Properties

Label 378.2.f.d.253.2
Level $378$
Weight $2$
Character 378.253
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.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 253.2
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 378.253
Dual form 378.2.f.d.127.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 2.98735i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 2.98735i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +3.44949 q^{10} +(1.00000 + 1.73205i) q^{11} +(2.44949 - 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} +7.44949 q^{19} +(1.72474 + 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-3.44949 - 5.97469i) q^{25} +4.89898 q^{26} -1.00000 q^{28} +(1.44949 + 2.51059i) q^{29} +(-3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{34} +3.44949 q^{35} -7.79796 q^{37} +(3.72474 + 6.45145i) q^{38} +(-1.72474 + 2.98735i) q^{40} +(-4.89898 + 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} -2.00000 q^{44} -1.00000 q^{46} +(-4.89898 - 8.48528i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(3.44949 - 5.97469i) q^{50} +(2.44949 + 4.24264i) q^{52} +1.10102 q^{53} +6.89898 q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.44949 + 2.51059i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(-5.72474 - 9.91555i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-8.44949 - 14.6349i) q^{65} +(1.55051 - 2.68556i) q^{67} +(1.00000 - 1.73205i) q^{68} +(1.72474 + 2.98735i) q^{70} -9.89898 q^{71} +2.89898 q^{73} +(-3.89898 - 6.75323i) q^{74} +(-3.72474 + 6.45145i) q^{76} +(-1.00000 + 1.73205i) q^{77} +(-3.94949 - 6.84072i) q^{79} -3.44949 q^{80} -9.79796 q^{82} +(1.00000 + 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +(-1.44949 + 2.51059i) q^{86} +(-1.00000 - 1.73205i) q^{88} +7.10102 q^{89} +4.89898 q^{91} +(-0.500000 - 0.866025i) q^{92} +(4.89898 - 8.48528i) q^{94} +(12.8485 - 22.2542i) q^{95} +(3.44949 + 5.97469i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} + 2q^{5} + 2q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} + 2q^{5} + 2q^{7} - 4q^{8} + 4q^{10} + 4q^{11} - 2q^{14} - 2q^{16} - 8q^{17} + 20q^{19} + 2q^{20} - 4q^{22} - 2q^{23} - 4q^{25} - 4q^{28} - 4q^{29} - 12q^{31} + 2q^{32} - 4q^{34} + 4q^{35} + 8q^{37} + 10q^{38} - 2q^{40} - 4q^{43} - 8q^{44} - 4q^{46} - 2q^{49} + 4q^{50} + 24q^{53} + 8q^{55} - 2q^{56} + 4q^{58} - 4q^{59} - 18q^{61} - 24q^{62} + 4q^{64} - 24q^{65} + 16q^{67} + 4q^{68} + 2q^{70} - 20q^{71} - 8q^{73} + 4q^{74} - 10q^{76} - 4q^{77} - 6q^{79} - 4q^{80} + 4q^{83} - 4q^{85} + 4q^{86} - 4q^{88} + 48q^{89} - 2q^{92} + 22q^{95} + 4q^{97} - 4q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.72474 2.98735i 0.771329 1.33598i −0.165505 0.986209i \(-0.552925\pi\)
0.936835 0.349773i \(-0.113741\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 3.44949 1.09082
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) 2.44949 4.24264i 0.679366 1.17670i −0.295806 0.955248i \(-0.595588\pi\)
0.975172 0.221449i \(-0.0710785\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 7.44949 1.70903 0.854515 0.519427i \(-0.173854\pi\)
0.854515 + 0.519427i \(0.173854\pi\)
\(20\) 1.72474 + 2.98735i 0.385665 + 0.667991i
\(21\) 0 0
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) −3.44949 5.97469i −0.689898 1.19494i
\(26\) 4.89898 0.960769
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 1.44949 + 2.51059i 0.269163 + 0.466205i 0.968646 0.248445i \(-0.0799195\pi\)
−0.699483 + 0.714650i \(0.746586\pi\)
\(30\) 0 0
\(31\) −3.00000 + 5.19615i −0.538816 + 0.933257i 0.460152 + 0.887840i \(0.347795\pi\)
−0.998968 + 0.0454165i \(0.985539\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.00000 1.73205i −0.171499 0.297044i
\(35\) 3.44949 0.583070
\(36\) 0 0
\(37\) −7.79796 −1.28198 −0.640988 0.767551i \(-0.721475\pi\)
−0.640988 + 0.767551i \(0.721475\pi\)
\(38\) 3.72474 + 6.45145i 0.604233 + 1.04656i
\(39\) 0 0
\(40\) −1.72474 + 2.98735i −0.272706 + 0.472341i
\(41\) −4.89898 + 8.48528i −0.765092 + 1.32518i 0.175106 + 0.984550i \(0.443973\pi\)
−0.940198 + 0.340629i \(0.889360\pi\)
\(42\) 0 0
\(43\) 1.44949 + 2.51059i 0.221045 + 0.382861i 0.955126 0.296201i \(-0.0957199\pi\)
−0.734080 + 0.679062i \(0.762387\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) −4.89898 8.48528i −0.714590 1.23771i −0.963118 0.269081i \(-0.913280\pi\)
0.248528 0.968625i \(-0.420053\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 3.44949 5.97469i 0.487832 0.844949i
\(51\) 0 0
\(52\) 2.44949 + 4.24264i 0.339683 + 0.588348i
\(53\) 1.10102 0.151237 0.0756184 0.997137i \(-0.475907\pi\)
0.0756184 + 0.997137i \(0.475907\pi\)
\(54\) 0 0
\(55\) 6.89898 0.930258
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 0 0
\(58\) −1.44949 + 2.51059i −0.190327 + 0.329657i
\(59\) −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i \(-0.874892\pi\)
0.793560 + 0.608492i \(0.208225\pi\)
\(60\) 0 0
\(61\) −5.72474 9.91555i −0.732978 1.26956i −0.955605 0.294652i \(-0.904796\pi\)
0.222626 0.974904i \(-0.428537\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −8.44949 14.6349i −1.04803 1.81524i
\(66\) 0 0
\(67\) 1.55051 2.68556i 0.189425 0.328094i −0.755634 0.654994i \(-0.772671\pi\)
0.945059 + 0.326901i \(0.106004\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0 0
\(70\) 1.72474 + 2.98735i 0.206146 + 0.357056i
\(71\) −9.89898 −1.17479 −0.587396 0.809299i \(-0.699847\pi\)
−0.587396 + 0.809299i \(0.699847\pi\)
\(72\) 0 0
\(73\) 2.89898 0.339300 0.169650 0.985504i \(-0.445736\pi\)
0.169650 + 0.985504i \(0.445736\pi\)
\(74\) −3.89898 6.75323i −0.453247 0.785047i
\(75\) 0 0
\(76\) −3.72474 + 6.45145i −0.427258 + 0.740032i
\(77\) −1.00000 + 1.73205i −0.113961 + 0.197386i
\(78\) 0 0
\(79\) −3.94949 6.84072i −0.444352 0.769641i 0.553655 0.832746i \(-0.313233\pi\)
−0.998007 + 0.0631057i \(0.979899\pi\)
\(80\) −3.44949 −0.385665
\(81\) 0 0
\(82\) −9.79796 −1.08200
\(83\) 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i \(-0.131657\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(84\) 0 0
\(85\) −3.44949 + 5.97469i −0.374150 + 0.648046i
\(86\) −1.44949 + 2.51059i −0.156302 + 0.270724i
\(87\) 0 0
\(88\) −1.00000 1.73205i −0.106600 0.184637i
\(89\) 7.10102 0.752707 0.376353 0.926476i \(-0.377178\pi\)
0.376353 + 0.926476i \(0.377178\pi\)
\(90\) 0 0
\(91\) 4.89898 0.513553
\(92\) −0.500000 0.866025i −0.0521286 0.0902894i
\(93\) 0 0
\(94\) 4.89898 8.48528i 0.505291 0.875190i
\(95\) 12.8485 22.2542i 1.31823 2.28323i
\(96\) 0 0
\(97\) 3.44949 + 5.97469i 0.350243 + 0.606638i 0.986292 0.165011i \(-0.0527658\pi\)
−0.636049 + 0.771649i \(0.719432\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 6.89898 0.689898
\(101\) 3.62372 + 6.27647i 0.360574 + 0.624533i 0.988055 0.154099i \(-0.0492475\pi\)
−0.627481 + 0.778632i \(0.715914\pi\)
\(102\) 0 0
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) −2.44949 + 4.24264i −0.240192 + 0.416025i
\(105\) 0 0
\(106\) 0.550510 + 0.953512i 0.0534703 + 0.0926132i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −16.6969 −1.59928 −0.799638 0.600482i \(-0.794975\pi\)
−0.799638 + 0.600482i \(0.794975\pi\)
\(110\) 3.44949 + 5.97469i 0.328896 + 0.569664i
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) −7.94949 + 13.7689i −0.747825 + 1.29527i 0.201038 + 0.979583i \(0.435569\pi\)
−0.948863 + 0.315688i \(0.897765\pi\)
\(114\) 0 0
\(115\) 1.72474 + 2.98735i 0.160833 + 0.278571i
\(116\) −2.89898 −0.269163
\(117\) 0 0
\(118\) −2.00000 −0.184115
\(119\) −1.00000 1.73205i −0.0916698 0.158777i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 5.72474 9.91555i 0.518294 0.897712i
\(123\) 0 0
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) −6.55051 −0.585895
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 8.44949 14.6349i 0.741069 1.28357i
\(131\) −6.72474 + 11.6476i −0.587544 + 1.01766i 0.407009 + 0.913424i \(0.366572\pi\)
−0.994553 + 0.104232i \(0.966762\pi\)
\(132\) 0 0
\(133\) 3.72474 + 6.45145i 0.322976 + 0.559411i
\(134\) 3.10102 0.267887
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) −5.89898 10.2173i −0.503984 0.872926i −0.999989 0.00460626i \(-0.998534\pi\)
0.496006 0.868319i \(-0.334800\pi\)
\(138\) 0 0
\(139\) −4.72474 + 8.18350i −0.400748 + 0.694115i −0.993816 0.111037i \(-0.964583\pi\)
0.593069 + 0.805152i \(0.297916\pi\)
\(140\) −1.72474 + 2.98735i −0.145768 + 0.252477i
\(141\) 0 0
\(142\) −4.94949 8.57277i −0.415352 0.719411i
\(143\) 9.79796 0.819346
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) 1.44949 + 2.51059i 0.119961 + 0.207778i
\(147\) 0 0
\(148\) 3.89898 6.75323i 0.320494 0.555112i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) −7.44949 −0.604233
\(153\) 0 0
\(154\) −2.00000 −0.161165
\(155\) 10.3485 + 17.9241i 0.831209 + 1.43970i
\(156\) 0 0
\(157\) −3.17423 + 5.49794i −0.253332 + 0.438783i −0.964441 0.264298i \(-0.914860\pi\)
0.711109 + 0.703081i \(0.248193\pi\)
\(158\) 3.94949 6.84072i 0.314205 0.544218i
\(159\) 0 0
\(160\) −1.72474 2.98735i −0.136353 0.236170i
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −0.202041 −0.0158251 −0.00791254 0.999969i \(-0.502519\pi\)
−0.00791254 + 0.999969i \(0.502519\pi\)
\(164\) −4.89898 8.48528i −0.382546 0.662589i
\(165\) 0 0
\(166\) −1.00000 + 1.73205i −0.0776151 + 0.134433i
\(167\) 9.34847 16.1920i 0.723406 1.25298i −0.236220 0.971700i \(-0.575909\pi\)
0.959627 0.281277i \(-0.0907579\pi\)
\(168\) 0 0
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) −6.89898 −0.529128
\(171\) 0 0
\(172\) −2.89898 −0.221045
\(173\) −6.44949 11.1708i −0.490346 0.849304i 0.509593 0.860416i \(-0.329796\pi\)
−0.999938 + 0.0111123i \(0.996463\pi\)
\(174\) 0 0
\(175\) 3.44949 5.97469i 0.260757 0.451644i
\(176\) 1.00000 1.73205i 0.0753778 0.130558i
\(177\) 0 0
\(178\) 3.55051 + 6.14966i 0.266122 + 0.460937i
\(179\) 8.69694 0.650040 0.325020 0.945707i \(-0.394629\pi\)
0.325020 + 0.945707i \(0.394629\pi\)
\(180\) 0 0
\(181\) 4.34847 0.323219 0.161610 0.986855i \(-0.448331\pi\)
0.161610 + 0.986855i \(0.448331\pi\)
\(182\) 2.44949 + 4.24264i 0.181568 + 0.314485i
\(183\) 0 0
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −13.4495 + 23.2952i −0.988826 + 1.71270i
\(186\) 0 0
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) 9.79796 0.714590
\(189\) 0 0
\(190\) 25.6969 1.86425
\(191\) 6.94949 + 12.0369i 0.502847 + 0.870957i 0.999995 + 0.00329106i \(0.00104758\pi\)
−0.497147 + 0.867666i \(0.665619\pi\)
\(192\) 0 0
\(193\) 4.05051 7.01569i 0.291562 0.505000i −0.682617 0.730776i \(-0.739158\pi\)
0.974179 + 0.225776i \(0.0724917\pi\)
\(194\) −3.44949 + 5.97469i −0.247659 + 0.428958i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) 12.6969 0.904619 0.452310 0.891861i \(-0.350600\pi\)
0.452310 + 0.891861i \(0.350600\pi\)
\(198\) 0 0
\(199\) 6.89898 0.489056 0.244528 0.969642i \(-0.421367\pi\)
0.244528 + 0.969642i \(0.421367\pi\)
\(200\) 3.44949 + 5.97469i 0.243916 + 0.422474i
\(201\) 0 0
\(202\) −3.62372 + 6.27647i −0.254964 + 0.441611i
\(203\) −1.44949 + 2.51059i −0.101734 + 0.176209i
\(204\) 0 0
\(205\) 16.8990 + 29.2699i 1.18028 + 2.04430i
\(206\) −14.0000 −0.975426
\(207\) 0 0
\(208\) −4.89898 −0.339683
\(209\) 7.44949 + 12.9029i 0.515292 + 0.892512i
\(210\) 0 0
\(211\) −1.55051 + 2.68556i −0.106742 + 0.184882i −0.914448 0.404703i \(-0.867375\pi\)
0.807707 + 0.589584i \(0.200708\pi\)
\(212\) −0.550510 + 0.953512i −0.0378092 + 0.0654875i
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 10.0000 0.681994
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) −8.34847 14.4600i −0.565430 0.979353i
\(219\) 0 0
\(220\) −3.44949 + 5.97469i −0.232565 + 0.402814i
\(221\) −4.89898 + 8.48528i −0.329541 + 0.570782i
\(222\) 0 0
\(223\) 10.4495 + 18.0990i 0.699750 + 1.21200i 0.968553 + 0.248807i \(0.0800384\pi\)
−0.268804 + 0.963195i \(0.586628\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −15.8990 −1.05758
\(227\) −0.275255 0.476756i −0.0182693 0.0316434i 0.856746 0.515738i \(-0.172482\pi\)
−0.875016 + 0.484095i \(0.839149\pi\)
\(228\) 0 0
\(229\) 11.6237 20.1329i 0.768117 1.33042i −0.170465 0.985364i \(-0.554527\pi\)
0.938583 0.345055i \(-0.112140\pi\)
\(230\) −1.72474 + 2.98735i −0.113726 + 0.196980i
\(231\) 0 0
\(232\) −1.44949 2.51059i −0.0951637 0.164828i
\(233\) 7.00000 0.458585 0.229293 0.973358i \(-0.426359\pi\)
0.229293 + 0.973358i \(0.426359\pi\)
\(234\) 0 0
\(235\) −33.7980 −2.20474
\(236\) −1.00000 1.73205i −0.0650945 0.112747i
\(237\) 0 0
\(238\) 1.00000 1.73205i 0.0648204 0.112272i
\(239\) −6.39898 + 11.0834i −0.413916 + 0.716923i −0.995314 0.0966962i \(-0.969172\pi\)
0.581398 + 0.813619i \(0.302506\pi\)
\(240\) 0 0
\(241\) 4.44949 + 7.70674i 0.286617 + 0.496435i 0.973000 0.230805i \(-0.0741360\pi\)
−0.686383 + 0.727240i \(0.740803\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) 11.4495 0.732978
\(245\) 1.72474 + 2.98735i 0.110190 + 0.190855i
\(246\) 0 0
\(247\) 18.2474 31.6055i 1.16106 2.01101i
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) 0 0
\(250\) −3.27526 5.67291i −0.207145 0.358786i
\(251\) −12.5505 −0.792181 −0.396091 0.918211i \(-0.629633\pi\)
−0.396091 + 0.918211i \(0.629633\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) −1.50000 2.59808i −0.0941184 0.163018i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 13.8990 24.0737i 0.866995 1.50168i 0.00194150 0.999998i \(-0.499382\pi\)
0.865053 0.501680i \(-0.167285\pi\)
\(258\) 0 0
\(259\) −3.89898 6.75323i −0.242271 0.419625i
\(260\) 16.8990 1.04803
\(261\) 0 0
\(262\) −13.4495 −0.830912
\(263\) 8.05051 + 13.9439i 0.496416 + 0.859817i 0.999991 0.00413383i \(-0.00131584\pi\)
−0.503576 + 0.863951i \(0.667983\pi\)
\(264\) 0 0
\(265\) 1.89898 3.28913i 0.116653 0.202050i
\(266\) −3.72474 + 6.45145i −0.228379 + 0.395564i
\(267\) 0 0
\(268\) 1.55051 + 2.68556i 0.0947125 + 0.164047i
\(269\) 3.65153 0.222638 0.111319 0.993785i \(-0.464493\pi\)
0.111319 + 0.993785i \(0.464493\pi\)
\(270\) 0 0
\(271\) 16.8990 1.02654 0.513270 0.858227i \(-0.328434\pi\)
0.513270 + 0.858227i \(0.328434\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) 5.89898 10.2173i 0.356370 0.617252i
\(275\) 6.89898 11.9494i 0.416024 0.720575i
\(276\) 0 0
\(277\) −5.34847 9.26382i −0.321358 0.556609i 0.659410 0.751783i \(-0.270806\pi\)
−0.980769 + 0.195174i \(0.937473\pi\)
\(278\) −9.44949 −0.566743
\(279\) 0 0
\(280\) −3.44949 −0.206146
\(281\) −9.50000 16.4545i −0.566722 0.981592i −0.996887 0.0788417i \(-0.974878\pi\)
0.430165 0.902750i \(-0.358455\pi\)
\(282\) 0 0
\(283\) 10.2753 17.7973i 0.610801 1.05794i −0.380305 0.924861i \(-0.624181\pi\)
0.991106 0.133077i \(-0.0424856\pi\)
\(284\) 4.94949 8.57277i 0.293698 0.508700i
\(285\) 0 0
\(286\) 4.89898 + 8.48528i 0.289683 + 0.501745i
\(287\) −9.79796 −0.578355
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 5.00000 + 8.66025i 0.293610 + 0.508548i
\(291\) 0 0
\(292\) −1.44949 + 2.51059i −0.0848250 + 0.146921i
\(293\) 13.6237 23.5970i 0.795906 1.37855i −0.126356 0.991985i \(-0.540328\pi\)
0.922262 0.386565i \(-0.126339\pi\)
\(294\) 0 0
\(295\) 3.44949 + 5.97469i 0.200837 + 0.347860i
\(296\) 7.79796 0.453247
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 2.44949 + 4.24264i 0.141658 + 0.245358i
\(300\) 0 0
\(301\) −1.44949 + 2.51059i −0.0835472 + 0.144708i
\(302\) −2.50000 + 4.33013i −0.143859 + 0.249171i
\(303\) 0 0
\(304\) −3.72474 6.45145i −0.213629 0.370016i
\(305\) −39.4949 −2.26147
\(306\) 0 0
\(307\) 0.752551 0.0429504 0.0214752 0.999769i \(-0.493164\pi\)
0.0214752 + 0.999769i \(0.493164\pi\)
\(308\) −1.00000 1.73205i −0.0569803 0.0986928i
\(309\) 0 0
\(310\) −10.3485 + 17.9241i −0.587754 + 1.01802i
\(311\) 0.651531 1.12848i 0.0369449 0.0639905i −0.846962 0.531654i \(-0.821571\pi\)
0.883907 + 0.467663i \(0.154904\pi\)
\(312\) 0 0
\(313\) −12.3485 21.3882i −0.697977 1.20893i −0.969167 0.246405i \(-0.920751\pi\)
0.271190 0.962526i \(-0.412583\pi\)
\(314\) −6.34847 −0.358265
\(315\) 0 0
\(316\) 7.89898 0.444352
\(317\) −4.34847 7.53177i −0.244234 0.423026i 0.717682 0.696371i \(-0.245203\pi\)
−0.961916 + 0.273345i \(0.911870\pi\)
\(318\) 0 0
\(319\) −2.89898 + 5.02118i −0.162312 + 0.281132i
\(320\) 1.72474 2.98735i 0.0964162 0.166998i
\(321\) 0 0
\(322\) −0.500000 0.866025i −0.0278639 0.0482617i
\(323\) −14.8990 −0.829001
\(324\) 0 0
\(325\) −33.7980 −1.87477
\(326\) −0.101021 0.174973i −0.00559501 0.00969084i
\(327\) 0 0
\(328\) 4.89898 8.48528i 0.270501 0.468521i
\(329\) 4.89898 8.48528i 0.270089 0.467809i
\(330\) 0 0
\(331\) 12.3485 + 21.3882i 0.678733 + 1.17560i 0.975363 + 0.220608i \(0.0708041\pi\)
−0.296629 + 0.954993i \(0.595863\pi\)
\(332\) −2.00000 −0.109764
\(333\) 0 0
\(334\) 18.6969 1.02305
\(335\) −5.34847 9.26382i −0.292218 0.506137i
\(336\) 0 0
\(337\) −17.6969 + 30.6520i −0.964014 + 1.66972i −0.251772 + 0.967787i \(0.581013\pi\)
−0.712242 + 0.701934i \(0.752320\pi\)
\(338\) 5.50000 9.52628i 0.299161 0.518161i
\(339\) 0 0
\(340\) −3.44949 5.97469i −0.187075 0.324023i
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −1.44949 2.51059i −0.0781512 0.135362i
\(345\) 0 0
\(346\) 6.44949 11.1708i 0.346727 0.600548i
\(347\) −9.79796 + 16.9706i −0.525982 + 0.911028i 0.473560 + 0.880762i \(0.342969\pi\)
−0.999542 + 0.0302659i \(0.990365\pi\)
\(348\) 0 0
\(349\) −10.4495 18.0990i −0.559348 0.968820i −0.997551 0.0699435i \(-0.977718\pi\)
0.438203 0.898876i \(-0.355615\pi\)
\(350\) 6.89898 0.368766
\(351\) 0 0
\(352\) 2.00000 0.106600
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 0 0
\(355\) −17.0732 + 29.5717i −0.906152 + 1.56950i
\(356\) −3.55051 + 6.14966i −0.188177 + 0.325932i
\(357\) 0 0
\(358\) 4.34847 + 7.53177i 0.229824 + 0.398066i
\(359\) −10.7980 −0.569894 −0.284947 0.958543i \(-0.591976\pi\)
−0.284947 + 0.958543i \(0.591976\pi\)
\(360\) 0 0
\(361\) 36.4949 1.92078
\(362\) 2.17423 + 3.76588i 0.114275 + 0.197931i
\(363\) 0 0
\(364\) −2.44949 + 4.24264i −0.128388 + 0.222375i
\(365\) 5.00000 8.66025i 0.261712 0.453298i
\(366\) 0 0
\(367\) −2.89898 5.02118i −0.151325 0.262103i 0.780389 0.625294i \(-0.215021\pi\)
−0.931715 + 0.363190i \(0.881687\pi\)
\(368\) 1.00000 0.0521286
\(369\) 0 0
\(370\) −26.8990 −1.39841
\(371\) 0.550510 + 0.953512i 0.0285811 + 0.0495039i
\(372\) 0 0
\(373\) −1.44949 + 2.51059i −0.0750517 + 0.129993i −0.901109 0.433593i \(-0.857246\pi\)
0.826057 + 0.563587i \(0.190579\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) 0 0
\(376\) 4.89898 + 8.48528i 0.252646 + 0.437595i
\(377\) 14.2020 0.731442
\(378\) 0 0
\(379\) −26.4949 −1.36095 −0.680476 0.732771i \(-0.738227\pi\)
−0.680476 + 0.732771i \(0.738227\pi\)
\(380\) 12.8485 + 22.2542i 0.659113 + 1.14162i
\(381\) 0 0
\(382\) −6.94949 + 12.0369i −0.355567 + 0.615860i
\(383\) 3.44949 5.97469i 0.176261 0.305292i −0.764336 0.644818i \(-0.776933\pi\)
0.940597 + 0.339526i \(0.110266\pi\)
\(384\) 0 0
\(385\) 3.44949 + 5.97469i 0.175802 + 0.304498i
\(386\) 8.10102 0.412331
\(387\) 0 0
\(388\) −6.89898 −0.350243
\(389\) −7.55051 13.0779i −0.382826 0.663074i 0.608639 0.793447i \(-0.291716\pi\)
−0.991465 + 0.130373i \(0.958382\pi\)
\(390\) 0 0
\(391\) 1.00000 1.73205i 0.0505722 0.0875936i
\(392\) 0.500000 0.866025i 0.0252538 0.0437409i
\(393\) 0 0
\(394\) 6.34847 + 10.9959i 0.319831 + 0.553964i
\(395\) −27.2474 −1.37097
\(396\) 0 0
\(397\) 9.30306 0.466907 0.233454 0.972368i \(-0.424997\pi\)
0.233454 + 0.972368i \(0.424997\pi\)
\(398\) 3.44949 + 5.97469i 0.172907 + 0.299484i
\(399\) 0 0
\(400\) −3.44949 + 5.97469i −0.172474 + 0.298735i
\(401\) −5.05051 + 8.74774i −0.252210 + 0.436841i −0.964134 0.265416i \(-0.914491\pi\)
0.711924 + 0.702257i \(0.247824\pi\)
\(402\) 0 0
\(403\) 14.6969 + 25.4558i 0.732107 + 1.26805i
\(404\) −7.24745 −0.360574
\(405\) 0 0
\(406\) −2.89898 −0.143874
\(407\) −7.79796 13.5065i −0.386530 0.669490i
\(408\) 0 0
\(409\) −2.89898 + 5.02118i −0.143345 + 0.248281i −0.928754 0.370696i \(-0.879119\pi\)
0.785409 + 0.618977i \(0.212453\pi\)
\(410\) −16.8990 + 29.2699i −0.834581 + 1.44554i
\(411\) 0 0
\(412\) −7.00000 12.1244i −0.344865 0.597324i
\(413\) −2.00000 −0.0984136
\(414\) 0 0
\(415\) 6.89898 0.338658
\(416\) −2.44949 4.24264i −0.120096 0.208013i
\(417\) 0 0
\(418\) −7.44949 + 12.9029i −0.364366 + 0.631101i
\(419\) 12.2753 21.2614i 0.599685 1.03869i −0.393182 0.919461i \(-0.628626\pi\)
0.992867 0.119225i \(-0.0380410\pi\)
\(420\) 0 0
\(421\) −6.55051 11.3458i −0.319252 0.552961i 0.661080 0.750316i \(-0.270098\pi\)
−0.980332 + 0.197354i \(0.936765\pi\)
\(422\) −3.10102 −0.150955
\(423\) 0 0
\(424\) −1.10102 −0.0534703
\(425\) 6.89898 + 11.9494i 0.334650 + 0.579630i
\(426\) 0 0
\(427\) 5.72474 9.91555i 0.277040 0.479847i
\(428\) −6.00000 + 10.3923i −0.290021 + 0.502331i
\(429\) 0 0
\(430\) 5.00000 + 8.66025i 0.241121 + 0.417635i
\(431\) 7.59592 0.365882 0.182941 0.983124i \(-0.441438\pi\)
0.182941 + 0.983124i \(0.441438\pi\)
\(432\) 0 0
\(433\) 11.7980 0.566974 0.283487 0.958976i \(-0.408509\pi\)
0.283487 + 0.958976i \(0.408509\pi\)
\(434\) −3.00000 5.19615i −0.144005 0.249423i
\(435\) 0 0
\(436\) 8.34847 14.4600i 0.399819 0.692507i
\(437\) −3.72474 + 6.45145i −0.178179 + 0.308615i
\(438\) 0 0
\(439\) −10.8990 18.8776i −0.520180 0.900978i −0.999725 0.0234607i \(-0.992532\pi\)
0.479545 0.877517i \(-0.340802\pi\)
\(440\) −6.89898 −0.328896
\(441\) 0 0
\(442\) −9.79796 −0.466041
\(443\) −2.55051 4.41761i −0.121178 0.209887i 0.799054 0.601259i \(-0.205334\pi\)
−0.920233 + 0.391372i \(0.872001\pi\)
\(444\) 0 0
\(445\) 12.2474 21.2132i 0.580585 1.00560i
\(446\) −10.4495 + 18.0990i −0.494798 + 0.857015i
\(447\) 0 0
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) 18.5959 0.877596 0.438798 0.898586i \(-0.355404\pi\)
0.438798 + 0.898586i \(0.355404\pi\)
\(450\) 0 0
\(451\) −19.5959 −0.922736
\(452\) −7.94949 13.7689i −0.373913 0.647636i
\(453\) 0 0
\(454\) 0.275255 0.476756i 0.0129184 0.0223753i
\(455\) 8.44949 14.6349i 0.396118 0.686097i
\(456\) 0 0
\(457\) −15.7474 27.2754i −0.736635 1.27589i −0.954002 0.299799i \(-0.903080\pi\)
0.217368 0.976090i \(-0.430253\pi\)
\(458\) 23.2474 1.08628
\(459\) 0 0
\(460\) −3.44949 −0.160833
\(461\) 10.1742 + 17.6223i 0.473861 + 0.820752i 0.999552 0.0299238i \(-0.00952645\pi\)
−0.525691 + 0.850676i \(0.676193\pi\)
\(462\) 0 0
\(463\) 12.8485 22.2542i 0.597119 1.03424i −0.396125 0.918197i \(-0.629645\pi\)
0.993244 0.116044i \(-0.0370213\pi\)
\(464\) 1.44949 2.51059i 0.0672909 0.116551i
\(465\) 0 0
\(466\) 3.50000 + 6.06218i 0.162134 + 0.280825i
\(467\) −10.0000 −0.462745 −0.231372 0.972865i \(-0.574322\pi\)
−0.231372 + 0.972865i \(0.574322\pi\)
\(468\) 0 0
\(469\) 3.10102 0.143192
\(470\) −16.8990 29.2699i −0.779492 1.35012i
\(471\) 0 0
\(472\) 1.00000 1.73205i 0.0460287 0.0797241i
\(473\) −2.89898 + 5.02118i −0.133295 + 0.230874i
\(474\) 0 0
\(475\) −25.6969 44.5084i −1.17906 2.04219i
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) −12.7980 −0.585365
\(479\) −14.7980 25.6308i −0.676136 1.17110i −0.976135 0.217163i \(-0.930320\pi\)
0.299999 0.953939i \(-0.403013\pi\)
\(480\) 0 0
\(481\) −19.1010 + 33.0839i −0.870932 + 1.50850i
\(482\) −4.44949 + 7.70674i −0.202669 + 0.351032i
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 23.7980 1.08061
\(486\) 0 0
\(487\) 22.3939 1.01476 0.507382 0.861721i \(-0.330613\pi\)
0.507382 + 0.861721i \(0.330613\pi\)
\(488\) 5.72474 + 9.91555i 0.259147 + 0.448856i
\(489\) 0 0
\(490\) −1.72474 + 2.98735i −0.0779160 + 0.134955i
\(491\) −1.89898 + 3.28913i −0.0856997 + 0.148436i −0.905689 0.423942i \(-0.860646\pi\)
0.819989 + 0.572379i \(0.193979\pi\)
\(492\) 0 0
\(493\) −2.89898 5.02118i −0.130563 0.226143i
\(494\) 36.4949 1.64198
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) −4.94949 8.57277i −0.222015 0.384541i
\(498\) 0 0
\(499\) −16.6969 + 28.9199i −0.747458 + 1.29463i 0.201580 + 0.979472i \(0.435392\pi\)
−0.949038 + 0.315163i \(0.897941\pi\)
\(500\) 3.27526 5.67291i 0.146474 0.253700i
\(501\) 0 0
\(502\) −6.27526 10.8691i −0.280078 0.485110i
\(503\) −24.4949 −1.09217 −0.546087 0.837729i \(-0.683883\pi\)
−0.546087 + 0.837729i \(0.683883\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) −1.00000 1.73205i −0.0444554 0.0769991i
\(507\) 0 0
\(508\) 1.50000 2.59808i 0.0665517 0.115271i
\(509\) −8.44949 + 14.6349i −0.374517 + 0.648683i −0.990255 0.139269i \(-0.955525\pi\)
0.615738 + 0.787951i \(0.288858\pi\)
\(510\) 0 0
\(511\) 1.44949 + 2.51059i 0.0641217 + 0.111062i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 27.7980 1.22612
\(515\) 24.1464 + 41.8228i 1.06402 + 1.84293i
\(516\) 0 0
\(517\) 9.79796 16.9706i 0.430914 0.746364i
\(518\) 3.89898 6.75323i 0.171311 0.296720i
\(519\) 0 0
\(520\) 8.44949 + 14.6349i 0.370535 + 0.641785i
\(521\) 38.6969 1.69534 0.847672 0.530521i \(-0.178004\pi\)
0.847672 + 0.530521i \(0.178004\pi\)
\(522\) 0 0
\(523\) 0.348469 0.0152375 0.00761875 0.999971i \(-0.497575\pi\)
0.00761875 + 0.999971i \(0.497575\pi\)
\(524\) −6.72474 11.6476i −0.293772 0.508828i
\(525\) 0 0
\(526\) −8.05051 + 13.9439i −0.351019 + 0.607983i
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 3.79796 0.164973
\(531\) 0 0
\(532\) −7.44949 −0.322976
\(533\) 24.0000 + 41.5692i 1.03956 + 1.80056i
\(534\) 0 0
\(535\) 20.6969 35.8481i 0.894807 1.54985i
\(536\) −1.55051 + 2.68556i −0.0669718 + 0.115999i
\(537\) 0 0
\(538\) 1.82577 + 3.16232i 0.0787143 + 0.136337i
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) 30.4949 1.31108 0.655539 0.755161i \(-0.272441\pi\)
0.655539 + 0.755161i \(0.272441\pi\)
\(542\) 8.44949 + 14.6349i 0.362937 + 0.628625i
\(543\) 0 0
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) −28.7980 + 49.8795i −1.23357 + 2.13660i
\(546\) 0 0
\(547\) −15.7980 27.3629i −0.675472 1.16995i −0.976331 0.216283i \(-0.930607\pi\)
0.300859 0.953669i \(-0.402727\pi\)
\(548\) 11.7980 0.503984
\(549\) 0 0
\(550\) 13.7980 0.588347
\(551\) 10.7980 + 18.7026i 0.460009 + 0.796758i
\(552\) 0 0
\(553\) 3.94949 6.84072i 0.167949 0.290897i
\(554\) 5.34847 9.26382i 0.227235 0.393582i
\(555\) 0 0
\(556\) −4.72474 8.18350i −0.200374 0.347058i
\(557\) 3.10102 0.131394 0.0656972 0.997840i \(-0.479073\pi\)
0.0656972 + 0.997840i \(0.479073\pi\)
\(558\) 0 0
\(559\) 14.2020 0.600682
\(560\) −1.72474 2.98735i −0.0728838 0.126238i
\(561\) 0 0
\(562\) 9.50000 16.4545i 0.400733 0.694090i
\(563\) 6.97219 12.0762i 0.293843 0.508951i −0.680872 0.732402i \(-0.738399\pi\)
0.974715 + 0.223451i \(0.0717324\pi\)
\(564\) 0 0
\(565\) 27.4217 + 47.4957i 1.15364 + 1.99816i
\(566\) 20.5505 0.863802
\(567\) 0 0
\(568\) 9.89898 0.415352
\(569\) −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i \(-0.950200\pi\)
0.358954 0.933355i \(-0.383134\pi\)
\(570\) 0 0
\(571\) −7.10102 + 12.2993i −0.297168 + 0.514711i −0.975487 0.220057i \(-0.929376\pi\)
0.678319 + 0.734768i \(0.262709\pi\)
\(572\) −4.89898 + 8.48528i −0.204837 + 0.354787i
\(573\) 0 0
\(574\) −4.89898 8.48528i −0.204479 0.354169i
\(575\) 6.89898 0.287707
\(576\) 0 0
\(577\) 23.5959 0.982311 0.491155 0.871072i \(-0.336575\pi\)
0.491155 + 0.871072i \(0.336575\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) 0 0
\(580\) −5.00000 + 8.66025i −0.207614 + 0.359597i
\(581\) −1.00000 + 1.73205i −0.0414870 + 0.0718576i
\(582\) 0 0
\(583\) 1.10102 + 1.90702i 0.0455996 + 0.0789808i
\(584\) −2.89898 −0.119961
\(585\) 0 0
\(586\) 27.2474 1.12558
\(587\) −9.07321 15.7153i −0.374492 0.648639i 0.615759 0.787934i \(-0.288849\pi\)
−0.990251 + 0.139296i \(0.955516\pi\)
\(588\) 0 0
\(589\) −22.3485 + 38.7087i −0.920853 + 1.59496i
\(590\) −3.44949 + 5.97469i −0.142013 + 0.245974i
\(591\) 0 0
\(592\) 3.89898 + 6.75323i 0.160247 + 0.277556i
\(593\) 14.6969 0.603531 0.301765 0.953382i \(-0.402424\pi\)
0.301765 + 0.953382i \(0.402424\pi\)
\(594\) 0 0
\(595\) −6.89898 −0.282831
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) −2.44949 + 4.24264i −0.100167 + 0.173494i
\(599\) −7.10102 + 12.2993i −0.290140 + 0.502537i −0.973843 0.227224i \(-0.927035\pi\)
0.683703 + 0.729761i \(0.260368\pi\)
\(600\) 0 0
\(601\) 6.34847 + 10.9959i 0.258959 + 0.448531i 0.965963 0.258679i \(-0.0832871\pi\)
−0.707004 + 0.707210i \(0.749954\pi\)
\(602\) −2.89898 −0.118154
\(603\) 0 0
\(604\) −5.00000 −0.203447
\(605\) −12.0732 20.9114i −0.490846 0.850170i
\(606\) 0 0
\(607\) 4.34847 7.53177i 0.176499 0.305705i −0.764180 0.645003i \(-0.776856\pi\)
0.940679 + 0.339298i \(0.110189\pi\)
\(608\) 3.72474 6.45145i 0.151058 0.261641i
\(609\) 0 0
\(610\) −19.7474 34.2036i −0.799551 1.38486i
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) 14.6969 0.593604 0.296802 0.954939i \(-0.404080\pi\)
0.296802 + 0.954939i \(0.404080\pi\)
\(614\) 0.376276 + 0.651729i 0.0151852 + 0.0263016i
\(615\) 0 0
\(616\) 1.00000 1.73205i 0.0402911 0.0697863i
\(617\) 21.6969 37.5802i 0.873486 1.51292i 0.0151189 0.999886i \(-0.495187\pi\)
0.858367 0.513036i \(-0.171479\pi\)
\(618\) 0 0
\(619\) 2.07321 + 3.59091i 0.0833295 + 0.144331i 0.904678 0.426096i \(-0.140111\pi\)
−0.821349 + 0.570426i \(0.806778\pi\)
\(620\) −20.6969 −0.831209
\(621\) 0 0
\(622\) 1.30306 0.0522480
\(623\) 3.55051 + 6.14966i 0.142248 + 0.246381i
\(624\) 0 0
\(625\) 5.94949 10.3048i 0.237980 0.412193i
\(626\) 12.3485 21.3882i 0.493544 0.854843i
\(627\) 0 0
\(628\) −3.17423 5.49794i −0.126666 0.219392i
\(629\) 15.5959 0.621850
\(630\) 0 0
\(631\) 18.1010 0.720590 0.360295 0.932838i \(-0.382676\pi\)
0.360295 + 0.932838i \(0.382676\pi\)
\(632\) 3.94949 + 6.84072i 0.157102 + 0.272109i
\(633\) 0 0
\(634\) 4.34847 7.53177i 0.172700 0.299125i
\(635\) −5.17423 + 8.96204i −0.205333 + 0.355648i
\(636\) 0 0
\(637\) 2.44949 + 4.24264i 0.0970523 + 0.168100i
\(638\) −5.79796 −0.229543
\(639\) 0 0
\(640\) 3.44949 0.136353
\(641\) 20.7474 + 35.9356i 0.819475 + 1.41937i 0.906070 + 0.423129i \(0.139068\pi\)
−0.0865947 + 0.996244i \(0.527599\pi\)
\(642\) 0 0
\(643\) −9.69694 + 16.7956i −0.382410 + 0.662353i −0.991406 0.130820i \(-0.958239\pi\)
0.608996 + 0.793173i \(0.291572\pi\)
\(644\) 0.500000 0.866025i 0.0197028 0.0341262i
\(645\) 0 0
\(646\) −7.44949 12.9029i −0.293096 0.507658i
\(647\) 21.3031 0.837510 0.418755 0.908099i \(-0.362467\pi\)
0.418755 + 0.908099i \(0.362467\pi\)
\(648\) 0 0
\(649\) −4.00000 −0.157014
\(650\) −16.8990 29.2699i −0.662833 1.14806i
\(651\) 0 0
\(652\) 0.101021 0.174973i 0.00395627 0.00685246i
\(653\) −4.89898 + 8.48528i −0.191712 + 0.332055i −0.945818 0.324698i \(-0.894737\pi\)
0.754106 + 0.656753i \(0.228071\pi\)
\(654\) 0 0
\(655\) 23.1969 + 40.1783i 0.906379 + 1.56990i
\(656\) 9.79796 0.382546
\(657\) 0 0
\(658\) 9.79796 0.381964
\(659\) 2.34847 + 4.06767i 0.0914834 + 0.158454i 0.908136 0.418676i \(-0.137506\pi\)
−0.816652 + 0.577130i \(0.804172\pi\)
\(660\) 0 0
\(661\) −4.72474 + 8.18350i −0.183771 + 0.318301i −0.943162 0.332334i \(-0.892164\pi\)
0.759391 + 0.650635i \(0.225497\pi\)
\(662\) −12.3485 + 21.3882i −0.479937 + 0.831275i
\(663\) 0 0
\(664\) −1.00000 1.73205i −0.0388075 0.0672166i
\(665\) 25.6969 0.996485
\(666\) 0 0
\(667\) −2.89898 −0.112249
\(668\) 9.34847 + 16.1920i 0.361703 + 0.626488i
\(669\) 0 0
\(670\) 5.34847 9.26382i 0.206629 0.357893i
\(671\) 11.4495 19.8311i 0.442003 0.765571i
\(672\) 0 0
\(673\) −15.2980 26.4968i −0.589693 1.02138i −0.994272 0.106875i \(-0.965915\pi\)
0.404579 0.914503i \(-0.367418\pi\)
\(674\) −35.3939 −1.36332
\(675\) 0 0
\(676\) 11.0000 0.423077
\(677\) −7.34847 12.7279i −0.282425 0.489174i 0.689557 0.724232i \(-0.257805\pi\)
−0.971981 + 0.235058i \(0.924472\pi\)
\(678\) 0 0
\(679\) −3.44949 + 5.97469i −0.132379 + 0.229288i
\(680\) 3.44949 5.97469i 0.132282 0.229119i
\(681\) 0 0
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) −32.2020 −1.23218 −0.616088 0.787677i \(-0.711284\pi\)
−0.616088 + 0.787677i \(0.711284\pi\)
\(684\) 0 0
\(685\) −40.6969 −1.55495
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) 1.44949 2.51059i 0.0552613 0.0957153i
\(689\) 2.69694 4.67123i 0.102745 0.177960i
\(690\) 0 0
\(691\) −3.47730 6.02285i −0.132283 0.229120i 0.792274 0.610166i \(-0.208897\pi\)
−0.924556 + 0.381046i \(0.875564\pi\)
\(692\) 12.8990 0.490346
\(693\) 0 0
\(694\) −19.5959 −0.743851
\(695\) 16.2980 + 28.2289i 0.618217 + 1.07078i
\(696\) 0 0
\(697\) 9.79796 16.9706i 0.371124 0.642806i
\(698\) 10.4495 18.0990i 0.395519 0.685059i
\(699\) 0 0
\(700\) 3.44949 + 5.97469i 0.130378 + 0.225822i
\(701\) −51.3939 −1.94112 −0.970560 0.240860i \(-0.922571\pi\)
−0.970560 + 0.240860i \(0.922571\pi\)
\(702\) 0 0
\(703\) −58.0908 −2.19094
\(704\) 1.00000 + 1.73205i 0.0376889 + 0.0652791i
\(705\) 0 0
\(706\) 3.00000 5.19615i 0.112906 0.195560i
\(707\) −3.62372 + 6.27647i −0.136284 + 0.236051i
\(708\) 0 0
\(709\) 5.79796 + 10.0424i 0.217747 + 0.377149i 0.954119 0.299428i \(-0.0967959\pi\)
−0.736372 + 0.676577i \(0.763463\pi\)
\(710\) −34.1464 −1.28149
\(711\) 0 0
\(712\) −7.10102 −0.266122
\(713\) −3.00000 5.19615i −0.112351 0.194597i
\(714\) 0 0
\(715\) 16.8990 29.2699i 0.631986 1.09463i
\(716\) −4.34847 + 7.53177i −0.162510 + 0.281475i
\(717\) 0 0
\(718\) −5.39898 9.35131i −0.201488 0.348988i
\(719\) 9.79796 0.365402 0.182701 0.983169i \(-0.441516\pi\)
0.182701 + 0.983169i \(0.441516\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 18.2474 + 31.6055i 0.679100 + 1.17624i
\(723\) 0 0
\(724\) −2.17423 + 3.76588i −0.0808048 + 0.139958i
\(725\) 10.0000 17.3205i 0.371391 0.643268i
\(726\) 0 0
\(727\) −20.2474 35.0696i −0.750936 1.30066i −0.947369 0.320143i \(-0.896269\pi\)
0.196433 0.980517i \(-0.437064\pi\)
\(728\) −4.89898 −0.181568
\(729\) 0 0
\(730\) 10.0000 0.370117
\(731\) −2.89898 5.02118i −0.107223 0.185715i
\(732\) 0 0
\(733\) 6.27526 10.8691i 0.231782 0.401458i −0.726551 0.687113i \(-0.758878\pi\)
0.958333 + 0.285655i \(0.0922111\pi\)
\(734\) 2.89898 5.02118i 0.107003 0.185335i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) 6.20204 0.228455
\(738\) 0 0
\(739\) −25.5959 −0.941561 −0.470781 0.882250i \(-0.656028\pi\)
−0.470781 + 0.882250i \(0.656028\pi\)
\(740\) −13.4495 23.2952i −0.494413 0.856349i
\(741\) 0 0
\(742\) −0.550510 + 0.953512i −0.0202099 + 0.0350045i
\(743\) 18.0000 31.1769i 0.660356 1.14377i −0.320166 0.947361i \(-0.603739\pi\)
0.980522 0.196409i \(-0.0629279\pi\)
\(744\) 0 0
\(745\) 10.3485 + 17.9241i 0.379139 + 0.656687i
\(746\) −2.89898 −0.106139
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) 6.00000 + 10.3923i 0.219235 + 0.379727i
\(750\) 0 0
\(751\) −20.2980 + 35.1571i −0.740683 + 1.28290i 0.211502 + 0.977378i \(0.432165\pi\)
−0.952185 + 0.305523i \(0.901169\pi\)
\(752\) −4.89898 + 8.48528i −0.178647 + 0.309426i
\(753\) 0 0
\(754\) 7.10102 + 12.2993i 0.258604 + 0.447915i
\(755\) 17.2474 0.627699
\(756\) 0 0
\(757\) 23.3939 0.850265 0.425132 0.905131i \(-0.360228\pi\)
0.425132 + 0.905131i \(0.360228\pi\)
\(758\) −13.2474 22.9453i −0.481169 0.833409i
\(759\) 0 0
\(760\) −12.8485 + 22.2542i −0.466063 + 0.807245i
\(761\) 1.00000 1.73205i 0.0362500 0.0627868i −0.847331 0.531065i \(-0.821792\pi\)
0.883581 + 0.468278i \(0.155125\pi\)
\(762\) 0 0
\(763\) −8.34847 14.4600i −0.302235 0.523486i
\(764\) −13.8990 −0.502847
\(765\) 0 0
\(766\) 6.89898 0.249270
\(767\) 4.89898 + 8.48528i 0.176892 + 0.306386i
\(768\) 0 0
\(769\) −27.0454 + 46.8440i −0.975282 + 1.68924i −0.296282 + 0.955100i \(0.595747\pi\)
−0.679000 + 0.734138i \(0.737586\pi\)
\(770\) −3.44949 + 5.97469i −0.124311 + 0.215313i
\(771\) 0 0
\(772\) 4.05051 + 7.01569i 0.145781 + 0.252500i
\(773\) 19.9444 0.717350 0.358675 0.933463i \(-0.383229\pi\)
0.358675 + 0.933463i \(0.383229\pi\)
\(774\) 0 0
\(775\) 41.3939 1.48691
\(776\) −3.44949 5.97469i −0.123829 0.214479i
\(777\) 0 0
\(778\) 7.55051 13.0779i 0.270699 0.468864i
\(779\) −36.4949 + 63.2110i −1.30757 + 2.26477i
\(780\) 0 0
\(781\) −9.89898 17.1455i −0.354213 0.613515i
\(782\) 2.00000 0.0715199
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 10.9495 + 18.9651i 0.390804 + 0.676892i
\(786\) 0 0
\(787\) −23.6969 + 41.0443i −0.844705 + 1.46307i 0.0411728 + 0.999152i \(0.486891\pi\)
−0.885877 + 0.463919i \(0.846443\pi\)
\(788\) −6.34847 + 10.9959i −0.226155 + 0.391712i
\(789\) 0 0
\(790\) −13.6237 23.5970i −0.484710 0.839543i
\(791\)