Properties

Label 912.2.bo.e.289.1
Level $912$
Weight $2$
Character 912.289
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 228)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 289.1
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 912.289
Dual form 912.2.bo.e.385.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.173648 - 0.984808i) q^{3} +(1.93969 - 1.62760i) q^{5} +(-1.61334 + 2.79439i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\) \(q+(-0.173648 - 0.984808i) q^{3} +(1.93969 - 1.62760i) q^{5} +(-1.61334 + 2.79439i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(1.55303 + 2.68993i) q^{11} +(-1.05303 + 5.97205i) q^{13} +(-1.93969 - 1.62760i) q^{15} +(5.58512 + 2.03282i) q^{17} +(-4.34002 + 0.405223i) q^{19} +(3.03209 + 1.10359i) q^{21} +(5.14543 + 4.31753i) q^{23} +(0.245100 - 1.39003i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-6.69846 + 2.43804i) q^{29} +(3.81908 - 6.61484i) q^{31} +(2.37939 - 1.99654i) q^{33} +(1.41875 + 8.04612i) q^{35} +2.10607 q^{37} +6.06418 q^{39} +(-1.22281 - 6.93491i) q^{41} +(7.17752 - 6.02265i) q^{43} +(-1.26604 + 2.19285i) q^{45} +(-4.37211 + 1.59132i) q^{47} +(-1.70574 - 2.95442i) q^{49} +(1.03209 - 5.85327i) q^{51} +(-4.86824 - 4.08494i) q^{53} +(7.39053 + 2.68993i) q^{55} +(1.15270 + 4.20372i) q^{57} +(-0.252374 - 0.0918566i) q^{59} +(1.21688 + 1.02108i) q^{61} +(0.560307 - 3.17766i) q^{63} +(7.67752 + 13.2979i) q^{65} +(-1.22668 + 0.446476i) q^{67} +(3.35844 - 5.81699i) q^{69} +(6.34002 - 5.31991i) q^{71} +(0.159978 + 0.907278i) q^{73} -1.41147 q^{75} -10.0223 q^{77} +(2.09492 + 11.8809i) q^{79} +(0.766044 - 0.642788i) q^{81} +(0.0432332 - 0.0748822i) q^{83} +(14.1420 - 5.14728i) q^{85} +(3.56418 + 6.17334i) q^{87} +(-1.22803 + 6.96448i) q^{89} +(-14.9893 - 12.5775i) q^{91} +(-7.17752 - 2.61240i) q^{93} +(-7.75877 + 7.84981i) q^{95} +(-3.12701 - 1.13814i) q^{97} +(-2.37939 - 1.99654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{5} - 3 q^{7} + O(q^{10}) \) \( 6 q + 6 q^{5} - 3 q^{7} - 3 q^{11} + 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 9 q^{21} + 15 q^{23} + 3 q^{27} - 12 q^{29} + 6 q^{31} + 3 q^{33} + 6 q^{35} - 12 q^{37} + 18 q^{39} - 18 q^{41} + 18 q^{43} - 3 q^{45} + 3 q^{47} - 3 q^{51} - 24 q^{53} + 27 q^{55} + 9 q^{57} - 18 q^{59} - 9 q^{61} + 9 q^{63} + 21 q^{65} + 6 q^{67} + 12 q^{69} + 18 q^{71} + 21 q^{73} + 12 q^{75} - 48 q^{77} - 6 q^{79} - 15 q^{83} + 27 q^{85} + 3 q^{87} + 15 q^{89} - 30 q^{91} - 18 q^{93} - 24 q^{95} + 9 q^{97} - 3 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(1\) \(1\) \(1\)

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 0
\(3\) −0.173648 0.984808i −0.100256 0.568579i
\(4\) 0 0
\(5\) 1.93969 1.62760i 0.867457 0.727883i −0.0961041 0.995371i \(-0.530638\pi\)
0.963561 + 0.267489i \(0.0861937\pi\)
\(6\) 0 0
\(7\) −1.61334 + 2.79439i −0.609786 + 1.05618i 0.381490 + 0.924373i \(0.375411\pi\)
−0.991275 + 0.131806i \(0.957922\pi\)
\(8\) 0 0
\(9\) −0.939693 + 0.342020i −0.313231 + 0.114007i
\(10\) 0 0
\(11\) 1.55303 + 2.68993i 0.468257 + 0.811045i 0.999342 0.0362735i \(-0.0115487\pi\)
−0.531085 + 0.847319i \(0.678215\pi\)
\(12\) 0 0
\(13\) −1.05303 + 5.97205i −0.292059 + 1.65635i 0.386862 + 0.922137i \(0.373559\pi\)
−0.678921 + 0.734211i \(0.737552\pi\)
\(14\) 0 0
\(15\) −1.93969 1.62760i −0.500826 0.420243i
\(16\) 0 0
\(17\) 5.58512 + 2.03282i 1.35459 + 0.493031i 0.914378 0.404862i \(-0.132681\pi\)
0.440213 + 0.897893i \(0.354903\pi\)
\(18\) 0 0
\(19\) −4.34002 + 0.405223i −0.995669 + 0.0929645i
\(20\) 0 0
\(21\) 3.03209 + 1.10359i 0.661656 + 0.240823i
\(22\) 0 0
\(23\) 5.14543 + 4.31753i 1.07290 + 0.900267i 0.995312 0.0967189i \(-0.0308348\pi\)
0.0775845 + 0.996986i \(0.475279\pi\)
\(24\) 0 0
\(25\) 0.245100 1.39003i 0.0490200 0.278006i
\(26\) 0 0
\(27\) 0.500000 + 0.866025i 0.0962250 + 0.166667i
\(28\) 0 0
\(29\) −6.69846 + 2.43804i −1.24387 + 0.452733i −0.878327 0.478060i \(-0.841340\pi\)
−0.365546 + 0.930793i \(0.619118\pi\)
\(30\) 0 0
\(31\) 3.81908 6.61484i 0.685927 1.18806i −0.287218 0.957865i \(-0.592730\pi\)
0.973145 0.230195i \(-0.0739363\pi\)
\(32\) 0 0
\(33\) 2.37939 1.99654i 0.414198 0.347553i
\(34\) 0 0
\(35\) 1.41875 + 8.04612i 0.239812 + 1.36004i
\(36\) 0 0
\(37\) 2.10607 0.346235 0.173118 0.984901i \(-0.444616\pi\)
0.173118 + 0.984901i \(0.444616\pi\)
\(38\) 0 0
\(39\) 6.06418 0.971046
\(40\) 0 0
\(41\) −1.22281 6.93491i −0.190971 1.08305i −0.918041 0.396487i \(-0.870229\pi\)
0.727069 0.686564i \(-0.240882\pi\)
\(42\) 0 0
\(43\) 7.17752 6.02265i 1.09456 0.918446i 0.0975139 0.995234i \(-0.468911\pi\)
0.997047 + 0.0767882i \(0.0244665\pi\)
\(44\) 0 0
\(45\) −1.26604 + 2.19285i −0.188731 + 0.326891i
\(46\) 0 0
\(47\) −4.37211 + 1.59132i −0.637738 + 0.232118i −0.640596 0.767878i \(-0.721313\pi\)
0.00285780 + 0.999996i \(0.499090\pi\)
\(48\) 0 0
\(49\) −1.70574 2.95442i −0.243677 0.422060i
\(50\) 0 0
\(51\) 1.03209 5.85327i 0.144521 0.819621i
\(52\) 0 0
\(53\) −4.86824 4.08494i −0.668704 0.561110i 0.243977 0.969781i \(-0.421548\pi\)
−0.912682 + 0.408671i \(0.865992\pi\)
\(54\) 0 0
\(55\) 7.39053 + 2.68993i 0.996539 + 0.362710i
\(56\) 0 0
\(57\) 1.15270 + 4.20372i 0.152679 + 0.556797i
\(58\) 0 0
\(59\) −0.252374 0.0918566i −0.0328563 0.0119587i 0.325540 0.945528i \(-0.394454\pi\)
−0.358396 + 0.933570i \(0.616676\pi\)
\(60\) 0 0
\(61\) 1.21688 + 1.02108i 0.155806 + 0.130737i 0.717358 0.696705i \(-0.245351\pi\)
−0.561552 + 0.827441i \(0.689796\pi\)
\(62\) 0 0
\(63\) 0.560307 3.17766i 0.0705921 0.400348i
\(64\) 0 0
\(65\) 7.67752 + 13.2979i 0.952279 + 1.64940i
\(66\) 0 0
\(67\) −1.22668 + 0.446476i −0.149863 + 0.0545457i −0.415863 0.909427i \(-0.636520\pi\)
0.266000 + 0.963973i \(0.414298\pi\)
\(68\) 0 0
\(69\) 3.35844 5.81699i 0.404309 0.700283i
\(70\) 0 0
\(71\) 6.34002 5.31991i 0.752422 0.631357i −0.183720 0.982979i \(-0.558814\pi\)
0.936142 + 0.351621i \(0.114370\pi\)
\(72\) 0 0
\(73\) 0.159978 + 0.907278i 0.0187240 + 0.106189i 0.992737 0.120301i \(-0.0383860\pi\)
−0.974013 + 0.226490i \(0.927275\pi\)
\(74\) 0 0
\(75\) −1.41147 −0.162983
\(76\) 0 0
\(77\) −10.0223 −1.14215
\(78\) 0 0
\(79\) 2.09492 + 11.8809i 0.235697 + 1.33671i 0.841140 + 0.540817i \(0.181885\pi\)
−0.605443 + 0.795888i \(0.707004\pi\)
\(80\) 0 0
\(81\) 0.766044 0.642788i 0.0851160 0.0714208i
\(82\) 0 0
\(83\) 0.0432332 0.0748822i 0.00474546 0.00821939i −0.863643 0.504104i \(-0.831823\pi\)
0.868388 + 0.495885i \(0.165156\pi\)
\(84\) 0 0
\(85\) 14.1420 5.14728i 1.53392 0.558301i
\(86\) 0 0
\(87\) 3.56418 + 6.17334i 0.382120 + 0.661851i
\(88\) 0 0
\(89\) −1.22803 + 6.96448i −0.130170 + 0.738233i 0.847931 + 0.530106i \(0.177848\pi\)
−0.978102 + 0.208127i \(0.933263\pi\)
\(90\) 0 0
\(91\) −14.9893 12.5775i −1.57131 1.31848i
\(92\) 0 0
\(93\) −7.17752 2.61240i −0.744274 0.270894i
\(94\) 0 0
\(95\) −7.75877 + 7.84981i −0.796033 + 0.805373i
\(96\) 0 0
\(97\) −3.12701 1.13814i −0.317500 0.115561i 0.178354 0.983966i \(-0.442923\pi\)
−0.495854 + 0.868406i \(0.665145\pi\)
\(98\) 0 0
\(99\) −2.37939 1.99654i −0.239137 0.200660i
\(100\) 0 0
\(101\) −1.86824 + 10.5953i −0.185897 + 1.05427i 0.738901 + 0.673814i \(0.235345\pi\)
−0.924798 + 0.380459i \(0.875766\pi\)
\(102\) 0 0
\(103\) 2.96451 + 5.13468i 0.292102 + 0.505935i 0.974306 0.225226i \(-0.0723121\pi\)
−0.682205 + 0.731161i \(0.738979\pi\)
\(104\) 0 0
\(105\) 7.67752 2.79439i 0.749249 0.272704i
\(106\) 0 0
\(107\) 1.29086 2.23583i 0.124792 0.216146i −0.796860 0.604165i \(-0.793507\pi\)
0.921652 + 0.388018i \(0.126840\pi\)
\(108\) 0 0
\(109\) 3.66250 3.07321i 0.350804 0.294360i −0.450309 0.892873i \(-0.648686\pi\)
0.801113 + 0.598513i \(0.204242\pi\)
\(110\) 0 0
\(111\) −0.365715 2.07407i −0.0347121 0.196862i
\(112\) 0 0
\(113\) 16.6655 1.56776 0.783879 0.620914i \(-0.213238\pi\)
0.783879 + 0.620914i \(0.213238\pi\)
\(114\) 0 0
\(115\) 17.0077 1.58598
\(116\) 0 0
\(117\) −1.05303 5.97205i −0.0973530 0.552116i
\(118\) 0 0
\(119\) −14.6912 + 12.3274i −1.34674 + 1.13005i
\(120\) 0 0
\(121\) 0.676174 1.17117i 0.0614704 0.106470i
\(122\) 0 0
\(123\) −6.61721 + 2.40847i −0.596654 + 0.217164i
\(124\) 0 0
\(125\) 4.54323 + 7.86911i 0.406359 + 0.703835i
\(126\) 0 0
\(127\) −0.906260 + 5.13965i −0.0804175 + 0.456070i 0.917834 + 0.396964i \(0.129936\pi\)
−0.998252 + 0.0591064i \(0.981175\pi\)
\(128\) 0 0
\(129\) −7.17752 6.02265i −0.631945 0.530265i
\(130\) 0 0
\(131\) −8.13563 2.96113i −0.710813 0.258715i −0.0387926 0.999247i \(-0.512351\pi\)
−0.672021 + 0.740532i \(0.734573\pi\)
\(132\) 0 0
\(133\) 5.86959 12.7815i 0.508958 1.10829i
\(134\) 0 0
\(135\) 2.37939 + 0.866025i 0.204785 + 0.0745356i
\(136\) 0 0
\(137\) −10.4684 8.78401i −0.894374 0.750469i 0.0747087 0.997205i \(-0.476197\pi\)
−0.969083 + 0.246737i \(0.920642\pi\)
\(138\) 0 0
\(139\) 2.37551 13.4722i 0.201489 1.14270i −0.701382 0.712786i \(-0.747433\pi\)
0.902870 0.429913i \(-0.141456\pi\)
\(140\) 0 0
\(141\) 2.32635 + 4.02936i 0.195914 + 0.339333i
\(142\) 0 0
\(143\) −17.6998 + 6.44220i −1.48013 + 0.538724i
\(144\) 0 0
\(145\) −9.02481 + 15.6314i −0.749470 + 1.29812i
\(146\) 0 0
\(147\) −2.61334 + 2.19285i −0.215545 + 0.180863i
\(148\) 0 0
\(149\) 4.12314 + 23.3835i 0.337781 + 1.91565i 0.397838 + 0.917456i \(0.369761\pi\)
−0.0600574 + 0.998195i \(0.519128\pi\)
\(150\) 0 0
\(151\) −8.33544 −0.678328 −0.339164 0.940727i \(-0.610144\pi\)
−0.339164 + 0.940727i \(0.610144\pi\)
\(152\) 0 0
\(153\) −5.94356 −0.480509
\(154\) 0 0
\(155\) −3.35844 19.0467i −0.269756 1.52986i
\(156\) 0 0
\(157\) 16.6197 13.9456i 1.32640 1.11298i 0.341495 0.939884i \(-0.389067\pi\)
0.984905 0.173098i \(-0.0553776\pi\)
\(158\) 0 0
\(159\) −3.17752 + 5.50362i −0.251994 + 0.436466i
\(160\) 0 0
\(161\) −20.3662 + 7.41268i −1.60508 + 0.584201i
\(162\) 0 0
\(163\) −11.4927 19.9060i −0.900180 1.55916i −0.827260 0.561819i \(-0.810102\pi\)
−0.0729198 0.997338i \(-0.523232\pi\)
\(164\) 0 0
\(165\) 1.36571 7.74535i 0.106321 0.602975i
\(166\) 0 0
\(167\) 5.85710 + 4.91469i 0.453236 + 0.380310i 0.840635 0.541602i \(-0.182182\pi\)
−0.387399 + 0.921912i \(0.626626\pi\)
\(168\) 0 0
\(169\) −22.3405 8.13127i −1.71850 0.625483i
\(170\) 0 0
\(171\) 3.93969 1.86516i 0.301276 0.142632i
\(172\) 0 0
\(173\) −11.0360 4.01676i −0.839048 0.305389i −0.113481 0.993540i \(-0.536200\pi\)
−0.725567 + 0.688151i \(0.758422\pi\)
\(174\) 0 0
\(175\) 3.48886 + 2.92750i 0.263733 + 0.221298i
\(176\) 0 0
\(177\) −0.0466368 + 0.264490i −0.00350544 + 0.0198803i
\(178\) 0 0
\(179\) −2.09879 3.63522i −0.156871 0.271709i 0.776868 0.629664i \(-0.216807\pi\)
−0.933739 + 0.357955i \(0.883474\pi\)
\(180\) 0 0
\(181\) −11.5842 + 4.21632i −0.861050 + 0.313397i −0.734537 0.678568i \(-0.762601\pi\)
−0.126513 + 0.991965i \(0.540379\pi\)
\(182\) 0 0
\(183\) 0.794263 1.37570i 0.0587136 0.101695i
\(184\) 0 0
\(185\) 4.08512 3.42782i 0.300344 0.252019i
\(186\) 0 0
\(187\) 3.20574 + 18.1806i 0.234427 + 1.32950i
\(188\) 0 0
\(189\) −3.22668 −0.234707
\(190\) 0 0
\(191\) 10.2044 0.738364 0.369182 0.929357i \(-0.379638\pi\)
0.369182 + 0.929357i \(0.379638\pi\)
\(192\) 0 0
\(193\) −3.76945 21.3776i −0.271331 1.53879i −0.750381 0.661006i \(-0.770130\pi\)
0.479050 0.877788i \(-0.340981\pi\)
\(194\) 0 0
\(195\) 11.7626 9.87003i 0.842340 0.706807i
\(196\) 0 0
\(197\) 8.34255 14.4497i 0.594382 1.02950i −0.399252 0.916841i \(-0.630730\pi\)
0.993634 0.112658i \(-0.0359366\pi\)
\(198\) 0 0
\(199\) −2.31180 + 0.841428i −0.163879 + 0.0596472i −0.422657 0.906290i \(-0.638903\pi\)
0.258778 + 0.965937i \(0.416680\pi\)
\(200\) 0 0
\(201\) 0.652704 + 1.13052i 0.0460382 + 0.0797404i
\(202\) 0 0
\(203\) 3.99407 22.6515i 0.280329 1.58982i
\(204\) 0 0
\(205\) −13.6591 11.4613i −0.953993 0.800495i
\(206\) 0 0
\(207\) −6.31180 2.29731i −0.438701 0.159674i
\(208\) 0 0
\(209\) −7.83022 11.0450i −0.541628 0.764002i
\(210\) 0 0
\(211\) −1.15745 0.421278i −0.0796822 0.0290020i 0.301871 0.953349i \(-0.402389\pi\)
−0.381554 + 0.924347i \(0.624611\pi\)
\(212\) 0 0
\(213\) −6.34002 5.31991i −0.434411 0.364514i
\(214\) 0 0
\(215\) 4.11974 23.3642i 0.280964 1.59342i
\(216\) 0 0
\(217\) 12.3229 + 21.3440i 0.836536 + 1.44892i
\(218\) 0 0
\(219\) 0.865715 0.315094i 0.0584996 0.0212921i
\(220\) 0 0
\(221\) −18.0214 + 31.2140i −1.21225 + 2.09968i
\(222\) 0 0
\(223\) −5.03983 + 4.22892i −0.337492 + 0.283189i −0.795744 0.605633i \(-0.792920\pi\)
0.458252 + 0.888822i \(0.348476\pi\)
\(224\) 0 0
\(225\) 0.245100 + 1.39003i 0.0163400 + 0.0926687i
\(226\) 0 0
\(227\) −9.72967 −0.645781 −0.322891 0.946436i \(-0.604655\pi\)
−0.322891 + 0.946436i \(0.604655\pi\)
\(228\) 0 0
\(229\) −9.86753 −0.652064 −0.326032 0.945359i \(-0.605712\pi\)
−0.326032 + 0.945359i \(0.605712\pi\)
\(230\) 0 0
\(231\) 1.74035 + 9.87003i 0.114507 + 0.649400i
\(232\) 0 0
\(233\) 16.7121 14.0231i 1.09485 0.918687i 0.0977803 0.995208i \(-0.468826\pi\)
0.997068 + 0.0765212i \(0.0243813\pi\)
\(234\) 0 0
\(235\) −5.89053 + 10.2027i −0.384256 + 0.665551i
\(236\) 0 0
\(237\) 11.3366 4.12619i 0.736393 0.268025i
\(238\) 0 0
\(239\) 10.6557 + 18.4562i 0.689260 + 1.19383i 0.972078 + 0.234659i \(0.0753974\pi\)
−0.282818 + 0.959174i \(0.591269\pi\)
\(240\) 0 0
\(241\) 2.71688 15.4082i 0.175010 0.992529i −0.763123 0.646253i \(-0.776335\pi\)
0.938133 0.346276i \(-0.112554\pi\)
\(242\) 0 0
\(243\) −0.766044 0.642788i −0.0491418 0.0412348i
\(244\) 0 0
\(245\) −8.11721 2.95442i −0.518590 0.188751i
\(246\) 0 0
\(247\) 2.15018 26.3455i 0.136813 1.67633i
\(248\) 0 0
\(249\) −0.0812519 0.0295733i −0.00514913 0.00187413i
\(250\) 0 0
\(251\) 7.75356 + 6.50601i 0.489400 + 0.410655i 0.853811 0.520583i \(-0.174285\pi\)
−0.364411 + 0.931238i \(0.618730\pi\)
\(252\) 0 0
\(253\) −3.62284 + 20.5461i −0.227766 + 1.29172i
\(254\) 0 0
\(255\) −7.52481 13.0334i −0.471222 0.816181i
\(256\) 0 0
\(257\) 4.49020 1.63430i 0.280091 0.101945i −0.198155 0.980171i \(-0.563495\pi\)
0.478246 + 0.878226i \(0.341273\pi\)
\(258\) 0 0
\(259\) −3.39780 + 5.88517i −0.211129 + 0.365687i
\(260\) 0 0
\(261\) 5.46064 4.58202i 0.338005 0.283620i
\(262\) 0 0
\(263\) 3.76651 + 21.3609i 0.232253 + 1.31717i 0.848322 + 0.529480i \(0.177613\pi\)
−0.616069 + 0.787692i \(0.711276\pi\)
\(264\) 0 0
\(265\) −16.0915 −0.988494
\(266\) 0 0
\(267\) 7.07192 0.432794
\(268\) 0 0
\(269\) −0.561185 3.18264i −0.0342160 0.194049i 0.962909 0.269828i \(-0.0869668\pi\)
−0.997125 + 0.0757790i \(0.975856\pi\)
\(270\) 0 0
\(271\) 8.97952 7.53471i 0.545467 0.457701i −0.327935 0.944700i \(-0.606353\pi\)
0.873403 + 0.486999i \(0.161908\pi\)
\(272\) 0 0
\(273\) −9.78359 + 16.9457i −0.592130 + 1.02560i
\(274\) 0 0
\(275\) 4.11974 1.49946i 0.248430 0.0904209i
\(276\) 0 0
\(277\) −4.38666 7.59792i −0.263569 0.456515i 0.703619 0.710578i \(-0.251566\pi\)
−0.967188 + 0.254063i \(0.918233\pi\)
\(278\) 0 0
\(279\) −1.32635 + 7.52211i −0.0794066 + 0.450337i
\(280\) 0 0
\(281\) 19.4702 + 16.3374i 1.16149 + 0.974609i 0.999925 0.0122521i \(-0.00390007\pi\)
0.161569 + 0.986861i \(0.448345\pi\)
\(282\) 0 0
\(283\) −2.51114 0.913982i −0.149272 0.0543306i 0.266304 0.963889i \(-0.414198\pi\)
−0.415576 + 0.909559i \(0.636420\pi\)
\(284\) 0 0
\(285\) 9.07785 + 6.27779i 0.537725 + 0.371864i
\(286\) 0 0
\(287\) 21.3516 + 7.77136i 1.26035 + 0.458729i
\(288\) 0 0
\(289\) 14.0385 + 11.7797i 0.825793 + 0.692923i
\(290\) 0 0
\(291\) −0.577848 + 3.27714i −0.0338741 + 0.192109i
\(292\) 0 0
\(293\) −9.97683 17.2804i −0.582853 1.00953i −0.995139 0.0984765i \(-0.968603\pi\)
0.412287 0.911054i \(-0.364730\pi\)
\(294\) 0 0
\(295\) −0.639033 + 0.232589i −0.0372059 + 0.0135419i
\(296\) 0 0
\(297\) −1.55303 + 2.68993i −0.0901161 + 0.156086i
\(298\) 0 0
\(299\) −31.2028 + 26.1823i −1.80450 + 1.51416i
\(300\) 0 0
\(301\) 5.24985 + 29.7734i 0.302596 + 1.71611i
\(302\) 0 0
\(303\) 10.7588 0.618075
\(304\) 0 0
\(305\) 4.02229 0.230316
\(306\) 0 0
\(307\) 4.16431 + 23.6170i 0.237670 + 1.34789i 0.836917 + 0.547330i \(0.184356\pi\)
−0.599247 + 0.800564i \(0.704533\pi\)
\(308\) 0 0
\(309\) 4.54189 3.81110i 0.258379 0.216806i
\(310\) 0 0
\(311\) −0.0812519 + 0.140732i −0.00460737 + 0.00798020i −0.868320 0.496005i \(-0.834800\pi\)
0.863713 + 0.503985i \(0.168133\pi\)
\(312\) 0 0
\(313\) −6.31655 + 2.29904i −0.357033 + 0.129949i −0.514308 0.857606i \(-0.671951\pi\)
0.157275 + 0.987555i \(0.449729\pi\)
\(314\) 0 0
\(315\) −4.08512 7.07564i −0.230171 0.398667i
\(316\) 0 0
\(317\) 2.48024 14.0661i 0.139304 0.790032i −0.832461 0.554083i \(-0.813069\pi\)
0.971765 0.235949i \(-0.0758199\pi\)
\(318\) 0 0
\(319\) −16.9611 14.2321i −0.949640 0.796842i
\(320\) 0 0
\(321\) −2.42602 0.883000i −0.135407 0.0492842i
\(322\) 0 0
\(323\) −25.0633 6.55926i −1.39456 0.364967i
\(324\) 0 0
\(325\) 8.04323 + 2.92750i 0.446158 + 0.162388i
\(326\) 0 0
\(327\) −3.66250 3.07321i −0.202537 0.169949i
\(328\) 0 0
\(329\) 2.60694 14.7847i 0.143725 0.815108i
\(330\) 0 0
\(331\) −16.6532 28.8441i −0.915341 1.58542i −0.806401 0.591369i \(-0.798588\pi\)
−0.108940 0.994048i \(-0.534746\pi\)
\(332\) 0 0
\(333\) −1.97906 + 0.720317i −0.108452 + 0.0394731i
\(334\) 0 0
\(335\) −1.65270 + 2.86257i −0.0902968 + 0.156399i
\(336\) 0 0
\(337\) −1.41669 + 1.18874i −0.0771720 + 0.0647550i −0.680558 0.732695i \(-0.738262\pi\)
0.603386 + 0.797450i \(0.293818\pi\)
\(338\) 0 0
\(339\) −2.89393 16.4123i −0.157177 0.891394i
\(340\) 0 0
\(341\) 23.7246 1.28476
\(342\) 0 0
\(343\) −11.5790 −0.625209
\(344\) 0 0
\(345\) −2.95336 16.7494i −0.159004 0.901755i
\(346\) 0 0
\(347\) 5.28493 4.43458i 0.283710 0.238061i −0.489816 0.871826i \(-0.662936\pi\)
0.773525 + 0.633765i \(0.218491\pi\)
\(348\) 0 0
\(349\) 5.61081 9.71822i 0.300340 0.520204i −0.675873 0.737018i \(-0.736233\pi\)
0.976213 + 0.216814i \(0.0695665\pi\)
\(350\) 0 0
\(351\) −5.69846 + 2.07407i −0.304161 + 0.110706i
\(352\) 0 0
\(353\) 0.954241 + 1.65279i 0.0507891 + 0.0879693i 0.890302 0.455370i \(-0.150493\pi\)
−0.839513 + 0.543339i \(0.817160\pi\)
\(354\) 0 0
\(355\) 3.63903 20.6380i 0.193140 1.09535i
\(356\) 0 0
\(357\) 14.6912 + 12.3274i 0.777540 + 0.652434i
\(358\) 0 0
\(359\) 8.95558 + 3.25957i 0.472658 + 0.172033i 0.567356 0.823473i \(-0.307966\pi\)
−0.0946982 + 0.995506i \(0.530189\pi\)
\(360\) 0 0
\(361\) 18.6716 3.51735i 0.982715 0.185124i
\(362\) 0 0
\(363\) −1.27079 0.462531i −0.0666993 0.0242766i
\(364\) 0 0
\(365\) 1.78699 + 1.49946i 0.0935353 + 0.0784854i
\(366\) 0 0
\(367\) −3.11216 + 17.6499i −0.162453 + 0.921319i 0.789198 + 0.614139i \(0.210496\pi\)
−0.951651 + 0.307180i \(0.900615\pi\)
\(368\) 0 0
\(369\) 3.52094 + 6.09845i 0.183293 + 0.317473i
\(370\) 0 0
\(371\) 19.2690 7.01336i 1.00040 0.364115i
\(372\) 0 0
\(373\) 15.2344 26.3868i 0.788808 1.36626i −0.137889 0.990448i \(-0.544032\pi\)
0.926697 0.375809i \(-0.122635\pi\)
\(374\) 0 0
\(375\) 6.96064 5.84067i 0.359446 0.301611i
\(376\) 0 0
\(377\) −7.50640 42.5709i −0.386599 2.19251i
\(378\) 0 0
\(379\) −6.57903 −0.337942 −0.168971 0.985621i \(-0.554044\pi\)
−0.168971 + 0.985621i \(0.554044\pi\)
\(380\) 0 0
\(381\) 5.21894 0.267374
\(382\) 0 0
\(383\) −3.99525 22.6582i −0.204148 1.15778i −0.898775 0.438410i \(-0.855542\pi\)
0.694627 0.719370i \(-0.255569\pi\)
\(384\) 0 0
\(385\) −19.4402 + 16.3122i −0.990762 + 0.831348i
\(386\) 0 0
\(387\) −4.68479 + 8.11430i −0.238141 + 0.412473i
\(388\) 0 0
\(389\) −25.6587 + 9.33900i −1.30095 + 0.473506i −0.897305 0.441411i \(-0.854478\pi\)
−0.403642 + 0.914917i \(0.632256\pi\)
\(390\) 0 0
\(391\) 19.9611 + 34.5736i 1.00948 + 1.74846i
\(392\) 0 0
\(393\) −1.50340 + 8.52623i −0.0758367 + 0.430091i
\(394\) 0 0
\(395\) 23.4008 + 19.6356i 1.17742 + 0.987974i
\(396\) 0 0
\(397\) 5.52734 + 2.01179i 0.277409 + 0.100969i 0.476978 0.878915i \(-0.341732\pi\)
−0.199569 + 0.979884i \(0.563954\pi\)
\(398\) 0 0
\(399\) −13.6065 3.56093i −0.681179 0.178270i
\(400\) 0 0
\(401\) 4.02987 + 1.46675i 0.201242 + 0.0732461i 0.440675 0.897667i \(-0.354739\pi\)
−0.239433 + 0.970913i \(0.576961\pi\)
\(402\) 0 0
\(403\) 35.4825 + 29.7734i 1.76751 + 1.48312i
\(404\) 0 0
\(405\) 0.439693 2.49362i 0.0218485 0.123909i
\(406\) 0 0
\(407\) 3.27079 + 5.66518i 0.162127 + 0.280812i
\(408\) 0 0
\(409\) 30.4714 11.0907i 1.50671 0.548398i 0.548924 0.835872i \(-0.315038\pi\)
0.957788 + 0.287474i \(0.0928155\pi\)
\(410\) 0 0
\(411\) −6.83275 + 11.8347i −0.337035 + 0.583761i
\(412\) 0 0
\(413\) 0.663848 0.557035i 0.0326658 0.0274099i
\(414\) 0 0
\(415\) −0.0380187 0.215615i −0.00186626 0.0105841i
\(416\) 0 0
\(417\) −13.6800 −0.669915
\(418\) 0 0
\(419\) −9.86577 −0.481974 −0.240987 0.970528i \(-0.577471\pi\)
−0.240987 + 0.970528i \(0.577471\pi\)
\(420\) 0 0
\(421\) 3.83884 + 21.7711i 0.187094 + 1.06106i 0.923236 + 0.384234i \(0.125534\pi\)
−0.736142 + 0.676827i \(0.763355\pi\)
\(422\) 0 0
\(423\) 3.56418 2.99070i 0.173296 0.145413i
\(424\) 0 0
\(425\) 4.19459 7.26525i 0.203468 0.352416i
\(426\) 0 0
\(427\) −4.81655 + 1.75308i −0.233089 + 0.0848376i
\(428\) 0 0
\(429\) 9.41787 + 16.3122i 0.454699 + 0.787562i
\(430\) 0 0
\(431\) 4.39693 24.9362i 0.211792 1.20113i −0.674594 0.738189i \(-0.735681\pi\)
0.886387 0.462946i \(-0.153208\pi\)
\(432\) 0 0
\(433\) 9.81702 + 8.23746i 0.471776 + 0.395867i 0.847442 0.530888i \(-0.178142\pi\)
−0.375666 + 0.926755i \(0.622586\pi\)
\(434\) 0 0
\(435\) 16.9611 + 6.17334i 0.813223 + 0.295989i
\(436\) 0 0
\(437\) −24.0808 16.6531i −1.15194 0.796627i
\(438\) 0 0
\(439\) −4.90895 1.78671i −0.234291 0.0852751i 0.222206 0.975000i \(-0.428674\pi\)
−0.456498 + 0.889725i \(0.650896\pi\)
\(440\) 0 0
\(441\) 2.61334 + 2.19285i 0.124445 + 0.104422i
\(442\) 0 0
\(443\) 3.02141 17.1353i 0.143552 0.814121i −0.824967 0.565181i \(-0.808806\pi\)
0.968519 0.248941i \(-0.0800825\pi\)
\(444\) 0 0
\(445\) 8.95336 + 15.5077i 0.424430 + 0.735135i
\(446\) 0 0
\(447\) 22.3123 8.12100i 1.05533 0.384110i
\(448\) 0 0
\(449\) −11.8255 + 20.4823i −0.558079 + 0.966621i 0.439578 + 0.898204i \(0.355128\pi\)
−0.997657 + 0.0684163i \(0.978205\pi\)
\(450\) 0 0
\(451\) 16.7554 14.0594i 0.788979 0.662032i
\(452\) 0 0
\(453\) 1.44743 + 8.20880i 0.0680064 + 0.385683i
\(454\) 0 0
\(455\) −49.5458 −2.32274
\(456\) 0 0
\(457\) −24.2695 −1.13528 −0.567640 0.823277i \(-0.692143\pi\)
−0.567640 + 0.823277i \(0.692143\pi\)
\(458\) 0 0
\(459\) 1.03209 + 5.85327i 0.0481738 + 0.273207i
\(460\) 0 0
\(461\) 5.34318 4.48346i 0.248857 0.208815i −0.509823 0.860279i \(-0.670289\pi\)
0.758680 + 0.651464i \(0.225845\pi\)
\(462\) 0 0
\(463\) 14.0385 24.3154i 0.652424 1.13003i −0.330109 0.943943i \(-0.607086\pi\)
0.982533 0.186088i \(-0.0595811\pi\)
\(464\) 0 0
\(465\) −18.1741 + 6.61484i −0.842804 + 0.306756i
\(466\) 0 0
\(467\) 1.91147 + 3.31077i 0.0884525 + 0.153204i 0.906857 0.421438i \(-0.138475\pi\)
−0.818405 + 0.574642i \(0.805141\pi\)
\(468\) 0 0
\(469\) 0.731429 4.14814i 0.0337743 0.191543i
\(470\) 0 0
\(471\) −16.6197 13.9456i −0.765797 0.642580i
\(472\) 0 0
\(473\) 27.3475 + 9.95366i 1.25744 + 0.457670i
\(474\) 0 0
\(475\) −0.500467 + 6.13208i −0.0229630 + 0.281359i
\(476\) 0 0
\(477\) 5.97178 + 2.17355i 0.273429 + 0.0995201i
\(478\) 0 0
\(479\) 23.7010 + 19.8875i 1.08293 + 0.908683i 0.996160 0.0875461i \(-0.0279025\pi\)
0.0867654 + 0.996229i \(0.472347\pi\)
\(480\) 0 0
\(481\) −2.21776 + 12.5775i −0.101121 + 0.573486i
\(482\) 0 0
\(483\) 10.8366 + 18.7696i 0.493083 + 0.854045i
\(484\) 0 0
\(485\) −7.91787 + 2.88187i −0.359532 + 0.130859i
\(486\) 0 0
\(487\) −1.43242 + 2.48102i −0.0649091 + 0.112426i −0.896654 0.442733i \(-0.854009\pi\)
0.831745 + 0.555159i \(0.187342\pi\)
\(488\) 0 0
\(489\) −17.6079 + 14.7748i −0.796256 + 0.668138i
\(490\) 0 0
\(491\) 7.24985 + 41.1159i 0.327181 + 1.85554i 0.493883 + 0.869529i \(0.335577\pi\)
−0.166702 + 0.986007i \(0.553312\pi\)
\(492\) 0 0
\(493\) −42.3678 −1.90815
\(494\) 0 0
\(495\) −7.86484 −0.353498
\(496\) 0 0
\(497\) 4.63728 + 26.2993i 0.208010 + 1.17969i
\(498\) 0 0
\(499\) −7.26991 + 6.10018i −0.325446 + 0.273082i −0.790841 0.612021i \(-0.790357\pi\)
0.465395 + 0.885103i \(0.345912\pi\)
\(500\) 0 0
\(501\) 3.82295 6.62154i 0.170797 0.295829i
\(502\) 0 0
\(503\) −11.8785 + 4.32342i −0.529636 + 0.192772i −0.592976 0.805220i \(-0.702047\pi\)
0.0633395 + 0.997992i \(0.479825\pi\)
\(504\) 0 0
\(505\) 13.6211 + 23.5924i 0.606130 + 1.04985i
\(506\) 0 0
\(507\) −4.12836 + 23.4131i −0.183347 + 1.03981i
\(508\) 0 0
\(509\) −14.9349 12.5319i −0.661980 0.555467i 0.248700 0.968581i \(-0.419997\pi\)
−0.910679 + 0.413114i \(0.864441\pi\)
\(510\) 0 0
\(511\) −2.79339 1.01671i −0.123572 0.0449766i
\(512\) 0 0
\(513\) −2.52094 3.55596i −0.111302 0.156999i
\(514\) 0 0
\(515\) 14.1074 + 5.13468i 0.621647 + 0.226261i
\(516\) 0 0
\(517\) −11.0706 9.28931i −0.486883 0.408544i
\(518\) 0 0
\(519\) −2.03936 + 11.5658i −0.0895181 + 0.507682i
\(520\) 0 0
\(521\) −10.1416 17.5657i −0.444310 0.769567i 0.553694 0.832720i \(-0.313218\pi\)
−0.998004 + 0.0631531i \(0.979884\pi\)
\(522\) 0 0
\(523\) 14.3461 5.22156i 0.627312 0.228323i −0.00874906 0.999962i \(-0.502785\pi\)
0.636061 + 0.771639i \(0.280563\pi\)
\(524\) 0 0
\(525\) 2.27719 3.94421i 0.0993847 0.172139i
\(526\) 0 0
\(527\) 34.7768 29.1812i 1.51490 1.27115i
\(528\) 0 0
\(529\) 3.84049 + 21.7805i 0.166978 + 0.946978i
\(530\) 0 0
\(531\) 0.268571 0.0116550
\(532\) 0 0
\(533\) 42.7033 1.84968
\(534\) 0 0
\(535\) −1.13516 6.43783i −0.0490774 0.278332i
\(536\) 0 0
\(537\) −3.21554 + 2.69816i −0.138761 + 0.116434i
\(538\) 0 0
\(539\) 5.29813 9.17664i 0.228207 0.395266i
\(540\) 0 0
\(541\) 19.3726 7.05104i 0.832892 0.303148i 0.109847 0.993949i \(-0.464964\pi\)
0.723045 + 0.690801i \(0.242742\pi\)
\(542\) 0 0
\(543\) 6.16385 + 10.6761i 0.264516 + 0.458155i
\(544\) 0 0
\(545\) 2.10220 11.9221i 0.0900482 0.510689i
\(546\) 0 0
\(547\) 21.7645 + 18.2625i 0.930581 + 0.780850i 0.975922 0.218122i \(-0.0699929\pi\)
−0.0453408 + 0.998972i \(0.514437\pi\)
\(548\) 0 0
\(549\) −1.49273 0.543308i −0.0637080 0.0231878i
\(550\) 0 0
\(551\) 28.0835 13.2955i 1.19640 0.566408i
\(552\) 0 0
\(553\) −36.5797 13.3139i −1.55553 0.566165i
\(554\) 0 0
\(555\) −4.08512 3.42782i −0.173404 0.145503i
\(556\) 0 0
\(557\) −6.56717 + 37.2443i −0.278260 + 1.57809i 0.450152 + 0.892952i \(0.351370\pi\)
−0.728412 + 0.685139i \(0.759741\pi\)
\(558\) 0 0
\(559\) 28.4094 + 49.2065i 1.20159 + 2.08122i
\(560\) 0 0
\(561\) 17.3478 6.31407i 0.732423 0.266580i
\(562\) 0 0
\(563\) 4.82042 8.34922i 0.203157 0.351877i −0.746387 0.665512i \(-0.768213\pi\)
0.949544 + 0.313634i \(0.101547\pi\)
\(564\) 0 0
\(565\) 32.3259 27.1247i 1.35996 1.14114i
\(566\) 0 0
\(567\) 0.560307 + 3.17766i 0.0235307 + 0.133449i
\(568\) 0 0
\(569\) 21.1129 0.885098 0.442549 0.896744i \(-0.354074\pi\)
0.442549 + 0.896744i \(0.354074\pi\)
\(570\) 0 0
\(571\) 2.11112 0.0883476 0.0441738 0.999024i \(-0.485934\pi\)
0.0441738 + 0.999024i \(0.485934\pi\)
\(572\) 0 0
\(573\) −1.77197 10.0494i −0.0740253 0.419818i
\(574\) 0 0
\(575\) 7.26264 6.09408i 0.302873 0.254141i
\(576\) 0 0
\(577\) −11.5715 + 20.0423i −0.481726 + 0.834374i −0.999780 0.0209742i \(-0.993323\pi\)
0.518054 + 0.855348i \(0.326657\pi\)
\(578\) 0 0
\(579\) −20.3983 + 7.42436i −0.847723 + 0.308546i
\(580\) 0 0
\(581\) 0.139500 + 0.241621i 0.00578743 + 0.0100241i
\(582\) 0 0
\(583\) 3.42767 19.4393i 0.141960 0.805093i
\(584\) 0 0
\(585\) −11.7626 9.87003i −0.486325 0.408075i
\(586\) 0 0
\(587\) −18.0052 6.55336i −0.743155 0.270486i −0.0574324 0.998349i \(-0.518291\pi\)
−0.685722 + 0.727863i \(0.740514\pi\)
\(588\) 0 0
\(589\) −13.8944 + 30.2561i −0.572509 + 1.24668i
\(590\) 0 0
\(591\) −15.6789 5.70664i −0.644942 0.234740i
\(592\) 0 0
\(593\) 28.4978 + 23.9125i 1.17026 + 0.981968i 0.999994 0.00342988i \(-0.00109177\pi\)
0.170269 + 0.985398i \(0.445536\pi\)
\(594\) 0 0
\(595\) −8.43242 + 47.8226i −0.345695 + 1.96054i
\(596\) 0 0
\(597\) 1.23009 + 2.13057i 0.0503440 + 0.0871984i
\(598\) 0 0
\(599\) 29.0412 10.5701i 1.18659 0.431884i 0.328065 0.944655i \(-0.393603\pi\)
0.858525 + 0.512772i \(0.171381\pi\)
\(600\) 0 0
\(601\) 21.7802 37.7244i 0.888432 1.53881i 0.0467035 0.998909i \(-0.485128\pi\)
0.841729 0.539901i \(-0.181538\pi\)
\(602\) 0 0
\(603\) 1.00000 0.839100i 0.0407231 0.0341708i
\(604\) 0 0
\(605\) −0.594618 3.37225i −0.0241747 0.137101i
\(606\) 0 0
\(607\) −20.9659 −0.850978 −0.425489 0.904964i \(-0.639898\pi\)
−0.425489 + 0.904964i \(0.639898\pi\)
\(608\) 0 0
\(609\) −23.0009 −0.932045
\(610\) 0 0
\(611\) −4.89945 27.7862i −0.198211 1.12411i
\(612\) 0 0
\(613\) 4.82951 4.05244i 0.195062 0.163676i −0.540026 0.841649i \(-0.681585\pi\)
0.735088 + 0.677972i \(0.237141\pi\)
\(614\) 0 0
\(615\) −8.91534 + 15.4418i −0.359501 + 0.622675i
\(616\) 0 0
\(617\) 36.1241 13.1481i 1.45430 0.529322i 0.510512 0.859871i \(-0.329456\pi\)
0.943789 + 0.330549i \(0.107234\pi\)
\(618\) 0 0
\(619\) −9.31908 16.1411i −0.374565 0.648766i 0.615697 0.787983i \(-0.288875\pi\)
−0.990262 + 0.139217i \(0.955541\pi\)
\(620\) 0 0
\(621\) −1.16637 + 6.61484i −0.0468050 + 0.265444i
\(622\) 0 0
\(623\) −17.4802 14.6677i −0.700331 0.587647i
\(624\) 0 0
\(625\) 28.2520 + 10.2829i 1.13008 + 0.411315i
\(626\) 0 0
\(627\) −9.51754 + 9.62922i −0.380094 + 0.384554i
\(628\) 0 0
\(629\) 11.7626 + 4.28125i 0.469007 + 0.170705i
\(630\) 0 0
\(631\) −11.8407 9.93556i −0.471372 0.395528i 0.375923 0.926651i \(-0.377326\pi\)
−0.847295 + 0.531123i \(0.821770\pi\)
\(632\) 0 0
\(633\) −0.213888 + 1.21302i −0.00850130 + 0.0482133i
\(634\) 0 0
\(635\) 6.60741 + 11.4444i 0.262207 + 0.454156i
\(636\) 0 0
\(637\) 19.4402 7.07564i 0.770247 0.280347i
\(638\) 0 0
\(639\) −4.13816 + 7.16750i −0.163703 + 0.283542i
\(640\) 0 0
\(641\) −19.1630 + 16.0796i −0.756892 + 0.635108i −0.937316 0.348481i \(-0.886697\pi\)
0.180424 + 0.983589i \(0.442253\pi\)
\(642\) 0 0
\(643\) −3.96333 22.4771i −0.156298 0.886412i −0.957589 0.288137i \(-0.906964\pi\)
0.801291 0.598275i \(-0.204147\pi\)
\(644\) 0 0
\(645\) −23.7246 −0.934156
\(646\) 0 0
\(647\) −46.1252 −1.81337 −0.906684 0.421811i \(-0.861395\pi\)
−0.906684 + 0.421811i \(0.861395\pi\)
\(648\) 0 0
\(649\) −0.144857 0.821525i −0.00568614 0.0322477i
\(650\) 0 0
\(651\) 18.8799 15.8421i 0.739960 0.620900i
\(652\) 0 0
\(653\) 7.33868 12.7110i 0.287185 0.497418i −0.685952 0.727647i \(-0.740614\pi\)
0.973137 + 0.230228i \(0.0739473\pi\)
\(654\) 0 0
\(655\) −20.6001 + 7.49784i −0.804914 + 0.292965i
\(656\) 0 0
\(657\) −0.460637 0.797847i −0.0179712 0.0311270i
\(658\) 0 0
\(659\) 3.73648 21.1906i 0.145553 0.825470i −0.821369 0.570397i \(-0.806789\pi\)
0.966922 0.255073i \(-0.0820995\pi\)
\(660\) 0 0
\(661\) −24.0494 20.1798i −0.935413 0.784904i 0.0413686 0.999144i \(-0.486828\pi\)
−0.976781 + 0.214240i \(0.931273\pi\)
\(662\) 0 0
\(663\) 33.8692 + 12.3274i 1.31537 + 0.478755i
\(664\) 0 0
\(665\) −9.41787 34.3454i −0.365209 1.33186i
\(666\) 0 0
\(667\) −44.9928 16.3760i −1.74213 0.634083i
\(668\) 0 0
\(669\) 5.03983 + 4.22892i 0.194851 + 0.163499i
\(670\) 0 0
\(671\) −0.856792 + 4.85911i −0.0330761 + 0.187584i
\(672\) 0 0
\(673\) −5.83662 10.1093i −0.224985 0.389686i 0.731330 0.682024i \(-0.238900\pi\)
−0.956315 + 0.292338i \(0.905567\pi\)
\(674\) 0 0
\(675\) 1.32635 0.482753i 0.0510513 0.0185812i
\(676\) 0 0
\(677\) −20.6866 + 35.8302i −0.795051 + 1.37707i 0.127756 + 0.991806i \(0.459223\pi\)
−0.922807 + 0.385263i \(0.874111\pi\)
\(678\) 0 0
\(679\) 8.22534 6.90188i 0.315659 0.264870i
\(680\) 0 0
\(681\) 1.68954 + 9.58186i 0.0647433 + 0.367178i
\(682\) 0 0
\(683\) 29.5117 1.12923 0.564616 0.825354i \(-0.309024\pi\)
0.564616 + 0.825354i \(0.309024\pi\)
\(684\) 0 0
\(685\) −34.6023 −1.32208
\(686\) 0 0
\(687\) 1.71348 + 9.71762i 0.0653733 + 0.370750i
\(688\) 0 0
\(689\) 29.5219 24.7718i 1.12469 0.943730i
\(690\) 0 0
\(691\) −2.23917 + 3.87836i −0.0851820 + 0.147540i −0.905469 0.424413i \(-0.860481\pi\)
0.820287 + 0.571953i \(0.193814\pi\)
\(692\) 0 0
\(693\) 9.41787 3.42782i 0.357755 0.130212i
\(694\) 0 0
\(695\) −17.3195 29.9983i −0.656968 1.13790i
\(696\) 0 0
\(697\) 7.26786 41.2181i 0.275290 1.56125i
\(698\) 0 0
\(699\) −16.7121 14.0231i −0.632111 0.530404i
\(700\) 0 0
\(701\) −5.55690 2.02255i −0.209881 0.0763906i 0.234940 0.972010i \(-0.424511\pi\)
−0.444821 + 0.895619i \(0.646733\pi\)
\(702\) 0 0
\(703\) −9.14038 + 0.853427i −0.344736 + 0.0321876i
\(704\) 0 0
\(705\) 11.0706 + 4.02936i 0.416942 + 0.151754i
\(706\) 0 0
\(707\) −26.5933 22.3145i −1.00015 0.839221i
\(708\) 0 0
\(709\) 5.19830 29.4810i 0.195226 1.10718i −0.716870 0.697207i \(-0.754426\pi\)
0.912096 0.409976i \(-0.134463\pi\)
\(710\) 0 0
\(711\) −6.03209 10.4479i −0.226221 0.391826i
\(712\) 0 0
\(713\) 48.2105 17.5472i 1.80550 0.657148i
\(714\) 0 0
\(715\) −23.8469 + 41.3040i −0.891823 + 1.54468i
\(716\) 0 0
\(717\) 16.3255 13.6987i 0.609686 0.511587i
\(718\) 0 0
\(719\) −8.29709 47.0552i −0.309429 1.75486i −0.601886 0.798582i \(-0.705584\pi\)
0.292456 0.956279i \(-0.405527\pi\)
\(720\) 0 0
\(721\) −19.1310 −0.712477
\(722\) 0 0
\(723\) −15.6459 −0.581877
\(724\) 0 0
\(725\) 1.74716 + 9.90863i 0.0648879 + 0.367997i
\(726\) 0 0
\(727\) 32.0933 26.9295i 1.19028 0.998760i 0.190421 0.981702i \(-0.439015\pi\)
0.999855 0.0170574i \(-0.00542981\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) 52.3303 19.0467i 1.93551 0.704466i
\(732\) 0 0
\(733\) −10.8068 18.7178i −0.399156 0.691359i 0.594466 0.804121i \(-0.297364\pi\)
−0.993622 + 0.112762i \(0.964030\pi\)
\(734\) 0 0
\(735\) −1.50000 + 8.50692i −0.0553283 + 0.313783i
\(736\) 0 0
\(737\) −3.10607 2.60630i −0.114413 0.0960043i
\(738\) 0 0
\(739\) 30.4688 + 11.0898i 1.12081 + 0.407943i 0.834949 0.550327i \(-0.185497\pi\)
0.285865 + 0.958270i \(0.407719\pi\)
\(740\) 0 0
\(741\) −26.3187 + 2.45734i −0.966840 + 0.0902728i
\(742\) 0 0
\(743\) −25.2754 9.19951i −0.927266 0.337497i −0.166141 0.986102i \(-0.553131\pi\)
−0.761125 + 0.648605i \(0.775353\pi\)
\(744\) 0 0
\(745\) 46.0565 + 38.6460i 1.68738 + 1.41588i
\(746\) 0 0
\(747\) −0.0150147 + 0.0851529i −0.000549361 + 0.00311558i
\(748\) 0 0
\(749\) 4.16519 + 7.21432i 0.152193 + 0.263606i
\(750\) 0 0
\(751\) −5.38103 + 1.95854i −0.196357 + 0.0714680i −0.438327 0.898816i \(-0.644429\pi\)
0.241970 + 0.970284i \(0.422206\pi\)
\(752\) 0 0
\(753\) 5.06077 8.76552i 0.184425 0.319433i
\(754\) 0 0
\(755\) −16.1682 + 13.5667i −0.588421 + 0.493743i
\(756\) 0 0
\(757\) 1.50269 + 8.52217i 0.0546161 + 0.309744i 0.999862 0.0166157i \(-0.00528920\pi\)
−0.945246 + 0.326359i \(0.894178\pi\)
\(758\) 0 0
\(759\) 20.8631 0.757282
\(760\) 0 0
\(761\) −37.7279 −1.36764 −0.683818 0.729653i \(-0.739682\pi\)
−0.683818 + 0.729653i \(0.739682\pi\)
\(762\) 0 0
\(763\) 2.67886 + 15.1926i 0.0969813 + 0.550009i
\(764\) 0 0
\(765\) −11.5287 + 9.67372i −0.416820 + 0.349754i
\(766\) 0 0
\(767\) 0.814330 1.41046i 0.0294038 0.0509288i
\(768\) 0 0
\(769\) −34.5724 + 12.5833i −1.24671 + 0.453766i −0.879289 0.476288i \(-0.841982\pi\)
−0.367423 + 0.930054i \(0.619760\pi\)
\(770\) 0 0
\(771\) −2.38919 4.13819i −0.0860444 0.149033i
\(772\) 0 0
\(773\) 3.46750 19.6652i 0.124717 0.707307i −0.856758 0.515719i \(-0.827525\pi\)
0.981475 0.191588i \(-0.0613639\pi\)
\(774\) 0 0
\(775\) −8.25877 6.92993i −0.296664 0.248930i
\(776\) 0 0
\(777\) 6.38578 + 2.32423i 0.229089 + 0.0833814i
\(778\) 0 0
\(779\) 8.11721 + 29.6021i 0.290829 + 1.06061i
\(780\) 0 0
\(781\) 24.1565 + 8.79224i 0.864386 + 0.314611i
\(782\) 0 0
\(783\) −5.46064 4.58202i −0.195147 0.163748i
\(784\) 0 0
\(785\) 9.53936 54.1004i 0.340474 1.93093i
\(786\) 0 0
\(787\) 4.18392 + 7.24675i 0.149140 + 0.258319i 0.930910 0.365249i \(-0.119016\pi\)
−0.781770 + 0.623567i \(0.785683\pi\)
\(788\) 0 0
\(789\) 20.3824 7.41858i 0.725632 0.264108i
\(790\) 0 0
\(791\) −26.8871 + 46.5699i −0.955996 + 1.65583i
\(792\) 0 0
\(793\) −7.37939 + 6.19204i −0.262050 + 0.219886i
\(794\) 0 </