Properties

Label 378.2.g.h.163.2
Level $378$
Weight $2$
Character 378.163
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 163.2
Root \(1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.2.g.h.109.2

$q$-expansion

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

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 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 −0.621252 0.783611i \(-0.713376\pi\)
0.989253 + 0.146214i \(0.0467089\pi\)
\(6\) 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 0.714894 0.699233i \(-0.246475\pi\)
−0.963000 + 0.269500i \(0.913142\pi\)
\(12\) 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 0.748815 0.662780i \(-0.230623\pi\)
−0.948391 + 0.317103i \(0.897290\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −1.64575 −0.368001
\(21\) 0 0
\(22\) −1.64575 −0.350875
\(23\) 4.64575 8.04668i 0.968706 1.67785i 0.269396 0.963029i \(-0.413176\pi\)
0.699310 0.714819i \(-0.253491\pi\)
\(24\) 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 0.835573 0.549380i \(-0.185136\pi\)
−0.893563 + 0.448938i \(0.851803\pi\)
\(32\) 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 −0.981236 0.192809i \(-0.938240\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 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 0.123441 + 0.992352i \(0.460607\pi\)
−0.921123 + 0.389273i \(0.872726\pi\)
\(48\) 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 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 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 0.841928 + 0.539590i \(0.181421\pi\)
0.0463350 + 0.998926i \(0.485246\pi\)
\(60\) 0 0
\(61\) −6.32288 + 10.9515i −0.809561 + 1.40220i 0.103607 + 0.994618i \(0.466962\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(62\) −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 −0.999972 0.00750349i \(-0.997612\pi\)
0.493488 0.869753i \(-0.335722\pi\)
\(68\) −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 0.989609 + 0.143782i \(0.0459264\pi\)
−0.370286 + 0.928918i \(0.620740\pi\)
\(74\) 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 −0.0183890 0.999831i \(-0.505854\pi\)
0.875073 0.483990i \(-0.160813\pi\)
\(80\) 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 0.415843 + 0.909436i \(0.363486\pi\)
−0.995517 + 0.0945873i \(0.969847\pi\)
\(90\) 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 0.975312 + 0.220831i \(0.0708770\pi\)
−0.296411 + 0.955061i \(0.595790\pi\)
\(102\) 0 0
\(103\) 5.96863 10.3380i 0.588106 1.01863i −0.406374 0.913707i \(-0.633207\pi\)
0.994480 0.104923i \(-0.0334597\pi\)
\(104\) −0.645751 −0.0633211
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) 0 0
\(109\) 4.32288 + 7.48744i 0.414056 + 0.717167i 0.995329 0.0965423i \(-0.0307783\pi\)
−0.581272 + 0.813709i \(0.697445\pi\)
\(110\) −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 −0.685652 0.727930i \(-0.740483\pi\)
0.973232 + 0.229827i \(0.0738160\pi\)
\(132\) 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 0.596430 0.802665i \(-0.296585\pi\)
−0.993343 + 0.115191i \(0.963252\pi\)
\(138\) 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 −0.684342 0.729161i \(-0.739910\pi\)
0.973643 + 0.228077i \(0.0732437\pi\)
\(150\) 0 0
\(151\) −3.61438 6.26029i −0.294134 0.509455i 0.680649 0.732610i \(-0.261698\pi\)
−0.974783 + 0.223155i \(0.928365\pi\)
\(152\) 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 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −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 −0.845780 0.533533i \(-0.820864\pi\)
0.884943 + 0.465700i \(0.154198\pi\)
\(164\) −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 −0.713346 0.700812i \(-0.752821\pi\)
0.963594 + 0.267369i \(0.0861544\pi\)
\(174\) 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 0.885200 0.465210i \(-0.154021\pi\)
−0.845484 + 0.534001i \(0.820688\pi\)
\(180\) 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 0.274526 0.961580i \(-0.411479\pi\)
0.695489 0.718537i \(-0.255188\pi\)
\(192\) 0 0
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) −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 −0.933353 0.358961i \(-0.883131\pi\)
0.155807 0.987787i \(-0.450202\pi\)
\(200\) −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 0.948242 0.317547i \(-0.102859\pi\)
−0.749125 + 0.662428i \(0.769526\pi\)
\(228\) 0 0
\(229\) 7.32288 12.6836i 0.483909 0.838155i −0.515920 0.856637i \(-0.672550\pi\)
0.999829 + 0.0184814i \(0.00588315\pi\)
\(230\) −15.2915 −1.00829
\(231\) 0 0
\(232\) 7.64575 0.501968
\(233\) −4.35425 + 7.54178i −0.285256 + 0.494078i −0.972671 0.232186i \(-0.925412\pi\)
0.687415 + 0.726265i \(0.258745\pi\)
\(234\) 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 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) −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 −0.999984 0.00563467i \(-0.998206\pi\)
0.504872 + 0.863194i \(0.331540\pi\)
\(258\) 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 0.983907 0.178682i \(-0.0571834\pi\)
−0.646697 + 0.762747i \(0.723850\pi\)
\(264\) 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 −0.896453 0.443139i \(-0.853865\pi\)
0.0644567 0.997921i \(-0.479469\pi\)
\(270\) 0 0
\(271\) 10.6144 18.3846i 0.644778 1.11679i −0.339575 0.940579i \(-0.610283\pi\)
0.984353 0.176209i \(-0.0563833\pi\)
\(272\) 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 0.998965 + 0.0454837i \(0.0144829\pi\)
−0.460093 + 0.887871i \(0.652184\pi\)
\(278\) −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 0.716096 0.698002i \(-0.245927\pi\)
−0.962535 + 0.271156i \(0.912594\pi\)
\(284\) 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 0.978779 + 0.204921i \(0.0656936\pi\)
−0.311923 + 0.950107i \(0.600973\pi\)
\(312\) 0 0
\(313\) −11.6458 + 20.1710i −0.658257 + 1.14013i 0.322810 + 0.946464i \(0.395373\pi\)
−0.981067 + 0.193670i \(0.937961\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −15.2288 −0.856684
\(317\) −10.4059 + 18.0235i −0.584452 + 1.01230i 0.410491 + 0.911865i \(0.365357\pi\)
−0.994943 + 0.100437i \(0.967976\pi\)
\(318\) 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 −0.864296 0.502984i \(-0.832236\pi\)
0.867745 + 0.497010i \(0.165569\pi\)
\(332\) −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 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 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 0.661004 0.750382i \(-0.270130\pi\)
−0.980352 + 0.197256i \(0.936797\pi\)
\(354\) 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 0.0814209 + 0.996680i \(0.474054\pi\)
−0.903860 + 0.427827i \(0.859279\pi\)
\(360\) 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 0.889450 0.457032i \(-0.151087\pi\)
−0.840526 + 0.541771i \(0.817754\pi\)
\(368\) 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 −0.567495 0.823377i \(-0.692087\pi\)
0.996813 + 0.0797767i \(0.0254207\pi\)
\(374\) 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 −0.873377 0.487045i \(-0.838075\pi\)
0.858482 + 0.512844i \(0.171408\pi\)
\(384\) 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 0.955042 0.296471i \(-0.0958099\pi\)
−0.734273 + 0.678855i \(0.762477\pi\)
\(390\) 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 −0.687665 0.726028i \(-0.741364\pi\)
0.972591 + 0.232521i \(0.0746974\pi\)
\(398\) −21.9373 −1.09962
\(399\) 0 0
\(400\) −2.29150 −0.114575
\(401\) 13.4059 23.2197i 0.669458 1.15953i −0.308598 0.951192i \(-0.599860\pi\)
0.978056 0.208342i \(-0.0668068\pi\)
\(402\) 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 0.995656 0.0931066i \(-0.0296798\pi\)
−0.578461 + 0.815710i \(0.696346\pi\)
\(410\) −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 0.740186 0.672402i \(-0.234737\pi\)
−0.952410 + 0.304819i \(0.901404\pi\)
\(432\) 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 −0.585205 0.810885i \(-0.698986\pi\)
0.994850 + 0.101360i \(0.0323194\pi\)
\(440\) 2.70850 0.129123
\(441\) 0 0
\(442\) −1.06275 −0.0505497
\(443\) −4.35425 + 7.54178i −0.206877 + 0.358321i −0.950729 0.310023i \(-0.899663\pi\)
0.743852 + 0.668344i \(0.232997\pi\)
\(444\) 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 −0.891579 0.452866i \(-0.850402\pi\)
0.837983 + 0.545697i \(0.183735\pi\)
\(458\) −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 0.384893 + 0.922961i \(0.374238\pi\)
−0.991754 + 0.128153i \(0.959095\pi\)
\(468\) 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 0.846614 0.532207i \(-0.178637\pi\)
−0.884212 + 0.467086i \(0.845304\pi\)
\(480\) 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 0.941337 0.337467i \(-0.109570\pi\)
−0.762923 + 0.646489i \(0.776237\pi\)
\(488\) 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 0.103700 + 0.994609i \(0.466932\pi\)
−0.913206 + 0.407498i \(0.866401\pi\)
\(500\) −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 0.0365105 0.999333i \(-0.488376\pi\)
0.847193 0.531286i \(-0.178291\pi\)
\(510\) 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 −0.858387 0.513003i \(-0.828533\pi\)
−0.0150801 0.999886i \(-0.504800\pi\)
\(522\) 0 0
\(523\) 0.500000 0.866025i 0.0218635 0.0378686i −0.854887 0.518815i \(-0.826373\pi\)
0.876750 + 0.480946i \(0.159707\pi\)
\(524\) −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 0.0391415 0.999234i \(-0.487538\pi\)
0.845791 0.533514i \(-0.179129\pi\)
\(542\) −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 −0.974126 0.226004i \(-0.927434\pi\)
0.291338 0.956620i \(-0.405899\pi\)
\(558\) 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 −0.958517 0.285034i \(-0.907995\pi\)
0.232412 0.972617i \(-0.425338\pi\)
\(564\) 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 −0.876949 0.480584i \(-0.840425\pi\)
0.854672 + 0.519168i \(0.173758\pi\)
\(570\) 0 0
\(571\) 0.645751 + 1.11847i 0.0270239 + 0.0468067i 0.879221 0.476414i \(-0.158064\pi\)
−0.852197 + 0.523221i \(0.824730\pi\)
\(572\) −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 0.998502 0.0547129i \(-0.0174244\pi\)
−0.546634 + 0.837372i \(0.684091\pi\)
\(578\) −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 −0.485255 0.874373i \(-0.661273\pi\)
0.999856 0.0169436i \(-0.00539357\pi\)
\(594\) 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 0.551297 0.834309i \(-0.314133\pi\)
−0.998181 + 0.0602830i \(0.980800\pi\)
\(600\) 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 0.459446 + 0.888206i \(0.348048\pi\)
−0.998932 + 0.0462106i \(0.985285\pi\)
\(608\) −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 −0.999256 0.0385780i \(-0.987717\pi\)
0.466218 0.884670i \(-0.345616\pi\)
\(614\) −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 0.842081 0.539351i \(-0.181331\pi\)
−0.888132 + 0.459588i \(0.847997\pi\)
\(620\) 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 0.935768 0.352617i \(-0.114708\pi\)
−0.773259 + 0.634090i \(0.781375\pi\)
\(642\) 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 0.566884 0.823798i \(-0.308149\pi\)
−0.996872 + 0.0790370i \(0.974815\pi\)
\(648\) 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 −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 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 −0.941979 0.335673i \(-0.891036\pi\)
0.180288 0.983614i \(-0.442297\pi\)
\(662\) −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 −0.969232 0.246150i \(-0.920834\pi\)
0.697788 + 0.716304i \(0.254168\pi\)
\(678\) 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 0.993500 0.113831i \(-0.0363121\pi\)
−0.595330 + 0.803481i \(0.702979\pi\)
\(684\) 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 −0.999440 0.0334536i \(-0.989349\pi\)
0.528692 + 0.848814i \(0.322683\pi\)
\(692\) −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 −0.759077 0.651000i \(-0.774350\pi\)
0.943322 + 0.331880i \(0.107683\pi\)
\(710\) 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 −0.792633 0.609699i \(-0.791290\pi\)
0.924331 + 0.381591i \(0.124624\pi\)
\(720\) 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 −0.935581 0.353112i \(-0.885123\pi\)
0.773594 + 0.633681i \(0.218457\pi\)
\(734\) 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 0.598395 0.801202i \(-0.295806\pi\)
−0.993058 + 0.117624i \(0.962472\pi\)
\(740\) 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 −0.870169 0.492753i \(-0.835990\pi\)
0.861822 + 0.507212i \(0.169324\pi\)
\(752\) −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 −0.983832 0.179093i \(-0.942684\pi\)
0.647015 + 0.762477i \(0.276017\pi\)
\(762\) 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 0.972047 + 0.234785i \(0.0754386\pi\)
−0.282694 + 0.959210i \(0.591228\pi\)
\(774\) 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 0.993392 0.114769i \(-0.0366128\pi\)
−0.596089 + 0.802918i \(0.703279\pi\)
\(788\) 7.64575 + 13.2428i 0.272369 + 0.471756i
\(789\) 0 0
\(790\) −25.0627 −0.891692
\(791\)