Properties

Label 378.2.g.h.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.h.163.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.82288 - 3.15731i) q^{5} -2.64575 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.82288 - 3.15731i) q^{5} -2.64575 q^{7} -1.00000 q^{8} +(1.82288 - 3.15731i) q^{10} +(1.82288 - 3.15731i) q^{11} -4.64575 q^{13} +(-1.32288 - 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82288 - 3.15731i) q^{17} +(-1.00000 - 1.73205i) q^{19} +3.64575 q^{20} +3.64575 q^{22} +(-0.645751 - 1.11847i) q^{23} +(-4.14575 + 7.18065i) q^{25} +(-2.32288 - 4.02334i) q^{26} +(1.32288 - 2.29129i) q^{28} -2.35425 q^{29} +(2.32288 - 4.02334i) q^{31} +(0.500000 - 0.866025i) q^{32} +3.64575 q^{34} +(4.82288 + 8.35347i) q^{35} +(5.96863 + 10.3380i) q^{37} +(1.00000 - 1.73205i) q^{38} +(1.82288 + 3.15731i) q^{40} -10.9373 q^{41} +5.00000 q^{43} +(1.82288 + 3.15731i) q^{44} +(0.645751 - 1.11847i) q^{46} +(2.46863 + 4.27579i) q^{47} +7.00000 q^{49} -8.29150 q^{50} +(2.32288 - 4.02334i) q^{52} +(3.00000 - 5.19615i) q^{53} -13.2915 q^{55} +2.64575 q^{56} +(-1.17712 - 2.03884i) q^{58} +(4.17712 - 7.23499i) q^{59} +(-3.67712 - 6.36897i) q^{61} +4.64575 q^{62} +1.00000 q^{64} +(8.46863 + 14.6681i) q^{65} +(1.14575 - 1.98450i) q^{67} +(1.82288 + 3.15731i) q^{68} +(-4.82288 + 8.35347i) q^{70} -15.6458 q^{71} +(-5.29150 + 9.16515i) q^{73} +(-5.96863 + 10.3380i) q^{74} +2.00000 q^{76} +(-4.82288 + 8.35347i) q^{77} +(-5.61438 - 9.72439i) q^{79} +(-1.82288 + 3.15731i) q^{80} +(-5.46863 - 9.47194i) q^{82} +13.2915 q^{83} -13.2915 q^{85} +(2.50000 + 4.33013i) q^{86} +(-1.82288 + 3.15731i) q^{88} +(2.46863 + 4.27579i) q^{89} +12.2915 q^{91} +1.29150 q^{92} +(-2.46863 + 4.27579i) q^{94} +(-3.64575 + 6.31463i) q^{95} +13.5830 q^{97} +(3.50000 + 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8}+O(q^{10}) \) 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
\(5\) −1.82288 3.15731i −0.815215 1.41199i −0.909174 0.416417i \(-0.863286\pi\)
0.0939588 0.995576i \(-0.470048\pi\)
\(6\) 0 0
\(7\) −2.64575 −1.00000
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.82288 3.15731i 0.576444 0.998430i
\(11\) 1.82288 3.15731i 0.549618 0.951966i −0.448683 0.893691i \(-0.648107\pi\)
0.998301 0.0582747i \(-0.0185599\pi\)
\(12\) 0 0
\(13\) −4.64575 −1.28850 −0.644250 0.764815i \(-0.722830\pi\)
−0.644250 + 0.764815i \(0.722830\pi\)
\(14\) −1.32288 2.29129i −0.353553 0.612372i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.82288 3.15731i 0.442112 0.765761i −0.555734 0.831360i \(-0.687563\pi\)
0.997846 + 0.0655994i \(0.0208959\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 3.64575 0.815215
\(21\) 0 0
\(22\) 3.64575 0.777277
\(23\) −0.645751 1.11847i −0.134648 0.233218i 0.790815 0.612056i \(-0.209657\pi\)
−0.925463 + 0.378838i \(0.876324\pi\)
\(24\) 0 0
\(25\) −4.14575 + 7.18065i −0.829150 + 1.43613i
\(26\) −2.32288 4.02334i −0.455553 0.789042i
\(27\) 0 0
\(28\) 1.32288 2.29129i 0.250000 0.433013i
\(29\) −2.35425 −0.437173 −0.218587 0.975818i \(-0.570145\pi\)
−0.218587 + 0.975818i \(0.570145\pi\)
\(30\) 0 0
\(31\) 2.32288 4.02334i 0.417201 0.722613i −0.578456 0.815714i \(-0.696345\pi\)
0.995657 + 0.0931007i \(0.0296779\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.64575 0.625241
\(35\) 4.82288 + 8.35347i 0.815215 + 1.41199i
\(36\) 0 0
\(37\) 5.96863 + 10.3380i 0.981236 + 1.69955i 0.657596 + 0.753371i \(0.271573\pi\)
0.323640 + 0.946180i \(0.395093\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) 0 0
\(40\) 1.82288 + 3.15731i 0.288222 + 0.499215i
\(41\) −10.9373 −1.70811 −0.854056 0.520181i \(-0.825864\pi\)
−0.854056 + 0.520181i \(0.825864\pi\)
\(42\) 0 0
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 1.82288 + 3.15731i 0.274809 + 0.475983i
\(45\) 0 0
\(46\) 0.645751 1.11847i 0.0952108 0.164910i
\(47\) 2.46863 + 4.27579i 0.360086 + 0.623688i 0.987975 0.154616i \(-0.0494139\pi\)
−0.627888 + 0.778303i \(0.716081\pi\)
\(48\) 0 0
\(49\) 7.00000 1.00000
\(50\) −8.29150 −1.17260
\(51\) 0 0
\(52\) 2.32288 4.02334i 0.322125 0.557937i
\(53\) 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
\(55\) −13.2915 −1.79223
\(56\) 2.64575 0.353553
\(57\) 0 0
\(58\) −1.17712 2.03884i −0.154564 0.267713i
\(59\) 4.17712 7.23499i 0.543815 0.941916i −0.454865 0.890560i \(-0.650313\pi\)
0.998680 0.0513554i \(-0.0163541\pi\)
\(60\) 0 0
\(61\) −3.67712 6.36897i −0.470808 0.815463i 0.528635 0.848849i \(-0.322704\pi\)
−0.999443 + 0.0333867i \(0.989371\pi\)
\(62\) 4.64575 0.590011
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 8.46863 + 14.6681i 1.05040 + 1.81935i
\(66\) 0 0
\(67\) 1.14575 1.98450i 0.139976 0.242445i −0.787511 0.616300i \(-0.788631\pi\)
0.927487 + 0.373855i \(0.121964\pi\)
\(68\) 1.82288 + 3.15731i 0.221056 + 0.382880i
\(69\) 0 0
\(70\) −4.82288 + 8.35347i −0.576444 + 0.998430i
\(71\) −15.6458 −1.85681 −0.928405 0.371571i \(-0.878819\pi\)
−0.928405 + 0.371571i \(0.878819\pi\)
\(72\) 0 0
\(73\) −5.29150 + 9.16515i −0.619324 + 1.07270i 0.370286 + 0.928918i \(0.379260\pi\)
−0.989609 + 0.143782i \(0.954074\pi\)
\(74\) −5.96863 + 10.3380i −0.693839 + 1.20176i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) −4.82288 + 8.35347i −0.549618 + 0.951966i
\(78\) 0 0
\(79\) −5.61438 9.72439i −0.631667 1.09408i −0.987211 0.159420i \(-0.949038\pi\)
0.355544 0.934660i \(-0.384296\pi\)
\(80\) −1.82288 + 3.15731i −0.203804 + 0.352998i
\(81\) 0 0
\(82\) −5.46863 9.47194i −0.603909 1.04600i
\(83\) 13.2915 1.45893 0.729466 0.684017i \(-0.239769\pi\)
0.729466 + 0.684017i \(0.239769\pi\)
\(84\) 0 0
\(85\) −13.2915 −1.44167
\(86\) 2.50000 + 4.33013i 0.269582 + 0.466930i
\(87\) 0 0
\(88\) −1.82288 + 3.15731i −0.194319 + 0.336571i
\(89\) 2.46863 + 4.27579i 0.261674 + 0.453233i 0.966687 0.255962i \(-0.0823922\pi\)
−0.705013 + 0.709194i \(0.749059\pi\)
\(90\) 0 0
\(91\) 12.2915 1.28850
\(92\) 1.29150 0.134648
\(93\) 0 0
\(94\) −2.46863 + 4.27579i −0.254619 + 0.441014i
\(95\) −3.64575 + 6.31463i −0.374046 + 0.647867i
\(96\) 0 0
\(97\) 13.5830 1.37915 0.689573 0.724217i \(-0.257798\pi\)
0.689573 + 0.724217i \(0.257798\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) 0 0
\(100\) −4.14575 7.18065i −0.414575 0.718065i
\(101\) 4.17712 7.23499i 0.415639 0.719909i −0.579856 0.814719i \(-0.696891\pi\)
0.995495 + 0.0948105i \(0.0302245\pi\)
\(102\) 0 0
\(103\) −1.96863 3.40976i −0.193975 0.335974i 0.752589 0.658490i \(-0.228805\pi\)
−0.946564 + 0.322516i \(0.895471\pi\)
\(104\) 4.64575 0.455553
\(105\) 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
\(109\) 1.67712 2.90486i 0.160639 0.278236i −0.774459 0.632624i \(-0.781978\pi\)
0.935098 + 0.354389i \(0.115311\pi\)
\(110\) −6.64575 11.5108i −0.633648 1.09751i
\(111\) 0 0
\(112\) 1.32288 + 2.29129i 0.125000 + 0.216506i
\(113\) −2.35425 −0.221469 −0.110735 0.993850i \(-0.535320\pi\)
−0.110735 + 0.993850i \(0.535320\pi\)
\(114\) 0 0
\(115\) −2.35425 + 4.07768i −0.219535 + 0.380245i
\(116\) 1.17712 2.03884i 0.109293 0.189301i
\(117\) 0 0
\(118\) 8.35425 0.769071
\(119\) −4.82288 + 8.35347i −0.442112 + 0.765761i
\(120\) 0 0
\(121\) −1.14575 1.98450i −0.104159 0.180409i
\(122\) 3.67712 6.36897i 0.332911 0.576619i
\(123\) 0 0
\(124\) 2.32288 + 4.02334i 0.208600 + 0.361306i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 1.35425 0.120170 0.0600851 0.998193i \(-0.480863\pi\)
0.0600851 + 0.998193i \(0.480863\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −8.46863 + 14.6681i −0.742748 + 1.28648i
\(131\) −7.29150 12.6293i −0.637062 1.10342i −0.986074 0.166305i \(-0.946816\pi\)
0.349013 0.937118i \(-0.386517\pi\)
\(132\) 0 0
\(133\) 2.64575 + 4.58258i 0.229416 + 0.397360i
\(134\) 2.29150 0.197956
\(135\) 0 0
\(136\) −1.82288 + 3.15731i −0.156310 + 0.270737i
\(137\) 0.645751 1.11847i 0.0551703 0.0955577i −0.837121 0.547017i \(-0.815763\pi\)
0.892292 + 0.451460i \(0.149097\pi\)
\(138\) 0 0
\(139\) 1.58301 0.134269 0.0671344 0.997744i \(-0.478614\pi\)
0.0671344 + 0.997744i \(0.478614\pi\)
\(140\) −9.64575 −0.815215
\(141\) 0 0
\(142\) −7.82288 13.5496i −0.656481 1.13706i
\(143\) −8.46863 + 14.6681i −0.708182 + 1.22661i
\(144\) 0 0
\(145\) 4.29150 + 7.43310i 0.356390 + 0.617285i
\(146\) −10.5830 −0.875856
\(147\) 0 0
\(148\) −11.9373 −0.981236
\(149\) 11.4686 + 19.8642i 0.939547 + 1.62734i 0.766319 + 0.642461i \(0.222086\pi\)
0.173228 + 0.984882i \(0.444580\pi\)
\(150\) 0 0
\(151\) 9.61438 16.6526i 0.782407 1.35517i −0.148129 0.988968i \(-0.547325\pi\)
0.930536 0.366201i \(-0.119342\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) 0 0
\(154\) −9.64575 −0.777277
\(155\) −16.9373 −1.36043
\(156\) 0 0
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) 5.61438 9.72439i 0.446656 0.773631i
\(159\) 0 0
\(160\) −3.64575 −0.288222
\(161\) 1.70850 + 2.95920i 0.134648 + 0.233218i
\(162\) 0 0
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) 5.46863 9.47194i 0.427028 0.739634i
\(165\) 0 0
\(166\) 6.64575 + 11.5108i 0.515810 + 0.893410i
\(167\) 8.58301 0.664173 0.332086 0.943249i \(-0.392247\pi\)
0.332086 + 0.943249i \(0.392247\pi\)
\(168\) 0 0
\(169\) 8.58301 0.660231
\(170\) −6.64575 11.5108i −0.509706 0.882836i
\(171\) 0 0
\(172\) −2.50000 + 4.33013i −0.190623 + 0.330169i
\(173\) −7.29150 12.6293i −0.554363 0.960184i −0.997953 0.0639546i \(-0.979629\pi\)
0.443590 0.896230i \(-0.353705\pi\)
\(174\) 0 0
\(175\) 10.9686 18.9982i 0.829150 1.43613i
\(176\) −3.64575 −0.274809
\(177\) 0 0
\(178\) −2.46863 + 4.27579i −0.185031 + 0.320484i
\(179\) 8.46863 14.6681i 0.632975 1.09634i −0.353965 0.935259i \(-0.615167\pi\)
0.986940 0.161086i \(-0.0514997\pi\)
\(180\) 0 0
\(181\) −2.70850 −0.201321 −0.100661 0.994921i \(-0.532096\pi\)
−0.100661 + 0.994921i \(0.532096\pi\)
\(182\) 6.14575 + 10.6448i 0.455553 + 0.789042i
\(183\) 0 0
\(184\) 0.645751 + 1.11847i 0.0476054 + 0.0824550i
\(185\) 21.7601 37.6897i 1.59984 2.77100i
\(186\) 0 0
\(187\) −6.64575 11.5108i −0.485985 0.841752i
\(188\) −4.93725 −0.360086
\(189\) 0 0
\(190\) −7.29150 −0.528981
\(191\) −10.4059 18.0235i −0.752943 1.30414i −0.946390 0.323025i \(-0.895300\pi\)
0.193447 0.981111i \(-0.438033\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) 6.79150 + 11.7632i 0.487601 + 0.844551i
\(195\) 0 0
\(196\) −3.50000 + 6.06218i −0.250000 + 0.433013i
\(197\) −4.70850 −0.335467 −0.167733 0.985832i \(-0.553645\pi\)
−0.167733 + 0.985832i \(0.553645\pi\)
\(198\) 0 0
\(199\) −3.03137 + 5.25049i −0.214888 + 0.372198i −0.953238 0.302221i \(-0.902272\pi\)
0.738350 + 0.674418i \(0.235605\pi\)
\(200\) 4.14575 7.18065i 0.293149 0.507749i
\(201\) 0 0
\(202\) 8.35425 0.587803
\(203\) 6.22876 0.437173
\(204\) 0 0
\(205\) 19.9373 + 34.5323i 1.39248 + 2.41184i
\(206\) 1.96863 3.40976i 0.137161 0.237569i
\(207\) 0 0
\(208\) 2.32288 + 4.02334i 0.161062 + 0.278968i
\(209\) −7.29150 −0.504364
\(210\) 0 0
\(211\) 14.8745 1.02400 0.512002 0.858984i \(-0.328904\pi\)
0.512002 + 0.858984i \(0.328904\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) −9.11438 15.7866i −0.621595 1.07663i
\(216\) 0 0
\(217\) −6.14575 + 10.6448i −0.417201 + 0.722613i
\(218\) 3.35425 0.227178
\(219\) 0 0
\(220\) 6.64575 11.5108i 0.448056 0.776057i
\(221\) −8.46863 + 14.6681i −0.569661 + 0.986683i
\(222\) 0 0
\(223\) −13.8745 −0.929106 −0.464553 0.885545i \(-0.653785\pi\)
−0.464553 + 0.885545i \(0.653785\pi\)
\(224\) −1.32288 + 2.29129i −0.0883883 + 0.153093i
\(225\) 0 0
\(226\) −1.17712 2.03884i −0.0783011 0.135622i
\(227\) 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
\(229\) 4.67712 + 8.10102i 0.309073 + 0.535330i 0.978160 0.207854i \(-0.0666479\pi\)
−0.669087 + 0.743184i \(0.733315\pi\)
\(230\) −4.70850 −0.310469
\(231\) 0 0
\(232\) 2.35425 0.154564
\(233\) −9.64575 16.7069i −0.631914 1.09451i −0.987160 0.159735i \(-0.948936\pi\)
0.355246 0.934773i \(-0.384397\pi\)
\(234\) 0 0
\(235\) 9.00000 15.5885i 0.587095 1.01688i
\(236\) 4.17712 + 7.23499i 0.271908 + 0.470958i
\(237\) 0 0
\(238\) −9.64575 −0.625241
\(239\) 10.9373 0.707472 0.353736 0.935345i \(-0.384911\pi\)
0.353736 + 0.935345i \(0.384911\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 1.14575 1.98450i 0.0736517 0.127568i
\(243\) 0 0
\(244\) 7.35425 0.470808
\(245\) −12.7601 22.1012i −0.815215 1.41199i
\(246\) 0 0
\(247\) 4.64575 + 8.04668i 0.295602 + 0.511998i
\(248\) −2.32288 + 4.02334i −0.147503 + 0.255482i
\(249\) 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
\(253\) −4.70850 −0.296021
\(254\) 0.677124 + 1.17281i 0.0424866 + 0.0735889i
\(255\) 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
\(259\) −15.7915 27.3517i −0.981236 1.69955i
\(260\) −16.9373 −1.05040
\(261\) 0 0
\(262\) 7.29150 12.6293i 0.450471 0.780238i
\(263\) −2.46863 + 4.27579i −0.152222 + 0.263656i −0.932044 0.362345i \(-0.881976\pi\)
0.779822 + 0.626001i \(0.215310\pi\)
\(264\) 0 0
\(265\) −21.8745 −1.34374
\(266\) −2.64575 + 4.58258i −0.162221 + 0.280976i
\(267\) 0 0
\(268\) 1.14575 + 1.98450i 0.0699879 + 0.121223i
\(269\) −8.35425 + 14.4700i −0.509368 + 0.882250i 0.490574 + 0.871400i \(0.336787\pi\)
−0.999941 + 0.0108507i \(0.996546\pi\)
\(270\) 0 0
\(271\) −2.61438 4.52824i −0.158812 0.275071i 0.775628 0.631190i \(-0.217433\pi\)
−0.934441 + 0.356119i \(0.884100\pi\)
\(272\) −3.64575 −0.221056
\(273\) 0 0
\(274\) 1.29150 0.0780225
\(275\) 15.1144 + 26.1789i 0.911431 + 1.57865i
\(276\) 0 0
\(277\) 1.03137 1.78639i 0.0619692 0.107334i −0.833376 0.552706i \(-0.813595\pi\)
0.895346 + 0.445372i \(0.146929\pi\)
\(278\) 0.791503 + 1.37092i 0.0474712 + 0.0822225i
\(279\) 0 0
\(280\) −4.82288 8.35347i −0.288222 0.499215i
\(281\) −19.5203 −1.16448 −0.582241 0.813017i \(-0.697824\pi\)
−0.582241 + 0.813017i \(0.697824\pi\)
\(282\) 0 0
\(283\) 1.14575 1.98450i 0.0681078 0.117966i −0.829961 0.557822i \(-0.811637\pi\)
0.898068 + 0.439856i \(0.144970\pi\)
\(284\) 7.82288 13.5496i 0.464202 0.804022i
\(285\) 0 0
\(286\) −16.9373 −1.00152
\(287\) 28.9373 1.70811
\(288\) 0 0
\(289\) 1.85425 + 3.21165i 0.109073 + 0.188921i
\(290\) −4.29150 + 7.43310i −0.252006 + 0.436487i
\(291\) 0 0
\(292\) −5.29150 9.16515i −0.309662 0.536350i
\(293\) −7.06275 −0.412610 −0.206305 0.978488i \(-0.566144\pi\)
−0.206305 + 0.978488i \(0.566144\pi\)
\(294\) 0 0
\(295\) −30.4575 −1.77330
\(296\) −5.96863 10.3380i −0.346919 0.600882i
\(297\) 0 0
\(298\) −11.4686 + 19.8642i −0.664360 + 1.15070i
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) −13.2288 −0.762493
\(302\) 19.2288 1.10649
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) −13.4059 + 23.2197i −0.767619 + 1.32955i
\(306\) 0 0
\(307\) 7.58301 0.432785 0.216392 0.976306i \(-0.430571\pi\)
0.216392 + 0.976306i \(0.430571\pi\)
\(308\) −4.82288 8.35347i −0.274809 0.475983i
\(309\) 0 0
\(310\) −8.46863 14.6681i −0.480986 0.833092i
\(311\) −6.76013 + 11.7089i −0.383332 + 0.663950i −0.991536 0.129830i \(-0.958557\pi\)
0.608204 + 0.793780i \(0.291890\pi\)
\(312\) 0 0
\(313\) −6.35425 11.0059i −0.359163 0.622089i 0.628658 0.777682i \(-0.283605\pi\)
−0.987821 + 0.155593i \(0.950271\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 11.2288 0.631667
\(317\) 13.4059 + 23.2197i 0.752949 + 1.30415i 0.946387 + 0.323034i \(0.104703\pi\)
−0.193438 + 0.981112i \(0.561964\pi\)
\(318\) 0 0
\(319\) −4.29150 + 7.43310i −0.240278 + 0.416174i
\(320\) −1.82288 3.15731i −0.101902 0.176499i
\(321\) 0 0
\(322\) −1.70850 + 2.95920i −0.0952108 + 0.164910i
\(323\) −7.29150 −0.405710
\(324\) 0 0
\(325\) 19.2601 33.3595i 1.06836 1.85045i
\(326\) −0.500000 + 0.866025i −0.0276924 + 0.0479647i
\(327\) 0 0
\(328\) 10.9373 0.603909
\(329\) −6.53137 11.3127i −0.360086 0.623688i
\(330\) 0 0
\(331\) 15.9373 + 27.6041i 0.875991 + 1.51726i 0.855704 + 0.517466i \(0.173125\pi\)
0.0202871 + 0.999794i \(0.493542\pi\)
\(332\) −6.64575 + 11.5108i −0.364733 + 0.631736i
\(333\) 0 0
\(334\) 4.29150 + 7.43310i 0.234821 + 0.406721i
\(335\) −8.35425 −0.456441
\(336\) 0 0
\(337\) −30.5830 −1.66596 −0.832981 0.553301i \(-0.813368\pi\)
−0.832981 + 0.553301i \(0.813368\pi\)
\(338\) 4.29150 + 7.43310i 0.233427 + 0.404307i
\(339\) 0 0
\(340\) 6.64575 11.5108i 0.360416 0.624260i
\(341\) −8.46863 14.6681i −0.458602 0.794322i
\(342\) 0 0
\(343\) −18.5203 −1.00000
\(344\) −5.00000 −0.269582
\(345\) 0 0
\(346\) 7.29150 12.6293i 0.391994 0.678953i
\(347\) −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
\(349\) −1.22876 −0.0657738 −0.0328869 0.999459i \(-0.510470\pi\)
−0.0328869 + 0.999459i \(0.510470\pi\)
\(350\) 21.9373 1.17260
\(351\) 0 0
\(352\) −1.82288 3.15731i −0.0971596 0.168285i
\(353\) −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
\(355\) 28.5203 + 49.3985i 1.51370 + 2.62180i
\(356\) −4.93725 −0.261674
\(357\) 0 0
\(358\) 16.9373 0.895162
\(359\) 5.58301 + 9.67005i 0.294660 + 0.510366i 0.974906 0.222618i \(-0.0714604\pi\)
−0.680246 + 0.732984i \(0.738127\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −1.35425 2.34563i −0.0711777 0.123283i
\(363\) 0 0
\(364\) −6.14575 + 10.6448i −0.322125 + 0.557937i
\(365\) 38.5830 2.01953
\(366\) 0 0
\(367\) −14.9373 + 25.8721i −0.779718 + 1.35051i 0.152386 + 0.988321i \(0.451304\pi\)
−0.932104 + 0.362191i \(0.882029\pi\)
\(368\) −0.645751 + 1.11847i −0.0336621 + 0.0583045i
\(369\) 0 0
\(370\) 43.5203 2.26251
\(371\) −7.93725 + 13.7477i −0.412082 + 0.713746i
\(372\) 0 0
\(373\) −2.29150 3.96900i −0.118650 0.205507i 0.800583 0.599222i \(-0.204523\pi\)
−0.919233 + 0.393715i \(0.871190\pi\)
\(374\) 6.64575 11.5108i 0.343644 0.595208i
\(375\) 0 0
\(376\) −2.46863 4.27579i −0.127310 0.220507i
\(377\) 10.9373 0.563297
\(378\) 0 0
\(379\) 25.5830 1.31411 0.657055 0.753842i \(-0.271802\pi\)
0.657055 + 0.753842i \(0.271802\pi\)
\(380\) −3.64575 6.31463i −0.187023 0.323934i
\(381\) 0 0
\(382\) 10.4059 18.0235i 0.532411 0.922163i
\(383\) 10.2915 + 17.8254i 0.525871 + 0.910836i 0.999546 + 0.0301357i \(0.00959395\pi\)
−0.473675 + 0.880700i \(0.657073\pi\)
\(384\) 0 0
\(385\) 35.1660 1.79223
\(386\) 7.00000 0.356291
\(387\) 0 0
\(388\) −6.79150 + 11.7632i −0.344786 + 0.597187i
\(389\) 9.64575 16.7069i 0.489059 0.847075i −0.510862 0.859663i \(-0.670674\pi\)
0.999921 + 0.0125878i \(0.00400694\pi\)
\(390\) 0 0
\(391\) −4.70850 −0.238119
\(392\) −7.00000 −0.353553
\(393\) 0 0
\(394\) −2.35425 4.07768i −0.118605 0.205430i
\(395\) −20.4686 + 35.4527i −1.02989 + 1.78382i
\(396\) 0 0
\(397\) 8.32288 + 14.4156i 0.417713 + 0.723500i 0.995709 0.0925393i \(-0.0294984\pi\)
−0.577996 + 0.816040i \(0.696165\pi\)
\(398\) −6.06275 −0.303898
\(399\) 0 0
\(400\) 8.29150 0.414575
\(401\) −10.4059 18.0235i −0.519645 0.900051i −0.999739 0.0228345i \(-0.992731\pi\)
0.480094 0.877217i \(-0.340602\pi\)
\(402\) 0 0
\(403\) −10.7915 + 18.6914i −0.537563 + 0.931086i
\(404\) 4.17712 + 7.23499i 0.207820 + 0.359954i
\(405\) 0 0
\(406\) 3.11438 + 5.39426i 0.154564 + 0.267713i
\(407\) 43.5203 2.15722
\(408\) 0 0
\(409\) −7.43725 + 12.8817i −0.367749 + 0.636959i −0.989213 0.146483i \(-0.953205\pi\)
0.621465 + 0.783442i \(0.286538\pi\)
\(410\) −19.9373 + 34.5323i −0.984631 + 1.70543i
\(411\) 0 0
\(412\) 3.93725 0.193975
\(413\) −11.0516 + 19.1420i −0.543815 + 0.941916i
\(414\) 0 0
\(415\) −24.2288 41.9654i −1.18934 2.06000i
\(416\) −2.32288 + 4.02334i −0.113888 + 0.197260i
\(417\) 0 0
\(418\) −3.64575 6.31463i −0.178320 0.308858i
\(419\) −28.9373 −1.41368 −0.706839 0.707375i \(-0.749879\pi\)
−0.706839 + 0.707375i \(0.749879\pi\)
\(420\) 0 0
\(421\) −14.7085 −0.716848 −0.358424 0.933559i \(-0.616686\pi\)
−0.358424 + 0.933559i \(0.616686\pi\)
\(422\) 7.43725 + 12.8817i 0.362040 + 0.627071i
\(423\) 0 0
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 15.1144 + 26.1789i 0.733155 + 1.26986i
\(426\) 0 0
\(427\) 9.72876 + 16.8507i 0.470808 + 0.815463i
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) 9.11438 15.7866i 0.439534 0.761296i
\(431\) 19.4059 33.6120i 0.934748 1.61903i 0.159666 0.987171i \(-0.448958\pi\)
0.775082 0.631861i \(-0.217709\pi\)
\(432\) 0 0
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) −12.2915 −0.590011
\(435\) 0 0
\(436\) 1.67712 + 2.90486i 0.0803197 + 0.139118i
\(437\) −1.29150 + 2.23695i −0.0617809 + 0.107008i
\(438\) 0 0
\(439\) −12.5830 21.7944i −0.600554 1.04019i −0.992737 0.120303i \(-0.961613\pi\)
0.392183 0.919887i \(-0.371720\pi\)
\(440\) 13.2915 0.633648
\(441\) 0 0
\(442\) −16.9373 −0.805623
\(443\) −9.64575 16.7069i −0.458283 0.793770i 0.540587 0.841288i \(-0.318202\pi\)
−0.998870 + 0.0475179i \(0.984869\pi\)
\(444\) 0 0
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) −6.93725 12.0157i −0.328488 0.568959i
\(447\) 0 0
\(448\) −2.64575 −0.125000
\(449\) −2.35425 −0.111104 −0.0555519 0.998456i \(-0.517692\pi\)
−0.0555519 + 0.998456i \(0.517692\pi\)
\(450\) 0 0
\(451\) −19.9373 + 34.5323i −0.938809 + 1.62606i
\(452\) 1.17712 2.03884i 0.0553673 0.0958989i
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) −22.4059 38.8081i −1.05040 1.81935i
\(456\) 0 0
\(457\) 4.14575 + 7.18065i 0.193930 + 0.335897i 0.946549 0.322559i \(-0.104543\pi\)
−0.752619 + 0.658456i \(0.771210\pi\)
\(458\) −4.67712 + 8.10102i −0.218548 + 0.378536i
\(459\) 0 0
\(460\) −2.35425 4.07768i −0.109767 0.190123i
\(461\) −24.2288 −1.12845 −0.564223 0.825623i \(-0.690824\pi\)
−0.564223 + 0.825623i \(0.690824\pi\)
\(462\) 0 0
\(463\) 18.7085 0.869458 0.434729 0.900561i \(-0.356844\pi\)
0.434729 + 0.900561i \(0.356844\pi\)
\(464\) 1.17712 + 2.03884i 0.0546466 + 0.0946507i
\(465\) 0 0
\(466\) 9.64575 16.7069i 0.446831 0.773934i
\(467\) 0.114378 + 0.198109i 0.00529280 + 0.00916739i 0.868660 0.495409i \(-0.164982\pi\)
−0.863367 + 0.504577i \(0.831649\pi\)
\(468\) 0 0
\(469\) −3.03137 + 5.25049i −0.139976 + 0.242445i
\(470\) 18.0000 0.830278
\(471\) 0 0
\(472\) −4.17712 + 7.23499i −0.192268 + 0.333017i
\(473\) 9.11438 15.7866i 0.419080 0.725867i
\(474\) 0 0
\(475\) 16.5830 0.760880
\(476\) −4.82288 8.35347i −0.221056 0.382880i
\(477\) 0 0
\(478\) 5.46863 + 9.47194i 0.250129 + 0.433236i
\(479\) 1.82288 3.15731i 0.0832893 0.144261i −0.821372 0.570393i \(-0.806791\pi\)
0.904661 + 0.426132i \(0.140124\pi\)
\(480\) 0 0
\(481\) −27.7288 48.0276i −1.26432 2.18987i
\(482\) −5.00000 −0.227744
\(483\) 0 0
\(484\) 2.29150 0.104159
\(485\) −24.7601 42.8858i −1.12430 1.94734i
\(486\) 0 0
\(487\) −11.9373 + 20.6759i −0.540929 + 0.936916i 0.457922 + 0.888992i \(0.348594\pi\)
−0.998851 + 0.0479237i \(0.984740\pi\)
\(488\) 3.67712 + 6.36897i 0.166456 + 0.288310i
\(489\) 0 0
\(490\) 12.7601 22.1012i 0.576444 0.998430i
\(491\) −25.7490 −1.16204 −0.581018 0.813890i \(-0.697346\pi\)
−0.581018 + 0.813890i \(0.697346\pi\)
\(492\) 0 0
\(493\) −4.29150 + 7.43310i −0.193280 + 0.334770i
\(494\) −4.64575 + 8.04668i −0.209022 + 0.362037i
\(495\) 0 0
\(496\) −4.64575 −0.208600
\(497\) 41.3948 1.85681
\(498\) 0 0
\(499\) 3.08301 + 5.33992i 0.138014 + 0.239048i 0.926745 0.375691i \(-0.122595\pi\)
−0.788731 + 0.614739i \(0.789261\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) 9.00000 + 15.5885i 0.401690 + 0.695747i
\(503\) −3.87451 −0.172756 −0.0863779 0.996262i \(-0.527529\pi\)
−0.0863779 + 0.996262i \(0.527529\pi\)
\(504\) 0 0
\(505\) −30.4575 −1.35534
\(506\) −2.35425 4.07768i −0.104659 0.181275i
\(507\) 0 0
\(508\) −0.677124 + 1.17281i −0.0300425 + 0.0520352i
\(509\) 4.06275 + 7.03688i 0.180078 + 0.311904i 0.941907 0.335874i \(-0.109032\pi\)
−0.761829 + 0.647778i \(0.775698\pi\)
\(510\) 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
\(515\) −7.17712 + 12.4311i −0.316262 + 0.547782i
\(516\) 0 0
\(517\) 18.0000 0.791639
\(518\) 15.7915 27.3517i 0.693839 1.20176i
\(519\) 0 0
\(520\) −8.46863 14.6681i −0.371374 0.643238i
\(521\) −4.06275 + 7.03688i −0.177992 + 0.308291i −0.941193 0.337870i \(-0.890293\pi\)
0.763201 + 0.646162i \(0.223627\pi\)
\(522\) 0 0
\(523\) 0.500000 + 0.866025i 0.0218635 + 0.0378686i 0.876750 0.480946i \(-0.159707\pi\)
−0.854887 + 0.518815i \(0.826373\pi\)
\(524\) 14.5830 0.637062
\(525\) 0 0
\(526\) −4.93725 −0.215275
\(527\) −8.46863 14.6681i −0.368899 0.638952i
\(528\) 0 0
\(529\) 10.6660 18.4741i 0.463740 0.803221i
\(530\) −10.9373 18.9439i −0.475084 0.822870i
\(531\) 0 0
\(532\) −5.29150 −0.229416
\(533\) 50.8118 2.20090
\(534\) 0 0
\(535\) −10.9373 + 18.9439i −0.472859 + 0.819015i
\(536\) −1.14575 + 1.98450i −0.0494889 + 0.0857173i
\(537\) 0 0
\(538\) −16.7085 −0.720354
\(539\) 12.7601 22.1012i 0.549618 0.951966i
\(540\) 0 0
\(541\) −0.583005 1.00979i −0.0250654 0.0434145i 0.853221 0.521550i \(-0.174646\pi\)
−0.878286 + 0.478136i \(0.841313\pi\)
\(542\) 2.61438 4.52824i 0.112297 0.194504i
\(543\) 0 0
\(544\) −1.82288 3.15731i −0.0781551 0.135369i
\(545\) −12.2288 −0.523822
\(546\) 0 0
\(547\) 18.2915 0.782088 0.391044 0.920372i \(-0.372114\pi\)
0.391044 + 0.920372i \(0.372114\pi\)
\(548\) 0.645751 + 1.11847i 0.0275851 + 0.0477788i
\(549\) 0 0
\(550\) −15.1144 + 26.1789i −0.644479 + 1.11627i
\(551\) 2.35425 + 4.07768i 0.100294 + 0.173715i
\(552\) 0 0
\(553\) 14.8542 + 25.7283i 0.631667 + 1.09408i
\(554\) 2.06275 0.0876377
\(555\) 0 0
\(556\) −0.791503 + 1.37092i −0.0335672 + 0.0581401i
\(557\) −2.88562 + 4.99804i −0.122268 + 0.211774i −0.920662 0.390362i \(-0.872350\pi\)
0.798394 + 0.602136i \(0.205683\pi\)
\(558\) 0 0
\(559\) −23.2288 −0.982472
\(560\) 4.82288 8.35347i 0.203804 0.352998i
\(561\) 0 0
\(562\) −9.76013 16.9050i −0.411706 0.713096i
\(563\) 9.22876 15.9847i 0.388946 0.673674i −0.603362 0.797467i \(-0.706173\pi\)
0.992308 + 0.123793i \(0.0395060\pi\)
\(564\) 0 0
\(565\) 4.29150 + 7.43310i 0.180545 + 0.312713i
\(566\) 2.29150 0.0963190
\(567\) 0 0
\(568\) 15.6458 0.656481
\(569\) −8.46863 14.6681i −0.355023 0.614918i 0.632099 0.774888i \(-0.282194\pi\)
−0.987122 + 0.159970i \(0.948860\pi\)
\(570\) 0 0
\(571\) −4.64575 + 8.04668i −0.194419 + 0.336743i −0.946710 0.322088i \(-0.895615\pi\)
0.752291 + 0.658831i \(0.228949\pi\)
\(572\) −8.46863 14.6681i −0.354091 0.613304i
\(573\) 0 0
\(574\) 14.4686 + 25.0604i 0.603909 + 1.04600i
\(575\) 10.7085 0.446575
\(576\) 0 0
\(577\) 16.1458 27.9653i 0.672156 1.16421i −0.305135 0.952309i \(-0.598702\pi\)
0.977291 0.211900i \(-0.0679651\pi\)
\(578\) −1.85425 + 3.21165i −0.0771266 + 0.133587i
\(579\) 0 0
\(580\) −8.58301 −0.356390
\(581\) −35.1660 −1.45893
\(582\) 0 0
\(583\) −10.9373 18.9439i −0.452975 0.784575i
\(584\) 5.29150 9.16515i 0.218964 0.379257i
\(585\) 0 0
\(586\) −3.53137 6.11652i −0.145880 0.252671i
\(587\) −11.7712 −0.485851 −0.242926 0.970045i \(-0.578107\pi\)
−0.242926 + 0.970045i \(0.578107\pi\)
\(588\) 0 0
\(589\) −9.29150 −0.382850
\(590\) −15.2288 26.3770i −0.626958 1.08592i
\(591\) 0 0
\(592\) 5.96863 10.3380i 0.245309 0.424888i
\(593\) 20.4686 + 35.4527i 0.840546 + 1.45587i 0.889434 + 0.457064i \(0.151099\pi\)
−0.0488882 + 0.998804i \(0.515568\pi\)
\(594\) 0 0
\(595\) 35.1660 1.44167
\(596\) −22.9373 −0.939547
\(597\) 0 0
\(598\) −3.00000 + 5.19615i −0.122679 + 0.212486i
\(599\) 4.93725 8.55157i 0.201731 0.349408i −0.747355 0.664424i \(-0.768677\pi\)
0.949086 + 0.315017i \(0.102010\pi\)
\(600\) 0 0
\(601\) 26.8745 1.09623 0.548117 0.836402i \(-0.315345\pi\)
0.548117 + 0.836402i \(0.315345\pi\)
\(602\) −6.61438 11.4564i −0.269582 0.466930i
\(603\) 0 0
\(604\) 9.61438 + 16.6526i 0.391204 + 0.677584i
\(605\) −4.17712 + 7.23499i −0.169824 + 0.294144i
\(606\) 0 0
\(607\) −2.70850 4.69126i −0.109935 0.190412i 0.805809 0.592176i \(-0.201731\pi\)
−0.915744 + 0.401763i \(0.868397\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) −26.8118 −1.08558
\(611\) −11.4686 19.8642i −0.463971 0.803621i
\(612\) 0 0
\(613\) 21.1974 36.7149i 0.856154 1.48290i −0.0194158 0.999811i \(-0.506181\pi\)
0.875570 0.483091i \(-0.160486\pi\)
\(614\) 3.79150 + 6.56708i 0.153013 + 0.265026i
\(615\) 0 0
\(616\) 4.82288 8.35347i 0.194319 0.336571i
\(617\) −1.52026 −0.0612033 −0.0306017 0.999532i \(-0.509742\pi\)
−0.0306017 + 0.999532i \(0.509742\pi\)
\(618\) 0 0
\(619\) 4.14575 7.18065i 0.166632 0.288615i −0.770602 0.637317i \(-0.780044\pi\)
0.937234 + 0.348702i \(0.113378\pi\)
\(620\) 8.46863 14.6681i 0.340108 0.589085i
\(621\) 0 0
\(622\) −13.5203 −0.542113
\(623\) −6.53137 11.3127i −0.261674 0.453233i
\(624\) 0 0
\(625\) −1.14575 1.98450i −0.0458301 0.0793800i
\(626\) 6.35425 11.0059i 0.253967 0.439883i
\(627\) 0 0
\(628\) 2.00000 + 3.46410i 0.0798087 + 0.138233i
\(629\) 43.5203 1.73527
\(630\) 0 0
\(631\) 6.06275 0.241354 0.120677 0.992692i \(-0.461493\pi\)
0.120677 + 0.992692i \(0.461493\pi\)
\(632\) 5.61438 + 9.72439i 0.223328 + 0.386815i
\(633\) 0 0
\(634\) −13.4059 + 23.2197i −0.532416 + 0.922171i
\(635\) −2.46863 4.27579i −0.0979645 0.169679i
\(636\) 0 0
\(637\) −32.5203 −1.28850
\(638\) −8.58301 −0.339804
\(639\) 0 0
\(640\) 1.82288 3.15731i 0.0720555 0.124804i
\(641\) −9.11438 + 15.7866i −0.359996 + 0.623532i −0.987960 0.154711i \(-0.950555\pi\)
0.627963 + 0.778243i \(0.283889\pi\)
\(642\) 0 0
\(643\) −3.12549 −0.123257 −0.0616287 0.998099i \(-0.519629\pi\)
−0.0616287 + 0.998099i \(0.519629\pi\)
\(644\) −3.41699 −0.134648
\(645\) 0 0
\(646\) −3.64575 6.31463i −0.143440 0.248446i
\(647\) 4.93725 8.55157i 0.194103 0.336197i −0.752503 0.658589i \(-0.771154\pi\)
0.946606 + 0.322392i \(0.104487\pi\)
\(648\) 0 0
\(649\) −15.2288 26.3770i −0.597781 1.03539i
\(650\) 38.5203 1.51089
\(651\) 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
\(655\) −26.5830 + 46.0431i −1.03868 + 1.79905i
\(656\) 5.46863 + 9.47194i 0.213514 + 0.369817i
\(657\) 0 0
\(658\) 6.53137 11.3127i 0.254619 0.441014i
\(659\) 24.2288 0.943818 0.471909 0.881647i \(-0.343565\pi\)
0.471909 + 0.881647i \(0.343565\pi\)
\(660\) 0 0
\(661\) 1.58301 2.74185i 0.0615718 0.106645i −0.833596 0.552374i \(-0.813722\pi\)
0.895168 + 0.445729i \(0.147055\pi\)
\(662\) −15.9373 + 27.6041i −0.619419 + 1.07287i
\(663\) 0 0
\(664\) −13.2915 −0.515810
\(665\) 9.64575 16.7069i 0.374046 0.647867i
\(666\) 0 0
\(667\) 1.52026 + 2.63317i 0.0588647 + 0.101957i
\(668\) −4.29150 + 7.43310i −0.166043 + 0.287595i
\(669\) 0 0
\(670\) −4.17712 7.23499i −0.161376 0.279512i
\(671\) −26.8118 −1.03506
\(672\) 0 0
\(673\) 15.7490 0.607080 0.303540 0.952819i \(-0.401831\pi\)
0.303540 + 0.952819i \(0.401831\pi\)
\(674\) −15.2915 26.4857i −0.589007 1.02019i
\(675\) 0 0
\(676\) −4.29150 + 7.43310i −0.165058 + 0.285888i
\(677\) −22.9373 39.7285i −0.881550 1.52689i −0.849617 0.527400i \(-0.823167\pi\)
−0.0319331 0.999490i \(-0.510166\pi\)
\(678\) 0 0
\(679\) −35.9373 −1.37915
\(680\) 13.2915 0.509706
\(681\) 0 0
\(682\) 8.46863 14.6681i 0.324280 0.561670i
\(683\) −13.4059 + 23.2197i −0.512962 + 0.888476i 0.486925 + 0.873444i \(0.338118\pi\)
−0.999887 + 0.0150322i \(0.995215\pi\)
\(684\) 0 0
\(685\) −4.70850 −0.179902
\(686\) −9.26013 16.0390i −0.353553 0.612372i
\(687\) 0 0
\(688\) −2.50000 4.33013i −0.0953116 0.165085i
\(689\) −13.9373 + 24.1400i −0.530967 + 0.919662i
\(690\) 0 0
\(691\) 19.3745 + 33.5576i 0.737041 + 1.27659i 0.953822 + 0.300372i \(0.0971109\pi\)
−0.216781 + 0.976220i \(0.569556\pi\)
\(692\) 14.5830 0.554363
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −2.88562 4.99804i −0.109458 0.189587i
\(696\) 0 0
\(697\) −19.9373 + 34.5323i −0.755177 + 1.30801i
\(698\) −0.614378 1.06413i −0.0232546 0.0402781i
\(699\) 0 0
\(700\) 10.9686 + 18.9982i 0.414575 + 0.718065i
\(701\) 26.5830 1.00403 0.502013 0.864860i \(-0.332593\pi\)
0.502013 + 0.864860i \(0.332593\pi\)
\(702\) 0 0
\(703\) 11.9373 20.6759i 0.450222 0.779807i
\(704\) 1.82288 3.15731i 0.0687022 0.118996i
\(705\) 0 0
\(706\) −12.0000 −0.451626
\(707\) −11.0516 + 19.1420i −0.415639 + 0.719909i
\(708\) 0 0
\(709\) −18.9059 32.7459i −0.710025 1.22980i −0.964847 0.262812i \(-0.915350\pi\)
0.254822 0.966988i \(-0.417983\pi\)
\(710\) −28.5203 + 49.3985i −1.07035 + 1.85389i
\(711\) 0 0
\(712\) −2.46863 4.27579i −0.0925157 0.160242i
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) 61.7490 2.30928
\(716\) 8.46863 + 14.6681i 0.316487 + 0.548172i
\(717\) 0 0
\(718\) −5.58301 + 9.67005i −0.208356 + 0.360883i
\(719\) 11.4686 + 19.8642i 0.427708 + 0.740811i 0.996669 0.0815529i \(-0.0259880\pi\)
−0.568961 + 0.822364i \(0.692655\pi\)
\(720\) 0 0
\(721\) 5.20850 + 9.02138i 0.193975 + 0.335974i
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 1.35425 2.34563i 0.0503303 0.0871746i
\(725\) 9.76013 16.9050i 0.362482 0.627837i
\(726\) 0 0
\(727\) −1.22876 −0.0455721 −0.0227860 0.999740i \(-0.507254\pi\)
−0.0227860 + 0.999740i \(0.507254\pi\)
\(728\) −12.2915 −0.455553
\(729\) 0 0
\(730\) 19.2915 + 33.4139i 0.714011 + 1.23670i
\(731\) 9.11438 15.7866i 0.337107 0.583887i
\(732\) 0 0
\(733\) −17.6144 30.5090i −0.650602 1.12688i −0.982977 0.183728i \(-0.941183\pi\)
0.332375 0.943147i \(-0.392150\pi\)
\(734\) −29.8745 −1.10269
\(735\) 0 0
\(736\) −1.29150 −0.0476054
\(737\) −4.17712 7.23499i −0.153866 0.266504i
\(738\) 0 0
\(739\) 15.7288 27.2430i 0.578592 1.00215i −0.417050 0.908884i \(-0.636936\pi\)
0.995641 0.0932664i \(-0.0297308\pi\)
\(740\) 21.7601 + 37.6897i 0.799918 + 1.38550i
\(741\) 0 0
\(742\) −15.8745 −0.582772
\(743\) 28.9373 1.06160 0.530802 0.847496i \(-0.321891\pi\)
0.530802 + 0.847496i \(0.321891\pi\)
\(744\) 0 0
\(745\) 41.8118 72.4201i 1.53186 2.65327i
\(746\) 2.29150 3.96900i 0.0838979 0.145315i
\(747\) 0 0
\(748\) 13.2915 0.485985
\(749\) 7.93725 + 13.7477i 0.290021 + 0.502331i
\(750\) 0 0
\(751\) 26.2288 + 45.4295i 0.957101 + 1.65775i 0.729485 + 0.683996i \(0.239760\pi\)
0.227615 + 0.973751i \(0.426907\pi\)
\(752\) 2.46863 4.27579i 0.0900216 0.155922i
\(753\) 0 0
\(754\) 5.46863 + 9.47194i 0.199156 + 0.344948i
\(755\) −70.1033 −2.55132
\(756\) 0 0
\(757\) 48.9778 1.78013 0.890064 0.455836i \(-0.150660\pi\)
0.890064 + 0.455836i \(0.150660\pi\)
\(758\) 12.7915 + 22.1555i 0.464608 + 0.804725i
\(759\) 0 0
\(760\) 3.64575 6.31463i 0.132245 0.229056i
\(761\) 1.29150 + 2.23695i 0.0468169 + 0.0810893i 0.888484 0.458907i \(-0.151759\pi\)
−0.841667 + 0.539996i \(0.818426\pi\)
\(762\) 0 0
\(763\) −4.43725 + 7.68555i −0.160639 + 0.278236i
\(764\) 20.8118 0.752943
\(765\) 0 0
\(766\) −10.2915 + 17.8254i −0.371847 + 0.644058i
\(767\) −19.4059 + 33.6120i −0.700706 + 1.21366i
\(768\) 0 0
\(769\) 40.5830 1.46346 0.731730 0.681594i \(-0.238713\pi\)
0.731730 + 0.681594i \(0.238713\pi\)
\(770\) 17.5830 + 30.4547i 0.633648 + 1.09751i
\(771\) 0 0
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) −23.1660 + 40.1247i −0.833223 + 1.44319i 0.0622452 + 0.998061i \(0.480174\pi\)
−0.895469 + 0.445125i \(0.853159\pi\)
\(774\) 0 0
\(775\) 19.2601 + 33.3595i 0.691844 + 1.19831i
\(776\) −13.5830 −0.487601
\(777\) 0 0
\(778\) 19.2915 0.691634
\(779\) 10.9373 + 18.9439i 0.391868 + 0.678735i
\(780\) 0 0
\(781\) −28.5203 + 49.3985i −1.02054 + 1.76762i
\(782\) −2.35425 4.07768i −0.0841878 0.145817i
\(783\) 0 0
\(784\) −3.50000 6.06218i −0.125000 0.216506i
\(785\) −14.5830 −0.520490
\(786\) 0 0
\(787\) 5.85425 10.1399i 0.208681 0.361447i −0.742618 0.669715i \(-0.766416\pi\)
0.951299 + 0.308268i \(0.0997495\pi\)
\(788\) 2.35425 4.07768i 0.0838666 0.145261i
\(789\) 0