Properties

Label 2646.2.m.a.881.8
Level $2646$
Weight $2$
Character 2646.881
Analytic conductor $21.128$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + 2785 x^{8} - 2640 x^{7} - 2601 x^{6} + 10260 x^{5} - 10611 x^{4} - 1944 x^{3} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.8
Root \(1.73109 - 0.0577511i\) of defining polynomial
Character \(\chi\) \(=\) 2646.881
Dual form 2646.2.m.a.1763.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.14095 - 1.97618i) q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.14095 - 1.97618i) q^{5} -1.00000i q^{8} -2.28190i q^{10} +(-0.946590 + 0.546514i) q^{11} +(-5.91448 - 3.41473i) q^{13} +(-0.500000 - 0.866025i) q^{16} +6.71727 q^{17} -2.86351i q^{19} +(-1.14095 - 1.97618i) q^{20} +(-0.546514 + 0.946590i) q^{22} +(-3.38264 - 1.95297i) q^{23} +(-0.103535 - 0.179327i) q^{25} -6.82946 q^{26} +(-1.59933 + 0.923371i) q^{29} +(1.75081 + 1.01083i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.81732 - 3.35863i) q^{34} -7.15840 q^{37} +(-1.43175 - 2.47987i) q^{38} +(-1.97618 - 1.14095i) q^{40} +(2.45515 - 4.25245i) q^{41} +(-3.74246 - 6.48214i) q^{43} +1.09303i q^{44} -3.90593 q^{46} +(-3.40174 - 5.89199i) q^{47} +(-0.179327 - 0.103535i) q^{50} +(-5.91448 + 3.41473i) q^{52} -0.256424i q^{53} +2.49418i q^{55} +(-0.923371 + 1.59933i) q^{58} +(-0.971009 + 1.68184i) q^{59} +(-1.15315 + 0.665771i) q^{61} +2.02166 q^{62} -1.00000 q^{64} +(-13.4963 + 7.79207i) q^{65} +(-2.54959 + 4.41602i) q^{67} +(3.35863 - 5.81732i) q^{68} +0.233507i q^{71} -6.80432i q^{73} +(-6.19935 + 3.57920i) q^{74} +(-2.47987 - 1.43175i) q^{76} +(3.63624 + 6.29816i) q^{79} -2.28190 q^{80} -4.91031i q^{82} +(-2.91353 - 5.04638i) q^{83} +(7.66407 - 13.2746i) q^{85} +(-6.48214 - 3.74246i) q^{86} +(0.546514 + 0.946590i) q^{88} +17.9941 q^{89} +(-3.38264 + 1.95297i) q^{92} +(-5.89199 - 3.40174i) q^{94} +(-5.65882 - 3.26712i) q^{95} +(4.13903 - 2.38967i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} + 48 q^{89} - 6 q^{92} - 66 q^{95} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.14095 1.97618i 0.510248 0.883776i −0.489681 0.871902i \(-0.662887\pi\)
0.999929 0.0118746i \(-0.00377989\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.28190i 0.721600i
\(11\) −0.946590 + 0.546514i −0.285408 + 0.164780i −0.635869 0.771797i \(-0.719358\pi\)
0.350461 + 0.936577i \(0.386025\pi\)
\(12\) 0 0
\(13\) −5.91448 3.41473i −1.64038 0.947075i −0.980697 0.195533i \(-0.937356\pi\)
−0.659685 0.751542i \(-0.729310\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 6.71727 1.62918 0.814588 0.580040i \(-0.196963\pi\)
0.814588 + 0.580040i \(0.196963\pi\)
\(18\) 0 0
\(19\) 2.86351i 0.656934i −0.944515 0.328467i \(-0.893468\pi\)
0.944515 0.328467i \(-0.106532\pi\)
\(20\) −1.14095 1.97618i −0.255124 0.441888i
\(21\) 0 0
\(22\) −0.546514 + 0.946590i −0.116517 + 0.201814i
\(23\) −3.38264 1.95297i −0.705328 0.407221i 0.104001 0.994577i \(-0.466836\pi\)
−0.809329 + 0.587356i \(0.800169\pi\)
\(24\) 0 0
\(25\) −0.103535 0.179327i −0.0207069 0.0358655i
\(26\) −6.82946 −1.33937
\(27\) 0 0
\(28\) 0 0
\(29\) −1.59933 + 0.923371i −0.296987 + 0.171466i −0.641089 0.767467i \(-0.721517\pi\)
0.344101 + 0.938933i \(0.388184\pi\)
\(30\) 0 0
\(31\) 1.75081 + 1.01083i 0.314455 + 0.181551i 0.648918 0.760858i \(-0.275222\pi\)
−0.334463 + 0.942409i \(0.608555\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 5.81732 3.35863i 0.997663 0.576001i
\(35\) 0 0
\(36\) 0 0
\(37\) −7.15840 −1.17683 −0.588416 0.808558i \(-0.700248\pi\)
−0.588416 + 0.808558i \(0.700248\pi\)
\(38\) −1.43175 2.47987i −0.232261 0.402288i
\(39\) 0 0
\(40\) −1.97618 1.14095i −0.312462 0.180400i
\(41\) 2.45515 4.25245i 0.383431 0.664121i −0.608120 0.793845i \(-0.708076\pi\)
0.991550 + 0.129724i \(0.0414092\pi\)
\(42\) 0 0
\(43\) −3.74246 6.48214i −0.570721 0.988517i −0.996492 0.0836863i \(-0.973331\pi\)
0.425772 0.904831i \(-0.360003\pi\)
\(44\) 1.09303i 0.164780i
\(45\) 0 0
\(46\) −3.90593 −0.575898
\(47\) −3.40174 5.89199i −0.496195 0.859435i 0.503795 0.863823i \(-0.331937\pi\)
−0.999990 + 0.00438774i \(0.998603\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.179327 0.103535i −0.0253607 0.0146420i
\(51\) 0 0
\(52\) −5.91448 + 3.41473i −0.820191 + 0.473538i
\(53\) 0.256424i 0.0352225i −0.999845 0.0176112i \(-0.994394\pi\)
0.999845 0.0176112i \(-0.00560612\pi\)
\(54\) 0 0
\(55\) 2.49418i 0.336315i
\(56\) 0 0
\(57\) 0 0
\(58\) −0.923371 + 1.59933i −0.121245 + 0.210002i
\(59\) −0.971009 + 1.68184i −0.126415 + 0.218957i −0.922285 0.386510i \(-0.873680\pi\)
0.795870 + 0.605467i \(0.207014\pi\)
\(60\) 0 0
\(61\) −1.15315 + 0.665771i −0.147646 + 0.0852432i −0.572003 0.820252i \(-0.693833\pi\)
0.424357 + 0.905495i \(0.360500\pi\)
\(62\) 2.02166 0.256752
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −13.4963 + 7.79207i −1.67400 + 0.966487i
\(66\) 0 0
\(67\) −2.54959 + 4.41602i −0.311482 + 0.539503i −0.978683 0.205375i \(-0.934159\pi\)
0.667201 + 0.744877i \(0.267492\pi\)
\(68\) 3.35863 5.81732i 0.407294 0.705454i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.233507i 0.0277121i 0.999904 + 0.0138561i \(0.00441066\pi\)
−0.999904 + 0.0138561i \(0.995589\pi\)
\(72\) 0 0
\(73\) 6.80432i 0.796386i −0.917302 0.398193i \(-0.869638\pi\)
0.917302 0.398193i \(-0.130362\pi\)
\(74\) −6.19935 + 3.57920i −0.720660 + 0.416073i
\(75\) 0 0
\(76\) −2.47987 1.43175i −0.284461 0.164233i
\(77\) 0 0
\(78\) 0 0
\(79\) 3.63624 + 6.29816i 0.409109 + 0.708598i 0.994790 0.101944i \(-0.0325062\pi\)
−0.585681 + 0.810542i \(0.699173\pi\)
\(80\) −2.28190 −0.255124
\(81\) 0 0
\(82\) 4.91031i 0.542253i
\(83\) −2.91353 5.04638i −0.319801 0.553912i 0.660645 0.750698i \(-0.270283\pi\)
−0.980446 + 0.196786i \(0.936950\pi\)
\(84\) 0 0
\(85\) 7.66407 13.2746i 0.831285 1.43983i
\(86\) −6.48214 3.74246i −0.698987 0.403560i
\(87\) 0 0
\(88\) 0.546514 + 0.946590i 0.0582586 + 0.100907i
\(89\) 17.9941 1.90737 0.953687 0.300800i \(-0.0972535\pi\)
0.953687 + 0.300800i \(0.0972535\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.38264 + 1.95297i −0.352664 + 0.203611i
\(93\) 0 0
\(94\) −5.89199 3.40174i −0.607713 0.350863i
\(95\) −5.65882 3.26712i −0.580583 0.335200i
\(96\) 0 0
\(97\) 4.13903 2.38967i 0.420255 0.242634i −0.274931 0.961464i \(-0.588655\pi\)
0.695186 + 0.718830i \(0.255322\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.207069 −0.0207069
\(101\) −5.22981 9.05829i −0.520385 0.901334i −0.999719 0.0237012i \(-0.992455\pi\)
0.479334 0.877633i \(-0.340878\pi\)
\(102\) 0 0
\(103\) −11.0398 6.37383i −1.08778 0.628033i −0.154799 0.987946i \(-0.549473\pi\)
−0.932986 + 0.359914i \(0.882806\pi\)
\(104\) −3.41473 + 5.91448i −0.334842 + 0.579963i
\(105\) 0 0
\(106\) −0.128212 0.222069i −0.0124530 0.0215693i
\(107\) 9.53627i 0.921906i 0.887425 + 0.460953i \(0.152492\pi\)
−0.887425 + 0.460953i \(0.847508\pi\)
\(108\) 0 0
\(109\) 5.76503 0.552189 0.276095 0.961130i \(-0.410960\pi\)
0.276095 + 0.961130i \(0.410960\pi\)
\(110\) 1.24709 + 2.16002i 0.118905 + 0.205950i
\(111\) 0 0
\(112\) 0 0
\(113\) 10.3333 + 5.96592i 0.972073 + 0.561227i 0.899868 0.436163i \(-0.143663\pi\)
0.0722053 + 0.997390i \(0.476996\pi\)
\(114\) 0 0
\(115\) −7.71884 + 4.45647i −0.719785 + 0.415568i
\(116\) 1.84674i 0.171466i
\(117\) 0 0
\(118\) 1.94202i 0.178777i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.90265 + 8.49163i −0.445695 + 0.771966i
\(122\) −0.665771 + 1.15315i −0.0602760 + 0.104401i
\(123\) 0 0
\(124\) 1.75081 1.01083i 0.157228 0.0907754i
\(125\) 10.9370 0.978234
\(126\) 0 0
\(127\) −10.9133 −0.968400 −0.484200 0.874957i \(-0.660889\pi\)
−0.484200 + 0.874957i \(0.660889\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −7.79207 + 13.4963i −0.683410 + 1.18370i
\(131\) 0.989677 1.71417i 0.0864684 0.149768i −0.819548 0.573011i \(-0.805775\pi\)
0.906016 + 0.423243i \(0.139108\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 5.09918i 0.440502i
\(135\) 0 0
\(136\) 6.71727i 0.576001i
\(137\) 2.86923 1.65655i 0.245135 0.141528i −0.372400 0.928072i \(-0.621465\pi\)
0.617534 + 0.786544i \(0.288132\pi\)
\(138\) 0 0
\(139\) 3.00698 + 1.73608i 0.255048 + 0.147252i 0.622074 0.782959i \(-0.286290\pi\)
−0.367025 + 0.930211i \(0.619624\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.116753 + 0.202223i 0.00979772 + 0.0169701i
\(143\) 7.46479 0.624237
\(144\) 0 0
\(145\) 4.21408i 0.349961i
\(146\) −3.40216 5.89272i −0.281565 0.487685i
\(147\) 0 0
\(148\) −3.57920 + 6.19935i −0.294208 + 0.509584i
\(149\) −11.5534 6.67036i −0.946492 0.546457i −0.0545027 0.998514i \(-0.517357\pi\)
−0.891989 + 0.452056i \(0.850691\pi\)
\(150\) 0 0
\(151\) 2.66995 + 4.62450i 0.217278 + 0.376336i 0.953975 0.299887i \(-0.0969489\pi\)
−0.736697 + 0.676223i \(0.763616\pi\)
\(152\) −2.86351 −0.232261
\(153\) 0 0
\(154\) 0 0
\(155\) 3.99518 2.30662i 0.320901 0.185272i
\(156\) 0 0
\(157\) 15.3003 + 8.83364i 1.22110 + 0.705002i 0.965152 0.261689i \(-0.0842796\pi\)
0.255946 + 0.966691i \(0.417613\pi\)
\(158\) 6.29816 + 3.63624i 0.501054 + 0.289284i
\(159\) 0 0
\(160\) −1.97618 + 1.14095i −0.156231 + 0.0902000i
\(161\) 0 0
\(162\) 0 0
\(163\) −15.8983 −1.24525 −0.622625 0.782520i \(-0.713934\pi\)
−0.622625 + 0.782520i \(0.713934\pi\)
\(164\) −2.45515 4.25245i −0.191715 0.332061i
\(165\) 0 0
\(166\) −5.04638 2.91353i −0.391675 0.226134i
\(167\) 2.85878 4.95155i 0.221219 0.383163i −0.733959 0.679193i \(-0.762330\pi\)
0.955178 + 0.296031i \(0.0956631\pi\)
\(168\) 0 0
\(169\) 16.8207 + 29.1344i 1.29390 + 2.24110i
\(170\) 15.3281i 1.17561i
\(171\) 0 0
\(172\) −7.48493 −0.570721
\(173\) −7.60258 13.1681i −0.578013 1.00115i −0.995707 0.0925606i \(-0.970495\pi\)
0.417694 0.908588i \(-0.362839\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.946590 + 0.546514i 0.0713519 + 0.0411950i
\(177\) 0 0
\(178\) 15.5834 8.99707i 1.16802 0.674359i
\(179\) 4.05972i 0.303438i −0.988424 0.151719i \(-0.951519\pi\)
0.988424 0.151719i \(-0.0484809\pi\)
\(180\) 0 0
\(181\) 3.68452i 0.273869i 0.990580 + 0.136934i \(0.0437249\pi\)
−0.990580 + 0.136934i \(0.956275\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.95297 + 3.38264i −0.143975 + 0.249371i
\(185\) −8.16737 + 14.1463i −0.600477 + 1.04006i
\(186\) 0 0
\(187\) −6.35850 + 3.67108i −0.464979 + 0.268456i
\(188\) −6.80349 −0.496195
\(189\) 0 0
\(190\) −6.53424 −0.474044
\(191\) 22.3425 12.8994i 1.61664 0.933370i 0.628864 0.777516i \(-0.283520\pi\)
0.987780 0.155854i \(-0.0498130\pi\)
\(192\) 0 0
\(193\) 4.64331 8.04245i 0.334233 0.578908i −0.649104 0.760699i \(-0.724856\pi\)
0.983337 + 0.181791i \(0.0581894\pi\)
\(194\) 2.38967 4.13903i 0.171568 0.297165i
\(195\) 0 0
\(196\) 0 0
\(197\) 5.86237i 0.417677i −0.977950 0.208838i \(-0.933032\pi\)
0.977950 0.208838i \(-0.0669683\pi\)
\(198\) 0 0
\(199\) 16.0638i 1.13873i 0.822083 + 0.569367i \(0.192812\pi\)
−0.822083 + 0.569367i \(0.807188\pi\)
\(200\) −0.179327 + 0.103535i −0.0126804 + 0.00732101i
\(201\) 0 0
\(202\) −9.05829 5.22981i −0.637339 0.367968i
\(203\) 0 0
\(204\) 0 0
\(205\) −5.60242 9.70367i −0.391290 0.677734i
\(206\) −12.7477 −0.888172
\(207\) 0 0
\(208\) 6.82946i 0.473538i
\(209\) 1.56495 + 2.71057i 0.108250 + 0.187494i
\(210\) 0 0
\(211\) 12.3741 21.4325i 0.851867 1.47548i −0.0276550 0.999618i \(-0.508804\pi\)
0.879522 0.475859i \(-0.157863\pi\)
\(212\) −0.222069 0.128212i −0.0152518 0.00880562i
\(213\) 0 0
\(214\) 4.76813 + 8.25865i 0.325943 + 0.564550i
\(215\) −17.0799 −1.16484
\(216\) 0 0
\(217\) 0 0
\(218\) 4.99266 2.88251i 0.338146 0.195228i
\(219\) 0 0
\(220\) 2.16002 + 1.24709i 0.145629 + 0.0840788i
\(221\) −39.7291 22.9376i −2.67247 1.54295i
\(222\) 0 0
\(223\) −3.20041 + 1.84776i −0.214315 + 0.123735i −0.603315 0.797503i \(-0.706154\pi\)
0.389000 + 0.921238i \(0.372821\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 11.9318 0.793694
\(227\) 2.30549 + 3.99322i 0.153020 + 0.265039i 0.932336 0.361592i \(-0.117767\pi\)
−0.779316 + 0.626631i \(0.784433\pi\)
\(228\) 0 0
\(229\) −13.8220 7.98016i −0.913386 0.527344i −0.0318672 0.999492i \(-0.510145\pi\)
−0.881519 + 0.472148i \(0.843479\pi\)
\(230\) −4.45647 + 7.71884i −0.293851 + 0.508965i
\(231\) 0 0
\(232\) 0.923371 + 1.59933i 0.0606223 + 0.105001i
\(233\) 7.13153i 0.467202i −0.972333 0.233601i \(-0.924949\pi\)
0.972333 0.233601i \(-0.0750510\pi\)
\(234\) 0 0
\(235\) −15.5249 −1.01273
\(236\) 0.971009 + 1.68184i 0.0632073 + 0.109478i
\(237\) 0 0
\(238\) 0 0
\(239\) −13.6219 7.86462i −0.881129 0.508720i −0.0100987 0.999949i \(-0.503215\pi\)
−0.871031 + 0.491229i \(0.836548\pi\)
\(240\) 0 0
\(241\) 1.39292 0.804201i 0.0897257 0.0518031i −0.454466 0.890764i \(-0.650170\pi\)
0.544191 + 0.838961i \(0.316837\pi\)
\(242\) 9.80529i 0.630308i
\(243\) 0 0
\(244\) 1.33154i 0.0852432i
\(245\) 0 0
\(246\) 0 0
\(247\) −9.77810 + 16.9362i −0.622166 + 1.07762i
\(248\) 1.01083 1.75081i 0.0641879 0.111177i
\(249\) 0 0
\(250\) 9.47171 5.46850i 0.599044 0.345858i
\(251\) −18.3728 −1.15968 −0.579841 0.814729i \(-0.696885\pi\)
−0.579841 + 0.814729i \(0.696885\pi\)
\(252\) 0 0
\(253\) 4.26929 0.268408
\(254\) −9.45121 + 5.45666i −0.593021 + 0.342381i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.73678 15.1326i 0.544986 0.943943i −0.453622 0.891194i \(-0.649868\pi\)
0.998608 0.0527487i \(-0.0167982\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 15.5841i 0.966487i
\(261\) 0 0
\(262\) 1.97935i 0.122285i
\(263\) 23.9148 13.8072i 1.47465 0.851389i 0.475057 0.879955i \(-0.342428\pi\)
0.999592 + 0.0285666i \(0.00909427\pi\)
\(264\) 0 0
\(265\) −0.506740 0.292567i −0.0311288 0.0179722i
\(266\) 0 0
\(267\) 0 0
\(268\) 2.54959 + 4.41602i 0.155741 + 0.269751i
\(269\) 6.77214 0.412904 0.206452 0.978457i \(-0.433808\pi\)
0.206452 + 0.978457i \(0.433808\pi\)
\(270\) 0 0
\(271\) 8.35798i 0.507711i 0.967242 + 0.253856i \(0.0816988\pi\)
−0.967242 + 0.253856i \(0.918301\pi\)
\(272\) −3.35863 5.81732i −0.203647 0.352727i
\(273\) 0 0
\(274\) 1.65655 2.86923i 0.100076 0.173336i
\(275\) 0.196010 + 0.113166i 0.0118198 + 0.00682419i
\(276\) 0 0
\(277\) 8.10617 + 14.0403i 0.487053 + 0.843600i 0.999889 0.0148865i \(-0.00473868\pi\)
−0.512837 + 0.858486i \(0.671405\pi\)
\(278\) 3.47216 0.208246
\(279\) 0 0
\(280\) 0 0
\(281\) 25.3352 14.6273i 1.51137 0.872590i 0.511458 0.859308i \(-0.329105\pi\)
0.999912 0.0132818i \(-0.00422786\pi\)
\(282\) 0 0
\(283\) −1.24230 0.717242i −0.0738470 0.0426356i 0.462622 0.886556i \(-0.346909\pi\)
−0.536469 + 0.843920i \(0.680242\pi\)
\(284\) 0.202223 + 0.116753i 0.0119997 + 0.00692803i
\(285\) 0 0
\(286\) 6.46469 3.73239i 0.382265 0.220701i
\(287\) 0 0
\(288\) 0 0
\(289\) 28.1217 1.65422
\(290\) 2.10704 + 3.64950i 0.123730 + 0.214306i
\(291\) 0 0
\(292\) −5.89272 3.40216i −0.344845 0.199096i
\(293\) −10.8260 + 18.7511i −0.632459 + 1.09545i 0.354588 + 0.935023i \(0.384621\pi\)
−0.987047 + 0.160429i \(0.948712\pi\)
\(294\) 0 0
\(295\) 2.21575 + 3.83779i 0.129006 + 0.223444i
\(296\) 7.15840i 0.416073i
\(297\) 0 0
\(298\) −13.3407 −0.772808
\(299\) 13.3377 + 23.1016i 0.771338 + 1.33600i
\(300\) 0 0
\(301\) 0 0
\(302\) 4.62450 + 2.66995i 0.266110 + 0.153639i
\(303\) 0 0
\(304\) −2.47987 + 1.43175i −0.142230 + 0.0821167i
\(305\) 3.03844i 0.173981i
\(306\) 0 0
\(307\) 13.4732i 0.768957i 0.923134 + 0.384479i \(0.125619\pi\)
−0.923134 + 0.384479i \(0.874381\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2.30662 3.99518i 0.131007 0.226911i
\(311\) 14.3669 24.8842i 0.814672 1.41105i −0.0948916 0.995488i \(-0.530250\pi\)
0.909563 0.415565i \(-0.136416\pi\)
\(312\) 0 0
\(313\) 20.4636 11.8147i 1.15667 0.667805i 0.206167 0.978517i \(-0.433901\pi\)
0.950504 + 0.310712i \(0.100567\pi\)
\(314\) 17.6673 0.997023
\(315\) 0 0
\(316\) 7.27248 0.409109
\(317\) −0.760093 + 0.438840i −0.0426911 + 0.0246477i −0.521194 0.853438i \(-0.674513\pi\)
0.478503 + 0.878086i \(0.341180\pi\)
\(318\) 0 0
\(319\) 1.00927 1.74811i 0.0565083 0.0978753i
\(320\) −1.14095 + 1.97618i −0.0637811 + 0.110472i
\(321\) 0 0
\(322\) 0 0
\(323\) 19.2349i 1.07026i
\(324\) 0 0
\(325\) 1.41417i 0.0784441i
\(326\) −13.7683 + 7.94915i −0.762557 + 0.440262i
\(327\) 0 0
\(328\) −4.25245 2.45515i −0.234802 0.135563i
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0915 + 17.4790i 0.554680 + 0.960733i 0.997928 + 0.0643345i \(0.0204925\pi\)
−0.443249 + 0.896399i \(0.646174\pi\)
\(332\) −5.82706 −0.319801
\(333\) 0 0
\(334\) 5.71756i 0.312851i
\(335\) 5.81791 + 10.0769i 0.317866 + 0.550561i
\(336\) 0 0
\(337\) 0.757605 1.31221i 0.0412694 0.0714807i −0.844653 0.535314i \(-0.820193\pi\)
0.885922 + 0.463834i \(0.153526\pi\)
\(338\) 29.1344 + 16.8207i 1.58470 + 0.914927i
\(339\) 0 0
\(340\) −7.66407 13.2746i −0.415642 0.719914i
\(341\) −2.20974 −0.119664
\(342\) 0 0
\(343\) 0 0
\(344\) −6.48214 + 3.74246i −0.349494 + 0.201780i
\(345\) 0 0
\(346\) −13.1681 7.60258i −0.707919 0.408717i
\(347\) 31.2622 + 18.0492i 1.67824 + 0.968934i 0.962781 + 0.270281i \(0.0871167\pi\)
0.715461 + 0.698652i \(0.246217\pi\)
\(348\) 0 0
\(349\) 16.7962 9.69727i 0.899078 0.519083i 0.0221769 0.999754i \(-0.492940\pi\)
0.876901 + 0.480671i \(0.159607\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.09303 0.0582586
\(353\) 2.01909 + 3.49717i 0.107465 + 0.186136i 0.914743 0.404037i \(-0.132393\pi\)
−0.807277 + 0.590172i \(0.799060\pi\)
\(354\) 0 0
\(355\) 0.461452 + 0.266419i 0.0244913 + 0.0141401i
\(356\) 8.99707 15.5834i 0.476844 0.825918i
\(357\) 0 0
\(358\) −2.02986 3.51582i −0.107281 0.185817i
\(359\) 24.5546i 1.29594i 0.761666 + 0.647970i \(0.224382\pi\)
−0.761666 + 0.647970i \(0.775618\pi\)
\(360\) 0 0
\(361\) 10.8003 0.568438
\(362\) 1.84226 + 3.19089i 0.0968272 + 0.167710i
\(363\) 0 0
\(364\) 0 0
\(365\) −13.4466 7.76339i −0.703827 0.406354i
\(366\) 0 0
\(367\) −6.28109 + 3.62639i −0.327870 + 0.189296i −0.654895 0.755720i \(-0.727287\pi\)
0.327025 + 0.945016i \(0.393954\pi\)
\(368\) 3.90593i 0.203611i
\(369\) 0 0
\(370\) 16.3347i 0.849203i
\(371\) 0 0
\(372\) 0 0
\(373\) 14.8921 25.7939i 0.771083 1.33556i −0.165887 0.986145i \(-0.553049\pi\)
0.936970 0.349410i \(-0.113618\pi\)
\(374\) −3.67108 + 6.35850i −0.189827 + 0.328790i
\(375\) 0 0
\(376\) −5.89199 + 3.40174i −0.303856 + 0.175432i
\(377\) 12.6122 0.649564
\(378\) 0 0
\(379\) 6.11280 0.313993 0.156997 0.987599i \(-0.449819\pi\)
0.156997 + 0.987599i \(0.449819\pi\)
\(380\) −5.65882 + 3.26712i −0.290291 + 0.167600i
\(381\) 0 0
\(382\) 12.8994 22.3425i 0.659992 1.14314i
\(383\) −16.2451 + 28.1374i −0.830088 + 1.43775i 0.0678797 + 0.997694i \(0.478377\pi\)
−0.897968 + 0.440061i \(0.854957\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.28662i 0.472677i
\(387\) 0 0
\(388\) 4.77934i 0.242634i
\(389\) 1.80316 1.04105i 0.0914236 0.0527834i −0.453591 0.891210i \(-0.649857\pi\)
0.545015 + 0.838426i \(0.316524\pi\)
\(390\) 0 0
\(391\) −22.7221 13.1186i −1.14910 0.663435i
\(392\) 0 0
\(393\) 0 0
\(394\) −2.93119 5.07696i −0.147671 0.255774i
\(395\) 16.5951 0.834989
\(396\) 0 0
\(397\) 18.9364i 0.950393i 0.879880 + 0.475196i \(0.157623\pi\)
−0.879880 + 0.475196i \(0.842377\pi\)
\(398\) 8.03191 + 13.9117i 0.402603 + 0.697329i
\(399\) 0 0
\(400\) −0.103535 + 0.179327i −0.00517674 + 0.00896637i
\(401\) 3.35718 + 1.93827i 0.167650 + 0.0967926i 0.581477 0.813563i \(-0.302475\pi\)
−0.413827 + 0.910355i \(0.635808\pi\)
\(402\) 0 0
\(403\) −6.90343 11.9571i −0.343884 0.595625i
\(404\) −10.4596 −0.520385
\(405\) 0 0
\(406\) 0 0
\(407\) 6.77606 3.91216i 0.335877 0.193919i
\(408\) 0 0
\(409\) −14.0286 8.09940i −0.693669 0.400490i 0.111316 0.993785i \(-0.464493\pi\)
−0.804985 + 0.593295i \(0.797827\pi\)
\(410\) −9.70367 5.60242i −0.479230 0.276684i
\(411\) 0 0
\(412\) −11.0398 + 6.37383i −0.543892 + 0.314016i
\(413\) 0 0
\(414\) 0 0
\(415\) −13.2968 −0.652713
\(416\) 3.41473 + 5.91448i 0.167421 + 0.289981i
\(417\) 0 0
\(418\) 2.71057 + 1.56495i 0.132578 + 0.0765441i
\(419\) −1.63790 + 2.83692i −0.0800165 + 0.138593i −0.903257 0.429100i \(-0.858831\pi\)
0.823240 + 0.567693i \(0.192164\pi\)
\(420\) 0 0
\(421\) −0.844823 1.46328i −0.0411741 0.0713157i 0.844704 0.535234i \(-0.179777\pi\)
−0.885878 + 0.463918i \(0.846443\pi\)
\(422\) 24.7482i 1.20472i
\(423\) 0 0
\(424\) −0.256424 −0.0124530
\(425\) −0.695470 1.20459i −0.0337353 0.0584312i
\(426\) 0 0
\(427\) 0 0
\(428\) 8.25865 + 4.76813i 0.399197 + 0.230476i
\(429\) 0 0
\(430\) −14.7916 + 8.53993i −0.713314 + 0.411832i
\(431\) 0.0181384i 0.000873697i −1.00000 0.000436848i \(-0.999861\pi\)
1.00000 0.000436848i \(-0.000139053\pi\)
\(432\) 0 0
\(433\) 5.36964i 0.258048i −0.991641 0.129024i \(-0.958815\pi\)
0.991641 0.129024i \(-0.0411845\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.88251 4.99266i 0.138047 0.239105i
\(437\) −5.59233 + 9.68621i −0.267518 + 0.463354i
\(438\) 0 0
\(439\) 18.9141 10.9201i 0.902720 0.521186i 0.0246384 0.999696i \(-0.492157\pi\)
0.878082 + 0.478511i \(0.158823\pi\)
\(440\) 2.49418 0.118905
\(441\) 0 0
\(442\) −45.8753 −2.18206
\(443\) 1.81806 1.04966i 0.0863785 0.0498707i −0.456189 0.889883i \(-0.650786\pi\)
0.542567 + 0.840012i \(0.317452\pi\)
\(444\) 0 0
\(445\) 20.5304 35.5597i 0.973235 1.68569i
\(446\) −1.84776 + 3.20041i −0.0874938 + 0.151544i
\(447\) 0 0
\(448\) 0 0
\(449\) 27.1356i 1.28061i 0.768122 + 0.640303i \(0.221191\pi\)
−0.768122 + 0.640303i \(0.778809\pi\)
\(450\) 0 0
\(451\) 5.36710i 0.252727i
\(452\) 10.3333 5.96592i 0.486036 0.280613i
\(453\) 0 0
\(454\) 3.99322 + 2.30549i 0.187411 + 0.108202i
\(455\) 0 0
\(456\) 0 0
\(457\) −4.21598 7.30229i −0.197215 0.341587i 0.750409 0.660974i \(-0.229856\pi\)
−0.947624 + 0.319387i \(0.896523\pi\)
\(458\) −15.9603 −0.745777
\(459\) 0 0
\(460\) 8.91294i 0.415568i
\(461\) 4.67153 + 8.09133i 0.217575 + 0.376851i 0.954066 0.299596i \(-0.0968520\pi\)
−0.736491 + 0.676447i \(0.763519\pi\)
\(462\) 0 0
\(463\) −12.7281 + 22.0458i −0.591526 + 1.02455i 0.402501 + 0.915420i \(0.368141\pi\)
−0.994027 + 0.109134i \(0.965192\pi\)
\(464\) 1.59933 + 0.923371i 0.0742469 + 0.0428664i
\(465\) 0 0
\(466\) −3.56577 6.17609i −0.165181 0.286102i
\(467\) 20.6398 0.955094 0.477547 0.878606i \(-0.341526\pi\)
0.477547 + 0.878606i \(0.341526\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −13.4449 + 7.76244i −0.620169 + 0.358055i
\(471\) 0 0
\(472\) 1.68184 + 0.971009i 0.0774128 + 0.0446943i
\(473\) 7.08516 + 4.09062i 0.325776 + 0.188087i
\(474\) 0 0
\(475\) −0.513506 + 0.296473i −0.0235613 + 0.0136031i
\(476\) 0 0
\(477\) 0 0
\(478\) −15.7292 −0.719439
\(479\) 3.07442 + 5.32505i 0.140474 + 0.243308i 0.927675 0.373388i \(-0.121804\pi\)
−0.787201 + 0.616696i \(0.788471\pi\)
\(480\) 0 0
\(481\) 42.3382 + 24.4440i 1.93046 + 1.11455i
\(482\) 0.804201 1.39292i 0.0366303 0.0634456i
\(483\) 0 0
\(484\) 4.90265 + 8.49163i 0.222848 + 0.385983i
\(485\) 10.9060i 0.495215i
\(486\) 0 0
\(487\) 19.7273 0.893929 0.446965 0.894552i \(-0.352505\pi\)
0.446965 + 0.894552i \(0.352505\pi\)
\(488\) 0.665771 + 1.15315i 0.0301380 + 0.0522006i
\(489\) 0 0
\(490\) 0 0
\(491\) −3.42935 1.97994i −0.154764 0.0893533i 0.420618 0.907238i \(-0.361813\pi\)
−0.575382 + 0.817885i \(0.695147\pi\)
\(492\) 0 0
\(493\) −10.7431 + 6.20253i −0.483845 + 0.279348i
\(494\) 19.5562i 0.879875i
\(495\) 0 0
\(496\) 2.02166i 0.0907754i
\(497\) 0 0
\(498\) 0 0
\(499\) 18.4092 31.8856i 0.824108 1.42740i −0.0784916 0.996915i \(-0.525010\pi\)
0.902599 0.430482i \(-0.141656\pi\)
\(500\) 5.46850 9.47171i 0.244559 0.423588i
\(501\) 0 0
\(502\) −15.9113 + 9.18641i −0.710158 + 0.410010i
\(503\) 12.3802 0.552004 0.276002 0.961157i \(-0.410990\pi\)
0.276002 + 0.961157i \(0.410990\pi\)
\(504\) 0 0
\(505\) −23.8678 −1.06210
\(506\) 3.69731 2.13465i 0.164366 0.0948966i
\(507\) 0 0
\(508\) −5.45666 + 9.45121i −0.242100 + 0.419329i
\(509\) −7.54528 + 13.0688i −0.334438 + 0.579264i −0.983377 0.181577i \(-0.941880\pi\)
0.648938 + 0.760841i \(0.275213\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 17.4736i 0.770726i
\(515\) −25.1917 + 14.5445i −1.11008 + 0.640905i
\(516\) 0 0
\(517\) 6.44011 + 3.71820i 0.283236 + 0.163526i
\(518\) 0 0
\(519\) 0 0
\(520\) 7.79207 + 13.4963i 0.341705 + 0.591850i
\(521\) 24.9816 1.09446 0.547231 0.836981i \(-0.315682\pi\)
0.547231 + 0.836981i \(0.315682\pi\)
\(522\) 0 0
\(523\) 25.0359i 1.09474i 0.836889 + 0.547372i \(0.184372\pi\)
−0.836889 + 0.547372i \(0.815628\pi\)
\(524\) −0.989677 1.71417i −0.0432342 0.0748839i
\(525\) 0 0
\(526\) 13.8072 23.9148i 0.602023 1.04273i
\(527\) 11.7607 + 6.79003i 0.512303 + 0.295778i
\(528\) 0 0
\(529\) −3.87185 6.70625i −0.168341 0.291576i
\(530\) −0.585133 −0.0254166
\(531\) 0 0
\(532\) 0 0
\(533\) −29.0419 + 16.7674i −1.25795 + 0.726275i
\(534\) 0 0
\(535\) 18.8454 + 10.8804i 0.814759 + 0.470401i
\(536\) 4.41602 + 2.54959i 0.190743 + 0.110126i
\(537\) 0 0
\(538\) 5.86484 3.38607i 0.252851 0.145984i
\(539\) 0 0
\(540\) 0 0
\(541\) −14.4608 −0.621720 −0.310860 0.950456i \(-0.600617\pi\)
−0.310860 + 0.950456i \(0.600617\pi\)
\(542\) 4.17899 + 7.23822i 0.179503 + 0.310908i
\(543\) 0 0
\(544\) −5.81732 3.35863i −0.249416 0.144000i
\(545\) 6.57761 11.3928i 0.281754 0.488012i
\(546\) 0 0
\(547\) 16.9160 + 29.2994i 0.723277 + 1.25275i 0.959679 + 0.281098i \(0.0906985\pi\)
−0.236402 + 0.971655i \(0.575968\pi\)
\(548\) 3.31310i 0.141528i
\(549\) 0 0
\(550\) 0.226333 0.00965086
\(551\) 2.64408 + 4.57968i 0.112642 + 0.195101i
\(552\) 0 0
\(553\) 0 0
\(554\) 14.0403 + 8.10617i 0.596515 + 0.344398i
\(555\) 0 0
\(556\) 3.00698 1.73608i 0.127524 0.0736261i
\(557\) 5.88269i 0.249257i 0.992203 + 0.124629i \(0.0397740\pi\)
−0.992203 + 0.124629i \(0.960226\pi\)
\(558\) 0 0
\(559\) 51.1180i 2.16206i
\(560\) 0 0
\(561\) 0 0
\(562\) 14.6273 25.3352i 0.617014 1.06870i
\(563\) −7.78184 + 13.4785i −0.327966 + 0.568053i −0.982108 0.188318i \(-0.939696\pi\)
0.654142 + 0.756371i \(0.273030\pi\)
\(564\) 0 0
\(565\) 23.5795 13.6136i 0.991997 0.572730i
\(566\) −1.43448 −0.0602958
\(567\) 0 0
\(568\) 0.233507 0.00979772
\(569\) 22.6993 13.1055i 0.951606 0.549410i 0.0580267 0.998315i \(-0.481519\pi\)
0.893580 + 0.448905i \(0.148186\pi\)
\(570\) 0 0
\(571\) −12.8090 + 22.1859i −0.536041 + 0.928451i 0.463071 + 0.886321i \(0.346748\pi\)
−0.999112 + 0.0421295i \(0.986586\pi\)
\(572\) 3.73239 6.46469i 0.156059 0.270302i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.808799i 0.0337292i
\(576\) 0 0
\(577\) 32.3939i 1.34858i −0.738468 0.674288i \(-0.764451\pi\)
0.738468 0.674288i \(-0.235549\pi\)
\(578\) 24.3541 14.0608i 1.01300 0.584853i
\(579\) 0 0
\(580\) 3.64950 + 2.10704i 0.151537 + 0.0874901i
\(581\) 0 0
\(582\) 0 0
\(583\) 0.140139 + 0.242728i 0.00580397 + 0.0100528i
\(584\) −6.80432 −0.281565
\(585\) 0 0
\(586\) 21.6519i 0.894432i
\(587\) −4.76851 8.25931i −0.196818 0.340898i 0.750677 0.660669i \(-0.229727\pi\)
−0.947495 + 0.319771i \(0.896394\pi\)
\(588\) 0 0
\(589\) 2.89453 5.01347i 0.119267 0.206576i
\(590\) 3.83779 + 2.21575i 0.157999 + 0.0912208i
\(591\) 0 0
\(592\) 3.57920 + 6.19935i 0.147104 + 0.254792i
\(593\) 3.78817 0.155562 0.0777808 0.996970i \(-0.475217\pi\)
0.0777808 + 0.996970i \(0.475217\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −11.5534 + 6.67036i −0.473246 + 0.273229i
\(597\) 0 0
\(598\) 23.1016 + 13.3377i 0.944693 + 0.545419i
\(599\) 31.2971 + 18.0694i 1.27876 + 0.738295i 0.976621 0.214968i \(-0.0689647\pi\)
0.302143 + 0.953263i \(0.402298\pi\)
\(600\) 0 0
\(601\) 13.8275 7.98332i 0.564036 0.325646i −0.190728 0.981643i \(-0.561085\pi\)
0.754764 + 0.655997i \(0.227751\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.33991 0.217278
\(605\) 11.1873 + 19.3771i 0.454830 + 0.787789i
\(606\) 0 0
\(607\) −19.6190 11.3270i −0.796309 0.459749i 0.0458701 0.998947i \(-0.485394\pi\)
−0.842179 + 0.539198i \(0.818727\pi\)
\(608\) −1.43175 + 2.47987i −0.0580653 + 0.100572i
\(609\) 0 0
\(610\) 1.51922 + 2.63137i 0.0615115 + 0.106541i
\(611\) 46.4641i 1.87974i
\(612\) 0 0
\(613\) 3.69517 0.149246 0.0746232 0.997212i \(-0.476225\pi\)
0.0746232 + 0.997212i \(0.476225\pi\)
\(614\) 6.73661 + 11.6682i 0.271868 + 0.470888i
\(615\) 0 0
\(616\) 0 0
\(617\) −22.5187 13.0011i −0.906567 0.523407i −0.0272418 0.999629i \(-0.508672\pi\)
−0.879325 + 0.476222i \(0.842006\pi\)
\(618\) 0 0
\(619\) 20.5526 11.8660i 0.826079 0.476937i −0.0264296 0.999651i \(-0.508414\pi\)
0.852508 + 0.522714i \(0.175080\pi\)
\(620\) 4.61324i 0.185272i
\(621\) 0 0
\(622\) 28.7338i 1.15212i
\(623\) 0 0
\(624\) 0 0
\(625\) 12.9962 22.5101i 0.519849 0.900406i
\(626\) 11.8147 20.4636i 0.472209 0.817890i
\(627\) 0 0
\(628\) 15.3003 8.83364i 0.610549 0.352501i
\(629\) −48.0848 −1.91727
\(630\) 0 0
\(631\) −0.664631 −0.0264586 −0.0132293 0.999912i \(-0.504211\pi\)
−0.0132293 + 0.999912i \(0.504211\pi\)
\(632\) 6.29816 3.63624i 0.250527 0.144642i
\(633\) 0 0
\(634\) −0.438840 + 0.760093i −0.0174286 + 0.0301872i
\(635\) −12.4515 + 21.5667i −0.494125 + 0.855849i
\(636\) 0 0
\(637\) 0 0
\(638\) 2.01854i 0.0799148i
\(639\) 0 0
\(640\) 2.28190i 0.0902000i
\(641\) 7.27466 4.20003i 0.287332 0.165891i −0.349406 0.936971i \(-0.613617\pi\)
0.636738 + 0.771080i \(0.280283\pi\)
\(642\) 0 0
\(643\) 0.237974 + 0.137394i 0.00938478 + 0.00541831i 0.504685 0.863304i \(-0.331609\pi\)
−0.495300 + 0.868722i \(0.664942\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −9.61747 16.6580i −0.378394 0.655398i
\(647\) −34.1015 −1.34067 −0.670335 0.742059i \(-0.733850\pi\)
−0.670335 + 0.742059i \(0.733850\pi\)
\(648\) 0 0
\(649\) 2.12268i 0.0833225i
\(650\) 0.707086 + 1.22471i 0.0277342 + 0.0480370i
\(651\) 0 0
\(652\) −7.94915 + 13.7683i −0.311313 + 0.539209i
\(653\) −1.48356 0.856531i −0.0580560 0.0335187i 0.470691 0.882298i \(-0.344005\pi\)
−0.528747 + 0.848779i \(0.677338\pi\)
\(654\) 0 0
\(655\) −2.25834 3.91157i −0.0882408 0.152838i
\(656\) −4.91031 −0.191715
\(657\) 0 0
\(658\) 0 0
\(659\) −30.0556 + 17.3526i −1.17080 + 0.675961i −0.953868 0.300226i \(-0.902938\pi\)
−0.216930 + 0.976187i \(0.569604\pi\)
\(660\) 0 0
\(661\) 33.2075 + 19.1724i 1.29162 + 0.745718i 0.978942 0.204140i \(-0.0654397\pi\)
0.312681 + 0.949858i \(0.398773\pi\)
\(662\) 17.4790 + 10.0915i 0.679341 + 0.392218i
\(663\) 0 0
\(664\) −5.04638 + 2.91353i −0.195838 + 0.113067i
\(665\) 0 0
\(666\) 0 0
\(667\) 7.21325 0.279298
\(668\) −2.85878 4.95155i −0.110610 0.191581i
\(669\) 0 0
\(670\) 10.0769 + 5.81791i 0.389305 + 0.224765i
\(671\) 0.727706 1.26042i 0.0280928 0.0486581i
\(672\) 0 0
\(673\) −8.33538 14.4373i −0.321305 0.556517i 0.659452 0.751746i \(-0.270788\pi\)
−0.980758 + 0.195229i \(0.937455\pi\)
\(674\) 1.51521i 0.0583637i
\(675\) 0 0
\(676\) 33.6415 1.29390
\(677\) −10.4682 18.1315i −0.402327 0.696850i 0.591680 0.806173i \(-0.298465\pi\)
−0.994006 + 0.109323i \(0.965132\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −13.2746 7.66407i −0.509056 0.293903i
\(681\) 0 0
\(682\) −1.91369 + 1.10487i −0.0732789 + 0.0423076i
\(683\) 7.64415i 0.292495i −0.989248 0.146248i \(-0.953280\pi\)
0.989248 0.146248i \(-0.0467197\pi\)
\(684\) 0 0
\(685\) 7.56016i 0.288859i
\(686\) 0 0
\(687\) 0 0
\(688\) −3.74246 + 6.48214i −0.142680 + 0.247129i
\(689\) −0.875617 + 1.51661i −0.0333583 + 0.0577783i
\(690\) 0 0
\(691\) −9.10461 + 5.25655i −0.346356 + 0.199969i −0.663079 0.748549i \(-0.730751\pi\)
0.316723 + 0.948518i \(0.397417\pi\)
\(692\) −15.2052 −0.578013
\(693\) 0 0
\(694\) 36.0985 1.37028
\(695\) 6.86162 3.96156i 0.260276 0.150270i
\(696\) 0 0
\(697\) 16.4919 28.5648i 0.624676 1.08197i
\(698\) 9.69727 16.7962i 0.367047 0.635744i
\(699\) 0 0
\(700\) 0 0
\(701\) 15.7336i 0.594250i 0.954839 + 0.297125i \(0.0960277\pi\)
−0.954839 + 0.297125i \(0.903972\pi\)
\(702\) 0 0
\(703\) 20.4981i 0.773102i
\(704\) 0.946590 0.546514i 0.0356759 0.0205975i
\(705\) 0 0
\(706\) 3.49717 + 2.01909i 0.131618 + 0.0759895i
\(707\) 0 0
\(708\) 0 0
\(709\) 1.44973 + 2.51100i 0.0544456 + 0.0943025i 0.891964 0.452107i \(-0.149328\pi\)
−0.837518 + 0.546410i \(0.815994\pi\)
\(710\) 0.532839 0.0199971
\(711\) 0 0
\(712\) 17.9941i 0.674359i
\(713\) −3.94824 6.83855i −0.147863 0.256106i
\(714\) 0 0
\(715\) 8.51695 14.7518i 0.318516 0.551686i
\(716\) −3.51582 2.02986i −0.131392 0.0758595i
\(717\) 0 0
\(718\) 12.2773 + 21.2649i 0.458184 + 0.793598i
\(719\) −41.1289 −1.53385 −0.766924 0.641738i \(-0.778214\pi\)
−0.766924 + 0.641738i \(0.778214\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 9.35335 5.40016i 0.348096 0.200973i
\(723\) 0 0
\(724\) 3.19089 + 1.84226i 0.118589 + 0.0684671i
\(725\) 0.331172 + 0.191202i 0.0122994 + 0.00710106i
\(726\) 0 0
\(727\) 33.6212 19.4112i 1.24694 0.719921i 0.276442 0.961031i \(-0.410845\pi\)
0.970498 + 0.241109i \(0.0775112\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −15.5268 −0.574672
\(731\) −25.1391 43.5423i −0.929804 1.61047i
\(732\) 0 0
\(733\) 22.5362 + 13.0113i 0.832394 + 0.480583i 0.854672 0.519169i \(-0.173758\pi\)
−0.0222778 + 0.999752i \(0.507092\pi\)
\(734\) −3.62639 + 6.28109i −0.133852 + 0.231839i
\(735\) 0 0
\(736\) 1.95297 + 3.38264i 0.0719873 + 0.124686i
\(737\) 5.57355i 0.205304i
\(738\) 0 0
\(739\) 7.40008 0.272216 0.136108 0.990694i \(-0.456541\pi\)
0.136108 + 0.990694i \(0.456541\pi\)
\(740\) 8.16737 + 14.1463i 0.300239 + 0.520028i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.3241 + 14.0435i 0.892366 + 0.515208i 0.874716 0.484636i \(-0.161048\pi\)
0.0176504 + 0.999844i \(0.494381\pi\)
\(744\) 0 0
\(745\) −26.3637 + 15.2211i −0.965892 + 0.557658i
\(746\) 29.7842i 1.09048i
\(747\) 0 0
\(748\) 7.34216i 0.268456i
\(749\) 0 0
\(750\) 0 0
\(751\) −21.1897 + 36.7016i −0.773221 + 1.33926i 0.162567 + 0.986697i \(0.448023\pi\)
−0.935789 + 0.352561i \(0.885311\pi\)
\(752\) −3.40174 + 5.89199i −0.124049 + 0.214859i
\(753\) 0 0
\(754\) 10.9225 6.30612i 0.397775 0.229655i
\(755\) 12.1851 0.443463
\(756\) 0 0
\(757\) −41.6462 −1.51366 −0.756828 0.653614i \(-0.773252\pi\)
−0.756828 + 0.653614i \(0.773252\pi\)
\(758\) 5.29384 3.05640i 0.192281 0.111013i
\(759\) 0 0
\(760\) −3.26712 + 5.65882i −0.118511 + 0.205267i
\(761\) −17.4823 + 30.2802i −0.633732 + 1.09766i 0.353051 + 0.935604i \(0.385144\pi\)
−0.986782 + 0.162051i \(0.948189\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 25.7989i 0.933370i
\(765\) 0 0
\(766\) 32.4903i 1.17392i
\(767\) 11.4860 6.63146i 0.414737 0.239448i
\(768\) 0 0
\(769\) −18.9307 10.9296i −0.682658 0.394133i 0.118198 0.992990i \(-0.462288\pi\)
−0.800856 + 0.598857i \(0.795622\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.64331 8.04245i −0.167116 0.289454i
\(773\) −21.2736 −0.765158 −0.382579 0.923923i \(-0.624964\pi\)
−0.382579 + 0.923923i \(0.624964\pi\)
\(774\) 0 0
\(775\) 0.418625i 0.0150374i
\(776\) −2.38967 4.13903i −0.0857842 0.148583i
\(777\) 0 0
\(778\) 1.04105 1.80316i 0.0373235 0.0646463i
\(779\) −12.1769 7.03035i −0.436284 0.251889i
\(780\) 0 0
\(781\) −0.127615 0.221035i −0.00456641 0.00790925i
\(782\) −26.2372 −0.938239
\(783\) 0 0
\(784\) 0 0
\(785\) 34.9138 20.1575i 1.24613 0.719452i
\(786\) 0 0
\(787\) −40.7238 23.5119i −1.45165 0.838108i −0.453070 0.891475i \(-0.649671\pi\)
−0.998575 + 0.0533671i \(0.983005\pi\)
\(788\) −5.07696 2.93119i −0.180859 0.104419i
\(789\) 0 0
\(790\) 14.3718 8.29754i 0.511325 0.295213i
\(791\) 0