Properties

Label 378.2.f.d.253.1
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 253.1
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 378.253
Dual form 378.2.f.d.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.724745 + 1.25529i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.724745 + 1.25529i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -1.44949 q^{10} +(1.00000 + 1.73205i) q^{11} +(-2.44949 + 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} +2.55051 q^{19} +(-0.724745 - 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.44949 + 2.51059i) q^{25} -4.89898 q^{26} -1.00000 q^{28} +(-3.44949 - 5.97469i) q^{29} +(-3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{34} -1.44949 q^{35} +11.7980 q^{37} +(1.27526 + 2.20881i) q^{38} +(0.724745 - 1.25529i) q^{40} +(4.89898 - 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} -2.00000 q^{44} -1.00000 q^{46} +(4.89898 + 8.48528i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-1.44949 + 2.51059i) q^{50} +(-2.44949 - 4.24264i) q^{52} +10.8990 q^{53} -2.89898 q^{55} +(-0.500000 - 0.866025i) q^{56} +(3.44949 - 5.97469i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(-3.27526 - 5.67291i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-3.55051 - 6.14966i) q^{65} +(6.44949 - 11.1708i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-0.724745 - 1.25529i) q^{70} -0.101021 q^{71} -6.89898 q^{73} +(5.89898 + 10.2173i) q^{74} +(-1.27526 + 2.20881i) q^{76} +(-1.00000 + 1.73205i) q^{77} +(0.949490 + 1.64456i) q^{79} +1.44949 q^{80} +9.79796 q^{82} +(1.00000 + 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +(3.44949 - 5.97469i) q^{86} +(-1.00000 - 1.73205i) q^{88} +16.8990 q^{89} -4.89898 q^{91} +(-0.500000 - 0.866025i) q^{92} +(-4.89898 + 8.48528i) q^{94} +(-1.84847 + 3.20164i) q^{95} +(-1.44949 - 2.51059i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 4 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 4 q^{8} + 4 q^{10} + 4 q^{11} - 2 q^{14} - 2 q^{16} - 8 q^{17} + 20 q^{19} + 2 q^{20} - 4 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{28} - 4 q^{29} - 12 q^{31} + 2 q^{32} - 4 q^{34} + 4 q^{35} + 8 q^{37} + 10 q^{38} - 2 q^{40} - 4 q^{43} - 8 q^{44} - 4 q^{46} - 2 q^{49} + 4 q^{50} + 24 q^{53} + 8 q^{55} - 2 q^{56} + 4 q^{58} - 4 q^{59} - 18 q^{61} - 24 q^{62} + 4 q^{64} - 24 q^{65} + 16 q^{67} + 4 q^{68} + 2 q^{70} - 20 q^{71} - 8 q^{73} + 4 q^{74} - 10 q^{76} - 4 q^{77} - 6 q^{79} - 4 q^{80} + 4 q^{83} - 4 q^{85} + 4 q^{86} - 4 q^{88} + 48 q^{89} - 2 q^{92} + 22 q^{95} + 4 q^{97} - 4 q^{98} + O(q^{100}) \)

Character values

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

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

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
\(5\) −0.724745 + 1.25529i −0.324116 + 0.561385i −0.981333 0.192316i \(-0.938400\pi\)
0.657217 + 0.753701i \(0.271733\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.44949 −0.458369
\(11\) 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 \(0.404412\pi\)
−0.975172 + 0.221449i \(0.928921\pi\)
\(14\) −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
\(19\) 2.55051 0.585127 0.292564 0.956246i \(-0.405492\pi\)
0.292564 + 0.956246i \(0.405492\pi\)
\(20\) −0.724745 1.25529i −0.162058 0.280692i
\(21\) 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
\(25\) 1.44949 + 2.51059i 0.289898 + 0.502118i
\(26\) −4.89898 −0.960769
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −3.44949 5.97469i −0.640554 1.10947i −0.985309 0.170780i \(-0.945371\pi\)
0.344755 0.938693i \(-0.387962\pi\)
\(30\) 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
\(35\) −1.44949 −0.245008
\(36\) 0 0
\(37\) 11.7980 1.93957 0.969786 0.243956i \(-0.0784453\pi\)
0.969786 + 0.243956i \(0.0784453\pi\)
\(38\) 1.27526 + 2.20881i 0.206874 + 0.358316i
\(39\) 0 0
\(40\) 0.724745 1.25529i 0.114592 0.198480i
\(41\) 4.89898 8.48528i 0.765092 1.32518i −0.175106 0.984550i \(-0.556027\pi\)
0.940198 0.340629i \(-0.110640\pi\)
\(42\) 0 0
\(43\) −3.44949 5.97469i −0.526042 0.911132i −0.999540 0.0303367i \(-0.990342\pi\)
0.473497 0.880795i \(-0.342991\pi\)
\(44\) −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 \(0.0867199\pi\)
−0.248528 + 0.968625i \(0.579947\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −1.44949 + 2.51059i −0.204989 + 0.355051i
\(51\) 0 0
\(52\) −2.44949 4.24264i −0.339683 0.588348i
\(53\) 10.8990 1.49709 0.748545 0.663084i \(-0.230753\pi\)
0.748545 + 0.663084i \(0.230753\pi\)
\(54\) 0 0
\(55\) −2.89898 −0.390898
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 0 0
\(58\) 3.44949 5.97469i 0.452940 0.784515i
\(59\) −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
\(61\) −3.27526 5.67291i −0.419353 0.726341i 0.576521 0.817082i \(-0.304410\pi\)
−0.995875 + 0.0907408i \(0.971077\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.55051 6.14966i −0.440387 0.762772i
\(66\) 0 0
\(67\) 6.44949 11.1708i 0.787931 1.36474i −0.139302 0.990250i \(-0.544486\pi\)
0.927233 0.374486i \(-0.122181\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0 0
\(70\) −0.724745 1.25529i −0.0866236 0.150036i
\(71\) −0.101021 −0.0119889 −0.00599446 0.999982i \(-0.501908\pi\)
−0.00599446 + 0.999982i \(0.501908\pi\)
\(72\) 0 0
\(73\) −6.89898 −0.807464 −0.403732 0.914877i \(-0.632287\pi\)
−0.403732 + 0.914877i \(0.632287\pi\)
\(74\) 5.89898 + 10.2173i 0.685742 + 1.18774i
\(75\) 0 0
\(76\) −1.27526 + 2.20881i −0.146282 + 0.253368i
\(77\) −1.00000 + 1.73205i −0.113961 + 0.197386i
\(78\) 0 0
\(79\) 0.949490 + 1.64456i 0.106826 + 0.185028i 0.914483 0.404625i \(-0.132598\pi\)
−0.807657 + 0.589653i \(0.799265\pi\)
\(80\) 1.44949 0.162058
\(81\) 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
\(85\) 1.44949 2.51059i 0.157219 0.272312i
\(86\) 3.44949 5.97469i 0.371968 0.644268i
\(87\) 0 0
\(88\) −1.00000 1.73205i −0.106600 0.184637i
\(89\) 16.8990 1.79129 0.895644 0.444771i \(-0.146715\pi\)
0.895644 + 0.444771i \(0.146715\pi\)
\(90\) 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
\(95\) −1.84847 + 3.20164i −0.189649 + 0.328482i
\(96\) 0 0
\(97\) −1.44949 2.51059i −0.147173 0.254912i 0.783008 0.622011i \(-0.213684\pi\)
−0.930182 + 0.367099i \(0.880351\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −2.89898 −0.289898
\(101\) −8.62372 14.9367i −0.858093 1.48626i −0.873746 0.486383i \(-0.838316\pi\)
0.0156533 0.999877i \(-0.495017\pi\)
\(102\) 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
\(106\) 5.44949 + 9.43879i 0.529301 + 0.916777i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 12.6969 1.21615 0.608073 0.793881i \(-0.291943\pi\)
0.608073 + 0.793881i \(0.291943\pi\)
\(110\) −1.44949 2.51059i −0.138203 0.239375i
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) −3.05051 + 5.28364i −0.286968 + 0.497043i −0.973084 0.230449i \(-0.925981\pi\)
0.686117 + 0.727492i \(0.259314\pi\)
\(114\) 0 0
\(115\) −0.724745 1.25529i −0.0675828 0.117057i
\(116\) 6.89898 0.640554
\(117\) 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
\(122\) 3.27526 5.67291i 0.296528 0.513601i
\(123\) 0 0
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) −11.4495 −1.02407
\(126\) 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
\(130\) 3.55051 6.14966i 0.311400 0.539361i
\(131\) −4.27526 + 7.40496i −0.373531 + 0.646974i −0.990106 0.140322i \(-0.955186\pi\)
0.616575 + 0.787296i \(0.288520\pi\)
\(132\) 0 0
\(133\) 1.27526 + 2.20881i 0.110579 + 0.191528i
\(134\) 12.8990 1.11430
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) 3.89898 + 6.75323i 0.333112 + 0.576967i 0.983120 0.182960i \(-0.0585678\pi\)
−0.650008 + 0.759927i \(0.725235\pi\)
\(138\) 0 0
\(139\) −2.27526 + 3.94086i −0.192985 + 0.334259i −0.946238 0.323471i \(-0.895150\pi\)
0.753253 + 0.657730i \(0.228483\pi\)
\(140\) 0.724745 1.25529i 0.0612521 0.106092i
\(141\) 0 0
\(142\) −0.0505103 0.0874863i −0.00423873 0.00734169i
\(143\) −9.79796 −0.819346
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) −3.44949 5.97469i −0.285482 0.494469i
\(147\) 0 0
\(148\) −5.89898 + 10.2173i −0.484893 + 0.839860i
\(149\) −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 \(0.768119\pi\)
\(152\) −2.55051 −0.206874
\(153\) 0 0
\(154\) −2.00000 −0.161165
\(155\) −4.34847 7.53177i −0.349277 0.604966i
\(156\) 0 0
\(157\) 4.17423 7.22999i 0.333140 0.577016i −0.649986 0.759947i \(-0.725225\pi\)
0.983126 + 0.182931i \(0.0585584\pi\)
\(158\) −0.949490 + 1.64456i −0.0755373 + 0.130835i
\(159\) 0 0
\(160\) 0.724745 + 1.25529i 0.0572961 + 0.0992398i
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −19.7980 −1.55070 −0.775348 0.631534i \(-0.782425\pi\)
−0.775348 + 0.631534i \(0.782425\pi\)
\(164\) 4.89898 + 8.48528i 0.382546 + 0.662589i
\(165\) 0 0
\(166\) −1.00000 + 1.73205i −0.0776151 + 0.134433i
\(167\) −5.34847 + 9.26382i −0.413877 + 0.716856i −0.995310 0.0967384i \(-0.969159\pi\)
0.581433 + 0.813594i \(0.302492\pi\)
\(168\) 0 0
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) 2.89898 0.222342
\(171\) 0 0
\(172\) 6.89898 0.526042
\(173\) −1.55051 2.68556i −0.117883 0.204180i 0.801045 0.598604i \(-0.204277\pi\)
−0.918929 + 0.394424i \(0.870944\pi\)
\(174\) 0 0
\(175\) −1.44949 + 2.51059i −0.109571 + 0.189783i
\(176\) 1.00000 1.73205i 0.0753778 0.130558i
\(177\) 0 0
\(178\) 8.44949 + 14.6349i 0.633316 + 1.09694i
\(179\) −20.6969 −1.54696 −0.773481 0.633820i \(-0.781486\pi\)
−0.773481 + 0.633820i \(0.781486\pi\)
\(180\) 0 0
\(181\) −10.3485 −0.769196 −0.384598 0.923084i \(-0.625660\pi\)
−0.384598 + 0.923084i \(0.625660\pi\)
\(182\) −2.44949 4.24264i −0.181568 0.314485i
\(183\) 0 0
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −8.55051 + 14.8099i −0.628646 + 1.08885i
\(186\) 0 0
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) −9.79796 −0.714590
\(189\) 0 0
\(190\) −3.69694 −0.268204
\(191\) 2.05051 + 3.55159i 0.148370 + 0.256984i 0.930625 0.365974i \(-0.119264\pi\)
−0.782255 + 0.622958i \(0.785931\pi\)
\(192\) 0 0
\(193\) 8.94949 15.5010i 0.644198 1.11578i −0.340288 0.940321i \(-0.610524\pi\)
0.984486 0.175463i \(-0.0561422\pi\)
\(194\) 1.44949 2.51059i 0.104067 0.180250i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) −16.6969 −1.18961 −0.594804 0.803871i \(-0.702770\pi\)
−0.594804 + 0.803871i \(0.702770\pi\)
\(198\) 0 0
\(199\) −2.89898 −0.205503 −0.102752 0.994707i \(-0.532765\pi\)
−0.102752 + 0.994707i \(0.532765\pi\)
\(200\) −1.44949 2.51059i −0.102494 0.177526i
\(201\) 0 0
\(202\) 8.62372 14.9367i 0.606763 1.05094i
\(203\) 3.44949 5.97469i 0.242107 0.419341i
\(204\) 0 0
\(205\) 7.10102 + 12.2993i 0.495957 + 0.859022i
\(206\) −14.0000 −0.975426
\(207\) 0 0
\(208\) 4.89898 0.339683
\(209\) 2.55051 + 4.41761i 0.176422 + 0.305573i
\(210\) 0 0
\(211\) −6.44949 + 11.1708i −0.444001 + 0.769033i −0.997982 0.0634968i \(-0.979775\pi\)
0.553981 + 0.832529i \(0.313108\pi\)
\(212\) −5.44949 + 9.43879i −0.374272 + 0.648259i
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 10.0000 0.681994
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) 6.34847 + 10.9959i 0.429973 + 0.744734i
\(219\) 0 0
\(220\) 1.44949 2.51059i 0.0977246 0.169264i
\(221\) 4.89898 8.48528i 0.329541 0.570782i
\(222\) 0 0
\(223\) 5.55051 + 9.61377i 0.371690 + 0.643785i 0.989826 0.142286i \(-0.0454452\pi\)
−0.618136 + 0.786071i \(0.712112\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −6.10102 −0.405834
\(227\) −2.72474 4.71940i −0.180848 0.313237i 0.761322 0.648374i \(-0.224551\pi\)
−0.942169 + 0.335137i \(0.891217\pi\)
\(228\) 0 0
\(229\) −0.623724 + 1.08032i −0.0412169 + 0.0713897i −0.885898 0.463880i \(-0.846457\pi\)
0.844681 + 0.535270i \(0.179790\pi\)
\(230\) 0.724745 1.25529i 0.0477883 0.0827717i
\(231\) 0 0
\(232\) 3.44949 + 5.97469i 0.226470 + 0.392258i
\(233\) 7.00000 0.458585 0.229293 0.973358i \(-0.426359\pi\)
0.229293 + 0.973358i \(0.426359\pi\)
\(234\) 0 0
\(235\) −14.2020 −0.926439
\(236\) −1.00000 1.73205i −0.0650945 0.112747i
\(237\) 0 0
\(238\) 1.00000 1.73205i 0.0648204 0.112272i
\(239\) 3.39898 5.88721i 0.219862 0.380812i −0.734904 0.678171i \(-0.762773\pi\)
0.954766 + 0.297360i \(0.0961061\pi\)
\(240\) 0 0
\(241\) −0.449490 0.778539i −0.0289542 0.0501501i 0.851185 0.524865i \(-0.175884\pi\)
−0.880139 + 0.474715i \(0.842551\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) 6.55051 0.419353
\(245\) −0.724745 1.25529i −0.0463023 0.0801979i
\(246\) 0 0
\(247\) −6.24745 + 10.8209i −0.397516 + 0.688517i
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) 0 0
\(250\) −5.72474 9.91555i −0.362065 0.627114i
\(251\) −17.4495 −1.10140 −0.550701 0.834703i \(-0.685640\pi\)
−0.550701 + 0.834703i \(0.685640\pi\)
\(252\) 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
\(257\) 4.10102 7.10318i 0.255815 0.443084i −0.709302 0.704905i \(-0.750990\pi\)
0.965116 + 0.261821i \(0.0843230\pi\)
\(258\) 0 0
\(259\) 5.89898 + 10.2173i 0.366545 + 0.634874i
\(260\) 7.10102 0.440387
\(261\) 0 0
\(262\) −8.55051 −0.528252
\(263\) 12.9495 + 22.4292i 0.798500 + 1.38304i 0.920593 + 0.390523i \(0.127706\pi\)
−0.122093 + 0.992519i \(0.538961\pi\)
\(264\) 0 0
\(265\) −7.89898 + 13.6814i −0.485230 + 0.840444i
\(266\) −1.27526 + 2.20881i −0.0781909 + 0.135431i
\(267\) 0 0
\(268\) 6.44949 + 11.1708i 0.393965 + 0.682368i
\(269\) 18.3485 1.11873 0.559363 0.828923i \(-0.311046\pi\)
0.559363 + 0.828923i \(0.311046\pi\)
\(270\) 0 0
\(271\) 7.10102 0.431356 0.215678 0.976465i \(-0.430804\pi\)
0.215678 + 0.976465i \(0.430804\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) −3.89898 + 6.75323i −0.235546 + 0.407978i
\(275\) −2.89898 + 5.02118i −0.174815 + 0.302789i
\(276\) 0 0
\(277\) 9.34847 + 16.1920i 0.561695 + 0.972884i 0.997349 + 0.0727700i \(0.0231839\pi\)
−0.435654 + 0.900114i \(0.643483\pi\)
\(278\) −4.55051 −0.272921
\(279\) 0 0
\(280\) 1.44949 0.0866236
\(281\) −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
\(283\) 12.7247 22.0399i 0.756408 1.31014i −0.188264 0.982118i \(-0.560286\pi\)
0.944672 0.328018i \(-0.106381\pi\)
\(284\) 0.0505103 0.0874863i 0.00299723 0.00519136i
\(285\) 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
\(292\) 3.44949 5.97469i 0.201866 0.349642i
\(293\) 1.37628 2.38378i 0.0804029 0.139262i −0.823020 0.568012i \(-0.807713\pi\)
0.903423 + 0.428750i \(0.141046\pi\)
\(294\) 0 0
\(295\) −1.44949 2.51059i −0.0843926 0.146172i
\(296\) −11.7980 −0.685742
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) −2.44949 4.24264i −0.141658 0.245358i
\(300\) 0 0
\(301\) 3.44949 5.97469i 0.198825 0.344375i
\(302\) −2.50000 + 4.33013i −0.143859 + 0.249171i
\(303\) 0 0
\(304\) −1.27526 2.20881i −0.0731409 0.126684i
\(305\) 9.49490 0.543676
\(306\) 0 0
\(307\) 25.2474 1.44095 0.720474 0.693482i \(-0.243924\pi\)
0.720474 + 0.693482i \(0.243924\pi\)
\(308\) −1.00000 1.73205i −0.0569803 0.0986928i
\(309\) 0 0
\(310\) 4.34847 7.53177i 0.246976 0.427776i
\(311\) 15.3485 26.5843i 0.870332 1.50746i 0.00867810 0.999962i \(-0.497238\pi\)
0.861654 0.507497i \(-0.169429\pi\)
\(312\) 0 0
\(313\) 2.34847 + 4.06767i 0.132743 + 0.229918i 0.924733 0.380616i \(-0.124288\pi\)
−0.791990 + 0.610534i \(0.790955\pi\)
\(314\) 8.34847 0.471131
\(315\) 0 0
\(316\) −1.89898 −0.106826
\(317\) 10.3485 + 17.9241i 0.581228 + 1.00672i 0.995334 + 0.0964878i \(0.0307609\pi\)
−0.414106 + 0.910229i \(0.635906\pi\)
\(318\) 0 0
\(319\) 6.89898 11.9494i 0.386269 0.669037i
\(320\) −0.724745 + 1.25529i −0.0405145 + 0.0701731i
\(321\) 0 0
\(322\) −0.500000 0.866025i −0.0278639 0.0482617i
\(323\) −5.10102 −0.283828
\(324\) 0 0
\(325\) −14.2020 −0.787787
\(326\) −9.89898 17.1455i −0.548254 0.949603i
\(327\) 0 0
\(328\) −4.89898 + 8.48528i −0.270501 + 0.468521i
\(329\) −4.89898 + 8.48528i −0.270089 + 0.467809i
\(330\) 0 0
\(331\) −2.34847 4.06767i −0.129084 0.223579i 0.794238 0.607606i \(-0.207870\pi\)
−0.923322 + 0.384027i \(0.874537\pi\)
\(332\) −2.00000 −0.109764
\(333\) 0 0
\(334\) −10.6969 −0.585310
\(335\) 9.34847 + 16.1920i 0.510761 + 0.884665i
\(336\) 0 0
\(337\) 11.6969 20.2597i 0.637173 1.10362i −0.348877 0.937168i \(-0.613437\pi\)
0.986050 0.166447i \(-0.0532296\pi\)
\(338\) 5.50000 9.52628i 0.299161 0.518161i
\(339\) 0 0
\(340\) 1.44949 + 2.51059i 0.0786096 + 0.136156i
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 3.44949 + 5.97469i 0.185984 + 0.322134i
\(345\) 0 0
\(346\) 1.55051 2.68556i 0.0833559 0.144377i
\(347\) 9.79796 16.9706i 0.525982 0.911028i −0.473560 0.880762i \(-0.657031\pi\)
0.999542 0.0302659i \(-0.00963541\pi\)
\(348\) 0 0
\(349\) −5.55051 9.61377i −0.297112 0.514613i 0.678362 0.734728i \(-0.262690\pi\)
−0.975474 + 0.220115i \(0.929357\pi\)
\(350\) −2.89898 −0.154957
\(351\) 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
\(355\) 0.0732141 0.126811i 0.00388580 0.00673040i
\(356\) −8.44949 + 14.6349i −0.447822 + 0.775651i
\(357\) 0 0
\(358\) −10.3485 17.9241i −0.546934 0.947317i
\(359\) 8.79796 0.464339 0.232169 0.972675i \(-0.425418\pi\)
0.232169 + 0.972675i \(0.425418\pi\)
\(360\) 0 0
\(361\) −12.4949 −0.657626
\(362\) −5.17423 8.96204i −0.271952 0.471034i
\(363\) 0 0
\(364\) 2.44949 4.24264i 0.128388 0.222375i
\(365\) 5.00000 8.66025i 0.261712 0.453298i
\(366\) 0 0
\(367\) 6.89898 + 11.9494i 0.360124 + 0.623753i 0.987981 0.154576i \(-0.0494011\pi\)
−0.627857 + 0.778329i \(0.716068\pi\)
\(368\) 1.00000 0.0521286
\(369\) 0 0
\(370\) −17.1010 −0.889040
\(371\) 5.44949 + 9.43879i 0.282923 + 0.490038i
\(372\) 0 0
\(373\) 3.44949 5.97469i 0.178608 0.309358i −0.762796 0.646639i \(-0.776174\pi\)
0.941404 + 0.337281i \(0.109507\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) 0 0
\(376\) −4.89898 8.48528i −0.252646 0.437595i
\(377\) 33.7980 1.74068
\(378\) 0 0
\(379\) 22.4949 1.15549 0.577743 0.816219i \(-0.303934\pi\)
0.577743 + 0.816219i \(0.303934\pi\)
\(380\) −1.84847 3.20164i −0.0948245 0.164241i
\(381\) 0 0
\(382\) −2.05051 + 3.55159i −0.104913 + 0.181715i
\(383\) −1.44949 + 2.51059i −0.0740655 + 0.128285i −0.900679 0.434484i \(-0.856931\pi\)
0.826614 + 0.562769i \(0.190264\pi\)
\(384\) 0 0
\(385\) −1.44949 2.51059i −0.0738728 0.127952i
\(386\) 17.8990 0.911034
\(387\) 0 0
\(388\) 2.89898 0.147173
\(389\) −12.4495 21.5631i −0.631214 1.09330i −0.987304 0.158843i \(-0.949224\pi\)
0.356090 0.934452i \(-0.384110\pi\)
\(390\) 0 0
\(391\) 1.00000 1.73205i 0.0505722 0.0875936i
\(392\) 0.500000 0.866025i 0.0252538 0.0437409i
\(393\) 0 0
\(394\) −8.34847 14.4600i −0.420590 0.728483i
\(395\) −2.75255 −0.138496
\(396\) 0 0
\(397\) 38.6969 1.94214 0.971072 0.238788i \(-0.0767500\pi\)
0.971072 + 0.238788i \(0.0767500\pi\)
\(398\) −1.44949 2.51059i −0.0726564 0.125844i
\(399\) 0 0
\(400\) 1.44949 2.51059i 0.0724745 0.125529i
\(401\) −9.94949 + 17.2330i −0.496854 + 0.860576i −0.999993 0.00362911i \(-0.998845\pi\)
0.503140 + 0.864205i \(0.332178\pi\)
\(402\) 0 0
\(403\) −14.6969 25.4558i −0.732107 1.26805i
\(404\) 17.2474 0.858093
\(405\) 0 0
\(406\) 6.89898 0.342391
\(407\) 11.7980 + 20.4347i 0.584803 + 1.01291i
\(408\) 0 0
\(409\) 6.89898 11.9494i 0.341133 0.590859i −0.643511 0.765437i \(-0.722523\pi\)
0.984643 + 0.174578i \(0.0558562\pi\)
\(410\) −7.10102 + 12.2993i −0.350694 + 0.607421i
\(411\) 0 0
\(412\) −7.00000 12.1244i −0.344865 0.597324i
\(413\) −2.00000 −0.0984136
\(414\) 0 0
\(415\) −2.89898 −0.142305
\(416\) 2.44949 + 4.24264i 0.120096 + 0.208013i
\(417\) 0 0
\(418\) −2.55051 + 4.41761i −0.124750 + 0.216073i
\(419\) 14.7247 25.5040i 0.719351 1.24595i −0.241906 0.970300i \(-0.577773\pi\)
0.961257 0.275653i \(-0.0888940\pi\)
\(420\) 0 0
\(421\) −11.4495 19.8311i −0.558014 0.966509i −0.997662 0.0683385i \(-0.978230\pi\)
0.439648 0.898170i \(-0.355103\pi\)
\(422\) −12.8990 −0.627912
\(423\) 0 0
\(424\) −10.8990 −0.529301
\(425\) −2.89898 5.02118i −0.140621 0.243563i
\(426\) 0 0
\(427\) 3.27526 5.67291i 0.158501 0.274531i
\(428\) −6.00000 + 10.3923i −0.290021 + 0.502331i
\(429\) 0 0
\(430\) 5.00000 + 8.66025i 0.241121 + 0.417635i
\(431\) −31.5959 −1.52192 −0.760961 0.648798i \(-0.775272\pi\)
−0.760961 + 0.648798i \(0.775272\pi\)
\(432\) 0 0
\(433\) −7.79796 −0.374746 −0.187373 0.982289i \(-0.559997\pi\)
−0.187373 + 0.982289i \(0.559997\pi\)
\(434\) −3.00000 5.19615i −0.144005 0.249423i
\(435\) 0 0
\(436\) −6.34847 + 10.9959i −0.304037 + 0.526607i
\(437\) −1.27526 + 2.20881i −0.0610037 + 0.105662i
\(438\) 0 0
\(439\) −1.10102 1.90702i −0.0525488 0.0910173i 0.838554 0.544818i \(-0.183401\pi\)
−0.891103 + 0.453801i \(0.850068\pi\)
\(440\) 2.89898 0.138203
\(441\) 0 0
\(442\) 9.79796 0.466041
\(443\) −7.44949 12.9029i −0.353936 0.613035i 0.632999 0.774152i \(-0.281824\pi\)
−0.986935 + 0.161117i \(0.948490\pi\)
\(444\) 0 0
\(445\) −12.2474 + 21.2132i −0.580585 + 1.00560i
\(446\) −5.55051 + 9.61377i −0.262824 + 0.455225i
\(447\) 0 0
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) −20.5959 −0.971981 −0.485991 0.873964i \(-0.661541\pi\)
−0.485991 + 0.873964i \(0.661541\pi\)
\(450\) 0 0
\(451\) 19.5959 0.922736
\(452\) −3.05051 5.28364i −0.143484 0.248521i
\(453\) 0 0
\(454\) 2.72474 4.71940i 0.127879 0.221492i
\(455\) 3.55051 6.14966i 0.166450 0.288301i
\(456\) 0 0
\(457\) 8.74745 + 15.1510i 0.409188 + 0.708735i 0.994799 0.101857i \(-0.0324785\pi\)
−0.585611 + 0.810593i \(0.699145\pi\)
\(458\) −1.24745 −0.0582895
\(459\) 0 0
\(460\) 1.44949 0.0675828
\(461\) 2.82577 + 4.89437i 0.131609 + 0.227954i 0.924297 0.381674i \(-0.124652\pi\)
−0.792688 + 0.609628i \(0.791319\pi\)
\(462\) 0 0
\(463\) −1.84847 + 3.20164i −0.0859057 + 0.148793i −0.905777 0.423755i \(-0.860712\pi\)
0.819871 + 0.572548i \(0.194045\pi\)
\(464\) −3.44949 + 5.97469i −0.160139 + 0.277368i
\(465\) 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
\(469\) 12.8990 0.595620
\(470\) −7.10102 12.2993i −0.327546 0.567326i
\(471\) 0 0
\(472\) 1.00000 1.73205i 0.0460287 0.0797241i
\(473\) 6.89898 11.9494i 0.317215 0.549433i
\(474\) 0 0
\(475\) 3.69694 + 6.40329i 0.169627 + 0.293803i
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) 6.79796 0.310931
\(479\) 4.79796 + 8.31031i 0.219224 + 0.379708i 0.954571 0.297983i \(-0.0963140\pi\)
−0.735347 + 0.677691i \(0.762981\pi\)
\(480\) 0 0
\(481\) −28.8990 + 50.0545i −1.31768 + 2.28229i
\(482\) 0.449490 0.778539i 0.0204737 0.0354615i
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 4.20204 0.190805
\(486\) 0 0
\(487\) −36.3939 −1.64916 −0.824582 0.565742i \(-0.808590\pi\)
−0.824582 + 0.565742i \(0.808590\pi\)
\(488\) 3.27526 + 5.67291i 0.148264 + 0.256800i
\(489\) 0 0
\(490\) 0.724745 1.25529i 0.0327406 0.0567084i
\(491\) 7.89898 13.6814i 0.356476 0.617434i −0.630893 0.775869i \(-0.717312\pi\)
0.987369 + 0.158435i \(0.0506448\pi\)
\(492\) 0 0
\(493\) 6.89898 + 11.9494i 0.310714 + 0.538173i
\(494\) −12.4949 −0.562172
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) −0.0505103 0.0874863i −0.00226569 0.00392430i
\(498\) 0 0
\(499\) 12.6969 21.9917i 0.568393 0.984486i −0.428332 0.903621i \(-0.640899\pi\)
0.996725 0.0808642i \(-0.0257680\pi\)
\(500\) 5.72474 9.91555i 0.256018 0.443437i
\(501\) 0 0
\(502\) −8.72474 15.1117i −0.389404 0.674468i
\(503\) 24.4949 1.09217 0.546087 0.837729i \(-0.316117\pi\)
0.546087 + 0.837729i \(0.316117\pi\)
\(504\) 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
\(509\) −3.55051 + 6.14966i −0.157374 + 0.272579i −0.933921 0.357480i \(-0.883636\pi\)
0.776547 + 0.630059i \(0.216969\pi\)
\(510\) 0 0
\(511\) −3.44949 5.97469i −0.152596 0.264305i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 8.20204 0.361777
\(515\) −10.1464 17.5741i −0.447105 0.774409i
\(516\) 0 0
\(517\) −9.79796 + 16.9706i −0.430914 + 0.746364i
\(518\) −5.89898 + 10.2173i −0.259186 + 0.448924i
\(519\) 0 0
\(520\) 3.55051 + 6.14966i 0.155700 + 0.269681i
\(521\) 9.30306 0.407575 0.203787 0.979015i \(-0.434675\pi\)
0.203787 + 0.979015i \(0.434675\pi\)
\(522\) 0 0
\(523\) −14.3485 −0.627415 −0.313707 0.949520i \(-0.601571\pi\)
−0.313707 + 0.949520i \(0.601571\pi\)
\(524\) −4.27526 7.40496i −0.186765 0.323487i
\(525\) 0 0
\(526\) −12.9495 + 22.4292i −0.564625 + 0.977958i
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) −15.7980 −0.686219
\(531\) 0 0
\(532\) −2.55051 −0.110579
\(533\) 24.0000 + 41.5692i 1.03956 + 1.80056i
\(534\) 0 0
\(535\) −8.69694 + 15.0635i −0.376001 + 0.651254i
\(536\) −6.44949 + 11.1708i −0.278576 + 0.482507i
\(537\) 0 0
\(538\) 9.17423 + 15.8902i 0.395529 + 0.685077i
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −18.4949 −0.795158 −0.397579 0.917568i \(-0.630149\pi\)
−0.397579 + 0.917568i \(0.630149\pi\)
\(542\) 3.55051 + 6.14966i 0.152507 + 0.264151i
\(543\) 0 0
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) −9.20204 + 15.9384i −0.394172 + 0.682726i
\(546\) 0 0
\(547\) 3.79796 + 6.57826i 0.162389 + 0.281266i 0.935725 0.352730i \(-0.114747\pi\)
−0.773336 + 0.633996i \(0.781413\pi\)
\(548\) −7.79796 −0.333112
\(549\) 0 0
\(550\) −5.79796 −0.247226
\(551\) −8.79796 15.2385i −0.374806 0.649182i
\(552\) 0 0
\(553\) −0.949490 + 1.64456i −0.0403764 + 0.0699340i
\(554\) −9.34847 + 16.1920i −0.397178 + 0.687933i
\(555\) 0 0
\(556\) −2.27526 3.94086i −0.0964923 0.167130i
\(557\) 12.8990 0.546547 0.273274 0.961936i \(-0.411894\pi\)
0.273274 + 0.961936i \(0.411894\pi\)
\(558\) 0 0
\(559\) 33.7980 1.42950
\(560\) 0.724745 + 1.25529i 0.0306261 + 0.0530459i
\(561\) 0 0
\(562\) 9.50000 16.4545i 0.400733 0.694090i
\(563\) −19.9722 + 34.5929i −0.841728 + 1.45791i 0.0467054 + 0.998909i \(0.485128\pi\)
−0.888433 + 0.459006i \(0.848206\pi\)
\(564\) 0 0
\(565\) −4.42168 7.65858i −0.186022 0.322199i
\(566\) 25.4495 1.06972
\(567\) 0 0
\(568\) 0.101021 0.00423873
\(569\) −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
\(571\) −16.8990 + 29.2699i −0.707200 + 1.22491i 0.258691 + 0.965960i \(0.416709\pi\)
−0.965892 + 0.258947i \(0.916625\pi\)
\(572\) 4.89898 8.48528i 0.204837 0.354787i
\(573\) 0 0
\(574\) 4.89898 + 8.48528i 0.204479 + 0.354169i
\(575\) −2.89898 −0.120896
\(576\) 0 0
\(577\) −15.5959 −0.649267 −0.324633 0.945840i \(-0.605241\pi\)
−0.324633 + 0.945840i \(0.605241\pi\)
\(578\) −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
\(583\) 10.8990 + 18.8776i 0.451390 + 0.781830i
\(584\) 6.89898 0.285482
\(585\) 0 0
\(586\) 2.75255 0.113707
\(587\) 8.07321 + 13.9832i 0.333217 + 0.577149i 0.983141 0.182850i \(-0.0585324\pi\)
−0.649924 + 0.760000i \(0.725199\pi\)
\(588\) 0 0
\(589\) −7.65153 + 13.2528i −0.315276 + 0.546074i
\(590\) 1.44949 2.51059i 0.0596745 0.103359i
\(591\) 0 0
\(592\) −5.89898 10.2173i −0.242447 0.419930i
\(593\) −14.6969 −0.603531 −0.301765 0.953382i \(-0.597576\pi\)
−0.301765 + 0.953382i \(0.597576\pi\)
\(594\) 0 0
\(595\) 2.89898 0.118847
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) 2.44949 4.24264i 0.100167 0.173494i
\(599\) −16.8990 + 29.2699i −0.690474 + 1.19594i 0.281209 + 0.959646i \(0.409264\pi\)
−0.971683 + 0.236289i \(0.924069\pi\)
\(600\) 0 0
\(601\) −8.34847 14.4600i −0.340541 0.589835i 0.643992 0.765032i \(-0.277277\pi\)
−0.984533 + 0.175198i \(0.943944\pi\)
\(602\) 6.89898 0.281181
\(603\) 0 0
\(604\) −5.00000 −0.203447
\(605\) 5.07321 + 8.78706i 0.206255 + 0.357245i
\(606\) 0 0
\(607\) −10.3485 + 17.9241i −0.420031 + 0.727516i −0.995942 0.0899969i \(-0.971314\pi\)
0.575911 + 0.817513i \(0.304648\pi\)
\(608\) 1.27526 2.20881i 0.0517184 0.0895789i
\(609\) 0 0
\(610\) 4.74745 + 8.22282i 0.192219 + 0.332932i
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) −14.6969 −0.593604 −0.296802 0.954939i \(-0.595920\pi\)
−0.296802 + 0.954939i \(0.595920\pi\)
\(614\) 12.6237 + 21.8649i 0.509452 + 0.882397i
\(615\) 0 0
\(616\) 1.00000 1.73205i 0.0402911 0.0697863i
\(617\) −7.69694 + 13.3315i −0.309867 + 0.536706i −0.978333 0.207037i \(-0.933618\pi\)
0.668466 + 0.743743i \(0.266951\pi\)
\(618\) 0 0
\(619\) −15.0732 26.1076i −0.605844 1.04935i −0.991918 0.126884i \(-0.959502\pi\)
0.386074 0.922468i \(-0.373831\pi\)
\(620\) 8.69694 0.349277
\(621\) 0 0
\(622\) 30.6969 1.23084
\(623\) 8.44949 + 14.6349i 0.338522 + 0.586337i
\(624\) 0 0
\(625\) 1.05051 1.81954i 0.0420204 0.0727815i
\(626\) −2.34847 + 4.06767i −0.0938637 + 0.162577i
\(627\) 0 0
\(628\) 4.17423 + 7.22999i 0.166570 + 0.288508i
\(629\) −23.5959 −0.940831
\(630\) 0 0
\(631\) 27.8990 1.11064 0.555320 0.831636i \(-0.312596\pi\)
0.555320 + 0.831636i \(0.312596\pi\)
\(632\) −0.949490 1.64456i −0.0377687 0.0654173i
\(633\) 0 0
\(634\) −10.3485 + 17.9241i −0.410990 + 0.711856i
\(635\) 2.17423 3.76588i 0.0862819 0.149445i
\(636\) 0 0
\(637\) −2.44949 4.24264i −0.0970523 0.168100i
\(638\) 13.7980 0.546266
\(639\) 0 0
\(640\) −1.44949 −0.0572961
\(641\) −3.74745 6.49077i −0.148015 0.256370i 0.782479 0.622678i \(-0.213955\pi\)
−0.930494 + 0.366308i \(0.880622\pi\)
\(642\) 0 0
\(643\) 19.6969 34.1161i 0.776771 1.34541i −0.157022 0.987595i \(-0.550189\pi\)
0.933793 0.357812i \(-0.116477\pi\)
\(644\) 0.500000 0.866025i 0.0197028 0.0341262i
\(645\) 0 0
\(646\) −2.55051 4.41761i −0.100348 0.173809i
\(647\) 50.6969 1.99310 0.996551 0.0829807i \(-0.0264440\pi\)
0.996551 + 0.0829807i \(0.0264440\pi\)
\(648\) 0 0
\(649\) −4.00000 −0.157014
\(650\) −7.10102 12.2993i −0.278525 0.482419i
\(651\) 0 0
\(652\) 9.89898 17.1455i 0.387674 0.671471i
\(653\) 4.89898 8.48528i 0.191712 0.332055i −0.754106 0.656753i \(-0.771929\pi\)
0.945818 + 0.324698i \(0.105263\pi\)
\(654\) 0 0
\(655\) −6.19694 10.7334i −0.242134 0.419389i
\(656\) −9.79796 −0.382546
\(657\) 0 0
\(658\) −9.79796 −0.381964
\(659\) −12.3485 21.3882i −0.481028 0.833165i 0.518735 0.854935i \(-0.326403\pi\)
−0.999763 + 0.0217701i \(0.993070\pi\)
\(660\) 0 0
\(661\) −2.27526 + 3.94086i −0.0884972 + 0.153282i −0.906876 0.421397i \(-0.861540\pi\)
0.818379 + 0.574679i \(0.194873\pi\)
\(662\) 2.34847 4.06767i 0.0912758 0.158094i
\(663\) 0 0
\(664\) −1.00000 1.73205i −0.0388075 0.0672166i
\(665\) −3.69694 −0.143361
\(666\) 0 0
\(667\) 6.89898 0.267130
\(668\) −5.34847 9.26382i −0.206938 0.358428i
\(669\) 0 0
\(670\) −9.34847 + 16.1920i −0.361163 + 0.625552i
\(671\) 6.55051 11.3458i 0.252880 0.438000i
\(672\) 0 0
\(673\) 4.29796 + 7.44428i 0.165674 + 0.286956i 0.936894 0.349612i \(-0.113687\pi\)
−0.771220 + 0.636568i \(0.780353\pi\)
\(674\) 23.3939 0.901098
\(675\) 0 0
\(676\) 11.0000 0.423077
\(677\) 7.34847 + 12.7279i 0.282425 + 0.489174i 0.971981 0.235058i \(-0.0755280\pi\)
−0.689557 + 0.724232i \(0.742195\pi\)
\(678\) 0 0
\(679\) 1.44949 2.51059i 0.0556263 0.0963476i
\(680\) −1.44949 + 2.51059i −0.0555854 + 0.0962767i
\(681\) 0 0
\(682\) −6.00000 10.3923i −0.229752 0.397942i
\(683\) −51.7980 −1.98199 −0.990997 0.133885i \(-0.957255\pi\)
−0.990997 + 0.133885i \(0.957255\pi\)
\(684\) 0 0
\(685\) −11.3031 −0.431868
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) −3.44949 + 5.97469i −0.131511 + 0.227783i
\(689\) −26.6969 + 46.2405i −1.01707 + 1.76162i
\(690\) 0 0
\(691\) −25.5227 44.2066i −0.970929 1.68170i −0.692762 0.721167i \(-0.743606\pi\)
−0.278168 0.960533i \(-0.589727\pi\)
\(692\) 3.10102 0.117883
\(693\) 0 0
\(694\) 19.5959 0.743851
\(695\) −3.29796 5.71223i −0.125099 0.216677i
\(696\) 0 0
\(697\) −9.79796 + 16.9706i −0.371124 + 0.642806i
\(698\) 5.55051 9.61377i 0.210090 0.363886i
\(699\) 0 0
\(700\) −1.44949 2.51059i −0.0547856 0.0948914i
\(701\) 7.39388 0.279263 0.139631 0.990204i \(-0.455408\pi\)
0.139631 + 0.990204i \(0.455408\pi\)
\(702\) 0 0
\(703\) 30.0908 1.13490
\(704\) 1.00000 + 1.73205i 0.0376889 + 0.0652791i
\(705\) 0 0
\(706\) 3.00000 5.19615i 0.112906 0.195560i
\(707\) 8.62372 14.9367i 0.324329 0.561754i
\(708\) 0 0
\(709\) −13.7980 23.8988i −0.518193 0.897537i −0.999777 0.0211367i \(-0.993271\pi\)
0.481583 0.876400i \(-0.340062\pi\)
\(710\) 0.146428 0.00549535
\(711\) 0 0
\(712\) −16.8990 −0.633316
\(713\) −3.00000 5.19615i −0.112351 0.194597i
\(714\) 0 0
\(715\) 7.10102 12.2993i 0.265563 0.459969i
\(716\) 10.3485 17.9241i 0.386740 0.669854i
\(717\) 0 0
\(718\) 4.39898 + 7.61926i 0.164168 + 0.284348i
\(719\) −9.79796 −0.365402 −0.182701 0.983169i \(-0.558484\pi\)
−0.182701 + 0.983169i \(0.558484\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) −6.24745 10.8209i −0.232506 0.402712i
\(723\) 0 0
\(724\) 5.17423 8.96204i 0.192299 0.333071i
\(725\) 10.0000 17.3205i 0.371391 0.643268i
\(726\) 0 0
\(727\) 4.24745 + 7.35680i 0.157529 + 0.272848i 0.933977 0.357333i \(-0.116314\pi\)
−0.776448 + 0.630181i \(0.782981\pi\)
\(728\) 4.89898 0.181568
\(729\) 0 0
\(730\) 10.0000 0.370117
\(731\) 6.89898 + 11.9494i 0.255168 + 0.441964i
\(732\) 0 0
\(733\) 8.72474 15.1117i 0.322256 0.558163i −0.658697 0.752408i \(-0.728892\pi\)
0.980953 + 0.194245i \(0.0622255\pi\)
\(734\) −6.89898 + 11.9494i −0.254646 + 0.441060i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) 25.7980 0.950280
\(738\) 0 0
\(739\) 13.5959 0.500134 0.250067 0.968229i \(-0.419547\pi\)
0.250067 + 0.968229i \(0.419547\pi\)
\(740\) −8.55051 14.8099i −0.314323 0.544423i
\(741\) 0 0
\(742\) −5.44949 + 9.43879i −0.200057 + 0.346509i
\(743\) 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
\(745\) −4.34847 7.53177i −0.159316 0.275943i
\(746\) 6.89898 0.252590
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) 6.00000 + 10.3923i 0.219235 + 0.379727i
\(750\) 0 0
\(751\) −0.702041 + 1.21597i −0.0256178 + 0.0443714i −0.878550 0.477650i \(-0.841489\pi\)
0.852932 + 0.522022i \(0.174822\pi\)
\(752\) 4.89898 8.48528i 0.178647 0.309426i
\(753\) 0 0
\(754\) 16.8990 + 29.2699i 0.615425 + 1.06595i
\(755\) −7.24745 −0.263762
\(756\) 0 0
\(757\) −35.3939 −1.28641 −0.643206 0.765693i \(-0.722396\pi\)
−0.643206 + 0.765693i \(0.722396\pi\)
\(758\) 11.2474 + 19.4812i 0.408526 + 0.707587i
\(759\) 0 0
\(760\) 1.84847 3.20164i 0.0670510 0.116136i
\(761\) 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
\(763\) 6.34847 + 10.9959i 0.229830 + 0.398077i
\(764\) −4.10102 −0.148370
\(765\) 0 0
\(766\) −2.89898 −0.104744
\(767\) −4.89898 8.48528i −0.176892 0.306386i
\(768\) 0 0
\(769\) 17.0454 29.5235i 0.614673 1.06465i −0.375769 0.926714i \(-0.622621\pi\)
0.990442 0.137932i \(-0.0440454\pi\)
\(770\) 1.44949 2.51059i 0.0522360 0.0904754i
\(771\) 0 0
\(772\) 8.94949 + 15.5010i 0.322099 + 0.557892i
\(773\) −33.9444 −1.22089 −0.610447 0.792057i \(-0.709010\pi\)
−0.610447 + 0.792057i \(0.709010\pi\)
\(774\) 0 0
\(775\) −17.3939 −0.624807
\(776\) 1.44949 + 2.51059i 0.0520336 + 0.0901249i
\(777\) 0 0
\(778\) 12.4495 21.5631i 0.446336 0.773076i
\(779\) 12.4949 21.6418i 0.447676 0.775398i
\(780\) 0 0
\(781\) −0.101021 0.174973i −0.00361480 0.00626101i
\(782\) 2.00000 0.0715199
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 6.05051 + 10.4798i 0.215952 + 0.374040i
\(786\) 0 0
\(787\) 5.69694 9.86739i 0.203074 0.351734i −0.746443 0.665449i \(-0.768240\pi\)
0.949517 + 0.313715i \(0.101573\pi\)
\(788\) 8.34847 14.4600i 0.297402 0.515115i
\(789\) 0 0
\(790\) −1.37628 2.38378i −0.04896