Properties

Label 756.2.ba.a.71.8
Level $756$
Weight $2$
Character 756.71
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.8
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.09990 + 0.888937i) q^{2} +(0.419581 - 1.95549i) q^{4} +(2.42137 + 1.39798i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.27681 + 2.52384i) q^{8} +O(q^{10})\) \(q+(-1.09990 + 0.888937i) q^{2} +(0.419581 - 1.95549i) q^{4} +(2.42137 + 1.39798i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.27681 + 2.52384i) q^{8} +(-3.90599 + 0.614803i) q^{10} +(0.140963 + 0.244156i) q^{11} +(-2.43776 + 4.22232i) q^{13} +(0.508077 - 1.31979i) q^{14} +(-3.64790 - 1.64098i) q^{16} +5.66309i q^{17} -7.39353i q^{19} +(3.74970 - 4.14841i) q^{20} +(-0.372086 - 0.143241i) q^{22} +(-3.28934 + 5.69730i) q^{23} +(1.40869 + 2.43992i) q^{25} +(-1.07208 - 6.81116i) q^{26} +(0.614378 + 1.90330i) q^{28} +(0.243350 - 0.140498i) q^{29} +(8.09138 + 4.67156i) q^{31} +(5.47107 - 1.43784i) q^{32} +(-5.03413 - 6.22886i) q^{34} -2.79596 q^{35} +4.22211 q^{37} +(6.57238 + 8.13218i) q^{38} +(-0.436639 + 7.89610i) q^{40} +(0.644767 + 0.372257i) q^{41} +(-6.31743 + 3.64737i) q^{43} +(0.536590 - 0.173210i) q^{44} +(-1.44658 - 9.19051i) q^{46} +(-2.59024 - 4.48642i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.71837 - 1.43145i) q^{50} +(7.23387 + 6.53862i) q^{52} +8.11915i q^{53} +0.788256i q^{55} +(-2.36767 - 1.54730i) q^{56} +(-0.142768 + 0.370857i) q^{58} +(0.215457 - 0.373183i) q^{59} +(2.95890 + 5.12497i) q^{61} +(-13.0525 + 2.05446i) q^{62} +(-4.73951 + 6.44493i) q^{64} +(-11.8054 + 6.81586i) q^{65} +(-2.11124 - 1.21893i) q^{67} +(11.0741 + 2.37612i) q^{68} +(3.07529 - 2.48543i) q^{70} -2.47114 q^{71} +0.714758 q^{73} +(-4.64392 + 3.75319i) q^{74} +(-14.4580 - 3.10218i) q^{76} +(-0.244156 - 0.140963i) q^{77} +(2.15347 - 1.24331i) q^{79} +(-6.53888 - 9.07310i) q^{80} +(-1.04010 + 0.163711i) q^{82} +(4.10072 + 7.10266i) q^{83} +(-7.91688 + 13.7124i) q^{85} +(3.70629 - 9.62757i) q^{86} +(-0.436226 + 0.667509i) q^{88} +0.354223i q^{89} -4.87551i q^{91} +(9.76089 + 8.82276i) q^{92} +(6.83716 + 2.63208i) q^{94} +(10.3360 - 17.9025i) q^{95} +(-0.138992 - 0.240741i) q^{97} +(0.219890 + 1.39701i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09990 + 0.888937i −0.777750 + 0.628574i
\(3\) 0 0
\(4\) 0.419581 1.95549i 0.209791 0.977746i
\(5\) 2.42137 + 1.39798i 1.08287 + 0.625195i 0.931669 0.363308i \(-0.118353\pi\)
0.151201 + 0.988503i \(0.451686\pi\)
\(6\) 0 0
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 1.27681 + 2.52384i 0.451421 + 0.892311i
\(9\) 0 0
\(10\) −3.90599 + 0.614803i −1.23518 + 0.194418i
\(11\) 0.140963 + 0.244156i 0.0425021 + 0.0736157i 0.886494 0.462740i \(-0.153134\pi\)
−0.843992 + 0.536356i \(0.819800\pi\)
\(12\) 0 0
\(13\) −2.43776 + 4.22232i −0.676112 + 1.17106i 0.300031 + 0.953930i \(0.403003\pi\)
−0.976143 + 0.217131i \(0.930330\pi\)
\(14\) 0.508077 1.31979i 0.135789 0.352730i
\(15\) 0 0
\(16\) −3.64790 1.64098i −0.911976 0.410244i
\(17\) 5.66309i 1.37350i 0.726894 + 0.686750i \(0.240963\pi\)
−0.726894 + 0.686750i \(0.759037\pi\)
\(18\) 0 0
\(19\) 7.39353i 1.69619i −0.529843 0.848096i \(-0.677749\pi\)
0.529843 0.848096i \(-0.322251\pi\)
\(20\) 3.74970 4.14841i 0.838458 0.927612i
\(21\) 0 0
\(22\) −0.372086 0.143241i −0.0793289 0.0305390i
\(23\) −3.28934 + 5.69730i −0.685875 + 1.18797i 0.287286 + 0.957845i \(0.407247\pi\)
−0.973161 + 0.230125i \(0.926086\pi\)
\(24\) 0 0
\(25\) 1.40869 + 2.43992i 0.281738 + 0.487985i
\(26\) −1.07208 6.81116i −0.210251 1.33578i
\(27\) 0 0
\(28\) 0.614378 + 1.90330i 0.116107 + 0.359689i
\(29\) 0.243350 0.140498i 0.0451889 0.0260898i −0.477235 0.878776i \(-0.658361\pi\)
0.522424 + 0.852686i \(0.325028\pi\)
\(30\) 0 0
\(31\) 8.09138 + 4.67156i 1.45325 + 0.839037i 0.998665 0.0516641i \(-0.0164525\pi\)
0.454590 + 0.890701i \(0.349786\pi\)
\(32\) 5.47107 1.43784i 0.967158 0.254177i
\(33\) 0 0
\(34\) −5.03413 6.22886i −0.863346 1.06824i
\(35\) −2.79596 −0.472603
\(36\) 0 0
\(37\) 4.22211 0.694111 0.347056 0.937845i \(-0.387182\pi\)
0.347056 + 0.937845i \(0.387182\pi\)
\(38\) 6.57238 + 8.13218i 1.06618 + 1.31921i
\(39\) 0 0
\(40\) −0.436639 + 7.89610i −0.0690387 + 1.24848i
\(41\) 0.644767 + 0.372257i 0.100696 + 0.0581367i 0.549502 0.835492i \(-0.314817\pi\)
−0.448806 + 0.893629i \(0.648151\pi\)
\(42\) 0 0
\(43\) −6.31743 + 3.64737i −0.963400 + 0.556219i −0.897218 0.441588i \(-0.854415\pi\)
−0.0661820 + 0.997808i \(0.521082\pi\)
\(44\) 0.536590 0.173210i 0.0808941 0.0261124i
\(45\) 0 0
\(46\) −1.44658 9.19051i −0.213287 1.35507i
\(47\) −2.59024 4.48642i −0.377825 0.654412i 0.612921 0.790144i \(-0.289994\pi\)
−0.990745 + 0.135733i \(0.956661\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −3.71837 1.43145i −0.525856 0.202437i
\(51\) 0 0
\(52\) 7.23387 + 6.53862i 1.00316 + 0.906743i
\(53\) 8.11915i 1.11525i 0.830093 + 0.557625i \(0.188287\pi\)
−0.830093 + 0.557625i \(0.811713\pi\)
\(54\) 0 0
\(55\) 0.788256i 0.106288i
\(56\) −2.36767 1.54730i −0.316393 0.206767i
\(57\) 0 0
\(58\) −0.142768 + 0.370857i −0.0187463 + 0.0486959i
\(59\) 0.215457 0.373183i 0.0280501 0.0485843i −0.851660 0.524095i \(-0.824404\pi\)
0.879710 + 0.475511i \(0.157737\pi\)
\(60\) 0 0
\(61\) 2.95890 + 5.12497i 0.378848 + 0.656185i 0.990895 0.134637i \(-0.0429869\pi\)
−0.612047 + 0.790822i \(0.709654\pi\)
\(62\) −13.0525 + 2.05446i −1.65767 + 0.260916i
\(63\) 0 0
\(64\) −4.73951 + 6.44493i −0.592438 + 0.805616i
\(65\) −11.8054 + 6.81586i −1.46428 + 0.845404i
\(66\) 0 0
\(67\) −2.11124 1.21893i −0.257930 0.148916i 0.365460 0.930827i \(-0.380912\pi\)
−0.623390 + 0.781911i \(0.714245\pi\)
\(68\) 11.0741 + 2.37612i 1.34293 + 0.288147i
\(69\) 0 0
\(70\) 3.07529 2.48543i 0.367567 0.297066i
\(71\) −2.47114 −0.293270 −0.146635 0.989191i \(-0.546844\pi\)
−0.146635 + 0.989191i \(0.546844\pi\)
\(72\) 0 0
\(73\) 0.714758 0.0836560 0.0418280 0.999125i \(-0.486682\pi\)
0.0418280 + 0.999125i \(0.486682\pi\)
\(74\) −4.64392 + 3.75319i −0.539845 + 0.436300i
\(75\) 0 0
\(76\) −14.4580 3.10218i −1.65844 0.355845i
\(77\) −0.244156 0.140963i −0.0278241 0.0160643i
\(78\) 0 0
\(79\) 2.15347 1.24331i 0.242285 0.139883i −0.373942 0.927452i \(-0.621994\pi\)
0.616226 + 0.787569i \(0.288661\pi\)
\(80\) −6.53888 9.07310i −0.731069 1.01440i
\(81\) 0 0
\(82\) −1.04010 + 0.163711i −0.114859 + 0.0180788i
\(83\) 4.10072 + 7.10266i 0.450113 + 0.779618i 0.998393 0.0566769i \(-0.0180505\pi\)
−0.548280 + 0.836295i \(0.684717\pi\)
\(84\) 0 0
\(85\) −7.91688 + 13.7124i −0.858706 + 1.48732i
\(86\) 3.70629 9.62757i 0.399660 1.03817i
\(87\) 0 0
\(88\) −0.436226 + 0.667509i −0.0465018 + 0.0711568i
\(89\) 0.354223i 0.0375476i 0.999824 + 0.0187738i \(0.00597624\pi\)
−0.999824 + 0.0187738i \(0.994024\pi\)
\(90\) 0 0
\(91\) 4.87551i 0.511093i
\(92\) 9.76089 + 8.82276i 1.01764 + 0.919836i
\(93\) 0 0
\(94\) 6.83716 + 2.63208i 0.705199 + 0.271478i
\(95\) 10.3360 17.9025i 1.06045 1.83675i
\(96\) 0 0
\(97\) −0.138992 0.240741i −0.0141125 0.0244435i 0.858883 0.512172i \(-0.171159\pi\)
−0.872995 + 0.487728i \(0.837826\pi\)
\(98\) 0.219890 + 1.39701i 0.0222122 + 0.141120i
\(99\) 0 0
\(100\) 5.36231 1.73094i 0.536231 0.173094i
\(101\) −12.2098 + 7.04936i −1.21493 + 0.701437i −0.963828 0.266525i \(-0.914125\pi\)
−0.251097 + 0.967962i \(0.580791\pi\)
\(102\) 0 0
\(103\) −9.34581 5.39581i −0.920870 0.531665i −0.0369577 0.999317i \(-0.511767\pi\)
−0.883913 + 0.467652i \(0.845100\pi\)
\(104\) −13.7690 0.761398i −1.35016 0.0746613i
\(105\) 0 0
\(106\) −7.21741 8.93029i −0.701017 0.867387i
\(107\) −3.76330 −0.363811 −0.181906 0.983316i \(-0.558227\pi\)
−0.181906 + 0.983316i \(0.558227\pi\)
\(108\) 0 0
\(109\) 6.11566 0.585774 0.292887 0.956147i \(-0.405384\pi\)
0.292887 + 0.956147i \(0.405384\pi\)
\(110\) −0.700710 0.867006i −0.0668101 0.0826658i
\(111\) 0 0
\(112\) 3.97966 0.402825i 0.376043 0.0380634i
\(113\) −1.77771 1.02636i −0.167233 0.0965519i 0.414048 0.910255i \(-0.364115\pi\)
−0.581280 + 0.813703i \(0.697448\pi\)
\(114\) 0 0
\(115\) −15.9294 + 9.19686i −1.48543 + 0.857611i
\(116\) −0.172638 0.534819i −0.0160290 0.0496567i
\(117\) 0 0
\(118\) 0.0947537 + 0.601993i 0.00872278 + 0.0554180i
\(119\) −2.83154 4.90438i −0.259567 0.449583i
\(120\) 0 0
\(121\) 5.46026 9.45745i 0.496387 0.859768i
\(122\) −7.81028 3.00670i −0.707110 0.272214i
\(123\) 0 0
\(124\) 12.5302 13.8625i 1.12524 1.24489i
\(125\) 6.10251i 0.545825i
\(126\) 0 0
\(127\) 12.5913i 1.11729i 0.829406 + 0.558647i \(0.188679\pi\)
−0.829406 + 0.558647i \(0.811321\pi\)
\(128\) −0.516127 11.3019i −0.0456196 0.998959i
\(129\) 0 0
\(130\) 6.92597 17.9911i 0.607447 1.57792i
\(131\) 4.13063 7.15447i 0.360895 0.625089i −0.627213 0.778848i \(-0.715805\pi\)
0.988108 + 0.153759i \(0.0491379\pi\)
\(132\) 0 0
\(133\) 3.69676 + 6.40298i 0.320550 + 0.555209i
\(134\) 3.40572 0.536060i 0.294209 0.0463085i
\(135\) 0 0
\(136\) −14.2927 + 7.23069i −1.22559 + 0.620027i
\(137\) 14.5034 8.37353i 1.23911 0.715399i 0.270195 0.962806i \(-0.412912\pi\)
0.968912 + 0.247407i \(0.0795784\pi\)
\(138\) 0 0
\(139\) 20.1639 + 11.6416i 1.71028 + 0.987430i 0.934169 + 0.356831i \(0.116143\pi\)
0.776110 + 0.630598i \(0.217190\pi\)
\(140\) −1.17313 + 5.46748i −0.0991477 + 0.462086i
\(141\) 0 0
\(142\) 2.71802 2.19669i 0.228091 0.184342i
\(143\) −1.37454 −0.114945
\(144\) 0 0
\(145\) 0.785654 0.0652450
\(146\) −0.786165 + 0.635375i −0.0650635 + 0.0525840i
\(147\) 0 0
\(148\) 1.77152 8.25631i 0.145618 0.678665i
\(149\) 9.96222 + 5.75169i 0.816137 + 0.471197i 0.849083 0.528260i \(-0.177155\pi\)
−0.0329454 + 0.999457i \(0.510489\pi\)
\(150\) 0 0
\(151\) −4.20513 + 2.42783i −0.342209 + 0.197574i −0.661248 0.750167i \(-0.729973\pi\)
0.319040 + 0.947741i \(0.396640\pi\)
\(152\) 18.6601 9.44014i 1.51353 0.765696i
\(153\) 0 0
\(154\) 0.393856 0.0619928i 0.0317378 0.00499553i
\(155\) 13.0615 + 22.6232i 1.04912 + 1.81714i
\(156\) 0 0
\(157\) 10.1032 17.4992i 0.806322 1.39659i −0.109073 0.994034i \(-0.534788\pi\)
0.915395 0.402557i \(-0.131878\pi\)
\(158\) −1.26339 + 3.28182i −0.100510 + 0.261088i
\(159\) 0 0
\(160\) 15.2576 + 4.16690i 1.20622 + 0.329422i
\(161\) 6.57868i 0.518473i
\(162\) 0 0
\(163\) 16.5798i 1.29863i −0.760518 0.649317i \(-0.775055\pi\)
0.760518 0.649317i \(-0.224945\pi\)
\(164\) 0.998477 1.10465i 0.0779680 0.0862584i
\(165\) 0 0
\(166\) −10.8242 4.16696i −0.840122 0.323419i
\(167\) 3.38550 5.86386i 0.261978 0.453759i −0.704789 0.709417i \(-0.748958\pi\)
0.966768 + 0.255657i \(0.0822918\pi\)
\(168\) 0 0
\(169\) −5.38531 9.32763i −0.414255 0.717510i
\(170\) −3.48168 22.1200i −0.267033 1.69652i
\(171\) 0 0
\(172\) 4.48173 + 13.8841i 0.341729 + 1.05865i
\(173\) 8.38112 4.83884i 0.637204 0.367890i −0.146332 0.989235i \(-0.546747\pi\)
0.783537 + 0.621345i \(0.213414\pi\)
\(174\) 0 0
\(175\) −2.43992 1.40869i −0.184441 0.106487i
\(176\) −0.113567 1.12197i −0.00856045 0.0845720i
\(177\) 0 0
\(178\) −0.314882 0.389612i −0.0236014 0.0292027i
\(179\) 6.71304 0.501756 0.250878 0.968019i \(-0.419281\pi\)
0.250878 + 0.968019i \(0.419281\pi\)
\(180\) 0 0
\(181\) 10.5763 0.786129 0.393065 0.919511i \(-0.371415\pi\)
0.393065 + 0.919511i \(0.371415\pi\)
\(182\) 4.33402 + 5.36260i 0.321259 + 0.397502i
\(183\) 0 0
\(184\) −18.5789 1.02738i −1.36966 0.0757393i
\(185\) 10.2233 + 5.90243i 0.751632 + 0.433955i
\(186\) 0 0
\(187\) −1.38268 + 0.798288i −0.101111 + 0.0583766i
\(188\) −9.85997 + 3.18277i −0.719113 + 0.232127i
\(189\) 0 0
\(190\) 4.54556 + 28.8791i 0.329770 + 2.09511i
\(191\) 4.68386 + 8.11268i 0.338912 + 0.587013i 0.984228 0.176903i \(-0.0566078\pi\)
−0.645316 + 0.763915i \(0.723274\pi\)
\(192\) 0 0
\(193\) −0.439681 + 0.761550i −0.0316489 + 0.0548176i −0.881416 0.472341i \(-0.843409\pi\)
0.849767 + 0.527158i \(0.176743\pi\)
\(194\) 0.366882 + 0.141237i 0.0263406 + 0.0101402i
\(195\) 0 0
\(196\) −1.48372 1.34111i −0.105980 0.0957939i
\(197\) 14.4709i 1.03101i −0.856887 0.515504i \(-0.827605\pi\)
0.856887 0.515504i \(-0.172395\pi\)
\(198\) 0 0
\(199\) 0.507764i 0.0359945i 0.999838 + 0.0179972i \(0.00572901\pi\)
−0.999838 + 0.0179972i \(0.994271\pi\)
\(200\) −4.35934 + 6.67063i −0.308252 + 0.471685i
\(201\) 0 0
\(202\) 7.16323 18.6074i 0.504003 1.30921i
\(203\) −0.140498 + 0.243350i −0.00986103 + 0.0170798i
\(204\) 0 0
\(205\) 1.04081 + 1.80274i 0.0726936 + 0.125909i
\(206\) 15.0760 2.37297i 1.05040 0.165332i
\(207\) 0 0
\(208\) 15.8214 11.4023i 1.09702 0.790608i
\(209\) 1.80517 1.04222i 0.124866 0.0720916i
\(210\) 0 0
\(211\) 10.0333 + 5.79273i 0.690721 + 0.398788i 0.803882 0.594789i \(-0.202764\pi\)
−0.113161 + 0.993577i \(0.536098\pi\)
\(212\) 15.8769 + 3.40664i 1.09043 + 0.233969i
\(213\) 0 0
\(214\) 4.13927 3.34533i 0.282954 0.228682i
\(215\) −20.3958 −1.39098
\(216\) 0 0
\(217\) −9.34312 −0.634252
\(218\) −6.72665 + 5.43644i −0.455586 + 0.368202i
\(219\) 0 0
\(220\) 1.54143 + 0.330737i 0.103923 + 0.0222983i
\(221\) −23.9113 13.8052i −1.60845 0.928640i
\(222\) 0 0
\(223\) 11.5096 6.64507i 0.770739 0.444987i −0.0623990 0.998051i \(-0.519875\pi\)
0.833138 + 0.553065i \(0.186542\pi\)
\(224\) −4.01917 + 3.98074i −0.268542 + 0.265974i
\(225\) 0 0
\(226\) 2.86768 0.451373i 0.190755 0.0300249i
\(227\) −4.25510 7.37006i −0.282421 0.489168i 0.689559 0.724229i \(-0.257804\pi\)
−0.971981 + 0.235061i \(0.924471\pi\)
\(228\) 0 0
\(229\) 5.27466 9.13598i 0.348559 0.603722i −0.637435 0.770505i \(-0.720004\pi\)
0.985994 + 0.166782i \(0.0533377\pi\)
\(230\) 9.34542 24.2759i 0.616219 1.60071i
\(231\) 0 0
\(232\) 0.665306 + 0.434786i 0.0436795 + 0.0285451i
\(233\) 2.54006i 0.166405i −0.996533 0.0832024i \(-0.973485\pi\)
0.996533 0.0832024i \(-0.0265148\pi\)
\(234\) 0 0
\(235\) 14.4844i 0.944857i
\(236\) −0.639354 0.577905i −0.0416184 0.0376184i
\(237\) 0 0
\(238\) 7.47411 + 2.87728i 0.484475 + 0.186507i
\(239\) −12.3345 + 21.3640i −0.797855 + 1.38193i 0.123155 + 0.992387i \(0.460699\pi\)
−0.921010 + 0.389538i \(0.872635\pi\)
\(240\) 0 0
\(241\) −7.33435 12.7035i −0.472447 0.818303i 0.527056 0.849831i \(-0.323296\pi\)
−0.999503 + 0.0315281i \(0.989963\pi\)
\(242\) 2.40131 + 15.2561i 0.154362 + 0.980700i
\(243\) 0 0
\(244\) 11.2633 3.63577i 0.721061 0.232756i
\(245\) 2.42137 1.39798i 0.154696 0.0893136i
\(246\) 0 0
\(247\) 31.2178 + 18.0236i 1.98634 + 1.14682i
\(248\) −1.45909 + 26.3860i −0.0926526 + 1.67551i
\(249\) 0 0
\(250\) 5.42475 + 6.71218i 0.343091 + 0.424516i
\(251\) −15.0697 −0.951191 −0.475595 0.879664i \(-0.657767\pi\)
−0.475595 + 0.879664i \(0.657767\pi\)
\(252\) 0 0
\(253\) −1.85471 −0.116604
\(254\) −11.1928 13.8492i −0.702301 0.868975i
\(255\) 0 0
\(256\) 10.6144 + 11.9722i 0.663400 + 0.748265i
\(257\) −3.71863 2.14695i −0.231962 0.133923i 0.379515 0.925186i \(-0.376091\pi\)
−0.611477 + 0.791262i \(0.709424\pi\)
\(258\) 0 0
\(259\) −3.65646 + 2.11106i −0.227201 + 0.131175i
\(260\) 8.37504 + 25.9452i 0.519398 + 1.60905i
\(261\) 0 0
\(262\) 1.81657 + 11.5411i 0.112228 + 0.713012i
\(263\) 4.80188 + 8.31711i 0.296097 + 0.512855i 0.975239 0.221152i \(-0.0709815\pi\)
−0.679143 + 0.734006i \(0.737648\pi\)
\(264\) 0 0
\(265\) −11.3504 + 19.6595i −0.697250 + 1.20767i
\(266\) −9.75794 3.75648i −0.598297 0.230325i
\(267\) 0 0
\(268\) −3.26944 + 3.61708i −0.199713 + 0.220949i
\(269\) 21.0329i 1.28240i −0.767375 0.641199i \(-0.778437\pi\)
0.767375 0.641199i \(-0.221563\pi\)
\(270\) 0 0
\(271\) 12.1109i 0.735682i −0.929889 0.367841i \(-0.880097\pi\)
0.929889 0.367841i \(-0.119903\pi\)
\(272\) 9.29299 20.6584i 0.563470 1.25260i
\(273\) 0 0
\(274\) −8.50879 + 22.1027i −0.514035 + 1.33527i
\(275\) −0.397148 + 0.687880i −0.0239489 + 0.0414807i
\(276\) 0 0
\(277\) 1.37227 + 2.37683i 0.0824514 + 0.142810i 0.904302 0.426893i \(-0.140392\pi\)
−0.821851 + 0.569703i \(0.807058\pi\)
\(278\) −32.5270 + 5.11975i −1.95084 + 0.307062i
\(279\) 0 0
\(280\) −3.56991 7.05654i −0.213343 0.421709i
\(281\) −5.21831 + 3.01279i −0.311298 + 0.179728i −0.647507 0.762059i \(-0.724188\pi\)
0.336209 + 0.941787i \(0.390855\pi\)
\(282\) 0 0
\(283\) −24.0259 13.8713i −1.42819 0.824565i −0.431211 0.902251i \(-0.641914\pi\)
−0.996978 + 0.0776854i \(0.975247\pi\)
\(284\) −1.03684 + 4.83230i −0.0615254 + 0.286744i
\(285\) 0 0
\(286\) 1.51186 1.22188i 0.0893982 0.0722511i
\(287\) −0.744513 −0.0439472
\(288\) 0 0
\(289\) −15.0705 −0.886503
\(290\) −0.864144 + 0.698397i −0.0507443 + 0.0410113i
\(291\) 0 0
\(292\) 0.299899 1.39770i 0.0175502 0.0817944i
\(293\) −10.8328 6.25434i −0.632861 0.365383i 0.148998 0.988837i \(-0.452395\pi\)
−0.781859 + 0.623455i \(0.785729\pi\)
\(294\) 0 0
\(295\) 1.04340 0.602409i 0.0607493 0.0350736i
\(296\) 5.39084 + 10.6559i 0.313336 + 0.619363i
\(297\) 0 0
\(298\) −16.0704 + 2.52948i −0.930933 + 0.146529i
\(299\) −16.0372 27.7773i −0.927456 1.60640i
\(300\) 0 0
\(301\) 3.64737 6.31743i 0.210231 0.364131i
\(302\) 2.46705 6.40848i 0.141963 0.368767i
\(303\) 0 0
\(304\) −12.1326 + 26.9709i −0.695852 + 1.54689i
\(305\) 16.5459i 0.947417i
\(306\) 0 0
\(307\) 2.72302i 0.155411i −0.996976 0.0777054i \(-0.975241\pi\)
0.996976 0.0777054i \(-0.0247594\pi\)
\(308\) −0.378096 + 0.418299i −0.0215440 + 0.0238348i
\(309\) 0 0
\(310\) −34.4770 13.2725i −1.95816 0.753826i
\(311\) 4.22803 7.32317i 0.239750 0.415259i −0.720893 0.693047i \(-0.756268\pi\)
0.960642 + 0.277788i \(0.0896013\pi\)
\(312\) 0 0
\(313\) −13.8676 24.0195i −0.783845 1.35766i −0.929687 0.368352i \(-0.879922\pi\)
0.145841 0.989308i \(-0.453411\pi\)
\(314\) 4.44318 + 28.2286i 0.250743 + 1.59303i
\(315\) 0 0
\(316\) −1.52772 4.73277i −0.0859411 0.266239i
\(317\) 20.7198 11.9626i 1.16374 0.671886i 0.211544 0.977369i \(-0.432151\pi\)
0.952198 + 0.305482i \(0.0988176\pi\)
\(318\) 0 0
\(319\) 0.0686069 + 0.0396102i 0.00384125 + 0.00221774i
\(320\) −20.4860 + 8.97982i −1.14520 + 0.501987i
\(321\) 0 0
\(322\) 5.84803 + 7.23592i 0.325898 + 0.403242i
\(323\) 41.8702 2.32972
\(324\) 0 0
\(325\) −13.7362 −0.761946
\(326\) 14.7384 + 18.2363i 0.816287 + 1.01001i
\(327\) 0 0
\(328\) −0.116269 + 2.10259i −0.00641988 + 0.116096i
\(329\) 4.48642 + 2.59024i 0.247344 + 0.142804i
\(330\) 0 0
\(331\) 24.6873 14.2532i 1.35694 0.783427i 0.367727 0.929934i \(-0.380136\pi\)
0.989210 + 0.146506i \(0.0468029\pi\)
\(332\) 15.6098 5.03879i 0.856698 0.276539i
\(333\) 0 0
\(334\) 1.48888 + 9.45919i 0.0814677 + 0.517584i
\(335\) −3.40807 5.90295i −0.186203 0.322513i
\(336\) 0 0
\(337\) 2.26282 3.91932i 0.123264 0.213499i −0.797789 0.602937i \(-0.793997\pi\)
0.921053 + 0.389437i \(0.127331\pi\)
\(338\) 14.2150 + 5.47230i 0.773194 + 0.297654i
\(339\) 0 0
\(340\) 23.4928 + 21.2349i 1.27408 + 1.15162i
\(341\) 2.63408i 0.142643i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −17.2715 11.2872i −0.931219 0.608563i
\(345\) 0 0
\(346\) −4.91700 + 12.7725i −0.264340 + 0.686656i
\(347\) −14.9377 + 25.8728i −0.801895 + 1.38892i 0.116472 + 0.993194i \(0.462841\pi\)
−0.918367 + 0.395729i \(0.870492\pi\)
\(348\) 0 0
\(349\) −9.43250 16.3376i −0.504910 0.874530i −0.999984 0.00567921i \(-0.998192\pi\)
0.495074 0.868851i \(-0.335141\pi\)
\(350\) 3.93592 0.619514i 0.210384 0.0331144i
\(351\) 0 0
\(352\) 1.12228 + 1.13311i 0.0598176 + 0.0603950i
\(353\) −26.5534 + 15.3306i −1.41330 + 0.815967i −0.995697 0.0926650i \(-0.970461\pi\)
−0.417598 + 0.908632i \(0.637128\pi\)
\(354\) 0 0
\(355\) −5.98355 3.45460i −0.317574 0.183351i
\(356\) 0.692681 + 0.148625i 0.0367120 + 0.00787713i
\(357\) 0 0
\(358\) −7.38370 + 5.96747i −0.390241 + 0.315391i
\(359\) 18.8963 0.997310 0.498655 0.866801i \(-0.333828\pi\)
0.498655 + 0.866801i \(0.333828\pi\)
\(360\) 0 0
\(361\) −35.6642 −1.87706
\(362\) −11.6329 + 9.40165i −0.611412 + 0.494140i
\(363\) 0 0
\(364\) −9.53403 2.04567i −0.499719 0.107222i
\(365\) 1.73069 + 0.999216i 0.0905886 + 0.0523014i
\(366\) 0 0
\(367\) −4.63257 + 2.67462i −0.241818 + 0.139614i −0.616012 0.787737i \(-0.711253\pi\)
0.374194 + 0.927351i \(0.377919\pi\)
\(368\) 21.3483 15.3855i 1.11286 0.802024i
\(369\) 0 0
\(370\) −16.4915 + 2.59577i −0.857355 + 0.134947i
\(371\) −4.05957 7.03139i −0.210763 0.365052i
\(372\) 0 0
\(373\) −7.51238 + 13.0118i −0.388976 + 0.673727i −0.992312 0.123760i \(-0.960505\pi\)
0.603336 + 0.797487i \(0.293838\pi\)
\(374\) 0.811183 2.10715i 0.0419453 0.108958i
\(375\) 0 0
\(376\) 8.01575 12.2656i 0.413381 0.632552i
\(377\) 1.37000i 0.0705586i
\(378\) 0 0
\(379\) 3.97151i 0.204003i 0.994784 + 0.102001i \(0.0325246\pi\)
−0.994784 + 0.102001i \(0.967475\pi\)
\(380\) −30.6714 27.7235i −1.57341 1.42219i
\(381\) 0 0
\(382\) −12.3635 4.75952i −0.632569 0.243518i
\(383\) 10.0601 17.4246i 0.514047 0.890355i −0.485821 0.874059i \(-0.661479\pi\)
0.999867 0.0162963i \(-0.00518751\pi\)
\(384\) 0 0
\(385\) −0.394128 0.682649i −0.0200866 0.0347910i
\(386\) −0.193363 1.22848i −0.00984191 0.0625281i
\(387\) 0 0
\(388\) −0.529086 + 0.170787i −0.0268603 + 0.00867041i
\(389\) 30.9005 17.8404i 1.56672 0.904545i 0.570169 0.821527i \(-0.306878\pi\)
0.996548 0.0830175i \(-0.0264558\pi\)
\(390\) 0 0
\(391\) −32.2643 18.6278i −1.63168 0.942049i
\(392\) 2.82411 + 0.156168i 0.142639 + 0.00788767i
\(393\) 0 0
\(394\) 12.8637 + 15.9166i 0.648064 + 0.801866i
\(395\) 6.95247 0.349817
\(396\) 0 0
\(397\) 26.7209 1.34108 0.670541 0.741873i \(-0.266062\pi\)
0.670541 + 0.741873i \(0.266062\pi\)
\(398\) −0.451371 0.558492i −0.0226252 0.0279947i
\(399\) 0 0
\(400\) −1.13491 11.2122i −0.0567456 0.560612i
\(401\) −19.5104 11.2643i −0.974302 0.562514i −0.0737572 0.997276i \(-0.523499\pi\)
−0.900545 + 0.434762i \(0.856832\pi\)
\(402\) 0 0
\(403\) −39.4496 + 22.7762i −1.96513 + 1.13457i
\(404\) 8.66195 + 26.8340i 0.430948 + 1.33504i
\(405\) 0 0
\(406\) −0.0617882 0.392556i −0.00306650 0.0194822i
\(407\) 0.595164 + 1.03085i 0.0295012 + 0.0510975i
\(408\) 0 0
\(409\) −7.38017 + 12.7828i −0.364926 + 0.632070i −0.988764 0.149483i \(-0.952239\pi\)
0.623839 + 0.781553i \(0.285572\pi\)
\(410\) −2.74732 1.05763i −0.135681 0.0522325i
\(411\) 0 0
\(412\) −14.4728 + 16.0117i −0.713023 + 0.788839i
\(413\) 0.430914i 0.0212039i
\(414\) 0 0
\(415\) 22.9309i 1.12563i
\(416\) −7.26612 + 26.6057i −0.356251 + 1.30445i
\(417\) 0 0
\(418\) −1.05905 + 2.75102i −0.0518000 + 0.134557i
\(419\) −15.0986 + 26.1515i −0.737614 + 1.27759i 0.215953 + 0.976404i \(0.430714\pi\)
−0.953567 + 0.301181i \(0.902619\pi\)
\(420\) 0 0
\(421\) 12.0519 + 20.8744i 0.587372 + 1.01736i 0.994575 + 0.104021i \(0.0331708\pi\)
−0.407203 + 0.913338i \(0.633496\pi\)
\(422\) −16.1850 + 2.54752i −0.787875 + 0.124011i
\(423\) 0 0
\(424\) −20.4914 + 10.3666i −0.995151 + 0.503448i
\(425\) −13.8175 + 7.97754i −0.670247 + 0.386967i
\(426\) 0 0
\(427\) −5.12497 2.95890i −0.248014 0.143191i
\(428\) −1.57901 + 7.35910i −0.0763242 + 0.355715i
\(429\) 0 0
\(430\) 22.4334 18.1306i 1.08184 0.874335i
\(431\) −26.8450 −1.29308 −0.646538 0.762882i \(-0.723784\pi\)
−0.646538 + 0.762882i \(0.723784\pi\)
\(432\) 0 0
\(433\) 16.4401 0.790063 0.395031 0.918668i \(-0.370734\pi\)
0.395031 + 0.918668i \(0.370734\pi\)
\(434\) 10.2765 8.30545i 0.493290 0.398674i
\(435\) 0 0
\(436\) 2.56602 11.9591i 0.122890 0.572739i
\(437\) 42.1232 + 24.3198i 2.01502 + 1.16337i
\(438\) 0 0
\(439\) −10.2179 + 5.89931i −0.487674 + 0.281559i −0.723609 0.690210i \(-0.757518\pi\)
0.235935 + 0.971769i \(0.424185\pi\)
\(440\) −1.98943 + 1.00645i −0.0948423 + 0.0479808i
\(441\) 0 0
\(442\) 38.5722 6.07126i 1.83469 0.288780i
\(443\) 8.35739 + 14.4754i 0.397071 + 0.687748i 0.993363 0.115020i \(-0.0366932\pi\)
−0.596292 + 0.802768i \(0.703360\pi\)
\(444\) 0 0
\(445\) −0.495197 + 0.857706i −0.0234746 + 0.0406592i
\(446\) −6.75241 + 17.5402i −0.319736 + 0.830555i
\(447\) 0 0
\(448\) 0.882071 7.95122i 0.0416740 0.375660i
\(449\) 36.4399i 1.71970i 0.510543 + 0.859852i \(0.329444\pi\)
−0.510543 + 0.859852i \(0.670556\pi\)
\(450\) 0 0
\(451\) 0.209898i 0.00988372i
\(452\) −2.75293 + 3.04566i −0.129487 + 0.143256i
\(453\) 0 0
\(454\) 11.2317 + 4.32384i 0.527131 + 0.202928i
\(455\) 6.81586 11.8054i 0.319533 0.553447i
\(456\) 0 0
\(457\) 16.3554 + 28.3283i 0.765072 + 1.32514i 0.940208 + 0.340600i \(0.110630\pi\)
−0.175136 + 0.984544i \(0.556036\pi\)
\(458\) 2.31969 + 14.7375i 0.108392 + 0.688640i
\(459\) 0 0
\(460\) 11.3007 + 35.0087i 0.526898 + 1.63229i
\(461\) 23.5218 13.5803i 1.09552 0.632498i 0.160479 0.987039i \(-0.448696\pi\)
0.935040 + 0.354541i \(0.115363\pi\)
\(462\) 0 0
\(463\) 15.5298 + 8.96612i 0.721730 + 0.416691i 0.815389 0.578913i \(-0.196523\pi\)
−0.0936592 + 0.995604i \(0.529856\pi\)
\(464\) −1.11827 + 0.113192i −0.0519144 + 0.00525482i
\(465\) 0 0
\(466\) 2.25795 + 2.79382i 0.104598 + 0.129421i
\(467\) 24.3536 1.12695 0.563474 0.826134i \(-0.309464\pi\)
0.563474 + 0.826134i \(0.309464\pi\)
\(468\) 0 0
\(469\) 2.43786 0.112570
\(470\) 12.8757 + 15.9314i 0.593912 + 0.734862i
\(471\) 0 0
\(472\) 1.21695 + 0.0672950i 0.0560147 + 0.00309750i
\(473\) −1.78105 1.02829i −0.0818930 0.0472809i
\(474\) 0 0
\(475\) 18.0396 10.4152i 0.827716 0.477882i
\(476\) −10.7785 + 3.47928i −0.494033 + 0.159472i
\(477\) 0 0
\(478\) −5.42448 34.4630i −0.248110 1.57630i
\(479\) −8.74315 15.1436i −0.399485 0.691928i 0.594177 0.804334i \(-0.297478\pi\)
−0.993662 + 0.112406i \(0.964144\pi\)
\(480\) 0 0
\(481\) −10.2925 + 17.8271i −0.469297 + 0.812846i
\(482\) 19.3597 + 7.45283i 0.881809 + 0.339467i
\(483\) 0 0
\(484\) −16.2029 14.6457i −0.736497 0.665712i
\(485\) 0.777231i 0.0352922i
\(486\) 0 0
\(487\) 5.76620i 0.261291i −0.991429 0.130646i \(-0.958295\pi\)
0.991429 0.130646i \(-0.0417050\pi\)
\(488\) −9.15662 + 14.0114i −0.414501 + 0.634266i
\(489\) 0 0
\(490\) −1.42056 + 3.69009i −0.0641744 + 0.166701i
\(491\) 16.6911 28.9099i 0.753261 1.30469i −0.192973 0.981204i \(-0.561813\pi\)
0.946234 0.323482i \(-0.104854\pi\)
\(492\) 0 0
\(493\) 0.795653 + 1.37811i 0.0358344 + 0.0620670i
\(494\) −50.3585 + 7.92642i −2.26574 + 0.356626i
\(495\) 0 0
\(496\) −21.8506 30.3192i −0.981123 1.36137i
\(497\) 2.14007 1.23557i 0.0959953 0.0554229i
\(498\) 0 0
\(499\) 35.1612 + 20.3003i 1.57403 + 0.908766i 0.995667 + 0.0929863i \(0.0296413\pi\)
0.578362 + 0.815780i \(0.303692\pi\)
\(500\) −11.9334 2.56050i −0.533678 0.114509i
\(501\) 0 0
\(502\) 16.5752 13.3960i 0.739789 0.597893i
\(503\) 16.0809 0.717012 0.358506 0.933528i \(-0.383286\pi\)
0.358506 + 0.933528i \(0.383286\pi\)
\(504\) 0 0
\(505\) −39.4194 −1.75414
\(506\) 2.04000 1.64872i 0.0906891 0.0732944i
\(507\) 0 0
\(508\) 24.6221 + 5.28305i 1.09243 + 0.234398i
\(509\) −0.457413 0.264088i −0.0202745 0.0117055i 0.489829 0.871819i \(-0.337059\pi\)
−0.510103 + 0.860113i \(0.670393\pi\)
\(510\) 0 0
\(511\) −0.618998 + 0.357379i −0.0273829 + 0.0158095i
\(512\) −22.3174 3.73279i −0.986299 0.164968i
\(513\) 0 0
\(514\) 5.99864 0.944185i 0.264589 0.0416462i
\(515\) −15.0865 26.1305i −0.664788 1.15145i
\(516\) 0 0
\(517\) 0.730257 1.26484i 0.0321167 0.0556277i
\(518\) 2.14516 5.57232i 0.0942528 0.244834i
\(519\) 0 0
\(520\) −32.2754 21.0924i −1.41537 0.924963i
\(521\) 39.2616i 1.72008i −0.510224 0.860042i \(-0.670437\pi\)
0.510224 0.860042i \(-0.329563\pi\)
\(522\) 0 0
\(523\) 12.1444i 0.531036i 0.964106 + 0.265518i \(0.0855430\pi\)
−0.964106 + 0.265518i \(0.914457\pi\)
\(524\) −12.2574 11.0793i −0.535466 0.484002i
\(525\) 0 0
\(526\) −12.6750 4.87945i −0.552656 0.212754i
\(527\) −26.4554 + 45.8222i −1.15242 + 1.99605i
\(528\) 0 0
\(529\) −10.1395 17.5621i −0.440848 0.763572i
\(530\) −4.99168 31.7133i −0.216825 1.37754i
\(531\) 0 0
\(532\) 14.0721 4.54242i 0.610102 0.196939i
\(533\) −3.14357 + 1.81494i −0.136163 + 0.0786138i
\(534\) 0 0
\(535\) −9.11233 5.26101i −0.393961 0.227453i
\(536\) 0.380715 6.88478i 0.0164444 0.297377i
\(537\) 0 0
\(538\) 18.6969 + 23.1342i 0.806081 + 0.997385i
\(539\) 0.281927 0.0121434
\(540\) 0 0
\(541\) −22.5265 −0.968490 −0.484245 0.874933i \(-0.660906\pi\)
−0.484245 + 0.874933i \(0.660906\pi\)
\(542\) 10.7658 + 13.3208i 0.462430 + 0.572177i
\(543\) 0 0
\(544\) 8.14261 + 30.9831i 0.349112 + 1.32839i
\(545\) 14.8083 + 8.54957i 0.634317 + 0.366223i
\(546\) 0 0
\(547\) −7.89651 + 4.55905i −0.337631 + 0.194931i −0.659224 0.751947i \(-0.729115\pi\)
0.321593 + 0.946878i \(0.395782\pi\)
\(548\) −10.2890 31.8746i −0.439525 1.36162i
\(549\) 0 0
\(550\) −0.174657 1.10964i −0.00744742 0.0473153i
\(551\) −1.03878 1.79921i −0.0442534 0.0766491i
\(552\) 0 0
\(553\) −1.24331 + 2.15347i −0.0528708 + 0.0915750i
\(554\) −3.62222 1.39443i −0.153893 0.0592438i
\(555\) 0 0
\(556\) 31.2255 34.5457i 1.32426 1.46506i
\(557\) 11.9979i 0.508369i −0.967156 0.254184i \(-0.918193\pi\)
0.967156 0.254184i \(-0.0818070\pi\)
\(558\) 0 0
\(559\) 35.5656i 1.50427i
\(560\) 10.1994 + 4.58810i 0.431003 + 0.193883i
\(561\) 0 0
\(562\) 3.06146 7.95253i 0.129140 0.335457i
\(563\) −9.48276 + 16.4246i −0.399651 + 0.692216i −0.993683 0.112226i \(-0.964202\pi\)
0.594032 + 0.804441i \(0.297535\pi\)
\(564\) 0 0
\(565\) −2.86966 4.97040i −0.120728 0.209106i
\(566\) 38.7569 6.10033i 1.62907 0.256416i
\(567\) 0 0
\(568\) −3.15518 6.23676i −0.132388 0.261688i
\(569\) −20.5929 + 11.8893i −0.863301 + 0.498427i −0.865116 0.501571i \(-0.832756\pi\)
0.00181529 + 0.999998i \(0.499422\pi\)
\(570\) 0 0
\(571\) 9.65431 + 5.57392i 0.404020 + 0.233261i 0.688217 0.725505i \(-0.258394\pi\)
−0.284197 + 0.958766i \(0.591727\pi\)
\(572\) −0.576730 + 2.68790i −0.0241143 + 0.112387i
\(573\) 0 0
\(574\) 0.818894 0.661826i 0.0341800 0.0276241i
\(575\) −18.5346 −0.772948
\(576\) 0 0
\(577\) 26.0394 1.08404 0.542018 0.840367i \(-0.317660\pi\)
0.542018 + 0.840367i \(0.317660\pi\)
\(578\) 16.5762 13.3968i 0.689478 0.557232i
\(579\) 0 0
\(580\) 0.329645 1.53634i 0.0136878 0.0637930i
\(581\) −7.10266 4.10072i −0.294668 0.170127i
\(582\) 0 0
\(583\) −1.98234 + 1.14450i −0.0821000 + 0.0474005i
\(584\) 0.912610 + 1.80393i 0.0377641 + 0.0746472i
\(585\) 0 0
\(586\) 17.4748 2.75053i 0.721878 0.113623i
\(587\) 1.53840 + 2.66458i 0.0634965 + 0.109979i 0.896026 0.444001i \(-0.146441\pi\)
−0.832530 + 0.553981i \(0.813108\pi\)
\(588\) 0 0
\(589\) 34.5393 59.8238i 1.42317 2.46500i
\(590\) −0.612140 + 1.59011i −0.0252014 + 0.0654639i
\(591\) 0 0
\(592\) −15.4019 6.92839i −0.633013 0.284755i
\(593\) 4.35742i 0.178938i −0.995990 0.0894688i \(-0.971483\pi\)
0.995990 0.0894688i \(-0.0285169\pi\)
\(594\) 0 0
\(595\) 15.8338i 0.649121i
\(596\) 15.4274 17.0678i 0.631929 0.699122i
\(597\) 0 0
\(598\) 42.3317 + 16.2963i 1.73107 + 0.666404i
\(599\) 16.0003 27.7133i 0.653753 1.13233i −0.328452 0.944521i \(-0.606527\pi\)
0.982205 0.187812i \(-0.0601397\pi\)
\(600\) 0 0
\(601\) −17.6951 30.6489i −0.721799 1.25019i −0.960278 0.279045i \(-0.909982\pi\)
0.238478 0.971148i \(-0.423351\pi\)
\(602\) 1.60404 + 10.1909i 0.0653758 + 0.415349i
\(603\) 0 0
\(604\) 2.98322 + 9.24178i 0.121385 + 0.376043i
\(605\) 26.4426 15.2667i 1.07505 0.620678i
\(606\) 0 0
\(607\) −2.32842 1.34431i −0.0945076 0.0545640i 0.452001 0.892017i \(-0.350710\pi\)
−0.546509 + 0.837453i \(0.684044\pi\)
\(608\) −10.6307 40.4505i −0.431132 1.64048i
\(609\) 0 0
\(610\) −14.7083 18.1989i −0.595521 0.736854i
\(611\) 25.2574 1.02181
\(612\) 0 0
\(613\) 41.2533 1.66621 0.833103 0.553117i \(-0.186562\pi\)
0.833103 + 0.553117i \(0.186562\pi\)
\(614\) 2.42059 + 2.99506i 0.0976872 + 0.120871i
\(615\) 0 0
\(616\) 0.0440279 0.796193i 0.00177394 0.0320795i
\(617\) −23.5137 13.5756i −0.946626 0.546534i −0.0545945 0.998509i \(-0.517387\pi\)
−0.892031 + 0.451974i \(0.850720\pi\)
\(618\) 0 0
\(619\) −8.12323 + 4.68995i −0.326500 + 0.188505i −0.654286 0.756247i \(-0.727031\pi\)
0.327786 + 0.944752i \(0.393698\pi\)
\(620\) 49.7198 16.0494i 1.99679 0.644559i
\(621\) 0 0
\(622\) 1.85940 + 11.8132i 0.0745553 + 0.473668i
\(623\) −0.177112 0.306766i −0.00709583 0.0122903i
\(624\) 0 0
\(625\) 15.5746 26.9761i 0.622985 1.07904i
\(626\) 36.6049 + 14.0917i 1.46302 + 0.563216i
\(627\) 0 0
\(628\) −29.9805 27.0991i −1.19635 1.08137i
\(629\) 23.9102i 0.953362i
\(630\) 0 0
\(631\) 17.3945i 0.692463i 0.938149 + 0.346232i \(0.112539\pi\)
−0.938149 + 0.346232i \(0.887461\pi\)
\(632\) 5.88748 + 3.84755i 0.234192 + 0.153047i
\(633\) 0 0
\(634\) −12.1558 + 31.5763i −0.482770 + 1.25406i
\(635\) −17.6023 + 30.4881i −0.698526 + 1.20988i
\(636\) 0 0
\(637\) 2.43776 + 4.22232i 0.0965874 + 0.167294i
\(638\) −0.110672 + 0.0174198i −0.00438155 + 0.000689655i
\(639\) 0 0
\(640\) 14.5501 28.0877i 0.575144 1.11026i
\(641\) −25.0358 + 14.4544i −0.988854 + 0.570915i −0.904932 0.425557i \(-0.860078\pi\)
−0.0839224 + 0.996472i \(0.526745\pi\)
\(642\) 0 0
\(643\) 12.0530 + 6.95879i 0.475323 + 0.274428i 0.718465 0.695563i \(-0.244845\pi\)
−0.243142 + 0.969991i \(0.578178\pi\)
\(644\) −12.8646 2.76029i −0.506935 0.108771i
\(645\) 0 0
\(646\) −46.0532 + 37.2200i −1.81194 + 1.46440i
\(647\) 20.5491 0.807868 0.403934 0.914788i \(-0.367643\pi\)
0.403934 + 0.914788i \(0.367643\pi\)
\(648\) 0 0
\(649\) 0.121486 0.00476875
\(650\) 15.1085 12.2106i 0.592604 0.478939i
\(651\) 0 0
\(652\) −32.4218 6.95659i −1.26973 0.272441i
\(653\) 4.02988 + 2.32665i 0.157701 + 0.0910489i 0.576774 0.816904i \(-0.304311\pi\)
−0.419073 + 0.907953i \(0.637645\pi\)
\(654\) 0 0
\(655\) 20.0036 11.5491i 0.781605 0.451260i
\(656\) −1.74118 2.41600i −0.0679818 0.0943291i
\(657\) 0 0
\(658\) −7.23719 + 1.13913i −0.282135 + 0.0444080i
\(659\) −13.4746 23.3387i −0.524895 0.909145i −0.999580 0.0289894i \(-0.990771\pi\)
0.474684 0.880156i \(-0.342562\pi\)
\(660\) 0 0
\(661\) −15.9921 + 27.6992i −0.622022 + 1.07737i 0.367087 + 0.930187i \(0.380355\pi\)
−0.989109 + 0.147186i \(0.952978\pi\)
\(662\) −14.4835 + 37.6226i −0.562916 + 1.46225i
\(663\) 0 0
\(664\) −12.6901 + 19.4183i −0.492472 + 0.753576i
\(665\) 20.6720i 0.801625i
\(666\) 0 0
\(667\) 1.84858i 0.0715775i
\(668\) −10.0463 9.08070i −0.388701 0.351343i
\(669\) 0 0
\(670\) 8.99591 + 3.46312i 0.347542 + 0.133792i
\(671\) −0.834193 + 1.44487i −0.0322037 + 0.0557784i
\(672\) 0 0
\(673\) 3.85968 + 6.68517i 0.148780 + 0.257694i 0.930777 0.365588i \(-0.119132\pi\)
−0.781997 + 0.623282i \(0.785799\pi\)
\(674\) 0.995143 + 6.32239i 0.0383315 + 0.243529i
\(675\) 0 0
\(676\) −20.4997 + 6.61724i −0.788449 + 0.254509i
\(677\) 7.42656 4.28773i 0.285426 0.164791i −0.350451 0.936581i \(-0.613972\pi\)
0.635877 + 0.771790i \(0.280638\pi\)
\(678\) 0 0
\(679\) 0.240741 + 0.138992i 0.00923879 + 0.00533402i
\(680\) −44.7163 2.47272i −1.71479 0.0948246i
\(681\) 0 0
\(682\) −2.34153 2.89723i −0.0896617 0.110941i
\(683\) −5.18082 −0.198238 −0.0991192 0.995076i \(-0.531603\pi\)
−0.0991192 + 0.995076i \(0.531603\pi\)
\(684\) 0 0
\(685\) 46.8241 1.78906
\(686\) −0.888937 1.09990i −0.0339398 0.0419946i
\(687\) 0 0
\(688\) 29.0306 2.93850i 1.10678 0.112029i
\(689\) −34.2816 19.7925i −1.30603 0.754034i
\(690\) 0 0
\(691\) 13.4870 7.78675i 0.513071 0.296222i −0.221024 0.975268i \(-0.570940\pi\)
0.734095 + 0.679047i \(0.237607\pi\)
\(692\) −5.94576 18.4195i −0.226024 0.700204i
\(693\) 0 0
\(694\) −6.56928 41.7362i −0.249366 1.58429i
\(695\) 32.5495 + 56.3774i 1.23467 + 2.13852i
\(696\) 0 0
\(697\) −2.10812 + 3.65137i −0.0798508 + 0.138306i
\(698\) 24.8979 + 9.58487i 0.942401 + 0.362793i
\(699\) 0 0
\(700\) −3.77843 + 4.18019i −0.142811 + 0.157996i
\(701\) 10.5008i 0.396609i 0.980140 + 0.198304i \(0.0635435\pi\)
−0.980140 + 0.198304i \(0.936457\pi\)
\(702\) 0 0
\(703\) 31.2163i 1.17735i
\(704\) −2.24166 0.248680i −0.0844859 0.00937246i
\(705\) 0 0
\(706\) 15.5783 40.4665i 0.586296 1.52298i
\(707\) 7.04936 12.2098i 0.265118 0.459199i
\(708\) 0 0
\(709\) 3.56049 + 6.16695i 0.133717 + 0.231605i 0.925107 0.379708i \(-0.123975\pi\)
−0.791390 + 0.611312i \(0.790642\pi\)
\(710\) 9.65226 1.51926i 0.362243 0.0570170i
\(711\) 0 0
\(712\) −0.894002 + 0.452276i −0.0335041 + 0.0169498i
\(713\) −53.2306 + 30.7327i −1.99350 + 1.15095i
\(714\) 0 0
\(715\) −3.32827 1.92157i −0.124470 0.0718628i
\(716\) 2.81666 13.1273i 0.105264 0.490590i
\(717\) 0 0
\(718\) −20.7842 + 16.7976i −0.775658 + 0.626882i
\(719\) −11.4166 −0.425766 −0.212883 0.977078i \(-0.568285\pi\)
−0.212883 + 0.977078i \(0.568285\pi\)
\(720\) 0 0
\(721\) 10.7916 0.401901
\(722\) 39.2273 31.7033i 1.45989 1.17987i
\(723\) 0 0
\(724\) 4.43761 20.6818i 0.164922 0.768635i
\(725\) 0.685609 + 0.395837i 0.0254629 + 0.0147010i
\(726\) 0 0
\(727\) −11.2371 + 6.48771i −0.416759 + 0.240616i −0.693690 0.720274i \(-0.744016\pi\)
0.276931 + 0.960890i \(0.410683\pi\)
\(728\) 12.3050 6.22511i 0.456054 0.230718i
\(729\) 0 0
\(730\) −2.79184 + 0.439435i −0.103331 + 0.0162642i
\(731\) −20.6554 35.7762i −0.763967 1.32323i
\(732\) 0 0
\(733\) −12.2933 + 21.2926i −0.454063 + 0.786460i −0.998634 0.0522545i \(-0.983359\pi\)
0.544571 + 0.838715i \(0.316693\pi\)
\(734\) 2.71782 7.05989i 0.100317 0.260585i
\(735\) 0 0
\(736\) −9.80440 + 35.8999i −0.361395 + 1.32329i
\(737\) 0.687297i 0.0253169i
\(738\) 0 0
\(739\) 42.1439i 1.55029i 0.631785 + 0.775144i \(0.282322\pi\)
−0.631785 + 0.775144i \(0.717678\pi\)
\(740\) 15.8317 17.5150i 0.581983 0.643866i
\(741\) 0 0
\(742\) 10.7156 + 4.12515i 0.393382 + 0.151439i
\(743\) −0.0854917 + 0.148076i −0.00313639 + 0.00543238i −0.867589 0.497281i \(-0.834332\pi\)
0.864453 + 0.502714i \(0.167665\pi\)
\(744\) 0 0
\(745\) 16.0815 + 27.8540i 0.589180 + 1.02049i
\(746\) −3.30379 20.9898i −0.120960 0.768491i
\(747\) 0 0
\(748\) 0.980902 + 3.03876i 0.0358653 + 0.111108i
\(749\) 3.25911 1.88165i 0.119085 0.0687539i
\(750\) 0 0
\(751\) −10.7780 6.22269i −0.393295 0.227069i 0.290292 0.956938i \(-0.406248\pi\)
−0.683587 + 0.729869i \(0.739581\pi\)
\(752\) 2.08682 + 20.6165i 0.0760986 + 0.751808i
\(753\) 0 0
\(754\) −1.21784 1.50687i −0.0443513 0.0548770i
\(755\) −13.5762 −0.494090
\(756\) 0 0
\(757\) 34.3261 1.24760 0.623801 0.781583i \(-0.285587\pi\)
0.623801 + 0.781583i \(0.285587\pi\)
\(758\) −3.53043 4.36829i −0.128231 0.158663i
\(759\) 0 0
\(760\) 58.3800 + 3.22830i 2.11767 + 0.117103i
\(761\) 9.19028 + 5.30601i 0.333148 + 0.192343i 0.657238 0.753683i \(-0.271725\pi\)
−0.324090 + 0.946026i \(0.605058\pi\)
\(762\) 0 0
\(763\) −5.29632 + 3.05783i −0.191740 + 0.110701i
\(764\) 17.8295 5.75532i 0.645050 0.208220i
\(765\) 0 0
\(766\) 4.42422 + 28.1082i 0.159854 + 1.01559i
\(767\) 1.05046 + 1.81946i 0.0379301 + 0.0656968i
\(768\) 0 0
\(769\) −4.39685 + 7.61557i −0.158554 + 0.274624i −0.934348 0.356363i \(-0.884017\pi\)
0.775793 + 0.630987i \(0.217350\pi\)
\(770\) 1.04034 + 0.400494i 0.0374911 + 0.0144328i
\(771\) 0 0
\(772\) 1.30472 + 1.17933i 0.0469580 + 0.0424449i
\(773\) 1.24418i 0.0447501i −0.999750 0.0223751i \(-0.992877\pi\)
0.999750 0.0223751i \(-0.00712279\pi\)
\(774\) 0 0
\(775\) 26.3231i 0.945555i
\(776\) 0.430125 0.658174i 0.0154406 0.0236271i
\(777\) 0 0
\(778\) −18.1286 + 47.0914i −0.649942 + 1.68831i
\(779\) 2.75229 4.76710i 0.0986110 0.170799i
\(780\) 0 0
\(781\) −0.348340 0.603343i −0.0124646 0.0215893i
\(782\) 52.0466 8.19213i 1.86118 0.292950i
\(783\) 0 0
\(784\) −3.24508 + 2.33869i −0.115896 + 0.0835246i
\(785\) 48.9271 28.2481i 1.74628 1.00822i
\(786\) 0 0
\(787\) −8.14573 4.70294i −0.290364 0.167642i 0.347742 0.937590i \(-0.386948\pi\)
−0.638106 + 0.769949i \(0.720282\pi\)
\(788\) −28.2977 6.07171i −1.00806 0.216296i
\(789\) 0 0
\(790\)