Properties

Label 2646.2.m.a.1763.8
Level $2646$
Weight $2$
Character 2646.1763
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 1763.8
Root \(1.73109 + 0.0577511i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1763
Dual form 2646.2.m.a.881.8

$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

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

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 0.999929 + 0.0118746i \(0.00377989\pi\)
−0.489681 + 0.871902i \(0.662887\pi\)
\(6\) 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 0.350461 0.936577i \(-0.386025\pi\)
−0.635869 + 0.771797i \(0.719358\pi\)
\(12\) 0 0
\(13\) −5.91448 + 3.41473i −1.64038 + 0.947075i −0.659685 + 0.751542i \(0.729310\pi\)
−0.980697 + 0.195533i \(0.937356\pi\)
\(14\) 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 \(0.106532\pi\)
−0.944515 + 0.328467i \(0.893468\pi\)
\(20\) −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 −0.809329 0.587356i \(-0.800169\pi\)
0.104001 + 0.994577i \(0.466836\pi\)
\(24\) 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 0.344101 0.938933i \(-0.388184\pi\)
−0.641089 + 0.767467i \(0.721517\pi\)
\(30\) 0 0
\(31\) 1.75081 1.01083i 0.314455 0.181551i −0.334463 0.942409i \(-0.608555\pi\)
0.648918 + 0.760858i \(0.275222\pi\)
\(32\) −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 0.991550 0.129724i \(-0.0414092\pi\)
−0.608120 + 0.793845i \(0.708076\pi\)
\(42\) 0 0
\(43\) −3.74246 + 6.48214i −0.570721 + 0.988517i 0.425772 + 0.904831i \(0.360003\pi\)
−0.996492 + 0.0836863i \(0.973331\pi\)
\(44\) 1.09303i 0.164780i
\(45\) 0 0
\(46\) −3.90593 −0.575898
\(47\) −3.40174 + 5.89199i −0.496195 + 0.859435i −0.999990 0.00438774i \(-0.998603\pi\)
0.503795 + 0.863823i \(0.331937\pi\)
\(48\) 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 \(0.00560612\pi\)
−0.999845 + 0.0176112i \(0.994394\pi\)
\(54\) 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 0.795870 0.605467i \(-0.207014\pi\)
−0.922285 + 0.386510i \(0.873680\pi\)
\(60\) 0 0
\(61\) −1.15315 0.665771i −0.147646 0.0852432i 0.424357 0.905495i \(-0.360500\pi\)
−0.572003 + 0.820252i \(0.693833\pi\)
\(62\) 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 0.667201 0.744877i \(-0.267492\pi\)
−0.978683 + 0.205375i \(0.934159\pi\)
\(68\) 3.35863 + 5.81732i 0.407294 + 0.705454i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.233507i 0.0277121i −0.999904 0.0138561i \(-0.995589\pi\)
0.999904 0.0138561i \(-0.00441066\pi\)
\(72\) 0 0
\(73\) 6.80432i 0.796386i 0.917302 + 0.398193i \(0.130362\pi\)
−0.917302 + 0.398193i \(0.869638\pi\)
\(74\) −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 −0.585681 0.810542i \(-0.699173\pi\)
0.994790 + 0.101944i \(0.0325062\pi\)
\(80\) −2.28190 −0.255124
\(81\) 0 0
\(82\) 4.91031i 0.542253i
\(83\) −2.91353 + 5.04638i −0.319801 + 0.553912i −0.980446 0.196786i \(-0.936950\pi\)
0.660645 + 0.750698i \(0.270283\pi\)
\(84\) 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 0.695186 0.718830i \(-0.255322\pi\)
−0.274931 + 0.961464i \(0.588655\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.207069 −0.0207069
\(101\) −5.22981 + 9.05829i −0.520385 + 0.901334i 0.479334 + 0.877633i \(0.340878\pi\)
−0.999719 + 0.0237012i \(0.992455\pi\)
\(102\) 0 0
\(103\) −11.0398 + 6.37383i −1.08778 + 0.628033i −0.932986 0.359914i \(-0.882806\pi\)
−0.154799 + 0.987946i \(0.549473\pi\)
\(104\) −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 \(-0.847508\pi\)
0.887425 0.460953i \(-0.152492\pi\)
\(108\) 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 0.0722053 0.997390i \(-0.476996\pi\)
0.899868 + 0.436163i \(0.143663\pi\)
\(114\) 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 0.906016 0.423243i \(-0.139108\pi\)
−0.819548 + 0.573011i \(0.805775\pi\)
\(132\) 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 0.617534 0.786544i \(-0.288132\pi\)
−0.372400 + 0.928072i \(0.621465\pi\)
\(138\) 0 0
\(139\) 3.00698 1.73608i 0.255048 0.147252i −0.367025 0.930211i \(-0.619624\pi\)
0.622074 + 0.782959i \(0.286290\pi\)
\(140\) 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 −0.891989 0.452056i \(-0.850691\pi\)
−0.0545027 + 0.998514i \(0.517357\pi\)
\(150\) 0 0
\(151\) 2.66995 4.62450i 0.217278 0.376336i −0.736697 0.676223i \(-0.763616\pi\)
0.953975 + 0.299887i \(0.0969489\pi\)
\(152\) −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 0.255946 0.966691i \(-0.417613\pi\)
0.965152 + 0.261689i \(0.0842796\pi\)
\(158\) 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 0.955178 0.296031i \(-0.0956631\pi\)
−0.733959 + 0.679193i \(0.762330\pi\)
\(168\) 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 0.417694 + 0.908588i \(0.362839\pi\)
−0.995707 + 0.0925606i \(0.970495\pi\)
\(174\) 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 \(0.0484809\pi\)
−0.988424 + 0.151719i \(0.951519\pi\)
\(180\) 0 0
\(181\) 3.68452i 0.273869i −0.990580 0.136934i \(-0.956275\pi\)
0.990580 0.136934i \(-0.0437249\pi\)
\(182\) 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 0.987780 + 0.155854i \(0.0498130\pi\)
0.628864 + 0.777516i \(0.283520\pi\)
\(192\) 0 0
\(193\) 4.64331 + 8.04245i 0.334233 + 0.578908i 0.983337 0.181791i \(-0.0581894\pi\)
−0.649104 + 0.760699i \(0.724856\pi\)
\(194\) 2.38967 + 4.13903i 0.171568 + 0.297165i
\(195\) 0 0
\(196\) 0 0
\(197\) 5.86237i 0.417677i 0.977950 + 0.208838i \(0.0669683\pi\)
−0.977950 + 0.208838i \(0.933032\pi\)
\(198\) 0 0
\(199\) 16.0638i 1.13873i −0.822083 0.569367i \(-0.807188\pi\)
0.822083 0.569367i \(-0.192812\pi\)
\(200\) −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 0.879522 + 0.475859i \(0.157863\pi\)
−0.0276550 + 0.999618i \(0.508804\pi\)
\(212\) −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 0.389000 0.921238i \(-0.372821\pi\)
−0.603315 + 0.797503i \(0.706154\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 11.9318 0.793694
\(227\) 2.30549 3.99322i 0.153020 0.265039i −0.779316 0.626631i \(-0.784433\pi\)
0.932336 + 0.361592i \(0.117767\pi\)
\(228\) 0 0
\(229\) −13.8220 + 7.98016i −0.913386 + 0.527344i −0.881519 0.472148i \(-0.843479\pi\)
−0.0318672 + 0.999492i \(0.510145\pi\)
\(230\) −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 \(0.0750510\pi\)
−0.972333 + 0.233601i \(0.924949\pi\)
\(234\) 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 −0.871031 0.491229i \(-0.836548\pi\)
−0.0100987 + 0.999949i \(0.503215\pi\)
\(240\) 0 0
\(241\) 1.39292 + 0.804201i 0.0897257 + 0.0518031i 0.544191 0.838961i \(-0.316837\pi\)
−0.454466 + 0.890764i \(0.650170\pi\)
\(242\) 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 0.998608 + 0.0527487i \(0.0167982\pi\)
−0.453622 + 0.891194i \(0.649868\pi\)
\(258\) 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 0.999592 0.0285666i \(-0.00909427\pi\)
0.475057 + 0.879955i \(0.342428\pi\)
\(264\) 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 \(-0.918301\pi\)
0.967242 0.253856i \(-0.0816988\pi\)
\(272\) −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 −0.512837 0.858486i \(-0.671405\pi\)
0.999889 + 0.0148865i \(0.00473868\pi\)
\(278\) 3.47216 0.208246
\(279\) 0 0
\(280\) 0 0
\(281\) 25.3352 + 14.6273i 1.51137 + 0.872590i 0.999912 + 0.0132818i \(0.00422786\pi\)
0.511458 + 0.859308i \(0.329105\pi\)
\(282\) 0 0
\(283\) −1.24230 + 0.717242i −0.0738470 + 0.0426356i −0.536469 0.843920i \(-0.680242\pi\)
0.462622 + 0.886556i \(0.346909\pi\)
\(284\) 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 −0.987047 0.160429i \(-0.948712\pi\)
0.354588 0.935023i \(-0.384621\pi\)
\(294\) 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 \(-0.874381\pi\)
0.923134 0.384479i \(-0.125619\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2.30662 + 3.99518i 0.131007 + 0.226911i
\(311\) 14.3669 + 24.8842i 0.814672 + 1.41105i 0.909563 + 0.415565i \(0.136416\pi\)
−0.0948916 + 0.995488i \(0.530250\pi\)
\(312\) 0 0
\(313\) 20.4636 + 11.8147i 1.15667 + 0.667805i 0.950504 0.310712i \(-0.100567\pi\)
0.206167 + 0.978517i \(0.433901\pi\)
\(314\) 17.6673 0.997023
\(315\) 0 0
\(316\) 7.27248 0.409109
\(317\) −0.760093 0.438840i −0.0426911 0.0246477i 0.478503 0.878086i \(-0.341180\pi\)
−0.521194 + 0.853438i \(0.674513\pi\)
\(318\) 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 −0.443249 0.896399i \(-0.646174\pi\)
0.997928 0.0643345i \(-0.0204925\pi\)
\(332\) −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 0.885922 0.463834i \(-0.153526\pi\)
−0.844653 + 0.535314i \(0.820193\pi\)
\(338\) 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 0.715461 0.698652i \(-0.246217\pi\)
0.962781 0.270281i \(-0.0871167\pi\)
\(348\) 0 0
\(349\) 16.7962 + 9.69727i 0.899078 + 0.519083i 0.876901 0.480671i \(-0.159607\pi\)
0.0221769 + 0.999754i \(0.492940\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.09303 0.0582586
\(353\) 2.01909 3.49717i 0.107465 0.186136i −0.807277 0.590172i \(-0.799060\pi\)
0.914743 + 0.404037i \(0.132393\pi\)
\(354\) 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 \(-0.775618\pi\)
0.761666 0.647970i \(-0.224382\pi\)
\(360\) 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 0.327025 0.945016i \(-0.393954\pi\)
−0.654895 + 0.755720i \(0.727287\pi\)
\(368\) 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 0.936970 + 0.349410i \(0.113618\pi\)
−0.165887 + 0.986145i \(0.553049\pi\)
\(374\) −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 −0.897968 0.440061i \(-0.854957\pi\)
0.0678797 0.997694i \(-0.478377\pi\)
\(384\) 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 0.545015 0.838426i \(-0.316524\pi\)
−0.453591 + 0.891210i \(0.649857\pi\)
\(390\) 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 \(-0.842377\pi\)
0.879880 0.475196i \(-0.157623\pi\)
\(398\) 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 −0.413827 0.910355i \(-0.635808\pi\)
0.581477 + 0.813563i \(0.302475\pi\)
\(402\) 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 −0.804985 0.593295i \(-0.797827\pi\)
0.111316 + 0.993785i \(0.464493\pi\)
\(410\) −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 0.823240 0.567693i \(-0.192164\pi\)
−0.903257 + 0.429100i \(0.858831\pi\)
\(420\) 0 0
\(421\) −0.844823 + 1.46328i −0.0411741 + 0.0713157i −0.885878 0.463918i \(-0.846443\pi\)
0.844704 + 0.535234i \(0.179777\pi\)
\(422\) 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 \(0.000139053\pi\)
−1.00000 0.000436848i \(0.999861\pi\)
\(432\) 0 0
\(433\) 5.36964i 0.258048i 0.991641 + 0.129024i \(0.0411845\pi\)
−0.991641 + 0.129024i \(0.958815\pi\)
\(434\) 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 0.878082 0.478511i \(-0.158823\pi\)
0.0246384 + 0.999696i \(0.492157\pi\)
\(440\) 2.49418 0.118905
\(441\) 0 0
\(442\) −45.8753 −2.18206
\(443\) 1.81806 + 1.04966i 0.0863785 + 0.0498707i 0.542567 0.840012i \(-0.317452\pi\)
−0.456189 + 0.889883i \(0.650786\pi\)
\(444\) 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 \(-0.778809\pi\)
0.768122 0.640303i \(-0.221191\pi\)
\(450\) 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 −0.947624 0.319387i \(-0.896523\pi\)
0.750409 + 0.660974i \(0.229856\pi\)
\(458\) −15.9603 −0.745777
\(459\) 0 0
\(460\) 8.91294i 0.415568i
\(461\) 4.67153 8.09133i 0.217575 0.376851i −0.736491 0.676447i \(-0.763519\pi\)
0.954066 + 0.299596i \(0.0968520\pi\)
\(462\) 0 0
\(463\) −12.7281 22.0458i −0.591526 1.02455i −0.994027 0.109134i \(-0.965192\pi\)
0.402501 0.915420i \(-0.368141\pi\)
\(464\) 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 −0.787201 0.616696i \(-0.788471\pi\)
0.927675 + 0.373388i \(0.121804\pi\)
\(480\) 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 −0.575382 0.817885i \(-0.695147\pi\)
0.420618 + 0.907238i \(0.361813\pi\)
\(492\) 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 0.902599 + 0.430482i \(0.141656\pi\)
−0.0784916 + 0.996915i \(0.525010\pi\)
\(500\) 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 0.648938 0.760841i \(-0.275213\pi\)
−0.983377 + 0.181577i \(0.941880\pi\)
\(510\) 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 \(-0.815628\pi\)
0.836889 0.547372i \(-0.184372\pi\)
\(524\) −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 −0.236402 0.971655i \(-0.575968\pi\)
0.959679 0.281098i \(-0.0906985\pi\)
\(548\) 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 \(-0.960226\pi\)
0.992203 0.124629i \(-0.0397740\pi\)
\(558\) 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 0.654142 0.756371i \(-0.273030\pi\)
−0.982108 + 0.188318i \(0.939696\pi\)
\(564\) 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 0.893580 0.448905i \(-0.148186\pi\)
0.0580267 + 0.998315i \(0.481519\pi\)
\(570\) 0 0
\(571\) −12.8090 22.1859i −0.536041 0.928451i −0.999112 0.0421295i \(-0.986586\pi\)
0.463071 0.886321i \(-0.346748\pi\)
\(572\) 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 \(0.235549\pi\)
−0.738468 + 0.674288i \(0.764451\pi\)
\(578\) 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 −0.947495 0.319771i \(-0.896394\pi\)
0.750677 + 0.660669i \(0.229727\pi\)
\(588\) 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 0.302143 0.953263i \(-0.402298\pi\)
0.976621 + 0.214968i \(0.0689647\pi\)
\(600\) 0 0
\(601\) 13.8275 + 7.98332i 0.564036 + 0.325646i 0.754764 0.655997i \(-0.227751\pi\)
−0.190728 + 0.981643i \(0.561085\pi\)
\(602\) 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 −0.842179 0.539198i \(-0.818727\pi\)
0.0458701 + 0.998947i \(0.485394\pi\)
\(608\) −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 −0.879325 0.476222i \(-0.842006\pi\)
−0.0272418 + 0.999629i \(0.508672\pi\)
\(618\) 0 0
\(619\) 20.5526 + 11.8660i 0.826079 + 0.476937i 0.852508 0.522714i \(-0.175080\pi\)
−0.0264296 + 0.999651i \(0.508414\pi\)
\(620\) 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 0.636738 0.771080i \(-0.280283\pi\)
−0.349406 + 0.936971i \(0.613617\pi\)
\(642\) 0 0
\(643\) 0.237974 0.137394i 0.00938478 0.00541831i −0.495300 0.868722i \(-0.664942\pi\)
0.504685 + 0.863304i \(0.331609\pi\)
\(644\) 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 −0.528747 0.848779i \(-0.677338\pi\)
0.470691 + 0.882298i \(0.344005\pi\)
\(654\) 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 −0.216930 0.976187i \(-0.569604\pi\)
−0.953868 + 0.300226i \(0.902938\pi\)
\(660\) 0 0
\(661\) 33.2075 19.1724i 1.29162 0.745718i 0.312681 0.949858i \(-0.398773\pi\)
0.978942 + 0.204140i \(0.0654397\pi\)
\(662\) 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 −0.980758 0.195229i \(-0.937455\pi\)
0.659452 + 0.751746i \(0.270788\pi\)
\(674\) 1.51521i 0.0583637i
\(675\) 0 0
\(676\) 33.6415 1.29390
\(677\) −10.4682 + 18.1315i −0.402327 + 0.696850i −0.994006 0.109323i \(-0.965132\pi\)
0.591680 + 0.806173i \(0.298465\pi\)
\(678\) 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 \(0.0467197\pi\)
−0.989248 + 0.146248i \(0.953280\pi\)
\(684\) 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 0.316723 0.948518i \(-0.397417\pi\)
−0.663079 + 0.748549i \(0.730751\pi\)
\(692\) −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 \(-0.903972\pi\)
0.954839 0.297125i \(-0.0960277\pi\)
\(702\) 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 −0.837518 0.546410i \(-0.815994\pi\)
0.891964 + 0.452107i \(0.149328\pi\)
\(710\) 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 0.970498 0.241109i \(-0.0775112\pi\)
0.276442 + 0.961031i \(0.410845\pi\)
\(728\) 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 −0.0222778 0.999752i \(-0.507092\pi\)
0.854672 + 0.519169i \(0.173758\pi\)
\(734\) −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 0.0176504 0.999844i \(-0.494381\pi\)
0.874716 + 0.484636i \(0.161048\pi\)
\(744\) 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 −0.935789 0.352561i \(-0.885311\pi\)
0.162567 0.986697i \(-0.448023\pi\)
\(752\) −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 −0.986782 0.162051i \(-0.948189\pi\)
0.353051 0.935604i \(-0.385144\pi\)
\(762\) 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 −0.800856 0.598857i \(-0.795622\pi\)
0.118198 + 0.992990i \(0.462288\pi\)
\(770\) 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 −0.998575 0.0533671i \(-0.983005\pi\)
−0.453070 + 0.891475i \(0.649671\pi\)
\(788\) −5.07696 + 2.93119i −0.180859 + 0.104419i
\(789\) 0 0
\(790\) 14.3718 + 8.29754i 0.511325 + 0.295213i
\(791\) 0