Properties

Label 1536.2.j.b.1153.1
Level $1536$
Weight $2$
Character 1536.1153
Analytic conductor $12.265$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1536 = 2^{9} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1536.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.2650217505\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1153.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1536.1153
Dual form 1536.2.j.b.385.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{3} +(-1.00000 + 1.00000i) q^{5} -2.82843i q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{3} +(-1.00000 + 1.00000i) q^{5} -2.82843i q^{7} +1.00000i q^{9} +(3.00000 + 3.00000i) q^{13} +1.41421 q^{15} -4.00000 q^{17} +(5.65685 + 5.65685i) q^{19} +(-2.00000 + 2.00000i) q^{21} -5.65685i q^{23} +3.00000i q^{25} +(0.707107 - 0.707107i) q^{27} +(-1.00000 - 1.00000i) q^{29} -2.82843 q^{31} +(2.82843 + 2.82843i) q^{35} +(3.00000 - 3.00000i) q^{37} -4.24264i q^{39} -4.00000i q^{41} +(-1.00000 - 1.00000i) q^{45} +11.3137 q^{47} -1.00000 q^{49} +(2.82843 + 2.82843i) q^{51} +(5.00000 - 5.00000i) q^{53} -8.00000i q^{57} +(8.48528 - 8.48528i) q^{59} +(-1.00000 - 1.00000i) q^{61} +2.82843 q^{63} -6.00000 q^{65} +(2.82843 + 2.82843i) q^{67} +(-4.00000 + 4.00000i) q^{69} -11.3137i q^{71} +14.0000i q^{73} +(2.12132 - 2.12132i) q^{75} +8.48528 q^{79} -1.00000 q^{81} +(11.3137 + 11.3137i) q^{83} +(4.00000 - 4.00000i) q^{85} +1.41421i q^{87} -6.00000i q^{89} +(8.48528 - 8.48528i) q^{91} +(2.00000 + 2.00000i) q^{93} -11.3137 q^{95} +16.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{5} + O(q^{10}) \) \( 4q - 4q^{5} + 12q^{13} - 16q^{17} - 8q^{21} - 4q^{29} + 12q^{37} - 4q^{45} - 4q^{49} + 20q^{53} - 4q^{61} - 24q^{65} - 16q^{69} - 4q^{81} + 16q^{85} + 8q^{93} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1536\mathbb{Z}\right)^\times\).

\(n\) \(511\) \(517\) \(1025\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 0 0
\(5\) −1.00000 + 1.00000i −0.447214 + 0.447214i −0.894427 0.447214i \(-0.852416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) 2.82843i 1.06904i −0.845154 0.534522i \(-0.820491\pi\)
0.845154 0.534522i \(-0.179509\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(12\) 0 0
\(13\) 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i \(-0.0497784\pi\)
−0.155747 + 0.987797i \(0.549778\pi\)
\(14\) 0 0
\(15\) 1.41421 0.365148
\(16\) 0 0
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) 5.65685 + 5.65685i 1.29777 + 1.29777i 0.929861 + 0.367910i \(0.119927\pi\)
0.367910 + 0.929861i \(0.380073\pi\)
\(20\) 0 0
\(21\) −2.00000 + 2.00000i −0.436436 + 0.436436i
\(22\) 0 0
\(23\) 5.65685i 1.17954i −0.807573 0.589768i \(-0.799219\pi\)
0.807573 0.589768i \(-0.200781\pi\)
\(24\) 0 0
\(25\) 3.00000i 0.600000i
\(26\) 0 0
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0 0
\(29\) −1.00000 1.00000i −0.185695 0.185695i 0.608137 0.793832i \(-0.291917\pi\)
−0.793832 + 0.608137i \(0.791917\pi\)
\(30\) 0 0
\(31\) −2.82843 −0.508001 −0.254000 0.967204i \(-0.581746\pi\)
−0.254000 + 0.967204i \(0.581746\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.82843 + 2.82843i 0.478091 + 0.478091i
\(36\) 0 0
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 0 0
\(39\) 4.24264i 0.679366i
\(40\) 0 0
\(41\) 4.00000i 0.624695i −0.949968 0.312348i \(-0.898885\pi\)
0.949968 0.312348i \(-0.101115\pi\)
\(42\) 0 0
\(43\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(44\) 0 0
\(45\) −1.00000 1.00000i −0.149071 0.149071i
\(46\) 0 0
\(47\) 11.3137 1.65027 0.825137 0.564933i \(-0.191098\pi\)
0.825137 + 0.564933i \(0.191098\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 2.82843 + 2.82843i 0.396059 + 0.396059i
\(52\) 0 0
\(53\) 5.00000 5.00000i 0.686803 0.686803i −0.274721 0.961524i \(-0.588586\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.00000i 1.05963i
\(58\) 0 0
\(59\) 8.48528 8.48528i 1.10469 1.10469i 0.110853 0.993837i \(-0.464642\pi\)
0.993837 0.110853i \(-0.0353582\pi\)
\(60\) 0 0
\(61\) −1.00000 1.00000i −0.128037 0.128037i 0.640184 0.768221i \(-0.278858\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) 0 0
\(63\) 2.82843 0.356348
\(64\) 0 0
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) 2.82843 + 2.82843i 0.345547 + 0.345547i 0.858448 0.512901i \(-0.171429\pi\)
−0.512901 + 0.858448i \(0.671429\pi\)
\(68\) 0 0
\(69\) −4.00000 + 4.00000i −0.481543 + 0.481543i
\(70\) 0 0
\(71\) 11.3137i 1.34269i −0.741145 0.671345i \(-0.765717\pi\)
0.741145 0.671345i \(-0.234283\pi\)
\(72\) 0 0
\(73\) 14.0000i 1.63858i 0.573382 + 0.819288i \(0.305631\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(74\) 0 0
\(75\) 2.12132 2.12132i 0.244949 0.244949i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 8.48528 0.954669 0.477334 0.878722i \(-0.341603\pi\)
0.477334 + 0.878722i \(0.341603\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) 11.3137 + 11.3137i 1.24184 + 1.24184i 0.959237 + 0.282604i \(0.0911983\pi\)
0.282604 + 0.959237i \(0.408802\pi\)
\(84\) 0 0
\(85\) 4.00000 4.00000i 0.433861 0.433861i
\(86\) 0 0
\(87\) 1.41421i 0.151620i
\(88\) 0 0
\(89\) 6.00000i 0.635999i −0.948091 0.317999i \(-0.896989\pi\)
0.948091 0.317999i \(-0.103011\pi\)
\(90\) 0 0
\(91\) 8.48528 8.48528i 0.889499 0.889499i
\(92\) 0 0
\(93\) 2.00000 + 2.00000i 0.207390 + 0.207390i
\(94\) 0 0
\(95\) −11.3137 −1.16076
\(96\) 0 0
\(97\) 16.0000 1.62455 0.812277 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −11.0000 + 11.0000i −1.09454 + 1.09454i −0.0995037 + 0.995037i \(0.531726\pi\)
−0.995037 + 0.0995037i \(0.968274\pi\)
\(102\) 0 0
\(103\) 19.7990i 1.95085i −0.220326 0.975426i \(-0.570712\pi\)
0.220326 0.975426i \(-0.429288\pi\)
\(104\) 0 0
\(105\) 4.00000i 0.390360i
\(106\) 0 0
\(107\) −8.48528 + 8.48528i −0.820303 + 0.820303i −0.986151 0.165848i \(-0.946964\pi\)
0.165848 + 0.986151i \(0.446964\pi\)
\(108\) 0 0
\(109\) −3.00000 3.00000i −0.287348 0.287348i 0.548683 0.836031i \(-0.315129\pi\)
−0.836031 + 0.548683i \(0.815129\pi\)
\(110\) 0 0
\(111\) −4.24264 −0.402694
\(112\) 0 0
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) 5.65685 + 5.65685i 0.527504 + 0.527504i
\(116\) 0 0
\(117\) −3.00000 + 3.00000i −0.277350 + 0.277350i
\(118\) 0 0
\(119\) 11.3137i 1.03713i
\(120\) 0 0
\(121\) 11.0000i 1.00000i
\(122\) 0 0
\(123\) −2.82843 + 2.82843i −0.255031 + 0.255031i
\(124\) 0 0
\(125\) −8.00000 8.00000i −0.715542 0.715542i
\(126\) 0 0
\(127\) 8.48528 0.752947 0.376473 0.926427i \(-0.377137\pi\)
0.376473 + 0.926427i \(0.377137\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.82843 2.82843i −0.247121 0.247121i 0.572667 0.819788i \(-0.305909\pi\)
−0.819788 + 0.572667i \(0.805909\pi\)
\(132\) 0 0
\(133\) 16.0000 16.0000i 1.38738 1.38738i
\(134\) 0 0
\(135\) 1.41421i 0.121716i
\(136\) 0 0
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) 0 0
\(139\) −2.82843 + 2.82843i −0.239904 + 0.239904i −0.816810 0.576906i \(-0.804260\pi\)
0.576906 + 0.816810i \(0.304260\pi\)
\(140\) 0 0
\(141\) −8.00000 8.00000i −0.673722 0.673722i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 2.00000 0.166091
\(146\) 0 0
\(147\) 0.707107 + 0.707107i 0.0583212 + 0.0583212i
\(148\) 0 0
\(149\) −9.00000 + 9.00000i −0.737309 + 0.737309i −0.972056 0.234748i \(-0.924574\pi\)
0.234748 + 0.972056i \(0.424574\pi\)
\(150\) 0 0
\(151\) 2.82843i 0.230174i −0.993355 0.115087i \(-0.963285\pi\)
0.993355 0.115087i \(-0.0367147\pi\)
\(152\) 0 0
\(153\) 4.00000i 0.323381i
\(154\) 0 0
\(155\) 2.82843 2.82843i 0.227185 0.227185i
\(156\) 0 0
\(157\) 15.0000 + 15.0000i 1.19713 + 1.19713i 0.975022 + 0.222108i \(0.0712939\pi\)
0.222108 + 0.975022i \(0.428706\pi\)
\(158\) 0 0
\(159\) −7.07107 −0.560772
\(160\) 0 0
\(161\) −16.0000 −1.26098
\(162\) 0 0
\(163\) −11.3137 11.3137i −0.886158 0.886158i 0.107994 0.994152i \(-0.465557\pi\)
−0.994152 + 0.107994i \(0.965557\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 11.3137i 0.875481i −0.899101 0.437741i \(-0.855779\pi\)
0.899101 0.437741i \(-0.144221\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) −5.65685 + 5.65685i −0.432590 + 0.432590i
\(172\) 0 0
\(173\) 5.00000 + 5.00000i 0.380143 + 0.380143i 0.871154 0.491011i \(-0.163372\pi\)
−0.491011 + 0.871154i \(0.663372\pi\)
\(174\) 0 0
\(175\) 8.48528 0.641427
\(176\) 0 0
\(177\) −12.0000 −0.901975
\(178\) 0 0
\(179\) −2.82843 2.82843i −0.211407 0.211407i 0.593458 0.804865i \(-0.297762\pi\)
−0.804865 + 0.593458i \(0.797762\pi\)
\(180\) 0 0
\(181\) 9.00000 9.00000i 0.668965 0.668965i −0.288512 0.957476i \(-0.593160\pi\)
0.957476 + 0.288512i \(0.0931604\pi\)
\(182\) 0 0
\(183\) 1.41421i 0.104542i
\(184\) 0 0
\(185\) 6.00000i 0.441129i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −2.00000 2.00000i −0.145479 0.145479i
\(190\) 0 0
\(191\) 5.65685 0.409316 0.204658 0.978834i \(-0.434392\pi\)
0.204658 + 0.978834i \(0.434392\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 4.24264 + 4.24264i 0.303822 + 0.303822i
\(196\) 0 0
\(197\) −5.00000 + 5.00000i −0.356235 + 0.356235i −0.862423 0.506188i \(-0.831054\pi\)
0.506188 + 0.862423i \(0.331054\pi\)
\(198\) 0 0
\(199\) 8.48528i 0.601506i 0.953702 + 0.300753i \(0.0972379\pi\)
−0.953702 + 0.300753i \(0.902762\pi\)
\(200\) 0 0
\(201\) 4.00000i 0.282138i
\(202\) 0 0
\(203\) −2.82843 + 2.82843i −0.198517 + 0.198517i
\(204\) 0 0
\(205\) 4.00000 + 4.00000i 0.279372 + 0.279372i
\(206\) 0 0
\(207\) 5.65685 0.393179
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −8.48528 8.48528i −0.584151 0.584151i 0.351890 0.936041i \(-0.385539\pi\)
−0.936041 + 0.351890i \(0.885539\pi\)
\(212\) 0 0
\(213\) −8.00000 + 8.00000i −0.548151 + 0.548151i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 8.00000i 0.543075i
\(218\) 0 0
\(219\) 9.89949 9.89949i 0.668946 0.668946i
\(220\) 0 0
\(221\) −12.0000 12.0000i −0.807207 0.807207i
\(222\) 0 0
\(223\) −25.4558 −1.70465 −0.852325 0.523013i \(-0.824808\pi\)
−0.852325 + 0.523013i \(0.824808\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) −5.65685 5.65685i −0.375459 0.375459i 0.494002 0.869461i \(-0.335534\pi\)
−0.869461 + 0.494002i \(0.835534\pi\)
\(228\) 0 0
\(229\) 17.0000 17.0000i 1.12339 1.12339i 0.132164 0.991228i \(-0.457808\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.0000i 0.655122i −0.944830 0.327561i \(-0.893773\pi\)
0.944830 0.327561i \(-0.106227\pi\)
\(234\) 0 0
\(235\) −11.3137 + 11.3137i −0.738025 + 0.738025i
\(236\) 0 0
\(237\) −6.00000 6.00000i −0.389742 0.389742i
\(238\) 0 0
\(239\) −5.65685 −0.365911 −0.182956 0.983121i \(-0.558567\pi\)
−0.182956 + 0.983121i \(0.558567\pi\)
\(240\) 0 0
\(241\) −8.00000 −0.515325 −0.257663 0.966235i \(-0.582952\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(242\) 0 0
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 1.00000 1.00000i 0.0638877 0.0638877i
\(246\) 0 0
\(247\) 33.9411i 2.15962i
\(248\) 0 0
\(249\) 16.0000i 1.01396i
\(250\) 0 0
\(251\) −5.65685 + 5.65685i −0.357057 + 0.357057i −0.862727 0.505670i \(-0.831245\pi\)
0.505670 + 0.862727i \(0.331245\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −5.65685 −0.354246
\(256\) 0 0
\(257\) 2.00000 0.124757 0.0623783 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 0 0
\(259\) −8.48528 8.48528i −0.527250 0.527250i
\(260\) 0 0
\(261\) 1.00000 1.00000i 0.0618984 0.0618984i
\(262\) 0 0
\(263\) 28.2843i 1.74408i 0.489432 + 0.872041i \(0.337204\pi\)
−0.489432 + 0.872041i \(0.662796\pi\)
\(264\) 0 0
\(265\) 10.0000i 0.614295i
\(266\) 0 0
\(267\) −4.24264 + 4.24264i −0.259645 + 0.259645i
\(268\) 0 0
\(269\) 15.0000 + 15.0000i 0.914566 + 0.914566i 0.996627 0.0820612i \(-0.0261503\pi\)
−0.0820612 + 0.996627i \(0.526150\pi\)
\(270\) 0 0
\(271\) −8.48528 −0.515444 −0.257722 0.966219i \(-0.582972\pi\)
−0.257722 + 0.966219i \(0.582972\pi\)
\(272\) 0 0
\(273\) −12.0000 −0.726273
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.00000 + 1.00000i −0.0600842 + 0.0600842i −0.736510 0.676426i \(-0.763528\pi\)
0.676426 + 0.736510i \(0.263528\pi\)
\(278\) 0 0
\(279\) 2.82843i 0.169334i
\(280\) 0 0
\(281\) 22.0000i 1.31241i 0.754583 + 0.656205i \(0.227839\pi\)
−0.754583 + 0.656205i \(0.772161\pi\)
\(282\) 0 0
\(283\) 2.82843 2.82843i 0.168133 0.168133i −0.618026 0.786158i \(-0.712067\pi\)
0.786158 + 0.618026i \(0.212067\pi\)
\(284\) 0 0
\(285\) 8.00000 + 8.00000i 0.473879 + 0.473879i
\(286\) 0 0
\(287\) −11.3137 −0.667827
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −11.3137 11.3137i −0.663221 0.663221i
\(292\) 0 0
\(293\) −13.0000 + 13.0000i −0.759468 + 0.759468i −0.976226 0.216757i \(-0.930452\pi\)
0.216757 + 0.976226i \(0.430452\pi\)
\(294\) 0 0
\(295\) 16.9706i 0.988064i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 16.9706 16.9706i 0.981433 0.981433i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 15.5563 0.893689
\(304\) 0 0
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) 2.82843 + 2.82843i 0.161427 + 0.161427i 0.783199 0.621772i \(-0.213587\pi\)
−0.621772 + 0.783199i \(0.713587\pi\)
\(308\) 0 0
\(309\) −14.0000 + 14.0000i −0.796432 + 0.796432i
\(310\) 0 0
\(311\) 28.2843i 1.60385i 0.597422 + 0.801927i \(0.296192\pi\)
−0.597422 + 0.801927i \(0.703808\pi\)
\(312\) 0 0
\(313\) 16.0000i 0.904373i 0.891923 + 0.452187i \(0.149356\pi\)
−0.891923 + 0.452187i \(0.850644\pi\)
\(314\) 0 0
\(315\) −2.82843 + 2.82843i −0.159364 + 0.159364i
\(316\) 0 0
\(317\) 15.0000 + 15.0000i 0.842484 + 0.842484i 0.989181 0.146697i \(-0.0468644\pi\)
−0.146697 + 0.989181i \(0.546864\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) −22.6274 22.6274i −1.25902 1.25902i
\(324\) 0 0
\(325\) −9.00000 + 9.00000i −0.499230 + 0.499230i
\(326\) 0 0
\(327\) 4.24264i 0.234619i
\(328\) 0 0
\(329\) 32.0000i 1.76422i
\(330\) 0 0
\(331\) 2.82843 2.82843i 0.155464 0.155464i −0.625089 0.780553i \(-0.714937\pi\)
0.780553 + 0.625089i \(0.214937\pi\)
\(332\) 0 0
\(333\) 3.00000 + 3.00000i 0.164399 + 0.164399i
\(334\) 0 0
\(335\) −5.65685 −0.309067
\(336\) 0 0
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) 0 0
\(339\) −12.7279 12.7279i −0.691286 0.691286i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 16.9706i 0.916324i
\(344\) 0 0
\(345\) 8.00000i 0.430706i
\(346\) 0 0
\(347\) −22.6274 + 22.6274i −1.21470 + 1.21470i −0.245241 + 0.969462i \(0.578867\pi\)
−0.969462 + 0.245241i \(0.921133\pi\)
\(348\) 0 0
\(349\) 9.00000 + 9.00000i 0.481759 + 0.481759i 0.905693 0.423934i \(-0.139351\pi\)
−0.423934 + 0.905693i \(0.639351\pi\)
\(350\) 0 0
\(351\) 4.24264 0.226455
\(352\) 0 0
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) 11.3137 + 11.3137i 0.600469 + 0.600469i
\(356\) 0 0
\(357\) 8.00000 8.00000i 0.423405 0.423405i
\(358\) 0 0
\(359\) 11.3137i 0.597115i −0.954392 0.298557i \(-0.903495\pi\)
0.954392 0.298557i \(-0.0965054\pi\)
\(360\) 0 0
\(361\) 45.0000i 2.36842i
\(362\) 0 0
\(363\) 7.77817 7.77817i 0.408248 0.408248i
\(364\) 0 0
\(365\) −14.0000 14.0000i −0.732793 0.732793i
\(366\) 0 0
\(367\) 2.82843 0.147643 0.0738213 0.997271i \(-0.476481\pi\)
0.0738213 + 0.997271i \(0.476481\pi\)
\(368\) 0 0
\(369\) 4.00000 0.208232
\(370\) 0 0
\(371\) −14.1421 14.1421i −0.734223 0.734223i
\(372\) 0 0
\(373\) 3.00000 3.00000i 0.155334 0.155334i −0.625161 0.780496i \(-0.714967\pi\)
0.780496 + 0.625161i \(0.214967\pi\)
\(374\) 0 0
\(375\) 11.3137i 0.584237i
\(376\) 0 0
\(377\) 6.00000i 0.309016i
\(378\) 0 0
\(379\) −11.3137 + 11.3137i −0.581146 + 0.581146i −0.935218 0.354072i \(-0.884797\pi\)
0.354072 + 0.935218i \(0.384797\pi\)
\(380\) 0 0
\(381\) −6.00000 6.00000i −0.307389 0.307389i
\(382\) 0 0
\(383\) 28.2843 1.44526 0.722629 0.691236i \(-0.242933\pi\)
0.722629 + 0.691236i \(0.242933\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7.00000 + 7.00000i −0.354914 + 0.354914i −0.861934 0.507020i \(-0.830747\pi\)
0.507020 + 0.861934i \(0.330747\pi\)
\(390\) 0 0
\(391\) 22.6274i 1.14432i
\(392\) 0 0
\(393\) 4.00000i 0.201773i
\(394\) 0 0
\(395\) −8.48528 + 8.48528i −0.426941 + 0.426941i
\(396\) 0 0
\(397\) −15.0000 15.0000i −0.752828 0.752828i 0.222178 0.975006i \(-0.428683\pi\)
−0.975006 + 0.222178i \(0.928683\pi\)
\(398\) 0 0
\(399\) −22.6274 −1.13279
\(400\) 0 0
\(401\) 20.0000 0.998752 0.499376 0.866385i \(-0.333563\pi\)
0.499376 + 0.866385i \(0.333563\pi\)
\(402\) 0 0
\(403\) −8.48528 8.48528i −0.422682 0.422682i
\(404\) 0 0
\(405\) 1.00000 1.00000i 0.0496904 0.0496904i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 32.0000i 1.58230i −0.611623 0.791149i \(-0.709483\pi\)
0.611623 0.791149i \(-0.290517\pi\)
\(410\) 0 0
\(411\) −8.48528 + 8.48528i −0.418548 + 0.418548i
\(412\) 0 0
\(413\) −24.0000 24.0000i −1.18096 1.18096i
\(414\) 0 0
\(415\) −22.6274 −1.11074
\(416\) 0 0
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) −5.65685 5.65685i −0.276355 0.276355i 0.555297 0.831652i \(-0.312605\pi\)
−0.831652 + 0.555297i \(0.812605\pi\)
\(420\) 0 0
\(421\) 9.00000 9.00000i 0.438633 0.438633i −0.452919 0.891552i \(-0.649617\pi\)
0.891552 + 0.452919i \(0.149617\pi\)
\(422\) 0 0
\(423\) 11.3137i 0.550091i
\(424\) 0 0
\(425\) 12.0000i 0.582086i
\(426\) 0 0
\(427\) −2.82843 + 2.82843i −0.136877 + 0.136877i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11.3137 −0.544962 −0.272481 0.962161i \(-0.587844\pi\)
−0.272481 + 0.962161i \(0.587844\pi\)
\(432\) 0 0
\(433\) −8.00000 −0.384455 −0.192228 0.981350i \(-0.561571\pi\)
−0.192228 + 0.981350i \(0.561571\pi\)
\(434\) 0 0
\(435\) −1.41421 1.41421i −0.0678064 0.0678064i
\(436\) 0 0
\(437\) 32.0000 32.0000i 1.53077 1.53077i
\(438\) 0 0
\(439\) 2.82843i 0.134993i 0.997719 + 0.0674967i \(0.0215012\pi\)
−0.997719 + 0.0674967i \(0.978499\pi\)
\(440\) 0 0
\(441\) 1.00000i 0.0476190i
\(442\) 0 0
\(443\) 16.9706 16.9706i 0.806296 0.806296i −0.177775 0.984071i \(-0.556890\pi\)
0.984071 + 0.177775i \(0.0568900\pi\)
\(444\) 0 0
\(445\) 6.00000 + 6.00000i 0.284427 + 0.284427i
\(446\) 0 0
\(447\) 12.7279 0.602010
\(448\) 0 0
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −2.00000 + 2.00000i −0.0939682 + 0.0939682i
\(454\) 0 0
\(455\) 16.9706i 0.795592i
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) −2.82843 + 2.82843i −0.132020 + 0.132020i
\(460\) 0 0
\(461\) 11.0000 + 11.0000i 0.512321 + 0.512321i 0.915237 0.402916i \(-0.132003\pi\)
−0.402916 + 0.915237i \(0.632003\pi\)
\(462\) 0 0
\(463\) −31.1127 −1.44593 −0.722965 0.690885i \(-0.757221\pi\)
−0.722965 + 0.690885i \(0.757221\pi\)
\(464\) 0 0
\(465\) −4.00000 −0.185496
\(466\) 0 0
\(467\) −5.65685 5.65685i −0.261768 0.261768i 0.564004 0.825772i \(-0.309260\pi\)
−0.825772 + 0.564004i \(0.809260\pi\)
\(468\) 0 0
\(469\) 8.00000 8.00000i 0.369406 0.369406i
\(470\) 0 0
\(471\) 21.2132i 0.977453i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −16.9706 + 16.9706i −0.778663 + 0.778663i
\(476\) 0 0
\(477\) 5.00000 + 5.00000i 0.228934 + 0.228934i
\(478\) 0 0
\(479\) −28.2843 −1.29234 −0.646171 0.763193i \(-0.723631\pi\)
−0.646171 + 0.763193i \(0.723631\pi\)
\(480\) 0 0
\(481\) 18.0000 0.820729
\(482\) 0 0
\(483\) 11.3137 + 11.3137i 0.514792 + 0.514792i
\(484\) 0 0
\(485\) −16.0000 + 16.0000i −0.726523 + 0.726523i
\(486\) 0 0
\(487\) 2.82843i 0.128168i 0.997944 + 0.0640841i \(0.0204126\pi\)
−0.997944 + 0.0640841i \(0.979587\pi\)
\(488\) 0 0
\(489\) 16.0000i 0.723545i
\(490\) 0 0
\(491\) −8.48528 + 8.48528i −0.382935 + 0.382935i −0.872159 0.489223i \(-0.837280\pi\)
0.489223 + 0.872159i \(0.337280\pi\)
\(492\) 0 0
\(493\) 4.00000 + 4.00000i 0.180151 + 0.180151i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −32.0000 −1.43540
\(498\) 0 0
\(499\) −19.7990 19.7990i −0.886325 0.886325i 0.107843 0.994168i \(-0.465605\pi\)
−0.994168 + 0.107843i \(0.965605\pi\)
\(500\) 0 0
\(501\) −8.00000 + 8.00000i −0.357414 + 0.357414i
\(502\) 0 0
\(503\) 11.3137i 0.504453i −0.967668 0.252227i \(-0.918837\pi\)
0.967668 0.252227i \(-0.0811629\pi\)
\(504\) 0 0
\(505\) 22.0000i 0.978987i
\(506\) 0 0
\(507\) 3.53553 3.53553i 0.157019 0.157019i
\(508\) 0 0
\(509\) −23.0000 23.0000i −1.01946 1.01946i −0.999807 0.0196502i \(-0.993745\pi\)
−0.0196502 0.999807i \(-0.506255\pi\)
\(510\) 0 0
\(511\) 39.5980 1.75171
\(512\) 0 0
\(513\) 8.00000 0.353209
\(514\) 0 0
\(515\) 19.7990 + 19.7990i 0.872448 + 0.872448i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 7.07107i 0.310385i
\(520\) 0 0
\(521\) 12.0000i 0.525730i 0.964833 + 0.262865i \(0.0846673\pi\)
−0.964833 + 0.262865i \(0.915333\pi\)
\(522\) 0 0
\(523\) 5.65685 5.65685i 0.247357 0.247357i −0.572528 0.819885i \(-0.694037\pi\)
0.819885 + 0.572528i \(0.194037\pi\)
\(524\) 0 0
\(525\) −6.00000 6.00000i −0.261861 0.261861i
\(526\) 0 0
\(527\) 11.3137 0.492833
\(528\) 0 0
\(529\) −9.00000 −0.391304
\(530\) 0 0
\(531\) 8.48528 + 8.48528i 0.368230 + 0.368230i
\(532\) 0 0
\(533\) 12.0000 12.0000i 0.519778 0.519778i
\(534\) 0 0
\(535\) 16.9706i 0.733701i
\(536\) 0 0
\(537\) 4.00000i 0.172613i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 3.00000 + 3.00000i 0.128980 + 0.128980i 0.768650 0.639670i \(-0.220929\pi\)
−0.639670 + 0.768650i \(0.720929\pi\)
\(542\) 0 0
\(543\) −12.7279 −0.546207
\(544\) 0 0
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) −5.65685 5.65685i −0.241870 0.241870i 0.575754 0.817623i \(-0.304709\pi\)
−0.817623 + 0.575754i \(0.804709\pi\)
\(548\) 0 0
\(549\) 1.00000 1.00000i 0.0426790 0.0426790i
\(550\) 0 0
\(551\) 11.3137i 0.481980i
\(552\) 0 0
\(553\) 24.0000i 1.02058i
\(554\) 0 0
\(555\) 4.24264 4.24264i 0.180090 0.180090i
\(556\) 0 0
\(557\) 21.0000 + 21.0000i 0.889799 + 0.889799i 0.994503 0.104705i \(-0.0333898\pi\)
−0.104705 + 0.994503i \(0.533390\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.65685 + 5.65685i 0.238408 + 0.238408i 0.816191 0.577783i \(-0.196082\pi\)
−0.577783 + 0.816191i \(0.696082\pi\)
\(564\) 0 0
\(565\) −18.0000 + 18.0000i −0.757266 + 0.757266i
\(566\) 0 0
\(567\) 2.82843i 0.118783i
\(568\) 0 0
\(569\) 20.0000i 0.838444i 0.907884 + 0.419222i \(0.137697\pi\)
−0.907884 + 0.419222i \(0.862303\pi\)
\(570\) 0 0
\(571\) 14.1421 14.1421i 0.591830 0.591830i −0.346296 0.938125i \(-0.612561\pi\)
0.938125 + 0.346296i \(0.112561\pi\)
\(572\) 0 0
\(573\) −4.00000 4.00000i −0.167102 0.167102i
\(574\) 0 0
\(575\) 16.9706 0.707721
\(576\) 0 0
\(577\) 22.0000 0.915872 0.457936 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 32.0000 32.0000i 1.32758 1.32758i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 6.00000i 0.248069i
\(586\) 0 0
\(587\) 2.82843 2.82843i 0.116742 0.116742i −0.646323 0.763064i \(-0.723694\pi\)
0.763064 + 0.646323i \(0.223694\pi\)
\(588\) 0 0
\(589\) −16.0000 16.0000i −0.659269 0.659269i
\(590\) 0 0
\(591\) 7.07107 0.290865
\(592\) 0 0
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 0 0
\(595\) −11.3137 11.3137i −0.463817 0.463817i
\(596\) 0 0
\(597\) 6.00000 6.00000i 0.245564 0.245564i
\(598\) 0 0
\(599\) 39.5980i 1.61793i −0.587857 0.808965i \(-0.700028\pi\)
0.587857 0.808965i \(-0.299972\pi\)
\(600\) 0 0
\(601\) 14.0000i 0.571072i −0.958368 0.285536i \(-0.907828\pi\)
0.958368 0.285536i \(-0.0921716\pi\)
\(602\) 0 0
\(603\) −2.82843 + 2.82843i −0.115182 + 0.115182i
\(604\) 0 0
\(605\) −11.0000 11.0000i −0.447214 0.447214i
\(606\) 0 0
\(607\) 42.4264 1.72203 0.861017 0.508576i \(-0.169828\pi\)
0.861017 + 0.508576i \(0.169828\pi\)
\(608\) 0 0
\(609\) 4.00000 0.162088
\(610\) 0 0
\(611\) 33.9411 + 33.9411i 1.37311 + 1.37311i
\(612\) 0 0
\(613\) −11.0000 + 11.0000i −0.444286 + 0.444286i −0.893449 0.449164i \(-0.851722\pi\)
0.449164 + 0.893449i \(0.351722\pi\)
\(614\) 0 0
\(615\) 5.65685i 0.228106i
\(616\) 0 0
\(617\) 6.00000i 0.241551i −0.992680 0.120775i \(-0.961462\pi\)
0.992680 0.120775i \(-0.0385381\pi\)
\(618\) 0 0
\(619\) 31.1127 31.1127i 1.25052 1.25052i 0.295040 0.955485i \(-0.404667\pi\)
0.955485 0.295040i \(-0.0953330\pi\)
\(620\) 0 0
\(621\) −4.00000 4.00000i −0.160514 0.160514i
\(622\) 0 0
\(623\) −16.9706 −0.679911
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.0000 + 12.0000i −0.478471 + 0.478471i
\(630\) 0 0
\(631\) 8.48528i 0.337794i 0.985634 + 0.168897i \(0.0540205\pi\)
−0.985634 + 0.168897i \(0.945980\pi\)
\(632\) 0 0
\(633\) 12.0000i 0.476957i
\(634\) 0 0
\(635\) −8.48528 + 8.48528i −0.336728 + 0.336728i
\(636\) 0 0
\(637\) −3.00000 3.00000i −0.118864 0.118864i
\(638\) 0 0
\(639\) 11.3137 0.447563
\(640\) 0 0
\(641\) −12.0000 −0.473972 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) 0 0
\(643\) 11.3137 + 11.3137i 0.446169 + 0.446169i 0.894079 0.447910i \(-0.147831\pi\)
−0.447910 + 0.894079i \(0.647831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 39.5980i 1.55676i 0.627795 + 0.778379i \(0.283958\pi\)
−0.627795 + 0.778379i \(0.716042\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 5.65685 5.65685i 0.221710 0.221710i
\(652\) 0 0
\(653\) 3.00000 + 3.00000i 0.117399 + 0.117399i 0.763366 0.645967i \(-0.223545\pi\)
−0.645967 + 0.763366i \(0.723545\pi\)
\(654\) 0 0
\(655\) 5.65685 0.221032
\(656\) 0 0
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) −14.1421 14.1421i −0.550899 0.550899i 0.375801 0.926700i \(-0.377368\pi\)
−0.926700 + 0.375801i \(0.877368\pi\)
\(660\) 0 0
\(661\) −19.0000 + 19.0000i −0.739014 + 0.739014i −0.972387 0.233373i \(-0.925024\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(662\) 0 0
\(663\) 16.9706i 0.659082i
\(664\) 0 0
\(665\) 32.0000i 1.24091i
\(666\) 0 0
\(667\) −5.65685 + 5.65685i −0.219034 + 0.219034i
\(668\) 0 0
\(669\) 18.0000 + 18.0000i 0.695920 + 0.695920i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −8.00000 −0.308377 −0.154189 0.988041i \(-0.549276\pi\)
−0.154189 + 0.988041i \(0.549276\pi\)
\(674\) 0 0
\(675\) 2.12132 + 2.12132i 0.0816497 + 0.0816497i
\(676\) 0 0
\(677\) −23.0000 + 23.0000i −0.883962 + 0.883962i −0.993935 0.109973i \(-0.964924\pi\)
0.109973 + 0.993935i \(0.464924\pi\)
\(678\) 0 0
\(679\) 45.2548i 1.73672i
\(680\) 0 0
\(681\) 8.00000i 0.306561i
\(682\) 0 0
\(683\) 22.6274 22.6274i 0.865814 0.865814i −0.126192 0.992006i \(-0.540275\pi\)
0.992006 + 0.126192i \(0.0402755\pi\)
\(684\) 0 0
\(685\) 12.0000 + 12.0000i 0.458496 + 0.458496i
\(686\) 0 0
\(687\) −24.0416 −0.917245
\(688\) 0 0
\(689\) 30.0000 1.14291
\(690\) 0 0
\(691\) 28.2843 + 28.2843i 1.07598 + 1.07598i 0.996865 + 0.0791192i \(0.0252108\pi\)
0.0791192 + 0.996865i \(0.474789\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.65685i 0.214577i
\(696\) 0 0
\(697\) 16.0000i 0.606043i
\(698\) 0 0
\(699\) −7.07107 + 7.07107i −0.267452 + 0.267452i
\(700\) 0 0
\(701\) 33.0000 + 33.0000i 1.24639 + 1.24639i 0.957302 + 0.289091i \(0.0933531\pi\)
0.289091 + 0.957302i \(0.406647\pi\)
\(702\) 0 0
\(703\) 33.9411 1.28011
\(704\) 0 0
\(705\) 16.0000 0.602595
\(706\) 0 0
\(707\) 31.1127 + 31.1127i 1.17011 + 1.17011i
\(708\) 0 0
\(709\) −25.0000 + 25.0000i −0.938895 + 0.938895i −0.998238 0.0593429i \(-0.981099\pi\)
0.0593429 + 0.998238i \(0.481099\pi\)
\(710\) 0 0
\(711\) 8.48528i 0.318223i
\(712\) 0 0
\(713\) 16.0000i 0.599205i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 4.00000 + 4.00000i 0.149383 + 0.149383i
\(718\) 0 0
\(719\) −16.9706 −0.632895 −0.316448 0.948610i \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(720\) 0 0
\(721\) −56.0000 −2.08555
\(722\) 0 0
\(723\) 5.65685 + 5.65685i 0.210381 + 0.210381i
\(724\) 0 0
\(725\) 3.00000 3.00000i 0.111417 0.111417i
\(726\) 0 0
\(727\) 42.4264i 1.57351i −0.617266 0.786754i \(-0.711760\pi\)
0.617266 0.786754i \(-0.288240\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −3.00000 3.00000i −0.110808 0.110808i 0.649529 0.760337i \(-0.274966\pi\)
−0.760337 + 0.649529i \(0.774966\pi\)
\(734\) 0 0
\(735\) −1.41421 −0.0521641
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 25.4558 + 25.4558i 0.936408 + 0.936408i 0.998096 0.0616872i \(-0.0196481\pi\)
−0.0616872 + 0.998096i \(0.519648\pi\)
\(740\) 0 0
\(741\) 24.0000 24.0000i 0.881662 0.881662i
\(742\) 0 0
\(743\) 11.3137i 0.415060i 0.978229 + 0.207530i \(0.0665424\pi\)
−0.978229 + 0.207530i \(0.933458\pi\)
\(744\) 0 0
\(745\) 18.0000i 0.659469i
\(746\) 0 0
\(747\) −11.3137 + 11.3137i −0.413947 + 0.413947i
\(748\) 0 0
\(749\) 24.0000 + 24.0000i 0.876941 + 0.876941i
\(750\) 0 0
\(751\) −8.48528 −0.309632 −0.154816 0.987943i \(-0.549479\pi\)
−0.154816 + 0.987943i \(0.549479\pi\)
\(752\) 0 0
\(753\) 8.00000 0.291536
\(754\) 0 0
\(755\) 2.82843 + 2.82843i 0.102937 + 0.102937i
\(756\) 0 0
\(757\) −15.0000 + 15.0000i −0.545184 + 0.545184i −0.925044 0.379860i \(-0.875972\pi\)
0.379860 + 0.925044i \(0.375972\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 36.0000i 1.30500i −0.757789 0.652499i \(-0.773720\pi\)
0.757789 0.652499i \(-0.226280\pi\)
\(762\) 0 0
\(763\) −8.48528 + 8.48528i −0.307188 + 0.307188i
\(764\) 0 0
\(765\) 4.00000 + 4.00000i 0.144620 + 0.144620i
\(766\) 0 0
\(767\) 50.9117 1.83831
\(768\) 0 0
\(769\) −32.0000 −1.15395 −0.576975 0.816762i \(-0.695767\pi\)
−0.576975 + 0.816762i \(0.695767\pi\)
\(770\) 0 0
\(771\) −1.41421 1.41421i −0.0509317 0.0509317i
\(772\) 0 0
\(773\) 13.0000 13.0000i 0.467578 0.467578i −0.433551 0.901129i \(-0.642740\pi\)
0.901129 + 0.433551i \(0.142740\pi\)
\(774\) 0 0
\(775\) 8.48528i 0.304800i
\(776\) 0 0
\(777\) 12.0000i 0.430498i
\(778\) 0 0
\(779\) 22.6274 22.6274i 0.810711 0.810711i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.41421 −0.0505399
\(784\) 0 0
\(785\) −30.0000 −1.07075
\(786\) 0 0
\(787\) 22.6274 + 22.6274i 0.806580 + 0.806580i 0.984115 0.177534i \(-0.0568121\pi\)
−0.177534 + 0.984115i \(0.556812\pi\)
\(788\) 0 0
\(789\) 20.0000 20.0000i 0.712019 0.712019i
\(790\) 0 0
\(791\) 50.9117i 1.81021i
\(792\) 0 0
\(793\) 6.00000i 0.213066i
\(794\) 0 0
\(795\) 7.07107 7.07107i 0.250785 0.250785i
\(796\) 0 0
\(797\) −35.0000 35.0000i −1.23976 1.23976i −0.960097 0.279666i \(-0.909776\pi\)
−0.279666 0.960097i \(-0.590224\pi\)
\(798\) 0 0
\(799\) −45.2548 −1.60100