Properties

Label 378.2.g.h.109.2
Level $378$
Weight $2$
Character 378.109
Analytic conductor $3.018$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
Defining polynomial: \(x^{4} + 7 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.2
Root \(1.32288 + 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.2.g.h.163.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} +2.64575 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.822876 + 1.42526i) q^{5} +2.64575 q^{7} -1.00000 q^{8} +(-0.822876 + 1.42526i) q^{10} +(-0.822876 + 1.42526i) q^{11} +0.645751 q^{13} +(1.32288 + 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.822876 + 1.42526i) q^{17} +(-1.00000 - 1.73205i) q^{19} -1.64575 q^{20} -1.64575 q^{22} +(4.64575 + 8.04668i) q^{23} +(1.14575 - 1.98450i) q^{25} +(0.322876 + 0.559237i) q^{26} +(-1.32288 + 2.29129i) q^{28} -7.64575 q^{29} +(-0.322876 + 0.559237i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.64575 q^{34} +(2.17712 + 3.77089i) q^{35} +(-1.96863 - 3.40976i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.822876 - 1.42526i) q^{40} +4.93725 q^{41} +5.00000 q^{43} +(-0.822876 - 1.42526i) q^{44} +(-4.64575 + 8.04668i) q^{46} +(-5.46863 - 9.47194i) q^{47} +7.00000 q^{49} +2.29150 q^{50} +(-0.322876 + 0.559237i) q^{52} +(3.00000 - 5.19615i) q^{53} -2.70850 q^{55} -2.64575 q^{56} +(-3.82288 - 6.62141i) q^{58} +(6.82288 - 11.8176i) q^{59} +(-6.32288 - 10.9515i) q^{61} -0.645751 q^{62} +1.00000 q^{64} +(0.531373 + 0.920365i) q^{65} +(-4.14575 + 7.18065i) q^{67} +(-0.822876 - 1.42526i) q^{68} +(-2.17712 + 3.77089i) q^{70} -10.3542 q^{71} +(5.29150 - 9.16515i) q^{73} +(1.96863 - 3.40976i) q^{74} +2.00000 q^{76} +(-2.17712 + 3.77089i) q^{77} +(7.61438 + 13.1885i) q^{79} +(0.822876 - 1.42526i) q^{80} +(2.46863 + 4.27579i) q^{82} +2.70850 q^{83} -2.70850 q^{85} +(2.50000 + 4.33013i) q^{86} +(0.822876 - 1.42526i) q^{88} +(-5.46863 - 9.47194i) q^{89} +1.70850 q^{91} -9.29150 q^{92} +(5.46863 - 9.47194i) q^{94} +(1.64575 - 2.85052i) q^{95} -7.58301 q^{97} +(3.50000 + 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} + 2 q^{10} + 2 q^{11} - 8 q^{13} - 2 q^{16} + 2 q^{17} - 4 q^{19} + 4 q^{20} + 4 q^{22} + 8 q^{23} - 6 q^{25} - 4 q^{26} - 20 q^{29} + 4 q^{31} + 2 q^{32} + 4 q^{34} + 14 q^{35} + 8 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} + 20 q^{43} + 2 q^{44} - 8 q^{46} - 6 q^{47} + 28 q^{49} - 12 q^{50} + 4 q^{52} + 12 q^{53} - 32 q^{55} - 10 q^{58} + 22 q^{59} - 20 q^{61} + 8 q^{62} + 4 q^{64} + 18 q^{65} - 6 q^{67} + 2 q^{68} - 14 q^{70} - 52 q^{71} - 8 q^{74} + 8 q^{76} - 14 q^{77} + 4 q^{79} - 2 q^{80} - 6 q^{82} + 32 q^{83} - 32 q^{85} + 10 q^{86} - 2 q^{88} - 6 q^{89} + 28 q^{91} - 16 q^{92} + 6 q^{94} - 4 q^{95} + 12 q^{97} + 14 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.822876 + 1.42526i 0.368001 + 0.637397i 0.989253 0.146214i \(-0.0467089\pi\)
−0.621252 + 0.783611i \(0.713376\pi\)
\(6\) 0 0
\(7\) 2.64575 1.00000
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.822876 + 1.42526i −0.260216 + 0.450708i
\(11\) −0.822876 + 1.42526i −0.248106 + 0.429733i −0.963000 0.269500i \(-0.913142\pi\)
0.714894 + 0.699233i \(0.246475\pi\)
\(12\) 0 0
\(13\) 0.645751 0.179099 0.0895496 0.995982i \(-0.471457\pi\)
0.0895496 + 0.995982i \(0.471457\pi\)
\(14\) 1.32288 + 2.29129i 0.353553 + 0.612372i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.822876 + 1.42526i −0.199577 + 0.345677i −0.948391 0.317103i \(-0.897290\pi\)
0.748815 + 0.662780i \(0.230623\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) −1.64575 −0.368001
\(21\) 0 0
\(22\) −1.64575 −0.350875
\(23\) 4.64575 + 8.04668i 0.968706 + 1.67785i 0.699310 + 0.714819i \(0.253491\pi\)
0.269396 + 0.963029i \(0.413176\pi\)
\(24\) 0 0
\(25\) 1.14575 1.98450i 0.229150 0.396900i
\(26\) 0.322876 + 0.559237i 0.0633211 + 0.109675i
\(27\) 0 0
\(28\) −1.32288 + 2.29129i −0.250000 + 0.433013i
\(29\) −7.64575 −1.41978 −0.709890 0.704312i \(-0.751255\pi\)
−0.709890 + 0.704312i \(0.751255\pi\)
\(30\) 0 0
\(31\) −0.322876 + 0.559237i −0.0579902 + 0.100442i −0.893563 0.448938i \(-0.851803\pi\)
0.835573 + 0.549380i \(0.185136\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.64575 −0.282244
\(35\) 2.17712 + 3.77089i 0.368001 + 0.637397i
\(36\) 0 0
\(37\) −1.96863 3.40976i −0.323640 0.560561i 0.657596 0.753371i \(-0.271573\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) 0 0
\(40\) −0.822876 1.42526i −0.130108 0.225354i
\(41\) 4.93725 0.771070 0.385535 0.922693i \(-0.374017\pi\)
0.385535 + 0.922693i \(0.374017\pi\)
\(42\) 0 0
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) −0.822876 1.42526i −0.124053 0.214866i
\(45\) 0 0
\(46\) −4.64575 + 8.04668i −0.684979 + 1.18642i
\(47\) −5.46863 9.47194i −0.797681 1.38162i −0.921123 0.389273i \(-0.872726\pi\)
0.123441 0.992352i \(-0.460607\pi\)
\(48\) 0 0
\(49\) 7.00000 1.00000
\(50\) 2.29150 0.324067
\(51\) 0 0
\(52\) −0.322876 + 0.559237i −0.0447748 + 0.0775522i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) −2.70850 −0.365214
\(56\) −2.64575 −0.353553
\(57\) 0 0
\(58\) −3.82288 6.62141i −0.501968 0.869434i
\(59\) 6.82288 11.8176i 0.888263 1.53852i 0.0463350 0.998926i \(-0.485246\pi\)
0.841928 0.539590i \(-0.181421\pi\)
\(60\) 0 0
\(61\) −6.32288 10.9515i −0.809561 1.40220i −0.913168 0.407583i \(-0.866372\pi\)
0.103607 0.994618i \(-0.466962\pi\)
\(62\) −0.645751 −0.0820105
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.531373 + 0.920365i 0.0659087 + 0.114157i
\(66\) 0 0
\(67\) −4.14575 + 7.18065i −0.506484 + 0.877256i 0.493488 + 0.869753i \(0.335722\pi\)
−0.999972 + 0.00750349i \(0.997612\pi\)
\(68\) −0.822876 1.42526i −0.0997883 0.172838i
\(69\) 0 0
\(70\) −2.17712 + 3.77089i −0.260216 + 0.450708i
\(71\) −10.3542 −1.22882 −0.614412 0.788986i \(-0.710607\pi\)
−0.614412 + 0.788986i \(0.710607\pi\)
\(72\) 0 0
\(73\) 5.29150 9.16515i 0.619324 1.07270i −0.370286 0.928918i \(-0.620740\pi\)
0.989609 0.143782i \(-0.0459264\pi\)
\(74\) 1.96863 3.40976i 0.228848 0.396377i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) −2.17712 + 3.77089i −0.248106 + 0.429733i
\(78\) 0 0
\(79\) 7.61438 + 13.1885i 0.856684 + 1.48382i 0.875073 + 0.483990i \(0.160813\pi\)
−0.0183890 + 0.999831i \(0.505854\pi\)
\(80\) 0.822876 1.42526i 0.0920003 0.159349i
\(81\) 0 0
\(82\) 2.46863 + 4.27579i 0.272614 + 0.472182i
\(83\) 2.70850 0.297296 0.148648 0.988890i \(-0.452508\pi\)
0.148648 + 0.988890i \(0.452508\pi\)
\(84\) 0 0
\(85\) −2.70850 −0.293778
\(86\) 2.50000 + 4.33013i 0.269582 + 0.466930i
\(87\) 0 0
\(88\) 0.822876 1.42526i 0.0877188 0.151933i
\(89\) −5.46863 9.47194i −0.579673 1.00402i −0.995517 0.0945873i \(-0.969847\pi\)
0.415843 0.909436i \(-0.363486\pi\)
\(90\) 0 0
\(91\) 1.70850 0.179099
\(92\) −9.29150 −0.968706
\(93\) 0 0
\(94\) 5.46863 9.47194i 0.564046 0.976956i
\(95\) 1.64575 2.85052i 0.168851 0.292458i
\(96\) 0 0
\(97\) −7.58301 −0.769938 −0.384969 0.922930i \(-0.625788\pi\)
−0.384969 + 0.922930i \(0.625788\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) 0 0
\(100\) 1.14575 + 1.98450i 0.114575 + 0.198450i
\(101\) 6.82288 11.8176i 0.678902 1.17589i −0.296411 0.955061i \(-0.595790\pi\)
0.975312 0.220831i \(-0.0708770\pi\)
\(102\) 0 0
\(103\) 5.96863 + 10.3380i 0.588106 + 1.01863i 0.994480 + 0.104923i \(0.0334597\pi\)
−0.406374 + 0.913707i \(0.633207\pi\)
\(104\) −0.645751 −0.0633211
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 0 0
\(109\) 4.32288 7.48744i 0.414056 0.717167i −0.581272 0.813709i \(-0.697445\pi\)
0.995329 + 0.0965423i \(0.0307783\pi\)
\(110\) −1.35425 2.34563i −0.129123 0.223647i
\(111\) 0 0
\(112\) −1.32288 2.29129i −0.125000 0.216506i
\(113\) −7.64575 −0.719252 −0.359626 0.933097i \(-0.617096\pi\)
−0.359626 + 0.933097i \(0.617096\pi\)
\(114\) 0 0
\(115\) −7.64575 + 13.2428i −0.712970 + 1.23490i
\(116\) 3.82288 6.62141i 0.354945 0.614783i
\(117\) 0 0
\(118\) 13.6458 1.25619
\(119\) −2.17712 + 3.77089i −0.199577 + 0.345677i
\(120\) 0 0
\(121\) 4.14575 + 7.18065i 0.376886 + 0.652787i
\(122\) 6.32288 10.9515i 0.572446 0.991506i
\(123\) 0 0
\(124\) −0.322876 0.559237i −0.0289951 0.0502210i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 6.64575 0.589715 0.294858 0.955541i \(-0.404728\pi\)
0.294858 + 0.955541i \(0.404728\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.531373 + 0.920365i −0.0466045 + 0.0807214i
\(131\) 3.29150 + 5.70105i 0.287580 + 0.498103i 0.973232 0.229827i \(-0.0738160\pi\)
−0.685652 + 0.727930i \(0.740483\pi\)
\(132\) 0 0
\(133\) −2.64575 4.58258i −0.229416 0.397360i
\(134\) −8.29150 −0.716277
\(135\) 0 0
\(136\) 0.822876 1.42526i 0.0705610 0.122215i
\(137\) −4.64575 + 8.04668i −0.396913 + 0.687474i −0.993343 0.115191i \(-0.963252\pi\)
0.596430 + 0.802665i \(0.296585\pi\)
\(138\) 0 0
\(139\) −19.5830 −1.66101 −0.830504 0.557012i \(-0.811948\pi\)
−0.830504 + 0.557012i \(0.811948\pi\)
\(140\) −4.35425 −0.368001
\(141\) 0 0
\(142\) −5.17712 8.96704i −0.434455 0.752497i
\(143\) −0.531373 + 0.920365i −0.0444356 + 0.0769648i
\(144\) 0 0
\(145\) −6.29150 10.8972i −0.522481 0.904963i
\(146\) 10.5830 0.875856
\(147\) 0 0
\(148\) 3.93725 0.323640
\(149\) 3.53137 + 6.11652i 0.289301 + 0.501085i 0.973643 0.228077i \(-0.0732437\pi\)
−0.684342 + 0.729161i \(0.739910\pi\)
\(150\) 0 0
\(151\) −3.61438 + 6.26029i −0.294134 + 0.509455i −0.974783 0.223155i \(-0.928365\pi\)
0.680649 + 0.732610i \(0.261698\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) 0 0
\(154\) −4.35425 −0.350875
\(155\) −1.06275 −0.0853618
\(156\) 0 0
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) −7.61438 + 13.1885i −0.605767 + 1.04922i
\(159\) 0 0
\(160\) 1.64575 0.130108
\(161\) 12.2915 + 21.2895i 0.968706 + 1.67785i
\(162\) 0 0
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) −2.46863 + 4.27579i −0.192767 + 0.333883i
\(165\) 0 0
\(166\) 1.35425 + 2.34563i 0.105110 + 0.182056i
\(167\) −12.5830 −0.973702 −0.486851 0.873485i \(-0.661855\pi\)
−0.486851 + 0.873485i \(0.661855\pi\)
\(168\) 0 0
\(169\) −12.5830 −0.967923
\(170\) −1.35425 2.34563i −0.103866 0.179901i
\(171\) 0 0
\(172\) −2.50000 + 4.33013i −0.190623 + 0.330169i
\(173\) 3.29150 + 5.70105i 0.250248 + 0.433443i 0.963594 0.267369i \(-0.0861544\pi\)
−0.713346 + 0.700812i \(0.752821\pi\)
\(174\) 0 0
\(175\) 3.03137 5.25049i 0.229150 0.396900i
\(176\) 1.64575 0.124053
\(177\) 0 0
\(178\) 5.46863 9.47194i 0.409891 0.709952i
\(179\) 0.531373 0.920365i 0.0397167 0.0687913i −0.845484 0.534001i \(-0.820688\pi\)
0.885200 + 0.465210i \(0.154021\pi\)
\(180\) 0 0
\(181\) −13.2915 −0.987950 −0.493975 0.869476i \(-0.664457\pi\)
−0.493975 + 0.869476i \(0.664457\pi\)
\(182\) 0.854249 + 1.47960i 0.0633211 + 0.109675i
\(183\) 0 0
\(184\) −4.64575 8.04668i −0.342489 0.593209i
\(185\) 3.23987 5.61162i 0.238200 0.412575i
\(186\) 0 0
\(187\) −1.35425 2.34563i −0.0990325 0.171529i
\(188\) 10.9373 0.797681
\(189\) 0 0
\(190\) 3.29150 0.238791
\(191\) 13.4059 + 23.2197i 0.970015 + 1.68012i 0.695489 + 0.718537i \(0.255188\pi\)
0.274526 + 0.961580i \(0.411479\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) −3.79150 6.56708i −0.272214 0.471489i
\(195\) 0 0
\(196\) −3.50000 + 6.06218i −0.250000 + 0.433013i
\(197\) −15.2915 −1.08947 −0.544737 0.838607i \(-0.683371\pi\)
−0.544737 + 0.838607i \(0.683371\pi\)
\(198\) 0 0
\(199\) −10.9686 + 18.9982i −0.777545 + 1.34675i 0.155807 + 0.987787i \(0.450202\pi\)
−0.933353 + 0.358961i \(0.883131\pi\)
\(200\) −1.14575 + 1.98450i −0.0810169 + 0.140325i
\(201\) 0 0
\(202\) 13.6458 0.960112
\(203\) −20.2288 −1.41978
\(204\) 0 0
\(205\) 4.06275 + 7.03688i 0.283754 + 0.491477i
\(206\) −5.96863 + 10.3380i −0.415854 + 0.720280i
\(207\) 0 0
\(208\) −0.322876 0.559237i −0.0223874 0.0387761i
\(209\) 3.29150 0.227678
\(210\) 0 0
\(211\) −16.8745 −1.16169 −0.580845 0.814015i \(-0.697278\pi\)
−0.580845 + 0.814015i \(0.697278\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 4.11438 + 7.12631i 0.280598 + 0.486010i
\(216\) 0 0
\(217\) −0.854249 + 1.47960i −0.0579902 + 0.100442i
\(218\) 8.64575 0.585564
\(219\) 0 0
\(220\) 1.35425 2.34563i 0.0913034 0.158142i
\(221\) −0.531373 + 0.920365i −0.0357440 + 0.0619105i
\(222\) 0 0
\(223\) 17.8745 1.19697 0.598483 0.801136i \(-0.295770\pi\)
0.598483 + 0.801136i \(0.295770\pi\)
\(224\) 1.32288 2.29129i 0.0883883 0.153093i
\(225\) 0 0
\(226\) −3.82288 6.62141i −0.254294 0.440450i
\(227\) 3.00000 5.19615i 0.199117 0.344881i −0.749125 0.662428i \(-0.769526\pi\)
0.948242 + 0.317547i \(0.102859\pi\)
\(228\) 0 0
\(229\) 7.32288 + 12.6836i 0.483909 + 0.838155i 0.999829 0.0184814i \(-0.00588315\pi\)
−0.515920 + 0.856637i \(0.672550\pi\)
\(230\) −15.2915 −1.00829
\(231\) 0 0
\(232\) 7.64575 0.501968
\(233\) −4.35425 7.54178i −0.285256 0.494078i 0.687415 0.726265i \(-0.258745\pi\)
−0.972671 + 0.232186i \(0.925412\pi\)
\(234\) 0 0
\(235\) 9.00000 15.5885i 0.587095 1.01688i
\(236\) 6.82288 + 11.8176i 0.444131 + 0.769258i
\(237\) 0 0
\(238\) −4.35425 −0.282244
\(239\) −4.93725 −0.319364 −0.159682 0.987168i \(-0.551047\pi\)
−0.159682 + 0.987168i \(0.551047\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) −4.14575 + 7.18065i −0.266499 + 0.461590i
\(243\) 0 0
\(244\) 12.6458 0.809561
\(245\) 5.76013 + 9.97684i 0.368001 + 0.637397i
\(246\) 0 0
\(247\) −0.645751 1.11847i −0.0410882 0.0711668i
\(248\) 0.322876 0.559237i 0.0205026 0.0355116i
\(249\) 0 0
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 0 0
\(253\) −15.2915 −0.961369
\(254\) 3.32288 + 5.75539i 0.208496 + 0.361125i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.93725 13.7477i −0.495112 0.857560i 0.504872 0.863194i \(-0.331540\pi\)
−0.999984 + 0.00563467i \(0.998206\pi\)
\(258\) 0 0
\(259\) −5.20850 9.02138i −0.323640 0.560561i
\(260\) −1.06275 −0.0659087
\(261\) 0 0
\(262\) −3.29150 + 5.70105i −0.203350 + 0.352212i
\(263\) 5.46863 9.47194i 0.337210 0.584065i −0.646697 0.762747i \(-0.723850\pi\)
0.983907 + 0.178682i \(0.0571834\pi\)
\(264\) 0 0
\(265\) 9.87451 0.606586
\(266\) 2.64575 4.58258i 0.162221 0.280976i
\(267\) 0 0
\(268\) −4.14575 7.18065i −0.253242 0.438628i
\(269\) −13.6458 + 23.6351i −0.831996 + 1.44106i 0.0644567 + 0.997921i \(0.479469\pi\)
−0.896453 + 0.443139i \(0.853865\pi\)
\(270\) 0 0
\(271\) 10.6144 + 18.3846i 0.644778 + 1.11679i 0.984353 + 0.176209i \(0.0563833\pi\)
−0.339575 + 0.940579i \(0.610283\pi\)
\(272\) 1.64575 0.0997883
\(273\) 0 0
\(274\) −9.29150 −0.561320
\(275\) 1.88562 + 3.26599i 0.113707 + 0.196947i
\(276\) 0 0
\(277\) 8.96863 15.5341i 0.538873 0.933355i −0.460093 0.887871i \(-0.652184\pi\)
0.998965 0.0454837i \(-0.0144829\pi\)
\(278\) −9.79150 16.9594i −0.587255 1.01716i
\(279\) 0 0
\(280\) −2.17712 3.77089i −0.130108 0.225354i
\(281\) 17.5203 1.04517 0.522586 0.852587i \(-0.324968\pi\)
0.522586 + 0.852587i \(0.324968\pi\)
\(282\) 0 0
\(283\) −4.14575 + 7.18065i −0.246439 + 0.426845i −0.962535 0.271156i \(-0.912594\pi\)
0.716096 + 0.698002i \(0.245927\pi\)
\(284\) 5.17712 8.96704i 0.307206 0.532096i
\(285\) 0 0
\(286\) −1.06275 −0.0628415
\(287\) 13.0627 0.771070
\(288\) 0 0
\(289\) 7.14575 + 12.3768i 0.420338 + 0.728047i
\(290\) 6.29150 10.8972i 0.369450 0.639906i
\(291\) 0 0
\(292\) 5.29150 + 9.16515i 0.309662 + 0.536350i
\(293\) −22.9373 −1.34001 −0.670004 0.742357i \(-0.733708\pi\)
−0.670004 + 0.742357i \(0.733708\pi\)
\(294\) 0 0
\(295\) 22.4575 1.30753
\(296\) 1.96863 + 3.40976i 0.114424 + 0.198188i
\(297\) 0 0
\(298\) −3.53137 + 6.11652i −0.204567 + 0.354320i
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) 13.2288 0.762493
\(302\) −7.22876 −0.415968
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) 10.4059 18.0235i 0.595839 1.03202i
\(306\) 0 0
\(307\) −13.5830 −0.775223 −0.387612 0.921823i \(-0.626700\pi\)
−0.387612 + 0.921823i \(0.626700\pi\)
\(308\) −2.17712 3.77089i −0.124053 0.214866i
\(309\) 0 0
\(310\) −0.531373 0.920365i −0.0301800 0.0522732i
\(311\) 11.7601 20.3691i 0.666856 1.15503i −0.311923 0.950107i \(-0.600973\pi\)
0.978779 0.204921i \(-0.0656936\pi\)
\(312\) 0 0
\(313\) −11.6458 20.1710i −0.658257 1.14013i −0.981067 0.193670i \(-0.937961\pi\)
0.322810 0.946464i \(-0.395373\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −15.2288 −0.856684
\(317\) −10.4059 18.0235i −0.584452 1.01230i −0.994943 0.100437i \(-0.967976\pi\)
0.410491 0.911865i \(-0.365357\pi\)
\(318\) 0 0
\(319\) 6.29150 10.8972i 0.352257 0.610126i
\(320\) 0.822876 + 1.42526i 0.0460001 + 0.0796746i
\(321\) 0 0
\(322\) −12.2915 + 21.2895i −0.684979 + 1.18642i
\(323\) 3.29150 0.183144
\(324\) 0 0
\(325\) 0.739870 1.28149i 0.0410406 0.0710844i
\(326\) −0.500000 + 0.866025i −0.0276924 + 0.0479647i
\(327\) 0 0
\(328\) −4.93725 −0.272614
\(329\) −14.4686 25.0604i −0.797681 1.38162i
\(330\) 0 0
\(331\) 0.0627461 + 0.108679i 0.00344884 + 0.00597356i 0.867745 0.497010i \(-0.165569\pi\)
−0.864296 + 0.502984i \(0.832236\pi\)
\(332\) −1.35425 + 2.34563i −0.0743241 + 0.128733i
\(333\) 0 0
\(334\) −6.29150 10.8972i −0.344256 0.596268i
\(335\) −13.6458 −0.745547
\(336\) 0 0
\(337\) −9.41699 −0.512976 −0.256488 0.966547i \(-0.582565\pi\)
−0.256488 + 0.966547i \(0.582565\pi\)
\(338\) −6.29150 10.8972i −0.342213 0.592730i
\(339\) 0 0
\(340\) 1.35425 2.34563i 0.0734444 0.127210i
\(341\) −0.531373 0.920365i −0.0287755 0.0498406i
\(342\) 0 0
\(343\) 18.5203 1.00000
\(344\) −5.00000 −0.269582
\(345\) 0 0
\(346\) −3.29150 + 5.70105i −0.176952 + 0.306490i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) 25.2288 1.35046 0.675232 0.737605i \(-0.264043\pi\)
0.675232 + 0.737605i \(0.264043\pi\)
\(350\) 6.06275 0.324067
\(351\) 0 0
\(352\) 0.822876 + 1.42526i 0.0438594 + 0.0759667i
\(353\) −6.00000 + 10.3923i −0.319348 + 0.553127i −0.980352 0.197256i \(-0.936797\pi\)
0.661004 + 0.750382i \(0.270130\pi\)
\(354\) 0 0
\(355\) −8.52026 14.7575i −0.452208 0.783248i
\(356\) 10.9373 0.579673
\(357\) 0 0
\(358\) 1.06275 0.0561679
\(359\) −15.5830 26.9906i −0.822440 1.42451i −0.903860 0.427827i \(-0.859279\pi\)
0.0814209 0.996680i \(-0.474054\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −6.64575 11.5108i −0.349293 0.604993i
\(363\) 0 0
\(364\) −0.854249 + 1.47960i −0.0447748 + 0.0775522i
\(365\) 17.4170 0.911647
\(366\) 0 0
\(367\) 0.937254 1.62337i 0.0489243 0.0847393i −0.840526 0.541771i \(-0.817754\pi\)
0.889450 + 0.457032i \(0.151087\pi\)
\(368\) 4.64575 8.04668i 0.242177 0.419462i
\(369\) 0 0
\(370\) 6.47974 0.336866
\(371\) 7.93725 13.7477i 0.412082 0.713746i
\(372\) 0 0
\(373\) 8.29150 + 14.3613i 0.429318 + 0.743600i 0.996813 0.0797767i \(-0.0254207\pi\)
−0.567495 + 0.823377i \(0.692087\pi\)
\(374\) 1.35425 2.34563i 0.0700265 0.121290i
\(375\) 0 0
\(376\) 5.46863 + 9.47194i 0.282023 + 0.488478i
\(377\) −4.93725 −0.254282
\(378\) 0 0
\(379\) 4.41699 0.226886 0.113443 0.993545i \(-0.463812\pi\)
0.113443 + 0.993545i \(0.463812\pi\)
\(380\) 1.64575 + 2.85052i 0.0844253 + 0.146229i
\(381\) 0 0
\(382\) −13.4059 + 23.2197i −0.685905 + 1.18802i
\(383\) −0.291503 0.504897i −0.0148951 0.0257990i 0.858482 0.512844i \(-0.171408\pi\)
−0.873377 + 0.487045i \(0.838075\pi\)
\(384\) 0 0
\(385\) −7.16601 −0.365214
\(386\) 7.00000 0.356291
\(387\) 0 0
\(388\) 3.79150 6.56708i 0.192484 0.333393i
\(389\) 4.35425 7.54178i 0.220769 0.382383i −0.734273 0.678855i \(-0.762477\pi\)
0.955042 + 0.296471i \(0.0958099\pi\)
\(390\) 0 0
\(391\) −15.2915 −0.773325
\(392\) −7.00000 −0.353553
\(393\) 0 0
\(394\) −7.64575 13.2428i −0.385187 0.667164i
\(395\) −12.5314 + 21.7050i −0.630522 + 1.09210i
\(396\) 0 0
\(397\) 5.67712 + 9.83307i 0.284927 + 0.493508i 0.972591 0.232521i \(-0.0746974\pi\)
−0.687665 + 0.726028i \(0.741364\pi\)
\(398\) −21.9373 −1.09962
\(399\) 0 0
\(400\) −2.29150 −0.114575
\(401\) 13.4059 + 23.2197i 0.669458 + 1.15953i 0.978056 + 0.208342i \(0.0668068\pi\)
−0.308598 + 0.951192i \(0.599860\pi\)
\(402\) 0 0
\(403\) −0.208497 + 0.361128i −0.0103860 + 0.0179891i
\(404\) 6.82288 + 11.8176i 0.339451 + 0.587946i
\(405\) 0 0
\(406\) −10.1144 17.5186i −0.501968 0.869434i
\(407\) 6.47974 0.321189
\(408\) 0 0
\(409\) 8.43725 14.6138i 0.417195 0.722604i −0.578461 0.815710i \(-0.696346\pi\)
0.995656 + 0.0931066i \(0.0296798\pi\)
\(410\) −4.06275 + 7.03688i −0.200645 + 0.347527i
\(411\) 0 0
\(412\) −11.9373 −0.588106
\(413\) 18.0516 31.2663i 0.888263 1.53852i
\(414\) 0 0
\(415\) 2.22876 + 3.86032i 0.109405 + 0.189496i
\(416\) 0.322876 0.559237i 0.0158303 0.0274189i
\(417\) 0 0
\(418\) 1.64575 + 2.85052i 0.0804963 + 0.139424i
\(419\) −13.0627 −0.638157 −0.319078 0.947728i \(-0.603373\pi\)
−0.319078 + 0.947728i \(0.603373\pi\)
\(420\) 0 0
\(421\) −25.2915 −1.23263 −0.616316 0.787499i \(-0.711376\pi\)
−0.616316 + 0.787499i \(0.711376\pi\)
\(422\) −8.43725 14.6138i −0.410719 0.711386i
\(423\) 0 0
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 1.88562 + 3.26599i 0.0914661 + 0.158424i
\(426\) 0 0
\(427\) −16.7288 28.9751i −0.809561 1.40220i
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) −4.11438 + 7.12631i −0.198413 + 0.343661i
\(431\) −4.40588 + 7.63121i −0.212224 + 0.367582i −0.952410 0.304819i \(-0.901404\pi\)
0.740186 + 0.672402i \(0.234737\pi\)
\(432\) 0 0
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) −1.70850 −0.0820105
\(435\) 0 0
\(436\) 4.32288 + 7.48744i 0.207028 + 0.358583i
\(437\) 9.29150 16.0934i 0.444473 0.769850i
\(438\) 0 0
\(439\) 8.58301 + 14.8662i 0.409644 + 0.709525i 0.994850 0.101360i \(-0.0323194\pi\)
−0.585205 + 0.810885i \(0.698986\pi\)
\(440\) 2.70850 0.129123
\(441\) 0 0
\(442\) −1.06275 −0.0505497
\(443\) −4.35425 7.54178i −0.206877 0.358321i 0.743852 0.668344i \(-0.232997\pi\)
−0.950729 + 0.310023i \(0.899663\pi\)
\(444\) 0 0
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) 8.93725 + 15.4798i 0.423191 + 0.732989i
\(447\) 0 0
\(448\) 2.64575 0.125000
\(449\) −7.64575 −0.360825 −0.180413 0.983591i \(-0.557743\pi\)
−0.180413 + 0.983591i \(0.557743\pi\)
\(450\) 0 0
\(451\) −4.06275 + 7.03688i −0.191307 + 0.331354i
\(452\) 3.82288 6.62141i 0.179813 0.311445i
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) 1.40588 + 2.43506i 0.0659087 + 0.114157i
\(456\) 0 0
\(457\) −1.14575 1.98450i −0.0535960 0.0928310i 0.837983 0.545697i \(-0.183735\pi\)
−0.891579 + 0.452866i \(0.850402\pi\)
\(458\) −7.32288 + 12.6836i −0.342176 + 0.592665i
\(459\) 0 0
\(460\) −7.64575 13.2428i −0.356485 0.617450i
\(461\) 2.22876 0.103804 0.0519018 0.998652i \(-0.483472\pi\)
0.0519018 + 0.998652i \(0.483472\pi\)
\(462\) 0 0
\(463\) 29.2915 1.36129 0.680646 0.732613i \(-0.261699\pi\)
0.680646 + 0.732613i \(0.261699\pi\)
\(464\) 3.82288 + 6.62141i 0.177473 + 0.307391i
\(465\) 0 0
\(466\) 4.35425 7.54178i 0.201707 0.349366i
\(467\) −13.1144 22.7148i −0.606861 1.05111i −0.991754 0.128153i \(-0.959095\pi\)
0.384893 0.922961i \(-0.374238\pi\)
\(468\) 0 0
\(469\) −10.9686 + 18.9982i −0.506484 + 0.877256i
\(470\) 18.0000 0.830278
\(471\) 0 0
\(472\) −6.82288 + 11.8176i −0.314048 + 0.543948i
\(473\) −4.11438 + 7.12631i −0.189179 + 0.327668i
\(474\) 0 0
\(475\) −4.58301 −0.210283
\(476\) −2.17712 3.77089i −0.0997883 0.172838i
\(477\) 0 0
\(478\) −2.46863 4.27579i −0.112912 0.195570i
\(479\) −0.822876 + 1.42526i −0.0375981 + 0.0651219i −0.884212 0.467086i \(-0.845304\pi\)
0.846614 + 0.532207i \(0.178637\pi\)
\(480\) 0 0
\(481\) −1.27124 2.20186i −0.0579637 0.100396i
\(482\) −5.00000 −0.227744
\(483\) 0 0
\(484\) −8.29150 −0.376886
\(485\) −6.23987 10.8078i −0.283338 0.490756i
\(486\) 0 0
\(487\) 3.93725 6.81952i 0.178414 0.309022i −0.762923 0.646489i \(-0.776237\pi\)
0.941337 + 0.337467i \(0.109570\pi\)
\(488\) 6.32288 + 10.9515i 0.286223 + 0.495753i
\(489\) 0 0
\(490\) −5.76013 + 9.97684i −0.260216 + 0.450708i
\(491\) 37.7490 1.70359 0.851795 0.523876i \(-0.175514\pi\)
0.851795 + 0.523876i \(0.175514\pi\)
\(492\) 0 0
\(493\) 6.29150 10.8972i 0.283355 0.490785i
\(494\) 0.645751 1.11847i 0.0290537 0.0503225i
\(495\) 0 0
\(496\) 0.645751 0.0289951
\(497\) −27.3948 −1.22882
\(498\) 0 0
\(499\) −18.0830 31.3207i −0.809506 1.40211i −0.913206 0.407498i \(-0.866401\pi\)
0.103700 0.994609i \(-0.466932\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) 9.00000 + 15.5885i 0.401690 + 0.695747i
\(503\) 27.8745 1.24286 0.621431 0.783469i \(-0.286551\pi\)
0.621431 + 0.783469i \(0.286551\pi\)
\(504\) 0 0
\(505\) 22.4575 0.999346
\(506\) −7.64575 13.2428i −0.339895 0.588716i
\(507\) 0 0
\(508\) −3.32288 + 5.75539i −0.147429 + 0.255354i
\(509\) 19.9373 + 34.5323i 0.883703 + 1.53062i 0.847193 + 0.531286i \(0.178291\pi\)
0.0365105 + 0.999333i \(0.488376\pi\)
\(510\) 0 0
\(511\) 14.0000 24.2487i 0.619324 1.07270i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 7.93725 13.7477i 0.350097 0.606386i
\(515\) −9.82288 + 17.0137i −0.432848 + 0.749714i
\(516\) 0 0
\(517\) 18.0000 0.791639
\(518\) 5.20850 9.02138i 0.228848 0.396377i
\(519\) 0 0
\(520\) −0.531373 0.920365i −0.0233022 0.0403607i
\(521\) −19.9373 + 34.5323i −0.873467 + 1.51289i −0.0150801 + 0.999886i \(0.504800\pi\)
−0.858387 + 0.513003i \(0.828533\pi\)
\(522\) 0 0
\(523\) 0.500000 + 0.866025i 0.0218635 + 0.0378686i 0.876750 0.480946i \(-0.159707\pi\)
−0.854887 + 0.518815i \(0.826373\pi\)
\(524\) −6.58301 −0.287580
\(525\) 0 0
\(526\) 10.9373 0.476887
\(527\) −0.531373 0.920365i −0.0231470 0.0400917i
\(528\) 0 0
\(529\) −31.6660 + 54.8471i −1.37678 + 2.38466i
\(530\) 4.93725 + 8.55157i 0.214461 + 0.371457i
\(531\) 0 0
\(532\) 5.29150 0.229416
\(533\) 3.18824 0.138098
\(534\) 0 0
\(535\) 4.93725 8.55157i 0.213456 0.369717i
\(536\) 4.14575 7.18065i 0.179069 0.310157i
\(537\) 0 0
\(538\) −27.2915 −1.17662
\(539\) −5.76013 + 9.97684i −0.248106 + 0.429733i
\(540\) 0 0
\(541\) 20.5830 + 35.6508i 0.884933 + 1.53275i 0.845791 + 0.533514i \(0.179129\pi\)
0.0391415 + 0.999234i \(0.487538\pi\)
\(542\) −10.6144 + 18.3846i −0.455927 + 0.789688i
\(543\) 0 0
\(544\) 0.822876 + 1.42526i 0.0352805 + 0.0611076i
\(545\) 14.2288 0.609493
\(546\) 0 0
\(547\) 7.70850 0.329592 0.164796 0.986328i \(-0.447303\pi\)
0.164796 + 0.986328i \(0.447303\pi\)
\(548\) −4.64575 8.04668i −0.198457 0.343737i
\(549\) 0 0
\(550\) −1.88562 + 3.26599i −0.0804032 + 0.139262i
\(551\) 7.64575 + 13.2428i 0.325720 + 0.564164i
\(552\) 0 0
\(553\) 20.1458 + 34.8935i 0.856684 + 1.48382i
\(554\) 17.9373 0.762081
\(555\) 0 0
\(556\) 9.79150 16.9594i 0.415252 0.719238i
\(557\) −16.1144 + 27.9109i −0.682788 + 1.18262i 0.291338 + 0.956620i \(0.405899\pi\)
−0.974126 + 0.226004i \(0.927434\pi\)
\(558\) 0 0
\(559\) 3.22876 0.136562
\(560\) 2.17712 3.77089i 0.0920003 0.159349i
\(561\) 0 0
\(562\) 8.76013 + 15.1730i 0.369524 + 0.640034i
\(563\) −17.2288 + 29.8411i −0.726106 + 1.25765i 0.232412 + 0.972617i \(0.425338\pi\)
−0.958517 + 0.285034i \(0.907995\pi\)
\(564\) 0 0
\(565\) −6.29150 10.8972i −0.264686 0.458449i
\(566\) −8.29150 −0.348518
\(567\) 0 0
\(568\) 10.3542 0.434455
\(569\) −0.531373 0.920365i −0.0222763 0.0385837i 0.854672 0.519168i \(-0.173758\pi\)
−0.876949 + 0.480584i \(0.840425\pi\)
\(570\) 0 0
\(571\) 0.645751 1.11847i 0.0270239 0.0468067i −0.852197 0.523221i \(-0.824730\pi\)
0.879221 + 0.476414i \(0.158064\pi\)
\(572\) −0.531373 0.920365i −0.0222178 0.0384824i
\(573\) 0 0
\(574\) 6.53137 + 11.3127i 0.272614 + 0.472182i
\(575\) 21.2915 0.887917
\(576\) 0 0
\(577\) 10.8542 18.8001i 0.451868 0.782659i −0.546634 0.837372i \(-0.684091\pi\)
0.998502 + 0.0547129i \(0.0174244\pi\)
\(578\) −7.14575 + 12.3768i −0.297224 + 0.514807i
\(579\) 0 0
\(580\) 12.5830 0.522481
\(581\) 7.16601 0.297296
\(582\) 0 0
\(583\) 4.93725 + 8.55157i 0.204480 + 0.354170i
\(584\) −5.29150 + 9.16515i −0.218964 + 0.379257i
\(585\) 0 0
\(586\) −11.4686 19.8642i −0.473765 0.820584i
\(587\) −38.2288 −1.57787 −0.788935 0.614477i \(-0.789367\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(588\) 0 0
\(589\) 1.29150 0.0532154
\(590\) 11.2288 + 19.4488i 0.462281 + 0.800693i
\(591\) 0 0
\(592\) −1.96863 + 3.40976i −0.0809101 + 0.140140i
\(593\) 12.5314 + 21.7050i 0.514602 + 0.891316i 0.999856 + 0.0169436i \(0.00539357\pi\)
−0.485255 + 0.874373i \(0.661273\pi\)
\(594\) 0 0
\(595\) −7.16601 −0.293778
\(596\) −7.06275 −0.289301
\(597\) 0 0
\(598\) −3.00000 + 5.19615i −0.122679 + 0.212486i
\(599\) −10.9373 + 18.9439i −0.446884 + 0.774026i −0.998181 0.0602830i \(-0.980800\pi\)
0.551297 + 0.834309i \(0.314133\pi\)
\(600\) 0 0
\(601\) −4.87451 −0.198835 −0.0994177 0.995046i \(-0.531698\pi\)
−0.0994177 + 0.995046i \(0.531698\pi\)
\(602\) 6.61438 + 11.4564i 0.269582 + 0.466930i
\(603\) 0 0
\(604\) −3.61438 6.26029i −0.147067 0.254727i
\(605\) −6.82288 + 11.8176i −0.277389 + 0.480452i
\(606\) 0 0
\(607\) −13.2915 23.0216i −0.539485 0.934416i −0.998932 0.0462106i \(-0.985285\pi\)
0.459446 0.888206i \(-0.348048\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 20.8118 0.842644
\(611\) −3.53137 6.11652i −0.142864 0.247448i
\(612\) 0 0
\(613\) −13.1974 + 22.8585i −0.533037 + 0.923248i 0.466218 + 0.884670i \(0.345616\pi\)
−0.999256 + 0.0385780i \(0.987717\pi\)
\(614\) −6.79150 11.7632i −0.274083 0.474725i
\(615\) 0 0
\(616\) 2.17712 3.77089i 0.0877188 0.151933i
\(617\) 35.5203 1.42999 0.714996 0.699129i \(-0.246429\pi\)
0.714996 + 0.699129i \(0.246429\pi\)
\(618\) 0 0
\(619\) −1.14575 + 1.98450i −0.0460516 + 0.0797638i −0.888132 0.459588i \(-0.847997\pi\)
0.842081 + 0.539351i \(0.181331\pi\)
\(620\) 0.531373 0.920365i 0.0213405 0.0369628i
\(621\) 0 0
\(622\) 23.5203 0.943076
\(623\) −14.4686 25.0604i −0.579673 1.00402i
\(624\) 0 0
\(625\) 4.14575 + 7.18065i 0.165830 + 0.287226i
\(626\) 11.6458 20.1710i 0.465458 0.806197i
\(627\) 0 0
\(628\) 2.00000 + 3.46410i 0.0798087 + 0.138233i
\(629\) 6.47974 0.258364
\(630\) 0 0
\(631\) 21.9373 0.873308 0.436654 0.899629i \(-0.356163\pi\)
0.436654 + 0.899629i \(0.356163\pi\)
\(632\) −7.61438 13.1885i −0.302884 0.524610i
\(633\) 0 0
\(634\) 10.4059 18.0235i 0.413270 0.715805i
\(635\) 5.46863 + 9.47194i 0.217016 + 0.375882i
\(636\) 0 0
\(637\) 4.52026 0.179099
\(638\) 12.5830 0.498166
\(639\) 0 0
\(640\) −0.822876 + 1.42526i −0.0325270 + 0.0563384i
\(641\) 4.11438 7.12631i 0.162508 0.281472i −0.773259 0.634090i \(-0.781375\pi\)
0.935768 + 0.352617i \(0.114708\pi\)
\(642\) 0 0
\(643\) −34.8745 −1.37532 −0.687658 0.726035i \(-0.741361\pi\)
−0.687658 + 0.726035i \(0.741361\pi\)
\(644\) −24.5830 −0.968706
\(645\) 0 0
\(646\) 1.64575 + 2.85052i 0.0647512 + 0.112152i
\(647\) −10.9373 + 18.9439i −0.429988 + 0.744761i −0.996872 0.0790370i \(-0.974815\pi\)
0.566884 + 0.823798i \(0.308149\pi\)
\(648\) 0 0
\(649\) 11.2288 + 19.4488i 0.440767 + 0.763431i
\(650\) 1.47974 0.0580402
\(651\) 0 0
\(652\) −1.00000 −0.0391630
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 0 0
\(655\) −5.41699 + 9.38251i −0.211659 + 0.366605i
\(656\) −2.46863 4.27579i −0.0963837 0.166941i
\(657\) 0 0
\(658\) 14.4686 25.0604i 0.564046 0.976956i
\(659\) −2.22876 −0.0868200 −0.0434100 0.999057i \(-0.513822\pi\)
−0.0434100 + 0.999057i \(0.513822\pi\)
\(660\) 0 0
\(661\) −19.5830 + 33.9188i −0.761691 + 1.31929i 0.180288 + 0.983614i \(0.442297\pi\)
−0.941979 + 0.335673i \(0.891036\pi\)
\(662\) −0.0627461 + 0.108679i −0.00243870 + 0.00422394i
\(663\) 0 0
\(664\) −2.70850 −0.105110
\(665\) 4.35425 7.54178i 0.168851 0.292458i
\(666\) 0 0
\(667\) −35.5203 61.5229i −1.37535 2.38218i
\(668\) 6.29150 10.8972i 0.243426 0.421625i
\(669\) 0 0
\(670\) −6.82288 11.8176i −0.263591 0.456552i
\(671\) 20.8118 0.803429
\(672\) 0 0
\(673\) −47.7490 −1.84059 −0.920295 0.391226i \(-0.872051\pi\)
−0.920295 + 0.391226i \(0.872051\pi\)
\(674\) −4.70850 8.15536i −0.181365 0.314133i
\(675\) 0 0
\(676\) 6.29150 10.8972i 0.241981 0.419123i
\(677\) −7.06275 12.2330i −0.271443 0.470154i 0.697788 0.716304i \(-0.254168\pi\)
−0.969232 + 0.246150i \(0.920834\pi\)
\(678\) 0 0
\(679\) −20.0627 −0.769938
\(680\) 2.70850 0.103866
\(681\) 0 0
\(682\) 0.531373 0.920365i 0.0203473 0.0352426i
\(683\) 10.4059 18.0235i 0.398170 0.689651i −0.595330 0.803481i \(-0.702979\pi\)
0.993500 + 0.113831i \(0.0363121\pi\)
\(684\) 0 0
\(685\) −15.2915 −0.584258
\(686\) 9.26013 + 16.0390i 0.353553 + 0.612372i
\(687\) 0 0
\(688\) −2.50000 4.33013i −0.0953116 0.165085i
\(689\) 1.93725 3.35542i 0.0738035 0.127831i
\(690\) 0 0
\(691\) −12.3745 21.4333i −0.470748 0.815360i 0.528692 0.848814i \(-0.322683\pi\)
−0.999440 + 0.0334536i \(0.989349\pi\)
\(692\) −6.58301 −0.250248
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −16.1144 27.9109i −0.611253 1.05872i
\(696\) 0 0
\(697\) −4.06275 + 7.03688i −0.153887 + 0.266541i
\(698\) 12.6144 + 21.8487i 0.477461 + 0.826987i
\(699\) 0 0
\(700\) 3.03137 + 5.25049i 0.114575 + 0.198450i
\(701\) 5.41699 0.204597 0.102299 0.994754i \(-0.467380\pi\)
0.102299 + 0.994754i \(0.467380\pi\)
\(702\) 0 0
\(703\) −3.93725 + 6.81952i −0.148496 + 0.257203i
\(704\) −0.822876 + 1.42526i −0.0310133 + 0.0537166i
\(705\) 0 0
\(706\) −12.0000 −0.451626
\(707\) 18.0516 31.2663i 0.678902 1.17589i
\(708\) 0 0
\(709\) 4.90588 + 8.49723i 0.184244 + 0.319120i 0.943322 0.331880i \(-0.107683\pi\)
−0.759077 + 0.651000i \(0.774350\pi\)
\(710\) 8.52026 14.7575i 0.319760 0.553840i
\(711\) 0 0
\(712\) 5.46863 + 9.47194i 0.204945 + 0.354976i
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) −1.74902 −0.0654095
\(716\) 0.531373 + 0.920365i 0.0198583 + 0.0343957i
\(717\) 0 0
\(718\) 15.5830 26.9906i 0.581553 1.00728i
\(719\) 3.53137 + 6.11652i 0.131698 + 0.228108i 0.924331 0.381591i \(-0.124624\pi\)
−0.792633 + 0.609699i \(0.791290\pi\)
\(720\) 0 0
\(721\) 15.7915 + 27.3517i 0.588106 + 1.01863i
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 6.64575 11.5108i 0.246987 0.427795i
\(725\) −8.76013 + 15.1730i −0.325343 + 0.563511i
\(726\) 0 0
\(727\) 25.2288 0.935683 0.467841 0.883812i \(-0.345032\pi\)
0.467841 + 0.883812i \(0.345032\pi\)
\(728\) −1.70850 −0.0633211
\(729\) 0 0
\(730\) 8.70850 + 15.0836i 0.322316 + 0.558268i
\(731\) −4.11438 + 7.12631i −0.152176 + 0.263576i
\(732\) 0 0
\(733\) −4.38562 7.59612i −0.161987 0.280569i 0.773594 0.633681i \(-0.218457\pi\)
−0.935581 + 0.353112i \(0.885123\pi\)
\(734\) 1.87451 0.0691893
\(735\) 0 0
\(736\) 9.29150 0.342489
\(737\) −6.82288 11.8176i −0.251324 0.435306i
\(738\) 0 0
\(739\) −10.7288 + 18.5828i −0.394664 + 0.683578i −0.993058 0.117624i \(-0.962472\pi\)
0.598395 + 0.801202i \(0.295806\pi\)
\(740\) 3.23987 + 5.61162i 0.119100 + 0.206287i
\(741\) 0 0
\(742\) 15.8745 0.582772
\(743\) 13.0627 0.479226 0.239613 0.970869i \(-0.422979\pi\)
0.239613 + 0.970869i \(0.422979\pi\)
\(744\) 0 0
\(745\) −5.81176 + 10.0663i −0.212926 + 0.368799i
\(746\) −8.29150 + 14.3613i −0.303573 + 0.525805i
\(747\) 0 0
\(748\) 2.70850 0.0990325
\(749\) −7.93725 13.7477i −0.290021 0.502331i
\(750\) 0 0
\(751\) −0.228757 0.396218i −0.00834745 0.0144582i 0.861822 0.507212i \(-0.169324\pi\)
−0.870169 + 0.492753i \(0.835990\pi\)
\(752\) −5.46863 + 9.47194i −0.199420 + 0.345406i
\(753\) 0 0
\(754\) −2.46863 4.27579i −0.0899021 0.155715i
\(755\) −11.8967 −0.432967
\(756\) 0 0
\(757\) −40.9778 −1.48936 −0.744681 0.667420i \(-0.767398\pi\)
−0.744681 + 0.667420i \(0.767398\pi\)
\(758\) 2.20850 + 3.82523i 0.0802162 + 0.138939i
\(759\) 0 0
\(760\) −1.64575 + 2.85052i −0.0596977 + 0.103399i
\(761\) −9.29150 16.0934i −0.336817 0.583384i 0.647015 0.762477i \(-0.276017\pi\)
−0.983832 + 0.179093i \(0.942684\pi\)
\(762\) 0 0
\(763\) 11.4373 19.8099i 0.414056 0.717167i
\(764\) −26.8118 −0.970015
\(765\) 0 0
\(766\) 0.291503 0.504897i 0.0105324 0.0182427i
\(767\) 4.40588 7.63121i 0.159087 0.275547i
\(768\) 0 0
\(769\) 19.4170 0.700195 0.350097 0.936713i \(-0.386148\pi\)
0.350097 + 0.936713i \(0.386148\pi\)
\(770\) −3.58301 6.20595i −0.129123 0.223647i
\(771\) 0 0
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) 19.1660 33.1965i 0.689353 1.19400i −0.282694 0.959210i \(-0.591228\pi\)
0.972047 0.234785i \(-0.0754386\pi\)
\(774\) 0 0
\(775\) 0.739870 + 1.28149i 0.0265769 + 0.0460326i
\(776\) 7.58301 0.272214
\(777\) 0 0
\(778\) 8.70850 0.312215
\(779\) −4.93725 8.55157i −0.176895 0.306392i
\(780\) 0 0
\(781\) 8.52026 14.7575i 0.304879 0.528066i
\(782\) −7.64575 13.2428i −0.273412 0.473563i
\(783\) 0 0
\(784\) −3.50000 6.06218i −0.125000 0.216506i
\(785\) 6.58301 0.234958
\(786\) 0 0
\(787\) 11.1458 19.3050i 0.397303 0.688149i −0.596089 0.802918i \(-0.703279\pi\)
0.993392 + 0.114769i \(0.0366128\pi\)
\(788\) 7.64575 13.2428i 0.272369 0.471756i
\(789\) 0 0
\(790\) −25.0627 −0.891692
\(791\)