Properties

Label 1512.2.s.o.865.3
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 3 x^{7} + 4 x^{6} + 28 x^{5} + 14 x^{4} - 52 x^{3} + 306 x^{2} + 1052 x + 1051\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.3
Root \(2.45973 - 2.20662i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.o.1297.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.26913 + 2.19820i) q^{5} +(2.64086 + 0.160857i) q^{7} +O(q^{10})\) \(q+(1.26913 + 2.19820i) q^{5} +(2.64086 + 0.160857i) q^{7} +(1.19060 - 2.06219i) q^{11} -0.461738 q^{13} +(3.64086 - 6.30615i) q^{17} +(4.32198 + 7.48589i) q^{19} +(-1.49052 - 2.58165i) q^{23} +(-0.721387 + 1.24948i) q^{25} -3.55723 q^{29} +(4.15034 - 7.18860i) q^{31} +(2.99800 + 6.00928i) q^{35} +(1.10259 + 1.90975i) q^{37} -6.81998 q^{41} +2.38121 q^{43} +(4.21938 + 7.30819i) q^{47} +(6.94825 + 0.849602i) q^{49} +(0.181122 - 0.313712i) q^{53} +6.04413 q^{55} +(-3.73397 + 6.46743i) q^{59} +(-3.08801 - 5.34859i) q^{61} +(-0.586006 - 1.01499i) q^{65} +(-5.87173 + 10.1701i) q^{67} -9.72048 q^{71} +(-4.67912 + 8.10447i) q^{73} +(3.47593 - 5.25442i) q^{77} +(4.97903 + 8.62394i) q^{79} +3.20118 q^{83} +18.4829 q^{85} +(-3.29320 - 5.70399i) q^{89} +(-1.21938 - 0.0742739i) q^{91} +(-10.9703 + 19.0011i) q^{95} +15.6400 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 8q + 2q^{5} - 4q^{7} + q^{11} - 20q^{13} + 4q^{17} + q^{19} - 12q^{23} - 14q^{25} - 12q^{29} + 8q^{31} - 9q^{35} + 12q^{41} + 2q^{43} + 9q^{47} + 6q^{49} - 7q^{53} - 36q^{55} + 4q^{59} - 25q^{61} + 28q^{65} - 30q^{67} + 22q^{71} + 4q^{73} + 37q^{77} + 7q^{79} - 58q^{83} + 14q^{85} - 9q^{89} + 15q^{91} + 4q^{95} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.26913 + 2.19820i 0.567573 + 0.983065i 0.996805 + 0.0798707i \(0.0254507\pi\)
−0.429233 + 0.903194i \(0.641216\pi\)
\(6\) 0 0
\(7\) 2.64086 + 0.160857i 0.998150 + 0.0607983i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.19060 2.06219i 0.358981 0.621773i −0.628810 0.777559i \(-0.716458\pi\)
0.987791 + 0.155786i \(0.0497911\pi\)
\(12\) 0 0
\(13\) −0.461738 −0.128063 −0.0640315 0.997948i \(-0.520396\pi\)
−0.0640315 + 0.997948i \(0.520396\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.64086 6.30615i 0.883037 1.52947i 0.0350909 0.999384i \(-0.488828\pi\)
0.847947 0.530082i \(-0.177839\pi\)
\(18\) 0 0
\(19\) 4.32198 + 7.48589i 0.991530 + 1.71738i 0.608243 + 0.793751i \(0.291875\pi\)
0.383287 + 0.923629i \(0.374792\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.49052 2.58165i −0.310794 0.538312i 0.667740 0.744394i \(-0.267262\pi\)
−0.978535 + 0.206083i \(0.933928\pi\)
\(24\) 0 0
\(25\) −0.721387 + 1.24948i −0.144277 + 0.249896i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.55723 −0.660560 −0.330280 0.943883i \(-0.607143\pi\)
−0.330280 + 0.943883i \(0.607143\pi\)
\(30\) 0 0
\(31\) 4.15034 7.18860i 0.745423 1.29111i −0.204574 0.978851i \(-0.565581\pi\)
0.949997 0.312259i \(-0.101086\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.99800 + 6.00928i 0.506754 + 1.01575i
\(36\) 0 0
\(37\) 1.10259 + 1.90975i 0.181265 + 0.313961i 0.942312 0.334737i \(-0.108647\pi\)
−0.761046 + 0.648698i \(0.775314\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.81998 −1.06510 −0.532551 0.846398i \(-0.678766\pi\)
−0.532551 + 0.846398i \(0.678766\pi\)
\(42\) 0 0
\(43\) 2.38121 0.363131 0.181565 0.983379i \(-0.441884\pi\)
0.181565 + 0.983379i \(0.441884\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.21938 + 7.30819i 0.615460 + 1.06601i 0.990304 + 0.138920i \(0.0443632\pi\)
−0.374843 + 0.927088i \(0.622303\pi\)
\(48\) 0 0
\(49\) 6.94825 + 0.849602i 0.992607 + 0.121372i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.181122 0.313712i 0.0248790 0.0430917i −0.853318 0.521391i \(-0.825413\pi\)
0.878197 + 0.478299i \(0.158747\pi\)
\(54\) 0 0
\(55\) 6.04413 0.814990
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.73397 + 6.46743i −0.486121 + 0.841987i −0.999873 0.0159521i \(-0.994922\pi\)
0.513751 + 0.857939i \(0.328255\pi\)
\(60\) 0 0
\(61\) −3.08801 5.34859i −0.395379 0.684817i 0.597770 0.801667i \(-0.296053\pi\)
−0.993149 + 0.116851i \(0.962720\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.586006 1.01499i −0.0726851 0.125894i
\(66\) 0 0
\(67\) −5.87173 + 10.1701i −0.717345 + 1.24248i 0.244702 + 0.969598i \(0.421310\pi\)
−0.962048 + 0.272881i \(0.912024\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9.72048 −1.15361 −0.576804 0.816882i \(-0.695701\pi\)
−0.576804 + 0.816882i \(0.695701\pi\)
\(72\) 0 0
\(73\) −4.67912 + 8.10447i −0.547649 + 0.948557i 0.450786 + 0.892632i \(0.351144\pi\)
−0.998435 + 0.0559244i \(0.982189\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.47593 5.25442i 0.396119 0.598797i
\(78\) 0 0
\(79\) 4.97903 + 8.62394i 0.560185 + 0.970269i 0.997480 + 0.0709506i \(0.0226033\pi\)
−0.437295 + 0.899318i \(0.644063\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.20118 0.351376 0.175688 0.984446i \(-0.443785\pi\)
0.175688 + 0.984446i \(0.443785\pi\)
\(84\) 0 0
\(85\) 18.4829 2.00475
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.29320 5.70399i −0.349078 0.604621i 0.637008 0.770858i \(-0.280172\pi\)
−0.986086 + 0.166236i \(0.946839\pi\)
\(90\) 0 0
\(91\) −1.21938 0.0742739i −0.127826 0.00778602i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −10.9703 + 19.0011i −1.12553 + 1.94948i
\(96\) 0 0
\(97\) 15.6400 1.58800 0.793998 0.607920i \(-0.207996\pi\)
0.793998 + 0.607920i \(0.207996\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.08911 15.7428i 0.904400 1.56647i 0.0826792 0.996576i \(-0.473652\pi\)
0.821721 0.569890i \(-0.193014\pi\)
\(102\) 0 0
\(103\) −3.91199 6.77577i −0.385460 0.667636i 0.606373 0.795180i \(-0.292624\pi\)
−0.991833 + 0.127544i \(0.959291\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.27223 + 7.39972i 0.413012 + 0.715358i 0.995218 0.0976837i \(-0.0311433\pi\)
−0.582205 + 0.813042i \(0.697810\pi\)
\(108\) 0 0
\(109\) 3.28171 5.68409i 0.314331 0.544438i −0.664964 0.746875i \(-0.731553\pi\)
0.979295 + 0.202438i \(0.0648864\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −15.9770 −1.50299 −0.751496 0.659737i \(-0.770668\pi\)
−0.751496 + 0.659737i \(0.770668\pi\)
\(114\) 0 0
\(115\) 3.78333 6.55291i 0.352797 0.611062i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 10.6294 16.0680i 0.974393 1.47295i
\(120\) 0 0
\(121\) 2.66492 + 4.61578i 0.242266 + 0.419617i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.02917 0.807594
\(126\) 0 0
\(127\) 19.9730 1.77232 0.886160 0.463380i \(-0.153364\pi\)
0.886160 + 0.463380i \(0.153364\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.73634 + 15.1318i 0.763298 + 1.32207i 0.941142 + 0.338012i \(0.109755\pi\)
−0.177844 + 0.984059i \(0.556912\pi\)
\(132\) 0 0
\(133\) 10.2096 + 20.4644i 0.885282 + 1.77449i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.74345 6.48385i 0.319825 0.553953i −0.660627 0.750715i \(-0.729709\pi\)
0.980451 + 0.196762i \(0.0630427\pi\)
\(138\) 0 0
\(139\) −13.3772 −1.13464 −0.567320 0.823498i \(-0.692020\pi\)
−0.567320 + 0.823498i \(0.692020\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.549747 + 0.952190i −0.0459722 + 0.0796261i
\(144\) 0 0
\(145\) −4.51459 7.81949i −0.374916 0.649373i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.19571 5.53513i −0.261803 0.453455i 0.704918 0.709288i \(-0.250984\pi\)
−0.966721 + 0.255833i \(0.917650\pi\)
\(150\) 0 0
\(151\) −2.89741 + 5.01845i −0.235787 + 0.408396i −0.959501 0.281704i \(-0.909100\pi\)
0.723714 + 0.690100i \(0.242434\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 21.0693 1.69233
\(156\) 0 0
\(157\) −1.83818 + 3.18381i −0.146702 + 0.254096i −0.930007 0.367542i \(-0.880199\pi\)
0.783304 + 0.621638i \(0.213533\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.52097 7.05754i −0.277491 0.556212i
\(162\) 0 0
\(163\) −4.42147 7.65822i −0.346316 0.599838i 0.639276 0.768978i \(-0.279234\pi\)
−0.985592 + 0.169140i \(0.945901\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.91071 −0.612149 −0.306075 0.952008i \(-0.599016\pi\)
−0.306075 + 0.952008i \(0.599016\pi\)
\(168\) 0 0
\(169\) −12.7868 −0.983600
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −5.52206 9.56450i −0.419835 0.727175i 0.576088 0.817388i \(-0.304579\pi\)
−0.995923 + 0.0902127i \(0.971245\pi\)
\(174\) 0 0
\(175\) −2.10607 + 3.18365i −0.159204 + 0.240662i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.28809 2.23105i 0.0962767 0.166756i −0.813864 0.581055i \(-0.802640\pi\)
0.910141 + 0.414299i \(0.135973\pi\)
\(180\) 0 0
\(181\) −20.8641 −1.55082 −0.775408 0.631460i \(-0.782456\pi\)
−0.775408 + 0.631460i \(0.782456\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.79867 + 4.84745i −0.205763 + 0.356391i
\(186\) 0 0
\(187\) −8.66964 15.0163i −0.633987 1.09810i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.19060 3.79424i −0.158507 0.274541i 0.775824 0.630950i \(-0.217335\pi\)
−0.934330 + 0.356408i \(0.884001\pi\)
\(192\) 0 0
\(193\) −7.40999 + 12.8345i −0.533383 + 0.923846i 0.465857 + 0.884860i \(0.345746\pi\)
−0.999240 + 0.0389858i \(0.987587\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.18623 0.440750 0.220375 0.975415i \(-0.429272\pi\)
0.220375 + 0.975415i \(0.429272\pi\)
\(198\) 0 0
\(199\) 2.41947 4.19064i 0.171512 0.297067i −0.767437 0.641125i \(-0.778468\pi\)
0.938949 + 0.344058i \(0.111802\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −9.39412 0.572206i −0.659338 0.0401610i
\(204\) 0 0
\(205\) −8.65544 14.9917i −0.604522 1.04706i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 20.5831 1.42376
\(210\) 0 0
\(211\) 10.7183 0.737877 0.368939 0.929454i \(-0.379721\pi\)
0.368939 + 0.929454i \(0.379721\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.02206 + 5.23437i 0.206103 + 0.356981i
\(216\) 0 0
\(217\) 12.1168 18.3164i 0.822541 1.24340i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.68112 + 2.91179i −0.113084 + 0.195868i
\(222\) 0 0
\(223\) −21.2398 −1.42232 −0.711160 0.703030i \(-0.751830\pi\)
−0.711160 + 0.703030i \(0.751830\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.45226 + 5.97948i −0.229134 + 0.396872i −0.957552 0.288261i \(-0.906923\pi\)
0.728418 + 0.685134i \(0.240256\pi\)
\(228\) 0 0
\(229\) −0.392301 0.679486i −0.0259240 0.0449017i 0.852772 0.522283i \(-0.174919\pi\)
−0.878696 + 0.477381i \(0.841586\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.73197 6.46396i −0.244489 0.423468i 0.717499 0.696560i \(-0.245287\pi\)
−0.961988 + 0.273092i \(0.911954\pi\)
\(234\) 0 0
\(235\) −10.7099 + 18.5501i −0.698637 + 1.21007i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −15.0314 −0.972298 −0.486149 0.873876i \(-0.661599\pi\)
−0.486149 + 0.873876i \(0.661599\pi\)
\(240\) 0 0
\(241\) 6.93877 12.0183i 0.446965 0.774167i −0.551221 0.834359i \(-0.685838\pi\)
0.998187 + 0.0601923i \(0.0191714\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.95064 + 16.3519i 0.444060 + 1.04468i
\(246\) 0 0
\(247\) −1.99562 3.45652i −0.126978 0.219933i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3.38121 −0.213420 −0.106710 0.994290i \(-0.534032\pi\)
−0.106710 + 0.994290i \(0.534032\pi\)
\(252\) 0 0
\(253\) −7.09847 −0.446277
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.39269 + 5.87632i 0.211630 + 0.366555i 0.952225 0.305398i \(-0.0987894\pi\)
−0.740595 + 0.671952i \(0.765456\pi\)
\(258\) 0 0
\(259\) 2.60460 + 5.22074i 0.161842 + 0.324401i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.883211 + 1.52977i −0.0544611 + 0.0943294i −0.891971 0.452093i \(-0.850677\pi\)
0.837510 + 0.546423i \(0.184011\pi\)
\(264\) 0 0
\(265\) 0.919470 0.0564826
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.88431 + 17.1201i −0.602657 + 1.04383i 0.389760 + 0.920916i \(0.372558\pi\)
−0.992417 + 0.122916i \(0.960775\pi\)
\(270\) 0 0
\(271\) −5.38321 9.32399i −0.327007 0.566392i 0.654910 0.755707i \(-0.272707\pi\)
−0.981916 + 0.189315i \(0.939373\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.71777 + 2.97527i 0.103586 + 0.179415i
\(276\) 0 0
\(277\) −8.41476 + 14.5748i −0.505594 + 0.875714i 0.494385 + 0.869243i \(0.335393\pi\)
−0.999979 + 0.00647123i \(0.997940\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.08053 −0.482044 −0.241022 0.970520i \(-0.577483\pi\)
−0.241022 + 0.970520i \(0.577483\pi\)
\(282\) 0 0
\(283\) −0.217047 + 0.375936i −0.0129021 + 0.0223471i −0.872404 0.488785i \(-0.837440\pi\)
0.859502 + 0.511132i \(0.170774\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.0106 1.09704i −1.06313 0.0647564i
\(288\) 0 0
\(289\) −18.0117 31.1971i −1.05951 1.83513i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −29.1458 −1.70272 −0.851358 0.524584i \(-0.824221\pi\)
−0.851358 + 0.524584i \(0.824221\pi\)
\(294\) 0 0
\(295\) −18.9556 −1.10364
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.688229 + 1.19205i 0.0398013 + 0.0689379i
\(300\) 0 0
\(301\) 6.28843 + 0.383035i 0.362459 + 0.0220777i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.83818 13.5761i 0.448813 0.777366i
\(306\) 0 0
\(307\) −2.73324 −0.155994 −0.0779972 0.996954i \(-0.524853\pi\)
−0.0779972 + 0.996954i \(0.524853\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.423810 0.734061i 0.0240321 0.0416248i −0.853759 0.520668i \(-0.825683\pi\)
0.877791 + 0.479043i \(0.159016\pi\)
\(312\) 0 0
\(313\) −2.96174 5.12988i −0.167407 0.289958i 0.770100 0.637923i \(-0.220206\pi\)
−0.937508 + 0.347965i \(0.886873\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.15034 8.92065i −0.289272 0.501034i 0.684364 0.729140i \(-0.260080\pi\)
−0.973636 + 0.228107i \(0.926746\pi\)
\(318\) 0 0
\(319\) −4.23525 + 7.33566i −0.237128 + 0.410718i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 62.9428 3.50223
\(324\) 0 0
\(325\) 0.333092 0.576932i 0.0184766 0.0320024i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 9.96721 + 19.9786i 0.549510 + 1.10146i
\(330\) 0 0
\(331\) 7.41437 + 12.8421i 0.407530 + 0.705863i 0.994612 0.103664i \(-0.0330567\pi\)
−0.587082 + 0.809528i \(0.699723\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −29.8080 −1.62858
\(336\) 0 0
\(337\) −24.4701 −1.33297 −0.666487 0.745517i \(-0.732203\pi\)
−0.666487 + 0.745517i \(0.732203\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −9.88282 17.1175i −0.535185 0.926967i
\(342\) 0 0
\(343\) 18.2127 + 3.36135i 0.983392 + 0.181496i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.04975 + 7.01437i −0.217402 + 0.376551i −0.954013 0.299766i \(-0.903092\pi\)
0.736611 + 0.676317i \(0.236425\pi\)
\(348\) 0 0
\(349\) −9.77262 −0.523117 −0.261558 0.965188i \(-0.584236\pi\)
−0.261558 + 0.965188i \(0.584236\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 13.8247 23.9452i 0.735817 1.27447i −0.218547 0.975826i \(-0.570132\pi\)
0.954364 0.298646i \(-0.0965350\pi\)
\(354\) 0 0
\(355\) −12.3366 21.3676i −0.654757 1.13407i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.65854 13.2650i −0.404202 0.700099i 0.590026 0.807384i \(-0.299118\pi\)
−0.994228 + 0.107285i \(0.965784\pi\)
\(360\) 0 0
\(361\) −27.8590 + 48.2532i −1.46626 + 2.53964i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −23.7537 −1.24332
\(366\) 0 0
\(367\) 14.9503 25.8946i 0.780397 1.35169i −0.151314 0.988486i \(-0.548350\pi\)
0.931711 0.363201i \(-0.118316\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.528780 0.799335i 0.0274529 0.0414994i
\(372\) 0 0
\(373\) −6.83894 11.8454i −0.354107 0.613331i 0.632858 0.774268i \(-0.281882\pi\)
−0.986965 + 0.160937i \(0.948548\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.64251 0.0845934
\(378\) 0 0
\(379\) 35.6036 1.82883 0.914416 0.404776i \(-0.132651\pi\)
0.914416 + 0.404776i \(0.132651\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.62266 6.27463i −0.185109 0.320618i 0.758504 0.651668i \(-0.225931\pi\)
−0.943613 + 0.331050i \(0.892597\pi\)
\(384\) 0 0
\(385\) 15.9617 + 0.972242i 0.813483 + 0.0495501i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.11518 10.5918i 0.310052 0.537025i −0.668321 0.743873i \(-0.732987\pi\)
0.978373 + 0.206847i \(0.0663203\pi\)
\(390\) 0 0
\(391\) −21.7071 −1.09777
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −12.6381 + 21.8898i −0.635891 + 1.10140i
\(396\) 0 0
\(397\) −18.3826 31.8397i −0.922598 1.59799i −0.795379 0.606112i \(-0.792728\pi\)
−0.127219 0.991875i \(-0.540605\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 19.3870 + 33.5793i 0.968141 + 1.67687i 0.700927 + 0.713233i \(0.252770\pi\)
0.267215 + 0.963637i \(0.413897\pi\)
\(402\) 0 0
\(403\) −1.91637 + 3.31925i −0.0954611 + 0.165344i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.25101 0.260283
\(408\) 0 0
\(409\) 7.45973 12.9206i 0.368860 0.638885i −0.620527 0.784185i \(-0.713081\pi\)
0.989388 + 0.145300i \(0.0464148\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.9012 + 16.4789i −0.536414 + 0.810874i
\(414\) 0 0
\(415\) 4.06272 + 7.03684i 0.199431 + 0.345425i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 29.1418 1.42367 0.711835 0.702346i \(-0.247864\pi\)
0.711835 + 0.702346i \(0.247864\pi\)
\(420\) 0 0
\(421\) 12.7049 0.619197 0.309598 0.950867i \(-0.399805\pi\)
0.309598 + 0.950867i \(0.399805\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.25293 + 9.09835i 0.254805 + 0.441335i
\(426\) 0 0
\(427\) −7.29463 14.6216i −0.353012 0.707588i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 15.7466 27.2738i 0.758485 1.31373i −0.185138 0.982712i \(-0.559273\pi\)
0.943623 0.331022i \(-0.107393\pi\)
\(432\) 0 0
\(433\) −37.4599 −1.80021 −0.900105 0.435674i \(-0.856510\pi\)
−0.900105 + 0.435674i \(0.856510\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.8840 22.3157i 0.616324 1.06750i
\(438\) 0 0
\(439\) −11.4652 19.8583i −0.547205 0.947786i −0.998465 0.0553937i \(-0.982359\pi\)
0.451260 0.892393i \(-0.350975\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.6561 + 18.4570i 0.506289 + 0.876918i 0.999974 + 0.00727709i \(0.00231639\pi\)
−0.493685 + 0.869641i \(0.664350\pi\)
\(444\) 0 0
\(445\) 8.35900 14.4782i 0.396255 0.686333i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 11.5729 0.546157 0.273078 0.961992i \(-0.411958\pi\)
0.273078 + 0.961992i \(0.411958\pi\)
\(450\) 0 0
\(451\) −8.11989 + 14.0641i −0.382351 + 0.662251i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.38429 2.77471i −0.0648965 0.130081i
\(456\) 0 0
\(457\) 2.18422 + 3.78318i 0.102174 + 0.176970i 0.912580 0.408898i \(-0.134087\pi\)
−0.810406 + 0.585868i \(0.800754\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 23.7118 1.10437 0.552184 0.833722i \(-0.313794\pi\)
0.552184 + 0.833722i \(0.313794\pi\)
\(462\) 0 0
\(463\) −17.9888 −0.836009 −0.418004 0.908445i \(-0.637270\pi\)
−0.418004 + 0.908445i \(0.637270\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −19.0603 33.0135i −0.882007 1.52768i −0.849106 0.528222i \(-0.822859\pi\)
−0.0329003 0.999459i \(-0.510474\pi\)
\(468\) 0 0
\(469\) −17.1423 + 25.9133i −0.791559 + 1.19657i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.83508 4.91049i 0.130357 0.225785i
\(474\) 0 0
\(475\) −12.4713 −0.572221
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.5599 + 21.7544i −0.573878 + 0.993986i 0.422284 + 0.906463i \(0.361228\pi\)
−0.996163 + 0.0875226i \(0.972105\pi\)
\(480\) 0 0
\(481\) −0.509110 0.881804i −0.0232134 0.0402068i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 19.8491 + 34.3797i 0.901303 + 1.56110i
\(486\) 0 0
\(487\) −9.03388 + 15.6471i −0.409364 + 0.709040i −0.994819 0.101666i \(-0.967583\pi\)
0.585454 + 0.810705i \(0.300916\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.327654 −0.0147868 −0.00739341 0.999973i \(-0.502353\pi\)
−0.00739341 + 0.999973i \(0.502353\pi\)
\(492\) 0 0
\(493\) −12.9514 + 22.4324i −0.583299 + 1.01030i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −25.6704 1.56361i −1.15147 0.0701375i
\(498\) 0 0
\(499\) −15.8610 27.4721i −0.710036 1.22982i −0.964843 0.262827i \(-0.915345\pi\)
0.254807 0.966992i \(-0.417988\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −5.18155 −0.231034 −0.115517 0.993306i \(-0.536852\pi\)
−0.115517 + 0.993306i \(0.536852\pi\)
\(504\) 0 0
\(505\) 46.1411 2.05325
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11.6104 20.1098i −0.514622 0.891352i −0.999856 0.0169675i \(-0.994599\pi\)
0.485234 0.874384i \(-0.338735\pi\)
\(510\) 0 0
\(511\) −13.6605 + 20.6501i −0.604307 + 0.913506i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 9.92966 17.1987i 0.437553 0.757864i
\(516\) 0 0
\(517\) 20.0945 0.883753
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.26713 + 12.5870i −0.318379 + 0.551448i −0.980150 0.198258i \(-0.936472\pi\)
0.661771 + 0.749706i \(0.269805\pi\)
\(522\) 0 0
\(523\) −3.12827 5.41833i −0.136790 0.236927i 0.789490 0.613764i \(-0.210345\pi\)
−0.926280 + 0.376837i \(0.877012\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −30.2216 52.3453i −1.31647 2.28020i
\(528\) 0 0
\(529\) 7.05671 12.2226i 0.306814 0.531417i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.14904 0.136400
\(534\) 0 0
\(535\) −10.8440 + 18.7824i −0.468829 + 0.812035i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10.0247 13.3170i 0.431792 0.573606i
\(540\) 0 0
\(541\) 2.45463 + 4.25155i 0.105533 + 0.182788i 0.913956 0.405814i \(-0.133012\pi\)
−0.808423 + 0.588602i \(0.799679\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 16.6597 0.713623
\(546\) 0 0
\(547\) 8.88087 0.379719 0.189859 0.981811i \(-0.439197\pi\)
0.189859 + 0.981811i \(0.439197\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −15.3743 26.6290i −0.654965 1.13443i
\(552\) 0 0
\(553\) 11.7617 + 23.5755i 0.500158 + 1.00253i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.4047 + 28.4138i −0.695090 + 1.20393i 0.275061 + 0.961427i \(0.411302\pi\)
−0.970150 + 0.242504i \(0.922031\pi\)
\(558\) 0 0
\(559\) −1.09949 −0.0465036
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.56981 9.64719i 0.234739 0.406581i −0.724457 0.689319i \(-0.757910\pi\)
0.959197 + 0.282739i \(0.0912430\pi\)
\(564\) 0 0
\(565\) −20.2769 35.1207i −0.853057 1.47754i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.6416 + 18.4318i 0.446120 + 0.772702i 0.998129 0.0611354i \(-0.0194721\pi\)
−0.552010 + 0.833838i \(0.686139\pi\)
\(570\) 0 0
\(571\) 2.00310 3.46947i 0.0838272 0.145193i −0.821064 0.570837i \(-0.806619\pi\)
0.904891 + 0.425644i \(0.139952\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.30096 0.179362
\(576\) 0 0
\(577\) 13.9834 24.2200i 0.582137 1.00829i −0.413089 0.910691i \(-0.635550\pi\)
0.995226 0.0976001i \(-0.0311166\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.45387 + 0.514934i 0.350726 + 0.0213630i
\(582\) 0 0
\(583\) −0.431289 0.747014i −0.0178622 0.0309382i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 32.7133 1.35022 0.675110 0.737717i \(-0.264096\pi\)
0.675110 + 0.737717i \(0.264096\pi\)
\(588\) 0 0
\(589\) 71.7507 2.95644
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15.7076 27.2063i −0.645032 1.11723i −0.984294 0.176537i \(-0.943511\pi\)
0.339262 0.940692i \(-0.389823\pi\)
\(594\) 0 0
\(595\) 48.8107 + 2.97311i 2.00104 + 0.121886i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.70680 + 9.88447i −0.233174 + 0.403868i −0.958740 0.284283i \(-0.908244\pi\)
0.725567 + 0.688152i \(0.241578\pi\)
\(600\) 0 0
\(601\) 7.69610 0.313930 0.156965 0.987604i \(-0.449829\pi\)
0.156965 + 0.987604i \(0.449829\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.76428 + 11.7161i −0.275007 + 0.476326i
\(606\) 0 0
\(607\) −0.228866 0.396407i −0.00928938 0.0160897i 0.861343 0.508023i \(-0.169624\pi\)
−0.870633 + 0.491934i \(0.836290\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.94825 3.37447i −0.0788178 0.136516i
\(612\) 0 0
\(613\) −5.34094 + 9.25078i −0.215719 + 0.373636i −0.953495 0.301410i \(-0.902543\pi\)
0.737776 + 0.675046i \(0.235876\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28.0379 −1.12876 −0.564382 0.825514i \(-0.690886\pi\)
−0.564382 + 0.825514i \(0.690886\pi\)
\(618\) 0 0
\(619\) 17.6447 30.5616i 0.709201 1.22837i −0.255953 0.966689i \(-0.582389\pi\)
0.965154 0.261683i \(-0.0842776\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.77934 15.5931i −0.311673 0.624726i
\(624\) 0 0
\(625\) 15.0661 + 26.0953i 0.602645 + 1.04381i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16.0576 0.640257
\(630\) 0 0
\(631\) −4.12466 −0.164200 −0.0821001 0.996624i \(-0.526163\pi\)
−0.0821001 + 0.996624i \(0.526163\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 25.3484 + 43.9047i 1.00592 + 1.74230i
\(636\) 0 0
\(637\) −3.20827 0.392294i −0.127116 0.0155432i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16.4998 + 28.5785i −0.651704 + 1.12878i 0.331006 + 0.943629i \(0.392612\pi\)
−0.982709 + 0.185155i \(0.940721\pi\)
\(642\) 0 0
\(643\) 3.45306 0.136175 0.0680876 0.997679i \(-0.478310\pi\)
0.0680876 + 0.997679i \(0.478310\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.0623 + 26.0887i −0.592161 + 1.02565i 0.401779 + 0.915736i \(0.368392\pi\)
−0.993941 + 0.109917i \(0.964941\pi\)
\(648\) 0 0
\(649\) 8.89136 + 15.4003i 0.349016 + 0.604514i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 23.7003 + 41.0501i 0.927464 + 1.60641i 0.787550 + 0.616250i \(0.211349\pi\)
0.139913 + 0.990164i \(0.455318\pi\)
\(654\) 0 0
\(655\) −22.1751 + 38.4085i −0.866454 + 1.50074i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −33.8623 −1.31909 −0.659544 0.751666i \(-0.729251\pi\)
−0.659544 + 0.751666i \(0.729251\pi\)
\(660\) 0 0
\(661\) 1.57142 2.72178i 0.0611212 0.105865i −0.833846 0.551998i \(-0.813866\pi\)
0.894967 + 0.446133i \(0.147199\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −32.0275 + 48.4146i −1.24197 + 1.87744i
\(666\) 0 0
\(667\) 5.30211 + 9.18352i 0.205298 + 0.355587i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −14.7064 −0.567734
\(672\) 0 0
\(673\) 4.50186 0.173534 0.0867670 0.996229i \(-0.472346\pi\)
0.0867670 + 0.996229i \(0.472346\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.5827 + 18.3298i 0.406727 + 0.704472i 0.994521 0.104539i \(-0.0333366\pi\)
−0.587794 + 0.809011i \(0.700003\pi\)
\(678\) 0 0
\(679\) 41.3029 + 2.51580i 1.58506 + 0.0965475i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.44153 + 16.3532i −0.361270 + 0.625738i −0.988170 0.153361i \(-0.950990\pi\)
0.626900 + 0.779100i \(0.284323\pi\)
\(684\) 0 0
\(685\) 19.0037 0.726095
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.0836309 + 0.144853i −0.00318608 + 0.00551846i
\(690\) 0 0
\(691\) 13.3286 + 23.0857i 0.507042 + 0.878223i 0.999967 + 0.00815061i \(0.00259445\pi\)
−0.492925 + 0.870072i \(0.664072\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −16.9774 29.4058i −0.643990 1.11542i
\(696\) 0 0
\(697\) −24.8306 + 43.0078i −0.940524 + 1.62904i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −7.77329 −0.293593 −0.146797 0.989167i \(-0.546896\pi\)
−0.146797 + 0.989167i \(0.546896\pi\)
\(702\) 0 0
\(703\) −9.53078 + 16.5078i −0.359460 + 0.622603i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 26.5354 40.1124i 0.997965 1.50858i
\(708\) 0 0
\(709\) 20.1123 + 34.8355i 0.755332 + 1.30827i 0.945209 + 0.326466i \(0.105858\pi\)
−0.189877 + 0.981808i \(0.560809\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −24.7446 −0.926693
\(714\) 0 0
\(715\) −2.79080 −0.104370
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.1822 28.0284i −0.603495 1.04528i −0.992287 0.123959i \(-0.960441\pi\)
0.388792 0.921325i \(-0.372892\pi\)
\(720\) 0 0
\(721\) −9.24108 18.5231i −0.344156 0.689836i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.56614 4.44468i 0.0953039 0.165071i
\(726\) 0 0
\(727\) 35.4282 1.31396 0.656980 0.753908i \(-0.271834\pi\)
0.656980 + 0.753908i \(0.271834\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.66964 15.0163i 0.320658 0.555396i
\(732\) 0 0
\(733\) −2.49927 4.32887i −0.0923128 0.159890i 0.816171 0.577810i \(-0.196093\pi\)
−0.908484 + 0.417920i \(0.862759\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.9818 + 24.2172i 0.515026 + 0.892052i
\(738\) 0 0
\(739\) 16.5002 28.5792i 0.606969 1.05130i −0.384768 0.923014i \(-0.625718\pi\)
0.991737 0.128288i \(-0.0409483\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 45.0817 1.65389 0.826944 0.562285i \(-0.190078\pi\)
0.826944 + 0.562285i \(0.190078\pi\)
\(744\) 0 0
\(745\) 8.11154 14.0496i 0.297184 0.514738i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10.0921 + 20.2288i 0.368756 + 0.739145i
\(750\) 0 0
\(751\) −13.2833 23.0074i −0.484715 0.839552i 0.515130 0.857112i \(-0.327743\pi\)
−0.999846 + 0.0175601i \(0.994410\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −14.7087 −0.535306
\(756\) 0 0
\(757\) −15.6833 −0.570021 −0.285010 0.958524i \(-0.591997\pi\)
−0.285010 + 0.958524i \(0.591997\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 22.3282 + 38.6735i 0.809396 + 1.40191i 0.913283 + 0.407326i \(0.133539\pi\)
−0.103887 + 0.994589i \(0.533128\pi\)
\(762\) 0 0
\(763\) 9.58086 14.4830i 0.346851 0.524320i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.72412 2.98626i 0.0622542 0.107827i
\(768\) 0 0
\(769\) −7.15705 −0.258090 −0.129045 0.991639i \(-0.541191\pi\)
−0.129045 + 0.991639i \(0.541191\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.9545 36.2942i 0.753679 1.30541i −0.192349 0.981327i \(-0.561611\pi\)
0.946028 0.324084i \(-0.105056\pi\)
\(774\) 0 0
\(775\) 5.98800 + 10.3715i 0.215095 + 0.372556i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −29.4758 51.0536i −1.05608 1.82918i
\(780\) 0 0
\(781\) −11.5732 + 20.0454i −0.414123 + 0.717282i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −9.33155 −0.333057
\(786\) 0 0
\(787\) −4.62627 + 8.01294i −0.164909 + 0.285630i −0.936623 0.350339i \(-0.886066\pi\)
0.771714 + 0.635970i \(0.219400\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −42.1930 2.57002i −1.50021 0.0913794i
\(792\) 0 0
\(793\) 1.42585 + 2.46965i 0.0506335 + 0.0876997i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −0.389964 −0.0138132 −0.00690662 0.999976i \(-0.502198\pi\)
−0.00690662 + 0.999976i \(0.502198\pi\)
\(798\) 0 0
\(799\) 61.4487 2.17390
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 11.1420 + 19.2984i 0.393191 + 0.681027i
\(804\) 0 0
\(805\) 11.0453 16.6967i 0.389296 0.588482i