Properties

Label 756.2.ba.a.71.5
Level $756$
Weight $2$
Character 756.71
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 71.5
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31979 + 0.508077i) q^{2} +(1.48372 - 1.34111i) q^{4} +(2.42137 + 1.39798i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.27681 + 2.52384i) q^{8} +O(q^{10})\) \(q+(-1.31979 + 0.508077i) q^{2} +(1.48372 - 1.34111i) q^{4} +(2.42137 + 1.39798i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-1.27681 + 2.52384i) q^{8} +(-3.90599 - 0.614803i) q^{10} +(-0.140963 - 0.244156i) q^{11} +(-2.43776 + 4.22232i) q^{13} +(-0.888937 + 1.09990i) q^{14} +(0.402825 - 3.97966i) q^{16} +5.66309i q^{17} +7.39353i q^{19} +(5.46748 - 1.17313i) q^{20} +(0.310093 + 0.250615i) q^{22} +(3.28934 - 5.69730i) q^{23} +(1.40869 + 2.43992i) q^{25} +(1.07208 - 6.81116i) q^{26} +(0.614378 - 1.90330i) q^{28} +(0.243350 - 0.140498i) q^{29} +(-8.09138 - 4.67156i) q^{31} +(1.49033 + 5.45701i) q^{32} +(-2.87728 - 7.47411i) q^{34} +2.79596 q^{35} +4.22211 q^{37} +(-3.75648 - 9.75794i) q^{38} +(-6.61990 + 4.32619i) q^{40} +(0.644767 + 0.372257i) q^{41} +(6.31743 - 3.64737i) q^{43} +(-0.536590 - 0.173210i) q^{44} +(-1.44658 + 9.19051i) q^{46} +(2.59024 + 4.48642i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.09885 - 2.50448i) q^{50} +(2.04567 + 9.53403i) q^{52} +8.11915i q^{53} -0.788256i q^{55} +(0.156168 + 2.82411i) q^{56} +(-0.249788 + 0.309069i) q^{58} +(-0.215457 + 0.373183i) q^{59} +(2.95890 + 5.12497i) q^{61} +(13.0525 + 2.05446i) q^{62} +(-4.73951 - 6.44493i) q^{64} +(-11.8054 + 6.81586i) q^{65} +(2.11124 + 1.21893i) q^{67} +(7.59485 + 8.40241i) q^{68} +(-3.69009 + 1.42056i) q^{70} +2.47114 q^{71} +0.714758 q^{73} +(-5.57232 + 2.14516i) q^{74} +(9.91556 + 10.9699i) q^{76} +(-0.244156 - 0.140963i) q^{77} +(-2.15347 + 1.24331i) q^{79} +(6.53888 - 9.07310i) q^{80} +(-1.04010 - 0.163711i) q^{82} +(-4.10072 - 7.10266i) q^{83} +(-7.91688 + 13.7124i) q^{85} +(-6.48457 + 8.02353i) q^{86} +(0.796193 - 0.0440279i) q^{88} +0.354223i q^{89} +4.87551i q^{91} +(-2.76029 - 12.8646i) q^{92} +(-5.69802 - 4.60511i) q^{94} +(-10.3360 + 17.9025i) q^{95} +(-0.138992 - 0.240741i) q^{97} +(-0.219890 + 1.39701i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31979 + 0.508077i −0.933236 + 0.359265i
\(3\) 0 0
\(4\) 1.48372 1.34111i 0.741858 0.670557i
\(5\) 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 0.843992 0.536356i \(-0.180200\pi\)
−0.886494 + 0.462740i \(0.846866\pi\)
\(12\) 0 0
\(13\) −2.43776 + 4.22232i −0.676112 + 1.17106i 0.300031 + 0.953930i \(0.403003\pi\)
−0.976143 + 0.217131i \(0.930330\pi\)
\(14\) −0.888937 + 1.09990i −0.237578 + 0.293962i
\(15\) 0 0
\(16\) 0.402825 3.97966i 0.100706 0.994916i
\(17\) 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 \(0.322251\pi\)
−0.529843 + 0.848096i \(0.677749\pi\)
\(20\) 5.46748 1.17313i 1.22256 0.262320i
\(21\) 0 0
\(22\) 0.310093 + 0.250615i 0.0661120 + 0.0534314i
\(23\) 3.28934 5.69730i 0.685875 1.18797i −0.287286 0.957845i \(-0.592753\pi\)
0.973161 0.230125i \(-0.0739135\pi\)
\(24\) 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 −0.454590 0.890701i \(-0.650214\pi\)
−0.998665 + 0.0516641i \(0.983547\pi\)
\(32\) 1.49033 + 5.45701i 0.263456 + 0.964672i
\(33\) 0 0
\(34\) −2.87728 7.47411i −0.493450 1.28180i
\(35\) 2.79596 0.472603
\(36\) 0 0
\(37\) 4.22211 0.694111 0.347056 0.937845i \(-0.387182\pi\)
0.347056 + 0.937845i \(0.387182\pi\)
\(38\) −3.75648 9.75794i −0.609382 1.58295i
\(39\) 0 0
\(40\) −6.61990 + 4.32619i −1.04670 + 0.684031i
\(41\) 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 0.0661820 0.997808i \(-0.478918\pi\)
0.897218 + 0.441588i \(0.145585\pi\)
\(44\) −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 0.990745 0.135733i \(-0.0433389\pi\)
−0.612921 + 0.790144i \(0.710006\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −3.09885 2.50448i −0.438244 0.354186i
\(51\) 0 0
\(52\) 2.04567 + 9.53403i 0.283684 + 1.32213i
\(53\) 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
\(56\) 0.156168 + 2.82411i 0.0208688 + 0.377388i
\(57\) 0 0
\(58\) −0.249788 + 0.309069i −0.0327988 + 0.0405828i
\(59\) −0.215457 + 0.373183i −0.0280501 + 0.0485843i −0.879710 0.475511i \(-0.842263\pi\)
0.851660 + 0.524095i \(0.175596\pi\)
\(60\) 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 0.623390 0.781911i \(-0.285755\pi\)
−0.365460 + 0.930827i \(0.619088\pi\)
\(68\) 7.59485 + 8.40241i 0.921010 + 1.01894i
\(69\) 0 0
\(70\) −3.69009 + 1.42056i −0.441050 + 0.169790i
\(71\) 2.47114 0.293270 0.146635 0.989191i \(-0.453156\pi\)
0.146635 + 0.989191i \(0.453156\pi\)
\(72\) 0 0
\(73\) 0.714758 0.0836560 0.0418280 0.999125i \(-0.486682\pi\)
0.0418280 + 0.999125i \(0.486682\pi\)
\(74\) −5.57232 + 2.14516i −0.647769 + 0.249370i
\(75\) 0 0
\(76\) 9.91556 + 10.9699i 1.13739 + 1.25833i
\(77\) −0.244156 0.140963i −0.0278241 0.0160643i
\(78\) 0 0
\(79\) −2.15347 + 1.24331i −0.242285 + 0.139883i −0.616226 0.787569i \(-0.711339\pi\)
0.373942 + 0.927452i \(0.378006\pi\)
\(80\) 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 0.548280 0.836295i \(-0.315283\pi\)
−0.998393 + 0.0566769i \(0.981950\pi\)
\(84\) 0 0
\(85\) −7.91688 + 13.7124i −0.858706 + 1.48732i
\(86\) −6.48457 + 8.02353i −0.699249 + 0.865199i
\(87\) 0 0
\(88\) 0.796193 0.0440279i 0.0848745 0.00469339i
\(89\) 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
\(92\) −2.76029 12.8646i −0.287780 1.34122i
\(93\) 0 0
\(94\) −5.69802 4.60511i −0.587706 0.474981i
\(95\) −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 0.883913 0.467652i \(-0.154900\pi\)
0.0369577 + 0.999317i \(0.488233\pi\)
\(104\) −7.54389 11.5436i −0.739739 1.13194i
\(105\) 0 0
\(106\) −4.12515 10.7156i −0.400670 1.04079i
\(107\) 3.76330 0.363811 0.181906 0.983316i \(-0.441773\pi\)
0.181906 + 0.983316i \(0.441773\pi\)
\(108\) 0 0
\(109\) 6.11566 0.585774 0.292887 0.956147i \(-0.405384\pi\)
0.292887 + 0.956147i \(0.405384\pi\)
\(110\) 0.400494 + 1.04034i 0.0381856 + 0.0991921i
\(111\) 0 0
\(112\) −1.64098 3.64790i −0.155058 0.344694i
\(113\) −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
\(122\) −6.50902 5.26055i −0.589299 0.476268i
\(123\) 0 0
\(124\) −18.2704 + 3.92020i −1.64073 + 0.352044i
\(125\) 6.10251i 0.545825i
\(126\) 0 0
\(127\) 12.5913i 1.11729i −0.829406 0.558647i \(-0.811321\pi\)
0.829406 0.558647i \(-0.188679\pi\)
\(128\) 9.52969 + 6.09794i 0.842314 + 0.538987i
\(129\) 0 0
\(130\) 12.1178 14.9936i 1.06280 1.31503i
\(131\) −4.13063 + 7.15447i −0.360895 + 0.625089i −0.988108 0.153759i \(-0.950862\pi\)
0.627213 + 0.778848i \(0.284195\pi\)
\(132\) 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 \(-0.883857\pi\)
−0.776110 0.630598i \(-0.782810\pi\)
\(140\) 4.14841 3.74970i 0.350604 0.316907i
\(141\) 0 0
\(142\) −3.26140 + 1.25553i −0.273690 + 0.105362i
\(143\) 1.37454 0.114945
\(144\) 0 0
\(145\) 0.785654 0.0652450
\(146\) −0.943333 + 0.363152i −0.0780708 + 0.0300547i
\(147\) 0 0
\(148\) 6.26442 5.66234i 0.514932 0.465441i
\(149\) 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 −0.319040 0.947741i \(-0.603360\pi\)
0.661248 + 0.750167i \(0.270027\pi\)
\(152\) −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 \(-0.131878\pi\)
\(158\) 2.21045 2.73504i 0.175854 0.217588i
\(159\) 0 0
\(160\) −4.02014 + 15.2969i −0.317820 + 1.20932i
\(161\) 6.57868i 0.518473i
\(162\) 0 0
\(163\) 16.5798i 1.29863i 0.760518 + 0.649317i \(0.224945\pi\)
−0.760518 + 0.649317i \(0.775055\pi\)
\(164\) 1.45589 0.312384i 0.113686 0.0243931i
\(165\) 0 0
\(166\) 9.02081 + 7.29057i 0.700150 + 0.565858i
\(167\) −3.38550 + 5.86386i −0.261978 + 0.453759i −0.966768 0.255657i \(-0.917708\pi\)
0.704789 + 0.709417i \(0.251042\pi\)
\(168\) 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
\(176\) −1.02844 + 0.462635i −0.0775217 + 0.0348724i
\(177\) 0 0
\(178\) −0.179973 0.467502i −0.0134895 0.0350408i
\(179\) −6.71304 −0.501756 −0.250878 0.968019i \(-0.580719\pi\)
−0.250878 + 0.968019i \(0.580719\pi\)
\(180\) 0 0
\(181\) 10.5763 0.786129 0.393065 0.919511i \(-0.371415\pi\)
0.393065 + 0.919511i \(0.371415\pi\)
\(182\) −2.47713 6.43467i −0.183617 0.476970i
\(183\) 0 0
\(184\) 10.1792 + 15.5761i 0.750421 + 1.14829i
\(185\) 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 0.645316 0.763915i \(-0.276726\pi\)
−0.984228 + 0.176903i \(0.943392\pi\)
\(192\) 0 0
\(193\) −0.439681 + 0.761550i −0.0316489 + 0.0548176i −0.881416 0.472341i \(-0.843409\pi\)
0.849767 + 0.527158i \(0.176743\pi\)
\(194\) 0.305756 + 0.247110i 0.0219520 + 0.0177415i
\(195\) 0 0
\(196\) −0.419581 1.95549i −0.0299701 0.139678i
\(197\) 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 \(-0.994271\pi\)
0.999838 0.0179972i \(-0.00572901\pi\)
\(200\) −7.95660 + 0.439984i −0.562617 + 0.0311116i
\(201\) 0 0
\(202\) 12.5329 15.5072i 0.881810 1.09109i
\(203\) 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 0.113161 0.993577i \(-0.463902\pi\)
−0.803882 + 0.594789i \(0.797236\pi\)
\(212\) 10.8887 + 12.0465i 0.747839 + 0.827358i
\(213\) 0 0
\(214\) −4.96678 + 1.91204i −0.339522 + 0.130705i
\(215\) 20.3958 1.39098
\(216\) 0 0
\(217\) −9.34312 −0.634252
\(218\) −8.07142 + 3.10723i −0.546665 + 0.210448i
\(219\) 0 0
\(220\) −1.05714 1.16955i −0.0712724 0.0788509i
\(221\) −23.9113 13.8052i −1.60845 0.928640i
\(222\) 0 0
\(223\) −11.5096 + 6.64507i −0.770739 + 0.444987i −0.833138 0.553065i \(-0.813458\pi\)
0.0623990 + 0.998051i \(0.480125\pi\)
\(224\) 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 0.971981 0.235061i \(-0.0755291\pi\)
−0.689559 + 0.724229i \(0.742196\pi\)
\(228\) 0 0
\(229\) 5.27466 9.13598i 0.348559 0.603722i −0.637435 0.770505i \(-0.720004\pi\)
0.985994 + 0.166782i \(0.0533377\pi\)
\(230\) −16.3509 + 20.2313i −1.07814 + 1.33401i
\(231\) 0 0
\(232\) 0.0438826 + 0.793565i 0.00288103 + 0.0521001i
\(233\) 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
\(236\) 0.180804 + 0.842650i 0.0117693 + 0.0548518i
\(237\) 0 0
\(238\) −6.22886 5.03413i −0.403757 0.326314i
\(239\) 12.3345 21.3640i 0.797855 1.38193i −0.123155 0.992387i \(-0.539301\pi\)
0.921010 0.389538i \(-0.127365\pi\)
\(240\) 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
\(248\) 22.1214 14.4566i 1.40471 0.917996i
\(249\) 0 0
\(250\) 3.10054 + 8.05406i 0.196096 + 0.509383i
\(251\) 15.0697 0.951191 0.475595 0.879664i \(-0.342233\pi\)
0.475595 + 0.879664i \(0.342233\pi\)
\(252\) 0 0
\(253\) −1.85471 −0.116604
\(254\) 6.39733 + 16.6179i 0.401404 + 1.04270i
\(255\) 0 0
\(256\) −15.6755 3.20622i −0.979717 0.200389i
\(257\) −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 0.679143 0.734006i \(-0.262352\pi\)
−0.975239 + 0.221152i \(0.929018\pi\)
\(264\) 0 0
\(265\) −11.3504 + 19.6595i −0.697250 + 1.20767i
\(266\) −8.13218 6.57238i −0.498616 0.402979i
\(267\) 0 0
\(268\) 4.76721 1.02288i 0.291204 0.0624822i
\(269\) 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 \(0.119903\pi\)
−0.929889 + 0.367841i \(0.880097\pi\)
\(272\) 22.5372 + 2.28123i 1.36652 + 0.138320i
\(273\) 0 0
\(274\) −14.8871 + 18.4202i −0.899361 + 1.11280i
\(275\) 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 0.996978 0.0776854i \(-0.0247530\pi\)
0.431211 + 0.902251i \(0.358086\pi\)
\(284\) 3.66647 3.31408i 0.217565 0.196655i
\(285\) 0 0
\(286\) −1.81411 + 0.698371i −0.107270 + 0.0412955i
\(287\) 0.744513 0.0439472
\(288\) 0 0
\(289\) −15.0705 −0.886503
\(290\) −1.03690 + 0.399172i −0.0608889 + 0.0234402i
\(291\) 0 0
\(292\) 1.06050 0.958572i 0.0620609 0.0560962i
\(293\) −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
\(302\) −4.31638 + 5.34077i −0.248380 + 0.307327i
\(303\) 0 0
\(304\) 29.4238 + 2.97830i 1.68757 + 0.170817i
\(305\) 16.5459i 0.947417i
\(306\) 0 0
\(307\) 2.72302i 0.155411i 0.996976 + 0.0777054i \(0.0247594\pi\)
−0.996976 + 0.0777054i \(0.975241\pi\)
\(308\) −0.551306 + 0.118291i −0.0314136 + 0.00674027i
\(309\) 0 0
\(310\) 28.7328 + 23.2217i 1.63191 + 1.31890i
\(311\) −4.22803 + 7.32317i −0.239750 + 0.415259i −0.960642 0.277788i \(-0.910399\pi\)
0.720893 + 0.693047i \(0.243732\pi\)
\(312\) 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
\(320\) −2.46623 22.2313i −0.137867 1.24277i
\(321\) 0 0
\(322\) 3.34247 + 8.68251i 0.186269 + 0.483857i
\(323\) −41.8702 −2.32972
\(324\) 0 0
\(325\) −13.7362 −0.761946
\(326\) −8.42384 21.8820i −0.466553 1.21193i
\(327\) 0 0
\(328\) −1.76276 + 1.15199i −0.0973322 + 0.0636078i
\(329\) 4.48642 + 2.59024i 0.247344 + 0.142804i
\(330\) 0 0
\(331\) −24.6873 + 14.2532i −1.35694 + 0.783427i −0.989210 0.146506i \(-0.953197\pi\)
−0.367727 + 0.929934i \(0.619864\pi\)
\(332\) −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 \(0.127331\pi\)
\(338\) 11.8467 + 9.57440i 0.644373 + 0.520779i
\(339\) 0 0
\(340\) 6.64354 + 30.9628i 0.360297 + 1.67919i
\(341\) 2.63408i 0.142643i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 1.13920 + 20.6012i 0.0614218 + 1.11074i
\(345\) 0 0
\(346\) −8.60285 + 10.6445i −0.462492 + 0.572253i
\(347\) 14.9377 25.8728i 0.801895 1.38892i −0.116472 0.993194i \(-0.537159\pi\)
0.918367 0.395729i \(-0.129508\pi\)
\(348\) 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
\(356\) 0.475054 + 0.525567i 0.0251778 + 0.0278550i
\(357\) 0 0
\(358\) 8.85983 3.41074i 0.468257 0.180263i
\(359\) −18.8963 −0.997310 −0.498655 0.866801i \(-0.666172\pi\)
−0.498655 + 0.866801i \(0.666172\pi\)
\(360\) 0 0
\(361\) −35.6642 −1.87706
\(362\) −13.9585 + 5.37357i −0.733644 + 0.282428i
\(363\) 0 0
\(364\) 6.53862 + 7.23387i 0.342717 + 0.379158i
\(365\) 1.73069 + 0.999216i 0.0905886 + 0.0523014i
\(366\) 0 0
\(367\) 4.63257 2.67462i 0.241818 0.139614i −0.374194 0.927351i \(-0.622081\pi\)
0.616012 + 0.787737i \(0.288747\pi\)
\(368\) −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 \(0.293838\pi\)
\(374\) −1.41926 + 1.75608i −0.0733880 + 0.0908048i
\(375\) 0 0
\(376\) −14.6302 + 0.809023i −0.754497 + 0.0417222i
\(377\) 1.37000i 0.0705586i
\(378\) 0 0
\(379\) 3.97151i 0.204003i −0.994784 0.102001i \(-0.967475\pi\)
0.994784 0.102001i \(-0.0325246\pi\)
\(380\) 8.67358 + 40.4239i 0.444945 + 2.07370i
\(381\) 0 0
\(382\) 10.3036 + 8.32731i 0.527178 + 0.426062i
\(383\) −10.0601 + 17.4246i −0.514047 + 0.890355i 0.485821 + 0.874059i \(0.338521\pi\)
−0.999867 + 0.0162963i \(0.994812\pi\)
\(384\) 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
\(392\) 1.54730 + 2.36767i 0.0781505 + 0.119585i
\(393\) 0 0
\(394\) 7.35232 + 19.0986i 0.370404 + 0.962173i
\(395\) −6.95247 −0.349817
\(396\) 0 0
\(397\) 26.7209 1.34108 0.670541 0.741873i \(-0.266062\pi\)
0.670541 + 0.741873i \(0.266062\pi\)
\(398\) 0.257983 + 0.670145i 0.0129315 + 0.0335913i
\(399\) 0 0
\(400\) 10.2775 4.62326i 0.513877 0.231163i
\(401\) −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 \(0.285572\pi\)
\(410\) −2.28959 1.85044i −0.113075 0.0913865i
\(411\) 0 0
\(412\) 21.1029 4.52796i 1.03967 0.223076i
\(413\) 0.430914i 0.0212039i
\(414\) 0 0
\(415\) 22.9309i 1.12563i
\(416\) −26.6743 7.01021i −1.30781 0.343704i
\(417\) 0 0
\(418\) −1.85293 + 2.29268i −0.0906298 + 0.112139i
\(419\) 15.0986 26.1515i 0.737614 1.27759i −0.215953 0.976404i \(-0.569286\pi\)
0.953567 0.301181i \(-0.0973810\pi\)
\(420\) 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
\(428\) 5.58366 5.04701i 0.269896 0.243956i
\(429\) 0 0
\(430\) −26.9183 + 10.3626i −1.29811 + 0.499731i
\(431\) 26.8450 1.29308 0.646538 0.762882i \(-0.276216\pi\)
0.646538 + 0.762882i \(0.276216\pi\)
\(432\) 0 0
\(433\) 16.4401 0.790063 0.395031 0.918668i \(-0.370734\pi\)
0.395031 + 0.918668i \(0.370734\pi\)
\(434\) 12.3310 4.74702i 0.591907 0.227864i
\(435\) 0 0
\(436\) 9.07390 8.20180i 0.434561 0.392795i
\(437\) 42.1232 + 24.3198i 2.01502 + 1.16337i
\(438\) 0 0
\(439\) 10.2179 5.89931i 0.487674 0.281559i −0.235935 0.971769i \(-0.575815\pi\)
0.723609 + 0.690210i \(0.242482\pi\)
\(440\) 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 0.596292 0.802768i \(-0.296640\pi\)
−0.993363 + 0.115020i \(0.963307\pi\)
\(444\) 0 0
\(445\) −0.495197 + 0.857706i −0.0234746 + 0.0406592i
\(446\) 11.8141 14.6179i 0.559414 0.692177i
\(447\) 0 0
\(448\) −7.32700 3.21172i −0.346168 0.151739i
\(449\) 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
\(452\) −4.01408 + 0.861283i −0.188807 + 0.0405114i
\(453\) 0 0
\(454\) −9.36042 7.56504i −0.439306 0.355045i
\(455\) −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 0.0936592 0.995604i \(-0.470144\pi\)
−0.815389 + 0.578913i \(0.803477\pi\)
\(464\) −0.461108 1.02505i −0.0214064 0.0475866i
\(465\) 0 0
\(466\) 1.29055 + 3.35236i 0.0597834 + 0.155295i
\(467\) −24.3536 −1.12695 −0.563474 0.826134i \(-0.690536\pi\)
−0.563474 + 0.826134i \(0.690536\pi\)
\(468\) 0 0
\(469\) 2.43786 0.112570
\(470\) −7.35918 19.1164i −0.339454 0.881774i
\(471\) 0 0
\(472\) −0.666754 1.02026i −0.0306899 0.0469614i
\(473\) −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 0.993662 0.112406i \(-0.0358557\pi\)
−0.594177 + 0.804334i \(0.702522\pi\)
\(480\) 0 0
\(481\) −10.2925 + 17.8271i −0.469297 + 0.812846i
\(482\) 16.1342 + 13.0396i 0.734892 + 0.593936i
\(483\) 0 0
\(484\) −4.58204 21.3550i −0.208275 0.970681i
\(485\) 0.777231i 0.0352922i
\(486\) 0 0
\(487\) 5.76620i 0.261291i 0.991429 + 0.130646i \(0.0417050\pi\)
−0.991429 + 0.130646i \(0.958295\pi\)
\(488\) −16.7125 + 0.924170i −0.756541 + 0.0418352i
\(489\) 0 0
\(490\) −2.48543 + 3.07529i −0.112280 + 0.138927i
\(491\) −16.6911 + 28.9099i −0.753261 + 1.30469i 0.192973 + 0.981204i \(0.438187\pi\)
−0.946234 + 0.323482i \(0.895146\pi\)
\(492\) 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 \(-0.970359\pi\)
−0.578362 0.815780i \(-0.696308\pi\)
\(500\) −8.18416 9.05439i −0.366007 0.404925i
\(501\) 0 0
\(502\) −19.8889 + 7.65656i −0.887685 + 0.341729i
\(503\) −16.0809 −0.717012 −0.358506 0.933528i \(-0.616714\pi\)
−0.358506 + 0.933528i \(0.616714\pi\)
\(504\) 0 0
\(505\) −39.4194 −1.75414
\(506\) 2.44783 0.942333i 0.108819 0.0418918i
\(507\) 0 0
\(508\) −16.8863 18.6818i −0.749209 0.828873i
\(509\) −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
\(518\) −3.75319 + 4.64392i −0.164906 + 0.204042i
\(519\) 0 0
\(520\) −2.12884 38.4975i −0.0933557 1.68823i
\(521\) 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 \(-0.914457\pi\)
0.964106 0.265518i \(-0.0855430\pi\)
\(524\) 3.46627 + 16.1548i 0.151425 + 0.705728i
\(525\) 0 0
\(526\) 10.5632 + 8.53715i 0.460579 + 0.372237i
\(527\) 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
\(536\) −5.77203 + 3.77210i −0.249314 + 0.162930i
\(537\) 0 0
\(538\) 10.6863 + 27.7591i 0.460720 + 1.19678i
\(539\) −0.281927 −0.0121434
\(540\) 0 0
\(541\) −22.5265 −0.968490 −0.484245 0.874933i \(-0.660906\pi\)
−0.484245 + 0.874933i \(0.660906\pi\)
\(542\) −6.15325 15.9838i −0.264305 0.686565i
\(543\) 0 0
\(544\) −30.9035 + 8.43987i −1.32498 + 0.361856i
\(545\) 14.8083 + 8.54957i 0.634317 + 0.366223i
\(546\) 0 0
\(547\) 7.89651 4.55905i 0.337631 0.194931i −0.321593 0.946878i \(-0.604218\pi\)
0.659224 + 0.751947i \(0.270885\pi\)
\(548\) 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
\(554\) −3.01872 2.43972i −0.128253 0.103654i
\(555\) 0 0
\(556\) −45.5302 + 9.76921i −1.93091 + 0.414307i
\(557\) 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
\(560\) 1.12628 11.1270i 0.0475941 0.470201i
\(561\) 0 0
\(562\) 5.35637 6.62757i 0.225945 0.279567i
\(563\) 9.48276 16.4246i 0.399651 0.692216i −0.594032 0.804441i \(-0.702465\pi\)
0.993683 + 0.112226i \(0.0357980\pi\)
\(564\) 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 0.284197 0.958766i \(-0.408273\pi\)
−0.688217 + 0.725505i \(0.741606\pi\)
\(572\) 2.03942 1.84341i 0.0852726 0.0770769i
\(573\) 0 0
\(574\) −0.982605 + 0.378270i −0.0410131 + 0.0157887i
\(575\) 18.5346 0.772948
\(576\) 0 0
\(577\) 26.0394 1.08404 0.542018 0.840367i \(-0.317660\pi\)
0.542018 + 0.840367i \(0.317660\pi\)
\(578\) 19.8900 7.65700i 0.827316 0.318489i
\(579\) 0 0
\(580\) 1.16569 1.05365i 0.0484025 0.0437505i
\(581\) −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 0.832530 0.553981i \(-0.186892\pi\)
−0.896026 + 0.444001i \(0.853559\pi\)
\(588\) 0 0
\(589\) 34.5393 59.8238i 1.42317 2.46500i
\(590\) 1.07101 1.32519i 0.0440927 0.0545570i
\(591\) 0 0
\(592\) 1.70077 16.8026i 0.0699013 0.690582i
\(593\) 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
\(596\) 22.4948 4.82660i 0.921422 0.197705i
\(597\) 0 0
\(598\) −35.2788 28.5122i −1.44266 1.16595i
\(599\) −16.0003 + 27.7133i −0.653753 + 1.13233i 0.328452 + 0.944521i \(0.393473\pi\)
−0.982205 + 0.187812i \(0.939860\pi\)
\(600\) 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 0.546509 0.837453i \(-0.315956\pi\)
−0.452001 + 0.892017i \(0.649290\pi\)
\(608\) −40.3465 + 11.0188i −1.63627 + 0.446871i
\(609\) 0 0
\(610\) −8.40660 21.8372i −0.340373 0.884163i
\(611\) −25.2574 −1.02181
\(612\) 0 0
\(613\) 41.2533 1.66621 0.833103 0.553117i \(-0.186562\pi\)
0.833103 + 0.553117i \(0.186562\pi\)
\(614\) −1.38350 3.59383i −0.0558336 0.145035i
\(615\) 0 0
\(616\) 0.667509 0.436226i 0.0268947 0.0175760i
\(617\) −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 −0.327786 0.944752i \(-0.606302\pi\)
0.654286 + 0.756247i \(0.272969\pi\)
\(620\) −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
\(626\) 30.5062 + 24.6549i 1.21927 + 0.985409i
\(627\) 0 0
\(628\) −8.47821 39.5134i −0.338318 1.57676i
\(629\) 23.9102i 0.953362i
\(630\) 0 0
\(631\) 17.3945i 0.692463i −0.938149 0.346232i \(-0.887461\pi\)
0.938149 0.346232i \(-0.112539\pi\)
\(632\) −0.388330 7.02248i −0.0154469 0.279339i
\(633\) 0 0
\(634\) −21.2680 + 26.3154i −0.844660 + 1.04512i
\(635\) 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 0.243142 0.969991i \(-0.421822\pi\)
−0.718465 + 0.695563i \(0.755155\pi\)
\(644\) −8.82276 9.76089i −0.347665 0.384633i
\(645\) 0 0
\(646\) 55.2600 21.2733i 2.17418 0.836986i
\(647\) −20.5491 −0.807868 −0.403934 0.914788i \(-0.632357\pi\)
−0.403934 + 0.914788i \(0.632357\pi\)
\(648\) 0 0
\(649\) 0.121486 0.00476875
\(650\) 18.1289 6.97903i 0.711075 0.273740i
\(651\) 0 0
\(652\) 22.2355 + 24.5998i 0.870808 + 0.963402i
\(653\) 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 \(0.00922889\pi\)
−0.474684 + 0.880156i \(0.657438\pi\)
\(660\) 0 0
\(661\) −15.9921 + 27.6992i −0.622022 + 1.07737i 0.367087 + 0.930187i \(0.380355\pi\)
−0.989109 + 0.147186i \(0.952978\pi\)
\(662\) 25.3404 31.3544i 0.984884 1.21862i
\(663\) 0 0
\(664\) 23.1618 1.28080i 0.898852 0.0497048i
\(665\) 20.6720i 0.801625i
\(666\) 0 0
\(667\) 1.84858i 0.0715775i
\(668\) 2.84099 + 13.2407i 0.109921 + 0.512296i
\(669\) 0 0
\(670\) −7.49711 6.05912i −0.289638 0.234084i
\(671\) 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
\(680\) −24.4996 37.4891i −0.939516 1.43764i
\(681\) 0 0
\(682\) −1.33831 3.47644i −0.0512467 0.133120i
\(683\) 5.18082 0.198238 0.0991192 0.995076i \(-0.468397\pi\)
0.0991192 + 0.995076i \(0.468397\pi\)
\(684\) 0 0
\(685\) 46.8241 1.78906
\(686\) 0.508077 + 1.31979i 0.0193985 + 0.0503900i
\(687\) 0 0
\(688\) −11.9705 26.6105i −0.456371 1.01452i
\(689\) −34.2816 19.7925i −1.30603 0.754034i
\(690\) 0 0
\(691\) −13.4870 + 7.78675i −0.513071 + 0.296222i −0.734095 0.679047i \(-0.762393\pi\)
0.221024 + 0.975268i \(0.429060\pi\)
\(692\) 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
\(698\) 20.7497 + 16.7698i 0.785388 + 0.634746i
\(699\) 0 0
\(700\) 5.50937 1.18212i 0.208235 0.0446799i
\(701\) 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
\(704\) −0.905469 + 2.06568i −0.0341261 + 0.0778531i
\(705\) 0 0
\(706\) 27.2559 33.7245i 1.02579 1.26924i
\(707\) −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
\(716\) −9.96024 + 9.00295i −0.372232 + 0.336456i
\(717\) 0 0
\(718\) 24.9393 9.60078i 0.930725 0.358298i
\(719\) 11.4166 0.425766 0.212883 0.977078i \(-0.431715\pi\)
0.212883 + 0.977078i \(0.431715\pi\)
\(720\) 0 0
\(721\) 10.7916 0.401901
\(722\) 47.0695 18.1202i 1.75174 0.674363i
\(723\) 0 0
\(724\) 15.6922 14.1840i 0.583196 0.527144i
\(725\) 0.685609 + 0.395837i 0.0254629 + 0.0147010i
\(726\) 0 0
\(727\) 11.2371 6.48771i 0.416759 0.240616i −0.276931 0.960890i \(-0.589317\pi\)
0.693690 + 0.720274i \(0.255984\pi\)
\(728\) −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 \(0.316693\pi\)
\(734\) −4.75514 + 5.88365i −0.175515 + 0.217170i
\(735\) 0 0
\(736\) 35.9924 + 9.45909i 1.32670 + 0.348667i
\(737\) 0.687297i 0.0253169i
\(738\) 0 0
\(739\) 42.1439i 1.55029i −0.631785 0.775144i \(-0.717678\pi\)
0.631785 0.775144i \(-0.282322\pi\)
\(740\) 23.0843 4.95309i 0.848596 0.182079i
\(741\) 0 0
\(742\) −8.93029 7.21741i −0.327841 0.264960i
\(743\) 0.0854917 0.148076i 0.00313639 0.00543238i −0.864453 0.502714i \(-0.832335\pi\)
0.867589 + 0.497281i \(0.165668\pi\)
\(744\) 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 0.683587 0.729869i \(-0.260419\pi\)
−0.290292 + 0.956938i \(0.593752\pi\)
\(752\) 18.8979 8.50103i 0.689134 0.310001i
\(753\) 0 0
\(754\) −0.696066 1.80812i −0.0253492 0.0658478i
\(755\) 13.5762 0.494090
\(756\) 0 0
\(757\) 34.3261 1.24760 0.623801 0.781583i \(-0.285587\pi\)
0.623801 + 0.781583i \(0.285587\pi\)
\(758\) 2.01783 + 5.24158i 0.0732910 + 0.190383i
\(759\) 0 0
\(760\) −31.9858 48.9444i −1.16025 1.77540i
\(761\) 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 \(0.217350\pi\)
\(770\) 0.867006 + 0.700710i 0.0312447 + 0.0252518i
\(771\) 0 0
\(772\) 0.368964 + 1.71959i 0.0132793 + 0.0618893i
\(773\) 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
\(776\) 0.785058 0.0434121i 0.0281819 0.00155840i
\(777\) 0 0
\(778\) −31.7180 + 39.2455i −1.13715 + 1.40702i
\(779\) −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 0.638106 0.769949i \(-0.279718\pi\)
−0.347742 + 0.937590i \(0.613052\pi\)
\(788\) −19.4071 21.4707i −0.691349 0.764861i
\(789\) 0 0
\(790\)