Properties

Label 2520.2.bi.q.1801.1
Level $2520$
Weight $2$
Character 2520.1801
Analytic conductor $20.122$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bi (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.11337408.1
Defining polynomial: \(x^{6} + 18 x^{4} + 81 x^{2} + 12\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1801.1
Root \(-0.391571i\) of defining polynomial
Character \(\chi\) \(=\) 2520.1801
Dual form 2520.2.bi.q.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(-0.292113 - 2.62958i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(-0.292113 - 2.62958i) q^{7} +(0.839111 + 1.45338i) q^{11} -4.84667 q^{13} +(1.00000 + 1.73205i) q^{17} +(-3.42334 + 5.92939i) q^{19} +(-1.13122 + 1.95934i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.32178 q^{29} +(-4.58423 - 7.94011i) q^{31} +(-2.42334 - 1.06181i) q^{35} +(1.42334 - 2.46529i) q^{37} -9.52489 q^{41} +6.58423 q^{43} +(-6.10156 + 10.5682i) q^{47} +(-6.82934 + 1.53627i) q^{49} +(3.74511 + 6.48673i) q^{53} +1.67822 q^{55} +(4.00000 + 6.92820i) q^{59} +(3.24511 - 5.62070i) q^{61} +(-2.42334 + 4.19734i) q^{65} +(2.87634 + 4.98196i) q^{67} +(5.84667 + 10.1267i) q^{73} +(3.57666 - 2.63106i) q^{77} +(-2.84667 + 4.93058i) q^{79} +12.5842 q^{83} +2.00000 q^{85} +(-2.92334 + 5.06337i) q^{89} +(1.41577 + 12.7447i) q^{91} +(3.42334 + 5.92939i) q^{95} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{5} + 6q^{7} + O(q^{10}) \) \( 6q + 3q^{5} + 6q^{7} + 3q^{11} + 6q^{13} + 6q^{17} - 3q^{19} + 3q^{23} - 3q^{25} - 24q^{29} - 12q^{31} + 3q^{35} - 9q^{37} - 18q^{41} + 24q^{43} - 15q^{47} - 12q^{49} + 9q^{53} + 6q^{55} + 24q^{59} + 6q^{61} + 3q^{65} - 6q^{67} + 39q^{77} + 18q^{79} + 60q^{83} + 12q^{85} + 24q^{91} + 3q^{95} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 0
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −0.292113 2.62958i −0.110408 0.993886i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.839111 + 1.45338i 0.253001 + 0.438211i 0.964351 0.264627i \(-0.0852490\pi\)
−0.711349 + 0.702839i \(0.751916\pi\)
\(12\) 0 0
\(13\) −4.84667 −1.34422 −0.672112 0.740449i \(-0.734613\pi\)
−0.672112 + 0.740449i \(0.734613\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) −3.42334 + 5.92939i −0.785367 + 1.36030i 0.143412 + 0.989663i \(0.454192\pi\)
−0.928779 + 0.370633i \(0.879141\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.13122 + 1.95934i −0.235876 + 0.408550i −0.959527 0.281617i \(-0.909129\pi\)
0.723651 + 0.690166i \(0.242463\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.32178 −0.616839 −0.308419 0.951250i \(-0.599800\pi\)
−0.308419 + 0.951250i \(0.599800\pi\)
\(30\) 0 0
\(31\) −4.58423 7.94011i −0.823351 1.42609i −0.903173 0.429277i \(-0.858768\pi\)
0.0798217 0.996809i \(-0.474565\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.42334 1.06181i −0.409619 0.179479i
\(36\) 0 0
\(37\) 1.42334 2.46529i 0.233995 0.405291i −0.724985 0.688765i \(-0.758153\pi\)
0.958980 + 0.283473i \(0.0914867\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9.52489 −1.48754 −0.743769 0.668437i \(-0.766964\pi\)
−0.743769 + 0.668437i \(0.766964\pi\)
\(42\) 0 0
\(43\) 6.58423 1.00408 0.502042 0.864843i \(-0.332582\pi\)
0.502042 + 0.864843i \(0.332582\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.10156 + 10.5682i −0.890004 + 1.54153i −0.0501344 + 0.998742i \(0.515965\pi\)
−0.839869 + 0.542789i \(0.817368\pi\)
\(48\) 0 0
\(49\) −6.82934 + 1.53627i −0.975620 + 0.219466i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.74511 + 6.48673i 0.514431 + 0.891021i 0.999860 + 0.0167445i \(0.00533020\pi\)
−0.485429 + 0.874276i \(0.661336\pi\)
\(54\) 0 0
\(55\) 1.67822 0.226291
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.00000 + 6.92820i 0.520756 + 0.901975i 0.999709 + 0.0241347i \(0.00768307\pi\)
−0.478953 + 0.877841i \(0.658984\pi\)
\(60\) 0 0
\(61\) 3.24511 5.62070i 0.415494 0.719657i −0.579986 0.814627i \(-0.696942\pi\)
0.995480 + 0.0949692i \(0.0302753\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.42334 + 4.19734i −0.300578 + 0.520616i
\(66\) 0 0
\(67\) 2.87634 + 4.98196i 0.351401 + 0.608644i 0.986495 0.163791i \(-0.0523722\pi\)
−0.635094 + 0.772434i \(0.719039\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 5.84667 + 10.1267i 0.684301 + 1.18524i 0.973656 + 0.228022i \(0.0732260\pi\)
−0.289355 + 0.957222i \(0.593441\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.57666 2.63106i 0.407599 0.299837i
\(78\) 0 0
\(79\) −2.84667 + 4.93058i −0.320276 + 0.554734i −0.980545 0.196295i \(-0.937109\pi\)
0.660269 + 0.751029i \(0.270442\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.5842 1.38130 0.690649 0.723190i \(-0.257325\pi\)
0.690649 + 0.723190i \(0.257325\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.92334 + 5.06337i −0.309873 + 0.536716i −0.978334 0.207031i \(-0.933620\pi\)
0.668461 + 0.743747i \(0.266953\pi\)
\(90\) 0 0
\(91\) 1.41577 + 12.7447i 0.148414 + 1.33601i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.42334 + 5.92939i 0.351227 + 0.608343i
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.50756 14.7355i −0.846534 1.46624i −0.884282 0.466953i \(-0.845352\pi\)
0.0377483 0.999287i \(-0.487981\pi\)
\(102\) 0 0
\(103\) −3.55456 + 6.15668i −0.350241 + 0.606635i −0.986292 0.165012i \(-0.947234\pi\)
0.636050 + 0.771648i \(0.280567\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.876338 + 1.51786i −0.0847188 + 0.146737i −0.905271 0.424834i \(-0.860333\pi\)
0.820553 + 0.571571i \(0.193666\pi\)
\(108\) 0 0
\(109\) −9.77001 16.9222i −0.935797 1.62085i −0.773206 0.634154i \(-0.781348\pi\)
−0.162591 0.986694i \(-0.551985\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −10.3369 −0.972414 −0.486207 0.873844i \(-0.661620\pi\)
−0.486207 + 0.873844i \(0.661620\pi\)
\(114\) 0 0
\(115\) 1.13122 + 1.95934i 0.105487 + 0.182709i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.26245 3.13553i 0.390738 0.287434i
\(120\) 0 0
\(121\) 4.09179 7.08718i 0.371981 0.644289i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −19.1836 −1.70227 −0.851133 0.524949i \(-0.824084\pi\)
−0.851133 + 0.524949i \(0.824084\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.91357 + 15.4387i −0.778782 + 1.34889i 0.153862 + 0.988092i \(0.450829\pi\)
−0.932644 + 0.360797i \(0.882505\pi\)
\(132\) 0 0
\(133\) 16.5918 + 7.26987i 1.43869 + 0.630378i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000 + 3.46410i 0.170872 + 0.295958i 0.938725 0.344668i \(-0.112008\pi\)
−0.767853 + 0.640626i \(0.778675\pi\)
\(138\) 0 0
\(139\) −5.16845 −0.438382 −0.219191 0.975682i \(-0.570342\pi\)
−0.219191 + 0.975682i \(0.570342\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.06689 7.04407i −0.340091 0.589054i
\(144\) 0 0
\(145\) −1.66089 + 2.87674i −0.137929 + 0.238901i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.398443 0.690123i 0.0326417 0.0565371i −0.849243 0.528002i \(-0.822941\pi\)
0.881885 + 0.471465i \(0.156275\pi\)
\(150\) 0 0
\(151\) 8.26245 + 14.3110i 0.672388 + 1.16461i 0.977225 + 0.212206i \(0.0680648\pi\)
−0.304837 + 0.952405i \(0.598602\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.16845 −0.736428
\(156\) 0 0
\(157\) −4.10156 7.10411i −0.327340 0.566969i 0.654643 0.755938i \(-0.272819\pi\)
−0.981983 + 0.188969i \(0.939486\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.48267 + 2.40229i 0.432095 + 0.189327i
\(162\) 0 0
\(163\) −1.84667 + 3.19853i −0.144643 + 0.250528i −0.929240 0.369478i \(-0.879537\pi\)
0.784597 + 0.620006i \(0.212870\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.262447 0.0203087 0.0101544 0.999948i \(-0.496768\pi\)
0.0101544 + 0.999948i \(0.496768\pi\)
\(168\) 0 0
\(169\) 10.4902 0.806941
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.42334 + 16.3217i −0.716443 + 1.24092i 0.245957 + 0.969281i \(0.420898\pi\)
−0.962400 + 0.271635i \(0.912436\pi\)
\(174\) 0 0
\(175\) −2.13122 + 1.56777i −0.161105 + 0.118512i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −6.00756 10.4054i −0.449026 0.777736i 0.549297 0.835627i \(-0.314896\pi\)
−0.998323 + 0.0578912i \(0.981562\pi\)
\(180\) 0 0
\(181\) −6.03466 −0.448553 −0.224276 0.974526i \(-0.572002\pi\)
−0.224276 + 0.974526i \(0.572002\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.42334 2.46529i −0.104646 0.181252i
\(186\) 0 0
\(187\) −1.67822 + 2.90676i −0.122724 + 0.212564i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.41577 2.45219i 0.102442 0.177434i −0.810248 0.586087i \(-0.800668\pi\)
0.912690 + 0.408652i \(0.134001\pi\)
\(192\) 0 0
\(193\) −6.49023 11.2414i −0.467177 0.809174i 0.532120 0.846669i \(-0.321396\pi\)
−0.999297 + 0.0374948i \(0.988062\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.84667 0.345311 0.172656 0.984982i \(-0.444765\pi\)
0.172656 + 0.984982i \(0.444765\pi\)
\(198\) 0 0
\(199\) 7.69334 + 13.3253i 0.545367 + 0.944603i 0.998584 + 0.0532026i \(0.0169429\pi\)
−0.453217 + 0.891400i \(0.649724\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.970334 + 8.73487i 0.0681041 + 0.613068i
\(204\) 0 0
\(205\) −4.76245 + 8.24880i −0.332624 + 0.576121i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −11.4902 −0.794796
\(210\) 0 0
\(211\) 9.18357 0.632223 0.316112 0.948722i \(-0.397623\pi\)
0.316112 + 0.948722i \(0.397623\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.29211 5.70211i 0.224520 0.388880i
\(216\) 0 0
\(217\) −19.5400 + 14.3740i −1.32646 + 0.975769i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.84667 8.39468i −0.326022 0.564687i
\(222\) 0 0
\(223\) −12.9805 −0.869236 −0.434618 0.900615i \(-0.643117\pi\)
−0.434618 + 0.900615i \(0.643117\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.0151 19.0788i −0.731099 1.26630i −0.956414 0.292015i \(-0.905674\pi\)
0.225314 0.974286i \(-0.427659\pi\)
\(228\) 0 0
\(229\) −2.15333 + 3.72967i −0.142296 + 0.246464i −0.928361 0.371680i \(-0.878782\pi\)
0.786065 + 0.618144i \(0.212115\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.00000 15.5885i 0.589610 1.02123i −0.404674 0.914461i \(-0.632615\pi\)
0.994283 0.106773i \(-0.0340517\pi\)
\(234\) 0 0
\(235\) 6.10156 + 10.5682i 0.398022 + 0.689394i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.8618 −0.702591 −0.351296 0.936265i \(-0.614259\pi\)
−0.351296 + 0.936265i \(0.614259\pi\)
\(240\) 0 0
\(241\) −0.101557 0.175902i −0.00654187 0.0113309i 0.862736 0.505655i \(-0.168749\pi\)
−0.869278 + 0.494324i \(0.835416\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.08423 + 6.68251i −0.133156 + 0.426930i
\(246\) 0 0
\(247\) 16.5918 28.7378i 1.05571 1.82854i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.03466 −0.317785 −0.158893 0.987296i \(-0.550792\pi\)
−0.158893 + 0.987296i \(0.550792\pi\)
\(252\) 0 0
\(253\) −3.79689 −0.238708
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.6933 20.2535i 0.729411 1.26338i −0.227722 0.973726i \(-0.573128\pi\)
0.957133 0.289650i \(-0.0935390\pi\)
\(258\) 0 0
\(259\) −6.89844 3.02263i −0.428648 0.187817i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 13.5546 + 23.4772i 0.835810 + 1.44767i 0.893369 + 0.449323i \(0.148335\pi\)
−0.0575594 + 0.998342i \(0.518332\pi\)
\(264\) 0 0
\(265\) 7.49023 0.460121
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.24511 + 5.62070i 0.197858 + 0.342700i 0.947834 0.318765i \(-0.103268\pi\)
−0.749976 + 0.661466i \(0.769935\pi\)
\(270\) 0 0
\(271\) 11.6933 20.2535i 0.710320 1.23031i −0.254417 0.967095i \(-0.581884\pi\)
0.964737 0.263216i \(-0.0847831\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.839111 1.45338i 0.0506003 0.0876422i
\(276\) 0 0
\(277\) −1.83155 3.17234i −0.110047 0.190607i 0.805742 0.592267i \(-0.201767\pi\)
−0.915789 + 0.401660i \(0.868434\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −13.8965 −0.828993 −0.414497 0.910051i \(-0.636042\pi\)
−0.414497 + 0.910051i \(0.636042\pi\)
\(282\) 0 0
\(283\) 10.1685 + 17.6123i 0.604452 + 1.04694i 0.992138 + 0.125150i \(0.0399411\pi\)
−0.387686 + 0.921791i \(0.626726\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.78234 + 25.0464i 0.164236 + 1.47844i
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −18.8467 −1.10103 −0.550517 0.834824i \(-0.685569\pi\)
−0.550517 + 0.834824i \(0.685569\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.48267 9.49626i 0.317071 0.549183i
\(300\) 0 0
\(301\) −1.92334 17.3137i −0.110859 0.997946i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.24511 5.62070i −0.185815 0.321841i
\(306\) 0 0
\(307\) −2.39623 −0.136760 −0.0683802 0.997659i \(-0.521783\pi\)
−0.0683802 + 0.997659i \(0.521783\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.83155 4.90439i −0.160562 0.278102i 0.774508 0.632564i \(-0.217997\pi\)
−0.935071 + 0.354462i \(0.884664\pi\)
\(312\) 0 0
\(313\) −14.8618 + 25.7414i −0.840038 + 1.45499i 0.0498231 + 0.998758i \(0.484134\pi\)
−0.889861 + 0.456231i \(0.849199\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.52489 16.4976i 0.534971 0.926597i −0.464193 0.885734i \(-0.653656\pi\)
0.999165 0.0408636i \(-0.0130109\pi\)
\(318\) 0 0
\(319\) −2.78734 4.82781i −0.156061 0.270306i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −13.6933 −0.761918
\(324\) 0 0
\(325\) 2.42334 + 4.19734i 0.134422 + 0.232827i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 29.5722 + 12.9574i 1.63037 + 0.714365i
\(330\) 0 0
\(331\) −1.16089 + 2.01072i −0.0638083 + 0.110519i −0.896165 0.443722i \(-0.853658\pi\)
0.832356 + 0.554241i \(0.186991\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.75268 0.314302
\(336\) 0 0
\(337\) −16.4062 −0.893704 −0.446852 0.894608i \(-0.647455\pi\)
−0.446852 + 0.894608i \(0.647455\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 7.69334 13.3253i 0.416618 0.721603i
\(342\) 0 0
\(343\) 6.03466 + 17.5095i 0.325841 + 0.945425i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.29211 + 3.97006i 0.123047 + 0.213124i 0.920968 0.389639i \(-0.127400\pi\)
−0.797921 + 0.602762i \(0.794067\pi\)
\(348\) 0 0
\(349\) 12.3716 0.662235 0.331117 0.943590i \(-0.392574\pi\)
0.331117 + 0.943590i \(0.392574\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.69334 + 16.7894i 0.515925 + 0.893608i 0.999829 + 0.0184869i \(0.00588489\pi\)
−0.483904 + 0.875121i \(0.660782\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.90600 + 8.49745i −0.258929 + 0.448478i −0.965955 0.258709i \(-0.916703\pi\)
0.707026 + 0.707187i \(0.250036\pi\)
\(360\) 0 0
\(361\) −13.9385 24.1421i −0.733603 1.27064i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11.6933 0.612058
\(366\) 0 0
\(367\) 6.35901 + 11.0141i 0.331937 + 0.574933i 0.982892 0.184184i \(-0.0589644\pi\)
−0.650954 + 0.759117i \(0.725631\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 15.9634 11.7429i 0.828776 0.609662i
\(372\) 0 0
\(373\) 8.20311 14.2082i 0.424741 0.735673i −0.571655 0.820494i \(-0.693698\pi\)
0.996396 + 0.0848208i \(0.0270318\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 16.0996 0.829170
\(378\) 0 0
\(379\) 14.4707 0.743309 0.371655 0.928371i \(-0.378791\pi\)
0.371655 + 0.928371i \(0.378791\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.77478 + 3.07401i −0.0906871 + 0.157075i −0.907800 0.419402i \(-0.862240\pi\)
0.817113 + 0.576477i \(0.195573\pi\)
\(384\) 0 0
\(385\) −0.490230 4.41301i −0.0249844 0.224908i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.49023 + 7.77731i 0.227664 + 0.394325i 0.957115 0.289707i \(-0.0935580\pi\)
−0.729452 + 0.684032i \(0.760225\pi\)
\(390\) 0 0
\(391\) −4.52489 −0.228834
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.84667 + 4.93058i 0.143232 + 0.248084i
\(396\) 0 0
\(397\) 14.0498 24.3349i 0.705139 1.22134i −0.261503 0.965203i \(-0.584218\pi\)
0.966642 0.256133i \(-0.0824486\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.3467 + 23.1171i −0.666501 + 1.15441i 0.312375 + 0.949959i \(0.398875\pi\)
−0.978876 + 0.204455i \(0.934458\pi\)
\(402\) 0 0
\(403\) 22.2182 + 38.4831i 1.10677 + 1.91698i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.77735 0.236804
\(408\) 0 0
\(409\) −14.0325 24.3049i −0.693860 1.20180i −0.970563 0.240846i \(-0.922575\pi\)
0.276703 0.960955i \(-0.410758\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 17.0498 12.5421i 0.838965 0.617157i
\(414\) 0 0
\(415\) 6.29211 10.8983i 0.308868 0.534974i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.8769 0.922198 0.461099 0.887349i \(-0.347455\pi\)
0.461099 + 0.887349i \(0.347455\pi\)
\(420\) 0 0
\(421\) −28.1836 −1.37358 −0.686792 0.726854i \(-0.740982\pi\)
−0.686792 + 0.726854i \(0.740982\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) −15.7280 6.89140i −0.761132 0.333498i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.41577 + 2.45219i 0.0681955 + 0.118118i 0.898107 0.439777i \(-0.144943\pi\)
−0.829912 + 0.557895i \(0.811609\pi\)
\(432\) 0 0
\(433\) −2.33690 −0.112304 −0.0561522 0.998422i \(-0.517883\pi\)
−0.0561522 + 0.998422i \(0.517883\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.74511 13.4149i −0.370499 0.641723i
\(438\) 0 0
\(439\) 3.03466 5.25619i 0.144837 0.250864i −0.784475 0.620160i \(-0.787068\pi\)
0.929312 + 0.369296i \(0.120401\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.80188 10.0492i 0.275656 0.477450i −0.694645 0.719353i \(-0.744438\pi\)
0.970300 + 0.241903i \(0.0777717\pi\)
\(444\) 0 0
\(445\) 2.92334 + 5.06337i 0.138579 + 0.240027i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4.13821 −0.195294 −0.0976470 0.995221i \(-0.531132\pi\)
−0.0976470 + 0.995221i \(0.531132\pi\)
\(450\) 0 0
\(451\) −7.99244 13.8433i −0.376349 0.651856i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 11.7451 + 5.14625i 0.550619 + 0.241260i
\(456\) 0 0
\(457\) 6.32178 10.9496i 0.295720 0.512203i −0.679432 0.733739i \(-0.737774\pi\)
0.975152 + 0.221536i \(0.0711070\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −20.7129 −0.964695 −0.482348 0.875980i \(-0.660216\pi\)
−0.482348 + 0.875980i \(0.660216\pi\)
\(462\) 0 0
\(463\) −16.3811 −0.761295 −0.380647 0.924720i \(-0.624299\pi\)
−0.380647 + 0.924720i \(0.624299\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −0.861215 + 1.49167i −0.0398523 + 0.0690262i −0.885264 0.465090i \(-0.846022\pi\)
0.845411 + 0.534116i \(0.179355\pi\)
\(468\) 0 0
\(469\) 12.2602 9.01884i 0.566125 0.416452i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.52489 + 9.56940i 0.254035 + 0.440001i
\(474\) 0 0
\(475\) 6.84667 0.314147
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.890881 1.54305i −0.0407054 0.0705038i 0.844955 0.534838i \(-0.179627\pi\)
−0.885660 + 0.464334i \(0.846294\pi\)
\(480\) 0 0
\(481\) −6.89844 + 11.9485i −0.314542 + 0.544803i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) 5.50977 + 9.54320i 0.249672 + 0.432444i 0.963435 0.267943i \(-0.0863440\pi\)
−0.713763 + 0.700387i \(0.753011\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 20.9311 0.944608 0.472304 0.881436i \(-0.343422\pi\)
0.472304 + 0.881436i \(0.343422\pi\)
\(492\) 0 0
\(493\) −3.32178 5.75349i −0.149605 0.259124i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.75268 6.49983i 0.167993 0.290972i −0.769721 0.638380i \(-0.779605\pi\)
0.937714 + 0.347408i \(0.112938\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −20.5842 −0.917805 −0.458903 0.888487i \(-0.651757\pi\)
−0.458903 + 0.888487i \(0.651757\pi\)
\(504\) 0 0
\(505\) −17.0151 −0.757163
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.82934 11.8288i 0.302705 0.524301i −0.674043 0.738693i \(-0.735444\pi\)
0.976748 + 0.214392i \(0.0687769\pi\)
\(510\) 0 0
\(511\) 24.9211 18.3324i 1.10245 0.810978i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3.55456 + 6.15668i 0.156633 + 0.271296i
\(516\) 0 0
\(517\) −20.4795 −0.900688
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −21.0820 36.5151i −0.923620 1.59976i −0.793766 0.608224i \(-0.791882\pi\)
−0.129854 0.991533i \(-0.541451\pi\)
\(522\) 0 0
\(523\) 15.3218 26.5381i 0.669975 1.16043i −0.307936 0.951407i \(-0.599638\pi\)
0.977911 0.209023i \(-0.0670284\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.16845 15.8802i 0.399384 0.691753i
\(528\) 0 0
\(529\) 8.94067 + 15.4857i 0.388725 + 0.673291i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 46.1640 1.99959
\(534\) 0 0
\(535\) 0.876338 + 1.51786i 0.0378874 + 0.0656229i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7.96335 8.63654i −0.343006 0.372002i
\(540\) 0 0
\(541\) 16.8445 29.1755i 0.724200 1.25435i −0.235102 0.971971i \(-0.575543\pi\)
0.959302 0.282381i \(-0.0911241\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −19.5400 −0.837002
\(546\) 0 0
\(547\) −3.03979 −0.129972 −0.0649861 0.997886i \(-0.520700\pi\)
−0.0649861 + 0.997886i \(0.520700\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 11.3716 19.6961i 0.484445 0.839083i
\(552\) 0 0
\(553\) 13.7969 + 6.04526i 0.586703 + 0.257070i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.08202 + 15.7305i 0.384817 + 0.666523i 0.991744 0.128235i \(-0.0409311\pi\)
−0.606926 + 0.794758i \(0.707598\pi\)
\(558\) 0 0
\(559\) −31.9116 −1.34972
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −18.4952 32.0347i −0.779481 1.35010i −0.932241 0.361837i \(-0.882150\pi\)
0.152760 0.988263i \(-0.451184\pi\)
\(564\) 0 0
\(565\) −5.16845 + 8.95202i −0.217438 + 0.376614i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16.3047 28.2405i 0.683527 1.18390i −0.290370 0.956915i \(-0.593778\pi\)
0.973897 0.226990i \(-0.0728884\pi\)
\(570\) 0 0
\(571\) −20.2182 35.0190i −0.846107 1.46550i −0.884656 0.466243i \(-0.845607\pi\)
0.0385496 0.999257i \(-0.487726\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.26245 0.0943505
\(576\) 0 0
\(577\) 19.0151 + 32.9352i 0.791610 + 1.37111i 0.924970 + 0.380041i \(0.124090\pi\)
−0.133360 + 0.991068i \(0.542577\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.67601 33.0912i −0.152507 1.37285i
\(582\) 0 0
\(583\) −6.28513 + 10.8862i −0.260304 + 0.450859i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −34.0302 −1.40458 −0.702289 0.711892i \(-0.747839\pi\)
−0.702289 + 0.711892i \(0.747839\pi\)
\(588\) 0 0
\(589\) 62.7734 2.58653
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −16.8618 + 29.2055i −0.692431 + 1.19933i 0.278608 + 0.960405i \(0.410127\pi\)
−0.971039 + 0.238921i \(0.923206\pi\)
\(594\) 0 0
\(595\) −0.584225 5.25915i −0.0239509 0.215604i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3.15333 + 5.46172i 0.128841 + 0.223160i 0.923228 0.384253i \(-0.125541\pi\)
−0.794387 + 0.607413i \(0.792207\pi\)
\(600\) 0 0
\(601\) −11.2871 −0.460411 −0.230206 0.973142i \(-0.573940\pi\)
−0.230206 + 0.973142i \(0.573940\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.09179 7.08718i −0.166355 0.288135i
\(606\) 0 0
\(607\) 7.73057 13.3897i 0.313774 0.543473i −0.665402 0.746485i \(-0.731740\pi\)
0.979176 + 0.203012i \(0.0650732\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 29.5722 51.2206i 1.19637 2.07217i
\(612\) 0 0
\(613\) 11.0820 + 19.1946i 0.447598 + 0.775263i 0.998229 0.0594857i \(-0.0189461\pi\)
−0.550631 + 0.834749i \(0.685613\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.9805 0.603091 0.301545 0.953452i \(-0.402498\pi\)
0.301545 + 0.953452i \(0.402498\pi\)
\(618\) 0 0
\(619\) −11.8196 20.4721i −0.475069 0.822843i 0.524524 0.851396i \(-0.324243\pi\)
−0.999592 + 0.0285529i \(0.990910\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 14.1685 + 6.20806i 0.567647 + 0.248721i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.69334 0.227008
\(630\) 0 0
\(631\) −13.7818 −0.548643 −0.274322 0.961638i \(-0.588453\pi\)
−0.274322 + 0.961638i \(0.588453\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.59179 + 16.6135i −0.380638 + 0.659285i
\(636\) 0 0
\(637\) 33.0996 7.44577i 1.31145 0.295012i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 21.9309 + 37.9854i 0.866218 + 1.50033i 0.865832 + 0.500334i \(0.166790\pi\)
0.000386062 1.00000i \(0.499877\pi\)
\(642\) 0 0
\(643\) 7.04979 0.278016 0.139008 0.990291i \(-0.455609\pi\)
0.139008 + 0.990291i \(0.455609\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12.2403 21.2009i −0.481217 0.833493i 0.518550 0.855047i \(-0.326472\pi\)
−0.999768 + 0.0215540i \(0.993139\pi\)
\(648\) 0 0
\(649\) −6.71288 + 11.6271i −0.263504 + 0.456402i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.408213 0.707046i 0.0159746 0.0276688i −0.857928 0.513771i \(-0.828248\pi\)
0.873902 + 0.486102i \(0.161582\pi\)
\(654\) 0 0
\(655\) 8.91357 + 15.4387i 0.348282 + 0.603242i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −21.2871 −0.829228 −0.414614 0.909997i \(-0.636083\pi\)
−0.414614 + 0.909997i \(0.636083\pi\)
\(660\) 0 0
\(661\) −12.9731 22.4701i −0.504596 0.873986i −0.999986 0.00531513i \(-0.998308\pi\)
0.495390 0.868671i \(-0.335025\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 14.5918 10.7340i 0.565845 0.416246i
\(666\) 0 0
\(667\) 3.75767 6.50848i 0.145498 0.252009i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.8920 0.420483
\(672\) 0 0
\(673\) 22.0693 0.850710 0.425355 0.905027i \(-0.360149\pi\)
0.425355 + 0.905027i \(0.360149\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.74511 4.75468i 0.105503 0.182737i −0.808440 0.588578i \(-0.799688\pi\)
0.913944 + 0.405841i \(0.133021\pi\)
\(678\) 0 0
\(679\) 0.584225 + 5.25915i 0.0224205 + 0.201828i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9.61389 + 16.6517i 0.367865 + 0.637161i 0.989232 0.146359i \(-0.0467554\pi\)
−0.621366 + 0.783520i \(0.713422\pi\)
\(684\) 0 0
\(685\) 4.00000 0.152832
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −18.1513 31.4390i −0.691511 1.19773i
\(690\) 0 0
\(691\) −7.10912 + 12.3134i −0.270444 + 0.468422i −0.968975 0.247157i \(-0.920504\pi\)
0.698532 + 0.715579i \(0.253837\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.58423 + 4.47601i −0.0980253 + 0.169785i
\(696\) 0 0
\(697\) −9.52489 16.4976i −0.360781 0.624891i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −14.1533 −0.534564 −0.267282 0.963618i \(-0.586125\pi\)
−0.267282 + 0.963618i \(0.586125\pi\)
\(702\) 0 0
\(703\) 9.74511 + 16.8790i 0.367544 + 0.636605i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −36.2630 + 26.6757i −1.36381 + 1.00324i
\(708\) 0 0
\(709\) −8.52268 + 14.7617i −0.320076 + 0.554388i −0.980503 0.196502i \(-0.937042\pi\)
0.660427 + 0.750890i \(0.270375\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 20.7431 0.776836
\(714\) 0 0
\(715\) −8.13379 −0.304186
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5.75268 + 9.96393i −0.214539 + 0.371592i −0.953130 0.302562i \(-0.902158\pi\)
0.738591 + 0.674154i \(0.235491\pi\)
\(720\) 0 0
\(721\) 17.2278 + 7.54854i 0.641596 + 0.281122i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.66089 + 2.87674i 0.0616839 + 0.106840i
\(726\) 0 0
\(727\) 16.4114 0.608664 0.304332 0.952566i \(-0.401567\pi\)
0.304332 + 0.952566i \(0.401567\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.58423 + 11.4042i 0.243526 + 0.421800i
\(732\) 0 0
\(733\) 4.55712 7.89317i 0.168321 0.291541i −0.769509 0.638637i \(-0.779499\pi\)
0.937830 + 0.347096i \(0.112832\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.82713 + 8.36084i −0.177810 + 0.307975i
\(738\) 0 0
\(739\) 17.4978 + 30.3071i 0.643667 + 1.11486i 0.984608 + 0.174779i \(0.0559210\pi\)
−0.340941 + 0.940085i \(0.610746\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 43.5305 1.59698 0.798489 0.602009i \(-0.205633\pi\)
0.798489 + 0.602009i \(0.205633\pi\)
\(744\) 0 0
\(745\) −0.398443 0.690123i −0.0145978 0.0252842i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.24732 + 1.86101i 0.155194 + 0.0679999i
\(750\) 0 0
\(751\) −3.15333 + 5.46172i −0.115067 + 0.199301i −0.917806 0.397028i \(-0.870041\pi\)
0.802740 + 0.596329i \(0.203375\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.5249 0.601402
\(756\) 0 0
\(757\) 24.3369 0.884540 0.442270 0.896882i \(-0.354173\pi\)
0.442270 + 0.896882i \(0.354173\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −14.1016 + 24.4246i −0.511181 + 0.885392i 0.488735 + 0.872432i \(0.337459\pi\)
−0.999916 + 0.0129592i \(0.995875\pi\)
\(762\) 0 0
\(763\) −41.6441 + 30.6342i −1.50762 + 1.10903i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −19.3867 33.5787i −0.700013 1.21246i
\(768\) 0 0
\(769\) −41.8965 −1.51082 −0.755412 0.655250i \(-0.772563\pi\)
−0.755412 + 0.655250i \(0.772563\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 19.9287 + 34.5175i 0.716785 + 1.24151i 0.962267 + 0.272107i \(0.0877205\pi\)
−0.245482 + 0.969401i \(0.578946\pi\)
\(774\) 0 0
\(775\) −4.58423 + 7.94011i −0.164670 + 0.285217i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 32.6069 56.4768i 1.16826 2.02349i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8.20311 −0.292782
\(786\) 0 0
\(787\) −17.6637 30.5944i −0.629642 1.09057i −0.987623 0.156843i \(-0.949868\pi\)
0.357981 0.933729i \(-0.383465\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.01954 + 27.1817i 0.107363 + 0.966469i
\(792\) 0 0
\(793\) −15.7280 + 27.2417i −0.558518 + 0.967381i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −29.6933 −1.05179 −0.525896 0.850549i \(-0.676270\pi\)
−0.525896 + 0.850549i \(0.676270\pi\)
\(798\) 0 0
\(799\) −24.4062 −0.863430
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −9.81201 + 16.9949i −0.346258 + 0.599737i
\(804\) 0