Properties

Label 378.2.g.g.109.1
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: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
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 109.1
Root \(1.32288 + 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.2.g.g.163.1

$q$-expansion

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

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 0.621252 0.783611i \(-0.286624\pi\)
−0.989253 + 0.146214i \(0.953291\pi\)
\(6\) 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 \(-0.753525\pi\)
0.963000 + 0.269500i \(0.0868584\pi\)
\(12\) 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 \(-0.769377\pi\)
0.948391 + 0.317103i \(0.102710\pi\)
\(18\) 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 \(-0.746509\pi\)
−0.269396 0.963029i \(-0.586824\pi\)
\(24\) 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 \(-0.248745\pi\)
0.709890 + 0.704312i \(0.248745\pi\)
\(30\) 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 \(-0.625983\pi\)
−0.385535 + 0.922693i \(0.625983\pi\)
\(42\) 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 \(0.127274\pi\)
−0.123441 + 0.992352i \(0.539393\pi\)
\(48\) 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 \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 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 \(0.514754\pi\)
−0.841928 + 0.539590i \(0.818579\pi\)
\(60\) 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 \(-0.289393\pi\)
0.614412 + 0.788986i \(0.289393\pi\)
\(72\) 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 \(-0.547492\pi\)
−0.148648 + 0.988890i \(0.547492\pi\)
\(84\) 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 \(0.0301532\pi\)
−0.415843 + 0.909436i \(0.636514\pi\)
\(90\) 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 \(0.404210\pi\)
−0.975312 + 0.220831i \(0.929123\pi\)
\(102\) 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 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) 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 \(-0.382904\pi\)
0.359626 + 0.933097i \(0.382904\pi\)
\(114\) 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 \(-0.259517\pi\)
−0.973232 + 0.229827i \(0.926184\pi\)
\(132\) 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 \(-0.703415\pi\)
0.993343 + 0.115191i \(0.0367480\pi\)
\(138\) 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 \(-0.260090\pi\)
−0.973643 + 0.228077i \(0.926756\pi\)
\(150\) 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 \(-0.338145\pi\)
0.486851 + 0.873485i \(0.338145\pi\)
\(168\) 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 \(-0.247179\pi\)
−0.963594 + 0.267369i \(0.913846\pi\)
\(174\) 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 \(-0.845979\pi\)
0.845484 + 0.534001i \(0.179312\pi\)
\(180\) 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 \(-0.744812\pi\)
−0.274526 0.961580i \(-0.588521\pi\)
\(192\) 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 \(-0.316629\pi\)
0.544737 + 0.838607i \(0.316629\pi\)
\(198\) 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 −0.948242 0.317547i \(-0.897141\pi\)
0.749125 + 0.662428i \(0.230474\pi\)
\(228\) 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 0.972671 0.232186i \(-0.0745879\pi\)
−0.687415 + 0.726265i \(0.741255\pi\)
\(234\) 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 \(-0.448953\pi\)
0.159682 + 0.987168i \(0.448953\pi\)
\(240\) 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 \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 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 \(-0.00179358\pi\)
−0.504872 + 0.863194i \(0.668460\pi\)
\(258\) 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 \(-0.942817\pi\)
0.646697 + 0.762747i \(0.276150\pi\)
\(264\) 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 \(-0.520531\pi\)
0.896453 0.443139i \(-0.146135\pi\)
\(270\) 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 \(-0.675032\pi\)
−0.522586 + 0.852587i \(0.675032\pi\)
\(282\) 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 \(-0.266292\pi\)
0.670004 + 0.742357i \(0.266292\pi\)
\(294\) 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 \(0.399027\pi\)
−0.978779 + 0.204921i \(0.934306\pi\)
\(312\) 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 \(0.0320240\pi\)
−0.410491 + 0.911865i \(0.634643\pi\)
\(318\) 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 −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 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 \(-0.729870\pi\)
0.980352 + 0.197256i \(0.0632029\pi\)
\(354\) 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 \(0.140721\pi\)
−0.0814209 + 0.996680i \(0.525946\pi\)
\(360\) 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 0.873377 0.487045i \(-0.161925\pi\)
−0.858482 + 0.512844i \(0.828592\pi\)
\(384\) 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 \(-0.904190\pi\)
0.734273 + 0.678855i \(0.237523\pi\)
\(390\) 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 \(-0.933193\pi\)
0.308598 0.951192i \(-0.400140\pi\)
\(402\) 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 \(-0.396627\pi\)
0.319078 + 0.947728i \(0.396627\pi\)
\(420\) 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 \(-0.765263\pi\)
0.952410 + 0.304819i \(0.0985961\pi\)
\(432\) 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 0.950729 0.310023i \(-0.100337\pi\)
−0.743852 + 0.668344i \(0.767003\pi\)
\(444\) 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 \(-0.442257\pi\)
0.180413 + 0.983591i \(0.442257\pi\)
\(450\) 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 \(-0.516528\pi\)
−0.0519018 + 0.998652i \(0.516528\pi\)
\(462\) 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 \(0.0409049\pi\)
−0.384893 + 0.922961i \(0.625762\pi\)
\(468\) 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 \(-0.821363\pi\)
0.884212 + 0.467086i \(0.154696\pi\)
\(480\) 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 \(-0.824486\pi\)
−0.851795 + 0.523876i \(0.824486\pi\)
\(492\) 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 \(-0.713449\pi\)
−0.621431 + 0.783469i \(0.713449\pi\)
\(504\) 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 \(-0.821709\pi\)
−0.0365105 0.999333i \(-0.511624\pi\)
\(510\) 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 \(-0.495200\pi\)
0.858387 0.513003i \(-0.171467\pi\)
\(522\) 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 \(-0.594101\pi\)
0.974126 0.226004i \(-0.0725661\pi\)
\(558\) 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 \(-0.574662\pi\)
0.958517 0.285034i \(-0.0920050\pi\)
\(564\) 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 \(-0.159575\pi\)
−0.854672 + 0.519168i \(0.826242\pi\)
\(570\) 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 \(-0.210633\pi\)
0.788935 + 0.614477i \(0.210633\pi\)
\(588\) 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 \(-0.994606\pi\)
0.485255 0.874373i \(-0.338727\pi\)
\(594\) 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 \(-0.685867\pi\)
0.998181 + 0.0602830i \(0.0192003\pi\)
\(600\) 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 \(-0.753571\pi\)
−0.714996 + 0.699129i \(0.753571\pi\)
\(618\) 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 −0.935768 0.352617i \(-0.885292\pi\)
0.773259 + 0.634090i \(0.218625\pi\)
\(642\) 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 \(-0.691851\pi\)
0.996872 + 0.0790370i \(0.0251845\pi\)
\(648\) 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 \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) 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 \(-0.486178\pi\)
0.0434100 + 0.999057i \(0.486178\pi\)
\(660\) 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 0.969232 0.246150i \(-0.0791657\pi\)
−0.697788 + 0.716304i \(0.745832\pi\)
\(678\) 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 \(-0.963688\pi\)
0.595330 + 0.803481i \(0.297021\pi\)
\(684\) 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 \(-0.532620\pi\)
−0.102299 + 0.994754i \(0.532620\pi\)
\(702\) 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 0.792633 0.609699i \(-0.208710\pi\)
−0.924331 + 0.381591i \(0.875376\pi\)
\(720\) 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 \(-0.577021\pi\)
−0.239613 + 0.970869i \(0.577021\pi\)
\(744\) 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 0.983832 0.179093i \(-0.0573164\pi\)
−0.647015 + 0.762477i \(0.723983\pi\)
\(762\) 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 \(0.408772\pi\)
−0.972047 + 0.234785i \(0.924561\pi\)
\(774\) 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