Properties

Label 912.2.bo.e.385.1
Level $912$
Weight $2$
Character 912.385
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
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 385.1
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 912.385
Dual form 912.2.bo.e.289.1

$q$-expansion

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

Character values

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

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\) \(1\) \(1\)

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 0.963561 0.267489i \(-0.0861937\pi\)
−0.0961041 + 0.995371i \(0.530638\pi\)
\(6\) 0 0
\(7\) −1.61334 2.79439i −0.609786 1.05618i −0.991275 0.131806i \(-0.957922\pi\)
0.381490 0.924373i \(-0.375411\pi\)
\(8\) 0 0
\(9\) −0.939693 0.342020i −0.313231 0.114007i
\(10\) 0 0
\(11\) 1.55303 2.68993i 0.468257 0.811045i −0.531085 0.847319i \(-0.678215\pi\)
0.999342 + 0.0362735i \(0.0115487\pi\)
\(12\) 0 0
\(13\) −1.05303 5.97205i −0.292059 1.65635i −0.678921 0.734211i \(-0.737552\pi\)
0.386862 0.922137i \(-0.373559\pi\)
\(14\) 0 0
\(15\) −1.93969 + 1.62760i −0.500826 + 0.420243i
\(16\) 0 0
\(17\) 5.58512 2.03282i 1.35459 0.493031i 0.440213 0.897893i \(-0.354903\pi\)
0.914378 + 0.404862i \(0.132681\pi\)
\(18\) 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 0.0775845 0.996986i \(-0.475279\pi\)
0.995312 + 0.0967189i \(0.0308348\pi\)
\(24\) 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 −0.365546 0.930793i \(-0.619118\pi\)
−0.878327 + 0.478060i \(0.841340\pi\)
\(30\) 0 0
\(31\) 3.81908 + 6.61484i 0.685927 + 1.18806i 0.973145 + 0.230195i \(0.0739363\pi\)
−0.287218 + 0.957865i \(0.592730\pi\)
\(32\) 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 0.727069 + 0.686564i \(0.240882\pi\)
−0.918041 + 0.396487i \(0.870229\pi\)
\(42\) 0 0
\(43\) 7.17752 + 6.02265i 1.09456 + 0.918446i 0.997047 0.0767882i \(-0.0244665\pi\)
0.0975139 + 0.995234i \(0.468911\pi\)
\(44\) 0 0
\(45\) −1.26604 2.19285i −0.188731 0.326891i
\(46\) 0 0
\(47\) −4.37211 1.59132i −0.637738 0.232118i 0.00285780 0.999996i \(-0.499090\pi\)
−0.640596 + 0.767878i \(0.721313\pi\)
\(48\) 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 −0.912682 0.408671i \(-0.865992\pi\)
0.243977 + 0.969781i \(0.421548\pi\)
\(54\) 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 −0.358396 0.933570i \(-0.616676\pi\)
0.325540 + 0.945528i \(0.394454\pi\)
\(60\) 0 0
\(61\) 1.21688 1.02108i 0.155806 0.130737i −0.561552 0.827441i \(-0.689796\pi\)
0.717358 + 0.696705i \(0.245351\pi\)
\(62\) 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 0.266000 0.963973i \(-0.414298\pi\)
−0.415863 + 0.909427i \(0.636520\pi\)
\(68\) 0 0
\(69\) 3.35844 + 5.81699i 0.404309 + 0.700283i
\(70\) 0 0
\(71\) 6.34002 + 5.31991i 0.752422 + 0.631357i 0.936142 0.351621i \(-0.114370\pi\)
−0.183720 + 0.982979i \(0.558814\pi\)
\(72\) 0 0
\(73\) 0.159978 0.907278i 0.0187240 0.106189i −0.974013 0.226490i \(-0.927275\pi\)
0.992737 + 0.120301i \(0.0383860\pi\)
\(74\) 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 −0.605443 0.795888i \(-0.707004\pi\)
0.841140 0.540817i \(-0.181885\pi\)
\(80\) 0 0
\(81\) 0.766044 + 0.642788i 0.0851160 + 0.0714208i
\(82\) 0 0
\(83\) 0.0432332 + 0.0748822i 0.00474546 + 0.00821939i 0.868388 0.495885i \(-0.165156\pi\)
−0.863643 + 0.504104i \(0.831823\pi\)
\(84\) 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 −0.978102 0.208127i \(-0.933263\pi\)
0.847931 0.530106i \(-0.177848\pi\)
\(90\) 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 −0.495854 0.868406i \(-0.665145\pi\)
0.178354 + 0.983966i \(0.442923\pi\)
\(98\) 0 0
\(99\) −2.37939 + 1.99654i −0.239137 + 0.200660i
\(100\) 0 0
\(101\) −1.86824 10.5953i −0.185897 1.05427i −0.924798 0.380459i \(-0.875766\pi\)
0.738901 0.673814i \(-0.235345\pi\)
\(102\) 0 0
\(103\) 2.96451 5.13468i 0.292102 0.505935i −0.682205 0.731161i \(-0.738979\pi\)
0.974306 + 0.225226i \(0.0723121\pi\)
\(104\) 0 0
\(105\) 7.67752 + 2.79439i 0.749249 + 0.272704i
\(106\) 0 0
\(107\) 1.29086 + 2.23583i 0.124792 + 0.216146i 0.921652 0.388018i \(-0.126840\pi\)
−0.796860 + 0.604165i \(0.793507\pi\)
\(108\) 0 0
\(109\) 3.66250 + 3.07321i 0.350804 + 0.294360i 0.801113 0.598513i \(-0.204242\pi\)
−0.450309 + 0.892873i \(0.648686\pi\)
\(110\) 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 −0.998252 0.0591064i \(-0.981175\pi\)
0.917834 0.396964i \(-0.129936\pi\)
\(128\) 0 0
\(129\) −7.17752 + 6.02265i −0.631945 + 0.530265i
\(130\) 0 0
\(131\) −8.13563 + 2.96113i −0.710813 + 0.258715i −0.672021 0.740532i \(-0.734573\pi\)
−0.0387926 + 0.999247i \(0.512351\pi\)
\(132\) 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 −0.969083 0.246737i \(-0.920642\pi\)
0.0747087 + 0.997205i \(0.476197\pi\)
\(138\) 0 0
\(139\) 2.37551 + 13.4722i 0.201489 + 1.14270i 0.902870 + 0.429913i \(0.141456\pi\)
−0.701382 + 0.712786i \(0.747433\pi\)
\(140\) 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 −0.0600574 0.998195i \(-0.519128\pi\)
0.397838 0.917456i \(-0.369761\pi\)
\(150\) 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 0.984905 + 0.173098i \(0.0553776\pi\)
0.341495 + 0.939884i \(0.389067\pi\)
\(158\) 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 −0.0729198 + 0.997338i \(0.523232\pi\)
−0.827260 + 0.561819i \(0.810102\pi\)
\(164\) 0 0
\(165\) 1.36571 + 7.74535i 0.106321 + 0.602975i
\(166\) 0 0
\(167\) 5.85710 4.91469i 0.453236 0.380310i −0.387399 0.921912i \(-0.626626\pi\)
0.840635 + 0.541602i \(0.182182\pi\)
\(168\) 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 −0.725567 0.688151i \(-0.758422\pi\)
−0.113481 + 0.993540i \(0.536200\pi\)
\(174\) 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 −0.933739 0.357955i \(-0.883474\pi\)
0.776868 + 0.629664i \(0.216807\pi\)
\(180\) 0 0
\(181\) −11.5842 4.21632i −0.861050 0.313397i −0.126513 0.991965i \(-0.540379\pi\)
−0.734537 + 0.678568i \(0.762601\pi\)
\(182\) 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 0.479050 + 0.877788i \(0.340981\pi\)
−0.750381 + 0.661006i \(0.770130\pi\)
\(194\) 0 0
\(195\) 11.7626 + 9.87003i 0.842340 + 0.706807i
\(196\) 0 0
\(197\) 8.34255 + 14.4497i 0.594382 + 1.02950i 0.993634 + 0.112658i \(0.0359366\pi\)
−0.399252 + 0.916841i \(0.630730\pi\)
\(198\) 0 0
\(199\) −2.31180 0.841428i −0.163879 0.0596472i 0.258778 0.965937i \(-0.416680\pi\)
−0.422657 + 0.906290i \(0.638903\pi\)
\(200\) 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 −0.381554 0.924347i \(-0.624611\pi\)
0.301871 + 0.953349i \(0.402389\pi\)
\(212\) 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 0.458252 0.888822i \(-0.348476\pi\)
−0.795744 + 0.605633i \(0.792920\pi\)
\(224\) 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 0.997068 0.0765212i \(-0.0243813\pi\)
0.0977803 + 0.995208i \(0.468826\pi\)
\(234\) 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 −0.282818 0.959174i \(-0.591269\pi\)
0.972078 0.234659i \(-0.0753974\pi\)
\(240\) 0 0
\(241\) 2.71688 + 15.4082i 0.175010 + 0.992529i 0.938133 + 0.346276i \(0.112554\pi\)
−0.763123 + 0.646253i \(0.776335\pi\)
\(242\) 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 −0.364411 0.931238i \(-0.618730\pi\)
0.853811 + 0.520583i \(0.174285\pi\)
\(252\) 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 0.478246 0.878226i \(-0.341273\pi\)
−0.198155 + 0.980171i \(0.563495\pi\)
\(258\) 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 −0.616069 0.787692i \(-0.711276\pi\)
0.848322 0.529480i \(-0.177613\pi\)
\(264\) 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 −0.997125 0.0757790i \(-0.975856\pi\)
0.962909 + 0.269828i \(0.0869668\pi\)
\(270\) 0 0
\(271\) 8.97952 + 7.53471i 0.545467 + 0.457701i 0.873403 0.486999i \(-0.161908\pi\)
−0.327935 + 0.944700i \(0.606353\pi\)
\(272\) 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 −0.967188 0.254063i \(-0.918233\pi\)
0.703619 + 0.710578i \(0.251566\pi\)
\(278\) 0 0
\(279\) −1.32635 7.52211i −0.0794066 0.450337i
\(280\) 0 0
\(281\) 19.4702 16.3374i 1.16149 0.974609i 0.161569 0.986861i \(-0.448345\pi\)
0.999925 + 0.0122521i \(0.00390007\pi\)
\(282\) 0 0
\(283\) −2.51114 + 0.913982i −0.149272 + 0.0543306i −0.415576 0.909559i \(-0.636420\pi\)
0.266304 + 0.963889i \(0.414198\pi\)
\(284\) 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 0.412287 + 0.911054i \(0.364730\pi\)
−0.995139 + 0.0984765i \(0.968603\pi\)
\(294\) 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 −0.599247 0.800564i \(-0.704533\pi\)
0.836917 0.547330i \(-0.184356\pi\)
\(308\) 0 0
\(309\) 4.54189 + 3.81110i 0.258379 + 0.216806i
\(310\) 0 0
\(311\) −0.0812519 0.140732i −0.00460737 0.00798020i 0.863713 0.503985i \(-0.168133\pi\)
−0.868320 + 0.496005i \(0.834800\pi\)
\(312\) 0 0
\(313\) −6.31655 2.29904i −0.357033 0.129949i 0.157275 0.987555i \(-0.449729\pi\)
−0.514308 + 0.857606i \(0.671951\pi\)
\(314\) 0 0
\(315\) −4.08512 + 7.07564i −0.230171 + 0.398667i
\(316\) 0 0
\(317\) 2.48024 + 14.0661i 0.139304 + 0.790032i 0.971765 + 0.235949i \(0.0758199\pi\)
−0.832461 + 0.554083i \(0.813069\pi\)
\(318\) 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 −0.108940 + 0.994048i \(0.534746\pi\)
−0.806401 + 0.591369i \(0.798588\pi\)
\(332\) 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 0.603386 0.797450i \(-0.293818\pi\)
−0.680558 + 0.732695i \(0.738262\pi\)
\(338\) 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 0.773525 0.633765i \(-0.218491\pi\)
−0.489816 + 0.871826i \(0.662936\pi\)
\(348\) 0 0
\(349\) 5.61081 + 9.71822i 0.300340 + 0.520204i 0.976213 0.216814i \(-0.0695665\pi\)
−0.675873 + 0.737018i \(0.736233\pi\)
\(350\) 0 0
\(351\) −5.69846 2.07407i −0.304161 0.110706i
\(352\) 0 0
\(353\) 0.954241 1.65279i 0.0507891 0.0879693i −0.839513 0.543339i \(-0.817160\pi\)
0.890302 + 0.455370i \(0.150493\pi\)
\(354\) 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 −0.0946982 0.995506i \(-0.530189\pi\)
0.567356 + 0.823473i \(0.307966\pi\)
\(360\) 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 −0.951651 0.307180i \(-0.900615\pi\)
0.789198 0.614139i \(-0.210496\pi\)
\(368\) 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 0.926697 + 0.375809i \(0.122635\pi\)
−0.137889 + 0.990448i \(0.544032\pi\)
\(374\) 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 0.694627 + 0.719370i \(0.255569\pi\)
−0.898775 + 0.438410i \(0.855542\pi\)
\(384\) 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 −0.403642 0.914917i \(-0.632256\pi\)
−0.897305 + 0.441411i \(0.854478\pi\)
\(390\) 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 −0.199569 0.979884i \(-0.563954\pi\)
0.476978 + 0.878915i \(0.341732\pi\)
\(398\) 0 0
\(399\) −13.6065 + 3.56093i −0.681179 + 0.178270i
\(400\) 0 0
\(401\) 4.02987 1.46675i 0.201242 0.0732461i −0.239433 0.970913i \(-0.576961\pi\)
0.440675 + 0.897667i \(0.354739\pi\)
\(402\) 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 0.957788 0.287474i \(-0.0928155\pi\)
0.548924 + 0.835872i \(0.315038\pi\)
\(410\) 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 −0.736142 0.676827i \(-0.763355\pi\)
0.923236 0.384234i \(-0.125534\pi\)
\(422\) 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 0.886387 + 0.462946i \(0.153208\pi\)
−0.674594 + 0.738189i \(0.735681\pi\)
\(432\) 0 0
\(433\) 9.81702 8.23746i 0.471776 0.395867i −0.375666 0.926755i \(-0.622586\pi\)
0.847442 + 0.530888i \(0.178142\pi\)
\(434\) 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 −0.456498 0.889725i \(-0.650896\pi\)
0.222206 + 0.975000i \(0.428674\pi\)
\(440\) 0 0
\(441\) 2.61334 2.19285i 0.124445 0.104422i
\(442\) 0 0
\(443\) 3.02141 + 17.1353i 0.143552 + 0.814121i 0.968519 + 0.248941i \(0.0800825\pi\)
−0.824967 + 0.565181i \(0.808806\pi\)
\(444\) 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 −0.997657 0.0684163i \(-0.978205\pi\)
0.439578 0.898204i \(-0.355128\pi\)
\(450\) 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 0.758680 0.651464i \(-0.225845\pi\)
−0.509823 + 0.860279i \(0.670289\pi\)
\(462\) 0 0
\(463\) 14.0385 + 24.3154i 0.652424 + 1.13003i 0.982533 + 0.186088i \(0.0595811\pi\)
−0.330109 + 0.943943i \(0.607086\pi\)
\(464\) 0 0
\(465\) −18.1741 6.61484i −0.842804 0.306756i
\(466\) 0 0
\(467\) 1.91147 3.31077i 0.0884525 0.153204i −0.818405 0.574642i \(-0.805141\pi\)
0.906857 + 0.421438i \(0.138475\pi\)
\(468\) 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 0.0867654 0.996229i \(-0.472347\pi\)
0.996160 + 0.0875461i \(0.0279025\pi\)
\(480\) 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 0.831745 0.555159i \(-0.187342\pi\)
−0.896654 + 0.442733i \(0.854009\pi\)
\(488\) 0 0
\(489\) −17.6079 14.7748i −0.796256 0.668138i
\(490\) 0 0
\(491\) 7.24985 41.1159i 0.327181 1.85554i −0.166702 0.986007i \(-0.553312\pi\)
0.493883 0.869529i \(-0.335577\pi\)
\(492\) 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 0.465395 0.885103i \(-0.345912\pi\)
−0.790841 + 0.612021i \(0.790357\pi\)
\(500\) 0 0
\(501\) 3.82295 + 6.62154i 0.170797 + 0.295829i
\(502\) 0 0
\(503\) −11.8785 4.32342i −0.529636 0.192772i 0.0633395 0.997992i \(-0.479825\pi\)
−0.592976 + 0.805220i \(0.702047\pi\)
\(504\) 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 −0.910679 0.413114i \(-0.864441\pi\)
0.248700 + 0.968581i \(0.419997\pi\)
\(510\) 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 −0.998004 0.0631531i \(-0.979884\pi\)
0.553694 + 0.832720i \(0.313218\pi\)
\(522\) 0 0
\(523\) 14.3461 + 5.22156i 0.627312 + 0.228323i 0.636061 0.771639i \(-0.280563\pi\)
−0.00874906 + 0.999962i \(0.502785\pi\)
\(524\) 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 0.723045 0.690801i \(-0.242742\pi\)
0.109847 + 0.993949i \(0.464964\pi\)
\(542\) 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 −0.0453408 0.998972i \(-0.514437\pi\)
0.975922 + 0.218122i \(0.0699929\pi\)
\(548\) 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 −0.728412 0.685139i \(-0.759741\pi\)
0.450152 0.892952i \(-0.351370\pi\)
\(558\) 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 0.949544 0.313634i \(-0.101547\pi\)
−0.746387 + 0.665512i \(0.768213\pi\)
\(564\) 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 0.518054 0.855348i \(-0.326657\pi\)
−0.999780 + 0.0209742i \(0.993323\pi\)
\(578\) 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 −0.685722 0.727863i \(-0.740514\pi\)
−0.0574324 + 0.998349i \(0.518291\pi\)
\(588\) 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 0.170269 0.985398i \(-0.445536\pi\)
0.999994 + 0.00342988i \(0.00109177\pi\)
\(594\) 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 0.858525 0.512772i \(-0.171381\pi\)
0.328065 + 0.944655i \(0.393603\pi\)
\(600\) 0 0
\(601\) 21.7802 + 37.7244i 0.888432 + 1.53881i 0.841729 + 0.539901i \(0.181538\pi\)
0.0467035 + 0.998909i \(0.485128\pi\)
\(602\) 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 0.735088 0.677972i \(-0.237141\pi\)
−0.540026 + 0.841649i \(0.681585\pi\)
\(614\) 0 0
\(615\) −8.91534 15.4418i −0.359501 0.622675i
\(616\) 0 0
\(617\) 36.1241 + 13.1481i 1.45430 + 0.529322i 0.943789 0.330549i \(-0.107234\pi\)
0.510512 + 0.859871i \(0.329456\pi\)
\(618\) 0 0
\(619\) −9.31908 + 16.1411i −0.374565 + 0.648766i −0.990262 0.139217i \(-0.955541\pi\)
0.615697 + 0.787983i \(0.288875\pi\)
\(620\) 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 −0.847295 0.531123i \(-0.821770\pi\)
0.375923 + 0.926651i \(0.377326\pi\)
\(632\) 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 0.180424 0.983589i \(-0.442253\pi\)
−0.937316 + 0.348481i \(0.886697\pi\)
\(642\) 0 0
\(643\) −3.96333 + 22.4771i −0.156298 + 0.886412i 0.801291 + 0.598275i \(0.204147\pi\)
−0.957589 + 0.288137i \(0.906964\pi\)
\(644\) 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 0.973137 0.230228i \(-0.0739473\pi\)
−0.685952 + 0.727647i \(0.740614\pi\)
\(654\) 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 0.966922 + 0.255073i \(0.0820995\pi\)
−0.821369 + 0.570397i \(0.806789\pi\)
\(660\) 0 0
\(661\) −24.0494 + 20.1798i −0.935413 + 0.784904i −0.976781 0.214240i \(-0.931273\pi\)
0.0413686 + 0.999144i \(0.486828\pi\)
\(662\) 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 −0.956315 0.292338i \(-0.905567\pi\)
0.731330 + 0.682024i \(0.238900\pi\)
\(674\) 0 0
\(675\) 1.32635 + 0.482753i 0.0510513 + 0.0185812i
\(676\) 0 0
\(677\) −20.6866 35.8302i −0.795051 1.37707i −0.922807 0.385263i \(-0.874111\pi\)
0.127756 0.991806i \(-0.459223\pi\)
\(678\) 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 0.820287 0.571953i \(-0.193814\pi\)
−0.905469 + 0.424413i \(0.860481\pi\)
\(692\) 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 −0.444821 0.895619i \(-0.646733\pi\)
0.234940 + 0.972010i \(0.424511\pi\)
\(702\) 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 0.912096 + 0.409976i \(0.134463\pi\)
−0.716870 + 0.697207i \(0.754426\pi\)
\(710\) 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 0.292456 + 0.956279i \(0.405527\pi\)
−0.601886 + 0.798582i \(0.705584\pi\)
\(720\) 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 0.999855 + 0.0170574i \(0.00542981\pi\)
0.190421 + 0.981702i \(0.439015\pi\)
\(728\) 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 −0.993622 0.112762i \(-0.964030\pi\)
0.594466 + 0.804121i \(0.297364\pi\)
\(734\) 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 0.285865 0.958270i \(-0.407719\pi\)
0.834949 + 0.550327i \(0.185497\pi\)
\(740\) 0 0
\(741\) −26.3187 2.45734i −0.966840 0.0902728i
\(742\) 0 0
\(743\) −25.2754 + 9.19951i −0.927266 + 0.337497i −0.761125 0.648605i \(-0.775353\pi\)
−0.166141 + 0.986102i \(0.553131\pi\)
\(744\) 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 0.241970 0.970284i \(-0.422206\pi\)
−0.438327 + 0.898816i \(0.644429\pi\)
\(752\) 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 −0.945246 0.326359i \(-0.894178\pi\)
0.999862 + 0.0166157i \(0.00528920\pi\)
\(758\) 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 −0.367423 0.930054i \(-0.619760\pi\)
−0.879289 + 0.476288i \(0.841982\pi\)
\(770\) 0 0
\(771\) −2.38919 + 4.13819i −0.0860444 + 0.149033i
\(772\) 0 0
\(773\) 3.46750 + 19.6652i 0.124717 + 0.707307i 0.981475 + 0.191588i \(0.0613639\pi\)
−0.856758 + 0.515719i \(0.827525\pi\)
\(774\) 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 −0.781770 0.623567i \(-0.785683\pi\)
0.930910 + 0.365249i \(0.119016\pi\)
\(788\) 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