482918i \(0.984622\pi\)